%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP051^1 : TPTP v9.3.1. Released v7.5.0.
% 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 : n004.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 10:23:50 AM UTC 2026
% Result : Theorem 78.15s 13.23s
% Output : CNFRefutation 78.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 349
% Syntax : Number of formulae : 4949 (2173 unt; 0 typ; 0 def)
% Number of atoms : 30902 (11588 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 58837 (9761 ~;7783 |; 150 &;40147 @)
% ( 0 <=>; 996 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 11 ( 10 usr)
% Number of type conns : 2504 (2504 >; 0 *; 0 +; 0 <<)
% Number of symbols : 157 ( 154 usr; 9 con; 0-5 aty)
% Number of variables : 13553 ( 500 ^;12939 !; 114 ?;13553 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_list_P559422087at_nat,type,
list_P559422087at_nat: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_product_prod_nat_nat,type,
product_prod_nat_nat: $tType ).
thf(tp_set_Pr1986765409at_nat,type,
set_Pr1986765409at_nat: $tType ).
thf(tp_set_li664300135at_nat,type,
set_li664300135at_nat: $tType ).
thf(tp_set_nat,type,
set_nat: $tType ).
thf(tp_set_se1612935105at_nat,type,
set_se1612935105at_nat: $tType ).
thf(tp_set_set_nat,type,
set_set_nat: $tType ).
thf(tp_adjacent_nodes_a,type,
adjacent_nodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
thf(tp_adjacent_nodes_b,type,
adjacent_nodes_b: ( product_prod_nat_nat > b ) > nat > set_nat ).
thf(tp_c,type,
c: product_prod_nat_nat > a ).
thf(tp_c2,type,
c2: product_prod_nat_nat > b ).
thf(tp_collec1606769740at_nat,type,
collec1606769740at_nat: ( set_Pr1986765409at_nat > $o ) > set_se1612935105at_nat ).
thf(tp_collec7649004at_nat,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(tp_collect_nat,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(tp_collect_set_nat,type,
collect_set_nat: ( set_nat > $o ) > set_set_nat ).
thf(tp_connected_a,type,
connected_a: ( product_prod_nat_nat > a ) > nat > nat > $o ).
thf(tp_connected_b,type,
connected_b: ( product_prod_nat_nat > b ) > nat > nat > $o ).
thf(tp_dist_a,type,
dist_a: ( product_prod_nat_nat > a ) > nat > nat > nat > $o ).
thf(tp_dist_b,type,
dist_b: ( product_prod_nat_nat > b ) > nat > nat > nat > $o ).
thf(tp_e_a,type,
e_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
thf(tp_e_b,type,
e_b: ( product_prod_nat_nat > b ) > set_Pr1986765409at_nat ).
thf(tp_edges,type,
edges: set_Pr1986765409at_nat ).
thf(tp_edmond1022345716sure_a,type,
edmond1022345716sure_a: ( product_prod_nat_nat > a ) > nat > nat > nat ).
thf(tp_edmond1022345717sure_b,type,
edmond1022345717sure_b: ( product_prod_nat_nat > b ) > nat > nat > nat ).
thf(tp_edmond1517640972ysis_a,type,
edmond1517640972ysis_a: ( product_prod_nat_nat > a ) > $o ).
thf(tp_edmond1517640973ysis_b,type,
edmond1517640973ysis_b: ( product_prod_nat_nat > b ) > $o ).
thf(tp_edmond475474835dges_a,type,
edmond475474835dges_a: ( product_prod_nat_nat > a ) > nat > nat > set_Pr1986765409at_nat ).
thf(tp_edmond475474836dges_b,type,
edmond475474836dges_b: ( product_prod_nat_nat > b ) > nat > nat > set_Pr1986765409at_nat ).
thf(tp_edmond771116670s_uE_a,type,
edmond771116670s_uE_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
thf(tp_edmond771116671s_uE_b,type,
edmond771116671s_uE_b: ( product_prod_nat_nat > b ) > set_Pr1986765409at_nat ).
thf(tp_finite1299096496at_nat,type,
finite1299096496at_nat: set_li664300135at_nat > $o ).
thf(tp_finite1457549322at_nat,type,
finite1457549322at_nat: set_se1612935105at_nat > $o ).
thf(tp_finite1701894793at_nat,type,
finite1701894793at_nat: set_se1612935105at_nat > nat ).
thf(tp_finite2012248349et_nat,type,
finite2012248349et_nat: set_set_nat > $o ).
thf(tp_finite447719721at_nat,type,
finite447719721at_nat: set_Pr1986765409at_nat > nat ).
thf(tp_finite772653738at_nat,type,
finite772653738at_nat: set_Pr1986765409at_nat > $o ).
thf(tp_finite83082927at_nat,type,
finite83082927at_nat: set_li664300135at_nat > nat ).
thf(tp_finite_Graph_a,type,
finite_Graph_a: ( product_prod_nat_nat > a ) > $o ).
thf(tp_finite_Graph_b,type,
finite_Graph_b: ( product_prod_nat_nat > b ) > $o ).
thf(tp_finite_card_nat,type,
finite_card_nat: set_nat > nat ).
thf(tp_finite_card_set_nat,type,
finite_card_set_nat: set_set_nat > nat ).
thf(tp_finite_finite_nat,type,
finite_finite_nat: set_nat > $o ).
thf(tp_incoming_a,type,
incoming_a: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
thf(tp_incoming_b,type,
incoming_b: ( product_prod_nat_nat > b ) > set_nat > set_Pr1986765409at_nat ).
thf(tp_isPath_a,type,
isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(tp_isPath_b,type,
isPath_b: ( product_prod_nat_nat > b ) > nat > list_P559422087at_nat > nat > $o ).
thf(tp_isShortestPath_a,type,
isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(tp_isShortestPath_b,type,
isShortestPath_b: ( product_prod_nat_nat > b ) > nat > list_P559422087at_nat > nat > $o ).
thf(tp_isSimplePath_a,type,
isSimplePath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(tp_isSimplePath_b,type,
isSimplePath_b: ( product_prod_nat_nat > b ) > nat > list_P559422087at_nat > nat > $o ).
thf(tp_member1608759472at_nat,type,
member1608759472at_nat: list_P559422087at_nat > set_li664300135at_nat > $o ).
thf(tp_member298845450at_nat,type,
member298845450at_nat: set_Pr1986765409at_nat > set_se1612935105at_nat > $o ).
thf(tp_member701585322at_nat,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(tp_member_nat,type,
member_nat: nat > set_nat > $o ).
thf(tp_member_set_nat,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(tp_min_dist_a,type,
min_dist_a: ( product_prod_nat_nat > a ) > nat > nat > nat ).
thf(tp_min_dist_b,type,
min_dist_b: ( product_prod_nat_nat > b ) > nat > nat > nat ).
thf(tp_ord_le116442893at_nat,type,
ord_le116442893at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(tp_ord_le1613022364et_nat,type,
ord_le1613022364et_nat: set_set_nat > set_set_nat > $o ).
thf(tp_ord_le2096002913at_nat,type,
ord_le2096002913at_nat: set_se1612935105at_nat > set_se1612935105at_nat > $o ).
thf(tp_ord_le841296385at_nat,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(tp_ord_less_eq_set_nat,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(tp_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(tp_ord_less_set_nat,type,
ord_less_set_nat: set_nat > set_nat > $o ).
thf(tp_outgoing_a,type,
outgoing_a: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
thf(tp_outgoing_b,type,
outgoing_b: ( product_prod_nat_nat > b ) > set_nat > set_Pr1986765409at_nat ).
thf(tp_p,type,
p: list_P559422087at_nat ).
thf(tp_p2,type,
p2: list_P559422087at_nat ).
thf(tp_reachableNodes_a,type,
reachableNodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
thf(tp_reachableNodes_b,type,
reachableNodes_b: ( product_prod_nat_nat > b ) > nat > set_nat ).
thf(tp_s,type,
s: nat ).
thf(tp_sK10_SY1291,type,
sK10_SY1291: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(tp_sK11_SY1034,type,
sK11_SY1034: set_li664300135at_nat > nat ).
thf(tp_sK12_SY1312,type,
sK12_SY1312: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(tp_sK13_SY1163,type,
sK13_SY1163: nat > nat > list_P559422087at_nat ).
thf(tp_sK14_SY873,type,
sK14_SY873: nat > nat > ( nat > nat ) > nat ).
thf(tp_sK15_SY1305,type,
sK15_SY1305: nat > nat > list_P559422087at_nat ).
thf(tp_sK16_SY1359,type,
sK16_SY1359: nat > nat > ( product_prod_nat_nat > a ) > list_P559422087at_nat ).
thf(tp_sK17_SY1174,type,
sK17_SY1174: set_Pr1986765409at_nat > nat > set_Pr1986765409at_nat ).
thf(tp_sK18_SY1504,type,
sK18_SY1504: ( nat > nat ) > nat > nat > nat ).
thf(tp_sK19_SY1227,type,
sK19_SY1227: ( nat > $o ) > ( nat > $o ) > nat ).
thf(tp_sK1_SX0,type,
sK1_SX0: list_P559422087at_nat ).
thf(tp_sK20_SY1230,type,
sK20_SY1230: set_Pr1986765409at_nat > ( set_Pr1986765409at_nat > $o ) > set_Pr1986765409at_nat ).
thf(tp_sK21_SY1397,type,
sK21_SY1397: nat > nat > ( product_prod_nat_nat > b ) > list_P559422087at_nat ).
thf(tp_sK22_SY1261,type,
sK22_SY1261: set_nat > ( set_nat > $o ) > set_nat ).
thf(tp_sK23_SY1404,type,
sK23_SY1404: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).
thf(tp_sK24_SY974,type,
sK24_SY974: nat > ( nat > $o ) > nat ).
thf(tp_sK25_SY1407,type,
sK25_SY1407: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).
thf(tp_sK26_SY1292,type,
sK26_SY1292: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(tp_sK27_SY1309,type,
sK27_SY1309: set_nat > nat > set_nat ).
thf(tp_sK28_SY1344,type,
sK28_SY1344: nat > nat > nat > nat ).
thf(tp_sK29_SY1165,type,
sK29_SY1165: nat > set_nat > nat ).
thf(tp_sK2_SY793,type,
sK2_SY793: nat > list_P559422087at_nat ).
thf(tp_sK30_SY1447,type,
sK30_SY1447: list_P559422087at_nat > nat > nat > ( product_prod_nat_nat > b ) > list_P559422087at_nat ).
thf(tp_sK31_SY1379,type,
sK31_SY1379: nat > nat > ( nat > $o ) > nat ).
thf(tp_sK32_SY1199,type,
sK32_SY1199: set_nat > set_set_nat > set_nat ).
thf(tp_sK33_SY1214,type,
sK33_SY1214: set_Pr1986765409at_nat > set_se1612935105at_nat > set_Pr1986765409at_nat ).
thf(tp_sK34_SY1223,type,
sK34_SY1223: set_Pr1986765409at_nat > set_se1612935105at_nat > set_Pr1986765409at_nat ).
thf(tp_sK35_SY1245,type,
sK35_SY1245: nat > set_nat > nat ).
thf(tp_sK36_SY1400,type,
sK36_SY1400: ( nat > $o ) > nat > nat > nat ).
thf(tp_sK37_SY1310,type,
sK37_SY1310: set_nat > set_set_nat > set_nat ).
thf(tp_sK38_SY1423,type,
sK38_SY1423: nat > nat > nat > nat ).
thf(tp_sK39_SY1473,type,
sK39_SY1473: list_P559422087at_nat > nat > nat > ( product_prod_nat_nat > a ) > list_P559422087at_nat ).
thf(tp_sK3_SY1117,type,
sK3_SY1117: set_nat > set_nat > nat ).
thf(tp_sK40_SY1428,type,
sK40_SY1428: ( nat > $o ) > nat > nat > nat ).
thf(tp_sK41_SY1438,type,
sK41_SY1438: nat > nat > nat > ( product_prod_nat_nat > a ) > nat ).
thf(tp_sK42_SY1444,type,
sK42_SY1444: ( nat > $o ) > nat > nat > ( product_prod_nat_nat > a ) > nat ).
thf(tp_sK43_SY1370,type,
sK43_SY1370: nat > nat > nat > nat ).
thf(tp_sK44_SY1448,type,
sK44_SY1448: nat > nat > nat > ( product_prod_nat_nat > b ) > nat ).
thf(tp_sK45_SY1455,type,
sK45_SY1455: ( nat > $o ) > nat > nat > ( product_prod_nat_nat > b ) > nat ).
thf(tp_sK46_SY1241,type,
sK46_SY1241: ( nat > $o ) > nat > nat ).
thf(tp_sK47_SY1417,type,
sK47_SY1417: nat > nat > nat > nat ).
thf(tp_sK48_SY1446,type,
sK48_SY1446: nat > nat > nat > ( product_prod_nat_nat > b ) > nat ).
thf(tp_sK49_SY1449,type,
sK49_SY1449: nat > nat > nat > ( product_prod_nat_nat > a ) > nat ).
thf(tp_sK4_SY1126,type,
sK4_SY1126: ( nat > $o ) > ( nat > $o ) > nat ).
thf(tp_sK50_SY1164,type,
sK50_SY1164: nat > nat > list_P559422087at_nat ).
thf(tp_sK51_SY1177,type,
sK51_SY1177: nat > nat > nat ).
thf(tp_sK52_SY852,type,
sK52_SY852: nat > nat > ( nat > $o ) > nat ).
thf(tp_sK53_SY1258,type,
sK53_SY1258: nat > nat > nat ).
thf(tp_sK54_SY1277,type,
sK54_SY1277: nat > nat > list_P559422087at_nat ).
thf(tp_sK55_SY1353,type,
sK55_SY1353: nat > nat > nat > list_P559422087at_nat ).
thf(tp_sK56_SY1443,type,
sK56_SY1443: nat > nat > nat > nat > nat ).
thf(tp_sK57_SY1378,type,
sK57_SY1378: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).
thf(tp_sK58_SY852,type,
sK58_SY852: nat > nat > ( nat > $o ) > nat ).
thf(tp_sK59_SY1382,type,
sK59_SY1382: nat > nat > nat > list_P559422087at_nat ).
thf(tp_sK5_SY879,type,
sK5_SY879: nat > ( nat > $o ) > nat ).
thf(tp_sK60_SY1399,type,
sK60_SY1399: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).
thf(tp_sK61_SY1466,type,
sK61_SY1466: nat > nat > nat > nat > nat ).
thf(tp_sK62_SY1479,type,
sK62_SY1479: nat > nat > nat > nat > ( product_prod_nat_nat > a ) > nat ).
thf(tp_sK63_SY1494,type,
sK63_SY1494: nat > nat > nat > nat > ( product_prod_nat_nat > b ) > nat ).
thf(tp_sK64_SY1164,type,
sK64_SY1164: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).
thf(tp_sK65_SY1177,type,
sK65_SY1177: nat > nat > nat > nat ).
thf(tp_sK66_SY1258,type,
sK66_SY1258: nat > nat > nat > nat ).
thf(tp_sK67_SY1277,type,
sK67_SY1277: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).
thf(tp_sK68_SY1501,type,
sK68_SY1501: nat > nat > ( product_prod_nat_nat > a ) > nat ).
thf(tp_sK69_SY1507,type,
sK69_SY1507: nat > nat > ( product_prod_nat_nat > a ) > list_P559422087at_nat ).
thf(tp_sK6_SY885,type,
sK6_SY885: list_P559422087at_nat > ( list_P559422087at_nat > $o ) > list_P559422087at_nat ).
thf(tp_sK70_SY1510,type,
sK70_SY1510: nat > nat > ( product_prod_nat_nat > b ) > list_P559422087at_nat ).
thf(tp_sK71_SY1512,type,
sK71_SY1512: nat > nat > ( product_prod_nat_nat > b ) > nat ).
thf(tp_sK72_SY1520,type,
sK72_SY1520: nat > nat > nat > ( product_prod_nat_nat > b ) > list_P559422087at_nat ).
thf(tp_sK73_SY1521,type,
sK73_SY1521: list_P559422087at_nat > nat > nat > ( product_prod_nat_nat > a ) > list_P559422087at_nat ).
thf(tp_sK74_SY1524,type,
sK74_SY1524: list_P559422087at_nat > nat > nat > ( product_prod_nat_nat > b ) > list_P559422087at_nat ).
thf(tp_sK75_SY1529,type,
sK75_SY1529: nat > nat > nat > ( product_prod_nat_nat > a ) > list_P559422087at_nat ).
thf(tp_sK76_SY1501,type,
sK76_SY1501: nat > nat > nat > ( product_prod_nat_nat > a ) > nat ).
thf(tp_sK77_SY1507,type,
sK77_SY1507: list_P559422087at_nat > nat > nat > ( product_prod_nat_nat > a ) > list_P559422087at_nat ).
thf(tp_sK78_SY1510,type,
sK78_SY1510: list_P559422087at_nat > nat > nat > ( product_prod_nat_nat > b ) > list_P559422087at_nat ).
thf(tp_sK79_SY1512,type,
sK79_SY1512: nat > nat > nat > ( product_prod_nat_nat > b ) > nat ).
thf(tp_sK7_SY922,type,
sK7_SY922: nat > ( nat > $o ) > nat ).
thf(tp_sK80_SY1353,type,
sK80_SY1353: list_P559422087at_nat > nat > nat > nat > list_P559422087at_nat ).
thf(tp_sK81_SY1382,type,
sK81_SY1382: list_P559422087at_nat > nat > nat > nat > list_P559422087at_nat ).
thf(tp_sK82_SY1520,type,
sK82_SY1520: list_P559422087at_nat > nat > nat > nat > ( product_prod_nat_nat > b ) > list_P559422087at_nat ).
thf(tp_sK83_SY1529,type,
sK83_SY1529: list_P559422087at_nat > nat > nat > nat > ( product_prod_nat_nat > a ) > list_P559422087at_nat ).
thf(tp_sK8_SY1267,type,
sK8_SY1267: nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(tp_sK9_SY1268,type,
sK9_SY1268: nat > set_nat > set_nat ).
thf(tp_set_Pr2131844118at_nat,type,
set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
thf(tp_size_s1990949619at_nat,type,
size_s1990949619at_nat: list_P559422087at_nat > nat ).
thf(tp_t,type,
t: nat ).
thf(tp_v_a,type,
v_a: ( product_prod_nat_nat > a ) > set_nat ).
thf(tp_v_b,type,
v_b: ( product_prod_nat_nat > b ) > set_nat ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(1,axiom,
! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C3: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( ord_le841296385at_nat @ B2 @ C3 )
=> ( ord_le841296385at_nat @ A2 @ C3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_subset__trans) ).
thf(2,axiom,
! [A2: set_nat,B2: set_nat,C3: set_nat] :
( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( ord_less_eq_set_nat @ B2 @ C3 )
=> ( ord_less_eq_set_nat @ A2 @ C3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_subset__trans) ).
thf(3,axiom,
( ( ^ [Y4: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] : ( Y4 = Z ) )
= ( ^ [A4: set_Pr1986765409at_nat,B5: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A4 @ B5 )
& ( ord_le841296385at_nat @ B5 @ A4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_set__eq__subset) ).
thf(4,axiom,
( ( ^ [Y4: set_nat,Z: set_nat] : ( Y4 = Z ) )
= ( ^ [A4: set_nat,B5: set_nat] :
( ( ord_less_eq_set_nat @ A4 @ B5 )
& ( ord_less_eq_set_nat @ B5 @ A4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_set__eq__subset) ).
thf(5,axiom,
! [P2: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
( ( ord_le841296385at_nat @ ( collec7649004at_nat @ P2 ) @ ( collec7649004at_nat @ Q ) )
= ( ! [X: product_prod_nat_nat] :
( ( P2 @ X )
=> ( Q @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_Collect__mono__iff) ).
thf(6,axiom,
! [P2: nat > $o,Q: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q ) )
= ( ! [X: nat] :
( ( P2 @ X )
=> ( Q @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_Collect__mono__iff) ).
thf(7,axiom,
ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_SP__EDGES) ).
thf(8,axiom,
! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
( ! [X2: product_prod_nat_nat] :
( ( member701585322at_nat @ X2 @ A2 )
=> ( member701585322at_nat @ X2 @ B2 ) )
=> ( ord_le841296385at_nat @ A2 @ B2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_subsetI) ).
thf(9,axiom,
! [A2: set_nat,B2: set_nat] :
( ! [X2: nat] :
( ( member_nat @ X2 @ A2 )
=> ( member_nat @ X2 @ B2 ) )
=> ( ord_less_eq_set_nat @ A2 @ B2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_subsetI) ).
thf(10,axiom,
! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( ord_le841296385at_nat @ B2 @ A2 )
=> ( A2 = B2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_subset__antisym) ).
thf(11,axiom,
! [A2: set_nat,B2: set_nat] :
( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( ord_less_eq_set_nat @ B2 @ A2 )
=> ( A2 = B2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_subset__antisym) ).
thf(12,axiom,
! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( A2 != B2 )
=> ( ord_le116442893at_nat @ A2 @ B2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_psubsetI) ).
thf(13,axiom,
! [A2: set_nat,B2: set_nat] :
( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( A2 != B2 )
=> ( ord_less_set_nat @ A2 @ B2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_psubsetI) ).
thf(14,axiom,
ord_le841296385at_nat @ edges @ ( e_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334__092_060open_062edges_A_092_060subseteq_062_AE_092_060close_062) ).
thf(15,axiom,
! [U3: set_nat] :
( ( finite_finite_nat @ ( v_b @ c2 ) )
=> ( finite772653738at_nat @ ( incoming_b @ c2 @ U3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_g_H_Ofinite__incoming_H) ).
thf(16,axiom,
! [U3: set_nat] :
( ( finite_finite_nat @ ( v_b @ c2 ) )
=> ( finite772653738at_nat @ ( outgoing_b @ c2 @ U3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_g_H_Ofinite__outgoing_H) ).
thf(17,axiom,
! [U3: set_nat] : ( ord_le841296385at_nat @ ( outgoing_b @ c2 @ U3 ) @ ( e_b @ c2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_g_H_Ooutgoing_H__edges) ).
thf(18,axiom,
! [U3: set_nat] : ( ord_le841296385at_nat @ ( incoming_b @ c2 @ U3 ) @ ( e_b @ c2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_g_H_Oincoming_H__edges) ).
thf(19,axiom,
! [C: product_prod_nat_nat > b,U3: set_nat] :
( ( finite_finite_nat @ ( v_b @ C ) )
=> ( finite772653738at_nat @ ( incoming_b @ C @ U3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_Graph_Ofinite__incoming_H) ).
thf(20,axiom,
! [C: product_prod_nat_nat > a,U3: set_nat] :
( ( finite_finite_nat @ ( v_a @ C ) )
=> ( finite772653738at_nat @ ( incoming_a @ C @ U3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_Graph_Ofinite__incoming_H) ).
thf(21,axiom,
! [C: product_prod_nat_nat > b,U3: set_nat] :
( ( finite_finite_nat @ ( v_b @ C ) )
=> ( finite772653738at_nat @ ( outgoing_b @ C @ U3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_Graph_Ofinite__outgoing_H) ).
thf(22,axiom,
! [C: product_prod_nat_nat > a,U3: set_nat] :
( ( finite_finite_nat @ ( v_a @ C ) )
=> ( finite772653738at_nat @ ( outgoing_a @ C @ U3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_Graph_Ofinite__outgoing_H) ).
thf(23,axiom,
! [C: product_prod_nat_nat > b,U3: set_nat] : ( ord_le841296385at_nat @ ( incoming_b @ C @ U3 ) @ ( e_b @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_Graph_Oincoming_H__edges) ).
thf(24,axiom,
! [C: product_prod_nat_nat > a,U3: set_nat] : ( ord_le841296385at_nat @ ( incoming_a @ C @ U3 ) @ ( e_a @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_Graph_Oincoming_H__edges) ).
thf(25,axiom,
! [C: product_prod_nat_nat > b,U3: set_nat] : ( ord_le841296385at_nat @ ( outgoing_b @ C @ U3 ) @ ( e_b @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_Graph_Ooutgoing_H__edges) ).
thf(26,axiom,
! [C: product_prod_nat_nat > a,U3: set_nat] : ( ord_le841296385at_nat @ ( outgoing_a @ C @ U3 ) @ ( e_a @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_Graph_Ooutgoing_H__edges) ).
thf(27,axiom,
outgoing_b = outgoing_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_Graph_Ooutgoing_H_Ocong) ).
thf(28,axiom,
outgoing_a = outgoing_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_Graph_Ooutgoing_H_Ocong) ).
thf(29,axiom,
incoming_b = incoming_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_Graph_Oincoming_H_Ocong) ).
thf(30,axiom,
incoming_a = incoming_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_Graph_Oincoming_H_Ocong) ).
thf(31,axiom,
! [U3: set_nat] :
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( incoming_a @ c @ U3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_finite__incoming_H) ).
thf(32,axiom,
! [U3: set_nat] :
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( outgoing_a @ c @ U3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_finite__outgoing_H) ).
thf(33,axiom,
( ( finite_finite_nat @ ( v_b @ c2 ) )
=> ( finite772653738at_nat @ ( e_b @ c2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_g_H_OVfin__imp__Efin) ).
thf(34,axiom,
finite772653738at_nat @ ( e_b @ c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_g_H_Ofinite__E) ).
thf(35,axiom,
ord_le841296385at_nat @ ( edmond475474836dges_b @ c2 @ s @ t ) @ ( e_b @ c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_g_H_OspEdges__ss__E) ).
thf(36,axiom,
( ( finite772653738at_nat @ ( e_b @ c2 ) )
=> ( finite_finite_nat @ ( v_b @ c2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_g_H_OEfin__imp__Vfin) ).
thf(37,axiom,
( ( finite772653738at_nat @ ( e_b @ c2 ) )
=> ( finite_Graph_b @ c2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_g_H_OFinite__Graph__EI) ).
thf(38,axiom,
ord_le841296385at_nat @ ( e_b @ c2 ) @ ( edmond771116671s_uE_b @ c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_g_H_OE__ss__uE) ).
thf(39,axiom,
! [U3: set_nat] : ( ord_le841296385at_nat @ ( outgoing_a @ c @ U3 ) @ ( e_a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_outgoing_H__edges) ).
thf(40,axiom,
! [U3: set_nat] : ( ord_le841296385at_nat @ ( incoming_a @ c @ U3 ) @ ( e_a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_incoming_H__edges) ).
thf(41,axiom,
! [C: product_prod_nat_nat > a,U: nat] :
( ( finite_Graph_a @ C )
=> ( finite_finite_nat @ ( adjacent_nodes_a @ C @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_Finite__Graph_Oadjacent__nodes__finite) ).
thf(42,axiom,
! [C: product_prod_nat_nat > b,U: nat] :
( ( finite_Graph_b @ C )
=> ( finite_finite_nat @ ( adjacent_nodes_b @ C @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_Finite__Graph_Oadjacent__nodes__finite) ).
thf(43,axiom,
! [C: product_prod_nat_nat > a,U: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ C @ U ) @ ( v_a @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_Graph_Oadjacent__nodes__ss__V) ).
thf(44,axiom,
! [C: product_prod_nat_nat > b,U: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_b @ C @ U ) @ ( v_b @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_Graph_Oadjacent__nodes__ss__V) ).
thf(45,axiom,
! [C: product_prod_nat_nat > b,S: nat,T: nat] :
( ( edmond1517640973ysis_b @ C )
=> ( ord_le841296385at_nat @ ( edmond475474836dges_b @ C @ S @ T ) @ ( e_b @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_ek__analysis_OspEdges__ss__E) ).
thf(46,axiom,
! [C: product_prod_nat_nat > a,S: nat,T: nat] :
( ( edmond1517640972ysis_a @ C )
=> ( ord_le841296385at_nat @ ( edmond475474835dges_a @ C @ S @ T ) @ ( e_a @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_ek__analysis_OspEdges__ss__E) ).
thf(47,axiom,
! [C: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ C )
=> ( ord_le841296385at_nat @ ( e_a @ C ) @ ( edmond771116670s_uE_a @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_ek__analysis_OE__ss__uE) ).
thf(48,axiom,
! [C: product_prod_nat_nat > b] :
( ( edmond1517640973ysis_b @ C )
=> ( ord_le841296385at_nat @ ( e_b @ C ) @ ( edmond771116671s_uE_b @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_ek__analysis_OE__ss__uE) ).
thf(49,axiom,
! [C: product_prod_nat_nat > a] :
( ( finite_Graph_a @ C )
=> ( finite772653738at_nat @ ( e_a @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_Finite__Graph_Ofinite__E) ).
thf(50,axiom,
! [C: product_prod_nat_nat > b] :
( ( finite_Graph_b @ C )
=> ( finite772653738at_nat @ ( e_b @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_Finite__Graph_Ofinite__E) ).
thf(51,axiom,
! [C: product_prod_nat_nat > a] :
( ( finite772653738at_nat @ ( e_a @ C ) )
=> ( finite_Graph_a @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_Graph_OFinite__Graph__EI) ).
thf(52,axiom,
! [C: product_prod_nat_nat > b] :
( ( finite772653738at_nat @ ( e_b @ C ) )
=> ( finite_Graph_b @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_Graph_OFinite__Graph__EI) ).
thf(53,axiom,
! [C: product_prod_nat_nat > b] :
( ( finite_finite_nat @ ( v_b @ C ) )
=> ( finite772653738at_nat @ ( e_b @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_Graph_OVfin__imp__Efin) ).
thf(54,axiom,
! [C: product_prod_nat_nat > a] :
( ( finite_finite_nat @ ( v_a @ C ) )
=> ( finite772653738at_nat @ ( e_a @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_Graph_OVfin__imp__Efin) ).
thf(55,axiom,
! [C: product_prod_nat_nat > b] :
( ( finite772653738at_nat @ ( e_b @ C ) )
=> ( finite_finite_nat @ ( v_b @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_Graph_OEfin__imp__Vfin) ).
thf(56,axiom,
! [C: product_prod_nat_nat > a] :
( ( finite772653738at_nat @ ( e_a @ C ) )
=> ( finite_finite_nat @ ( v_a @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_Graph_OEfin__imp__Vfin) ).
thf(57,axiom,
! [S: nat,C: product_prod_nat_nat > b] :
( ( member_nat @ S @ ( v_b @ C ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_b @ C @ S ) @ ( v_b @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_Graph_Oreachable__ss__V) ).
thf(58,axiom,
! [S: nat,C: product_prod_nat_nat > a] :
( ( member_nat @ S @ ( v_a @ C ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_a @ C @ S ) @ ( v_a @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_Graph_Oreachable__ss__V) ).
thf(59,axiom,
e_b = e_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_Graph_OE_Ocong) ).
thf(60,axiom,
e_a = e_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_Graph_OE_Ocong) ).
thf(61,axiom,
adjacent_nodes_a = adjacent_nodes_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_Graph_Oadjacent__nodes_Ocong) ).
thf(62,axiom,
adjacent_nodes_b = adjacent_nodes_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_Graph_Oadjacent__nodes_Ocong) ).
thf(63,axiom,
reachableNodes_b = reachableNodes_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_Graph_OreachableNodes_Ocong) ).
thf(64,axiom,
reachableNodes_a = reachableNodes_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_Graph_OreachableNodes_Ocong) ).
thf(65,axiom,
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( e_a @ c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_Vfin__imp__Efin) ).
thf(66,axiom,
! [U: nat] : ( finite_finite_nat @ ( adjacent_nodes_a @ c @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_adjacent__nodes__finite) ).
thf(67,axiom,
! [U: nat] : ( finite_finite_nat @ ( adjacent_nodes_b @ c2 @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_g_H_Oadjacent__nodes__finite) ).
thf(68,axiom,
finite772653738at_nat @ ( e_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_finite__E) ).
thf(69,axiom,
( ( finite772653738at_nat @ ( e_a @ c ) )
=> ( finite_finite_nat @ ( v_a @ c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_Efin__imp__Vfin) ).
thf(70,axiom,
( ( finite772653738at_nat @ ( e_a @ c ) )
=> ( finite_Graph_a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_Finite__Graph__EI) ).
thf(71,axiom,
ord_le841296385at_nat @ ( e_a @ c ) @ ( edmond771116670s_uE_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_E__ss__uE) ).
thf(72,axiom,
ord_le841296385at_nat @ ( edmond475474835dges_a @ c @ s @ t ) @ ( e_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_spEdges__ss__E) ).
thf(73,axiom,
! [S: nat] :
( ( member_nat @ S @ ( v_b @ c2 ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_b @ c2 @ S ) @ ( v_b @ c2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_g_H_Oreachable__ss__V) ).
thf(74,axiom,
! [S: nat] :
( ( member_nat @ S @ ( v_a @ c ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_a @ c @ S ) @ ( v_a @ c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_reachable__ss__V) ).
thf(75,axiom,
! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_set_nat @ A2 @ B2 )
=> ( ord_less_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_psubset__card__mono) ).
thf(76,axiom,
! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le116442893at_nat @ A2 @ B2 )
=> ( ord_less_nat @ ( finite447719721at_nat @ A2 ) @ ( finite447719721at_nat @ B2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_psubset__card__mono) ).
thf(77,axiom,
! [C: product_prod_nat_nat > b,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( finite_Graph_b @ C )
=> ( ( member_nat @ U @ ( v_b @ C ) )
=> ( ( isSimplePath_b @ C @ U @ P5 @ V )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_b @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_Finite__Graph_OsimplePath__length__less__V) ).
thf(78,axiom,
! [C: product_prod_nat_nat > a,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( finite_Graph_a @ C )
=> ( ( member_nat @ U @ ( v_a @ C ) )
=> ( ( isSimplePath_a @ C @ U @ P5 @ V )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_a @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_Finite__Graph_OsimplePath__length__less__V) ).
thf(79,axiom,
! [A2: set_se1612935105at_nat,A: set_Pr1986765409at_nat] :
( ( finite1457549322at_nat @ A2 )
=> ( ( member298845450at_nat @ A @ A2 )
=> ? [X2: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ X2 @ A2 )
& ( ord_le841296385at_nat @ A @ X2 )
& ! [Xa: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ Xa @ A2 )
=> ( ( ord_le841296385at_nat @ X2 @ Xa )
=> ( X2 = Xa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_finite__has__maximal2) ).
thf(80,axiom,
! [A2: set_set_nat,A: set_nat] :
( ( finite2012248349et_nat @ A2 )
=> ( ( member_set_nat @ A @ A2 )
=> ? [X2: set_nat] :
( ( member_set_nat @ X2 @ A2 )
& ( ord_less_eq_set_nat @ A @ X2 )
& ! [Xa: set_nat] :
( ( member_set_nat @ Xa @ A2 )
=> ( ( ord_less_eq_set_nat @ X2 @ Xa )
=> ( X2 = Xa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_finite__has__maximal2) ).
thf(81,axiom,
! [A2: set_nat,A: nat] :
( ( finite_finite_nat @ A2 )
=> ( ( member_nat @ A @ A2 )
=> ? [X2: nat] :
( ( member_nat @ X2 @ A2 )
& ( ord_less_eq_nat @ A @ X2 )
& ! [Xa: nat] :
( ( member_nat @ Xa @ A2 )
=> ( ( ord_less_eq_nat @ X2 @ Xa )
=> ( X2 = Xa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_finite__has__maximal2) ).
thf(82,axiom,
! [A2: set_se1612935105at_nat,A: set_Pr1986765409at_nat] :
( ( finite1457549322at_nat @ A2 )
=> ( ( member298845450at_nat @ A @ A2 )
=> ? [X2: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ X2 @ A2 )
& ( ord_le841296385at_nat @ X2 @ A )
& ! [Xa: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ Xa @ A2 )
=> ( ( ord_le841296385at_nat @ Xa @ X2 )
=> ( X2 = Xa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_finite__has__minimal2) ).
thf(83,axiom,
! [A2: set_set_nat,A: set_nat] :
( ( finite2012248349et_nat @ A2 )
=> ( ( member_set_nat @ A @ A2 )
=> ? [X2: set_nat] :
( ( member_set_nat @ X2 @ A2 )
& ( ord_less_eq_set_nat @ X2 @ A )
& ! [Xa: set_nat] :
( ( member_set_nat @ Xa @ A2 )
=> ( ( ord_less_eq_set_nat @ Xa @ X2 )
=> ( X2 = Xa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_finite__has__minimal2) ).
thf(84,axiom,
! [A2: set_nat,A: nat] :
( ( finite_finite_nat @ A2 )
=> ( ( member_nat @ A @ A2 )
=> ? [X2: nat] :
( ( member_nat @ X2 @ A2 )
& ( ord_less_eq_nat @ X2 @ A )
& ! [Xa: nat] :
( ( member_nat @ Xa @ A2 )
=> ( ( ord_less_eq_nat @ Xa @ X2 )
=> ( X2 = Xa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_finite__has__minimal2) ).
thf(85,axiom,
! [C: product_prod_nat_nat > b,S: nat,T: nat] :
( ( edmond1517640973ysis_b @ C )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474836dges_b @ C @ S @ T ) ) @ ( finite447719721at_nat @ ( edmond771116671s_uE_b @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_ek__analysis_Ocard__spEdges__le) ).
thf(86,axiom,
! [C: product_prod_nat_nat > a,S: nat,T: nat] :
( ( edmond1517640972ysis_a @ C )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ C @ S @ T ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_ek__analysis_Ocard__spEdges__le) ).
thf(87,axiom,
( isShortestPath_b
= ( ^ [C2: product_prod_nat_nat > b,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isSimplePath_b @ C2 @ U2 @ P3 @ V4 )
& ( ( size_s1990949619at_nat @ P3 )
= ( min_dist_b @ C2 @ U2 @ V4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_Graph_OisShortestPath__alt) ).
thf(88,axiom,
( isShortestPath_a
= ( ^ [C2: product_prod_nat_nat > a,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isSimplePath_a @ C2 @ U2 @ P3 @ V4 )
& ( ( size_s1990949619at_nat @ P3 )
= ( min_dist_a @ C2 @ U2 @ V4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_Graph_OisShortestPath__alt) ).
thf(89,axiom,
! [A2: set_nat,P2: set_nat > $o] :
( ( finite_finite_nat @ A2 )
=> ( ! [A3: set_nat] :
( ( finite_finite_nat @ A3 )
=> ( ! [B4: set_nat] :
( ( ord_less_set_nat @ B4 @ A3 )
=> ( P2 @ B4 ) )
=> ( P2 @ A3 ) ) )
=> ( P2 @ A2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_finite__psubset__induct) ).
thf(90,axiom,
! [A2: set_Pr1986765409at_nat,P2: set_Pr1986765409at_nat > $o] :
( ( finite772653738at_nat @ A2 )
=> ( ! [A3: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A3 )
=> ( ! [B4: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ B4 @ A3 )
=> ( P2 @ B4 ) )
=> ( P2 @ A3 ) ) )
=> ( P2 @ A2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_finite__psubset__induct) ).
thf(91,axiom,
! [C: product_prod_nat_nat > a] :
( ( finite_Graph_a @ C )
=> ( finite_finite_nat @ ( v_a @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_Finite__Graph_Ofinite__V) ).
thf(92,axiom,
! [C: product_prod_nat_nat > b] :
( ( finite_Graph_b @ C )
=> ( finite_finite_nat @ ( v_b @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_Finite__Graph_Ofinite__V) ).
thf(93,axiom,
! [C: product_prod_nat_nat > a] :
( ( finite_finite_nat @ ( v_a @ C ) )
=> ( finite_Graph_a @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_Finite__Graph_Ointro) ).
thf(94,axiom,
! [C: product_prod_nat_nat > b] :
( ( finite_finite_nat @ ( v_b @ C ) )
=> ( finite_Graph_b @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_Finite__Graph_Ointro) ).
thf(95,axiom,
( finite_Graph_a
= ( ^ [C2: product_prod_nat_nat > a] : ( finite_finite_nat @ ( v_a @ C2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_Finite__Graph__def) ).
thf(96,axiom,
( finite_Graph_b
= ( ^ [C2: product_prod_nat_nat > b] : ( finite_finite_nat @ ( v_b @ C2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_Finite__Graph__def) ).
thf(97,axiom,
! [F2: set_Pr1986765409at_nat,C3: nat] :
( ! [G: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ G @ F2 )
=> ( ( finite772653738at_nat @ G )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ G ) @ C3 ) ) )
=> ( ( finite772653738at_nat @ F2 )
& ( ord_less_eq_nat @ ( finite447719721at_nat @ F2 ) @ C3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_finite__if__finite__subsets__card__bdd) ).
thf(98,axiom,
! [F2: set_nat,C3: nat] :
( ! [G: set_nat] :
( ( ord_less_eq_set_nat @ G @ F2 )
=> ( ( finite_finite_nat @ G )
=> ( ord_less_eq_nat @ ( finite_card_nat @ G ) @ C3 ) ) )
=> ( ( finite_finite_nat @ F2 )
& ( ord_less_eq_nat @ ( finite_card_nat @ F2 ) @ C3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_finite__if__finite__subsets__card__bdd) ).
thf(99,axiom,
! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( ord_less_eq_nat @ ( finite447719721at_nat @ B2 ) @ ( finite447719721at_nat @ A2 ) )
=> ( A2 = B2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_card__seteq) ).
thf(100,axiom,
! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( ord_less_eq_nat @ ( finite_card_nat @ B2 ) @ ( finite_card_nat @ A2 ) )
=> ( A2 = B2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_card__seteq) ).
thf(101,axiom,
! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ A2 ) @ ( finite447719721at_nat @ B2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_card__mono) ).
thf(102,axiom,
! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_card__mono) ).
thf(103,axiom,
! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( ord_less_nat @ ( finite447719721at_nat @ A2 ) @ ( finite447719721at_nat @ B2 ) )
=> ( ord_le116442893at_nat @ A2 @ B2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_card__psubset) ).
thf(104,axiom,
! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( ord_less_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) )
=> ( ord_less_set_nat @ A2 @ B2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_card__psubset) ).
thf(105,axiom,
! [M4: set_li664300135at_nat] :
( ( finite1299096496at_nat @ M4 )
=> ? [N3: nat] :
! [X4: list_P559422087at_nat] :
( ( member1608759472at_nat @ X4 @ M4 )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ X4 ) @ N3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_finite__maxlen) ).
thf(106,axiom,
! [C: product_prod_nat_nat > b,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isShortestPath_b @ C @ S @ P5 @ T )
=> ( isSimplePath_b @ C @ S @ P5 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_Graph_OshortestPath__is__simple) ).
thf(107,axiom,
! [C: product_prod_nat_nat > a,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isShortestPath_a @ C @ S @ P5 @ T )
=> ( isSimplePath_a @ C @ S @ P5 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_Graph_OshortestPath__is__simple) ).
thf(108,axiom,
! [C: product_prod_nat_nat > b,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isPath_b @ C @ S @ P5 @ T )
=> ? [P: list_P559422087at_nat] : ( isSimplePath_b @ C @ S @ P @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_Graph_OisSPath__pathLE) ).
thf(109,axiom,
! [C: product_prod_nat_nat > a,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isPath_a @ C @ S @ P5 @ T )
=> ? [P: list_P559422087at_nat] : ( isSimplePath_a @ C @ S @ P @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_Graph_OisSPath__pathLE) ).
thf(110,axiom,
! [A2: set_Pr1986765409at_nat,N: nat] :
( ~ ( finite772653738at_nat @ A2 )
=> ? [B3: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B3 )
& ( ( finite447719721at_nat @ B3 )
= N )
& ( ord_le841296385at_nat @ B3 @ A2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_infinite__arbitrarily__large) ).
thf(111,axiom,
! [A2: set_nat,N: nat] :
( ~ ( finite_finite_nat @ A2 )
=> ? [B3: set_nat] :
( ( finite_finite_nat @ B3 )
& ( ( finite_card_nat @ B3 )
= N )
& ( ord_less_eq_set_nat @ B3 @ A2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_infinite__arbitrarily__large) ).
thf(112,axiom,
! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( ( finite447719721at_nat @ A2 )
= ( finite447719721at_nat @ B2 ) )
=> ( A2 = B2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_card__subset__eq) ).
thf(113,axiom,
! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( ( finite_card_nat @ A2 )
= ( finite_card_nat @ B2 ) )
=> ( A2 = B2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_card__subset__eq) ).
thf(114,axiom,
! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( finite772653738at_nat @ A2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_rev__finite__subset) ).
thf(115,axiom,
! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( finite_finite_nat @ A2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_rev__finite__subset) ).
thf(116,axiom,
! [S2: set_Pr1986765409at_nat,T2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ S2 @ T2 )
=> ( ~ ( finite772653738at_nat @ S2 )
=> ~ ( finite772653738at_nat @ T2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_infinite__super) ).
thf(117,axiom,
! [S2: set_nat,T2: set_nat] :
( ( ord_less_eq_set_nat @ S2 @ T2 )
=> ( ~ ( finite_finite_nat @ S2 )
=> ~ ( finite_finite_nat @ T2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_infinite__super) ).
thf(118,axiom,
! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( finite772653738at_nat @ B2 )
=> ( finite772653738at_nat @ A2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_finite__subset) ).
thf(119,axiom,
! [A2: set_nat,B2: set_nat] :
( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( finite_finite_nat @ B2 )
=> ( finite_finite_nat @ A2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_finite__subset) ).
thf(120,axiom,
! [A2: set_set_nat,B2: set_set_nat] :
( ( ord_le1613022364et_nat @ A2 @ B2 )
=> ( ( finite2012248349et_nat @ B2 )
=> ( finite2012248349et_nat @ A2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_finite__subset) ).
thf(121,axiom,
! [A2: set_se1612935105at_nat,B2: set_se1612935105at_nat] :
( ( ord_le2096002913at_nat @ A2 @ B2 )
=> ( ( finite1457549322at_nat @ B2 )
=> ( finite1457549322at_nat @ A2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_finite__subset) ).
thf(122,axiom,
isSimplePath_b = isSimplePath_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_Graph_OisSimplePath_Ocong) ).
thf(123,axiom,
isSimplePath_a = isSimplePath_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_Graph_OisSimplePath_Ocong) ).
thf(124,axiom,
! [U: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ c @ U ) @ ( v_a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_adjacent__nodes__ss__V) ).
thf(125,axiom,
! [U: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_b @ c2 @ U ) @ ( v_b @ c2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_g_H_Oadjacent__nodes__ss__V) ).
thf(126,axiom,
( ( v_b @ c2 )
= ( v_a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_Veq) ).
thf(127,axiom,
! [V: nat,D: nat,V3: nat] :
( ( dist_a @ c @ V @ D @ V3 )
=> ( connected_a @ c @ V @ V3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_connected__distI) ).
thf(128,axiom,
! [V: nat] : ( dist_a @ c @ V @ zero_zero_nat @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_dist__z) ).
thf(129,axiom,
! [V: nat,V3: nat] :
( ( dist_a @ c @ V @ zero_zero_nat @ V3 )
= ( V3 = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_dist__z__iff) ).
thf(130,axiom,
finite_finite_nat @ ( v_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_finite__V) ).
thf(131,axiom,
finite_finite_nat @ ( v_b @ c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_g_H_Ofinite__V) ).
thf(132,axiom,
! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_a @ c @ U @ P5 @ V )
= ( ( isSimplePath_a @ c @ U @ P5 @ V )
& ( ( size_s1990949619at_nat @ P5 )
= ( min_dist_a @ c @ U @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_isShortestPath__alt) ).
thf(133,axiom,
! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( member_nat @ S @ ( v_b @ c2 ) )
=> ( ( isShortestPath_b @ c2 @ S @ P5 @ T )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_g_H_OisShortestPath__length__less__V) ).
thf(134,axiom,
! [S: nat,T: nat] :
( ( member_nat @ S @ ( v_b @ c2 ) )
=> ( ( connected_b @ c2 @ S @ T )
=> ( ord_less_nat @ ( min_dist_b @ c2 @ S @ T ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_g_H_Omin__dist__less__V) ).
thf(135,axiom,
! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( member_nat @ U @ ( v_b @ c2 ) )
=> ( ( isSimplePath_b @ c2 @ U @ P5 @ V )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_g_H_OsimplePath__length__less__V) ).
thf(136,axiom,
! [V: nat,V3: nat] :
( ( connected_a @ c @ V @ V3 )
=> ( dist_a @ c @ V @ ( min_dist_a @ c @ V @ V3 ) @ V3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_min__dist__is__dist) ).
thf(137,axiom,
! [V: nat,D: nat,V3: nat] :
( ( dist_a @ c @ V @ D @ V3 )
= ( ? [P3: list_P559422087at_nat] :
( ( isPath_a @ c @ V @ P3 @ V3 )
& ( ( size_s1990949619at_nat @ P3 )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_dist__def) ).
thf(138,axiom,
! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isPath_a @ c @ U @ P5 @ V )
=> ( dist_a @ c @ U @ ( size_s1990949619at_nat @ P5 ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_isPath__distD) ).
thf(139,axiom,
! [V: nat,D: nat,V3: nat] :
( ( dist_a @ c @ V @ D @ V3 )
=> ( ! [D6: nat] :
( ( dist_a @ c @ V @ D6 @ V3 )
=> ( ord_less_eq_nat @ D @ D6 ) )
=> ( ( min_dist_a @ c @ V @ V3 )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_min__distI__eq) ).
thf(140,axiom,
! [V: nat,D: nat,V3: nat] :
( ( dist_a @ c @ V @ D @ V3 )
=> ( ord_less_eq_nat @ ( min_dist_a @ c @ V @ V3 ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_min__dist__minD) ).
thf(141,axiom,
! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isShortestPath_b @ c2 @ S @ P5 @ T )
=> ( isSimplePath_b @ c2 @ S @ P5 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_g_H_OshortestPath__is__simple) ).
thf(142,axiom,
! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isShortestPath_a @ c @ S @ P5 @ T )
=> ( isSimplePath_a @ c @ S @ P5 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_shortestPath__is__simple) ).
thf(143,axiom,
! [V: nat,V3: nat] :
( ( connected_a @ c @ V @ V3 )
= ( ? [D3: nat] : ( dist_a @ c @ V @ D3 @ V3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_connected__by__dist) ).
thf(144,axiom,
! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isPath_a @ c @ S @ P5 @ T )
=> ? [P: list_P559422087at_nat] : ( isSimplePath_a @ c @ S @ P @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_isSPath__pathLE) ).
thf(145,axiom,
! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isPath_b @ c2 @ S @ P5 @ T )
=> ? [P: list_P559422087at_nat] : ( isSimplePath_b @ c2 @ S @ P @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_g_H_OisSPath__pathLE) ).
thf(146,axiom,
! [U: nat,V: nat] :
( ( connected_b @ c2 @ U @ V )
=> ( ( member_nat @ V @ ( v_b @ c2 ) )
= ( member_nat @ U @ ( v_b @ c2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_g_H_Oconnected__inV__iff) ).
thf(147,axiom,
! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_b @ c2 @ U @ P5 @ V )
= ( ( isSimplePath_b @ c2 @ U @ P5 @ V )
& ( ( size_s1990949619at_nat @ P5 )
= ( min_dist_b @ c2 @ U @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_g_H_OisShortestPath__alt) ).
thf(148,axiom,
! [V: nat,V3: nat,Q: nat > $o] :
( ( connected_a @ c @ V @ V3 )
=> ( ! [D4: nat] :
( ( dist_a @ c @ V @ D4 @ V3 )
=> ( ! [D5: nat] :
( ( dist_a @ c @ V @ D5 @ V3 )
=> ( ord_less_eq_nat @ D4 @ D5 ) )
=> ( Q @ D4 ) ) )
=> ( Q @ ( min_dist_a @ c @ V @ V3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_min__distI2) ).
thf(149,axiom,
! [A2: set_nat] :
( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A2 ) )
=> ( finite_finite_nat @ A2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_card__ge__0__finite) ).
thf(150,axiom,
! [A2: set_Pr1986765409at_nat] :
( ( ord_less_nat @ zero_zero_nat @ ( finite447719721at_nat @ A2 ) )
=> ( finite772653738at_nat @ A2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_card__ge__0__finite) ).
thf(151,axiom,
! [A2: set_set_nat] :
( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A2 ) )
=> ( finite2012248349et_nat @ A2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_card__ge__0__finite) ).
thf(152,axiom,
! [A2: set_se1612935105at_nat] :
( ( ord_less_nat @ zero_zero_nat @ ( finite1701894793at_nat @ A2 ) )
=> ( finite1457549322at_nat @ A2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_card__ge__0__finite) ).
thf(153,axiom,
! [A2: set_li664300135at_nat] :
( ( ord_less_nat @ zero_zero_nat @ ( finite83082927at_nat @ A2 ) )
=> ( finite1299096496at_nat @ A2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_card__ge__0__finite) ).
thf(154,axiom,
! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( member_nat @ U @ ( v_a @ c ) )
=> ( ( isSimplePath_a @ c @ U @ P5 @ V )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_simplePath__length__less__V) ).
thf(155,axiom,
ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474836dges_b @ c2 @ s @ t ) ) @ ( finite447719721at_nat @ ( edmond771116671s_uE_b @ c2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_g_H_Ocard__spEdges__le) ).
thf(156,axiom,
ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_card__spEdges__le) ).
thf(157,axiom,
! [A2: set_nat] :
( ~ ( finite_finite_nat @ A2 )
=> ( ( finite_card_nat @ A2 )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_card_Oinfinite) ).
thf(158,axiom,
! [A2: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ A2 )
=> ( ( finite447719721at_nat @ A2 )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_card_Oinfinite) ).
thf(159,axiom,
! [A2: set_set_nat] :
( ~ ( finite2012248349et_nat @ A2 )
=> ( ( finite_card_set_nat @ A2 )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_card_Oinfinite) ).
thf(160,axiom,
! [A2: set_se1612935105at_nat] :
( ~ ( finite1457549322at_nat @ A2 )
=> ( ( finite1701894793at_nat @ A2 )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_card_Oinfinite) ).
thf(161,axiom,
! [A2: set_li664300135at_nat] :
( ~ ( finite1299096496at_nat @ A2 )
=> ( ( finite83082927at_nat @ A2 )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_card_Oinfinite) ).
thf(162,axiom,
( dist_a
= ( ^ [C2: product_prod_nat_nat > a,V4: nat,D3: nat,V5: nat] :
? [P3: list_P559422087at_nat] :
( ( isPath_a @ C2 @ V4 @ P3 @ V5 )
& ( ( size_s1990949619at_nat @ P3 )
= D3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_Graph_Odist__def) ).
thf(163,axiom,
( dist_b
= ( ^ [C2: product_prod_nat_nat > b,V4: nat,D3: nat,V5: nat] :
? [P3: list_P559422087at_nat] :
( ( isPath_b @ C2 @ V4 @ P3 @ V5 )
& ( ( size_s1990949619at_nat @ P3 )
= D3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_Graph_Odist__def) ).
thf(164,axiom,
! [C: product_prod_nat_nat > a,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isPath_a @ C @ U @ P5 @ V )
=> ( dist_a @ C @ U @ ( size_s1990949619at_nat @ P5 ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_Graph_OisPath__distD) ).
thf(165,axiom,
! [C: product_prod_nat_nat > b,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isPath_b @ C @ U @ P5 @ V )
=> ( dist_b @ C @ U @ ( size_s1990949619at_nat @ P5 ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_Graph_OisPath__distD) ).
thf(166,axiom,
! [C: product_prod_nat_nat > a,V: nat,V3: nat] :
( ( connected_a @ C @ V @ V3 )
=> ( dist_a @ C @ V @ ( min_dist_a @ C @ V @ V3 ) @ V3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_Graph_Omin__dist__is__dist) ).
thf(167,axiom,
! [C: product_prod_nat_nat > b,V: nat,V3: nat] :
( ( connected_b @ C @ V @ V3 )
=> ( dist_b @ C @ V @ ( min_dist_b @ C @ V @ V3 ) @ V3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_Graph_Omin__dist__is__dist) ).
thf(168,axiom,
! [C: product_prod_nat_nat > a,Src: nat,V: nat,D: nat,D2: nat] :
( ( connected_a @ C @ Src @ V )
=> ( ( ( min_dist_a @ C @ Src @ V )
= D )
=> ( ( ord_less_nat @ D2 @ D )
=> ? [V2: nat] :
( ( connected_a @ C @ Src @ V2 )
& ( ( min_dist_a @ C @ Src @ V2 )
= D2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Graph_Omin__dist__less) ).
thf(169,axiom,
! [C: product_prod_nat_nat > b,Src: nat,V: nat,D: nat,D2: nat] :
( ( connected_b @ C @ Src @ V )
=> ( ( ( min_dist_b @ C @ Src @ V )
= D )
=> ( ( ord_less_nat @ D2 @ D )
=> ? [V2: nat] :
( ( connected_b @ C @ Src @ V2 )
& ( ( min_dist_b @ C @ Src @ V2 )
= D2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_Graph_Omin__dist__less) ).
thf(170,axiom,
! [C: product_prod_nat_nat > a,V: nat,V3: nat] :
( ( connected_a @ C @ V @ V3 )
=> ( ( ( min_dist_a @ C @ V @ V3 )
= zero_zero_nat )
= ( V3 = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_Graph_Omin__dist__z__iff) ).
thf(171,axiom,
! [C: product_prod_nat_nat > b,V: nat,V3: nat] :
( ( connected_b @ C @ V @ V3 )
=> ( ( ( min_dist_b @ C @ V @ V3 )
= zero_zero_nat )
= ( V3 = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_Graph_Omin__dist__z__iff) ).
thf(172,axiom,
! [C: product_prod_nat_nat > b,U: nat,V: nat] :
( ( connected_b @ C @ U @ V )
=> ~ ! [P4: list_P559422087at_nat] :
~ ( isShortestPath_b @ C @ U @ P4 @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_Graph_Oobtain__shortest__path) ).
thf(173,axiom,
! [C: product_prod_nat_nat > a,U: nat,V: nat] :
( ( connected_a @ C @ U @ V )
=> ~ ! [P4: list_P559422087at_nat] :
~ ( isShortestPath_a @ C @ U @ P4 @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_Graph_Oobtain__shortest__path) ).
thf(174,axiom,
( connected_a
= ( ^ [C2: product_prod_nat_nat > a,V4: nat,V5: nat] :
? [D3: nat] : ( dist_a @ C2 @ V4 @ D3 @ V5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_Graph_Oconnected__by__dist) ).
thf(175,axiom,
( connected_b
= ( ^ [C2: product_prod_nat_nat > b,V4: nat,V5: nat] :
? [D3: nat] : ( dist_b @ C2 @ V4 @ D3 @ V5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_Graph_Oconnected__by__dist) ).
thf(176,axiom,
! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
( ( dist_a @ C @ V @ D @ V3 )
=> ( connected_a @ C @ V @ V3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Graph_Oconnected__distI) ).
thf(177,axiom,
! [C: product_prod_nat_nat > b,V: nat,D: nat,V3: nat] :
( ( dist_b @ C @ V @ D @ V3 )
=> ( connected_b @ C @ V @ V3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_Graph_Oconnected__distI) ).
thf(178,axiom,
! [C: product_prod_nat_nat > b,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_b @ C @ U @ P5 @ V )
=> ( isPath_b @ C @ U @ P5 @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Graph_OshortestPath__is__path) ).
thf(179,axiom,
! [C: product_prod_nat_nat > a,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_a @ C @ U @ P5 @ V )
=> ( isPath_a @ C @ U @ P5 @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_Graph_OshortestPath__is__path) ).
thf(180,axiom,
! [C: product_prod_nat_nat > a,U: nat,V: nat] :
( ( connected_a @ C @ U @ V )
=> ( ( member_nat @ V @ ( v_a @ C ) )
= ( member_nat @ U @ ( v_a @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_Graph_Oconnected__inV__iff) ).
thf(181,axiom,
! [C: product_prod_nat_nat > b,U: nat,V: nat] :
( ( connected_b @ C @ U @ V )
=> ( ( member_nat @ V @ ( v_b @ C ) )
= ( member_nat @ U @ ( v_b @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_Graph_Oconnected__inV__iff) ).
thf(182,axiom,
( connected_a
= ( ^ [C2: product_prod_nat_nat > a,U2: nat,V4: nat] :
? [P3: list_P559422087at_nat] : ( isPath_a @ C2 @ U2 @ P3 @ V4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_Graph_Oconnected__def) ).
thf(183,axiom,
( connected_b
= ( ^ [C2: product_prod_nat_nat > b,U2: nat,V4: nat] :
? [P3: list_P559422087at_nat] : ( isPath_b @ C2 @ U2 @ P3 @ V4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_Graph_Oconnected__def) ).
thf(184,axiom,
! [C: product_prod_nat_nat > a,V: nat,V3: nat] :
( ( dist_a @ C @ V @ zero_zero_nat @ V3 )
= ( V3 = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_Graph_Odist__z__iff) ).
thf(185,axiom,
! [C: product_prod_nat_nat > b,V: nat,V3: nat] :
( ( dist_b @ C @ V @ zero_zero_nat @ V3 )
= ( V3 = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_Graph_Odist__z__iff) ).
thf(186,axiom,
! [C: product_prod_nat_nat > a,V: nat] : ( dist_a @ C @ V @ zero_zero_nat @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_Graph_Odist__z) ).
thf(187,axiom,
! [C: product_prod_nat_nat > b,V: nat] : ( dist_b @ C @ V @ zero_zero_nat @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_Graph_Odist__z) ).
thf(188,axiom,
! [C: product_prod_nat_nat > b,V: nat] :
( ( min_dist_b @ C @ V @ V )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_Graph_Omin__dist__z) ).
thf(189,axiom,
! [C: product_prod_nat_nat > a,V: nat] :
( ( min_dist_a @ C @ V @ V )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_Graph_Omin__dist__z) ).
thf(190,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_bot__nat__0_Oextremum__strict) ).
thf(191,axiom,
! [P2: nat > $o,N: nat] :
( ( P2 @ zero_zero_nat )
=> ( ! [N3: nat] :
( ( ord_less_nat @ zero_zero_nat @ N3 )
=> ( ~ ( P2 @ N3 )
=> ? [M3: nat] :
( ( ord_less_nat @ M3 @ N3 )
& ~ ( P2 @ M3 ) ) ) )
=> ( P2 @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_infinite__descent0) ).
thf(192,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_gr__implies__not0) ).
thf(193,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_less__zeroE) ).
thf(194,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_not__less0) ).
thf(195,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_not__gr0) ).
thf(196,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_gr0I) ).
thf(197,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_zero__less__iff__neq__zero) ).
thf(198,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_gr__implies__not__zero) ).
thf(199,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_not__less__zero) ).
thf(200,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_gr__zeroI) ).
thf(201,axiom,
! [C: product_prod_nat_nat > b,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( finite_Graph_b @ C )
=> ( ( member_nat @ S @ ( v_b @ C ) )
=> ( ( isShortestPath_b @ C @ S @ P5 @ T )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_b @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_Finite__Graph_OisShortestPath__length__less__V) ).
thf(202,axiom,
! [C: product_prod_nat_nat > a,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( finite_Graph_a @ C )
=> ( ( member_nat @ S @ ( v_a @ C ) )
=> ( ( isShortestPath_a @ C @ S @ P5 @ T )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_a @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_Finite__Graph_OisShortestPath__length__less__V) ).
thf(203,axiom,
! [C: product_prod_nat_nat > a,S: nat,T: nat] :
( ( finite_Graph_a @ C )
=> ( ( member_nat @ S @ ( v_a @ C ) )
=> ( ( connected_a @ C @ S @ T )
=> ( ord_less_nat @ ( min_dist_a @ C @ S @ T ) @ ( finite_card_nat @ ( v_a @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_Finite__Graph_Omin__dist__less__V) ).
thf(204,axiom,
! [C: product_prod_nat_nat > b,S: nat,T: nat] :
( ( finite_Graph_b @ C )
=> ( ( member_nat @ S @ ( v_b @ C ) )
=> ( ( connected_b @ C @ S @ T )
=> ( ord_less_nat @ ( min_dist_b @ C @ S @ T ) @ ( finite_card_nat @ ( v_b @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_Finite__Graph_Omin__dist__less__V) ).
thf(205,axiom,
isShortestPath_b = isShortestPath_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Graph_OisShortestPath_Ocong) ).
thf(206,axiom,
isShortestPath_a = isShortestPath_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Graph_OisShortestPath_Ocong) ).
thf(207,axiom,
dist_a = dist_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Graph_Odist_Ocong) ).
thf(208,axiom,
dist_b = dist_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_Graph_Odist_Ocong) ).
thf(209,axiom,
! [C: product_prod_nat_nat > a,V: nat] : ( connected_a @ C @ V @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Graph_Oconnected__refl) ).
thf(210,axiom,
! [C: product_prod_nat_nat > b,V: nat] : ( connected_b @ C @ V @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_Graph_Oconnected__refl) ).
thf(211,axiom,
connected_a = connected_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Graph_Oconnected_Ocong) ).
thf(212,axiom,
connected_b = connected_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_Graph_Oconnected_Ocong) ).
thf(213,axiom,
min_dist_b = min_dist_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_Graph_Omin__dist_Ocong) ).
thf(214,axiom,
min_dist_a = min_dist_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_Graph_Omin__dist_Ocong) ).
thf(215,axiom,
v_b = v_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_Graph_OV_Ocong) ).
thf(216,axiom,
v_a = v_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_Graph_OV_Ocong) ).
thf(217,axiom,
isPath_a = isPath_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_Graph_OisPath_Ocong) ).
thf(218,axiom,
isPath_b = isPath_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Graph_OisPath_Ocong) ).
thf(219,axiom,
! [X3: list_P559422087at_nat,Y3: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ X3 )
!= ( size_s1990949619at_nat @ Y3 ) )
=> ( X3 != Y3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_size__neq__size__imp__neq) ).
thf(220,axiom,
! [X3: nat,Y3: nat] :
( ( X3 != Y3 )
=> ( ~ ( ord_less_nat @ X3 @ Y3 )
=> ( ord_less_nat @ Y3 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_linorder__neqE__nat) ).
thf(221,axiom,
! [P2: nat > $o,N: nat] :
( ! [N3: nat] :
( ~ ( P2 @ N3 )
=> ? [M3: nat] :
( ( ord_less_nat @ M3 @ N3 )
& ~ ( P2 @ M3 ) ) )
=> ( P2 @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_infinite__descent) ).
thf(222,axiom,
! [P2: nat > $o,N: nat] :
( ! [N3: nat] :
( ! [M3: nat] :
( ( ord_less_nat @ M3 @ N3 )
=> ( P2 @ M3 ) )
=> ( P2 @ N3 ) )
=> ( P2 @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_nat__less__induct) ).
thf(223,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_less__irrefl__nat) ).
thf(224,axiom,
! [S: nat,T: nat] :
( ( ord_less_nat @ S @ T )
=> ( S != T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_less__not__refl3) ).
thf(225,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
=> ( M != N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_less__not__refl2) ).
thf(226,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_less__not__refl) ).
thf(227,axiom,
! [M: nat,N: nat] :
( ( M != N )
= ( ( ord_less_nat @ M @ N )
| ( ord_less_nat @ N @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_nat__neq__iff) ).
thf(228,axiom,
! [X3: nat] :
( ( zero_zero_nat = X3 )
= ( X3 = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_zero__reorient) ).
thf(229,axiom,
( isShortestPath_b
= ( ^ [C2: product_prod_nat_nat > b,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isPath_b @ C2 @ U2 @ P3 @ V4 )
& ! [P6: list_P559422087at_nat] :
( ( isPath_b @ C2 @ U2 @ P6 @ V4 )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P3 ) @ ( size_s1990949619at_nat @ P6 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Graph_OisShortestPath__def) ).
thf(230,axiom,
( isShortestPath_a
= ( ^ [C2: product_prod_nat_nat > a,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isPath_a @ C2 @ U2 @ P3 @ V4 )
& ! [P6: list_P559422087at_nat] :
( ( isPath_a @ C2 @ U2 @ P6 @ V4 )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P3 ) @ ( size_s1990949619at_nat @ P6 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_Graph_OisShortestPath__def) ).
thf(231,axiom,
! [C: product_prod_nat_nat > a,V: nat,V3: nat,Q: nat > $o] :
( ( connected_a @ C @ V @ V3 )
=> ( ! [D4: nat] :
( ( dist_a @ C @ V @ D4 @ V3 )
=> ( ! [D5: nat] :
( ( dist_a @ C @ V @ D5 @ V3 )
=> ( ord_less_eq_nat @ D4 @ D5 ) )
=> ( Q @ D4 ) ) )
=> ( Q @ ( min_dist_a @ C @ V @ V3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_Graph_Omin__distI2) ).
thf(232,axiom,
! [C: product_prod_nat_nat > b,V: nat,V3: nat,Q: nat > $o] :
( ( connected_b @ C @ V @ V3 )
=> ( ! [D4: nat] :
( ( dist_b @ C @ V @ D4 @ V3 )
=> ( ! [D5: nat] :
( ( dist_b @ C @ V @ D5 @ V3 )
=> ( ord_less_eq_nat @ D4 @ D5 ) )
=> ( Q @ D4 ) ) )
=> ( Q @ ( min_dist_b @ C @ V @ V3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_Graph_Omin__distI2) ).
thf(233,axiom,
! [C: product_prod_nat_nat > b,V: nat,D: nat,V3: nat] :
( ( dist_b @ C @ V @ D @ V3 )
=> ( ! [D6: nat] :
( ( dist_b @ C @ V @ D6 @ V3 )
=> ( ord_less_eq_nat @ D @ D6 ) )
=> ( ( min_dist_b @ C @ V @ V3 )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Graph_Omin__distI__eq) ).
thf(234,axiom,
! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
( ( dist_a @ C @ V @ D @ V3 )
=> ( ! [D6: nat] :
( ( dist_a @ C @ V @ D6 @ V3 )
=> ( ord_less_eq_nat @ D @ D6 ) )
=> ( ( min_dist_a @ C @ V @ V3 )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_Graph_Omin__distI__eq) ).
thf(235,axiom,
! [C: product_prod_nat_nat > b,V: nat,D: nat,V3: nat] :
( ( dist_b @ C @ V @ D @ V3 )
=> ( ord_less_eq_nat @ ( min_dist_b @ C @ V @ V3 ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_Graph_Omin__dist__minD) ).
thf(236,axiom,
! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
( ( dist_a @ C @ V @ D @ V3 )
=> ( ord_less_eq_nat @ ( min_dist_a @ C @ V @ V3 ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_Graph_Omin__dist__minD) ).
thf(237,axiom,
! [C: product_prod_nat_nat > a,Src: nat,V: nat,D2: nat] :
( ( connected_a @ C @ Src @ V )
=> ( ( ord_less_eq_nat @ D2 @ ( min_dist_a @ C @ Src @ V ) )
=> ? [V2: nat] :
( ( connected_a @ C @ Src @ V2 )
& ( ( min_dist_a @ C @ Src @ V2 )
= D2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_Graph_Omin__dist__le) ).
thf(238,axiom,
! [C: product_prod_nat_nat > b,Src: nat,V: nat,D2: nat] :
( ( connected_b @ C @ Src @ V )
=> ( ( ord_less_eq_nat @ D2 @ ( min_dist_b @ C @ Src @ V ) )
=> ? [V2: nat] :
( ( connected_b @ C @ Src @ V2 )
& ( ( min_dist_b @ C @ Src @ V2 )
= D2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_Graph_Omin__dist__le) ).
thf(239,axiom,
! [P2: nat > $o,N: nat] :
( ( P2 @ N )
=> ( ~ ( P2 @ zero_zero_nat )
=> ? [K2: nat] :
( ( ord_less_eq_nat @ K2 @ N )
& ! [I3: nat] :
( ( ord_less_nat @ I3 @ K2 )
=> ~ ( P2 @ I3 ) )
& ( P2 @ K2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_ex__least__nat__le) ).
thf(240,axiom,
! [F: nat > nat,I: nat,J: nat] :
( ! [I2: nat,J2: nat] :
( ( ord_less_nat @ I2 @ J2 )
=> ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
=> ( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_less__mono__imp__le__mono) ).
thf(241,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( M != N )
=> ( ord_less_nat @ M @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_le__neq__implies__less) ).
thf(242,axiom,
! [M: nat,N: nat] :
( ( ( ord_less_nat @ M @ N )
| ( M = N ) )
=> ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_less__or__eq__imp__le) ).
thf(243,axiom,
( ord_less_eq_nat
= ( ^ [M2: nat,N2: nat] :
( ( ord_less_nat @ M2 @ N2 )
| ( M2 = N2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_le__eq__less__or__eq) ).
thf(244,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_less__imp__le__nat) ).
thf(245,axiom,
( ord_less_nat
= ( ^ [M2: nat,N2: nat] :
( ( ord_less_eq_nat @ M2 @ N2 )
& ( M2 != N2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_nat__less__le) ).
thf(246,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_bot__nat__0_Oextremum__uniqueI) ).
thf(247,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_bot__nat__0_Oextremum__unique) ).
thf(248,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_le__0__eq) ).
thf(249,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_less__eq__nat_Osimps_I1_J) ).
thf(250,axiom,
! [P2: nat > $o,K: nat,B: nat] :
( ( P2 @ K )
=> ( ! [Y: nat] :
( ( P2 @ Y )
=> ( ord_less_eq_nat @ Y @ B ) )
=> ? [X2: nat] :
( ( P2 @ X2 )
& ! [Y2: nat] :
( ( P2 @ Y2 )
=> ( ord_less_eq_nat @ Y2 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Nat_Oex__has__greatest__nat) ).
thf(251,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
| ( ord_less_eq_nat @ N @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_nat__le__linear) ).
thf(252,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_eq_nat @ N @ M )
=> ( M = N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_le__antisym) ).
thf(253,axiom,
! [M: nat,N: nat] :
( ( M = N )
=> ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_eq__imp__le) ).
thf(254,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_less_eq_nat @ J @ K )
=> ( ord_less_eq_nat @ I @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_le__trans) ).
thf(255,axiom,
! [N: nat] : ( ord_less_eq_nat @ N @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_le__refl) ).
thf(256,axiom,
! [X3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_zero__le) ).
thf(257,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_bot__nat__0_Oextremum) ).
thf(258,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_le0) ).
thf(259,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_le__zero__eq) ).
thf(260,axiom,
! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_b @ c2 @ U @ P5 @ V )
= ( ( isPath_b @ c2 @ U @ P5 @ V )
& ! [P6: list_P559422087at_nat] :
( ( isPath_b @ c2 @ U @ P6 @ V )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P5 ) @ ( size_s1990949619at_nat @ P6 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_g_H_OisShortestPath__def) ).
thf(261,axiom,
! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_a @ c @ U @ P5 @ V )
= ( ( isPath_a @ c @ U @ P5 @ V )
& ( ( size_s1990949619at_nat @ P5 )
= ( min_dist_a @ c @ U @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_isShortestPath__min__dist__def) ).
thf(262,axiom,
! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_a @ c @ U @ P5 @ V )
= ( ( isPath_a @ c @ U @ P5 @ V )
& ! [P6: list_P559422087at_nat] :
( ( isPath_a @ c @ U @ P6 @ V )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P5 ) @ ( size_s1990949619at_nat @ P6 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_isShortestPath__def) ).
thf(263,axiom,
! [Src: nat,V: nat,D2: nat] :
( ( connected_a @ c @ Src @ V )
=> ( ( ord_less_eq_nat @ D2 @ ( min_dist_a @ c @ Src @ V ) )
=> ? [V2: nat] :
( ( connected_a @ c @ Src @ V2 )
& ( ( min_dist_a @ c @ Src @ V2 )
= D2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_min__dist__le) ).
thf(264,axiom,
! [V: nat,D: nat,V3: nat] :
( ( dist_b @ c2 @ V @ D @ V3 )
=> ( ord_less_eq_nat @ ( min_dist_b @ c2 @ V @ V3 ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_g_H_Omin__dist__minD) ).
thf(265,axiom,
! [V: nat,D: nat,V3: nat] :
( ( dist_b @ c2 @ V @ D @ V3 )
=> ( ! [D6: nat] :
( ( dist_b @ c2 @ V @ D6 @ V3 )
=> ( ord_less_eq_nat @ D @ D6 ) )
=> ( ( min_dist_b @ c2 @ V @ V3 )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_g_H_Omin__distI__eq) ).
thf(266,axiom,
! [Src: nat,V: nat,D2: nat] :
( ( connected_b @ c2 @ Src @ V )
=> ( ( ord_less_eq_nat @ D2 @ ( min_dist_b @ c2 @ Src @ V ) )
=> ? [V2: nat] :
( ( connected_b @ c2 @ Src @ V2 )
& ( ( min_dist_b @ c2 @ Src @ V2 )
= D2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_g_H_Omin__dist__le) ).
thf(267,axiom,
! [U: nat,V: nat] :
( ( connected_b @ c2 @ U @ V )
=> ~ ! [P4: list_P559422087at_nat] :
~ ( isShortestPath_b @ c2 @ U @ P4 @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_g_H_Oobtain__shortest__path) ).
thf(268,axiom,
! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_b @ c2 @ U @ P5 @ V )
=> ( isPath_b @ c2 @ U @ P5 @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_g_H_OshortestPath__is__path) ).
thf(269,axiom,
! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_a @ c @ U @ P5 @ V )
=> ( isPath_a @ c @ U @ P5 @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_shortestPath__is__path) ).
thf(270,axiom,
! [U: nat,V: nat] :
( ( connected_a @ c @ U @ V )
= ( ? [P3: list_P559422087at_nat] : ( isPath_a @ c @ U @ P3 @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_connected__def) ).
thf(271,axiom,
! [S: nat,T: nat] :
( ( member_nat @ S @ ( v_a @ c ) )
=> ( ( connected_a @ c @ S @ T )
=> ( ord_less_nat @ ( min_dist_a @ c @ S @ T ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_min__dist__less__V) ).
thf(272,axiom,
! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( member_nat @ S @ ( v_a @ c ) )
=> ( ( isShortestPath_a @ c @ S @ P5 @ T )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_isShortestPath__length__less__V) ).
thf(273,axiom,
! [V: nat,V3: nat,Q: nat > $o] :
( ( connected_b @ c2 @ V @ V3 )
=> ( ! [D4: nat] :
( ( dist_b @ c2 @ V @ D4 @ V3 )
=> ( ! [D5: nat] :
( ( dist_b @ c2 @ V @ D5 @ V3 )
=> ( ord_less_eq_nat @ D4 @ D5 ) )
=> ( Q @ D4 ) ) )
=> ( Q @ ( min_dist_b @ c2 @ V @ V3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_g_H_Omin__distI2) ).
thf(274,axiom,
! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_b @ c2 @ U @ P5 @ V )
= ( ( isPath_b @ c2 @ U @ P5 @ V )
& ( ( size_s1990949619at_nat @ P5 )
= ( min_dist_b @ c2 @ U @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_g_H_OisShortestPath__min__dist__def) ).
thf(275,axiom,
( isShortestPath_b
= ( ^ [C2: product_prod_nat_nat > b,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isPath_b @ C2 @ U2 @ P3 @ V4 )
& ( ( size_s1990949619at_nat @ P3 )
= ( min_dist_b @ C2 @ U2 @ V4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Graph_OisShortestPath__min__dist__def) ).
thf(276,axiom,
( isShortestPath_a
= ( ^ [C2: product_prod_nat_nat > a,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isPath_a @ C2 @ U2 @ P3 @ V4 )
& ( ( size_s1990949619at_nat @ P3 )
= ( min_dist_a @ C2 @ U2 @ V4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Graph_OisShortestPath__min__dist__def) ).
thf(277,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_not__gr__zero) ).
thf(278,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_neq0__conv) ).
thf(279,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_less__nat__zero__code) ).
thf(280,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_bot__nat__0_Onot__eq__extremum) ).
thf(281,axiom,
! [N: nat] :
? [Xs2: list_P559422087at_nat] :
( ( size_s1990949619at_nat @ Xs2 )
= N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_Ex__list__of__length) ).
thf(282,axiom,
! [Xs: list_P559422087at_nat,Ys2: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Xs )
!= ( size_s1990949619at_nat @ Ys2 ) )
=> ( Xs != Ys2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_neq__if__length__neq) ).
thf(283,axiom,
! [C: product_prod_nat_nat > b,S: nat,T: nat] :
( ( edmond1517640973ysis_b @ C )
=> ( finite772653738at_nat @ ( edmond475474836dges_b @ C @ S @ T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_ek__analysis_Ofinite__spEdges) ).
thf(284,axiom,
! [C: product_prod_nat_nat > a,S: nat,T: nat] :
( ( edmond1517640972ysis_a @ C )
=> ( finite772653738at_nat @ ( edmond475474835dges_a @ C @ S @ T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_ek__analysis_Ofinite__spEdges) ).
thf(285,axiom,
! [C: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ C )
=> ( finite772653738at_nat @ ( edmond771116670s_uE_a @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_ek__analysis_Ofinite__uE) ).
thf(286,axiom,
! [C: product_prod_nat_nat > b] :
( ( edmond1517640973ysis_b @ C )
=> ( finite772653738at_nat @ ( edmond771116671s_uE_b @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_ek__analysis_Ofinite__uE) ).
thf(287,axiom,
! [V: nat,V3: nat] :
( ( connected_a @ c @ V @ V3 )
=> ( ( ( min_dist_a @ c @ V @ V3 )
= zero_zero_nat )
= ( V3 = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_min__dist__z__iff) ).
thf(288,axiom,
! [P2: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
( ! [X2: product_prod_nat_nat] :
( ( P2 @ X2 )
= ( Q @ X2 ) )
=> ( ( collec7649004at_nat @ P2 )
= ( collec7649004at_nat @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Collect__cong) ).
thf(289,axiom,
! [P2: nat > $o,Q: nat > $o] :
( ! [X2: nat] :
( ( P2 @ X2 )
= ( Q @ X2 ) )
=> ( ( collect_nat @ P2 )
= ( collect_nat @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Collect__cong) ).
thf(290,axiom,
! [A2: set_nat] :
( ( collect_nat
@ ^ [X: nat] : ( member_nat @ X @ A2 ) )
= A2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Collect__mem__eq) ).
thf(291,axiom,
! [A2: set_Pr1986765409at_nat] :
( ( collec7649004at_nat
@ ^ [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ A2 ) )
= A2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Collect__mem__eq) ).
thf(292,axiom,
! [A2: set_set_nat] :
( ( collect_set_nat
@ ^ [X: set_nat] : ( member_set_nat @ X @ A2 ) )
= A2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Collect__mem__eq) ).
thf(293,axiom,
! [A2: set_se1612935105at_nat] :
( ( collec1606769740at_nat
@ ^ [X: set_Pr1986765409at_nat] : ( member298845450at_nat @ X @ A2 ) )
= A2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Collect__mem__eq) ).
thf(294,axiom,
! [A: nat,P2: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ P2 ) )
= ( P2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_mem__Collect__eq) ).
thf(295,axiom,
! [A: product_prod_nat_nat,P2: product_prod_nat_nat > $o] :
( ( member701585322at_nat @ A @ ( collec7649004at_nat @ P2 ) )
= ( P2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_mem__Collect__eq) ).
thf(296,axiom,
! [A: set_nat,P2: set_nat > $o] :
( ( member_set_nat @ A @ ( collect_set_nat @ P2 ) )
= ( P2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_mem__Collect__eq) ).
thf(297,axiom,
! [A: set_Pr1986765409at_nat,P2: set_Pr1986765409at_nat > $o] :
( ( member298845450at_nat @ A @ ( collec1606769740at_nat @ P2 ) )
= ( P2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_mem__Collect__eq) ).
thf(298,axiom,
! [V: nat,V3: nat] :
( ( connected_b @ c2 @ V @ V3 )
=> ( ( ( min_dist_b @ c2 @ V @ V3 )
= zero_zero_nat )
= ( V3 = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_g_H_Omin__dist__z__iff) ).
thf(299,axiom,
finite772653738at_nat @ ( edmond771116670s_uE_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_finite__uE) ).
thf(300,axiom,
finite772653738at_nat @ ( edmond771116671s_uE_b @ c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_g_H_Ofinite__uE) ).
thf(301,axiom,
! [V: nat,D: nat,V3: nat] :
( ( dist_b @ c2 @ V @ D @ V3 )
=> ( connected_b @ c2 @ V @ V3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_g_H_Oconnected__distI) ).
thf(302,axiom,
! [V: nat] : ( dist_b @ c2 @ V @ zero_zero_nat @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_g_H_Odist__z) ).
thf(303,axiom,
! [V: nat,V3: nat] :
( ( dist_b @ c2 @ V @ zero_zero_nat @ V3 )
= ( V3 = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_g_H_Odist__z__iff) ).
thf(304,axiom,
! [V: nat] : ( connected_a @ c @ V @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_connected__refl) ).
thf(305,axiom,
! [V: nat] : ( connected_b @ c2 @ V @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_g_H_Oconnected__refl) ).
thf(306,axiom,
! [V: nat,V3: nat] :
( ( connected_b @ c2 @ V @ V3 )
=> ( dist_b @ c2 @ V @ ( min_dist_b @ c2 @ V @ V3 ) @ V3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_g_H_Omin__dist__is__dist) ).
thf(307,axiom,
! [V: nat,D: nat,V3: nat] :
( ( dist_b @ c2 @ V @ D @ V3 )
= ( ? [P3: list_P559422087at_nat] :
( ( isPath_b @ c2 @ V @ P3 @ V3 )
& ( ( size_s1990949619at_nat @ P3 )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_g_H_Odist__def) ).
thf(308,axiom,
! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isPath_b @ c2 @ U @ P5 @ V )
=> ( dist_b @ c2 @ U @ ( size_s1990949619at_nat @ P5 ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_g_H_OisPath__distD) ).
thf(309,axiom,
! [U: nat,V: nat] :
( ( connected_a @ c @ U @ V )
=> ~ ! [P4: list_P559422087at_nat] :
~ ( isShortestPath_a @ c @ U @ P4 @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_obtain__shortest__path) ).
thf(310,axiom,
! [V: nat,V3: nat] :
( ( connected_b @ c2 @ V @ V3 )
= ( ? [D3: nat] : ( dist_b @ c2 @ V @ D3 @ V3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_g_H_Oconnected__by__dist) ).
thf(311,axiom,
! [U: nat,V: nat] :
( ( connected_a @ c @ U @ V )
=> ( ( member_nat @ V @ ( v_a @ c ) )
= ( member_nat @ U @ ( v_a @ c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_connected__inV__iff) ).
thf(312,axiom,
! [U: nat,V: nat] :
( ( connected_b @ c2 @ U @ V )
= ( ? [P3: list_P559422087at_nat] : ( isPath_b @ c2 @ U @ P3 @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_g_H_Oconnected__def) ).
thf(313,axiom,
! [V: nat] :
( ( min_dist_b @ c2 @ V @ V )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_g_H_Omin__dist__z) ).
thf(314,axiom,
! [V: nat] :
( ( min_dist_a @ c @ V @ V )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_min__dist__z) ).
thf(315,axiom,
finite772653738at_nat @ ( edmond475474836dges_b @ c2 @ s @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_g_H_Ofinite__spEdges) ).
thf(316,axiom,
finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_finite__spEdges) ).
thf(317,axiom,
! [P2: list_P559422087at_nat > $o,Xs: list_P559422087at_nat] :
( ! [Xs2: list_P559422087at_nat] :
( ! [Ys: list_P559422087at_nat] :
( ( ord_less_nat @ ( size_s1990949619at_nat @ Ys ) @ ( size_s1990949619at_nat @ Xs2 ) )
=> ( P2 @ Ys ) )
=> ( P2 @ Xs2 ) )
=> ( P2 @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_length__induct) ).
thf(318,axiom,
! [Src: nat,V: nat,D: nat,D2: nat] :
( ( connected_b @ c2 @ Src @ V )
=> ( ( ( min_dist_b @ c2 @ Src @ V )
= D )
=> ( ( ord_less_nat @ D2 @ D )
=> ? [V2: nat] :
( ( connected_b @ c2 @ Src @ V2 )
& ( ( min_dist_b @ c2 @ Src @ V2 )
= D2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_g_H_Omin__dist__less) ).
thf(319,axiom,
! [Src: nat,V: nat,D: nat,D2: nat] :
( ( connected_a @ c @ Src @ V )
=> ( ( ( min_dist_a @ c @ Src @ V )
= D )
=> ( ( ord_less_nat @ D2 @ D )
=> ? [V2: nat] :
( ( connected_a @ c @ Src @ V2 )
& ( ( min_dist_a @ c @ Src @ V2 )
= D2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_min__dist__less) ).
thf(320,axiom,
connected_a @ c @ s @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_CONN) ).
thf(321,axiom,
~ ! [P: list_P559422087at_nat] :
( ( isPath_b @ c2 @ s @ P @ t )
=> ( ( size_s1990949619at_nat @ P )
!= ( min_dist_b @ c2 @ s @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062p_H_O_A_092_060lbrakk_062g_H_OisPath_As_Ap_H_At_059_Alength_Ap_H_A_061_Ag_H_Omin__dist_As_At_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(322,axiom,
dist_b @ c2 @ s @ ( min_dist_b @ c2 @ s @ t ) @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26__092_060open_062g_H_Odist_As_A_Ig_H_Omin__dist_As_At_J_At_092_060close_062) ).
thf(323,axiom,
( ~ ( connected_b @ c2 @ s @ t )
=> ( ord_less_nat @ ( edmond1022345717sure_b @ c2 @ s @ t ) @ ( edmond1022345716sure_a @ c @ s @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25__092_060open_062_092_060not_062_Ag_H_Oconnected_As_At_A_092_060Longrightarrow_062_Ag_H_OekMeasure_A_060_AekMeasure_092_060close_062) ).
thf(324,axiom,
! [C: product_prod_nat_nat > b] :
( ( edmond1517640973ysis_b @ C )
=> ( finite_Graph_b @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_ek__analysis_Oaxioms) ).
thf(325,axiom,
! [C: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ C )
=> ( finite_Graph_a @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_ek__analysis_Oaxioms) ).
thf(326,axiom,
! [C: product_prod_nat_nat > b] :
( ( finite_Graph_b @ C )
=> ( edmond1517640973ysis_b @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_ek__analysis_Ointro) ).
thf(327,axiom,
! [C: product_prod_nat_nat > a] :
( ( finite_Graph_a @ C )
=> ( edmond1517640972ysis_a @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_ek__analysis_Ointro) ).
thf(328,axiom,
edmond1517640973ysis_b = finite_Graph_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_ek__analysis__def) ).
thf(329,axiom,
edmond1517640972ysis_a = finite_Graph_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_ek__analysis__def) ).
thf(330,axiom,
isPath_b @ c2 @ s @ p2 @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_P_H) ).
thf(331,axiom,
member_nat @ s @ ( v_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_SV) ).
thf(332,axiom,
connected_b @ c2 @ s @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_CONN2) ).
thf(333,axiom,
isShortestPath_a @ c @ s @ p @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_SP) ).
thf(334,axiom,
( ( edmond771116671s_uE_b @ c2 )
= ( edmond771116670s_uE_a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_uE__eq) ).
thf(335,axiom,
ord_less_nat @ ( size_s1990949619at_nat @ p ) @ ( size_s1990949619at_nat @ p2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__092_060open_062length_Ap_A_060_Alength_Ap_H_092_060close_062) ).
thf(336,axiom,
finite_Graph_a @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_Finite__Graph__axioms) ).
thf(337,axiom,
finite_Graph_b @ c2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_g_H_OFinite__Graph__axioms) ).
thf(338,axiom,
edmond475474836dges_b = edmond475474836dges_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_ek__analysis__defs_OspEdges_Ocong) ).
thf(339,axiom,
edmond475474835dges_a = edmond475474835dges_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_ek__analysis__defs_OspEdges_Ocong) ).
thf(340,axiom,
edmond771116670s_uE_a = edmond771116670s_uE_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_ek__analysis__defs_OuE_Ocong) ).
thf(341,axiom,
edmond771116671s_uE_b = edmond771116671s_uE_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_ek__analysis__defs_OuE_Ocong) ).
thf(342,axiom,
ord_less_nat @ ( min_dist_b @ c2 @ s @ t ) @ ( min_dist_a @ c @ s @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_SHORTER) ).
thf(343,axiom,
edmond1517640973ysis_b @ c2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_g_H_Oek__analysis__axioms) ).
thf(344,axiom,
edmond1022345716sure_a = edmond1022345716sure_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_ek__analysis__defs_OekMeasure_Ocong) ).
thf(345,axiom,
edmond1022345717sure_b = edmond1022345717sure_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_ek__analysis__defs_OekMeasure_Ocong) ).
thf(346,axiom,
( ( size_s1990949619at_nat @ p2 )
= ( min_dist_b @ c2 @ s @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_LENP_H) ).
thf(347,axiom,
( ( size_s1990949619at_nat @ p )
= ( min_dist_a @ c @ s @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_LENP) ).
thf(348,axiom,
edmond1517640972ysis_a @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_ek__analysis__axioms) ).
thf(349,conjecture,
$false,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(350,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[349]) ).
thf(351,plain,
$false = $false,
inference(unfold_def,[status(thm)],[350]) ).
thf(352,plain,
( ( ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C3: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( ord_le841296385at_nat @ B2 @ C3 )
=> ( ord_le841296385at_nat @ A2 @ C3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(353,plain,
( ( ! [A2: set_nat,B2: set_nat,C3: set_nat] :
( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( ord_less_eq_set_nat @ B2 @ C3 )
=> ( ord_less_eq_set_nat @ A2 @ C3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(354,plain,
( ( ( ^ [Y4: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] : ( Y4 = Z ) )
= ( ^ [A4: set_Pr1986765409at_nat,B5: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A4 @ B5 )
& ( ord_le841296385at_nat @ B5 @ A4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(355,plain,
( ( ( ^ [Y4: set_nat,Z: set_nat] : ( Y4 = Z ) )
= ( ^ [A4: set_nat,B5: set_nat] :
( ( ord_less_eq_set_nat @ A4 @ B5 )
& ( ord_less_eq_set_nat @ B5 @ A4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(356,plain,
( ( ! [P2: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
( ( ord_le841296385at_nat @ ( collec7649004at_nat @ P2 ) @ ( collec7649004at_nat @ Q ) )
= ( ! [X: product_prod_nat_nat] :
( ( P2 @ X )
=> ( Q @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(357,plain,
( ( ! [P2: nat > $o,Q: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q ) )
= ( ! [X: nat] :
( ( P2 @ X )
=> ( Q @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(358,plain,
( ( ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(359,plain,
( ( ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
( ! [X2: product_prod_nat_nat] :
( ( member701585322at_nat @ X2 @ A2 )
=> ( member701585322at_nat @ X2 @ B2 ) )
=> ( ord_le841296385at_nat @ A2 @ B2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(360,plain,
( ( ! [A2: set_nat,B2: set_nat] :
( ! [X2: nat] :
( ( member_nat @ X2 @ A2 )
=> ( member_nat @ X2 @ B2 ) )
=> ( ord_less_eq_set_nat @ A2 @ B2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(361,plain,
( ( ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( ord_le841296385at_nat @ B2 @ A2 )
=> ( A2 = B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(362,plain,
( ( ! [A2: set_nat,B2: set_nat] :
( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( ord_less_eq_set_nat @ B2 @ A2 )
=> ( A2 = B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(363,plain,
( ( ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( A2 != B2 )
=> ( ord_le116442893at_nat @ A2 @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(364,plain,
( ( ! [A2: set_nat,B2: set_nat] :
( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( A2 != B2 )
=> ( ord_less_set_nat @ A2 @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(365,plain,
( ( ord_le841296385at_nat @ edges @ ( e_a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(366,plain,
( ( ! [U3: set_nat] :
( ( finite_finite_nat @ ( v_b @ c2 ) )
=> ( finite772653738at_nat @ ( incoming_b @ c2 @ U3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(367,plain,
( ( ! [U3: set_nat] :
( ( finite_finite_nat @ ( v_b @ c2 ) )
=> ( finite772653738at_nat @ ( outgoing_b @ c2 @ U3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(368,plain,
( ( ! [U3: set_nat] : ( ord_le841296385at_nat @ ( outgoing_b @ c2 @ U3 ) @ ( e_b @ c2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(369,plain,
( ( ! [U3: set_nat] : ( ord_le841296385at_nat @ ( incoming_b @ c2 @ U3 ) @ ( e_b @ c2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(370,plain,
( ( ! [C: product_prod_nat_nat > b,U3: set_nat] :
( ( finite_finite_nat @ ( v_b @ C ) )
=> ( finite772653738at_nat @ ( incoming_b @ C @ U3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(371,plain,
( ( ! [C: product_prod_nat_nat > a,U3: set_nat] :
( ( finite_finite_nat @ ( v_a @ C ) )
=> ( finite772653738at_nat @ ( incoming_a @ C @ U3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(372,plain,
( ( ! [C: product_prod_nat_nat > b,U3: set_nat] :
( ( finite_finite_nat @ ( v_b @ C ) )
=> ( finite772653738at_nat @ ( outgoing_b @ C @ U3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(373,plain,
( ( ! [C: product_prod_nat_nat > a,U3: set_nat] :
( ( finite_finite_nat @ ( v_a @ C ) )
=> ( finite772653738at_nat @ ( outgoing_a @ C @ U3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(374,plain,
( ( ! [C: product_prod_nat_nat > b,U3: set_nat] : ( ord_le841296385at_nat @ ( incoming_b @ C @ U3 ) @ ( e_b @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(375,plain,
( ( ! [C: product_prod_nat_nat > a,U3: set_nat] : ( ord_le841296385at_nat @ ( incoming_a @ C @ U3 ) @ ( e_a @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(376,plain,
( ( ! [C: product_prod_nat_nat > b,U3: set_nat] : ( ord_le841296385at_nat @ ( outgoing_b @ C @ U3 ) @ ( e_b @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(377,plain,
( ( ! [C: product_prod_nat_nat > a,U3: set_nat] : ( ord_le841296385at_nat @ ( outgoing_a @ C @ U3 ) @ ( e_a @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(378,plain,
( ( outgoing_b = outgoing_b )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(379,plain,
( ( outgoing_a = outgoing_a )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(380,plain,
( ( incoming_b = incoming_b )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(381,plain,
( ( incoming_a = incoming_a )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(382,plain,
( ( ! [U3: set_nat] :
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( incoming_a @ c @ U3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(383,plain,
( ( ! [U3: set_nat] :
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( outgoing_a @ c @ U3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(384,plain,
( ( ( finite_finite_nat @ ( v_b @ c2 ) )
=> ( finite772653738at_nat @ ( e_b @ c2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(385,plain,
( ( finite772653738at_nat @ ( e_b @ c2 ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(386,plain,
( ( ord_le841296385at_nat @ ( edmond475474836dges_b @ c2 @ s @ t ) @ ( e_b @ c2 ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(387,plain,
( ( ( finite772653738at_nat @ ( e_b @ c2 ) )
=> ( finite_finite_nat @ ( v_b @ c2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(388,plain,
( ( ( finite772653738at_nat @ ( e_b @ c2 ) )
=> ( finite_Graph_b @ c2 ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(389,plain,
( ( ord_le841296385at_nat @ ( e_b @ c2 ) @ ( edmond771116671s_uE_b @ c2 ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(390,plain,
( ( ! [U3: set_nat] : ( ord_le841296385at_nat @ ( outgoing_a @ c @ U3 ) @ ( e_a @ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(391,plain,
( ( ! [U3: set_nat] : ( ord_le841296385at_nat @ ( incoming_a @ c @ U3 ) @ ( e_a @ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(392,plain,
( ( ! [C: product_prod_nat_nat > a,U: nat] :
( ( finite_Graph_a @ C )
=> ( finite_finite_nat @ ( adjacent_nodes_a @ C @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(393,plain,
( ( ! [C: product_prod_nat_nat > b,U: nat] :
( ( finite_Graph_b @ C )
=> ( finite_finite_nat @ ( adjacent_nodes_b @ C @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(394,plain,
( ( ! [C: product_prod_nat_nat > a,U: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ C @ U ) @ ( v_a @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(395,plain,
( ( ! [C: product_prod_nat_nat > b,U: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_b @ C @ U ) @ ( v_b @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(396,plain,
( ( ! [C: product_prod_nat_nat > b,S: nat,T: nat] :
( ( edmond1517640973ysis_b @ C )
=> ( ord_le841296385at_nat @ ( edmond475474836dges_b @ C @ S @ T ) @ ( e_b @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(397,plain,
( ( ! [C: product_prod_nat_nat > a,S: nat,T: nat] :
( ( edmond1517640972ysis_a @ C )
=> ( ord_le841296385at_nat @ ( edmond475474835dges_a @ C @ S @ T ) @ ( e_a @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(398,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ C )
=> ( ord_le841296385at_nat @ ( e_a @ C ) @ ( edmond771116670s_uE_a @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(399,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( edmond1517640973ysis_b @ C )
=> ( ord_le841296385at_nat @ ( e_b @ C ) @ ( edmond771116671s_uE_b @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(400,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( finite_Graph_a @ C )
=> ( finite772653738at_nat @ ( e_a @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(401,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( finite_Graph_b @ C )
=> ( finite772653738at_nat @ ( e_b @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(402,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( finite772653738at_nat @ ( e_a @ C ) )
=> ( finite_Graph_a @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(403,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( finite772653738at_nat @ ( e_b @ C ) )
=> ( finite_Graph_b @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(404,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( finite_finite_nat @ ( v_b @ C ) )
=> ( finite772653738at_nat @ ( e_b @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(405,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( finite_finite_nat @ ( v_a @ C ) )
=> ( finite772653738at_nat @ ( e_a @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(406,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( finite772653738at_nat @ ( e_b @ C ) )
=> ( finite_finite_nat @ ( v_b @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(407,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( finite772653738at_nat @ ( e_a @ C ) )
=> ( finite_finite_nat @ ( v_a @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(408,plain,
( ( ! [S: nat,C: product_prod_nat_nat > b] :
( ( member_nat @ S @ ( v_b @ C ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_b @ C @ S ) @ ( v_b @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(409,plain,
( ( ! [S: nat,C: product_prod_nat_nat > a] :
( ( member_nat @ S @ ( v_a @ C ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_a @ C @ S ) @ ( v_a @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(410,plain,
( ( e_b = e_b )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(411,plain,
( ( e_a = e_a )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(412,plain,
( ( adjacent_nodes_a = adjacent_nodes_a )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(413,plain,
( ( adjacent_nodes_b = adjacent_nodes_b )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(414,plain,
( ( reachableNodes_b = reachableNodes_b )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(415,plain,
( ( reachableNodes_a = reachableNodes_a )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(416,plain,
( ( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( e_a @ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(417,plain,
( ( ! [U: nat] : ( finite_finite_nat @ ( adjacent_nodes_a @ c @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(418,plain,
( ( ! [U: nat] : ( finite_finite_nat @ ( adjacent_nodes_b @ c2 @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(419,plain,
( ( finite772653738at_nat @ ( e_a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(420,plain,
( ( ( finite772653738at_nat @ ( e_a @ c ) )
=> ( finite_finite_nat @ ( v_a @ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(421,plain,
( ( ( finite772653738at_nat @ ( e_a @ c ) )
=> ( finite_Graph_a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(422,plain,
( ( ord_le841296385at_nat @ ( e_a @ c ) @ ( edmond771116670s_uE_a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(423,plain,
( ( ord_le841296385at_nat @ ( edmond475474835dges_a @ c @ s @ t ) @ ( e_a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(424,plain,
( ( ! [S: nat] :
( ( member_nat @ S @ ( v_b @ c2 ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_b @ c2 @ S ) @ ( v_b @ c2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(425,plain,
( ( ! [S: nat] :
( ( member_nat @ S @ ( v_a @ c ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_a @ c @ S ) @ ( v_a @ c ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(426,plain,
( ( ! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_set_nat @ A2 @ B2 )
=> ( ord_less_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(427,plain,
( ( ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le116442893at_nat @ A2 @ B2 )
=> ( ord_less_nat @ ( finite447719721at_nat @ A2 ) @ ( finite447719721at_nat @ B2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(428,plain,
( ( ! [C: product_prod_nat_nat > b,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( finite_Graph_b @ C )
=> ( ( member_nat @ U @ ( v_b @ C ) )
=> ( ( isSimplePath_b @ C @ U @ P5 @ V )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_b @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(429,plain,
( ( ! [C: product_prod_nat_nat > a,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( finite_Graph_a @ C )
=> ( ( member_nat @ U @ ( v_a @ C ) )
=> ( ( isSimplePath_a @ C @ U @ P5 @ V )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_a @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(430,plain,
( ( ! [A2: set_se1612935105at_nat,A: set_Pr1986765409at_nat] :
( ( finite1457549322at_nat @ A2 )
=> ( ( member298845450at_nat @ A @ A2 )
=> ? [X2: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ X2 @ A2 )
& ( ord_le841296385at_nat @ A @ X2 )
& ! [Xa: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ Xa @ A2 )
=> ( ( ord_le841296385at_nat @ X2 @ Xa )
=> ( X2 = Xa ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(431,plain,
( ( ! [A2: set_set_nat,A: set_nat] :
( ( finite2012248349et_nat @ A2 )
=> ( ( member_set_nat @ A @ A2 )
=> ? [X2: set_nat] :
( ( member_set_nat @ X2 @ A2 )
& ( ord_less_eq_set_nat @ A @ X2 )
& ! [Xa: set_nat] :
( ( member_set_nat @ Xa @ A2 )
=> ( ( ord_less_eq_set_nat @ X2 @ Xa )
=> ( X2 = Xa ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(432,plain,
( ( ! [A2: set_nat,A: nat] :
( ( finite_finite_nat @ A2 )
=> ( ( member_nat @ A @ A2 )
=> ? [X2: nat] :
( ( member_nat @ X2 @ A2 )
& ( ord_less_eq_nat @ A @ X2 )
& ! [Xa: nat] :
( ( member_nat @ Xa @ A2 )
=> ( ( ord_less_eq_nat @ X2 @ Xa )
=> ( X2 = Xa ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(433,plain,
( ( ! [A2: set_se1612935105at_nat,A: set_Pr1986765409at_nat] :
( ( finite1457549322at_nat @ A2 )
=> ( ( member298845450at_nat @ A @ A2 )
=> ? [X2: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ X2 @ A2 )
& ( ord_le841296385at_nat @ X2 @ A )
& ! [Xa: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ Xa @ A2 )
=> ( ( ord_le841296385at_nat @ Xa @ X2 )
=> ( X2 = Xa ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(434,plain,
( ( ! [A2: set_set_nat,A: set_nat] :
( ( finite2012248349et_nat @ A2 )
=> ( ( member_set_nat @ A @ A2 )
=> ? [X2: set_nat] :
( ( member_set_nat @ X2 @ A2 )
& ( ord_less_eq_set_nat @ X2 @ A )
& ! [Xa: set_nat] :
( ( member_set_nat @ Xa @ A2 )
=> ( ( ord_less_eq_set_nat @ Xa @ X2 )
=> ( X2 = Xa ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(435,plain,
( ( ! [A2: set_nat,A: nat] :
( ( finite_finite_nat @ A2 )
=> ( ( member_nat @ A @ A2 )
=> ? [X2: nat] :
( ( member_nat @ X2 @ A2 )
& ( ord_less_eq_nat @ X2 @ A )
& ! [Xa: nat] :
( ( member_nat @ Xa @ A2 )
=> ( ( ord_less_eq_nat @ Xa @ X2 )
=> ( X2 = Xa ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(436,plain,
( ( ! [C: product_prod_nat_nat > b,S: nat,T: nat] :
( ( edmond1517640973ysis_b @ C )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474836dges_b @ C @ S @ T ) ) @ ( finite447719721at_nat @ ( edmond771116671s_uE_b @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(437,plain,
( ( ! [C: product_prod_nat_nat > a,S: nat,T: nat] :
( ( edmond1517640972ysis_a @ C )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ C @ S @ T ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(438,plain,
( ( isShortestPath_b
= ( ^ [C2: product_prod_nat_nat > b,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isSimplePath_b @ C2 @ U2 @ P3 @ V4 )
& ( ( size_s1990949619at_nat @ P3 )
= ( min_dist_b @ C2 @ U2 @ V4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(439,plain,
( ( isShortestPath_a
= ( ^ [C2: product_prod_nat_nat > a,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isSimplePath_a @ C2 @ U2 @ P3 @ V4 )
& ( ( size_s1990949619at_nat @ P3 )
= ( min_dist_a @ C2 @ U2 @ V4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(440,plain,
( ( ! [A2: set_nat,P2: set_nat > $o] :
( ( finite_finite_nat @ A2 )
=> ( ! [A3: set_nat] :
( ( finite_finite_nat @ A3 )
=> ( ! [B4: set_nat] :
( ( ord_less_set_nat @ B4 @ A3 )
=> ( P2 @ B4 ) )
=> ( P2 @ A3 ) ) )
=> ( P2 @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(441,plain,
( ( ! [A2: set_Pr1986765409at_nat,P2: set_Pr1986765409at_nat > $o] :
( ( finite772653738at_nat @ A2 )
=> ( ! [A3: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A3 )
=> ( ! [B4: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ B4 @ A3 )
=> ( P2 @ B4 ) )
=> ( P2 @ A3 ) ) )
=> ( P2 @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(442,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( finite_Graph_a @ C )
=> ( finite_finite_nat @ ( v_a @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(443,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( finite_Graph_b @ C )
=> ( finite_finite_nat @ ( v_b @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(444,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( finite_finite_nat @ ( v_a @ C ) )
=> ( finite_Graph_a @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(445,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( finite_finite_nat @ ( v_b @ C ) )
=> ( finite_Graph_b @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(446,plain,
( ( finite_Graph_a
= ( ^ [C2: product_prod_nat_nat > a] : ( finite_finite_nat @ ( v_a @ C2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(447,plain,
( ( finite_Graph_b
= ( ^ [C2: product_prod_nat_nat > b] : ( finite_finite_nat @ ( v_b @ C2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(448,plain,
( ( ! [F2: set_Pr1986765409at_nat,C3: nat] :
( ! [G: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ G @ F2 )
=> ( ( finite772653738at_nat @ G )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ G ) @ C3 ) ) )
=> ( ( finite772653738at_nat @ F2 )
& ( ord_less_eq_nat @ ( finite447719721at_nat @ F2 ) @ C3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(449,plain,
( ( ! [F2: set_nat,C3: nat] :
( ! [G: set_nat] :
( ( ord_less_eq_set_nat @ G @ F2 )
=> ( ( finite_finite_nat @ G )
=> ( ord_less_eq_nat @ ( finite_card_nat @ G ) @ C3 ) ) )
=> ( ( finite_finite_nat @ F2 )
& ( ord_less_eq_nat @ ( finite_card_nat @ F2 ) @ C3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(450,plain,
( ( ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( ord_less_eq_nat @ ( finite447719721at_nat @ B2 ) @ ( finite447719721at_nat @ A2 ) )
=> ( A2 = B2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(451,plain,
( ( ! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( ord_less_eq_nat @ ( finite_card_nat @ B2 ) @ ( finite_card_nat @ A2 ) )
=> ( A2 = B2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(452,plain,
( ( ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ A2 ) @ ( finite447719721at_nat @ B2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(453,plain,
( ( ! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(454,plain,
( ( ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( ord_less_nat @ ( finite447719721at_nat @ A2 ) @ ( finite447719721at_nat @ B2 ) )
=> ( ord_le116442893at_nat @ A2 @ B2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(455,plain,
( ( ! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( ord_less_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) )
=> ( ord_less_set_nat @ A2 @ B2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(456,plain,
( ( ! [M4: set_li664300135at_nat] :
( ( finite1299096496at_nat @ M4 )
=> ? [N3: nat] :
! [X4: list_P559422087at_nat] :
( ( member1608759472at_nat @ X4 @ M4 )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ X4 ) @ N3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(457,plain,
( ( ! [C: product_prod_nat_nat > b,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isShortestPath_b @ C @ S @ P5 @ T )
=> ( isSimplePath_b @ C @ S @ P5 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(458,plain,
( ( ! [C: product_prod_nat_nat > a,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isShortestPath_a @ C @ S @ P5 @ T )
=> ( isSimplePath_a @ C @ S @ P5 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(459,plain,
( ( ! [C: product_prod_nat_nat > b,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isPath_b @ C @ S @ P5 @ T )
=> ? [P: list_P559422087at_nat] : ( isSimplePath_b @ C @ S @ P @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(460,plain,
( ( ! [C: product_prod_nat_nat > a,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isPath_a @ C @ S @ P5 @ T )
=> ? [P: list_P559422087at_nat] : ( isSimplePath_a @ C @ S @ P @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(461,plain,
( ( ! [A2: set_Pr1986765409at_nat,N: nat] :
( ~ ( finite772653738at_nat @ A2 )
=> ? [B3: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B3 )
& ( ( finite447719721at_nat @ B3 )
= N )
& ( ord_le841296385at_nat @ B3 @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(462,plain,
( ( ! [A2: set_nat,N: nat] :
( ~ ( finite_finite_nat @ A2 )
=> ? [B3: set_nat] :
( ( finite_finite_nat @ B3 )
& ( ( finite_card_nat @ B3 )
= N )
& ( ord_less_eq_set_nat @ B3 @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(463,plain,
( ( ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( ( finite447719721at_nat @ A2 )
= ( finite447719721at_nat @ B2 ) )
=> ( A2 = B2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(464,plain,
( ( ! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( ( finite_card_nat @ A2 )
= ( finite_card_nat @ B2 ) )
=> ( A2 = B2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(465,plain,
( ( ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( finite772653738at_nat @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(466,plain,
( ( ! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( finite_finite_nat @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(467,plain,
( ( ! [S2: set_Pr1986765409at_nat,T2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ S2 @ T2 )
=> ( ~ ( finite772653738at_nat @ S2 )
=> ~ ( finite772653738at_nat @ T2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(468,plain,
( ( ! [S2: set_nat,T2: set_nat] :
( ( ord_less_eq_set_nat @ S2 @ T2 )
=> ( ~ ( finite_finite_nat @ S2 )
=> ~ ( finite_finite_nat @ T2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(469,plain,
( ( ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( finite772653738at_nat @ B2 )
=> ( finite772653738at_nat @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(470,plain,
( ( ! [A2: set_nat,B2: set_nat] :
( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( finite_finite_nat @ B2 )
=> ( finite_finite_nat @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(471,plain,
( ( ! [A2: set_set_nat,B2: set_set_nat] :
( ( ord_le1613022364et_nat @ A2 @ B2 )
=> ( ( finite2012248349et_nat @ B2 )
=> ( finite2012248349et_nat @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(472,plain,
( ( ! [A2: set_se1612935105at_nat,B2: set_se1612935105at_nat] :
( ( ord_le2096002913at_nat @ A2 @ B2 )
=> ( ( finite1457549322at_nat @ B2 )
=> ( finite1457549322at_nat @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(473,plain,
( ( isSimplePath_b = isSimplePath_b )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(474,plain,
( ( isSimplePath_a = isSimplePath_a )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(475,plain,
( ( ! [U: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ c @ U ) @ ( v_a @ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(476,plain,
( ( ! [U: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_b @ c2 @ U ) @ ( v_b @ c2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(477,plain,
( ( ( v_b @ c2 )
= ( v_a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(478,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_a @ c @ V @ D @ V3 )
=> ( connected_a @ c @ V @ V3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(479,plain,
( ( ! [V: nat] : ( dist_a @ c @ V @ zero_zero_nat @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(480,plain,
( ( ! [V: nat,V3: nat] :
( ( dist_a @ c @ V @ zero_zero_nat @ V3 )
= ( V3 = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(481,plain,
( ( finite_finite_nat @ ( v_a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(482,plain,
( ( finite_finite_nat @ ( v_b @ c2 ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(483,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_a @ c @ U @ P5 @ V )
= ( ( isSimplePath_a @ c @ U @ P5 @ V )
& ( ( size_s1990949619at_nat @ P5 )
= ( min_dist_a @ c @ U @ V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(484,plain,
( ( ! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( member_nat @ S @ ( v_b @ c2 ) )
=> ( ( isShortestPath_b @ c2 @ S @ P5 @ T )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(485,plain,
( ( ! [S: nat,T: nat] :
( ( member_nat @ S @ ( v_b @ c2 ) )
=> ( ( connected_b @ c2 @ S @ T )
=> ( ord_less_nat @ ( min_dist_b @ c2 @ S @ T ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(486,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( member_nat @ U @ ( v_b @ c2 ) )
=> ( ( isSimplePath_b @ c2 @ U @ P5 @ V )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(487,plain,
( ( ! [V: nat,V3: nat] :
( ( connected_a @ c @ V @ V3 )
=> ( dist_a @ c @ V @ ( min_dist_a @ c @ V @ V3 ) @ V3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(488,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_a @ c @ V @ D @ V3 )
= ( ? [P3: list_P559422087at_nat] :
( ( isPath_a @ c @ V @ P3 @ V3 )
& ( ( size_s1990949619at_nat @ P3 )
= D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(489,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isPath_a @ c @ U @ P5 @ V )
=> ( dist_a @ c @ U @ ( size_s1990949619at_nat @ P5 ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(490,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_a @ c @ V @ D @ V3 )
=> ( ! [D6: nat] :
( ( dist_a @ c @ V @ D6 @ V3 )
=> ( ord_less_eq_nat @ D @ D6 ) )
=> ( ( min_dist_a @ c @ V @ V3 )
= D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(491,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_a @ c @ V @ D @ V3 )
=> ( ord_less_eq_nat @ ( min_dist_a @ c @ V @ V3 ) @ D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(492,plain,
( ( ! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isShortestPath_b @ c2 @ S @ P5 @ T )
=> ( isSimplePath_b @ c2 @ S @ P5 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(493,plain,
( ( ! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isShortestPath_a @ c @ S @ P5 @ T )
=> ( isSimplePath_a @ c @ S @ P5 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(494,plain,
( ( ! [V: nat,V3: nat] :
( ( connected_a @ c @ V @ V3 )
= ( ? [D3: nat] : ( dist_a @ c @ V @ D3 @ V3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(495,plain,
( ( ! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isPath_a @ c @ S @ P5 @ T )
=> ? [P: list_P559422087at_nat] : ( isSimplePath_a @ c @ S @ P @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(496,plain,
( ( ! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isPath_b @ c2 @ S @ P5 @ T )
=> ? [P: list_P559422087at_nat] : ( isSimplePath_b @ c2 @ S @ P @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(497,plain,
( ( ! [U: nat,V: nat] :
( ( connected_b @ c2 @ U @ V )
=> ( ( member_nat @ V @ ( v_b @ c2 ) )
= ( member_nat @ U @ ( v_b @ c2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(498,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_b @ c2 @ U @ P5 @ V )
= ( ( isSimplePath_b @ c2 @ U @ P5 @ V )
& ( ( size_s1990949619at_nat @ P5 )
= ( min_dist_b @ c2 @ U @ V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(499,plain,
( ( ! [V: nat,V3: nat,Q: nat > $o] :
( ( connected_a @ c @ V @ V3 )
=> ( ! [D4: nat] :
( ( dist_a @ c @ V @ D4 @ V3 )
=> ( ! [D5: nat] :
( ( dist_a @ c @ V @ D5 @ V3 )
=> ( ord_less_eq_nat @ D4 @ D5 ) )
=> ( Q @ D4 ) ) )
=> ( Q @ ( min_dist_a @ c @ V @ V3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(500,plain,
( ( ! [A2: set_nat] :
( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A2 ) )
=> ( finite_finite_nat @ A2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(501,plain,
( ( ! [A2: set_Pr1986765409at_nat] :
( ( ord_less_nat @ zero_zero_nat @ ( finite447719721at_nat @ A2 ) )
=> ( finite772653738at_nat @ A2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(502,plain,
( ( ! [A2: set_set_nat] :
( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A2 ) )
=> ( finite2012248349et_nat @ A2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(503,plain,
( ( ! [A2: set_se1612935105at_nat] :
( ( ord_less_nat @ zero_zero_nat @ ( finite1701894793at_nat @ A2 ) )
=> ( finite1457549322at_nat @ A2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(504,plain,
( ( ! [A2: set_li664300135at_nat] :
( ( ord_less_nat @ zero_zero_nat @ ( finite83082927at_nat @ A2 ) )
=> ( finite1299096496at_nat @ A2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(505,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( member_nat @ U @ ( v_a @ c ) )
=> ( ( isSimplePath_a @ c @ U @ P5 @ V )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(506,plain,
( ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474836dges_b @ c2 @ s @ t ) ) @ ( finite447719721at_nat @ ( edmond771116671s_uE_b @ c2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(507,plain,
( ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(508,plain,
( ( ! [A2: set_nat] :
( ~ ( finite_finite_nat @ A2 )
=> ( ( finite_card_nat @ A2 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(509,plain,
( ( ! [A2: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ A2 )
=> ( ( finite447719721at_nat @ A2 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(510,plain,
( ( ! [A2: set_set_nat] :
( ~ ( finite2012248349et_nat @ A2 )
=> ( ( finite_card_set_nat @ A2 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(511,plain,
( ( ! [A2: set_se1612935105at_nat] :
( ~ ( finite1457549322at_nat @ A2 )
=> ( ( finite1701894793at_nat @ A2 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(512,plain,
( ( ! [A2: set_li664300135at_nat] :
( ~ ( finite1299096496at_nat @ A2 )
=> ( ( finite83082927at_nat @ A2 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(513,plain,
( ( dist_a
= ( ^ [C2: product_prod_nat_nat > a,V4: nat,D3: nat,V5: nat] :
? [P3: list_P559422087at_nat] :
( ( isPath_a @ C2 @ V4 @ P3 @ V5 )
& ( ( size_s1990949619at_nat @ P3 )
= D3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(514,plain,
( ( dist_b
= ( ^ [C2: product_prod_nat_nat > b,V4: nat,D3: nat,V5: nat] :
? [P3: list_P559422087at_nat] :
( ( isPath_b @ C2 @ V4 @ P3 @ V5 )
& ( ( size_s1990949619at_nat @ P3 )
= D3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(515,plain,
( ( ! [C: product_prod_nat_nat > a,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isPath_a @ C @ U @ P5 @ V )
=> ( dist_a @ C @ U @ ( size_s1990949619at_nat @ P5 ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(516,plain,
( ( ! [C: product_prod_nat_nat > b,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isPath_b @ C @ U @ P5 @ V )
=> ( dist_b @ C @ U @ ( size_s1990949619at_nat @ P5 ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(517,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat,V3: nat] :
( ( connected_a @ C @ V @ V3 )
=> ( dist_a @ C @ V @ ( min_dist_a @ C @ V @ V3 ) @ V3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(518,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat,V3: nat] :
( ( connected_b @ C @ V @ V3 )
=> ( dist_b @ C @ V @ ( min_dist_b @ C @ V @ V3 ) @ V3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(519,plain,
( ( ! [C: product_prod_nat_nat > a,Src: nat,V: nat,D: nat,D2: nat] :
( ( connected_a @ C @ Src @ V )
=> ( ( ( min_dist_a @ C @ Src @ V )
= D )
=> ( ( ord_less_nat @ D2 @ D )
=> ? [V2: nat] :
( ( connected_a @ C @ Src @ V2 )
& ( ( min_dist_a @ C @ Src @ V2 )
= D2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(520,plain,
( ( ! [C: product_prod_nat_nat > b,Src: nat,V: nat,D: nat,D2: nat] :
( ( connected_b @ C @ Src @ V )
=> ( ( ( min_dist_b @ C @ Src @ V )
= D )
=> ( ( ord_less_nat @ D2 @ D )
=> ? [V2: nat] :
( ( connected_b @ C @ Src @ V2 )
& ( ( min_dist_b @ C @ Src @ V2 )
= D2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(521,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat,V3: nat] :
( ( connected_a @ C @ V @ V3 )
=> ( ( ( min_dist_a @ C @ V @ V3 )
= zero_zero_nat )
= ( V3 = V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(522,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat,V3: nat] :
( ( connected_b @ C @ V @ V3 )
=> ( ( ( min_dist_b @ C @ V @ V3 )
= zero_zero_nat )
= ( V3 = V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(523,plain,
( ( ! [C: product_prod_nat_nat > b,U: nat,V: nat] :
( ( connected_b @ C @ U @ V )
=> ~ ! [P4: list_P559422087at_nat] :
~ ( isShortestPath_b @ C @ U @ P4 @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(524,plain,
( ( ! [C: product_prod_nat_nat > a,U: nat,V: nat] :
( ( connected_a @ C @ U @ V )
=> ~ ! [P4: list_P559422087at_nat] :
~ ( isShortestPath_a @ C @ U @ P4 @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(525,plain,
( ( connected_a
= ( ^ [C2: product_prod_nat_nat > a,V4: nat,V5: nat] :
? [D3: nat] : ( dist_a @ C2 @ V4 @ D3 @ V5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(526,plain,
( ( connected_b
= ( ^ [C2: product_prod_nat_nat > b,V4: nat,V5: nat] :
? [D3: nat] : ( dist_b @ C2 @ V4 @ D3 @ V5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(527,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
( ( dist_a @ C @ V @ D @ V3 )
=> ( connected_a @ C @ V @ V3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(528,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat,D: nat,V3: nat] :
( ( dist_b @ C @ V @ D @ V3 )
=> ( connected_b @ C @ V @ V3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(529,plain,
( ( ! [C: product_prod_nat_nat > b,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_b @ C @ U @ P5 @ V )
=> ( isPath_b @ C @ U @ P5 @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(530,plain,
( ( ! [C: product_prod_nat_nat > a,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_a @ C @ U @ P5 @ V )
=> ( isPath_a @ C @ U @ P5 @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(531,plain,
( ( ! [C: product_prod_nat_nat > a,U: nat,V: nat] :
( ( connected_a @ C @ U @ V )
=> ( ( member_nat @ V @ ( v_a @ C ) )
= ( member_nat @ U @ ( v_a @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(532,plain,
( ( ! [C: product_prod_nat_nat > b,U: nat,V: nat] :
( ( connected_b @ C @ U @ V )
=> ( ( member_nat @ V @ ( v_b @ C ) )
= ( member_nat @ U @ ( v_b @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(533,plain,
( ( connected_a
= ( ^ [C2: product_prod_nat_nat > a,U2: nat,V4: nat] :
? [P3: list_P559422087at_nat] : ( isPath_a @ C2 @ U2 @ P3 @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(534,plain,
( ( connected_b
= ( ^ [C2: product_prod_nat_nat > b,U2: nat,V4: nat] :
? [P3: list_P559422087at_nat] : ( isPath_b @ C2 @ U2 @ P3 @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(535,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat,V3: nat] :
( ( dist_a @ C @ V @ zero_zero_nat @ V3 )
= ( V3 = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(536,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat,V3: nat] :
( ( dist_b @ C @ V @ zero_zero_nat @ V3 )
= ( V3 = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(537,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat] : ( dist_a @ C @ V @ zero_zero_nat @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(538,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat] : ( dist_b @ C @ V @ zero_zero_nat @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(539,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat] :
( ( min_dist_b @ C @ V @ V )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(540,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat] :
( ( min_dist_a @ C @ V @ V )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(541,plain,
( ( ! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(542,plain,
( ( ! [P2: nat > $o,N: nat] :
( ( P2 @ zero_zero_nat )
=> ( ! [N3: nat] :
( ( ord_less_nat @ zero_zero_nat @ N3 )
=> ( ~ ( P2 @ N3 )
=> ? [M3: nat] :
( ( ord_less_nat @ M3 @ N3 )
& ~ ( P2 @ M3 ) ) ) )
=> ( P2 @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(543,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(544,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(545,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(546,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(547,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(548,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(549,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(550,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(551,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(552,plain,
( ( ! [C: product_prod_nat_nat > b,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( finite_Graph_b @ C )
=> ( ( member_nat @ S @ ( v_b @ C ) )
=> ( ( isShortestPath_b @ C @ S @ P5 @ T )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_b @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(553,plain,
( ( ! [C: product_prod_nat_nat > a,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( finite_Graph_a @ C )
=> ( ( member_nat @ S @ ( v_a @ C ) )
=> ( ( isShortestPath_a @ C @ S @ P5 @ T )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_a @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(554,plain,
( ( ! [C: product_prod_nat_nat > a,S: nat,T: nat] :
( ( finite_Graph_a @ C )
=> ( ( member_nat @ S @ ( v_a @ C ) )
=> ( ( connected_a @ C @ S @ T )
=> ( ord_less_nat @ ( min_dist_a @ C @ S @ T ) @ ( finite_card_nat @ ( v_a @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(555,plain,
( ( ! [C: product_prod_nat_nat > b,S: nat,T: nat] :
( ( finite_Graph_b @ C )
=> ( ( member_nat @ S @ ( v_b @ C ) )
=> ( ( connected_b @ C @ S @ T )
=> ( ord_less_nat @ ( min_dist_b @ C @ S @ T ) @ ( finite_card_nat @ ( v_b @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(556,plain,
( ( isShortestPath_b = isShortestPath_b )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(557,plain,
( ( isShortestPath_a = isShortestPath_a )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(558,plain,
( ( dist_a = dist_a )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(559,plain,
( ( dist_b = dist_b )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(560,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat] : ( connected_a @ C @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(561,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat] : ( connected_b @ C @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(562,plain,
( ( connected_a = connected_a )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(563,plain,
( ( connected_b = connected_b )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(564,plain,
( ( min_dist_b = min_dist_b )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(565,plain,
( ( min_dist_a = min_dist_a )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(566,plain,
( ( v_b = v_b )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(567,plain,
( ( v_a = v_a )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(568,plain,
( ( isPath_a = isPath_a )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(569,plain,
( ( isPath_b = isPath_b )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(570,plain,
( ( ! [X3: list_P559422087at_nat,Y3: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ X3 )
!= ( size_s1990949619at_nat @ Y3 ) )
=> ( X3 != Y3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(571,plain,
( ( ! [X3: nat,Y3: nat] :
( ( X3 != Y3 )
=> ( ~ ( ord_less_nat @ X3 @ Y3 )
=> ( ord_less_nat @ Y3 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(572,plain,
( ( ! [P2: nat > $o,N: nat] :
( ! [N3: nat] :
( ~ ( P2 @ N3 )
=> ? [M3: nat] :
( ( ord_less_nat @ M3 @ N3 )
& ~ ( P2 @ M3 ) ) )
=> ( P2 @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(573,plain,
( ( ! [P2: nat > $o,N: nat] :
( ! [N3: nat] :
( ! [M3: nat] :
( ( ord_less_nat @ M3 @ N3 )
=> ( P2 @ M3 ) )
=> ( P2 @ N3 ) )
=> ( P2 @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(574,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(575,plain,
( ( ! [S: nat,T: nat] :
( ( ord_less_nat @ S @ T )
=> ( S != T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(576,plain,
( ( ! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
=> ( M != N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(577,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(578,plain,
( ( ! [M: nat,N: nat] :
( ( M != N )
= ( ( ord_less_nat @ M @ N )
| ( ord_less_nat @ N @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(579,plain,
( ( ! [X3: nat] :
( ( zero_zero_nat = X3 )
= ( X3 = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(580,plain,
( ( isShortestPath_b
= ( ^ [C2: product_prod_nat_nat > b,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isPath_b @ C2 @ U2 @ P3 @ V4 )
& ! [P6: list_P559422087at_nat] :
( ( isPath_b @ C2 @ U2 @ P6 @ V4 )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P3 ) @ ( size_s1990949619at_nat @ P6 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(581,plain,
( ( isShortestPath_a
= ( ^ [C2: product_prod_nat_nat > a,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isPath_a @ C2 @ U2 @ P3 @ V4 )
& ! [P6: list_P559422087at_nat] :
( ( isPath_a @ C2 @ U2 @ P6 @ V4 )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P3 ) @ ( size_s1990949619at_nat @ P6 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(582,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat,V3: nat,Q: nat > $o] :
( ( connected_a @ C @ V @ V3 )
=> ( ! [D4: nat] :
( ( dist_a @ C @ V @ D4 @ V3 )
=> ( ! [D5: nat] :
( ( dist_a @ C @ V @ D5 @ V3 )
=> ( ord_less_eq_nat @ D4 @ D5 ) )
=> ( Q @ D4 ) ) )
=> ( Q @ ( min_dist_a @ C @ V @ V3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(583,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat,V3: nat,Q: nat > $o] :
( ( connected_b @ C @ V @ V3 )
=> ( ! [D4: nat] :
( ( dist_b @ C @ V @ D4 @ V3 )
=> ( ! [D5: nat] :
( ( dist_b @ C @ V @ D5 @ V3 )
=> ( ord_less_eq_nat @ D4 @ D5 ) )
=> ( Q @ D4 ) ) )
=> ( Q @ ( min_dist_b @ C @ V @ V3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(584,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat,D: nat,V3: nat] :
( ( dist_b @ C @ V @ D @ V3 )
=> ( ! [D6: nat] :
( ( dist_b @ C @ V @ D6 @ V3 )
=> ( ord_less_eq_nat @ D @ D6 ) )
=> ( ( min_dist_b @ C @ V @ V3 )
= D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(585,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
( ( dist_a @ C @ V @ D @ V3 )
=> ( ! [D6: nat] :
( ( dist_a @ C @ V @ D6 @ V3 )
=> ( ord_less_eq_nat @ D @ D6 ) )
=> ( ( min_dist_a @ C @ V @ V3 )
= D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(586,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat,D: nat,V3: nat] :
( ( dist_b @ C @ V @ D @ V3 )
=> ( ord_less_eq_nat @ ( min_dist_b @ C @ V @ V3 ) @ D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(587,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
( ( dist_a @ C @ V @ D @ V3 )
=> ( ord_less_eq_nat @ ( min_dist_a @ C @ V @ V3 ) @ D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(588,plain,
( ( ! [C: product_prod_nat_nat > a,Src: nat,V: nat,D2: nat] :
( ( connected_a @ C @ Src @ V )
=> ( ( ord_less_eq_nat @ D2 @ ( min_dist_a @ C @ Src @ V ) )
=> ? [V2: nat] :
( ( connected_a @ C @ Src @ V2 )
& ( ( min_dist_a @ C @ Src @ V2 )
= D2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(589,plain,
( ( ! [C: product_prod_nat_nat > b,Src: nat,V: nat,D2: nat] :
( ( connected_b @ C @ Src @ V )
=> ( ( ord_less_eq_nat @ D2 @ ( min_dist_b @ C @ Src @ V ) )
=> ? [V2: nat] :
( ( connected_b @ C @ Src @ V2 )
& ( ( min_dist_b @ C @ Src @ V2 )
= D2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(590,plain,
( ( ! [P2: nat > $o,N: nat] :
( ( P2 @ N )
=> ( ~ ( P2 @ zero_zero_nat )
=> ? [K2: nat] :
( ( ord_less_eq_nat @ K2 @ N )
& ! [I3: nat] :
( ( ord_less_nat @ I3 @ K2 )
=> ~ ( P2 @ I3 ) )
& ( P2 @ K2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(591,plain,
( ( ! [F: nat > nat,I: nat,J: nat] :
( ! [I2: nat,J2: nat] :
( ( ord_less_nat @ I2 @ J2 )
=> ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
=> ( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(592,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( M != N )
=> ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(593,plain,
( ( ! [M: nat,N: nat] :
( ( ( ord_less_nat @ M @ N )
| ( M = N ) )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(594,plain,
( ( ord_less_eq_nat
= ( ^ [M2: nat,N2: nat] :
( ( ord_less_nat @ M2 @ N2 )
| ( M2 = N2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(595,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(596,plain,
( ( ord_less_nat
= ( ^ [M2: nat,N2: nat] :
( ( ord_less_eq_nat @ M2 @ N2 )
& ( M2 != N2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(597,plain,
( ( ! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(598,plain,
( ( ! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(599,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(600,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(601,plain,
( ( ! [P2: nat > $o,K: nat,B: nat] :
( ( P2 @ K )
=> ( ! [Y: nat] :
( ( P2 @ Y )
=> ( ord_less_eq_nat @ Y @ B ) )
=> ? [X2: nat] :
( ( P2 @ X2 )
& ! [Y2: nat] :
( ( P2 @ Y2 )
=> ( ord_less_eq_nat @ Y2 @ X2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(602,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
| ( ord_less_eq_nat @ N @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(603,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_eq_nat @ N @ M )
=> ( M = N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(604,plain,
( ( ! [M: nat,N: nat] :
( ( M = N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(605,plain,
( ( ! [I: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_less_eq_nat @ J @ K )
=> ( ord_less_eq_nat @ I @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(606,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ N @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(607,plain,
( ( ! [X3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X3 ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(608,plain,
( ( ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(609,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(610,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(611,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_b @ c2 @ U @ P5 @ V )
= ( ( isPath_b @ c2 @ U @ P5 @ V )
& ! [P6: list_P559422087at_nat] :
( ( isPath_b @ c2 @ U @ P6 @ V )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P5 ) @ ( size_s1990949619at_nat @ P6 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(612,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_a @ c @ U @ P5 @ V )
= ( ( isPath_a @ c @ U @ P5 @ V )
& ( ( size_s1990949619at_nat @ P5 )
= ( min_dist_a @ c @ U @ V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(613,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_a @ c @ U @ P5 @ V )
= ( ( isPath_a @ c @ U @ P5 @ V )
& ! [P6: list_P559422087at_nat] :
( ( isPath_a @ c @ U @ P6 @ V )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P5 ) @ ( size_s1990949619at_nat @ P6 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(614,plain,
( ( ! [Src: nat,V: nat,D2: nat] :
( ( connected_a @ c @ Src @ V )
=> ( ( ord_less_eq_nat @ D2 @ ( min_dist_a @ c @ Src @ V ) )
=> ? [V2: nat] :
( ( connected_a @ c @ Src @ V2 )
& ( ( min_dist_a @ c @ Src @ V2 )
= D2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(615,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_b @ c2 @ V @ D @ V3 )
=> ( ord_less_eq_nat @ ( min_dist_b @ c2 @ V @ V3 ) @ D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(616,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_b @ c2 @ V @ D @ V3 )
=> ( ! [D6: nat] :
( ( dist_b @ c2 @ V @ D6 @ V3 )
=> ( ord_less_eq_nat @ D @ D6 ) )
=> ( ( min_dist_b @ c2 @ V @ V3 )
= D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(617,plain,
( ( ! [Src: nat,V: nat,D2: nat] :
( ( connected_b @ c2 @ Src @ V )
=> ( ( ord_less_eq_nat @ D2 @ ( min_dist_b @ c2 @ Src @ V ) )
=> ? [V2: nat] :
( ( connected_b @ c2 @ Src @ V2 )
& ( ( min_dist_b @ c2 @ Src @ V2 )
= D2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(618,plain,
( ( ! [U: nat,V: nat] :
( ( connected_b @ c2 @ U @ V )
=> ~ ! [P4: list_P559422087at_nat] :
~ ( isShortestPath_b @ c2 @ U @ P4 @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(619,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_b @ c2 @ U @ P5 @ V )
=> ( isPath_b @ c2 @ U @ P5 @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(620,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_a @ c @ U @ P5 @ V )
=> ( isPath_a @ c @ U @ P5 @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(621,plain,
( ( ! [U: nat,V: nat] :
( ( connected_a @ c @ U @ V )
= ( ? [P3: list_P559422087at_nat] : ( isPath_a @ c @ U @ P3 @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(622,plain,
( ( ! [S: nat,T: nat] :
( ( member_nat @ S @ ( v_a @ c ) )
=> ( ( connected_a @ c @ S @ T )
=> ( ord_less_nat @ ( min_dist_a @ c @ S @ T ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(623,plain,
( ( ! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( member_nat @ S @ ( v_a @ c ) )
=> ( ( isShortestPath_a @ c @ S @ P5 @ T )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(624,plain,
( ( ! [V: nat,V3: nat,Q: nat > $o] :
( ( connected_b @ c2 @ V @ V3 )
=> ( ! [D4: nat] :
( ( dist_b @ c2 @ V @ D4 @ V3 )
=> ( ! [D5: nat] :
( ( dist_b @ c2 @ V @ D5 @ V3 )
=> ( ord_less_eq_nat @ D4 @ D5 ) )
=> ( Q @ D4 ) ) )
=> ( Q @ ( min_dist_b @ c2 @ V @ V3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(625,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_b @ c2 @ U @ P5 @ V )
= ( ( isPath_b @ c2 @ U @ P5 @ V )
& ( ( size_s1990949619at_nat @ P5 )
= ( min_dist_b @ c2 @ U @ V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(626,plain,
( ( isShortestPath_b
= ( ^ [C2: product_prod_nat_nat > b,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isPath_b @ C2 @ U2 @ P3 @ V4 )
& ( ( size_s1990949619at_nat @ P3 )
= ( min_dist_b @ C2 @ U2 @ V4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(627,plain,
( ( isShortestPath_a
= ( ^ [C2: product_prod_nat_nat > a,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isPath_a @ C2 @ U2 @ P3 @ V4 )
& ( ( size_s1990949619at_nat @ P3 )
= ( min_dist_a @ C2 @ U2 @ V4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(628,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(629,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(630,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(631,plain,
( ( ! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(632,plain,
( ( ! [N: nat] :
? [Xs2: list_P559422087at_nat] :
( ( size_s1990949619at_nat @ Xs2 )
= N ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(633,plain,
( ( ! [Xs: list_P559422087at_nat,Ys2: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Xs )
!= ( size_s1990949619at_nat @ Ys2 ) )
=> ( Xs != Ys2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(634,plain,
( ( ! [C: product_prod_nat_nat > b,S: nat,T: nat] :
( ( edmond1517640973ysis_b @ C )
=> ( finite772653738at_nat @ ( edmond475474836dges_b @ C @ S @ T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(635,plain,
( ( ! [C: product_prod_nat_nat > a,S: nat,T: nat] :
( ( edmond1517640972ysis_a @ C )
=> ( finite772653738at_nat @ ( edmond475474835dges_a @ C @ S @ T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(636,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ C )
=> ( finite772653738at_nat @ ( edmond771116670s_uE_a @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(637,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( edmond1517640973ysis_b @ C )
=> ( finite772653738at_nat @ ( edmond771116671s_uE_b @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(638,plain,
( ( ! [V: nat,V3: nat] :
( ( connected_a @ c @ V @ V3 )
=> ( ( ( min_dist_a @ c @ V @ V3 )
= zero_zero_nat )
= ( V3 = V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(639,plain,
( ( ! [P2: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
( ! [X2: product_prod_nat_nat] :
( ( P2 @ X2 )
= ( Q @ X2 ) )
=> ( ( collec7649004at_nat @ P2 )
= ( collec7649004at_nat @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(640,plain,
( ( ! [P2: nat > $o,Q: nat > $o] :
( ! [X2: nat] :
( ( P2 @ X2 )
= ( Q @ X2 ) )
=> ( ( collect_nat @ P2 )
= ( collect_nat @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(641,plain,
( ( ! [A2: set_nat] :
( ( collect_nat
@ ^ [X: nat] : ( member_nat @ X @ A2 ) )
= A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(642,plain,
( ( ! [A2: set_Pr1986765409at_nat] :
( ( collec7649004at_nat
@ ^ [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ A2 ) )
= A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(643,plain,
( ( ! [A2: set_set_nat] :
( ( collect_set_nat
@ ^ [X: set_nat] : ( member_set_nat @ X @ A2 ) )
= A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(644,plain,
( ( ! [A2: set_se1612935105at_nat] :
( ( collec1606769740at_nat
@ ^ [X: set_Pr1986765409at_nat] : ( member298845450at_nat @ X @ A2 ) )
= A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(645,plain,
( ( ! [A: nat,P2: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ P2 ) )
= ( P2 @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(646,plain,
( ( ! [A: product_prod_nat_nat,P2: product_prod_nat_nat > $o] :
( ( member701585322at_nat @ A @ ( collec7649004at_nat @ P2 ) )
= ( P2 @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(647,plain,
( ( ! [A: set_nat,P2: set_nat > $o] :
( ( member_set_nat @ A @ ( collect_set_nat @ P2 ) )
= ( P2 @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(648,plain,
( ( ! [A: set_Pr1986765409at_nat,P2: set_Pr1986765409at_nat > $o] :
( ( member298845450at_nat @ A @ ( collec1606769740at_nat @ P2 ) )
= ( P2 @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(649,plain,
( ( ! [V: nat,V3: nat] :
( ( connected_b @ c2 @ V @ V3 )
=> ( ( ( min_dist_b @ c2 @ V @ V3 )
= zero_zero_nat )
= ( V3 = V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(650,plain,
( ( finite772653738at_nat @ ( edmond771116670s_uE_a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(651,plain,
( ( finite772653738at_nat @ ( edmond771116671s_uE_b @ c2 ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(652,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_b @ c2 @ V @ D @ V3 )
=> ( connected_b @ c2 @ V @ V3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(653,plain,
( ( ! [V: nat] : ( dist_b @ c2 @ V @ zero_zero_nat @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(654,plain,
( ( ! [V: nat,V3: nat] :
( ( dist_b @ c2 @ V @ zero_zero_nat @ V3 )
= ( V3 = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(655,plain,
( ( ! [V: nat] : ( connected_a @ c @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(656,plain,
( ( ! [V: nat] : ( connected_b @ c2 @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(657,plain,
( ( ! [V: nat,V3: nat] :
( ( connected_b @ c2 @ V @ V3 )
=> ( dist_b @ c2 @ V @ ( min_dist_b @ c2 @ V @ V3 ) @ V3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(658,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_b @ c2 @ V @ D @ V3 )
= ( ? [P3: list_P559422087at_nat] :
( ( isPath_b @ c2 @ V @ P3 @ V3 )
& ( ( size_s1990949619at_nat @ P3 )
= D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(659,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isPath_b @ c2 @ U @ P5 @ V )
=> ( dist_b @ c2 @ U @ ( size_s1990949619at_nat @ P5 ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(660,plain,
( ( ! [U: nat,V: nat] :
( ( connected_a @ c @ U @ V )
=> ~ ! [P4: list_P559422087at_nat] :
~ ( isShortestPath_a @ c @ U @ P4 @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(661,plain,
( ( ! [V: nat,V3: nat] :
( ( connected_b @ c2 @ V @ V3 )
= ( ? [D3: nat] : ( dist_b @ c2 @ V @ D3 @ V3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(662,plain,
( ( ! [U: nat,V: nat] :
( ( connected_a @ c @ U @ V )
=> ( ( member_nat @ V @ ( v_a @ c ) )
= ( member_nat @ U @ ( v_a @ c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(663,plain,
( ( ! [U: nat,V: nat] :
( ( connected_b @ c2 @ U @ V )
= ( ? [P3: list_P559422087at_nat] : ( isPath_b @ c2 @ U @ P3 @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(664,plain,
( ( ! [V: nat] :
( ( min_dist_b @ c2 @ V @ V )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(665,plain,
( ( ! [V: nat] :
( ( min_dist_a @ c @ V @ V )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(666,plain,
( ( finite772653738at_nat @ ( edmond475474836dges_b @ c2 @ s @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(667,plain,
( ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(668,plain,
( ( ! [P2: list_P559422087at_nat > $o,Xs: list_P559422087at_nat] :
( ! [Xs2: list_P559422087at_nat] :
( ! [Ys: list_P559422087at_nat] :
( ( ord_less_nat @ ( size_s1990949619at_nat @ Ys ) @ ( size_s1990949619at_nat @ Xs2 ) )
=> ( P2 @ Ys ) )
=> ( P2 @ Xs2 ) )
=> ( P2 @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(669,plain,
( ( ! [Src: nat,V: nat,D: nat,D2: nat] :
( ( connected_b @ c2 @ Src @ V )
=> ( ( ( min_dist_b @ c2 @ Src @ V )
= D )
=> ( ( ord_less_nat @ D2 @ D )
=> ? [V2: nat] :
( ( connected_b @ c2 @ Src @ V2 )
& ( ( min_dist_b @ c2 @ Src @ V2 )
= D2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(670,plain,
( ( ! [Src: nat,V: nat,D: nat,D2: nat] :
( ( connected_a @ c @ Src @ V )
=> ( ( ( min_dist_a @ c @ Src @ V )
= D )
=> ( ( ord_less_nat @ D2 @ D )
=> ? [V2: nat] :
( ( connected_a @ c @ Src @ V2 )
& ( ( min_dist_a @ c @ Src @ V2 )
= D2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(671,plain,
( ( connected_a @ c @ s @ t )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(672,plain,
( ( ~ ! [P: list_P559422087at_nat] :
( ( isPath_b @ c2 @ s @ P @ t )
=> ( ( size_s1990949619at_nat @ P )
!= ( min_dist_b @ c2 @ s @ t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(673,plain,
( ( dist_b @ c2 @ s @ ( min_dist_b @ c2 @ s @ t ) @ t )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(674,plain,
( ( ~ ( connected_b @ c2 @ s @ t )
=> ( ord_less_nat @ ( edmond1022345717sure_b @ c2 @ s @ t ) @ ( edmond1022345716sure_a @ c @ s @ t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(675,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( edmond1517640973ysis_b @ C )
=> ( finite_Graph_b @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(676,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ C )
=> ( finite_Graph_a @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(677,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( finite_Graph_b @ C )
=> ( edmond1517640973ysis_b @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(678,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( finite_Graph_a @ C )
=> ( edmond1517640972ysis_a @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(679,plain,
( ( edmond1517640973ysis_b = finite_Graph_b )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(680,plain,
( ( edmond1517640972ysis_a = finite_Graph_a )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(681,plain,
( ( isPath_b @ c2 @ s @ p2 @ t )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(682,plain,
( ( member_nat @ s @ ( v_a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(683,plain,
( ( connected_b @ c2 @ s @ t )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(684,plain,
( ( isShortestPath_a @ c @ s @ p @ t )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(685,plain,
( ( ( edmond771116671s_uE_b @ c2 )
= ( edmond771116670s_uE_a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(686,plain,
( ( ord_less_nat @ ( size_s1990949619at_nat @ p ) @ ( size_s1990949619at_nat @ p2 ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(687,plain,
( ( finite_Graph_a @ c )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(688,plain,
( ( finite_Graph_b @ c2 )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(689,plain,
( ( edmond475474836dges_b = edmond475474836dges_b )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(690,plain,
( ( edmond475474835dges_a = edmond475474835dges_a )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(691,plain,
( ( edmond771116670s_uE_a = edmond771116670s_uE_a )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(692,plain,
( ( edmond771116671s_uE_b = edmond771116671s_uE_b )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(693,plain,
( ( ord_less_nat @ ( min_dist_b @ c2 @ s @ t ) @ ( min_dist_a @ c @ s @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(694,plain,
( ( edmond1517640973ysis_b @ c2 )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(695,plain,
( ( edmond1022345716sure_a = edmond1022345716sure_a )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(696,plain,
( ( edmond1022345717sure_b = edmond1022345717sure_b )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(697,plain,
( ( ( size_s1990949619at_nat @ p2 )
= ( min_dist_b @ c2 @ s @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(698,plain,
( ( ( size_s1990949619at_nat @ p )
= ( min_dist_a @ c @ s @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(699,plain,
( ( edmond1517640972ysis_a @ c )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(700,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[351]) ).
thf(701,plain,
( ( edmond1517640972ysis_a @ c )
= $true ),
inference(copy,[status(thm)],[699]) ).
thf(702,plain,
( ( ( size_s1990949619at_nat @ p )
= ( min_dist_a @ c @ s @ t ) )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(703,plain,
( ( ( size_s1990949619at_nat @ p2 )
= ( min_dist_b @ c2 @ s @ t ) )
= $true ),
inference(copy,[status(thm)],[697]) ).
thf(704,plain,
( ( edmond1022345717sure_b = edmond1022345717sure_b )
= $true ),
inference(copy,[status(thm)],[696]) ).
thf(705,plain,
( ( edmond1022345716sure_a = edmond1022345716sure_a )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(706,plain,
( ( edmond1517640973ysis_b @ c2 )
= $true ),
inference(copy,[status(thm)],[694]) ).
thf(707,plain,
( ( ord_less_nat @ ( min_dist_b @ c2 @ s @ t ) @ ( min_dist_a @ c @ s @ t ) )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(708,plain,
( ( edmond771116671s_uE_b = edmond771116671s_uE_b )
= $true ),
inference(copy,[status(thm)],[692]) ).
thf(709,plain,
( ( edmond771116670s_uE_a = edmond771116670s_uE_a )
= $true ),
inference(copy,[status(thm)],[691]) ).
thf(710,plain,
( ( edmond475474835dges_a = edmond475474835dges_a )
= $true ),
inference(copy,[status(thm)],[690]) ).
thf(711,plain,
( ( edmond475474836dges_b = edmond475474836dges_b )
= $true ),
inference(copy,[status(thm)],[689]) ).
thf(712,plain,
( ( finite_Graph_b @ c2 )
= $true ),
inference(copy,[status(thm)],[688]) ).
thf(713,plain,
( ( finite_Graph_a @ c )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(714,plain,
( ( ord_less_nat @ ( size_s1990949619at_nat @ p ) @ ( size_s1990949619at_nat @ p2 ) )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(715,plain,
( ( ( edmond771116671s_uE_b @ c2 )
= ( edmond771116670s_uE_a @ c ) )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(716,plain,
( ( isShortestPath_a @ c @ s @ p @ t )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(717,plain,
( ( connected_b @ c2 @ s @ t )
= $true ),
inference(copy,[status(thm)],[683]) ).
thf(718,plain,
( ( member_nat @ s @ ( v_a @ c ) )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(719,plain,
( ( isPath_b @ c2 @ s @ p2 @ t )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(720,plain,
( ( edmond1517640972ysis_a = finite_Graph_a )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(721,plain,
( ( edmond1517640973ysis_b = finite_Graph_b )
= $true ),
inference(copy,[status(thm)],[679]) ).
thf(722,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( finite_Graph_a @ C )
=> ( edmond1517640972ysis_a @ C ) ) )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(723,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( finite_Graph_b @ C )
=> ( edmond1517640973ysis_b @ C ) ) )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(724,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ C )
=> ( finite_Graph_a @ C ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(725,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( edmond1517640973ysis_b @ C )
=> ( finite_Graph_b @ C ) ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(726,plain,
( ( ~ ( connected_b @ c2 @ s @ t )
=> ( ord_less_nat @ ( edmond1022345717sure_b @ c2 @ s @ t ) @ ( edmond1022345716sure_a @ c @ s @ t ) ) )
= $true ),
inference(copy,[status(thm)],[674]) ).
thf(727,plain,
( ( dist_b @ c2 @ s @ ( min_dist_b @ c2 @ s @ t ) @ t )
= $true ),
inference(copy,[status(thm)],[673]) ).
thf(728,plain,
( ( ~ ! [P: list_P559422087at_nat] :
( ( isPath_b @ c2 @ s @ P @ t )
=> ( ( size_s1990949619at_nat @ P )
!= ( min_dist_b @ c2 @ s @ t ) ) ) )
= $true ),
inference(copy,[status(thm)],[672]) ).
thf(729,plain,
( ( connected_a @ c @ s @ t )
= $true ),
inference(copy,[status(thm)],[671]) ).
thf(730,plain,
( ( ! [Src: nat,V: nat,D: nat,D2: nat] :
( ( connected_a @ c @ Src @ V )
=> ( ( ( min_dist_a @ c @ Src @ V )
= D )
=> ( ( ord_less_nat @ D2 @ D )
=> ? [V2: nat] :
( ( connected_a @ c @ Src @ V2 )
& ( ( min_dist_a @ c @ Src @ V2 )
= D2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[670]) ).
thf(731,plain,
( ( ! [Src: nat,V: nat,D: nat,D2: nat] :
( ( connected_b @ c2 @ Src @ V )
=> ( ( ( min_dist_b @ c2 @ Src @ V )
= D )
=> ( ( ord_less_nat @ D2 @ D )
=> ? [V2: nat] :
( ( connected_b @ c2 @ Src @ V2 )
& ( ( min_dist_b @ c2 @ Src @ V2 )
= D2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[669]) ).
thf(732,plain,
( ( ! [P2: list_P559422087at_nat > $o,Xs: list_P559422087at_nat] :
( ! [Xs2: list_P559422087at_nat] :
( ! [Ys: list_P559422087at_nat] :
( ( ord_less_nat @ ( size_s1990949619at_nat @ Ys ) @ ( size_s1990949619at_nat @ Xs2 ) )
=> ( P2 @ Ys ) )
=> ( P2 @ Xs2 ) )
=> ( P2 @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[668]) ).
thf(733,plain,
( ( finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) )
= $true ),
inference(copy,[status(thm)],[667]) ).
thf(734,plain,
( ( finite772653738at_nat @ ( edmond475474836dges_b @ c2 @ s @ t ) )
= $true ),
inference(copy,[status(thm)],[666]) ).
thf(735,plain,
( ( ! [V: nat] :
( ( min_dist_a @ c @ V @ V )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[665]) ).
thf(736,plain,
( ( ! [V: nat] :
( ( min_dist_b @ c2 @ V @ V )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[664]) ).
thf(737,plain,
( ( ! [U: nat,V: nat] :
( ( connected_b @ c2 @ U @ V )
= ( ? [P3: list_P559422087at_nat] : ( isPath_b @ c2 @ U @ P3 @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[663]) ).
thf(738,plain,
( ( ! [U: nat,V: nat] :
( ( connected_a @ c @ U @ V )
=> ( ( member_nat @ V @ ( v_a @ c ) )
= ( member_nat @ U @ ( v_a @ c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[662]) ).
thf(739,plain,
( ( ! [V: nat,V3: nat] :
( ( connected_b @ c2 @ V @ V3 )
= ( ? [D3: nat] : ( dist_b @ c2 @ V @ D3 @ V3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[661]) ).
thf(740,plain,
( ( ! [U: nat,V: nat] :
( ( connected_a @ c @ U @ V )
=> ~ ! [P4: list_P559422087at_nat] :
~ ( isShortestPath_a @ c @ U @ P4 @ V ) ) )
= $true ),
inference(copy,[status(thm)],[660]) ).
thf(741,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isPath_b @ c2 @ U @ P5 @ V )
=> ( dist_b @ c2 @ U @ ( size_s1990949619at_nat @ P5 ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(742,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_b @ c2 @ V @ D @ V3 )
= ( ? [P3: list_P559422087at_nat] :
( ( isPath_b @ c2 @ V @ P3 @ V3 )
& ( ( size_s1990949619at_nat @ P3 )
= D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(743,plain,
( ( ! [V: nat,V3: nat] :
( ( connected_b @ c2 @ V @ V3 )
=> ( dist_b @ c2 @ V @ ( min_dist_b @ c2 @ V @ V3 ) @ V3 ) ) )
= $true ),
inference(copy,[status(thm)],[657]) ).
thf(744,plain,
( ( ! [V: nat] : ( connected_b @ c2 @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(745,plain,
( ( ! [V: nat] : ( connected_a @ c @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[655]) ).
thf(746,plain,
( ( ! [V: nat,V3: nat] :
( ( dist_b @ c2 @ V @ zero_zero_nat @ V3 )
= ( V3 = V ) ) )
= $true ),
inference(copy,[status(thm)],[654]) ).
thf(747,plain,
( ( ! [V: nat] : ( dist_b @ c2 @ V @ zero_zero_nat @ V ) )
= $true ),
inference(copy,[status(thm)],[653]) ).
thf(748,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_b @ c2 @ V @ D @ V3 )
=> ( connected_b @ c2 @ V @ V3 ) ) )
= $true ),
inference(copy,[status(thm)],[652]) ).
thf(749,plain,
( ( finite772653738at_nat @ ( edmond771116671s_uE_b @ c2 ) )
= $true ),
inference(copy,[status(thm)],[651]) ).
thf(750,plain,
( ( finite772653738at_nat @ ( edmond771116670s_uE_a @ c ) )
= $true ),
inference(copy,[status(thm)],[650]) ).
thf(751,plain,
( ( ! [V: nat,V3: nat] :
( ( connected_b @ c2 @ V @ V3 )
=> ( ( ( min_dist_b @ c2 @ V @ V3 )
= zero_zero_nat )
= ( V3 = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[649]) ).
thf(752,plain,
( ( ! [A: set_Pr1986765409at_nat,P2: set_Pr1986765409at_nat > $o] :
( ( member298845450at_nat @ A @ ( collec1606769740at_nat @ P2 ) )
= ( P2 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[648]) ).
thf(753,plain,
( ( ! [A: set_nat,P2: set_nat > $o] :
( ( member_set_nat @ A @ ( collect_set_nat @ P2 ) )
= ( P2 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[647]) ).
thf(754,plain,
( ( ! [A: product_prod_nat_nat,P2: product_prod_nat_nat > $o] :
( ( member701585322at_nat @ A @ ( collec7649004at_nat @ P2 ) )
= ( P2 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[646]) ).
thf(755,plain,
( ( ! [A: nat,P2: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ P2 ) )
= ( P2 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[645]) ).
thf(756,plain,
( ( ! [A2: set_se1612935105at_nat] :
( ( collec1606769740at_nat
@ ^ [X: set_Pr1986765409at_nat] : ( member298845450at_nat @ X @ A2 ) )
= A2 ) )
= $true ),
inference(copy,[status(thm)],[644]) ).
thf(757,plain,
( ( ! [A2: set_set_nat] :
( ( collect_set_nat
@ ^ [X: set_nat] : ( member_set_nat @ X @ A2 ) )
= A2 ) )
= $true ),
inference(copy,[status(thm)],[643]) ).
thf(758,plain,
( ( ! [A2: set_Pr1986765409at_nat] :
( ( collec7649004at_nat
@ ^ [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ A2 ) )
= A2 ) )
= $true ),
inference(copy,[status(thm)],[642]) ).
thf(759,plain,
( ( ! [A2: set_nat] :
( ( collect_nat
@ ^ [X: nat] : ( member_nat @ X @ A2 ) )
= A2 ) )
= $true ),
inference(copy,[status(thm)],[641]) ).
thf(760,plain,
( ( ! [P2: nat > $o,Q: nat > $o] :
( ! [X2: nat] :
( ( P2 @ X2 )
= ( Q @ X2 ) )
=> ( ( collect_nat @ P2 )
= ( collect_nat @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[640]) ).
thf(761,plain,
( ( ! [P2: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
( ! [X2: product_prod_nat_nat] :
( ( P2 @ X2 )
= ( Q @ X2 ) )
=> ( ( collec7649004at_nat @ P2 )
= ( collec7649004at_nat @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[639]) ).
thf(762,plain,
( ( ! [V: nat,V3: nat] :
( ( connected_a @ c @ V @ V3 )
=> ( ( ( min_dist_a @ c @ V @ V3 )
= zero_zero_nat )
= ( V3 = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[638]) ).
thf(763,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( edmond1517640973ysis_b @ C )
=> ( finite772653738at_nat @ ( edmond771116671s_uE_b @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[637]) ).
thf(764,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ C )
=> ( finite772653738at_nat @ ( edmond771116670s_uE_a @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[636]) ).
thf(765,plain,
( ( ! [C: product_prod_nat_nat > a,S: nat,T: nat] :
( ( edmond1517640972ysis_a @ C )
=> ( finite772653738at_nat @ ( edmond475474835dges_a @ C @ S @ T ) ) ) )
= $true ),
inference(copy,[status(thm)],[635]) ).
thf(766,plain,
( ( ! [C: product_prod_nat_nat > b,S: nat,T: nat] :
( ( edmond1517640973ysis_b @ C )
=> ( finite772653738at_nat @ ( edmond475474836dges_b @ C @ S @ T ) ) ) )
= $true ),
inference(copy,[status(thm)],[634]) ).
thf(767,plain,
( ( ! [Xs: list_P559422087at_nat,Ys2: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Xs )
!= ( size_s1990949619at_nat @ Ys2 ) )
=> ( Xs != Ys2 ) ) )
= $true ),
inference(copy,[status(thm)],[633]) ).
thf(768,plain,
( ( ! [N: nat] :
? [Xs2: list_P559422087at_nat] :
( ( size_s1990949619at_nat @ Xs2 )
= N ) )
= $true ),
inference(copy,[status(thm)],[632]) ).
thf(769,plain,
( ( ! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ) )
= $true ),
inference(copy,[status(thm)],[631]) ).
thf(770,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[630]) ).
thf(771,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[629]) ).
thf(772,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[628]) ).
thf(773,plain,
( ( isShortestPath_a
= ( ^ [C2: product_prod_nat_nat > a,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isPath_a @ C2 @ U2 @ P3 @ V4 )
& ( ( size_s1990949619at_nat @ P3 )
= ( min_dist_a @ C2 @ U2 @ V4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[627]) ).
thf(774,plain,
( ( isShortestPath_b
= ( ^ [C2: product_prod_nat_nat > b,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isPath_b @ C2 @ U2 @ P3 @ V4 )
& ( ( size_s1990949619at_nat @ P3 )
= ( min_dist_b @ C2 @ U2 @ V4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[626]) ).
thf(775,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_b @ c2 @ U @ P5 @ V )
= ( ( isPath_b @ c2 @ U @ P5 @ V )
& ( ( size_s1990949619at_nat @ P5 )
= ( min_dist_b @ c2 @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[625]) ).
thf(776,plain,
( ( ! [V: nat,V3: nat,Q: nat > $o] :
( ( connected_b @ c2 @ V @ V3 )
=> ( ! [D4: nat] :
( ( dist_b @ c2 @ V @ D4 @ V3 )
=> ( ! [D5: nat] :
( ( dist_b @ c2 @ V @ D5 @ V3 )
=> ( ord_less_eq_nat @ D4 @ D5 ) )
=> ( Q @ D4 ) ) )
=> ( Q @ ( min_dist_b @ c2 @ V @ V3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[624]) ).
thf(777,plain,
( ( ! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( member_nat @ S @ ( v_a @ c ) )
=> ( ( isShortestPath_a @ c @ S @ P5 @ T )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[623]) ).
thf(778,plain,
( ( ! [S: nat,T: nat] :
( ( member_nat @ S @ ( v_a @ c ) )
=> ( ( connected_a @ c @ S @ T )
=> ( ord_less_nat @ ( min_dist_a @ c @ S @ T ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[622]) ).
thf(779,plain,
( ( ! [U: nat,V: nat] :
( ( connected_a @ c @ U @ V )
= ( ? [P3: list_P559422087at_nat] : ( isPath_a @ c @ U @ P3 @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[621]) ).
thf(780,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_a @ c @ U @ P5 @ V )
=> ( isPath_a @ c @ U @ P5 @ V ) ) )
= $true ),
inference(copy,[status(thm)],[620]) ).
thf(781,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_b @ c2 @ U @ P5 @ V )
=> ( isPath_b @ c2 @ U @ P5 @ V ) ) )
= $true ),
inference(copy,[status(thm)],[619]) ).
thf(782,plain,
( ( ! [U: nat,V: nat] :
( ( connected_b @ c2 @ U @ V )
=> ~ ! [P4: list_P559422087at_nat] :
~ ( isShortestPath_b @ c2 @ U @ P4 @ V ) ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(783,plain,
( ( ! [Src: nat,V: nat,D2: nat] :
( ( connected_b @ c2 @ Src @ V )
=> ( ( ord_less_eq_nat @ D2 @ ( min_dist_b @ c2 @ Src @ V ) )
=> ? [V2: nat] :
( ( connected_b @ c2 @ Src @ V2 )
& ( ( min_dist_b @ c2 @ Src @ V2 )
= D2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[617]) ).
thf(784,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_b @ c2 @ V @ D @ V3 )
=> ( ! [D6: nat] :
( ( dist_b @ c2 @ V @ D6 @ V3 )
=> ( ord_less_eq_nat @ D @ D6 ) )
=> ( ( min_dist_b @ c2 @ V @ V3 )
= D ) ) ) )
= $true ),
inference(copy,[status(thm)],[616]) ).
thf(785,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_b @ c2 @ V @ D @ V3 )
=> ( ord_less_eq_nat @ ( min_dist_b @ c2 @ V @ V3 ) @ D ) ) )
= $true ),
inference(copy,[status(thm)],[615]) ).
thf(786,plain,
( ( ! [Src: nat,V: nat,D2: nat] :
( ( connected_a @ c @ Src @ V )
=> ( ( ord_less_eq_nat @ D2 @ ( min_dist_a @ c @ Src @ V ) )
=> ? [V2: nat] :
( ( connected_a @ c @ Src @ V2 )
& ( ( min_dist_a @ c @ Src @ V2 )
= D2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[614]) ).
thf(787,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_a @ c @ U @ P5 @ V )
= ( ( isPath_a @ c @ U @ P5 @ V )
& ! [P6: list_P559422087at_nat] :
( ( isPath_a @ c @ U @ P6 @ V )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P5 ) @ ( size_s1990949619at_nat @ P6 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[613]) ).
thf(788,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_a @ c @ U @ P5 @ V )
= ( ( isPath_a @ c @ U @ P5 @ V )
& ( ( size_s1990949619at_nat @ P5 )
= ( min_dist_a @ c @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[612]) ).
thf(789,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_b @ c2 @ U @ P5 @ V )
= ( ( isPath_b @ c2 @ U @ P5 @ V )
& ! [P6: list_P559422087at_nat] :
( ( isPath_b @ c2 @ U @ P6 @ V )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P5 ) @ ( size_s1990949619at_nat @ P6 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[611]) ).
thf(790,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[610]) ).
thf(791,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(copy,[status(thm)],[609]) ).
thf(792,plain,
( ( ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) )
= $true ),
inference(copy,[status(thm)],[608]) ).
thf(793,plain,
( ( ! [X3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X3 ) )
= $true ),
inference(copy,[status(thm)],[607]) ).
thf(794,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ N @ N ) )
= $true ),
inference(copy,[status(thm)],[606]) ).
thf(795,plain,
( ( ! [I: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_less_eq_nat @ J @ K )
=> ( ord_less_eq_nat @ I @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[605]) ).
thf(796,plain,
( ( ! [M: nat,N: nat] :
( ( M = N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[604]) ).
thf(797,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_eq_nat @ N @ M )
=> ( M = N ) ) ) )
= $true ),
inference(copy,[status(thm)],[603]) ).
thf(798,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
| ( ord_less_eq_nat @ N @ M ) ) )
= $true ),
inference(copy,[status(thm)],[602]) ).
thf(799,plain,
( ( ! [P2: nat > $o,K: nat,B: nat] :
( ( P2 @ K )
=> ( ! [Y: nat] :
( ( P2 @ Y )
=> ( ord_less_eq_nat @ Y @ B ) )
=> ? [X2: nat] :
( ( P2 @ X2 )
& ! [Y2: nat] :
( ( P2 @ Y2 )
=> ( ord_less_eq_nat @ Y2 @ X2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[601]) ).
thf(800,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(801,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[599]) ).
thf(802,plain,
( ( ! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(803,plain,
( ( ! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[597]) ).
thf(804,plain,
( ( ord_less_nat
= ( ^ [M2: nat,N2: nat] :
( ( ord_less_eq_nat @ M2 @ N2 )
& ( M2 != N2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[596]) ).
thf(805,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(806,plain,
( ( ord_less_eq_nat
= ( ^ [M2: nat,N2: nat] :
( ( ord_less_nat @ M2 @ N2 )
| ( M2 = N2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[594]) ).
thf(807,plain,
( ( ! [M: nat,N: nat] :
( ( ( ord_less_nat @ M @ N )
| ( M = N ) )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(808,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( M != N )
=> ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(809,plain,
( ( ! [F: nat > nat,I: nat,J: nat] :
( ! [I2: nat,J2: nat] :
( ( ord_less_nat @ I2 @ J2 )
=> ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
=> ( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(810,plain,
( ( ! [P2: nat > $o,N: nat] :
( ( P2 @ N )
=> ( ~ ( P2 @ zero_zero_nat )
=> ? [K2: nat] :
( ( ord_less_eq_nat @ K2 @ N )
& ! [I3: nat] :
( ( ord_less_nat @ I3 @ K2 )
=> ~ ( P2 @ I3 ) )
& ( P2 @ K2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(811,plain,
( ( ! [C: product_prod_nat_nat > b,Src: nat,V: nat,D2: nat] :
( ( connected_b @ C @ Src @ V )
=> ( ( ord_less_eq_nat @ D2 @ ( min_dist_b @ C @ Src @ V ) )
=> ? [V2: nat] :
( ( connected_b @ C @ Src @ V2 )
& ( ( min_dist_b @ C @ Src @ V2 )
= D2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(812,plain,
( ( ! [C: product_prod_nat_nat > a,Src: nat,V: nat,D2: nat] :
( ( connected_a @ C @ Src @ V )
=> ( ( ord_less_eq_nat @ D2 @ ( min_dist_a @ C @ Src @ V ) )
=> ? [V2: nat] :
( ( connected_a @ C @ Src @ V2 )
& ( ( min_dist_a @ C @ Src @ V2 )
= D2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(813,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
( ( dist_a @ C @ V @ D @ V3 )
=> ( ord_less_eq_nat @ ( min_dist_a @ C @ V @ V3 ) @ D ) ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(814,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat,D: nat,V3: nat] :
( ( dist_b @ C @ V @ D @ V3 )
=> ( ord_less_eq_nat @ ( min_dist_b @ C @ V @ V3 ) @ D ) ) )
= $true ),
inference(copy,[status(thm)],[586]) ).
thf(815,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
( ( dist_a @ C @ V @ D @ V3 )
=> ( ! [D6: nat] :
( ( dist_a @ C @ V @ D6 @ V3 )
=> ( ord_less_eq_nat @ D @ D6 ) )
=> ( ( min_dist_a @ C @ V @ V3 )
= D ) ) ) )
= $true ),
inference(copy,[status(thm)],[585]) ).
thf(816,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat,D: nat,V3: nat] :
( ( dist_b @ C @ V @ D @ V3 )
=> ( ! [D6: nat] :
( ( dist_b @ C @ V @ D6 @ V3 )
=> ( ord_less_eq_nat @ D @ D6 ) )
=> ( ( min_dist_b @ C @ V @ V3 )
= D ) ) ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(817,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat,V3: nat,Q: nat > $o] :
( ( connected_b @ C @ V @ V3 )
=> ( ! [D4: nat] :
( ( dist_b @ C @ V @ D4 @ V3 )
=> ( ! [D5: nat] :
( ( dist_b @ C @ V @ D5 @ V3 )
=> ( ord_less_eq_nat @ D4 @ D5 ) )
=> ( Q @ D4 ) ) )
=> ( Q @ ( min_dist_b @ C @ V @ V3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(818,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat,V3: nat,Q: nat > $o] :
( ( connected_a @ C @ V @ V3 )
=> ( ! [D4: nat] :
( ( dist_a @ C @ V @ D4 @ V3 )
=> ( ! [D5: nat] :
( ( dist_a @ C @ V @ D5 @ V3 )
=> ( ord_less_eq_nat @ D4 @ D5 ) )
=> ( Q @ D4 ) ) )
=> ( Q @ ( min_dist_a @ C @ V @ V3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[582]) ).
thf(819,plain,
( ( isShortestPath_a
= ( ^ [C2: product_prod_nat_nat > a,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isPath_a @ C2 @ U2 @ P3 @ V4 )
& ! [P6: list_P559422087at_nat] :
( ( isPath_a @ C2 @ U2 @ P6 @ V4 )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P3 ) @ ( size_s1990949619at_nat @ P6 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[581]) ).
thf(820,plain,
( ( isShortestPath_b
= ( ^ [C2: product_prod_nat_nat > b,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isPath_b @ C2 @ U2 @ P3 @ V4 )
& ! [P6: list_P559422087at_nat] :
( ( isPath_b @ C2 @ U2 @ P6 @ V4 )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P3 ) @ ( size_s1990949619at_nat @ P6 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(821,plain,
( ( ! [X3: nat] :
( ( zero_zero_nat = X3 )
= ( X3 = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(822,plain,
( ( ! [M: nat,N: nat] :
( ( M != N )
= ( ( ord_less_nat @ M @ N )
| ( ord_less_nat @ N @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(823,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ N ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(824,plain,
( ( ! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
=> ( M != N ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(825,plain,
( ( ! [S: nat,T: nat] :
( ( ord_less_nat @ S @ T )
=> ( S != T ) ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(826,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ N ) )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(827,plain,
( ( ! [P2: nat > $o,N: nat] :
( ! [N3: nat] :
( ! [M3: nat] :
( ( ord_less_nat @ M3 @ N3 )
=> ( P2 @ M3 ) )
=> ( P2 @ N3 ) )
=> ( P2 @ N ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(828,plain,
( ( ! [P2: nat > $o,N: nat] :
( ! [N3: nat] :
( ~ ( P2 @ N3 )
=> ? [M3: nat] :
( ( ord_less_nat @ M3 @ N3 )
& ~ ( P2 @ M3 ) ) )
=> ( P2 @ N ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(829,plain,
( ( ! [X3: nat,Y3: nat] :
( ( X3 != Y3 )
=> ( ~ ( ord_less_nat @ X3 @ Y3 )
=> ( ord_less_nat @ Y3 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[571]) ).
thf(830,plain,
( ( ! [X3: list_P559422087at_nat,Y3: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ X3 )
!= ( size_s1990949619at_nat @ Y3 ) )
=> ( X3 != Y3 ) ) )
= $true ),
inference(copy,[status(thm)],[570]) ).
thf(831,plain,
( ( isPath_b = isPath_b )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(832,plain,
( ( isPath_a = isPath_a )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(833,plain,
( ( v_a = v_a )
= $true ),
inference(copy,[status(thm)],[567]) ).
thf(834,plain,
( ( v_b = v_b )
= $true ),
inference(copy,[status(thm)],[566]) ).
thf(835,plain,
( ( min_dist_a = min_dist_a )
= $true ),
inference(copy,[status(thm)],[565]) ).
thf(836,plain,
( ( min_dist_b = min_dist_b )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(837,plain,
( ( connected_b = connected_b )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(838,plain,
( ( connected_a = connected_a )
= $true ),
inference(copy,[status(thm)],[562]) ).
thf(839,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat] : ( connected_b @ C @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[561]) ).
thf(840,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat] : ( connected_a @ C @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(841,plain,
( ( dist_b = dist_b )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(842,plain,
( ( dist_a = dist_a )
= $true ),
inference(copy,[status(thm)],[558]) ).
thf(843,plain,
( ( isShortestPath_a = isShortestPath_a )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(844,plain,
( ( isShortestPath_b = isShortestPath_b )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(845,plain,
( ( ! [C: product_prod_nat_nat > b,S: nat,T: nat] :
( ( finite_Graph_b @ C )
=> ( ( member_nat @ S @ ( v_b @ C ) )
=> ( ( connected_b @ C @ S @ T )
=> ( ord_less_nat @ ( min_dist_b @ C @ S @ T ) @ ( finite_card_nat @ ( v_b @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[555]) ).
thf(846,plain,
( ( ! [C: product_prod_nat_nat > a,S: nat,T: nat] :
( ( finite_Graph_a @ C )
=> ( ( member_nat @ S @ ( v_a @ C ) )
=> ( ( connected_a @ C @ S @ T )
=> ( ord_less_nat @ ( min_dist_a @ C @ S @ T ) @ ( finite_card_nat @ ( v_a @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(847,plain,
( ( ! [C: product_prod_nat_nat > a,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( finite_Graph_a @ C )
=> ( ( member_nat @ S @ ( v_a @ C ) )
=> ( ( isShortestPath_a @ C @ S @ P5 @ T )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_a @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(848,plain,
( ( ! [C: product_prod_nat_nat > b,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( finite_Graph_b @ C )
=> ( ( member_nat @ S @ ( v_b @ C ) )
=> ( ( isShortestPath_b @ C @ S @ P5 @ T )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_b @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(849,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[551]) ).
thf(850,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[550]) ).
thf(851,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[549]) ).
thf(852,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(853,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[547]) ).
thf(854,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[546]) ).
thf(855,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[545]) ).
thf(856,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(857,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(858,plain,
( ( ! [P2: nat > $o,N: nat] :
( ( P2 @ zero_zero_nat )
=> ( ! [N3: nat] :
( ( ord_less_nat @ zero_zero_nat @ N3 )
=> ( ~ ( P2 @ N3 )
=> ? [M3: nat] :
( ( ord_less_nat @ M3 @ N3 )
& ~ ( P2 @ M3 ) ) ) )
=> ( P2 @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(859,plain,
( ( ! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(860,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat] :
( ( min_dist_a @ C @ V @ V )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(861,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat] :
( ( min_dist_b @ C @ V @ V )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(862,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat] : ( dist_b @ C @ V @ zero_zero_nat @ V ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(863,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat] : ( dist_a @ C @ V @ zero_zero_nat @ V ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(864,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat,V3: nat] :
( ( dist_b @ C @ V @ zero_zero_nat @ V3 )
= ( V3 = V ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(865,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat,V3: nat] :
( ( dist_a @ C @ V @ zero_zero_nat @ V3 )
= ( V3 = V ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(866,plain,
( ( connected_b
= ( ^ [C2: product_prod_nat_nat > b,U2: nat,V4: nat] :
? [P3: list_P559422087at_nat] : ( isPath_b @ C2 @ U2 @ P3 @ V4 ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(867,plain,
( ( connected_a
= ( ^ [C2: product_prod_nat_nat > a,U2: nat,V4: nat] :
? [P3: list_P559422087at_nat] : ( isPath_a @ C2 @ U2 @ P3 @ V4 ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(868,plain,
( ( ! [C: product_prod_nat_nat > b,U: nat,V: nat] :
( ( connected_b @ C @ U @ V )
=> ( ( member_nat @ V @ ( v_b @ C ) )
= ( member_nat @ U @ ( v_b @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(869,plain,
( ( ! [C: product_prod_nat_nat > a,U: nat,V: nat] :
( ( connected_a @ C @ U @ V )
=> ( ( member_nat @ V @ ( v_a @ C ) )
= ( member_nat @ U @ ( v_a @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(870,plain,
( ( ! [C: product_prod_nat_nat > a,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_a @ C @ U @ P5 @ V )
=> ( isPath_a @ C @ U @ P5 @ V ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(871,plain,
( ( ! [C: product_prod_nat_nat > b,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_b @ C @ U @ P5 @ V )
=> ( isPath_b @ C @ U @ P5 @ V ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(872,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat,D: nat,V3: nat] :
( ( dist_b @ C @ V @ D @ V3 )
=> ( connected_b @ C @ V @ V3 ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(873,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
( ( dist_a @ C @ V @ D @ V3 )
=> ( connected_a @ C @ V @ V3 ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(874,plain,
( ( connected_b
= ( ^ [C2: product_prod_nat_nat > b,V4: nat,V5: nat] :
? [D3: nat] : ( dist_b @ C2 @ V4 @ D3 @ V5 ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(875,plain,
( ( connected_a
= ( ^ [C2: product_prod_nat_nat > a,V4: nat,V5: nat] :
? [D3: nat] : ( dist_a @ C2 @ V4 @ D3 @ V5 ) ) )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(876,plain,
( ( ! [C: product_prod_nat_nat > a,U: nat,V: nat] :
( ( connected_a @ C @ U @ V )
=> ~ ! [P4: list_P559422087at_nat] :
~ ( isShortestPath_a @ C @ U @ P4 @ V ) ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(877,plain,
( ( ! [C: product_prod_nat_nat > b,U: nat,V: nat] :
( ( connected_b @ C @ U @ V )
=> ~ ! [P4: list_P559422087at_nat] :
~ ( isShortestPath_b @ C @ U @ P4 @ V ) ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(878,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat,V3: nat] :
( ( connected_b @ C @ V @ V3 )
=> ( ( ( min_dist_b @ C @ V @ V3 )
= zero_zero_nat )
= ( V3 = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(879,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat,V3: nat] :
( ( connected_a @ C @ V @ V3 )
=> ( ( ( min_dist_a @ C @ V @ V3 )
= zero_zero_nat )
= ( V3 = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(880,plain,
( ( ! [C: product_prod_nat_nat > b,Src: nat,V: nat,D: nat,D2: nat] :
( ( connected_b @ C @ Src @ V )
=> ( ( ( min_dist_b @ C @ Src @ V )
= D )
=> ( ( ord_less_nat @ D2 @ D )
=> ? [V2: nat] :
( ( connected_b @ C @ Src @ V2 )
& ( ( min_dist_b @ C @ Src @ V2 )
= D2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(881,plain,
( ( ! [C: product_prod_nat_nat > a,Src: nat,V: nat,D: nat,D2: nat] :
( ( connected_a @ C @ Src @ V )
=> ( ( ( min_dist_a @ C @ Src @ V )
= D )
=> ( ( ord_less_nat @ D2 @ D )
=> ? [V2: nat] :
( ( connected_a @ C @ Src @ V2 )
& ( ( min_dist_a @ C @ Src @ V2 )
= D2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(882,plain,
( ( ! [C: product_prod_nat_nat > b,V: nat,V3: nat] :
( ( connected_b @ C @ V @ V3 )
=> ( dist_b @ C @ V @ ( min_dist_b @ C @ V @ V3 ) @ V3 ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(883,plain,
( ( ! [C: product_prod_nat_nat > a,V: nat,V3: nat] :
( ( connected_a @ C @ V @ V3 )
=> ( dist_a @ C @ V @ ( min_dist_a @ C @ V @ V3 ) @ V3 ) ) )
= $true ),
inference(copy,[status(thm)],[517]) ).
thf(884,plain,
( ( ! [C: product_prod_nat_nat > b,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isPath_b @ C @ U @ P5 @ V )
=> ( dist_b @ C @ U @ ( size_s1990949619at_nat @ P5 ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(885,plain,
( ( ! [C: product_prod_nat_nat > a,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isPath_a @ C @ U @ P5 @ V )
=> ( dist_a @ C @ U @ ( size_s1990949619at_nat @ P5 ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(886,plain,
( ( dist_b
= ( ^ [C2: product_prod_nat_nat > b,V4: nat,D3: nat,V5: nat] :
? [P3: list_P559422087at_nat] :
( ( isPath_b @ C2 @ V4 @ P3 @ V5 )
& ( ( size_s1990949619at_nat @ P3 )
= D3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(887,plain,
( ( dist_a
= ( ^ [C2: product_prod_nat_nat > a,V4: nat,D3: nat,V5: nat] :
? [P3: list_P559422087at_nat] :
( ( isPath_a @ C2 @ V4 @ P3 @ V5 )
& ( ( size_s1990949619at_nat @ P3 )
= D3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[513]) ).
thf(888,plain,
( ( ! [A2: set_li664300135at_nat] :
( ~ ( finite1299096496at_nat @ A2 )
=> ( ( finite83082927at_nat @ A2 )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(889,plain,
( ( ! [A2: set_se1612935105at_nat] :
( ~ ( finite1457549322at_nat @ A2 )
=> ( ( finite1701894793at_nat @ A2 )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[511]) ).
thf(890,plain,
( ( ! [A2: set_set_nat] :
( ~ ( finite2012248349et_nat @ A2 )
=> ( ( finite_card_set_nat @ A2 )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(891,plain,
( ( ! [A2: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ A2 )
=> ( ( finite447719721at_nat @ A2 )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(892,plain,
( ( ! [A2: set_nat] :
( ~ ( finite_finite_nat @ A2 )
=> ( ( finite_card_nat @ A2 )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(893,plain,
( ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ c ) ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(894,plain,
( ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474836dges_b @ c2 @ s @ t ) ) @ ( finite447719721at_nat @ ( edmond771116671s_uE_b @ c2 ) ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(895,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( member_nat @ U @ ( v_a @ c ) )
=> ( ( isSimplePath_a @ c @ U @ P5 @ V )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(896,plain,
( ( ! [A2: set_li664300135at_nat] :
( ( ord_less_nat @ zero_zero_nat @ ( finite83082927at_nat @ A2 ) )
=> ( finite1299096496at_nat @ A2 ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(897,plain,
( ( ! [A2: set_se1612935105at_nat] :
( ( ord_less_nat @ zero_zero_nat @ ( finite1701894793at_nat @ A2 ) )
=> ( finite1457549322at_nat @ A2 ) ) )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(898,plain,
( ( ! [A2: set_set_nat] :
( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A2 ) )
=> ( finite2012248349et_nat @ A2 ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(899,plain,
( ( ! [A2: set_Pr1986765409at_nat] :
( ( ord_less_nat @ zero_zero_nat @ ( finite447719721at_nat @ A2 ) )
=> ( finite772653738at_nat @ A2 ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(900,plain,
( ( ! [A2: set_nat] :
( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A2 ) )
=> ( finite_finite_nat @ A2 ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(901,plain,
( ( ! [V: nat,V3: nat,Q: nat > $o] :
( ( connected_a @ c @ V @ V3 )
=> ( ! [D4: nat] :
( ( dist_a @ c @ V @ D4 @ V3 )
=> ( ! [D5: nat] :
( ( dist_a @ c @ V @ D5 @ V3 )
=> ( ord_less_eq_nat @ D4 @ D5 ) )
=> ( Q @ D4 ) ) )
=> ( Q @ ( min_dist_a @ c @ V @ V3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(902,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_b @ c2 @ U @ P5 @ V )
= ( ( isSimplePath_b @ c2 @ U @ P5 @ V )
& ( ( size_s1990949619at_nat @ P5 )
= ( min_dist_b @ c2 @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(903,plain,
( ( ! [U: nat,V: nat] :
( ( connected_b @ c2 @ U @ V )
=> ( ( member_nat @ V @ ( v_b @ c2 ) )
= ( member_nat @ U @ ( v_b @ c2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(904,plain,
( ( ! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isPath_b @ c2 @ S @ P5 @ T )
=> ? [P: list_P559422087at_nat] : ( isSimplePath_b @ c2 @ S @ P @ T ) ) )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(905,plain,
( ( ! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isPath_a @ c @ S @ P5 @ T )
=> ? [P: list_P559422087at_nat] : ( isSimplePath_a @ c @ S @ P @ T ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(906,plain,
( ( ! [V: nat,V3: nat] :
( ( connected_a @ c @ V @ V3 )
= ( ? [D3: nat] : ( dist_a @ c @ V @ D3 @ V3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(907,plain,
( ( ! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isShortestPath_a @ c @ S @ P5 @ T )
=> ( isSimplePath_a @ c @ S @ P5 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(908,plain,
( ( ! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isShortestPath_b @ c2 @ S @ P5 @ T )
=> ( isSimplePath_b @ c2 @ S @ P5 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(909,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_a @ c @ V @ D @ V3 )
=> ( ord_less_eq_nat @ ( min_dist_a @ c @ V @ V3 ) @ D ) ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(910,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_a @ c @ V @ D @ V3 )
=> ( ! [D6: nat] :
( ( dist_a @ c @ V @ D6 @ V3 )
=> ( ord_less_eq_nat @ D @ D6 ) )
=> ( ( min_dist_a @ c @ V @ V3 )
= D ) ) ) )
= $true ),
inference(copy,[status(thm)],[490]) ).
thf(911,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isPath_a @ c @ U @ P5 @ V )
=> ( dist_a @ c @ U @ ( size_s1990949619at_nat @ P5 ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(912,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_a @ c @ V @ D @ V3 )
= ( ? [P3: list_P559422087at_nat] :
( ( isPath_a @ c @ V @ P3 @ V3 )
& ( ( size_s1990949619at_nat @ P3 )
= D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(913,plain,
( ( ! [V: nat,V3: nat] :
( ( connected_a @ c @ V @ V3 )
=> ( dist_a @ c @ V @ ( min_dist_a @ c @ V @ V3 ) @ V3 ) ) )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(914,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( member_nat @ U @ ( v_b @ c2 ) )
=> ( ( isSimplePath_b @ c2 @ U @ P5 @ V )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(915,plain,
( ( ! [S: nat,T: nat] :
( ( member_nat @ S @ ( v_b @ c2 ) )
=> ( ( connected_b @ c2 @ S @ T )
=> ( ord_less_nat @ ( min_dist_b @ c2 @ S @ T ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(916,plain,
( ( ! [S: nat,P5: list_P559422087at_nat,T: nat] :
( ( member_nat @ S @ ( v_b @ c2 ) )
=> ( ( isShortestPath_b @ c2 @ S @ P5 @ T )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(917,plain,
( ( ! [U: nat,P5: list_P559422087at_nat,V: nat] :
( ( isShortestPath_a @ c @ U @ P5 @ V )
= ( ( isSimplePath_a @ c @ U @ P5 @ V )
& ( ( size_s1990949619at_nat @ P5 )
= ( min_dist_a @ c @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(918,plain,
( ( finite_finite_nat @ ( v_b @ c2 ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(919,plain,
( ( finite_finite_nat @ ( v_a @ c ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(920,plain,
( ( ! [V: nat,V3: nat] :
( ( dist_a @ c @ V @ zero_zero_nat @ V3 )
= ( V3 = V ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(921,plain,
( ( ! [V: nat] : ( dist_a @ c @ V @ zero_zero_nat @ V ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(922,plain,
( ( ! [V: nat,D: nat,V3: nat] :
( ( dist_a @ c @ V @ D @ V3 )
=> ( connected_a @ c @ V @ V3 ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(923,plain,
( ( ( v_b @ c2 )
= ( v_a @ c ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(924,plain,
( ( ! [U: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_b @ c2 @ U ) @ ( v_b @ c2 ) ) )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(925,plain,
( ( ! [U: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ c @ U ) @ ( v_a @ c ) ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(926,plain,
( ( isSimplePath_a = isSimplePath_a )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(927,plain,
( ( isSimplePath_b = isSimplePath_b )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(928,plain,
( ( ! [A2: set_se1612935105at_nat,B2: set_se1612935105at_nat] :
( ( ord_le2096002913at_nat @ A2 @ B2 )
=> ( ( finite1457549322at_nat @ B2 )
=> ( finite1457549322at_nat @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(929,plain,
( ( ! [A2: set_set_nat,B2: set_set_nat] :
( ( ord_le1613022364et_nat @ A2 @ B2 )
=> ( ( finite2012248349et_nat @ B2 )
=> ( finite2012248349et_nat @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(930,plain,
( ( ! [A2: set_nat,B2: set_nat] :
( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( finite_finite_nat @ B2 )
=> ( finite_finite_nat @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(931,plain,
( ( ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( finite772653738at_nat @ B2 )
=> ( finite772653738at_nat @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(932,plain,
( ( ! [S2: set_nat,T2: set_nat] :
( ( ord_less_eq_set_nat @ S2 @ T2 )
=> ( ~ ( finite_finite_nat @ S2 )
=> ~ ( finite_finite_nat @ T2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(933,plain,
( ( ! [S2: set_Pr1986765409at_nat,T2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ S2 @ T2 )
=> ( ~ ( finite772653738at_nat @ S2 )
=> ~ ( finite772653738at_nat @ T2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(934,plain,
( ( ! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( finite_finite_nat @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(935,plain,
( ( ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( finite772653738at_nat @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(936,plain,
( ( ! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( ( finite_card_nat @ A2 )
= ( finite_card_nat @ B2 ) )
=> ( A2 = B2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(937,plain,
( ( ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( ( finite447719721at_nat @ A2 )
= ( finite447719721at_nat @ B2 ) )
=> ( A2 = B2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(938,plain,
( ( ! [A2: set_nat,N: nat] :
( ~ ( finite_finite_nat @ A2 )
=> ? [B3: set_nat] :
( ( finite_finite_nat @ B3 )
& ( ( finite_card_nat @ B3 )
= N )
& ( ord_less_eq_set_nat @ B3 @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(939,plain,
( ( ! [A2: set_Pr1986765409at_nat,N: nat] :
( ~ ( finite772653738at_nat @ A2 )
=> ? [B3: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B3 )
& ( ( finite447719721at_nat @ B3 )
= N )
& ( ord_le841296385at_nat @ B3 @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(940,plain,
( ( ! [C: product_prod_nat_nat > a,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isPath_a @ C @ S @ P5 @ T )
=> ? [P: list_P559422087at_nat] : ( isSimplePath_a @ C @ S @ P @ T ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(941,plain,
( ( ! [C: product_prod_nat_nat > b,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isPath_b @ C @ S @ P5 @ T )
=> ? [P: list_P559422087at_nat] : ( isSimplePath_b @ C @ S @ P @ T ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(942,plain,
( ( ! [C: product_prod_nat_nat > a,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isShortestPath_a @ C @ S @ P5 @ T )
=> ( isSimplePath_a @ C @ S @ P5 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(943,plain,
( ( ! [C: product_prod_nat_nat > b,S: nat,P5: list_P559422087at_nat,T: nat] :
( ( isShortestPath_b @ C @ S @ P5 @ T )
=> ( isSimplePath_b @ C @ S @ P5 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(944,plain,
( ( ! [M4: set_li664300135at_nat] :
( ( finite1299096496at_nat @ M4 )
=> ? [N3: nat] :
! [X4: list_P559422087at_nat] :
( ( member1608759472at_nat @ X4 @ M4 )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ X4 ) @ N3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(945,plain,
( ( ! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( ord_less_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) )
=> ( ord_less_set_nat @ A2 @ B2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(946,plain,
( ( ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( ord_less_nat @ ( finite447719721at_nat @ A2 ) @ ( finite447719721at_nat @ B2 ) )
=> ( ord_le116442893at_nat @ A2 @ B2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(947,plain,
( ( ! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(948,plain,
( ( ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ A2 ) @ ( finite447719721at_nat @ B2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(949,plain,
( ( ! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( ord_less_eq_nat @ ( finite_card_nat @ B2 ) @ ( finite_card_nat @ A2 ) )
=> ( A2 = B2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(950,plain,
( ( ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( ord_less_eq_nat @ ( finite447719721at_nat @ B2 ) @ ( finite447719721at_nat @ A2 ) )
=> ( A2 = B2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(951,plain,
( ( ! [F2: set_nat,C3: nat] :
( ! [G: set_nat] :
( ( ord_less_eq_set_nat @ G @ F2 )
=> ( ( finite_finite_nat @ G )
=> ( ord_less_eq_nat @ ( finite_card_nat @ G ) @ C3 ) ) )
=> ( ( finite_finite_nat @ F2 )
& ( ord_less_eq_nat @ ( finite_card_nat @ F2 ) @ C3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(952,plain,
( ( ! [F2: set_Pr1986765409at_nat,C3: nat] :
( ! [G: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ G @ F2 )
=> ( ( finite772653738at_nat @ G )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ G ) @ C3 ) ) )
=> ( ( finite772653738at_nat @ F2 )
& ( ord_less_eq_nat @ ( finite447719721at_nat @ F2 ) @ C3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(953,plain,
( ( finite_Graph_b
= ( ^ [C2: product_prod_nat_nat > b] : ( finite_finite_nat @ ( v_b @ C2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(954,plain,
( ( finite_Graph_a
= ( ^ [C2: product_prod_nat_nat > a] : ( finite_finite_nat @ ( v_a @ C2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(955,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( finite_finite_nat @ ( v_b @ C ) )
=> ( finite_Graph_b @ C ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(956,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( finite_finite_nat @ ( v_a @ C ) )
=> ( finite_Graph_a @ C ) ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(957,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( finite_Graph_b @ C )
=> ( finite_finite_nat @ ( v_b @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(958,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( finite_Graph_a @ C )
=> ( finite_finite_nat @ ( v_a @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(959,plain,
( ( ! [A2: set_Pr1986765409at_nat,P2: set_Pr1986765409at_nat > $o] :
( ( finite772653738at_nat @ A2 )
=> ( ! [A3: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A3 )
=> ( ! [B4: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ B4 @ A3 )
=> ( P2 @ B4 ) )
=> ( P2 @ A3 ) ) )
=> ( P2 @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(960,plain,
( ( ! [A2: set_nat,P2: set_nat > $o] :
( ( finite_finite_nat @ A2 )
=> ( ! [A3: set_nat] :
( ( finite_finite_nat @ A3 )
=> ( ! [B4: set_nat] :
( ( ord_less_set_nat @ B4 @ A3 )
=> ( P2 @ B4 ) )
=> ( P2 @ A3 ) ) )
=> ( P2 @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(961,plain,
( ( isShortestPath_a
= ( ^ [C2: product_prod_nat_nat > a,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isSimplePath_a @ C2 @ U2 @ P3 @ V4 )
& ( ( size_s1990949619at_nat @ P3 )
= ( min_dist_a @ C2 @ U2 @ V4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(962,plain,
( ( isShortestPath_b
= ( ^ [C2: product_prod_nat_nat > b,U2: nat,P3: list_P559422087at_nat,V4: nat] :
( ( isSimplePath_b @ C2 @ U2 @ P3 @ V4 )
& ( ( size_s1990949619at_nat @ P3 )
= ( min_dist_b @ C2 @ U2 @ V4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(963,plain,
( ( ! [C: product_prod_nat_nat > a,S: nat,T: nat] :
( ( edmond1517640972ysis_a @ C )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ C @ S @ T ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(964,plain,
( ( ! [C: product_prod_nat_nat > b,S: nat,T: nat] :
( ( edmond1517640973ysis_b @ C )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474836dges_b @ C @ S @ T ) ) @ ( finite447719721at_nat @ ( edmond771116671s_uE_b @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(965,plain,
( ( ! [A2: set_nat,A: nat] :
( ( finite_finite_nat @ A2 )
=> ( ( member_nat @ A @ A2 )
=> ? [X2: nat] :
( ( member_nat @ X2 @ A2 )
& ( ord_less_eq_nat @ X2 @ A )
& ! [Xa: nat] :
( ( member_nat @ Xa @ A2 )
=> ( ( ord_less_eq_nat @ Xa @ X2 )
=> ( X2 = Xa ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(966,plain,
( ( ! [A2: set_set_nat,A: set_nat] :
( ( finite2012248349et_nat @ A2 )
=> ( ( member_set_nat @ A @ A2 )
=> ? [X2: set_nat] :
( ( member_set_nat @ X2 @ A2 )
& ( ord_less_eq_set_nat @ X2 @ A )
& ! [Xa: set_nat] :
( ( member_set_nat @ Xa @ A2 )
=> ( ( ord_less_eq_set_nat @ Xa @ X2 )
=> ( X2 = Xa ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(967,plain,
( ( ! [A2: set_se1612935105at_nat,A: set_Pr1986765409at_nat] :
( ( finite1457549322at_nat @ A2 )
=> ( ( member298845450at_nat @ A @ A2 )
=> ? [X2: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ X2 @ A2 )
& ( ord_le841296385at_nat @ X2 @ A )
& ! [Xa: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ Xa @ A2 )
=> ( ( ord_le841296385at_nat @ Xa @ X2 )
=> ( X2 = Xa ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(968,plain,
( ( ! [A2: set_nat,A: nat] :
( ( finite_finite_nat @ A2 )
=> ( ( member_nat @ A @ A2 )
=> ? [X2: nat] :
( ( member_nat @ X2 @ A2 )
& ( ord_less_eq_nat @ A @ X2 )
& ! [Xa: nat] :
( ( member_nat @ Xa @ A2 )
=> ( ( ord_less_eq_nat @ X2 @ Xa )
=> ( X2 = Xa ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(969,plain,
( ( ! [A2: set_set_nat,A: set_nat] :
( ( finite2012248349et_nat @ A2 )
=> ( ( member_set_nat @ A @ A2 )
=> ? [X2: set_nat] :
( ( member_set_nat @ X2 @ A2 )
& ( ord_less_eq_set_nat @ A @ X2 )
& ! [Xa: set_nat] :
( ( member_set_nat @ Xa @ A2 )
=> ( ( ord_less_eq_set_nat @ X2 @ Xa )
=> ( X2 = Xa ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(970,plain,
( ( ! [A2: set_se1612935105at_nat,A: set_Pr1986765409at_nat] :
( ( finite1457549322at_nat @ A2 )
=> ( ( member298845450at_nat @ A @ A2 )
=> ? [X2: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ X2 @ A2 )
& ( ord_le841296385at_nat @ A @ X2 )
& ! [Xa: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ Xa @ A2 )
=> ( ( ord_le841296385at_nat @ X2 @ Xa )
=> ( X2 = Xa ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(971,plain,
( ( ! [C: product_prod_nat_nat > a,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( finite_Graph_a @ C )
=> ( ( member_nat @ U @ ( v_a @ C ) )
=> ( ( isSimplePath_a @ C @ U @ P5 @ V )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_a @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(972,plain,
( ( ! [C: product_prod_nat_nat > b,U: nat,P5: list_P559422087at_nat,V: nat] :
( ( finite_Graph_b @ C )
=> ( ( member_nat @ U @ ( v_b @ C ) )
=> ( ( isSimplePath_b @ C @ U @ P5 @ V )
=> ( ord_less_nat @ ( size_s1990949619at_nat @ P5 ) @ ( finite_card_nat @ ( v_b @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(973,plain,
( ( ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ B2 )
=> ( ( ord_le116442893at_nat @ A2 @ B2 )
=> ( ord_less_nat @ ( finite447719721at_nat @ A2 ) @ ( finite447719721at_nat @ B2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(974,plain,
( ( ! [B2: set_nat,A2: set_nat] :
( ( finite_finite_nat @ B2 )
=> ( ( ord_less_set_nat @ A2 @ B2 )
=> ( ord_less_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(975,plain,
( ( ! [S: nat] :
( ( member_nat @ S @ ( v_a @ c ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_a @ c @ S ) @ ( v_a @ c ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(976,plain,
( ( ! [S: nat] :
( ( member_nat @ S @ ( v_b @ c2 ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_b @ c2 @ S ) @ ( v_b @ c2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(977,plain,
( ( ord_le841296385at_nat @ ( edmond475474835dges_a @ c @ s @ t ) @ ( e_a @ c ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(978,plain,
( ( ord_le841296385at_nat @ ( e_a @ c ) @ ( edmond771116670s_uE_a @ c ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(979,plain,
( ( ( finite772653738at_nat @ ( e_a @ c ) )
=> ( finite_Graph_a @ c ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(980,plain,
( ( ( finite772653738at_nat @ ( e_a @ c ) )
=> ( finite_finite_nat @ ( v_a @ c ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(981,plain,
( ( finite772653738at_nat @ ( e_a @ c ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(982,plain,
( ( ! [U: nat] : ( finite_finite_nat @ ( adjacent_nodes_b @ c2 @ U ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(983,plain,
( ( ! [U: nat] : ( finite_finite_nat @ ( adjacent_nodes_a @ c @ U ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(984,plain,
( ( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( e_a @ c ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(985,plain,
( ( reachableNodes_a = reachableNodes_a )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(986,plain,
( ( reachableNodes_b = reachableNodes_b )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(987,plain,
( ( adjacent_nodes_b = adjacent_nodes_b )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(988,plain,
( ( adjacent_nodes_a = adjacent_nodes_a )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(989,plain,
( ( e_a = e_a )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(990,plain,
( ( e_b = e_b )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(991,plain,
( ( ! [S: nat,C: product_prod_nat_nat > a] :
( ( member_nat @ S @ ( v_a @ C ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_a @ C @ S ) @ ( v_a @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(992,plain,
( ( ! [S: nat,C: product_prod_nat_nat > b] :
( ( member_nat @ S @ ( v_b @ C ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_b @ C @ S ) @ ( v_b @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(993,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( finite772653738at_nat @ ( e_a @ C ) )
=> ( finite_finite_nat @ ( v_a @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(994,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( finite772653738at_nat @ ( e_b @ C ) )
=> ( finite_finite_nat @ ( v_b @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(995,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( finite_finite_nat @ ( v_a @ C ) )
=> ( finite772653738at_nat @ ( e_a @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(996,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( finite_finite_nat @ ( v_b @ C ) )
=> ( finite772653738at_nat @ ( e_b @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(997,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( finite772653738at_nat @ ( e_b @ C ) )
=> ( finite_Graph_b @ C ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(998,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( finite772653738at_nat @ ( e_a @ C ) )
=> ( finite_Graph_a @ C ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(999,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( finite_Graph_b @ C )
=> ( finite772653738at_nat @ ( e_b @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(1000,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( finite_Graph_a @ C )
=> ( finite772653738at_nat @ ( e_a @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(1001,plain,
( ( ! [C: product_prod_nat_nat > b] :
( ( edmond1517640973ysis_b @ C )
=> ( ord_le841296385at_nat @ ( e_b @ C ) @ ( edmond771116671s_uE_b @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(1002,plain,
( ( ! [C: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ C )
=> ( ord_le841296385at_nat @ ( e_a @ C ) @ ( edmond771116670s_uE_a @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(1003,plain,
( ( ! [C: product_prod_nat_nat > a,S: nat,T: nat] :
( ( edmond1517640972ysis_a @ C )
=> ( ord_le841296385at_nat @ ( edmond475474835dges_a @ C @ S @ T ) @ ( e_a @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(1004,plain,
( ( ! [C: product_prod_nat_nat > b,S: nat,T: nat] :
( ( edmond1517640973ysis_b @ C )
=> ( ord_le841296385at_nat @ ( edmond475474836dges_b @ C @ S @ T ) @ ( e_b @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(1005,plain,
( ( ! [C: product_prod_nat_nat > b,U: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_b @ C @ U ) @ ( v_b @ C ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(1006,plain,
( ( ! [C: product_prod_nat_nat > a,U: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ C @ U ) @ ( v_a @ C ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(1007,plain,
( ( ! [C: product_prod_nat_nat > b,U: nat] :
( ( finite_Graph_b @ C )
=> ( finite_finite_nat @ ( adjacent_nodes_b @ C @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(1008,plain,
( ( ! [C: product_prod_nat_nat > a,U: nat] :
( ( finite_Graph_a @ C )
=> ( finite_finite_nat @ ( adjacent_nodes_a @ C @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(1009,plain,
( ( ! [U3: set_nat] : ( ord_le841296385at_nat @ ( incoming_a @ c @ U3 ) @ ( e_a @ c ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(1010,plain,
( ( ! [U3: set_nat] : ( ord_le841296385at_nat @ ( outgoing_a @ c @ U3 ) @ ( e_a @ c ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(1011,plain,
( ( ord_le841296385at_nat @ ( e_b @ c2 ) @ ( edmond771116671s_uE_b @ c2 ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(1012,plain,
( ( ( finite772653738at_nat @ ( e_b @ c2 ) )
=> ( finite_Graph_b @ c2 ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(1013,plain,
( ( ( finite772653738at_nat @ ( e_b @ c2 ) )
=> ( finite_finite_nat @ ( v_b @ c2 ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(1014,plain,
( ( ord_le841296385at_nat @ ( edmond475474836dges_b @ c2 @ s @ t ) @ ( e_b @ c2 ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(1015,plain,
( ( finite772653738at_nat @ ( e_b @ c2 ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(1016,plain,
( ( ( finite_finite_nat @ ( v_b @ c2 ) )
=> ( finite772653738at_nat @ ( e_b @ c2 ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(1017,plain,
( ( ! [U3: set_nat] :
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( outgoing_a @ c @ U3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(1018,plain,
( ( ! [U3: set_nat] :
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( incoming_a @ c @ U3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(1019,plain,
( ( incoming_a = incoming_a )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(1020,plain,
( ( incoming_b = incoming_b )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(1021,plain,
( ( outgoing_a = outgoing_a )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(1022,plain,
( ( outgoing_b = outgoing_b )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(1023,plain,
( ( ! [C: product_prod_nat_nat > a,U3: set_nat] : ( ord_le841296385at_nat @ ( outgoing_a @ C @ U3 ) @ ( e_a @ C ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(1024,plain,
( ( ! [C: product_prod_nat_nat > b,U3: set_nat] : ( ord_le841296385at_nat @ ( outgoing_b @ C @ U3 ) @ ( e_b @ C ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(1025,plain,
( ( ! [C: product_prod_nat_nat > a,U3: set_nat] : ( ord_le841296385at_nat @ ( incoming_a @ C @ U3 ) @ ( e_a @ C ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(1026,plain,
( ( ! [C: product_prod_nat_nat > b,U3: set_nat] : ( ord_le841296385at_nat @ ( incoming_b @ C @ U3 ) @ ( e_b @ C ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(1027,plain,
( ( ! [C: product_prod_nat_nat > a,U3: set_nat] :
( ( finite_finite_nat @ ( v_a @ C ) )
=> ( finite772653738at_nat @ ( outgoing_a @ C @ U3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(1028,plain,
( ( ! [C: product_prod_nat_nat > b,U3: set_nat] :
( ( finite_finite_nat @ ( v_b @ C ) )
=> ( finite772653738at_nat @ ( outgoing_b @ C @ U3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(1029,plain,
( ( ! [C: product_prod_nat_nat > a,U3: set_nat] :
( ( finite_finite_nat @ ( v_a @ C ) )
=> ( finite772653738at_nat @ ( incoming_a @ C @ U3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(1030,plain,
( ( ! [C: product_prod_nat_nat > b,U3: set_nat] :
( ( finite_finite_nat @ ( v_b @ C ) )
=> ( finite772653738at_nat @ ( incoming_b @ C @ U3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(1031,plain,
( ( ! [U3: set_nat] : ( ord_le841296385at_nat @ ( incoming_b @ c2 @ U3 ) @ ( e_b @ c2 ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(1032,plain,
( ( ! [U3: set_nat] : ( ord_le841296385at_nat @ ( outgoing_b @ c2 @ U3 ) @ ( e_b @ c2 ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(1033,plain,
( ( ! [U3: set_nat] :
( ( finite_finite_nat @ ( v_b @ c2 ) )
=> ( finite772653738at_nat @ ( outgoing_b @ c2 @ U3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(1034,plain,
( ( ! [U3: set_nat] :
( ( finite_finite_nat @ ( v_b @ c2 ) )
=> ( finite772653738at_nat @ ( incoming_b @ c2 @ U3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(1035,plain,
( ( ord_le841296385at_nat @ edges @ ( e_a @ c ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(1036,plain,
( ( ! [A2: set_nat,B2: set_nat] :
( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( A2 != B2 )
=> ( ord_less_set_nat @ A2 @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(1037,plain,
( ( ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( A2 != B2 )
=> ( ord_le116442893at_nat @ A2 @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(1038,plain,
( ( ! [A2: set_nat,B2: set_nat] :
( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( ord_less_eq_set_nat @ B2 @ A2 )
=> ( A2 = B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(1039,plain,
( ( ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( ord_le841296385at_nat @ B2 @ A2 )
=> ( A2 = B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(1040,plain,
( ( ! [A2: set_nat,B2: set_nat] :
( ! [X2: nat] :
( ( member_nat @ X2 @ A2 )
=> ( member_nat @ X2 @ B2 ) )
=> ( ord_less_eq_set_nat @ A2 @ B2 ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(1041,plain,
( ( ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
( ! [X2: product_prod_nat_nat] :
( ( member701585322at_nat @ X2 @ A2 )
=> ( member701585322at_nat @ X2 @ B2 ) )
=> ( ord_le841296385at_nat @ A2 @ B2 ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(1042,plain,
( ( ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(1043,plain,
( ( ! [P2: nat > $o,Q: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q ) )
= ( ! [X: nat] :
( ( P2 @ X )
=> ( Q @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(1044,plain,
( ( ! [P2: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
( ( ord_le841296385at_nat @ ( collec7649004at_nat @ P2 ) @ ( collec7649004at_nat @ Q ) )
= ( ! [X: product_prod_nat_nat] :
( ( P2 @ X )
=> ( Q @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(1045,plain,
( ( ( ^ [Y4: set_nat,Z: set_nat] : ( Y4 = Z ) )
= ( ^ [A4: set_nat,B5: set_nat] :
( ( ord_less_eq_set_nat @ A4 @ B5 )
& ( ord_less_eq_set_nat @ B5 @ A4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(1046,plain,
( ( ( ^ [Y4: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] : ( Y4 = Z ) )
= ( ^ [A4: set_Pr1986765409at_nat,B5: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A4 @ B5 )
& ( ord_le841296385at_nat @ B5 @ A4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(1047,plain,
( ( ! [A2: set_nat,B2: set_nat,C3: set_nat] :
( ( ord_less_eq_set_nat @ A2 @ B2 )
=> ( ( ord_less_eq_set_nat @ B2 @ C3 )
=> ( ord_less_eq_set_nat @ A2 @ C3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(1048,plain,
( ( ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C3: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A2 @ B2 )
=> ( ( ord_le841296385at_nat @ B2 @ C3 )
=> ( ord_le841296385at_nat @ A2 @ C3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(1049,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[700]) ).
thf(1050,plain,
( ( ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[771]) ).
thf(1051,plain,
( ( ! [SX0: product_prod_nat_nat > b] :
( ~ ( finite_Graph_b @ SX0 )
| ( finite_finite_nat @ ( v_b @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[957]) ).
thf(1052,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( member_nat @ SX0 @ ( v_a @ c ) )
| ~ ( isSimplePath_a @ c @ SX0 @ SX1 @ SX2 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SX1 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[895]) ).
thf(1053,plain,
( ( isShortestPath_a
= ( ^ [SX0: product_prod_nat_nat > a,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isSimplePath_a @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ( size_s1990949619at_nat @ SX2 )
!= ( min_dist_a @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[961]) ).
thf(1054,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ( isShortestPath_b @ c2 @ SX0 @ SX1 @ SX2 )
= ( ~ ( ~ ( isPath_b @ c2 @ SX0 @ SX1 @ SX2 )
| ( ( size_s1990949619at_nat @ SX1 )
!= ( min_dist_b @ c2 @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[775]) ).
thf(1055,plain,
( ( ! [SX0: product_prod_nat_nat > a] :
( ~ ( finite_Graph_a @ SX0 )
| ( finite772653738at_nat @ ( e_a @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1000]) ).
thf(1056,plain,
( ( ! [SX0: set_nat] :
( ~ ( finite_finite_nat @ ( v_a @ c ) )
| ( finite772653738at_nat @ ( outgoing_a @ c @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1017]) ).
thf(1057,plain,
( ( ! [SX0: nat,SX1: product_prod_nat_nat > b] :
( ~ ( member_nat @ SX0 @ ( v_b @ SX1 ) )
| ( ord_less_eq_set_nat @ ( reachableNodes_b @ SX1 @ SX0 ) @ ( v_b @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[992]) ).
thf(1058,plain,
( ( ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[769]) ).
thf(1059,plain,
( ( ! [SX0: set_nat,SX1: set_nat] :
( ~ ! [SX2: nat] :
( ~ ( member_nat @ SX2 @ SX0 )
| ( member_nat @ SX2 @ SX1 ) )
| ( ord_less_eq_set_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1040]) ).
thf(1060,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
( ~ ( finite_Graph_a @ SX0 )
| ~ ( member_nat @ SX1 @ ( v_a @ SX0 ) )
| ~ ( isShortestPath_a @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SX2 ) @ ( finite_card_nat @ ( v_a @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[847]) ).
thf(1061,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat] :
( ~ ( finite_Graph_a @ SX0 )
| ( finite_finite_nat @ ( adjacent_nodes_a @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1008]) ).
thf(1062,plain,
( ( ( ^ [SX0: set_nat,SX1: set_nat] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_nat,SX1: set_nat] :
~ ( ~ ( ord_less_eq_set_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_nat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1045]) ).
thf(1063,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
( ~ ( finite_Graph_b @ SX0 )
| ~ ( member_nat @ SX1 @ ( v_b @ SX0 ) )
| ~ ( isShortestPath_b @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SX2 ) @ ( finite_card_nat @ ( v_b @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[848]) ).
thf(1064,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
( ~ ( isShortestPath_a @ SX0 @ SX1 @ SX2 @ SX3 )
| ( isPath_a @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[870]) ).
thf(1065,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[825]) ).
thf(1066,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX0 != SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[796]) ).
thf(1067,plain,
( ( ! [SX0: nat > $o,SX1: nat > $o] :
( ~ ! [SX2: nat] :
( ( SX0 @ SX2 )
= ( SX1 @ SX2 ) )
| ( ( collect_nat @ SX0 )
= ( collect_nat @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[760]) ).
thf(1068,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat] :
( ~ ( connected_a @ SX0 @ SX1 @ SX2 )
| ( ( member_nat @ SX2 @ ( v_a @ SX0 ) )
= ( member_nat @ SX1 @ ( v_a @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[869]) ).
thf(1069,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( dist_a @ c @ SX0 @ SX1 @ SX2 )
| ~ ! [SX3: nat] :
( ~ ( dist_a @ c @ SX0 @ SX3 @ SX2 )
| ( ord_less_eq_nat @ SX1 @ SX3 ) )
| ( ( min_dist_a @ c @ SX0 @ SX2 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[910]) ).
thf(1070,plain,
( ( dist_b
= ( ^ [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat,SX3: nat] :
~ ! [SX4: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SX0 @ SX1 @ SX4 @ SX3 )
| ( ( size_s1990949619at_nat @ SX4 )
!= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[886]) ).
thf(1071,plain,
( ( isShortestPath_a
= ( ^ [SX0: product_prod_nat_nat > a,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isPath_a @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ! [SX4: list_P559422087at_nat] :
( ~ ( isPath_a @ SX0 @ SX1 @ SX4 @ SX3 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SX2 ) @ ( size_s1990949619at_nat @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[819]) ).
thf(1072,plain,
( ( ! [SX0: product_prod_nat_nat > b] :
( ~ ( edmond1517640973ysis_b @ SX0 )
| ( finite772653738at_nat @ ( edmond771116671s_uE_b @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[763]) ).
thf(1073,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( dist_a @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ! [SX4: nat] :
( ~ ( dist_a @ SX0 @ SX1 @ SX4 @ SX3 )
| ( ord_less_eq_nat @ SX2 @ SX4 ) )
| ( ( min_dist_a @ SX0 @ SX1 @ SX3 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[815]) ).
thf(1074,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( connected_b @ c2 @ SX0 @ SX1 )
| ( ( ( min_dist_b @ c2 @ SX0 @ SX1 )
= zero_zero_nat )
= ( SX1 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[751]) ).
thf(1075,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( dist_a @ c @ SX0 @ SX1 @ SX2 )
= ( ~ ! [SX3: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SX0 @ SX3 @ SX2 )
| ( ( size_s1990949619at_nat @ SX3 )
!= SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[912]) ).
thf(1076,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SX0 )
| ~ ( ord_le116442893at_nat @ SX1 @ SX0 )
| ( ord_less_nat @ ( finite447719721at_nat @ SX1 ) @ ( finite447719721at_nat @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[973]) ).
thf(1077,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
( ~ ( connected_a @ SX0 @ SX1 @ SX2 )
| ( ( min_dist_a @ SX0 @ SX1 @ SX2 )
!= SX3 )
| ~ ( ord_less_nat @ SX4 @ SX3 )
| ~ ! [SX5: nat] :
~ ~ ( ~ ( connected_a @ SX0 @ SX1 @ SX5 )
| ( ( min_dist_a @ SX0 @ SX1 @ SX5 )
!= SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[881]) ).
thf(1078,plain,
( ( connected_a
= ( ^ [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat] :
~ ! [SX3: nat] :
~ ( dist_a @ SX0 @ SX1 @ SX3 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[875]) ).
thf(1079,plain,
( ( ! [SX0: set_nat] :
( ~ ( finite_finite_nat @ ( v_b @ c2 ) )
| ( finite772653738at_nat @ ( outgoing_b @ c2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1033]) ).
thf(1080,plain,
( ( ! [SX0: product_prod_nat_nat > a] :
( ~ ( edmond1517640972ysis_a @ SX0 )
| ( ord_le841296385at_nat @ ( e_a @ SX0 ) @ ( edmond771116670s_uE_a @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1002]) ).
thf(1081,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat] :
( ~ ( connected_a @ SX0 @ SX1 @ SX2 )
| ~ ! [SX3: list_P559422087at_nat] :
~ ( isShortestPath_a @ SX0 @ SX1 @ SX3 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[876]) ).
thf(1082,plain,
( ( ! [SX0: product_prod_nat_nat > b] :
( ~ ( finite_finite_nat @ ( v_b @ SX0 ) )
| ( finite772653738at_nat @ ( e_b @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[996]) ).
thf(1083,plain,
( ( ! [SX0: set_nat,SX1: set_nat] :
( ~ ( finite_finite_nat @ SX0 )
| ~ ( ord_less_eq_set_nat @ SX1 @ SX0 )
| ( ord_less_eq_nat @ ( finite_card_nat @ SX1 ) @ ( finite_card_nat @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[947]) ).
thf(1084,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat] :
( ~ ( connected_b @ SX0 @ SX1 @ SX2 )
| ( dist_b @ SX0 @ SX1 @ ( min_dist_b @ SX0 @ SX1 @ SX2 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[882]) ).
thf(1085,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( connected_b @ c2 @ SX0 @ SX1 )
| ( ( min_dist_b @ c2 @ SX0 @ SX1 )
!= SX2 )
| ~ ( ord_less_nat @ SX3 @ SX2 )
| ~ ! [SX4: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SX0 @ SX4 )
| ( ( min_dist_b @ c2 @ SX0 @ SX4 )
!= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[731]) ).
thf(1086,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat,SX3: nat > $o] :
( ~ ( connected_a @ SX0 @ SX1 @ SX2 )
| ~ ! [SX4: nat] :
( ~ ( dist_a @ SX0 @ SX1 @ SX4 @ SX2 )
| ~ ! [SX5: nat] :
( ~ ( dist_a @ SX0 @ SX1 @ SX5 @ SX2 )
| ( ord_less_eq_nat @ SX4 @ SX5 ) )
| ( SX3 @ SX4 ) )
| ( SX3 @ ( min_dist_a @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[818]) ).
thf(1087,plain,
( ( ! [SX0: nat] :
~ ! [SX1: list_P559422087at_nat] :
( ( size_s1990949619at_nat @ SX1 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[768]) ).
thf(1088,plain,
( ( ! [SX0: set_set_nat,SX1: set_set_nat] :
( ~ ( ord_le1613022364et_nat @ SX0 @ SX1 )
| ~ ( finite2012248349et_nat @ SX1 )
| ( finite2012248349et_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[929]) ).
thf(1089,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( connected_b @ c2 @ SX0 @ SX1 )
| ( dist_b @ c2 @ SX0 @ ( min_dist_b @ c2 @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[743]) ).
thf(1090,plain,
( ( ~ ~ ( connected_b @ c2 @ s @ t )
| ( ord_less_nat @ ( edmond1022345717sure_b @ c2 @ s @ t ) @ ( edmond1022345716sure_a @ c @ s @ t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[726]) ).
thf(1091,plain,
( ( ! [SX0: set_nat,SX1: set_nat] :
( ~ ( finite_finite_nat @ SX0 )
| ~ ( ord_less_eq_set_nat @ SX1 @ SX0 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SX0 ) @ ( finite_card_nat @ SX1 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[949]) ).
thf(1092,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( connected_b @ SX0 @ SX1 @ SX2 )
| ~ ( ord_less_eq_nat @ SX3 @ ( min_dist_b @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX4: nat] :
~ ~ ( ~ ( connected_b @ SX0 @ SX1 @ SX4 )
| ( ( min_dist_b @ SX0 @ SX1 @ SX4 )
!= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[811]) ).
thf(1093,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( connected_b @ c2 @ SX0 @ SX1 )
| ~ ! [SX2: list_P559422087at_nat] :
~ ( isShortestPath_b @ c2 @ SX0 @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[782]) ).
thf(1094,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( connected_a @ c @ SX0 @ SX1 )
= ( ~ ! [SX2: list_P559422087at_nat] :
~ ( isPath_a @ c @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[779]) ).
thf(1095,plain,
( ( ! [SX0: set_nat,SX1: nat] :
( ~ ( finite_finite_nat @ SX0 )
| ~ ( member_nat @ SX1 @ SX0 )
| ~ ! [SX2: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SX2 @ SX0 )
| ~ ( ord_less_eq_nat @ SX2 @ SX1 ) )
| ~ ! [SX3: nat] :
( ~ ( member_nat @ SX3 @ SX0 )
| ~ ( ord_less_eq_nat @ SX3 @ SX2 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[965]) ).
thf(1096,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
( ~ ( finite_Graph_a @ SX0 )
| ~ ( member_nat @ SX1 @ ( v_a @ SX0 ) )
| ~ ( isSimplePath_a @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SX2 ) @ ( finite_card_nat @ ( v_a @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[971]) ).
thf(1097,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
( ~ ( isPath_b @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ! [SX4: list_P559422087at_nat] :
~ ( isSimplePath_b @ SX0 @ SX1 @ SX4 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[941]) ).
thf(1098,plain,
( ( ! [SX0: nat] :
( ~ ( member_nat @ SX0 @ ( v_a @ c ) )
| ( ord_less_eq_set_nat @ ( reachableNodes_a @ c @ SX0 ) @ ( v_a @ c ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[975]) ).
thf(1099,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: set_nat] :
( ~ ( finite_finite_nat @ ( v_a @ SX0 ) )
| ( finite772653738at_nat @ ( incoming_a @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1029]) ).
thf(1100,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( connected_b @ c2 @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ ( min_dist_b @ c2 @ SX0 @ SX1 ) )
| ~ ! [SX3: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SX0 @ SX3 )
| ( ( min_dist_b @ c2 @ SX0 @ SX3 )
!= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[783]) ).
thf(1101,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: nat] :
( ~ ~ ( finite772653738at_nat @ SX0 )
| ~ ! [SX2: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( finite772653738at_nat @ SX2 )
| ( ( finite447719721at_nat @ SX2 )
!= SX1 ) )
| ~ ( ord_le841296385at_nat @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[939]) ).
thf(1102,plain,
( ( ! [SX0: set_nat,SX1: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_nat @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1038]) ).
thf(1103,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
( ~ ( isPath_a @ SX0 @ SX1 @ SX2 @ SX3 )
| ( dist_a @ SX0 @ SX1 @ ( size_s1990949619at_nat @ SX2 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[885]) ).
thf(1104,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( connected_a @ c @ SX0 @ SX1 )
= ( ~ ! [SX2: nat] :
~ ( dist_a @ c @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[906]) ).
thf(1105,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( dist_b @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ! [SX4: nat] :
( ~ ( dist_b @ SX0 @ SX1 @ SX4 @ SX3 )
| ( ord_less_eq_nat @ SX2 @ SX4 ) )
| ( ( min_dist_b @ SX0 @ SX1 @ SX3 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[816]) ).
thf(1106,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat] :
( ~ ( edmond1517640972ysis_a @ SX0 )
| ( ord_le841296385at_nat @ ( edmond475474835dges_a @ SX0 @ SX1 @ SX2 ) @ ( e_a @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1003]) ).
thf(1107,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( dist_a @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ord_less_eq_nat @ ( min_dist_a @ SX0 @ SX1 @ SX3 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[813]) ).
thf(1108,plain,
( ( ! [SX0: product_prod_nat_nat > b] :
( ~ ( finite_Graph_b @ SX0 )
| ( finite772653738at_nat @ ( e_b @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[999]) ).
thf(1109,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( connected_a @ SX0 @ SX1 @ SX2 )
| ~ ( ord_less_eq_nat @ SX3 @ ( min_dist_a @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX4: nat] :
~ ~ ( ~ ( connected_a @ SX0 @ SX1 @ SX4 )
| ( ( min_dist_a @ SX0 @ SX1 @ SX4 )
!= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[812]) ).
thf(1110,plain,
( ( ! [SX0: product_prod_nat_nat > a] :
( ~ ( edmond1517640972ysis_a @ SX0 )
| ( finite772653738at_nat @ ( edmond771116670s_uE_a @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[764]) ).
thf(1111,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
( ~ ( isShortestPath_b @ SX0 @ SX1 @ SX2 @ SX3 )
| ( isPath_b @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[871]) ).
thf(1112,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) )
| ( ord_less_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[808]) ).
thf(1113,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: set_nat] :
( ~ ( finite_finite_nat @ ( v_b @ SX0 ) )
| ( finite772653738at_nat @ ( outgoing_b @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1028]) ).
thf(1114,plain,
( ( ! [SX0: product_prod_nat_nat > a] :
( ~ ( finite_finite_nat @ ( v_a @ SX0 ) )
| ( finite772653738at_nat @ ( e_a @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[995]) ).
thf(1115,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) )
| ( ord_le116442893at_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1037]) ).
thf(1116,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ( isShortestPath_b @ c2 @ SX0 @ SX1 @ SX2 )
= ( ~ ( ~ ( isPath_b @ c2 @ SX0 @ SX1 @ SX2 )
| ~ ! [SX3: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SX0 @ SX3 @ SX2 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SX1 ) @ ( size_s1990949619at_nat @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[789]) ).
thf(1117,plain,
( ( ! [SX0: nat > $o,SX1: nat,SX2: nat] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX3: nat] :
( ~ ( SX0 @ SX3 )
| ( ord_less_eq_nat @ SX3 @ SX2 ) )
| ~ ! [SX3: nat] :
~ ~ ( ~ ( SX0 @ SX3 )
| ~ ! [SX4: nat] :
( ~ ( SX0 @ SX4 )
| ( ord_less_eq_nat @ SX4 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[799]) ).
thf(1118,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( member_nat @ SX0 @ ( v_a @ c ) )
| ~ ( connected_a @ c @ SX0 @ SX1 )
| ( ord_less_nat @ ( min_dist_a @ c @ SX0 @ SX1 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[778]) ).
thf(1119,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat] :
( ~ ( edmond1517640973ysis_b @ SX0 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474836dges_b @ SX0 @ SX1 @ SX2 ) ) @ ( finite447719721at_nat @ ( edmond771116671s_uE_b @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[964]) ).
thf(1120,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( dist_a @ c @ SX0 @ SX1 @ SX2 )
| ( ord_less_eq_nat @ ( min_dist_a @ c @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[909]) ).
thf(1121,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( dist_b @ c2 @ SX0 @ SX1 @ SX2 )
= ( ~ ! [SX3: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SX0 @ SX3 @ SX2 )
| ( ( size_s1990949619at_nat @ SX3 )
!= SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[742]) ).
thf(1122,plain,
( ( ! [SX0: set_set_nat,SX1: set_nat] :
( ~ ( finite2012248349et_nat @ SX0 )
| ~ ( member_set_nat @ SX1 @ SX0 )
| ~ ! [SX2: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SX2 @ SX0 )
| ~ ( ord_less_eq_set_nat @ SX1 @ SX2 ) )
| ~ ! [SX3: set_nat] :
( ~ ( member_set_nat @ SX3 @ SX0 )
| ~ ( ord_less_eq_set_nat @ SX2 @ SX3 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[969]) ).
thf(1123,plain,
( ( isShortestPath_b
= ( ^ [SX0: product_prod_nat_nat > b,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isPath_b @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ! [SX4: list_P559422087at_nat] :
( ~ ( isPath_b @ SX0 @ SX1 @ SX4 @ SX3 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SX2 ) @ ( size_s1990949619at_nat @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[820]) ).
thf(1124,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat] :
( ~ ( edmond1517640972ysis_a @ SX0 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ SX0 @ SX1 @ SX2 ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[963]) ).
thf(1125,plain,
( ( ! [SX0: nat > nat,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat,SX4: nat] :
( ~ ( ord_less_nat @ SX3 @ SX4 )
| ( ord_less_nat @ ( SX0 @ SX3 ) @ ( SX0 @ SX4 ) ) )
| ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ( ord_less_eq_nat @ ( SX0 @ SX1 ) @ ( SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[809]) ).
thf(1126,plain,
( ( isShortestPath_a
= ( ^ [SX0: product_prod_nat_nat > a,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isPath_a @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ( size_s1990949619at_nat @ SX2 )
!= ( min_dist_a @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[773]) ).
thf(1127,plain,
( ( ! [SX0: set_nat] :
( ~ ( finite_finite_nat @ ( v_b @ c2 ) )
| ( finite772653738at_nat @ ( incoming_b @ c2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1034]) ).
thf(1128,plain,
( ( ! [SX0: product_prod_nat_nat > a] :
( ~ ( finite_finite_nat @ ( v_a @ SX0 ) )
| ( finite_Graph_a @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[956]) ).
thf(1129,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ! [SX2: nat] :
( ~ ~ ( SX0 @ SX2 )
| ~ ! [SX3: nat] :
~ ~ ( ~ ( ord_less_nat @ SX3 @ SX2 )
| ~ ~ ( SX0 @ SX3 ) ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[828]) ).
thf(1130,plain,
( ( ! [SX0: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[849]) ).
thf(1131,plain,
( ( ! [SX0: set_se1612935105at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ( finite1457549322at_nat @ SX0 )
| ~ ( member298845450at_nat @ SX1 @ SX0 )
| ~ ! [SX2: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SX2 @ SX0 )
| ~ ( ord_le841296385at_nat @ SX2 @ SX1 ) )
| ~ ! [SX3: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SX3 @ SX0 )
| ~ ( ord_le841296385at_nat @ SX3 @ SX2 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[967]) ).
thf(1132,plain,
( ( ! [SX0: list_P559422087at_nat > $o,SX1: list_P559422087at_nat] :
( ~ ! [SX2: list_P559422087at_nat] :
( ~ ! [SX3: list_P559422087at_nat] :
( ~ ( ord_less_nat @ ( size_s1990949619at_nat @ SX3 ) @ ( size_s1990949619at_nat @ SX2 ) )
| ( SX0 @ SX3 ) )
| ( SX0 @ SX2 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[732]) ).
thf(1133,plain,
( ( ! [SX0: set_nat,SX1: set_nat,SX2: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_nat @ SX1 @ SX2 )
| ( ord_less_eq_set_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1047]) ).
thf(1134,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat,SX3: nat > $o] :
( ~ ( connected_b @ SX0 @ SX1 @ SX2 )
| ~ ! [SX4: nat] :
( ~ ( dist_b @ SX0 @ SX1 @ SX4 @ SX2 )
| ~ ! [SX5: nat] :
( ~ ( dist_b @ SX0 @ SX1 @ SX5 @ SX2 )
| ( ord_less_eq_nat @ SX4 @ SX5 ) )
| ( SX3 @ SX4 ) )
| ( SX3 @ ( min_dist_b @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[817]) ).
thf(1135,plain,
( ( ! [SX0: set_se1612935105at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ( finite1457549322at_nat @ SX0 )
| ~ ( member298845450at_nat @ SX1 @ SX0 )
| ~ ! [SX2: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SX2 @ SX0 )
| ~ ( ord_le841296385at_nat @ SX1 @ SX2 ) )
| ~ ! [SX3: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SX3 @ SX0 )
| ~ ( ord_le841296385at_nat @ SX2 @ SX3 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[970]) ).
thf(1136,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( connected_b @ c2 @ SX0 @ SX1 )
| ( ( member_nat @ SX1 @ ( v_b @ c2 ) )
= ( member_nat @ SX0 @ ( v_b @ c2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[903]) ).
thf(1137,plain,
( ( ! [SX0: product_prod_nat_nat > a] :
( ~ ( finite772653738at_nat @ ( e_a @ SX0 ) )
| ( finite_Graph_a @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[998]) ).
thf(1138,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( dist_b @ c2 @ SX0 @ SX1 @ SX2 )
| ( connected_b @ c2 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[748]) ).
thf(1139,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( isPath_b @ c2 @ SX0 @ SX1 @ SX2 )
| ( dist_b @ c2 @ SX0 @ ( size_s1990949619at_nat @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[741]) ).
thf(1140,plain,
( ( ! [SX0: nat > $o,SX1: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ SX0 ) @ ( collect_nat @ SX1 ) )
= ( ! [SX2: nat] :
( ~ ( SX0 @ SX2 )
| ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1043]) ).
thf(1141,plain,
( ( ( ^ [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
~ ( ~ ( ord_le841296385at_nat @ SX0 @ SX1 )
| ~ ( ord_le841296385at_nat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1046]) ).
thf(1142,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat > $o] :
( ~ ( finite772653738at_nat @ SX0 )
| ~ ! [SX2: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SX2 )
| ~ ! [SX3: set_Pr1986765409at_nat] :
( ~ ( ord_le116442893at_nat @ SX3 @ SX2 )
| ( SX1 @ SX3 ) )
| ( SX1 @ SX2 ) )
| ( SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[959]) ).
thf(1143,plain,
( ( isShortestPath_b
= ( ^ [SX0: product_prod_nat_nat > b,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isPath_b @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ( size_s1990949619at_nat @ SX2 )
!= ( min_dist_b @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[774]) ).
thf(1144,plain,
( ( ~ ( finite_finite_nat @ ( v_a @ c ) )
| ( finite772653738at_nat @ ( e_a @ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[984]) ).
thf(1145,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[797]) ).
thf(1146,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[851]) ).
thf(1147,plain,
( ( connected_a
= ( ^ [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat] :
~ ! [SX3: list_P559422087at_nat] :
~ ( isPath_a @ SX0 @ SX1 @ SX3 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[867]) ).
thf(1148,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( isShortestPath_a @ c @ SX0 @ SX1 @ SX2 )
| ( isSimplePath_a @ c @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[907]) ).
thf(1149,plain,
( ( ! [SX0: set_nat,SX1: set_nat] :
( ~ ( finite_finite_nat @ SX0 )
| ~ ( ord_less_eq_set_nat @ SX1 @ SX0 )
| ~ ( ord_less_nat @ ( finite_card_nat @ SX1 ) @ ( finite_card_nat @ SX0 ) )
| ( ord_less_set_nat @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[945]) ).
thf(1150,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( connected_a @ c @ SX0 @ SX1 )
| ( ( ( min_dist_a @ c @ SX0 @ SX1 )
= zero_zero_nat )
= ( SX1 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[762]) ).
thf(1151,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ! [SX2: nat] :
( ~ ! [SX3: nat] :
( ~ ( ord_less_nat @ SX3 @ SX2 )
| ( SX0 @ SX3 ) )
| ( SX0 @ SX2 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[827]) ).
thf(1152,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( connected_a @ c @ SX0 @ SX1 )
| ( ( member_nat @ SX1 @ ( v_a @ c ) )
= ( member_nat @ SX0 @ ( v_a @ c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[738]) ).
thf(1153,plain,
( ( ! [SX0: set_nat,SX1: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX0 @ SX1 )
| ~ ~ ( finite_finite_nat @ SX0 )
| ~ ( finite_finite_nat @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[932]) ).
thf(1154,plain,
( ( ! [SX0: set_Pr1986765409at_nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( finite447719721at_nat @ SX0 ) )
| ( finite772653738at_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[899]) ).
thf(1155,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ( SX0 @ SX1 )
| ~ ~ ( SX0 @ zero_zero_nat )
| ~ ! [SX2: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_eq_nat @ SX2 @ SX1 )
| ~ ! [SX3: nat] :
( ~ ( ord_less_nat @ SX3 @ SX2 )
| ~ ( SX0 @ SX3 ) ) )
| ~ ( SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[810]) ).
thf(1156,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[857]) ).
thf(1157,plain,
( ( ~ ! [SX0: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ s @ SX0 @ t )
| ( ( size_s1990949619at_nat @ SX0 )
!= ( min_dist_b @ c2 @ s @ t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[728]) ).
thf(1158,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SX0 )
| ~ ( ord_le841296385at_nat @ SX1 @ SX0 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SX0 ) @ ( finite447719721at_nat @ SX1 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[950]) ).
thf(1159,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat] :
( ~ ( connected_b @ SX0 @ SX1 @ SX2 )
| ~ ! [SX3: list_P559422087at_nat] :
~ ( isShortestPath_b @ SX0 @ SX1 @ SX3 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[877]) ).
thf(1160,plain,
( ( ! [SX0: set_nat,SX1: nat] :
( ~ ( finite_finite_nat @ SX0 )
| ~ ( member_nat @ SX1 @ SX0 )
| ~ ! [SX2: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SX2 @ SX0 )
| ~ ( ord_less_eq_nat @ SX1 @ SX2 ) )
| ~ ! [SX3: nat] :
( ~ ( member_nat @ SX3 @ SX0 )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[968]) ).
thf(1161,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat] :
( ~ ( finite_Graph_a @ SX0 )
| ~ ( member_nat @ SX1 @ ( v_a @ SX0 ) )
| ~ ( connected_a @ SX0 @ SX1 @ SX2 )
| ( ord_less_nat @ ( min_dist_a @ SX0 @ SX1 @ SX2 ) @ ( finite_card_nat @ ( v_a @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[846]) ).
thf(1162,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SX0 @ SX1 )
| ~ ~ ( finite772653738at_nat @ SX0 )
| ~ ( finite772653738at_nat @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[933]) ).
thf(1163,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
( ~ ( isShortestPath_b @ SX0 @ SX1 @ SX2 @ SX3 )
| ( isSimplePath_b @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[943]) ).
thf(1164,plain,
( ( ! [SX0: set_nat] :
( ~ ~ ( finite_finite_nat @ SX0 )
| ( ( finite_card_nat @ SX0 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[892]) ).
thf(1165,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ( SX0 != SX1 ) )
| ~ ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[829]) ).
thf(1166,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SX0 )
| ~ ( ord_le841296385at_nat @ SX1 @ SX0 )
| ~ ( ord_less_nat @ ( finite447719721at_nat @ SX1 ) @ ( finite447719721at_nat @ SX0 ) )
| ( ord_le116442893at_nat @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[946]) ).
thf(1167,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( isPath_a @ c @ SX0 @ SX1 @ SX2 )
| ( dist_a @ c @ SX0 @ ( size_s1990949619at_nat @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[911]) ).
thf(1168,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ( isShortestPath_a @ c @ SX0 @ SX1 @ SX2 )
= ( ~ ( ~ ( isPath_a @ c @ SX0 @ SX1 @ SX2 )
| ~ ! [SX3: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SX0 @ SX3 @ SX2 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SX1 ) @ ( size_s1990949619at_nat @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[787]) ).
thf(1169,plain,
( ( ! [SX0: set_nat,SX1: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX0 @ SX1 )
| ~ ( finite_finite_nat @ SX1 )
| ( finite_finite_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[930]) ).
thf(1170,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat > $o] :
( ~ ( connected_a @ c @ SX0 @ SX1 )
| ~ ! [SX3: nat] :
( ~ ( dist_a @ c @ SX0 @ SX3 @ SX1 )
| ~ ! [SX4: nat] :
( ~ ( dist_a @ c @ SX0 @ SX4 @ SX1 )
| ( ord_less_eq_nat @ SX3 @ SX4 ) )
| ( SX2 @ SX3 ) )
| ( SX2 @ ( min_dist_a @ c @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[901]) ).
thf(1171,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( connected_a @ c @ SX0 @ SX1 )
| ( dist_a @ c @ SX0 @ ( min_dist_a @ c @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[913]) ).
thf(1172,plain,
( ( ! [SX0: set_Pr1986765409at_nat] :
( ~ ~ ( finite772653738at_nat @ SX0 )
| ( ( finite447719721at_nat @ SX0 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[891]) ).
thf(1173,plain,
( ( ! [SX0: set_nat,SX1: set_nat] :
( ~ ( finite_finite_nat @ SX0 )
| ~ ( ord_less_eq_set_nat @ SX1 @ SX0 )
| ( ( finite_card_nat @ SX1 )
!= ( finite_card_nat @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[936]) ).
thf(1174,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( dist_b @ SX0 @ SX1 @ SX2 @ SX3 )
| ( connected_b @ SX0 @ SX1 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[872]) ).
thf(1175,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( connected_b @ c2 @ SX0 @ SX1 )
= ( ~ ! [SX2: nat] :
~ ( dist_b @ c2 @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[739]) ).
thf(1176,plain,
( ( ! [SX0: product_prod_nat_nat > a] :
( ~ ( finite_Graph_a @ SX0 )
| ( edmond1517640972ysis_a @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[722]) ).
thf(1177,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
( ~ ( finite_Graph_b @ SX0 )
| ~ ( member_nat @ SX1 @ ( v_b @ SX0 ) )
| ~ ( isSimplePath_b @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SX2 ) @ ( finite_card_nat @ ( v_b @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[972]) ).
thf(1178,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( member_nat @ SX0 @ ( v_b @ c2 ) )
| ~ ( connected_b @ c2 @ SX0 @ SX1 )
| ( ord_less_nat @ ( min_dist_b @ c2 @ SX0 @ SX1 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[915]) ).
thf(1179,plain,
( ( ! [SX0: set_nat,SX1: set_nat > $o] :
( ~ ( finite_finite_nat @ SX0 )
| ~ ! [SX2: set_nat] :
( ~ ( finite_finite_nat @ SX2 )
| ~ ! [SX3: set_nat] :
( ~ ( ord_less_set_nat @ SX3 @ SX2 )
| ( SX1 @ SX3 ) )
| ( SX1 @ SX2 ) )
| ( SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[960]) ).
thf(1180,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX0 != SX1 )
= ( ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[822]) ).
thf(1181,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( isPath_b @ c2 @ SX0 @ SX1 @ SX2 )
| ~ ! [SX3: list_P559422087at_nat] :
~ ( isSimplePath_b @ c2 @ SX0 @ SX3 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[904]) ).
thf(1182,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ( SX0 @ zero_zero_nat )
| ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX2 )
| ~ ~ ( SX0 @ SX2 )
| ~ ! [SX3: nat] :
~ ~ ( ~ ( ord_less_nat @ SX3 @ SX2 )
| ~ ~ ( SX0 @ SX3 ) ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[858]) ).
thf(1183,plain,
( ( ! [SX0: set_nat,SX1: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) )
| ( ord_less_set_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1036]) ).
thf(1184,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: nat] :
( ~ ! [SX2: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SX2 @ SX0 )
| ~ ( finite772653738at_nat @ SX2 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ SX2 ) @ SX1 ) )
| ~ ( ~ ( finite772653738at_nat @ SX0 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[952]) ).
thf(1185,plain,
( ( ! [SX0: nat,SX1: product_prod_nat_nat > a] :
( ~ ( member_nat @ SX0 @ ( v_a @ SX1 ) )
| ( ord_less_eq_set_nat @ ( reachableNodes_a @ SX1 @ SX0 ) @ ( v_a @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[991]) ).
thf(1186,plain,
( ( ! [SX0: set_nat,SX1: nat] :
( ~ ! [SX2: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX2 @ SX0 )
| ~ ( finite_finite_nat @ SX2 )
| ( ord_less_eq_nat @ ( finite_card_nat @ SX2 ) @ SX1 ) )
| ~ ( ~ ( finite_finite_nat @ SX0 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[951]) ).
thf(1187,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
( ~ ( isPath_b @ SX0 @ SX1 @ SX2 @ SX3 )
| ( dist_b @ SX0 @ SX1 @ ( size_s1990949619at_nat @ SX2 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[884]) ).
thf(1188,plain,
( ( ! [SX0: set_set_nat] :
( ~ ~ ( finite2012248349et_nat @ SX0 )
| ( ( finite_card_set_nat @ SX0 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[890]) ).
thf(1189,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ( isShortestPath_a @ c @ SX0 @ SX1 @ SX2 )
= ( ~ ( ~ ( isPath_a @ c @ SX0 @ SX1 @ SX2 )
| ( ( size_s1990949619at_nat @ SX1 )
!= ( min_dist_a @ c @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[788]) ).
thf(1190,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[805]) ).
thf(1191,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SX0 )
| ~ ( ord_le841296385at_nat @ SX1 @ SX0 )
| ( finite772653738at_nat @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[935]) ).
thf(1192,plain,
( ( ! [SX0: product_prod_nat_nat > b] :
( ~ ( finite_finite_nat @ ( v_b @ SX0 ) )
| ( finite_Graph_b @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[955]) ).
thf(1193,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat] :
( ~ ( connected_a @ SX0 @ SX1 @ SX2 )
| ( ( ( min_dist_a @ SX0 @ SX1 @ SX2 )
= zero_zero_nat )
= ( SX2 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[879]) ).
thf(1194,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
( ~ ( isShortestPath_a @ SX0 @ SX1 @ SX2 @ SX3 )
| ( isSimplePath_a @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[942]) ).
thf(1195,plain,
( ( ! [SX0: set_se1612935105at_nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( finite1701894793at_nat @ SX0 ) )
| ( finite1457549322at_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[897]) ).
thf(1196,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( isPath_a @ c @ SX0 @ SX1 @ SX2 )
| ~ ! [SX3: list_P559422087at_nat] :
~ ( isSimplePath_a @ c @ SX0 @ SX3 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[905]) ).
thf(1197,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( connected_b @ c2 @ SX0 @ SX1 )
= ( ~ ! [SX2: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[737]) ).
thf(1198,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ( ord_less_eq_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[795]) ).
thf(1199,plain,
( ( ! [SX0: product_prod_nat_nat > b] :
( ~ ( finite_Graph_b @ SX0 )
| ( edmond1517640973ysis_b @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[723]) ).
thf(1200,plain,
( ( ! [SX0: product_prod_nat_nat > a] :
( ~ ( edmond1517640972ysis_a @ SX0 )
| ( finite_Graph_a @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[724]) ).
thf(1201,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: set_nat] :
( ~ ( finite_finite_nat @ ( v_b @ SX0 ) )
| ( finite772653738at_nat @ ( incoming_b @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1030]) ).
thf(1202,plain,
( ( ~ ( finite772653738at_nat @ ( e_b @ c2 ) )
| ( finite_Graph_b @ c2 ) )
= $true ),
inference(unfold_def,[status(thm)],[1012]) ).
thf(1203,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SX0 @ SX1 )
| ~ ( finite772653738at_nat @ SX1 )
| ( finite772653738at_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[931]) ).
thf(1204,plain,
( ( ! [SX0: product_prod_nat_nat > b] :
( ~ ( finite772653738at_nat @ ( e_b @ SX0 ) )
| ( finite_finite_nat @ ( v_b @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[994]) ).
thf(1205,plain,
( ( dist_a
= ( ^ [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat,SX3: nat] :
~ ! [SX4: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SX0 @ SX1 @ SX4 @ SX3 )
| ( ( size_s1990949619at_nat @ SX4 )
!= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[887]) ).
thf(1206,plain,
( ( ! [SX0: product_prod_nat_nat > b] :
( ~ ( finite772653738at_nat @ ( e_b @ SX0 ) )
| ( finite_Graph_b @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[997]) ).
thf(1207,plain,
( ( ! [SX0: product_prod_nat_nat > b] :
( ~ ( edmond1517640973ysis_b @ SX0 )
| ( finite_Graph_b @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[725]) ).
thf(1208,plain,
( ( ! [SX0: product_prod_nat_nat > b] :
( ~ ( edmond1517640973ysis_b @ SX0 )
| ( ord_le841296385at_nat @ ( e_b @ SX0 ) @ ( edmond771116671s_uE_b @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1001]) ).
thf(1209,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ( isShortestPath_a @ c @ SX0 @ SX1 @ SX2 )
= ( ~ ( ~ ( isSimplePath_a @ c @ SX0 @ SX1 @ SX2 )
| ( ( size_s1990949619at_nat @ SX1 )
!= ( min_dist_a @ c @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[917]) ).
thf(1210,plain,
( ( ! [SX0: list_P559422087at_nat,SX1: list_P559422087at_nat] :
( ~ ( ( ( size_s1990949619at_nat @ SX0 )
!= ( size_s1990949619at_nat @ SX1 ) ) )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[830]) ).
thf(1211,plain,
( ( ! [SX0: set_set_nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ SX0 ) )
| ( finite2012248349et_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[898]) ).
thf(1212,plain,
( ( connected_b
= ( ^ [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat] :
~ ! [SX3: list_P559422087at_nat] :
~ ( isPath_b @ SX0 @ SX1 @ SX3 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[866]) ).
thf(1213,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SX0 )
| ~ ( ord_le841296385at_nat @ SX1 @ SX0 )
| ( ( finite447719721at_nat @ SX1 )
!= ( finite447719721at_nat @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[937]) ).
thf(1214,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( dist_b @ c2 @ SX0 @ SX1 @ SX2 )
| ( ord_less_eq_nat @ ( min_dist_b @ c2 @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[785]) ).
thf(1215,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat] :
( ~ ( connected_b @ SX0 @ SX1 @ SX2 )
| ( ( member_nat @ SX2 @ ( v_b @ SX0 ) )
= ( member_nat @ SX1 @ ( v_b @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[868]) ).
thf(1216,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat] :
( ~ ( connected_b @ SX0 @ SX1 @ SX2 )
| ( ( ( min_dist_b @ SX0 @ SX1 @ SX2 )
= zero_zero_nat )
= ( SX2 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[878]) ).
thf(1217,plain,
( ( ! [SX0: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[853]) ).
thf(1218,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat] :
( ~ ( finite_Graph_b @ SX0 )
| ~ ( member_nat @ SX1 @ ( v_b @ SX0 ) )
| ~ ( connected_b @ SX0 @ SX1 @ SX2 )
| ( ord_less_nat @ ( min_dist_b @ SX0 @ SX1 @ SX2 ) @ ( finite_card_nat @ ( v_b @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[845]) ).
thf(1219,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ! [SX2: product_prod_nat_nat] :
( ~ ( member701585322at_nat @ SX2 @ SX0 )
| ( member701585322at_nat @ SX2 @ SX1 ) )
| ( ord_le841296385at_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1041]) ).
thf(1220,plain,
( ( ! [SX0: product_prod_nat_nat > $o,SX1: product_prod_nat_nat > $o] :
( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SX0 ) @ ( collec7649004at_nat @ SX1 ) )
= ( ! [SX2: product_prod_nat_nat] :
( ~ ( SX0 @ SX2 )
| ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1044]) ).
thf(1221,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( connected_a @ c @ SX0 @ SX1 )
| ( ( min_dist_a @ c @ SX0 @ SX1 )
!= SX2 )
| ~ ( ord_less_nat @ SX3 @ SX2 )
| ~ ! [SX4: nat] :
~ ~ ( ~ ( connected_a @ c @ SX0 @ SX4 )
| ( ( min_dist_a @ c @ SX0 @ SX4 )
!= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[730]) ).
thf(1222,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: set_nat] :
( ~ ( finite_finite_nat @ ( v_a @ SX0 ) )
| ( finite772653738at_nat @ ( outgoing_a @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1027]) ).
thf(1223,plain,
( ( isShortestPath_b
= ( ^ [SX0: product_prod_nat_nat > b,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isSimplePath_b @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ( size_s1990949619at_nat @ SX2 )
!= ( min_dist_b @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[962]) ).
thf(1224,plain,
( ( ! [SX0: set_li664300135at_nat] :
( ~ ( finite1299096496at_nat @ SX0 )
| ~ ! [SX1: nat] :
~ ! [SX2: list_P559422087at_nat] :
( ~ ( member1608759472at_nat @ SX2 @ SX0 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SX2 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[944]) ).
thf(1225,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( connected_a @ c @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ ( min_dist_a @ c @ SX0 @ SX1 ) )
| ~ ! [SX3: nat] :
~ ~ ( ~ ( connected_a @ c @ SX0 @ SX3 )
| ( ( min_dist_a @ c @ SX0 @ SX3 )
!= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[786]) ).
thf(1226,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
( ~ ( connected_b @ SX0 @ SX1 @ SX2 )
| ( ( min_dist_b @ SX0 @ SX1 @ SX2 )
!= SX3 )
| ~ ( ord_less_nat @ SX4 @ SX3 )
| ~ ! [SX5: nat] :
~ ~ ( ~ ( connected_b @ SX0 @ SX1 @ SX5 )
| ( ( min_dist_b @ SX0 @ SX1 @ SX5 )
!= SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[880]) ).
thf(1227,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( connected_a @ c @ SX0 @ SX1 )
| ~ ! [SX2: list_P559422087at_nat] :
~ ( isShortestPath_a @ c @ SX0 @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[740]) ).
thf(1228,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( member_nat @ SX0 @ ( v_a @ c ) )
| ~ ( isShortestPath_a @ c @ SX0 @ SX1 @ SX2 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SX1 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[777]) ).
thf(1229,plain,
( ( ~ ( finite772653738at_nat @ ( e_a @ c ) )
| ( finite_Graph_a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[979]) ).
thf(1230,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( dist_a @ SX0 @ SX1 @ SX2 @ SX3 )
| ( connected_a @ SX0 @ SX1 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[873]) ).
thf(1231,plain,
( ( ! [SX0: set_nat,SX1: set_nat] :
( ~ ( finite_finite_nat @ SX0 )
| ~ ( ord_less_eq_set_nat @ SX1 @ SX0 )
| ( finite_finite_nat @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[934]) ).
thf(1232,plain,
( ( ! [SX0: set_nat,SX1: nat] :
( ~ ~ ( finite_finite_nat @ SX0 )
| ~ ! [SX2: set_nat] :
~ ~ ( ~ ~ ( ~ ( finite_finite_nat @ SX2 )
| ( ( finite_card_nat @ SX2 )
!= SX1 ) )
| ~ ( ord_less_eq_set_nat @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[938]) ).
thf(1233,plain,
( ( ! [SX0: nat] :
( ( ord_less_nat @ zero_zero_nat @ SX0 )
= ( SX0 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[852]) ).
thf(1234,plain,
( ( ! [SX0: set_li664300135at_nat] :
( ~ ~ ( finite1299096496at_nat @ SX0 )
| ( ( finite83082927at_nat @ SX0 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[888]) ).
thf(1235,plain,
( ( ! [SX0: set_set_nat,SX1: set_nat] :
( ~ ( finite2012248349et_nat @ SX0 )
| ~ ( member_set_nat @ SX1 @ SX0 )
| ~ ! [SX2: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SX2 @ SX0 )
| ~ ( ord_less_eq_set_nat @ SX2 @ SX1 ) )
| ~ ! [SX3: set_nat] :
( ~ ( member_set_nat @ SX3 @ SX0 )
| ~ ( ord_less_eq_set_nat @ SX3 @ SX2 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[966]) ).
thf(1236,plain,
( ( ! [SX0: product_prod_nat_nat > $o,SX1: product_prod_nat_nat > $o] :
( ~ ! [SX2: product_prod_nat_nat] :
( ( SX0 @ SX2 )
= ( SX1 @ SX2 ) )
| ( ( collec7649004at_nat @ SX0 )
= ( collec7649004at_nat @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[761]) ).
thf(1237,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( member_nat @ SX0 @ ( v_b @ c2 ) )
| ~ ( isSimplePath_b @ c2 @ SX0 @ SX1 @ SX2 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SX1 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[914]) ).
thf(1238,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( isShortestPath_b @ c2 @ SX0 @ SX1 @ SX2 )
| ( isSimplePath_b @ c2 @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[908]) ).
thf(1239,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat] :
( ~ ( edmond1517640973ysis_b @ SX0 )
| ( ord_le841296385at_nat @ ( edmond475474836dges_b @ SX0 @ SX1 @ SX2 ) @ ( e_b @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1004]) ).
thf(1240,plain,
( ( ! [SX0: nat] :
( ~ ( member_nat @ SX0 @ ( v_b @ c2 ) )
| ( ord_less_eq_set_nat @ ( reachableNodes_b @ c2 @ SX0 ) @ ( v_b @ c2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[976]) ).
thf(1241,plain,
( ( ! [SX0: set_nat,SX1: set_nat] :
( ~ ( finite_finite_nat @ SX0 )
| ~ ( ord_less_set_nat @ SX1 @ SX0 )
| ( ord_less_nat @ ( finite_card_nat @ SX1 ) @ ( finite_card_nat @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[974]) ).
thf(1242,plain,
( ( ~ ( finite772653738at_nat @ ( e_a @ c ) )
| ( finite_finite_nat @ ( v_a @ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[980]) ).
thf(1243,plain,
( ( ! [SX0: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[803]) ).
thf(1244,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( dist_b @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ord_less_eq_nat @ ( min_dist_b @ SX0 @ SX1 @ SX3 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[814]) ).
thf(1245,plain,
( ( ! [SX0: set_nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ SX0 ) )
| ( finite_finite_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[900]) ).
thf(1246,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( dist_b @ c2 @ SX0 @ SX1 @ SX2 )
| ~ ! [SX3: nat] :
( ~ ( dist_b @ c2 @ SX0 @ SX3 @ SX2 )
| ( ord_less_eq_nat @ SX1 @ SX3 ) )
| ( ( min_dist_b @ c2 @ SX0 @ SX2 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[784]) ).
thf(1247,plain,
( ( ! [SX0: set_se1612935105at_nat,SX1: set_se1612935105at_nat] :
( ~ ( ord_le2096002913at_nat @ SX0 @ SX1 )
| ~ ( finite1457549322at_nat @ SX1 )
| ( finite1457549322at_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[928]) ).
thf(1248,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat] :
( ~ ( edmond1517640973ysis_b @ SX0 )
| ( finite772653738at_nat @ ( edmond475474836dges_b @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[766]) ).
thf(1249,plain,
( ( connected_b
= ( ^ [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat] :
~ ! [SX3: nat] :
~ ( dist_b @ SX0 @ SX1 @ SX3 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[874]) ).
thf(1250,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat,SX2: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SX0 @ SX1 )
| ~ ( ord_le841296385at_nat @ SX1 @ SX2 )
| ( ord_le841296385at_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1048]) ).
thf(1251,plain,
( ( ! [SX0: set_li664300135at_nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ ( finite83082927at_nat @ SX0 ) )
| ( finite1299096496at_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[896]) ).
thf(1252,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat] :
( ~ ( edmond1517640972ysis_a @ SX0 )
| ( finite772653738at_nat @ ( edmond475474835dges_a @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[765]) ).
thf(1253,plain,
( ( ! [SX0: product_prod_nat_nat > b,SX1: nat] :
( ~ ( finite_Graph_b @ SX0 )
| ( finite_finite_nat @ ( adjacent_nodes_b @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1007]) ).
thf(1254,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
( ~ ( isPath_a @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ! [SX4: list_P559422087at_nat] :
~ ( isSimplePath_a @ SX0 @ SX1 @ SX4 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[940]) ).
thf(1255,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[824]) ).
thf(1256,plain,
( ( ~ ( finite772653738at_nat @ ( e_b @ c2 ) )
| ( finite_finite_nat @ ( v_b @ c2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1013]) ).
thf(1257,plain,
( ( ~ ( finite_finite_nat @ ( v_b @ c2 ) )
| ( finite772653738at_nat @ ( e_b @ c2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1016]) ).
thf(1258,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ( isShortestPath_b @ c2 @ SX0 @ SX1 @ SX2 )
= ( ~ ( ~ ( isSimplePath_b @ c2 @ SX0 @ SX1 @ SX2 )
| ( ( size_s1990949619at_nat @ SX1 )
!= ( min_dist_b @ c2 @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[902]) ).
thf(1259,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( dist_a @ c @ SX0 @ SX1 @ SX2 )
| ( connected_a @ c @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[922]) ).
thf(1260,plain,
( ( ! [SX0: product_prod_nat_nat > a] :
( ~ ( finite_Graph_a @ SX0 )
| ( finite_finite_nat @ ( v_a @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[958]) ).
thf(1261,plain,
( ( ! [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat] :
( ~ ( connected_a @ SX0 @ SX1 @ SX2 )
| ( dist_a @ SX0 @ SX1 @ ( min_dist_a @ SX0 @ SX1 @ SX2 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[883]) ).
thf(1262,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ( ord_less_nat @ SX0 @ SX1 )
| ( SX0 = SX1 ) )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[807]) ).
thf(1263,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SX0 )
| ~ ( ord_le841296385at_nat @ SX1 @ SX0 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ SX1 ) @ ( finite447719721at_nat @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[948]) ).
thf(1264,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[804]) ).
thf(1265,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( member_nat @ SX0 @ ( v_b @ c2 ) )
| ~ ( isShortestPath_b @ c2 @ SX0 @ SX1 @ SX2 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SX1 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[916]) ).
thf(1266,plain,
( ( ! [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SX0 @ SX1 )
| ~ ( ord_le841296385at_nat @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1039]) ).
thf(1267,plain,
( ( ! [SX0: product_prod_nat_nat > a] :
( ~ ( finite772653738at_nat @ ( e_a @ SX0 ) )
| ( finite_finite_nat @ ( v_a @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[993]) ).
thf(1268,plain,
( ( ! [SX0: set_se1612935105at_nat] :
( ~ ~ ( finite1457549322at_nat @ SX0 )
| ( ( finite1701894793at_nat @ SX0 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[889]) ).
thf(1269,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat > $o] :
( ~ ( connected_b @ c2 @ SX0 @ SX1 )
| ~ ! [SX3: nat] :
( ~ ( dist_b @ c2 @ SX0 @ SX3 @ SX1 )
| ~ ! [SX4: nat] :
( ~ ( dist_b @ c2 @ SX0 @ SX4 @ SX1 )
| ( ord_less_eq_nat @ SX3 @ SX4 ) )
| ( SX2 @ SX3 ) )
| ( SX2 @ ( min_dist_b @ c2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[776]) ).
thf(1270,plain,
( ( ! [SX0: list_P559422087at_nat,SX1: list_P559422087at_nat] :
( ~ ( ( ( size_s1990949619at_nat @ SX0 )
!= ( size_s1990949619at_nat @ SX1 ) ) )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[767]) ).
thf(1271,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( isShortestPath_b @ c2 @ SX0 @ SX1 @ SX2 )
| ( isPath_b @ c2 @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[781]) ).
thf(1272,plain,
( ( ! [SX0: set_nat] :
( ~ ( finite_finite_nat @ ( v_a @ c ) )
| ( finite772653738at_nat @ ( incoming_a @ c @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1018]) ).
thf(1273,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( isShortestPath_a @ c @ SX0 @ SX1 @ SX2 )
| ( isPath_a @ c @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[780]) ).
thf(1274,plain,
( ( ! [SV1: product_prod_nat_nat > b] :
( ( edmond1022345717sure_b @ SV1 )
= ( edmond1022345717sure_b @ SV1 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[704]) ).
thf(1275,plain,
( ( edmond1022345717sure_b = edmond1022345717sure_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[704]) ).
thf(1276,plain,
( ( ! [SV2: product_prod_nat_nat > a] :
( ( edmond1022345716sure_a @ SV2 )
= ( edmond1022345716sure_a @ SV2 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[705]) ).
thf(1277,plain,
( ( edmond1022345716sure_a = edmond1022345716sure_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[705]) ).
thf(1278,plain,
( ( ! [SV3: product_prod_nat_nat > b] :
( ( edmond771116671s_uE_b @ SV3 )
= ( edmond771116671s_uE_b @ SV3 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[708]) ).
thf(1279,plain,
( ( edmond771116671s_uE_b = edmond771116671s_uE_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[708]) ).
thf(1280,plain,
( ( ! [SV4: product_prod_nat_nat > a] :
( ( edmond771116670s_uE_a @ SV4 )
= ( edmond771116670s_uE_a @ SV4 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[709]) ).
thf(1281,plain,
( ( edmond771116670s_uE_a = edmond771116670s_uE_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[709]) ).
thf(1282,plain,
( ( ! [SV5: product_prod_nat_nat > a] :
( ( edmond475474835dges_a @ SV5 )
= ( edmond475474835dges_a @ SV5 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[710]) ).
thf(1283,plain,
( ( edmond475474835dges_a = edmond475474835dges_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[710]) ).
thf(1284,plain,
( ( ! [SV6: product_prod_nat_nat > b] :
( ( edmond475474836dges_b @ SV6 )
= ( edmond475474836dges_b @ SV6 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[711]) ).
thf(1285,plain,
( ( edmond475474836dges_b = edmond475474836dges_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[711]) ).
thf(1286,plain,
( ( ! [SV7: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ SV7 )
= ( finite_Graph_a @ SV7 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[720]) ).
thf(1287,plain,
( ( edmond1517640972ysis_a = finite_Graph_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[720]) ).
thf(1288,plain,
( ( ! [SV8: product_prod_nat_nat > b] :
( ( edmond1517640973ysis_b @ SV8 )
= ( finite_Graph_b @ SV8 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[721]) ).
thf(1289,plain,
( ( edmond1517640973ysis_b = finite_Graph_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[721]) ).
thf(1290,plain,
! [SV9: nat] :
( ( ( min_dist_a @ c @ SV9 @ SV9 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(1291,plain,
! [SV10: nat] :
( ( ( min_dist_b @ c2 @ SV10 @ SV10 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(1292,plain,
! [SV11: nat] :
( ( connected_b @ c2 @ SV11 @ SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(1293,plain,
! [SV12: nat] :
( ( connected_a @ c @ SV12 @ SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(1294,plain,
! [SV13: nat] :
( ( ! [SY694: nat] :
( ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SY694 )
= ( SY694 = SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(1295,plain,
! [SV14: nat] :
( ( dist_b @ c2 @ SV14 @ zero_zero_nat @ SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(1296,plain,
! [SV15: set_Pr1986765409at_nat] :
( ( ! [SY695: set_Pr1986765409at_nat > $o] :
( ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SY695 ) )
= ( SY695 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(1297,plain,
! [SV16: set_nat] :
( ( ! [SY696: set_nat > $o] :
( ( member_set_nat @ SV16 @ ( collect_set_nat @ SY696 ) )
= ( SY696 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(1298,plain,
! [SV17: product_prod_nat_nat] :
( ( ! [SY697: product_prod_nat_nat > $o] :
( ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SY697 ) )
= ( SY697 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(1299,plain,
! [SV18: nat] :
( ( ! [SY698: nat > $o] :
( ( member_nat @ SV18 @ ( collect_nat @ SY698 ) )
= ( SY698 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(1300,plain,
! [SV19: set_se1612935105at_nat] :
( ( ( collec1606769740at_nat
@ ^ [SY699: set_Pr1986765409at_nat] : ( member298845450at_nat @ SY699 @ SV19 ) )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(1301,plain,
! [SV20: set_set_nat] :
( ( ( collect_set_nat
@ ^ [SY700: set_nat] : ( member_set_nat @ SY700 @ SV20 ) )
= SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(1302,plain,
! [SV21: set_Pr1986765409at_nat] :
( ( ( collec7649004at_nat
@ ^ [SY701: product_prod_nat_nat] : ( member701585322at_nat @ SY701 @ SV21 ) )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(1303,plain,
! [SV22: set_nat] :
( ( ( collect_nat
@ ^ [SY702: nat] : ( member_nat @ SY702 @ SV22 ) )
= SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(1304,plain,
! [SV23: nat] :
( ( ~ ( ord_less_nat @ SV23 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(1305,plain,
! [SV24: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV24 ) )
= ( SV24 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(1306,plain,
! [SV25: nat] :
( ( ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
= ( SV25 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1307,plain,
! [SV26: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(1308,plain,
! [SV27: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV27 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(1309,plain,
! [SV28: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV28 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(1310,plain,
! [SV29: nat] :
( ( ord_less_eq_nat @ SV29 @ SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1311,plain,
! [SV30: nat] :
( ( ! [SY703: nat] :
( ( ord_less_eq_nat @ SV30 @ SY703 )
| ( ord_less_eq_nat @ SY703 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1312,plain,
! [SV31: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1313,plain,
! [SV32: nat] :
( ( ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
= ( SV32 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1314,plain,
! [SV33: nat] :
( ( ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
= ( SV33 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1315,plain,
( ( ! [SV34: nat] :
( ( ord_less_eq_nat @ SV34 )
= ( ^ [SY704: nat] :
( ( ord_less_nat @ SV34 @ SY704 )
| ( SV34 = SY704 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[806]) ).
thf(1316,plain,
( ( ord_less_eq_nat
= ( ^ [M2: nat,N2: nat] :
( ( ord_less_nat @ M2 @ N2 )
| ( M2 = N2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[806]) ).
thf(1317,plain,
! [SV35: nat] :
( ( ( zero_zero_nat = SV35 )
= ( SV35 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1318,plain,
! [SV36: nat] :
( ( ~ ( ord_less_nat @ SV36 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1319,plain,
! [SV37: nat] :
( ( ~ ( ord_less_nat @ SV37 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1320,plain,
( ( ! [SV38: product_prod_nat_nat > b] :
( ( isPath_b @ SV38 )
= ( isPath_b @ SV38 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[831]) ).
thf(1321,plain,
( ( isPath_b = isPath_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[831]) ).
thf(1322,plain,
( ( ! [SV39: product_prod_nat_nat > a] :
( ( isPath_a @ SV39 )
= ( isPath_a @ SV39 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[832]) ).
thf(1323,plain,
( ( isPath_a = isPath_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[832]) ).
thf(1324,plain,
( ( ! [SV40: product_prod_nat_nat > a] :
( ( v_a @ SV40 )
= ( v_a @ SV40 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[833]) ).
thf(1325,plain,
( ( v_a = v_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[833]) ).
thf(1326,plain,
( ( ! [SV41: product_prod_nat_nat > b] :
( ( v_b @ SV41 )
= ( v_b @ SV41 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[834]) ).
thf(1327,plain,
( ( v_b = v_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[834]) ).
thf(1328,plain,
( ( ! [SV42: product_prod_nat_nat > a] :
( ( min_dist_a @ SV42 )
= ( min_dist_a @ SV42 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[835]) ).
thf(1329,plain,
( ( min_dist_a = min_dist_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[835]) ).
thf(1330,plain,
( ( ! [SV43: product_prod_nat_nat > b] :
( ( min_dist_b @ SV43 )
= ( min_dist_b @ SV43 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[836]) ).
thf(1331,plain,
( ( min_dist_b = min_dist_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[836]) ).
thf(1332,plain,
( ( ! [SV44: product_prod_nat_nat > b] :
( ( connected_b @ SV44 )
= ( connected_b @ SV44 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[837]) ).
thf(1333,plain,
( ( connected_b = connected_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[837]) ).
thf(1334,plain,
( ( ! [SV45: product_prod_nat_nat > a] :
( ( connected_a @ SV45 )
= ( connected_a @ SV45 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[838]) ).
thf(1335,plain,
( ( connected_a = connected_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[838]) ).
thf(1336,plain,
! [SV46: product_prod_nat_nat > b] :
( ( ! [SY705: nat] : ( connected_b @ SV46 @ SY705 @ SY705 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1337,plain,
! [SV47: product_prod_nat_nat > a] :
( ( ! [SY706: nat] : ( connected_a @ SV47 @ SY706 @ SY706 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1338,plain,
( ( ! [SV48: product_prod_nat_nat > b] :
( ( dist_b @ SV48 )
= ( dist_b @ SV48 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[841]) ).
thf(1339,plain,
( ( dist_b = dist_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[841]) ).
thf(1340,plain,
( ( ! [SV49: product_prod_nat_nat > a] :
( ( dist_a @ SV49 )
= ( dist_a @ SV49 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[842]) ).
thf(1341,plain,
( ( dist_a = dist_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[842]) ).
thf(1342,plain,
( ( ! [SV50: product_prod_nat_nat > a] :
( ( isShortestPath_a @ SV50 )
= ( isShortestPath_a @ SV50 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[843]) ).
thf(1343,plain,
( ( isShortestPath_a = isShortestPath_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[843]) ).
thf(1344,plain,
( ( ! [SV51: product_prod_nat_nat > b] :
( ( isShortestPath_b @ SV51 )
= ( isShortestPath_b @ SV51 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[844]) ).
thf(1345,plain,
( ( isShortestPath_b = isShortestPath_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[844]) ).
thf(1346,plain,
! [SV52: nat] :
( ( ~ ( ord_less_nat @ SV52 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1347,plain,
! [SV53: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 ) )
= ( SV53 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1348,plain,
! [SV54: nat] :
( ( ~ ( ord_less_nat @ SV54 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1349,plain,
! [SV55: nat] :
( ( ~ ( ord_less_nat @ SV55 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1350,plain,
! [SV56: nat] :
( ( ~ ( ord_less_nat @ SV56 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1351,plain,
! [SV57: product_prod_nat_nat > a] :
( ( ! [SY707: nat] :
( ( min_dist_a @ SV57 @ SY707 @ SY707 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1352,plain,
! [SV58: product_prod_nat_nat > b] :
( ( ! [SY708: nat] :
( ( min_dist_b @ SV58 @ SY708 @ SY708 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1353,plain,
! [SV59: product_prod_nat_nat > b] :
( ( ! [SY709: nat] : ( dist_b @ SV59 @ SY709 @ zero_zero_nat @ SY709 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1354,plain,
! [SV60: product_prod_nat_nat > a] :
( ( ! [SY710: nat] : ( dist_a @ SV60 @ SY710 @ zero_zero_nat @ SY710 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1355,plain,
! [SV61: product_prod_nat_nat > b] :
( ( ! [SY711: nat,SY712: nat] :
( ( dist_b @ SV61 @ SY711 @ zero_zero_nat @ SY712 )
= ( SY712 = SY711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1356,plain,
! [SV62: product_prod_nat_nat > a] :
( ( ! [SY713: nat,SY714: nat] :
( ( dist_a @ SV62 @ SY713 @ zero_zero_nat @ SY714 )
= ( SY714 = SY713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1357,plain,
! [SV63: nat] :
( ( ! [SY715: nat] :
( ( dist_a @ c @ SV63 @ zero_zero_nat @ SY715 )
= ( SY715 = SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1358,plain,
! [SV64: nat] :
( ( dist_a @ c @ SV64 @ zero_zero_nat @ SV64 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1359,plain,
! [SV65: nat] :
( ( ord_less_eq_set_nat @ ( adjacent_nodes_b @ c2 @ SV65 ) @ ( v_b @ c2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1360,plain,
! [SV66: nat] :
( ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ c @ SV66 ) @ ( v_a @ c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1361,plain,
( ( ! [SV67: product_prod_nat_nat > a] :
( ( isSimplePath_a @ SV67 )
= ( isSimplePath_a @ SV67 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[926]) ).
thf(1362,plain,
( ( isSimplePath_a = isSimplePath_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[926]) ).
thf(1363,plain,
( ( ! [SV68: product_prod_nat_nat > b] :
( ( isSimplePath_b @ SV68 )
= ( isSimplePath_b @ SV68 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[927]) ).
thf(1364,plain,
( ( isSimplePath_b = isSimplePath_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[927]) ).
thf(1365,plain,
( ( ! [SV69: product_prod_nat_nat > b] :
( ( finite_Graph_b @ SV69 )
= ( finite_finite_nat @ ( v_b @ SV69 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[953]) ).
thf(1366,plain,
( ( finite_Graph_b
= ( ^ [C2: product_prod_nat_nat > b] : ( finite_finite_nat @ ( v_b @ C2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[953]) ).
thf(1367,plain,
( ( ! [SV70: product_prod_nat_nat > a] :
( ( finite_Graph_a @ SV70 )
= ( finite_finite_nat @ ( v_a @ SV70 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[954]) ).
thf(1368,plain,
( ( finite_Graph_a
= ( ^ [C2: product_prod_nat_nat > a] : ( finite_finite_nat @ ( v_a @ C2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[954]) ).
thf(1369,plain,
! [SV71: nat] :
( ( finite_finite_nat @ ( adjacent_nodes_b @ c2 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1370,plain,
! [SV72: nat] :
( ( finite_finite_nat @ ( adjacent_nodes_a @ c @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1371,plain,
( ( ! [SV73: product_prod_nat_nat > a] :
( ( reachableNodes_a @ SV73 )
= ( reachableNodes_a @ SV73 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[985]) ).
thf(1372,plain,
( ( reachableNodes_a = reachableNodes_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[985]) ).
thf(1373,plain,
( ( ! [SV74: product_prod_nat_nat > b] :
( ( reachableNodes_b @ SV74 )
= ( reachableNodes_b @ SV74 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[986]) ).
thf(1374,plain,
( ( reachableNodes_b = reachableNodes_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[986]) ).
thf(1375,plain,
( ( ! [SV75: product_prod_nat_nat > b] :
( ( adjacent_nodes_b @ SV75 )
= ( adjacent_nodes_b @ SV75 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[987]) ).
thf(1376,plain,
( ( adjacent_nodes_b = adjacent_nodes_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[987]) ).
thf(1377,plain,
( ( ! [SV76: product_prod_nat_nat > a] :
( ( adjacent_nodes_a @ SV76 )
= ( adjacent_nodes_a @ SV76 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[988]) ).
thf(1378,plain,
( ( adjacent_nodes_a = adjacent_nodes_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[988]) ).
thf(1379,plain,
( ( ! [SV77: product_prod_nat_nat > a] :
( ( e_a @ SV77 )
= ( e_a @ SV77 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[989]) ).
thf(1380,plain,
( ( e_a = e_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[989]) ).
thf(1381,plain,
( ( ! [SV78: product_prod_nat_nat > b] :
( ( e_b @ SV78 )
= ( e_b @ SV78 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[990]) ).
thf(1382,plain,
( ( e_b = e_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[990]) ).
thf(1383,plain,
! [SV79: product_prod_nat_nat > b] :
( ( ! [SY716: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_b @ SV79 @ SY716 ) @ ( v_b @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1384,plain,
! [SV80: product_prod_nat_nat > a] :
( ( ! [SY717: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ SV80 @ SY717 ) @ ( v_a @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1385,plain,
! [SV81: set_nat] :
( ( ord_le841296385at_nat @ ( incoming_a @ c @ SV81 ) @ ( e_a @ c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1386,plain,
! [SV82: set_nat] :
( ( ord_le841296385at_nat @ ( outgoing_a @ c @ SV82 ) @ ( e_a @ c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1387,plain,
( ( ! [SV83: product_prod_nat_nat > a] :
( ( incoming_a @ SV83 )
= ( incoming_a @ SV83 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1019]) ).
thf(1388,plain,
( ( incoming_a = incoming_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1019]) ).
thf(1389,plain,
( ( ! [SV84: product_prod_nat_nat > b] :
( ( incoming_b @ SV84 )
= ( incoming_b @ SV84 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1020]) ).
thf(1390,plain,
( ( incoming_b = incoming_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1020]) ).
thf(1391,plain,
( ( ! [SV85: product_prod_nat_nat > a] :
( ( outgoing_a @ SV85 )
= ( outgoing_a @ SV85 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1021]) ).
thf(1392,plain,
( ( outgoing_a = outgoing_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1021]) ).
thf(1393,plain,
( ( ! [SV86: product_prod_nat_nat > b] :
( ( outgoing_b @ SV86 )
= ( outgoing_b @ SV86 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1022]) ).
thf(1394,plain,
( ( outgoing_b = outgoing_b )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1022]) ).
thf(1395,plain,
! [SV87: product_prod_nat_nat > a] :
( ( ! [SY718: set_nat] : ( ord_le841296385at_nat @ ( outgoing_a @ SV87 @ SY718 ) @ ( e_a @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1396,plain,
! [SV88: product_prod_nat_nat > b] :
( ( ! [SY719: set_nat] : ( ord_le841296385at_nat @ ( outgoing_b @ SV88 @ SY719 ) @ ( e_b @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1397,plain,
! [SV89: product_prod_nat_nat > a] :
( ( ! [SY720: set_nat] : ( ord_le841296385at_nat @ ( incoming_a @ SV89 @ SY720 ) @ ( e_a @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1398,plain,
! [SV90: product_prod_nat_nat > b] :
( ( ! [SY721: set_nat] : ( ord_le841296385at_nat @ ( incoming_b @ SV90 @ SY721 ) @ ( e_b @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1399,plain,
! [SV91: set_nat] :
( ( ord_le841296385at_nat @ ( incoming_b @ c2 @ SV91 ) @ ( e_b @ c2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1400,plain,
! [SV92: set_nat] :
( ( ord_le841296385at_nat @ ( outgoing_b @ c2 @ SV92 ) @ ( e_b @ c2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1401,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1402,plain,
! [SV93: nat] :
( ( ( SV93 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1403,plain,
! [SV94: product_prod_nat_nat > b] :
( ( ~ ( finite_Graph_b @ SV94 )
| ( finite_finite_nat @ ( v_b @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1404,plain,
! [SV95: nat] :
( ( ! [SY722: list_P559422087at_nat,SY723: nat] :
( ~ ( member_nat @ SV95 @ ( v_a @ c ) )
| ~ ( isSimplePath_a @ c @ SV95 @ SY722 @ SY723 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY722 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1405,plain,
( ( ! [SV96: product_prod_nat_nat > a] :
( ( isShortestPath_a @ SV96 )
= ( ^ [SY724: nat,SY725: list_P559422087at_nat,SY726: nat] :
~ ( ~ ( isSimplePath_a @ SV96 @ SY724 @ SY725 @ SY726 )
| ( ( size_s1990949619at_nat @ SY725 )
!= ( min_dist_a @ SV96 @ SY724 @ SY726 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1053]) ).
thf(1406,plain,
( ( isShortestPath_a
= ( ^ [SX0: product_prod_nat_nat > a,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isSimplePath_a @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ( size_s1990949619at_nat @ SX2 )
!= ( min_dist_a @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1053]) ).
thf(1407,plain,
! [SV97: nat] :
( ( ! [SY727: list_P559422087at_nat,SY728: nat] :
( ( isShortestPath_b @ c2 @ SV97 @ SY727 @ SY728 )
= ( ~ ( ~ ( isPath_b @ c2 @ SV97 @ SY727 @ SY728 )
| ( ( size_s1990949619at_nat @ SY727 )
!= ( min_dist_b @ c2 @ SV97 @ SY728 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1408,plain,
! [SV98: product_prod_nat_nat > a] :
( ( ~ ( finite_Graph_a @ SV98 )
| ( finite772653738at_nat @ ( e_a @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1409,plain,
! [SV99: set_nat] :
( ( ~ ( finite_finite_nat @ ( v_a @ c ) )
| ( finite772653738at_nat @ ( outgoing_a @ c @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1410,plain,
! [SV100: nat] :
( ( ! [SY729: product_prod_nat_nat > b] :
( ~ ( member_nat @ SV100 @ ( v_b @ SY729 ) )
| ( ord_less_eq_set_nat @ ( reachableNodes_b @ SY729 @ SV100 ) @ ( v_b @ SY729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1411,plain,
! [SV101: nat] :
( ( ( SV101 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1412,plain,
! [SV102: set_nat] :
( ( ! [SY730: set_nat] :
( ~ ! [SY731: nat] :
( ~ ( member_nat @ SY731 @ SV102 )
| ( member_nat @ SY731 @ SY730 ) )
| ( ord_less_eq_set_nat @ SV102 @ SY730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1413,plain,
! [SV103: product_prod_nat_nat > a] :
( ( ! [SY732: nat,SY733: list_P559422087at_nat,SY734: nat] :
( ~ ( finite_Graph_a @ SV103 )
| ~ ( member_nat @ SY732 @ ( v_a @ SV103 ) )
| ~ ( isShortestPath_a @ SV103 @ SY732 @ SY733 @ SY734 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY733 ) @ ( finite_card_nat @ ( v_a @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1414,plain,
! [SV104: product_prod_nat_nat > a] :
( ( ! [SY735: nat] :
( ~ ( finite_Graph_a @ SV104 )
| ( finite_finite_nat @ ( adjacent_nodes_a @ SV104 @ SY735 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1415,plain,
( ( ! [SV105: set_nat] :
( ( ^ [SY736: set_nat] : ( SV105 = SY736 ) )
= ( ^ [SY737: set_nat] :
~ ( ~ ( ord_less_eq_set_nat @ SV105 @ SY737 )
| ~ ( ord_less_eq_set_nat @ SY737 @ SV105 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1062]) ).
thf(1416,plain,
( ( ( ^ [SX0: set_nat,SX1: set_nat] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_nat,SX1: set_nat] :
~ ( ~ ( ord_less_eq_set_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_nat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1062]) ).
thf(1417,plain,
! [SV106: product_prod_nat_nat > b] :
( ( ! [SY738: nat,SY739: list_P559422087at_nat,SY740: nat] :
( ~ ( finite_Graph_b @ SV106 )
| ~ ( member_nat @ SY738 @ ( v_b @ SV106 ) )
| ~ ( isShortestPath_b @ SV106 @ SY738 @ SY739 @ SY740 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY739 ) @ ( finite_card_nat @ ( v_b @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1418,plain,
! [SV107: product_prod_nat_nat > a] :
( ( ! [SY741: nat,SY742: list_P559422087at_nat,SY743: nat] :
( ~ ( isShortestPath_a @ SV107 @ SY741 @ SY742 @ SY743 )
| ( isPath_a @ SV107 @ SY741 @ SY742 @ SY743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1419,plain,
! [SV108: nat] :
( ( ! [SY744: nat] :
( ~ ( ord_less_nat @ SV108 @ SY744 )
| ( SV108 != SY744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1420,plain,
! [SV109: nat] :
( ( ! [SY745: nat] :
( ( SV109 != SY745 )
| ( ord_less_eq_nat @ SV109 @ SY745 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1421,plain,
! [SV110: nat > $o] :
( ( ! [SY746: nat > $o] :
( ~ ! [SY747: nat] :
( ( SV110 @ SY747 )
= ( SY746 @ SY747 ) )
| ( ( collect_nat @ SV110 )
= ( collect_nat @ SY746 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1422,plain,
! [SV111: product_prod_nat_nat > a] :
( ( ! [SY748: nat,SY749: nat] :
( ~ ( connected_a @ SV111 @ SY748 @ SY749 )
| ( ( member_nat @ SY749 @ ( v_a @ SV111 ) )
= ( member_nat @ SY748 @ ( v_a @ SV111 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1423,plain,
! [SV112: nat] :
( ( ! [SY750: nat,SY751: nat] :
( ~ ( dist_a @ c @ SV112 @ SY750 @ SY751 )
| ~ ! [SY752: nat] :
( ~ ( dist_a @ c @ SV112 @ SY752 @ SY751 )
| ( ord_less_eq_nat @ SY750 @ SY752 ) )
| ( ( min_dist_a @ c @ SV112 @ SY751 )
= SY750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1424,plain,
( ( ! [SV113: product_prod_nat_nat > b] :
( ( dist_b @ SV113 )
= ( ^ [SY753: nat,SY754: nat,SY755: nat] :
~ ! [SY756: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV113 @ SY753 @ SY756 @ SY755 )
| ( ( size_s1990949619at_nat @ SY756 )
!= SY754 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1070]) ).
thf(1425,plain,
( ( dist_b
= ( ^ [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat,SX3: nat] :
~ ! [SX4: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SX0 @ SX1 @ SX4 @ SX3 )
| ( ( size_s1990949619at_nat @ SX4 )
!= SX2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1070]) ).
thf(1426,plain,
( ( ! [SV114: product_prod_nat_nat > a] :
( ( isShortestPath_a @ SV114 )
= ( ^ [SY757: nat,SY758: list_P559422087at_nat,SY759: nat] :
~ ( ~ ( isPath_a @ SV114 @ SY757 @ SY758 @ SY759 )
| ~ ! [SY760: list_P559422087at_nat] :
( ~ ( isPath_a @ SV114 @ SY757 @ SY760 @ SY759 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY758 ) @ ( size_s1990949619at_nat @ SY760 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1071]) ).
thf(1427,plain,
( ( isShortestPath_a
= ( ^ [SX0: product_prod_nat_nat > a,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isPath_a @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ! [SX4: list_P559422087at_nat] :
( ~ ( isPath_a @ SX0 @ SX1 @ SX4 @ SX3 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SX2 ) @ ( size_s1990949619at_nat @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1071]) ).
thf(1428,plain,
! [SV115: product_prod_nat_nat > b] :
( ( ~ ( edmond1517640973ysis_b @ SV115 )
| ( finite772653738at_nat @ ( edmond771116671s_uE_b @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1429,plain,
! [SV116: product_prod_nat_nat > a] :
( ( ! [SY761: nat,SY762: nat,SY763: nat] :
( ~ ( dist_a @ SV116 @ SY761 @ SY762 @ SY763 )
| ~ ! [SY764: nat] :
( ~ ( dist_a @ SV116 @ SY761 @ SY764 @ SY763 )
| ( ord_less_eq_nat @ SY762 @ SY764 ) )
| ( ( min_dist_a @ SV116 @ SY761 @ SY763 )
= SY762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1430,plain,
! [SV117: nat] :
( ( ! [SY765: nat] :
( ~ ( connected_b @ c2 @ SV117 @ SY765 )
| ( ( ( min_dist_b @ c2 @ SV117 @ SY765 )
= zero_zero_nat )
= ( SY765 = SV117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1431,plain,
! [SV118: nat] :
( ( ! [SY766: nat,SY767: nat] :
( ( dist_a @ c @ SV118 @ SY766 @ SY767 )
= ( ~ ! [SY768: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY768 @ SY767 )
| ( ( size_s1990949619at_nat @ SY768 )
!= SY766 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1432,plain,
! [SV119: set_Pr1986765409at_nat] :
( ( ! [SY769: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SV119 )
| ~ ( ord_le116442893at_nat @ SY769 @ SV119 )
| ( ord_less_nat @ ( finite447719721at_nat @ SY769 ) @ ( finite447719721at_nat @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1433,plain,
! [SV120: product_prod_nat_nat > a] :
( ( ! [SY770: nat,SY771: nat,SY772: nat,SY773: nat] :
( ~ ( connected_a @ SV120 @ SY770 @ SY771 )
| ( ( min_dist_a @ SV120 @ SY770 @ SY771 )
!= SY772 )
| ~ ( ord_less_nat @ SY773 @ SY772 )
| ~ ! [SY774: nat] :
~ ~ ( ~ ( connected_a @ SV120 @ SY770 @ SY774 )
| ( ( min_dist_a @ SV120 @ SY770 @ SY774 )
!= SY773 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1434,plain,
( ( ! [SV121: product_prod_nat_nat > a] :
( ( connected_a @ SV121 )
= ( ^ [SY775: nat,SY776: nat] :
~ ! [SY777: nat] :
~ ( dist_a @ SV121 @ SY775 @ SY777 @ SY776 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1078]) ).
thf(1435,plain,
( ( connected_a
= ( ^ [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat] :
~ ! [SX3: nat] :
~ ( dist_a @ SX0 @ SX1 @ SX3 @ SX2 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1078]) ).
thf(1436,plain,
! [SV122: set_nat] :
( ( ~ ( finite_finite_nat @ ( v_b @ c2 ) )
| ( finite772653738at_nat @ ( outgoing_b @ c2 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1437,plain,
! [SV123: product_prod_nat_nat > a] :
( ( ~ ( edmond1517640972ysis_a @ SV123 )
| ( ord_le841296385at_nat @ ( e_a @ SV123 ) @ ( edmond771116670s_uE_a @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1438,plain,
! [SV124: product_prod_nat_nat > a] :
( ( ! [SY778: nat,SY779: nat] :
( ~ ( connected_a @ SV124 @ SY778 @ SY779 )
| ~ ! [SY780: list_P559422087at_nat] :
~ ( isShortestPath_a @ SV124 @ SY778 @ SY780 @ SY779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1439,plain,
! [SV125: product_prod_nat_nat > b] :
( ( ~ ( finite_finite_nat @ ( v_b @ SV125 ) )
| ( finite772653738at_nat @ ( e_b @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1440,plain,
! [SV126: set_nat] :
( ( ! [SY781: set_nat] :
( ~ ( finite_finite_nat @ SV126 )
| ~ ( ord_less_eq_set_nat @ SY781 @ SV126 )
| ( ord_less_eq_nat @ ( finite_card_nat @ SY781 ) @ ( finite_card_nat @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1441,plain,
! [SV127: product_prod_nat_nat > b] :
( ( ! [SY782: nat,SY783: nat] :
( ~ ( connected_b @ SV127 @ SY782 @ SY783 )
| ( dist_b @ SV127 @ SY782 @ ( min_dist_b @ SV127 @ SY782 @ SY783 ) @ SY783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1442,plain,
! [SV128: nat] :
( ( ! [SY784: nat,SY785: nat,SY786: nat] :
( ~ ( connected_b @ c2 @ SV128 @ SY784 )
| ( ( min_dist_b @ c2 @ SV128 @ SY784 )
!= SY785 )
| ~ ( ord_less_nat @ SY786 @ SY785 )
| ~ ! [SY787: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV128 @ SY787 )
| ( ( min_dist_b @ c2 @ SV128 @ SY787 )
!= SY786 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1443,plain,
! [SV129: product_prod_nat_nat > a] :
( ( ! [SY788: nat,SY789: nat,SY790: nat > $o] :
( ~ ( connected_a @ SV129 @ SY788 @ SY789 )
| ~ ! [SY791: nat] :
( ~ ( dist_a @ SV129 @ SY788 @ SY791 @ SY789 )
| ~ ! [SY792: nat] :
( ~ ( dist_a @ SV129 @ SY788 @ SY792 @ SY789 )
| ( ord_less_eq_nat @ SY791 @ SY792 ) )
| ( SY790 @ SY791 ) )
| ( SY790 @ ( min_dist_a @ SV129 @ SY788 @ SY789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1444,plain,
! [SV130: nat] :
( ( ~ ! [SY793: list_P559422087at_nat] :
( ( size_s1990949619at_nat @ SY793 )
!= SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1445,plain,
! [SV131: set_set_nat] :
( ( ! [SY794: set_set_nat] :
( ~ ( ord_le1613022364et_nat @ SV131 @ SY794 )
| ~ ( finite2012248349et_nat @ SY794 )
| ( finite2012248349et_nat @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1446,plain,
! [SV132: nat] :
( ( ! [SY795: nat] :
( ~ ( connected_b @ c2 @ SV132 @ SY795 )
| ( dist_b @ c2 @ SV132 @ ( min_dist_b @ c2 @ SV132 @ SY795 ) @ SY795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1447,plain,
( ( ( ~ ~ ( connected_b @ c2 @ s @ t ) )
= $true )
| ( ( ord_less_nat @ ( edmond1022345717sure_b @ c2 @ s @ t ) @ ( edmond1022345716sure_a @ c @ s @ t ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1448,plain,
! [SV133: set_nat] :
( ( ! [SY796: set_nat] :
( ~ ( finite_finite_nat @ SV133 )
| ~ ( ord_less_eq_set_nat @ SY796 @ SV133 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV133 ) @ ( finite_card_nat @ SY796 ) )
| ( SY796 = SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1449,plain,
! [SV134: product_prod_nat_nat > b] :
( ( ! [SY797: nat,SY798: nat,SY799: nat] :
( ~ ( connected_b @ SV134 @ SY797 @ SY798 )
| ~ ( ord_less_eq_nat @ SY799 @ ( min_dist_b @ SV134 @ SY797 @ SY798 ) )
| ~ ! [SY800: nat] :
~ ~ ( ~ ( connected_b @ SV134 @ SY797 @ SY800 )
| ( ( min_dist_b @ SV134 @ SY797 @ SY800 )
!= SY799 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1450,plain,
! [SV135: nat] :
( ( ! [SY801: nat] :
( ~ ( connected_b @ c2 @ SV135 @ SY801 )
| ~ ! [SY802: list_P559422087at_nat] :
~ ( isShortestPath_b @ c2 @ SV135 @ SY802 @ SY801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1451,plain,
! [SV136: nat] :
( ( ! [SY803: nat] :
( ( connected_a @ c @ SV136 @ SY803 )
= ( ~ ! [SY804: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY804 @ SY803 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1452,plain,
! [SV137: set_nat] :
( ( ! [SY805: nat] :
( ~ ( finite_finite_nat @ SV137 )
| ~ ( member_nat @ SY805 @ SV137 )
| ~ ! [SY806: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY806 @ SV137 )
| ~ ( ord_less_eq_nat @ SY806 @ SY805 ) )
| ~ ! [SY807: nat] :
( ~ ( member_nat @ SY807 @ SV137 )
| ~ ( ord_less_eq_nat @ SY807 @ SY806 )
| ( SY806 = SY807 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1453,plain,
! [SV138: product_prod_nat_nat > a] :
( ( ! [SY808: nat,SY809: list_P559422087at_nat,SY810: nat] :
( ~ ( finite_Graph_a @ SV138 )
| ~ ( member_nat @ SY808 @ ( v_a @ SV138 ) )
| ~ ( isSimplePath_a @ SV138 @ SY808 @ SY809 @ SY810 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY809 ) @ ( finite_card_nat @ ( v_a @ SV138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1454,plain,
! [SV139: product_prod_nat_nat > b] :
( ( ! [SY811: nat,SY812: list_P559422087at_nat,SY813: nat] :
( ~ ( isPath_b @ SV139 @ SY811 @ SY812 @ SY813 )
| ~ ! [SY814: list_P559422087at_nat] :
~ ( isSimplePath_b @ SV139 @ SY811 @ SY814 @ SY813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1455,plain,
! [SV140: nat] :
( ( ~ ( member_nat @ SV140 @ ( v_a @ c ) )
| ( ord_less_eq_set_nat @ ( reachableNodes_a @ c @ SV140 ) @ ( v_a @ c ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1456,plain,
! [SV141: product_prod_nat_nat > a] :
( ( ! [SY815: set_nat] :
( ~ ( finite_finite_nat @ ( v_a @ SV141 ) )
| ( finite772653738at_nat @ ( incoming_a @ SV141 @ SY815 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1457,plain,
! [SV142: nat] :
( ( ! [SY816: nat,SY817: nat] :
( ~ ( connected_b @ c2 @ SV142 @ SY816 )
| ~ ( ord_less_eq_nat @ SY817 @ ( min_dist_b @ c2 @ SV142 @ SY816 ) )
| ~ ! [SY818: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV142 @ SY818 )
| ( ( min_dist_b @ c2 @ SV142 @ SY818 )
!= SY817 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1458,plain,
! [SV143: set_Pr1986765409at_nat] :
( ( ! [SY819: nat] :
( ~ ~ ( finite772653738at_nat @ SV143 )
| ~ ! [SY820: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( finite772653738at_nat @ SY820 )
| ( ( finite447719721at_nat @ SY820 )
!= SY819 ) )
| ~ ( ord_le841296385at_nat @ SY820 @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1459,plain,
! [SV144: set_nat] :
( ( ! [SY821: set_nat] :
( ~ ( ord_less_eq_set_nat @ SV144 @ SY821 )
| ~ ( ord_less_eq_set_nat @ SY821 @ SV144 )
| ( SV144 = SY821 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1460,plain,
! [SV145: product_prod_nat_nat > a] :
( ( ! [SY822: nat,SY823: list_P559422087at_nat,SY824: nat] :
( ~ ( isPath_a @ SV145 @ SY822 @ SY823 @ SY824 )
| ( dist_a @ SV145 @ SY822 @ ( size_s1990949619at_nat @ SY823 ) @ SY824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1461,plain,
! [SV146: nat] :
( ( ! [SY825: nat] :
( ( connected_a @ c @ SV146 @ SY825 )
= ( ~ ! [SY826: nat] :
~ ( dist_a @ c @ SV146 @ SY826 @ SY825 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1462,plain,
! [SV147: product_prod_nat_nat > b] :
( ( ! [SY827: nat,SY828: nat,SY829: nat] :
( ~ ( dist_b @ SV147 @ SY827 @ SY828 @ SY829 )
| ~ ! [SY830: nat] :
( ~ ( dist_b @ SV147 @ SY827 @ SY830 @ SY829 )
| ( ord_less_eq_nat @ SY828 @ SY830 ) )
| ( ( min_dist_b @ SV147 @ SY827 @ SY829 )
= SY828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1463,plain,
! [SV148: product_prod_nat_nat > a] :
( ( ! [SY831: nat,SY832: nat] :
( ~ ( edmond1517640972ysis_a @ SV148 )
| ( ord_le841296385at_nat @ ( edmond475474835dges_a @ SV148 @ SY831 @ SY832 ) @ ( e_a @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1464,plain,
! [SV149: product_prod_nat_nat > a] :
( ( ! [SY833: nat,SY834: nat,SY835: nat] :
( ~ ( dist_a @ SV149 @ SY833 @ SY834 @ SY835 )
| ( ord_less_eq_nat @ ( min_dist_a @ SV149 @ SY833 @ SY835 ) @ SY834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1465,plain,
! [SV150: product_prod_nat_nat > b] :
( ( ~ ( finite_Graph_b @ SV150 )
| ( finite772653738at_nat @ ( e_b @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1466,plain,
! [SV151: product_prod_nat_nat > a] :
( ( ! [SY836: nat,SY837: nat,SY838: nat] :
( ~ ( connected_a @ SV151 @ SY836 @ SY837 )
| ~ ( ord_less_eq_nat @ SY838 @ ( min_dist_a @ SV151 @ SY836 @ SY837 ) )
| ~ ! [SY839: nat] :
~ ~ ( ~ ( connected_a @ SV151 @ SY836 @ SY839 )
| ( ( min_dist_a @ SV151 @ SY836 @ SY839 )
!= SY838 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1467,plain,
! [SV152: product_prod_nat_nat > a] :
( ( ~ ( edmond1517640972ysis_a @ SV152 )
| ( finite772653738at_nat @ ( edmond771116670s_uE_a @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1468,plain,
! [SV153: product_prod_nat_nat > b] :
( ( ! [SY840: nat,SY841: list_P559422087at_nat,SY842: nat] :
( ~ ( isShortestPath_b @ SV153 @ SY840 @ SY841 @ SY842 )
| ( isPath_b @ SV153 @ SY840 @ SY841 @ SY842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1469,plain,
! [SV154: nat] :
( ( ! [SY843: nat] :
( ~ ( ord_less_eq_nat @ SV154 @ SY843 )
| ~ ( ( SV154 != SY843 ) )
| ( ord_less_nat @ SV154 @ SY843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1470,plain,
! [SV155: product_prod_nat_nat > b] :
( ( ! [SY844: set_nat] :
( ~ ( finite_finite_nat @ ( v_b @ SV155 ) )
| ( finite772653738at_nat @ ( outgoing_b @ SV155 @ SY844 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1471,plain,
! [SV156: product_prod_nat_nat > a] :
( ( ~ ( finite_finite_nat @ ( v_a @ SV156 ) )
| ( finite772653738at_nat @ ( e_a @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1472,plain,
! [SV157: set_Pr1986765409at_nat] :
( ( ! [SY845: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SV157 @ SY845 )
| ~ ( ( SV157 != SY845 ) )
| ( ord_le116442893at_nat @ SV157 @ SY845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1473,plain,
! [SV158: nat] :
( ( ! [SY846: list_P559422087at_nat,SY847: nat] :
( ( isShortestPath_b @ c2 @ SV158 @ SY846 @ SY847 )
= ( ~ ( ~ ( isPath_b @ c2 @ SV158 @ SY846 @ SY847 )
| ~ ! [SY848: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY848 @ SY847 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY846 ) @ ( size_s1990949619at_nat @ SY848 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1474,plain,
! [SV159: nat > $o] :
( ( ! [SY849: nat,SY850: nat] :
( ~ ( SV159 @ SY849 )
| ~ ! [SY851: nat] :
( ~ ( SV159 @ SY851 )
| ( ord_less_eq_nat @ SY851 @ SY850 ) )
| ~ ! [SY852: nat] :
~ ~ ( ~ ( SV159 @ SY852 )
| ~ ! [SY853: nat] :
( ~ ( SV159 @ SY853 )
| ( ord_less_eq_nat @ SY853 @ SY852 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1475,plain,
! [SV160: nat] :
( ( ! [SY854: nat] :
( ~ ( member_nat @ SV160 @ ( v_a @ c ) )
| ~ ( connected_a @ c @ SV160 @ SY854 )
| ( ord_less_nat @ ( min_dist_a @ c @ SV160 @ SY854 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1476,plain,
! [SV161: product_prod_nat_nat > b] :
( ( ! [SY855: nat,SY856: nat] :
( ~ ( edmond1517640973ysis_b @ SV161 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474836dges_b @ SV161 @ SY855 @ SY856 ) ) @ ( finite447719721at_nat @ ( edmond771116671s_uE_b @ SV161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1477,plain,
! [SV162: nat] :
( ( ! [SY857: nat,SY858: nat] :
( ~ ( dist_a @ c @ SV162 @ SY857 @ SY858 )
| ( ord_less_eq_nat @ ( min_dist_a @ c @ SV162 @ SY858 ) @ SY857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1478,plain,
! [SV163: nat] :
( ( ! [SY859: nat,SY860: nat] :
( ( dist_b @ c2 @ SV163 @ SY859 @ SY860 )
= ( ~ ! [SY861: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY861 @ SY860 )
| ( ( size_s1990949619at_nat @ SY861 )
!= SY859 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1479,plain,
! [SV164: set_set_nat] :
( ( ! [SY862: set_nat] :
( ~ ( finite2012248349et_nat @ SV164 )
| ~ ( member_set_nat @ SY862 @ SV164 )
| ~ ! [SY863: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SY863 @ SV164 )
| ~ ( ord_less_eq_set_nat @ SY862 @ SY863 ) )
| ~ ! [SY864: set_nat] :
( ~ ( member_set_nat @ SY864 @ SV164 )
| ~ ( ord_less_eq_set_nat @ SY863 @ SY864 )
| ( SY863 = SY864 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1480,plain,
( ( ! [SV165: product_prod_nat_nat > b] :
( ( isShortestPath_b @ SV165 )
= ( ^ [SY865: nat,SY866: list_P559422087at_nat,SY867: nat] :
~ ( ~ ( isPath_b @ SV165 @ SY865 @ SY866 @ SY867 )
| ~ ! [SY868: list_P559422087at_nat] :
( ~ ( isPath_b @ SV165 @ SY865 @ SY868 @ SY867 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY866 ) @ ( size_s1990949619at_nat @ SY868 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1123]) ).
thf(1481,plain,
( ( isShortestPath_b
= ( ^ [SX0: product_prod_nat_nat > b,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isPath_b @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ! [SX4: list_P559422087at_nat] :
( ~ ( isPath_b @ SX0 @ SX1 @ SX4 @ SX3 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SX2 ) @ ( size_s1990949619at_nat @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1123]) ).
thf(1482,plain,
! [SV166: product_prod_nat_nat > a] :
( ( ! [SY869: nat,SY870: nat] :
( ~ ( edmond1517640972ysis_a @ SV166 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ SV166 @ SY869 @ SY870 ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ SV166 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1483,plain,
! [SV167: nat > nat] :
( ( ! [SY871: nat,SY872: nat] :
( ~ ! [SY873: nat,SY874: nat] :
( ~ ( ord_less_nat @ SY873 @ SY874 )
| ( ord_less_nat @ ( SV167 @ SY873 ) @ ( SV167 @ SY874 ) ) )
| ~ ( ord_less_eq_nat @ SY871 @ SY872 )
| ( ord_less_eq_nat @ ( SV167 @ SY871 ) @ ( SV167 @ SY872 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1484,plain,
( ( ! [SV168: product_prod_nat_nat > a] :
( ( isShortestPath_a @ SV168 )
= ( ^ [SY875: nat,SY876: list_P559422087at_nat,SY877: nat] :
~ ( ~ ( isPath_a @ SV168 @ SY875 @ SY876 @ SY877 )
| ( ( size_s1990949619at_nat @ SY876 )
!= ( min_dist_a @ SV168 @ SY875 @ SY877 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1126]) ).
thf(1485,plain,
( ( isShortestPath_a
= ( ^ [SX0: product_prod_nat_nat > a,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isPath_a @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ( size_s1990949619at_nat @ SX2 )
!= ( min_dist_a @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1126]) ).
thf(1486,plain,
! [SV169: set_nat] :
( ( ~ ( finite_finite_nat @ ( v_b @ c2 ) )
| ( finite772653738at_nat @ ( incoming_b @ c2 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1487,plain,
! [SV170: product_prod_nat_nat > a] :
( ( ~ ( finite_finite_nat @ ( v_a @ SV170 ) )
| ( finite_Graph_a @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1488,plain,
! [SV171: nat > $o] :
( ( ! [SY878: nat] :
( ~ ! [SY879: nat] :
( ~ ~ ( SV171 @ SY879 )
| ~ ! [SY880: nat] :
~ ~ ( ~ ( ord_less_nat @ SY880 @ SY879 )
| ~ ~ ( SV171 @ SY880 ) ) )
| ( SV171 @ SY878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1489,plain,
! [SV172: nat] :
( ( ~ ( ( SV172 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1490,plain,
! [SV173: set_se1612935105at_nat] :
( ( ! [SY881: set_Pr1986765409at_nat] :
( ~ ( finite1457549322at_nat @ SV173 )
| ~ ( member298845450at_nat @ SY881 @ SV173 )
| ~ ! [SY882: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SY882 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY882 @ SY881 ) )
| ~ ! [SY883: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY883 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY883 @ SY882 )
| ( SY882 = SY883 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1491,plain,
! [SV174: list_P559422087at_nat > $o] :
( ( ! [SY884: list_P559422087at_nat] :
( ~ ! [SY885: list_P559422087at_nat] :
( ~ ! [SY886: list_P559422087at_nat] :
( ~ ( ord_less_nat @ ( size_s1990949619at_nat @ SY886 ) @ ( size_s1990949619at_nat @ SY885 ) )
| ( SV174 @ SY886 ) )
| ( SV174 @ SY885 ) )
| ( SV174 @ SY884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1492,plain,
! [SV175: set_nat] :
( ( ! [SY887: set_nat,SY888: set_nat] :
( ~ ( ord_less_eq_set_nat @ SV175 @ SY887 )
| ~ ( ord_less_eq_set_nat @ SY887 @ SY888 )
| ( ord_less_eq_set_nat @ SV175 @ SY888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1493,plain,
! [SV176: product_prod_nat_nat > b] :
( ( ! [SY889: nat,SY890: nat,SY891: nat > $o] :
( ~ ( connected_b @ SV176 @ SY889 @ SY890 )
| ~ ! [SY892: nat] :
( ~ ( dist_b @ SV176 @ SY889 @ SY892 @ SY890 )
| ~ ! [SY893: nat] :
( ~ ( dist_b @ SV176 @ SY889 @ SY893 @ SY890 )
| ( ord_less_eq_nat @ SY892 @ SY893 ) )
| ( SY891 @ SY892 ) )
| ( SY891 @ ( min_dist_b @ SV176 @ SY889 @ SY890 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1494,plain,
! [SV177: set_se1612935105at_nat] :
( ( ! [SY894: set_Pr1986765409at_nat] :
( ~ ( finite1457549322at_nat @ SV177 )
| ~ ( member298845450at_nat @ SY894 @ SV177 )
| ~ ! [SY895: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SY895 @ SV177 )
| ~ ( ord_le841296385at_nat @ SY894 @ SY895 ) )
| ~ ! [SY896: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY896 @ SV177 )
| ~ ( ord_le841296385at_nat @ SY895 @ SY896 )
| ( SY895 = SY896 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1495,plain,
! [SV178: nat] :
( ( ! [SY897: nat] :
( ~ ( connected_b @ c2 @ SV178 @ SY897 )
| ( ( member_nat @ SY897 @ ( v_b @ c2 ) )
= ( member_nat @ SV178 @ ( v_b @ c2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1496,plain,
! [SV179: product_prod_nat_nat > a] :
( ( ~ ( finite772653738at_nat @ ( e_a @ SV179 ) )
| ( finite_Graph_a @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1497,plain,
! [SV180: nat] :
( ( ! [SY898: nat,SY899: nat] :
( ~ ( dist_b @ c2 @ SV180 @ SY898 @ SY899 )
| ( connected_b @ c2 @ SV180 @ SY899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1498,plain,
! [SV181: nat] :
( ( ! [SY900: list_P559422087at_nat,SY901: nat] :
( ~ ( isPath_b @ c2 @ SV181 @ SY900 @ SY901 )
| ( dist_b @ c2 @ SV181 @ ( size_s1990949619at_nat @ SY900 ) @ SY901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1499,plain,
! [SV182: nat > $o] :
( ( ! [SY902: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SY902 ) )
= ( ! [SY903: nat] :
( ~ ( SV182 @ SY903 )
| ( SY902 @ SY903 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1500,plain,
( ( ! [SV183: set_Pr1986765409at_nat] :
( ( ^ [SY904: set_Pr1986765409at_nat] : ( SV183 = SY904 ) )
= ( ^ [SY905: set_Pr1986765409at_nat] :
~ ( ~ ( ord_le841296385at_nat @ SV183 @ SY905 )
| ~ ( ord_le841296385at_nat @ SY905 @ SV183 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1141]) ).
thf(1501,plain,
( ( ( ^ [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_Pr1986765409at_nat,SX1: set_Pr1986765409at_nat] :
~ ( ~ ( ord_le841296385at_nat @ SX0 @ SX1 )
| ~ ( ord_le841296385at_nat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1141]) ).
thf(1502,plain,
! [SV184: set_Pr1986765409at_nat] :
( ( ! [SY906: set_Pr1986765409at_nat > $o] :
( ~ ( finite772653738at_nat @ SV184 )
| ~ ! [SX2: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SX2 )
| ~ ! [SX3: set_Pr1986765409at_nat] :
( ~ ( ord_le116442893at_nat @ SX3 @ SX2 )
| ( SY906 @ SX3 ) )
| ( SY906 @ SX2 ) )
| ( SY906 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1503,plain,
( ( ! [SV185: product_prod_nat_nat > b] :
( ( isShortestPath_b @ SV185 )
= ( ^ [SY909: nat,SY910: list_P559422087at_nat,SY911: nat] :
~ ( ~ ( isPath_b @ SV185 @ SY909 @ SY910 @ SY911 )
| ( ( size_s1990949619at_nat @ SY910 )
!= ( min_dist_b @ SV185 @ SY909 @ SY911 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1143]) ).
thf(1504,plain,
( ( isShortestPath_b
= ( ^ [SX0: product_prod_nat_nat > b,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isPath_b @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ( size_s1990949619at_nat @ SX2 )
!= ( min_dist_b @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1143]) ).
thf(1505,plain,
( ( ( ~ ( finite_finite_nat @ ( v_a @ c ) ) )
= $true )
| ( ( finite772653738at_nat @ ( e_a @ c ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1506,plain,
! [SV186: nat] :
( ( ! [SY912: nat] :
( ~ ( ord_less_eq_nat @ SV186 @ SY912 )
| ~ ( ord_less_eq_nat @ SY912 @ SV186 )
| ( SV186 = SY912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1507,plain,
! [SV187: nat] :
( ( ! [SY913: nat] :
( ~ ( ord_less_nat @ SV187 @ SY913 )
| ( SY913 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1508,plain,
( ( ! [SV188: product_prod_nat_nat > a] :
( ( connected_a @ SV188 )
= ( ^ [SY914: nat,SY915: nat] :
~ ! [SY916: list_P559422087at_nat] :
~ ( isPath_a @ SV188 @ SY914 @ SY916 @ SY915 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1147]) ).
thf(1509,plain,
( ( connected_a
= ( ^ [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat] :
~ ! [SX3: list_P559422087at_nat] :
~ ( isPath_a @ SX0 @ SX1 @ SX3 @ SX2 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1147]) ).
thf(1510,plain,
! [SV189: nat] :
( ( ! [SY917: list_P559422087at_nat,SY918: nat] :
( ~ ( isShortestPath_a @ c @ SV189 @ SY917 @ SY918 )
| ( isSimplePath_a @ c @ SV189 @ SY917 @ SY918 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1511,plain,
! [SV190: set_nat] :
( ( ! [SY919: set_nat] :
( ~ ( finite_finite_nat @ SV190 )
| ~ ( ord_less_eq_set_nat @ SY919 @ SV190 )
| ~ ( ord_less_nat @ ( finite_card_nat @ SY919 ) @ ( finite_card_nat @ SV190 ) )
| ( ord_less_set_nat @ SY919 @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1512,plain,
! [SV191: nat] :
( ( ! [SY920: nat] :
( ~ ( connected_a @ c @ SV191 @ SY920 )
| ( ( ( min_dist_a @ c @ SV191 @ SY920 )
= zero_zero_nat )
= ( SY920 = SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1513,plain,
! [SV192: nat > $o] :
( ( ! [SY921: nat] :
( ~ ! [SY922: nat] :
( ~ ! [SY923: nat] :
( ~ ( ord_less_nat @ SY923 @ SY922 )
| ( SV192 @ SY923 ) )
| ( SV192 @ SY922 ) )
| ( SV192 @ SY921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1514,plain,
! [SV193: nat] :
( ( ! [SY924: nat] :
( ~ ( connected_a @ c @ SV193 @ SY924 )
| ( ( member_nat @ SY924 @ ( v_a @ c ) )
= ( member_nat @ SV193 @ ( v_a @ c ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1515,plain,
! [SV194: set_nat] :
( ( ! [SY925: set_nat] :
( ~ ( ord_less_eq_set_nat @ SV194 @ SY925 )
| ~ ~ ( finite_finite_nat @ SV194 )
| ~ ( finite_finite_nat @ SY925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1516,plain,
! [SV195: set_Pr1986765409at_nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ ( finite447719721at_nat @ SV195 ) )
| ( finite772653738at_nat @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1517,plain,
! [SV196: nat > $o] :
( ( ! [SY926: nat] :
( ~ ( SV196 @ SY926 )
| ~ ~ ( SV196 @ zero_zero_nat )
| ~ ! [SY927: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_eq_nat @ SY927 @ SY926 )
| ~ ! [SY928: nat] :
( ~ ( ord_less_nat @ SY928 @ SY927 )
| ~ ( SV196 @ SY928 ) ) )
| ~ ( SV196 @ SY927 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1518,plain,
! [SV197: nat] :
( ( ! [SY929: nat] :
( ~ ( ord_less_nat @ SV197 @ SY929 )
| ( SY929 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1519,plain,
( ( ! [SX0: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ s @ SX0 @ t )
| ( ( size_s1990949619at_nat @ SX0 )
!= ( min_dist_b @ c2 @ s @ t ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1520,plain,
! [SV198: set_Pr1986765409at_nat] :
( ( ! [SY930: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SV198 )
| ~ ( ord_le841296385at_nat @ SY930 @ SV198 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV198 ) @ ( finite447719721at_nat @ SY930 ) )
| ( SY930 = SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1521,plain,
! [SV199: product_prod_nat_nat > b] :
( ( ! [SY931: nat,SY932: nat] :
( ~ ( connected_b @ SV199 @ SY931 @ SY932 )
| ~ ! [SY933: list_P559422087at_nat] :
~ ( isShortestPath_b @ SV199 @ SY931 @ SY933 @ SY932 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1522,plain,
! [SV200: set_nat] :
( ( ! [SY934: nat] :
( ~ ( finite_finite_nat @ SV200 )
| ~ ( member_nat @ SY934 @ SV200 )
| ~ ! [SY935: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY935 @ SV200 )
| ~ ( ord_less_eq_nat @ SY934 @ SY935 ) )
| ~ ! [SY936: nat] :
( ~ ( member_nat @ SY936 @ SV200 )
| ~ ( ord_less_eq_nat @ SY935 @ SY936 )
| ( SY935 = SY936 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1523,plain,
! [SV201: product_prod_nat_nat > a] :
( ( ! [SY937: nat,SY938: nat] :
( ~ ( finite_Graph_a @ SV201 )
| ~ ( member_nat @ SY937 @ ( v_a @ SV201 ) )
| ~ ( connected_a @ SV201 @ SY937 @ SY938 )
| ( ord_less_nat @ ( min_dist_a @ SV201 @ SY937 @ SY938 ) @ ( finite_card_nat @ ( v_a @ SV201 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1524,plain,
! [SV202: set_Pr1986765409at_nat] :
( ( ! [SY939: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SV202 @ SY939 )
| ~ ~ ( finite772653738at_nat @ SV202 )
| ~ ( finite772653738at_nat @ SY939 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1525,plain,
! [SV203: product_prod_nat_nat > b] :
( ( ! [SY940: nat,SY941: list_P559422087at_nat,SY942: nat] :
( ~ ( isShortestPath_b @ SV203 @ SY940 @ SY941 @ SY942 )
| ( isSimplePath_b @ SV203 @ SY940 @ SY941 @ SY942 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1526,plain,
! [SV204: set_nat] :
( ( ~ ~ ( finite_finite_nat @ SV204 )
| ( ( finite_card_nat @ SV204 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1527,plain,
! [SV205: nat] :
( ( ! [SY943: nat] :
( ~ ( ( SV205 != SY943 ) )
| ~ ~ ( ord_less_nat @ SV205 @ SY943 )
| ( ord_less_nat @ SY943 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1528,plain,
! [SV206: set_Pr1986765409at_nat] :
( ( ! [SY944: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SV206 )
| ~ ( ord_le841296385at_nat @ SY944 @ SV206 )
| ~ ( ord_less_nat @ ( finite447719721at_nat @ SY944 ) @ ( finite447719721at_nat @ SV206 ) )
| ( ord_le116442893at_nat @ SY944 @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1529,plain,
! [SV207: nat] :
( ( ! [SY945: list_P559422087at_nat,SY946: nat] :
( ~ ( isPath_a @ c @ SV207 @ SY945 @ SY946 )
| ( dist_a @ c @ SV207 @ ( size_s1990949619at_nat @ SY945 ) @ SY946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1530,plain,
! [SV208: nat] :
( ( ! [SY947: list_P559422087at_nat,SY948: nat] :
( ( isShortestPath_a @ c @ SV208 @ SY947 @ SY948 )
= ( ~ ( ~ ( isPath_a @ c @ SV208 @ SY947 @ SY948 )
| ~ ! [SY949: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY949 @ SY948 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY947 ) @ ( size_s1990949619at_nat @ SY949 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1531,plain,
! [SV209: set_nat] :
( ( ! [SY950: set_nat] :
( ~ ( ord_less_eq_set_nat @ SV209 @ SY950 )
| ~ ( finite_finite_nat @ SY950 )
| ( finite_finite_nat @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1532,plain,
! [SV210: nat] :
( ( ! [SY951: nat,SY952: nat > $o] :
( ~ ( connected_a @ c @ SV210 @ SY951 )
| ~ ! [SY953: nat] :
( ~ ( dist_a @ c @ SV210 @ SY953 @ SY951 )
| ~ ! [SY954: nat] :
( ~ ( dist_a @ c @ SV210 @ SY954 @ SY951 )
| ( ord_less_eq_nat @ SY953 @ SY954 ) )
| ( SY952 @ SY953 ) )
| ( SY952 @ ( min_dist_a @ c @ SV210 @ SY951 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1533,plain,
! [SV211: nat] :
( ( ! [SY955: nat] :
( ~ ( connected_a @ c @ SV211 @ SY955 )
| ( dist_a @ c @ SV211 @ ( min_dist_a @ c @ SV211 @ SY955 ) @ SY955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1534,plain,
! [SV212: set_Pr1986765409at_nat] :
( ( ~ ~ ( finite772653738at_nat @ SV212 )
| ( ( finite447719721at_nat @ SV212 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1535,plain,
! [SV213: set_nat] :
( ( ! [SY956: set_nat] :
( ~ ( finite_finite_nat @ SV213 )
| ~ ( ord_less_eq_set_nat @ SY956 @ SV213 )
| ( ( finite_card_nat @ SY956 )
!= ( finite_card_nat @ SV213 ) )
| ( SY956 = SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1536,plain,
! [SV214: product_prod_nat_nat > b] :
( ( ! [SY957: nat,SY958: nat,SY959: nat] :
( ~ ( dist_b @ SV214 @ SY957 @ SY958 @ SY959 )
| ( connected_b @ SV214 @ SY957 @ SY959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1537,plain,
! [SV215: nat] :
( ( ! [SY960: nat] :
( ( connected_b @ c2 @ SV215 @ SY960 )
= ( ~ ! [SY961: nat] :
~ ( dist_b @ c2 @ SV215 @ SY961 @ SY960 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1538,plain,
! [SV216: product_prod_nat_nat > a] :
( ( ~ ( finite_Graph_a @ SV216 )
| ( edmond1517640972ysis_a @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1539,plain,
! [SV217: product_prod_nat_nat > b] :
( ( ! [SY962: nat,SY963: list_P559422087at_nat,SY964: nat] :
( ~ ( finite_Graph_b @ SV217 )
| ~ ( member_nat @ SY962 @ ( v_b @ SV217 ) )
| ~ ( isSimplePath_b @ SV217 @ SY962 @ SY963 @ SY964 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY963 ) @ ( finite_card_nat @ ( v_b @ SV217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1540,plain,
! [SV218: nat] :
( ( ! [SY965: nat] :
( ~ ( member_nat @ SV218 @ ( v_b @ c2 ) )
| ~ ( connected_b @ c2 @ SV218 @ SY965 )
| ( ord_less_nat @ ( min_dist_b @ c2 @ SV218 @ SY965 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1541,plain,
! [SV219: set_nat] :
( ( ! [SY966: set_nat > $o] :
( ~ ( finite_finite_nat @ SV219 )
| ~ ! [SX2: set_nat] :
( ~ ( finite_finite_nat @ SX2 )
| ~ ! [SX3: set_nat] :
( ~ ( ord_less_set_nat @ SX3 @ SX2 )
| ( SY966 @ SX3 ) )
| ( SY966 @ SX2 ) )
| ( SY966 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1542,plain,
! [SV220: nat] :
( ( ! [SY969: nat] :
( ( SV220 != SY969 )
= ( ( ord_less_nat @ SV220 @ SY969 )
| ( ord_less_nat @ SY969 @ SV220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1543,plain,
! [SV221: nat] :
( ( ! [SY970: list_P559422087at_nat,SY971: nat] :
( ~ ( isPath_b @ c2 @ SV221 @ SY970 @ SY971 )
| ~ ! [SY972: list_P559422087at_nat] :
~ ( isSimplePath_b @ c2 @ SV221 @ SY972 @ SY971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1544,plain,
! [SV222: nat > $o] :
( ( ! [SY973: nat] :
( ~ ( SV222 @ zero_zero_nat )
| ~ ! [SY974: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY974 )
| ~ ~ ( SV222 @ SY974 )
| ~ ! [SY975: nat] :
~ ~ ( ~ ( ord_less_nat @ SY975 @ SY974 )
| ~ ~ ( SV222 @ SY975 ) ) )
| ( SV222 @ SY973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1545,plain,
! [SV223: set_nat] :
( ( ! [SY976: set_nat] :
( ~ ( ord_less_eq_set_nat @ SV223 @ SY976 )
| ~ ( ( SV223 != SY976 ) )
| ( ord_less_set_nat @ SV223 @ SY976 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1546,plain,
! [SV224: set_Pr1986765409at_nat] :
( ( ! [SY977: nat] :
( ~ ! [SY978: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SY978 @ SV224 )
| ~ ( finite772653738at_nat @ SY978 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ SY978 ) @ SY977 ) )
| ~ ( ~ ( finite772653738at_nat @ SV224 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SY977 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1547,plain,
! [SV225: nat] :
( ( ! [SY979: product_prod_nat_nat > a] :
( ~ ( member_nat @ SV225 @ ( v_a @ SY979 ) )
| ( ord_less_eq_set_nat @ ( reachableNodes_a @ SY979 @ SV225 ) @ ( v_a @ SY979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1548,plain,
! [SV226: set_nat] :
( ( ! [SY980: nat] :
( ~ ! [SY981: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY981 @ SV226 )
| ~ ( finite_finite_nat @ SY981 )
| ( ord_less_eq_nat @ ( finite_card_nat @ SY981 ) @ SY980 ) )
| ~ ( ~ ( finite_finite_nat @ SV226 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SY980 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1549,plain,
! [SV227: product_prod_nat_nat > b] :
( ( ! [SY982: nat,SY983: list_P559422087at_nat,SY984: nat] :
( ~ ( isPath_b @ SV227 @ SY982 @ SY983 @ SY984 )
| ( dist_b @ SV227 @ SY982 @ ( size_s1990949619at_nat @ SY983 ) @ SY984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1550,plain,
! [SV228: set_set_nat] :
( ( ~ ~ ( finite2012248349et_nat @ SV228 )
| ( ( finite_card_set_nat @ SV228 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1551,plain,
! [SV229: nat] :
( ( ! [SY985: list_P559422087at_nat,SY986: nat] :
( ( isShortestPath_a @ c @ SV229 @ SY985 @ SY986 )
= ( ~ ( ~ ( isPath_a @ c @ SV229 @ SY985 @ SY986 )
| ( ( size_s1990949619at_nat @ SY985 )
!= ( min_dist_a @ c @ SV229 @ SY986 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1552,plain,
! [SV230: nat] :
( ( ! [SY987: nat] :
( ~ ( ord_less_nat @ SV230 @ SY987 )
| ( ord_less_eq_nat @ SV230 @ SY987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1553,plain,
! [SV231: set_Pr1986765409at_nat] :
( ( ! [SY988: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SV231 )
| ~ ( ord_le841296385at_nat @ SY988 @ SV231 )
| ( finite772653738at_nat @ SY988 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1554,plain,
! [SV232: product_prod_nat_nat > b] :
( ( ~ ( finite_finite_nat @ ( v_b @ SV232 ) )
| ( finite_Graph_b @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1555,plain,
! [SV233: product_prod_nat_nat > a] :
( ( ! [SY989: nat,SY990: nat] :
( ~ ( connected_a @ SV233 @ SY989 @ SY990 )
| ( ( ( min_dist_a @ SV233 @ SY989 @ SY990 )
= zero_zero_nat )
= ( SY990 = SY989 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1556,plain,
! [SV234: product_prod_nat_nat > a] :
( ( ! [SY991: nat,SY992: list_P559422087at_nat,SY993: nat] :
( ~ ( isShortestPath_a @ SV234 @ SY991 @ SY992 @ SY993 )
| ( isSimplePath_a @ SV234 @ SY991 @ SY992 @ SY993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1557,plain,
! [SV235: set_se1612935105at_nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ ( finite1701894793at_nat @ SV235 ) )
| ( finite1457549322at_nat @ SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1558,plain,
! [SV236: nat] :
( ( ! [SY994: list_P559422087at_nat,SY995: nat] :
( ~ ( isPath_a @ c @ SV236 @ SY994 @ SY995 )
| ~ ! [SY996: list_P559422087at_nat] :
~ ( isSimplePath_a @ c @ SV236 @ SY996 @ SY995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1559,plain,
! [SV237: nat] :
( ( ! [SY997: nat] :
( ( connected_b @ c2 @ SV237 @ SY997 )
= ( ~ ! [SY998: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY998 @ SY997 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1560,plain,
! [SV238: nat] :
( ( ! [SY999: nat,SY1000: nat] :
( ~ ( ord_less_eq_nat @ SV238 @ SY999 )
| ~ ( ord_less_eq_nat @ SY999 @ SY1000 )
| ( ord_less_eq_nat @ SV238 @ SY1000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1561,plain,
! [SV239: product_prod_nat_nat > b] :
( ( ~ ( finite_Graph_b @ SV239 )
| ( edmond1517640973ysis_b @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1562,plain,
! [SV240: product_prod_nat_nat > a] :
( ( ~ ( edmond1517640972ysis_a @ SV240 )
| ( finite_Graph_a @ SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1563,plain,
! [SV241: product_prod_nat_nat > b] :
( ( ! [SY1001: set_nat] :
( ~ ( finite_finite_nat @ ( v_b @ SV241 ) )
| ( finite772653738at_nat @ ( incoming_b @ SV241 @ SY1001 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1564,plain,
( ( ( ~ ( finite772653738at_nat @ ( e_b @ c2 ) ) )
= $true )
| ( ( finite_Graph_b @ c2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1565,plain,
! [SV242: set_Pr1986765409at_nat] :
( ( ! [SY1002: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SV242 @ SY1002 )
| ~ ( finite772653738at_nat @ SY1002 )
| ( finite772653738at_nat @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1566,plain,
! [SV243: product_prod_nat_nat > b] :
( ( ~ ( finite772653738at_nat @ ( e_b @ SV243 ) )
| ( finite_finite_nat @ ( v_b @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1567,plain,
( ( ! [SV244: product_prod_nat_nat > a] :
( ( dist_a @ SV244 )
= ( ^ [SY1003: nat,SY1004: nat,SY1005: nat] :
~ ! [SY1006: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV244 @ SY1003 @ SY1006 @ SY1005 )
| ( ( size_s1990949619at_nat @ SY1006 )
!= SY1004 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1205]) ).
thf(1568,plain,
( ( dist_a
= ( ^ [SX0: product_prod_nat_nat > a,SX1: nat,SX2: nat,SX3: nat] :
~ ! [SX4: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SX0 @ SX1 @ SX4 @ SX3 )
| ( ( size_s1990949619at_nat @ SX4 )
!= SX2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1205]) ).
thf(1569,plain,
! [SV245: product_prod_nat_nat > b] :
( ( ~ ( finite772653738at_nat @ ( e_b @ SV245 ) )
| ( finite_Graph_b @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1570,plain,
! [SV246: product_prod_nat_nat > b] :
( ( ~ ( edmond1517640973ysis_b @ SV246 )
| ( finite_Graph_b @ SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1571,plain,
! [SV247: product_prod_nat_nat > b] :
( ( ~ ( edmond1517640973ysis_b @ SV247 )
| ( ord_le841296385at_nat @ ( e_b @ SV247 ) @ ( edmond771116671s_uE_b @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1572,plain,
! [SV248: nat] :
( ( ! [SY1007: list_P559422087at_nat,SY1008: nat] :
( ( isShortestPath_a @ c @ SV248 @ SY1007 @ SY1008 )
= ( ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SY1007 @ SY1008 )
| ( ( size_s1990949619at_nat @ SY1007 )
!= ( min_dist_a @ c @ SV248 @ SY1008 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1573,plain,
! [SV249: list_P559422087at_nat] :
( ( ! [SY1009: list_P559422087at_nat] :
( ~ ( ( ( size_s1990949619at_nat @ SV249 )
!= ( size_s1990949619at_nat @ SY1009 ) ) )
| ( SV249 != SY1009 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1574,plain,
! [SV250: set_set_nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ SV250 ) )
| ( finite2012248349et_nat @ SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1575,plain,
( ( ! [SV251: product_prod_nat_nat > b] :
( ( connected_b @ SV251 )
= ( ^ [SY1010: nat,SY1011: nat] :
~ ! [SY1012: list_P559422087at_nat] :
~ ( isPath_b @ SV251 @ SY1010 @ SY1012 @ SY1011 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1212]) ).
thf(1576,plain,
( ( connected_b
= ( ^ [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat] :
~ ! [SX3: list_P559422087at_nat] :
~ ( isPath_b @ SX0 @ SX1 @ SX3 @ SX2 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1212]) ).
thf(1577,plain,
! [SV252: set_Pr1986765409at_nat] :
( ( ! [SY1013: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SV252 )
| ~ ( ord_le841296385at_nat @ SY1013 @ SV252 )
| ( ( finite447719721at_nat @ SY1013 )
!= ( finite447719721at_nat @ SV252 ) )
| ( SY1013 = SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1578,plain,
! [SV253: nat] :
( ( ! [SY1014: nat,SY1015: nat] :
( ~ ( dist_b @ c2 @ SV253 @ SY1014 @ SY1015 )
| ( ord_less_eq_nat @ ( min_dist_b @ c2 @ SV253 @ SY1015 ) @ SY1014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1579,plain,
! [SV254: product_prod_nat_nat > b] :
( ( ! [SY1016: nat,SY1017: nat] :
( ~ ( connected_b @ SV254 @ SY1016 @ SY1017 )
| ( ( member_nat @ SY1017 @ ( v_b @ SV254 ) )
= ( member_nat @ SY1016 @ ( v_b @ SV254 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1580,plain,
! [SV255: product_prod_nat_nat > b] :
( ( ! [SY1018: nat,SY1019: nat] :
( ~ ( connected_b @ SV255 @ SY1018 @ SY1019 )
| ( ( ( min_dist_b @ SV255 @ SY1018 @ SY1019 )
= zero_zero_nat )
= ( SY1019 = SY1018 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1581,plain,
! [SV256: nat] :
( ( ~ ( ( SV256 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1582,plain,
! [SV257: product_prod_nat_nat > b] :
( ( ! [SY1020: nat,SY1021: nat] :
( ~ ( finite_Graph_b @ SV257 )
| ~ ( member_nat @ SY1020 @ ( v_b @ SV257 ) )
| ~ ( connected_b @ SV257 @ SY1020 @ SY1021 )
| ( ord_less_nat @ ( min_dist_b @ SV257 @ SY1020 @ SY1021 ) @ ( finite_card_nat @ ( v_b @ SV257 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1583,plain,
! [SV258: set_Pr1986765409at_nat] :
( ( ! [SY1022: set_Pr1986765409at_nat] :
( ~ ! [SY1023: product_prod_nat_nat] :
( ~ ( member701585322at_nat @ SY1023 @ SV258 )
| ( member701585322at_nat @ SY1023 @ SY1022 ) )
| ( ord_le841296385at_nat @ SV258 @ SY1022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1584,plain,
! [SV259: product_prod_nat_nat > $o] :
( ( ! [SY1024: product_prod_nat_nat > $o] :
( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SY1024 ) )
= ( ! [SY1025: product_prod_nat_nat] :
( ~ ( SV259 @ SY1025 )
| ( SY1024 @ SY1025 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1585,plain,
! [SV260: nat] :
( ( ! [SY1026: nat,SY1027: nat,SY1028: nat] :
( ~ ( connected_a @ c @ SV260 @ SY1026 )
| ( ( min_dist_a @ c @ SV260 @ SY1026 )
!= SY1027 )
| ~ ( ord_less_nat @ SY1028 @ SY1027 )
| ~ ! [SY1029: nat] :
~ ~ ( ~ ( connected_a @ c @ SV260 @ SY1029 )
| ( ( min_dist_a @ c @ SV260 @ SY1029 )
!= SY1028 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1586,plain,
! [SV261: product_prod_nat_nat > a] :
( ( ! [SY1030: set_nat] :
( ~ ( finite_finite_nat @ ( v_a @ SV261 ) )
| ( finite772653738at_nat @ ( outgoing_a @ SV261 @ SY1030 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1587,plain,
( ( ! [SV262: product_prod_nat_nat > b] :
( ( isShortestPath_b @ SV262 )
= ( ^ [SY1031: nat,SY1032: list_P559422087at_nat,SY1033: nat] :
~ ( ~ ( isSimplePath_b @ SV262 @ SY1031 @ SY1032 @ SY1033 )
| ( ( size_s1990949619at_nat @ SY1032 )
!= ( min_dist_b @ SV262 @ SY1031 @ SY1033 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1223]) ).
thf(1588,plain,
( ( isShortestPath_b
= ( ^ [SX0: product_prod_nat_nat > b,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isSimplePath_b @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ( size_s1990949619at_nat @ SX2 )
!= ( min_dist_b @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1223]) ).
thf(1589,plain,
! [SV263: set_li664300135at_nat] :
( ( ~ ( finite1299096496at_nat @ SV263 )
| ~ ! [SY1034: nat] :
~ ! [SY1035: list_P559422087at_nat] :
( ~ ( member1608759472at_nat @ SY1035 @ SV263 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY1035 ) @ SY1034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1590,plain,
! [SV264: nat] :
( ( ! [SY1036: nat,SY1037: nat] :
( ~ ( connected_a @ c @ SV264 @ SY1036 )
| ~ ( ord_less_eq_nat @ SY1037 @ ( min_dist_a @ c @ SV264 @ SY1036 ) )
| ~ ! [SY1038: nat] :
~ ~ ( ~ ( connected_a @ c @ SV264 @ SY1038 )
| ( ( min_dist_a @ c @ SV264 @ SY1038 )
!= SY1037 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1591,plain,
! [SV265: product_prod_nat_nat > b] :
( ( ! [SY1039: nat,SY1040: nat,SY1041: nat,SY1042: nat] :
( ~ ( connected_b @ SV265 @ SY1039 @ SY1040 )
| ( ( min_dist_b @ SV265 @ SY1039 @ SY1040 )
!= SY1041 )
| ~ ( ord_less_nat @ SY1042 @ SY1041 )
| ~ ! [SY1043: nat] :
~ ~ ( ~ ( connected_b @ SV265 @ SY1039 @ SY1043 )
| ( ( min_dist_b @ SV265 @ SY1039 @ SY1043 )
!= SY1042 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1592,plain,
! [SV266: nat] :
( ( ! [SY1044: nat] :
( ~ ( connected_a @ c @ SV266 @ SY1044 )
| ~ ! [SY1045: list_P559422087at_nat] :
~ ( isShortestPath_a @ c @ SV266 @ SY1045 @ SY1044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1593,plain,
! [SV267: nat] :
( ( ! [SY1046: list_P559422087at_nat,SY1047: nat] :
( ~ ( member_nat @ SV267 @ ( v_a @ c ) )
| ~ ( isShortestPath_a @ c @ SV267 @ SY1046 @ SY1047 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY1046 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1594,plain,
( ( ( ~ ( finite772653738at_nat @ ( e_a @ c ) ) )
= $true )
| ( ( finite_Graph_a @ c )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1595,plain,
! [SV268: product_prod_nat_nat > a] :
( ( ! [SY1048: nat,SY1049: nat,SY1050: nat] :
( ~ ( dist_a @ SV268 @ SY1048 @ SY1049 @ SY1050 )
| ( connected_a @ SV268 @ SY1048 @ SY1050 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1596,plain,
! [SV269: set_nat] :
( ( ! [SY1051: set_nat] :
( ~ ( finite_finite_nat @ SV269 )
| ~ ( ord_less_eq_set_nat @ SY1051 @ SV269 )
| ( finite_finite_nat @ SY1051 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1597,plain,
! [SV270: set_nat] :
( ( ! [SY1052: nat] :
( ~ ~ ( finite_finite_nat @ SV270 )
| ~ ! [SY1053: set_nat] :
~ ~ ( ~ ~ ( ~ ( finite_finite_nat @ SY1053 )
| ( ( finite_card_nat @ SY1053 )
!= SY1052 ) )
| ~ ( ord_less_eq_set_nat @ SY1053 @ SV270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1598,plain,
! [SV271: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV271 )
= ( SV271 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1599,plain,
! [SV272: set_li664300135at_nat] :
( ( ~ ~ ( finite1299096496at_nat @ SV272 )
| ( ( finite83082927at_nat @ SV272 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1600,plain,
! [SV273: set_set_nat] :
( ( ! [SY1054: set_nat] :
( ~ ( finite2012248349et_nat @ SV273 )
| ~ ( member_set_nat @ SY1054 @ SV273 )
| ~ ! [SY1055: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SY1055 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1055 @ SY1054 ) )
| ~ ! [SY1056: set_nat] :
( ~ ( member_set_nat @ SY1056 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1056 @ SY1055 )
| ( SY1055 = SY1056 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1601,plain,
! [SV274: product_prod_nat_nat > $o] :
( ( ! [SY1057: product_prod_nat_nat > $o] :
( ~ ! [SY1058: product_prod_nat_nat] :
( ( SV274 @ SY1058 )
= ( SY1057 @ SY1058 ) )
| ( ( collec7649004at_nat @ SV274 )
= ( collec7649004at_nat @ SY1057 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1602,plain,
! [SV275: nat] :
( ( ! [SY1059: list_P559422087at_nat,SY1060: nat] :
( ~ ( member_nat @ SV275 @ ( v_b @ c2 ) )
| ~ ( isSimplePath_b @ c2 @ SV275 @ SY1059 @ SY1060 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY1059 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1603,plain,
! [SV276: nat] :
( ( ! [SY1061: list_P559422087at_nat,SY1062: nat] :
( ~ ( isShortestPath_b @ c2 @ SV276 @ SY1061 @ SY1062 )
| ( isSimplePath_b @ c2 @ SV276 @ SY1061 @ SY1062 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1604,plain,
! [SV277: product_prod_nat_nat > b] :
( ( ! [SY1063: nat,SY1064: nat] :
( ~ ( edmond1517640973ysis_b @ SV277 )
| ( ord_le841296385at_nat @ ( edmond475474836dges_b @ SV277 @ SY1063 @ SY1064 ) @ ( e_b @ SV277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1605,plain,
! [SV278: nat] :
( ( ~ ( member_nat @ SV278 @ ( v_b @ c2 ) )
| ( ord_less_eq_set_nat @ ( reachableNodes_b @ c2 @ SV278 ) @ ( v_b @ c2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1606,plain,
! [SV279: set_nat] :
( ( ! [SY1065: set_nat] :
( ~ ( finite_finite_nat @ SV279 )
| ~ ( ord_less_set_nat @ SY1065 @ SV279 )
| ( ord_less_nat @ ( finite_card_nat @ SY1065 ) @ ( finite_card_nat @ SV279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1607,plain,
( ( ( ~ ( finite772653738at_nat @ ( e_a @ c ) ) )
= $true )
| ( ( finite_finite_nat @ ( v_a @ c ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1608,plain,
! [SV280: nat] :
( ( ~ ( ord_less_eq_nat @ SV280 @ zero_zero_nat )
| ( SV280 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1609,plain,
! [SV281: product_prod_nat_nat > b] :
( ( ! [SY1066: nat,SY1067: nat,SY1068: nat] :
( ~ ( dist_b @ SV281 @ SY1066 @ SY1067 @ SY1068 )
| ( ord_less_eq_nat @ ( min_dist_b @ SV281 @ SY1066 @ SY1068 ) @ SY1067 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1610,plain,
! [SV282: set_nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ SV282 ) )
| ( finite_finite_nat @ SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1611,plain,
! [SV283: nat] :
( ( ! [SY1069: nat,SY1070: nat] :
( ~ ( dist_b @ c2 @ SV283 @ SY1069 @ SY1070 )
| ~ ! [SY1071: nat] :
( ~ ( dist_b @ c2 @ SV283 @ SY1071 @ SY1070 )
| ( ord_less_eq_nat @ SY1069 @ SY1071 ) )
| ( ( min_dist_b @ c2 @ SV283 @ SY1070 )
= SY1069 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1612,plain,
! [SV284: set_se1612935105at_nat] :
( ( ! [SY1072: set_se1612935105at_nat] :
( ~ ( ord_le2096002913at_nat @ SV284 @ SY1072 )
| ~ ( finite1457549322at_nat @ SY1072 )
| ( finite1457549322at_nat @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1613,plain,
! [SV285: product_prod_nat_nat > b] :
( ( ! [SY1073: nat,SY1074: nat] :
( ~ ( edmond1517640973ysis_b @ SV285 )
| ( finite772653738at_nat @ ( edmond475474836dges_b @ SV285 @ SY1073 @ SY1074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1614,plain,
( ( ! [SV286: product_prod_nat_nat > b] :
( ( connected_b @ SV286 )
= ( ^ [SY1075: nat,SY1076: nat] :
~ ! [SY1077: nat] :
~ ( dist_b @ SV286 @ SY1075 @ SY1077 @ SY1076 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1249]) ).
thf(1615,plain,
( ( connected_b
= ( ^ [SX0: product_prod_nat_nat > b,SX1: nat,SX2: nat] :
~ ! [SX3: nat] :
~ ( dist_b @ SX0 @ SX1 @ SX3 @ SX2 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1249]) ).
thf(1616,plain,
! [SV287: set_Pr1986765409at_nat] :
( ( ! [SY1078: set_Pr1986765409at_nat,SY1079: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SV287 @ SY1078 )
| ~ ( ord_le841296385at_nat @ SY1078 @ SY1079 )
| ( ord_le841296385at_nat @ SV287 @ SY1079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1617,plain,
! [SV288: set_li664300135at_nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ ( finite83082927at_nat @ SV288 ) )
| ( finite1299096496at_nat @ SV288 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1618,plain,
! [SV289: product_prod_nat_nat > a] :
( ( ! [SY1080: nat,SY1081: nat] :
( ~ ( edmond1517640972ysis_a @ SV289 )
| ( finite772653738at_nat @ ( edmond475474835dges_a @ SV289 @ SY1080 @ SY1081 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1619,plain,
! [SV290: product_prod_nat_nat > b] :
( ( ! [SY1082: nat] :
( ~ ( finite_Graph_b @ SV290 )
| ( finite_finite_nat @ ( adjacent_nodes_b @ SV290 @ SY1082 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1620,plain,
! [SV291: product_prod_nat_nat > a] :
( ( ! [SY1083: nat,SY1084: list_P559422087at_nat,SY1085: nat] :
( ~ ( isPath_a @ SV291 @ SY1083 @ SY1084 @ SY1085 )
| ~ ! [SY1086: list_P559422087at_nat] :
~ ( isSimplePath_a @ SV291 @ SY1083 @ SY1086 @ SY1085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1621,plain,
! [SV292: nat] :
( ( ! [SY1087: nat] :
( ~ ( ord_less_nat @ SV292 @ SY1087 )
| ( SY1087 != SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1622,plain,
( ( ( ~ ( finite772653738at_nat @ ( e_b @ c2 ) ) )
= $true )
| ( ( finite_finite_nat @ ( v_b @ c2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1623,plain,
( ( ( ~ ( finite_finite_nat @ ( v_b @ c2 ) ) )
= $true )
| ( ( finite772653738at_nat @ ( e_b @ c2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1624,plain,
! [SV293: nat] :
( ( ! [SY1088: list_P559422087at_nat,SY1089: nat] :
( ( isShortestPath_b @ c2 @ SV293 @ SY1088 @ SY1089 )
= ( ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SY1088 @ SY1089 )
| ( ( size_s1990949619at_nat @ SY1088 )
!= ( min_dist_b @ c2 @ SV293 @ SY1089 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1625,plain,
! [SV294: nat] :
( ( ! [SY1090: nat,SY1091: nat] :
( ~ ( dist_a @ c @ SV294 @ SY1090 @ SY1091 )
| ( connected_a @ c @ SV294 @ SY1091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1626,plain,
! [SV295: product_prod_nat_nat > a] :
( ( ~ ( finite_Graph_a @ SV295 )
| ( finite_finite_nat @ ( v_a @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1627,plain,
! [SV296: product_prod_nat_nat > a] :
( ( ! [SY1092: nat,SY1093: nat] :
( ~ ( connected_a @ SV296 @ SY1092 @ SY1093 )
| ( dist_a @ SV296 @ SY1092 @ ( min_dist_a @ SV296 @ SY1092 @ SY1093 ) @ SY1093 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1628,plain,
! [SV297: nat] :
( ( ! [SY1094: nat] :
( ~ ( ( ord_less_nat @ SV297 @ SY1094 )
| ( SV297 = SY1094 ) )
| ( ord_less_eq_nat @ SV297 @ SY1094 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1629,plain,
! [SV298: set_Pr1986765409at_nat] :
( ( ! [SY1095: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SV298 )
| ~ ( ord_le841296385at_nat @ SY1095 @ SV298 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ SY1095 ) @ ( finite447719721at_nat @ SV298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1630,plain,
( ( ! [SV299: nat] :
( ( ord_less_nat @ SV299 )
= ( ^ [SY1096: nat] :
~ ( ~ ( ord_less_eq_nat @ SV299 @ SY1096 )
| ~ ( ( SV299 != SY1096 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1264]) ).
thf(1631,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1264]) ).
thf(1632,plain,
! [SV300: nat] :
( ( ! [SY1097: list_P559422087at_nat,SY1098: nat] :
( ~ ( member_nat @ SV300 @ ( v_b @ c2 ) )
| ~ ( isShortestPath_b @ c2 @ SV300 @ SY1097 @ SY1098 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY1097 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1633,plain,
! [SV301: set_Pr1986765409at_nat] :
( ( ! [SY1099: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SV301 @ SY1099 )
| ~ ( ord_le841296385at_nat @ SY1099 @ SV301 )
| ( SV301 = SY1099 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1634,plain,
! [SV302: product_prod_nat_nat > a] :
( ( ~ ( finite772653738at_nat @ ( e_a @ SV302 ) )
| ( finite_finite_nat @ ( v_a @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1635,plain,
! [SV303: set_se1612935105at_nat] :
( ( ~ ~ ( finite1457549322at_nat @ SV303 )
| ( ( finite1701894793at_nat @ SV303 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1636,plain,
! [SV304: nat] :
( ( ! [SY1100: nat,SY1101: nat > $o] :
( ~ ( connected_b @ c2 @ SV304 @ SY1100 )
| ~ ! [SY1102: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1102 @ SY1100 )
| ~ ! [SY1103: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1103 @ SY1100 )
| ( ord_less_eq_nat @ SY1102 @ SY1103 ) )
| ( SY1101 @ SY1102 ) )
| ( SY1101 @ ( min_dist_b @ c2 @ SV304 @ SY1100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1637,plain,
! [SV305: list_P559422087at_nat] :
( ( ! [SY1104: list_P559422087at_nat] :
( ~ ( ( ( size_s1990949619at_nat @ SV305 )
!= ( size_s1990949619at_nat @ SY1104 ) ) )
| ( SV305 != SY1104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1638,plain,
! [SV306: nat] :
( ( ! [SY1105: list_P559422087at_nat,SY1106: nat] :
( ~ ( isShortestPath_b @ c2 @ SV306 @ SY1105 @ SY1106 )
| ( isPath_b @ c2 @ SV306 @ SY1105 @ SY1106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1639,plain,
! [SV307: set_nat] :
( ( ~ ( finite_finite_nat @ ( v_a @ c ) )
| ( finite772653738at_nat @ ( incoming_a @ c @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1640,plain,
! [SV308: nat] :
( ( ! [SY1107: list_P559422087at_nat,SY1108: nat] :
( ~ ( isShortestPath_a @ c @ SV308 @ SY1107 @ SY1108 )
| ( isPath_a @ c @ SV308 @ SY1107 @ SY1108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1641,plain,
! [SV309: product_prod_nat_nat > b] :
( ( ( edmond1022345717sure_b @ SV309 )
= ( edmond1022345717sure_b @ SV309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1642,plain,
! [SV310: product_prod_nat_nat > a] :
( ( ( edmond1022345716sure_a @ SV310 )
= ( edmond1022345716sure_a @ SV310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1643,plain,
! [SV311: product_prod_nat_nat > b] :
( ( ( edmond771116671s_uE_b @ SV311 )
= ( edmond771116671s_uE_b @ SV311 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1644,plain,
! [SV312: product_prod_nat_nat > a] :
( ( ( edmond771116670s_uE_a @ SV312 )
= ( edmond771116670s_uE_a @ SV312 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1645,plain,
! [SV313: product_prod_nat_nat > a] :
( ( ( edmond475474835dges_a @ SV313 )
= ( edmond475474835dges_a @ SV313 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1646,plain,
! [SV314: product_prod_nat_nat > b] :
( ( ( edmond475474836dges_b @ SV314 )
= ( edmond475474836dges_b @ SV314 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1647,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( edmond1517640972ysis_a @ SV315 )
= ( finite_Graph_a @ SV315 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1648,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( edmond1517640973ysis_b @ SV316 )
= ( finite_Graph_b @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1649,plain,
! [SV317: nat,SV13: nat] :
( ( ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
= ( SV317 = SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1650,plain,
! [SV318: set_Pr1986765409at_nat > $o,SV15: set_Pr1986765409at_nat] :
( ( ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
= ( SV318 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1651,plain,
! [SV319: set_nat > $o,SV16: set_nat] :
( ( ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
= ( SV319 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1652,plain,
! [SV320: product_prod_nat_nat > $o,SV17: product_prod_nat_nat] :
( ( ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
= ( SV320 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1653,plain,
! [SV321: nat > $o,SV18: nat] :
( ( ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
= ( SV321 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1654,plain,
! [SV23: nat] :
( ( ord_less_nat @ SV23 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1655,plain,
! [SV24: nat] :
( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV24 )
| ( SV24 = zero_zero_nat ) )
| ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV24 )
| ( SV24 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1305]) ).
thf(1656,plain,
! [SV24: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV24 ) )
= ( SV24 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1305]) ).
thf(1657,plain,
! [SV25: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
| ( SV25 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
| ( SV25 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1306]) ).
thf(1658,plain,
! [SV25: nat] :
( ( ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
= ( SV25 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1306]) ).
thf(1659,plain,
! [SV322: nat,SV30: nat] :
( ( ( ord_less_eq_nat @ SV30 @ SV322 )
| ( ord_less_eq_nat @ SV322 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1660,plain,
! [SV32: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
| ( SV32 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
| ( SV32 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1313]) ).
thf(1661,plain,
! [SV32: nat] :
( ( ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
= ( SV32 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1313]) ).
thf(1662,plain,
! [SV33: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
| ( SV33 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
| ( SV33 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1314]) ).
thf(1663,plain,
! [SV33: nat] :
( ( ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
= ( SV33 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1314]) ).
thf(1664,plain,
! [SV323: nat] :
( ( ( ord_less_eq_nat @ SV323 )
= ( ^ [SY1109: nat] :
( ( ord_less_nat @ SV323 @ SY1109 )
| ( SV323 = SY1109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1665,plain,
! [SV35: nat] :
( ( ~ ( ( zero_zero_nat = SV35 )
| ( SV35 = zero_zero_nat ) )
| ~ ( ( zero_zero_nat != SV35 )
| ( SV35 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1317]) ).
thf(1666,plain,
! [SV35: nat] :
( ( ( zero_zero_nat = SV35 )
= ( SV35 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1317]) ).
thf(1667,plain,
! [SV36: nat] :
( ( ord_less_nat @ SV36 @ SV36 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1668,plain,
! [SV37: nat] :
( ( ord_less_nat @ SV37 @ SV37 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1669,plain,
! [SV324: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV324 )
= ( isPath_b @ SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1670,plain,
! [SV325: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV325 )
= ( isPath_a @ SV325 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1671,plain,
! [SV326: product_prod_nat_nat > a] :
( ( ( v_a @ SV326 )
= ( v_a @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1672,plain,
! [SV327: product_prod_nat_nat > b] :
( ( ( v_b @ SV327 )
= ( v_b @ SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1673,plain,
! [SV328: product_prod_nat_nat > a] :
( ( ( min_dist_a @ SV328 )
= ( min_dist_a @ SV328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1674,plain,
! [SV329: product_prod_nat_nat > b] :
( ( ( min_dist_b @ SV329 )
= ( min_dist_b @ SV329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1675,plain,
! [SV330: product_prod_nat_nat > b] :
( ( ( connected_b @ SV330 )
= ( connected_b @ SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1676,plain,
! [SV331: product_prod_nat_nat > a] :
( ( ( connected_a @ SV331 )
= ( connected_a @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1677,plain,
! [SV332: nat,SV46: product_prod_nat_nat > b] :
( ( connected_b @ SV46 @ SV332 @ SV332 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1678,plain,
! [SV333: nat,SV47: product_prod_nat_nat > a] :
( ( connected_a @ SV47 @ SV333 @ SV333 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1679,plain,
! [SV334: product_prod_nat_nat > b] :
( ( ( dist_b @ SV334 )
= ( dist_b @ SV334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1680,plain,
! [SV335: product_prod_nat_nat > a] :
( ( ( dist_a @ SV335 )
= ( dist_a @ SV335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1681,plain,
! [SV336: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV336 )
= ( isShortestPath_a @ SV336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1682,plain,
! [SV337: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV337 )
= ( isShortestPath_b @ SV337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1683,plain,
! [SV52: nat] :
( ( ord_less_nat @ SV52 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1684,plain,
! [SV53: nat] :
( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ( SV53 = zero_zero_nat ) )
| ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ( SV53 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1347]) ).
thf(1685,plain,
! [SV53: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 ) )
= ( SV53 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1347]) ).
thf(1686,plain,
! [SV54: nat] :
( ( ord_less_nat @ SV54 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1687,plain,
! [SV55: nat] :
( ( ord_less_nat @ SV55 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1688,plain,
! [SV56: nat] :
( ( ord_less_nat @ SV56 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1689,plain,
! [SV338: nat,SV57: product_prod_nat_nat > a] :
( ( ( min_dist_a @ SV57 @ SV338 @ SV338 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1690,plain,
! [SV339: nat,SV58: product_prod_nat_nat > b] :
( ( ( min_dist_b @ SV58 @ SV339 @ SV339 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1691,plain,
! [SV340: nat,SV59: product_prod_nat_nat > b] :
( ( dist_b @ SV59 @ SV340 @ zero_zero_nat @ SV340 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1692,plain,
! [SV341: nat,SV60: product_prod_nat_nat > a] :
( ( dist_a @ SV60 @ SV341 @ zero_zero_nat @ SV341 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1693,plain,
! [SV342: nat,SV61: product_prod_nat_nat > b] :
( ( ! [SY1110: nat] :
( ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SY1110 )
= ( SY1110 = SV342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1694,plain,
! [SV343: nat,SV62: product_prod_nat_nat > a] :
( ( ! [SY1111: nat] :
( ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SY1111 )
= ( SY1111 = SV343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1695,plain,
! [SV344: nat,SV63: nat] :
( ( ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
= ( SV344 = SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1696,plain,
! [SV345: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV345 )
= ( isSimplePath_a @ SV345 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1697,plain,
! [SV346: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV346 )
= ( isSimplePath_b @ SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1698,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( finite_Graph_b @ SV347 )
= ( finite_finite_nat @ ( v_b @ SV347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1699,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( finite_Graph_a @ SV348 )
= ( finite_finite_nat @ ( v_a @ SV348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1700,plain,
! [SV349: product_prod_nat_nat > a] :
( ( ( reachableNodes_a @ SV349 )
= ( reachableNodes_a @ SV349 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1701,plain,
! [SV350: product_prod_nat_nat > b] :
( ( ( reachableNodes_b @ SV350 )
= ( reachableNodes_b @ SV350 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1702,plain,
! [SV351: product_prod_nat_nat > b] :
( ( ( adjacent_nodes_b @ SV351 )
= ( adjacent_nodes_b @ SV351 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1703,plain,
! [SV352: product_prod_nat_nat > a] :
( ( ( adjacent_nodes_a @ SV352 )
= ( adjacent_nodes_a @ SV352 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1704,plain,
! [SV353: product_prod_nat_nat > a] :
( ( ( e_a @ SV353 )
= ( e_a @ SV353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1705,plain,
! [SV354: product_prod_nat_nat > b] :
( ( ( e_b @ SV354 )
= ( e_b @ SV354 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1706,plain,
! [SV355: nat,SV79: product_prod_nat_nat > b] :
( ( ord_less_eq_set_nat @ ( adjacent_nodes_b @ SV79 @ SV355 ) @ ( v_b @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1707,plain,
! [SV356: nat,SV80: product_prod_nat_nat > a] :
( ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ SV80 @ SV356 ) @ ( v_a @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1708,plain,
! [SV357: product_prod_nat_nat > a] :
( ( ( incoming_a @ SV357 )
= ( incoming_a @ SV357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1709,plain,
! [SV358: product_prod_nat_nat > b] :
( ( ( incoming_b @ SV358 )
= ( incoming_b @ SV358 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1710,plain,
! [SV359: product_prod_nat_nat > a] :
( ( ( outgoing_a @ SV359 )
= ( outgoing_a @ SV359 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1711,plain,
! [SV360: product_prod_nat_nat > b] :
( ( ( outgoing_b @ SV360 )
= ( outgoing_b @ SV360 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1712,plain,
! [SV361: set_nat,SV87: product_prod_nat_nat > a] :
( ( ord_le841296385at_nat @ ( outgoing_a @ SV87 @ SV361 ) @ ( e_a @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1713,plain,
! [SV362: set_nat,SV88: product_prod_nat_nat > b] :
( ( ord_le841296385at_nat @ ( outgoing_b @ SV88 @ SV362 ) @ ( e_b @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1714,plain,
! [SV363: set_nat,SV89: product_prod_nat_nat > a] :
( ( ord_le841296385at_nat @ ( incoming_a @ SV89 @ SV363 ) @ ( e_a @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1715,plain,
! [SV364: set_nat,SV90: product_prod_nat_nat > b] :
( ( ord_le841296385at_nat @ ( incoming_b @ SV90 @ SV364 ) @ ( e_b @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1716,plain,
! [SV93: nat] :
( ( ~ ( ( SV93 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV93 ) )
| ~ ( ~ ( ( SV93 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV93 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1402]) ).
thf(1717,plain,
! [SV93: nat] :
( ( ( SV93 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV93 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1402]) ).
thf(1718,plain,
! [SV94: product_prod_nat_nat > b] :
( ( ( ~ ( finite_Graph_b @ SV94 ) )
= $true )
| ( ( finite_finite_nat @ ( v_b @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1719,plain,
! [SV365: list_P559422087at_nat,SV95: nat] :
( ( ! [SY1112: nat] :
( ~ ( member_nat @ SV95 @ ( v_a @ c ) )
| ~ ( isSimplePath_a @ c @ SV95 @ SV365 @ SY1112 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV365 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1720,plain,
! [SV366: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV366 )
= ( ^ [SY1113: nat,SY1114: list_P559422087at_nat,SY1115: nat] :
~ ( ~ ( isSimplePath_a @ SV366 @ SY1113 @ SY1114 @ SY1115 )
| ( ( size_s1990949619at_nat @ SY1114 )
!= ( min_dist_a @ SV366 @ SY1113 @ SY1115 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1721,plain,
! [SV367: list_P559422087at_nat,SV97: nat] :
( ( ! [SY1116: nat] :
( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SY1116 )
= ( ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SY1116 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SY1116 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1722,plain,
! [SV98: product_prod_nat_nat > a] :
( ( ( ~ ( finite_Graph_a @ SV98 ) )
= $true )
| ( ( finite772653738at_nat @ ( e_a @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1723,plain,
! [SV99: set_nat] :
( ( ( ~ ( finite_finite_nat @ ( v_a @ c ) ) )
= $true )
| ( ( finite772653738at_nat @ ( outgoing_a @ c @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1724,plain,
! [SV368: product_prod_nat_nat > b,SV100: nat] :
( ( ~ ( member_nat @ SV100 @ ( v_b @ SV368 ) )
| ( ord_less_eq_set_nat @ ( reachableNodes_b @ SV368 @ SV100 ) @ ( v_b @ SV368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1725,plain,
! [SV101: nat] :
( ( ~ ( ( SV101 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV101 ) )
| ~ ( ~ ( ( SV101 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV101 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1411]) ).
thf(1726,plain,
! [SV101: nat] :
( ( ( SV101 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV101 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1411]) ).
thf(1727,plain,
! [SV369: set_nat,SV102: set_nat] :
( ( ~ ! [SY1117: nat] :
( ~ ( member_nat @ SY1117 @ SV102 )
| ( member_nat @ SY1117 @ SV369 ) )
| ( ord_less_eq_set_nat @ SV102 @ SV369 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1728,plain,
! [SV370: nat,SV103: product_prod_nat_nat > a] :
( ( ! [SY1118: list_P559422087at_nat,SY1119: nat] :
( ~ ( finite_Graph_a @ SV103 )
| ~ ( member_nat @ SV370 @ ( v_a @ SV103 ) )
| ~ ( isShortestPath_a @ SV103 @ SV370 @ SY1118 @ SY1119 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY1118 ) @ ( finite_card_nat @ ( v_a @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1729,plain,
! [SV371: nat,SV104: product_prod_nat_nat > a] :
( ( ~ ( finite_Graph_a @ SV104 )
| ( finite_finite_nat @ ( adjacent_nodes_a @ SV104 @ SV371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1730,plain,
! [SV372: set_nat] :
( ( ( ^ [SY1120: set_nat] : ( SV372 = SY1120 ) )
= ( ^ [SY1121: set_nat] :
~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SY1121 )
| ~ ( ord_less_eq_set_nat @ SY1121 @ SV372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1731,plain,
! [SV373: nat,SV106: product_prod_nat_nat > b] :
( ( ! [SY1122: list_P559422087at_nat,SY1123: nat] :
( ~ ( finite_Graph_b @ SV106 )
| ~ ( member_nat @ SV373 @ ( v_b @ SV106 ) )
| ~ ( isShortestPath_b @ SV106 @ SV373 @ SY1122 @ SY1123 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY1122 ) @ ( finite_card_nat @ ( v_b @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1732,plain,
! [SV374: nat,SV107: product_prod_nat_nat > a] :
( ( ! [SY1124: list_P559422087at_nat,SY1125: nat] :
( ~ ( isShortestPath_a @ SV107 @ SV374 @ SY1124 @ SY1125 )
| ( isPath_a @ SV107 @ SV374 @ SY1124 @ SY1125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1733,plain,
! [SV375: nat,SV108: nat] :
( ( ~ ( ord_less_nat @ SV108 @ SV375 )
| ( SV108 != SV375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1734,plain,
! [SV376: nat,SV109: nat] :
( ( ( SV109 != SV376 )
| ( ord_less_eq_nat @ SV109 @ SV376 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1735,plain,
! [SV377: nat > $o,SV110: nat > $o] :
( ( ~ ! [SY1126: nat] :
( ( SV110 @ SY1126 )
= ( SV377 @ SY1126 ) )
| ( ( collect_nat @ SV110 )
= ( collect_nat @ SV377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1736,plain,
! [SV378: nat,SV111: product_prod_nat_nat > a] :
( ( ! [SY1127: nat] :
( ~ ( connected_a @ SV111 @ SV378 @ SY1127 )
| ( ( member_nat @ SY1127 @ ( v_a @ SV111 ) )
= ( member_nat @ SV378 @ ( v_a @ SV111 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1737,plain,
! [SV379: nat,SV112: nat] :
( ( ! [SY1128: nat] :
( ~ ( dist_a @ c @ SV112 @ SV379 @ SY1128 )
| ~ ! [SY1129: nat] :
( ~ ( dist_a @ c @ SV112 @ SY1129 @ SY1128 )
| ( ord_less_eq_nat @ SV379 @ SY1129 ) )
| ( ( min_dist_a @ c @ SV112 @ SY1128 )
= SV379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1738,plain,
! [SV380: product_prod_nat_nat > b] :
( ( ( dist_b @ SV380 )
= ( ^ [SY1130: nat,SY1131: nat,SY1132: nat] :
~ ! [SY1133: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SY1130 @ SY1133 @ SY1132 )
| ( ( size_s1990949619at_nat @ SY1133 )
!= SY1131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1739,plain,
! [SV381: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV381 )
= ( ^ [SY1134: nat,SY1135: list_P559422087at_nat,SY1136: nat] :
~ ( ~ ( isPath_a @ SV381 @ SY1134 @ SY1135 @ SY1136 )
| ~ ! [SY1137: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SY1134 @ SY1137 @ SY1136 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY1135 ) @ ( size_s1990949619at_nat @ SY1137 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1740,plain,
! [SV115: product_prod_nat_nat > b] :
( ( ( ~ ( edmond1517640973ysis_b @ SV115 ) )
= $true )
| ( ( finite772653738at_nat @ ( edmond771116671s_uE_b @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1428]) ).
thf(1741,plain,
! [SV382: nat,SV116: product_prod_nat_nat > a] :
( ( ! [SY1138: nat,SY1139: nat] :
( ~ ( dist_a @ SV116 @ SV382 @ SY1138 @ SY1139 )
| ~ ! [SY1140: nat] :
( ~ ( dist_a @ SV116 @ SV382 @ SY1140 @ SY1139 )
| ( ord_less_eq_nat @ SY1138 @ SY1140 ) )
| ( ( min_dist_a @ SV116 @ SV382 @ SY1139 )
= SY1138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1742,plain,
! [SV383: nat,SV117: nat] :
( ( ~ ( connected_b @ c2 @ SV117 @ SV383 )
| ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
= zero_zero_nat )
= ( SV383 = SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1743,plain,
! [SV384: nat,SV118: nat] :
( ( ! [SY1141: nat] :
( ( dist_a @ c @ SV118 @ SV384 @ SY1141 )
= ( ~ ! [SY1142: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1142 @ SY1141 )
| ( ( size_s1990949619at_nat @ SY1142 )
!= SV384 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1744,plain,
! [SV385: set_Pr1986765409at_nat,SV119: set_Pr1986765409at_nat] :
( ( ~ ( finite772653738at_nat @ SV119 )
| ~ ( ord_le116442893at_nat @ SV385 @ SV119 )
| ( ord_less_nat @ ( finite447719721at_nat @ SV385 ) @ ( finite447719721at_nat @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1745,plain,
! [SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ! [SY1143: nat,SY1144: nat,SY1145: nat] :
( ~ ( connected_a @ SV120 @ SV386 @ SY1143 )
| ( ( min_dist_a @ SV120 @ SV386 @ SY1143 )
!= SY1144 )
| ~ ( ord_less_nat @ SY1145 @ SY1144 )
| ~ ! [SY1146: nat] :
~ ~ ( ~ ( connected_a @ SV120 @ SV386 @ SY1146 )
| ( ( min_dist_a @ SV120 @ SV386 @ SY1146 )
!= SY1145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1746,plain,
! [SV387: product_prod_nat_nat > a] :
( ( ( connected_a @ SV387 )
= ( ^ [SY1147: nat,SY1148: nat] :
~ ! [SY1149: nat] :
~ ( dist_a @ SV387 @ SY1147 @ SY1149 @ SY1148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1747,plain,
! [SV122: set_nat] :
( ( ( ~ ( finite_finite_nat @ ( v_b @ c2 ) ) )
= $true )
| ( ( finite772653738at_nat @ ( outgoing_b @ c2 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1748,plain,
! [SV123: product_prod_nat_nat > a] :
( ( ( ~ ( edmond1517640972ysis_a @ SV123 ) )
= $true )
| ( ( ord_le841296385at_nat @ ( e_a @ SV123 ) @ ( edmond771116670s_uE_a @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1749,plain,
! [SV388: nat,SV124: product_prod_nat_nat > a] :
( ( ! [SY1150: nat] :
( ~ ( connected_a @ SV124 @ SV388 @ SY1150 )
| ~ ! [SY1151: list_P559422087at_nat] :
~ ( isShortestPath_a @ SV124 @ SV388 @ SY1151 @ SY1150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1750,plain,
! [SV125: product_prod_nat_nat > b] :
( ( ( ~ ( finite_finite_nat @ ( v_b @ SV125 ) ) )
= $true )
| ( ( finite772653738at_nat @ ( e_b @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1751,plain,
! [SV389: set_nat,SV126: set_nat] :
( ( ~ ( finite_finite_nat @ SV126 )
| ~ ( ord_less_eq_set_nat @ SV389 @ SV126 )
| ( ord_less_eq_nat @ ( finite_card_nat @ SV389 ) @ ( finite_card_nat @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1752,plain,
! [SV390: nat,SV127: product_prod_nat_nat > b] :
( ( ! [SY1152: nat] :
( ~ ( connected_b @ SV127 @ SV390 @ SY1152 )
| ( dist_b @ SV127 @ SV390 @ ( min_dist_b @ SV127 @ SV390 @ SY1152 ) @ SY1152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1753,plain,
! [SV391: nat,SV128: nat] :
( ( ! [SY1153: nat,SY1154: nat] :
( ~ ( connected_b @ c2 @ SV128 @ SV391 )
| ( ( min_dist_b @ c2 @ SV128 @ SV391 )
!= SY1153 )
| ~ ( ord_less_nat @ SY1154 @ SY1153 )
| ~ ! [SY787: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV128 @ SY787 )
| ( ( min_dist_b @ c2 @ SV128 @ SY787 )
!= SY1154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1754,plain,
! [SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ! [SY1156: nat,SY1157: nat > $o] :
( ~ ( connected_a @ SV129 @ SV392 @ SY1156 )
| ~ ! [SY1158: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1158 @ SY1156 )
| ~ ! [SY1159: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1159 @ SY1156 )
| ( ord_less_eq_nat @ SY1158 @ SY1159 ) )
| ( SY1157 @ SY1158 ) )
| ( SY1157 @ ( min_dist_a @ SV129 @ SV392 @ SY1156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1755,plain,
! [SV130: nat] :
( ( ! [SY793: list_P559422087at_nat] :
( ( size_s1990949619at_nat @ SY793 )
!= SV130 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1756,plain,
! [SV393: set_set_nat,SV131: set_set_nat] :
( ( ~ ( ord_le1613022364et_nat @ SV131 @ SV393 )
| ~ ( finite2012248349et_nat @ SV393 )
| ( finite2012248349et_nat @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1757,plain,
! [SV394: nat,SV132: nat] :
( ( ~ ( connected_b @ c2 @ SV132 @ SV394 )
| ( dist_b @ c2 @ SV132 @ ( min_dist_b @ c2 @ SV132 @ SV394 ) @ SV394 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1758,plain,
( ( ( ~ ( connected_b @ c2 @ s @ t ) )
= $false )
| ( ( ord_less_nat @ ( edmond1022345717sure_b @ c2 @ s @ t ) @ ( edmond1022345716sure_a @ c @ s @ t ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1759,plain,
! [SV395: set_nat,SV133: set_nat] :
( ( ~ ( finite_finite_nat @ SV133 )
| ~ ( ord_less_eq_set_nat @ SV395 @ SV133 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV133 ) @ ( finite_card_nat @ SV395 ) )
| ( SV395 = SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1760,plain,
! [SV396: nat,SV134: product_prod_nat_nat > b] :
( ( ! [SY1160: nat,SY1161: nat] :
( ~ ( connected_b @ SV134 @ SV396 @ SY1160 )
| ~ ( ord_less_eq_nat @ SY1161 @ ( min_dist_b @ SV134 @ SV396 @ SY1160 ) )
| ~ ! [SY1162: nat] :
~ ~ ( ~ ( connected_b @ SV134 @ SV396 @ SY1162 )
| ( ( min_dist_b @ SV134 @ SV396 @ SY1162 )
!= SY1161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1761,plain,
! [SV397: nat,SV135: nat] :
( ( ~ ( connected_b @ c2 @ SV135 @ SV397 )
| ~ ! [SY1163: list_P559422087at_nat] :
~ ( isShortestPath_b @ c2 @ SV135 @ SY1163 @ SV397 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1762,plain,
! [SV398: nat,SV136: nat] :
( ( ( connected_a @ c @ SV136 @ SV398 )
= ( ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1763,plain,
! [SV399: nat,SV137: set_nat] :
( ( ~ ( finite_finite_nat @ SV137 )
| ~ ( member_nat @ SV399 @ SV137 )
| ~ ! [SY1165: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY1165 @ SV137 )
| ~ ( ord_less_eq_nat @ SY1165 @ SV399 ) )
| ~ ! [SY807: nat] :
( ~ ( member_nat @ SY807 @ SV137 )
| ~ ( ord_less_eq_nat @ SY807 @ SY1165 )
| ( SY1165 = SY807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1764,plain,
! [SV400: nat,SV138: product_prod_nat_nat > a] :
( ( ! [SY1167: list_P559422087at_nat,SY1168: nat] :
( ~ ( finite_Graph_a @ SV138 )
| ~ ( member_nat @ SV400 @ ( v_a @ SV138 ) )
| ~ ( isSimplePath_a @ SV138 @ SV400 @ SY1167 @ SY1168 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY1167 ) @ ( finite_card_nat @ ( v_a @ SV138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1765,plain,
! [SV401: nat,SV139: product_prod_nat_nat > b] :
( ( ! [SY1169: list_P559422087at_nat,SY1170: nat] :
( ~ ( isPath_b @ SV139 @ SV401 @ SY1169 @ SY1170 )
| ~ ! [SY1171: list_P559422087at_nat] :
~ ( isSimplePath_b @ SV139 @ SV401 @ SY1171 @ SY1170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1766,plain,
! [SV140: nat] :
( ( ( ~ ( member_nat @ SV140 @ ( v_a @ c ) ) )
= $true )
| ( ( ord_less_eq_set_nat @ ( reachableNodes_a @ c @ SV140 ) @ ( v_a @ c ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1455]) ).
thf(1767,plain,
! [SV402: set_nat,SV141: product_prod_nat_nat > a] :
( ( ~ ( finite_finite_nat @ ( v_a @ SV141 ) )
| ( finite772653738at_nat @ ( incoming_a @ SV141 @ SV402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1768,plain,
! [SV403: nat,SV142: nat] :
( ( ! [SY1172: nat] :
( ~ ( connected_b @ c2 @ SV142 @ SV403 )
| ~ ( ord_less_eq_nat @ SY1172 @ ( min_dist_b @ c2 @ SV142 @ SV403 ) )
| ~ ! [SY818: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV142 @ SY818 )
| ( ( min_dist_b @ c2 @ SV142 @ SY818 )
!= SY1172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1769,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ~ ~ ( finite772653738at_nat @ SV143 )
| ~ ! [SY1174: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( finite772653738at_nat @ SY1174 )
| ( ( finite447719721at_nat @ SY1174 )
!= SV404 ) )
| ~ ( ord_le841296385at_nat @ SY1174 @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1770,plain,
! [SV405: set_nat,SV144: set_nat] :
( ( ~ ( ord_less_eq_set_nat @ SV144 @ SV405 )
| ~ ( ord_less_eq_set_nat @ SV405 @ SV144 )
| ( SV144 = SV405 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1771,plain,
! [SV406: nat,SV145: product_prod_nat_nat > a] :
( ( ! [SY1175: list_P559422087at_nat,SY1176: nat] :
( ~ ( isPath_a @ SV145 @ SV406 @ SY1175 @ SY1176 )
| ( dist_a @ SV145 @ SV406 @ ( size_s1990949619at_nat @ SY1175 ) @ SY1176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1772,plain,
! [SV407: nat,SV146: nat] :
( ( ( connected_a @ c @ SV146 @ SV407 )
= ( ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1773,plain,
! [SV408: nat,SV147: product_prod_nat_nat > b] :
( ( ! [SY1178: nat,SY1179: nat] :
( ~ ( dist_b @ SV147 @ SV408 @ SY1178 @ SY1179 )
| ~ ! [SY1180: nat] :
( ~ ( dist_b @ SV147 @ SV408 @ SY1180 @ SY1179 )
| ( ord_less_eq_nat @ SY1178 @ SY1180 ) )
| ( ( min_dist_b @ SV147 @ SV408 @ SY1179 )
= SY1178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1774,plain,
! [SV409: nat,SV148: product_prod_nat_nat > a] :
( ( ! [SY1181: nat] :
( ~ ( edmond1517640972ysis_a @ SV148 )
| ( ord_le841296385at_nat @ ( edmond475474835dges_a @ SV148 @ SV409 @ SY1181 ) @ ( e_a @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1775,plain,
! [SV410: nat,SV149: product_prod_nat_nat > a] :
( ( ! [SY1182: nat,SY1183: nat] :
( ~ ( dist_a @ SV149 @ SV410 @ SY1182 @ SY1183 )
| ( ord_less_eq_nat @ ( min_dist_a @ SV149 @ SV410 @ SY1183 ) @ SY1182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1776,plain,
! [SV150: product_prod_nat_nat > b] :
( ( ( ~ ( finite_Graph_b @ SV150 ) )
= $true )
| ( ( finite772653738at_nat @ ( e_b @ SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1465]) ).
thf(1777,plain,
! [SV411: nat,SV151: product_prod_nat_nat > a] :
( ( ! [SY1184: nat,SY1185: nat] :
( ~ ( connected_a @ SV151 @ SV411 @ SY1184 )
| ~ ( ord_less_eq_nat @ SY1185 @ ( min_dist_a @ SV151 @ SV411 @ SY1184 ) )
| ~ ! [SY1186: nat] :
~ ~ ( ~ ( connected_a @ SV151 @ SV411 @ SY1186 )
| ( ( min_dist_a @ SV151 @ SV411 @ SY1186 )
!= SY1185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1778,plain,
! [SV152: product_prod_nat_nat > a] :
( ( ( ~ ( edmond1517640972ysis_a @ SV152 ) )
= $true )
| ( ( finite772653738at_nat @ ( edmond771116670s_uE_a @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1467]) ).
thf(1779,plain,
! [SV412: nat,SV153: product_prod_nat_nat > b] :
( ( ! [SY1187: list_P559422087at_nat,SY1188: nat] :
( ~ ( isShortestPath_b @ SV153 @ SV412 @ SY1187 @ SY1188 )
| ( isPath_b @ SV153 @ SV412 @ SY1187 @ SY1188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1780,plain,
! [SV413: nat,SV154: nat] :
( ( ~ ( ord_less_eq_nat @ SV154 @ SV413 )
| ~ ( ( SV154 != SV413 ) )
| ( ord_less_nat @ SV154 @ SV413 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1781,plain,
! [SV414: set_nat,SV155: product_prod_nat_nat > b] :
( ( ~ ( finite_finite_nat @ ( v_b @ SV155 ) )
| ( finite772653738at_nat @ ( outgoing_b @ SV155 @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1782,plain,
! [SV156: product_prod_nat_nat > a] :
( ( ( ~ ( finite_finite_nat @ ( v_a @ SV156 ) ) )
= $true )
| ( ( finite772653738at_nat @ ( e_a @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1471]) ).
thf(1783,plain,
! [SV415: set_Pr1986765409at_nat,SV157: set_Pr1986765409at_nat] :
( ( ~ ( ord_le841296385at_nat @ SV157 @ SV415 )
| ~ ( ( SV157 != SV415 ) )
| ( ord_le116442893at_nat @ SV157 @ SV415 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1784,plain,
! [SV416: list_P559422087at_nat,SV158: nat] :
( ( ! [SY1189: nat] :
( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SY1189 )
= ( ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SY1189 )
| ~ ! [SY1190: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1190 @ SY1189 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1190 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1785,plain,
! [SV417: nat,SV159: nat > $o] :
( ( ! [SY1191: nat] :
( ~ ( SV159 @ SV417 )
| ~ ! [SY851: nat] :
( ~ ( SV159 @ SY851 )
| ( ord_less_eq_nat @ SY851 @ SY1191 ) )
| ~ ! [SY852: nat] :
~ ~ ( ~ ( SV159 @ SY852 )
| ~ ! [SY853: nat] :
( ~ ( SV159 @ SY853 )
| ( ord_less_eq_nat @ SY853 @ SY852 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1786,plain,
! [SV418: nat,SV160: nat] :
( ( ~ ( member_nat @ SV160 @ ( v_a @ c ) )
| ~ ( connected_a @ c @ SV160 @ SV418 )
| ( ord_less_nat @ ( min_dist_a @ c @ SV160 @ SV418 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1787,plain,
! [SV419: nat,SV161: product_prod_nat_nat > b] :
( ( ! [SY1195: nat] :
( ~ ( edmond1517640973ysis_b @ SV161 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474836dges_b @ SV161 @ SV419 @ SY1195 ) ) @ ( finite447719721at_nat @ ( edmond771116671s_uE_b @ SV161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1788,plain,
! [SV420: nat,SV162: nat] :
( ( ! [SY1196: nat] :
( ~ ( dist_a @ c @ SV162 @ SV420 @ SY1196 )
| ( ord_less_eq_nat @ ( min_dist_a @ c @ SV162 @ SY1196 ) @ SV420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1789,plain,
! [SV421: nat,SV163: nat] :
( ( ! [SY1197: nat] :
( ( dist_b @ c2 @ SV163 @ SV421 @ SY1197 )
= ( ~ ! [SY1198: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1198 @ SY1197 )
| ( ( size_s1990949619at_nat @ SY1198 )
!= SV421 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1790,plain,
! [SV422: set_nat,SV164: set_set_nat] :
( ( ~ ( finite2012248349et_nat @ SV164 )
| ~ ( member_set_nat @ SV422 @ SV164 )
| ~ ! [SY1199: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SY1199 @ SV164 )
| ~ ( ord_less_eq_set_nat @ SV422 @ SY1199 ) )
| ~ ! [SY864: set_nat] :
( ~ ( member_set_nat @ SY864 @ SV164 )
| ~ ( ord_less_eq_set_nat @ SY1199 @ SY864 )
| ( SY1199 = SY864 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1791,plain,
! [SV423: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV423 )
= ( ^ [SY1201: nat,SY1202: list_P559422087at_nat,SY1203: nat] :
~ ( ~ ( isPath_b @ SV423 @ SY1201 @ SY1202 @ SY1203 )
| ~ ! [SY1204: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SY1201 @ SY1204 @ SY1203 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY1202 ) @ ( size_s1990949619at_nat @ SY1204 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1792,plain,
! [SV424: nat,SV166: product_prod_nat_nat > a] :
( ( ! [SY1205: nat] :
( ~ ( edmond1517640972ysis_a @ SV166 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ SV166 @ SV424 @ SY1205 ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ SV166 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1793,plain,
! [SV425: nat,SV167: nat > nat] :
( ( ! [SY1206: nat] :
( ~ ! [SY873: nat,SY874: nat] :
( ~ ( ord_less_nat @ SY873 @ SY874 )
| ( ord_less_nat @ ( SV167 @ SY873 ) @ ( SV167 @ SY874 ) ) )
| ~ ( ord_less_eq_nat @ SV425 @ SY1206 )
| ( ord_less_eq_nat @ ( SV167 @ SV425 ) @ ( SV167 @ SY1206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1794,plain,
! [SV426: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV426 )
= ( ^ [SY1209: nat,SY1210: list_P559422087at_nat,SY1211: nat] :
~ ( ~ ( isPath_a @ SV426 @ SY1209 @ SY1210 @ SY1211 )
| ( ( size_s1990949619at_nat @ SY1210 )
!= ( min_dist_a @ SV426 @ SY1209 @ SY1211 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1795,plain,
! [SV169: set_nat] :
( ( ( ~ ( finite_finite_nat @ ( v_b @ c2 ) ) )
= $true )
| ( ( finite772653738at_nat @ ( incoming_b @ c2 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1486]) ).
thf(1796,plain,
! [SV170: product_prod_nat_nat > a] :
( ( ( ~ ( finite_finite_nat @ ( v_a @ SV170 ) ) )
= $true )
| ( ( finite_Graph_a @ SV170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1487]) ).
thf(1797,plain,
! [SV427: nat,SV171: nat > $o] :
( ( ~ ! [SY879: nat] :
( ~ ~ ( SV171 @ SY879 )
| ~ ! [SY880: nat] :
~ ~ ( ~ ( ord_less_nat @ SY880 @ SY879 )
| ~ ~ ( SV171 @ SY880 ) ) )
| ( SV171 @ SV427 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1798,plain,
! [SV172: nat] :
( ( ( ~ ( ( SV172 != zero_zero_nat ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV172 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1799,plain,
! [SV428: set_Pr1986765409at_nat,SV173: set_se1612935105at_nat] :
( ( ~ ( finite1457549322at_nat @ SV173 )
| ~ ( member298845450at_nat @ SV428 @ SV173 )
| ~ ! [SY1214: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SY1214 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY1214 @ SV428 ) )
| ~ ! [SY883: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY883 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY883 @ SY1214 )
| ( SY1214 = SY883 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1800,plain,
! [SV429: list_P559422087at_nat,SV174: list_P559422087at_nat > $o] :
( ( ~ ! [SY885: list_P559422087at_nat] :
( ~ ! [SY886: list_P559422087at_nat] :
( ~ ( ord_less_nat @ ( size_s1990949619at_nat @ SY886 ) @ ( size_s1990949619at_nat @ SY885 ) )
| ( SV174 @ SY886 ) )
| ( SV174 @ SY885 ) )
| ( SV174 @ SV429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1801,plain,
! [SV430: set_nat,SV175: set_nat] :
( ( ! [SY1218: set_nat] :
( ~ ( ord_less_eq_set_nat @ SV175 @ SV430 )
| ~ ( ord_less_eq_set_nat @ SV430 @ SY1218 )
| ( ord_less_eq_set_nat @ SV175 @ SY1218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1802,plain,
! [SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ! [SY1219: nat,SY1220: nat > $o] :
( ~ ( connected_b @ SV176 @ SV431 @ SY1219 )
| ~ ! [SY1221: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1221 @ SY1219 )
| ~ ! [SY1222: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1222 @ SY1219 )
| ( ord_less_eq_nat @ SY1221 @ SY1222 ) )
| ( SY1220 @ SY1221 ) )
| ( SY1220 @ ( min_dist_b @ SV176 @ SV431 @ SY1219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1803,plain,
! [SV432: set_Pr1986765409at_nat,SV177: set_se1612935105at_nat] :
( ( ~ ( finite1457549322at_nat @ SV177 )
| ~ ( member298845450at_nat @ SV432 @ SV177 )
| ~ ! [SY1223: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SY1223 @ SV177 )
| ~ ( ord_le841296385at_nat @ SV432 @ SY1223 ) )
| ~ ! [SY896: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY896 @ SV177 )
| ~ ( ord_le841296385at_nat @ SY1223 @ SY896 )
| ( SY1223 = SY896 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1804,plain,
! [SV433: nat,SV178: nat] :
( ( ~ ( connected_b @ c2 @ SV178 @ SV433 )
| ( ( member_nat @ SV433 @ ( v_b @ c2 ) )
= ( member_nat @ SV178 @ ( v_b @ c2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1805,plain,
! [SV179: product_prod_nat_nat > a] :
( ( ( ~ ( finite772653738at_nat @ ( e_a @ SV179 ) ) )
= $true )
| ( ( finite_Graph_a @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1806,plain,
! [SV434: nat,SV180: nat] :
( ( ! [SY1225: nat] :
( ~ ( dist_b @ c2 @ SV180 @ SV434 @ SY1225 )
| ( connected_b @ c2 @ SV180 @ SY1225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1807,plain,
! [SV435: list_P559422087at_nat,SV181: nat] :
( ( ! [SY1226: nat] :
( ~ ( isPath_b @ c2 @ SV181 @ SV435 @ SY1226 )
| ( dist_b @ c2 @ SV181 @ ( size_s1990949619at_nat @ SV435 ) @ SY1226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1808,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
= ( ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1809,plain,
! [SV437: set_Pr1986765409at_nat] :
( ( ( ^ [SY1228: set_Pr1986765409at_nat] : ( SV437 = SY1228 ) )
= ( ^ [SY1229: set_Pr1986765409at_nat] :
~ ( ~ ( ord_le841296385at_nat @ SV437 @ SY1229 )
| ~ ( ord_le841296385at_nat @ SY1229 @ SV437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1810,plain,
! [SV438: set_Pr1986765409at_nat > $o,SV184: set_Pr1986765409at_nat] :
( ( ~ ( finite772653738at_nat @ SV184 )
| ~ ! [SY1230: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SY1230 )
| ~ ! [SY1231: set_Pr1986765409at_nat] :
( ~ ( ord_le116442893at_nat @ SY1231 @ SY1230 )
| ( SV438 @ SY1231 ) )
| ( SV438 @ SY1230 ) )
| ( SV438 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1811,plain,
! [SV439: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV439 )
= ( ^ [SY1232: nat,SY1233: list_P559422087at_nat,SY1234: nat] :
~ ( ~ ( isPath_b @ SV439 @ SY1232 @ SY1233 @ SY1234 )
| ( ( size_s1990949619at_nat @ SY1233 )
!= ( min_dist_b @ SV439 @ SY1232 @ SY1234 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1812,plain,
( ( ( finite_finite_nat @ ( v_a @ c ) )
= $false )
| ( ( finite772653738at_nat @ ( e_a @ c ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1813,plain,
! [SV440: nat,SV186: nat] :
( ( ~ ( ord_less_eq_nat @ SV186 @ SV440 )
| ~ ( ord_less_eq_nat @ SV440 @ SV186 )
| ( SV186 = SV440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1814,plain,
! [SV441: nat,SV187: nat] :
( ( ~ ( ord_less_nat @ SV187 @ SV441 )
| ( SV441 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1815,plain,
! [SV442: product_prod_nat_nat > a] :
( ( ( connected_a @ SV442 )
= ( ^ [SY1235: nat,SY1236: nat] :
~ ! [SY1237: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SY1235 @ SY1237 @ SY1236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1816,plain,
! [SV443: list_P559422087at_nat,SV189: nat] :
( ( ! [SY1238: nat] :
( ~ ( isShortestPath_a @ c @ SV189 @ SV443 @ SY1238 )
| ( isSimplePath_a @ c @ SV189 @ SV443 @ SY1238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1817,plain,
! [SV444: set_nat,SV190: set_nat] :
( ( ~ ( finite_finite_nat @ SV190 )
| ~ ( ord_less_eq_set_nat @ SV444 @ SV190 )
| ~ ( ord_less_nat @ ( finite_card_nat @ SV444 ) @ ( finite_card_nat @ SV190 ) )
| ( ord_less_set_nat @ SV444 @ SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1818,plain,
! [SV445: nat,SV191: nat] :
( ( ~ ( connected_a @ c @ SV191 @ SV445 )
| ( ( ( min_dist_a @ c @ SV191 @ SV445 )
= zero_zero_nat )
= ( SV445 = SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1819,plain,
! [SV446: nat,SV192: nat > $o] :
( ( ~ ! [SY922: nat] :
( ~ ! [SY923: nat] :
( ~ ( ord_less_nat @ SY923 @ SY922 )
| ( SV192 @ SY923 ) )
| ( SV192 @ SY922 ) )
| ( SV192 @ SV446 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1820,plain,
! [SV447: nat,SV193: nat] :
( ( ~ ( connected_a @ c @ SV193 @ SV447 )
| ( ( member_nat @ SV447 @ ( v_a @ c ) )
= ( member_nat @ SV193 @ ( v_a @ c ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1821,plain,
! [SV448: set_nat,SV194: set_nat] :
( ( ~ ( ord_less_eq_set_nat @ SV194 @ SV448 )
| ~ ~ ( finite_finite_nat @ SV194 )
| ~ ( finite_finite_nat @ SV448 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1822,plain,
! [SV195: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( finite447719721at_nat @ SV195 ) ) )
= $true )
| ( ( finite772653738at_nat @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1516]) ).
thf(1823,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ~ ( SV196 @ SV449 )
| ~ ~ ( SV196 @ zero_zero_nat )
| ~ ! [SY1241: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_eq_nat @ SY1241 @ SV449 )
| ~ ! [SY928: nat] :
( ~ ( ord_less_nat @ SY928 @ SY1241 )
| ~ ( SV196 @ SY928 ) ) )
| ~ ( SV196 @ SY1241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1824,plain,
! [SV450: nat,SV197: nat] :
( ( ~ ( ord_less_nat @ SV197 @ SV450 )
| ( SV450 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1825,plain,
( ( ~ ( isPath_b @ c2 @ s @ sK1_SX0 @ t )
| ( ( size_s1990949619at_nat @ sK1_SX0 )
!= ( min_dist_b @ c2 @ s @ t ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1519]) ).
thf(1826,plain,
! [SV451: set_Pr1986765409at_nat,SV198: set_Pr1986765409at_nat] :
( ( ~ ( finite772653738at_nat @ SV198 )
| ~ ( ord_le841296385at_nat @ SV451 @ SV198 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV198 ) @ ( finite447719721at_nat @ SV451 ) )
| ( SV451 = SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1827,plain,
! [SV452: nat,SV199: product_prod_nat_nat > b] :
( ( ! [SY1243: nat] :
( ~ ( connected_b @ SV199 @ SV452 @ SY1243 )
| ~ ! [SY1244: list_P559422087at_nat] :
~ ( isShortestPath_b @ SV199 @ SV452 @ SY1244 @ SY1243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1828,plain,
! [SV453: nat,SV200: set_nat] :
( ( ~ ( finite_finite_nat @ SV200 )
| ~ ( member_nat @ SV453 @ SV200 )
| ~ ! [SY1245: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY1245 @ SV200 )
| ~ ( ord_less_eq_nat @ SV453 @ SY1245 ) )
| ~ ! [SY936: nat] :
( ~ ( member_nat @ SY936 @ SV200 )
| ~ ( ord_less_eq_nat @ SY1245 @ SY936 )
| ( SY1245 = SY936 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1829,plain,
! [SV454: nat,SV201: product_prod_nat_nat > a] :
( ( ! [SY1247: nat] :
( ~ ( finite_Graph_a @ SV201 )
| ~ ( member_nat @ SV454 @ ( v_a @ SV201 ) )
| ~ ( connected_a @ SV201 @ SV454 @ SY1247 )
| ( ord_less_nat @ ( min_dist_a @ SV201 @ SV454 @ SY1247 ) @ ( finite_card_nat @ ( v_a @ SV201 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1830,plain,
! [SV455: set_Pr1986765409at_nat,SV202: set_Pr1986765409at_nat] :
( ( ~ ( ord_le841296385at_nat @ SV202 @ SV455 )
| ~ ~ ( finite772653738at_nat @ SV202 )
| ~ ( finite772653738at_nat @ SV455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1831,plain,
! [SV456: nat,SV203: product_prod_nat_nat > b] :
( ( ! [SY1248: list_P559422087at_nat,SY1249: nat] :
( ~ ( isShortestPath_b @ SV203 @ SV456 @ SY1248 @ SY1249 )
| ( isSimplePath_b @ SV203 @ SV456 @ SY1248 @ SY1249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1832,plain,
! [SV204: set_nat] :
( ( ( ~ ~ ( finite_finite_nat @ SV204 ) )
= $true )
| ( ( ( finite_card_nat @ SV204 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1833,plain,
! [SV457: nat,SV205: nat] :
( ( ~ ( ( SV205 != SV457 ) )
| ~ ~ ( ord_less_nat @ SV205 @ SV457 )
| ( ord_less_nat @ SV457 @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1834,plain,
! [SV458: set_Pr1986765409at_nat,SV206: set_Pr1986765409at_nat] :
( ( ~ ( finite772653738at_nat @ SV206 )
| ~ ( ord_le841296385at_nat @ SV458 @ SV206 )
| ~ ( ord_less_nat @ ( finite447719721at_nat @ SV458 ) @ ( finite447719721at_nat @ SV206 ) )
| ( ord_le116442893at_nat @ SV458 @ SV206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1835,plain,
! [SV459: list_P559422087at_nat,SV207: nat] :
( ( ! [SY1250: nat] :
( ~ ( isPath_a @ c @ SV207 @ SV459 @ SY1250 )
| ( dist_a @ c @ SV207 @ ( size_s1990949619at_nat @ SV459 ) @ SY1250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1836,plain,
! [SV460: list_P559422087at_nat,SV208: nat] :
( ( ! [SY1251: nat] :
( ( isShortestPath_a @ c @ SV208 @ SV460 @ SY1251 )
= ( ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SY1251 )
| ~ ! [SY1252: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1252 @ SY1251 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1252 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1837,plain,
! [SV461: set_nat,SV209: set_nat] :
( ( ~ ( ord_less_eq_set_nat @ SV209 @ SV461 )
| ~ ( finite_finite_nat @ SV461 )
| ( finite_finite_nat @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1838,plain,
! [SV462: nat,SV210: nat] :
( ( ! [SY1253: nat > $o] :
( ~ ( connected_a @ c @ SV210 @ SV462 )
| ~ ! [SY1254: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1254 @ SV462 )
| ~ ! [SY1255: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1255 @ SV462 )
| ( ord_less_eq_nat @ SY1254 @ SY1255 ) )
| ( SY1253 @ SY1254 ) )
| ( SY1253 @ ( min_dist_a @ c @ SV210 @ SV462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1839,plain,
! [SV463: nat,SV211: nat] :
( ( ~ ( connected_a @ c @ SV211 @ SV463 )
| ( dist_a @ c @ SV211 @ ( min_dist_a @ c @ SV211 @ SV463 ) @ SV463 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1840,plain,
! [SV212: set_Pr1986765409at_nat] :
( ( ( ~ ~ ( finite772653738at_nat @ SV212 ) )
= $true )
| ( ( ( finite447719721at_nat @ SV212 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1534]) ).
thf(1841,plain,
! [SV464: set_nat,SV213: set_nat] :
( ( ~ ( finite_finite_nat @ SV213 )
| ~ ( ord_less_eq_set_nat @ SV464 @ SV213 )
| ( ( finite_card_nat @ SV464 )
!= ( finite_card_nat @ SV213 ) )
| ( SV464 = SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1842,plain,
! [SV465: nat,SV214: product_prod_nat_nat > b] :
( ( ! [SY1256: nat,SY1257: nat] :
( ~ ( dist_b @ SV214 @ SV465 @ SY1256 @ SY1257 )
| ( connected_b @ SV214 @ SV465 @ SY1257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1843,plain,
! [SV466: nat,SV215: nat] :
( ( ( connected_b @ c2 @ SV215 @ SV466 )
= ( ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1844,plain,
! [SV216: product_prod_nat_nat > a] :
( ( ( ~ ( finite_Graph_a @ SV216 ) )
= $true )
| ( ( edmond1517640972ysis_a @ SV216 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1538]) ).
thf(1845,plain,
! [SV467: nat,SV217: product_prod_nat_nat > b] :
( ( ! [SY1259: list_P559422087at_nat,SY1260: nat] :
( ~ ( finite_Graph_b @ SV217 )
| ~ ( member_nat @ SV467 @ ( v_b @ SV217 ) )
| ~ ( isSimplePath_b @ SV217 @ SV467 @ SY1259 @ SY1260 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY1259 ) @ ( finite_card_nat @ ( v_b @ SV217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1846,plain,
! [SV468: nat,SV218: nat] :
( ( ~ ( member_nat @ SV218 @ ( v_b @ c2 ) )
| ~ ( connected_b @ c2 @ SV218 @ SV468 )
| ( ord_less_nat @ ( min_dist_b @ c2 @ SV218 @ SV468 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1847,plain,
! [SV469: set_nat > $o,SV219: set_nat] :
( ( ~ ( finite_finite_nat @ SV219 )
| ~ ! [SY1261: set_nat] :
( ~ ( finite_finite_nat @ SY1261 )
| ~ ! [SY1262: set_nat] :
( ~ ( ord_less_set_nat @ SY1262 @ SY1261 )
| ( SV469 @ SY1262 ) )
| ( SV469 @ SY1261 ) )
| ( SV469 @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1848,plain,
! [SV470: nat,SV220: nat] :
( ( ( SV220 != SV470 )
= ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1849,plain,
! [SV471: list_P559422087at_nat,SV221: nat] :
( ( ! [SY1263: nat] :
( ~ ( isPath_b @ c2 @ SV221 @ SV471 @ SY1263 )
| ~ ! [SY972: list_P559422087at_nat] :
~ ( isSimplePath_b @ c2 @ SV221 @ SY972 @ SY1263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1850,plain,
! [SV472: nat,SV222: nat > $o] :
( ( ~ ( SV222 @ zero_zero_nat )
| ~ ! [SY974: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY974 )
| ~ ~ ( SV222 @ SY974 )
| ~ ! [SY975: nat] :
~ ~ ( ~ ( ord_less_nat @ SY975 @ SY974 )
| ~ ~ ( SV222 @ SY975 ) ) )
| ( SV222 @ SV472 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1851,plain,
! [SV473: set_nat,SV223: set_nat] :
( ( ~ ( ord_less_eq_set_nat @ SV223 @ SV473 )
| ~ ( ( SV223 != SV473 ) )
| ( ord_less_set_nat @ SV223 @ SV473 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1852,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ~ ! [SY1267: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SY1267 @ SV224 )
| ~ ( finite772653738at_nat @ SY1267 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ SY1267 ) @ SV474 ) )
| ~ ( ~ ( finite772653738at_nat @ SV224 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1853,plain,
! [SV475: product_prod_nat_nat > a,SV225: nat] :
( ( ~ ( member_nat @ SV225 @ ( v_a @ SV475 ) )
| ( ord_less_eq_set_nat @ ( reachableNodes_a @ SV475 @ SV225 ) @ ( v_a @ SV475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1854,plain,
! [SV476: nat,SV226: set_nat] :
( ( ~ ! [SY1268: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY1268 @ SV226 )
| ~ ( finite_finite_nat @ SY1268 )
| ( ord_less_eq_nat @ ( finite_card_nat @ SY1268 ) @ SV476 ) )
| ~ ( ~ ( finite_finite_nat @ SV226 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1855,plain,
! [SV477: nat,SV227: product_prod_nat_nat > b] :
( ( ! [SY1269: list_P559422087at_nat,SY1270: nat] :
( ~ ( isPath_b @ SV227 @ SV477 @ SY1269 @ SY1270 )
| ( dist_b @ SV227 @ SV477 @ ( size_s1990949619at_nat @ SY1269 ) @ SY1270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1856,plain,
! [SV228: set_set_nat] :
( ( ( ~ ~ ( finite2012248349et_nat @ SV228 ) )
= $true )
| ( ( ( finite_card_set_nat @ SV228 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1550]) ).
thf(1857,plain,
! [SV478: list_P559422087at_nat,SV229: nat] :
( ( ! [SY1271: nat] :
( ( isShortestPath_a @ c @ SV229 @ SV478 @ SY1271 )
= ( ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SY1271 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SY1271 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1858,plain,
! [SV479: nat,SV230: nat] :
( ( ~ ( ord_less_nat @ SV230 @ SV479 )
| ( ord_less_eq_nat @ SV230 @ SV479 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1859,plain,
! [SV480: set_Pr1986765409at_nat,SV231: set_Pr1986765409at_nat] :
( ( ~ ( finite772653738at_nat @ SV231 )
| ~ ( ord_le841296385at_nat @ SV480 @ SV231 )
| ( finite772653738at_nat @ SV480 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1860,plain,
! [SV232: product_prod_nat_nat > b] :
( ( ( ~ ( finite_finite_nat @ ( v_b @ SV232 ) ) )
= $true )
| ( ( finite_Graph_b @ SV232 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1861,plain,
! [SV481: nat,SV233: product_prod_nat_nat > a] :
( ( ! [SY1272: nat] :
( ~ ( connected_a @ SV233 @ SV481 @ SY1272 )
| ( ( ( min_dist_a @ SV233 @ SV481 @ SY1272 )
= zero_zero_nat )
= ( SY1272 = SV481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1862,plain,
! [SV482: nat,SV234: product_prod_nat_nat > a] :
( ( ! [SY1273: list_P559422087at_nat,SY1274: nat] :
( ~ ( isShortestPath_a @ SV234 @ SV482 @ SY1273 @ SY1274 )
| ( isSimplePath_a @ SV234 @ SV482 @ SY1273 @ SY1274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1863,plain,
! [SV235: set_se1612935105at_nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( finite1701894793at_nat @ SV235 ) ) )
= $true )
| ( ( finite1457549322at_nat @ SV235 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1557]) ).
thf(1864,plain,
! [SV483: list_P559422087at_nat,SV236: nat] :
( ( ! [SY1275: nat] :
( ~ ( isPath_a @ c @ SV236 @ SV483 @ SY1275 )
| ~ ! [SY996: list_P559422087at_nat] :
~ ( isSimplePath_a @ c @ SV236 @ SY996 @ SY1275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1865,plain,
! [SV484: nat,SV237: nat] :
( ( ( connected_b @ c2 @ SV237 @ SV484 )
= ( ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1866,plain,
! [SV485: nat,SV238: nat] :
( ( ! [SY1278: nat] :
( ~ ( ord_less_eq_nat @ SV238 @ SV485 )
| ~ ( ord_less_eq_nat @ SV485 @ SY1278 )
| ( ord_less_eq_nat @ SV238 @ SY1278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1867,plain,
! [SV239: product_prod_nat_nat > b] :
( ( ( ~ ( finite_Graph_b @ SV239 ) )
= $true )
| ( ( edmond1517640973ysis_b @ SV239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1561]) ).
thf(1868,plain,
! [SV240: product_prod_nat_nat > a] :
( ( ( ~ ( edmond1517640972ysis_a @ SV240 ) )
= $true )
| ( ( finite_Graph_a @ SV240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1562]) ).
thf(1869,plain,
! [SV486: set_nat,SV241: product_prod_nat_nat > b] :
( ( ~ ( finite_finite_nat @ ( v_b @ SV241 ) )
| ( finite772653738at_nat @ ( incoming_b @ SV241 @ SV486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1870,plain,
( ( ( finite772653738at_nat @ ( e_b @ c2 ) )
= $false )
| ( ( finite_Graph_b @ c2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1871,plain,
! [SV487: set_Pr1986765409at_nat,SV242: set_Pr1986765409at_nat] :
( ( ~ ( ord_le841296385at_nat @ SV242 @ SV487 )
| ~ ( finite772653738at_nat @ SV487 )
| ( finite772653738at_nat @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1872,plain,
! [SV243: product_prod_nat_nat > b] :
( ( ( ~ ( finite772653738at_nat @ ( e_b @ SV243 ) ) )
= $true )
| ( ( finite_finite_nat @ ( v_b @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1566]) ).
thf(1873,plain,
! [SV488: product_prod_nat_nat > a] :
( ( ( dist_a @ SV488 )
= ( ^ [SY1279: nat,SY1280: nat,SY1281: nat] :
~ ! [SY1282: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SY1279 @ SY1282 @ SY1281 )
| ( ( size_s1990949619at_nat @ SY1282 )
!= SY1280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1874,plain,
! [SV245: product_prod_nat_nat > b] :
( ( ( ~ ( finite772653738at_nat @ ( e_b @ SV245 ) ) )
= $true )
| ( ( finite_Graph_b @ SV245 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1569]) ).
thf(1875,plain,
! [SV246: product_prod_nat_nat > b] :
( ( ( ~ ( edmond1517640973ysis_b @ SV246 ) )
= $true )
| ( ( finite_Graph_b @ SV246 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1876,plain,
! [SV247: product_prod_nat_nat > b] :
( ( ( ~ ( edmond1517640973ysis_b @ SV247 ) )
= $true )
| ( ( ord_le841296385at_nat @ ( e_b @ SV247 ) @ ( edmond771116671s_uE_b @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1877,plain,
! [SV489: list_P559422087at_nat,SV248: nat] :
( ( ! [SY1283: nat] :
( ( isShortestPath_a @ c @ SV248 @ SV489 @ SY1283 )
= ( ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SY1283 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SY1283 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1878,plain,
! [SV490: list_P559422087at_nat,SV249: list_P559422087at_nat] :
( ( ~ ( ( ( size_s1990949619at_nat @ SV249 )
!= ( size_s1990949619at_nat @ SV490 ) ) )
| ( SV249 != SV490 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1879,plain,
! [SV250: set_set_nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ SV250 ) ) )
= $true )
| ( ( finite2012248349et_nat @ SV250 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1574]) ).
thf(1880,plain,
! [SV491: product_prod_nat_nat > b] :
( ( ( connected_b @ SV491 )
= ( ^ [SY1284: nat,SY1285: nat] :
~ ! [SY1286: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SY1284 @ SY1286 @ SY1285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1881,plain,
! [SV492: set_Pr1986765409at_nat,SV252: set_Pr1986765409at_nat] :
( ( ~ ( finite772653738at_nat @ SV252 )
| ~ ( ord_le841296385at_nat @ SV492 @ SV252 )
| ( ( finite447719721at_nat @ SV492 )
!= ( finite447719721at_nat @ SV252 ) )
| ( SV492 = SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1882,plain,
! [SV493: nat,SV253: nat] :
( ( ! [SY1287: nat] :
( ~ ( dist_b @ c2 @ SV253 @ SV493 @ SY1287 )
| ( ord_less_eq_nat @ ( min_dist_b @ c2 @ SV253 @ SY1287 ) @ SV493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1883,plain,
! [SV494: nat,SV254: product_prod_nat_nat > b] :
( ( ! [SY1288: nat] :
( ~ ( connected_b @ SV254 @ SV494 @ SY1288 )
| ( ( member_nat @ SY1288 @ ( v_b @ SV254 ) )
= ( member_nat @ SV494 @ ( v_b @ SV254 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1884,plain,
! [SV495: nat,SV255: product_prod_nat_nat > b] :
( ( ! [SY1289: nat] :
( ~ ( connected_b @ SV255 @ SV495 @ SY1289 )
| ( ( ( min_dist_b @ SV255 @ SV495 @ SY1289 )
= zero_zero_nat )
= ( SY1289 = SV495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1885,plain,
! [SV256: nat] :
( ( ( ~ ( ( SV256 != zero_zero_nat ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1581]) ).
thf(1886,plain,
! [SV496: nat,SV257: product_prod_nat_nat > b] :
( ( ! [SY1290: nat] :
( ~ ( finite_Graph_b @ SV257 )
| ~ ( member_nat @ SV496 @ ( v_b @ SV257 ) )
| ~ ( connected_b @ SV257 @ SV496 @ SY1290 )
| ( ord_less_nat @ ( min_dist_b @ SV257 @ SV496 @ SY1290 ) @ ( finite_card_nat @ ( v_b @ SV257 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1887,plain,
! [SV497: set_Pr1986765409at_nat,SV258: set_Pr1986765409at_nat] :
( ( ~ ! [SY1291: product_prod_nat_nat] :
( ~ ( member701585322at_nat @ SY1291 @ SV258 )
| ( member701585322at_nat @ SY1291 @ SV497 ) )
| ( ord_le841296385at_nat @ SV258 @ SV497 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1888,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
= ( ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1889,plain,
! [SV499: nat,SV260: nat] :
( ( ! [SY1293: nat,SY1294: nat] :
( ~ ( connected_a @ c @ SV260 @ SV499 )
| ( ( min_dist_a @ c @ SV260 @ SV499 )
!= SY1293 )
| ~ ( ord_less_nat @ SY1294 @ SY1293 )
| ~ ! [SY1029: nat] :
~ ~ ( ~ ( connected_a @ c @ SV260 @ SY1029 )
| ( ( min_dist_a @ c @ SV260 @ SY1029 )
!= SY1294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1890,plain,
! [SV500: set_nat,SV261: product_prod_nat_nat > a] :
( ( ~ ( finite_finite_nat @ ( v_a @ SV261 ) )
| ( finite772653738at_nat @ ( outgoing_a @ SV261 @ SV500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1891,plain,
! [SV501: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV501 )
= ( ^ [SY1296: nat,SY1297: list_P559422087at_nat,SY1298: nat] :
~ ( ~ ( isSimplePath_b @ SV501 @ SY1296 @ SY1297 @ SY1298 )
| ( ( size_s1990949619at_nat @ SY1297 )
!= ( min_dist_b @ SV501 @ SY1296 @ SY1298 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1892,plain,
! [SV263: set_li664300135at_nat] :
( ( ( ~ ( finite1299096496at_nat @ SV263 ) )
= $true )
| ( ( ~ ! [SY1034: nat] :
~ ! [SY1035: list_P559422087at_nat] :
( ~ ( member1608759472at_nat @ SY1035 @ SV263 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY1035 ) @ SY1034 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1589]) ).
thf(1893,plain,
! [SV502: nat,SV264: nat] :
( ( ! [SY1299: nat] :
( ~ ( connected_a @ c @ SV264 @ SV502 )
| ~ ( ord_less_eq_nat @ SY1299 @ ( min_dist_a @ c @ SV264 @ SV502 ) )
| ~ ! [SY1038: nat] :
~ ~ ( ~ ( connected_a @ c @ SV264 @ SY1038 )
| ( ( min_dist_a @ c @ SV264 @ SY1038 )
!= SY1299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1894,plain,
! [SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ! [SY1301: nat,SY1302: nat,SY1303: nat] :
( ~ ( connected_b @ SV265 @ SV503 @ SY1301 )
| ( ( min_dist_b @ SV265 @ SV503 @ SY1301 )
!= SY1302 )
| ~ ( ord_less_nat @ SY1303 @ SY1302 )
| ~ ! [SY1304: nat] :
~ ~ ( ~ ( connected_b @ SV265 @ SV503 @ SY1304 )
| ( ( min_dist_b @ SV265 @ SV503 @ SY1304 )
!= SY1303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1895,plain,
! [SV504: nat,SV266: nat] :
( ( ~ ( connected_a @ c @ SV266 @ SV504 )
| ~ ! [SY1305: list_P559422087at_nat] :
~ ( isShortestPath_a @ c @ SV266 @ SY1305 @ SV504 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1896,plain,
! [SV505: list_P559422087at_nat,SV267: nat] :
( ( ! [SY1306: nat] :
( ~ ( member_nat @ SV267 @ ( v_a @ c ) )
| ~ ( isShortestPath_a @ c @ SV267 @ SV505 @ SY1306 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV505 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1897,plain,
( ( ( finite772653738at_nat @ ( e_a @ c ) )
= $false )
| ( ( finite_Graph_a @ c )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1898,plain,
! [SV506: nat,SV268: product_prod_nat_nat > a] :
( ( ! [SY1307: nat,SY1308: nat] :
( ~ ( dist_a @ SV268 @ SV506 @ SY1307 @ SY1308 )
| ( connected_a @ SV268 @ SV506 @ SY1308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1899,plain,
! [SV507: set_nat,SV269: set_nat] :
( ( ~ ( finite_finite_nat @ SV269 )
| ~ ( ord_less_eq_set_nat @ SV507 @ SV269 )
| ( finite_finite_nat @ SV507 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1900,plain,
! [SV508: nat,SV270: set_nat] :
( ( ~ ~ ( finite_finite_nat @ SV270 )
| ~ ! [SY1309: set_nat] :
~ ~ ( ~ ~ ( ~ ( finite_finite_nat @ SY1309 )
| ( ( finite_card_nat @ SY1309 )
!= SV508 ) )
| ~ ( ord_less_eq_set_nat @ SY1309 @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(1901,plain,
! [SV271: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV271 )
| ( SV271 != zero_zero_nat ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV271 )
| ~ ( ( SV271 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1598]) ).
thf(1902,plain,
! [SV271: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV271 )
= ( SV271 != zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1598]) ).
thf(1903,plain,
! [SV272: set_li664300135at_nat] :
( ( ( ~ ~ ( finite1299096496at_nat @ SV272 ) )
= $true )
| ( ( ( finite83082927at_nat @ SV272 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1904,plain,
! [SV509: set_nat,SV273: set_set_nat] :
( ( ~ ( finite2012248349et_nat @ SV273 )
| ~ ( member_set_nat @ SV509 @ SV273 )
| ~ ! [SY1310: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SY1310 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1310 @ SV509 ) )
| ~ ! [SY1056: set_nat] :
( ~ ( member_set_nat @ SY1056 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1056 @ SY1310 )
| ( SY1310 = SY1056 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1905,plain,
! [SV510: product_prod_nat_nat > $o,SV274: product_prod_nat_nat > $o] :
( ( ~ ! [SY1312: product_prod_nat_nat] :
( ( SV274 @ SY1312 )
= ( SV510 @ SY1312 ) )
| ( ( collec7649004at_nat @ SV274 )
= ( collec7649004at_nat @ SV510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(1906,plain,
! [SV511: list_P559422087at_nat,SV275: nat] :
( ( ! [SY1313: nat] :
( ~ ( member_nat @ SV275 @ ( v_b @ c2 ) )
| ~ ( isSimplePath_b @ c2 @ SV275 @ SV511 @ SY1313 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV511 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1907,plain,
! [SV512: list_P559422087at_nat,SV276: nat] :
( ( ! [SY1314: nat] :
( ~ ( isShortestPath_b @ c2 @ SV276 @ SV512 @ SY1314 )
| ( isSimplePath_b @ c2 @ SV276 @ SV512 @ SY1314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1908,plain,
! [SV513: nat,SV277: product_prod_nat_nat > b] :
( ( ! [SY1315: nat] :
( ~ ( edmond1517640973ysis_b @ SV277 )
| ( ord_le841296385at_nat @ ( edmond475474836dges_b @ SV277 @ SV513 @ SY1315 ) @ ( e_b @ SV277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1909,plain,
! [SV278: nat] :
( ( ( ~ ( member_nat @ SV278 @ ( v_b @ c2 ) ) )
= $true )
| ( ( ord_less_eq_set_nat @ ( reachableNodes_b @ c2 @ SV278 ) @ ( v_b @ c2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1605]) ).
thf(1910,plain,
! [SV514: set_nat,SV279: set_nat] :
( ( ~ ( finite_finite_nat @ SV279 )
| ~ ( ord_less_set_nat @ SV514 @ SV279 )
| ( ord_less_nat @ ( finite_card_nat @ SV514 ) @ ( finite_card_nat @ SV279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1911,plain,
( ( ( finite772653738at_nat @ ( e_a @ c ) )
= $false )
| ( ( finite_finite_nat @ ( v_a @ c ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1912,plain,
! [SV280: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV280 @ zero_zero_nat ) )
= $true )
| ( ( SV280 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1608]) ).
thf(1913,plain,
! [SV515: nat,SV281: product_prod_nat_nat > b] :
( ( ! [SY1316: nat,SY1317: nat] :
( ~ ( dist_b @ SV281 @ SV515 @ SY1316 @ SY1317 )
| ( ord_less_eq_nat @ ( min_dist_b @ SV281 @ SV515 @ SY1317 ) @ SY1316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1914,plain,
! [SV282: set_nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ SV282 ) ) )
= $true )
| ( ( finite_finite_nat @ SV282 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1610]) ).
thf(1915,plain,
! [SV516: nat,SV283: nat] :
( ( ! [SY1318: nat] :
( ~ ( dist_b @ c2 @ SV283 @ SV516 @ SY1318 )
| ~ ! [SY1319: nat] :
( ~ ( dist_b @ c2 @ SV283 @ SY1319 @ SY1318 )
| ( ord_less_eq_nat @ SV516 @ SY1319 ) )
| ( ( min_dist_b @ c2 @ SV283 @ SY1318 )
= SV516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1916,plain,
! [SV517: set_se1612935105at_nat,SV284: set_se1612935105at_nat] :
( ( ~ ( ord_le2096002913at_nat @ SV284 @ SV517 )
| ~ ( finite1457549322at_nat @ SV517 )
| ( finite1457549322at_nat @ SV284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1917,plain,
! [SV518: nat,SV285: product_prod_nat_nat > b] :
( ( ! [SY1320: nat] :
( ~ ( edmond1517640973ysis_b @ SV285 )
| ( finite772653738at_nat @ ( edmond475474836dges_b @ SV285 @ SV518 @ SY1320 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1918,plain,
! [SV519: product_prod_nat_nat > b] :
( ( ( connected_b @ SV519 )
= ( ^ [SY1321: nat,SY1322: nat] :
~ ! [SY1323: nat] :
~ ( dist_b @ SV519 @ SY1321 @ SY1323 @ SY1322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1919,plain,
! [SV520: set_Pr1986765409at_nat,SV287: set_Pr1986765409at_nat] :
( ( ! [SY1324: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SV287 @ SV520 )
| ~ ( ord_le841296385at_nat @ SV520 @ SY1324 )
| ( ord_le841296385at_nat @ SV287 @ SY1324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1920,plain,
! [SV288: set_li664300135at_nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( finite83082927at_nat @ SV288 ) ) )
= $true )
| ( ( finite1299096496at_nat @ SV288 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1617]) ).
thf(1921,plain,
! [SV521: nat,SV289: product_prod_nat_nat > a] :
( ( ! [SY1325: nat] :
( ~ ( edmond1517640972ysis_a @ SV289 )
| ( finite772653738at_nat @ ( edmond475474835dges_a @ SV289 @ SV521 @ SY1325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(1922,plain,
! [SV522: nat,SV290: product_prod_nat_nat > b] :
( ( ~ ( finite_Graph_b @ SV290 )
| ( finite_finite_nat @ ( adjacent_nodes_b @ SV290 @ SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1923,plain,
! [SV523: nat,SV291: product_prod_nat_nat > a] :
( ( ! [SY1326: list_P559422087at_nat,SY1327: nat] :
( ~ ( isPath_a @ SV291 @ SV523 @ SY1326 @ SY1327 )
| ~ ! [SY1328: list_P559422087at_nat] :
~ ( isSimplePath_a @ SV291 @ SV523 @ SY1328 @ SY1327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1924,plain,
! [SV524: nat,SV292: nat] :
( ( ~ ( ord_less_nat @ SV292 @ SV524 )
| ( SV524 != SV292 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1925,plain,
( ( ( finite772653738at_nat @ ( e_b @ c2 ) )
= $false )
| ( ( finite_finite_nat @ ( v_b @ c2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1926,plain,
( ( ( finite_finite_nat @ ( v_b @ c2 ) )
= $false )
| ( ( finite772653738at_nat @ ( e_b @ c2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1927,plain,
! [SV525: list_P559422087at_nat,SV293: nat] :
( ( ! [SY1329: nat] :
( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SY1329 )
= ( ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SY1329 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SY1329 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1928,plain,
! [SV526: nat,SV294: nat] :
( ( ! [SY1330: nat] :
( ~ ( dist_a @ c @ SV294 @ SV526 @ SY1330 )
| ( connected_a @ c @ SV294 @ SY1330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1929,plain,
! [SV295: product_prod_nat_nat > a] :
( ( ( ~ ( finite_Graph_a @ SV295 ) )
= $true )
| ( ( finite_finite_nat @ ( v_a @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1626]) ).
thf(1930,plain,
! [SV527: nat,SV296: product_prod_nat_nat > a] :
( ( ! [SY1331: nat] :
( ~ ( connected_a @ SV296 @ SV527 @ SY1331 )
| ( dist_a @ SV296 @ SV527 @ ( min_dist_a @ SV296 @ SV527 @ SY1331 ) @ SY1331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(1931,plain,
! [SV528: nat,SV297: nat] :
( ( ~ ( ( ord_less_nat @ SV297 @ SV528 )
| ( SV297 = SV528 ) )
| ( ord_less_eq_nat @ SV297 @ SV528 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1932,plain,
! [SV529: set_Pr1986765409at_nat,SV298: set_Pr1986765409at_nat] :
( ( ~ ( finite772653738at_nat @ SV298 )
| ~ ( ord_le841296385at_nat @ SV529 @ SV298 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ SV529 ) @ ( finite447719721at_nat @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(1933,plain,
! [SV530: nat] :
( ( ( ord_less_nat @ SV530 )
= ( ^ [SY1332: nat] :
~ ( ~ ( ord_less_eq_nat @ SV530 @ SY1332 )
| ~ ( ( SV530 != SY1332 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(1934,plain,
! [SV531: list_P559422087at_nat,SV300: nat] :
( ( ! [SY1333: nat] :
( ~ ( member_nat @ SV300 @ ( v_b @ c2 ) )
| ~ ( isShortestPath_b @ c2 @ SV300 @ SV531 @ SY1333 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV531 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1935,plain,
! [SV532: set_Pr1986765409at_nat,SV301: set_Pr1986765409at_nat] :
( ( ~ ( ord_le841296385at_nat @ SV301 @ SV532 )
| ~ ( ord_le841296385at_nat @ SV532 @ SV301 )
| ( SV301 = SV532 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1936,plain,
! [SV302: product_prod_nat_nat > a] :
( ( ( ~ ( finite772653738at_nat @ ( e_a @ SV302 ) ) )
= $true )
| ( ( finite_finite_nat @ ( v_a @ SV302 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1634]) ).
thf(1937,plain,
! [SV303: set_se1612935105at_nat] :
( ( ( ~ ~ ( finite1457549322at_nat @ SV303 ) )
= $true )
| ( ( ( finite1701894793at_nat @ SV303 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1635]) ).
thf(1938,plain,
! [SV533: nat,SV304: nat] :
( ( ! [SY1334: nat > $o] :
( ~ ( connected_b @ c2 @ SV304 @ SV533 )
| ~ ! [SY1335: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1335 @ SV533 )
| ~ ! [SY1336: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1336 @ SV533 )
| ( ord_less_eq_nat @ SY1335 @ SY1336 ) )
| ( SY1334 @ SY1335 ) )
| ( SY1334 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1939,plain,
! [SV534: list_P559422087at_nat,SV305: list_P559422087at_nat] :
( ( ~ ( ( ( size_s1990949619at_nat @ SV305 )
!= ( size_s1990949619at_nat @ SV534 ) ) )
| ( SV305 != SV534 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1940,plain,
! [SV535: list_P559422087at_nat,SV306: nat] :
( ( ! [SY1337: nat] :
( ~ ( isShortestPath_b @ c2 @ SV306 @ SV535 @ SY1337 )
| ( isPath_b @ c2 @ SV306 @ SV535 @ SY1337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1941,plain,
! [SV307: set_nat] :
( ( ( ~ ( finite_finite_nat @ ( v_a @ c ) ) )
= $true )
| ( ( finite772653738at_nat @ ( incoming_a @ c @ SV307 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1639]) ).
thf(1942,plain,
! [SV536: list_P559422087at_nat,SV308: nat] :
( ( ! [SY1338: nat] :
( ~ ( isShortestPath_a @ c @ SV308 @ SV536 @ SY1338 )
| ( isPath_a @ c @ SV308 @ SV536 @ SY1338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1943,plain,
! [SV309: product_prod_nat_nat > b] :
( ( ! [SV537: nat] :
( ( edmond1022345717sure_b @ SV309 @ SV537 )
= ( edmond1022345717sure_b @ SV309 @ SV537 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1641]) ).
thf(1944,plain,
! [SV309: product_prod_nat_nat > b] :
( ( ( edmond1022345717sure_b @ SV309 )
= ( edmond1022345717sure_b @ SV309 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1641]) ).
thf(1945,plain,
! [SV310: product_prod_nat_nat > a] :
( ( ! [SV538: nat] :
( ( edmond1022345716sure_a @ SV310 @ SV538 )
= ( edmond1022345716sure_a @ SV310 @ SV538 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1642]) ).
thf(1946,plain,
! [SV310: product_prod_nat_nat > a] :
( ( ( edmond1022345716sure_a @ SV310 )
= ( edmond1022345716sure_a @ SV310 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1642]) ).
thf(1947,plain,
! [SV313: product_prod_nat_nat > a] :
( ( ! [SV539: nat] :
( ( edmond475474835dges_a @ SV313 @ SV539 )
= ( edmond475474835dges_a @ SV313 @ SV539 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1645]) ).
thf(1948,plain,
! [SV313: product_prod_nat_nat > a] :
( ( ( edmond475474835dges_a @ SV313 )
= ( edmond475474835dges_a @ SV313 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1645]) ).
thf(1949,plain,
! [SV314: product_prod_nat_nat > b] :
( ( ! [SV540: nat] :
( ( edmond475474836dges_b @ SV314 @ SV540 )
= ( edmond475474836dges_b @ SV314 @ SV540 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1646]) ).
thf(1950,plain,
! [SV314: product_prod_nat_nat > b] :
( ( ( edmond475474836dges_b @ SV314 )
= ( edmond475474836dges_b @ SV314 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1646]) ).
thf(1951,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ~ ( ( edmond1517640972ysis_a @ SV315 )
| ( finite_Graph_a @ SV315 ) )
| ~ ( ~ ( edmond1517640972ysis_a @ SV315 )
| ~ ( finite_Graph_a @ SV315 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1647]) ).
thf(1952,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( edmond1517640972ysis_a @ SV315 )
= ( finite_Graph_a @ SV315 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1647]) ).
thf(1953,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ~ ( ( edmond1517640973ysis_b @ SV316 )
| ( finite_Graph_b @ SV316 ) )
| ~ ( ~ ( edmond1517640973ysis_b @ SV316 )
| ~ ( finite_Graph_b @ SV316 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1648]) ).
thf(1954,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( edmond1517640973ysis_b @ SV316 )
= ( finite_Graph_b @ SV316 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1648]) ).
thf(1955,plain,
! [SV317: nat,SV13: nat] :
( ( ~ ( ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
| ( SV317 = SV13 ) )
| ~ ( ~ ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
| ( SV317 != SV13 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1649]) ).
thf(1956,plain,
! [SV317: nat,SV13: nat] :
( ( ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
= ( SV317 = SV13 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1649]) ).
thf(1957,plain,
! [SV318: set_Pr1986765409at_nat > $o,SV15: set_Pr1986765409at_nat] :
( ( ~ ( ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
| ( SV318 @ SV15 ) )
| ~ ( ~ ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
| ~ ( SV318 @ SV15 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1650]) ).
thf(1958,plain,
! [SV318: set_Pr1986765409at_nat > $o,SV15: set_Pr1986765409at_nat] :
( ( ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
= ( SV318 @ SV15 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1650]) ).
thf(1959,plain,
! [SV319: set_nat > $o,SV16: set_nat] :
( ( ~ ( ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
| ( SV319 @ SV16 ) )
| ~ ( ~ ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
| ~ ( SV319 @ SV16 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1651]) ).
thf(1960,plain,
! [SV319: set_nat > $o,SV16: set_nat] :
( ( ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
= ( SV319 @ SV16 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1651]) ).
thf(1961,plain,
! [SV320: product_prod_nat_nat > $o,SV17: product_prod_nat_nat] :
( ( ~ ( ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
| ( SV320 @ SV17 ) )
| ~ ( ~ ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
| ~ ( SV320 @ SV17 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1652]) ).
thf(1962,plain,
! [SV320: product_prod_nat_nat > $o,SV17: product_prod_nat_nat] :
( ( ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
= ( SV320 @ SV17 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1652]) ).
thf(1963,plain,
! [SV321: nat > $o,SV18: nat] :
( ( ~ ( ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
| ( SV321 @ SV18 ) )
| ~ ( ~ ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
| ~ ( SV321 @ SV18 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1653]) ).
thf(1964,plain,
! [SV321: nat > $o,SV18: nat] :
( ( ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
= ( SV321 @ SV18 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1653]) ).
thf(1965,plain,
! [SV24: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV24 )
| ( SV24 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV24 )
| ( SV24 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1655]) ).
thf(1966,plain,
! [SV25: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
| ( SV25 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
| ( SV25 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1657]) ).
thf(1967,plain,
! [SV322: nat,SV30: nat] :
( ( ( ord_less_eq_nat @ SV30 @ SV322 )
= $true )
| ( ( ord_less_eq_nat @ SV322 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1659]) ).
thf(1968,plain,
! [SV32: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
| ( SV32 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
| ( SV32 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1660]) ).
thf(1969,plain,
! [SV33: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
| ( SV33 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
| ( SV33 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(1970,plain,
! [SV323: nat] :
( ( ! [SV541: nat] :
( ( ord_less_eq_nat @ SV323 @ SV541 )
= ( ( ord_less_nat @ SV323 @ SV541 )
| ( SV323 = SV541 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1664]) ).
thf(1971,plain,
! [SV323: nat] :
( ( ( ord_less_eq_nat @ SV323 )
= ( ^ [SY1109: nat] :
( ( ord_less_nat @ SV323 @ SY1109 )
| ( SV323 = SY1109 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1664]) ).
thf(1972,plain,
! [SV35: nat] :
( ( ( ~ ( ( zero_zero_nat = SV35 )
| ( SV35 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( zero_zero_nat != SV35 )
| ( SV35 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1665]) ).
thf(1973,plain,
! [SV324: product_prod_nat_nat > b] :
( ( ! [SV542: nat] :
( ( isPath_b @ SV324 @ SV542 )
= ( isPath_b @ SV324 @ SV542 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1669]) ).
thf(1974,plain,
! [SV324: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV324 )
= ( isPath_b @ SV324 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1669]) ).
thf(1975,plain,
! [SV325: product_prod_nat_nat > a] :
( ( ! [SV543: nat] :
( ( isPath_a @ SV325 @ SV543 )
= ( isPath_a @ SV325 @ SV543 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1670]) ).
thf(1976,plain,
! [SV325: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV325 )
= ( isPath_a @ SV325 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1670]) ).
thf(1977,plain,
! [SV328: product_prod_nat_nat > a] :
( ( ! [SV544: nat] :
( ( min_dist_a @ SV328 @ SV544 )
= ( min_dist_a @ SV328 @ SV544 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1673]) ).
thf(1978,plain,
! [SV328: product_prod_nat_nat > a] :
( ( ( min_dist_a @ SV328 )
= ( min_dist_a @ SV328 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1673]) ).
thf(1979,plain,
! [SV329: product_prod_nat_nat > b] :
( ( ! [SV545: nat] :
( ( min_dist_b @ SV329 @ SV545 )
= ( min_dist_b @ SV329 @ SV545 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1674]) ).
thf(1980,plain,
! [SV329: product_prod_nat_nat > b] :
( ( ( min_dist_b @ SV329 )
= ( min_dist_b @ SV329 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1674]) ).
thf(1981,plain,
! [SV330: product_prod_nat_nat > b] :
( ( ! [SV546: nat] :
( ( connected_b @ SV330 @ SV546 )
= ( connected_b @ SV330 @ SV546 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1675]) ).
thf(1982,plain,
! [SV330: product_prod_nat_nat > b] :
( ( ( connected_b @ SV330 )
= ( connected_b @ SV330 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1675]) ).
thf(1983,plain,
! [SV331: product_prod_nat_nat > a] :
( ( ! [SV547: nat] :
( ( connected_a @ SV331 @ SV547 )
= ( connected_a @ SV331 @ SV547 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1676]) ).
thf(1984,plain,
! [SV331: product_prod_nat_nat > a] :
( ( ( connected_a @ SV331 )
= ( connected_a @ SV331 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1676]) ).
thf(1985,plain,
! [SV334: product_prod_nat_nat > b] :
( ( ! [SV548: nat] :
( ( dist_b @ SV334 @ SV548 )
= ( dist_b @ SV334 @ SV548 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1679]) ).
thf(1986,plain,
! [SV334: product_prod_nat_nat > b] :
( ( ( dist_b @ SV334 )
= ( dist_b @ SV334 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1679]) ).
thf(1987,plain,
! [SV335: product_prod_nat_nat > a] :
( ( ! [SV549: nat] :
( ( dist_a @ SV335 @ SV549 )
= ( dist_a @ SV335 @ SV549 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1680]) ).
thf(1988,plain,
! [SV335: product_prod_nat_nat > a] :
( ( ( dist_a @ SV335 )
= ( dist_a @ SV335 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1680]) ).
thf(1989,plain,
! [SV336: product_prod_nat_nat > a] :
( ( ! [SV550: nat] :
( ( isShortestPath_a @ SV336 @ SV550 )
= ( isShortestPath_a @ SV336 @ SV550 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1681]) ).
thf(1990,plain,
! [SV336: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV336 )
= ( isShortestPath_a @ SV336 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1681]) ).
thf(1991,plain,
! [SV337: product_prod_nat_nat > b] :
( ( ! [SV551: nat] :
( ( isShortestPath_b @ SV337 @ SV551 )
= ( isShortestPath_b @ SV337 @ SV551 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1682]) ).
thf(1992,plain,
! [SV337: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV337 )
= ( isShortestPath_b @ SV337 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1682]) ).
thf(1993,plain,
! [SV53: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ( SV53 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ( SV53 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1994,plain,
! [SV552: nat,SV342: nat,SV61: product_prod_nat_nat > b] :
( ( ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
= ( SV552 = SV342 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(1995,plain,
! [SV553: nat,SV343: nat,SV62: product_prod_nat_nat > a] :
( ( ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
= ( SV553 = SV343 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(1996,plain,
! [SV344: nat,SV63: nat] :
( ( ~ ( ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
| ( SV344 = SV63 ) )
| ~ ( ~ ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
| ( SV344 != SV63 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1695]) ).
thf(1997,plain,
! [SV344: nat,SV63: nat] :
( ( ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
= ( SV344 = SV63 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1695]) ).
thf(1998,plain,
! [SV345: product_prod_nat_nat > a] :
( ( ! [SV554: nat] :
( ( isSimplePath_a @ SV345 @ SV554 )
= ( isSimplePath_a @ SV345 @ SV554 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1696]) ).
thf(1999,plain,
! [SV345: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV345 )
= ( isSimplePath_a @ SV345 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1696]) ).
thf(2000,plain,
! [SV346: product_prod_nat_nat > b] :
( ( ! [SV555: nat] :
( ( isSimplePath_b @ SV346 @ SV555 )
= ( isSimplePath_b @ SV346 @ SV555 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1697]) ).
thf(2001,plain,
! [SV346: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV346 )
= ( isSimplePath_b @ SV346 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1697]) ).
thf(2002,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ~ ( ( finite_Graph_b @ SV347 )
| ( finite_finite_nat @ ( v_b @ SV347 ) ) )
| ~ ( ~ ( finite_Graph_b @ SV347 )
| ~ ( finite_finite_nat @ ( v_b @ SV347 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1698]) ).
thf(2003,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( finite_Graph_b @ SV347 )
= ( finite_finite_nat @ ( v_b @ SV347 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1698]) ).
thf(2004,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ~ ( ( finite_Graph_a @ SV348 )
| ( finite_finite_nat @ ( v_a @ SV348 ) ) )
| ~ ( ~ ( finite_Graph_a @ SV348 )
| ~ ( finite_finite_nat @ ( v_a @ SV348 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1699]) ).
thf(2005,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( finite_Graph_a @ SV348 )
= ( finite_finite_nat @ ( v_a @ SV348 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1699]) ).
thf(2006,plain,
! [SV349: product_prod_nat_nat > a] :
( ( ! [SV556: nat] :
( ( reachableNodes_a @ SV349 @ SV556 )
= ( reachableNodes_a @ SV349 @ SV556 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1700]) ).
thf(2007,plain,
! [SV349: product_prod_nat_nat > a] :
( ( ( reachableNodes_a @ SV349 )
= ( reachableNodes_a @ SV349 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1700]) ).
thf(2008,plain,
! [SV350: product_prod_nat_nat > b] :
( ( ! [SV557: nat] :
( ( reachableNodes_b @ SV350 @ SV557 )
= ( reachableNodes_b @ SV350 @ SV557 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1701]) ).
thf(2009,plain,
! [SV350: product_prod_nat_nat > b] :
( ( ( reachableNodes_b @ SV350 )
= ( reachableNodes_b @ SV350 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1701]) ).
thf(2010,plain,
! [SV351: product_prod_nat_nat > b] :
( ( ! [SV558: nat] :
( ( adjacent_nodes_b @ SV351 @ SV558 )
= ( adjacent_nodes_b @ SV351 @ SV558 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1702]) ).
thf(2011,plain,
! [SV351: product_prod_nat_nat > b] :
( ( ( adjacent_nodes_b @ SV351 )
= ( adjacent_nodes_b @ SV351 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1702]) ).
thf(2012,plain,
! [SV352: product_prod_nat_nat > a] :
( ( ! [SV559: nat] :
( ( adjacent_nodes_a @ SV352 @ SV559 )
= ( adjacent_nodes_a @ SV352 @ SV559 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1703]) ).
thf(2013,plain,
! [SV352: product_prod_nat_nat > a] :
( ( ( adjacent_nodes_a @ SV352 )
= ( adjacent_nodes_a @ SV352 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1703]) ).
thf(2014,plain,
! [SV357: product_prod_nat_nat > a] :
( ( ! [SV560: set_nat] :
( ( incoming_a @ SV357 @ SV560 )
= ( incoming_a @ SV357 @ SV560 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1708]) ).
thf(2015,plain,
! [SV357: product_prod_nat_nat > a] :
( ( ( incoming_a @ SV357 )
= ( incoming_a @ SV357 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1708]) ).
thf(2016,plain,
! [SV358: product_prod_nat_nat > b] :
( ( ! [SV561: set_nat] :
( ( incoming_b @ SV358 @ SV561 )
= ( incoming_b @ SV358 @ SV561 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1709]) ).
thf(2017,plain,
! [SV358: product_prod_nat_nat > b] :
( ( ( incoming_b @ SV358 )
= ( incoming_b @ SV358 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1709]) ).
thf(2018,plain,
! [SV359: product_prod_nat_nat > a] :
( ( ! [SV562: set_nat] :
( ( outgoing_a @ SV359 @ SV562 )
= ( outgoing_a @ SV359 @ SV562 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1710]) ).
thf(2019,plain,
! [SV359: product_prod_nat_nat > a] :
( ( ( outgoing_a @ SV359 )
= ( outgoing_a @ SV359 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1710]) ).
thf(2020,plain,
! [SV360: product_prod_nat_nat > b] :
( ( ! [SV563: set_nat] :
( ( outgoing_b @ SV360 @ SV563 )
= ( outgoing_b @ SV360 @ SV563 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1711]) ).
thf(2021,plain,
! [SV360: product_prod_nat_nat > b] :
( ( ( outgoing_b @ SV360 )
= ( outgoing_b @ SV360 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1711]) ).
thf(2022,plain,
! [SV93: nat] :
( ( ( ~ ( ( SV93 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV93 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV93 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1716]) ).
thf(2023,plain,
! [SV94: product_prod_nat_nat > b] :
( ( ( finite_Graph_b @ SV94 )
= $false )
| ( ( finite_finite_nat @ ( v_b @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1718]) ).
thf(2024,plain,
! [SV564: nat,SV365: list_P559422087at_nat,SV95: nat] :
( ( ~ ( member_nat @ SV95 @ ( v_a @ c ) )
| ~ ( isSimplePath_a @ c @ SV95 @ SV365 @ SV564 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV365 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(2025,plain,
! [SV366: product_prod_nat_nat > a] :
( ( ! [SV565: nat] :
( ( isShortestPath_a @ SV366 @ SV565 )
= ( ^ [SY1339: list_P559422087at_nat,SY1340: nat] :
~ ( ~ ( isSimplePath_a @ SV366 @ SV565 @ SY1339 @ SY1340 )
| ( ( size_s1990949619at_nat @ SY1339 )
!= ( min_dist_a @ SV366 @ SV565 @ SY1340 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1720]) ).
thf(2026,plain,
! [SV366: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV366 )
= ( ^ [SY1113: nat,SY1114: list_P559422087at_nat,SY1115: nat] :
~ ( ~ ( isSimplePath_a @ SV366 @ SY1113 @ SY1114 @ SY1115 )
| ( ( size_s1990949619at_nat @ SY1114 )
!= ( min_dist_a @ SV366 @ SY1113 @ SY1115 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1720]) ).
thf(2027,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= ( ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2028,plain,
! [SV98: product_prod_nat_nat > a] :
( ( ( finite_Graph_a @ SV98 )
= $false )
| ( ( finite772653738at_nat @ ( e_a @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(2029,plain,
! [SV99: set_nat] :
( ( ( finite_finite_nat @ ( v_a @ c ) )
= $false )
| ( ( finite772653738at_nat @ ( outgoing_a @ c @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(2030,plain,
! [SV368: product_prod_nat_nat > b,SV100: nat] :
( ( ( ~ ( member_nat @ SV100 @ ( v_b @ SV368 ) ) )
= $true )
| ( ( ord_less_eq_set_nat @ ( reachableNodes_b @ SV368 @ SV100 ) @ ( v_b @ SV368 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(2031,plain,
! [SV101: nat] :
( ( ( ~ ( ( SV101 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV101 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV101 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV101 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1725]) ).
thf(2032,plain,
! [SV369: set_nat,SV102: set_nat] :
( ( ( ~ ! [SY1117: nat] :
( ~ ( member_nat @ SY1117 @ SV102 )
| ( member_nat @ SY1117 @ SV369 ) ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV102 @ SV369 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(2033,plain,
! [SV567: list_P559422087at_nat,SV370: nat,SV103: product_prod_nat_nat > a] :
( ( ! [SY1341: nat] :
( ~ ( finite_Graph_a @ SV103 )
| ~ ( member_nat @ SV370 @ ( v_a @ SV103 ) )
| ~ ( isShortestPath_a @ SV103 @ SV370 @ SV567 @ SY1341 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV567 ) @ ( finite_card_nat @ ( v_a @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2034,plain,
! [SV371: nat,SV104: product_prod_nat_nat > a] :
( ( ( ~ ( finite_Graph_a @ SV104 ) )
= $true )
| ( ( finite_finite_nat @ ( adjacent_nodes_a @ SV104 @ SV371 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1729]) ).
thf(2035,plain,
! [SV372: set_nat] :
( ( ! [SV568: set_nat] :
( ( SV372 = SV568 )
= ( ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV568 )
| ~ ( ord_less_eq_set_nat @ SV568 @ SV372 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1730]) ).
thf(2036,plain,
! [SV372: set_nat] :
( ( ( ^ [SY1120: set_nat] : ( SV372 = SY1120 ) )
= ( ^ [SY1121: set_nat] :
~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SY1121 )
| ~ ( ord_less_eq_set_nat @ SY1121 @ SV372 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1730]) ).
thf(2037,plain,
! [SV569: list_P559422087at_nat,SV373: nat,SV106: product_prod_nat_nat > b] :
( ( ! [SY1342: nat] :
( ~ ( finite_Graph_b @ SV106 )
| ~ ( member_nat @ SV373 @ ( v_b @ SV106 ) )
| ~ ( isShortestPath_b @ SV106 @ SV373 @ SV569 @ SY1342 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV569 ) @ ( finite_card_nat @ ( v_b @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2038,plain,
! [SV570: list_P559422087at_nat,SV374: nat,SV107: product_prod_nat_nat > a] :
( ( ! [SY1343: nat] :
( ~ ( isShortestPath_a @ SV107 @ SV374 @ SV570 @ SY1343 )
| ( isPath_a @ SV107 @ SV374 @ SV570 @ SY1343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2039,plain,
! [SV375: nat,SV108: nat] :
( ( ( ~ ( ord_less_nat @ SV108 @ SV375 ) )
= $true )
| ( ( SV108 != SV375 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(2040,plain,
! [SV376: nat,SV109: nat] :
( ( ( SV109 != SV376 )
= $true )
| ( ( ord_less_eq_nat @ SV109 @ SV376 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1734]) ).
thf(2041,plain,
! [SV377: nat > $o,SV110: nat > $o] :
( ( ( ~ ! [SY1126: nat] :
( ( SV110 @ SY1126 )
= ( SV377 @ SY1126 ) ) )
= $true )
| ( ( ( collect_nat @ SV110 )
= ( collect_nat @ SV377 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1735]) ).
thf(2042,plain,
! [SV571: nat,SV378: nat,SV111: product_prod_nat_nat > a] :
( ( ~ ( connected_a @ SV111 @ SV378 @ SV571 )
| ( ( member_nat @ SV571 @ ( v_a @ SV111 ) )
= ( member_nat @ SV378 @ ( v_a @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(2043,plain,
! [SV572: nat,SV379: nat,SV112: nat] :
( ( ~ ( dist_a @ c @ SV112 @ SV379 @ SV572 )
| ~ ! [SY1344: nat] :
( ~ ( dist_a @ c @ SV112 @ SY1344 @ SV572 )
| ( ord_less_eq_nat @ SV379 @ SY1344 ) )
| ( ( min_dist_a @ c @ SV112 @ SV572 )
= SV379 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2044,plain,
! [SV380: product_prod_nat_nat > b] :
( ( ! [SV573: nat] :
( ( dist_b @ SV380 @ SV573 )
= ( ^ [SY1345: nat,SY1346: nat] :
~ ! [SY1347: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV573 @ SY1347 @ SY1346 )
| ( ( size_s1990949619at_nat @ SY1347 )
!= SY1345 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1738]) ).
thf(2045,plain,
! [SV380: product_prod_nat_nat > b] :
( ( ( dist_b @ SV380 )
= ( ^ [SY1130: nat,SY1131: nat,SY1132: nat] :
~ ! [SY1133: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SY1130 @ SY1133 @ SY1132 )
| ( ( size_s1990949619at_nat @ SY1133 )
!= SY1131 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1738]) ).
thf(2046,plain,
! [SV381: product_prod_nat_nat > a] :
( ( ! [SV574: nat] :
( ( isShortestPath_a @ SV381 @ SV574 )
= ( ^ [SY1348: list_P559422087at_nat,SY1349: nat] :
~ ( ~ ( isPath_a @ SV381 @ SV574 @ SY1348 @ SY1349 )
| ~ ! [SY1350: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV574 @ SY1350 @ SY1349 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY1348 ) @ ( size_s1990949619at_nat @ SY1350 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1739]) ).
thf(2047,plain,
! [SV381: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV381 )
= ( ^ [SY1134: nat,SY1135: list_P559422087at_nat,SY1136: nat] :
~ ( ~ ( isPath_a @ SV381 @ SY1134 @ SY1135 @ SY1136 )
| ~ ! [SY1137: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SY1134 @ SY1137 @ SY1136 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY1135 ) @ ( size_s1990949619at_nat @ SY1137 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1739]) ).
thf(2048,plain,
! [SV115: product_prod_nat_nat > b] :
( ( ( edmond1517640973ysis_b @ SV115 )
= $false )
| ( ( finite772653738at_nat @ ( edmond771116671s_uE_b @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(2049,plain,
! [SV575: nat,SV382: nat,SV116: product_prod_nat_nat > a] :
( ( ! [SY1351: nat] :
( ~ ( dist_a @ SV116 @ SV382 @ SV575 @ SY1351 )
| ~ ! [SY1352: nat] :
( ~ ( dist_a @ SV116 @ SV382 @ SY1352 @ SY1351 )
| ( ord_less_eq_nat @ SV575 @ SY1352 ) )
| ( ( min_dist_a @ SV116 @ SV382 @ SY1351 )
= SV575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2050,plain,
! [SV383: nat,SV117: nat] :
( ( ( ~ ( connected_b @ c2 @ SV117 @ SV383 ) )
= $true )
| ( ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
= zero_zero_nat )
= ( SV383 = SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1742]) ).
thf(2051,plain,
! [SV576: nat,SV384: nat,SV118: nat] :
( ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= ( ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(2052,plain,
! [SV385: set_Pr1986765409at_nat,SV119: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV119 ) )
= $true )
| ( ( ~ ( ord_le116442893at_nat @ SV385 @ SV119 )
| ( ord_less_nat @ ( finite447719721at_nat @ SV385 ) @ ( finite447719721at_nat @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1744]) ).
thf(2053,plain,
! [SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ! [SY1354: nat,SY1355: nat] :
( ~ ( connected_a @ SV120 @ SV386 @ SV577 )
| ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
!= SY1354 )
| ~ ( ord_less_nat @ SY1355 @ SY1354 )
| ~ ! [SY1146: nat] :
~ ~ ( ~ ( connected_a @ SV120 @ SV386 @ SY1146 )
| ( ( min_dist_a @ SV120 @ SV386 @ SY1146 )
!= SY1355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2054,plain,
! [SV387: product_prod_nat_nat > a] :
( ( ! [SV578: nat] :
( ( connected_a @ SV387 @ SV578 )
= ( ^ [SY1357: nat] :
~ ! [SY1358: nat] :
~ ( dist_a @ SV387 @ SV578 @ SY1358 @ SY1357 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1746]) ).
thf(2055,plain,
! [SV387: product_prod_nat_nat > a] :
( ( ( connected_a @ SV387 )
= ( ^ [SY1147: nat,SY1148: nat] :
~ ! [SY1149: nat] :
~ ( dist_a @ SV387 @ SY1147 @ SY1149 @ SY1148 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1746]) ).
thf(2056,plain,
! [SV122: set_nat] :
( ( ( finite_finite_nat @ ( v_b @ c2 ) )
= $false )
| ( ( finite772653738at_nat @ ( outgoing_b @ c2 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(2057,plain,
! [SV123: product_prod_nat_nat > a] :
( ( ( edmond1517640972ysis_a @ SV123 )
= $false )
| ( ( ord_le841296385at_nat @ ( e_a @ SV123 ) @ ( edmond771116670s_uE_a @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(2058,plain,
! [SV579: nat,SV388: nat,SV124: product_prod_nat_nat > a] :
( ( ~ ( connected_a @ SV124 @ SV388 @ SV579 )
| ~ ! [SY1359: list_P559422087at_nat] :
~ ( isShortestPath_a @ SV124 @ SV388 @ SY1359 @ SV579 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2059,plain,
! [SV125: product_prod_nat_nat > b] :
( ( ( finite_finite_nat @ ( v_b @ SV125 ) )
= $false )
| ( ( finite772653738at_nat @ ( e_b @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1750]) ).
thf(2060,plain,
! [SV389: set_nat,SV126: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV126 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_nat @ SV389 @ SV126 )
| ( ord_less_eq_nat @ ( finite_card_nat @ SV389 ) @ ( finite_card_nat @ SV126 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1751]) ).
thf(2061,plain,
! [SV580: nat,SV390: nat,SV127: product_prod_nat_nat > b] :
( ( ~ ( connected_b @ SV127 @ SV390 @ SV580 )
| ( dist_b @ SV127 @ SV390 @ ( min_dist_b @ SV127 @ SV390 @ SV580 ) @ SV580 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2062,plain,
! [SV581: nat,SV391: nat,SV128: nat] :
( ( ! [SY1360: nat] :
( ~ ( connected_b @ c2 @ SV128 @ SV391 )
| ( ( min_dist_b @ c2 @ SV128 @ SV391 )
!= SV581 )
| ~ ( ord_less_nat @ SY1360 @ SV581 )
| ~ ! [SY787: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV128 @ SY787 )
| ( ( min_dist_b @ c2 @ SV128 @ SY787 )
!= SY1360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2063,plain,
! [SV582: nat,SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ! [SY1362: nat > $o] :
( ~ ( connected_a @ SV129 @ SV392 @ SV582 )
| ~ ! [SY1363: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1363 @ SV582 )
| ~ ! [SY1364: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1364 @ SV582 )
| ( ord_less_eq_nat @ SY1363 @ SY1364 ) )
| ( SY1362 @ SY1363 ) )
| ( SY1362 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2064,plain,
! [SV130: nat] :
( ( ( size_s1990949619at_nat @ ( sK2_SY793 @ SV130 ) )
!= SV130 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1755]) ).
thf(2065,plain,
! [SV393: set_set_nat,SV131: set_set_nat] :
( ( ( ~ ( ord_le1613022364et_nat @ SV131 @ SV393 ) )
= $true )
| ( ( ~ ( finite2012248349et_nat @ SV393 )
| ( finite2012248349et_nat @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(2066,plain,
! [SV394: nat,SV132: nat] :
( ( ( ~ ( connected_b @ c2 @ SV132 @ SV394 ) )
= $true )
| ( ( dist_b @ c2 @ SV132 @ ( min_dist_b @ c2 @ SV132 @ SV394 ) @ SV394 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1757]) ).
thf(2067,plain,
( ( ( connected_b @ c2 @ s @ t )
= $true )
| ( ( ord_less_nat @ ( edmond1022345717sure_b @ c2 @ s @ t ) @ ( edmond1022345716sure_a @ c @ s @ t ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1758]) ).
thf(2068,plain,
! [SV395: set_nat,SV133: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV133 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_nat @ SV395 @ SV133 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV133 ) @ ( finite_card_nat @ SV395 ) )
| ( SV395 = SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(2069,plain,
! [SV583: nat,SV396: nat,SV134: product_prod_nat_nat > b] :
( ( ! [SY1365: nat] :
( ~ ( connected_b @ SV134 @ SV396 @ SV583 )
| ~ ( ord_less_eq_nat @ SY1365 @ ( min_dist_b @ SV134 @ SV396 @ SV583 ) )
| ~ ! [SY1162: nat] :
~ ~ ( ~ ( connected_b @ SV134 @ SV396 @ SY1162 )
| ( ( min_dist_b @ SV134 @ SV396 @ SY1162 )
!= SY1365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2070,plain,
! [SV397: nat,SV135: nat] :
( ( ( ~ ( connected_b @ c2 @ SV135 @ SV397 ) )
= $true )
| ( ( ~ ! [SY1163: list_P559422087at_nat] :
~ ( isShortestPath_b @ c2 @ SV135 @ SY1163 @ SV397 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1761]) ).
thf(2071,plain,
! [SV398: nat,SV136: nat] :
( ( ~ ( ( connected_a @ c @ SV136 @ SV398 )
| ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) )
| ~ ( ~ ( connected_a @ c @ SV136 @ SV398 )
| ~ ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1762]) ).
thf(2072,plain,
! [SV398: nat,SV136: nat] :
( ( ( connected_a @ c @ SV136 @ SV398 )
= ( ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1762]) ).
thf(2073,plain,
! [SV399: nat,SV137: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV137 ) )
= $true )
| ( ( ~ ( member_nat @ SV399 @ SV137 )
| ~ ! [SY1165: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY1165 @ SV137 )
| ~ ( ord_less_eq_nat @ SY1165 @ SV399 ) )
| ~ ! [SY807: nat] :
( ~ ( member_nat @ SY807 @ SV137 )
| ~ ( ord_less_eq_nat @ SY807 @ SY1165 )
| ( SY1165 = SY807 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1763]) ).
thf(2074,plain,
! [SV584: list_P559422087at_nat,SV400: nat,SV138: product_prod_nat_nat > a] :
( ( ! [SY1367: nat] :
( ~ ( finite_Graph_a @ SV138 )
| ~ ( member_nat @ SV400 @ ( v_a @ SV138 ) )
| ~ ( isSimplePath_a @ SV138 @ SV400 @ SV584 @ SY1367 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV584 ) @ ( finite_card_nat @ ( v_a @ SV138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2075,plain,
! [SV585: list_P559422087at_nat,SV401: nat,SV139: product_prod_nat_nat > b] :
( ( ! [SY1368: nat] :
( ~ ( isPath_b @ SV139 @ SV401 @ SV585 @ SY1368 )
| ~ ! [SY1171: list_P559422087at_nat] :
~ ( isSimplePath_b @ SV139 @ SV401 @ SY1171 @ SY1368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2076,plain,
! [SV140: nat] :
( ( ( member_nat @ SV140 @ ( v_a @ c ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( reachableNodes_a @ c @ SV140 ) @ ( v_a @ c ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(2077,plain,
! [SV402: set_nat,SV141: product_prod_nat_nat > a] :
( ( ( ~ ( finite_finite_nat @ ( v_a @ SV141 ) ) )
= $true )
| ( ( finite772653738at_nat @ ( incoming_a @ SV141 @ SV402 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1767]) ).
thf(2078,plain,
! [SV586: nat,SV403: nat,SV142: nat] :
( ( ~ ( connected_b @ c2 @ SV142 @ SV403 )
| ~ ( ord_less_eq_nat @ SV586 @ ( min_dist_b @ c2 @ SV142 @ SV403 ) )
| ~ ! [SY1370: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV142 @ SY1370 )
| ( ( min_dist_b @ c2 @ SV142 @ SY1370 )
!= SV586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2079,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ( ~ ~ ( finite772653738at_nat @ SV143 ) )
= $true )
| ( ( ~ ! [SY1174: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( finite772653738at_nat @ SY1174 )
| ( ( finite447719721at_nat @ SY1174 )
!= SV404 ) )
| ~ ( ord_le841296385at_nat @ SY1174 @ SV143 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(2080,plain,
! [SV405: set_nat,SV144: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV144 @ SV405 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_nat @ SV405 @ SV144 )
| ( SV144 = SV405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(2081,plain,
! [SV587: list_P559422087at_nat,SV406: nat,SV145: product_prod_nat_nat > a] :
( ( ! [SY1371: nat] :
( ~ ( isPath_a @ SV145 @ SV406 @ SV587 @ SY1371 )
| ( dist_a @ SV145 @ SV406 @ ( size_s1990949619at_nat @ SV587 ) @ SY1371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2082,plain,
! [SV407: nat,SV146: nat] :
( ( ~ ( ( connected_a @ c @ SV146 @ SV407 )
| ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) )
| ~ ( ~ ( connected_a @ c @ SV146 @ SV407 )
| ~ ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1772]) ).
thf(2083,plain,
! [SV407: nat,SV146: nat] :
( ( ( connected_a @ c @ SV146 @ SV407 )
= ( ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1772]) ).
thf(2084,plain,
! [SV588: nat,SV408: nat,SV147: product_prod_nat_nat > b] :
( ( ! [SY1372: nat] :
( ~ ( dist_b @ SV147 @ SV408 @ SV588 @ SY1372 )
| ~ ! [SY1373: nat] :
( ~ ( dist_b @ SV147 @ SV408 @ SY1373 @ SY1372 )
| ( ord_less_eq_nat @ SV588 @ SY1373 ) )
| ( ( min_dist_b @ SV147 @ SV408 @ SY1372 )
= SV588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2085,plain,
! [SV589: nat,SV409: nat,SV148: product_prod_nat_nat > a] :
( ( ~ ( edmond1517640972ysis_a @ SV148 )
| ( ord_le841296385at_nat @ ( edmond475474835dges_a @ SV148 @ SV409 @ SV589 ) @ ( e_a @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2086,plain,
! [SV590: nat,SV410: nat,SV149: product_prod_nat_nat > a] :
( ( ! [SY1374: nat] :
( ~ ( dist_a @ SV149 @ SV410 @ SV590 @ SY1374 )
| ( ord_less_eq_nat @ ( min_dist_a @ SV149 @ SV410 @ SY1374 ) @ SV590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2087,plain,
! [SV150: product_prod_nat_nat > b] :
( ( ( finite_Graph_b @ SV150 )
= $false )
| ( ( finite772653738at_nat @ ( e_b @ SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(2088,plain,
! [SV591: nat,SV411: nat,SV151: product_prod_nat_nat > a] :
( ( ! [SY1375: nat] :
( ~ ( connected_a @ SV151 @ SV411 @ SV591 )
| ~ ( ord_less_eq_nat @ SY1375 @ ( min_dist_a @ SV151 @ SV411 @ SV591 ) )
| ~ ! [SY1186: nat] :
~ ~ ( ~ ( connected_a @ SV151 @ SV411 @ SY1186 )
| ( ( min_dist_a @ SV151 @ SV411 @ SY1186 )
!= SY1375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2089,plain,
! [SV152: product_prod_nat_nat > a] :
( ( ( edmond1517640972ysis_a @ SV152 )
= $false )
| ( ( finite772653738at_nat @ ( edmond771116670s_uE_a @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1778]) ).
thf(2090,plain,
! [SV592: list_P559422087at_nat,SV412: nat,SV153: product_prod_nat_nat > b] :
( ( ! [SY1377: nat] :
( ~ ( isShortestPath_b @ SV153 @ SV412 @ SV592 @ SY1377 )
| ( isPath_b @ SV153 @ SV412 @ SV592 @ SY1377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2091,plain,
! [SV413: nat,SV154: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV154 @ SV413 ) )
= $true )
| ( ( ~ ( ( SV154 != SV413 ) )
| ( ord_less_nat @ SV154 @ SV413 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1780]) ).
thf(2092,plain,
! [SV414: set_nat,SV155: product_prod_nat_nat > b] :
( ( ( ~ ( finite_finite_nat @ ( v_b @ SV155 ) ) )
= $true )
| ( ( finite772653738at_nat @ ( outgoing_b @ SV155 @ SV414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1781]) ).
thf(2093,plain,
! [SV156: product_prod_nat_nat > a] :
( ( ( finite_finite_nat @ ( v_a @ SV156 ) )
= $false )
| ( ( finite772653738at_nat @ ( e_a @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(2094,plain,
! [SV415: set_Pr1986765409at_nat,SV157: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV157 @ SV415 ) )
= $true )
| ( ( ~ ( ( SV157 != SV415 ) )
| ( ord_le116442893at_nat @ SV157 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1783]) ).
thf(2095,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= ( ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2096,plain,
! [SV594: nat,SV417: nat,SV159: nat > $o] :
( ( ~ ( SV159 @ SV417 )
| ~ ! [SY1379: nat] :
( ~ ( SV159 @ SY1379 )
| ( ord_less_eq_nat @ SY1379 @ SV594 ) )
| ~ ! [SY852: nat] :
~ ~ ( ~ ( SV159 @ SY852 )
| ~ ! [SY853: nat] :
( ~ ( SV159 @ SY853 )
| ( ord_less_eq_nat @ SY853 @ SY852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2097,plain,
! [SV418: nat,SV160: nat] :
( ( ( ~ ( member_nat @ SV160 @ ( v_a @ c ) ) )
= $true )
| ( ( ~ ( connected_a @ c @ SV160 @ SV418 )
| ( ord_less_nat @ ( min_dist_a @ c @ SV160 @ SV418 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1786]) ).
thf(2098,plain,
! [SV595: nat,SV419: nat,SV161: product_prod_nat_nat > b] :
( ( ~ ( edmond1517640973ysis_b @ SV161 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474836dges_b @ SV161 @ SV419 @ SV595 ) ) @ ( finite447719721at_nat @ ( edmond771116671s_uE_b @ SV161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2099,plain,
! [SV596: nat,SV420: nat,SV162: nat] :
( ( ~ ( dist_a @ c @ SV162 @ SV420 @ SV596 )
| ( ord_less_eq_nat @ ( min_dist_a @ c @ SV162 @ SV596 ) @ SV420 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2100,plain,
! [SV597: nat,SV421: nat,SV163: nat] :
( ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= ( ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2101,plain,
! [SV422: set_nat,SV164: set_set_nat] :
( ( ( ~ ( finite2012248349et_nat @ SV164 ) )
= $true )
| ( ( ~ ( member_set_nat @ SV422 @ SV164 )
| ~ ! [SY1199: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SY1199 @ SV164 )
| ~ ( ord_less_eq_set_nat @ SV422 @ SY1199 ) )
| ~ ! [SY864: set_nat] :
( ~ ( member_set_nat @ SY864 @ SV164 )
| ~ ( ord_less_eq_set_nat @ SY1199 @ SY864 )
| ( SY1199 = SY864 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(2102,plain,
! [SV423: product_prod_nat_nat > b] :
( ( ! [SV598: nat] :
( ( isShortestPath_b @ SV423 @ SV598 )
= ( ^ [SY1383: list_P559422087at_nat,SY1384: nat] :
~ ( ~ ( isPath_b @ SV423 @ SV598 @ SY1383 @ SY1384 )
| ~ ! [SY1385: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV598 @ SY1385 @ SY1384 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY1383 ) @ ( size_s1990949619at_nat @ SY1385 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1791]) ).
thf(2103,plain,
! [SV423: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV423 )
= ( ^ [SY1201: nat,SY1202: list_P559422087at_nat,SY1203: nat] :
~ ( ~ ( isPath_b @ SV423 @ SY1201 @ SY1202 @ SY1203 )
| ~ ! [SY1204: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SY1201 @ SY1204 @ SY1203 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY1202 ) @ ( size_s1990949619at_nat @ SY1204 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1791]) ).
thf(2104,plain,
! [SV599: nat,SV424: nat,SV166: product_prod_nat_nat > a] :
( ( ~ ( edmond1517640972ysis_a @ SV166 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ SV166 @ SV424 @ SV599 ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ SV166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2105,plain,
! [SV600: nat,SV425: nat,SV167: nat > nat] :
( ( ~ ! [SY873: nat,SY874: nat] :
( ~ ( ord_less_nat @ SY873 @ SY874 )
| ( ord_less_nat @ ( SV167 @ SY873 ) @ ( SV167 @ SY874 ) ) )
| ~ ( ord_less_eq_nat @ SV425 @ SV600 )
| ( ord_less_eq_nat @ ( SV167 @ SV425 ) @ ( SV167 @ SV600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2106,plain,
! [SV426: product_prod_nat_nat > a] :
( ( ! [SV601: nat] :
( ( isShortestPath_a @ SV426 @ SV601 )
= ( ^ [SY1388: list_P559422087at_nat,SY1389: nat] :
~ ( ~ ( isPath_a @ SV426 @ SV601 @ SY1388 @ SY1389 )
| ( ( size_s1990949619at_nat @ SY1388 )
!= ( min_dist_a @ SV426 @ SV601 @ SY1389 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1794]) ).
thf(2107,plain,
! [SV426: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV426 )
= ( ^ [SY1209: nat,SY1210: list_P559422087at_nat,SY1211: nat] :
~ ( ~ ( isPath_a @ SV426 @ SY1209 @ SY1210 @ SY1211 )
| ( ( size_s1990949619at_nat @ SY1210 )
!= ( min_dist_a @ SV426 @ SY1209 @ SY1211 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1794]) ).
thf(2108,plain,
! [SV169: set_nat] :
( ( ( finite_finite_nat @ ( v_b @ c2 ) )
= $false )
| ( ( finite772653738at_nat @ ( incoming_b @ c2 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(2109,plain,
! [SV170: product_prod_nat_nat > a] :
( ( ( finite_finite_nat @ ( v_a @ SV170 ) )
= $false )
| ( ( finite_Graph_a @ SV170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(2110,plain,
! [SV427: nat,SV171: nat > $o] :
( ( ( ~ ! [SY879: nat] :
( ~ ~ ( SV171 @ SY879 )
| ~ ! [SY880: nat] :
~ ~ ( ~ ( ord_less_nat @ SY880 @ SY879 )
| ~ ~ ( SV171 @ SY880 ) ) ) )
= $true )
| ( ( SV171 @ SV427 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1797]) ).
thf(2111,plain,
! [SV172: nat] :
( ( ( SV172 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(2112,plain,
! [SV428: set_Pr1986765409at_nat,SV173: set_se1612935105at_nat] :
( ( ( ~ ( finite1457549322at_nat @ SV173 ) )
= $true )
| ( ( ~ ( member298845450at_nat @ SV428 @ SV173 )
| ~ ! [SY1214: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SY1214 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY1214 @ SV428 ) )
| ~ ! [SY883: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY883 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY883 @ SY1214 )
| ( SY1214 = SY883 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(2113,plain,
! [SV429: list_P559422087at_nat,SV174: list_P559422087at_nat > $o] :
( ( ( ~ ! [SY885: list_P559422087at_nat] :
( ~ ! [SY886: list_P559422087at_nat] :
( ~ ( ord_less_nat @ ( size_s1990949619at_nat @ SY886 ) @ ( size_s1990949619at_nat @ SY885 ) )
| ( SV174 @ SY886 ) )
| ( SV174 @ SY885 ) ) )
= $true )
| ( ( SV174 @ SV429 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1800]) ).
thf(2114,plain,
! [SV602: set_nat,SV430: set_nat,SV175: set_nat] :
( ( ~ ( ord_less_eq_set_nat @ SV175 @ SV430 )
| ~ ( ord_less_eq_set_nat @ SV430 @ SV602 )
| ( ord_less_eq_set_nat @ SV175 @ SV602 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2115,plain,
! [SV603: nat,SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ! [SY1390: nat > $o] :
( ~ ( connected_b @ SV176 @ SV431 @ SV603 )
| ~ ! [SY1391: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1391 @ SV603 )
| ~ ! [SY1392: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1392 @ SV603 )
| ( ord_less_eq_nat @ SY1391 @ SY1392 ) )
| ( SY1390 @ SY1391 ) )
| ( SY1390 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2116,plain,
! [SV432: set_Pr1986765409at_nat,SV177: set_se1612935105at_nat] :
( ( ( ~ ( finite1457549322at_nat @ SV177 ) )
= $true )
| ( ( ~ ( member298845450at_nat @ SV432 @ SV177 )
| ~ ! [SY1223: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SY1223 @ SV177 )
| ~ ( ord_le841296385at_nat @ SV432 @ SY1223 ) )
| ~ ! [SY896: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY896 @ SV177 )
| ~ ( ord_le841296385at_nat @ SY1223 @ SY896 )
| ( SY1223 = SY896 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1803]) ).
thf(2117,plain,
! [SV433: nat,SV178: nat] :
( ( ( ~ ( connected_b @ c2 @ SV178 @ SV433 ) )
= $true )
| ( ( ( member_nat @ SV433 @ ( v_b @ c2 ) )
= ( member_nat @ SV178 @ ( v_b @ c2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1804]) ).
thf(2118,plain,
! [SV179: product_prod_nat_nat > a] :
( ( ( finite772653738at_nat @ ( e_a @ SV179 ) )
= $false )
| ( ( finite_Graph_a @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(2119,plain,
! [SV604: nat,SV434: nat,SV180: nat] :
( ( ~ ( dist_b @ c2 @ SV180 @ SV434 @ SV604 )
| ( connected_b @ c2 @ SV180 @ SV604 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2120,plain,
! [SV605: nat,SV435: list_P559422087at_nat,SV181: nat] :
( ( ~ ( isPath_b @ c2 @ SV181 @ SV435 @ SV605 )
| ( dist_b @ c2 @ SV181 @ ( size_s1990949619at_nat @ SV435 ) @ SV605 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2121,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ~ ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
| ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) )
| ~ ( ~ ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
| ~ ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1808]) ).
thf(2122,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
= ( ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1808]) ).
thf(2123,plain,
! [SV437: set_Pr1986765409at_nat] :
( ( ! [SV606: set_Pr1986765409at_nat] :
( ( SV437 = SV606 )
= ( ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV606 )
| ~ ( ord_le841296385at_nat @ SV606 @ SV437 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1809]) ).
thf(2124,plain,
! [SV437: set_Pr1986765409at_nat] :
( ( ( ^ [SY1228: set_Pr1986765409at_nat] : ( SV437 = SY1228 ) )
= ( ^ [SY1229: set_Pr1986765409at_nat] :
~ ( ~ ( ord_le841296385at_nat @ SV437 @ SY1229 )
| ~ ( ord_le841296385at_nat @ SY1229 @ SV437 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1809]) ).
thf(2125,plain,
! [SV438: set_Pr1986765409at_nat > $o,SV184: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV184 ) )
= $true )
| ( ( ~ ! [SY1230: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SY1230 )
| ~ ! [SY1231: set_Pr1986765409at_nat] :
( ~ ( ord_le116442893at_nat @ SY1231 @ SY1230 )
| ( SV438 @ SY1231 ) )
| ( SV438 @ SY1230 ) )
| ( SV438 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1810]) ).
thf(2126,plain,
! [SV439: product_prod_nat_nat > b] :
( ( ! [SV607: nat] :
( ( isShortestPath_b @ SV439 @ SV607 )
= ( ^ [SY1393: list_P559422087at_nat,SY1394: nat] :
~ ( ~ ( isPath_b @ SV439 @ SV607 @ SY1393 @ SY1394 )
| ( ( size_s1990949619at_nat @ SY1393 )
!= ( min_dist_b @ SV439 @ SV607 @ SY1394 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1811]) ).
thf(2127,plain,
! [SV439: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV439 )
= ( ^ [SY1232: nat,SY1233: list_P559422087at_nat,SY1234: nat] :
~ ( ~ ( isPath_b @ SV439 @ SY1232 @ SY1233 @ SY1234 )
| ( ( size_s1990949619at_nat @ SY1233 )
!= ( min_dist_b @ SV439 @ SY1232 @ SY1234 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1811]) ).
thf(2128,plain,
! [SV440: nat,SV186: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV186 @ SV440 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV440 @ SV186 )
| ( SV186 = SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(2129,plain,
! [SV441: nat,SV187: nat] :
( ( ( ~ ( ord_less_nat @ SV187 @ SV441 ) )
= $true )
| ( ( SV441 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1814]) ).
thf(2130,plain,
! [SV442: product_prod_nat_nat > a] :
( ( ! [SV608: nat] :
( ( connected_a @ SV442 @ SV608 )
= ( ^ [SY1395: nat] :
~ ! [SY1396: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV608 @ SY1396 @ SY1395 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1815]) ).
thf(2131,plain,
! [SV442: product_prod_nat_nat > a] :
( ( ( connected_a @ SV442 )
= ( ^ [SY1235: nat,SY1236: nat] :
~ ! [SY1237: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SY1235 @ SY1237 @ SY1236 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1815]) ).
thf(2132,plain,
! [SV609: nat,SV443: list_P559422087at_nat,SV189: nat] :
( ( ~ ( isShortestPath_a @ c @ SV189 @ SV443 @ SV609 )
| ( isSimplePath_a @ c @ SV189 @ SV443 @ SV609 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2133,plain,
! [SV444: set_nat,SV190: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV190 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_nat @ SV444 @ SV190 )
| ~ ( ord_less_nat @ ( finite_card_nat @ SV444 ) @ ( finite_card_nat @ SV190 ) )
| ( ord_less_set_nat @ SV444 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1817]) ).
thf(2134,plain,
! [SV445: nat,SV191: nat] :
( ( ( ~ ( connected_a @ c @ SV191 @ SV445 ) )
= $true )
| ( ( ( ( min_dist_a @ c @ SV191 @ SV445 )
= zero_zero_nat )
= ( SV445 = SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1818]) ).
thf(2135,plain,
! [SV446: nat,SV192: nat > $o] :
( ( ( ~ ! [SY922: nat] :
( ~ ! [SY923: nat] :
( ~ ( ord_less_nat @ SY923 @ SY922 )
| ( SV192 @ SY923 ) )
| ( SV192 @ SY922 ) ) )
= $true )
| ( ( SV192 @ SV446 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(2136,plain,
! [SV447: nat,SV193: nat] :
( ( ( ~ ( connected_a @ c @ SV193 @ SV447 ) )
= $true )
| ( ( ( member_nat @ SV447 @ ( v_a @ c ) )
= ( member_nat @ SV193 @ ( v_a @ c ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(2137,plain,
! [SV448: set_nat,SV194: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV194 @ SV448 ) )
= $true )
| ( ( ~ ~ ( finite_finite_nat @ SV194 )
| ~ ( finite_finite_nat @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(2138,plain,
! [SV195: set_Pr1986765409at_nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( finite447719721at_nat @ SV195 ) )
= $false )
| ( ( finite772653738at_nat @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(2139,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( ~ ( SV196 @ SV449 ) )
= $true )
| ( ( ~ ~ ( SV196 @ zero_zero_nat )
| ~ ! [SY1241: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_eq_nat @ SY1241 @ SV449 )
| ~ ! [SY928: nat] :
( ~ ( ord_less_nat @ SY928 @ SY1241 )
| ~ ( SV196 @ SY928 ) ) )
| ~ ( SV196 @ SY1241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1823]) ).
thf(2140,plain,
! [SV450: nat,SV197: nat] :
( ( ( ~ ( ord_less_nat @ SV197 @ SV450 ) )
= $true )
| ( ( SV450 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1824]) ).
thf(2141,plain,
( ( ~ ( isPath_b @ c2 @ s @ sK1_SX0 @ t ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1825]) ).
thf(2142,plain,
( ( ( size_s1990949619at_nat @ sK1_SX0 )
!= ( min_dist_b @ c2 @ s @ t ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1825]) ).
thf(2143,plain,
! [SV451: set_Pr1986765409at_nat,SV198: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV198 ) )
= $true )
| ( ( ~ ( ord_le841296385at_nat @ SV451 @ SV198 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV198 ) @ ( finite447719721at_nat @ SV451 ) )
| ( SV451 = SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1826]) ).
thf(2144,plain,
! [SV610: nat,SV452: nat,SV199: product_prod_nat_nat > b] :
( ( ~ ( connected_b @ SV199 @ SV452 @ SV610 )
| ~ ! [SY1397: list_P559422087at_nat] :
~ ( isShortestPath_b @ SV199 @ SV452 @ SY1397 @ SV610 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2145,plain,
! [SV453: nat,SV200: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV200 ) )
= $true )
| ( ( ~ ( member_nat @ SV453 @ SV200 )
| ~ ! [SY1245: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY1245 @ SV200 )
| ~ ( ord_less_eq_nat @ SV453 @ SY1245 ) )
| ~ ! [SY936: nat] :
( ~ ( member_nat @ SY936 @ SV200 )
| ~ ( ord_less_eq_nat @ SY1245 @ SY936 )
| ( SY1245 = SY936 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(2146,plain,
! [SV611: nat,SV454: nat,SV201: product_prod_nat_nat > a] :
( ( ~ ( finite_Graph_a @ SV201 )
| ~ ( member_nat @ SV454 @ ( v_a @ SV201 ) )
| ~ ( connected_a @ SV201 @ SV454 @ SV611 )
| ( ord_less_nat @ ( min_dist_a @ SV201 @ SV454 @ SV611 ) @ ( finite_card_nat @ ( v_a @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2147,plain,
! [SV455: set_Pr1986765409at_nat,SV202: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV202 @ SV455 ) )
= $true )
| ( ( ~ ~ ( finite772653738at_nat @ SV202 )
| ~ ( finite772653738at_nat @ SV455 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(2148,plain,
! [SV612: list_P559422087at_nat,SV456: nat,SV203: product_prod_nat_nat > b] :
( ( ! [SY1398: nat] :
( ~ ( isShortestPath_b @ SV203 @ SV456 @ SV612 @ SY1398 )
| ( isSimplePath_b @ SV203 @ SV456 @ SV612 @ SY1398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2149,plain,
! [SV204: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV204 ) )
= $false )
| ( ( ( finite_card_nat @ SV204 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(2150,plain,
! [SV457: nat,SV205: nat] :
( ( ( ~ ( ( SV205 != SV457 ) ) )
= $true )
| ( ( ~ ~ ( ord_less_nat @ SV205 @ SV457 )
| ( ord_less_nat @ SV457 @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(2151,plain,
! [SV458: set_Pr1986765409at_nat,SV206: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV206 ) )
= $true )
| ( ( ~ ( ord_le841296385at_nat @ SV458 @ SV206 )
| ~ ( ord_less_nat @ ( finite447719721at_nat @ SV458 ) @ ( finite447719721at_nat @ SV206 ) )
| ( ord_le116442893at_nat @ SV458 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(2152,plain,
! [SV613: nat,SV459: list_P559422087at_nat,SV207: nat] :
( ( ~ ( isPath_a @ c @ SV207 @ SV459 @ SV613 )
| ( dist_a @ c @ SV207 @ ( size_s1990949619at_nat @ SV459 ) @ SV613 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2153,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= ( ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2154,plain,
! [SV461: set_nat,SV209: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV209 @ SV461 ) )
= $true )
| ( ( ~ ( finite_finite_nat @ SV461 )
| ( finite_finite_nat @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1837]) ).
thf(2155,plain,
! [SV615: nat > $o,SV462: nat,SV210: nat] :
( ( ~ ( connected_a @ c @ SV210 @ SV462 )
| ~ ! [SY1400: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1400 @ SV462 )
| ~ ! [SY1255: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1255 @ SV462 )
| ( ord_less_eq_nat @ SY1400 @ SY1255 ) )
| ( SV615 @ SY1400 ) )
| ( SV615 @ ( min_dist_a @ c @ SV210 @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2156,plain,
! [SV463: nat,SV211: nat] :
( ( ( ~ ( connected_a @ c @ SV211 @ SV463 ) )
= $true )
| ( ( dist_a @ c @ SV211 @ ( min_dist_a @ c @ SV211 @ SV463 ) @ SV463 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1839]) ).
thf(2157,plain,
! [SV212: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV212 ) )
= $false )
| ( ( ( finite447719721at_nat @ SV212 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(2158,plain,
! [SV464: set_nat,SV213: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV213 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_nat @ SV464 @ SV213 )
| ( ( finite_card_nat @ SV464 )
!= ( finite_card_nat @ SV213 ) )
| ( SV464 = SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(2159,plain,
! [SV616: nat,SV465: nat,SV214: product_prod_nat_nat > b] :
( ( ! [SY1402: nat] :
( ~ ( dist_b @ SV214 @ SV465 @ SV616 @ SY1402 )
| ( connected_b @ SV214 @ SV465 @ SY1402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2160,plain,
! [SV466: nat,SV215: nat] :
( ( ~ ( ( connected_b @ c2 @ SV215 @ SV466 )
| ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) )
| ~ ( ~ ( connected_b @ c2 @ SV215 @ SV466 )
| ~ ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1843]) ).
thf(2161,plain,
! [SV466: nat,SV215: nat] :
( ( ( connected_b @ c2 @ SV215 @ SV466 )
= ( ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1843]) ).
thf(2162,plain,
! [SV216: product_prod_nat_nat > a] :
( ( ( finite_Graph_a @ SV216 )
= $false )
| ( ( edmond1517640972ysis_a @ SV216 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(2163,plain,
! [SV617: list_P559422087at_nat,SV467: nat,SV217: product_prod_nat_nat > b] :
( ( ! [SY1403: nat] :
( ~ ( finite_Graph_b @ SV217 )
| ~ ( member_nat @ SV467 @ ( v_b @ SV217 ) )
| ~ ( isSimplePath_b @ SV217 @ SV467 @ SV617 @ SY1403 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV617 ) @ ( finite_card_nat @ ( v_b @ SV217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2164,plain,
! [SV468: nat,SV218: nat] :
( ( ( ~ ( member_nat @ SV218 @ ( v_b @ c2 ) ) )
= $true )
| ( ( ~ ( connected_b @ c2 @ SV218 @ SV468 )
| ( ord_less_nat @ ( min_dist_b @ c2 @ SV218 @ SV468 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(2165,plain,
! [SV469: set_nat > $o,SV219: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV219 ) )
= $true )
| ( ( ~ ! [SY1261: set_nat] :
( ~ ( finite_finite_nat @ SY1261 )
| ~ ! [SY1262: set_nat] :
( ~ ( ord_less_set_nat @ SY1262 @ SY1261 )
| ( SV469 @ SY1262 ) )
| ( SV469 @ SY1261 ) )
| ( SV469 @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(2166,plain,
! [SV470: nat,SV220: nat] :
( ( ~ ( ( SV220 != SV470 )
| ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) )
| ~ ( ~ ( ( SV220 != SV470 ) )
| ~ ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1848]) ).
thf(2167,plain,
! [SV470: nat,SV220: nat] :
( ( ( SV220 != SV470 )
= ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1848]) ).
thf(2168,plain,
! [SV618: nat,SV471: list_P559422087at_nat,SV221: nat] :
( ( ~ ( isPath_b @ c2 @ SV221 @ SV471 @ SV618 )
| ~ ! [SY1404: list_P559422087at_nat] :
~ ( isSimplePath_b @ c2 @ SV221 @ SY1404 @ SV618 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2169,plain,
! [SV472: nat,SV222: nat > $o] :
( ( ( ~ ( SV222 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY974: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY974 )
| ~ ~ ( SV222 @ SY974 )
| ~ ! [SY975: nat] :
~ ~ ( ~ ( ord_less_nat @ SY975 @ SY974 )
| ~ ~ ( SV222 @ SY975 ) ) )
| ( SV222 @ SV472 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1850]) ).
thf(2170,plain,
! [SV473: set_nat,SV223: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV223 @ SV473 ) )
= $true )
| ( ( ~ ( ( SV223 != SV473 ) )
| ( ord_less_set_nat @ SV223 @ SV473 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1851]) ).
thf(2171,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( ~ ! [SY1267: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SY1267 @ SV224 )
| ~ ( finite772653738at_nat @ SY1267 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ SY1267 ) @ SV474 ) ) )
= $true )
| ( ( ~ ( ~ ( finite772653738at_nat @ SV224 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1852]) ).
thf(2172,plain,
! [SV475: product_prod_nat_nat > a,SV225: nat] :
( ( ( ~ ( member_nat @ SV225 @ ( v_a @ SV475 ) ) )
= $true )
| ( ( ord_less_eq_set_nat @ ( reachableNodes_a @ SV475 @ SV225 ) @ ( v_a @ SV475 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1853]) ).
thf(2173,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( ~ ! [SY1268: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY1268 @ SV226 )
| ~ ( finite_finite_nat @ SY1268 )
| ( ord_less_eq_nat @ ( finite_card_nat @ SY1268 ) @ SV476 ) ) )
= $true )
| ( ( ~ ( ~ ( finite_finite_nat @ SV226 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1854]) ).
thf(2174,plain,
! [SV619: list_P559422087at_nat,SV477: nat,SV227: product_prod_nat_nat > b] :
( ( ! [SY1405: nat] :
( ~ ( isPath_b @ SV227 @ SV477 @ SV619 @ SY1405 )
| ( dist_b @ SV227 @ SV477 @ ( size_s1990949619at_nat @ SV619 ) @ SY1405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2175,plain,
! [SV228: set_set_nat] :
( ( ( ~ ( finite2012248349et_nat @ SV228 ) )
= $false )
| ( ( ( finite_card_set_nat @ SV228 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1856]) ).
thf(2176,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
= ( ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2177,plain,
! [SV479: nat,SV230: nat] :
( ( ( ~ ( ord_less_nat @ SV230 @ SV479 ) )
= $true )
| ( ( ord_less_eq_nat @ SV230 @ SV479 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1858]) ).
thf(2178,plain,
! [SV480: set_Pr1986765409at_nat,SV231: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV231 ) )
= $true )
| ( ( ~ ( ord_le841296385at_nat @ SV480 @ SV231 )
| ( finite772653738at_nat @ SV480 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1859]) ).
thf(2179,plain,
! [SV232: product_prod_nat_nat > b] :
( ( ( finite_finite_nat @ ( v_b @ SV232 ) )
= $false )
| ( ( finite_Graph_b @ SV232 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(2180,plain,
! [SV621: nat,SV481: nat,SV233: product_prod_nat_nat > a] :
( ( ~ ( connected_a @ SV233 @ SV481 @ SV621 )
| ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
= zero_zero_nat )
= ( SV621 = SV481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2181,plain,
! [SV622: list_P559422087at_nat,SV482: nat,SV234: product_prod_nat_nat > a] :
( ( ! [SY1406: nat] :
( ~ ( isShortestPath_a @ SV234 @ SV482 @ SV622 @ SY1406 )
| ( isSimplePath_a @ SV234 @ SV482 @ SV622 @ SY1406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2182,plain,
! [SV235: set_se1612935105at_nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( finite1701894793at_nat @ SV235 ) )
= $false )
| ( ( finite1457549322at_nat @ SV235 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(2183,plain,
! [SV623: nat,SV483: list_P559422087at_nat,SV236: nat] :
( ( ~ ( isPath_a @ c @ SV236 @ SV483 @ SV623 )
| ~ ! [SY1407: list_P559422087at_nat] :
~ ( isSimplePath_a @ c @ SV236 @ SY1407 @ SV623 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2184,plain,
! [SV484: nat,SV237: nat] :
( ( ~ ( ( connected_b @ c2 @ SV237 @ SV484 )
| ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) )
| ~ ( ~ ( connected_b @ c2 @ SV237 @ SV484 )
| ~ ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1865]) ).
thf(2185,plain,
! [SV484: nat,SV237: nat] :
( ( ( connected_b @ c2 @ SV237 @ SV484 )
= ( ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1865]) ).
thf(2186,plain,
! [SV624: nat,SV485: nat,SV238: nat] :
( ( ~ ( ord_less_eq_nat @ SV238 @ SV485 )
| ~ ( ord_less_eq_nat @ SV485 @ SV624 )
| ( ord_less_eq_nat @ SV238 @ SV624 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2187,plain,
! [SV239: product_prod_nat_nat > b] :
( ( ( finite_Graph_b @ SV239 )
= $false )
| ( ( edmond1517640973ysis_b @ SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(2188,plain,
! [SV240: product_prod_nat_nat > a] :
( ( ( edmond1517640972ysis_a @ SV240 )
= $false )
| ( ( finite_Graph_a @ SV240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(2189,plain,
! [SV486: set_nat,SV241: product_prod_nat_nat > b] :
( ( ( ~ ( finite_finite_nat @ ( v_b @ SV241 ) ) )
= $true )
| ( ( finite772653738at_nat @ ( incoming_b @ SV241 @ SV486 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(2190,plain,
! [SV487: set_Pr1986765409at_nat,SV242: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV242 @ SV487 ) )
= $true )
| ( ( ~ ( finite772653738at_nat @ SV487 )
| ( finite772653738at_nat @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(2191,plain,
! [SV243: product_prod_nat_nat > b] :
( ( ( finite772653738at_nat @ ( e_b @ SV243 ) )
= $false )
| ( ( finite_finite_nat @ ( v_b @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(2192,plain,
! [SV488: product_prod_nat_nat > a] :
( ( ! [SV625: nat] :
( ( dist_a @ SV488 @ SV625 )
= ( ^ [SY1408: nat,SY1409: nat] :
~ ! [SY1410: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV625 @ SY1410 @ SY1409 )
| ( ( size_s1990949619at_nat @ SY1410 )
!= SY1408 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1873]) ).
thf(2193,plain,
! [SV488: product_prod_nat_nat > a] :
( ( ( dist_a @ SV488 )
= ( ^ [SY1279: nat,SY1280: nat,SY1281: nat] :
~ ! [SY1282: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SY1279 @ SY1282 @ SY1281 )
| ( ( size_s1990949619at_nat @ SY1282 )
!= SY1280 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1873]) ).
thf(2194,plain,
! [SV245: product_prod_nat_nat > b] :
( ( ( finite772653738at_nat @ ( e_b @ SV245 ) )
= $false )
| ( ( finite_Graph_b @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(2195,plain,
! [SV246: product_prod_nat_nat > b] :
( ( ( edmond1517640973ysis_b @ SV246 )
= $false )
| ( ( finite_Graph_b @ SV246 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1875]) ).
thf(2196,plain,
! [SV247: product_prod_nat_nat > b] :
( ( ( edmond1517640973ysis_b @ SV247 )
= $false )
| ( ( ord_le841296385at_nat @ ( e_b @ SV247 ) @ ( edmond771116671s_uE_b @ SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(2197,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
= ( ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2198,plain,
! [SV490: list_P559422087at_nat,SV249: list_P559422087at_nat] :
( ( ( ~ ( ( ( size_s1990949619at_nat @ SV249 )
!= ( size_s1990949619at_nat @ SV490 ) ) ) )
= $true )
| ( ( SV249 != SV490 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1878]) ).
thf(2199,plain,
! [SV250: set_set_nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ SV250 ) )
= $false )
| ( ( finite2012248349et_nat @ SV250 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(2200,plain,
! [SV491: product_prod_nat_nat > b] :
( ( ! [SV627: nat] :
( ( connected_b @ SV491 @ SV627 )
= ( ^ [SY1411: nat] :
~ ! [SY1412: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV627 @ SY1412 @ SY1411 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1880]) ).
thf(2201,plain,
! [SV491: product_prod_nat_nat > b] :
( ( ( connected_b @ SV491 )
= ( ^ [SY1284: nat,SY1285: nat] :
~ ! [SY1286: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SY1284 @ SY1286 @ SY1285 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1880]) ).
thf(2202,plain,
! [SV492: set_Pr1986765409at_nat,SV252: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV252 ) )
= $true )
| ( ( ~ ( ord_le841296385at_nat @ SV492 @ SV252 )
| ( ( finite447719721at_nat @ SV492 )
!= ( finite447719721at_nat @ SV252 ) )
| ( SV492 = SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(2203,plain,
! [SV628: nat,SV493: nat,SV253: nat] :
( ( ~ ( dist_b @ c2 @ SV253 @ SV493 @ SV628 )
| ( ord_less_eq_nat @ ( min_dist_b @ c2 @ SV253 @ SV628 ) @ SV493 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2204,plain,
! [SV629: nat,SV494: nat,SV254: product_prod_nat_nat > b] :
( ( ~ ( connected_b @ SV254 @ SV494 @ SV629 )
| ( ( member_nat @ SV629 @ ( v_b @ SV254 ) )
= ( member_nat @ SV494 @ ( v_b @ SV254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2205,plain,
! [SV630: nat,SV495: nat,SV255: product_prod_nat_nat > b] :
( ( ~ ( connected_b @ SV255 @ SV495 @ SV630 )
| ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
= zero_zero_nat )
= ( SV630 = SV495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2206,plain,
! [SV256: nat] :
( ( ( SV256 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(2207,plain,
! [SV631: nat,SV496: nat,SV257: product_prod_nat_nat > b] :
( ( ~ ( finite_Graph_b @ SV257 )
| ~ ( member_nat @ SV496 @ ( v_b @ SV257 ) )
| ~ ( connected_b @ SV257 @ SV496 @ SV631 )
| ( ord_less_nat @ ( min_dist_b @ SV257 @ SV496 @ SV631 ) @ ( finite_card_nat @ ( v_b @ SV257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2208,plain,
! [SV497: set_Pr1986765409at_nat,SV258: set_Pr1986765409at_nat] :
( ( ( ~ ! [SY1291: product_prod_nat_nat] :
( ~ ( member701585322at_nat @ SY1291 @ SV258 )
| ( member701585322at_nat @ SY1291 @ SV497 ) ) )
= $true )
| ( ( ord_le841296385at_nat @ SV258 @ SV497 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(2209,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ~ ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
| ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) )
| ~ ( ~ ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
| ~ ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1888]) ).
thf(2210,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
= ( ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1888]) ).
thf(2211,plain,
! [SV632: nat,SV499: nat,SV260: nat] :
( ( ! [SY1413: nat] :
( ~ ( connected_a @ c @ SV260 @ SV499 )
| ( ( min_dist_a @ c @ SV260 @ SV499 )
!= SV632 )
| ~ ( ord_less_nat @ SY1413 @ SV632 )
| ~ ! [SY1029: nat] :
~ ~ ( ~ ( connected_a @ c @ SV260 @ SY1029 )
| ( ( min_dist_a @ c @ SV260 @ SY1029 )
!= SY1413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2212,plain,
! [SV500: set_nat,SV261: product_prod_nat_nat > a] :
( ( ( ~ ( finite_finite_nat @ ( v_a @ SV261 ) ) )
= $true )
| ( ( finite772653738at_nat @ ( outgoing_a @ SV261 @ SV500 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(2213,plain,
! [SV501: product_prod_nat_nat > b] :
( ( ! [SV633: nat] :
( ( isShortestPath_b @ SV501 @ SV633 )
= ( ^ [SY1415: list_P559422087at_nat,SY1416: nat] :
~ ( ~ ( isSimplePath_b @ SV501 @ SV633 @ SY1415 @ SY1416 )
| ( ( size_s1990949619at_nat @ SY1415 )
!= ( min_dist_b @ SV501 @ SV633 @ SY1416 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1891]) ).
thf(2214,plain,
! [SV501: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV501 )
= ( ^ [SY1296: nat,SY1297: list_P559422087at_nat,SY1298: nat] :
~ ( ~ ( isSimplePath_b @ SV501 @ SY1296 @ SY1297 @ SY1298 )
| ( ( size_s1990949619at_nat @ SY1297 )
!= ( min_dist_b @ SV501 @ SY1296 @ SY1298 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1891]) ).
thf(2215,plain,
! [SV263: set_li664300135at_nat] :
( ( ( finite1299096496at_nat @ SV263 )
= $false )
| ( ( ~ ! [SY1034: nat] :
~ ! [SY1035: list_P559422087at_nat] :
( ~ ( member1608759472at_nat @ SY1035 @ SV263 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY1035 ) @ SY1034 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1892]) ).
thf(2216,plain,
! [SV634: nat,SV502: nat,SV264: nat] :
( ( ~ ( connected_a @ c @ SV264 @ SV502 )
| ~ ( ord_less_eq_nat @ SV634 @ ( min_dist_a @ c @ SV264 @ SV502 ) )
| ~ ! [SY1417: nat] :
~ ~ ( ~ ( connected_a @ c @ SV264 @ SY1417 )
| ( ( min_dist_a @ c @ SV264 @ SY1417 )
!= SV634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2217,plain,
! [SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ! [SY1418: nat,SY1419: nat] :
( ~ ( connected_b @ SV265 @ SV503 @ SV635 )
| ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
!= SY1418 )
| ~ ( ord_less_nat @ SY1419 @ SY1418 )
| ~ ! [SY1304: nat] :
~ ~ ( ~ ( connected_b @ SV265 @ SV503 @ SY1304 )
| ( ( min_dist_b @ SV265 @ SV503 @ SY1304 )
!= SY1419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2218,plain,
! [SV504: nat,SV266: nat] :
( ( ( ~ ( connected_a @ c @ SV266 @ SV504 ) )
= $true )
| ( ( ~ ! [SY1305: list_P559422087at_nat] :
~ ( isShortestPath_a @ c @ SV266 @ SY1305 @ SV504 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1895]) ).
thf(2219,plain,
! [SV636: nat,SV505: list_P559422087at_nat,SV267: nat] :
( ( ~ ( member_nat @ SV267 @ ( v_a @ c ) )
| ~ ( isShortestPath_a @ c @ SV267 @ SV505 @ SV636 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV505 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2220,plain,
! [SV637: nat,SV506: nat,SV268: product_prod_nat_nat > a] :
( ( ! [SY1421: nat] :
( ~ ( dist_a @ SV268 @ SV506 @ SV637 @ SY1421 )
| ( connected_a @ SV268 @ SV506 @ SY1421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2221,plain,
! [SV507: set_nat,SV269: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV269 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_nat @ SV507 @ SV269 )
| ( finite_finite_nat @ SV507 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(2222,plain,
! [SV508: nat,SV270: set_nat] :
( ( ( ~ ~ ( finite_finite_nat @ SV270 ) )
= $true )
| ( ( ~ ! [SY1309: set_nat] :
~ ~ ( ~ ~ ( ~ ( finite_finite_nat @ SY1309 )
| ( ( finite_card_nat @ SY1309 )
!= SV508 ) )
| ~ ( ord_less_eq_set_nat @ SY1309 @ SV270 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1900]) ).
thf(2223,plain,
! [SV271: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV271 )
| ( SV271 != zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV271 )
| ~ ( ( SV271 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(2224,plain,
! [SV272: set_li664300135at_nat] :
( ( ( ~ ( finite1299096496at_nat @ SV272 ) )
= $false )
| ( ( ( finite83082927at_nat @ SV272 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(2225,plain,
! [SV509: set_nat,SV273: set_set_nat] :
( ( ( ~ ( finite2012248349et_nat @ SV273 ) )
= $true )
| ( ( ~ ( member_set_nat @ SV509 @ SV273 )
| ~ ! [SY1310: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SY1310 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1310 @ SV509 ) )
| ~ ! [SY1056: set_nat] :
( ~ ( member_set_nat @ SY1056 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1056 @ SY1310 )
| ( SY1310 = SY1056 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(2226,plain,
! [SV510: product_prod_nat_nat > $o,SV274: product_prod_nat_nat > $o] :
( ( ( ~ ! [SY1312: product_prod_nat_nat] :
( ( SV274 @ SY1312 )
= ( SV510 @ SY1312 ) ) )
= $true )
| ( ( ( collec7649004at_nat @ SV274 )
= ( collec7649004at_nat @ SV510 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1905]) ).
thf(2227,plain,
! [SV638: nat,SV511: list_P559422087at_nat,SV275: nat] :
( ( ~ ( member_nat @ SV275 @ ( v_b @ c2 ) )
| ~ ( isSimplePath_b @ c2 @ SV275 @ SV511 @ SV638 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV511 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2228,plain,
! [SV639: nat,SV512: list_P559422087at_nat,SV276: nat] :
( ( ~ ( isShortestPath_b @ c2 @ SV276 @ SV512 @ SV639 )
| ( isSimplePath_b @ c2 @ SV276 @ SV512 @ SV639 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2229,plain,
! [SV640: nat,SV513: nat,SV277: product_prod_nat_nat > b] :
( ( ~ ( edmond1517640973ysis_b @ SV277 )
| ( ord_le841296385at_nat @ ( edmond475474836dges_b @ SV277 @ SV513 @ SV640 ) @ ( e_b @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2230,plain,
! [SV278: nat] :
( ( ( member_nat @ SV278 @ ( v_b @ c2 ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( reachableNodes_b @ c2 @ SV278 ) @ ( v_b @ c2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(2231,plain,
! [SV514: set_nat,SV279: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV279 ) )
= $true )
| ( ( ~ ( ord_less_set_nat @ SV514 @ SV279 )
| ( ord_less_nat @ ( finite_card_nat @ SV514 ) @ ( finite_card_nat @ SV279 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(2232,plain,
! [SV280: nat] :
( ( ( ord_less_eq_nat @ SV280 @ zero_zero_nat )
= $false )
| ( ( SV280 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(2233,plain,
! [SV641: nat,SV515: nat,SV281: product_prod_nat_nat > b] :
( ( ! [SY1422: nat] :
( ~ ( dist_b @ SV281 @ SV515 @ SV641 @ SY1422 )
| ( ord_less_eq_nat @ ( min_dist_b @ SV281 @ SV515 @ SY1422 ) @ SV641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2234,plain,
! [SV282: set_nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ SV282 ) )
= $false )
| ( ( finite_finite_nat @ SV282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(2235,plain,
! [SV642: nat,SV516: nat,SV283: nat] :
( ( ~ ( dist_b @ c2 @ SV283 @ SV516 @ SV642 )
| ~ ! [SY1423: nat] :
( ~ ( dist_b @ c2 @ SV283 @ SY1423 @ SV642 )
| ( ord_less_eq_nat @ SV516 @ SY1423 ) )
| ( ( min_dist_b @ c2 @ SV283 @ SV642 )
= SV516 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2236,plain,
! [SV517: set_se1612935105at_nat,SV284: set_se1612935105at_nat] :
( ( ( ~ ( ord_le2096002913at_nat @ SV284 @ SV517 ) )
= $true )
| ( ( ~ ( finite1457549322at_nat @ SV517 )
| ( finite1457549322at_nat @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(2237,plain,
! [SV643: nat,SV518: nat,SV285: product_prod_nat_nat > b] :
( ( ~ ( edmond1517640973ysis_b @ SV285 )
| ( finite772653738at_nat @ ( edmond475474836dges_b @ SV285 @ SV518 @ SV643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2238,plain,
! [SV519: product_prod_nat_nat > b] :
( ( ! [SV644: nat] :
( ( connected_b @ SV519 @ SV644 )
= ( ^ [SY1424: nat] :
~ ! [SY1425: nat] :
~ ( dist_b @ SV519 @ SV644 @ SY1425 @ SY1424 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1918]) ).
thf(2239,plain,
! [SV519: product_prod_nat_nat > b] :
( ( ( connected_b @ SV519 )
= ( ^ [SY1321: nat,SY1322: nat] :
~ ! [SY1323: nat] :
~ ( dist_b @ SV519 @ SY1321 @ SY1323 @ SY1322 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1918]) ).
thf(2240,plain,
! [SV645: set_Pr1986765409at_nat,SV520: set_Pr1986765409at_nat,SV287: set_Pr1986765409at_nat] :
( ( ~ ( ord_le841296385at_nat @ SV287 @ SV520 )
| ~ ( ord_le841296385at_nat @ SV520 @ SV645 )
| ( ord_le841296385at_nat @ SV287 @ SV645 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2241,plain,
! [SV288: set_li664300135at_nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( finite83082927at_nat @ SV288 ) )
= $false )
| ( ( finite1299096496at_nat @ SV288 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2242,plain,
! [SV646: nat,SV521: nat,SV289: product_prod_nat_nat > a] :
( ( ~ ( edmond1517640972ysis_a @ SV289 )
| ( finite772653738at_nat @ ( edmond475474835dges_a @ SV289 @ SV521 @ SV646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2243,plain,
! [SV522: nat,SV290: product_prod_nat_nat > b] :
( ( ( ~ ( finite_Graph_b @ SV290 ) )
= $true )
| ( ( finite_finite_nat @ ( adjacent_nodes_b @ SV290 @ SV522 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1922]) ).
thf(2244,plain,
! [SV647: list_P559422087at_nat,SV523: nat,SV291: product_prod_nat_nat > a] :
( ( ! [SY1426: nat] :
( ~ ( isPath_a @ SV291 @ SV523 @ SV647 @ SY1426 )
| ~ ! [SY1328: list_P559422087at_nat] :
~ ( isSimplePath_a @ SV291 @ SV523 @ SY1328 @ SY1426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2245,plain,
! [SV524: nat,SV292: nat] :
( ( ( ~ ( ord_less_nat @ SV292 @ SV524 ) )
= $true )
| ( ( SV524 != SV292 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1924]) ).
thf(2246,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
= ( ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2247,plain,
! [SV649: nat,SV526: nat,SV294: nat] :
( ( ~ ( dist_a @ c @ SV294 @ SV526 @ SV649 )
| ( connected_a @ c @ SV294 @ SV649 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2248,plain,
! [SV295: product_prod_nat_nat > a] :
( ( ( finite_Graph_a @ SV295 )
= $false )
| ( ( finite_finite_nat @ ( v_a @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1929]) ).
thf(2249,plain,
! [SV650: nat,SV527: nat,SV296: product_prod_nat_nat > a] :
( ( ~ ( connected_a @ SV296 @ SV527 @ SV650 )
| ( dist_a @ SV296 @ SV527 @ ( min_dist_a @ SV296 @ SV527 @ SV650 ) @ SV650 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2250,plain,
! [SV528: nat,SV297: nat] :
( ( ( ~ ( ( ord_less_nat @ SV297 @ SV528 )
| ( SV297 = SV528 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV297 @ SV528 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(2251,plain,
! [SV529: set_Pr1986765409at_nat,SV298: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV298 ) )
= $true )
| ( ( ~ ( ord_le841296385at_nat @ SV529 @ SV298 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ SV529 ) @ ( finite447719721at_nat @ SV298 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1932]) ).
thf(2252,plain,
! [SV530: nat] :
( ( ! [SV651: nat] :
( ( ord_less_nat @ SV530 @ SV651 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV651 )
| ~ ( ( SV530 != SV651 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1933]) ).
thf(2253,plain,
! [SV530: nat] :
( ( ( ord_less_nat @ SV530 )
= ( ^ [SY1332: nat] :
~ ( ~ ( ord_less_eq_nat @ SV530 @ SY1332 )
| ~ ( ( SV530 != SY1332 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1933]) ).
thf(2254,plain,
! [SV652: nat,SV531: list_P559422087at_nat,SV300: nat] :
( ( ~ ( member_nat @ SV300 @ ( v_b @ c2 ) )
| ~ ( isShortestPath_b @ c2 @ SV300 @ SV531 @ SV652 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV531 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2255,plain,
! [SV532: set_Pr1986765409at_nat,SV301: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV301 @ SV532 ) )
= $true )
| ( ( ~ ( ord_le841296385at_nat @ SV532 @ SV301 )
| ( SV301 = SV532 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(2256,plain,
! [SV302: product_prod_nat_nat > a] :
( ( ( finite772653738at_nat @ ( e_a @ SV302 ) )
= $false )
| ( ( finite_finite_nat @ ( v_a @ SV302 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(2257,plain,
! [SV303: set_se1612935105at_nat] :
( ( ( ~ ( finite1457549322at_nat @ SV303 ) )
= $false )
| ( ( ( finite1701894793at_nat @ SV303 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(2258,plain,
! [SV653: nat > $o,SV533: nat,SV304: nat] :
( ( ~ ( connected_b @ c2 @ SV304 @ SV533 )
| ~ ! [SY1428: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1428 @ SV533 )
| ~ ! [SY1336: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1336 @ SV533 )
| ( ord_less_eq_nat @ SY1428 @ SY1336 ) )
| ( SV653 @ SY1428 ) )
| ( SV653 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2259,plain,
! [SV534: list_P559422087at_nat,SV305: list_P559422087at_nat] :
( ( ( ~ ( ( ( size_s1990949619at_nat @ SV305 )
!= ( size_s1990949619at_nat @ SV534 ) ) ) )
= $true )
| ( ( SV305 != SV534 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1939]) ).
thf(2260,plain,
! [SV654: nat,SV535: list_P559422087at_nat,SV306: nat] :
( ( ~ ( isShortestPath_b @ c2 @ SV306 @ SV535 @ SV654 )
| ( isPath_b @ c2 @ SV306 @ SV535 @ SV654 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2261,plain,
! [SV307: set_nat] :
( ( ( finite_finite_nat @ ( v_a @ c ) )
= $false )
| ( ( finite772653738at_nat @ ( incoming_a @ c @ SV307 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(2262,plain,
! [SV655: nat,SV536: list_P559422087at_nat,SV308: nat] :
( ( ~ ( isShortestPath_a @ c @ SV308 @ SV536 @ SV655 )
| ( isPath_a @ c @ SV308 @ SV536 @ SV655 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2263,plain,
! [SV656: nat,SV309: product_prod_nat_nat > b] :
( ( ( edmond1022345717sure_b @ SV309 @ SV656 )
= ( edmond1022345717sure_b @ SV309 @ SV656 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2264,plain,
! [SV657: nat,SV310: product_prod_nat_nat > a] :
( ( ( edmond1022345716sure_a @ SV310 @ SV657 )
= ( edmond1022345716sure_a @ SV310 @ SV657 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2265,plain,
! [SV658: nat,SV313: product_prod_nat_nat > a] :
( ( ( edmond475474835dges_a @ SV313 @ SV658 )
= ( edmond475474835dges_a @ SV313 @ SV658 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2266,plain,
! [SV659: nat,SV314: product_prod_nat_nat > b] :
( ( ( edmond475474836dges_b @ SV314 @ SV659 )
= ( edmond475474836dges_b @ SV314 @ SV659 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2267,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( ~ ( ( edmond1517640972ysis_a @ SV315 )
| ( finite_Graph_a @ SV315 ) ) )
= $true )
| ( ( ~ ( ~ ( edmond1517640972ysis_a @ SV315 )
| ~ ( finite_Graph_a @ SV315 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1951]) ).
thf(2268,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( ~ ( ( edmond1517640973ysis_b @ SV316 )
| ( finite_Graph_b @ SV316 ) ) )
= $true )
| ( ( ~ ( ~ ( edmond1517640973ysis_b @ SV316 )
| ~ ( finite_Graph_b @ SV316 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(2269,plain,
! [SV317: nat,SV13: nat] :
( ( ( ~ ( ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
| ( SV317 = SV13 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
| ( SV317 != SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1955]) ).
thf(2270,plain,
! [SV318: set_Pr1986765409at_nat > $o,SV15: set_Pr1986765409at_nat] :
( ( ( ~ ( ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
| ( SV318 @ SV15 ) ) )
= $true )
| ( ( ~ ( ~ ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
| ~ ( SV318 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1957]) ).
thf(2271,plain,
! [SV319: set_nat > $o,SV16: set_nat] :
( ( ( ~ ( ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
| ( SV319 @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
| ~ ( SV319 @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2272,plain,
! [SV320: product_prod_nat_nat > $o,SV17: product_prod_nat_nat] :
( ( ( ~ ( ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
| ( SV320 @ SV17 ) ) )
= $true )
| ( ( ~ ( ~ ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
| ~ ( SV320 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2273,plain,
! [SV321: nat > $o,SV18: nat] :
( ( ( ~ ( ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
| ( SV321 @ SV18 ) ) )
= $true )
| ( ( ~ ( ~ ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
| ~ ( SV321 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1963]) ).
thf(2274,plain,
! [SV24: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV24 )
| ( SV24 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV24 )
| ( SV24 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(2275,plain,
! [SV25: nat] :
( ( ( ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
| ( SV25 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
| ( SV25 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2276,plain,
! [SV32: nat] :
( ( ( ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
| ( SV32 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
| ( SV32 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2277,plain,
! [SV33: nat] :
( ( ( ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
| ( SV33 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
| ( SV33 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1969]) ).
thf(2278,plain,
! [SV660: nat,SV323: nat] :
( ( ( ord_less_eq_nat @ SV323 @ SV660 )
= ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2279,plain,
! [SV35: nat] :
( ( ( ( zero_zero_nat = SV35 )
| ( SV35 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV35 )
| ( SV35 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2280,plain,
! [SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV324 @ SV661 )
= ( isPath_b @ SV324 @ SV661 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2281,plain,
! [SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV325 @ SV662 )
= ( isPath_a @ SV325 @ SV662 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2282,plain,
! [SV663: nat,SV328: product_prod_nat_nat > a] :
( ( ( min_dist_a @ SV328 @ SV663 )
= ( min_dist_a @ SV328 @ SV663 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2283,plain,
! [SV664: nat,SV329: product_prod_nat_nat > b] :
( ( ( min_dist_b @ SV329 @ SV664 )
= ( min_dist_b @ SV329 @ SV664 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2284,plain,
! [SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( connected_b @ SV330 @ SV665 )
= ( connected_b @ SV330 @ SV665 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2285,plain,
! [SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( connected_a @ SV331 @ SV666 )
= ( connected_a @ SV331 @ SV666 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2286,plain,
! [SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( dist_b @ SV334 @ SV667 )
= ( dist_b @ SV334 @ SV667 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2287,plain,
! [SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( dist_a @ SV335 @ SV668 )
= ( dist_a @ SV335 @ SV668 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2288,plain,
! [SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV336 @ SV669 )
= ( isShortestPath_a @ SV336 @ SV669 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2289,plain,
! [SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV337 @ SV670 )
= ( isShortestPath_b @ SV337 @ SV670 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2290,plain,
! [SV53: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ( SV53 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ( SV53 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2291,plain,
! [SV552: nat,SV342: nat,SV61: product_prod_nat_nat > b] :
( ( ~ ( ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
| ( SV552 = SV342 ) )
| ~ ( ~ ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
| ( SV552 != SV342 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1994]) ).
thf(2292,plain,
! [SV552: nat,SV342: nat,SV61: product_prod_nat_nat > b] :
( ( ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
= ( SV552 = SV342 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1994]) ).
thf(2293,plain,
! [SV553: nat,SV343: nat,SV62: product_prod_nat_nat > a] :
( ( ~ ( ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
| ( SV553 = SV343 ) )
| ~ ( ~ ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
| ( SV553 != SV343 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1995]) ).
thf(2294,plain,
! [SV553: nat,SV343: nat,SV62: product_prod_nat_nat > a] :
( ( ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
= ( SV553 = SV343 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1995]) ).
thf(2295,plain,
! [SV344: nat,SV63: nat] :
( ( ( ~ ( ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
| ( SV344 = SV63 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
| ( SV344 != SV63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2296,plain,
! [SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV345 @ SV671 )
= ( isSimplePath_a @ SV345 @ SV671 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2297,plain,
! [SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV346 @ SV672 )
= ( isSimplePath_b @ SV346 @ SV672 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2298,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( ~ ( ( finite_Graph_b @ SV347 )
| ( finite_finite_nat @ ( v_b @ SV347 ) ) ) )
= $true )
| ( ( ~ ( ~ ( finite_Graph_b @ SV347 )
| ~ ( finite_finite_nat @ ( v_b @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2002]) ).
thf(2299,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( ~ ( ( finite_Graph_a @ SV348 )
| ( finite_finite_nat @ ( v_a @ SV348 ) ) ) )
= $true )
| ( ( ~ ( ~ ( finite_Graph_a @ SV348 )
| ~ ( finite_finite_nat @ ( v_a @ SV348 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2004]) ).
thf(2300,plain,
! [SV673: nat,SV349: product_prod_nat_nat > a] :
( ( ( reachableNodes_a @ SV349 @ SV673 )
= ( reachableNodes_a @ SV349 @ SV673 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2301,plain,
! [SV674: nat,SV350: product_prod_nat_nat > b] :
( ( ( reachableNodes_b @ SV350 @ SV674 )
= ( reachableNodes_b @ SV350 @ SV674 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2302,plain,
! [SV675: nat,SV351: product_prod_nat_nat > b] :
( ( ( adjacent_nodes_b @ SV351 @ SV675 )
= ( adjacent_nodes_b @ SV351 @ SV675 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2303,plain,
! [SV676: nat,SV352: product_prod_nat_nat > a] :
( ( ( adjacent_nodes_a @ SV352 @ SV676 )
= ( adjacent_nodes_a @ SV352 @ SV676 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2304,plain,
! [SV677: set_nat,SV357: product_prod_nat_nat > a] :
( ( ( incoming_a @ SV357 @ SV677 )
= ( incoming_a @ SV357 @ SV677 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2305,plain,
! [SV678: set_nat,SV358: product_prod_nat_nat > b] :
( ( ( incoming_b @ SV358 @ SV678 )
= ( incoming_b @ SV358 @ SV678 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2306,plain,
! [SV679: set_nat,SV359: product_prod_nat_nat > a] :
( ( ( outgoing_a @ SV359 @ SV679 )
= ( outgoing_a @ SV359 @ SV679 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2307,plain,
! [SV680: set_nat,SV360: product_prod_nat_nat > b] :
( ( ( outgoing_b @ SV360 @ SV680 )
= ( outgoing_b @ SV360 @ SV680 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2308,plain,
! [SV93: nat] :
( ( ( ( SV93 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV93 ) )
= $false )
| ( ( ~ ( ~ ( ( SV93 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2309,plain,
! [SV564: nat,SV365: list_P559422087at_nat,SV95: nat] :
( ( ( ~ ( member_nat @ SV95 @ ( v_a @ c ) ) )
= $true )
| ( ( ~ ( isSimplePath_a @ c @ SV95 @ SV365 @ SV564 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV365 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2024]) ).
thf(2310,plain,
! [SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV366 @ SV681 )
= ( ^ [SY1430: list_P559422087at_nat,SY1431: nat] :
~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SY1430 @ SY1431 )
| ( ( size_s1990949619at_nat @ SY1430 )
!= ( min_dist_a @ SV366 @ SV681 @ SY1431 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2311,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ~ ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) )
| ~ ( ~ ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2027]) ).
thf(2312,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= ( ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2027]) ).
thf(2313,plain,
! [SV368: product_prod_nat_nat > b,SV100: nat] :
( ( ( member_nat @ SV100 @ ( v_b @ SV368 ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( reachableNodes_b @ SV368 @ SV100 ) @ ( v_b @ SV368 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2314,plain,
! [SV101: nat] :
( ( ( ( SV101 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV101 ) )
= $false )
| ( ( ~ ( ~ ( ( SV101 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV101 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2315,plain,
! [SV369: set_nat,SV102: set_nat] :
( ( ( ! [SY1117: nat] :
( ~ ( member_nat @ SY1117 @ SV102 )
| ( member_nat @ SY1117 @ SV369 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV102 @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2316,plain,
! [SV682: nat,SV567: list_P559422087at_nat,SV370: nat,SV103: product_prod_nat_nat > a] :
( ( ~ ( finite_Graph_a @ SV103 )
| ~ ( member_nat @ SV370 @ ( v_a @ SV103 ) )
| ~ ( isShortestPath_a @ SV103 @ SV370 @ SV567 @ SV682 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV567 ) @ ( finite_card_nat @ ( v_a @ SV103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2317,plain,
! [SV371: nat,SV104: product_prod_nat_nat > a] :
( ( ( finite_Graph_a @ SV104 )
= $false )
| ( ( finite_finite_nat @ ( adjacent_nodes_a @ SV104 @ SV371 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2318,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( SV372 = SV683 )
= ( ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2319,plain,
! [SV684: nat,SV569: list_P559422087at_nat,SV373: nat,SV106: product_prod_nat_nat > b] :
( ( ~ ( finite_Graph_b @ SV106 )
| ~ ( member_nat @ SV373 @ ( v_b @ SV106 ) )
| ~ ( isShortestPath_b @ SV106 @ SV373 @ SV569 @ SV684 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV569 ) @ ( finite_card_nat @ ( v_b @ SV106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2320,plain,
! [SV685: nat,SV570: list_P559422087at_nat,SV374: nat,SV107: product_prod_nat_nat > a] :
( ( ~ ( isShortestPath_a @ SV107 @ SV374 @ SV570 @ SV685 )
| ( isPath_a @ SV107 @ SV374 @ SV570 @ SV685 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2321,plain,
! [SV375: nat,SV108: nat] :
( ( ( ord_less_nat @ SV108 @ SV375 )
= $false )
| ( ( SV108 != SV375 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2322,plain,
! [SV376: nat,SV109: nat] :
( ( ( SV109 = SV376 )
= $false )
| ( ( ord_less_eq_nat @ SV109 @ SV376 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2323,plain,
! [SV377: nat > $o,SV110: nat > $o] :
( ( ( ! [SY1126: nat] :
( ( SV110 @ SY1126 )
= ( SV377 @ SY1126 ) ) )
= $false )
| ( ( ( collect_nat @ SV110 )
= ( collect_nat @ SV377 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2041]) ).
thf(2324,plain,
! [SV571: nat,SV378: nat,SV111: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV111 @ SV378 @ SV571 ) )
= $true )
| ( ( ( member_nat @ SV571 @ ( v_a @ SV111 ) )
= ( member_nat @ SV378 @ ( v_a @ SV111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2042]) ).
thf(2325,plain,
! [SV572: nat,SV379: nat,SV112: nat] :
( ( ( ~ ( dist_a @ c @ SV112 @ SV379 @ SV572 ) )
= $true )
| ( ( ~ ! [SY1344: nat] :
( ~ ( dist_a @ c @ SV112 @ SY1344 @ SV572 )
| ( ord_less_eq_nat @ SV379 @ SY1344 ) )
| ( ( min_dist_a @ c @ SV112 @ SV572 )
= SV379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2043]) ).
thf(2326,plain,
! [SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( dist_b @ SV380 @ SV686 )
= ( ^ [SY1432: nat,SY1433: nat] :
~ ! [SY1434: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1434 @ SY1433 )
| ( ( size_s1990949619at_nat @ SY1434 )
!= SY1432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2327,plain,
! [SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV381 @ SV687 )
= ( ^ [SY1435: list_P559422087at_nat,SY1436: nat] :
~ ( ~ ( isPath_a @ SV381 @ SV687 @ SY1435 @ SY1436 )
| ~ ! [SY1437: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1437 @ SY1436 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY1435 ) @ ( size_s1990949619at_nat @ SY1437 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2328,plain,
! [SV688: nat,SV575: nat,SV382: nat,SV116: product_prod_nat_nat > a] :
( ( ~ ( dist_a @ SV116 @ SV382 @ SV575 @ SV688 )
| ~ ! [SY1438: nat] :
( ~ ( dist_a @ SV116 @ SV382 @ SY1438 @ SV688 )
| ( ord_less_eq_nat @ SV575 @ SY1438 ) )
| ( ( min_dist_a @ SV116 @ SV382 @ SV688 )
= SV575 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2329,plain,
! [SV383: nat,SV117: nat] :
( ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false )
| ( ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
= zero_zero_nat )
= ( SV383 = SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2330,plain,
! [SV576: nat,SV384: nat,SV118: nat] :
( ( ~ ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) )
| ~ ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2051]) ).
thf(2331,plain,
! [SV576: nat,SV384: nat,SV118: nat] :
( ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= ( ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2051]) ).
thf(2332,plain,
! [SV385: set_Pr1986765409at_nat,SV119: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV119 )
= $false )
| ( ( ~ ( ord_le116442893at_nat @ SV385 @ SV119 )
| ( ord_less_nat @ ( finite447719721at_nat @ SV385 ) @ ( finite447719721at_nat @ SV119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2333,plain,
! [SV689: nat,SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ! [SY1439: nat] :
( ~ ( connected_a @ SV120 @ SV386 @ SV577 )
| ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
!= SV689 )
| ~ ( ord_less_nat @ SY1439 @ SV689 )
| ~ ! [SY1146: nat] :
~ ~ ( ~ ( connected_a @ SV120 @ SV386 @ SY1146 )
| ( ( min_dist_a @ SV120 @ SV386 @ SY1146 )
!= SY1439 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2334,plain,
! [SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( connected_a @ SV387 @ SV690 )
= ( ^ [SY1441: nat] :
~ ! [SY1442: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1442 @ SY1441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2335,plain,
! [SV579: nat,SV388: nat,SV124: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV124 @ SV388 @ SV579 ) )
= $true )
| ( ( ~ ! [SY1359: list_P559422087at_nat] :
~ ( isShortestPath_a @ SV124 @ SV388 @ SY1359 @ SV579 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2058]) ).
thf(2336,plain,
! [SV389: set_nat,SV126: set_nat] :
( ( ( finite_finite_nat @ SV126 )
= $false )
| ( ( ~ ( ord_less_eq_set_nat @ SV389 @ SV126 )
| ( ord_less_eq_nat @ ( finite_card_nat @ SV389 ) @ ( finite_card_nat @ SV126 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2060]) ).
thf(2337,plain,
! [SV580: nat,SV390: nat,SV127: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV127 @ SV390 @ SV580 ) )
= $true )
| ( ( dist_b @ SV127 @ SV390 @ ( min_dist_b @ SV127 @ SV390 @ SV580 ) @ SV580 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2061]) ).
thf(2338,plain,
! [SV691: nat,SV581: nat,SV391: nat,SV128: nat] :
( ( ~ ( connected_b @ c2 @ SV128 @ SV391 )
| ( ( min_dist_b @ c2 @ SV128 @ SV391 )
!= SV581 )
| ~ ( ord_less_nat @ SV691 @ SV581 )
| ~ ! [SY1443: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV128 @ SY1443 )
| ( ( min_dist_b @ c2 @ SV128 @ SY1443 )
!= SV691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2339,plain,
! [SV692: nat > $o,SV582: nat,SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ~ ( connected_a @ SV129 @ SV392 @ SV582 )
| ~ ! [SY1444: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1444 @ SV582 )
| ~ ! [SY1364: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1364 @ SV582 )
| ( ord_less_eq_nat @ SY1444 @ SY1364 ) )
| ( SV692 @ SY1444 ) )
| ( SV692 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2340,plain,
! [SV130: nat] :
( ( ( size_s1990949619at_nat @ ( sK2_SY793 @ SV130 ) )
= SV130 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2064]) ).
thf(2341,plain,
! [SV393: set_set_nat,SV131: set_set_nat] :
( ( ( ord_le1613022364et_nat @ SV131 @ SV393 )
= $false )
| ( ( ~ ( finite2012248349et_nat @ SV393 )
| ( finite2012248349et_nat @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2342,plain,
! [SV394: nat,SV132: nat] :
( ( ( connected_b @ c2 @ SV132 @ SV394 )
= $false )
| ( ( dist_b @ c2 @ SV132 @ ( min_dist_b @ c2 @ SV132 @ SV394 ) @ SV394 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2343,plain,
! [SV395: set_nat,SV133: set_nat] :
( ( ( finite_finite_nat @ SV133 )
= $false )
| ( ( ~ ( ord_less_eq_set_nat @ SV395 @ SV133 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV133 ) @ ( finite_card_nat @ SV395 ) )
| ( SV395 = SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2344,plain,
! [SV693: nat,SV583: nat,SV396: nat,SV134: product_prod_nat_nat > b] :
( ( ~ ( connected_b @ SV134 @ SV396 @ SV583 )
| ~ ( ord_less_eq_nat @ SV693 @ ( min_dist_b @ SV134 @ SV396 @ SV583 ) )
| ~ ! [SY1446: nat] :
~ ~ ( ~ ( connected_b @ SV134 @ SV396 @ SY1446 )
| ( ( min_dist_b @ SV134 @ SV396 @ SY1446 )
!= SV693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2345,plain,
! [SV397: nat,SV135: nat] :
( ( ( connected_b @ c2 @ SV135 @ SV397 )
= $false )
| ( ( ~ ! [SY1163: list_P559422087at_nat] :
~ ( isShortestPath_b @ c2 @ SV135 @ SY1163 @ SV397 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2346,plain,
! [SV398: nat,SV136: nat] :
( ( ( ~ ( ( connected_a @ c @ SV136 @ SV398 )
| ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) ) )
= $true )
| ( ( ~ ( ~ ( connected_a @ c @ SV136 @ SV398 )
| ~ ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2071]) ).
thf(2347,plain,
! [SV399: nat,SV137: set_nat] :
( ( ( finite_finite_nat @ SV137 )
= $false )
| ( ( ~ ( member_nat @ SV399 @ SV137 )
| ~ ! [SY1165: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY1165 @ SV137 )
| ~ ( ord_less_eq_nat @ SY1165 @ SV399 ) )
| ~ ! [SY807: nat] :
( ~ ( member_nat @ SY807 @ SV137 )
| ~ ( ord_less_eq_nat @ SY807 @ SY1165 )
| ( SY1165 = SY807 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2073]) ).
thf(2348,plain,
! [SV694: nat,SV584: list_P559422087at_nat,SV400: nat,SV138: product_prod_nat_nat > a] :
( ( ~ ( finite_Graph_a @ SV138 )
| ~ ( member_nat @ SV400 @ ( v_a @ SV138 ) )
| ~ ( isSimplePath_a @ SV138 @ SV400 @ SV584 @ SV694 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV584 ) @ ( finite_card_nat @ ( v_a @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2349,plain,
! [SV695: nat,SV585: list_P559422087at_nat,SV401: nat,SV139: product_prod_nat_nat > b] :
( ( ~ ( isPath_b @ SV139 @ SV401 @ SV585 @ SV695 )
| ~ ! [SY1447: list_P559422087at_nat] :
~ ( isSimplePath_b @ SV139 @ SV401 @ SY1447 @ SV695 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2350,plain,
! [SV402: set_nat,SV141: product_prod_nat_nat > a] :
( ( ( finite_finite_nat @ ( v_a @ SV141 ) )
= $false )
| ( ( finite772653738at_nat @ ( incoming_a @ SV141 @ SV402 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2077]) ).
thf(2351,plain,
! [SV586: nat,SV403: nat,SV142: nat] :
( ( ( ~ ( connected_b @ c2 @ SV142 @ SV403 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV586 @ ( min_dist_b @ c2 @ SV142 @ SV403 ) )
| ~ ! [SY1370: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV142 @ SY1370 )
| ( ( min_dist_b @ c2 @ SV142 @ SY1370 )
!= SV586 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2078]) ).
thf(2352,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV143 ) )
= $false )
| ( ( ~ ! [SY1174: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( finite772653738at_nat @ SY1174 )
| ( ( finite447719721at_nat @ SY1174 )
!= SV404 ) )
| ~ ( ord_le841296385at_nat @ SY1174 @ SV143 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2353,plain,
! [SV405: set_nat,SV144: set_nat] :
( ( ( ord_less_eq_set_nat @ SV144 @ SV405 )
= $false )
| ( ( ~ ( ord_less_eq_set_nat @ SV405 @ SV144 )
| ( SV144 = SV405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2354,plain,
! [SV696: nat,SV587: list_P559422087at_nat,SV406: nat,SV145: product_prod_nat_nat > a] :
( ( ~ ( isPath_a @ SV145 @ SV406 @ SV587 @ SV696 )
| ( dist_a @ SV145 @ SV406 @ ( size_s1990949619at_nat @ SV587 ) @ SV696 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2355,plain,
! [SV407: nat,SV146: nat] :
( ( ( ~ ( ( connected_a @ c @ SV146 @ SV407 )
| ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) ) )
= $true )
| ( ( ~ ( ~ ( connected_a @ c @ SV146 @ SV407 )
| ~ ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2082]) ).
thf(2356,plain,
! [SV697: nat,SV588: nat,SV408: nat,SV147: product_prod_nat_nat > b] :
( ( ~ ( dist_b @ SV147 @ SV408 @ SV588 @ SV697 )
| ~ ! [SY1448: nat] :
( ~ ( dist_b @ SV147 @ SV408 @ SY1448 @ SV697 )
| ( ord_less_eq_nat @ SV588 @ SY1448 ) )
| ( ( min_dist_b @ SV147 @ SV408 @ SV697 )
= SV588 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2357,plain,
! [SV589: nat,SV409: nat,SV148: product_prod_nat_nat > a] :
( ( ( ~ ( edmond1517640972ysis_a @ SV148 ) )
= $true )
| ( ( ord_le841296385at_nat @ ( edmond475474835dges_a @ SV148 @ SV409 @ SV589 ) @ ( e_a @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2085]) ).
thf(2358,plain,
! [SV698: nat,SV590: nat,SV410: nat,SV149: product_prod_nat_nat > a] :
( ( ~ ( dist_a @ SV149 @ SV410 @ SV590 @ SV698 )
| ( ord_less_eq_nat @ ( min_dist_a @ SV149 @ SV410 @ SV698 ) @ SV590 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2359,plain,
! [SV699: nat,SV591: nat,SV411: nat,SV151: product_prod_nat_nat > a] :
( ( ~ ( connected_a @ SV151 @ SV411 @ SV591 )
| ~ ( ord_less_eq_nat @ SV699 @ ( min_dist_a @ SV151 @ SV411 @ SV591 ) )
| ~ ! [SY1449: nat] :
~ ~ ( ~ ( connected_a @ SV151 @ SV411 @ SY1449 )
| ( ( min_dist_a @ SV151 @ SV411 @ SY1449 )
!= SV699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2360,plain,
! [SV700: nat,SV592: list_P559422087at_nat,SV412: nat,SV153: product_prod_nat_nat > b] :
( ( ~ ( isShortestPath_b @ SV153 @ SV412 @ SV592 @ SV700 )
| ( isPath_b @ SV153 @ SV412 @ SV592 @ SV700 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2361,plain,
! [SV413: nat,SV154: nat] :
( ( ( ord_less_eq_nat @ SV154 @ SV413 )
= $false )
| ( ( ~ ( ( SV154 != SV413 ) )
| ( ord_less_nat @ SV154 @ SV413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2362,plain,
! [SV414: set_nat,SV155: product_prod_nat_nat > b] :
( ( ( finite_finite_nat @ ( v_b @ SV155 ) )
= $false )
| ( ( finite772653738at_nat @ ( outgoing_b @ SV155 @ SV414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2363,plain,
! [SV415: set_Pr1986765409at_nat,SV157: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV157 @ SV415 )
= $false )
| ( ( ~ ( ( SV157 != SV415 ) )
| ( ord_le116442893at_nat @ SV157 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2364,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ~ ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) )
| ~ ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2095]) ).
thf(2365,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= ( ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2095]) ).
thf(2366,plain,
! [SV594: nat,SV417: nat,SV159: nat > $o] :
( ( ( ~ ( SV159 @ SV417 ) )
= $true )
| ( ( ~ ! [SY1379: nat] :
( ~ ( SV159 @ SY1379 )
| ( ord_less_eq_nat @ SY1379 @ SV594 ) )
| ~ ! [SY852: nat] :
~ ~ ( ~ ( SV159 @ SY852 )
| ~ ! [SY853: nat] :
( ~ ( SV159 @ SY853 )
| ( ord_less_eq_nat @ SY853 @ SY852 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2096]) ).
thf(2367,plain,
! [SV418: nat,SV160: nat] :
( ( ( member_nat @ SV160 @ ( v_a @ c ) )
= $false )
| ( ( ~ ( connected_a @ c @ SV160 @ SV418 )
| ( ord_less_nat @ ( min_dist_a @ c @ SV160 @ SV418 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2368,plain,
! [SV595: nat,SV419: nat,SV161: product_prod_nat_nat > b] :
( ( ( ~ ( edmond1517640973ysis_b @ SV161 ) )
= $true )
| ( ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474836dges_b @ SV161 @ SV419 @ SV595 ) ) @ ( finite447719721at_nat @ ( edmond771116671s_uE_b @ SV161 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2098]) ).
thf(2369,plain,
! [SV596: nat,SV420: nat,SV162: nat] :
( ( ( ~ ( dist_a @ c @ SV162 @ SV420 @ SV596 ) )
= $true )
| ( ( ord_less_eq_nat @ ( min_dist_a @ c @ SV162 @ SV596 ) @ SV420 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2099]) ).
thf(2370,plain,
! [SV597: nat,SV421: nat,SV163: nat] :
( ( ~ ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) )
| ~ ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2100]) ).
thf(2371,plain,
! [SV597: nat,SV421: nat,SV163: nat] :
( ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= ( ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2100]) ).
thf(2372,plain,
! [SV422: set_nat,SV164: set_set_nat] :
( ( ( finite2012248349et_nat @ SV164 )
= $false )
| ( ( ~ ( member_set_nat @ SV422 @ SV164 )
| ~ ! [SY1199: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SY1199 @ SV164 )
| ~ ( ord_less_eq_set_nat @ SV422 @ SY1199 ) )
| ~ ! [SY864: set_nat] :
( ~ ( member_set_nat @ SY864 @ SV164 )
| ~ ( ord_less_eq_set_nat @ SY1199 @ SY864 )
| ( SY1199 = SY864 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2373,plain,
! [SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV423 @ SV701 )
= ( ^ [SY1450: list_P559422087at_nat,SY1451: nat] :
~ ( ~ ( isPath_b @ SV423 @ SV701 @ SY1450 @ SY1451 )
| ~ ! [SY1452: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1452 @ SY1451 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY1450 ) @ ( size_s1990949619at_nat @ SY1452 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2374,plain,
! [SV599: nat,SV424: nat,SV166: product_prod_nat_nat > a] :
( ( ( ~ ( edmond1517640972ysis_a @ SV166 ) )
= $true )
| ( ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ SV166 @ SV424 @ SV599 ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ SV166 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2104]) ).
thf(2375,plain,
! [SV600: nat,SV425: nat,SV167: nat > nat] :
( ( ( ~ ! [SY873: nat,SY874: nat] :
( ~ ( ord_less_nat @ SY873 @ SY874 )
| ( ord_less_nat @ ( SV167 @ SY873 ) @ ( SV167 @ SY874 ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV425 @ SV600 )
| ( ord_less_eq_nat @ ( SV167 @ SV425 ) @ ( SV167 @ SV600 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2105]) ).
thf(2376,plain,
! [SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV426 @ SV702 )
= ( ^ [SY1453: list_P559422087at_nat,SY1454: nat] :
~ ( ~ ( isPath_a @ SV426 @ SV702 @ SY1453 @ SY1454 )
| ( ( size_s1990949619at_nat @ SY1453 )
!= ( min_dist_a @ SV426 @ SV702 @ SY1454 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2377,plain,
! [SV427: nat,SV171: nat > $o] :
( ( ( ! [SY879: nat] :
( ~ ~ ( SV171 @ SY879 )
| ~ ! [SY880: nat] :
~ ~ ( ~ ( ord_less_nat @ SY880 @ SY879 )
| ~ ~ ( SV171 @ SY880 ) ) ) )
= $false )
| ( ( SV171 @ SV427 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2378,plain,
! [SV172: nat] :
( ( ( SV172 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV172 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2111]) ).
thf(2379,plain,
! [SV428: set_Pr1986765409at_nat,SV173: set_se1612935105at_nat] :
( ( ( finite1457549322at_nat @ SV173 )
= $false )
| ( ( ~ ( member298845450at_nat @ SV428 @ SV173 )
| ~ ! [SY1214: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SY1214 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY1214 @ SV428 ) )
| ~ ! [SY883: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY883 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY883 @ SY1214 )
| ( SY1214 = SY883 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2112]) ).
thf(2380,plain,
! [SV429: list_P559422087at_nat,SV174: list_P559422087at_nat > $o] :
( ( ( ! [SY885: list_P559422087at_nat] :
( ~ ! [SY886: list_P559422087at_nat] :
( ~ ( ord_less_nat @ ( size_s1990949619at_nat @ SY886 ) @ ( size_s1990949619at_nat @ SY885 ) )
| ( SV174 @ SY886 ) )
| ( SV174 @ SY885 ) ) )
= $false )
| ( ( SV174 @ SV429 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2381,plain,
! [SV602: set_nat,SV430: set_nat,SV175: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV175 @ SV430 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_nat @ SV430 @ SV602 )
| ( ord_less_eq_set_nat @ SV175 @ SV602 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2114]) ).
thf(2382,plain,
! [SV703: nat > $o,SV603: nat,SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ~ ( connected_b @ SV176 @ SV431 @ SV603 )
| ~ ! [SY1455: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1455 @ SV603 )
| ~ ! [SY1392: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1392 @ SV603 )
| ( ord_less_eq_nat @ SY1455 @ SY1392 ) )
| ( SV703 @ SY1455 ) )
| ( SV703 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2383,plain,
! [SV432: set_Pr1986765409at_nat,SV177: set_se1612935105at_nat] :
( ( ( finite1457549322at_nat @ SV177 )
= $false )
| ( ( ~ ( member298845450at_nat @ SV432 @ SV177 )
| ~ ! [SY1223: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SY1223 @ SV177 )
| ~ ( ord_le841296385at_nat @ SV432 @ SY1223 ) )
| ~ ! [SY896: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY896 @ SV177 )
| ~ ( ord_le841296385at_nat @ SY1223 @ SY896 )
| ( SY1223 = SY896 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2384,plain,
! [SV433: nat,SV178: nat] :
( ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false )
| ( ( ( member_nat @ SV433 @ ( v_b @ c2 ) )
= ( member_nat @ SV178 @ ( v_b @ c2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2385,plain,
! [SV604: nat,SV434: nat,SV180: nat] :
( ( ( ~ ( dist_b @ c2 @ SV180 @ SV434 @ SV604 ) )
= $true )
| ( ( connected_b @ c2 @ SV180 @ SV604 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2119]) ).
thf(2386,plain,
! [SV605: nat,SV435: list_P559422087at_nat,SV181: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV181 @ SV435 @ SV605 ) )
= $true )
| ( ( dist_b @ c2 @ SV181 @ ( size_s1990949619at_nat @ SV435 ) @ SV605 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2120]) ).
thf(2387,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ~ ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
| ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
| ~ ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2121]) ).
thf(2388,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( SV437 = SV704 )
= ( ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2389,plain,
! [SV438: set_Pr1986765409at_nat > $o,SV184: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV184 )
= $false )
| ( ( ~ ! [SY1230: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SY1230 )
| ~ ! [SY1231: set_Pr1986765409at_nat] :
( ~ ( ord_le116442893at_nat @ SY1231 @ SY1230 )
| ( SV438 @ SY1231 ) )
| ( SV438 @ SY1230 ) )
| ( SV438 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2390,plain,
! [SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV439 @ SV705 )
= ( ^ [SY1457: list_P559422087at_nat,SY1458: nat] :
~ ( ~ ( isPath_b @ SV439 @ SV705 @ SY1457 @ SY1458 )
| ( ( size_s1990949619at_nat @ SY1457 )
!= ( min_dist_b @ SV439 @ SV705 @ SY1458 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2391,plain,
! [SV440: nat,SV186: nat] :
( ( ( ord_less_eq_nat @ SV186 @ SV440 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV440 @ SV186 )
| ( SV186 = SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2392,plain,
! [SV441: nat,SV187: nat] :
( ( ( ord_less_nat @ SV187 @ SV441 )
= $false )
| ( ( SV441 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2393,plain,
! [SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( connected_a @ SV442 @ SV706 )
= ( ^ [SY1459: nat] :
~ ! [SY1460: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1460 @ SY1459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2394,plain,
! [SV609: nat,SV443: list_P559422087at_nat,SV189: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV189 @ SV443 @ SV609 ) )
= $true )
| ( ( isSimplePath_a @ c @ SV189 @ SV443 @ SV609 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2132]) ).
thf(2395,plain,
! [SV444: set_nat,SV190: set_nat] :
( ( ( finite_finite_nat @ SV190 )
= $false )
| ( ( ~ ( ord_less_eq_set_nat @ SV444 @ SV190 )
| ~ ( ord_less_nat @ ( finite_card_nat @ SV444 ) @ ( finite_card_nat @ SV190 ) )
| ( ord_less_set_nat @ SV444 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2396,plain,
! [SV445: nat,SV191: nat] :
( ( ( connected_a @ c @ SV191 @ SV445 )
= $false )
| ( ( ( ( min_dist_a @ c @ SV191 @ SV445 )
= zero_zero_nat )
= ( SV445 = SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2397,plain,
! [SV446: nat,SV192: nat > $o] :
( ( ( ! [SY922: nat] :
( ~ ! [SY923: nat] :
( ~ ( ord_less_nat @ SY923 @ SY922 )
| ( SV192 @ SY923 ) )
| ( SV192 @ SY922 ) ) )
= $false )
| ( ( SV192 @ SV446 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2398,plain,
! [SV447: nat,SV193: nat] :
( ( ( connected_a @ c @ SV193 @ SV447 )
= $false )
| ( ( ( member_nat @ SV447 @ ( v_a @ c ) )
= ( member_nat @ SV193 @ ( v_a @ c ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2399,plain,
! [SV448: set_nat,SV194: set_nat] :
( ( ( ord_less_eq_set_nat @ SV194 @ SV448 )
= $false )
| ( ( ~ ~ ( finite_finite_nat @ SV194 )
| ~ ( finite_finite_nat @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2400,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( SV196 @ SV449 )
= $false )
| ( ( ~ ~ ( SV196 @ zero_zero_nat )
| ~ ! [SY1241: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_eq_nat @ SY1241 @ SV449 )
| ~ ! [SY928: nat] :
( ~ ( ord_less_nat @ SY928 @ SY1241 )
| ~ ( SV196 @ SY928 ) ) )
| ~ ( SV196 @ SY1241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2401,plain,
! [SV450: nat,SV197: nat] :
( ( ( ord_less_nat @ SV197 @ SV450 )
= $false )
| ( ( SV450 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2402,plain,
( ( isPath_b @ c2 @ s @ sK1_SX0 @ t )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2141]) ).
thf(2403,plain,
( ( ( size_s1990949619at_nat @ sK1_SX0 )
= ( min_dist_b @ c2 @ s @ t ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2142]) ).
thf(2404,plain,
! [SV451: set_Pr1986765409at_nat,SV198: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV198 )
= $false )
| ( ( ~ ( ord_le841296385at_nat @ SV451 @ SV198 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV198 ) @ ( finite447719721at_nat @ SV451 ) )
| ( SV451 = SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2405,plain,
! [SV610: nat,SV452: nat,SV199: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV199 @ SV452 @ SV610 ) )
= $true )
| ( ( ~ ! [SY1397: list_P559422087at_nat] :
~ ( isShortestPath_b @ SV199 @ SV452 @ SY1397 @ SV610 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2144]) ).
thf(2406,plain,
! [SV453: nat,SV200: set_nat] :
( ( ( finite_finite_nat @ SV200 )
= $false )
| ( ( ~ ( member_nat @ SV453 @ SV200 )
| ~ ! [SY1245: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY1245 @ SV200 )
| ~ ( ord_less_eq_nat @ SV453 @ SY1245 ) )
| ~ ! [SY936: nat] :
( ~ ( member_nat @ SY936 @ SV200 )
| ~ ( ord_less_eq_nat @ SY1245 @ SY936 )
| ( SY1245 = SY936 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2407,plain,
! [SV611: nat,SV454: nat,SV201: product_prod_nat_nat > a] :
( ( ( ~ ( finite_Graph_a @ SV201 ) )
= $true )
| ( ( ~ ( member_nat @ SV454 @ ( v_a @ SV201 ) )
| ~ ( connected_a @ SV201 @ SV454 @ SV611 )
| ( ord_less_nat @ ( min_dist_a @ SV201 @ SV454 @ SV611 ) @ ( finite_card_nat @ ( v_a @ SV201 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2146]) ).
thf(2408,plain,
! [SV455: set_Pr1986765409at_nat,SV202: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV202 @ SV455 )
= $false )
| ( ( ~ ~ ( finite772653738at_nat @ SV202 )
| ~ ( finite772653738at_nat @ SV455 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2409,plain,
! [SV707: nat,SV612: list_P559422087at_nat,SV456: nat,SV203: product_prod_nat_nat > b] :
( ( ~ ( isShortestPath_b @ SV203 @ SV456 @ SV612 @ SV707 )
| ( isSimplePath_b @ SV203 @ SV456 @ SV612 @ SV707 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2410,plain,
! [SV204: set_nat] :
( ( ( finite_finite_nat @ SV204 )
= $true )
| ( ( ( finite_card_nat @ SV204 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2149]) ).
thf(2411,plain,
! [SV457: nat,SV205: nat] :
( ( ( SV205 != SV457 )
= $false )
| ( ( ~ ~ ( ord_less_nat @ SV205 @ SV457 )
| ( ord_less_nat @ SV457 @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2412,plain,
! [SV458: set_Pr1986765409at_nat,SV206: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV206 )
= $false )
| ( ( ~ ( ord_le841296385at_nat @ SV458 @ SV206 )
| ~ ( ord_less_nat @ ( finite447719721at_nat @ SV458 ) @ ( finite447719721at_nat @ SV206 ) )
| ( ord_le116442893at_nat @ SV458 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2413,plain,
! [SV613: nat,SV459: list_P559422087at_nat,SV207: nat] :
( ( ( ~ ( isPath_a @ c @ SV207 @ SV459 @ SV613 ) )
= $true )
| ( ( dist_a @ c @ SV207 @ ( size_s1990949619at_nat @ SV459 ) @ SV613 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2414,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ~ ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) )
| ~ ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2153]) ).
thf(2415,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= ( ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2153]) ).
thf(2416,plain,
! [SV461: set_nat,SV209: set_nat] :
( ( ( ord_less_eq_set_nat @ SV209 @ SV461 )
= $false )
| ( ( ~ ( finite_finite_nat @ SV461 )
| ( finite_finite_nat @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2154]) ).
thf(2417,plain,
! [SV615: nat > $o,SV462: nat,SV210: nat] :
( ( ( ~ ( connected_a @ c @ SV210 @ SV462 ) )
= $true )
| ( ( ~ ! [SY1400: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1400 @ SV462 )
| ~ ! [SY1255: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1255 @ SV462 )
| ( ord_less_eq_nat @ SY1400 @ SY1255 ) )
| ( SV615 @ SY1400 ) )
| ( SV615 @ ( min_dist_a @ c @ SV210 @ SV462 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2418,plain,
! [SV463: nat,SV211: nat] :
( ( ( connected_a @ c @ SV211 @ SV463 )
= $false )
| ( ( dist_a @ c @ SV211 @ ( min_dist_a @ c @ SV211 @ SV463 ) @ SV463 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2419,plain,
! [SV212: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV212 )
= $true )
| ( ( ( finite447719721at_nat @ SV212 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2157]) ).
thf(2420,plain,
! [SV464: set_nat,SV213: set_nat] :
( ( ( finite_finite_nat @ SV213 )
= $false )
| ( ( ~ ( ord_less_eq_set_nat @ SV464 @ SV213 )
| ( ( finite_card_nat @ SV464 )
!= ( finite_card_nat @ SV213 ) )
| ( SV464 = SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2158]) ).
thf(2421,plain,
! [SV708: nat,SV616: nat,SV465: nat,SV214: product_prod_nat_nat > b] :
( ( ~ ( dist_b @ SV214 @ SV465 @ SV616 @ SV708 )
| ( connected_b @ SV214 @ SV465 @ SV708 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2422,plain,
! [SV466: nat,SV215: nat] :
( ( ( ~ ( ( connected_b @ c2 @ SV215 @ SV466 )
| ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) ) )
= $true )
| ( ( ~ ( ~ ( connected_b @ c2 @ SV215 @ SV466 )
| ~ ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2160]) ).
thf(2423,plain,
! [SV709: nat,SV617: list_P559422087at_nat,SV467: nat,SV217: product_prod_nat_nat > b] :
( ( ~ ( finite_Graph_b @ SV217 )
| ~ ( member_nat @ SV467 @ ( v_b @ SV217 ) )
| ~ ( isSimplePath_b @ SV217 @ SV467 @ SV617 @ SV709 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV617 ) @ ( finite_card_nat @ ( v_b @ SV217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2424,plain,
! [SV468: nat,SV218: nat] :
( ( ( member_nat @ SV218 @ ( v_b @ c2 ) )
= $false )
| ( ( ~ ( connected_b @ c2 @ SV218 @ SV468 )
| ( ord_less_nat @ ( min_dist_b @ c2 @ SV218 @ SV468 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2425,plain,
! [SV469: set_nat > $o,SV219: set_nat] :
( ( ( finite_finite_nat @ SV219 )
= $false )
| ( ( ~ ! [SY1261: set_nat] :
( ~ ( finite_finite_nat @ SY1261 )
| ~ ! [SY1262: set_nat] :
( ~ ( ord_less_set_nat @ SY1262 @ SY1261 )
| ( SV469 @ SY1262 ) )
| ( SV469 @ SY1261 ) )
| ( SV469 @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2426,plain,
! [SV470: nat,SV220: nat] :
( ( ( ~ ( ( SV220 != SV470 )
| ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV220 != SV470 ) )
| ~ ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2166]) ).
thf(2427,plain,
! [SV618: nat,SV471: list_P559422087at_nat,SV221: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV221 @ SV471 @ SV618 ) )
= $true )
| ( ( ~ ! [SY1404: list_P559422087at_nat] :
~ ( isSimplePath_b @ c2 @ SV221 @ SY1404 @ SV618 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2168]) ).
thf(2428,plain,
! [SV472: nat,SV222: nat > $o] :
( ( ( SV222 @ zero_zero_nat )
= $false )
| ( ( ~ ! [SY974: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY974 )
| ~ ~ ( SV222 @ SY974 )
| ~ ! [SY975: nat] :
~ ~ ( ~ ( ord_less_nat @ SY975 @ SY974 )
| ~ ~ ( SV222 @ SY975 ) ) )
| ( SV222 @ SV472 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2429,plain,
! [SV473: set_nat,SV223: set_nat] :
( ( ( ord_less_eq_set_nat @ SV223 @ SV473 )
= $false )
| ( ( ~ ( ( SV223 != SV473 ) )
| ( ord_less_set_nat @ SV223 @ SV473 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2170]) ).
thf(2430,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( ! [SY1267: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ SY1267 @ SV224 )
| ~ ( finite772653738at_nat @ SY1267 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ SY1267 ) @ SV474 ) ) )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat @ SV224 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2171]) ).
thf(2431,plain,
! [SV475: product_prod_nat_nat > a,SV225: nat] :
( ( ( member_nat @ SV225 @ ( v_a @ SV475 ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( reachableNodes_a @ SV475 @ SV225 ) @ ( v_a @ SV475 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2432,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( ! [SY1268: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY1268 @ SV226 )
| ~ ( finite_finite_nat @ SY1268 )
| ( ord_less_eq_nat @ ( finite_card_nat @ SY1268 ) @ SV476 ) ) )
= $false )
| ( ( ~ ( ~ ( finite_finite_nat @ SV226 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2433,plain,
! [SV710: nat,SV619: list_P559422087at_nat,SV477: nat,SV227: product_prod_nat_nat > b] :
( ( ~ ( isPath_b @ SV227 @ SV477 @ SV619 @ SV710 )
| ( dist_b @ SV227 @ SV477 @ ( size_s1990949619at_nat @ SV619 ) @ SV710 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2434,plain,
! [SV228: set_set_nat] :
( ( ( finite2012248349et_nat @ SV228 )
= $true )
| ( ( ( finite_card_set_nat @ SV228 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2175]) ).
thf(2435,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ~ ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
| ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) )
| ~ ( ~ ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
| ~ ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2176]) ).
thf(2436,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
= ( ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2176]) ).
thf(2437,plain,
! [SV479: nat,SV230: nat] :
( ( ( ord_less_nat @ SV230 @ SV479 )
= $false )
| ( ( ord_less_eq_nat @ SV230 @ SV479 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2438,plain,
! [SV480: set_Pr1986765409at_nat,SV231: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV231 )
= $false )
| ( ( ~ ( ord_le841296385at_nat @ SV480 @ SV231 )
| ( finite772653738at_nat @ SV480 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2178]) ).
thf(2439,plain,
! [SV621: nat,SV481: nat,SV233: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV233 @ SV481 @ SV621 ) )
= $true )
| ( ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
= zero_zero_nat )
= ( SV621 = SV481 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2180]) ).
thf(2440,plain,
! [SV711: nat,SV622: list_P559422087at_nat,SV482: nat,SV234: product_prod_nat_nat > a] :
( ( ~ ( isShortestPath_a @ SV234 @ SV482 @ SV622 @ SV711 )
| ( isSimplePath_a @ SV234 @ SV482 @ SV622 @ SV711 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2441,plain,
! [SV623: nat,SV483: list_P559422087at_nat,SV236: nat] :
( ( ( ~ ( isPath_a @ c @ SV236 @ SV483 @ SV623 ) )
= $true )
| ( ( ~ ! [SY1407: list_P559422087at_nat] :
~ ( isSimplePath_a @ c @ SV236 @ SY1407 @ SV623 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2442,plain,
! [SV484: nat,SV237: nat] :
( ( ( ~ ( ( connected_b @ c2 @ SV237 @ SV484 )
| ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) ) )
= $true )
| ( ( ~ ( ~ ( connected_b @ c2 @ SV237 @ SV484 )
| ~ ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2184]) ).
thf(2443,plain,
! [SV624: nat,SV485: nat,SV238: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV238 @ SV485 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV485 @ SV624 )
| ( ord_less_eq_nat @ SV238 @ SV624 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2186]) ).
thf(2444,plain,
! [SV486: set_nat,SV241: product_prod_nat_nat > b] :
( ( ( finite_finite_nat @ ( v_b @ SV241 ) )
= $false )
| ( ( finite772653738at_nat @ ( incoming_b @ SV241 @ SV486 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2189]) ).
thf(2445,plain,
! [SV487: set_Pr1986765409at_nat,SV242: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV242 @ SV487 )
= $false )
| ( ( ~ ( finite772653738at_nat @ SV487 )
| ( finite772653738at_nat @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2446,plain,
! [SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( dist_a @ SV488 @ SV712 )
= ( ^ [SY1461: nat,SY1462: nat] :
~ ! [SY1463: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1463 @ SY1462 )
| ( ( size_s1990949619at_nat @ SY1463 )
!= SY1461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2447,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ~ ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
| ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) )
| ~ ( ~ ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
| ~ ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2197]) ).
thf(2448,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
= ( ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2197]) ).
thf(2449,plain,
! [SV490: list_P559422087at_nat,SV249: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV249 )
!= ( size_s1990949619at_nat @ SV490 ) )
= $false )
| ( ( SV249 != SV490 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2198]) ).
thf(2450,plain,
! [SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( connected_b @ SV491 @ SV713 )
= ( ^ [SY1464: nat] :
~ ! [SY1465: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1465 @ SY1464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2451,plain,
! [SV492: set_Pr1986765409at_nat,SV252: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV252 )
= $false )
| ( ( ~ ( ord_le841296385at_nat @ SV492 @ SV252 )
| ( ( finite447719721at_nat @ SV492 )
!= ( finite447719721at_nat @ SV252 ) )
| ( SV492 = SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2202]) ).
thf(2452,plain,
! [SV628: nat,SV493: nat,SV253: nat] :
( ( ( ~ ( dist_b @ c2 @ SV253 @ SV493 @ SV628 ) )
= $true )
| ( ( ord_less_eq_nat @ ( min_dist_b @ c2 @ SV253 @ SV628 ) @ SV493 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2453,plain,
! [SV629: nat,SV494: nat,SV254: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV254 @ SV494 @ SV629 ) )
= $true )
| ( ( ( member_nat @ SV629 @ ( v_b @ SV254 ) )
= ( member_nat @ SV494 @ ( v_b @ SV254 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2204]) ).
thf(2454,plain,
! [SV630: nat,SV495: nat,SV255: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV255 @ SV495 @ SV630 ) )
= $true )
| ( ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
= zero_zero_nat )
= ( SV630 = SV495 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2205]) ).
thf(2455,plain,
! [SV256: nat] :
( ( ( SV256 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV256 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2206]) ).
thf(2456,plain,
! [SV631: nat,SV496: nat,SV257: product_prod_nat_nat > b] :
( ( ( ~ ( finite_Graph_b @ SV257 ) )
= $true )
| ( ( ~ ( member_nat @ SV496 @ ( v_b @ SV257 ) )
| ~ ( connected_b @ SV257 @ SV496 @ SV631 )
| ( ord_less_nat @ ( min_dist_b @ SV257 @ SV496 @ SV631 ) @ ( finite_card_nat @ ( v_b @ SV257 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2207]) ).
thf(2457,plain,
! [SV497: set_Pr1986765409at_nat,SV258: set_Pr1986765409at_nat] :
( ( ( ! [SY1291: product_prod_nat_nat] :
( ~ ( member701585322at_nat @ SY1291 @ SV258 )
| ( member701585322at_nat @ SY1291 @ SV497 ) ) )
= $false )
| ( ( ord_le841296385at_nat @ SV258 @ SV497 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2458,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
| ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
| ~ ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2459,plain,
! [SV714: nat,SV632: nat,SV499: nat,SV260: nat] :
( ( ~ ( connected_a @ c @ SV260 @ SV499 )
| ( ( min_dist_a @ c @ SV260 @ SV499 )
!= SV632 )
| ~ ( ord_less_nat @ SV714 @ SV632 )
| ~ ! [SY1466: nat] :
~ ~ ( ~ ( connected_a @ c @ SV260 @ SY1466 )
| ( ( min_dist_a @ c @ SV260 @ SY1466 )
!= SV714 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2460,plain,
! [SV500: set_nat,SV261: product_prod_nat_nat > a] :
( ( ( finite_finite_nat @ ( v_a @ SV261 ) )
= $false )
| ( ( finite772653738at_nat @ ( outgoing_a @ SV261 @ SV500 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2461,plain,
! [SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV501 @ SV715 )
= ( ^ [SY1467: list_P559422087at_nat,SY1468: nat] :
~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SY1467 @ SY1468 )
| ( ( size_s1990949619at_nat @ SY1467 )
!= ( min_dist_b @ SV501 @ SV715 @ SY1468 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(2462,plain,
! [SV263: set_li664300135at_nat] :
( ( ( ! [SY1034: nat] :
~ ! [SY1035: list_P559422087at_nat] :
( ~ ( member1608759472at_nat @ SY1035 @ SV263 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY1035 ) @ SY1034 ) ) )
= $false )
| ( ( finite1299096496at_nat @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2463,plain,
! [SV634: nat,SV502: nat,SV264: nat] :
( ( ( ~ ( connected_a @ c @ SV264 @ SV502 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV634 @ ( min_dist_a @ c @ SV264 @ SV502 ) )
| ~ ! [SY1417: nat] :
~ ~ ( ~ ( connected_a @ c @ SV264 @ SY1417 )
| ( ( min_dist_a @ c @ SV264 @ SY1417 )
!= SV634 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2216]) ).
thf(2464,plain,
! [SV716: nat,SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ! [SY1469: nat] :
( ~ ( connected_b @ SV265 @ SV503 @ SV635 )
| ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
!= SV716 )
| ~ ( ord_less_nat @ SY1469 @ SV716 )
| ~ ! [SY1304: nat] :
~ ~ ( ~ ( connected_b @ SV265 @ SV503 @ SY1304 )
| ( ( min_dist_b @ SV265 @ SV503 @ SY1304 )
!= SY1469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2465,plain,
! [SV504: nat,SV266: nat] :
( ( ( connected_a @ c @ SV266 @ SV504 )
= $false )
| ( ( ~ ! [SY1305: list_P559422087at_nat] :
~ ( isShortestPath_a @ c @ SV266 @ SY1305 @ SV504 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2466,plain,
! [SV636: nat,SV505: list_P559422087at_nat,SV267: nat] :
( ( ( ~ ( member_nat @ SV267 @ ( v_a @ c ) ) )
= $true )
| ( ( ~ ( isShortestPath_a @ c @ SV267 @ SV505 @ SV636 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV505 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2219]) ).
thf(2467,plain,
! [SV717: nat,SV637: nat,SV506: nat,SV268: product_prod_nat_nat > a] :
( ( ~ ( dist_a @ SV268 @ SV506 @ SV637 @ SV717 )
| ( connected_a @ SV268 @ SV506 @ SV717 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2468,plain,
! [SV507: set_nat,SV269: set_nat] :
( ( ( finite_finite_nat @ SV269 )
= $false )
| ( ( ~ ( ord_less_eq_set_nat @ SV507 @ SV269 )
| ( finite_finite_nat @ SV507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2221]) ).
thf(2469,plain,
! [SV508: nat,SV270: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV270 ) )
= $false )
| ( ( ~ ! [SY1309: set_nat] :
~ ~ ( ~ ~ ( ~ ( finite_finite_nat @ SY1309 )
| ( ( finite_card_nat @ SY1309 )
!= SV508 ) )
| ~ ( ord_less_eq_set_nat @ SY1309 @ SV270 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2222]) ).
thf(2470,plain,
! [SV271: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV271 )
| ( SV271 != zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV271 )
| ~ ( ( SV271 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2471,plain,
! [SV272: set_li664300135at_nat] :
( ( ( finite1299096496at_nat @ SV272 )
= $true )
| ( ( ( finite83082927at_nat @ SV272 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2224]) ).
thf(2472,plain,
! [SV509: set_nat,SV273: set_set_nat] :
( ( ( finite2012248349et_nat @ SV273 )
= $false )
| ( ( ~ ( member_set_nat @ SV509 @ SV273 )
| ~ ! [SY1310: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SY1310 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1310 @ SV509 ) )
| ~ ! [SY1056: set_nat] :
( ~ ( member_set_nat @ SY1056 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1056 @ SY1310 )
| ( SY1310 = SY1056 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2225]) ).
thf(2473,plain,
! [SV510: product_prod_nat_nat > $o,SV274: product_prod_nat_nat > $o] :
( ( ( ! [SY1312: product_prod_nat_nat] :
( ( SV274 @ SY1312 )
= ( SV510 @ SY1312 ) ) )
= $false )
| ( ( ( collec7649004at_nat @ SV274 )
= ( collec7649004at_nat @ SV510 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2226]) ).
thf(2474,plain,
! [SV638: nat,SV511: list_P559422087at_nat,SV275: nat] :
( ( ( ~ ( member_nat @ SV275 @ ( v_b @ c2 ) ) )
= $true )
| ( ( ~ ( isSimplePath_b @ c2 @ SV275 @ SV511 @ SV638 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV511 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2227]) ).
thf(2475,plain,
! [SV639: nat,SV512: list_P559422087at_nat,SV276: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV276 @ SV512 @ SV639 ) )
= $true )
| ( ( isSimplePath_b @ c2 @ SV276 @ SV512 @ SV639 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2228]) ).
thf(2476,plain,
! [SV640: nat,SV513: nat,SV277: product_prod_nat_nat > b] :
( ( ( ~ ( edmond1517640973ysis_b @ SV277 ) )
= $true )
| ( ( ord_le841296385at_nat @ ( edmond475474836dges_b @ SV277 @ SV513 @ SV640 ) @ ( e_b @ SV277 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2229]) ).
thf(2477,plain,
! [SV514: set_nat,SV279: set_nat] :
( ( ( finite_finite_nat @ SV279 )
= $false )
| ( ( ~ ( ord_less_set_nat @ SV514 @ SV279 )
| ( ord_less_nat @ ( finite_card_nat @ SV514 ) @ ( finite_card_nat @ SV279 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2231]) ).
thf(2478,plain,
! [SV718: nat,SV641: nat,SV515: nat,SV281: product_prod_nat_nat > b] :
( ( ~ ( dist_b @ SV281 @ SV515 @ SV641 @ SV718 )
| ( ord_less_eq_nat @ ( min_dist_b @ SV281 @ SV515 @ SV718 ) @ SV641 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2479,plain,
! [SV642: nat,SV516: nat,SV283: nat] :
( ( ( ~ ( dist_b @ c2 @ SV283 @ SV516 @ SV642 ) )
= $true )
| ( ( ~ ! [SY1423: nat] :
( ~ ( dist_b @ c2 @ SV283 @ SY1423 @ SV642 )
| ( ord_less_eq_nat @ SV516 @ SY1423 ) )
| ( ( min_dist_b @ c2 @ SV283 @ SV642 )
= SV516 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2235]) ).
thf(2480,plain,
! [SV517: set_se1612935105at_nat,SV284: set_se1612935105at_nat] :
( ( ( ord_le2096002913at_nat @ SV284 @ SV517 )
= $false )
| ( ( ~ ( finite1457549322at_nat @ SV517 )
| ( finite1457549322at_nat @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2236]) ).
thf(2481,plain,
! [SV643: nat,SV518: nat,SV285: product_prod_nat_nat > b] :
( ( ( ~ ( edmond1517640973ysis_b @ SV285 ) )
= $true )
| ( ( finite772653738at_nat @ ( edmond475474836dges_b @ SV285 @ SV518 @ SV643 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2237]) ).
thf(2482,plain,
! [SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( connected_b @ SV519 @ SV719 )
= ( ^ [SY1471: nat] :
~ ! [SY1472: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1472 @ SY1471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2483,plain,
! [SV645: set_Pr1986765409at_nat,SV520: set_Pr1986765409at_nat,SV287: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV287 @ SV520 ) )
= $true )
| ( ( ~ ( ord_le841296385at_nat @ SV520 @ SV645 )
| ( ord_le841296385at_nat @ SV287 @ SV645 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2240]) ).
thf(2484,plain,
! [SV646: nat,SV521: nat,SV289: product_prod_nat_nat > a] :
( ( ( ~ ( edmond1517640972ysis_a @ SV289 ) )
= $true )
| ( ( finite772653738at_nat @ ( edmond475474835dges_a @ SV289 @ SV521 @ SV646 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2242]) ).
thf(2485,plain,
! [SV522: nat,SV290: product_prod_nat_nat > b] :
( ( ( finite_Graph_b @ SV290 )
= $false )
| ( ( finite_finite_nat @ ( adjacent_nodes_b @ SV290 @ SV522 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2243]) ).
thf(2486,plain,
! [SV720: nat,SV647: list_P559422087at_nat,SV523: nat,SV291: product_prod_nat_nat > a] :
( ( ~ ( isPath_a @ SV291 @ SV523 @ SV647 @ SV720 )
| ~ ! [SY1473: list_P559422087at_nat] :
~ ( isSimplePath_a @ SV291 @ SV523 @ SY1473 @ SV720 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2487,plain,
! [SV524: nat,SV292: nat] :
( ( ( ord_less_nat @ SV292 @ SV524 )
= $false )
| ( ( SV524 != SV292 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2245]) ).
thf(2488,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ~ ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) )
| ~ ( ~ ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ~ ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2246]) ).
thf(2489,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
= ( ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2246]) ).
thf(2490,plain,
! [SV649: nat,SV526: nat,SV294: nat] :
( ( ( ~ ( dist_a @ c @ SV294 @ SV526 @ SV649 ) )
= $true )
| ( ( connected_a @ c @ SV294 @ SV649 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2247]) ).
thf(2491,plain,
! [SV650: nat,SV527: nat,SV296: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV296 @ SV527 @ SV650 ) )
= $true )
| ( ( dist_a @ SV296 @ SV527 @ ( min_dist_a @ SV296 @ SV527 @ SV650 ) @ SV650 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2492,plain,
! [SV528: nat,SV297: nat] :
( ( ( ( ord_less_nat @ SV297 @ SV528 )
| ( SV297 = SV528 ) )
= $false )
| ( ( ord_less_eq_nat @ SV297 @ SV528 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2493,plain,
! [SV529: set_Pr1986765409at_nat,SV298: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV298 )
= $false )
| ( ( ~ ( ord_le841296385at_nat @ SV529 @ SV298 )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ SV529 ) @ ( finite447719721at_nat @ SV298 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2251]) ).
thf(2494,plain,
! [SV721: nat,SV530: nat] :
( ( ( ord_less_nat @ SV530 @ SV721 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2495,plain,
! [SV652: nat,SV531: list_P559422087at_nat,SV300: nat] :
( ( ( ~ ( member_nat @ SV300 @ ( v_b @ c2 ) ) )
= $true )
| ( ( ~ ( isShortestPath_b @ c2 @ SV300 @ SV531 @ SV652 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV531 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2254]) ).
thf(2496,plain,
! [SV532: set_Pr1986765409at_nat,SV301: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV301 @ SV532 )
= $false )
| ( ( ~ ( ord_le841296385at_nat @ SV532 @ SV301 )
| ( SV301 = SV532 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2255]) ).
thf(2497,plain,
! [SV303: set_se1612935105at_nat] :
( ( ( finite1457549322at_nat @ SV303 )
= $true )
| ( ( ( finite1701894793at_nat @ SV303 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2257]) ).
thf(2498,plain,
! [SV653: nat > $o,SV533: nat,SV304: nat] :
( ( ( ~ ( connected_b @ c2 @ SV304 @ SV533 ) )
= $true )
| ( ( ~ ! [SY1428: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1428 @ SV533 )
| ~ ! [SY1336: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1336 @ SV533 )
| ( ord_less_eq_nat @ SY1428 @ SY1336 ) )
| ( SV653 @ SY1428 ) )
| ( SV653 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2258]) ).
thf(2499,plain,
! [SV534: list_P559422087at_nat,SV305: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV305 )
!= ( size_s1990949619at_nat @ SV534 ) )
= $false )
| ( ( SV305 != SV534 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2500,plain,
! [SV654: nat,SV535: list_P559422087at_nat,SV306: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV306 @ SV535 @ SV654 ) )
= $true )
| ( ( isPath_b @ c2 @ SV306 @ SV535 @ SV654 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2260]) ).
thf(2501,plain,
! [SV655: nat,SV536: list_P559422087at_nat,SV308: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV308 @ SV536 @ SV655 ) )
= $true )
| ( ( isPath_a @ c @ SV308 @ SV536 @ SV655 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2262]) ).
thf(2502,plain,
! [SV656: nat,SV309: product_prod_nat_nat > b] :
( ( ! [SV722: nat] :
( ( edmond1022345717sure_b @ SV309 @ SV656 @ SV722 )
= ( edmond1022345717sure_b @ SV309 @ SV656 @ SV722 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2263]) ).
thf(2503,plain,
! [SV656: nat,SV309: product_prod_nat_nat > b] :
( ( ( edmond1022345717sure_b @ SV309 @ SV656 )
= ( edmond1022345717sure_b @ SV309 @ SV656 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2263]) ).
thf(2504,plain,
! [SV657: nat,SV310: product_prod_nat_nat > a] :
( ( ! [SV723: nat] :
( ( edmond1022345716sure_a @ SV310 @ SV657 @ SV723 )
= ( edmond1022345716sure_a @ SV310 @ SV657 @ SV723 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2264]) ).
thf(2505,plain,
! [SV657: nat,SV310: product_prod_nat_nat > a] :
( ( ( edmond1022345716sure_a @ SV310 @ SV657 )
= ( edmond1022345716sure_a @ SV310 @ SV657 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2264]) ).
thf(2506,plain,
! [SV658: nat,SV313: product_prod_nat_nat > a] :
( ( ! [SV724: nat] :
( ( edmond475474835dges_a @ SV313 @ SV658 @ SV724 )
= ( edmond475474835dges_a @ SV313 @ SV658 @ SV724 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2265]) ).
thf(2507,plain,
! [SV658: nat,SV313: product_prod_nat_nat > a] :
( ( ( edmond475474835dges_a @ SV313 @ SV658 )
= ( edmond475474835dges_a @ SV313 @ SV658 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2265]) ).
thf(2508,plain,
! [SV659: nat,SV314: product_prod_nat_nat > b] :
( ( ! [SV725: nat] :
( ( edmond475474836dges_b @ SV314 @ SV659 @ SV725 )
= ( edmond475474836dges_b @ SV314 @ SV659 @ SV725 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2266]) ).
thf(2509,plain,
! [SV659: nat,SV314: product_prod_nat_nat > b] :
( ( ( edmond475474836dges_b @ SV314 @ SV659 )
= ( edmond475474836dges_b @ SV314 @ SV659 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2266]) ).
thf(2510,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( ( edmond1517640972ysis_a @ SV315 )
| ( finite_Graph_a @ SV315 ) )
= $false )
| ( ( ~ ( ~ ( edmond1517640972ysis_a @ SV315 )
| ~ ( finite_Graph_a @ SV315 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2267]) ).
thf(2511,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( ( edmond1517640973ysis_b @ SV316 )
| ( finite_Graph_b @ SV316 ) )
= $false )
| ( ( ~ ( ~ ( edmond1517640973ysis_b @ SV316 )
| ~ ( finite_Graph_b @ SV316 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2268]) ).
thf(2512,plain,
! [SV317: nat,SV13: nat] :
( ( ( ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
| ( SV317 = SV13 ) )
= $false )
| ( ( ~ ( ~ ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
| ( SV317 != SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2269]) ).
thf(2513,plain,
! [SV318: set_Pr1986765409at_nat > $o,SV15: set_Pr1986765409at_nat] :
( ( ( ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
| ( SV318 @ SV15 ) )
= $false )
| ( ( ~ ( ~ ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
| ~ ( SV318 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2270]) ).
thf(2514,plain,
! [SV319: set_nat > $o,SV16: set_nat] :
( ( ( ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
| ( SV319 @ SV16 ) )
= $false )
| ( ( ~ ( ~ ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
| ~ ( SV319 @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2271]) ).
thf(2515,plain,
! [SV320: product_prod_nat_nat > $o,SV17: product_prod_nat_nat] :
( ( ( ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
| ( SV320 @ SV17 ) )
= $false )
| ( ( ~ ( ~ ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
| ~ ( SV320 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2516,plain,
! [SV321: nat > $o,SV18: nat] :
( ( ( ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
| ( SV321 @ SV18 ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
| ~ ( SV321 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2517,plain,
! [SV24: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV24 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV24 )
| ( SV24 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2274]) ).
thf(2518,plain,
! [SV24: nat] :
( ( ( SV24 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV24 )
| ( SV24 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2274]) ).
thf(2519,plain,
! [SV25: nat] :
( ( ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
| ( SV25 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2275]) ).
thf(2520,plain,
! [SV25: nat] :
( ( ( SV25 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
| ( SV25 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2275]) ).
thf(2521,plain,
! [SV32: nat] :
( ( ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
| ( SV32 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2276]) ).
thf(2522,plain,
! [SV32: nat] :
( ( ( SV32 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
| ( SV32 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2276]) ).
thf(2523,plain,
! [SV33: nat] :
( ( ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
| ( SV33 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2277]) ).
thf(2524,plain,
! [SV33: nat] :
( ( ( SV33 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
| ( SV33 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2277]) ).
thf(2525,plain,
! [SV660: nat,SV323: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV323 @ SV660 )
| ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV323 @ SV660 )
| ~ ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2278]) ).
thf(2526,plain,
! [SV660: nat,SV323: nat] :
( ( ( ord_less_eq_nat @ SV323 @ SV660 )
= ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2278]) ).
thf(2527,plain,
! [SV35: nat] :
( ( ( zero_zero_nat = SV35 )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV35 )
| ( SV35 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2279]) ).
thf(2528,plain,
! [SV35: nat] :
( ( ( SV35 = zero_zero_nat )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV35 )
| ( SV35 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2279]) ).
thf(2529,plain,
! [SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ! [SV726: list_P559422087at_nat] :
( ( isPath_b @ SV324 @ SV661 @ SV726 )
= ( isPath_b @ SV324 @ SV661 @ SV726 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2280]) ).
thf(2530,plain,
! [SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV324 @ SV661 )
= ( isPath_b @ SV324 @ SV661 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2280]) ).
thf(2531,plain,
! [SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ! [SV727: list_P559422087at_nat] :
( ( isPath_a @ SV325 @ SV662 @ SV727 )
= ( isPath_a @ SV325 @ SV662 @ SV727 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2281]) ).
thf(2532,plain,
! [SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV325 @ SV662 )
= ( isPath_a @ SV325 @ SV662 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2281]) ).
thf(2533,plain,
! [SV663: nat,SV328: product_prod_nat_nat > a] :
( ( ! [SV728: nat] :
( ( min_dist_a @ SV328 @ SV663 @ SV728 )
= ( min_dist_a @ SV328 @ SV663 @ SV728 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2282]) ).
thf(2534,plain,
! [SV663: nat,SV328: product_prod_nat_nat > a] :
( ( ( min_dist_a @ SV328 @ SV663 )
= ( min_dist_a @ SV328 @ SV663 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2282]) ).
thf(2535,plain,
! [SV664: nat,SV329: product_prod_nat_nat > b] :
( ( ! [SV729: nat] :
( ( min_dist_b @ SV329 @ SV664 @ SV729 )
= ( min_dist_b @ SV329 @ SV664 @ SV729 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2283]) ).
thf(2536,plain,
! [SV664: nat,SV329: product_prod_nat_nat > b] :
( ( ( min_dist_b @ SV329 @ SV664 )
= ( min_dist_b @ SV329 @ SV664 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2283]) ).
thf(2537,plain,
! [SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ! [SV730: nat] :
( ( connected_b @ SV330 @ SV665 @ SV730 )
= ( connected_b @ SV330 @ SV665 @ SV730 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2284]) ).
thf(2538,plain,
! [SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( connected_b @ SV330 @ SV665 )
= ( connected_b @ SV330 @ SV665 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2284]) ).
thf(2539,plain,
! [SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ! [SV731: nat] :
( ( connected_a @ SV331 @ SV666 @ SV731 )
= ( connected_a @ SV331 @ SV666 @ SV731 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2285]) ).
thf(2540,plain,
! [SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( connected_a @ SV331 @ SV666 )
= ( connected_a @ SV331 @ SV666 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2285]) ).
thf(2541,plain,
! [SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ! [SV732: nat] :
( ( dist_b @ SV334 @ SV667 @ SV732 )
= ( dist_b @ SV334 @ SV667 @ SV732 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2286]) ).
thf(2542,plain,
! [SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( dist_b @ SV334 @ SV667 )
= ( dist_b @ SV334 @ SV667 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2286]) ).
thf(2543,plain,
! [SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ! [SV733: nat] :
( ( dist_a @ SV335 @ SV668 @ SV733 )
= ( dist_a @ SV335 @ SV668 @ SV733 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2287]) ).
thf(2544,plain,
! [SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( dist_a @ SV335 @ SV668 )
= ( dist_a @ SV335 @ SV668 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2287]) ).
thf(2545,plain,
! [SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ! [SV734: list_P559422087at_nat] :
( ( isShortestPath_a @ SV336 @ SV669 @ SV734 )
= ( isShortestPath_a @ SV336 @ SV669 @ SV734 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2288]) ).
thf(2546,plain,
! [SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV336 @ SV669 )
= ( isShortestPath_a @ SV336 @ SV669 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2288]) ).
thf(2547,plain,
! [SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ! [SV735: list_P559422087at_nat] :
( ( isShortestPath_b @ SV337 @ SV670 @ SV735 )
= ( isShortestPath_b @ SV337 @ SV670 @ SV735 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2289]) ).
thf(2548,plain,
! [SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV337 @ SV670 )
= ( isShortestPath_b @ SV337 @ SV670 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2289]) ).
thf(2549,plain,
! [SV53: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ( SV53 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2290]) ).
thf(2550,plain,
! [SV53: nat] :
( ( ( SV53 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ( SV53 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2290]) ).
thf(2551,plain,
! [SV552: nat,SV342: nat,SV61: product_prod_nat_nat > b] :
( ( ( ~ ( ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
| ( SV552 = SV342 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
| ( SV552 != SV342 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2291]) ).
thf(2552,plain,
! [SV553: nat,SV343: nat,SV62: product_prod_nat_nat > a] :
( ( ( ~ ( ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
| ( SV553 = SV343 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
| ( SV553 != SV343 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2293]) ).
thf(2553,plain,
! [SV344: nat,SV63: nat] :
( ( ( ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
| ( SV344 = SV63 ) )
= $false )
| ( ( ~ ( ~ ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
| ( SV344 != SV63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2554,plain,
! [SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ! [SV736: list_P559422087at_nat] :
( ( isSimplePath_a @ SV345 @ SV671 @ SV736 )
= ( isSimplePath_a @ SV345 @ SV671 @ SV736 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2296]) ).
thf(2555,plain,
! [SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV345 @ SV671 )
= ( isSimplePath_a @ SV345 @ SV671 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2296]) ).
thf(2556,plain,
! [SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ! [SV737: list_P559422087at_nat] :
( ( isSimplePath_b @ SV346 @ SV672 @ SV737 )
= ( isSimplePath_b @ SV346 @ SV672 @ SV737 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2297]) ).
thf(2557,plain,
! [SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV346 @ SV672 )
= ( isSimplePath_b @ SV346 @ SV672 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2297]) ).
thf(2558,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( ( finite_Graph_b @ SV347 )
| ( finite_finite_nat @ ( v_b @ SV347 ) ) )
= $false )
| ( ( ~ ( ~ ( finite_Graph_b @ SV347 )
| ~ ( finite_finite_nat @ ( v_b @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2559,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( ( finite_Graph_a @ SV348 )
| ( finite_finite_nat @ ( v_a @ SV348 ) ) )
= $false )
| ( ( ~ ( ~ ( finite_Graph_a @ SV348 )
| ~ ( finite_finite_nat @ ( v_a @ SV348 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2560,plain,
! [SV93: nat] :
( ( ( SV93 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ( SV93 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV93 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2308]) ).
thf(2561,plain,
! [SV93: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV93 )
= $false )
| ( ( ~ ( ~ ( ( SV93 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV93 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2308]) ).
thf(2562,plain,
! [SV564: nat,SV365: list_P559422087at_nat,SV95: nat] :
( ( ( member_nat @ SV95 @ ( v_a @ c ) )
= $false )
| ( ( ~ ( isSimplePath_a @ c @ SV95 @ SV365 @ SV564 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV365 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2563,plain,
! [SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ! [SV738: list_P559422087at_nat] :
( ( isShortestPath_a @ SV366 @ SV681 @ SV738 )
= ( ^ [SY1474: nat] :
~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV738 @ SY1474 )
| ( ( size_s1990949619at_nat @ SV738 )
!= ( min_dist_a @ SV366 @ SV681 @ SY1474 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2310]) ).
thf(2564,plain,
! [SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV366 @ SV681 )
= ( ^ [SY1430: list_P559422087at_nat,SY1431: nat] :
~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SY1430 @ SY1431 )
| ( ( size_s1990949619at_nat @ SY1430 )
!= ( min_dist_a @ SV366 @ SV681 @ SY1431 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2310]) ).
thf(2565,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2311]) ).
thf(2566,plain,
! [SV101: nat] :
( ( ( SV101 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ( SV101 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV101 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2314]) ).
thf(2567,plain,
! [SV101: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV101 )
= $false )
| ( ( ~ ( ~ ( ( SV101 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV101 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2314]) ).
thf(2568,plain,
! [SV102: set_nat,SV369: set_nat] :
( ( ( ~ ( member_nat @ ( sK3_SY1117 @ SV369 @ SV102 ) @ SV102 )
| ( member_nat @ ( sK3_SY1117 @ SV369 @ SV102 ) @ SV369 ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV102 @ SV369 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2315]) ).
thf(2569,plain,
! [SV682: nat,SV567: list_P559422087at_nat,SV370: nat,SV103: product_prod_nat_nat > a] :
( ( ( ~ ( finite_Graph_a @ SV103 ) )
= $true )
| ( ( ~ ( member_nat @ SV370 @ ( v_a @ SV103 ) )
| ~ ( isShortestPath_a @ SV103 @ SV370 @ SV567 @ SV682 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV567 ) @ ( finite_card_nat @ ( v_a @ SV103 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2316]) ).
thf(2570,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ~ ( ( SV372 = SV683 )
| ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) )
| ~ ( ( SV372 != SV683 )
| ~ ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2318]) ).
thf(2571,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( SV372 = SV683 )
= ( ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2318]) ).
thf(2572,plain,
! [SV684: nat,SV569: list_P559422087at_nat,SV373: nat,SV106: product_prod_nat_nat > b] :
( ( ( ~ ( finite_Graph_b @ SV106 ) )
= $true )
| ( ( ~ ( member_nat @ SV373 @ ( v_b @ SV106 ) )
| ~ ( isShortestPath_b @ SV106 @ SV373 @ SV569 @ SV684 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV569 ) @ ( finite_card_nat @ ( v_b @ SV106 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2573,plain,
! [SV685: nat,SV570: list_P559422087at_nat,SV374: nat,SV107: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV107 @ SV374 @ SV570 @ SV685 ) )
= $true )
| ( ( isPath_a @ SV107 @ SV374 @ SV570 @ SV685 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2320]) ).
thf(2574,plain,
! [SV375: nat,SV108: nat] :
( ( ( SV108 = SV375 )
= $false )
| ( ( ord_less_nat @ SV108 @ SV375 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2575,plain,
! [SV377: nat > $o,SV110: nat > $o] :
( ( ( ( SV110 @ ( sK4_SY1126 @ SV377 @ SV110 ) )
= ( SV377 @ ( sK4_SY1126 @ SV377 @ SV110 ) ) )
= $false )
| ( ( ( collect_nat @ SV110 )
= ( collect_nat @ SV377 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2323]) ).
thf(2576,plain,
! [SV571: nat,SV378: nat,SV111: product_prod_nat_nat > a] :
( ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false )
| ( ( ( member_nat @ SV571 @ ( v_a @ SV111 ) )
= ( member_nat @ SV378 @ ( v_a @ SV111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2577,plain,
! [SV572: nat,SV379: nat,SV112: nat] :
( ( ( dist_a @ c @ SV112 @ SV379 @ SV572 )
= $false )
| ( ( ~ ! [SY1344: nat] :
( ~ ( dist_a @ c @ SV112 @ SY1344 @ SV572 )
| ( ord_less_eq_nat @ SV379 @ SY1344 ) )
| ( ( min_dist_a @ c @ SV112 @ SV572 )
= SV379 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2578,plain,
! [SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ! [SV739: nat] :
( ( dist_b @ SV380 @ SV686 @ SV739 )
= ( ^ [SY1475: nat] :
~ ! [SY1476: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1476 @ SY1475 )
| ( ( size_s1990949619at_nat @ SY1476 )
!= SV739 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2326]) ).
thf(2579,plain,
! [SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( dist_b @ SV380 @ SV686 )
= ( ^ [SY1432: nat,SY1433: nat] :
~ ! [SY1434: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1434 @ SY1433 )
| ( ( size_s1990949619at_nat @ SY1434 )
!= SY1432 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2326]) ).
thf(2580,plain,
! [SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ! [SV740: list_P559422087at_nat] :
( ( isShortestPath_a @ SV381 @ SV687 @ SV740 )
= ( ^ [SY1477: nat] :
~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV740 @ SY1477 )
| ~ ! [SY1478: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1478 @ SY1477 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV740 ) @ ( size_s1990949619at_nat @ SY1478 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2327]) ).
thf(2581,plain,
! [SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV381 @ SV687 )
= ( ^ [SY1435: list_P559422087at_nat,SY1436: nat] :
~ ( ~ ( isPath_a @ SV381 @ SV687 @ SY1435 @ SY1436 )
| ~ ! [SY1437: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1437 @ SY1436 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY1435 ) @ ( size_s1990949619at_nat @ SY1437 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2327]) ).
thf(2582,plain,
! [SV688: nat,SV575: nat,SV382: nat,SV116: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV116 @ SV382 @ SV575 @ SV688 ) )
= $true )
| ( ( ~ ! [SY1438: nat] :
( ~ ( dist_a @ SV116 @ SV382 @ SY1438 @ SV688 )
| ( ord_less_eq_nat @ SV575 @ SY1438 ) )
| ( ( min_dist_a @ SV116 @ SV382 @ SV688 )
= SV575 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2328]) ).
thf(2583,plain,
! [SV383: nat,SV117: nat] :
( ( ( ~ ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
= zero_zero_nat )
| ( SV383 = SV117 ) )
| ~ ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
!= zero_zero_nat )
| ( SV383 != SV117 ) ) )
= $true )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2329]) ).
thf(2584,plain,
! [SV383: nat,SV117: nat] :
( ( ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
= zero_zero_nat )
= ( SV383 = SV117 ) )
= $true )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2329]) ).
thf(2585,plain,
! [SV576: nat,SV384: nat,SV118: nat] :
( ( ( ~ ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) ) )
= $true )
| ( ( ~ ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2330]) ).
thf(2586,plain,
! [SV119: set_Pr1986765409at_nat,SV385: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le116442893at_nat @ SV385 @ SV119 ) )
= $true )
| ( ( ord_less_nat @ ( finite447719721at_nat @ SV385 ) @ ( finite447719721at_nat @ SV119 ) )
= $true )
| ( ( finite772653738at_nat @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2587,plain,
! [SV741: nat,SV689: nat,SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ~ ( connected_a @ SV120 @ SV386 @ SV577 )
| ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
!= SV689 )
| ~ ( ord_less_nat @ SV741 @ SV689 )
| ~ ! [SY1479: nat] :
~ ~ ( ~ ( connected_a @ SV120 @ SV386 @ SY1479 )
| ( ( min_dist_a @ SV120 @ SV386 @ SY1479 )
!= SV741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(2588,plain,
! [SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ! [SV742: nat] :
( ( connected_a @ SV387 @ SV690 @ SV742 )
= ( ~ ! [SY1480: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1480 @ SV742 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2334]) ).
thf(2589,plain,
! [SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( connected_a @ SV387 @ SV690 )
= ( ^ [SY1441: nat] :
~ ! [SY1442: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1442 @ SY1441 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2334]) ).
thf(2590,plain,
! [SV579: nat,SV388: nat,SV124: product_prod_nat_nat > a] :
( ( ( connected_a @ SV124 @ SV388 @ SV579 )
= $false )
| ( ( ~ ! [SY1359: list_P559422087at_nat] :
~ ( isShortestPath_a @ SV124 @ SV388 @ SY1359 @ SV579 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2591,plain,
! [SV126: set_nat,SV389: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV389 @ SV126 ) )
= $true )
| ( ( ord_less_eq_nat @ ( finite_card_nat @ SV389 ) @ ( finite_card_nat @ SV126 ) )
= $true )
| ( ( finite_finite_nat @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2336]) ).
thf(2592,plain,
! [SV580: nat,SV390: nat,SV127: product_prod_nat_nat > b] :
( ( ( connected_b @ SV127 @ SV390 @ SV580 )
= $false )
| ( ( dist_b @ SV127 @ SV390 @ ( min_dist_b @ SV127 @ SV390 @ SV580 ) @ SV580 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2593,plain,
! [SV691: nat,SV581: nat,SV391: nat,SV128: nat] :
( ( ( ~ ( connected_b @ c2 @ SV128 @ SV391 ) )
= $true )
| ( ( ( ( min_dist_b @ c2 @ SV128 @ SV391 )
!= SV581 )
| ~ ( ord_less_nat @ SV691 @ SV581 )
| ~ ! [SY1443: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV128 @ SY1443 )
| ( ( min_dist_b @ c2 @ SV128 @ SY1443 )
!= SV691 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2338]) ).
thf(2594,plain,
! [SV692: nat > $o,SV582: nat,SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV129 @ SV392 @ SV582 ) )
= $true )
| ( ( ~ ! [SY1444: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1444 @ SV582 )
| ~ ! [SY1364: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1364 @ SV582 )
| ( ord_less_eq_nat @ SY1444 @ SY1364 ) )
| ( SV692 @ SY1444 ) )
| ( SV692 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2339]) ).
thf(2595,plain,
! [SV131: set_set_nat,SV393: set_set_nat] :
( ( ( ~ ( finite2012248349et_nat @ SV393 ) )
= $true )
| ( ( finite2012248349et_nat @ SV131 )
= $true )
| ( ( ord_le1613022364et_nat @ SV131 @ SV393 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2341]) ).
thf(2596,plain,
! [SV133: set_nat,SV395: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV395 @ SV133 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV133 ) @ ( finite_card_nat @ SV395 ) )
| ( SV395 = SV133 ) )
= $true )
| ( ( finite_finite_nat @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2343]) ).
thf(2597,plain,
! [SV693: nat,SV583: nat,SV396: nat,SV134: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV134 @ SV396 @ SV583 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV693 @ ( min_dist_b @ SV134 @ SV396 @ SV583 ) )
| ~ ! [SY1446: nat] :
~ ~ ( ~ ( connected_b @ SV134 @ SV396 @ SY1446 )
| ( ( min_dist_b @ SV134 @ SV396 @ SY1446 )
!= SV693 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2344]) ).
thf(2598,plain,
! [SV397: nat,SV135: nat] :
( ( ( ! [SY1163: list_P559422087at_nat] :
~ ( isShortestPath_b @ c2 @ SV135 @ SY1163 @ SV397 ) )
= $false )
| ( ( connected_b @ c2 @ SV135 @ SV397 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2345]) ).
thf(2599,plain,
! [SV398: nat,SV136: nat] :
( ( ( ( connected_a @ c @ SV136 @ SV398 )
| ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) )
= $false )
| ( ( ~ ( ~ ( connected_a @ c @ SV136 @ SV398 )
| ~ ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2346]) ).
thf(2600,plain,
! [SV137: set_nat,SV399: nat] :
( ( ( ~ ( member_nat @ SV399 @ SV137 ) )
= $true )
| ( ( ~ ! [SY1165: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY1165 @ SV137 )
| ~ ( ord_less_eq_nat @ SY1165 @ SV399 ) )
| ~ ! [SY807: nat] :
( ~ ( member_nat @ SY807 @ SV137 )
| ~ ( ord_less_eq_nat @ SY807 @ SY1165 )
| ( SY1165 = SY807 ) ) ) )
= $true )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2601,plain,
! [SV694: nat,SV584: list_P559422087at_nat,SV400: nat,SV138: product_prod_nat_nat > a] :
( ( ( ~ ( finite_Graph_a @ SV138 ) )
= $true )
| ( ( ~ ( member_nat @ SV400 @ ( v_a @ SV138 ) )
| ~ ( isSimplePath_a @ SV138 @ SV400 @ SV584 @ SV694 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV584 ) @ ( finite_card_nat @ ( v_a @ SV138 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2602,plain,
! [SV695: nat,SV585: list_P559422087at_nat,SV401: nat,SV139: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV139 @ SV401 @ SV585 @ SV695 ) )
= $true )
| ( ( ~ ! [SY1447: list_P559422087at_nat] :
~ ( isSimplePath_b @ SV139 @ SV401 @ SY1447 @ SV695 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2349]) ).
thf(2603,plain,
! [SV586: nat,SV403: nat,SV142: nat] :
( ( ( connected_b @ c2 @ SV142 @ SV403 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV586 @ ( min_dist_b @ c2 @ SV142 @ SV403 ) )
| ~ ! [SY1370: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV142 @ SY1370 )
| ( ( min_dist_b @ c2 @ SV142 @ SY1370 )
!= SV586 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2351]) ).
thf(2604,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV143 )
= $true )
| ( ( ~ ! [SY1174: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( finite772653738at_nat @ SY1174 )
| ( ( finite447719721at_nat @ SY1174 )
!= SV404 ) )
| ~ ( ord_le841296385at_nat @ SY1174 @ SV143 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2352]) ).
thf(2605,plain,
! [SV144: set_nat,SV405: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV405 @ SV144 ) )
= $true )
| ( ( SV144 = SV405 )
= $true )
| ( ( ord_less_eq_set_nat @ SV144 @ SV405 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2353]) ).
thf(2606,plain,
! [SV696: nat,SV587: list_P559422087at_nat,SV406: nat,SV145: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV145 @ SV406 @ SV587 @ SV696 ) )
= $true )
| ( ( dist_a @ SV145 @ SV406 @ ( size_s1990949619at_nat @ SV587 ) @ SV696 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2607,plain,
! [SV407: nat,SV146: nat] :
( ( ( ( connected_a @ c @ SV146 @ SV407 )
| ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) )
= $false )
| ( ( ~ ( ~ ( connected_a @ c @ SV146 @ SV407 )
| ~ ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2608,plain,
! [SV697: nat,SV588: nat,SV408: nat,SV147: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV147 @ SV408 @ SV588 @ SV697 ) )
= $true )
| ( ( ~ ! [SY1448: nat] :
( ~ ( dist_b @ SV147 @ SV408 @ SY1448 @ SV697 )
| ( ord_less_eq_nat @ SV588 @ SY1448 ) )
| ( ( min_dist_b @ SV147 @ SV408 @ SV697 )
= SV588 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2356]) ).
thf(2609,plain,
! [SV589: nat,SV409: nat,SV148: product_prod_nat_nat > a] :
( ( ( edmond1517640972ysis_a @ SV148 )
= $false )
| ( ( ord_le841296385at_nat @ ( edmond475474835dges_a @ SV148 @ SV409 @ SV589 ) @ ( e_a @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2610,plain,
! [SV698: nat,SV590: nat,SV410: nat,SV149: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV149 @ SV410 @ SV590 @ SV698 ) )
= $true )
| ( ( ord_less_eq_nat @ ( min_dist_a @ SV149 @ SV410 @ SV698 ) @ SV590 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2358]) ).
thf(2611,plain,
! [SV699: nat,SV591: nat,SV411: nat,SV151: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV151 @ SV411 @ SV591 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV699 @ ( min_dist_a @ SV151 @ SV411 @ SV591 ) )
| ~ ! [SY1449: nat] :
~ ~ ( ~ ( connected_a @ SV151 @ SV411 @ SY1449 )
| ( ( min_dist_a @ SV151 @ SV411 @ SY1449 )
!= SV699 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2359]) ).
thf(2612,plain,
! [SV700: nat,SV592: list_P559422087at_nat,SV412: nat,SV153: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV153 @ SV412 @ SV592 @ SV700 ) )
= $true )
| ( ( isPath_b @ SV153 @ SV412 @ SV592 @ SV700 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2360]) ).
thf(2613,plain,
! [SV413: nat,SV154: nat] :
( ( ( ~ ( ( SV154 != SV413 ) ) )
= $true )
| ( ( ord_less_nat @ SV154 @ SV413 )
= $true )
| ( ( ord_less_eq_nat @ SV154 @ SV413 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2361]) ).
thf(2614,plain,
! [SV415: set_Pr1986765409at_nat,SV157: set_Pr1986765409at_nat] :
( ( ( ~ ( ( SV157 != SV415 ) ) )
= $true )
| ( ( ord_le116442893at_nat @ SV157 @ SV415 )
= $true )
| ( ( ord_le841296385at_nat @ SV157 @ SV415 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2615,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2616,plain,
! [SV594: nat,SV417: nat,SV159: nat > $o] :
( ( ( SV159 @ SV417 )
= $false )
| ( ( ~ ! [SY1379: nat] :
( ~ ( SV159 @ SY1379 )
| ( ord_less_eq_nat @ SY1379 @ SV594 ) )
| ~ ! [SY852: nat] :
~ ~ ( ~ ( SV159 @ SY852 )
| ~ ! [SY853: nat] :
( ~ ( SV159 @ SY853 )
| ( ord_less_eq_nat @ SY853 @ SY852 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2366]) ).
thf(2617,plain,
! [SV418: nat,SV160: nat] :
( ( ( ~ ( connected_a @ c @ SV160 @ SV418 ) )
= $true )
| ( ( ord_less_nat @ ( min_dist_a @ c @ SV160 @ SV418 ) @ ( finite_card_nat @ ( v_a @ c ) ) )
= $true )
| ( ( member_nat @ SV160 @ ( v_a @ c ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2367]) ).
thf(2618,plain,
! [SV595: nat,SV419: nat,SV161: product_prod_nat_nat > b] :
( ( ( edmond1517640973ysis_b @ SV161 )
= $false )
| ( ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474836dges_b @ SV161 @ SV419 @ SV595 ) ) @ ( finite447719721at_nat @ ( edmond771116671s_uE_b @ SV161 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2368]) ).
thf(2619,plain,
! [SV596: nat,SV420: nat,SV162: nat] :
( ( ( dist_a @ c @ SV162 @ SV420 @ SV596 )
= $false )
| ( ( ord_less_eq_nat @ ( min_dist_a @ c @ SV162 @ SV596 ) @ SV420 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2369]) ).
thf(2620,plain,
! [SV597: nat,SV421: nat,SV163: nat] :
( ( ( ~ ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) ) )
= $true )
| ( ( ~ ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2621,plain,
! [SV164: set_set_nat,SV422: set_nat] :
( ( ( ~ ( member_set_nat @ SV422 @ SV164 ) )
= $true )
| ( ( ~ ! [SY1199: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SY1199 @ SV164 )
| ~ ( ord_less_eq_set_nat @ SV422 @ SY1199 ) )
| ~ ! [SY864: set_nat] :
( ~ ( member_set_nat @ SY864 @ SV164 )
| ~ ( ord_less_eq_set_nat @ SY1199 @ SY864 )
| ( SY1199 = SY864 ) ) ) )
= $true )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(2622,plain,
! [SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ! [SV743: list_P559422087at_nat] :
( ( isShortestPath_b @ SV423 @ SV701 @ SV743 )
= ( ^ [SY1481: nat] :
~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV743 @ SY1481 )
| ~ ! [SY1482: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1482 @ SY1481 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV743 ) @ ( size_s1990949619at_nat @ SY1482 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2373]) ).
thf(2623,plain,
! [SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV423 @ SV701 )
= ( ^ [SY1450: list_P559422087at_nat,SY1451: nat] :
~ ( ~ ( isPath_b @ SV423 @ SV701 @ SY1450 @ SY1451 )
| ~ ! [SY1452: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1452 @ SY1451 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY1450 ) @ ( size_s1990949619at_nat @ SY1452 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2373]) ).
thf(2624,plain,
! [SV599: nat,SV424: nat,SV166: product_prod_nat_nat > a] :
( ( ( edmond1517640972ysis_a @ SV166 )
= $false )
| ( ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ SV166 @ SV424 @ SV599 ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ SV166 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2625,plain,
! [SV600: nat,SV425: nat,SV167: nat > nat] :
( ( ( ! [SY873: nat,SY874: nat] :
( ~ ( ord_less_nat @ SY873 @ SY874 )
| ( ord_less_nat @ ( SV167 @ SY873 ) @ ( SV167 @ SY874 ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV425 @ SV600 )
| ( ord_less_eq_nat @ ( SV167 @ SV425 ) @ ( SV167 @ SV600 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2626,plain,
! [SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ! [SV744: list_P559422087at_nat] :
( ( isShortestPath_a @ SV426 @ SV702 @ SV744 )
= ( ^ [SY1483: nat] :
~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV744 @ SY1483 )
| ( ( size_s1990949619at_nat @ SV744 )
!= ( min_dist_a @ SV426 @ SV702 @ SY1483 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2376]) ).
thf(2627,plain,
! [SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV426 @ SV702 )
= ( ^ [SY1453: list_P559422087at_nat,SY1454: nat] :
~ ( ~ ( isPath_a @ SV426 @ SV702 @ SY1453 @ SY1454 )
| ( ( size_s1990949619at_nat @ SY1453 )
!= ( min_dist_a @ SV426 @ SV702 @ SY1454 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2376]) ).
thf(2628,plain,
! [SV427: nat,SV171: nat > $o] :
( ( ( ~ ~ ( SV171 @ ( sK5_SY879 @ SV427 @ SV171 ) )
| ~ ! [SY1484: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1484 @ ( sK5_SY879 @ SV427 @ SV171 ) )
| ~ ~ ( SV171 @ SY1484 ) ) )
= $false )
| ( ( SV171 @ SV427 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2377]) ).
thf(2629,plain,
! [SV173: set_se1612935105at_nat,SV428: set_Pr1986765409at_nat] :
( ( ( ~ ( member298845450at_nat @ SV428 @ SV173 ) )
= $true )
| ( ( ~ ! [SY1214: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SY1214 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY1214 @ SV428 ) )
| ~ ! [SY883: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY883 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY883 @ SY1214 )
| ( SY1214 = SY883 ) ) ) )
= $true )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2630,plain,
! [SV174: list_P559422087at_nat > $o,SV429: list_P559422087at_nat] :
( ( ( ~ ! [SY1485: list_P559422087at_nat] :
( ~ ( ord_less_nat @ ( size_s1990949619at_nat @ SY1485 ) @ ( size_s1990949619at_nat @ ( sK6_SY885 @ SV429 @ SV174 ) ) )
| ( SV174 @ SY1485 ) )
| ( SV174 @ ( sK6_SY885 @ SV429 @ SV174 ) ) )
= $false )
| ( ( SV174 @ SV429 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2380]) ).
thf(2631,plain,
! [SV602: set_nat,SV430: set_nat,SV175: set_nat] :
( ( ( ord_less_eq_set_nat @ SV175 @ SV430 )
= $false )
| ( ( ~ ( ord_less_eq_set_nat @ SV430 @ SV602 )
| ( ord_less_eq_set_nat @ SV175 @ SV602 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2381]) ).
thf(2632,plain,
! [SV703: nat > $o,SV603: nat,SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV176 @ SV431 @ SV603 ) )
= $true )
| ( ( ~ ! [SY1455: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1455 @ SV603 )
| ~ ! [SY1392: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1392 @ SV603 )
| ( ord_less_eq_nat @ SY1455 @ SY1392 ) )
| ( SV703 @ SY1455 ) )
| ( SV703 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2633,plain,
! [SV177: set_se1612935105at_nat,SV432: set_Pr1986765409at_nat] :
( ( ( ~ ( member298845450at_nat @ SV432 @ SV177 ) )
= $true )
| ( ( ~ ! [SY1223: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SY1223 @ SV177 )
| ~ ( ord_le841296385at_nat @ SV432 @ SY1223 ) )
| ~ ! [SY896: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY896 @ SV177 )
| ~ ( ord_le841296385at_nat @ SY1223 @ SY896 )
| ( SY1223 = SY896 ) ) ) )
= $true )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2383]) ).
thf(2634,plain,
! [SV178: nat,SV433: nat] :
( ( ( ~ ( ( member_nat @ SV433 @ ( v_b @ c2 ) )
| ( member_nat @ SV178 @ ( v_b @ c2 ) ) )
| ~ ( ~ ( member_nat @ SV433 @ ( v_b @ c2 ) )
| ~ ( member_nat @ SV178 @ ( v_b @ c2 ) ) ) )
= $true )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2384]) ).
thf(2635,plain,
! [SV178: nat,SV433: nat] :
( ( ( ( member_nat @ SV433 @ ( v_b @ c2 ) )
= ( member_nat @ SV178 @ ( v_b @ c2 ) ) )
= $true )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2384]) ).
thf(2636,plain,
! [SV604: nat,SV434: nat,SV180: nat] :
( ( ( dist_b @ c2 @ SV180 @ SV434 @ SV604 )
= $false )
| ( ( connected_b @ c2 @ SV180 @ SV604 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2637,plain,
! [SV605: nat,SV435: list_P559422087at_nat,SV181: nat] :
( ( ( isPath_b @ c2 @ SV181 @ SV435 @ SV605 )
= $false )
| ( ( dist_b @ c2 @ SV181 @ ( size_s1990949619at_nat @ SV435 ) @ SV605 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2386]) ).
thf(2638,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
| ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
| ~ ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2639,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ~ ( ( SV437 = SV704 )
| ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) )
| ~ ( ( SV437 != SV704 )
| ~ ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2388]) ).
thf(2640,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( SV437 = SV704 )
= ( ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2388]) ).
thf(2641,plain,
! [SV184: set_Pr1986765409at_nat,SV438: set_Pr1986765409at_nat > $o] :
( ( ( ~ ! [SY1230: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SY1230 )
| ~ ! [SY1231: set_Pr1986765409at_nat] :
( ~ ( ord_le116442893at_nat @ SY1231 @ SY1230 )
| ( SV438 @ SY1231 ) )
| ( SV438 @ SY1230 ) ) )
= $true )
| ( ( SV438 @ SV184 )
= $true )
| ( ( finite772653738at_nat @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2389]) ).
thf(2642,plain,
! [SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ! [SV745: list_P559422087at_nat] :
( ( isShortestPath_b @ SV439 @ SV705 @ SV745 )
= ( ^ [SY1486: nat] :
~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV745 @ SY1486 )
| ( ( size_s1990949619at_nat @ SV745 )
!= ( min_dist_b @ SV439 @ SV705 @ SY1486 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2390]) ).
thf(2643,plain,
! [SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV439 @ SV705 )
= ( ^ [SY1457: list_P559422087at_nat,SY1458: nat] :
~ ( ~ ( isPath_b @ SV439 @ SV705 @ SY1457 @ SY1458 )
| ( ( size_s1990949619at_nat @ SY1457 )
!= ( min_dist_b @ SV439 @ SV705 @ SY1458 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2390]) ).
thf(2644,plain,
! [SV186: nat,SV440: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV440 @ SV186 ) )
= $true )
| ( ( SV186 = SV440 )
= $true )
| ( ( ord_less_eq_nat @ SV186 @ SV440 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2391]) ).
thf(2645,plain,
! [SV187: nat,SV441: nat] :
( ( ( SV441 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV187 @ SV441 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2646,plain,
! [SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ! [SV746: nat] :
( ( connected_a @ SV442 @ SV706 @ SV746 )
= ( ~ ! [SY1487: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1487 @ SV746 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2393]) ).
thf(2647,plain,
! [SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( connected_a @ SV442 @ SV706 )
= ( ^ [SY1459: nat] :
~ ! [SY1460: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1460 @ SY1459 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2393]) ).
thf(2648,plain,
! [SV609: nat,SV443: list_P559422087at_nat,SV189: nat] :
( ( ( isShortestPath_a @ c @ SV189 @ SV443 @ SV609 )
= $false )
| ( ( isSimplePath_a @ c @ SV189 @ SV443 @ SV609 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2649,plain,
! [SV190: set_nat,SV444: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV444 @ SV190 ) )
= $true )
| ( ( ~ ( ord_less_nat @ ( finite_card_nat @ SV444 ) @ ( finite_card_nat @ SV190 ) )
| ( ord_less_set_nat @ SV444 @ SV190 ) )
= $true )
| ( ( finite_finite_nat @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2650,plain,
! [SV445: nat,SV191: nat] :
( ( ( ~ ( ( ( min_dist_a @ c @ SV191 @ SV445 )
= zero_zero_nat )
| ( SV445 = SV191 ) )
| ~ ( ( ( min_dist_a @ c @ SV191 @ SV445 )
!= zero_zero_nat )
| ( SV445 != SV191 ) ) )
= $true )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2396]) ).
thf(2651,plain,
! [SV445: nat,SV191: nat] :
( ( ( ( ( min_dist_a @ c @ SV191 @ SV445 )
= zero_zero_nat )
= ( SV445 = SV191 ) )
= $true )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2396]) ).
thf(2652,plain,
! [SV192: nat > $o,SV446: nat] :
( ( ( ~ ! [SY1488: nat] :
( ~ ( ord_less_nat @ SY1488 @ ( sK7_SY922 @ SV446 @ SV192 ) )
| ( SV192 @ SY1488 ) )
| ( SV192 @ ( sK7_SY922 @ SV446 @ SV192 ) ) )
= $false )
| ( ( SV192 @ SV446 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2397]) ).
thf(2653,plain,
! [SV193: nat,SV447: nat] :
( ( ( ~ ( ( member_nat @ SV447 @ ( v_a @ c ) )
| ( member_nat @ SV193 @ ( v_a @ c ) ) )
| ~ ( ~ ( member_nat @ SV447 @ ( v_a @ c ) )
| ~ ( member_nat @ SV193 @ ( v_a @ c ) ) ) )
= $true )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2398]) ).
thf(2654,plain,
! [SV193: nat,SV447: nat] :
( ( ( ( member_nat @ SV447 @ ( v_a @ c ) )
= ( member_nat @ SV193 @ ( v_a @ c ) ) )
= $true )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2398]) ).
thf(2655,plain,
! [SV448: set_nat,SV194: set_nat] :
( ( ( ~ ~ ( finite_finite_nat @ SV194 ) )
= $true )
| ( ( ~ ( finite_finite_nat @ SV448 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV194 @ SV448 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2399]) ).
thf(2656,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( ~ ~ ( SV196 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY1241: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_eq_nat @ SY1241 @ SV449 )
| ~ ! [SY928: nat] :
( ~ ( ord_less_nat @ SY928 @ SY1241 )
| ~ ( SV196 @ SY928 ) ) )
| ~ ( SV196 @ SY1241 ) ) )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2400]) ).
thf(2657,plain,
! [SV197: nat,SV450: nat] :
( ( ( SV450 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV197 @ SV450 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2658,plain,
! [SV198: set_Pr1986765409at_nat,SV451: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV451 @ SV198 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV198 ) @ ( finite447719721at_nat @ SV451 ) )
| ( SV451 = SV198 ) )
= $true )
| ( ( finite772653738at_nat @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2404]) ).
thf(2659,plain,
! [SV610: nat,SV452: nat,SV199: product_prod_nat_nat > b] :
( ( ( connected_b @ SV199 @ SV452 @ SV610 )
= $false )
| ( ( ~ ! [SY1397: list_P559422087at_nat] :
~ ( isShortestPath_b @ SV199 @ SV452 @ SY1397 @ SV610 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2405]) ).
thf(2660,plain,
! [SV200: set_nat,SV453: nat] :
( ( ( ~ ( member_nat @ SV453 @ SV200 ) )
= $true )
| ( ( ~ ! [SY1245: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY1245 @ SV200 )
| ~ ( ord_less_eq_nat @ SV453 @ SY1245 ) )
| ~ ! [SY936: nat] :
( ~ ( member_nat @ SY936 @ SV200 )
| ~ ( ord_less_eq_nat @ SY1245 @ SY936 )
| ( SY1245 = SY936 ) ) ) )
= $true )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2406]) ).
thf(2661,plain,
! [SV611: nat,SV454: nat,SV201: product_prod_nat_nat > a] :
( ( ( finite_Graph_a @ SV201 )
= $false )
| ( ( ~ ( member_nat @ SV454 @ ( v_a @ SV201 ) )
| ~ ( connected_a @ SV201 @ SV454 @ SV611 )
| ( ord_less_nat @ ( min_dist_a @ SV201 @ SV454 @ SV611 ) @ ( finite_card_nat @ ( v_a @ SV201 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2407]) ).
thf(2662,plain,
! [SV455: set_Pr1986765409at_nat,SV202: set_Pr1986765409at_nat] :
( ( ( ~ ~ ( finite772653738at_nat @ SV202 ) )
= $true )
| ( ( ~ ( finite772653738at_nat @ SV455 ) )
= $true )
| ( ( ord_le841296385at_nat @ SV202 @ SV455 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2408]) ).
thf(2663,plain,
! [SV707: nat,SV612: list_P559422087at_nat,SV456: nat,SV203: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV203 @ SV456 @ SV612 @ SV707 ) )
= $true )
| ( ( isSimplePath_b @ SV203 @ SV456 @ SV612 @ SV707 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2664,plain,
! [SV457: nat,SV205: nat] :
( ( ( SV205 = SV457 )
= $true )
| ( ( ~ ~ ( ord_less_nat @ SV205 @ SV457 )
| ( ord_less_nat @ SV457 @ SV205 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2411]) ).
thf(2665,plain,
! [SV206: set_Pr1986765409at_nat,SV458: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV458 @ SV206 ) )
= $true )
| ( ( ~ ( ord_less_nat @ ( finite447719721at_nat @ SV458 ) @ ( finite447719721at_nat @ SV206 ) )
| ( ord_le116442893at_nat @ SV458 @ SV206 ) )
= $true )
| ( ( finite772653738at_nat @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2666,plain,
! [SV613: nat,SV459: list_P559422087at_nat,SV207: nat] :
( ( ( isPath_a @ c @ SV207 @ SV459 @ SV613 )
= $false )
| ( ( dist_a @ c @ SV207 @ ( size_s1990949619at_nat @ SV459 ) @ SV613 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2667,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2414]) ).
thf(2668,plain,
! [SV209: set_nat,SV461: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV461 ) )
= $true )
| ( ( finite_finite_nat @ SV209 )
= $true )
| ( ( ord_less_eq_set_nat @ SV209 @ SV461 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(2669,plain,
! [SV615: nat > $o,SV462: nat,SV210: nat] :
( ( ( connected_a @ c @ SV210 @ SV462 )
= $false )
| ( ( ~ ! [SY1400: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1400 @ SV462 )
| ~ ! [SY1255: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1255 @ SV462 )
| ( ord_less_eq_nat @ SY1400 @ SY1255 ) )
| ( SV615 @ SY1400 ) )
| ( SV615 @ ( min_dist_a @ c @ SV210 @ SV462 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2670,plain,
! [SV213: set_nat,SV464: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV464 @ SV213 ) )
= $true )
| ( ( ( ( finite_card_nat @ SV464 )
!= ( finite_card_nat @ SV213 ) )
| ( SV464 = SV213 ) )
= $true )
| ( ( finite_finite_nat @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2671,plain,
! [SV708: nat,SV616: nat,SV465: nat,SV214: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV214 @ SV465 @ SV616 @ SV708 ) )
= $true )
| ( ( connected_b @ SV214 @ SV465 @ SV708 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2421]) ).
thf(2672,plain,
! [SV466: nat,SV215: nat] :
( ( ( ( connected_b @ c2 @ SV215 @ SV466 )
| ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) )
= $false )
| ( ( ~ ( ~ ( connected_b @ c2 @ SV215 @ SV466 )
| ~ ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2422]) ).
thf(2673,plain,
! [SV709: nat,SV617: list_P559422087at_nat,SV467: nat,SV217: product_prod_nat_nat > b] :
( ( ( ~ ( finite_Graph_b @ SV217 ) )
= $true )
| ( ( ~ ( member_nat @ SV467 @ ( v_b @ SV217 ) )
| ~ ( isSimplePath_b @ SV217 @ SV467 @ SV617 @ SV709 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV617 ) @ ( finite_card_nat @ ( v_b @ SV217 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2423]) ).
thf(2674,plain,
! [SV468: nat,SV218: nat] :
( ( ( ~ ( connected_b @ c2 @ SV218 @ SV468 ) )
= $true )
| ( ( ord_less_nat @ ( min_dist_b @ c2 @ SV218 @ SV468 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) )
= $true )
| ( ( member_nat @ SV218 @ ( v_b @ c2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2424]) ).
thf(2675,plain,
! [SV219: set_nat,SV469: set_nat > $o] :
( ( ( ~ ! [SY1261: set_nat] :
( ~ ( finite_finite_nat @ SY1261 )
| ~ ! [SY1262: set_nat] :
( ~ ( ord_less_set_nat @ SY1262 @ SY1261 )
| ( SV469 @ SY1262 ) )
| ( SV469 @ SY1261 ) ) )
= $true )
| ( ( SV469 @ SV219 )
= $true )
| ( ( finite_finite_nat @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2425]) ).
thf(2676,plain,
! [SV470: nat,SV220: nat] :
( ( ( ( SV220 != SV470 )
| ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) )
= $false )
| ( ( ~ ( ~ ( ( SV220 != SV470 ) )
| ~ ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2426]) ).
thf(2677,plain,
! [SV618: nat,SV471: list_P559422087at_nat,SV221: nat] :
( ( ( isPath_b @ c2 @ SV221 @ SV471 @ SV618 )
= $false )
| ( ( ~ ! [SY1404: list_P559422087at_nat] :
~ ( isSimplePath_b @ c2 @ SV221 @ SY1404 @ SV618 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2427]) ).
thf(2678,plain,
! [SV472: nat,SV222: nat > $o] :
( ( ( ~ ! [SY974: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY974 )
| ~ ~ ( SV222 @ SY974 )
| ~ ! [SY975: nat] :
~ ~ ( ~ ( ord_less_nat @ SY975 @ SY974 )
| ~ ~ ( SV222 @ SY975 ) ) ) )
= $true )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2428]) ).
thf(2679,plain,
! [SV473: set_nat,SV223: set_nat] :
( ( ( ~ ( ( SV223 != SV473 ) ) )
= $true )
| ( ( ord_less_set_nat @ SV223 @ SV473 )
= $true )
| ( ( ord_less_eq_set_nat @ SV223 @ SV473 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2680,plain,
! [SV224: set_Pr1986765409at_nat,SV474: nat] :
( ( ( ~ ( ord_le841296385at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) @ SV224 )
| ~ ( finite772653738at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) ) @ SV474 ) )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat @ SV224 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2430]) ).
thf(2681,plain,
! [SV226: set_nat,SV476: nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) @ SV226 )
| ~ ( finite_finite_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) )
| ( ord_less_eq_nat @ ( finite_card_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) ) @ SV476 ) )
= $false )
| ( ( ~ ( ~ ( finite_finite_nat @ SV226 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2432]) ).
thf(2682,plain,
! [SV710: nat,SV619: list_P559422087at_nat,SV477: nat,SV227: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV227 @ SV477 @ SV619 @ SV710 ) )
= $true )
| ( ( dist_b @ SV227 @ SV477 @ ( size_s1990949619at_nat @ SV619 ) @ SV710 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2433]) ).
thf(2683,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
| ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
| ~ ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2435]) ).
thf(2684,plain,
! [SV231: set_Pr1986765409at_nat,SV480: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV480 @ SV231 ) )
= $true )
| ( ( finite772653738at_nat @ SV480 )
= $true )
| ( ( finite772653738at_nat @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2438]) ).
thf(2685,plain,
! [SV621: nat,SV481: nat,SV233: product_prod_nat_nat > a] :
( ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false )
| ( ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
= zero_zero_nat )
= ( SV621 = SV481 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2686,plain,
! [SV711: nat,SV622: list_P559422087at_nat,SV482: nat,SV234: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV234 @ SV482 @ SV622 @ SV711 ) )
= $true )
| ( ( isSimplePath_a @ SV234 @ SV482 @ SV622 @ SV711 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2440]) ).
thf(2687,plain,
! [SV623: nat,SV483: list_P559422087at_nat,SV236: nat] :
( ( ( isPath_a @ c @ SV236 @ SV483 @ SV623 )
= $false )
| ( ( ~ ! [SY1407: list_P559422087at_nat] :
~ ( isSimplePath_a @ c @ SV236 @ SY1407 @ SV623 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2441]) ).
thf(2688,plain,
! [SV484: nat,SV237: nat] :
( ( ( ( connected_b @ c2 @ SV237 @ SV484 )
| ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) )
= $false )
| ( ( ~ ( ~ ( connected_b @ c2 @ SV237 @ SV484 )
| ~ ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2442]) ).
thf(2689,plain,
! [SV624: nat,SV485: nat,SV238: nat] :
( ( ( ord_less_eq_nat @ SV238 @ SV485 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV485 @ SV624 )
| ( ord_less_eq_nat @ SV238 @ SV624 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2443]) ).
thf(2690,plain,
! [SV242: set_Pr1986765409at_nat,SV487: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV487 ) )
= $true )
| ( ( finite772653738at_nat @ SV242 )
= $true )
| ( ( ord_le841296385at_nat @ SV242 @ SV487 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2445]) ).
thf(2691,plain,
! [SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ! [SV747: nat] :
( ( dist_a @ SV488 @ SV712 @ SV747 )
= ( ^ [SY1489: nat] :
~ ! [SY1490: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1490 @ SY1489 )
| ( ( size_s1990949619at_nat @ SY1490 )
!= SV747 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2446]) ).
thf(2692,plain,
! [SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( dist_a @ SV488 @ SV712 )
= ( ^ [SY1461: nat,SY1462: nat] :
~ ! [SY1463: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1463 @ SY1462 )
| ( ( size_s1990949619at_nat @ SY1463 )
!= SY1461 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2446]) ).
thf(2693,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
| ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
| ~ ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2694,plain,
! [SV490: list_P559422087at_nat,SV249: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV249 )
= ( size_s1990949619at_nat @ SV490 ) )
= $true )
| ( ( SV249 != SV490 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2449]) ).
thf(2695,plain,
! [SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ! [SV748: nat] :
( ( connected_b @ SV491 @ SV713 @ SV748 )
= ( ~ ! [SY1491: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1491 @ SV748 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2450]) ).
thf(2696,plain,
! [SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( connected_b @ SV491 @ SV713 )
= ( ^ [SY1464: nat] :
~ ! [SY1465: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1465 @ SY1464 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2450]) ).
thf(2697,plain,
! [SV252: set_Pr1986765409at_nat,SV492: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV492 @ SV252 ) )
= $true )
| ( ( ( ( finite447719721at_nat @ SV492 )
!= ( finite447719721at_nat @ SV252 ) )
| ( SV492 = SV252 ) )
= $true )
| ( ( finite772653738at_nat @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2451]) ).
thf(2698,plain,
! [SV628: nat,SV493: nat,SV253: nat] :
( ( ( dist_b @ c2 @ SV253 @ SV493 @ SV628 )
= $false )
| ( ( ord_less_eq_nat @ ( min_dist_b @ c2 @ SV253 @ SV628 ) @ SV493 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2452]) ).
thf(2699,plain,
! [SV629: nat,SV494: nat,SV254: product_prod_nat_nat > b] :
( ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false )
| ( ( ( member_nat @ SV629 @ ( v_b @ SV254 ) )
= ( member_nat @ SV494 @ ( v_b @ SV254 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2453]) ).
thf(2700,plain,
! [SV630: nat,SV495: nat,SV255: product_prod_nat_nat > b] :
( ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false )
| ( ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
= zero_zero_nat )
= ( SV630 = SV495 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(2701,plain,
! [SV631: nat,SV496: nat,SV257: product_prod_nat_nat > b] :
( ( ( finite_Graph_b @ SV257 )
= $false )
| ( ( ~ ( member_nat @ SV496 @ ( v_b @ SV257 ) )
| ~ ( connected_b @ SV257 @ SV496 @ SV631 )
| ( ord_less_nat @ ( min_dist_b @ SV257 @ SV496 @ SV631 ) @ ( finite_card_nat @ ( v_b @ SV257 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2456]) ).
thf(2702,plain,
! [SV258: set_Pr1986765409at_nat,SV497: set_Pr1986765409at_nat] :
( ( ( ~ ( member701585322at_nat @ ( sK10_SY1291 @ SV497 @ SV258 ) @ SV258 )
| ( member701585322at_nat @ ( sK10_SY1291 @ SV497 @ SV258 ) @ SV497 ) )
= $false )
| ( ( ord_le841296385at_nat @ SV258 @ SV497 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2457]) ).
thf(2703,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
| ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
| ~ ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2458]) ).
thf(2704,plain,
! [SV714: nat,SV632: nat,SV499: nat,SV260: nat] :
( ( ( ~ ( connected_a @ c @ SV260 @ SV499 ) )
= $true )
| ( ( ( ( min_dist_a @ c @ SV260 @ SV499 )
!= SV632 )
| ~ ( ord_less_nat @ SV714 @ SV632 )
| ~ ! [SY1466: nat] :
~ ~ ( ~ ( connected_a @ c @ SV260 @ SY1466 )
| ( ( min_dist_a @ c @ SV260 @ SY1466 )
!= SV714 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2459]) ).
thf(2705,plain,
! [SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ! [SV749: list_P559422087at_nat] :
( ( isShortestPath_b @ SV501 @ SV715 @ SV749 )
= ( ^ [SY1492: nat] :
~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV749 @ SY1492 )
| ( ( size_s1990949619at_nat @ SV749 )
!= ( min_dist_b @ SV501 @ SV715 @ SY1492 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2461]) ).
thf(2706,plain,
! [SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV501 @ SV715 )
= ( ^ [SY1467: list_P559422087at_nat,SY1468: nat] :
~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SY1467 @ SY1468 )
| ( ( size_s1990949619at_nat @ SY1467 )
!= ( min_dist_b @ SV501 @ SV715 @ SY1468 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2461]) ).
thf(2707,plain,
! [SV263: set_li664300135at_nat] :
( ( ( ~ ! [SY1493: list_P559422087at_nat] :
( ~ ( member1608759472at_nat @ SY1493 @ SV263 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY1493 ) @ ( sK11_SY1034 @ SV263 ) ) ) )
= $false )
| ( ( finite1299096496at_nat @ SV263 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2462]) ).
thf(2708,plain,
! [SV634: nat,SV502: nat,SV264: nat] :
( ( ( connected_a @ c @ SV264 @ SV502 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV634 @ ( min_dist_a @ c @ SV264 @ SV502 ) )
| ~ ! [SY1417: nat] :
~ ~ ( ~ ( connected_a @ c @ SV264 @ SY1417 )
| ( ( min_dist_a @ c @ SV264 @ SY1417 )
!= SV634 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2463]) ).
thf(2709,plain,
! [SV750: nat,SV716: nat,SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ~ ( connected_b @ SV265 @ SV503 @ SV635 )
| ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
!= SV716 )
| ~ ( ord_less_nat @ SV750 @ SV716 )
| ~ ! [SY1494: nat] :
~ ~ ( ~ ( connected_b @ SV265 @ SV503 @ SY1494 )
| ( ( min_dist_b @ SV265 @ SV503 @ SY1494 )
!= SV750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(2710,plain,
! [SV504: nat,SV266: nat] :
( ( ( ! [SY1305: list_P559422087at_nat] :
~ ( isShortestPath_a @ c @ SV266 @ SY1305 @ SV504 ) )
= $false )
| ( ( connected_a @ c @ SV266 @ SV504 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2465]) ).
thf(2711,plain,
! [SV636: nat,SV505: list_P559422087at_nat,SV267: nat] :
( ( ( member_nat @ SV267 @ ( v_a @ c ) )
= $false )
| ( ( ~ ( isShortestPath_a @ c @ SV267 @ SV505 @ SV636 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV505 ) @ ( finite_card_nat @ ( v_a @ c ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2466]) ).
thf(2712,plain,
! [SV717: nat,SV637: nat,SV506: nat,SV268: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV268 @ SV506 @ SV637 @ SV717 ) )
= $true )
| ( ( connected_a @ SV268 @ SV506 @ SV717 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2467]) ).
thf(2713,plain,
! [SV269: set_nat,SV507: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV507 @ SV269 ) )
= $true )
| ( ( finite_finite_nat @ SV507 )
= $true )
| ( ( finite_finite_nat @ SV269 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2468]) ).
thf(2714,plain,
! [SV508: nat,SV270: set_nat] :
( ( ( finite_finite_nat @ SV270 )
= $true )
| ( ( ~ ! [SY1309: set_nat] :
~ ~ ( ~ ~ ( ~ ( finite_finite_nat @ SY1309 )
| ( ( finite_card_nat @ SY1309 )
!= SV508 ) )
| ~ ( ord_less_eq_set_nat @ SY1309 @ SV270 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2469]) ).
thf(2715,plain,
! [SV271: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV271 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV271 )
| ~ ( ( SV271 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2470]) ).
thf(2716,plain,
! [SV271: nat] :
( ( ( SV271 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV271 )
| ~ ( ( SV271 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2470]) ).
thf(2717,plain,
! [SV273: set_set_nat,SV509: set_nat] :
( ( ( ~ ( member_set_nat @ SV509 @ SV273 ) )
= $true )
| ( ( ~ ! [SY1310: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SY1310 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1310 @ SV509 ) )
| ~ ! [SY1056: set_nat] :
( ~ ( member_set_nat @ SY1056 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1056 @ SY1310 )
| ( SY1310 = SY1056 ) ) ) )
= $true )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2472]) ).
thf(2718,plain,
! [SV510: product_prod_nat_nat > $o,SV274: product_prod_nat_nat > $o] :
( ( ( ( SV274 @ ( sK12_SY1312 @ SV510 @ SV274 ) )
= ( SV510 @ ( sK12_SY1312 @ SV510 @ SV274 ) ) )
= $false )
| ( ( ( collec7649004at_nat @ SV274 )
= ( collec7649004at_nat @ SV510 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2473]) ).
thf(2719,plain,
! [SV638: nat,SV511: list_P559422087at_nat,SV275: nat] :
( ( ( member_nat @ SV275 @ ( v_b @ c2 ) )
= $false )
| ( ( ~ ( isSimplePath_b @ c2 @ SV275 @ SV511 @ SV638 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV511 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2720,plain,
! [SV639: nat,SV512: list_P559422087at_nat,SV276: nat] :
( ( ( isShortestPath_b @ c2 @ SV276 @ SV512 @ SV639 )
= $false )
| ( ( isSimplePath_b @ c2 @ SV276 @ SV512 @ SV639 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2475]) ).
thf(2721,plain,
! [SV640: nat,SV513: nat,SV277: product_prod_nat_nat > b] :
( ( ( edmond1517640973ysis_b @ SV277 )
= $false )
| ( ( ord_le841296385at_nat @ ( edmond475474836dges_b @ SV277 @ SV513 @ SV640 ) @ ( e_b @ SV277 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2476]) ).
thf(2722,plain,
! [SV279: set_nat,SV514: set_nat] :
( ( ( ~ ( ord_less_set_nat @ SV514 @ SV279 ) )
= $true )
| ( ( ord_less_nat @ ( finite_card_nat @ SV514 ) @ ( finite_card_nat @ SV279 ) )
= $true )
| ( ( finite_finite_nat @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2723,plain,
! [SV718: nat,SV641: nat,SV515: nat,SV281: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV281 @ SV515 @ SV641 @ SV718 ) )
= $true )
| ( ( ord_less_eq_nat @ ( min_dist_b @ SV281 @ SV515 @ SV718 ) @ SV641 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2724,plain,
! [SV642: nat,SV516: nat,SV283: nat] :
( ( ( dist_b @ c2 @ SV283 @ SV516 @ SV642 )
= $false )
| ( ( ~ ! [SY1423: nat] :
( ~ ( dist_b @ c2 @ SV283 @ SY1423 @ SV642 )
| ( ord_less_eq_nat @ SV516 @ SY1423 ) )
| ( ( min_dist_b @ c2 @ SV283 @ SV642 )
= SV516 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(2725,plain,
! [SV284: set_se1612935105at_nat,SV517: set_se1612935105at_nat] :
( ( ( ~ ( finite1457549322at_nat @ SV517 ) )
= $true )
| ( ( finite1457549322at_nat @ SV284 )
= $true )
| ( ( ord_le2096002913at_nat @ SV284 @ SV517 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2480]) ).
thf(2726,plain,
! [SV643: nat,SV518: nat,SV285: product_prod_nat_nat > b] :
( ( ( edmond1517640973ysis_b @ SV285 )
= $false )
| ( ( finite772653738at_nat @ ( edmond475474836dges_b @ SV285 @ SV518 @ SV643 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2727,plain,
! [SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ! [SV751: nat] :
( ( connected_b @ SV519 @ SV719 @ SV751 )
= ( ~ ! [SY1495: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1495 @ SV751 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2482]) ).
thf(2728,plain,
! [SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( connected_b @ SV519 @ SV719 )
= ( ^ [SY1471: nat] :
~ ! [SY1472: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1472 @ SY1471 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2482]) ).
thf(2729,plain,
! [SV645: set_Pr1986765409at_nat,SV520: set_Pr1986765409at_nat,SV287: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV287 @ SV520 )
= $false )
| ( ( ~ ( ord_le841296385at_nat @ SV520 @ SV645 )
| ( ord_le841296385at_nat @ SV287 @ SV645 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(2730,plain,
! [SV646: nat,SV521: nat,SV289: product_prod_nat_nat > a] :
( ( ( edmond1517640972ysis_a @ SV289 )
= $false )
| ( ( finite772653738at_nat @ ( edmond475474835dges_a @ SV289 @ SV521 @ SV646 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2731,plain,
! [SV720: nat,SV647: list_P559422087at_nat,SV523: nat,SV291: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV291 @ SV523 @ SV647 @ SV720 ) )
= $true )
| ( ( ~ ! [SY1473: list_P559422087at_nat] :
~ ( isSimplePath_a @ SV291 @ SV523 @ SY1473 @ SV720 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2486]) ).
thf(2732,plain,
! [SV292: nat,SV524: nat] :
( ( ( SV524 = SV292 )
= $false )
| ( ( ord_less_nat @ SV292 @ SV524 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2487]) ).
thf(2733,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ~ ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2488]) ).
thf(2734,plain,
! [SV649: nat,SV526: nat,SV294: nat] :
( ( ( dist_a @ c @ SV294 @ SV526 @ SV649 )
= $false )
| ( ( connected_a @ c @ SV294 @ SV649 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2490]) ).
thf(2735,plain,
! [SV650: nat,SV527: nat,SV296: product_prod_nat_nat > a] :
( ( ( connected_a @ SV296 @ SV527 @ SV650 )
= $false )
| ( ( dist_a @ SV296 @ SV527 @ ( min_dist_a @ SV296 @ SV527 @ SV650 ) @ SV650 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2491]) ).
thf(2736,plain,
! [SV528: nat,SV297: nat] :
( ( ( ord_less_nat @ SV297 @ SV528 )
= $false )
| ( ( ord_less_eq_nat @ SV297 @ SV528 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2492]) ).
thf(2737,plain,
! [SV528: nat,SV297: nat] :
( ( ( SV297 = SV528 )
= $false )
| ( ( ord_less_eq_nat @ SV297 @ SV528 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2492]) ).
thf(2738,plain,
! [SV298: set_Pr1986765409at_nat,SV529: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV529 @ SV298 ) )
= $true )
| ( ( ord_less_eq_nat @ ( finite447719721at_nat @ SV529 ) @ ( finite447719721at_nat @ SV298 ) )
= $true )
| ( ( finite772653738at_nat @ SV298 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2493]) ).
thf(2739,plain,
! [SV721: nat,SV530: nat] :
( ( ~ ( ( ord_less_nat @ SV530 @ SV721 )
| ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) )
| ~ ( ~ ( ord_less_nat @ SV530 @ SV721 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2494]) ).
thf(2740,plain,
! [SV721: nat,SV530: nat] :
( ( ( ord_less_nat @ SV530 @ SV721 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2494]) ).
thf(2741,plain,
! [SV652: nat,SV531: list_P559422087at_nat,SV300: nat] :
( ( ( member_nat @ SV300 @ ( v_b @ c2 ) )
= $false )
| ( ( ~ ( isShortestPath_b @ c2 @ SV300 @ SV531 @ SV652 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV531 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2495]) ).
thf(2742,plain,
! [SV301: set_Pr1986765409at_nat,SV532: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV532 @ SV301 ) )
= $true )
| ( ( SV301 = SV532 )
= $true )
| ( ( ord_le841296385at_nat @ SV301 @ SV532 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2496]) ).
thf(2743,plain,
! [SV653: nat > $o,SV533: nat,SV304: nat] :
( ( ( connected_b @ c2 @ SV304 @ SV533 )
= $false )
| ( ( ~ ! [SY1428: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1428 @ SV533 )
| ~ ! [SY1336: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1336 @ SV533 )
| ( ord_less_eq_nat @ SY1428 @ SY1336 ) )
| ( SV653 @ SY1428 ) )
| ( SV653 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2744,plain,
! [SV534: list_P559422087at_nat,SV305: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV305 )
= ( size_s1990949619at_nat @ SV534 ) )
= $true )
| ( ( SV305 != SV534 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2499]) ).
thf(2745,plain,
! [SV654: nat,SV535: list_P559422087at_nat,SV306: nat] :
( ( ( isShortestPath_b @ c2 @ SV306 @ SV535 @ SV654 )
= $false )
| ( ( isPath_b @ c2 @ SV306 @ SV535 @ SV654 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2500]) ).
thf(2746,plain,
! [SV655: nat,SV536: list_P559422087at_nat,SV308: nat] :
( ( ( isShortestPath_a @ c @ SV308 @ SV536 @ SV655 )
= $false )
| ( ( isPath_a @ c @ SV308 @ SV536 @ SV655 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2747,plain,
! [SV752: nat,SV656: nat,SV309: product_prod_nat_nat > b] :
( ( ( edmond1022345717sure_b @ SV309 @ SV656 @ SV752 )
= ( edmond1022345717sure_b @ SV309 @ SV656 @ SV752 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(2748,plain,
! [SV753: nat,SV657: nat,SV310: product_prod_nat_nat > a] :
( ( ( edmond1022345716sure_a @ SV310 @ SV657 @ SV753 )
= ( edmond1022345716sure_a @ SV310 @ SV657 @ SV753 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(2749,plain,
! [SV754: nat,SV658: nat,SV313: product_prod_nat_nat > a] :
( ( ( edmond475474835dges_a @ SV313 @ SV658 @ SV754 )
= ( edmond475474835dges_a @ SV313 @ SV658 @ SV754 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(2750,plain,
! [SV755: nat,SV659: nat,SV314: product_prod_nat_nat > b] :
( ( ( edmond475474836dges_b @ SV314 @ SV659 @ SV755 )
= ( edmond475474836dges_b @ SV314 @ SV659 @ SV755 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2508]) ).
thf(2751,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( edmond1517640972ysis_a @ SV315 )
= $false )
| ( ( ~ ( ~ ( edmond1517640972ysis_a @ SV315 )
| ~ ( finite_Graph_a @ SV315 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2510]) ).
thf(2752,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( finite_Graph_a @ SV315 )
= $false )
| ( ( ~ ( ~ ( edmond1517640972ysis_a @ SV315 )
| ~ ( finite_Graph_a @ SV315 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2510]) ).
thf(2753,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( edmond1517640973ysis_b @ SV316 )
= $false )
| ( ( ~ ( ~ ( edmond1517640973ysis_b @ SV316 )
| ~ ( finite_Graph_b @ SV316 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2511]) ).
thf(2754,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( finite_Graph_b @ SV316 )
= $false )
| ( ( ~ ( ~ ( edmond1517640973ysis_b @ SV316 )
| ~ ( finite_Graph_b @ SV316 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2511]) ).
thf(2755,plain,
! [SV317: nat,SV13: nat] :
( ( ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
= $false )
| ( ( ~ ( ~ ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
| ( SV317 != SV13 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2512]) ).
thf(2756,plain,
! [SV13: nat,SV317: nat] :
( ( ( SV317 = SV13 )
= $false )
| ( ( ~ ( ~ ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
| ( SV317 != SV13 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2512]) ).
thf(2757,plain,
! [SV318: set_Pr1986765409at_nat > $o,SV15: set_Pr1986765409at_nat] :
( ( ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
= $false )
| ( ( ~ ( ~ ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
| ~ ( SV318 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2513]) ).
thf(2758,plain,
! [SV15: set_Pr1986765409at_nat,SV318: set_Pr1986765409at_nat > $o] :
( ( ( SV318 @ SV15 )
= $false )
| ( ( ~ ( ~ ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
| ~ ( SV318 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2513]) ).
thf(2759,plain,
! [SV319: set_nat > $o,SV16: set_nat] :
( ( ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
= $false )
| ( ( ~ ( ~ ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
| ~ ( SV319 @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2514]) ).
thf(2760,plain,
! [SV16: set_nat,SV319: set_nat > $o] :
( ( ( SV319 @ SV16 )
= $false )
| ( ( ~ ( ~ ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
| ~ ( SV319 @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2514]) ).
thf(2761,plain,
! [SV320: product_prod_nat_nat > $o,SV17: product_prod_nat_nat] :
( ( ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
= $false )
| ( ( ~ ( ~ ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
| ~ ( SV320 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2515]) ).
thf(2762,plain,
! [SV17: product_prod_nat_nat,SV320: product_prod_nat_nat > $o] :
( ( ( SV320 @ SV17 )
= $false )
| ( ( ~ ( ~ ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
| ~ ( SV320 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2515]) ).
thf(2763,plain,
! [SV321: nat > $o,SV18: nat] :
( ( ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
| ~ ( SV321 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2516]) ).
thf(2764,plain,
! [SV18: nat,SV321: nat > $o] :
( ( ( SV321 @ SV18 )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
| ~ ( SV321 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2516]) ).
thf(2765,plain,
! [SV24: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV24 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV24 )
| ( SV24 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2517]) ).
thf(2766,plain,
! [SV24: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV24 )
| ( SV24 != zero_zero_nat ) )
= $false )
| ( ( SV24 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2767,plain,
! [SV25: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
| ( SV25 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(2768,plain,
! [SV25: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
| ( SV25 != zero_zero_nat ) )
= $false )
| ( ( SV25 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2520]) ).
thf(2769,plain,
! [SV32: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
| ( SV32 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2770,plain,
! [SV32: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
| ( SV32 != zero_zero_nat ) )
= $false )
| ( ( SV32 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2522]) ).
thf(2771,plain,
! [SV33: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
| ( SV33 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2523]) ).
thf(2772,plain,
! [SV33: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
| ( SV33 != zero_zero_nat ) )
= $false )
| ( ( SV33 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2524]) ).
thf(2773,plain,
! [SV660: nat,SV323: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV323 @ SV660 )
| ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV323 @ SV660 )
| ~ ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2525]) ).
thf(2774,plain,
! [SV35: nat] :
( ( ( ( zero_zero_nat != SV35 )
| ( SV35 != zero_zero_nat ) )
= $false )
| ( ( zero_zero_nat = SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2527]) ).
thf(2775,plain,
! [SV35: nat] :
( ( ( ( zero_zero_nat != SV35 )
| ( SV35 != zero_zero_nat ) )
= $false )
| ( ( SV35 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2528]) ).
thf(2776,plain,
! [SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV324 @ SV661 @ SV756 )
= ( isPath_b @ SV324 @ SV661 @ SV756 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(2777,plain,
! [SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV325 @ SV662 @ SV757 )
= ( isPath_a @ SV325 @ SV662 @ SV757 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2531]) ).
thf(2778,plain,
! [SV758: nat,SV663: nat,SV328: product_prod_nat_nat > a] :
( ( ( min_dist_a @ SV328 @ SV663 @ SV758 )
= ( min_dist_a @ SV328 @ SV663 @ SV758 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(2779,plain,
! [SV759: nat,SV664: nat,SV329: product_prod_nat_nat > b] :
( ( ( min_dist_b @ SV329 @ SV664 @ SV759 )
= ( min_dist_b @ SV329 @ SV664 @ SV759 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2535]) ).
thf(2780,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( connected_b @ SV330 @ SV665 @ SV760 )
= ( connected_b @ SV330 @ SV665 @ SV760 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(2781,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( connected_a @ SV331 @ SV666 @ SV761 )
= ( connected_a @ SV331 @ SV666 @ SV761 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(2782,plain,
! [SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( dist_b @ SV334 @ SV667 @ SV762 )
= ( dist_b @ SV334 @ SV667 @ SV762 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(2783,plain,
! [SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( dist_a @ SV335 @ SV668 @ SV763 )
= ( dist_a @ SV335 @ SV668 @ SV763 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(2784,plain,
! [SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 )
= ( isShortestPath_a @ SV336 @ SV669 @ SV764 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(2785,plain,
! [SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 )
= ( isShortestPath_b @ SV337 @ SV670 @ SV765 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(2786,plain,
! [SV53: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ( SV53 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2549]) ).
thf(2787,plain,
! [SV53: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ( SV53 != zero_zero_nat ) )
= $false )
| ( ( SV53 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2788,plain,
! [SV552: nat,SV342: nat,SV61: product_prod_nat_nat > b] :
( ( ( ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
| ( SV552 = SV342 ) )
= $false )
| ( ( ~ ( ~ ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
| ( SV552 != SV342 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2551]) ).
thf(2789,plain,
! [SV553: nat,SV343: nat,SV62: product_prod_nat_nat > a] :
( ( ( ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
| ( SV553 = SV343 ) )
= $false )
| ( ( ~ ( ~ ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
| ( SV553 != SV343 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2552]) ).
thf(2790,plain,
! [SV344: nat,SV63: nat] :
( ( ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
= $false )
| ( ( ~ ( ~ ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
| ( SV344 != SV63 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2553]) ).
thf(2791,plain,
! [SV63: nat,SV344: nat] :
( ( ( SV344 = SV63 )
= $false )
| ( ( ~ ( ~ ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
| ( SV344 != SV63 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2553]) ).
thf(2792,plain,
! [SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 )
= ( isSimplePath_a @ SV345 @ SV671 @ SV766 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(2793,plain,
! [SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 )
= ( isSimplePath_b @ SV346 @ SV672 @ SV767 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2556]) ).
thf(2794,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( finite_Graph_b @ SV347 )
= $false )
| ( ( ~ ( ~ ( finite_Graph_b @ SV347 )
| ~ ( finite_finite_nat @ ( v_b @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2558]) ).
thf(2795,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( finite_finite_nat @ ( v_b @ SV347 ) )
= $false )
| ( ( ~ ( ~ ( finite_Graph_b @ SV347 )
| ~ ( finite_finite_nat @ ( v_b @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2558]) ).
thf(2796,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( finite_Graph_a @ SV348 )
= $false )
| ( ( ~ ( ~ ( finite_Graph_a @ SV348 )
| ~ ( finite_finite_nat @ ( v_a @ SV348 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2559]) ).
thf(2797,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( finite_finite_nat @ ( v_a @ SV348 ) )
= $false )
| ( ( ~ ( ~ ( finite_Graph_a @ SV348 )
| ~ ( finite_finite_nat @ ( v_a @ SV348 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2559]) ).
thf(2798,plain,
! [SV93: nat] :
( ( ( SV93 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ( SV93 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV93 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2560]) ).
thf(2799,plain,
! [SV93: nat] :
( ( ( ~ ( ( SV93 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV93 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2561]) ).
thf(2800,plain,
! [SV564: nat,SV365: list_P559422087at_nat,SV95: nat] :
( ( ( ~ ( isSimplePath_a @ c @ SV95 @ SV365 @ SV564 ) )
= $true )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV365 ) @ ( finite_card_nat @ ( v_a @ c ) ) )
= $true )
| ( ( member_nat @ SV95 @ ( v_a @ c ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2562]) ).
thf(2801,plain,
! [SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 )
= ( ^ [SY1496: nat] :
~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SY1496 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SY1496 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2563]) ).
thf(2802,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2565]) ).
thf(2803,plain,
! [SV101: nat] :
( ( ( SV101 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ( SV101 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV101 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2566]) ).
thf(2804,plain,
! [SV101: nat] :
( ( ( ~ ( ( SV101 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV101 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2567]) ).
thf(2805,plain,
! [SV102: set_nat,SV369: set_nat] :
( ( ( ~ ( member_nat @ ( sK3_SY1117 @ SV369 @ SV102 ) @ SV102 ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV102 @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2568]) ).
thf(2806,plain,
! [SV102: set_nat,SV369: set_nat] :
( ( ( member_nat @ ( sK3_SY1117 @ SV369 @ SV102 ) @ SV369 )
= $false )
| ( ( ord_less_eq_set_nat @ SV102 @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2568]) ).
thf(2807,plain,
! [SV682: nat,SV567: list_P559422087at_nat,SV370: nat,SV103: product_prod_nat_nat > a] :
( ( ( finite_Graph_a @ SV103 )
= $false )
| ( ( ~ ( member_nat @ SV370 @ ( v_a @ SV103 ) )
| ~ ( isShortestPath_a @ SV103 @ SV370 @ SV567 @ SV682 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV567 ) @ ( finite_card_nat @ ( v_a @ SV103 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2569]) ).
thf(2808,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ~ ( ( SV372 = SV683 )
| ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) ) )
= $true )
| ( ( ~ ( ( SV372 != SV683 )
| ~ ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2570]) ).
thf(2809,plain,
! [SV684: nat,SV569: list_P559422087at_nat,SV373: nat,SV106: product_prod_nat_nat > b] :
( ( ( finite_Graph_b @ SV106 )
= $false )
| ( ( ~ ( member_nat @ SV373 @ ( v_b @ SV106 ) )
| ~ ( isShortestPath_b @ SV106 @ SV373 @ SV569 @ SV684 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV569 ) @ ( finite_card_nat @ ( v_b @ SV106 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2810,plain,
! [SV685: nat,SV570: list_P559422087at_nat,SV374: nat,SV107: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV107 @ SV374 @ SV570 @ SV685 )
= $false )
| ( ( isPath_a @ SV107 @ SV374 @ SV570 @ SV685 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2811,plain,
! [SV377: nat > $o,SV110: nat > $o] :
( ( ( ~ ( ( SV110 @ ( sK4_SY1126 @ SV377 @ SV110 ) )
| ( SV377 @ ( sK4_SY1126 @ SV377 @ SV110 ) ) )
| ~ ( ~ ( SV110 @ ( sK4_SY1126 @ SV377 @ SV110 ) )
| ~ ( SV377 @ ( sK4_SY1126 @ SV377 @ SV110 ) ) ) )
= $false )
| ( ( ( collect_nat @ SV110 )
= ( collect_nat @ SV377 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2575]) ).
thf(2812,plain,
! [SV377: nat > $o,SV110: nat > $o] :
( ( ( ( SV110 @ ( sK4_SY1126 @ SV377 @ SV110 ) )
= ( SV377 @ ( sK4_SY1126 @ SV377 @ SV110 ) ) )
= $false )
| ( ( ( collect_nat @ SV110 )
= ( collect_nat @ SV377 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2575]) ).
thf(2813,plain,
! [SV378: nat,SV111: product_prod_nat_nat > a,SV571: nat] :
( ( ( ~ ( ( member_nat @ SV571 @ ( v_a @ SV111 ) )
| ( member_nat @ SV378 @ ( v_a @ SV111 ) ) )
| ~ ( ~ ( member_nat @ SV571 @ ( v_a @ SV111 ) )
| ~ ( member_nat @ SV378 @ ( v_a @ SV111 ) ) ) )
= $true )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2576]) ).
thf(2814,plain,
! [SV378: nat,SV111: product_prod_nat_nat > a,SV571: nat] :
( ( ( ( member_nat @ SV571 @ ( v_a @ SV111 ) )
= ( member_nat @ SV378 @ ( v_a @ SV111 ) ) )
= $true )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2576]) ).
thf(2815,plain,
! [SV379: nat,SV572: nat,SV112: nat] :
( ( ( ~ ! [SY1344: nat] :
( ~ ( dist_a @ c @ SV112 @ SY1344 @ SV572 )
| ( ord_less_eq_nat @ SV379 @ SY1344 ) ) )
= $true )
| ( ( ( min_dist_a @ c @ SV112 @ SV572 )
= SV379 )
= $true )
| ( ( dist_a @ c @ SV112 @ SV379 @ SV572 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(2816,plain,
! [SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( dist_b @ SV380 @ SV686 @ SV769 )
= ( ^ [SY1497: nat] :
~ ! [SY1498: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1498 @ SY1497 )
| ( ( size_s1990949619at_nat @ SY1498 )
!= SV769 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2578]) ).
thf(2817,plain,
! [SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 )
= ( ^ [SY1499: nat] :
~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SY1499 )
| ~ ! [SY1500: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1500 @ SY1499 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1500 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(2818,plain,
! [SV688: nat,SV575: nat,SV382: nat,SV116: product_prod_nat_nat > a] :
( ( ( dist_a @ SV116 @ SV382 @ SV575 @ SV688 )
= $false )
| ( ( ~ ! [SY1438: nat] :
( ~ ( dist_a @ SV116 @ SV382 @ SY1438 @ SV688 )
| ( ord_less_eq_nat @ SV575 @ SY1438 ) )
| ( ( min_dist_a @ SV116 @ SV382 @ SV688 )
= SV575 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2819,plain,
! [SV383: nat,SV117: nat] :
( ( ( ~ ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
= zero_zero_nat )
| ( SV383 = SV117 ) ) )
= $true )
| ( ( ~ ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
!= zero_zero_nat )
| ( SV383 != SV117 ) ) )
= $true )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2583]) ).
thf(2820,plain,
! [SV576: nat,SV384: nat,SV118: nat] :
( ( ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2821,plain,
! [SV119: set_Pr1986765409at_nat,SV385: set_Pr1986765409at_nat] :
( ( ( ord_le116442893at_nat @ SV385 @ SV119 )
= $false )
| ( ( ord_less_nat @ ( finite447719721at_nat @ SV385 ) @ ( finite447719721at_nat @ SV119 ) )
= $true )
| ( ( finite772653738at_nat @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2586]) ).
thf(2822,plain,
! [SV741: nat,SV689: nat,SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV120 @ SV386 @ SV577 ) )
= $true )
| ( ( ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
!= SV689 )
| ~ ( ord_less_nat @ SV741 @ SV689 )
| ~ ! [SY1479: nat] :
~ ~ ( ~ ( connected_a @ SV120 @ SV386 @ SY1479 )
| ( ( min_dist_a @ SV120 @ SV386 @ SY1479 )
!= SV741 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2587]) ).
thf(2823,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( connected_a @ SV387 @ SV690 @ SV771 )
= ( ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(2824,plain,
! [SV579: nat,SV388: nat,SV124: product_prod_nat_nat > a] :
( ( ( ! [SY1359: list_P559422087at_nat] :
~ ( isShortestPath_a @ SV124 @ SV388 @ SY1359 @ SV579 ) )
= $false )
| ( ( connected_a @ SV124 @ SV388 @ SV579 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2590]) ).
thf(2825,plain,
! [SV126: set_nat,SV389: set_nat] :
( ( ( ord_less_eq_set_nat @ SV389 @ SV126 )
= $false )
| ( ( ord_less_eq_nat @ ( finite_card_nat @ SV389 ) @ ( finite_card_nat @ SV126 ) )
= $true )
| ( ( finite_finite_nat @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2591]) ).
thf(2826,plain,
! [SV691: nat,SV581: nat,SV391: nat,SV128: nat] :
( ( ( connected_b @ c2 @ SV128 @ SV391 )
= $false )
| ( ( ( ( min_dist_b @ c2 @ SV128 @ SV391 )
!= SV581 )
| ~ ( ord_less_nat @ SV691 @ SV581 )
| ~ ! [SY1443: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV128 @ SY1443 )
| ( ( min_dist_b @ c2 @ SV128 @ SY1443 )
!= SV691 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2593]) ).
thf(2827,plain,
! [SV692: nat > $o,SV582: nat,SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ( connected_a @ SV129 @ SV392 @ SV582 )
= $false )
| ( ( ~ ! [SY1444: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1444 @ SV582 )
| ~ ! [SY1364: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1364 @ SV582 )
| ( ord_less_eq_nat @ SY1444 @ SY1364 ) )
| ( SV692 @ SY1444 ) )
| ( SV692 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2828,plain,
! [SV131: set_set_nat,SV393: set_set_nat] :
( ( ( finite2012248349et_nat @ SV393 )
= $false )
| ( ( finite2012248349et_nat @ SV131 )
= $true )
| ( ( ord_le1613022364et_nat @ SV131 @ SV393 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2829,plain,
! [SV133: set_nat,SV395: set_nat] :
( ( ( ord_less_eq_set_nat @ SV395 @ SV133 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV133 ) @ ( finite_card_nat @ SV395 ) )
| ( SV395 = SV133 ) )
= $true )
| ( ( finite_finite_nat @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(2830,plain,
! [SV693: nat,SV583: nat,SV396: nat,SV134: product_prod_nat_nat > b] :
( ( ( connected_b @ SV134 @ SV396 @ SV583 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV693 @ ( min_dist_b @ SV134 @ SV396 @ SV583 ) )
| ~ ! [SY1446: nat] :
~ ~ ( ~ ( connected_b @ SV134 @ SV396 @ SY1446 )
| ( ( min_dist_b @ SV134 @ SV396 @ SY1446 )
!= SV693 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2597]) ).
thf(2831,plain,
! [SV397: nat,SV135: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV135 @ ( sK13_SY1163 @ SV397 @ SV135 ) @ SV397 ) )
= $false )
| ( ( connected_b @ c2 @ SV135 @ SV397 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2598]) ).
thf(2832,plain,
! [SV398: nat,SV136: nat] :
( ( ( connected_a @ c @ SV136 @ SV398 )
= $false )
| ( ( ~ ( ~ ( connected_a @ c @ SV136 @ SV398 )
| ~ ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2599]) ).
thf(2833,plain,
! [SV398: nat,SV136: nat] :
( ( ( ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) )
= $false )
| ( ( ~ ( ~ ( connected_a @ c @ SV136 @ SV398 )
| ~ ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2599]) ).
thf(2834,plain,
! [SV137: set_nat,SV399: nat] :
( ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( ~ ! [SY1165: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY1165 @ SV137 )
| ~ ( ord_less_eq_nat @ SY1165 @ SV399 ) )
| ~ ! [SY807: nat] :
( ~ ( member_nat @ SY807 @ SV137 )
| ~ ( ord_less_eq_nat @ SY807 @ SY1165 )
| ( SY1165 = SY807 ) ) ) )
= $true )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2600]) ).
thf(2835,plain,
! [SV694: nat,SV584: list_P559422087at_nat,SV400: nat,SV138: product_prod_nat_nat > a] :
( ( ( finite_Graph_a @ SV138 )
= $false )
| ( ( ~ ( member_nat @ SV400 @ ( v_a @ SV138 ) )
| ~ ( isSimplePath_a @ SV138 @ SV400 @ SV584 @ SV694 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV584 ) @ ( finite_card_nat @ ( v_a @ SV138 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2836,plain,
! [SV695: nat,SV585: list_P559422087at_nat,SV401: nat,SV139: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV139 @ SV401 @ SV585 @ SV695 )
= $false )
| ( ( ~ ! [SY1447: list_P559422087at_nat] :
~ ( isSimplePath_b @ SV139 @ SV401 @ SY1447 @ SV695 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2602]) ).
thf(2837,plain,
! [SV403: nat,SV142: nat,SV586: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV586 @ ( min_dist_b @ c2 @ SV142 @ SV403 ) ) )
= $true )
| ( ( ~ ! [SY1370: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV142 @ SY1370 )
| ( ( min_dist_b @ c2 @ SV142 @ SY1370 )
!= SV586 ) ) )
= $true )
| ( ( connected_b @ c2 @ SV142 @ SV403 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2603]) ).
thf(2838,plain,
! [SV143: set_Pr1986765409at_nat,SV404: nat] :
( ( ( ! [SY1174: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( finite772653738at_nat @ SY1174 )
| ( ( finite447719721at_nat @ SY1174 )
!= SV404 ) )
| ~ ( ord_le841296385at_nat @ SY1174 @ SV143 ) ) )
= $false )
| ( ( finite772653738at_nat @ SV143 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2604]) ).
thf(2839,plain,
! [SV144: set_nat,SV405: set_nat] :
( ( ( ord_less_eq_set_nat @ SV405 @ SV144 )
= $false )
| ( ( SV144 = SV405 )
= $true )
| ( ( ord_less_eq_set_nat @ SV144 @ SV405 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2605]) ).
thf(2840,plain,
! [SV696: nat,SV587: list_P559422087at_nat,SV406: nat,SV145: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV145 @ SV406 @ SV587 @ SV696 )
= $false )
| ( ( dist_a @ SV145 @ SV406 @ ( size_s1990949619at_nat @ SV587 ) @ SV696 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2606]) ).
thf(2841,plain,
! [SV407: nat,SV146: nat] :
( ( ( connected_a @ c @ SV146 @ SV407 )
= $false )
| ( ( ~ ( ~ ( connected_a @ c @ SV146 @ SV407 )
| ~ ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2607]) ).
thf(2842,plain,
! [SV407: nat,SV146: nat] :
( ( ( ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) )
= $false )
| ( ( ~ ( ~ ( connected_a @ c @ SV146 @ SV407 )
| ~ ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2607]) ).
thf(2843,plain,
! [SV697: nat,SV588: nat,SV408: nat,SV147: product_prod_nat_nat > b] :
( ( ( dist_b @ SV147 @ SV408 @ SV588 @ SV697 )
= $false )
| ( ( ~ ! [SY1448: nat] :
( ~ ( dist_b @ SV147 @ SV408 @ SY1448 @ SV697 )
| ( ord_less_eq_nat @ SV588 @ SY1448 ) )
| ( ( min_dist_b @ SV147 @ SV408 @ SV697 )
= SV588 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2844,plain,
! [SV698: nat,SV590: nat,SV410: nat,SV149: product_prod_nat_nat > a] :
( ( ( dist_a @ SV149 @ SV410 @ SV590 @ SV698 )
= $false )
| ( ( ord_less_eq_nat @ ( min_dist_a @ SV149 @ SV410 @ SV698 ) @ SV590 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2845,plain,
! [SV699: nat,SV591: nat,SV411: nat,SV151: product_prod_nat_nat > a] :
( ( ( connected_a @ SV151 @ SV411 @ SV591 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV699 @ ( min_dist_a @ SV151 @ SV411 @ SV591 ) )
| ~ ! [SY1449: nat] :
~ ~ ( ~ ( connected_a @ SV151 @ SV411 @ SY1449 )
| ( ( min_dist_a @ SV151 @ SV411 @ SY1449 )
!= SV699 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2611]) ).
thf(2846,plain,
! [SV700: nat,SV592: list_P559422087at_nat,SV412: nat,SV153: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV153 @ SV412 @ SV592 @ SV700 )
= $false )
| ( ( isPath_b @ SV153 @ SV412 @ SV592 @ SV700 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2612]) ).
thf(2847,plain,
! [SV413: nat,SV154: nat] :
( ( ( SV154 != SV413 )
= $false )
| ( ( ord_less_nat @ SV154 @ SV413 )
= $true )
| ( ( ord_less_eq_nat @ SV154 @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2613]) ).
thf(2848,plain,
! [SV415: set_Pr1986765409at_nat,SV157: set_Pr1986765409at_nat] :
( ( ( SV157 != SV415 )
= $false )
| ( ( ord_le116442893at_nat @ SV157 @ SV415 )
= $true )
| ( ( ord_le841296385at_nat @ SV157 @ SV415 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2614]) ).
thf(2849,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2615]) ).
thf(2850,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( ~ ! [SY1379: nat] :
( ~ ( SV159 @ SY1379 )
| ( ord_less_eq_nat @ SY1379 @ SV594 ) ) )
= $true )
| ( ( ~ ! [SY852: nat] :
~ ~ ( ~ ( SV159 @ SY852 )
| ~ ! [SY853: nat] :
( ~ ( SV159 @ SY853 )
| ( ord_less_eq_nat @ SY853 @ SY852 ) ) ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2616]) ).
thf(2851,plain,
! [SV418: nat,SV160: nat] :
( ( ( connected_a @ c @ SV160 @ SV418 )
= $false )
| ( ( ord_less_nat @ ( min_dist_a @ c @ SV160 @ SV418 ) @ ( finite_card_nat @ ( v_a @ c ) ) )
= $true )
| ( ( member_nat @ SV160 @ ( v_a @ c ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2617]) ).
thf(2852,plain,
! [SV597: nat,SV421: nat,SV163: nat] :
( ( ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2853,plain,
! [SV164: set_set_nat,SV422: set_nat] :
( ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( ~ ! [SY1199: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SY1199 @ SV164 )
| ~ ( ord_less_eq_set_nat @ SV422 @ SY1199 ) )
| ~ ! [SY864: set_nat] :
( ~ ( member_set_nat @ SY864 @ SV164 )
| ~ ( ord_less_eq_set_nat @ SY1199 @ SY864 )
| ( SY1199 = SY864 ) ) ) )
= $true )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2621]) ).
thf(2854,plain,
! [SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 )
= ( ^ [SY1502: nat] :
~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SY1502 )
| ~ ! [SY1503: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1503 @ SY1502 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1503 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(2855,plain,
! [SV167: nat > nat,SV425: nat,SV600: nat] :
( ( ( ! [SY1504: nat] :
( ~ ( ord_less_nat @ ( sK14_SY873 @ SV600 @ SV425 @ SV167 ) @ SY1504 )
| ( ord_less_nat @ ( SV167 @ ( sK14_SY873 @ SV600 @ SV425 @ SV167 ) ) @ ( SV167 @ SY1504 ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV425 @ SV600 )
| ( ord_less_eq_nat @ ( SV167 @ SV425 ) @ ( SV167 @ SV600 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2625]) ).
thf(2856,plain,
! [SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 )
= ( ^ [SY1505: nat] :
~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SY1505 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SY1505 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(2857,plain,
! [SV427: nat,SV171: nat > $o] :
( ( ( ~ ~ ( SV171 @ ( sK5_SY879 @ SV427 @ SV171 ) ) )
= $false )
| ( ( SV171 @ SV427 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2628]) ).
thf(2858,plain,
! [SV171: nat > $o,SV427: nat] :
( ( ( ~ ! [SY1484: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1484 @ ( sK5_SY879 @ SV427 @ SV171 ) )
| ~ ~ ( SV171 @ SY1484 ) ) )
= $false )
| ( ( SV171 @ SV427 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2628]) ).
thf(2859,plain,
! [SV173: set_se1612935105at_nat,SV428: set_Pr1986765409at_nat] :
( ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( ~ ! [SY1214: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SY1214 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY1214 @ SV428 ) )
| ~ ! [SY883: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY883 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY883 @ SY1214 )
| ( SY1214 = SY883 ) ) ) )
= $true )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2629]) ).
thf(2860,plain,
! [SV174: list_P559422087at_nat > $o,SV429: list_P559422087at_nat] :
( ( ( ~ ! [SY1485: list_P559422087at_nat] :
( ~ ( ord_less_nat @ ( size_s1990949619at_nat @ SY1485 ) @ ( size_s1990949619at_nat @ ( sK6_SY885 @ SV429 @ SV174 ) ) )
| ( SV174 @ SY1485 ) ) )
= $false )
| ( ( SV174 @ SV429 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2630]) ).
thf(2861,plain,
! [SV429: list_P559422087at_nat,SV174: list_P559422087at_nat > $o] :
( ( ( SV174 @ ( sK6_SY885 @ SV429 @ SV174 ) )
= $false )
| ( ( SV174 @ SV429 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2630]) ).
thf(2862,plain,
! [SV175: set_nat,SV602: set_nat,SV430: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV430 @ SV602 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV175 @ SV602 )
= $true )
| ( ( ord_less_eq_set_nat @ SV175 @ SV430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2631]) ).
thf(2863,plain,
! [SV703: nat > $o,SV603: nat,SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ( connected_b @ SV176 @ SV431 @ SV603 )
= $false )
| ( ( ~ ! [SY1455: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1455 @ SV603 )
| ~ ! [SY1392: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1392 @ SV603 )
| ( ord_less_eq_nat @ SY1455 @ SY1392 ) )
| ( SV703 @ SY1455 ) )
| ( SV703 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2632]) ).
thf(2864,plain,
! [SV177: set_se1612935105at_nat,SV432: set_Pr1986765409at_nat] :
( ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( ~ ! [SY1223: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SY1223 @ SV177 )
| ~ ( ord_le841296385at_nat @ SV432 @ SY1223 ) )
| ~ ! [SY896: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY896 @ SV177 )
| ~ ( ord_le841296385at_nat @ SY1223 @ SY896 )
| ( SY1223 = SY896 ) ) ) )
= $true )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2633]) ).
thf(2865,plain,
! [SV178: nat,SV433: nat] :
( ( ( ~ ( ( member_nat @ SV433 @ ( v_b @ c2 ) )
| ( member_nat @ SV178 @ ( v_b @ c2 ) ) ) )
= $true )
| ( ( ~ ( ~ ( member_nat @ SV433 @ ( v_b @ c2 ) )
| ~ ( member_nat @ SV178 @ ( v_b @ c2 ) ) ) )
= $true )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2634]) ).
thf(2866,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
| ~ ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2638]) ).
thf(2867,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
| ~ ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2638]) ).
thf(2868,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ~ ( ( SV437 = SV704 )
| ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) ) )
= $true )
| ( ( ~ ( ( SV437 != SV704 )
| ~ ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(2869,plain,
! [SV184: set_Pr1986765409at_nat,SV438: set_Pr1986765409at_nat > $o] :
( ( ( ! [SY1230: set_Pr1986765409at_nat] :
( ~ ( finite772653738at_nat @ SY1230 )
| ~ ! [SY1231: set_Pr1986765409at_nat] :
( ~ ( ord_le116442893at_nat @ SY1231 @ SY1230 )
| ( SV438 @ SY1231 ) )
| ( SV438 @ SY1230 ) ) )
= $false )
| ( ( SV438 @ SV184 )
= $true )
| ( ( finite772653738at_nat @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(2870,plain,
! [SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 )
= ( ^ [SY1506: nat] :
~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SY1506 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SY1506 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2642]) ).
thf(2871,plain,
! [SV186: nat,SV440: nat] :
( ( ( ord_less_eq_nat @ SV440 @ SV186 )
= $false )
| ( ( SV186 = SV440 )
= $true )
| ( ( ord_less_eq_nat @ SV186 @ SV440 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2644]) ).
thf(2872,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( connected_a @ SV442 @ SV706 @ SV775 )
= ( ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2646]) ).
thf(2873,plain,
! [SV190: set_nat,SV444: set_nat] :
( ( ( ord_less_eq_set_nat @ SV444 @ SV190 )
= $false )
| ( ( ~ ( ord_less_nat @ ( finite_card_nat @ SV444 ) @ ( finite_card_nat @ SV190 ) )
| ( ord_less_set_nat @ SV444 @ SV190 ) )
= $true )
| ( ( finite_finite_nat @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(2874,plain,
! [SV445: nat,SV191: nat] :
( ( ( ~ ( ( ( min_dist_a @ c @ SV191 @ SV445 )
= zero_zero_nat )
| ( SV445 = SV191 ) ) )
= $true )
| ( ( ~ ( ( ( min_dist_a @ c @ SV191 @ SV445 )
!= zero_zero_nat )
| ( SV445 != SV191 ) ) )
= $true )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2650]) ).
thf(2875,plain,
! [SV192: nat > $o,SV446: nat] :
( ( ( ~ ! [SY1488: nat] :
( ~ ( ord_less_nat @ SY1488 @ ( sK7_SY922 @ SV446 @ SV192 ) )
| ( SV192 @ SY1488 ) ) )
= $false )
| ( ( SV192 @ SV446 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2652]) ).
thf(2876,plain,
! [SV446: nat,SV192: nat > $o] :
( ( ( SV192 @ ( sK7_SY922 @ SV446 @ SV192 ) )
= $false )
| ( ( SV192 @ SV446 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2652]) ).
thf(2877,plain,
! [SV193: nat,SV447: nat] :
( ( ( ~ ( ( member_nat @ SV447 @ ( v_a @ c ) )
| ( member_nat @ SV193 @ ( v_a @ c ) ) ) )
= $true )
| ( ( ~ ( ~ ( member_nat @ SV447 @ ( v_a @ c ) )
| ~ ( member_nat @ SV193 @ ( v_a @ c ) ) ) )
= $true )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2653]) ).
thf(2878,plain,
! [SV448: set_nat,SV194: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV194 ) )
= $false )
| ( ( ~ ( finite_finite_nat @ SV448 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV194 @ SV448 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2655]) ).
thf(2879,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( ~ ( SV196 @ zero_zero_nat ) )
= $false )
| ( ( ~ ! [SY1241: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_eq_nat @ SY1241 @ SV449 )
| ~ ! [SY928: nat] :
( ~ ( ord_less_nat @ SY928 @ SY1241 )
| ~ ( SV196 @ SY928 ) ) )
| ~ ( SV196 @ SY1241 ) ) )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2656]) ).
thf(2880,plain,
! [SV198: set_Pr1986765409at_nat,SV451: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV451 @ SV198 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV198 ) @ ( finite447719721at_nat @ SV451 ) )
| ( SV451 = SV198 ) )
= $true )
| ( ( finite772653738at_nat @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2658]) ).
thf(2881,plain,
! [SV610: nat,SV452: nat,SV199: product_prod_nat_nat > b] :
( ( ( ! [SY1397: list_P559422087at_nat] :
~ ( isShortestPath_b @ SV199 @ SV452 @ SY1397 @ SV610 ) )
= $false )
| ( ( connected_b @ SV199 @ SV452 @ SV610 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(2882,plain,
! [SV200: set_nat,SV453: nat] :
( ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( ~ ! [SY1245: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY1245 @ SV200 )
| ~ ( ord_less_eq_nat @ SV453 @ SY1245 ) )
| ~ ! [SY936: nat] :
( ~ ( member_nat @ SY936 @ SV200 )
| ~ ( ord_less_eq_nat @ SY1245 @ SY936 )
| ( SY1245 = SY936 ) ) ) )
= $true )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2883,plain,
! [SV611: nat,SV201: product_prod_nat_nat > a,SV454: nat] :
( ( ( ~ ( member_nat @ SV454 @ ( v_a @ SV201 ) ) )
= $true )
| ( ( ~ ( connected_a @ SV201 @ SV454 @ SV611 )
| ( ord_less_nat @ ( min_dist_a @ SV201 @ SV454 @ SV611 ) @ ( finite_card_nat @ ( v_a @ SV201 ) ) ) )
= $true )
| ( ( finite_Graph_a @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2661]) ).
thf(2884,plain,
! [SV455: set_Pr1986765409at_nat,SV202: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV202 ) )
= $false )
| ( ( ~ ( finite772653738at_nat @ SV455 ) )
= $true )
| ( ( ord_le841296385at_nat @ SV202 @ SV455 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2662]) ).
thf(2885,plain,
! [SV707: nat,SV612: list_P559422087at_nat,SV456: nat,SV203: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV203 @ SV456 @ SV612 @ SV707 )
= $false )
| ( ( isSimplePath_b @ SV203 @ SV456 @ SV612 @ SV707 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2663]) ).
thf(2886,plain,
! [SV457: nat,SV205: nat] :
( ( ( ~ ~ ( ord_less_nat @ SV205 @ SV457 ) )
= $true )
| ( ( ord_less_nat @ SV457 @ SV205 )
= $true )
| ( ( SV205 = SV457 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2664]) ).
thf(2887,plain,
! [SV206: set_Pr1986765409at_nat,SV458: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV458 @ SV206 )
= $false )
| ( ( ~ ( ord_less_nat @ ( finite447719721at_nat @ SV458 ) @ ( finite447719721at_nat @ SV206 ) )
| ( ord_le116442893at_nat @ SV458 @ SV206 ) )
= $true )
| ( ( finite772653738at_nat @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2665]) ).
thf(2888,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2889,plain,
! [SV209: set_nat,SV461: set_nat] :
( ( ( finite_finite_nat @ SV461 )
= $false )
| ( ( finite_finite_nat @ SV209 )
= $true )
| ( ( ord_less_eq_set_nat @ SV209 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(2890,plain,
! [SV615: nat > $o,SV462: nat,SV210: nat] :
( ( ( ~ ! [SY1400: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1400 @ SV462 )
| ~ ! [SY1255: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1255 @ SV462 )
| ( ord_less_eq_nat @ SY1400 @ SY1255 ) )
| ( SV615 @ SY1400 ) ) )
= $true )
| ( ( SV615 @ ( min_dist_a @ c @ SV210 @ SV462 ) )
= $true )
| ( ( connected_a @ c @ SV210 @ SV462 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2669]) ).
thf(2891,plain,
! [SV213: set_nat,SV464: set_nat] :
( ( ( ord_less_eq_set_nat @ SV464 @ SV213 )
= $false )
| ( ( ( ( finite_card_nat @ SV464 )
!= ( finite_card_nat @ SV213 ) )
| ( SV464 = SV213 ) )
= $true )
| ( ( finite_finite_nat @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2670]) ).
thf(2892,plain,
! [SV708: nat,SV616: nat,SV465: nat,SV214: product_prod_nat_nat > b] :
( ( ( dist_b @ SV214 @ SV465 @ SV616 @ SV708 )
= $false )
| ( ( connected_b @ SV214 @ SV465 @ SV708 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2671]) ).
thf(2893,plain,
! [SV466: nat,SV215: nat] :
( ( ( connected_b @ c2 @ SV215 @ SV466 )
= $false )
| ( ( ~ ( ~ ( connected_b @ c2 @ SV215 @ SV466 )
| ~ ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2672]) ).
thf(2894,plain,
! [SV466: nat,SV215: nat] :
( ( ( ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) )
= $false )
| ( ( ~ ( ~ ( connected_b @ c2 @ SV215 @ SV466 )
| ~ ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2672]) ).
thf(2895,plain,
! [SV709: nat,SV617: list_P559422087at_nat,SV467: nat,SV217: product_prod_nat_nat > b] :
( ( ( finite_Graph_b @ SV217 )
= $false )
| ( ( ~ ( member_nat @ SV467 @ ( v_b @ SV217 ) )
| ~ ( isSimplePath_b @ SV217 @ SV467 @ SV617 @ SV709 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV617 ) @ ( finite_card_nat @ ( v_b @ SV217 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2673]) ).
thf(2896,plain,
! [SV468: nat,SV218: nat] :
( ( ( connected_b @ c2 @ SV218 @ SV468 )
= $false )
| ( ( ord_less_nat @ ( min_dist_b @ c2 @ SV218 @ SV468 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) )
= $true )
| ( ( member_nat @ SV218 @ ( v_b @ c2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2674]) ).
thf(2897,plain,
! [SV219: set_nat,SV469: set_nat > $o] :
( ( ( ! [SY1261: set_nat] :
( ~ ( finite_finite_nat @ SY1261 )
| ~ ! [SY1262: set_nat] :
( ~ ( ord_less_set_nat @ SY1262 @ SY1261 )
| ( SV469 @ SY1262 ) )
| ( SV469 @ SY1261 ) ) )
= $false )
| ( ( SV469 @ SV219 )
= $true )
| ( ( finite_finite_nat @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2675]) ).
thf(2898,plain,
! [SV470: nat,SV220: nat] :
( ( ( SV220 != SV470 )
= $false )
| ( ( ~ ( ~ ( ( SV220 != SV470 ) )
| ~ ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2676]) ).
thf(2899,plain,
! [SV470: nat,SV220: nat] :
( ( ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) )
= $false )
| ( ( ~ ( ~ ( ( SV220 != SV470 ) )
| ~ ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2676]) ).
thf(2900,plain,
! [SV471: list_P559422087at_nat,SV618: nat,SV221: nat] :
( ( ( ! [SY1404: list_P559422087at_nat] :
~ ( isSimplePath_b @ c2 @ SV221 @ SY1404 @ SV618 ) )
= $false )
| ( ( isPath_b @ c2 @ SV221 @ SV471 @ SV618 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2677]) ).
thf(2901,plain,
! [SV472: nat,SV222: nat > $o] :
( ( ( ! [SY974: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY974 )
| ~ ~ ( SV222 @ SY974 )
| ~ ! [SY975: nat] :
~ ~ ( ~ ( ord_less_nat @ SY975 @ SY974 )
| ~ ~ ( SV222 @ SY975 ) ) ) )
= $false )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2902,plain,
! [SV473: set_nat,SV223: set_nat] :
( ( ( SV223 != SV473 )
= $false )
| ( ( ord_less_set_nat @ SV223 @ SV473 )
= $true )
| ( ( ord_less_eq_set_nat @ SV223 @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2679]) ).
thf(2903,plain,
! [SV224: set_Pr1986765409at_nat,SV474: nat] :
( ( ( ~ ( ord_le841296385at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) @ SV224 ) )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat @ SV224 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2680]) ).
thf(2904,plain,
! [SV224: set_Pr1986765409at_nat,SV474: nat] :
( ( ( ~ ( finite772653738at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) )
| ( ord_less_eq_nat @ ( finite447719721at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) ) @ SV474 ) )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat @ SV224 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2680]) ).
thf(2905,plain,
! [SV226: set_nat,SV476: nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) @ SV226 ) )
= $false )
| ( ( ~ ( ~ ( finite_finite_nat @ SV226 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2681]) ).
thf(2906,plain,
! [SV226: set_nat,SV476: nat] :
( ( ( ~ ( finite_finite_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) )
| ( ord_less_eq_nat @ ( finite_card_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) ) @ SV476 ) )
= $false )
| ( ( ~ ( ~ ( finite_finite_nat @ SV226 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2681]) ).
thf(2907,plain,
! [SV710: nat,SV619: list_P559422087at_nat,SV477: nat,SV227: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV227 @ SV477 @ SV619 @ SV710 )
= $false )
| ( ( dist_b @ SV227 @ SV477 @ ( size_s1990949619at_nat @ SV619 ) @ SV710 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2908,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
| ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
| ~ ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2909,plain,
! [SV231: set_Pr1986765409at_nat,SV480: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV480 @ SV231 )
= $false )
| ( ( finite772653738at_nat @ SV480 )
= $true )
| ( ( finite772653738at_nat @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2684]) ).
thf(2910,plain,
! [SV621: nat,SV481: nat,SV233: product_prod_nat_nat > a] :
( ( ( ~ ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
= zero_zero_nat )
| ( SV621 = SV481 ) )
| ~ ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
!= zero_zero_nat )
| ( SV621 != SV481 ) ) )
= $true )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2685]) ).
thf(2911,plain,
! [SV621: nat,SV481: nat,SV233: product_prod_nat_nat > a] :
( ( ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
= zero_zero_nat )
= ( SV621 = SV481 ) )
= $true )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2685]) ).
thf(2912,plain,
! [SV711: nat,SV622: list_P559422087at_nat,SV482: nat,SV234: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV234 @ SV482 @ SV622 @ SV711 )
= $false )
| ( ( isSimplePath_a @ SV234 @ SV482 @ SV622 @ SV711 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2686]) ).
thf(2913,plain,
! [SV483: list_P559422087at_nat,SV623: nat,SV236: nat] :
( ( ( ! [SY1407: list_P559422087at_nat] :
~ ( isSimplePath_a @ c @ SV236 @ SY1407 @ SV623 ) )
= $false )
| ( ( isPath_a @ c @ SV236 @ SV483 @ SV623 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2687]) ).
thf(2914,plain,
! [SV484: nat,SV237: nat] :
( ( ( connected_b @ c2 @ SV237 @ SV484 )
= $false )
| ( ( ~ ( ~ ( connected_b @ c2 @ SV237 @ SV484 )
| ~ ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2688]) ).
thf(2915,plain,
! [SV484: nat,SV237: nat] :
( ( ( ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) )
= $false )
| ( ( ~ ( ~ ( connected_b @ c2 @ SV237 @ SV484 )
| ~ ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2688]) ).
thf(2916,plain,
! [SV238: nat,SV624: nat,SV485: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV485 @ SV624 ) )
= $true )
| ( ( ord_less_eq_nat @ SV238 @ SV624 )
= $true )
| ( ( ord_less_eq_nat @ SV238 @ SV485 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2689]) ).
thf(2917,plain,
! [SV242: set_Pr1986765409at_nat,SV487: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV487 )
= $false )
| ( ( finite772653738at_nat @ SV242 )
= $true )
| ( ( ord_le841296385at_nat @ SV242 @ SV487 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2690]) ).
thf(2918,plain,
! [SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( dist_a @ SV488 @ SV712 @ SV776 )
= ( ^ [SY1508: nat] :
~ ! [SY1509: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1509 @ SY1508 )
| ( ( size_s1990949619at_nat @ SY1509 )
!= SV776 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(2919,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
| ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
| ~ ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(2920,plain,
! [SV490: list_P559422087at_nat,SV249: list_P559422087at_nat] :
( ( ( SV249 = SV490 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV249 )
= ( size_s1990949619at_nat @ SV490 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2921,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( connected_b @ SV491 @ SV713 @ SV777 )
= ( ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(2922,plain,
! [SV252: set_Pr1986765409at_nat,SV492: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV492 @ SV252 )
= $false )
| ( ( ( ( finite447719721at_nat @ SV492 )
!= ( finite447719721at_nat @ SV252 ) )
| ( SV492 = SV252 ) )
= $true )
| ( ( finite772653738at_nat @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(2923,plain,
! [SV494: nat,SV254: product_prod_nat_nat > b,SV629: nat] :
( ( ( ~ ( ( member_nat @ SV629 @ ( v_b @ SV254 ) )
| ( member_nat @ SV494 @ ( v_b @ SV254 ) ) )
| ~ ( ~ ( member_nat @ SV629 @ ( v_b @ SV254 ) )
| ~ ( member_nat @ SV494 @ ( v_b @ SV254 ) ) ) )
= $true )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2699]) ).
thf(2924,plain,
! [SV494: nat,SV254: product_prod_nat_nat > b,SV629: nat] :
( ( ( ( member_nat @ SV629 @ ( v_b @ SV254 ) )
= ( member_nat @ SV494 @ ( v_b @ SV254 ) ) )
= $true )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2699]) ).
thf(2925,plain,
! [SV630: nat,SV495: nat,SV255: product_prod_nat_nat > b] :
( ( ( ~ ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
= zero_zero_nat )
| ( SV630 = SV495 ) )
| ~ ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
!= zero_zero_nat )
| ( SV630 != SV495 ) ) )
= $true )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2700]) ).
thf(2926,plain,
! [SV630: nat,SV495: nat,SV255: product_prod_nat_nat > b] :
( ( ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
= zero_zero_nat )
= ( SV630 = SV495 ) )
= $true )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2700]) ).
thf(2927,plain,
! [SV631: nat,SV257: product_prod_nat_nat > b,SV496: nat] :
( ( ( ~ ( member_nat @ SV496 @ ( v_b @ SV257 ) ) )
= $true )
| ( ( ~ ( connected_b @ SV257 @ SV496 @ SV631 )
| ( ord_less_nat @ ( min_dist_b @ SV257 @ SV496 @ SV631 ) @ ( finite_card_nat @ ( v_b @ SV257 ) ) ) )
= $true )
| ( ( finite_Graph_b @ SV257 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2701]) ).
thf(2928,plain,
! [SV258: set_Pr1986765409at_nat,SV497: set_Pr1986765409at_nat] :
( ( ( ~ ( member701585322at_nat @ ( sK10_SY1291 @ SV497 @ SV258 ) @ SV258 ) )
= $false )
| ( ( ord_le841296385at_nat @ SV258 @ SV497 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2702]) ).
thf(2929,plain,
! [SV258: set_Pr1986765409at_nat,SV497: set_Pr1986765409at_nat] :
( ( ( member701585322at_nat @ ( sK10_SY1291 @ SV497 @ SV258 ) @ SV497 )
= $false )
| ( ( ord_le841296385at_nat @ SV258 @ SV497 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2702]) ).
thf(2930,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
= $false )
| ( ( ~ ( ~ ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
| ~ ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2703]) ).
thf(2931,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
| ~ ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2703]) ).
thf(2932,plain,
! [SV714: nat,SV632: nat,SV499: nat,SV260: nat] :
( ( ( connected_a @ c @ SV260 @ SV499 )
= $false )
| ( ( ( ( min_dist_a @ c @ SV260 @ SV499 )
!= SV632 )
| ~ ( ord_less_nat @ SV714 @ SV632 )
| ~ ! [SY1466: nat] :
~ ~ ( ~ ( connected_a @ c @ SV260 @ SY1466 )
| ( ( min_dist_a @ c @ SV260 @ SY1466 )
!= SV714 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2933,plain,
! [SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 )
= ( ^ [SY1511: nat] :
~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SY1511 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SY1511 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2705]) ).
thf(2934,plain,
! [SV263: set_li664300135at_nat] :
( ( ( ! [SY1493: list_P559422087at_nat] :
( ~ ( member1608759472at_nat @ SY1493 @ SV263 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SY1493 ) @ ( sK11_SY1034 @ SV263 ) ) ) )
= $true )
| ( ( finite1299096496at_nat @ SV263 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2707]) ).
thf(2935,plain,
! [SV502: nat,SV264: nat,SV634: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV634 @ ( min_dist_a @ c @ SV264 @ SV502 ) ) )
= $true )
| ( ( ~ ! [SY1417: nat] :
~ ~ ( ~ ( connected_a @ c @ SV264 @ SY1417 )
| ( ( min_dist_a @ c @ SV264 @ SY1417 )
!= SV634 ) ) )
= $true )
| ( ( connected_a @ c @ SV264 @ SV502 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2708]) ).
thf(2936,plain,
! [SV750: nat,SV716: nat,SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV265 @ SV503 @ SV635 ) )
= $true )
| ( ( ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
!= SV716 )
| ~ ( ord_less_nat @ SV750 @ SV716 )
| ~ ! [SY1494: nat] :
~ ~ ( ~ ( connected_b @ SV265 @ SV503 @ SY1494 )
| ( ( min_dist_b @ SV265 @ SV503 @ SY1494 )
!= SV750 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2709]) ).
thf(2937,plain,
! [SV504: nat,SV266: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV266 @ ( sK15_SY1305 @ SV504 @ SV266 ) @ SV504 ) )
= $false )
| ( ( connected_a @ c @ SV266 @ SV504 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2710]) ).
thf(2938,plain,
! [SV636: nat,SV505: list_P559422087at_nat,SV267: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV267 @ SV505 @ SV636 ) )
= $true )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV505 ) @ ( finite_card_nat @ ( v_a @ c ) ) )
= $true )
| ( ( member_nat @ SV267 @ ( v_a @ c ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2711]) ).
thf(2939,plain,
! [SV717: nat,SV637: nat,SV506: nat,SV268: product_prod_nat_nat > a] :
( ( ( dist_a @ SV268 @ SV506 @ SV637 @ SV717 )
= $false )
| ( ( connected_a @ SV268 @ SV506 @ SV717 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2712]) ).
thf(2940,plain,
! [SV269: set_nat,SV507: set_nat] :
( ( ( ord_less_eq_set_nat @ SV507 @ SV269 )
= $false )
| ( ( finite_finite_nat @ SV507 )
= $true )
| ( ( finite_finite_nat @ SV269 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2713]) ).
thf(2941,plain,
! [SV270: set_nat,SV508: nat] :
( ( ( ! [SY1309: set_nat] :
~ ~ ( ~ ~ ( ~ ( finite_finite_nat @ SY1309 )
| ( ( finite_card_nat @ SY1309 )
!= SV508 ) )
| ~ ( ord_less_eq_set_nat @ SY1309 @ SV270 ) ) )
= $false )
| ( ( finite_finite_nat @ SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2714]) ).
thf(2942,plain,
! [SV271: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV271 )
| ~ ( ( SV271 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(2943,plain,
! [SV271: nat] :
( ( ( SV271 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV271 )
| ~ ( ( SV271 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2716]) ).
thf(2944,plain,
! [SV273: set_set_nat,SV509: set_nat] :
( ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( ~ ! [SY1310: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SY1310 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1310 @ SV509 ) )
| ~ ! [SY1056: set_nat] :
( ~ ( member_set_nat @ SY1056 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1056 @ SY1310 )
| ( SY1310 = SY1056 ) ) ) )
= $true )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2945,plain,
! [SV510: product_prod_nat_nat > $o,SV274: product_prod_nat_nat > $o] :
( ( ( ~ ( ( SV274 @ ( sK12_SY1312 @ SV510 @ SV274 ) )
| ( SV510 @ ( sK12_SY1312 @ SV510 @ SV274 ) ) )
| ~ ( ~ ( SV274 @ ( sK12_SY1312 @ SV510 @ SV274 ) )
| ~ ( SV510 @ ( sK12_SY1312 @ SV510 @ SV274 ) ) ) )
= $false )
| ( ( ( collec7649004at_nat @ SV274 )
= ( collec7649004at_nat @ SV510 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2718]) ).
thf(2946,plain,
! [SV510: product_prod_nat_nat > $o,SV274: product_prod_nat_nat > $o] :
( ( ( ( SV274 @ ( sK12_SY1312 @ SV510 @ SV274 ) )
= ( SV510 @ ( sK12_SY1312 @ SV510 @ SV274 ) ) )
= $false )
| ( ( ( collec7649004at_nat @ SV274 )
= ( collec7649004at_nat @ SV510 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2718]) ).
thf(2947,plain,
! [SV638: nat,SV511: list_P559422087at_nat,SV275: nat] :
( ( ( ~ ( isSimplePath_b @ c2 @ SV275 @ SV511 @ SV638 ) )
= $true )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV511 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) )
= $true )
| ( ( member_nat @ SV275 @ ( v_b @ c2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2719]) ).
thf(2948,plain,
! [SV279: set_nat,SV514: set_nat] :
( ( ( ord_less_set_nat @ SV514 @ SV279 )
= $false )
| ( ( ord_less_nat @ ( finite_card_nat @ SV514 ) @ ( finite_card_nat @ SV279 ) )
= $true )
| ( ( finite_finite_nat @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2722]) ).
thf(2949,plain,
! [SV718: nat,SV641: nat,SV515: nat,SV281: product_prod_nat_nat > b] :
( ( ( dist_b @ SV281 @ SV515 @ SV641 @ SV718 )
= $false )
| ( ( ord_less_eq_nat @ ( min_dist_b @ SV281 @ SV515 @ SV718 ) @ SV641 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2723]) ).
thf(2950,plain,
! [SV516: nat,SV642: nat,SV283: nat] :
( ( ( ~ ! [SY1423: nat] :
( ~ ( dist_b @ c2 @ SV283 @ SY1423 @ SV642 )
| ( ord_less_eq_nat @ SV516 @ SY1423 ) ) )
= $true )
| ( ( ( min_dist_b @ c2 @ SV283 @ SV642 )
= SV516 )
= $true )
| ( ( dist_b @ c2 @ SV283 @ SV516 @ SV642 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2724]) ).
thf(2951,plain,
! [SV284: set_se1612935105at_nat,SV517: set_se1612935105at_nat] :
( ( ( finite1457549322at_nat @ SV517 )
= $false )
| ( ( finite1457549322at_nat @ SV284 )
= $true )
| ( ( ord_le2096002913at_nat @ SV284 @ SV517 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2725]) ).
thf(2952,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( connected_b @ SV519 @ SV719 @ SV779 )
= ( ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(2953,plain,
! [SV287: set_Pr1986765409at_nat,SV645: set_Pr1986765409at_nat,SV520: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV520 @ SV645 ) )
= $true )
| ( ( ord_le841296385at_nat @ SV287 @ SV645 )
= $true )
| ( ( ord_le841296385at_nat @ SV287 @ SV520 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2729]) ).
thf(2954,plain,
! [SV720: nat,SV647: list_P559422087at_nat,SV523: nat,SV291: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV291 @ SV523 @ SV647 @ SV720 )
= $false )
| ( ( ~ ! [SY1473: list_P559422087at_nat] :
~ ( isSimplePath_a @ SV291 @ SV523 @ SY1473 @ SV720 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2731]) ).
thf(2955,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ~ ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2733]) ).
thf(2956,plain,
! [SV298: set_Pr1986765409at_nat,SV529: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV529 @ SV298 )
= $false )
| ( ( ord_less_eq_nat @ ( finite447719721at_nat @ SV529 ) @ ( finite447719721at_nat @ SV298 ) )
= $true )
| ( ( finite772653738at_nat @ SV298 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2738]) ).
thf(2957,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ( ord_less_nat @ SV530 @ SV721 )
| ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV530 @ SV721 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2739]) ).
thf(2958,plain,
! [SV652: nat,SV531: list_P559422087at_nat,SV300: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV300 @ SV531 @ SV652 ) )
= $true )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV531 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) )
= $true )
| ( ( member_nat @ SV300 @ ( v_b @ c2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2741]) ).
thf(2959,plain,
! [SV301: set_Pr1986765409at_nat,SV532: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV532 @ SV301 )
= $false )
| ( ( SV301 = SV532 )
= $true )
| ( ( ord_le841296385at_nat @ SV301 @ SV532 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2742]) ).
thf(2960,plain,
! [SV653: nat > $o,SV533: nat,SV304: nat] :
( ( ( ~ ! [SY1428: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1428 @ SV533 )
| ~ ! [SY1336: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1336 @ SV533 )
| ( ord_less_eq_nat @ SY1428 @ SY1336 ) )
| ( SV653 @ SY1428 ) ) )
= $true )
| ( ( SV653 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) )
= $true )
| ( ( connected_b @ c2 @ SV304 @ SV533 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2743]) ).
thf(2961,plain,
! [SV534: list_P559422087at_nat,SV305: list_P559422087at_nat] :
( ( ( SV305 = SV534 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV305 )
= ( size_s1990949619at_nat @ SV534 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2744]) ).
thf(2962,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( ~ ( edmond1517640972ysis_a @ SV315 )
| ~ ( finite_Graph_a @ SV315 ) )
= $false )
| ( ( edmond1517640972ysis_a @ SV315 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(2963,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( ~ ( edmond1517640972ysis_a @ SV315 )
| ~ ( finite_Graph_a @ SV315 ) )
= $false )
| ( ( finite_Graph_a @ SV315 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2752]) ).
thf(2964,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( ~ ( edmond1517640973ysis_b @ SV316 )
| ~ ( finite_Graph_b @ SV316 ) )
= $false )
| ( ( edmond1517640973ysis_b @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2965,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( ~ ( edmond1517640973ysis_b @ SV316 )
| ~ ( finite_Graph_b @ SV316 ) )
= $false )
| ( ( finite_Graph_b @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(2966,plain,
! [SV317: nat,SV13: nat] :
( ( ( ~ ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
| ( SV317 != SV13 ) )
= $false )
| ( ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(2967,plain,
! [SV317: nat,SV13: nat] :
( ( ( ~ ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
| ( SV317 != SV13 ) )
= $false )
| ( ( SV317 = SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(2968,plain,
! [SV318: set_Pr1986765409at_nat > $o,SV15: set_Pr1986765409at_nat] :
( ( ( ~ ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
| ~ ( SV318 @ SV15 ) )
= $false )
| ( ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(2969,plain,
! [SV318: set_Pr1986765409at_nat > $o,SV15: set_Pr1986765409at_nat] :
( ( ( ~ ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
| ~ ( SV318 @ SV15 ) )
= $false )
| ( ( SV318 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(2970,plain,
! [SV319: set_nat > $o,SV16: set_nat] :
( ( ( ~ ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
| ~ ( SV319 @ SV16 ) )
= $false )
| ( ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(2971,plain,
! [SV319: set_nat > $o,SV16: set_nat] :
( ( ( ~ ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
| ~ ( SV319 @ SV16 ) )
= $false )
| ( ( SV319 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(2972,plain,
! [SV320: product_prod_nat_nat > $o,SV17: product_prod_nat_nat] :
( ( ( ~ ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
| ~ ( SV320 @ SV17 ) )
= $false )
| ( ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2761]) ).
thf(2973,plain,
! [SV320: product_prod_nat_nat > $o,SV17: product_prod_nat_nat] :
( ( ( ~ ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
| ~ ( SV320 @ SV17 ) )
= $false )
| ( ( SV320 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2762]) ).
thf(2974,plain,
! [SV321: nat > $o,SV18: nat] :
( ( ( ~ ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
| ~ ( SV321 @ SV18 ) )
= $false )
| ( ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2763]) ).
thf(2975,plain,
! [SV321: nat > $o,SV18: nat] :
( ( ( ~ ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
| ~ ( SV321 @ SV18 ) )
= $false )
| ( ( SV321 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2764]) ).
thf(2976,plain,
! [SV24: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV24 )
| ( SV24 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(2977,plain,
! [SV24: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV24 ) )
= $false )
| ( ( SV24 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2766]) ).
thf(2978,plain,
! [SV24: nat] :
( ( ( SV24 != zero_zero_nat )
= $false )
| ( ( SV24 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2766]) ).
thf(2979,plain,
! [SV25: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV25 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2767]) ).
thf(2980,plain,
! [SV25: nat] :
( ( ( SV25 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2767]) ).
thf(2981,plain,
! [SV25: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV25 @ zero_zero_nat ) )
= $false )
| ( ( SV25 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2768]) ).
thf(2982,plain,
! [SV25: nat] :
( ( ( SV25 != zero_zero_nat )
= $false )
| ( ( SV25 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2768]) ).
thf(2983,plain,
! [SV32: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV32 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2769]) ).
thf(2984,plain,
! [SV32: nat] :
( ( ( SV32 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2769]) ).
thf(2985,plain,
! [SV32: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV32 @ zero_zero_nat ) )
= $false )
| ( ( SV32 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2770]) ).
thf(2986,plain,
! [SV32: nat] :
( ( ( SV32 != zero_zero_nat )
= $false )
| ( ( SV32 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2770]) ).
thf(2987,plain,
! [SV33: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV33 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2771]) ).
thf(2988,plain,
! [SV33: nat] :
( ( ( SV33 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2771]) ).
thf(2989,plain,
! [SV33: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV33 @ zero_zero_nat ) )
= $false )
| ( ( SV33 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2772]) ).
thf(2990,plain,
! [SV33: nat] :
( ( ( SV33 != zero_zero_nat )
= $false )
| ( ( SV33 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2772]) ).
thf(2991,plain,
! [SV660: nat,SV323: nat] :
( ( ( ( ord_less_eq_nat @ SV323 @ SV660 )
| ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV323 @ SV660 )
| ~ ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2773]) ).
thf(2992,plain,
! [SV35: nat] :
( ( ( zero_zero_nat != SV35 )
= $false )
| ( ( zero_zero_nat = SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2774]) ).
thf(2993,plain,
! [SV35: nat] :
( ( ( SV35 != zero_zero_nat )
= $false )
| ( ( zero_zero_nat = SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2774]) ).
thf(2994,plain,
! [SV35: nat] :
( ( ( zero_zero_nat != SV35 )
= $false )
| ( ( SV35 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2775]) ).
thf(2995,plain,
! [SV35: nat] :
( ( ( SV35 != zero_zero_nat )
= $false )
| ( ( SV35 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2775]) ).
thf(2996,plain,
! [SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ! [SV780: nat] :
( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV780 )
= ( isPath_b @ SV324 @ SV661 @ SV756 @ SV780 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2776]) ).
thf(2997,plain,
! [SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV324 @ SV661 @ SV756 )
= ( isPath_b @ SV324 @ SV661 @ SV756 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2776]) ).
thf(2998,plain,
! [SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ! [SV781: nat] :
( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV781 )
= ( isPath_a @ SV325 @ SV662 @ SV757 @ SV781 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2777]) ).
thf(2999,plain,
! [SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV325 @ SV662 @ SV757 )
= ( isPath_a @ SV325 @ SV662 @ SV757 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2777]) ).
thf(3000,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ~ ( ( connected_b @ SV330 @ SV665 @ SV760 )
| ( connected_b @ SV330 @ SV665 @ SV760 ) )
| ~ ( ~ ( connected_b @ SV330 @ SV665 @ SV760 )
| ~ ( connected_b @ SV330 @ SV665 @ SV760 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2780]) ).
thf(3001,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( connected_b @ SV330 @ SV665 @ SV760 )
= ( connected_b @ SV330 @ SV665 @ SV760 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2780]) ).
thf(3002,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ~ ( ( connected_a @ SV331 @ SV666 @ SV761 )
| ( connected_a @ SV331 @ SV666 @ SV761 ) )
| ~ ( ~ ( connected_a @ SV331 @ SV666 @ SV761 )
| ~ ( connected_a @ SV331 @ SV666 @ SV761 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2781]) ).
thf(3003,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( connected_a @ SV331 @ SV666 @ SV761 )
= ( connected_a @ SV331 @ SV666 @ SV761 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2781]) ).
thf(3004,plain,
! [SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ! [SV782: nat] :
( ( dist_b @ SV334 @ SV667 @ SV762 @ SV782 )
= ( dist_b @ SV334 @ SV667 @ SV762 @ SV782 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2782]) ).
thf(3005,plain,
! [SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( dist_b @ SV334 @ SV667 @ SV762 )
= ( dist_b @ SV334 @ SV667 @ SV762 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2782]) ).
thf(3006,plain,
! [SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ! [SV783: nat] :
( ( dist_a @ SV335 @ SV668 @ SV763 @ SV783 )
= ( dist_a @ SV335 @ SV668 @ SV763 @ SV783 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2783]) ).
thf(3007,plain,
! [SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( dist_a @ SV335 @ SV668 @ SV763 )
= ( dist_a @ SV335 @ SV668 @ SV763 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2783]) ).
thf(3008,plain,
! [SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ! [SV784: nat] :
( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV784 )
= ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV784 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2784]) ).
thf(3009,plain,
! [SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 )
= ( isShortestPath_a @ SV336 @ SV669 @ SV764 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2784]) ).
thf(3010,plain,
! [SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ! [SV785: nat] :
( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV785 )
= ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV785 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2785]) ).
thf(3011,plain,
! [SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 )
= ( isShortestPath_b @ SV337 @ SV670 @ SV765 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2785]) ).
thf(3012,plain,
! [SV53: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ( SV53 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(3013,plain,
! [SV53: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV53 ) )
= $false )
| ( ( SV53 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2787]) ).
thf(3014,plain,
! [SV53: nat] :
( ( ( SV53 != zero_zero_nat )
= $false )
| ( ( SV53 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2787]) ).
thf(3015,plain,
! [SV552: nat,SV342: nat,SV61: product_prod_nat_nat > b] :
( ( ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
= $false )
| ( ( ~ ( ~ ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
| ( SV552 != SV342 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2788]) ).
thf(3016,plain,
! [SV61: product_prod_nat_nat > b,SV342: nat,SV552: nat] :
( ( ( SV552 = SV342 )
= $false )
| ( ( ~ ( ~ ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
| ( SV552 != SV342 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2788]) ).
thf(3017,plain,
! [SV553: nat,SV343: nat,SV62: product_prod_nat_nat > a] :
( ( ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
= $false )
| ( ( ~ ( ~ ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
| ( SV553 != SV343 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2789]) ).
thf(3018,plain,
! [SV62: product_prod_nat_nat > a,SV343: nat,SV553: nat] :
( ( ( SV553 = SV343 )
= $false )
| ( ( ~ ( ~ ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
| ( SV553 != SV343 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2789]) ).
thf(3019,plain,
! [SV344: nat,SV63: nat] :
( ( ( ~ ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
| ( SV344 != SV63 ) )
= $false )
| ( ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(3020,plain,
! [SV344: nat,SV63: nat] :
( ( ( ~ ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
| ( SV344 != SV63 ) )
= $false )
| ( ( SV344 = SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(3021,plain,
! [SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ! [SV786: nat] :
( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV786 )
= ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV786 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2792]) ).
thf(3022,plain,
! [SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 )
= ( isSimplePath_a @ SV345 @ SV671 @ SV766 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2792]) ).
thf(3023,plain,
! [SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ! [SV787: nat] :
( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV787 )
= ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV787 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2793]) ).
thf(3024,plain,
! [SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 )
= ( isSimplePath_b @ SV346 @ SV672 @ SV767 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2793]) ).
thf(3025,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( ~ ( finite_Graph_b @ SV347 )
| ~ ( finite_finite_nat @ ( v_b @ SV347 ) ) )
= $false )
| ( ( finite_Graph_b @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2794]) ).
thf(3026,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( ~ ( finite_Graph_b @ SV347 )
| ~ ( finite_finite_nat @ ( v_b @ SV347 ) ) )
= $false )
| ( ( finite_finite_nat @ ( v_b @ SV347 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2795]) ).
thf(3027,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( ~ ( finite_Graph_a @ SV348 )
| ~ ( finite_finite_nat @ ( v_a @ SV348 ) ) )
= $false )
| ( ( finite_Graph_a @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2796]) ).
thf(3028,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( ~ ( finite_Graph_a @ SV348 )
| ~ ( finite_finite_nat @ ( v_a @ SV348 ) ) )
= $false )
| ( ( finite_finite_nat @ ( v_a @ SV348 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2797]) ).
thf(3029,plain,
! [SV93: nat] :
( ( ( ~ ( ( SV93 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV93 ) )
= $false )
| ( ( SV93 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(3030,plain,
! [SV93: nat] :
( ( ( ~ ( ( SV93 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2799]) ).
thf(3031,plain,
! [SV93: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV93 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2799]) ).
thf(3032,plain,
! [SV564: nat,SV365: list_P559422087at_nat,SV95: nat] :
( ( ( isSimplePath_a @ c @ SV95 @ SV365 @ SV564 )
= $false )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV365 ) @ ( finite_card_nat @ ( v_a @ c ) ) )
= $true )
| ( ( member_nat @ SV95 @ ( v_a @ c ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2800]) ).
thf(3033,plain,
! [SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ! [SV788: nat] :
( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV788 )
= ( ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV788 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV788 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2801]) ).
thf(3034,plain,
! [SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 )
= ( ^ [SY1496: nat] :
~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SY1496 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SY1496 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2801]) ).
thf(3035,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2802]) ).
thf(3036,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2802]) ).
thf(3037,plain,
! [SV101: nat] :
( ( ( ~ ( ( SV101 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV101 ) )
= $false )
| ( ( SV101 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2803]) ).
thf(3038,plain,
! [SV101: nat] :
( ( ( ~ ( ( SV101 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2804]) ).
thf(3039,plain,
! [SV101: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV101 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2804]) ).
thf(3040,plain,
! [SV102: set_nat,SV369: set_nat] :
( ( ( member_nat @ ( sK3_SY1117 @ SV369 @ SV102 ) @ SV102 )
= $true )
| ( ( ord_less_eq_set_nat @ SV102 @ SV369 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2805]) ).
thf(3041,plain,
! [SV682: nat,SV567: list_P559422087at_nat,SV103: product_prod_nat_nat > a,SV370: nat] :
( ( ( ~ ( member_nat @ SV370 @ ( v_a @ SV103 ) ) )
= $true )
| ( ( ~ ( isShortestPath_a @ SV103 @ SV370 @ SV567 @ SV682 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV567 ) @ ( finite_card_nat @ ( v_a @ SV103 ) ) ) )
= $true )
| ( ( finite_Graph_a @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2807]) ).
thf(3042,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ( SV372 = SV683 )
| ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) )
= $false )
| ( ( ~ ( ( SV372 != SV683 )
| ~ ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2808]) ).
thf(3043,plain,
! [SV684: nat,SV569: list_P559422087at_nat,SV106: product_prod_nat_nat > b,SV373: nat] :
( ( ( ~ ( member_nat @ SV373 @ ( v_b @ SV106 ) ) )
= $true )
| ( ( ~ ( isShortestPath_b @ SV106 @ SV373 @ SV569 @ SV684 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV569 ) @ ( finite_card_nat @ ( v_b @ SV106 ) ) ) )
= $true )
| ( ( finite_Graph_b @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2809]) ).
thf(3044,plain,
! [SV377: nat > $o,SV110: nat > $o] :
( ( ( ~ ( ( SV110 @ ( sK4_SY1126 @ SV377 @ SV110 ) )
| ( SV377 @ ( sK4_SY1126 @ SV377 @ SV110 ) ) ) )
= $false )
| ( ( ( collect_nat @ SV110 )
= ( collect_nat @ SV377 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2811]) ).
thf(3045,plain,
! [SV377: nat > $o,SV110: nat > $o] :
( ( ( ~ ( ~ ( SV110 @ ( sK4_SY1126 @ SV377 @ SV110 ) )
| ~ ( SV377 @ ( sK4_SY1126 @ SV377 @ SV110 ) ) ) )
= $false )
| ( ( ( collect_nat @ SV110 )
= ( collect_nat @ SV377 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2811]) ).
thf(3046,plain,
! [SV378: nat,SV111: product_prod_nat_nat > a,SV571: nat] :
( ( ( ~ ( ( member_nat @ SV571 @ ( v_a @ SV111 ) )
| ( member_nat @ SV378 @ ( v_a @ SV111 ) ) ) )
= $true )
| ( ( ~ ( ~ ( member_nat @ SV571 @ ( v_a @ SV111 ) )
| ~ ( member_nat @ SV378 @ ( v_a @ SV111 ) ) ) )
= $true )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2813]) ).
thf(3047,plain,
! [SV379: nat,SV572: nat,SV112: nat] :
( ( ( ! [SY1344: nat] :
( ~ ( dist_a @ c @ SV112 @ SY1344 @ SV572 )
| ( ord_less_eq_nat @ SV379 @ SY1344 ) ) )
= $false )
| ( ( ( min_dist_a @ c @ SV112 @ SV572 )
= SV379 )
= $true )
| ( ( dist_a @ c @ SV112 @ SV379 @ SV572 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2815]) ).
thf(3048,plain,
! [SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ! [SV789: nat] :
( ( dist_b @ SV380 @ SV686 @ SV769 @ SV789 )
= ( ~ ! [SY1513: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1513 @ SV789 )
| ( ( size_s1990949619at_nat @ SY1513 )
!= SV769 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2816]) ).
thf(3049,plain,
! [SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( dist_b @ SV380 @ SV686 @ SV769 )
= ( ^ [SY1497: nat] :
~ ! [SY1498: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1498 @ SY1497 )
| ( ( size_s1990949619at_nat @ SY1498 )
!= SV769 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2816]) ).
thf(3050,plain,
! [SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ! [SV790: nat] :
( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV790 )
= ( ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV790 )
| ~ ! [SY1514: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1514 @ SV790 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1514 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2817]) ).
thf(3051,plain,
! [SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 )
= ( ^ [SY1499: nat] :
~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SY1499 )
| ~ ! [SY1500: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1500 @ SY1499 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1500 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2817]) ).
thf(3052,plain,
! [SV575: nat,SV688: nat,SV382: nat,SV116: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1438: nat] :
( ~ ( dist_a @ SV116 @ SV382 @ SY1438 @ SV688 )
| ( ord_less_eq_nat @ SV575 @ SY1438 ) ) )
= $true )
| ( ( ( min_dist_a @ SV116 @ SV382 @ SV688 )
= SV575 )
= $true )
| ( ( dist_a @ SV116 @ SV382 @ SV575 @ SV688 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2818]) ).
thf(3053,plain,
! [SV383: nat,SV117: nat] :
( ( ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
= zero_zero_nat )
| ( SV383 = SV117 ) )
= $false )
| ( ( ~ ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
!= zero_zero_nat )
| ( SV383 != SV117 ) ) )
= $true )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2819]) ).
thf(3054,plain,
! [SV576: nat,SV384: nat,SV118: nat] :
( ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $false )
| ( ( ~ ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2820]) ).
thf(3055,plain,
! [SV384: nat,SV576: nat,SV118: nat] :
( ( ( ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2820]) ).
thf(3056,plain,
! [SV741: nat,SV689: nat,SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ( connected_a @ SV120 @ SV386 @ SV577 )
= $false )
| ( ( ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
!= SV689 )
| ~ ( ord_less_nat @ SV741 @ SV689 )
| ~ ! [SY1479: nat] :
~ ~ ( ~ ( connected_a @ SV120 @ SV386 @ SY1479 )
| ( ( min_dist_a @ SV120 @ SV386 @ SY1479 )
!= SV741 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2822]) ).
thf(3057,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ~ ( ( connected_a @ SV387 @ SV690 @ SV771 )
| ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) )
| ~ ( ~ ( connected_a @ SV387 @ SV690 @ SV771 )
| ~ ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2823]) ).
thf(3058,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( connected_a @ SV387 @ SV690 @ SV771 )
= ( ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2823]) ).
thf(3059,plain,
! [SV579: nat,SV388: nat,SV124: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV124 @ SV388 @ ( sK16_SY1359 @ SV579 @ SV388 @ SV124 ) @ SV579 ) )
= $false )
| ( ( connected_a @ SV124 @ SV388 @ SV579 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2824]) ).
thf(3060,plain,
! [SV691: nat,SV581: nat,SV391: nat,SV128: nat] :
( ( ( ( min_dist_b @ c2 @ SV128 @ SV391 )
!= SV581 )
= $true )
| ( ( ~ ( ord_less_nat @ SV691 @ SV581 )
| ~ ! [SY1443: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV128 @ SY1443 )
| ( ( min_dist_b @ c2 @ SV128 @ SY1443 )
!= SV691 ) ) )
= $true )
| ( ( connected_b @ c2 @ SV128 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2826]) ).
thf(3061,plain,
! [SV692: nat > $o,SV582: nat,SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1444: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1444 @ SV582 )
| ~ ! [SY1364: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1364 @ SV582 )
| ( ord_less_eq_nat @ SY1444 @ SY1364 ) )
| ( SV692 @ SY1444 ) ) )
= $true )
| ( ( SV692 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) )
= $true )
| ( ( connected_a @ SV129 @ SV392 @ SV582 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2827]) ).
thf(3062,plain,
! [SV395: set_nat,SV133: set_nat] :
( ( ( ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV133 ) @ ( finite_card_nat @ SV395 ) ) )
= $true )
| ( ( SV395 = SV133 )
= $true )
| ( ( ord_less_eq_set_nat @ SV395 @ SV133 )
= $false )
| ( ( finite_finite_nat @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2829]) ).
thf(3063,plain,
! [SV583: nat,SV396: nat,SV134: product_prod_nat_nat > b,SV693: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV693 @ ( min_dist_b @ SV134 @ SV396 @ SV583 ) ) )
= $true )
| ( ( ~ ! [SY1446: nat] :
~ ~ ( ~ ( connected_b @ SV134 @ SV396 @ SY1446 )
| ( ( min_dist_b @ SV134 @ SV396 @ SY1446 )
!= SV693 ) ) )
= $true )
| ( ( connected_b @ SV134 @ SV396 @ SV583 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2830]) ).
thf(3064,plain,
! [SV397: nat,SV135: nat] :
( ( ( isShortestPath_b @ c2 @ SV135 @ ( sK13_SY1163 @ SV397 @ SV135 ) @ SV397 )
= $true )
| ( ( connected_b @ c2 @ SV135 @ SV397 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2831]) ).
thf(3065,plain,
! [SV398: nat,SV136: nat] :
( ( ( ~ ( connected_a @ c @ SV136 @ SV398 )
| ~ ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) )
= $false )
| ( ( connected_a @ c @ SV136 @ SV398 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2832]) ).
thf(3066,plain,
! [SV398: nat,SV136: nat] :
( ( ( ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) )
= $true )
| ( ( ~ ( ~ ( connected_a @ c @ SV136 @ SV398 )
| ~ ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2833]) ).
thf(3067,plain,
! [SV399: nat,SV137: set_nat] :
( ( ( ! [SY1165: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY1165 @ SV137 )
| ~ ( ord_less_eq_nat @ SY1165 @ SV399 ) )
| ~ ! [SY807: nat] :
( ~ ( member_nat @ SY807 @ SV137 )
| ~ ( ord_less_eq_nat @ SY807 @ SY1165 )
| ( SY1165 = SY807 ) ) ) )
= $false )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2834]) ).
thf(3068,plain,
! [SV694: nat,SV584: list_P559422087at_nat,SV138: product_prod_nat_nat > a,SV400: nat] :
( ( ( ~ ( member_nat @ SV400 @ ( v_a @ SV138 ) ) )
= $true )
| ( ( ~ ( isSimplePath_a @ SV138 @ SV400 @ SV584 @ SV694 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV584 ) @ ( finite_card_nat @ ( v_a @ SV138 ) ) ) )
= $true )
| ( ( finite_Graph_a @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2835]) ).
thf(3069,plain,
! [SV585: list_P559422087at_nat,SV695: nat,SV401: nat,SV139: product_prod_nat_nat > b] :
( ( ( ! [SY1447: list_P559422087at_nat] :
~ ( isSimplePath_b @ SV139 @ SV401 @ SY1447 @ SV695 ) )
= $false )
| ( ( isPath_b @ SV139 @ SV401 @ SV585 @ SV695 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2836]) ).
thf(3070,plain,
! [SV403: nat,SV142: nat,SV586: nat] :
( ( ( ord_less_eq_nat @ SV586 @ ( min_dist_b @ c2 @ SV142 @ SV403 ) )
= $false )
| ( ( ~ ! [SY1370: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV142 @ SY1370 )
| ( ( min_dist_b @ c2 @ SV142 @ SY1370 )
!= SV586 ) ) )
= $true )
| ( ( connected_b @ c2 @ SV142 @ SV403 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(3071,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ( ~ ~ ( ~ ~ ( ~ ( finite772653738at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) )
| ( ( finite447719721at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) )
!= SV404 ) )
| ~ ( ord_le841296385at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) @ SV143 ) ) )
= $false )
| ( ( finite772653738at_nat @ SV143 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2838]) ).
thf(3072,plain,
! [SV407: nat,SV146: nat] :
( ( ( ~ ( connected_a @ c @ SV146 @ SV407 )
| ~ ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) )
= $false )
| ( ( connected_a @ c @ SV146 @ SV407 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2841]) ).
thf(3073,plain,
! [SV407: nat,SV146: nat] :
( ( ( ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) )
= $true )
| ( ( ~ ( ~ ( connected_a @ c @ SV146 @ SV407 )
| ~ ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2842]) ).
thf(3074,plain,
! [SV588: nat,SV697: nat,SV408: nat,SV147: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1448: nat] :
( ~ ( dist_b @ SV147 @ SV408 @ SY1448 @ SV697 )
| ( ord_less_eq_nat @ SV588 @ SY1448 ) ) )
= $true )
| ( ( ( min_dist_b @ SV147 @ SV408 @ SV697 )
= SV588 )
= $true )
| ( ( dist_b @ SV147 @ SV408 @ SV588 @ SV697 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2843]) ).
thf(3075,plain,
! [SV591: nat,SV411: nat,SV151: product_prod_nat_nat > a,SV699: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV699 @ ( min_dist_a @ SV151 @ SV411 @ SV591 ) ) )
= $true )
| ( ( ~ ! [SY1449: nat] :
~ ~ ( ~ ( connected_a @ SV151 @ SV411 @ SY1449 )
| ( ( min_dist_a @ SV151 @ SV411 @ SY1449 )
!= SV699 ) ) )
= $true )
| ( ( connected_a @ SV151 @ SV411 @ SV591 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2845]) ).
thf(3076,plain,
! [SV413: nat,SV154: nat] :
( ( ( SV154 = SV413 )
= $true )
| ( ( ord_less_nat @ SV154 @ SV413 )
= $true )
| ( ( ord_less_eq_nat @ SV154 @ SV413 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2847]) ).
thf(3077,plain,
! [SV415: set_Pr1986765409at_nat,SV157: set_Pr1986765409at_nat] :
( ( ( SV157 = SV415 )
= $true )
| ( ( ord_le116442893at_nat @ SV157 @ SV415 )
= $true )
| ( ( ord_le841296385at_nat @ SV157 @ SV415 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2848]) ).
thf(3078,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2849]) ).
thf(3079,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2849]) ).
thf(3080,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( ! [SY1379: nat] :
( ~ ( SV159 @ SY1379 )
| ( ord_less_eq_nat @ SY1379 @ SV594 ) ) )
= $false )
| ( ( ~ ! [SY852: nat] :
~ ~ ( ~ ( SV159 @ SY852 )
| ~ ! [SY853: nat] :
( ~ ( SV159 @ SY853 )
| ( ord_less_eq_nat @ SY853 @ SY852 ) ) ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2850]) ).
thf(3081,plain,
! [SV597: nat,SV421: nat,SV163: nat] :
( ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $false )
| ( ( ~ ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2852]) ).
thf(3082,plain,
! [SV421: nat,SV597: nat,SV163: nat] :
( ( ( ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2852]) ).
thf(3083,plain,
! [SV422: set_nat,SV164: set_set_nat] :
( ( ( ! [SY1199: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SY1199 @ SV164 )
| ~ ( ord_less_eq_set_nat @ SV422 @ SY1199 ) )
| ~ ! [SY864: set_nat] :
( ~ ( member_set_nat @ SY864 @ SV164 )
| ~ ( ord_less_eq_set_nat @ SY1199 @ SY864 )
| ( SY1199 = SY864 ) ) ) )
= $false )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2853]) ).
thf(3084,plain,
! [SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ! [SV791: nat] :
( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV791 )
= ( ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV791 )
| ~ ! [SY1515: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1515 @ SV791 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1515 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2854]) ).
thf(3085,plain,
! [SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 )
= ( ^ [SY1502: nat] :
~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SY1502 )
| ~ ! [SY1503: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1503 @ SY1502 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1503 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2854]) ).
thf(3086,plain,
! [SV167: nat > nat,SV425: nat,SV600: nat] :
( ( ( ~ ( ord_less_nat @ ( sK14_SY873 @ SV600 @ SV425 @ SV167 ) @ ( sK18_SY1504 @ SV167 @ SV425 @ SV600 ) )
| ( ord_less_nat @ ( SV167 @ ( sK14_SY873 @ SV600 @ SV425 @ SV167 ) ) @ ( SV167 @ ( sK18_SY1504 @ SV167 @ SV425 @ SV600 ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV425 @ SV600 )
| ( ord_less_eq_nat @ ( SV167 @ SV425 ) @ ( SV167 @ SV600 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2855]) ).
thf(3087,plain,
! [SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ! [SV792: nat] :
( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV792 )
= ( ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV792 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV792 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2856]) ).
thf(3088,plain,
! [SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 )
= ( ^ [SY1505: nat] :
~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SY1505 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SY1505 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2856]) ).
thf(3089,plain,
! [SV427: nat,SV171: nat > $o] :
( ( ( ~ ( SV171 @ ( sK5_SY879 @ SV427 @ SV171 ) ) )
= $true )
| ( ( SV171 @ SV427 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2857]) ).
thf(3090,plain,
! [SV171: nat > $o,SV427: nat] :
( ( ( ! [SY1484: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1484 @ ( sK5_SY879 @ SV427 @ SV171 ) )
| ~ ~ ( SV171 @ SY1484 ) ) )
= $true )
| ( ( SV171 @ SV427 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2858]) ).
thf(3091,plain,
! [SV428: set_Pr1986765409at_nat,SV173: set_se1612935105at_nat] :
( ( ( ! [SY1214: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SY1214 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY1214 @ SV428 ) )
| ~ ! [SY883: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY883 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY883 @ SY1214 )
| ( SY1214 = SY883 ) ) ) )
= $false )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2859]) ).
thf(3092,plain,
! [SV174: list_P559422087at_nat > $o,SV429: list_P559422087at_nat] :
( ( ( ! [SY1485: list_P559422087at_nat] :
( ~ ( ord_less_nat @ ( size_s1990949619at_nat @ SY1485 ) @ ( size_s1990949619at_nat @ ( sK6_SY885 @ SV429 @ SV174 ) ) )
| ( SV174 @ SY1485 ) ) )
= $true )
| ( ( SV174 @ SV429 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2860]) ).
thf(3093,plain,
! [SV175: set_nat,SV602: set_nat,SV430: set_nat] :
( ( ( ord_less_eq_set_nat @ SV430 @ SV602 )
= $false )
| ( ( ord_less_eq_set_nat @ SV175 @ SV602 )
= $true )
| ( ( ord_less_eq_set_nat @ SV175 @ SV430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2862]) ).
thf(3094,plain,
! [SV703: nat > $o,SV603: nat,SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1455: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1455 @ SV603 )
| ~ ! [SY1392: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1392 @ SV603 )
| ( ord_less_eq_nat @ SY1455 @ SY1392 ) )
| ( SV703 @ SY1455 ) ) )
= $true )
| ( ( SV703 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) )
= $true )
| ( ( connected_b @ SV176 @ SV431 @ SV603 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2863]) ).
thf(3095,plain,
! [SV432: set_Pr1986765409at_nat,SV177: set_se1612935105at_nat] :
( ( ( ! [SY1223: set_Pr1986765409at_nat] :
~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ SY1223 @ SV177 )
| ~ ( ord_le841296385at_nat @ SV432 @ SY1223 ) )
| ~ ! [SY896: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY896 @ SV177 )
| ~ ( ord_le841296385at_nat @ SY1223 @ SY896 )
| ( SY1223 = SY896 ) ) ) )
= $false )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2864]) ).
thf(3096,plain,
! [SV178: nat,SV433: nat] :
( ( ( ( member_nat @ SV433 @ ( v_b @ c2 ) )
| ( member_nat @ SV178 @ ( v_b @ c2 ) ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV433 @ ( v_b @ c2 ) )
| ~ ( member_nat @ SV178 @ ( v_b @ c2 ) ) ) )
= $true )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(3097,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ~ ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
| ~ ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2866]) ).
thf(3098,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ~ ( SV182 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
| ( SV436 @ ( sK19_SY1227 @ SV436 @ SV182 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
| ~ ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2867]) ).
thf(3099,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ( SV437 = SV704 )
| ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) )
= $false )
| ( ( ~ ( ( SV437 != SV704 )
| ~ ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2868]) ).
thf(3100,plain,
! [SV438: set_Pr1986765409at_nat > $o,SV184: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ ( sK20_SY1230 @ SV184 @ SV438 ) )
| ~ ! [SY1516: set_Pr1986765409at_nat] :
( ~ ( ord_le116442893at_nat @ SY1516 @ ( sK20_SY1230 @ SV184 @ SV438 ) )
| ( SV438 @ SY1516 ) )
| ( SV438 @ ( sK20_SY1230 @ SV184 @ SV438 ) ) )
= $false )
| ( ( SV438 @ SV184 )
= $true )
| ( ( finite772653738at_nat @ SV184 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2869]) ).
thf(3101,plain,
! [SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ! [SV793: nat] :
( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV793 )
= ( ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV793 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV793 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2870]) ).
thf(3102,plain,
! [SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 )
= ( ^ [SY1506: nat] :
~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SY1506 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SY1506 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2870]) ).
thf(3103,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ~ ( ( connected_a @ SV442 @ SV706 @ SV775 )
| ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) )
| ~ ( ~ ( connected_a @ SV442 @ SV706 @ SV775 )
| ~ ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2872]) ).
thf(3104,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( connected_a @ SV442 @ SV706 @ SV775 )
= ( ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2872]) ).
thf(3105,plain,
! [SV190: set_nat,SV444: set_nat] :
( ( ( ~ ( ord_less_nat @ ( finite_card_nat @ SV444 ) @ ( finite_card_nat @ SV190 ) ) )
= $true )
| ( ( ord_less_set_nat @ SV444 @ SV190 )
= $true )
| ( ( ord_less_eq_set_nat @ SV444 @ SV190 )
= $false )
| ( ( finite_finite_nat @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2873]) ).
thf(3106,plain,
! [SV445: nat,SV191: nat] :
( ( ( ( ( min_dist_a @ c @ SV191 @ SV445 )
= zero_zero_nat )
| ( SV445 = SV191 ) )
= $false )
| ( ( ~ ( ( ( min_dist_a @ c @ SV191 @ SV445 )
!= zero_zero_nat )
| ( SV445 != SV191 ) ) )
= $true )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(3107,plain,
! [SV192: nat > $o,SV446: nat] :
( ( ( ! [SY1488: nat] :
( ~ ( ord_less_nat @ SY1488 @ ( sK7_SY922 @ SV446 @ SV192 ) )
| ( SV192 @ SY1488 ) ) )
= $true )
| ( ( SV192 @ SV446 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2875]) ).
thf(3108,plain,
! [SV193: nat,SV447: nat] :
( ( ( ( member_nat @ SV447 @ ( v_a @ c ) )
| ( member_nat @ SV193 @ ( v_a @ c ) ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV447 @ ( v_a @ c ) )
| ~ ( member_nat @ SV193 @ ( v_a @ c ) ) ) )
= $true )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2877]) ).
thf(3109,plain,
! [SV448: set_nat,SV194: set_nat] :
( ( ( finite_finite_nat @ SV194 )
= $true )
| ( ( ~ ( finite_finite_nat @ SV448 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV194 @ SV448 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2878]) ).
thf(3110,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( ~ ! [SY1241: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_eq_nat @ SY1241 @ SV449 )
| ~ ! [SY928: nat] :
( ~ ( ord_less_nat @ SY928 @ SY1241 )
| ~ ( SV196 @ SY928 ) ) )
| ~ ( SV196 @ SY1241 ) ) )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2879]) ).
thf(3111,plain,
! [SV451: set_Pr1986765409at_nat,SV198: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV198 ) @ ( finite447719721at_nat @ SV451 ) ) )
= $true )
| ( ( SV451 = SV198 )
= $true )
| ( ( ord_le841296385at_nat @ SV451 @ SV198 )
= $false )
| ( ( finite772653738at_nat @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2880]) ).
thf(3112,plain,
! [SV610: nat,SV452: nat,SV199: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV199 @ SV452 @ ( sK21_SY1397 @ SV610 @ SV452 @ SV199 ) @ SV610 ) )
= $false )
| ( ( connected_b @ SV199 @ SV452 @ SV610 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2881]) ).
thf(3113,plain,
! [SV453: nat,SV200: set_nat] :
( ( ( ! [SY1245: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY1245 @ SV200 )
| ~ ( ord_less_eq_nat @ SV453 @ SY1245 ) )
| ~ ! [SY936: nat] :
( ~ ( member_nat @ SY936 @ SV200 )
| ~ ( ord_less_eq_nat @ SY1245 @ SY936 )
| ( SY1245 = SY936 ) ) ) )
= $false )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(3114,plain,
! [SV611: nat,SV201: product_prod_nat_nat > a,SV454: nat] :
( ( ( member_nat @ SV454 @ ( v_a @ SV201 ) )
= $false )
| ( ( ~ ( connected_a @ SV201 @ SV454 @ SV611 )
| ( ord_less_nat @ ( min_dist_a @ SV201 @ SV454 @ SV611 ) @ ( finite_card_nat @ ( v_a @ SV201 ) ) ) )
= $true )
| ( ( finite_Graph_a @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2883]) ).
thf(3115,plain,
! [SV455: set_Pr1986765409at_nat,SV202: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV202 )
= $true )
| ( ( ~ ( finite772653738at_nat @ SV455 ) )
= $true )
| ( ( ord_le841296385at_nat @ SV202 @ SV455 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2884]) ).
thf(3116,plain,
! [SV457: nat,SV205: nat] :
( ( ( ~ ( ord_less_nat @ SV205 @ SV457 ) )
= $false )
| ( ( ord_less_nat @ SV457 @ SV205 )
= $true )
| ( ( SV205 = SV457 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2886]) ).
thf(3117,plain,
! [SV206: set_Pr1986765409at_nat,SV458: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_less_nat @ ( finite447719721at_nat @ SV458 ) @ ( finite447719721at_nat @ SV206 ) ) )
= $true )
| ( ( ord_le116442893at_nat @ SV458 @ SV206 )
= $true )
| ( ( ord_le841296385at_nat @ SV458 @ SV206 )
= $false )
| ( ( finite772653738at_nat @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2887]) ).
thf(3118,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2888]) ).
thf(3119,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2888]) ).
thf(3120,plain,
! [SV615: nat > $o,SV462: nat,SV210: nat] :
( ( ( ! [SY1400: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1400 @ SV462 )
| ~ ! [SY1255: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1255 @ SV462 )
| ( ord_less_eq_nat @ SY1400 @ SY1255 ) )
| ( SV615 @ SY1400 ) ) )
= $false )
| ( ( SV615 @ ( min_dist_a @ c @ SV210 @ SV462 ) )
= $true )
| ( ( connected_a @ c @ SV210 @ SV462 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2890]) ).
thf(3121,plain,
! [SV213: set_nat,SV464: set_nat] :
( ( ( ( finite_card_nat @ SV464 )
!= ( finite_card_nat @ SV213 ) )
= $true )
| ( ( SV464 = SV213 )
= $true )
| ( ( ord_less_eq_set_nat @ SV464 @ SV213 )
= $false )
| ( ( finite_finite_nat @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2891]) ).
thf(3122,plain,
! [SV466: nat,SV215: nat] :
( ( ( ~ ( connected_b @ c2 @ SV215 @ SV466 )
| ~ ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) )
= $false )
| ( ( connected_b @ c2 @ SV215 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2893]) ).
thf(3123,plain,
! [SV466: nat,SV215: nat] :
( ( ( ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) )
= $true )
| ( ( ~ ( ~ ( connected_b @ c2 @ SV215 @ SV466 )
| ~ ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2894]) ).
thf(3124,plain,
! [SV709: nat,SV617: list_P559422087at_nat,SV217: product_prod_nat_nat > b,SV467: nat] :
( ( ( ~ ( member_nat @ SV467 @ ( v_b @ SV217 ) ) )
= $true )
| ( ( ~ ( isSimplePath_b @ SV217 @ SV467 @ SV617 @ SV709 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV617 ) @ ( finite_card_nat @ ( v_b @ SV217 ) ) ) )
= $true )
| ( ( finite_Graph_b @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2895]) ).
thf(3125,plain,
! [SV469: set_nat > $o,SV219: set_nat] :
( ( ( ~ ( finite_finite_nat @ ( sK22_SY1261 @ SV219 @ SV469 ) )
| ~ ! [SY1517: set_nat] :
( ~ ( ord_less_set_nat @ SY1517 @ ( sK22_SY1261 @ SV219 @ SV469 ) )
| ( SV469 @ SY1517 ) )
| ( SV469 @ ( sK22_SY1261 @ SV219 @ SV469 ) ) )
= $false )
| ( ( SV469 @ SV219 )
= $true )
| ( ( finite_finite_nat @ SV219 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2897]) ).
thf(3126,plain,
! [SV470: nat,SV220: nat] :
( ( ( SV220 = SV470 )
= $true )
| ( ( ~ ( ~ ( ( SV220 != SV470 ) )
| ~ ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2898]) ).
thf(3127,plain,
! [SV470: nat,SV220: nat] :
( ( ( ord_less_nat @ SV220 @ SV470 )
= $false )
| ( ( ~ ( ~ ( ( SV220 != SV470 ) )
| ~ ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2899]) ).
thf(3128,plain,
! [SV220: nat,SV470: nat] :
( ( ( ord_less_nat @ SV470 @ SV220 )
= $false )
| ( ( ~ ( ~ ( ( SV220 != SV470 ) )
| ~ ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2899]) ).
thf(3129,plain,
! [SV618: nat,SV471: list_P559422087at_nat,SV221: nat] :
( ( ( ~ ( isSimplePath_b @ c2 @ SV221 @ ( sK23_SY1404 @ SV471 @ SV618 @ SV221 ) @ SV618 ) )
= $false )
| ( ( isPath_b @ c2 @ SV221 @ SV471 @ SV618 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2900]) ).
thf(3130,plain,
! [SV222: nat > $o,SV472: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK24_SY974 @ SV472 @ SV222 ) )
| ~ ~ ( SV222 @ ( sK24_SY974 @ SV472 @ SV222 ) )
| ~ ! [SY1518: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1518 @ ( sK24_SY974 @ SV472 @ SV222 ) )
| ~ ~ ( SV222 @ SY1518 ) ) )
= $false )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2901]) ).
thf(3131,plain,
! [SV473: set_nat,SV223: set_nat] :
( ( ( SV223 = SV473 )
= $true )
| ( ( ord_less_set_nat @ SV223 @ SV473 )
= $true )
| ( ( ord_less_eq_set_nat @ SV223 @ SV473 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2902]) ).
thf(3132,plain,
! [SV224: set_Pr1986765409at_nat,SV474: nat] :
( ( ( ord_le841296385at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) @ SV224 )
= $true )
| ( ( ~ ( ~ ( finite772653738at_nat @ SV224 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2903]) ).
thf(3133,plain,
! [SV224: set_Pr1986765409at_nat,SV474: nat] :
( ( ( ~ ( finite772653738at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) ) )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat @ SV224 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2904]) ).
thf(3134,plain,
! [SV224: set_Pr1986765409at_nat,SV474: nat] :
( ( ( ord_less_eq_nat @ ( finite447719721at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) ) @ SV474 )
= $false )
| ( ( ~ ( ~ ( finite772653738at_nat @ SV224 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2904]) ).
thf(3135,plain,
! [SV226: set_nat,SV476: nat] :
( ( ( ord_less_eq_set_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) @ SV226 )
= $true )
| ( ( ~ ( ~ ( finite_finite_nat @ SV226 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2905]) ).
thf(3136,plain,
! [SV226: set_nat,SV476: nat] :
( ( ( ~ ( finite_finite_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) ) )
= $false )
| ( ( ~ ( ~ ( finite_finite_nat @ SV226 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2906]) ).
thf(3137,plain,
! [SV226: set_nat,SV476: nat] :
( ( ( ord_less_eq_nat @ ( finite_card_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) ) @ SV476 )
= $false )
| ( ( ~ ( ~ ( finite_finite_nat @ SV226 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2906]) ).
thf(3138,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
| ~ ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2908]) ).
thf(3139,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
| ~ ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2908]) ).
thf(3140,plain,
! [SV621: nat,SV481: nat,SV233: product_prod_nat_nat > a] :
( ( ( ~ ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
= zero_zero_nat )
| ( SV621 = SV481 ) ) )
= $true )
| ( ( ~ ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
!= zero_zero_nat )
| ( SV621 != SV481 ) ) )
= $true )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2910]) ).
thf(3141,plain,
! [SV623: nat,SV483: list_P559422087at_nat,SV236: nat] :
( ( ( ~ ( isSimplePath_a @ c @ SV236 @ ( sK25_SY1407 @ SV483 @ SV623 @ SV236 ) @ SV623 ) )
= $false )
| ( ( isPath_a @ c @ SV236 @ SV483 @ SV623 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2913]) ).
thf(3142,plain,
! [SV484: nat,SV237: nat] :
( ( ( ~ ( connected_b @ c2 @ SV237 @ SV484 )
| ~ ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) )
= $false )
| ( ( connected_b @ c2 @ SV237 @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2914]) ).
thf(3143,plain,
! [SV484: nat,SV237: nat] :
( ( ( ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) )
= $true )
| ( ( ~ ( ~ ( connected_b @ c2 @ SV237 @ SV484 )
| ~ ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2915]) ).
thf(3144,plain,
! [SV238: nat,SV624: nat,SV485: nat] :
( ( ( ord_less_eq_nat @ SV485 @ SV624 )
= $false )
| ( ( ord_less_eq_nat @ SV238 @ SV624 )
= $true )
| ( ( ord_less_eq_nat @ SV238 @ SV485 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2916]) ).
thf(3145,plain,
! [SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ! [SV794: nat] :
( ( dist_a @ SV488 @ SV712 @ SV776 @ SV794 )
= ( ~ ! [SY1519: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1519 @ SV794 )
| ( ( size_s1990949619at_nat @ SY1519 )
!= SV776 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2918]) ).
thf(3146,plain,
! [SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( dist_a @ SV488 @ SV712 @ SV776 )
= ( ^ [SY1508: nat] :
~ ! [SY1509: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1509 @ SY1508 )
| ( ( size_s1990949619at_nat @ SY1509 )
!= SV776 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2918]) ).
thf(3147,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
| ~ ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2919]) ).
thf(3148,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
| ~ ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2919]) ).
thf(3149,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ~ ( ( connected_b @ SV491 @ SV713 @ SV777 )
| ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) )
| ~ ( ~ ( connected_b @ SV491 @ SV713 @ SV777 )
| ~ ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2921]) ).
thf(3150,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( connected_b @ SV491 @ SV713 @ SV777 )
= ( ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2921]) ).
thf(3151,plain,
! [SV252: set_Pr1986765409at_nat,SV492: set_Pr1986765409at_nat] :
( ( ( ( finite447719721at_nat @ SV492 )
!= ( finite447719721at_nat @ SV252 ) )
= $true )
| ( ( SV492 = SV252 )
= $true )
| ( ( ord_le841296385at_nat @ SV492 @ SV252 )
= $false )
| ( ( finite772653738at_nat @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2922]) ).
thf(3152,plain,
! [SV494: nat,SV254: product_prod_nat_nat > b,SV629: nat] :
( ( ( ~ ( ( member_nat @ SV629 @ ( v_b @ SV254 ) )
| ( member_nat @ SV494 @ ( v_b @ SV254 ) ) ) )
= $true )
| ( ( ~ ( ~ ( member_nat @ SV629 @ ( v_b @ SV254 ) )
| ~ ( member_nat @ SV494 @ ( v_b @ SV254 ) ) ) )
= $true )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2923]) ).
thf(3153,plain,
! [SV630: nat,SV495: nat,SV255: product_prod_nat_nat > b] :
( ( ( ~ ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
= zero_zero_nat )
| ( SV630 = SV495 ) ) )
= $true )
| ( ( ~ ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
!= zero_zero_nat )
| ( SV630 != SV495 ) ) )
= $true )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2925]) ).
thf(3154,plain,
! [SV631: nat,SV257: product_prod_nat_nat > b,SV496: nat] :
( ( ( member_nat @ SV496 @ ( v_b @ SV257 ) )
= $false )
| ( ( ~ ( connected_b @ SV257 @ SV496 @ SV631 )
| ( ord_less_nat @ ( min_dist_b @ SV257 @ SV496 @ SV631 ) @ ( finite_card_nat @ ( v_b @ SV257 ) ) ) )
= $true )
| ( ( finite_Graph_b @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2927]) ).
thf(3155,plain,
! [SV258: set_Pr1986765409at_nat,SV497: set_Pr1986765409at_nat] :
( ( ( member701585322at_nat @ ( sK10_SY1291 @ SV497 @ SV258 ) @ SV258 )
= $true )
| ( ( ord_le841296385at_nat @ SV258 @ SV497 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2928]) ).
thf(3156,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
| ~ ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) )
= $false )
| ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2930]) ).
thf(3157,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ( SV259 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
| ( SV498 @ ( sK26_SY1292 @ SV498 @ SV259 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
| ~ ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2931]) ).
thf(3158,plain,
! [SV714: nat,SV632: nat,SV499: nat,SV260: nat] :
( ( ( ( min_dist_a @ c @ SV260 @ SV499 )
!= SV632 )
= $true )
| ( ( ~ ( ord_less_nat @ SV714 @ SV632 )
| ~ ! [SY1466: nat] :
~ ~ ( ~ ( connected_a @ c @ SV260 @ SY1466 )
| ( ( min_dist_a @ c @ SV260 @ SY1466 )
!= SV714 ) ) )
= $true )
| ( ( connected_a @ c @ SV260 @ SV499 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2932]) ).
thf(3159,plain,
! [SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ! [SV795: nat] :
( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV795 )
= ( ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV795 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV795 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2933]) ).
thf(3160,plain,
! [SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 )
= ( ^ [SY1511: nat] :
~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SY1511 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SY1511 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2933]) ).
thf(3161,plain,
! [SV263: set_li664300135at_nat,SV796: list_P559422087at_nat] :
( ( ( ~ ( member1608759472at_nat @ SV796 @ SV263 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV796 ) @ ( sK11_SY1034 @ SV263 ) ) )
= $true )
| ( ( finite1299096496at_nat @ SV263 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2934]) ).
thf(3162,plain,
! [SV502: nat,SV264: nat,SV634: nat] :
( ( ( ord_less_eq_nat @ SV634 @ ( min_dist_a @ c @ SV264 @ SV502 ) )
= $false )
| ( ( ~ ! [SY1417: nat] :
~ ~ ( ~ ( connected_a @ c @ SV264 @ SY1417 )
| ( ( min_dist_a @ c @ SV264 @ SY1417 )
!= SV634 ) ) )
= $true )
| ( ( connected_a @ c @ SV264 @ SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2935]) ).
thf(3163,plain,
! [SV750: nat,SV716: nat,SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ( connected_b @ SV265 @ SV503 @ SV635 )
= $false )
| ( ( ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
!= SV716 )
| ~ ( ord_less_nat @ SV750 @ SV716 )
| ~ ! [SY1494: nat] :
~ ~ ( ~ ( connected_b @ SV265 @ SV503 @ SY1494 )
| ( ( min_dist_b @ SV265 @ SV503 @ SY1494 )
!= SV750 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2936]) ).
thf(3164,plain,
! [SV504: nat,SV266: nat] :
( ( ( isShortestPath_a @ c @ SV266 @ ( sK15_SY1305 @ SV504 @ SV266 ) @ SV504 )
= $true )
| ( ( connected_a @ c @ SV266 @ SV504 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2937]) ).
thf(3165,plain,
! [SV636: nat,SV505: list_P559422087at_nat,SV267: nat] :
( ( ( isShortestPath_a @ c @ SV267 @ SV505 @ SV636 )
= $false )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV505 ) @ ( finite_card_nat @ ( v_a @ c ) ) )
= $true )
| ( ( member_nat @ SV267 @ ( v_a @ c ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2938]) ).
thf(3166,plain,
! [SV508: nat,SV270: set_nat] :
( ( ( ~ ~ ( ~ ~ ( ~ ( finite_finite_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) )
| ( ( finite_card_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) )
!= SV508 ) )
| ~ ( ord_less_eq_set_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) @ SV270 ) ) )
= $false )
| ( ( finite_finite_nat @ SV270 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2941]) ).
thf(3167,plain,
! [SV271: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV271 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2942]) ).
thf(3168,plain,
! [SV271: nat] :
( ( ( ~ ( ( SV271 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2942]) ).
thf(3169,plain,
! [SV271: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV271 )
| ~ ( ( SV271 != zero_zero_nat ) ) )
= $false )
| ( ( SV271 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2943]) ).
thf(3170,plain,
! [SV509: set_nat,SV273: set_set_nat] :
( ( ( ! [SY1310: set_nat] :
~ ~ ( ~ ~ ( ~ ( member_set_nat @ SY1310 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1310 @ SV509 ) )
| ~ ! [SY1056: set_nat] :
( ~ ( member_set_nat @ SY1056 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1056 @ SY1310 )
| ( SY1310 = SY1056 ) ) ) )
= $false )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2944]) ).
thf(3171,plain,
! [SV510: product_prod_nat_nat > $o,SV274: product_prod_nat_nat > $o] :
( ( ( ~ ( ( SV274 @ ( sK12_SY1312 @ SV510 @ SV274 ) )
| ( SV510 @ ( sK12_SY1312 @ SV510 @ SV274 ) ) ) )
= $false )
| ( ( ( collec7649004at_nat @ SV274 )
= ( collec7649004at_nat @ SV510 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2945]) ).
thf(3172,plain,
! [SV510: product_prod_nat_nat > $o,SV274: product_prod_nat_nat > $o] :
( ( ( ~ ( ~ ( SV274 @ ( sK12_SY1312 @ SV510 @ SV274 ) )
| ~ ( SV510 @ ( sK12_SY1312 @ SV510 @ SV274 ) ) ) )
= $false )
| ( ( ( collec7649004at_nat @ SV274 )
= ( collec7649004at_nat @ SV510 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2945]) ).
thf(3173,plain,
! [SV638: nat,SV511: list_P559422087at_nat,SV275: nat] :
( ( ( isSimplePath_b @ c2 @ SV275 @ SV511 @ SV638 )
= $false )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV511 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) )
= $true )
| ( ( member_nat @ SV275 @ ( v_b @ c2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2947]) ).
thf(3174,plain,
! [SV516: nat,SV642: nat,SV283: nat] :
( ( ( ! [SY1423: nat] :
( ~ ( dist_b @ c2 @ SV283 @ SY1423 @ SV642 )
| ( ord_less_eq_nat @ SV516 @ SY1423 ) ) )
= $false )
| ( ( ( min_dist_b @ c2 @ SV283 @ SV642 )
= SV516 )
= $true )
| ( ( dist_b @ c2 @ SV283 @ SV516 @ SV642 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2950]) ).
thf(3175,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ~ ( ( connected_b @ SV519 @ SV719 @ SV779 )
| ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) )
| ~ ( ~ ( connected_b @ SV519 @ SV719 @ SV779 )
| ~ ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2952]) ).
thf(3176,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( connected_b @ SV519 @ SV719 @ SV779 )
= ( ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[2952]) ).
thf(3177,plain,
! [SV287: set_Pr1986765409at_nat,SV645: set_Pr1986765409at_nat,SV520: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV520 @ SV645 )
= $false )
| ( ( ord_le841296385at_nat @ SV287 @ SV645 )
= $true )
| ( ( ord_le841296385at_nat @ SV287 @ SV520 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2953]) ).
thf(3178,plain,
! [SV647: list_P559422087at_nat,SV720: nat,SV523: nat,SV291: product_prod_nat_nat > a] :
( ( ( ! [SY1473: list_P559422087at_nat] :
~ ( isSimplePath_a @ SV291 @ SV523 @ SY1473 @ SV720 ) )
= $false )
| ( ( isPath_a @ SV291 @ SV523 @ SV647 @ SV720 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2954]) ).
thf(3179,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ~ ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2955]) ).
thf(3180,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ~ ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2955]) ).
thf(3181,plain,
! [SV721: nat,SV530: nat] :
( ( ( ( ord_less_nat @ SV530 @ SV721 )
| ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV530 @ SV721 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2957]) ).
thf(3182,plain,
! [SV652: nat,SV531: list_P559422087at_nat,SV300: nat] :
( ( ( isShortestPath_b @ c2 @ SV300 @ SV531 @ SV652 )
= $false )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV531 ) @ ( finite_card_nat @ ( v_b @ c2 ) ) )
= $true )
| ( ( member_nat @ SV300 @ ( v_b @ c2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2958]) ).
thf(3183,plain,
! [SV653: nat > $o,SV533: nat,SV304: nat] :
( ( ( ! [SY1428: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1428 @ SV533 )
| ~ ! [SY1336: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1336 @ SV533 )
| ( ord_less_eq_nat @ SY1428 @ SY1336 ) )
| ( SV653 @ SY1428 ) ) )
= $false )
| ( ( SV653 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) )
= $true )
| ( ( connected_b @ c2 @ SV304 @ SV533 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2960]) ).
thf(3184,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( ~ ( edmond1517640972ysis_a @ SV315 ) )
= $false )
| ( ( edmond1517640972ysis_a @ SV315 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2962]) ).
thf(3185,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( ~ ( finite_Graph_a @ SV315 ) )
= $false )
| ( ( edmond1517640972ysis_a @ SV315 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2962]) ).
thf(3186,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( ~ ( edmond1517640972ysis_a @ SV315 ) )
= $false )
| ( ( finite_Graph_a @ SV315 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2963]) ).
thf(3187,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( ~ ( finite_Graph_a @ SV315 ) )
= $false )
| ( ( finite_Graph_a @ SV315 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2963]) ).
thf(3188,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( ~ ( edmond1517640973ysis_b @ SV316 ) )
= $false )
| ( ( edmond1517640973ysis_b @ SV316 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2964]) ).
thf(3189,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( ~ ( finite_Graph_b @ SV316 ) )
= $false )
| ( ( edmond1517640973ysis_b @ SV316 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2964]) ).
thf(3190,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( ~ ( edmond1517640973ysis_b @ SV316 ) )
= $false )
| ( ( finite_Graph_b @ SV316 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2965]) ).
thf(3191,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( ~ ( finite_Graph_b @ SV316 ) )
= $false )
| ( ( finite_Graph_b @ SV316 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2965]) ).
thf(3192,plain,
! [SV317: nat,SV13: nat] :
( ( ( ~ ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 ) )
= $false )
| ( ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2966]) ).
thf(3193,plain,
! [SV13: nat,SV317: nat] :
( ( ( SV317 != SV13 )
= $false )
| ( ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2966]) ).
thf(3194,plain,
! [SV317: nat,SV13: nat] :
( ( ( ~ ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 ) )
= $false )
| ( ( SV317 = SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2967]) ).
thf(3195,plain,
! [SV13: nat,SV317: nat] :
( ( ( SV317 != SV13 )
= $false )
| ( ( SV317 = SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2967]) ).
thf(3196,plain,
! [SV318: set_Pr1986765409at_nat > $o,SV15: set_Pr1986765409at_nat] :
( ( ( ~ ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) ) )
= $false )
| ( ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2968]) ).
thf(3197,plain,
! [SV15: set_Pr1986765409at_nat,SV318: set_Pr1986765409at_nat > $o] :
( ( ( ~ ( SV318 @ SV15 ) )
= $false )
| ( ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2968]) ).
thf(3198,plain,
! [SV318: set_Pr1986765409at_nat > $o,SV15: set_Pr1986765409at_nat] :
( ( ( ~ ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) ) )
= $false )
| ( ( SV318 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2969]) ).
thf(3199,plain,
! [SV15: set_Pr1986765409at_nat,SV318: set_Pr1986765409at_nat > $o] :
( ( ( ~ ( SV318 @ SV15 ) )
= $false )
| ( ( SV318 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2969]) ).
thf(3200,plain,
! [SV319: set_nat > $o,SV16: set_nat] :
( ( ( ~ ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) ) )
= $false )
| ( ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2970]) ).
thf(3201,plain,
! [SV16: set_nat,SV319: set_nat > $o] :
( ( ( ~ ( SV319 @ SV16 ) )
= $false )
| ( ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2970]) ).
thf(3202,plain,
! [SV319: set_nat > $o,SV16: set_nat] :
( ( ( ~ ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) ) )
= $false )
| ( ( SV319 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2971]) ).
thf(3203,plain,
! [SV16: set_nat,SV319: set_nat > $o] :
( ( ( ~ ( SV319 @ SV16 ) )
= $false )
| ( ( SV319 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2971]) ).
thf(3204,plain,
! [SV320: product_prod_nat_nat > $o,SV17: product_prod_nat_nat] :
( ( ( ~ ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) ) )
= $false )
| ( ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2972]) ).
thf(3205,plain,
! [SV17: product_prod_nat_nat,SV320: product_prod_nat_nat > $o] :
( ( ( ~ ( SV320 @ SV17 ) )
= $false )
| ( ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2972]) ).
thf(3206,plain,
! [SV320: product_prod_nat_nat > $o,SV17: product_prod_nat_nat] :
( ( ( ~ ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) ) )
= $false )
| ( ( SV320 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2973]) ).
thf(3207,plain,
! [SV17: product_prod_nat_nat,SV320: product_prod_nat_nat > $o] :
( ( ( ~ ( SV320 @ SV17 ) )
= $false )
| ( ( SV320 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2973]) ).
thf(3208,plain,
! [SV321: nat > $o,SV18: nat] :
( ( ( ~ ( member_nat @ SV18 @ ( collect_nat @ SV321 ) ) )
= $false )
| ( ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2974]) ).
thf(3209,plain,
! [SV18: nat,SV321: nat > $o] :
( ( ( ~ ( SV321 @ SV18 ) )
= $false )
| ( ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2974]) ).
thf(3210,plain,
! [SV321: nat > $o,SV18: nat] :
( ( ( ~ ( member_nat @ SV18 @ ( collect_nat @ SV321 ) ) )
= $false )
| ( ( SV321 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2975]) ).
thf(3211,plain,
! [SV18: nat,SV321: nat > $o] :
( ( ( ~ ( SV321 @ SV18 ) )
= $false )
| ( ( SV321 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2975]) ).
thf(3212,plain,
! [SV24: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV24 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2976]) ).
thf(3213,plain,
! [SV24: nat] :
( ( ( SV24 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2976]) ).
thf(3214,plain,
! [SV24: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV24 ) )
= $true )
| ( ( SV24 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2977]) ).
thf(3215,plain,
! [SV24: nat] :
( ( ( SV24 = zero_zero_nat )
= $true )
| ( ( SV24 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2978]) ).
thf(3216,plain,
! [SV25: nat] :
( ( ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2979]) ).
thf(3217,plain,
! [SV25: nat] :
( ( ( SV25 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2980]) ).
thf(3218,plain,
! [SV25: nat] :
( ( ( ord_less_eq_nat @ SV25 @ zero_zero_nat )
= $true )
| ( ( SV25 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2981]) ).
thf(3219,plain,
! [SV25: nat] :
( ( ( SV25 = zero_zero_nat )
= $true )
| ( ( SV25 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2982]) ).
thf(3220,plain,
! [SV32: nat] :
( ( ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2983]) ).
thf(3221,plain,
! [SV32: nat] :
( ( ( SV32 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2984]) ).
thf(3222,plain,
! [SV32: nat] :
( ( ( ord_less_eq_nat @ SV32 @ zero_zero_nat )
= $true )
| ( ( SV32 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2985]) ).
thf(3223,plain,
! [SV32: nat] :
( ( ( SV32 = zero_zero_nat )
= $true )
| ( ( SV32 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2986]) ).
thf(3224,plain,
! [SV33: nat] :
( ( ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2987]) ).
thf(3225,plain,
! [SV33: nat] :
( ( ( SV33 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2988]) ).
thf(3226,plain,
! [SV33: nat] :
( ( ( ord_less_eq_nat @ SV33 @ zero_zero_nat )
= $true )
| ( ( SV33 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2989]) ).
thf(3227,plain,
! [SV33: nat] :
( ( ( SV33 = zero_zero_nat )
= $true )
| ( ( SV33 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2990]) ).
thf(3228,plain,
! [SV660: nat,SV323: nat] :
( ( ( ord_less_eq_nat @ SV323 @ SV660 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV323 @ SV660 )
| ~ ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2991]) ).
thf(3229,plain,
! [SV660: nat,SV323: nat] :
( ( ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV323 @ SV660 )
| ~ ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2991]) ).
thf(3230,plain,
! [SV35: nat] :
( ( ( zero_zero_nat = SV35 )
= $true )
| ( ( zero_zero_nat = SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2992]) ).
thf(3231,plain,
! [SV35: nat] :
( ( ( SV35 = zero_zero_nat )
= $true )
| ( ( zero_zero_nat = SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2993]) ).
thf(3232,plain,
! [SV35: nat] :
( ( ( zero_zero_nat = SV35 )
= $true )
| ( ( SV35 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2994]) ).
thf(3233,plain,
! [SV35: nat] :
( ( ( SV35 = zero_zero_nat )
= $true )
| ( ( SV35 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2995]) ).
thf(3234,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2996]) ).
thf(3235,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2998]) ).
thf(3236,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( ~ ( ( connected_b @ SV330 @ SV665 @ SV760 )
| ( connected_b @ SV330 @ SV665 @ SV760 ) ) )
= $true )
| ( ( ~ ( ~ ( connected_b @ SV330 @ SV665 @ SV760 )
| ~ ( connected_b @ SV330 @ SV665 @ SV760 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3000]) ).
thf(3237,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( ~ ( ( connected_a @ SV331 @ SV666 @ SV761 )
| ( connected_a @ SV331 @ SV666 @ SV761 ) ) )
= $true )
| ( ( ~ ( ~ ( connected_a @ SV331 @ SV666 @ SV761 )
| ~ ( connected_a @ SV331 @ SV666 @ SV761 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3002]) ).
thf(3238,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3004]) ).
thf(3239,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3006]) ).
thf(3240,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3008]) ).
thf(3241,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3010]) ).
thf(3242,plain,
! [SV53: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV53 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3012]) ).
thf(3243,plain,
! [SV53: nat] :
( ( ( SV53 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3012]) ).
thf(3244,plain,
! [SV53: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 ) )
= $true )
| ( ( SV53 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3013]) ).
thf(3245,plain,
! [SV53: nat] :
( ( ( SV53 = zero_zero_nat )
= $true )
| ( ( SV53 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3014]) ).
thf(3246,plain,
! [SV552: nat,SV342: nat,SV61: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
| ( SV552 != SV342 ) )
= $false )
| ( ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3015]) ).
thf(3247,plain,
! [SV552: nat,SV342: nat,SV61: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
| ( SV552 != SV342 ) )
= $false )
| ( ( SV552 = SV342 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3016]) ).
thf(3248,plain,
! [SV553: nat,SV343: nat,SV62: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
| ( SV553 != SV343 ) )
= $false )
| ( ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3017]) ).
thf(3249,plain,
! [SV553: nat,SV343: nat,SV62: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
| ( SV553 != SV343 ) )
= $false )
| ( ( SV553 = SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3018]) ).
thf(3250,plain,
! [SV344: nat,SV63: nat] :
( ( ( ~ ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 ) )
= $false )
| ( ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3019]) ).
thf(3251,plain,
! [SV63: nat,SV344: nat] :
( ( ( SV344 != SV63 )
= $false )
| ( ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3019]) ).
thf(3252,plain,
! [SV344: nat,SV63: nat] :
( ( ( ~ ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 ) )
= $false )
| ( ( SV344 = SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3020]) ).
thf(3253,plain,
! [SV63: nat,SV344: nat] :
( ( ( SV344 != SV63 )
= $false )
| ( ( SV344 = SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3020]) ).
thf(3254,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3021]) ).
thf(3255,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3023]) ).
thf(3256,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( ~ ( finite_Graph_b @ SV347 ) )
= $false )
| ( ( finite_Graph_b @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3025]) ).
thf(3257,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( ~ ( finite_finite_nat @ ( v_b @ SV347 ) ) )
= $false )
| ( ( finite_Graph_b @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3025]) ).
thf(3258,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( ~ ( finite_Graph_b @ SV347 ) )
= $false )
| ( ( finite_finite_nat @ ( v_b @ SV347 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3026]) ).
thf(3259,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( ~ ( finite_finite_nat @ ( v_b @ SV347 ) ) )
= $false )
| ( ( finite_finite_nat @ ( v_b @ SV347 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3026]) ).
thf(3260,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( ~ ( finite_Graph_a @ SV348 ) )
= $false )
| ( ( finite_Graph_a @ SV348 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3027]) ).
thf(3261,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( ~ ( finite_finite_nat @ ( v_a @ SV348 ) ) )
= $false )
| ( ( finite_Graph_a @ SV348 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3027]) ).
thf(3262,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( ~ ( finite_Graph_a @ SV348 ) )
= $false )
| ( ( finite_finite_nat @ ( v_a @ SV348 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3028]) ).
thf(3263,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( ~ ( finite_finite_nat @ ( v_a @ SV348 ) ) )
= $false )
| ( ( finite_finite_nat @ ( v_a @ SV348 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3028]) ).
thf(3264,plain,
! [SV93: nat] :
( ( ( ~ ( ( SV93 != zero_zero_nat ) ) )
= $false )
| ( ( SV93 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3029]) ).
thf(3265,plain,
! [SV93: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV93 ) )
= $false )
| ( ( SV93 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3029]) ).
thf(3266,plain,
! [SV93: nat] :
( ( ( SV93 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3030]) ).
thf(3267,plain,
! [SV93: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV93 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3031]) ).
thf(3268,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= ( ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3033]) ).
thf(3269,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3035]) ).
thf(3270,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3036]) ).
thf(3271,plain,
! [SV101: nat] :
( ( ( ~ ( ( SV101 != zero_zero_nat ) ) )
= $false )
| ( ( SV101 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3037]) ).
thf(3272,plain,
! [SV101: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV101 ) )
= $false )
| ( ( SV101 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3037]) ).
thf(3273,plain,
! [SV101: nat] :
( ( ( SV101 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3038]) ).
thf(3274,plain,
! [SV101: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV101 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3039]) ).
thf(3275,plain,
! [SV682: nat,SV567: list_P559422087at_nat,SV103: product_prod_nat_nat > a,SV370: nat] :
( ( ( member_nat @ SV370 @ ( v_a @ SV103 ) )
= $false )
| ( ( ~ ( isShortestPath_a @ SV103 @ SV370 @ SV567 @ SV682 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV567 ) @ ( finite_card_nat @ ( v_a @ SV103 ) ) ) )
= $true )
| ( ( finite_Graph_a @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3041]) ).
thf(3276,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( SV372 = SV683 )
= $false )
| ( ( ~ ( ( SV372 != SV683 )
| ~ ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3042]) ).
thf(3277,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) )
= $false )
| ( ( ~ ( ( SV372 != SV683 )
| ~ ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3042]) ).
thf(3278,plain,
! [SV684: nat,SV569: list_P559422087at_nat,SV106: product_prod_nat_nat > b,SV373: nat] :
( ( ( member_nat @ SV373 @ ( v_b @ SV106 ) )
= $false )
| ( ( ~ ( isShortestPath_b @ SV106 @ SV373 @ SV569 @ SV684 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV569 ) @ ( finite_card_nat @ ( v_b @ SV106 ) ) ) )
= $true )
| ( ( finite_Graph_b @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3043]) ).
thf(3279,plain,
! [SV377: nat > $o,SV110: nat > $o] :
( ( ( ( SV110 @ ( sK4_SY1126 @ SV377 @ SV110 ) )
| ( SV377 @ ( sK4_SY1126 @ SV377 @ SV110 ) ) )
= $true )
| ( ( ( collect_nat @ SV110 )
= ( collect_nat @ SV377 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3044]) ).
thf(3280,plain,
! [SV377: nat > $o,SV110: nat > $o] :
( ( ( ~ ( SV110 @ ( sK4_SY1126 @ SV377 @ SV110 ) )
| ~ ( SV377 @ ( sK4_SY1126 @ SV377 @ SV110 ) ) )
= $true )
| ( ( ( collect_nat @ SV110 )
= ( collect_nat @ SV377 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3045]) ).
thf(3281,plain,
! [SV378: nat,SV111: product_prod_nat_nat > a,SV571: nat] :
( ( ( ( member_nat @ SV571 @ ( v_a @ SV111 ) )
| ( member_nat @ SV378 @ ( v_a @ SV111 ) ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV571 @ ( v_a @ SV111 ) )
| ~ ( member_nat @ SV378 @ ( v_a @ SV111 ) ) ) )
= $true )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3282,plain,
! [SV572: nat,SV379: nat,SV112: nat] :
( ( ( ~ ( dist_a @ c @ SV112 @ ( sK28_SY1344 @ SV379 @ SV572 @ SV112 ) @ SV572 )
| ( ord_less_eq_nat @ SV379 @ ( sK28_SY1344 @ SV379 @ SV572 @ SV112 ) ) )
= $false )
| ( ( ( min_dist_a @ c @ SV112 @ SV572 )
= SV379 )
= $true )
| ( ( dist_a @ c @ SV112 @ SV379 @ SV572 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3047]) ).
thf(3283,plain,
! [SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= ( ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3048]) ).
thf(3284,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= ( ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3050]) ).
thf(3285,plain,
! [SV575: nat,SV688: nat,SV382: nat,SV116: product_prod_nat_nat > a] :
( ( ( ! [SY1438: nat] :
( ~ ( dist_a @ SV116 @ SV382 @ SY1438 @ SV688 )
| ( ord_less_eq_nat @ SV575 @ SY1438 ) ) )
= $false )
| ( ( ( min_dist_a @ SV116 @ SV382 @ SV688 )
= SV575 )
= $true )
| ( ( dist_a @ SV116 @ SV382 @ SV575 @ SV688 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3052]) ).
thf(3286,plain,
! [SV383: nat,SV117: nat] :
( ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
!= zero_zero_nat )
| ( SV383 != SV117 ) ) )
= $true )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3053]) ).
thf(3287,plain,
! [SV117: nat,SV383: nat] :
( ( ( SV383 = SV117 )
= $false )
| ( ( ~ ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
!= zero_zero_nat )
| ( SV383 != SV117 ) ) )
= $true )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3053]) ).
thf(3288,plain,
! [SV576: nat,SV384: nat,SV118: nat] :
( ( ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) )
= $false )
| ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3054]) ).
thf(3289,plain,
! [SV384: nat,SV576: nat,SV118: nat] :
( ( ( ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3055]) ).
thf(3290,plain,
! [SV741: nat,SV689: nat,SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
!= SV689 )
= $true )
| ( ( ~ ( ord_less_nat @ SV741 @ SV689 )
| ~ ! [SY1479: nat] :
~ ~ ( ~ ( connected_a @ SV120 @ SV386 @ SY1479 )
| ( ( min_dist_a @ SV120 @ SV386 @ SY1479 )
!= SV741 ) ) )
= $true )
| ( ( connected_a @ SV120 @ SV386 @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3056]) ).
thf(3291,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ~ ( ( connected_a @ SV387 @ SV690 @ SV771 )
| ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) ) )
= $true )
| ( ( ~ ( ~ ( connected_a @ SV387 @ SV690 @ SV771 )
| ~ ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3057]) ).
thf(3292,plain,
! [SV579: nat,SV388: nat,SV124: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV124 @ SV388 @ ( sK16_SY1359 @ SV579 @ SV388 @ SV124 ) @ SV579 )
= $true )
| ( ( connected_a @ SV124 @ SV388 @ SV579 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3059]) ).
thf(3293,plain,
! [SV691: nat,SV581: nat,SV391: nat,SV128: nat] :
( ( ( ( min_dist_b @ c2 @ SV128 @ SV391 )
= SV581 )
= $false )
| ( ( ~ ( ord_less_nat @ SV691 @ SV581 )
| ~ ! [SY1443: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV128 @ SY1443 )
| ( ( min_dist_b @ c2 @ SV128 @ SY1443 )
!= SV691 ) ) )
= $true )
| ( ( connected_b @ c2 @ SV128 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3060]) ).
thf(3294,plain,
! [SV692: nat > $o,SV582: nat,SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ( ! [SY1444: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1444 @ SV582 )
| ~ ! [SY1364: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1364 @ SV582 )
| ( ord_less_eq_nat @ SY1444 @ SY1364 ) )
| ( SV692 @ SY1444 ) ) )
= $false )
| ( ( SV692 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) )
= $true )
| ( ( connected_a @ SV129 @ SV392 @ SV582 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3061]) ).
thf(3295,plain,
! [SV395: set_nat,SV133: set_nat] :
( ( ( ord_less_eq_nat @ ( finite_card_nat @ SV133 ) @ ( finite_card_nat @ SV395 ) )
= $false )
| ( ( SV395 = SV133 )
= $true )
| ( ( ord_less_eq_set_nat @ SV395 @ SV133 )
= $false )
| ( ( finite_finite_nat @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3062]) ).
thf(3296,plain,
! [SV583: nat,SV396: nat,SV134: product_prod_nat_nat > b,SV693: nat] :
( ( ( ord_less_eq_nat @ SV693 @ ( min_dist_b @ SV134 @ SV396 @ SV583 ) )
= $false )
| ( ( ~ ! [SY1446: nat] :
~ ~ ( ~ ( connected_b @ SV134 @ SV396 @ SY1446 )
| ( ( min_dist_b @ SV134 @ SV396 @ SY1446 )
!= SV693 ) ) )
= $true )
| ( ( connected_b @ SV134 @ SV396 @ SV583 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3063]) ).
thf(3297,plain,
! [SV398: nat,SV136: nat] :
( ( ( ~ ( connected_a @ c @ SV136 @ SV398 ) )
= $false )
| ( ( connected_a @ c @ SV136 @ SV398 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3065]) ).
thf(3298,plain,
! [SV398: nat,SV136: nat] :
( ( ( ~ ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) )
= $false )
| ( ( connected_a @ c @ SV136 @ SV398 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3065]) ).
thf(3299,plain,
! [SV398: nat,SV808: list_P559422087at_nat,SV136: nat] :
( ( ( ~ ( isPath_a @ c @ SV136 @ SV808 @ SV398 ) )
= $true )
| ( ( ~ ( ~ ( connected_a @ c @ SV136 @ SV398 )
| ~ ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3066]) ).
thf(3300,plain,
! [SV137: set_nat,SV399: nat] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV137 )
| ~ ( ord_less_eq_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV399 ) )
| ~ ! [SY1522: nat] :
( ~ ( member_nat @ SY1522 @ SV137 )
| ~ ( ord_less_eq_nat @ SY1522 @ ( sK29_SY1165 @ SV399 @ SV137 ) )
| ( ( sK29_SY1165 @ SV399 @ SV137 )
= SY1522 ) ) ) )
= $false )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3067]) ).
thf(3301,plain,
! [SV694: nat,SV584: list_P559422087at_nat,SV138: product_prod_nat_nat > a,SV400: nat] :
( ( ( member_nat @ SV400 @ ( v_a @ SV138 ) )
= $false )
| ( ( ~ ( isSimplePath_a @ SV138 @ SV400 @ SV584 @ SV694 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV584 ) @ ( finite_card_nat @ ( v_a @ SV138 ) ) ) )
= $true )
| ( ( finite_Graph_a @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3068]) ).
thf(3302,plain,
! [SV695: nat,SV585: list_P559422087at_nat,SV401: nat,SV139: product_prod_nat_nat > b] :
( ( ( ~ ( isSimplePath_b @ SV139 @ SV401 @ ( sK30_SY1447 @ SV585 @ SV695 @ SV401 @ SV139 ) @ SV695 ) )
= $false )
| ( ( isPath_b @ SV139 @ SV401 @ SV585 @ SV695 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3069]) ).
thf(3303,plain,
! [SV403: nat,SV586: nat,SV142: nat] :
( ( ( ! [SY1370: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV142 @ SY1370 )
| ( ( min_dist_b @ c2 @ SV142 @ SY1370 )
!= SV586 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV586 @ ( min_dist_b @ c2 @ SV142 @ SV403 ) )
= $false )
| ( ( connected_b @ c2 @ SV142 @ SV403 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3070]) ).
thf(3304,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ( ~ ( ~ ~ ( ~ ( finite772653738at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) )
| ( ( finite447719721at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) )
!= SV404 ) )
| ~ ( ord_le841296385at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) @ SV143 ) ) )
= $true )
| ( ( finite772653738at_nat @ SV143 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3071]) ).
thf(3305,plain,
! [SV407: nat,SV146: nat] :
( ( ( ~ ( connected_a @ c @ SV146 @ SV407 ) )
= $false )
| ( ( connected_a @ c @ SV146 @ SV407 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3072]) ).
thf(3306,plain,
! [SV407: nat,SV146: nat] :
( ( ( ~ ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) )
= $false )
| ( ( connected_a @ c @ SV146 @ SV407 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3072]) ).
thf(3307,plain,
! [SV407: nat,SV809: nat,SV146: nat] :
( ( ( ~ ( dist_a @ c @ SV146 @ SV809 @ SV407 ) )
= $true )
| ( ( ~ ( ~ ( connected_a @ c @ SV146 @ SV407 )
| ~ ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3073]) ).
thf(3308,plain,
! [SV588: nat,SV697: nat,SV408: nat,SV147: product_prod_nat_nat > b] :
( ( ( ! [SY1448: nat] :
( ~ ( dist_b @ SV147 @ SV408 @ SY1448 @ SV697 )
| ( ord_less_eq_nat @ SV588 @ SY1448 ) ) )
= $false )
| ( ( ( min_dist_b @ SV147 @ SV408 @ SV697 )
= SV588 )
= $true )
| ( ( dist_b @ SV147 @ SV408 @ SV588 @ SV697 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3074]) ).
thf(3309,plain,
! [SV591: nat,SV411: nat,SV151: product_prod_nat_nat > a,SV699: nat] :
( ( ( ord_less_eq_nat @ SV699 @ ( min_dist_a @ SV151 @ SV411 @ SV591 ) )
= $false )
| ( ( ~ ! [SY1449: nat] :
~ ~ ( ~ ( connected_a @ SV151 @ SV411 @ SY1449 )
| ( ( min_dist_a @ SV151 @ SV411 @ SY1449 )
!= SV699 ) ) )
= $true )
| ( ( connected_a @ SV151 @ SV411 @ SV591 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3075]) ).
thf(3310,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3078]) ).
thf(3311,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3079]) ).
thf(3312,plain,
! [SV594: nat,SV417: nat,SV159: nat > $o] :
( ( ( ~ ( SV159 @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) )
| ( ord_less_eq_nat @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) @ SV594 ) )
= $false )
| ( ( ~ ! [SY852: nat] :
~ ~ ( ~ ( SV159 @ SY852 )
| ~ ! [SY853: nat] :
( ~ ( SV159 @ SY853 )
| ( ord_less_eq_nat @ SY853 @ SY852 ) ) ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3080]) ).
thf(3313,plain,
! [SV597: nat,SV421: nat,SV163: nat] :
( ( ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) )
= $false )
| ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3081]) ).
thf(3314,plain,
! [SV421: nat,SV597: nat,SV163: nat] :
( ( ( ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3082]) ).
thf(3315,plain,
! [SV164: set_set_nat,SV422: set_nat] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SV164 )
| ~ ( ord_less_eq_set_nat @ SV422 @ ( sK32_SY1199 @ SV422 @ SV164 ) ) )
| ~ ! [SY1523: set_nat] :
( ~ ( member_set_nat @ SY1523 @ SV164 )
| ~ ( ord_less_eq_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SY1523 )
| ( ( sK32_SY1199 @ SV422 @ SV164 )
= SY1523 ) ) ) )
= $false )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3083]) ).
thf(3316,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= ( ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3084]) ).
thf(3317,plain,
! [SV167: nat > nat,SV425: nat,SV600: nat] :
( ( ( ~ ( ord_less_nat @ ( sK14_SY873 @ SV600 @ SV425 @ SV167 ) @ ( sK18_SY1504 @ SV167 @ SV425 @ SV600 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV425 @ SV600 )
| ( ord_less_eq_nat @ ( SV167 @ SV425 ) @ ( SV167 @ SV600 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3086]) ).
thf(3318,plain,
! [SV425: nat,SV600: nat,SV167: nat > nat] :
( ( ( ord_less_nat @ ( SV167 @ ( sK14_SY873 @ SV600 @ SV425 @ SV167 ) ) @ ( SV167 @ ( sK18_SY1504 @ SV167 @ SV425 @ SV600 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV425 @ SV600 )
| ( ord_less_eq_nat @ ( SV167 @ SV425 ) @ ( SV167 @ SV600 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3086]) ).
thf(3319,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= ( ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3087]) ).
thf(3320,plain,
! [SV427: nat,SV171: nat > $o] :
( ( ( SV171 @ ( sK5_SY879 @ SV427 @ SV171 ) )
= $false )
| ( ( SV171 @ SV427 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3321,plain,
! [SV171: nat > $o,SV427: nat,SV812: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV812 @ ( sK5_SY879 @ SV427 @ SV171 ) )
| ~ ~ ( SV171 @ SV812 ) ) )
= $true )
| ( ( SV171 @ SV427 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3090]) ).
thf(3322,plain,
! [SV173: set_se1612935105at_nat,SV428: set_Pr1986765409at_nat] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV173 )
| ~ ( ord_le841296385at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV428 ) )
| ~ ! [SY1525: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY1525 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY1525 @ ( sK33_SY1214 @ SV428 @ SV173 ) )
| ( ( sK33_SY1214 @ SV428 @ SV173 )
= SY1525 ) ) ) )
= $false )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3091]) ).
thf(3323,plain,
! [SV174: list_P559422087at_nat > $o,SV429: list_P559422087at_nat,SV813: list_P559422087at_nat] :
( ( ( ~ ( ord_less_nat @ ( size_s1990949619at_nat @ SV813 ) @ ( size_s1990949619at_nat @ ( sK6_SY885 @ SV429 @ SV174 ) ) )
| ( SV174 @ SV813 ) )
= $true )
| ( ( SV174 @ SV429 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3092]) ).
thf(3324,plain,
! [SV703: nat > $o,SV603: nat,SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ( ! [SY1455: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1455 @ SV603 )
| ~ ! [SY1392: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1392 @ SV603 )
| ( ord_less_eq_nat @ SY1455 @ SY1392 ) )
| ( SV703 @ SY1455 ) ) )
= $false )
| ( ( SV703 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) )
= $true )
| ( ( connected_b @ SV176 @ SV431 @ SV603 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3094]) ).
thf(3325,plain,
! [SV177: set_se1612935105at_nat,SV432: set_Pr1986765409at_nat] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member298845450at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SV177 )
| ~ ( ord_le841296385at_nat @ SV432 @ ( sK34_SY1223 @ SV432 @ SV177 ) ) )
| ~ ! [SY1526: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY1526 @ SV177 )
| ~ ( ord_le841296385at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SY1526 )
| ( ( sK34_SY1223 @ SV432 @ SV177 )
= SY1526 ) ) ) )
= $false )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3095]) ).
thf(3326,plain,
! [SV178: nat,SV433: nat] :
( ( ( member_nat @ SV433 @ ( v_b @ c2 ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV433 @ ( v_b @ c2 ) )
| ~ ( member_nat @ SV178 @ ( v_b @ c2 ) ) ) )
= $true )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3327,plain,
! [SV433: nat,SV178: nat] :
( ( ( member_nat @ SV178 @ ( v_b @ c2 ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV433 @ ( v_b @ c2 ) )
| ~ ( member_nat @ SV178 @ ( v_b @ c2 ) ) ) )
= $true )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3328,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ~ ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3097]) ).
thf(3329,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ~ ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3097]) ).
thf(3330,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ~ ( SV182 @ ( sK19_SY1227 @ SV436 @ SV182 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
| ~ ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3098]) ).
thf(3331,plain,
! [SV182: nat > $o,SV436: nat > $o] :
( ( ( SV436 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
| ~ ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3098]) ).
thf(3332,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( SV437 = SV704 )
= $false )
| ( ( ~ ( ( SV437 != SV704 )
| ~ ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3099]) ).
thf(3333,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) )
= $false )
| ( ( ~ ( ( SV437 != SV704 )
| ~ ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3099]) ).
thf(3334,plain,
! [SV438: set_Pr1986765409at_nat > $o,SV184: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ ( sK20_SY1230 @ SV184 @ SV438 ) ) )
= $false )
| ( ( SV438 @ SV184 )
= $true )
| ( ( finite772653738at_nat @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3100]) ).
thf(3335,plain,
! [SV438: set_Pr1986765409at_nat > $o,SV184: set_Pr1986765409at_nat] :
( ( ( ~ ! [SY1516: set_Pr1986765409at_nat] :
( ~ ( ord_le116442893at_nat @ SY1516 @ ( sK20_SY1230 @ SV184 @ SV438 ) )
| ( SV438 @ SY1516 ) )
| ( SV438 @ ( sK20_SY1230 @ SV184 @ SV438 ) ) )
= $false )
| ( ( SV438 @ SV184 )
= $true )
| ( ( finite772653738at_nat @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3100]) ).
thf(3336,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= ( ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3101]) ).
thf(3337,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ~ ( ( connected_a @ SV442 @ SV706 @ SV775 )
| ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) ) )
= $true )
| ( ( ~ ( ~ ( connected_a @ SV442 @ SV706 @ SV775 )
| ~ ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3103]) ).
thf(3338,plain,
! [SV190: set_nat,SV444: set_nat] :
( ( ( ord_less_nat @ ( finite_card_nat @ SV444 ) @ ( finite_card_nat @ SV190 ) )
= $false )
| ( ( ord_less_set_nat @ SV444 @ SV190 )
= $true )
| ( ( ord_less_eq_set_nat @ SV444 @ SV190 )
= $false )
| ( ( finite_finite_nat @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3105]) ).
thf(3339,plain,
! [SV445: nat,SV191: nat] :
( ( ( ( min_dist_a @ c @ SV191 @ SV445 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( min_dist_a @ c @ SV191 @ SV445 )
!= zero_zero_nat )
| ( SV445 != SV191 ) ) )
= $true )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3340,plain,
! [SV191: nat,SV445: nat] :
( ( ( SV445 = SV191 )
= $false )
| ( ( ~ ( ( ( min_dist_a @ c @ SV191 @ SV445 )
!= zero_zero_nat )
| ( SV445 != SV191 ) ) )
= $true )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3341,plain,
! [SV192: nat > $o,SV446: nat,SV815: nat] :
( ( ( ~ ( ord_less_nat @ SV815 @ ( sK7_SY922 @ SV446 @ SV192 ) )
| ( SV192 @ SV815 ) )
= $true )
| ( ( SV192 @ SV446 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3107]) ).
thf(3342,plain,
! [SV193: nat,SV447: nat] :
( ( ( member_nat @ SV447 @ ( v_a @ c ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV447 @ ( v_a @ c ) )
| ~ ( member_nat @ SV193 @ ( v_a @ c ) ) ) )
= $true )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3108]) ).
thf(3343,plain,
! [SV447: nat,SV193: nat] :
( ( ( member_nat @ SV193 @ ( v_a @ c ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV447 @ ( v_a @ c ) )
| ~ ( member_nat @ SV193 @ ( v_a @ c ) ) ) )
= $true )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3108]) ).
thf(3344,plain,
! [SV194: set_nat,SV448: set_nat] :
( ( ( finite_finite_nat @ SV448 )
= $false )
| ( ( finite_finite_nat @ SV194 )
= $true )
| ( ( ord_less_eq_set_nat @ SV194 @ SV448 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3109]) ).
thf(3345,plain,
! [SV196: nat > $o,SV449: nat] :
( ( ( ! [SY1241: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_eq_nat @ SY1241 @ SV449 )
| ~ ! [SY928: nat] :
( ~ ( ord_less_nat @ SY928 @ SY1241 )
| ~ ( SV196 @ SY928 ) ) )
| ~ ( SV196 @ SY1241 ) ) )
= $false )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3110]) ).
thf(3346,plain,
! [SV451: set_Pr1986765409at_nat,SV198: set_Pr1986765409at_nat] :
( ( ( ord_less_eq_nat @ ( finite447719721at_nat @ SV198 ) @ ( finite447719721at_nat @ SV451 ) )
= $false )
| ( ( SV451 = SV198 )
= $true )
| ( ( ord_le841296385at_nat @ SV451 @ SV198 )
= $false )
| ( ( finite772653738at_nat @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3111]) ).
thf(3347,plain,
! [SV610: nat,SV452: nat,SV199: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV199 @ SV452 @ ( sK21_SY1397 @ SV610 @ SV452 @ SV199 ) @ SV610 )
= $true )
| ( ( connected_b @ SV199 @ SV452 @ SV610 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3112]) ).
thf(3348,plain,
! [SV200: set_nat,SV453: nat] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SV200 )
| ~ ( ord_less_eq_nat @ SV453 @ ( sK35_SY1245 @ SV453 @ SV200 ) ) )
| ~ ! [SY1527: nat] :
( ~ ( member_nat @ SY1527 @ SV200 )
| ~ ( ord_less_eq_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SY1527 )
| ( ( sK35_SY1245 @ SV453 @ SV200 )
= SY1527 ) ) ) )
= $false )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3113]) ).
thf(3349,plain,
! [SV611: nat,SV454: nat,SV201: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV201 @ SV454 @ SV611 ) )
= $true )
| ( ( ord_less_nat @ ( min_dist_a @ SV201 @ SV454 @ SV611 ) @ ( finite_card_nat @ ( v_a @ SV201 ) ) )
= $true )
| ( ( member_nat @ SV454 @ ( v_a @ SV201 ) )
= $false )
| ( ( finite_Graph_a @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3114]) ).
thf(3350,plain,
! [SV202: set_Pr1986765409at_nat,SV455: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV455 )
= $false )
| ( ( finite772653738at_nat @ SV202 )
= $true )
| ( ( ord_le841296385at_nat @ SV202 @ SV455 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3115]) ).
thf(3351,plain,
! [SV457: nat,SV205: nat] :
( ( ( ord_less_nat @ SV205 @ SV457 )
= $true )
| ( ( ord_less_nat @ SV457 @ SV205 )
= $true )
| ( ( SV205 = SV457 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3116]) ).
thf(3352,plain,
! [SV206: set_Pr1986765409at_nat,SV458: set_Pr1986765409at_nat] :
( ( ( ord_less_nat @ ( finite447719721at_nat @ SV458 ) @ ( finite447719721at_nat @ SV206 ) )
= $false )
| ( ( ord_le116442893at_nat @ SV458 @ SV206 )
= $true )
| ( ( ord_le841296385at_nat @ SV458 @ SV206 )
= $false )
| ( ( finite772653738at_nat @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3117]) ).
thf(3353,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) )
= $false )
| ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3354,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3119]) ).
thf(3355,plain,
! [SV462: nat,SV615: nat > $o,SV210: nat] :
( ( ( ~ ( dist_a @ c @ SV210 @ ( sK36_SY1400 @ SV615 @ SV462 @ SV210 ) @ SV462 )
| ~ ! [SY1528: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1528 @ SV462 )
| ( ord_less_eq_nat @ ( sK36_SY1400 @ SV615 @ SV462 @ SV210 ) @ SY1528 ) )
| ( SV615 @ ( sK36_SY1400 @ SV615 @ SV462 @ SV210 ) ) )
= $false )
| ( ( SV615 @ ( min_dist_a @ c @ SV210 @ SV462 ) )
= $true )
| ( ( connected_a @ c @ SV210 @ SV462 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3120]) ).
thf(3356,plain,
! [SV213: set_nat,SV464: set_nat] :
( ( ( ( finite_card_nat @ SV464 )
= ( finite_card_nat @ SV213 ) )
= $false )
| ( ( SV464 = SV213 )
= $true )
| ( ( ord_less_eq_set_nat @ SV464 @ SV213 )
= $false )
| ( ( finite_finite_nat @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3121]) ).
thf(3357,plain,
! [SV466: nat,SV215: nat] :
( ( ( ~ ( connected_b @ c2 @ SV215 @ SV466 ) )
= $false )
| ( ( connected_b @ c2 @ SV215 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3122]) ).
thf(3358,plain,
! [SV466: nat,SV215: nat] :
( ( ( ~ ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) )
= $false )
| ( ( connected_b @ c2 @ SV215 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3122]) ).
thf(3359,plain,
! [SV466: nat,SV816: nat,SV215: nat] :
( ( ( ~ ( dist_b @ c2 @ SV215 @ SV816 @ SV466 ) )
= $true )
| ( ( ~ ( ~ ( connected_b @ c2 @ SV215 @ SV466 )
| ~ ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3123]) ).
thf(3360,plain,
! [SV709: nat,SV617: list_P559422087at_nat,SV217: product_prod_nat_nat > b,SV467: nat] :
( ( ( member_nat @ SV467 @ ( v_b @ SV217 ) )
= $false )
| ( ( ~ ( isSimplePath_b @ SV217 @ SV467 @ SV617 @ SV709 )
| ( ord_less_nat @ ( size_s1990949619at_nat @ SV617 ) @ ( finite_card_nat @ ( v_b @ SV217 ) ) ) )
= $true )
| ( ( finite_Graph_b @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3124]) ).
thf(3361,plain,
! [SV469: set_nat > $o,SV219: set_nat] :
( ( ( ~ ( finite_finite_nat @ ( sK22_SY1261 @ SV219 @ SV469 ) ) )
= $false )
| ( ( SV469 @ SV219 )
= $true )
| ( ( finite_finite_nat @ SV219 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3125]) ).
thf(3362,plain,
! [SV469: set_nat > $o,SV219: set_nat] :
( ( ( ~ ! [SY1517: set_nat] :
( ~ ( ord_less_set_nat @ SY1517 @ ( sK22_SY1261 @ SV219 @ SV469 ) )
| ( SV469 @ SY1517 ) )
| ( SV469 @ ( sK22_SY1261 @ SV219 @ SV469 ) ) )
= $false )
| ( ( SV469 @ SV219 )
= $true )
| ( ( finite_finite_nat @ SV219 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3125]) ).
thf(3363,plain,
! [SV470: nat,SV220: nat] :
( ( ( ~ ( ( SV220 != SV470 ) )
| ~ ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) )
= $false )
| ( ( SV220 = SV470 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3126]) ).
thf(3364,plain,
! [SV470: nat,SV220: nat] :
( ( ( ~ ( ( SV220 != SV470 ) )
| ~ ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) )
= $false )
| ( ( ord_less_nat @ SV220 @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3127]) ).
thf(3365,plain,
! [SV470: nat,SV220: nat] :
( ( ( ~ ( ( SV220 != SV470 ) )
| ~ ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) )
= $false )
| ( ( ord_less_nat @ SV470 @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3128]) ).
thf(3366,plain,
! [SV618: nat,SV471: list_P559422087at_nat,SV221: nat] :
( ( ( isSimplePath_b @ c2 @ SV221 @ ( sK23_SY1404 @ SV471 @ SV618 @ SV221 ) @ SV618 )
= $true )
| ( ( isPath_b @ c2 @ SV221 @ SV471 @ SV618 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3129]) ).
thf(3367,plain,
! [SV222: nat > $o,SV472: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK24_SY974 @ SV472 @ SV222 ) ) )
= $false )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3130]) ).
thf(3368,plain,
! [SV472: nat,SV222: nat > $o] :
( ( ( ~ ~ ( SV222 @ ( sK24_SY974 @ SV472 @ SV222 ) )
| ~ ! [SY1518: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1518 @ ( sK24_SY974 @ SV472 @ SV222 ) )
| ~ ~ ( SV222 @ SY1518 ) ) )
= $false )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3130]) ).
thf(3369,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV224 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) )
= $false )
| ( ( ord_le841296385at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) @ SV224 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3132]) ).
thf(3370,plain,
! [SV224: set_Pr1986765409at_nat,SV474: nat] :
( ( ( finite772653738at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) )
= $true )
| ( ( ~ ( ~ ( finite772653738at_nat @ SV224 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3133]) ).
thf(3371,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV224 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) )
= $false )
| ( ( ord_less_eq_nat @ ( finite447719721at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) ) @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3134]) ).
thf(3372,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV226 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) @ SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3135]) ).
thf(3373,plain,
! [SV226: set_nat,SV476: nat] :
( ( ( finite_finite_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) )
= $true )
| ( ( ~ ( ~ ( finite_finite_nat @ SV226 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3136]) ).
thf(3374,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV226 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) )
= $false )
| ( ( ord_less_eq_nat @ ( finite_card_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) ) @ SV476 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3375,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
| ~ ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) )
= $false )
| ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3138]) ).
thf(3376,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
| ~ ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3139]) ).
thf(3377,plain,
! [SV621: nat,SV481: nat,SV233: product_prod_nat_nat > a] :
( ( ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
= zero_zero_nat )
| ( SV621 = SV481 ) )
= $false )
| ( ( ~ ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
!= zero_zero_nat )
| ( SV621 != SV481 ) ) )
= $true )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3140]) ).
thf(3378,plain,
! [SV623: nat,SV483: list_P559422087at_nat,SV236: nat] :
( ( ( isSimplePath_a @ c @ SV236 @ ( sK25_SY1407 @ SV483 @ SV623 @ SV236 ) @ SV623 )
= $true )
| ( ( isPath_a @ c @ SV236 @ SV483 @ SV623 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3141]) ).
thf(3379,plain,
! [SV484: nat,SV237: nat] :
( ( ( ~ ( connected_b @ c2 @ SV237 @ SV484 ) )
= $false )
| ( ( connected_b @ c2 @ SV237 @ SV484 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3142]) ).
thf(3380,plain,
! [SV484: nat,SV237: nat] :
( ( ( ~ ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) )
= $false )
| ( ( connected_b @ c2 @ SV237 @ SV484 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3142]) ).
thf(3381,plain,
! [SV484: nat,SV817: list_P559422087at_nat,SV237: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV237 @ SV817 @ SV484 ) )
= $true )
| ( ( ~ ( ~ ( connected_b @ c2 @ SV237 @ SV484 )
| ~ ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3143]) ).
thf(3382,plain,
! [SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= ( ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3145]) ).
thf(3383,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
| ~ ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) )
= $false )
| ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3147]) ).
thf(3384,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
| ~ ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3148]) ).
thf(3385,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ~ ( ( connected_b @ SV491 @ SV713 @ SV777 )
| ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) ) )
= $true )
| ( ( ~ ( ~ ( connected_b @ SV491 @ SV713 @ SV777 )
| ~ ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3149]) ).
thf(3386,plain,
! [SV252: set_Pr1986765409at_nat,SV492: set_Pr1986765409at_nat] :
( ( ( ( finite447719721at_nat @ SV492 )
= ( finite447719721at_nat @ SV252 ) )
= $false )
| ( ( SV492 = SV252 )
= $true )
| ( ( ord_le841296385at_nat @ SV492 @ SV252 )
= $false )
| ( ( finite772653738at_nat @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3151]) ).
thf(3387,plain,
! [SV494: nat,SV254: product_prod_nat_nat > b,SV629: nat] :
( ( ( ( member_nat @ SV629 @ ( v_b @ SV254 ) )
| ( member_nat @ SV494 @ ( v_b @ SV254 ) ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV629 @ ( v_b @ SV254 ) )
| ~ ( member_nat @ SV494 @ ( v_b @ SV254 ) ) ) )
= $true )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3152]) ).
thf(3388,plain,
! [SV630: nat,SV495: nat,SV255: product_prod_nat_nat > b] :
( ( ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
= zero_zero_nat )
| ( SV630 = SV495 ) )
= $false )
| ( ( ~ ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
!= zero_zero_nat )
| ( SV630 != SV495 ) ) )
= $true )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3153]) ).
thf(3389,plain,
! [SV631: nat,SV496: nat,SV257: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV257 @ SV496 @ SV631 ) )
= $true )
| ( ( ord_less_nat @ ( min_dist_b @ SV257 @ SV496 @ SV631 ) @ ( finite_card_nat @ ( v_b @ SV257 ) ) )
= $true )
| ( ( member_nat @ SV496 @ ( v_b @ SV257 ) )
= $false )
| ( ( finite_Graph_b @ SV257 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3154]) ).
thf(3390,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) ) )
= $false )
| ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3156]) ).
thf(3391,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) )
= $false )
| ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3156]) ).
thf(3392,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ( SV259 @ ( sK26_SY1292 @ SV498 @ SV259 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
| ~ ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3157]) ).
thf(3393,plain,
! [SV259: product_prod_nat_nat > $o,SV498: product_prod_nat_nat > $o] :
( ( ( SV498 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $false )
| ( ( ~ ( ~ ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
| ~ ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3157]) ).
thf(3394,plain,
! [SV714: nat,SV632: nat,SV499: nat,SV260: nat] :
( ( ( ( min_dist_a @ c @ SV260 @ SV499 )
= SV632 )
= $false )
| ( ( ~ ( ord_less_nat @ SV714 @ SV632 )
| ~ ! [SY1466: nat] :
~ ~ ( ~ ( connected_a @ c @ SV260 @ SY1466 )
| ( ( min_dist_a @ c @ SV260 @ SY1466 )
!= SV714 ) ) )
= $true )
| ( ( connected_a @ c @ SV260 @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3158]) ).
thf(3395,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= ( ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3159]) ).
thf(3396,plain,
! [SV263: set_li664300135at_nat,SV796: list_P559422087at_nat] :
( ( ( ~ ( member1608759472at_nat @ SV796 @ SV263 ) )
= $true )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV796 ) @ ( sK11_SY1034 @ SV263 ) )
= $true )
| ( ( finite1299096496at_nat @ SV263 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3161]) ).
thf(3397,plain,
! [SV502: nat,SV634: nat,SV264: nat] :
( ( ( ! [SY1417: nat] :
~ ~ ( ~ ( connected_a @ c @ SV264 @ SY1417 )
| ( ( min_dist_a @ c @ SV264 @ SY1417 )
!= SV634 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV634 @ ( min_dist_a @ c @ SV264 @ SV502 ) )
= $false )
| ( ( connected_a @ c @ SV264 @ SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3162]) ).
thf(3398,plain,
! [SV750: nat,SV716: nat,SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
!= SV716 )
= $true )
| ( ( ~ ( ord_less_nat @ SV750 @ SV716 )
| ~ ! [SY1494: nat] :
~ ~ ( ~ ( connected_b @ SV265 @ SV503 @ SY1494 )
| ( ( min_dist_b @ SV265 @ SV503 @ SY1494 )
!= SV750 ) ) )
= $true )
| ( ( connected_b @ SV265 @ SV503 @ SV635 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3163]) ).
thf(3399,plain,
! [SV508: nat,SV270: set_nat] :
( ( ( ~ ( ~ ~ ( ~ ( finite_finite_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) )
| ( ( finite_card_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) )
!= SV508 ) )
| ~ ( ord_less_eq_set_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) @ SV270 ) ) )
= $true )
| ( ( finite_finite_nat @ SV270 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3166]) ).
thf(3400,plain,
! [SV271: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV271 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3167]) ).
thf(3401,plain,
! [SV271: nat] :
( ( ( SV271 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3168]) ).
thf(3402,plain,
! [SV271: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV271 ) )
= $false )
| ( ( SV271 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3169]) ).
thf(3403,plain,
! [SV271: nat] :
( ( ( ~ ( ( SV271 != zero_zero_nat ) ) )
= $false )
| ( ( SV271 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3169]) ).
thf(3404,plain,
! [SV273: set_set_nat,SV509: set_nat] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV273 )
| ~ ( ord_less_eq_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV509 ) )
| ~ ! [SY1530: set_nat] :
( ~ ( member_set_nat @ SY1530 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1530 @ ( sK37_SY1310 @ SV509 @ SV273 ) )
| ( ( sK37_SY1310 @ SV509 @ SV273 )
= SY1530 ) ) ) )
= $false )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3170]) ).
thf(3405,plain,
! [SV510: product_prod_nat_nat > $o,SV274: product_prod_nat_nat > $o] :
( ( ( ( SV274 @ ( sK12_SY1312 @ SV510 @ SV274 ) )
| ( SV510 @ ( sK12_SY1312 @ SV510 @ SV274 ) ) )
= $true )
| ( ( ( collec7649004at_nat @ SV274 )
= ( collec7649004at_nat @ SV510 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3171]) ).
thf(3406,plain,
! [SV510: product_prod_nat_nat > $o,SV274: product_prod_nat_nat > $o] :
( ( ( ~ ( SV274 @ ( sK12_SY1312 @ SV510 @ SV274 ) )
| ~ ( SV510 @ ( sK12_SY1312 @ SV510 @ SV274 ) ) )
= $true )
| ( ( ( collec7649004at_nat @ SV274 )
= ( collec7649004at_nat @ SV510 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3172]) ).
thf(3407,plain,
! [SV642: nat,SV516: nat,SV283: nat] :
( ( ( ~ ( dist_b @ c2 @ SV283 @ ( sK38_SY1423 @ SV516 @ SV642 @ SV283 ) @ SV642 )
| ( ord_less_eq_nat @ SV516 @ ( sK38_SY1423 @ SV516 @ SV642 @ SV283 ) ) )
= $false )
| ( ( ( min_dist_b @ c2 @ SV283 @ SV642 )
= SV516 )
= $true )
| ( ( dist_b @ c2 @ SV283 @ SV516 @ SV642 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3174]) ).
thf(3408,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ~ ( ( connected_b @ SV519 @ SV719 @ SV779 )
| ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) ) )
= $true )
| ( ( ~ ( ~ ( connected_b @ SV519 @ SV719 @ SV779 )
| ~ ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3175]) ).
thf(3409,plain,
! [SV720: nat,SV647: list_P559422087at_nat,SV523: nat,SV291: product_prod_nat_nat > a] :
( ( ( ~ ( isSimplePath_a @ SV291 @ SV523 @ ( sK39_SY1473 @ SV647 @ SV720 @ SV523 @ SV291 ) @ SV720 ) )
= $false )
| ( ( isPath_a @ SV291 @ SV523 @ SV647 @ SV720 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3178]) ).
thf(3410,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ~ ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3179]) ).
thf(3411,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ~ ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3180]) ).
thf(3412,plain,
! [SV721: nat,SV530: nat] :
( ( ( ord_less_nat @ SV530 @ SV721 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV530 @ SV721 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3181]) ).
thf(3413,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV530 @ SV721 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3181]) ).
thf(3414,plain,
! [SV533: nat,SV653: nat > $o,SV304: nat] :
( ( ( ~ ( dist_b @ c2 @ SV304 @ ( sK40_SY1428 @ SV653 @ SV533 @ SV304 ) @ SV533 )
| ~ ! [SY1531: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1531 @ SV533 )
| ( ord_less_eq_nat @ ( sK40_SY1428 @ SV653 @ SV533 @ SV304 ) @ SY1531 ) )
| ( SV653 @ ( sK40_SY1428 @ SV653 @ SV533 @ SV304 ) ) )
= $false )
| ( ( SV653 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) )
= $true )
| ( ( connected_b @ c2 @ SV304 @ SV533 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3183]) ).
thf(3415,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( edmond1517640972ysis_a @ SV315 )
= $true )
| ( ( edmond1517640972ysis_a @ SV315 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3184]) ).
thf(3416,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( finite_Graph_a @ SV315 )
= $true )
| ( ( edmond1517640972ysis_a @ SV315 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3185]) ).
thf(3417,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( edmond1517640972ysis_a @ SV315 )
= $true )
| ( ( finite_Graph_a @ SV315 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3186]) ).
thf(3418,plain,
! [SV315: product_prod_nat_nat > a] :
( ( ( finite_Graph_a @ SV315 )
= $true )
| ( ( finite_Graph_a @ SV315 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3187]) ).
thf(3419,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( edmond1517640973ysis_b @ SV316 )
= $true )
| ( ( edmond1517640973ysis_b @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3188]) ).
thf(3420,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( finite_Graph_b @ SV316 )
= $true )
| ( ( edmond1517640973ysis_b @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3189]) ).
thf(3421,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( edmond1517640973ysis_b @ SV316 )
= $true )
| ( ( finite_Graph_b @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3190]) ).
thf(3422,plain,
! [SV316: product_prod_nat_nat > b] :
( ( ( finite_Graph_b @ SV316 )
= $true )
| ( ( finite_Graph_b @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3191]) ).
thf(3423,plain,
! [SV317: nat,SV13: nat] :
( ( ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
= $true )
| ( ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3192]) ).
thf(3424,plain,
! [SV13: nat,SV317: nat] :
( ( ( SV317 = SV13 )
= $true )
| ( ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3193]) ).
thf(3425,plain,
! [SV317: nat,SV13: nat] :
( ( ( dist_b @ c2 @ SV13 @ zero_zero_nat @ SV317 )
= $true )
| ( ( SV317 = SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3194]) ).
thf(3426,plain,
! [SV13: nat,SV317: nat] :
( ( ( SV317 = SV13 )
= $true )
| ( ( SV317 = SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3195]) ).
thf(3427,plain,
! [SV318: set_Pr1986765409at_nat > $o,SV15: set_Pr1986765409at_nat] :
( ( ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
= $true )
| ( ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3196]) ).
thf(3428,plain,
! [SV15: set_Pr1986765409at_nat,SV318: set_Pr1986765409at_nat > $o] :
( ( ( SV318 @ SV15 )
= $true )
| ( ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3197]) ).
thf(3429,plain,
! [SV318: set_Pr1986765409at_nat > $o,SV15: set_Pr1986765409at_nat] :
( ( ( member298845450at_nat @ SV15 @ ( collec1606769740at_nat @ SV318 ) )
= $true )
| ( ( SV318 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3198]) ).
thf(3430,plain,
! [SV15: set_Pr1986765409at_nat,SV318: set_Pr1986765409at_nat > $o] :
( ( ( SV318 @ SV15 )
= $true )
| ( ( SV318 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3199]) ).
thf(3431,plain,
! [SV319: set_nat > $o,SV16: set_nat] :
( ( ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
= $true )
| ( ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3200]) ).
thf(3432,plain,
! [SV16: set_nat,SV319: set_nat > $o] :
( ( ( SV319 @ SV16 )
= $true )
| ( ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3201]) ).
thf(3433,plain,
! [SV319: set_nat > $o,SV16: set_nat] :
( ( ( member_set_nat @ SV16 @ ( collect_set_nat @ SV319 ) )
= $true )
| ( ( SV319 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3202]) ).
thf(3434,plain,
! [SV16: set_nat,SV319: set_nat > $o] :
( ( ( SV319 @ SV16 )
= $true )
| ( ( SV319 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3203]) ).
thf(3435,plain,
! [SV320: product_prod_nat_nat > $o,SV17: product_prod_nat_nat] :
( ( ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
= $true )
| ( ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3204]) ).
thf(3436,plain,
! [SV17: product_prod_nat_nat,SV320: product_prod_nat_nat > $o] :
( ( ( SV320 @ SV17 )
= $true )
| ( ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3205]) ).
thf(3437,plain,
! [SV320: product_prod_nat_nat > $o,SV17: product_prod_nat_nat] :
( ( ( member701585322at_nat @ SV17 @ ( collec7649004at_nat @ SV320 ) )
= $true )
| ( ( SV320 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3206]) ).
thf(3438,plain,
! [SV17: product_prod_nat_nat,SV320: product_prod_nat_nat > $o] :
( ( ( SV320 @ SV17 )
= $true )
| ( ( SV320 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3207]) ).
thf(3439,plain,
! [SV321: nat > $o,SV18: nat] :
( ( ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
= $true )
| ( ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3208]) ).
thf(3440,plain,
! [SV18: nat,SV321: nat > $o] :
( ( ( SV321 @ SV18 )
= $true )
| ( ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3209]) ).
thf(3441,plain,
! [SV321: nat > $o,SV18: nat] :
( ( ( member_nat @ SV18 @ ( collect_nat @ SV321 ) )
= $true )
| ( ( SV321 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3210]) ).
thf(3442,plain,
! [SV18: nat,SV321: nat > $o] :
( ( ( SV321 @ SV18 )
= $true )
| ( ( SV321 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3211]) ).
thf(3443,plain,
! [SV24: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV24 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3212]) ).
thf(3444,plain,
! [SV24: nat] :
( ( ( SV24 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3213]) ).
thf(3445,plain,
! [SV24: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV24 )
= $false )
| ( ( SV24 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3214]) ).
thf(3446,plain,
! [SV660: nat,SV323: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV323 @ SV660 )
| ~ ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV323 @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3228]) ).
thf(3447,plain,
! [SV660: nat,SV323: nat] :
( ( ( ord_less_nat @ SV323 @ SV660 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV323 @ SV660 )
| ~ ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3229]) ).
thf(3448,plain,
! [SV660: nat,SV323: nat] :
( ( ( SV323 = SV660 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV323 @ SV660 )
| ~ ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3229]) ).
thf(3449,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ~ ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
| ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) )
| ~ ( ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
| ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3234]) ).
thf(3450,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3234]) ).
thf(3451,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ~ ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
| ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) )
| ~ ( ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
| ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3235]) ).
thf(3452,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3235]) ).
thf(3453,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( ( connected_b @ SV330 @ SV665 @ SV760 )
| ( connected_b @ SV330 @ SV665 @ SV760 ) )
= $false )
| ( ( ~ ( ~ ( connected_b @ SV330 @ SV665 @ SV760 )
| ~ ( connected_b @ SV330 @ SV665 @ SV760 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3236]) ).
thf(3454,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( ( connected_a @ SV331 @ SV666 @ SV761 )
| ( connected_a @ SV331 @ SV666 @ SV761 ) )
= $false )
| ( ( ~ ( ~ ( connected_a @ SV331 @ SV666 @ SV761 )
| ~ ( connected_a @ SV331 @ SV666 @ SV761 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3237]) ).
thf(3455,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ~ ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
| ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) )
| ~ ( ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
| ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3238]) ).
thf(3456,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3238]) ).
thf(3457,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ~ ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
| ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) )
| ~ ( ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
| ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3239]) ).
thf(3458,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3239]) ).
thf(3459,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ~ ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
| ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) )
| ~ ( ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
| ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3240]) ).
thf(3460,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3240]) ).
thf(3461,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ~ ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
| ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) )
| ~ ( ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
| ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3241]) ).
thf(3462,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3241]) ).
thf(3463,plain,
! [SV53: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3242]) ).
thf(3464,plain,
! [SV53: nat] :
( ( ( SV53 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3243]) ).
thf(3465,plain,
! [SV53: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $false )
| ( ( SV53 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3244]) ).
thf(3466,plain,
! [SV552: nat,SV342: nat,SV61: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 ) )
= $false )
| ( ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3246]) ).
thf(3467,plain,
! [SV61: product_prod_nat_nat > b,SV342: nat,SV552: nat] :
( ( ( SV552 != SV342 )
= $false )
| ( ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3246]) ).
thf(3468,plain,
! [SV552: nat,SV342: nat,SV61: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 ) )
= $false )
| ( ( SV552 = SV342 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3247]) ).
thf(3469,plain,
! [SV342: nat,SV552: nat] :
( ( ( SV552 != SV342 )
= $false )
| ( ( SV552 = SV342 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3247]) ).
thf(3470,plain,
! [SV553: nat,SV343: nat,SV62: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 ) )
= $false )
| ( ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3248]) ).
thf(3471,plain,
! [SV62: product_prod_nat_nat > a,SV343: nat,SV553: nat] :
( ( ( SV553 != SV343 )
= $false )
| ( ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3248]) ).
thf(3472,plain,
! [SV553: nat,SV343: nat,SV62: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 ) )
= $false )
| ( ( SV553 = SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3249]) ).
thf(3473,plain,
! [SV343: nat,SV553: nat] :
( ( ( SV553 != SV343 )
= $false )
| ( ( SV553 = SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3249]) ).
thf(3474,plain,
! [SV344: nat,SV63: nat] :
( ( ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
= $true )
| ( ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3250]) ).
thf(3475,plain,
! [SV63: nat,SV344: nat] :
( ( ( SV344 = SV63 )
= $true )
| ( ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3251]) ).
thf(3476,plain,
! [SV344: nat,SV63: nat] :
( ( ( dist_a @ c @ SV63 @ zero_zero_nat @ SV344 )
= $true )
| ( ( SV344 = SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3252]) ).
thf(3477,plain,
! [SV63: nat,SV344: nat] :
( ( ( SV344 = SV63 )
= $true )
| ( ( SV344 = SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3253]) ).
thf(3478,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ~ ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
| ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) )
| ~ ( ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
| ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3254]) ).
thf(3479,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3254]) ).
thf(3480,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ~ ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
| ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) )
| ~ ( ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
| ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3255]) ).
thf(3481,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3255]) ).
thf(3482,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( finite_Graph_b @ SV347 )
= $true )
| ( ( finite_Graph_b @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3256]) ).
thf(3483,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( finite_finite_nat @ ( v_b @ SV347 ) )
= $true )
| ( ( finite_Graph_b @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3257]) ).
thf(3484,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( finite_Graph_b @ SV347 )
= $true )
| ( ( finite_finite_nat @ ( v_b @ SV347 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3258]) ).
thf(3485,plain,
! [SV347: product_prod_nat_nat > b] :
( ( ( finite_finite_nat @ ( v_b @ SV347 ) )
= $true )
| ( ( finite_finite_nat @ ( v_b @ SV347 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3259]) ).
thf(3486,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( finite_Graph_a @ SV348 )
= $true )
| ( ( finite_Graph_a @ SV348 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3260]) ).
thf(3487,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( finite_finite_nat @ ( v_a @ SV348 ) )
= $true )
| ( ( finite_Graph_a @ SV348 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3261]) ).
thf(3488,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( finite_Graph_a @ SV348 )
= $true )
| ( ( finite_finite_nat @ ( v_a @ SV348 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3262]) ).
thf(3489,plain,
! [SV348: product_prod_nat_nat > a] :
( ( ( finite_finite_nat @ ( v_a @ SV348 ) )
= $true )
| ( ( finite_finite_nat @ ( v_a @ SV348 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3263]) ).
thf(3490,plain,
! [SV93: nat] :
( ( ( SV93 != zero_zero_nat )
= $true )
| ( ( SV93 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3264]) ).
thf(3491,plain,
! [SV93: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV93 )
= $true )
| ( ( SV93 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3265]) ).
thf(3492,plain,
! [SV93: nat] :
( ( ( SV93 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3266]) ).
thf(3493,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ~ ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) )
| ~ ( ~ ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ~ ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3268]) ).
thf(3494,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= ( ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3268]) ).
thf(3495,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3269]) ).
thf(3496,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3269]) ).
thf(3497,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3270]) ).
thf(3498,plain,
! [SV101: nat] :
( ( ( SV101 != zero_zero_nat )
= $true )
| ( ( SV101 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3271]) ).
thf(3499,plain,
! [SV101: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV101 )
= $true )
| ( ( SV101 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3272]) ).
thf(3500,plain,
! [SV101: nat] :
( ( ( SV101 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3273]) ).
thf(3501,plain,
! [SV682: nat,SV567: list_P559422087at_nat,SV370: nat,SV103: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV103 @ SV370 @ SV567 @ SV682 ) )
= $true )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV567 ) @ ( finite_card_nat @ ( v_a @ SV103 ) ) )
= $true )
| ( ( member_nat @ SV370 @ ( v_a @ SV103 ) )
= $false )
| ( ( finite_Graph_a @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3275]) ).
thf(3502,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ( SV372 != SV683 )
| ~ ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) )
= $false )
| ( ( SV372 = SV683 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3276]) ).
thf(3503,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) )
= $true )
| ( ( ~ ( ( SV372 != SV683 )
| ~ ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3277]) ).
thf(3504,plain,
! [SV684: nat,SV569: list_P559422087at_nat,SV373: nat,SV106: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV106 @ SV373 @ SV569 @ SV684 ) )
= $true )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV569 ) @ ( finite_card_nat @ ( v_b @ SV106 ) ) )
= $true )
| ( ( member_nat @ SV373 @ ( v_b @ SV106 ) )
= $false )
| ( ( finite_Graph_b @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3278]) ).
thf(3505,plain,
! [SV377: nat > $o,SV110: nat > $o] :
( ( ( SV110 @ ( sK4_SY1126 @ SV377 @ SV110 ) )
= $true )
| ( ( SV377 @ ( sK4_SY1126 @ SV377 @ SV110 ) )
= $true )
| ( ( ( collect_nat @ SV110 )
= ( collect_nat @ SV377 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3279]) ).
thf(3506,plain,
! [SV377: nat > $o,SV110: nat > $o] :
( ( ( ~ ( SV110 @ ( sK4_SY1126 @ SV377 @ SV110 ) ) )
= $true )
| ( ( ~ ( SV377 @ ( sK4_SY1126 @ SV377 @ SV110 ) ) )
= $true )
| ( ( ( collect_nat @ SV110 )
= ( collect_nat @ SV377 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3280]) ).
thf(3507,plain,
! [SV378: nat,SV111: product_prod_nat_nat > a,SV571: nat] :
( ( ( member_nat @ SV571 @ ( v_a @ SV111 ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV571 @ ( v_a @ SV111 ) )
| ~ ( member_nat @ SV378 @ ( v_a @ SV111 ) ) ) )
= $true )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3281]) ).
thf(3508,plain,
! [SV571: nat,SV111: product_prod_nat_nat > a,SV378: nat] :
( ( ( member_nat @ SV378 @ ( v_a @ SV111 ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV571 @ ( v_a @ SV111 ) )
| ~ ( member_nat @ SV378 @ ( v_a @ SV111 ) ) ) )
= $true )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3281]) ).
thf(3509,plain,
! [SV572: nat,SV379: nat,SV112: nat] :
( ( ( ~ ( dist_a @ c @ SV112 @ ( sK28_SY1344 @ SV379 @ SV572 @ SV112 ) @ SV572 ) )
= $false )
| ( ( ( min_dist_a @ c @ SV112 @ SV572 )
= SV379 )
= $true )
| ( ( dist_a @ c @ SV112 @ SV379 @ SV572 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3282]) ).
thf(3510,plain,
! [SV112: nat,SV572: nat,SV379: nat] :
( ( ( ord_less_eq_nat @ SV379 @ ( sK28_SY1344 @ SV379 @ SV572 @ SV112 ) )
= $false )
| ( ( ( min_dist_a @ c @ SV112 @ SV572 )
= SV379 )
= $true )
| ( ( dist_a @ c @ SV112 @ SV379 @ SV572 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3282]) ).
thf(3511,plain,
! [SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ~ ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) )
| ~ ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3283]) ).
thf(3512,plain,
! [SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= ( ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3283]) ).
thf(3513,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ~ ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) )
| ~ ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3284]) ).
thf(3514,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= ( ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3284]) ).
thf(3515,plain,
! [SV688: nat,SV575: nat,SV382: nat,SV116: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV116 @ SV382 @ ( sK41_SY1438 @ SV575 @ SV688 @ SV382 @ SV116 ) @ SV688 )
| ( ord_less_eq_nat @ SV575 @ ( sK41_SY1438 @ SV575 @ SV688 @ SV382 @ SV116 ) ) )
= $false )
| ( ( ( min_dist_a @ SV116 @ SV382 @ SV688 )
= SV575 )
= $true )
| ( ( dist_a @ SV116 @ SV382 @ SV575 @ SV688 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3285]) ).
thf(3516,plain,
! [SV383: nat,SV117: nat] :
( ( ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
!= zero_zero_nat )
| ( SV383 != SV117 ) )
= $false )
| ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
= zero_zero_nat )
= $false )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3286]) ).
thf(3517,plain,
! [SV383: nat,SV117: nat] :
( ( ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
!= zero_zero_nat )
| ( SV383 != SV117 ) )
= $false )
| ( ( SV383 = SV117 )
= $false )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3287]) ).
thf(3518,plain,
! [SV576: nat,SV384: nat,SV118: nat] :
( ( ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 ) )
= $false )
| ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3288]) ).
thf(3519,plain,
! [SV384: nat,SV576: nat,SV118: nat] :
( ( ( ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) )
= $false )
| ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3288]) ).
thf(3520,plain,
! [SV384: nat,SV576: nat,SV820: list_P559422087at_nat,SV118: nat] :
( ( ( ~ ~ ( ~ ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
| ( ( size_s1990949619at_nat @ SV820 )
!= SV384 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3289]) ).
thf(3521,plain,
! [SV741: nat,SV689: nat,SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
= SV689 )
= $false )
| ( ( ~ ( ord_less_nat @ SV741 @ SV689 )
| ~ ! [SY1479: nat] :
~ ~ ( ~ ( connected_a @ SV120 @ SV386 @ SY1479 )
| ( ( min_dist_a @ SV120 @ SV386 @ SY1479 )
!= SV741 ) ) )
= $true )
| ( ( connected_a @ SV120 @ SV386 @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3290]) ).
thf(3522,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ( connected_a @ SV387 @ SV690 @ SV771 )
| ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) )
= $false )
| ( ( ~ ( ~ ( connected_a @ SV387 @ SV690 @ SV771 )
| ~ ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3291]) ).
thf(3523,plain,
! [SV391: nat,SV128: nat,SV581: nat,SV691: nat] :
( ( ( ~ ( ord_less_nat @ SV691 @ SV581 ) )
= $true )
| ( ( ~ ! [SY1443: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV128 @ SY1443 )
| ( ( min_dist_b @ c2 @ SV128 @ SY1443 )
!= SV691 ) ) )
= $true )
| ( ( ( min_dist_b @ c2 @ SV128 @ SV391 )
= SV581 )
= $false )
| ( ( connected_b @ c2 @ SV128 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3293]) ).
thf(3524,plain,
! [SV582: nat,SV692: nat > $o,SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV129 @ SV392 @ ( sK42_SY1444 @ SV692 @ SV582 @ SV392 @ SV129 ) @ SV582 )
| ~ ! [SY1532: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1532 @ SV582 )
| ( ord_less_eq_nat @ ( sK42_SY1444 @ SV692 @ SV582 @ SV392 @ SV129 ) @ SY1532 ) )
| ( SV692 @ ( sK42_SY1444 @ SV692 @ SV582 @ SV392 @ SV129 ) ) )
= $false )
| ( ( SV692 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) )
= $true )
| ( ( connected_a @ SV129 @ SV392 @ SV582 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3294]) ).
thf(3525,plain,
! [SV583: nat,SV693: nat,SV396: nat,SV134: product_prod_nat_nat > b] :
( ( ( ! [SY1446: nat] :
~ ~ ( ~ ( connected_b @ SV134 @ SV396 @ SY1446 )
| ( ( min_dist_b @ SV134 @ SV396 @ SY1446 )
!= SV693 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV693 @ ( min_dist_b @ SV134 @ SV396 @ SV583 ) )
= $false )
| ( ( connected_b @ SV134 @ SV396 @ SV583 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3296]) ).
thf(3526,plain,
! [SV398: nat,SV136: nat] :
( ( ( connected_a @ c @ SV136 @ SV398 )
= $true )
| ( ( connected_a @ c @ SV136 @ SV398 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3297]) ).
thf(3527,plain,
! [SV398: nat,SV136: nat] :
( ( ( ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) )
= $true )
| ( ( connected_a @ c @ SV136 @ SV398 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3298]) ).
thf(3528,plain,
! [SV398: nat,SV808: list_P559422087at_nat,SV136: nat] :
( ( ( isPath_a @ c @ SV136 @ SV808 @ SV398 )
= $false )
| ( ( ~ ( ~ ( connected_a @ c @ SV136 @ SV398 )
| ~ ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3299]) ).
thf(3529,plain,
! [SV137: set_nat,SV399: nat] :
( ( ( ~ ( ~ ~ ( ~ ( member_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV137 )
| ~ ( ord_less_eq_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV399 ) )
| ~ ! [SY1522: nat] :
( ~ ( member_nat @ SY1522 @ SV137 )
| ~ ( ord_less_eq_nat @ SY1522 @ ( sK29_SY1165 @ SV399 @ SV137 ) )
| ( ( sK29_SY1165 @ SV399 @ SV137 )
= SY1522 ) ) ) )
= $true )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3300]) ).
thf(3530,plain,
! [SV694: nat,SV584: list_P559422087at_nat,SV400: nat,SV138: product_prod_nat_nat > a] :
( ( ( ~ ( isSimplePath_a @ SV138 @ SV400 @ SV584 @ SV694 ) )
= $true )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV584 ) @ ( finite_card_nat @ ( v_a @ SV138 ) ) )
= $true )
| ( ( member_nat @ SV400 @ ( v_a @ SV138 ) )
= $false )
| ( ( finite_Graph_a @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3301]) ).
thf(3531,plain,
! [SV695: nat,SV585: list_P559422087at_nat,SV401: nat,SV139: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV139 @ SV401 @ ( sK30_SY1447 @ SV585 @ SV695 @ SV401 @ SV139 ) @ SV695 )
= $true )
| ( ( isPath_b @ SV139 @ SV401 @ SV585 @ SV695 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3302]) ).
thf(3532,plain,
! [SV586: nat,SV403: nat,SV142: nat] :
( ( ( ~ ~ ( ~ ( connected_b @ c2 @ SV142 @ ( sK43_SY1370 @ SV403 @ SV586 @ SV142 ) )
| ( ( min_dist_b @ c2 @ SV142 @ ( sK43_SY1370 @ SV403 @ SV586 @ SV142 ) )
!= SV586 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV586 @ ( min_dist_b @ c2 @ SV142 @ SV403 ) )
= $false )
| ( ( connected_b @ c2 @ SV142 @ SV403 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3303]) ).
thf(3533,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ( ~ ~ ( ~ ( finite772653738at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) )
| ( ( finite447719721at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) )
!= SV404 ) )
| ~ ( ord_le841296385at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) @ SV143 ) )
= $false )
| ( ( finite772653738at_nat @ SV143 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3304]) ).
thf(3534,plain,
! [SV407: nat,SV146: nat] :
( ( ( connected_a @ c @ SV146 @ SV407 )
= $true )
| ( ( connected_a @ c @ SV146 @ SV407 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3305]) ).
thf(3535,plain,
! [SV407: nat,SV146: nat] :
( ( ( ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) )
= $true )
| ( ( connected_a @ c @ SV146 @ SV407 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3306]) ).
thf(3536,plain,
! [SV407: nat,SV809: nat,SV146: nat] :
( ( ( dist_a @ c @ SV146 @ SV809 @ SV407 )
= $false )
| ( ( ~ ( ~ ( connected_a @ c @ SV146 @ SV407 )
| ~ ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3307]) ).
thf(3537,plain,
! [SV697: nat,SV588: nat,SV408: nat,SV147: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV147 @ SV408 @ ( sK44_SY1448 @ SV588 @ SV697 @ SV408 @ SV147 ) @ SV697 )
| ( ord_less_eq_nat @ SV588 @ ( sK44_SY1448 @ SV588 @ SV697 @ SV408 @ SV147 ) ) )
= $false )
| ( ( ( min_dist_b @ SV147 @ SV408 @ SV697 )
= SV588 )
= $true )
| ( ( dist_b @ SV147 @ SV408 @ SV588 @ SV697 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3308]) ).
thf(3538,plain,
! [SV591: nat,SV699: nat,SV411: nat,SV151: product_prod_nat_nat > a] :
( ( ( ! [SY1449: nat] :
~ ~ ( ~ ( connected_a @ SV151 @ SV411 @ SY1449 )
| ( ( min_dist_a @ SV151 @ SV411 @ SY1449 )
!= SV699 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV699 @ ( min_dist_a @ SV151 @ SV411 @ SV591 ) )
= $false )
| ( ( connected_a @ SV151 @ SV411 @ SV591 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3309]) ).
thf(3539,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3310]) ).
thf(3540,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3310]) ).
thf(3541,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 ) )
= $true )
| ( ( ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3311]) ).
thf(3542,plain,
! [SV594: nat,SV417: nat,SV159: nat > $o] :
( ( ( ~ ( SV159 @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) ) )
= $false )
| ( ( ~ ! [SY852: nat] :
~ ~ ( ~ ( SV159 @ SY852 )
| ~ ! [SY853: nat] :
( ~ ( SV159 @ SY853 )
| ( ord_less_eq_nat @ SY853 @ SY852 ) ) ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3312]) ).
thf(3543,plain,
! [SV159: nat > $o,SV594: nat,SV417: nat] :
( ( ( ord_less_eq_nat @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) @ SV594 )
= $false )
| ( ( ~ ! [SY852: nat] :
~ ~ ( ~ ( SV159 @ SY852 )
| ~ ! [SY853: nat] :
( ~ ( SV159 @ SY853 )
| ( ord_less_eq_nat @ SY853 @ SY852 ) ) ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3312]) ).
thf(3544,plain,
! [SV597: nat,SV421: nat,SV163: nat] :
( ( ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 ) )
= $false )
| ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3313]) ).
thf(3545,plain,
! [SV421: nat,SV597: nat,SV163: nat] :
( ( ( ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) )
= $false )
| ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3313]) ).
thf(3546,plain,
! [SV421: nat,SV597: nat,SV821: list_P559422087at_nat,SV163: nat] :
( ( ( ~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
| ( ( size_s1990949619at_nat @ SV821 )
!= SV421 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3314]) ).
thf(3547,plain,
! [SV164: set_set_nat,SV422: set_nat] :
( ( ( ~ ( ~ ~ ( ~ ( member_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SV164 )
| ~ ( ord_less_eq_set_nat @ SV422 @ ( sK32_SY1199 @ SV422 @ SV164 ) ) )
| ~ ! [SY1523: set_nat] :
( ~ ( member_set_nat @ SY1523 @ SV164 )
| ~ ( ord_less_eq_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SY1523 )
| ( ( sK32_SY1199 @ SV422 @ SV164 )
= SY1523 ) ) ) )
= $true )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3315]) ).
thf(3548,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ~ ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) )
| ~ ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3316]) ).
thf(3549,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= ( ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3316]) ).
thf(3550,plain,
! [SV167: nat > nat,SV425: nat,SV600: nat] :
( ( ( ord_less_nat @ ( sK14_SY873 @ SV600 @ SV425 @ SV167 ) @ ( sK18_SY1504 @ SV167 @ SV425 @ SV600 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV425 @ SV600 )
| ( ord_less_eq_nat @ ( SV167 @ SV425 ) @ ( SV167 @ SV600 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3317]) ).
thf(3551,plain,
! [SV167: nat > nat,SV600: nat,SV425: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV425 @ SV600 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV167 @ SV425 ) @ ( SV167 @ SV600 ) )
= $true )
| ( ( ord_less_nat @ ( SV167 @ ( sK14_SY873 @ SV600 @ SV425 @ SV167 ) ) @ ( SV167 @ ( sK18_SY1504 @ SV167 @ SV425 @ SV600 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3318]) ).
thf(3552,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ~ ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) )
| ~ ( ~ ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ~ ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3319]) ).
thf(3553,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= ( ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3319]) ).
thf(3554,plain,
! [SV171: nat > $o,SV427: nat,SV812: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV812 @ ( sK5_SY879 @ SV427 @ SV171 ) )
| ~ ~ ( SV171 @ SV812 ) ) )
= $false )
| ( ( SV171 @ SV427 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3321]) ).
thf(3555,plain,
! [SV173: set_se1612935105at_nat,SV428: set_Pr1986765409at_nat] :
( ( ( ~ ( ~ ~ ( ~ ( member298845450at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV173 )
| ~ ( ord_le841296385at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV428 ) )
| ~ ! [SY1525: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY1525 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY1525 @ ( sK33_SY1214 @ SV428 @ SV173 ) )
| ( ( sK33_SY1214 @ SV428 @ SV173 )
= SY1525 ) ) ) )
= $true )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3322]) ).
thf(3556,plain,
! [SV174: list_P559422087at_nat > $o,SV429: list_P559422087at_nat,SV813: list_P559422087at_nat] :
( ( ( ~ ( ord_less_nat @ ( size_s1990949619at_nat @ SV813 ) @ ( size_s1990949619at_nat @ ( sK6_SY885 @ SV429 @ SV174 ) ) ) )
= $true )
| ( ( SV174 @ SV813 )
= $true )
| ( ( SV174 @ SV429 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3323]) ).
thf(3557,plain,
! [SV603: nat,SV703: nat > $o,SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV176 @ SV431 @ ( sK45_SY1455 @ SV703 @ SV603 @ SV431 @ SV176 ) @ SV603 )
| ~ ! [SY1533: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1533 @ SV603 )
| ( ord_less_eq_nat @ ( sK45_SY1455 @ SV703 @ SV603 @ SV431 @ SV176 ) @ SY1533 ) )
| ( SV703 @ ( sK45_SY1455 @ SV703 @ SV603 @ SV431 @ SV176 ) ) )
= $false )
| ( ( SV703 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) )
= $true )
| ( ( connected_b @ SV176 @ SV431 @ SV603 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3324]) ).
thf(3558,plain,
! [SV177: set_se1612935105at_nat,SV432: set_Pr1986765409at_nat] :
( ( ( ~ ( ~ ~ ( ~ ( member298845450at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SV177 )
| ~ ( ord_le841296385at_nat @ SV432 @ ( sK34_SY1223 @ SV432 @ SV177 ) ) )
| ~ ! [SY1526: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY1526 @ SV177 )
| ~ ( ord_le841296385at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SY1526 )
| ( ( sK34_SY1223 @ SV432 @ SV177 )
= SY1526 ) ) ) )
= $true )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3325]) ).
thf(3559,plain,
! [SV178: nat,SV433: nat] :
( ( ( ~ ( member_nat @ SV433 @ ( v_b @ c2 ) )
| ~ ( member_nat @ SV178 @ ( v_b @ c2 ) ) )
= $false )
| ( ( member_nat @ SV433 @ ( v_b @ c2 ) )
= $false )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3326]) ).
thf(3560,plain,
! [SV178: nat,SV433: nat] :
( ( ( ~ ( member_nat @ SV433 @ ( v_b @ c2 ) )
| ~ ( member_nat @ SV178 @ ( v_b @ c2 ) ) )
= $false )
| ( ( member_nat @ SV178 @ ( v_b @ c2 ) )
= $false )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3327]) ).
thf(3561,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
= $true )
| ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3328]) ).
thf(3562,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) )
= $true )
| ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3329]) ).
thf(3563,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( SV182 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
| ~ ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3330]) ).
thf(3564,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ~ ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
| ~ ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) )
= $false )
| ( ( SV436 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3565,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ( SV437 != SV704 )
| ~ ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) )
= $false )
| ( ( SV437 = SV704 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3332]) ).
thf(3566,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) )
= $true )
| ( ( ~ ( ( SV437 != SV704 )
| ~ ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3333]) ).
thf(3567,plain,
! [SV438: set_Pr1986765409at_nat > $o,SV184: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ ( sK20_SY1230 @ SV184 @ SV438 ) )
= $true )
| ( ( SV438 @ SV184 )
= $true )
| ( ( finite772653738at_nat @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3334]) ).
thf(3568,plain,
! [SV438: set_Pr1986765409at_nat > $o,SV184: set_Pr1986765409at_nat] :
( ( ( ~ ! [SY1516: set_Pr1986765409at_nat] :
( ~ ( ord_le116442893at_nat @ SY1516 @ ( sK20_SY1230 @ SV184 @ SV438 ) )
| ( SV438 @ SY1516 ) ) )
= $false )
| ( ( SV438 @ SV184 )
= $true )
| ( ( finite772653738at_nat @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3335]) ).
thf(3569,plain,
! [SV184: set_Pr1986765409at_nat,SV438: set_Pr1986765409at_nat > $o] :
( ( ( SV438 @ ( sK20_SY1230 @ SV184 @ SV438 ) )
= $false )
| ( ( SV438 @ SV184 )
= $true )
| ( ( finite772653738at_nat @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3335]) ).
thf(3570,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ~ ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) )
| ~ ( ~ ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ~ ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3336]) ).
thf(3571,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= ( ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3336]) ).
thf(3572,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ( connected_a @ SV442 @ SV706 @ SV775 )
| ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) )
= $false )
| ( ( ~ ( ~ ( connected_a @ SV442 @ SV706 @ SV775 )
| ~ ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3337]) ).
thf(3573,plain,
! [SV445: nat,SV191: nat] :
( ( ( ( ( min_dist_a @ c @ SV191 @ SV445 )
!= zero_zero_nat )
| ( SV445 != SV191 ) )
= $false )
| ( ( ( min_dist_a @ c @ SV191 @ SV445 )
= zero_zero_nat )
= $false )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3339]) ).
thf(3574,plain,
! [SV445: nat,SV191: nat] :
( ( ( ( ( min_dist_a @ c @ SV191 @ SV445 )
!= zero_zero_nat )
| ( SV445 != SV191 ) )
= $false )
| ( ( SV445 = SV191 )
= $false )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3340]) ).
thf(3575,plain,
! [SV192: nat > $o,SV446: nat,SV815: nat] :
( ( ( ~ ( ord_less_nat @ SV815 @ ( sK7_SY922 @ SV446 @ SV192 ) ) )
= $true )
| ( ( SV192 @ SV815 )
= $true )
| ( ( SV192 @ SV446 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3341]) ).
thf(3576,plain,
! [SV193: nat,SV447: nat] :
( ( ( ~ ( member_nat @ SV447 @ ( v_a @ c ) )
| ~ ( member_nat @ SV193 @ ( v_a @ c ) ) )
= $false )
| ( ( member_nat @ SV447 @ ( v_a @ c ) )
= $false )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3342]) ).
thf(3577,plain,
! [SV193: nat,SV447: nat] :
( ( ( ~ ( member_nat @ SV447 @ ( v_a @ c ) )
| ~ ( member_nat @ SV193 @ ( v_a @ c ) ) )
= $false )
| ( ( member_nat @ SV193 @ ( v_a @ c ) )
= $false )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3343]) ).
thf(3578,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ord_less_eq_nat @ ( sK46_SY1241 @ SV196 @ SV449 ) @ SV449 )
| ~ ! [SY1534: nat] :
( ~ ( ord_less_nat @ SY1534 @ ( sK46_SY1241 @ SV196 @ SV449 ) )
| ~ ( SV196 @ SY1534 ) ) )
| ~ ( SV196 @ ( sK46_SY1241 @ SV196 @ SV449 ) ) ) )
= $false )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3345]) ).
thf(3579,plain,
! [SV200: set_nat,SV453: nat] :
( ( ( ~ ( ~ ~ ( ~ ( member_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SV200 )
| ~ ( ord_less_eq_nat @ SV453 @ ( sK35_SY1245 @ SV453 @ SV200 ) ) )
| ~ ! [SY1527: nat] :
( ~ ( member_nat @ SY1527 @ SV200 )
| ~ ( ord_less_eq_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SY1527 )
| ( ( sK35_SY1245 @ SV453 @ SV200 )
= SY1527 ) ) ) )
= $true )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3348]) ).
thf(3580,plain,
! [SV611: nat,SV454: nat,SV201: product_prod_nat_nat > a] :
( ( ( connected_a @ SV201 @ SV454 @ SV611 )
= $false )
| ( ( ord_less_nat @ ( min_dist_a @ SV201 @ SV454 @ SV611 ) @ ( finite_card_nat @ ( v_a @ SV201 ) ) )
= $true )
| ( ( member_nat @ SV454 @ ( v_a @ SV201 ) )
= $false )
| ( ( finite_Graph_a @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3349]) ).
thf(3581,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 ) )
= $false )
| ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3353]) ).
thf(3582,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) )
= $false )
| ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3353]) ).
thf(3583,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 ) )
= $true )
| ( ( ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3354]) ).
thf(3584,plain,
! [SV462: nat,SV615: nat > $o,SV210: nat] :
( ( ( ~ ( dist_a @ c @ SV210 @ ( sK36_SY1400 @ SV615 @ SV462 @ SV210 ) @ SV462 ) )
= $false )
| ( ( SV615 @ ( min_dist_a @ c @ SV210 @ SV462 ) )
= $true )
| ( ( connected_a @ c @ SV210 @ SV462 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3355]) ).
thf(3585,plain,
! [SV615: nat > $o,SV462: nat,SV210: nat] :
( ( ( ~ ! [SY1528: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1528 @ SV462 )
| ( ord_less_eq_nat @ ( sK36_SY1400 @ SV615 @ SV462 @ SV210 ) @ SY1528 ) )
| ( SV615 @ ( sK36_SY1400 @ SV615 @ SV462 @ SV210 ) ) )
= $false )
| ( ( SV615 @ ( min_dist_a @ c @ SV210 @ SV462 ) )
= $true )
| ( ( connected_a @ c @ SV210 @ SV462 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3355]) ).
thf(3586,plain,
! [SV466: nat,SV215: nat] :
( ( ( connected_b @ c2 @ SV215 @ SV466 )
= $true )
| ( ( connected_b @ c2 @ SV215 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3357]) ).
thf(3587,plain,
! [SV466: nat,SV215: nat] :
( ( ( ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) )
= $true )
| ( ( connected_b @ c2 @ SV215 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3358]) ).
thf(3588,plain,
! [SV466: nat,SV816: nat,SV215: nat] :
( ( ( dist_b @ c2 @ SV215 @ SV816 @ SV466 )
= $false )
| ( ( ~ ( ~ ( connected_b @ c2 @ SV215 @ SV466 )
| ~ ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3359]) ).
thf(3589,plain,
! [SV709: nat,SV617: list_P559422087at_nat,SV467: nat,SV217: product_prod_nat_nat > b] :
( ( ( ~ ( isSimplePath_b @ SV217 @ SV467 @ SV617 @ SV709 ) )
= $true )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV617 ) @ ( finite_card_nat @ ( v_b @ SV217 ) ) )
= $true )
| ( ( member_nat @ SV467 @ ( v_b @ SV217 ) )
= $false )
| ( ( finite_Graph_b @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3360]) ).
thf(3590,plain,
! [SV469: set_nat > $o,SV219: set_nat] :
( ( ( finite_finite_nat @ ( sK22_SY1261 @ SV219 @ SV469 ) )
= $true )
| ( ( SV469 @ SV219 )
= $true )
| ( ( finite_finite_nat @ SV219 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3361]) ).
thf(3591,plain,
! [SV469: set_nat > $o,SV219: set_nat] :
( ( ( ~ ! [SY1517: set_nat] :
( ~ ( ord_less_set_nat @ SY1517 @ ( sK22_SY1261 @ SV219 @ SV469 ) )
| ( SV469 @ SY1517 ) ) )
= $false )
| ( ( SV469 @ SV219 )
= $true )
| ( ( finite_finite_nat @ SV219 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3362]) ).
thf(3592,plain,
! [SV219: set_nat,SV469: set_nat > $o] :
( ( ( SV469 @ ( sK22_SY1261 @ SV219 @ SV469 ) )
= $false )
| ( ( SV469 @ SV219 )
= $true )
| ( ( finite_finite_nat @ SV219 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3362]) ).
thf(3593,plain,
! [SV470: nat,SV220: nat] :
( ( ( ~ ( ( SV220 != SV470 ) ) )
= $false )
| ( ( SV220 = SV470 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3363]) ).
thf(3594,plain,
! [SV470: nat,SV220: nat] :
( ( ( ~ ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) )
= $false )
| ( ( SV220 = SV470 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3363]) ).
thf(3595,plain,
! [SV470: nat,SV220: nat] :
( ( ( ~ ( ( SV220 != SV470 ) ) )
= $false )
| ( ( ord_less_nat @ SV220 @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3364]) ).
thf(3596,plain,
! [SV470: nat,SV220: nat] :
( ( ( ~ ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) )
= $false )
| ( ( ord_less_nat @ SV220 @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3364]) ).
thf(3597,plain,
! [SV470: nat,SV220: nat] :
( ( ( ~ ( ( SV220 != SV470 ) ) )
= $false )
| ( ( ord_less_nat @ SV470 @ SV220 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3365]) ).
thf(3598,plain,
! [SV470: nat,SV220: nat] :
( ( ( ~ ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) ) )
= $false )
| ( ( ord_less_nat @ SV470 @ SV220 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3365]) ).
thf(3599,plain,
! [SV222: nat > $o,SV472: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( sK24_SY974 @ SV472 @ SV222 ) )
= $true )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3367]) ).
thf(3600,plain,
! [SV472: nat,SV222: nat > $o] :
( ( ( ~ ~ ( SV222 @ ( sK24_SY974 @ SV472 @ SV222 ) ) )
= $false )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3368]) ).
thf(3601,plain,
! [SV222: nat > $o,SV472: nat] :
( ( ( ~ ! [SY1518: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1518 @ ( sK24_SY974 @ SV472 @ SV222 ) )
| ~ ~ ( SV222 @ SY1518 ) ) )
= $false )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3368]) ).
thf(3602,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV224 ) )
= $false )
| ( ( ord_le841296385at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) @ SV224 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3369]) ).
thf(3603,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) )
= $false )
| ( ( ord_le841296385at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) @ SV224 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3369]) ).
thf(3604,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV224 )
| ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) )
= $false )
| ( ( finite772653738at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3370]) ).
thf(3605,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV224 ) )
= $false )
| ( ( ord_less_eq_nat @ ( finite447719721at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) ) @ SV474 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3371]) ).
thf(3606,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) )
= $false )
| ( ( ord_less_eq_nat @ ( finite447719721at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) ) @ SV474 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3371]) ).
thf(3607,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV226 ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) @ SV226 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3372]) ).
thf(3608,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) @ SV226 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3372]) ).
thf(3609,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV226 )
| ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) )
= $false )
| ( ( finite_finite_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3373]) ).
thf(3610,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV226 ) )
= $false )
| ( ( ord_less_eq_nat @ ( finite_card_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) ) @ SV476 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3374]) ).
thf(3611,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) )
= $false )
| ( ( ord_less_eq_nat @ ( finite_card_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) ) @ SV476 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3374]) ).
thf(3612,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 ) )
= $false )
| ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3375]) ).
thf(3613,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) )
= $false )
| ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3375]) ).
thf(3614,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
| ~ ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3376]) ).
thf(3615,plain,
! [SV621: nat,SV481: nat,SV233: product_prod_nat_nat > a] :
( ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
!= zero_zero_nat )
| ( SV621 != SV481 ) ) )
= $true )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3377]) ).
thf(3616,plain,
! [SV233: product_prod_nat_nat > a,SV481: nat,SV621: nat] :
( ( ( SV621 = SV481 )
= $false )
| ( ( ~ ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
!= zero_zero_nat )
| ( SV621 != SV481 ) ) )
= $true )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3377]) ).
thf(3617,plain,
! [SV484: nat,SV237: nat] :
( ( ( connected_b @ c2 @ SV237 @ SV484 )
= $true )
| ( ( connected_b @ c2 @ SV237 @ SV484 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3379]) ).
thf(3618,plain,
! [SV484: nat,SV237: nat] :
( ( ( ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) )
= $true )
| ( ( connected_b @ c2 @ SV237 @ SV484 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3380]) ).
thf(3619,plain,
! [SV484: nat,SV817: list_P559422087at_nat,SV237: nat] :
( ( ( isPath_b @ c2 @ SV237 @ SV817 @ SV484 )
= $false )
| ( ( ~ ( ~ ( connected_b @ c2 @ SV237 @ SV484 )
| ~ ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3381]) ).
thf(3620,plain,
! [SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ~ ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) )
| ~ ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3382]) ).
thf(3621,plain,
! [SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= ( ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3382]) ).
thf(3622,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 ) )
= $false )
| ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3383]) ).
thf(3623,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) )
= $false )
| ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3383]) ).
thf(3624,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
| ~ ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3384]) ).
thf(3625,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ( connected_b @ SV491 @ SV713 @ SV777 )
| ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) )
= $false )
| ( ( ~ ( ~ ( connected_b @ SV491 @ SV713 @ SV777 )
| ~ ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3385]) ).
thf(3626,plain,
! [SV494: nat,SV254: product_prod_nat_nat > b,SV629: nat] :
( ( ( member_nat @ SV629 @ ( v_b @ SV254 ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV629 @ ( v_b @ SV254 ) )
| ~ ( member_nat @ SV494 @ ( v_b @ SV254 ) ) ) )
= $true )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3387]) ).
thf(3627,plain,
! [SV629: nat,SV254: product_prod_nat_nat > b,SV494: nat] :
( ( ( member_nat @ SV494 @ ( v_b @ SV254 ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV629 @ ( v_b @ SV254 ) )
| ~ ( member_nat @ SV494 @ ( v_b @ SV254 ) ) ) )
= $true )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3387]) ).
thf(3628,plain,
! [SV630: nat,SV495: nat,SV255: product_prod_nat_nat > b] :
( ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
!= zero_zero_nat )
| ( SV630 != SV495 ) ) )
= $true )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3388]) ).
thf(3629,plain,
! [SV255: product_prod_nat_nat > b,SV495: nat,SV630: nat] :
( ( ( SV630 = SV495 )
= $false )
| ( ( ~ ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
!= zero_zero_nat )
| ( SV630 != SV495 ) ) )
= $true )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3388]) ).
thf(3630,plain,
! [SV631: nat,SV496: nat,SV257: product_prod_nat_nat > b] :
( ( ( connected_b @ SV257 @ SV496 @ SV631 )
= $false )
| ( ( ord_less_nat @ ( min_dist_b @ SV257 @ SV496 @ SV631 ) @ ( finite_card_nat @ ( v_b @ SV257 ) ) )
= $true )
| ( ( member_nat @ SV496 @ ( v_b @ SV257 ) )
= $false )
| ( ( finite_Graph_b @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3389]) ).
thf(3631,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
= $true )
| ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3390]) ).
thf(3632,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) )
= $true )
| ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3391]) ).
thf(3633,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( SV259 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $true )
| ( ( ~ ( ~ ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
| ~ ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3392]) ).
thf(3634,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
| ~ ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) )
= $false )
| ( ( SV498 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3393]) ).
thf(3635,plain,
! [SV499: nat,SV260: nat,SV632: nat,SV714: nat] :
( ( ( ~ ( ord_less_nat @ SV714 @ SV632 ) )
= $true )
| ( ( ~ ! [SY1466: nat] :
~ ~ ( ~ ( connected_a @ c @ SV260 @ SY1466 )
| ( ( min_dist_a @ c @ SV260 @ SY1466 )
!= SV714 ) ) )
= $true )
| ( ( ( min_dist_a @ c @ SV260 @ SV499 )
= SV632 )
= $false )
| ( ( connected_a @ c @ SV260 @ SV499 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3394]) ).
thf(3636,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ~ ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) )
| ~ ( ~ ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ~ ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3395]) ).
thf(3637,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= ( ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[3395]) ).
thf(3638,plain,
! [SV263: set_li664300135at_nat,SV796: list_P559422087at_nat] :
( ( ( member1608759472at_nat @ SV796 @ SV263 )
= $false )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV796 ) @ ( sK11_SY1034 @ SV263 ) )
= $true )
| ( ( finite1299096496at_nat @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3396]) ).
thf(3639,plain,
! [SV634: nat,SV502: nat,SV264: nat] :
( ( ( ~ ~ ( ~ ( connected_a @ c @ SV264 @ ( sK47_SY1417 @ SV502 @ SV634 @ SV264 ) )
| ( ( min_dist_a @ c @ SV264 @ ( sK47_SY1417 @ SV502 @ SV634 @ SV264 ) )
!= SV634 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV634 @ ( min_dist_a @ c @ SV264 @ SV502 ) )
= $false )
| ( ( connected_a @ c @ SV264 @ SV502 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3397]) ).
thf(3640,plain,
! [SV750: nat,SV716: nat,SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
= SV716 )
= $false )
| ( ( ~ ( ord_less_nat @ SV750 @ SV716 )
| ~ ! [SY1494: nat] :
~ ~ ( ~ ( connected_b @ SV265 @ SV503 @ SY1494 )
| ( ( min_dist_b @ SV265 @ SV503 @ SY1494 )
!= SV750 ) ) )
= $true )
| ( ( connected_b @ SV265 @ SV503 @ SV635 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3398]) ).
thf(3641,plain,
! [SV508: nat,SV270: set_nat] :
( ( ( ~ ~ ( ~ ( finite_finite_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) )
| ( ( finite_card_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) )
!= SV508 ) )
| ~ ( ord_less_eq_set_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) @ SV270 ) )
= $false )
| ( ( finite_finite_nat @ SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3399]) ).
thf(3642,plain,
! [SV271: nat] :
( ( ( SV271 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3401]) ).
thf(3643,plain,
! [SV271: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV271 )
= $true )
| ( ( SV271 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3402]) ).
thf(3644,plain,
! [SV271: nat] :
( ( ( SV271 != zero_zero_nat )
= $true )
| ( ( SV271 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3403]) ).
thf(3645,plain,
! [SV273: set_set_nat,SV509: set_nat] :
( ( ( ~ ( ~ ~ ( ~ ( member_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV273 )
| ~ ( ord_less_eq_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV509 ) )
| ~ ! [SY1530: set_nat] :
( ~ ( member_set_nat @ SY1530 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1530 @ ( sK37_SY1310 @ SV509 @ SV273 ) )
| ( ( sK37_SY1310 @ SV509 @ SV273 )
= SY1530 ) ) ) )
= $true )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3404]) ).
thf(3646,plain,
! [SV510: product_prod_nat_nat > $o,SV274: product_prod_nat_nat > $o] :
( ( ( SV274 @ ( sK12_SY1312 @ SV510 @ SV274 ) )
= $true )
| ( ( SV510 @ ( sK12_SY1312 @ SV510 @ SV274 ) )
= $true )
| ( ( ( collec7649004at_nat @ SV274 )
= ( collec7649004at_nat @ SV510 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3405]) ).
thf(3647,plain,
! [SV510: product_prod_nat_nat > $o,SV274: product_prod_nat_nat > $o] :
( ( ( ~ ( SV274 @ ( sK12_SY1312 @ SV510 @ SV274 ) ) )
= $true )
| ( ( ~ ( SV510 @ ( sK12_SY1312 @ SV510 @ SV274 ) ) )
= $true )
| ( ( ( collec7649004at_nat @ SV274 )
= ( collec7649004at_nat @ SV510 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3406]) ).
thf(3648,plain,
! [SV642: nat,SV516: nat,SV283: nat] :
( ( ( ~ ( dist_b @ c2 @ SV283 @ ( sK38_SY1423 @ SV516 @ SV642 @ SV283 ) @ SV642 ) )
= $false )
| ( ( ( min_dist_b @ c2 @ SV283 @ SV642 )
= SV516 )
= $true )
| ( ( dist_b @ c2 @ SV283 @ SV516 @ SV642 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3407]) ).
thf(3649,plain,
! [SV283: nat,SV642: nat,SV516: nat] :
( ( ( ord_less_eq_nat @ SV516 @ ( sK38_SY1423 @ SV516 @ SV642 @ SV283 ) )
= $false )
| ( ( ( min_dist_b @ c2 @ SV283 @ SV642 )
= SV516 )
= $true )
| ( ( dist_b @ c2 @ SV283 @ SV516 @ SV642 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3407]) ).
thf(3650,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ( connected_b @ SV519 @ SV719 @ SV779 )
| ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) )
= $false )
| ( ( ~ ( ~ ( connected_b @ SV519 @ SV719 @ SV779 )
| ~ ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3408]) ).
thf(3651,plain,
! [SV720: nat,SV647: list_P559422087at_nat,SV523: nat,SV291: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV291 @ SV523 @ ( sK39_SY1473 @ SV647 @ SV720 @ SV523 @ SV291 ) @ SV720 )
= $true )
| ( ( isPath_a @ SV291 @ SV523 @ SV647 @ SV720 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3409]) ).
thf(3652,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3410]) ).
thf(3653,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3410]) ).
thf(3654,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ~ ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3411]) ).
thf(3655,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ord_less_nat @ SV530 @ SV721 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV530 @ SV721 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3412]) ).
thf(3656,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV530 @ SV721 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3413]) ).
thf(3657,plain,
! [SV533: nat,SV653: nat > $o,SV304: nat] :
( ( ( ~ ( dist_b @ c2 @ SV304 @ ( sK40_SY1428 @ SV653 @ SV533 @ SV304 ) @ SV533 ) )
= $false )
| ( ( SV653 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) )
= $true )
| ( ( connected_b @ c2 @ SV304 @ SV533 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3414]) ).
thf(3658,plain,
! [SV653: nat > $o,SV533: nat,SV304: nat] :
( ( ( ~ ! [SY1531: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1531 @ SV533 )
| ( ord_less_eq_nat @ ( sK40_SY1428 @ SV653 @ SV533 @ SV304 ) @ SY1531 ) )
| ( SV653 @ ( sK40_SY1428 @ SV653 @ SV533 @ SV304 ) ) )
= $false )
| ( ( SV653 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) )
= $true )
| ( ( connected_b @ c2 @ SV304 @ SV533 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3414]) ).
thf(3659,plain,
! [SV24: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV24 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3443]) ).
thf(3660,plain,
! [SV660: nat,SV323: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV323 @ SV660 ) )
= $false )
| ( ( ord_less_eq_nat @ SV323 @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3446]) ).
thf(3661,plain,
! [SV660: nat,SV323: nat] :
( ( ( ~ ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV323 @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3446]) ).
thf(3662,plain,
! [SV660: nat,SV323: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV323 @ SV660 )
| ~ ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) )
= $false )
| ( ( ord_less_nat @ SV323 @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3447]) ).
thf(3663,plain,
! [SV660: nat,SV323: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV323 @ SV660 )
| ~ ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) )
= $false )
| ( ( SV323 = SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3448]) ).
thf(3664,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( ~ ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
| ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) ) )
= $true )
| ( ( ~ ( ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
| ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3449]) ).
thf(3665,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( ~ ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
| ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) ) )
= $true )
| ( ( ~ ( ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
| ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3451]) ).
thf(3666,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $false )
| ( ( ~ ( ~ ( connected_b @ SV330 @ SV665 @ SV760 )
| ~ ( connected_b @ SV330 @ SV665 @ SV760 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3453]) ).
thf(3667,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $false )
| ( ( ~ ( ~ ( connected_b @ SV330 @ SV665 @ SV760 )
| ~ ( connected_b @ SV330 @ SV665 @ SV760 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3453]) ).
thf(3668,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $false )
| ( ( ~ ( ~ ( connected_a @ SV331 @ SV666 @ SV761 )
| ~ ( connected_a @ SV331 @ SV666 @ SV761 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3454]) ).
thf(3669,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $false )
| ( ( ~ ( ~ ( connected_a @ SV331 @ SV666 @ SV761 )
| ~ ( connected_a @ SV331 @ SV666 @ SV761 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3454]) ).
thf(3670,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( ~ ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
| ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
| ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3455]) ).
thf(3671,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( ~ ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
| ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
| ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3457]) ).
thf(3672,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( ~ ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
| ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
| ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3459]) ).
thf(3673,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( ~ ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
| ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
| ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3461]) ).
thf(3674,plain,
! [SV53: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3463]) ).
thf(3675,plain,
! [SV552: nat,SV342: nat,SV61: product_prod_nat_nat > b] :
( ( ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
= $true )
| ( ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3466]) ).
thf(3676,plain,
! [SV61: product_prod_nat_nat > b,SV342: nat,SV552: nat] :
( ( ( SV552 = SV342 )
= $true )
| ( ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3467]) ).
thf(3677,plain,
! [SV552: nat,SV342: nat,SV61: product_prod_nat_nat > b] :
( ( ( dist_b @ SV61 @ SV342 @ zero_zero_nat @ SV552 )
= $true )
| ( ( SV552 = SV342 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3468]) ).
thf(3678,plain,
! [SV342: nat,SV552: nat] :
( ( ( SV552 = SV342 )
= $true )
| ( ( SV552 = SV342 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3469]) ).
thf(3679,plain,
! [SV553: nat,SV343: nat,SV62: product_prod_nat_nat > a] :
( ( ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
= $true )
| ( ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3470]) ).
thf(3680,plain,
! [SV62: product_prod_nat_nat > a,SV343: nat,SV553: nat] :
( ( ( SV553 = SV343 )
= $true )
| ( ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3471]) ).
thf(3681,plain,
! [SV553: nat,SV343: nat,SV62: product_prod_nat_nat > a] :
( ( ( dist_a @ SV62 @ SV343 @ zero_zero_nat @ SV553 )
= $true )
| ( ( SV553 = SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3472]) ).
thf(3682,plain,
! [SV343: nat,SV553: nat] :
( ( ( SV553 = SV343 )
= $true )
| ( ( SV553 = SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3473]) ).
thf(3683,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( ~ ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
| ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) ) )
= $true )
| ( ( ~ ( ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
| ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3478]) ).
thf(3684,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( ~ ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
| ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) ) )
= $true )
| ( ( ~ ( ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
| ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3480]) ).
thf(3685,plain,
! [SV93: nat] :
( ( ( SV93 = zero_zero_nat )
= $false )
| ( ( SV93 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3490]) ).
thf(3686,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ~ ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3493]) ).
thf(3687,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $true )
| ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3495]) ).
thf(3688,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) )
= $true )
| ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3496]) ).
thf(3689,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3497]) ).
thf(3690,plain,
! [SV101: nat] :
( ( ( SV101 = zero_zero_nat )
= $false )
| ( ( SV101 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3498]) ).
thf(3691,plain,
! [SV682: nat,SV567: list_P559422087at_nat,SV370: nat,SV103: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV103 @ SV370 @ SV567 @ SV682 )
= $false )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV567 ) @ ( finite_card_nat @ ( v_a @ SV103 ) ) )
= $true )
| ( ( member_nat @ SV370 @ ( v_a @ SV103 ) )
= $false )
| ( ( finite_Graph_a @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3501]) ).
thf(3692,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( SV372 != SV683 )
= $false )
| ( ( SV372 = SV683 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3502]) ).
thf(3693,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) )
= $false )
| ( ( SV372 = SV683 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3502]) ).
thf(3694,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) )
= $true )
| ( ( ~ ( ( SV372 != SV683 )
| ~ ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3503]) ).
thf(3695,plain,
! [SV684: nat,SV569: list_P559422087at_nat,SV373: nat,SV106: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV106 @ SV373 @ SV569 @ SV684 )
= $false )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV569 ) @ ( finite_card_nat @ ( v_b @ SV106 ) ) )
= $true )
| ( ( member_nat @ SV373 @ ( v_b @ SV106 ) )
= $false )
| ( ( finite_Graph_b @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3504]) ).
thf(3696,plain,
! [SV377: nat > $o,SV110: nat > $o] :
( ( ( SV110 @ ( sK4_SY1126 @ SV377 @ SV110 ) )
= $false )
| ( ( ~ ( SV377 @ ( sK4_SY1126 @ SV377 @ SV110 ) ) )
= $true )
| ( ( ( collect_nat @ SV110 )
= ( collect_nat @ SV377 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3506]) ).
thf(3697,plain,
! [SV378: nat,SV111: product_prod_nat_nat > a,SV571: nat] :
( ( ( ~ ( member_nat @ SV571 @ ( v_a @ SV111 ) )
| ~ ( member_nat @ SV378 @ ( v_a @ SV111 ) ) )
= $false )
| ( ( member_nat @ SV571 @ ( v_a @ SV111 ) )
= $false )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3507]) ).
thf(3698,plain,
! [SV378: nat,SV111: product_prod_nat_nat > a,SV571: nat] :
( ( ( ~ ( member_nat @ SV571 @ ( v_a @ SV111 ) )
| ~ ( member_nat @ SV378 @ ( v_a @ SV111 ) ) )
= $false )
| ( ( member_nat @ SV378 @ ( v_a @ SV111 ) )
= $false )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3508]) ).
thf(3699,plain,
! [SV572: nat,SV379: nat,SV112: nat] :
( ( ( dist_a @ c @ SV112 @ ( sK28_SY1344 @ SV379 @ SV572 @ SV112 ) @ SV572 )
= $true )
| ( ( ( min_dist_a @ c @ SV112 @ SV572 )
= SV379 )
= $true )
| ( ( dist_a @ c @ SV112 @ SV379 @ SV572 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3509]) ).
thf(3700,plain,
! [SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) ) )
= $true )
| ( ( ~ ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3511]) ).
thf(3701,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3513]) ).
thf(3702,plain,
! [SV688: nat,SV575: nat,SV382: nat,SV116: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV116 @ SV382 @ ( sK41_SY1438 @ SV575 @ SV688 @ SV382 @ SV116 ) @ SV688 ) )
= $false )
| ( ( ( min_dist_a @ SV116 @ SV382 @ SV688 )
= SV575 )
= $true )
| ( ( dist_a @ SV116 @ SV382 @ SV575 @ SV688 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3515]) ).
thf(3703,plain,
! [SV116: product_prod_nat_nat > a,SV382: nat,SV688: nat,SV575: nat] :
( ( ( ord_less_eq_nat @ SV575 @ ( sK41_SY1438 @ SV575 @ SV688 @ SV382 @ SV116 ) )
= $false )
| ( ( ( min_dist_a @ SV116 @ SV382 @ SV688 )
= SV575 )
= $true )
| ( ( dist_a @ SV116 @ SV382 @ SV575 @ SV688 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3515]) ).
thf(3704,plain,
! [SV383: nat,SV117: nat] :
( ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
!= zero_zero_nat )
= $false )
| ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
= zero_zero_nat )
= $false )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3516]) ).
thf(3705,plain,
! [SV117: nat,SV383: nat] :
( ( ( SV383 != SV117 )
= $false )
| ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
= zero_zero_nat )
= $false )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3516]) ).
thf(3706,plain,
! [SV383: nat,SV117: nat] :
( ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
!= zero_zero_nat )
= $false )
| ( ( SV383 = SV117 )
= $false )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3517]) ).
thf(3707,plain,
! [SV117: nat,SV383: nat] :
( ( ( SV383 != SV117 )
= $false )
| ( ( SV383 = SV117 )
= $false )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3517]) ).
thf(3708,plain,
! [SV576: nat,SV384: nat,SV118: nat] :
( ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $true )
| ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3518]) ).
thf(3709,plain,
! [SV384: nat,SV576: nat,SV118: nat] :
( ( ( ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) )
= $true )
| ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3519]) ).
thf(3710,plain,
! [SV384: nat,SV576: nat,SV820: list_P559422087at_nat,SV118: nat] :
( ( ( ~ ( ~ ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
| ( ( size_s1990949619at_nat @ SV820 )
!= SV384 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3520]) ).
thf(3711,plain,
! [SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a,SV689: nat,SV741: nat] :
( ( ( ~ ( ord_less_nat @ SV741 @ SV689 ) )
= $true )
| ( ( ~ ! [SY1479: nat] :
~ ~ ( ~ ( connected_a @ SV120 @ SV386 @ SY1479 )
| ( ( min_dist_a @ SV120 @ SV386 @ SY1479 )
!= SV741 ) ) )
= $true )
| ( ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
= SV689 )
= $false )
| ( ( connected_a @ SV120 @ SV386 @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3521]) ).
thf(3712,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( connected_a @ SV387 @ SV690 @ SV771 )
= $false )
| ( ( ~ ( ~ ( connected_a @ SV387 @ SV690 @ SV771 )
| ~ ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3522]) ).
thf(3713,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) )
= $false )
| ( ( ~ ( ~ ( connected_a @ SV387 @ SV690 @ SV771 )
| ~ ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3522]) ).
thf(3714,plain,
! [SV391: nat,SV128: nat,SV581: nat,SV691: nat] :
( ( ( ord_less_nat @ SV691 @ SV581 )
= $false )
| ( ( ~ ! [SY1443: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV128 @ SY1443 )
| ( ( min_dist_b @ c2 @ SV128 @ SY1443 )
!= SV691 ) ) )
= $true )
| ( ( ( min_dist_b @ c2 @ SV128 @ SV391 )
= SV581 )
= $false )
| ( ( connected_b @ c2 @ SV128 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3523]) ).
thf(3715,plain,
! [SV582: nat,SV692: nat > $o,SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV129 @ SV392 @ ( sK42_SY1444 @ SV692 @ SV582 @ SV392 @ SV129 ) @ SV582 ) )
= $false )
| ( ( SV692 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) )
= $true )
| ( ( connected_a @ SV129 @ SV392 @ SV582 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3524]) ).
thf(3716,plain,
! [SV692: nat > $o,SV582: nat,SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1532: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1532 @ SV582 )
| ( ord_less_eq_nat @ ( sK42_SY1444 @ SV692 @ SV582 @ SV392 @ SV129 ) @ SY1532 ) )
| ( SV692 @ ( sK42_SY1444 @ SV692 @ SV582 @ SV392 @ SV129 ) ) )
= $false )
| ( ( SV692 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) )
= $true )
| ( ( connected_a @ SV129 @ SV392 @ SV582 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3524]) ).
thf(3717,plain,
! [SV693: nat,SV583: nat,SV396: nat,SV134: product_prod_nat_nat > b] :
( ( ( ~ ~ ( ~ ( connected_b @ SV134 @ SV396 @ ( sK48_SY1446 @ SV583 @ SV693 @ SV396 @ SV134 ) )
| ( ( min_dist_b @ SV134 @ SV396 @ ( sK48_SY1446 @ SV583 @ SV693 @ SV396 @ SV134 ) )
!= SV693 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV693 @ ( min_dist_b @ SV134 @ SV396 @ SV583 ) )
= $false )
| ( ( connected_b @ SV134 @ SV396 @ SV583 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3525]) ).
thf(3718,plain,
! [SV398: nat,SV136: nat] :
( ( ( ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) )
= $false )
| ( ( connected_a @ c @ SV136 @ SV398 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3527]) ).
thf(3719,plain,
! [SV808: list_P559422087at_nat,SV398: nat,SV136: nat] :
( ( ( ~ ( connected_a @ c @ SV136 @ SV398 )
| ~ ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) )
= $false )
| ( ( isPath_a @ c @ SV136 @ SV808 @ SV398 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3528]) ).
thf(3720,plain,
! [SV137: set_nat,SV399: nat] :
( ( ( ~ ~ ( ~ ( member_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV137 )
| ~ ( ord_less_eq_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV399 ) )
| ~ ! [SY1522: nat] :
( ~ ( member_nat @ SY1522 @ SV137 )
| ~ ( ord_less_eq_nat @ SY1522 @ ( sK29_SY1165 @ SV399 @ SV137 ) )
| ( ( sK29_SY1165 @ SV399 @ SV137 )
= SY1522 ) ) )
= $false )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3529]) ).
thf(3721,plain,
! [SV694: nat,SV584: list_P559422087at_nat,SV400: nat,SV138: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV138 @ SV400 @ SV584 @ SV694 )
= $false )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV584 ) @ ( finite_card_nat @ ( v_a @ SV138 ) ) )
= $true )
| ( ( member_nat @ SV400 @ ( v_a @ SV138 ) )
= $false )
| ( ( finite_Graph_a @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3530]) ).
thf(3722,plain,
! [SV586: nat,SV403: nat,SV142: nat] :
( ( ( ~ ( ~ ( connected_b @ c2 @ SV142 @ ( sK43_SY1370 @ SV403 @ SV586 @ SV142 ) )
| ( ( min_dist_b @ c2 @ SV142 @ ( sK43_SY1370 @ SV403 @ SV586 @ SV142 ) )
!= SV586 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV586 @ ( min_dist_b @ c2 @ SV142 @ SV403 ) )
= $false )
| ( ( connected_b @ c2 @ SV142 @ SV403 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3532]) ).
thf(3723,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ( ~ ~ ( ~ ( finite772653738at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) )
| ( ( finite447719721at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) )
!= SV404 ) ) )
= $false )
| ( ( finite772653738at_nat @ SV143 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3533]) ).
thf(3724,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) @ SV143 ) )
= $false )
| ( ( finite772653738at_nat @ SV143 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3533]) ).
thf(3725,plain,
! [SV407: nat,SV146: nat] :
( ( ( ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) )
= $false )
| ( ( connected_a @ c @ SV146 @ SV407 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3535]) ).
thf(3726,plain,
! [SV809: nat,SV407: nat,SV146: nat] :
( ( ( ~ ( connected_a @ c @ SV146 @ SV407 )
| ~ ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) )
= $false )
| ( ( dist_a @ c @ SV146 @ SV809 @ SV407 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3536]) ).
thf(3727,plain,
! [SV697: nat,SV588: nat,SV408: nat,SV147: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV147 @ SV408 @ ( sK44_SY1448 @ SV588 @ SV697 @ SV408 @ SV147 ) @ SV697 ) )
= $false )
| ( ( ( min_dist_b @ SV147 @ SV408 @ SV697 )
= SV588 )
= $true )
| ( ( dist_b @ SV147 @ SV408 @ SV588 @ SV697 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3537]) ).
thf(3728,plain,
! [SV147: product_prod_nat_nat > b,SV408: nat,SV697: nat,SV588: nat] :
( ( ( ord_less_eq_nat @ SV588 @ ( sK44_SY1448 @ SV588 @ SV697 @ SV408 @ SV147 ) )
= $false )
| ( ( ( min_dist_b @ SV147 @ SV408 @ SV697 )
= SV588 )
= $true )
| ( ( dist_b @ SV147 @ SV408 @ SV588 @ SV697 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3537]) ).
thf(3729,plain,
! [SV699: nat,SV591: nat,SV411: nat,SV151: product_prod_nat_nat > a] :
( ( ( ~ ~ ( ~ ( connected_a @ SV151 @ SV411 @ ( sK49_SY1449 @ SV591 @ SV699 @ SV411 @ SV151 ) )
| ( ( min_dist_a @ SV151 @ SV411 @ ( sK49_SY1449 @ SV591 @ SV699 @ SV411 @ SV151 ) )
!= SV699 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV699 @ ( min_dist_a @ SV151 @ SV411 @ SV591 ) )
= $false )
| ( ( connected_a @ SV151 @ SV411 @ SV591 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3538]) ).
thf(3730,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $true )
| ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3539]) ).
thf(3731,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) )
= $true )
| ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3540]) ).
thf(3732,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3541]) ).
thf(3733,plain,
! [SV594: nat,SV417: nat,SV159: nat > $o] :
( ( ( SV159 @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) )
= $true )
| ( ( ~ ! [SY852: nat] :
~ ~ ( ~ ( SV159 @ SY852 )
| ~ ! [SY853: nat] :
( ~ ( SV159 @ SY853 )
| ( ord_less_eq_nat @ SY853 @ SY852 ) ) ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3542]) ).
thf(3734,plain,
! [SV594: nat,SV417: nat,SV159: nat > $o] :
( ( ( ! [SY852: nat] :
~ ~ ( ~ ( SV159 @ SY852 )
| ~ ! [SY853: nat] :
( ~ ( SV159 @ SY853 )
| ( ord_less_eq_nat @ SY853 @ SY852 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) @ SV594 )
= $false )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3543]) ).
thf(3735,plain,
! [SV597: nat,SV421: nat,SV163: nat] :
( ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $true )
| ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3544]) ).
thf(3736,plain,
! [SV421: nat,SV597: nat,SV163: nat] :
( ( ( ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) )
= $true )
| ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3545]) ).
thf(3737,plain,
! [SV421: nat,SV597: nat,SV821: list_P559422087at_nat,SV163: nat] :
( ( ( ~ ( ~ ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
| ( ( size_s1990949619at_nat @ SV821 )
!= SV421 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3546]) ).
thf(3738,plain,
! [SV164: set_set_nat,SV422: set_nat] :
( ( ( ~ ~ ( ~ ( member_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SV164 )
| ~ ( ord_less_eq_set_nat @ SV422 @ ( sK32_SY1199 @ SV422 @ SV164 ) ) )
| ~ ! [SY1523: set_nat] :
( ~ ( member_set_nat @ SY1523 @ SV164 )
| ~ ( ord_less_eq_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SY1523 )
| ( ( sK32_SY1199 @ SV422 @ SV164 )
= SY1523 ) ) )
= $false )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3547]) ).
thf(3739,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3548]) ).
thf(3740,plain,
! [SV167: nat > nat,SV600: nat,SV425: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV425 @ SV600 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV167 @ SV425 ) @ ( SV167 @ SV600 ) )
= $true )
| ( ( ord_less_nat @ ( sK14_SY873 @ SV600 @ SV425 @ SV167 ) @ ( sK18_SY1504 @ SV167 @ SV425 @ SV600 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3550]) ).
thf(3741,plain,
! [SV167: nat > nat,SV600: nat,SV425: nat] :
( ( ( ord_less_eq_nat @ SV425 @ SV600 )
= $false )
| ( ( ord_less_eq_nat @ ( SV167 @ SV425 ) @ ( SV167 @ SV600 ) )
= $true )
| ( ( ord_less_nat @ ( SV167 @ ( sK14_SY873 @ SV600 @ SV425 @ SV167 ) ) @ ( SV167 @ ( sK18_SY1504 @ SV167 @ SV425 @ SV600 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3551]) ).
thf(3742,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ~ ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3552]) ).
thf(3743,plain,
! [SV171: nat > $o,SV427: nat,SV812: nat] :
( ( ( ~ ( ord_less_nat @ SV812 @ ( sK5_SY879 @ SV427 @ SV171 ) )
| ~ ~ ( SV171 @ SV812 ) )
= $true )
| ( ( SV171 @ SV427 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3554]) ).
thf(3744,plain,
! [SV173: set_se1612935105at_nat,SV428: set_Pr1986765409at_nat] :
( ( ( ~ ~ ( ~ ( member298845450at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV173 )
| ~ ( ord_le841296385at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV428 ) )
| ~ ! [SY1525: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY1525 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY1525 @ ( sK33_SY1214 @ SV428 @ SV173 ) )
| ( ( sK33_SY1214 @ SV428 @ SV173 )
= SY1525 ) ) )
= $false )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3555]) ).
thf(3745,plain,
! [SV174: list_P559422087at_nat > $o,SV429: list_P559422087at_nat,SV813: list_P559422087at_nat] :
( ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV813 ) @ ( size_s1990949619at_nat @ ( sK6_SY885 @ SV429 @ SV174 ) ) )
= $false )
| ( ( SV174 @ SV813 )
= $true )
| ( ( SV174 @ SV429 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3556]) ).
thf(3746,plain,
! [SV603: nat,SV703: nat > $o,SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV176 @ SV431 @ ( sK45_SY1455 @ SV703 @ SV603 @ SV431 @ SV176 ) @ SV603 ) )
= $false )
| ( ( SV703 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) )
= $true )
| ( ( connected_b @ SV176 @ SV431 @ SV603 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3557]) ).
thf(3747,plain,
! [SV703: nat > $o,SV603: nat,SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1533: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1533 @ SV603 )
| ( ord_less_eq_nat @ ( sK45_SY1455 @ SV703 @ SV603 @ SV431 @ SV176 ) @ SY1533 ) )
| ( SV703 @ ( sK45_SY1455 @ SV703 @ SV603 @ SV431 @ SV176 ) ) )
= $false )
| ( ( SV703 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) )
= $true )
| ( ( connected_b @ SV176 @ SV431 @ SV603 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3557]) ).
thf(3748,plain,
! [SV177: set_se1612935105at_nat,SV432: set_Pr1986765409at_nat] :
( ( ( ~ ~ ( ~ ( member298845450at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SV177 )
| ~ ( ord_le841296385at_nat @ SV432 @ ( sK34_SY1223 @ SV432 @ SV177 ) ) )
| ~ ! [SY1526: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY1526 @ SV177 )
| ~ ( ord_le841296385at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SY1526 )
| ( ( sK34_SY1223 @ SV432 @ SV177 )
= SY1526 ) ) )
= $false )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3558]) ).
thf(3749,plain,
! [SV178: nat,SV433: nat] :
( ( ( ~ ( member_nat @ SV433 @ ( v_b @ c2 ) ) )
= $false )
| ( ( member_nat @ SV433 @ ( v_b @ c2 ) )
= $false )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3559]) ).
thf(3750,plain,
! [SV433: nat,SV178: nat] :
( ( ( ~ ( member_nat @ SV178 @ ( v_b @ c2 ) ) )
= $false )
| ( ( member_nat @ SV433 @ ( v_b @ c2 ) )
= $false )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3559]) ).
thf(3751,plain,
! [SV178: nat,SV433: nat] :
( ( ( ~ ( member_nat @ SV433 @ ( v_b @ c2 ) ) )
= $false )
| ( ( member_nat @ SV178 @ ( v_b @ c2 ) )
= $false )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3560]) ).
thf(3752,plain,
! [SV433: nat,SV178: nat] :
( ( ( ~ ( member_nat @ SV178 @ ( v_b @ c2 ) ) )
= $false )
| ( ( member_nat @ SV178 @ ( v_b @ c2 ) )
= $false )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3560]) ).
thf(3753,plain,
! [SV436: nat > $o,SV822: nat,SV182: nat > $o] :
( ( ( ~ ( SV182 @ SV822 )
| ( SV436 @ SV822 ) )
= $true )
| ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3562]) ).
thf(3754,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ~ ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
| ~ ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) )
= $false )
| ( ( SV182 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3563]) ).
thf(3755,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ~ ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) ) )
= $false )
| ( ( SV436 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3564]) ).
thf(3756,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ~ ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) )
= $false )
| ( ( SV436 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3564]) ).
thf(3757,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( SV437 != SV704 )
= $false )
| ( ( SV437 = SV704 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3565]) ).
thf(3758,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ~ ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) )
= $false )
| ( ( SV437 = SV704 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3565]) ).
thf(3759,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 ) )
= $true )
| ( ( ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) )
= $true )
| ( ( ~ ( ( SV437 != SV704 )
| ~ ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3566]) ).
thf(3760,plain,
! [SV438: set_Pr1986765409at_nat > $o,SV184: set_Pr1986765409at_nat] :
( ( ( ! [SY1516: set_Pr1986765409at_nat] :
( ~ ( ord_le116442893at_nat @ SY1516 @ ( sK20_SY1230 @ SV184 @ SV438 ) )
| ( SV438 @ SY1516 ) ) )
= $true )
| ( ( SV438 @ SV184 )
= $true )
| ( ( finite772653738at_nat @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3568]) ).
thf(3761,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ~ ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3570]) ).
thf(3762,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( connected_a @ SV442 @ SV706 @ SV775 )
= $false )
| ( ( ~ ( ~ ( connected_a @ SV442 @ SV706 @ SV775 )
| ~ ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3572]) ).
thf(3763,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) )
= $false )
| ( ( ~ ( ~ ( connected_a @ SV442 @ SV706 @ SV775 )
| ~ ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3572]) ).
thf(3764,plain,
! [SV445: nat,SV191: nat] :
( ( ( ( min_dist_a @ c @ SV191 @ SV445 )
!= zero_zero_nat )
= $false )
| ( ( ( min_dist_a @ c @ SV191 @ SV445 )
= zero_zero_nat )
= $false )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3573]) ).
thf(3765,plain,
! [SV191: nat,SV445: nat] :
( ( ( SV445 != SV191 )
= $false )
| ( ( ( min_dist_a @ c @ SV191 @ SV445 )
= zero_zero_nat )
= $false )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3573]) ).
thf(3766,plain,
! [SV445: nat,SV191: nat] :
( ( ( ( min_dist_a @ c @ SV191 @ SV445 )
!= zero_zero_nat )
= $false )
| ( ( SV445 = SV191 )
= $false )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3574]) ).
thf(3767,plain,
! [SV191: nat,SV445: nat] :
( ( ( SV445 != SV191 )
= $false )
| ( ( SV445 = SV191 )
= $false )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3574]) ).
thf(3768,plain,
! [SV192: nat > $o,SV446: nat,SV815: nat] :
( ( ( ord_less_nat @ SV815 @ ( sK7_SY922 @ SV446 @ SV192 ) )
= $false )
| ( ( SV192 @ SV815 )
= $true )
| ( ( SV192 @ SV446 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3575]) ).
thf(3769,plain,
! [SV193: nat,SV447: nat] :
( ( ( ~ ( member_nat @ SV447 @ ( v_a @ c ) ) )
= $false )
| ( ( member_nat @ SV447 @ ( v_a @ c ) )
= $false )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3576]) ).
thf(3770,plain,
! [SV447: nat,SV193: nat] :
( ( ( ~ ( member_nat @ SV193 @ ( v_a @ c ) ) )
= $false )
| ( ( member_nat @ SV447 @ ( v_a @ c ) )
= $false )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3576]) ).
thf(3771,plain,
! [SV193: nat,SV447: nat] :
( ( ( ~ ( member_nat @ SV447 @ ( v_a @ c ) ) )
= $false )
| ( ( member_nat @ SV193 @ ( v_a @ c ) )
= $false )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3577]) ).
thf(3772,plain,
! [SV447: nat,SV193: nat] :
( ( ( ~ ( member_nat @ SV193 @ ( v_a @ c ) ) )
= $false )
| ( ( member_nat @ SV193 @ ( v_a @ c ) )
= $false )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3577]) ).
thf(3773,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( ~ ( ~ ~ ( ~ ( ord_less_eq_nat @ ( sK46_SY1241 @ SV196 @ SV449 ) @ SV449 )
| ~ ! [SY1534: nat] :
( ~ ( ord_less_nat @ SY1534 @ ( sK46_SY1241 @ SV196 @ SV449 ) )
| ~ ( SV196 @ SY1534 ) ) )
| ~ ( SV196 @ ( sK46_SY1241 @ SV196 @ SV449 ) ) ) )
= $true )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3578]) ).
thf(3774,plain,
! [SV200: set_nat,SV453: nat] :
( ( ( ~ ~ ( ~ ( member_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SV200 )
| ~ ( ord_less_eq_nat @ SV453 @ ( sK35_SY1245 @ SV453 @ SV200 ) ) )
| ~ ! [SY1527: nat] :
( ~ ( member_nat @ SY1527 @ SV200 )
| ~ ( ord_less_eq_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SY1527 )
| ( ( sK35_SY1245 @ SV453 @ SV200 )
= SY1527 ) ) )
= $false )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3579]) ).
thf(3775,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $true )
| ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3581]) ).
thf(3776,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) )
= $true )
| ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3582]) ).
thf(3777,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3583]) ).
thf(3778,plain,
! [SV462: nat,SV615: nat > $o,SV210: nat] :
( ( ( dist_a @ c @ SV210 @ ( sK36_SY1400 @ SV615 @ SV462 @ SV210 ) @ SV462 )
= $true )
| ( ( SV615 @ ( min_dist_a @ c @ SV210 @ SV462 ) )
= $true )
| ( ( connected_a @ c @ SV210 @ SV462 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3584]) ).
thf(3779,plain,
! [SV615: nat > $o,SV462: nat,SV210: nat] :
( ( ( ~ ! [SY1528: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1528 @ SV462 )
| ( ord_less_eq_nat @ ( sK36_SY1400 @ SV615 @ SV462 @ SV210 ) @ SY1528 ) ) )
= $false )
| ( ( SV615 @ ( min_dist_a @ c @ SV210 @ SV462 ) )
= $true )
| ( ( connected_a @ c @ SV210 @ SV462 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3585]) ).
thf(3780,plain,
! [SV210: nat,SV462: nat,SV615: nat > $o] :
( ( ( SV615 @ ( sK36_SY1400 @ SV615 @ SV462 @ SV210 ) )
= $false )
| ( ( SV615 @ ( min_dist_a @ c @ SV210 @ SV462 ) )
= $true )
| ( ( connected_a @ c @ SV210 @ SV462 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3585]) ).
thf(3781,plain,
! [SV466: nat,SV215: nat] :
( ( ( ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) )
= $false )
| ( ( connected_b @ c2 @ SV215 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3587]) ).
thf(3782,plain,
! [SV816: nat,SV466: nat,SV215: nat] :
( ( ( ~ ( connected_b @ c2 @ SV215 @ SV466 )
| ~ ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) )
= $false )
| ( ( dist_b @ c2 @ SV215 @ SV816 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3588]) ).
thf(3783,plain,
! [SV709: nat,SV617: list_P559422087at_nat,SV467: nat,SV217: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV217 @ SV467 @ SV617 @ SV709 )
= $false )
| ( ( ord_less_nat @ ( size_s1990949619at_nat @ SV617 ) @ ( finite_card_nat @ ( v_b @ SV217 ) ) )
= $true )
| ( ( member_nat @ SV467 @ ( v_b @ SV217 ) )
= $false )
| ( ( finite_Graph_b @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3589]) ).
thf(3784,plain,
! [SV469: set_nat > $o,SV219: set_nat] :
( ( ( ! [SY1517: set_nat] :
( ~ ( ord_less_set_nat @ SY1517 @ ( sK22_SY1261 @ SV219 @ SV469 ) )
| ( SV469 @ SY1517 ) ) )
= $true )
| ( ( SV469 @ SV219 )
= $true )
| ( ( finite_finite_nat @ SV219 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3591]) ).
thf(3785,plain,
! [SV470: nat,SV220: nat] :
( ( ( SV220 != SV470 )
= $true )
| ( ( SV220 = SV470 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3593]) ).
thf(3786,plain,
! [SV470: nat,SV220: nat] :
( ( ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) )
= $true )
| ( ( SV220 = SV470 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3594]) ).
thf(3787,plain,
! [SV470: nat,SV220: nat] :
( ( ( SV220 != SV470 )
= $true )
| ( ( ord_less_nat @ SV220 @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3595]) ).
thf(3788,plain,
! [SV470: nat,SV220: nat] :
( ( ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) )
= $true )
| ( ( ord_less_nat @ SV220 @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3596]) ).
thf(3789,plain,
! [SV470: nat,SV220: nat] :
( ( ( SV220 != SV470 )
= $true )
| ( ( ord_less_nat @ SV470 @ SV220 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3597]) ).
thf(3790,plain,
! [SV470: nat,SV220: nat] :
( ( ( ( ord_less_nat @ SV220 @ SV470 )
| ( ord_less_nat @ SV470 @ SV220 ) )
= $true )
| ( ( ord_less_nat @ SV470 @ SV220 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3598]) ).
thf(3791,plain,
! [SV472: nat,SV222: nat > $o] :
( ( ( ~ ( SV222 @ ( sK24_SY974 @ SV472 @ SV222 ) ) )
= $true )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3600]) ).
thf(3792,plain,
! [SV222: nat > $o,SV472: nat] :
( ( ( ! [SY1518: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1518 @ ( sK24_SY974 @ SV472 @ SV222 ) )
| ~ ~ ( SV222 @ SY1518 ) ) )
= $true )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3601]) ).
thf(3793,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV224 )
= $true )
| ( ( ord_le841296385at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) @ SV224 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3602]) ).
thf(3794,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 )
= $true )
| ( ( ord_le841296385at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) @ SV224 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3603]) ).
thf(3795,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ SV224 ) )
= $false )
| ( ( finite772653738at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3604]) ).
thf(3796,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 ) )
= $false )
| ( ( finite772653738at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3604]) ).
thf(3797,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV224 )
= $true )
| ( ( ord_less_eq_nat @ ( finite447719721at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) ) @ SV474 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3605]) ).
thf(3798,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 )
= $true )
| ( ( ord_less_eq_nat @ ( finite447719721at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) ) @ SV474 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3606]) ).
thf(3799,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( finite_finite_nat @ SV226 )
= $true )
| ( ( ord_less_eq_set_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) @ SV226 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3607]) ).
thf(3800,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 )
= $true )
| ( ( ord_less_eq_set_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) @ SV226 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3608]) ).
thf(3801,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( ~ ( finite_finite_nat @ SV226 ) )
= $false )
| ( ( finite_finite_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3609]) ).
thf(3802,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( ~ ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 ) )
= $false )
| ( ( finite_finite_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3609]) ).
thf(3803,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( finite_finite_nat @ SV226 )
= $true )
| ( ( ord_less_eq_nat @ ( finite_card_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) ) @ SV476 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3610]) ).
thf(3804,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 )
= $true )
| ( ( ord_less_eq_nat @ ( finite_card_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) ) @ SV476 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3611]) ).
thf(3805,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
= $true )
| ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3612]) ).
thf(3806,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) )
= $true )
| ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3613]) ).
thf(3807,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
| ~ ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3614]) ).
thf(3808,plain,
! [SV621: nat,SV481: nat,SV233: product_prod_nat_nat > a] :
( ( ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
!= zero_zero_nat )
| ( SV621 != SV481 ) )
= $false )
| ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
= zero_zero_nat )
= $false )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3615]) ).
thf(3809,plain,
! [SV621: nat,SV481: nat,SV233: product_prod_nat_nat > a] :
( ( ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
!= zero_zero_nat )
| ( SV621 != SV481 ) )
= $false )
| ( ( SV621 = SV481 )
= $false )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3616]) ).
thf(3810,plain,
! [SV484: nat,SV237: nat] :
( ( ( ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) )
= $false )
| ( ( connected_b @ c2 @ SV237 @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3618]) ).
thf(3811,plain,
! [SV817: list_P559422087at_nat,SV484: nat,SV237: nat] :
( ( ( ~ ( connected_b @ c2 @ SV237 @ SV484 )
| ~ ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) )
= $false )
| ( ( isPath_b @ c2 @ SV237 @ SV817 @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3619]) ).
thf(3812,plain,
! [SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) ) )
= $true )
| ( ( ~ ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3620]) ).
thf(3813,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
= $true )
| ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3622]) ).
thf(3814,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) )
= $true )
| ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3623]) ).
thf(3815,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
| ~ ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3624]) ).
thf(3816,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( connected_b @ SV491 @ SV713 @ SV777 )
= $false )
| ( ( ~ ( ~ ( connected_b @ SV491 @ SV713 @ SV777 )
| ~ ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3625]) ).
thf(3817,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) )
= $false )
| ( ( ~ ( ~ ( connected_b @ SV491 @ SV713 @ SV777 )
| ~ ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3625]) ).
thf(3818,plain,
! [SV494: nat,SV254: product_prod_nat_nat > b,SV629: nat] :
( ( ( ~ ( member_nat @ SV629 @ ( v_b @ SV254 ) )
| ~ ( member_nat @ SV494 @ ( v_b @ SV254 ) ) )
= $false )
| ( ( member_nat @ SV629 @ ( v_b @ SV254 ) )
= $false )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3626]) ).
thf(3819,plain,
! [SV494: nat,SV254: product_prod_nat_nat > b,SV629: nat] :
( ( ( ~ ( member_nat @ SV629 @ ( v_b @ SV254 ) )
| ~ ( member_nat @ SV494 @ ( v_b @ SV254 ) ) )
= $false )
| ( ( member_nat @ SV494 @ ( v_b @ SV254 ) )
= $false )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3627]) ).
thf(3820,plain,
! [SV630: nat,SV495: nat,SV255: product_prod_nat_nat > b] :
( ( ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
!= zero_zero_nat )
| ( SV630 != SV495 ) )
= $false )
| ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
= zero_zero_nat )
= $false )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3628]) ).
thf(3821,plain,
! [SV630: nat,SV495: nat,SV255: product_prod_nat_nat > b] :
( ( ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
!= zero_zero_nat )
| ( SV630 != SV495 ) )
= $false )
| ( ( SV630 = SV495 )
= $false )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3629]) ).
thf(3822,plain,
! [SV498: product_prod_nat_nat > $o,SV823: product_prod_nat_nat,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ( SV259 @ SV823 )
| ( SV498 @ SV823 ) )
= $true )
| ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3632]) ).
thf(3823,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
| ~ ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) )
= $false )
| ( ( SV259 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3633]) ).
thf(3824,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) ) )
= $false )
| ( ( SV498 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3634]) ).
thf(3825,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) )
= $false )
| ( ( SV498 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3634]) ).
thf(3826,plain,
! [SV499: nat,SV260: nat,SV632: nat,SV714: nat] :
( ( ( ord_less_nat @ SV714 @ SV632 )
= $false )
| ( ( ~ ! [SY1466: nat] :
~ ~ ( ~ ( connected_a @ c @ SV260 @ SY1466 )
| ( ( min_dist_a @ c @ SV260 @ SY1466 )
!= SV714 ) ) )
= $true )
| ( ( ( min_dist_a @ c @ SV260 @ SV499 )
= SV632 )
= $false )
| ( ( connected_a @ c @ SV260 @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3635]) ).
thf(3827,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ~ ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3636]) ).
thf(3828,plain,
! [SV634: nat,SV502: nat,SV264: nat] :
( ( ( ~ ( ~ ( connected_a @ c @ SV264 @ ( sK47_SY1417 @ SV502 @ SV634 @ SV264 ) )
| ( ( min_dist_a @ c @ SV264 @ ( sK47_SY1417 @ SV502 @ SV634 @ SV264 ) )
!= SV634 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV634 @ ( min_dist_a @ c @ SV264 @ SV502 ) )
= $false )
| ( ( connected_a @ c @ SV264 @ SV502 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3639]) ).
thf(3829,plain,
! [SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b,SV716: nat,SV750: nat] :
( ( ( ~ ( ord_less_nat @ SV750 @ SV716 ) )
= $true )
| ( ( ~ ! [SY1494: nat] :
~ ~ ( ~ ( connected_b @ SV265 @ SV503 @ SY1494 )
| ( ( min_dist_b @ SV265 @ SV503 @ SY1494 )
!= SV750 ) ) )
= $true )
| ( ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
= SV716 )
= $false )
| ( ( connected_b @ SV265 @ SV503 @ SV635 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3640]) ).
thf(3830,plain,
! [SV508: nat,SV270: set_nat] :
( ( ( ~ ~ ( ~ ( finite_finite_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) )
| ( ( finite_card_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) )
!= SV508 ) ) )
= $false )
| ( ( finite_finite_nat @ SV270 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3641]) ).
thf(3831,plain,
! [SV508: nat,SV270: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) @ SV270 ) )
= $false )
| ( ( finite_finite_nat @ SV270 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3641]) ).
thf(3832,plain,
! [SV271: nat] :
( ( ( SV271 = zero_zero_nat )
= $false )
| ( ( SV271 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3644]) ).
thf(3833,plain,
! [SV273: set_set_nat,SV509: set_nat] :
( ( ( ~ ~ ( ~ ( member_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV273 )
| ~ ( ord_less_eq_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV509 ) )
| ~ ! [SY1530: set_nat] :
( ~ ( member_set_nat @ SY1530 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1530 @ ( sK37_SY1310 @ SV509 @ SV273 ) )
| ( ( sK37_SY1310 @ SV509 @ SV273 )
= SY1530 ) ) )
= $false )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3645]) ).
thf(3834,plain,
! [SV510: product_prod_nat_nat > $o,SV274: product_prod_nat_nat > $o] :
( ( ( SV274 @ ( sK12_SY1312 @ SV510 @ SV274 ) )
= $false )
| ( ( ~ ( SV510 @ ( sK12_SY1312 @ SV510 @ SV274 ) ) )
= $true )
| ( ( ( collec7649004at_nat @ SV274 )
= ( collec7649004at_nat @ SV510 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3647]) ).
thf(3835,plain,
! [SV642: nat,SV516: nat,SV283: nat] :
( ( ( dist_b @ c2 @ SV283 @ ( sK38_SY1423 @ SV516 @ SV642 @ SV283 ) @ SV642 )
= $true )
| ( ( ( min_dist_b @ c2 @ SV283 @ SV642 )
= SV516 )
= $true )
| ( ( dist_b @ c2 @ SV283 @ SV516 @ SV642 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3648]) ).
thf(3836,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( connected_b @ SV519 @ SV719 @ SV779 )
= $false )
| ( ( ~ ( ~ ( connected_b @ SV519 @ SV719 @ SV779 )
| ~ ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3650]) ).
thf(3837,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) )
= $false )
| ( ( ~ ( ~ ( connected_b @ SV519 @ SV719 @ SV779 )
| ~ ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3650]) ).
thf(3838,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $true )
| ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3652]) ).
thf(3839,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) )
= $true )
| ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3653]) ).
thf(3840,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ~ ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3654]) ).
thf(3841,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ord_less_nat @ SV530 @ SV721 ) )
= $false )
| ( ( ord_less_nat @ SV530 @ SV721 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3655]) ).
thf(3842,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV530 @ SV721 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3655]) ).
thf(3843,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV530 @ SV721 ) )
= $true )
| ( ( ~ ( ( SV530 != SV721 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV530 @ SV721 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3656]) ).
thf(3844,plain,
! [SV533: nat,SV653: nat > $o,SV304: nat] :
( ( ( dist_b @ c2 @ SV304 @ ( sK40_SY1428 @ SV653 @ SV533 @ SV304 ) @ SV533 )
= $true )
| ( ( SV653 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) )
= $true )
| ( ( connected_b @ c2 @ SV304 @ SV533 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3657]) ).
thf(3845,plain,
! [SV653: nat > $o,SV533: nat,SV304: nat] :
( ( ( ~ ! [SY1531: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1531 @ SV533 )
| ( ord_less_eq_nat @ ( sK40_SY1428 @ SV653 @ SV533 @ SV304 ) @ SY1531 ) ) )
= $false )
| ( ( SV653 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) )
= $true )
| ( ( connected_b @ c2 @ SV304 @ SV533 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3658]) ).
thf(3846,plain,
! [SV304: nat,SV533: nat,SV653: nat > $o] :
( ( ( SV653 @ ( sK40_SY1428 @ SV653 @ SV533 @ SV304 ) )
= $false )
| ( ( SV653 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) )
= $true )
| ( ( connected_b @ c2 @ SV304 @ SV533 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3658]) ).
thf(3847,plain,
! [SV660: nat,SV323: nat] :
( ( ( ord_less_eq_nat @ SV323 @ SV660 )
= $true )
| ( ( ord_less_eq_nat @ SV323 @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3660]) ).
thf(3848,plain,
! [SV660: nat,SV323: nat] :
( ( ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) )
= $true )
| ( ( ord_less_eq_nat @ SV323 @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3661]) ).
thf(3849,plain,
! [SV660: nat,SV323: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV323 @ SV660 ) )
= $false )
| ( ( ord_less_nat @ SV323 @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3662]) ).
thf(3850,plain,
! [SV660: nat,SV323: nat] :
( ( ( ~ ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) )
= $false )
| ( ( ord_less_nat @ SV323 @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3662]) ).
thf(3851,plain,
! [SV660: nat,SV323: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV323 @ SV660 ) )
= $false )
| ( ( SV323 = SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3663]) ).
thf(3852,plain,
! [SV660: nat,SV323: nat] :
( ( ( ~ ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) ) )
= $false )
| ( ( SV323 = SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3663]) ).
thf(3853,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
| ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) )
= $false )
| ( ( ~ ( ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
| ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3664]) ).
thf(3854,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
| ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) )
= $false )
| ( ( ~ ( ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
| ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3665]) ).
thf(3855,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV330 @ SV665 @ SV760 )
| ~ ( connected_b @ SV330 @ SV665 @ SV760 ) )
= $false )
| ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3666]) ).
thf(3856,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV330 @ SV665 @ SV760 )
| ~ ( connected_b @ SV330 @ SV665 @ SV760 ) )
= $false )
| ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3667]) ).
thf(3857,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV331 @ SV666 @ SV761 )
| ~ ( connected_a @ SV331 @ SV666 @ SV761 ) )
= $false )
| ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3668]) ).
thf(3858,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV331 @ SV666 @ SV761 )
| ~ ( connected_a @ SV331 @ SV666 @ SV761 ) )
= $false )
| ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3669]) ).
thf(3859,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
| ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) )
= $false )
| ( ( ~ ( ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
| ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3670]) ).
thf(3860,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
| ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) )
= $false )
| ( ( ~ ( ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
| ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3671]) ).
thf(3861,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
| ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
| ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3672]) ).
thf(3862,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
| ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
| ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3673]) ).
thf(3863,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
| ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) )
= $false )
| ( ( ~ ( ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
| ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3683]) ).
thf(3864,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
| ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) )
= $false )
| ( ( ~ ( ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
| ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3684]) ).
thf(3865,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ~ ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3686]) ).
thf(3866,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3688]) ).
thf(3867,plain,
! [SV566: nat,SV97: nat,SV367: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV367 )
= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $false )
| ( ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3689]) ).
thf(3868,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( SV372 = SV683 )
= $true )
| ( ( SV372 = SV683 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3692]) ).
thf(3869,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) )
= $true )
| ( ( SV372 = SV683 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3693]) ).
thf(3870,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ord_less_eq_set_nat @ SV372 @ SV683 )
= $false )
| ( ( ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) )
= $true )
| ( ( ~ ( ( SV372 != SV683 )
| ~ ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3694]) ).
thf(3871,plain,
! [SV110: nat > $o,SV377: nat > $o] :
( ( ( SV377 @ ( sK4_SY1126 @ SV377 @ SV110 ) )
= $false )
| ( ( SV110 @ ( sK4_SY1126 @ SV377 @ SV110 ) )
= $false )
| ( ( ( collect_nat @ SV110 )
= ( collect_nat @ SV377 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3696]) ).
thf(3872,plain,
! [SV378: nat,SV111: product_prod_nat_nat > a,SV571: nat] :
( ( ( ~ ( member_nat @ SV571 @ ( v_a @ SV111 ) ) )
= $false )
| ( ( member_nat @ SV571 @ ( v_a @ SV111 ) )
= $false )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3697]) ).
thf(3873,plain,
! [SV571: nat,SV111: product_prod_nat_nat > a,SV378: nat] :
( ( ( ~ ( member_nat @ SV378 @ ( v_a @ SV111 ) ) )
= $false )
| ( ( member_nat @ SV571 @ ( v_a @ SV111 ) )
= $false )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3697]) ).
thf(3874,plain,
! [SV378: nat,SV111: product_prod_nat_nat > a,SV571: nat] :
( ( ( ~ ( member_nat @ SV571 @ ( v_a @ SV111 ) ) )
= $false )
| ( ( member_nat @ SV378 @ ( v_a @ SV111 ) )
= $false )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3698]) ).
thf(3875,plain,
! [SV571: nat,SV111: product_prod_nat_nat > a,SV378: nat] :
( ( ( ~ ( member_nat @ SV378 @ ( v_a @ SV111 ) ) )
= $false )
| ( ( member_nat @ SV378 @ ( v_a @ SV111 ) )
= $false )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3698]) ).
thf(3876,plain,
! [SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3700]) ).
thf(3877,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3701]) ).
thf(3878,plain,
! [SV688: nat,SV575: nat,SV382: nat,SV116: product_prod_nat_nat > a] :
( ( ( dist_a @ SV116 @ SV382 @ ( sK41_SY1438 @ SV575 @ SV688 @ SV382 @ SV116 ) @ SV688 )
= $true )
| ( ( ( min_dist_a @ SV116 @ SV382 @ SV688 )
= SV575 )
= $true )
| ( ( dist_a @ SV116 @ SV382 @ SV575 @ SV688 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3702]) ).
thf(3879,plain,
! [SV383: nat,SV117: nat] :
( ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
= zero_zero_nat )
= $true )
| ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
= zero_zero_nat )
= $false )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3704]) ).
thf(3880,plain,
! [SV117: nat,SV383: nat] :
( ( ( SV383 = SV117 )
= $true )
| ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
= zero_zero_nat )
= $false )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3705]) ).
thf(3881,plain,
! [SV383: nat,SV117: nat] :
( ( ( ( min_dist_b @ c2 @ SV117 @ SV383 )
= zero_zero_nat )
= $true )
| ( ( SV383 = SV117 )
= $false )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3706]) ).
thf(3882,plain,
! [SV117: nat,SV383: nat] :
( ( ( SV383 = SV117 )
= $true )
| ( ( SV383 = SV117 )
= $false )
| ( ( connected_b @ c2 @ SV117 @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3707]) ).
thf(3883,plain,
! [SV384: nat,SV576: nat,SV118: nat] :
( ( ( ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) )
= $false )
| ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3709]) ).
thf(3884,plain,
! [SV384: nat,SV576: nat,SV820: list_P559422087at_nat,SV118: nat] :
( ( ( ~ ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
| ( ( size_s1990949619at_nat @ SV820 )
!= SV384 ) )
= $true )
| ( ( ~ ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3710]) ).
thf(3885,plain,
! [SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a,SV689: nat,SV741: nat] :
( ( ( ord_less_nat @ SV741 @ SV689 )
= $false )
| ( ( ~ ! [SY1479: nat] :
~ ~ ( ~ ( connected_a @ SV120 @ SV386 @ SY1479 )
| ( ( min_dist_a @ SV120 @ SV386 @ SY1479 )
!= SV741 ) ) )
= $true )
| ( ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
= SV689 )
= $false )
| ( ( connected_a @ SV120 @ SV386 @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3711]) ).
thf(3886,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV387 @ SV690 @ SV771 )
| ~ ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) )
= $false )
| ( ( connected_a @ SV387 @ SV690 @ SV771 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3712]) ).
thf(3887,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) )
= $true )
| ( ( ~ ( ~ ( connected_a @ SV387 @ SV690 @ SV771 )
| ~ ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3713]) ).
thf(3888,plain,
! [SV391: nat,SV581: nat,SV691: nat,SV128: nat] :
( ( ( ! [SY1443: nat] :
~ ~ ( ~ ( connected_b @ c2 @ SV128 @ SY1443 )
| ( ( min_dist_b @ c2 @ SV128 @ SY1443 )
!= SV691 ) ) )
= $false )
| ( ( ord_less_nat @ SV691 @ SV581 )
= $false )
| ( ( ( min_dist_b @ c2 @ SV128 @ SV391 )
= SV581 )
= $false )
| ( ( connected_b @ c2 @ SV128 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3714]) ).
thf(3889,plain,
! [SV582: nat,SV692: nat > $o,SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ( dist_a @ SV129 @ SV392 @ ( sK42_SY1444 @ SV692 @ SV582 @ SV392 @ SV129 ) @ SV582 )
= $true )
| ( ( SV692 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) )
= $true )
| ( ( connected_a @ SV129 @ SV392 @ SV582 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3715]) ).
thf(3890,plain,
! [SV692: nat > $o,SV582: nat,SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1532: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1532 @ SV582 )
| ( ord_less_eq_nat @ ( sK42_SY1444 @ SV692 @ SV582 @ SV392 @ SV129 ) @ SY1532 ) ) )
= $false )
| ( ( SV692 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) )
= $true )
| ( ( connected_a @ SV129 @ SV392 @ SV582 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3716]) ).
thf(3891,plain,
! [SV129: product_prod_nat_nat > a,SV392: nat,SV582: nat,SV692: nat > $o] :
( ( ( SV692 @ ( sK42_SY1444 @ SV692 @ SV582 @ SV392 @ SV129 ) )
= $false )
| ( ( SV692 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) )
= $true )
| ( ( connected_a @ SV129 @ SV392 @ SV582 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3716]) ).
thf(3892,plain,
! [SV693: nat,SV583: nat,SV396: nat,SV134: product_prod_nat_nat > b] :
( ( ( ~ ( ~ ( connected_b @ SV134 @ SV396 @ ( sK48_SY1446 @ SV583 @ SV693 @ SV396 @ SV134 ) )
| ( ( min_dist_b @ SV134 @ SV396 @ ( sK48_SY1446 @ SV583 @ SV693 @ SV396 @ SV134 ) )
!= SV693 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV693 @ ( min_dist_b @ SV134 @ SV396 @ SV583 ) )
= $false )
| ( ( connected_b @ SV134 @ SV396 @ SV583 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3717]) ).
thf(3893,plain,
! [SV398: nat,SV136: nat] :
( ( ( ~ ( isPath_a @ c @ SV136 @ ( sK50_SY1164 @ SV398 @ SV136 ) @ SV398 ) )
= $false )
| ( ( connected_a @ c @ SV136 @ SV398 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3718]) ).
thf(3894,plain,
! [SV808: list_P559422087at_nat,SV398: nat,SV136: nat] :
( ( ( ~ ( connected_a @ c @ SV136 @ SV398 ) )
= $false )
| ( ( isPath_a @ c @ SV136 @ SV808 @ SV398 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3719]) ).
thf(3895,plain,
! [SV808: list_P559422087at_nat,SV398: nat,SV136: nat] :
( ( ( ~ ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) )
= $false )
| ( ( isPath_a @ c @ SV136 @ SV808 @ SV398 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3719]) ).
thf(3896,plain,
! [SV137: set_nat,SV399: nat] :
( ( ( ~ ~ ( ~ ( member_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV137 )
| ~ ( ord_less_eq_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV399 ) ) )
= $false )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3720]) ).
thf(3897,plain,
! [SV399: nat,SV137: set_nat] :
( ( ( ~ ! [SY1522: nat] :
( ~ ( member_nat @ SY1522 @ SV137 )
| ~ ( ord_less_eq_nat @ SY1522 @ ( sK29_SY1165 @ SV399 @ SV137 ) )
| ( ( sK29_SY1165 @ SV399 @ SV137 )
= SY1522 ) ) )
= $false )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3720]) ).
thf(3898,plain,
! [SV586: nat,SV403: nat,SV142: nat] :
( ( ( ~ ( connected_b @ c2 @ SV142 @ ( sK43_SY1370 @ SV403 @ SV586 @ SV142 ) )
| ( ( min_dist_b @ c2 @ SV142 @ ( sK43_SY1370 @ SV403 @ SV586 @ SV142 ) )
!= SV586 ) )
= $false )
| ( ( ord_less_eq_nat @ SV586 @ ( min_dist_b @ c2 @ SV142 @ SV403 ) )
= $false )
| ( ( connected_b @ c2 @ SV142 @ SV403 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3722]) ).
thf(3899,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ( ~ ( ~ ( finite772653738at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) )
| ( ( finite447719721at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) )
!= SV404 ) ) )
= $true )
| ( ( finite772653738at_nat @ SV143 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3723]) ).
thf(3900,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) @ SV143 )
= $true )
| ( ( finite772653738at_nat @ SV143 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3724]) ).
thf(3901,plain,
! [SV407: nat,SV146: nat] :
( ( ( ~ ( dist_a @ c @ SV146 @ ( sK51_SY1177 @ SV407 @ SV146 ) @ SV407 ) )
= $false )
| ( ( connected_a @ c @ SV146 @ SV407 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3725]) ).
thf(3902,plain,
! [SV809: nat,SV407: nat,SV146: nat] :
( ( ( ~ ( connected_a @ c @ SV146 @ SV407 ) )
= $false )
| ( ( dist_a @ c @ SV146 @ SV809 @ SV407 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3726]) ).
thf(3903,plain,
! [SV809: nat,SV407: nat,SV146: nat] :
( ( ( ~ ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) )
= $false )
| ( ( dist_a @ c @ SV146 @ SV809 @ SV407 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3726]) ).
thf(3904,plain,
! [SV697: nat,SV588: nat,SV408: nat,SV147: product_prod_nat_nat > b] :
( ( ( dist_b @ SV147 @ SV408 @ ( sK44_SY1448 @ SV588 @ SV697 @ SV408 @ SV147 ) @ SV697 )
= $true )
| ( ( ( min_dist_b @ SV147 @ SV408 @ SV697 )
= SV588 )
= $true )
| ( ( dist_b @ SV147 @ SV408 @ SV588 @ SV697 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3727]) ).
thf(3905,plain,
! [SV699: nat,SV591: nat,SV411: nat,SV151: product_prod_nat_nat > a] :
( ( ( ~ ( ~ ( connected_a @ SV151 @ SV411 @ ( sK49_SY1449 @ SV591 @ SV699 @ SV411 @ SV151 ) )
| ( ( min_dist_a @ SV151 @ SV411 @ ( sK49_SY1449 @ SV591 @ SV699 @ SV411 @ SV151 ) )
!= SV699 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV699 @ ( min_dist_a @ SV151 @ SV411 @ SV591 ) )
= $false )
| ( ( connected_a @ SV151 @ SV411 @ SV591 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3729]) ).
thf(3906,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3731]) ).
thf(3907,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV158: nat] :
( ( ( ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3732]) ).
thf(3908,plain,
! [SV594: nat,SV417: nat,SV159: nat > $o] :
( ( ( ! [SY852: nat] :
~ ~ ( ~ ( SV159 @ SY852 )
| ~ ! [SY853: nat] :
( ~ ( SV159 @ SY853 )
| ( ord_less_eq_nat @ SY853 @ SY852 ) ) ) )
= $false )
| ( ( SV159 @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3733]) ).
thf(3909,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( ~ ~ ( ~ ( SV159 @ ( sK52_SY852 @ SV594 @ SV417 @ SV159 ) )
| ~ ! [SY1535: nat] :
( ~ ( SV159 @ SY1535 )
| ( ord_less_eq_nat @ SY1535 @ ( sK52_SY852 @ SV594 @ SV417 @ SV159 ) ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) @ SV594 )
= $false )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3734]) ).
thf(3910,plain,
! [SV421: nat,SV597: nat,SV163: nat] :
( ( ( ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) )
= $false )
| ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3736]) ).
thf(3911,plain,
! [SV421: nat,SV597: nat,SV821: list_P559422087at_nat,SV163: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
| ( ( size_s1990949619at_nat @ SV821 )
!= SV421 ) )
= $true )
| ( ( ~ ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3737]) ).
thf(3912,plain,
! [SV164: set_set_nat,SV422: set_nat] :
( ( ( ~ ~ ( ~ ( member_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SV164 )
| ~ ( ord_less_eq_set_nat @ SV422 @ ( sK32_SY1199 @ SV422 @ SV164 ) ) ) )
= $false )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3738]) ).
thf(3913,plain,
! [SV422: set_nat,SV164: set_set_nat] :
( ( ( ~ ! [SY1523: set_nat] :
( ~ ( member_set_nat @ SY1523 @ SV164 )
| ~ ( ord_less_eq_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SY1523 )
| ( ( sK32_SY1199 @ SV422 @ SV164 )
= SY1523 ) ) )
= $false )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3738]) ).
thf(3914,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3739]) ).
thf(3915,plain,
! [SV167: nat > nat,SV600: nat,SV425: nat] :
( ( ( ord_less_eq_nat @ SV425 @ SV600 )
= $false )
| ( ( ord_less_eq_nat @ ( SV167 @ SV425 ) @ ( SV167 @ SV600 ) )
= $true )
| ( ( ord_less_nat @ ( sK14_SY873 @ SV600 @ SV425 @ SV167 ) @ ( sK18_SY1504 @ SV167 @ SV425 @ SV600 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3740]) ).
thf(3916,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ~ ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3742]) ).
thf(3917,plain,
! [SV171: nat > $o,SV427: nat,SV812: nat] :
( ( ( ~ ( ord_less_nat @ SV812 @ ( sK5_SY879 @ SV427 @ SV171 ) ) )
= $true )
| ( ( ~ ~ ( SV171 @ SV812 ) )
= $true )
| ( ( SV171 @ SV427 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3743]) ).
thf(3918,plain,
! [SV173: set_se1612935105at_nat,SV428: set_Pr1986765409at_nat] :
( ( ( ~ ~ ( ~ ( member298845450at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV173 )
| ~ ( ord_le841296385at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV428 ) ) )
= $false )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3744]) ).
thf(3919,plain,
! [SV428: set_Pr1986765409at_nat,SV173: set_se1612935105at_nat] :
( ( ( ~ ! [SY1525: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY1525 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY1525 @ ( sK33_SY1214 @ SV428 @ SV173 ) )
| ( ( sK33_SY1214 @ SV428 @ SV173 )
= SY1525 ) ) )
= $false )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3744]) ).
thf(3920,plain,
! [SV603: nat,SV703: nat > $o,SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ( dist_b @ SV176 @ SV431 @ ( sK45_SY1455 @ SV703 @ SV603 @ SV431 @ SV176 ) @ SV603 )
= $true )
| ( ( SV703 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) )
= $true )
| ( ( connected_b @ SV176 @ SV431 @ SV603 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3746]) ).
thf(3921,plain,
! [SV703: nat > $o,SV603: nat,SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1533: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1533 @ SV603 )
| ( ord_less_eq_nat @ ( sK45_SY1455 @ SV703 @ SV603 @ SV431 @ SV176 ) @ SY1533 ) ) )
= $false )
| ( ( SV703 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) )
= $true )
| ( ( connected_b @ SV176 @ SV431 @ SV603 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3747]) ).
thf(3922,plain,
! [SV176: product_prod_nat_nat > b,SV431: nat,SV603: nat,SV703: nat > $o] :
( ( ( SV703 @ ( sK45_SY1455 @ SV703 @ SV603 @ SV431 @ SV176 ) )
= $false )
| ( ( SV703 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) )
= $true )
| ( ( connected_b @ SV176 @ SV431 @ SV603 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3747]) ).
thf(3923,plain,
! [SV177: set_se1612935105at_nat,SV432: set_Pr1986765409at_nat] :
( ( ( ~ ~ ( ~ ( member298845450at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SV177 )
| ~ ( ord_le841296385at_nat @ SV432 @ ( sK34_SY1223 @ SV432 @ SV177 ) ) ) )
= $false )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3748]) ).
thf(3924,plain,
! [SV432: set_Pr1986765409at_nat,SV177: set_se1612935105at_nat] :
( ( ( ~ ! [SY1526: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY1526 @ SV177 )
| ~ ( ord_le841296385at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SY1526 )
| ( ( sK34_SY1223 @ SV432 @ SV177 )
= SY1526 ) ) )
= $false )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3748]) ).
thf(3925,plain,
! [SV178: nat,SV433: nat] :
( ( ( member_nat @ SV433 @ ( v_b @ c2 ) )
= $true )
| ( ( member_nat @ SV433 @ ( v_b @ c2 ) )
= $false )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3749]) ).
thf(3926,plain,
! [SV433: nat,SV178: nat] :
( ( ( member_nat @ SV178 @ ( v_b @ c2 ) )
= $true )
| ( ( member_nat @ SV433 @ ( v_b @ c2 ) )
= $false )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3750]) ).
thf(3927,plain,
! [SV178: nat,SV433: nat] :
( ( ( member_nat @ SV433 @ ( v_b @ c2 ) )
= $true )
| ( ( member_nat @ SV178 @ ( v_b @ c2 ) )
= $false )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3751]) ).
thf(3928,plain,
! [SV433: nat,SV178: nat] :
( ( ( member_nat @ SV178 @ ( v_b @ c2 ) )
= $true )
| ( ( member_nat @ SV178 @ ( v_b @ c2 ) )
= $false )
| ( ( connected_b @ c2 @ SV178 @ SV433 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3752]) ).
thf(3929,plain,
! [SV436: nat > $o,SV822: nat,SV182: nat > $o] :
( ( ( ~ ( SV182 @ SV822 ) )
= $true )
| ( ( SV436 @ SV822 )
= $true )
| ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3753]) ).
thf(3930,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ~ ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) ) )
= $false )
| ( ( SV182 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3754]) ).
thf(3931,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ~ ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) )
= $false )
| ( ( SV182 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3754]) ).
thf(3932,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
= $true )
| ( ( SV436 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3755]) ).
thf(3933,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) )
= $true )
| ( ( SV436 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3756]) ).
thf(3934,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( SV437 = SV704 )
= $true )
| ( ( SV437 = SV704 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3757]) ).
thf(3935,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) )
= $true )
| ( ( SV437 = SV704 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3758]) ).
thf(3936,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV437 @ SV704 )
= $false )
| ( ( ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) )
= $true )
| ( ( ~ ( ( SV437 != SV704 )
| ~ ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3759]) ).
thf(3937,plain,
! [SV438: set_Pr1986765409at_nat > $o,SV184: set_Pr1986765409at_nat,SV824: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le116442893at_nat @ SV824 @ ( sK20_SY1230 @ SV184 @ SV438 ) )
| ( SV438 @ SV824 ) )
= $true )
| ( ( SV438 @ SV184 )
= $true )
| ( ( finite772653738at_nat @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3760]) ).
thf(3938,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ~ ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3761]) ).
thf(3939,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV442 @ SV706 @ SV775 )
| ~ ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) )
= $false )
| ( ( connected_a @ SV442 @ SV706 @ SV775 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3762]) ).
thf(3940,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) )
= $true )
| ( ( ~ ( ~ ( connected_a @ SV442 @ SV706 @ SV775 )
| ~ ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3763]) ).
thf(3941,plain,
! [SV445: nat,SV191: nat] :
( ( ( ( min_dist_a @ c @ SV191 @ SV445 )
= zero_zero_nat )
= $true )
| ( ( ( min_dist_a @ c @ SV191 @ SV445 )
= zero_zero_nat )
= $false )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3764]) ).
thf(3942,plain,
! [SV191: nat,SV445: nat] :
( ( ( SV445 = SV191 )
= $true )
| ( ( ( min_dist_a @ c @ SV191 @ SV445 )
= zero_zero_nat )
= $false )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3765]) ).
thf(3943,plain,
! [SV445: nat,SV191: nat] :
( ( ( ( min_dist_a @ c @ SV191 @ SV445 )
= zero_zero_nat )
= $true )
| ( ( SV445 = SV191 )
= $false )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3766]) ).
thf(3944,plain,
! [SV191: nat,SV445: nat] :
( ( ( SV445 = SV191 )
= $true )
| ( ( SV445 = SV191 )
= $false )
| ( ( connected_a @ c @ SV191 @ SV445 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3767]) ).
thf(3945,plain,
! [SV193: nat,SV447: nat] :
( ( ( member_nat @ SV447 @ ( v_a @ c ) )
= $true )
| ( ( member_nat @ SV447 @ ( v_a @ c ) )
= $false )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3769]) ).
thf(3946,plain,
! [SV447: nat,SV193: nat] :
( ( ( member_nat @ SV193 @ ( v_a @ c ) )
= $true )
| ( ( member_nat @ SV447 @ ( v_a @ c ) )
= $false )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3770]) ).
thf(3947,plain,
! [SV193: nat,SV447: nat] :
( ( ( member_nat @ SV447 @ ( v_a @ c ) )
= $true )
| ( ( member_nat @ SV193 @ ( v_a @ c ) )
= $false )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3771]) ).
thf(3948,plain,
! [SV447: nat,SV193: nat] :
( ( ( member_nat @ SV193 @ ( v_a @ c ) )
= $true )
| ( ( member_nat @ SV193 @ ( v_a @ c ) )
= $false )
| ( ( connected_a @ c @ SV193 @ SV447 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3772]) ).
thf(3949,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ ( sK46_SY1241 @ SV196 @ SV449 ) @ SV449 )
| ~ ! [SY1534: nat] :
( ~ ( ord_less_nat @ SY1534 @ ( sK46_SY1241 @ SV196 @ SV449 ) )
| ~ ( SV196 @ SY1534 ) ) )
| ~ ( SV196 @ ( sK46_SY1241 @ SV196 @ SV449 ) ) )
= $false )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3773]) ).
thf(3950,plain,
! [SV200: set_nat,SV453: nat] :
( ( ( ~ ~ ( ~ ( member_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SV200 )
| ~ ( ord_less_eq_nat @ SV453 @ ( sK35_SY1245 @ SV453 @ SV200 ) ) ) )
= $false )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3774]) ).
thf(3951,plain,
! [SV453: nat,SV200: set_nat] :
( ( ( ~ ! [SY1527: nat] :
( ~ ( member_nat @ SY1527 @ SV200 )
| ~ ( ord_less_eq_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SY1527 )
| ( ( sK35_SY1245 @ SV453 @ SV200 )
= SY1527 ) ) )
= $false )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3774]) ).
thf(3952,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) )
= $false )
| ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3776]) ).
thf(3953,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV208: nat] :
( ( ( ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3777]) ).
thf(3954,plain,
! [SV615: nat > $o,SV462: nat,SV210: nat] :
( ( ( ! [SY1528: nat] :
( ~ ( dist_a @ c @ SV210 @ SY1528 @ SV462 )
| ( ord_less_eq_nat @ ( sK36_SY1400 @ SV615 @ SV462 @ SV210 ) @ SY1528 ) ) )
= $true )
| ( ( SV615 @ ( min_dist_a @ c @ SV210 @ SV462 ) )
= $true )
| ( ( connected_a @ c @ SV210 @ SV462 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3779]) ).
thf(3955,plain,
! [SV466: nat,SV215: nat] :
( ( ( ~ ( dist_b @ c2 @ SV215 @ ( sK53_SY1258 @ SV466 @ SV215 ) @ SV466 ) )
= $false )
| ( ( connected_b @ c2 @ SV215 @ SV466 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3781]) ).
thf(3956,plain,
! [SV816: nat,SV466: nat,SV215: nat] :
( ( ( ~ ( connected_b @ c2 @ SV215 @ SV466 ) )
= $false )
| ( ( dist_b @ c2 @ SV215 @ SV816 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3782]) ).
thf(3957,plain,
! [SV816: nat,SV466: nat,SV215: nat] :
( ( ( ~ ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) )
= $false )
| ( ( dist_b @ c2 @ SV215 @ SV816 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3782]) ).
thf(3958,plain,
! [SV469: set_nat > $o,SV219: set_nat,SV825: set_nat] :
( ( ( ~ ( ord_less_set_nat @ SV825 @ ( sK22_SY1261 @ SV219 @ SV469 ) )
| ( SV469 @ SV825 ) )
= $true )
| ( ( SV469 @ SV219 )
= $true )
| ( ( finite_finite_nat @ SV219 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3784]) ).
thf(3959,plain,
! [SV470: nat,SV220: nat] :
( ( ( SV220 = SV470 )
= $false )
| ( ( SV220 = SV470 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3785]) ).
thf(3960,plain,
! [SV470: nat,SV220: nat] :
( ( ( ord_less_nat @ SV220 @ SV470 )
= $true )
| ( ( ord_less_nat @ SV470 @ SV220 )
= $true )
| ( ( SV220 = SV470 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3786]) ).
thf(3961,plain,
! [SV470: nat,SV220: nat] :
( ( ( SV220 = SV470 )
= $false )
| ( ( ord_less_nat @ SV220 @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3787]) ).
thf(3962,plain,
! [SV470: nat,SV220: nat] :
( ( ( ord_less_nat @ SV220 @ SV470 )
= $true )
| ( ( ord_less_nat @ SV470 @ SV220 )
= $true )
| ( ( ord_less_nat @ SV220 @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3788]) ).
thf(3963,plain,
! [SV470: nat,SV220: nat] :
( ( ( SV220 = SV470 )
= $false )
| ( ( ord_less_nat @ SV470 @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3789]) ).
thf(3964,plain,
! [SV470: nat,SV220: nat] :
( ( ( ord_less_nat @ SV220 @ SV470 )
= $true )
| ( ( ord_less_nat @ SV470 @ SV220 )
= $true )
| ( ( ord_less_nat @ SV470 @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3790]) ).
thf(3965,plain,
! [SV472: nat,SV222: nat > $o] :
( ( ( SV222 @ ( sK24_SY974 @ SV472 @ SV222 ) )
= $false )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3791]) ).
thf(3966,plain,
! [SV222: nat > $o,SV472: nat,SV826: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV826 @ ( sK24_SY974 @ SV472 @ SV222 ) )
| ~ ~ ( SV222 @ SV826 ) ) )
= $true )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3792]) ).
thf(3967,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ SV224 )
= $true )
| ( ( finite772653738at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3795]) ).
thf(3968,plain,
! [SV474: nat,SV224: set_Pr1986765409at_nat] :
( ( ( ord_less_eq_nat @ ( finite447719721at_nat @ SV224 ) @ SV474 )
= $true )
| ( ( finite772653738at_nat @ ( sK8_SY1267 @ SV474 @ SV224 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3796]) ).
thf(3969,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( finite_finite_nat @ SV226 )
= $true )
| ( ( finite_finite_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3801]) ).
thf(3970,plain,
! [SV476: nat,SV226: set_nat] :
( ( ( ord_less_eq_nat @ ( finite_card_nat @ SV226 ) @ SV476 )
= $true )
| ( ( finite_finite_nat @ ( sK9_SY1268 @ SV476 @ SV226 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3802]) ).
thf(3971,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) )
= $false )
| ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3806]) ).
thf(3972,plain,
! [SV620: nat,SV229: nat,SV478: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV478 )
= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $false )
| ( ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
| ~ ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3807]) ).
thf(3973,plain,
! [SV621: nat,SV481: nat,SV233: product_prod_nat_nat > a] :
( ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
!= zero_zero_nat )
= $false )
| ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
= zero_zero_nat )
= $false )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3808]) ).
thf(3974,plain,
! [SV233: product_prod_nat_nat > a,SV481: nat,SV621: nat] :
( ( ( SV621 != SV481 )
= $false )
| ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
= zero_zero_nat )
= $false )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3808]) ).
thf(3975,plain,
! [SV621: nat,SV481: nat,SV233: product_prod_nat_nat > a] :
( ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
!= zero_zero_nat )
= $false )
| ( ( SV621 = SV481 )
= $false )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3809]) ).
thf(3976,plain,
! [SV233: product_prod_nat_nat > a,SV481: nat,SV621: nat] :
( ( ( SV621 != SV481 )
= $false )
| ( ( SV621 = SV481 )
= $false )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3809]) ).
thf(3977,plain,
! [SV484: nat,SV237: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV237 @ ( sK54_SY1277 @ SV484 @ SV237 ) @ SV484 ) )
= $false )
| ( ( connected_b @ c2 @ SV237 @ SV484 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3810]) ).
thf(3978,plain,
! [SV817: list_P559422087at_nat,SV484: nat,SV237: nat] :
( ( ( ~ ( connected_b @ c2 @ SV237 @ SV484 ) )
= $false )
| ( ( isPath_b @ c2 @ SV237 @ SV817 @ SV484 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3811]) ).
thf(3979,plain,
! [SV817: list_P559422087at_nat,SV484: nat,SV237: nat] :
( ( ( ~ ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) )
= $false )
| ( ( isPath_b @ c2 @ SV237 @ SV817 @ SV484 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3811]) ).
thf(3980,plain,
! [SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3812]) ).
thf(3981,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) )
= $false )
| ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3814]) ).
thf(3982,plain,
! [SV626: nat,SV248: nat,SV489: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV489 )
= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $false )
| ( ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
| ~ ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3815]) ).
thf(3983,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV491 @ SV713 @ SV777 )
| ~ ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) )
= $false )
| ( ( connected_b @ SV491 @ SV713 @ SV777 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3816]) ).
thf(3984,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) )
= $true )
| ( ( ~ ( ~ ( connected_b @ SV491 @ SV713 @ SV777 )
| ~ ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3817]) ).
thf(3985,plain,
! [SV494: nat,SV254: product_prod_nat_nat > b,SV629: nat] :
( ( ( ~ ( member_nat @ SV629 @ ( v_b @ SV254 ) ) )
= $false )
| ( ( member_nat @ SV629 @ ( v_b @ SV254 ) )
= $false )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3818]) ).
thf(3986,plain,
! [SV629: nat,SV254: product_prod_nat_nat > b,SV494: nat] :
( ( ( ~ ( member_nat @ SV494 @ ( v_b @ SV254 ) ) )
= $false )
| ( ( member_nat @ SV629 @ ( v_b @ SV254 ) )
= $false )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3818]) ).
thf(3987,plain,
! [SV494: nat,SV254: product_prod_nat_nat > b,SV629: nat] :
( ( ( ~ ( member_nat @ SV629 @ ( v_b @ SV254 ) ) )
= $false )
| ( ( member_nat @ SV494 @ ( v_b @ SV254 ) )
= $false )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3819]) ).
thf(3988,plain,
! [SV629: nat,SV254: product_prod_nat_nat > b,SV494: nat] :
( ( ( ~ ( member_nat @ SV494 @ ( v_b @ SV254 ) ) )
= $false )
| ( ( member_nat @ SV494 @ ( v_b @ SV254 ) )
= $false )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3819]) ).
thf(3989,plain,
! [SV630: nat,SV495: nat,SV255: product_prod_nat_nat > b] :
( ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
!= zero_zero_nat )
= $false )
| ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
= zero_zero_nat )
= $false )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3820]) ).
thf(3990,plain,
! [SV255: product_prod_nat_nat > b,SV495: nat,SV630: nat] :
( ( ( SV630 != SV495 )
= $false )
| ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
= zero_zero_nat )
= $false )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3820]) ).
thf(3991,plain,
! [SV630: nat,SV495: nat,SV255: product_prod_nat_nat > b] :
( ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
!= zero_zero_nat )
= $false )
| ( ( SV630 = SV495 )
= $false )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3821]) ).
thf(3992,plain,
! [SV255: product_prod_nat_nat > b,SV495: nat,SV630: nat] :
( ( ( SV630 != SV495 )
= $false )
| ( ( SV630 = SV495 )
= $false )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3821]) ).
thf(3993,plain,
! [SV498: product_prod_nat_nat > $o,SV823: product_prod_nat_nat,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ( SV259 @ SV823 ) )
= $true )
| ( ( SV498 @ SV823 )
= $true )
| ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3822]) ).
thf(3994,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) ) )
= $false )
| ( ( SV259 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3823]) ).
thf(3995,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) )
= $false )
| ( ( SV259 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3823]) ).
thf(3996,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
= $true )
| ( ( SV498 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3824]) ).
thf(3997,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) )
= $true )
| ( ( SV498 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3825]) ).
thf(3998,plain,
! [SV499: nat,SV632: nat,SV714: nat,SV260: nat] :
( ( ( ! [SY1466: nat] :
~ ~ ( ~ ( connected_a @ c @ SV260 @ SY1466 )
| ( ( min_dist_a @ c @ SV260 @ SY1466 )
!= SV714 ) ) )
= $false )
| ( ( ord_less_nat @ SV714 @ SV632 )
= $false )
| ( ( ( min_dist_a @ c @ SV260 @ SV499 )
= SV632 )
= $false )
| ( ( connected_a @ c @ SV260 @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3826]) ).
thf(3999,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ~ ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3827]) ).
thf(4000,plain,
! [SV634: nat,SV502: nat,SV264: nat] :
( ( ( ~ ( connected_a @ c @ SV264 @ ( sK47_SY1417 @ SV502 @ SV634 @ SV264 ) )
| ( ( min_dist_a @ c @ SV264 @ ( sK47_SY1417 @ SV502 @ SV634 @ SV264 ) )
!= SV634 ) )
= $false )
| ( ( ord_less_eq_nat @ SV634 @ ( min_dist_a @ c @ SV264 @ SV502 ) )
= $false )
| ( ( connected_a @ c @ SV264 @ SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3828]) ).
thf(4001,plain,
! [SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b,SV716: nat,SV750: nat] :
( ( ( ord_less_nat @ SV750 @ SV716 )
= $false )
| ( ( ~ ! [SY1494: nat] :
~ ~ ( ~ ( connected_b @ SV265 @ SV503 @ SY1494 )
| ( ( min_dist_b @ SV265 @ SV503 @ SY1494 )
!= SV750 ) ) )
= $true )
| ( ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
= SV716 )
= $false )
| ( ( connected_b @ SV265 @ SV503 @ SV635 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3829]) ).
thf(4002,plain,
! [SV508: nat,SV270: set_nat] :
( ( ( ~ ( ~ ( finite_finite_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) )
| ( ( finite_card_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) )
!= SV508 ) ) )
= $true )
| ( ( finite_finite_nat @ SV270 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3830]) ).
thf(4003,plain,
! [SV508: nat,SV270: set_nat] :
( ( ( ord_less_eq_set_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) @ SV270 )
= $true )
| ( ( finite_finite_nat @ SV270 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3831]) ).
thf(4004,plain,
! [SV273: set_set_nat,SV509: set_nat] :
( ( ( ~ ~ ( ~ ( member_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV273 )
| ~ ( ord_less_eq_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV509 ) ) )
= $false )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3833]) ).
thf(4005,plain,
! [SV509: set_nat,SV273: set_set_nat] :
( ( ( ~ ! [SY1530: set_nat] :
( ~ ( member_set_nat @ SY1530 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1530 @ ( sK37_SY1310 @ SV509 @ SV273 ) )
| ( ( sK37_SY1310 @ SV509 @ SV273 )
= SY1530 ) ) )
= $false )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3833]) ).
thf(4006,plain,
! [SV274: product_prod_nat_nat > $o,SV510: product_prod_nat_nat > $o] :
( ( ( SV510 @ ( sK12_SY1312 @ SV510 @ SV274 ) )
= $false )
| ( ( SV274 @ ( sK12_SY1312 @ SV510 @ SV274 ) )
= $false )
| ( ( ( collec7649004at_nat @ SV274 )
= ( collec7649004at_nat @ SV510 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3834]) ).
thf(4007,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV519 @ SV719 @ SV779 )
| ~ ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) )
= $false )
| ( ( connected_b @ SV519 @ SV719 @ SV779 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3836]) ).
thf(4008,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) )
= $true )
| ( ( ~ ( ~ ( connected_b @ SV519 @ SV719 @ SV779 )
| ~ ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3837]) ).
thf(4009,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3839]) ).
thf(4010,plain,
! [SV648: nat,SV293: nat,SV525: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV525 )
= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $false )
| ( ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ~ ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3840]) ).
thf(4011,plain,
! [SV721: nat,SV530: nat] :
( ( ( ord_less_nat @ SV530 @ SV721 )
= $true )
| ( ( ord_less_nat @ SV530 @ SV721 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3841]) ).
thf(4012,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV530 @ SV721 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3842]) ).
thf(4013,plain,
! [SV721: nat,SV530: nat] :
( ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $false )
| ( ( ~ ( ( SV530 != SV721 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV530 @ SV721 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3843]) ).
thf(4014,plain,
! [SV653: nat > $o,SV533: nat,SV304: nat] :
( ( ( ! [SY1531: nat] :
( ~ ( dist_b @ c2 @ SV304 @ SY1531 @ SV533 )
| ( ord_less_eq_nat @ ( sK40_SY1428 @ SV653 @ SV533 @ SV304 ) @ SY1531 ) ) )
= $true )
| ( ( SV653 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) )
= $true )
| ( ( connected_b @ c2 @ SV304 @ SV533 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3845]) ).
thf(4015,plain,
! [SV660: nat,SV323: nat] :
( ( ( ord_less_nat @ SV323 @ SV660 )
= $true )
| ( ( SV323 = SV660 )
= $true )
| ( ( ord_less_eq_nat @ SV323 @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3848]) ).
thf(4016,plain,
! [SV660: nat,SV323: nat] :
( ( ( ord_less_eq_nat @ SV323 @ SV660 )
= $true )
| ( ( ord_less_nat @ SV323 @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3849]) ).
thf(4017,plain,
! [SV660: nat,SV323: nat] :
( ( ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) )
= $true )
| ( ( ord_less_nat @ SV323 @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3850]) ).
thf(4018,plain,
! [SV660: nat,SV323: nat] :
( ( ( ord_less_eq_nat @ SV323 @ SV660 )
= $true )
| ( ( SV323 = SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3851]) ).
thf(4019,plain,
! [SV660: nat,SV323: nat] :
( ( ( ( ord_less_nat @ SV323 @ SV660 )
| ( SV323 = SV660 ) )
= $true )
| ( ( SV323 = SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3852]) ).
thf(4020,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $false )
| ( ( ~ ( ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
| ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3853]) ).
thf(4021,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $false )
| ( ( ~ ( ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
| ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3853]) ).
thf(4022,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $false )
| ( ( ~ ( ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
| ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3854]) ).
thf(4023,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $false )
| ( ( ~ ( ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
| ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3854]) ).
thf(4024,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV330 @ SV665 @ SV760 ) )
= $false )
| ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3855]) ).
thf(4025,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV330 @ SV665 @ SV760 ) )
= $false )
| ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3855]) ).
thf(4026,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV330 @ SV665 @ SV760 ) )
= $false )
| ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3856]) ).
thf(4027,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV330 @ SV665 @ SV760 ) )
= $false )
| ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3856]) ).
thf(4028,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV331 @ SV666 @ SV761 ) )
= $false )
| ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3857]) ).
thf(4029,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV331 @ SV666 @ SV761 ) )
= $false )
| ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3857]) ).
thf(4030,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV331 @ SV666 @ SV761 ) )
= $false )
| ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3858]) ).
thf(4031,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV331 @ SV666 @ SV761 ) )
= $false )
| ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3858]) ).
thf(4032,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $false )
| ( ( ~ ( ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
| ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3859]) ).
thf(4033,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $false )
| ( ( ~ ( ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
| ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3859]) ).
thf(4034,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $false )
| ( ( ~ ( ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
| ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3860]) ).
thf(4035,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $false )
| ( ( ~ ( ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
| ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3860]) ).
thf(4036,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
| ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3861]) ).
thf(4037,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
| ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3861]) ).
thf(4038,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
| ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3862]) ).
thf(4039,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
| ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3862]) ).
thf(4040,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $false )
| ( ( ~ ( ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
| ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3863]) ).
thf(4041,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $false )
| ( ( ~ ( ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
| ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3863]) ).
thf(4042,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $false )
| ( ( ~ ( ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
| ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3864]) ).
thf(4043,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $false )
| ( ( ~ ( ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
| ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3864]) ).
thf(4044,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ~ ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3865]) ).
thf(4045,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ~ ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3865]) ).
thf(4046,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3866]) ).
thf(4047,plain,
! [SV566: nat,SV97: nat,SV367: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3866]) ).
thf(4048,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3867]) ).
thf(4049,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) )
= $false )
| ( ( SV372 = SV683 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3869]) ).
thf(4050,plain,
! [SV372: set_nat,SV683: set_nat] :
( ( ( ord_less_eq_set_nat @ SV683 @ SV372 )
= $false )
| ( ( ord_less_eq_set_nat @ SV372 @ SV683 )
= $false )
| ( ( ~ ( ( SV372 != SV683 )
| ~ ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3870]) ).
thf(4051,plain,
! [SV378: nat,SV111: product_prod_nat_nat > a,SV571: nat] :
( ( ( member_nat @ SV571 @ ( v_a @ SV111 ) )
= $true )
| ( ( member_nat @ SV571 @ ( v_a @ SV111 ) )
= $false )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3872]) ).
thf(4052,plain,
! [SV571: nat,SV111: product_prod_nat_nat > a,SV378: nat] :
( ( ( member_nat @ SV378 @ ( v_a @ SV111 ) )
= $true )
| ( ( member_nat @ SV571 @ ( v_a @ SV111 ) )
= $false )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3873]) ).
thf(4053,plain,
! [SV378: nat,SV111: product_prod_nat_nat > a,SV571: nat] :
( ( ( member_nat @ SV571 @ ( v_a @ SV111 ) )
= $true )
| ( ( member_nat @ SV378 @ ( v_a @ SV111 ) )
= $false )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3874]) ).
thf(4054,plain,
! [SV571: nat,SV111: product_prod_nat_nat > a,SV378: nat] :
( ( ( member_nat @ SV378 @ ( v_a @ SV111 ) )
= $true )
| ( ( member_nat @ SV378 @ ( v_a @ SV111 ) )
= $false )
| ( ( connected_a @ SV111 @ SV378 @ SV571 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3875]) ).
thf(4055,plain,
! [SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $false )
| ( ( ~ ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3876]) ).
thf(4056,plain,
! [SV769: nat,SV806: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3876]) ).
thf(4057,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3877]) ).
thf(4058,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3877]) ).
thf(4059,plain,
! [SV576: nat,SV384: nat,SV118: nat] :
( ( ( ~ ~ ( ~ ( isPath_a @ c @ SV118 @ ( sK55_SY1353 @ SV384 @ SV576 @ SV118 ) @ SV576 )
| ( ( size_s1990949619at_nat @ ( sK55_SY1353 @ SV384 @ SV576 @ SV118 ) )
!= SV384 ) ) )
= $false )
| ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3883]) ).
thf(4060,plain,
! [SV384: nat,SV576: nat,SV820: list_P559422087at_nat,SV118: nat] :
( ( ( ~ ( isPath_a @ c @ SV118 @ SV820 @ SV576 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV820 )
!= SV384 )
= $true )
| ( ( ~ ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3884]) ).
thf(4061,plain,
! [SV577: nat,SV689: nat,SV741: nat,SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ( ! [SY1479: nat] :
~ ~ ( ~ ( connected_a @ SV120 @ SV386 @ SY1479 )
| ( ( min_dist_a @ SV120 @ SV386 @ SY1479 )
!= SV741 ) ) )
= $false )
| ( ( ord_less_nat @ SV741 @ SV689 )
= $false )
| ( ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
= SV689 )
= $false )
| ( ( connected_a @ SV120 @ SV386 @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3885]) ).
thf(4062,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV387 @ SV690 @ SV771 ) )
= $false )
| ( ( connected_a @ SV387 @ SV690 @ SV771 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3886]) ).
thf(4063,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ~ ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) )
= $false )
| ( ( connected_a @ SV387 @ SV690 @ SV771 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3886]) ).
thf(4064,plain,
! [SV771: nat,SV827: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV387 @ SV690 @ SV827 @ SV771 ) )
= $true )
| ( ( ~ ( ~ ( connected_a @ SV387 @ SV690 @ SV771 )
| ~ ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3887]) ).
thf(4065,plain,
! [SV691: nat,SV581: nat,SV391: nat,SV128: nat] :
( ( ( ~ ~ ( ~ ( connected_b @ c2 @ SV128 @ ( sK56_SY1443 @ SV391 @ SV581 @ SV691 @ SV128 ) )
| ( ( min_dist_b @ c2 @ SV128 @ ( sK56_SY1443 @ SV391 @ SV581 @ SV691 @ SV128 ) )
!= SV691 ) ) )
= $false )
| ( ( ord_less_nat @ SV691 @ SV581 )
= $false )
| ( ( ( min_dist_b @ c2 @ SV128 @ SV391 )
= SV581 )
= $false )
| ( ( connected_b @ c2 @ SV128 @ SV391 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3888]) ).
thf(4066,plain,
! [SV692: nat > $o,SV582: nat,SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ( ! [SY1532: nat] :
( ~ ( dist_a @ SV129 @ SV392 @ SY1532 @ SV582 )
| ( ord_less_eq_nat @ ( sK42_SY1444 @ SV692 @ SV582 @ SV392 @ SV129 ) @ SY1532 ) ) )
= $true )
| ( ( SV692 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) )
= $true )
| ( ( connected_a @ SV129 @ SV392 @ SV582 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3890]) ).
thf(4067,plain,
! [SV693: nat,SV583: nat,SV396: nat,SV134: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV134 @ SV396 @ ( sK48_SY1446 @ SV583 @ SV693 @ SV396 @ SV134 ) )
| ( ( min_dist_b @ SV134 @ SV396 @ ( sK48_SY1446 @ SV583 @ SV693 @ SV396 @ SV134 ) )
!= SV693 ) )
= $false )
| ( ( ord_less_eq_nat @ SV693 @ ( min_dist_b @ SV134 @ SV396 @ SV583 ) )
= $false )
| ( ( connected_b @ SV134 @ SV396 @ SV583 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3892]) ).
thf(4068,plain,
! [SV398: nat,SV136: nat] :
( ( ( isPath_a @ c @ SV136 @ ( sK50_SY1164 @ SV398 @ SV136 ) @ SV398 )
= $true )
| ( ( connected_a @ c @ SV136 @ SV398 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3893]) ).
thf(4069,plain,
! [SV808: list_P559422087at_nat,SV398: nat,SV136: nat] :
( ( ( connected_a @ c @ SV136 @ SV398 )
= $true )
| ( ( isPath_a @ c @ SV136 @ SV808 @ SV398 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3894]) ).
thf(4070,plain,
! [SV808: list_P559422087at_nat,SV398: nat,SV136: nat] :
( ( ( ~ ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) )
= $true )
| ( ( isPath_a @ c @ SV136 @ SV808 @ SV398 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3895]) ).
thf(4071,plain,
! [SV137: set_nat,SV399: nat] :
( ( ( ~ ( ~ ( member_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV137 )
| ~ ( ord_less_eq_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV399 ) ) )
= $true )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3896]) ).
thf(4072,plain,
! [SV399: nat,SV137: set_nat] :
( ( ( ! [SY1522: nat] :
( ~ ( member_nat @ SY1522 @ SV137 )
| ~ ( ord_less_eq_nat @ SY1522 @ ( sK29_SY1165 @ SV399 @ SV137 ) )
| ( ( sK29_SY1165 @ SV399 @ SV137 )
= SY1522 ) ) )
= $true )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3897]) ).
thf(4073,plain,
! [SV586: nat,SV403: nat,SV142: nat] :
( ( ( ~ ( connected_b @ c2 @ SV142 @ ( sK43_SY1370 @ SV403 @ SV586 @ SV142 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV586 @ ( min_dist_b @ c2 @ SV142 @ SV403 ) )
= $false )
| ( ( connected_b @ c2 @ SV142 @ SV403 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3898]) ).
thf(4074,plain,
! [SV586: nat,SV403: nat,SV142: nat] :
( ( ( ( min_dist_b @ c2 @ SV142 @ ( sK43_SY1370 @ SV403 @ SV586 @ SV142 ) )
!= SV586 )
= $false )
| ( ( ord_less_eq_nat @ SV586 @ ( min_dist_b @ c2 @ SV142 @ SV403 ) )
= $false )
| ( ( connected_b @ c2 @ SV142 @ SV403 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3898]) ).
thf(4075,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) )
| ( ( finite447719721at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) )
!= SV404 ) )
= $false )
| ( ( finite772653738at_nat @ SV143 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3899]) ).
thf(4076,plain,
! [SV407: nat,SV146: nat] :
( ( ( dist_a @ c @ SV146 @ ( sK51_SY1177 @ SV407 @ SV146 ) @ SV407 )
= $true )
| ( ( connected_a @ c @ SV146 @ SV407 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3901]) ).
thf(4077,plain,
! [SV809: nat,SV407: nat,SV146: nat] :
( ( ( connected_a @ c @ SV146 @ SV407 )
= $true )
| ( ( dist_a @ c @ SV146 @ SV809 @ SV407 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3902]) ).
thf(4078,plain,
! [SV809: nat,SV407: nat,SV146: nat] :
( ( ( ~ ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) )
= $true )
| ( ( dist_a @ c @ SV146 @ SV809 @ SV407 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3903]) ).
thf(4079,plain,
! [SV699: nat,SV591: nat,SV411: nat,SV151: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV151 @ SV411 @ ( sK49_SY1449 @ SV591 @ SV699 @ SV411 @ SV151 ) )
| ( ( min_dist_a @ SV151 @ SV411 @ ( sK49_SY1449 @ SV591 @ SV699 @ SV411 @ SV151 ) )
!= SV699 ) )
= $false )
| ( ( ord_less_eq_nat @ SV699 @ ( min_dist_a @ SV151 @ SV411 @ SV591 ) )
= $false )
| ( ( connected_a @ SV151 @ SV411 @ SV591 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3905]) ).
thf(4080,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3906]) ).
thf(4081,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV158: nat] :
( ( ( ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3906]) ).
thf(4082,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3907]) ).
thf(4083,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( ~ ~ ( ~ ( SV159 @ ( sK58_SY852 @ SV594 @ SV417 @ SV159 ) )
| ~ ! [SY1536: nat] :
( ~ ( SV159 @ SY1536 )
| ( ord_less_eq_nat @ SY1536 @ ( sK58_SY852 @ SV594 @ SV417 @ SV159 ) ) ) ) )
= $false )
| ( ( SV159 @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3908]) ).
thf(4084,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( ~ ( ~ ( SV159 @ ( sK52_SY852 @ SV594 @ SV417 @ SV159 ) )
| ~ ! [SY1535: nat] :
( ~ ( SV159 @ SY1535 )
| ( ord_less_eq_nat @ SY1535 @ ( sK52_SY852 @ SV594 @ SV417 @ SV159 ) ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) @ SV594 )
= $false )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3909]) ).
thf(4085,plain,
! [SV597: nat,SV421: nat,SV163: nat] :
( ( ( ~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ ( sK59_SY1382 @ SV421 @ SV597 @ SV163 ) @ SV597 )
| ( ( size_s1990949619at_nat @ ( sK59_SY1382 @ SV421 @ SV597 @ SV163 ) )
!= SV421 ) ) )
= $false )
| ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3910]) ).
thf(4086,plain,
! [SV421: nat,SV597: nat,SV821: list_P559422087at_nat,SV163: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV821 )
!= SV421 )
= $true )
| ( ( ~ ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3911]) ).
thf(4087,plain,
! [SV164: set_set_nat,SV422: set_nat] :
( ( ( ~ ( ~ ( member_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SV164 )
| ~ ( ord_less_eq_set_nat @ SV422 @ ( sK32_SY1199 @ SV422 @ SV164 ) ) ) )
= $true )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3912]) ).
thf(4088,plain,
! [SV422: set_nat,SV164: set_set_nat] :
( ( ( ! [SY1523: set_nat] :
( ~ ( member_set_nat @ SY1523 @ SV164 )
| ~ ( ord_less_eq_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SY1523 )
| ( ( sK32_SY1199 @ SV422 @ SV164 )
= SY1523 ) ) )
= $true )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3913]) ).
thf(4089,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3914]) ).
thf(4090,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3914]) ).
thf(4091,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ~ ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3916]) ).
thf(4092,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ~ ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3916]) ).
thf(4093,plain,
! [SV171: nat > $o,SV427: nat,SV812: nat] :
( ( ( ord_less_nat @ SV812 @ ( sK5_SY879 @ SV427 @ SV171 ) )
= $false )
| ( ( ~ ~ ( SV171 @ SV812 ) )
= $true )
| ( ( SV171 @ SV427 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3917]) ).
thf(4094,plain,
! [SV173: set_se1612935105at_nat,SV428: set_Pr1986765409at_nat] :
( ( ( ~ ( ~ ( member298845450at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV173 )
| ~ ( ord_le841296385at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV428 ) ) )
= $true )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3918]) ).
thf(4095,plain,
! [SV428: set_Pr1986765409at_nat,SV173: set_se1612935105at_nat] :
( ( ( ! [SY1525: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY1525 @ SV173 )
| ~ ( ord_le841296385at_nat @ SY1525 @ ( sK33_SY1214 @ SV428 @ SV173 ) )
| ( ( sK33_SY1214 @ SV428 @ SV173 )
= SY1525 ) ) )
= $true )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3919]) ).
thf(4096,plain,
! [SV703: nat > $o,SV603: nat,SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ( ! [SY1533: nat] :
( ~ ( dist_b @ SV176 @ SV431 @ SY1533 @ SV603 )
| ( ord_less_eq_nat @ ( sK45_SY1455 @ SV703 @ SV603 @ SV431 @ SV176 ) @ SY1533 ) ) )
= $true )
| ( ( SV703 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) )
= $true )
| ( ( connected_b @ SV176 @ SV431 @ SV603 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3921]) ).
thf(4097,plain,
! [SV177: set_se1612935105at_nat,SV432: set_Pr1986765409at_nat] :
( ( ( ~ ( ~ ( member298845450at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SV177 )
| ~ ( ord_le841296385at_nat @ SV432 @ ( sK34_SY1223 @ SV432 @ SV177 ) ) ) )
= $true )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3923]) ).
thf(4098,plain,
! [SV432: set_Pr1986765409at_nat,SV177: set_se1612935105at_nat] :
( ( ( ! [SY1526: set_Pr1986765409at_nat] :
( ~ ( member298845450at_nat @ SY1526 @ SV177 )
| ~ ( ord_le841296385at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SY1526 )
| ( ( sK34_SY1223 @ SV432 @ SV177 )
= SY1526 ) ) )
= $true )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3924]) ).
thf(4099,plain,
! [SV436: nat > $o,SV822: nat,SV182: nat > $o] :
( ( ( SV182 @ SV822 )
= $false )
| ( ( SV436 @ SV822 )
= $true )
| ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3929]) ).
thf(4100,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ord_less_eq_set_nat @ ( collect_nat @ SV182 ) @ ( collect_nat @ SV436 ) )
= $true )
| ( ( SV182 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3930]) ).
thf(4101,plain,
! [SV436: nat > $o,SV182: nat > $o] :
( ( ( ! [SY1227: nat] :
( ~ ( SV182 @ SY1227 )
| ( SV436 @ SY1227 ) ) )
= $true )
| ( ( SV182 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3931]) ).
thf(4102,plain,
! [SV436: nat > $o,SV828: nat,SV182: nat > $o] :
( ( ( ~ ( SV182 @ SV828 )
| ( SV436 @ SV828 ) )
= $true )
| ( ( SV436 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3933]) ).
thf(4103,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) )
= $false )
| ( ( SV437 = SV704 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3935]) ).
thf(4104,plain,
! [SV437: set_Pr1986765409at_nat,SV704: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV704 @ SV437 )
= $false )
| ( ( ord_le841296385at_nat @ SV437 @ SV704 )
= $false )
| ( ( ~ ( ( SV437 != SV704 )
| ~ ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3936]) ).
thf(4105,plain,
! [SV438: set_Pr1986765409at_nat > $o,SV184: set_Pr1986765409at_nat,SV824: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le116442893at_nat @ SV824 @ ( sK20_SY1230 @ SV184 @ SV438 ) ) )
= $true )
| ( ( SV438 @ SV824 )
= $true )
| ( ( SV438 @ SV184 )
= $true )
| ( ( finite772653738at_nat @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3937]) ).
thf(4106,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ~ ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3938]) ).
thf(4107,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ~ ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3938]) ).
thf(4108,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV442 @ SV706 @ SV775 ) )
= $false )
| ( ( connected_a @ SV442 @ SV706 @ SV775 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3939]) ).
thf(4109,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ~ ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) )
= $false )
| ( ( connected_a @ SV442 @ SV706 @ SV775 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3939]) ).
thf(4110,plain,
! [SV775: nat,SV829: list_P559422087at_nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV442 @ SV706 @ SV829 @ SV775 ) )
= $true )
| ( ( ~ ( ~ ( connected_a @ SV442 @ SV706 @ SV775 )
| ~ ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3940]) ).
thf(4111,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ ( sK46_SY1241 @ SV196 @ SV449 ) @ SV449 )
| ~ ! [SY1534: nat] :
( ~ ( ord_less_nat @ SY1534 @ ( sK46_SY1241 @ SV196 @ SV449 ) )
| ~ ( SV196 @ SY1534 ) ) ) )
= $false )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3949]) ).
thf(4112,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( ~ ( SV196 @ ( sK46_SY1241 @ SV196 @ SV449 ) ) )
= $false )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3949]) ).
thf(4113,plain,
! [SV200: set_nat,SV453: nat] :
( ( ( ~ ( ~ ( member_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SV200 )
| ~ ( ord_less_eq_nat @ SV453 @ ( sK35_SY1245 @ SV453 @ SV200 ) ) ) )
= $true )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3950]) ).
thf(4114,plain,
! [SV453: nat,SV200: set_nat] :
( ( ( ! [SY1527: nat] :
( ~ ( member_nat @ SY1527 @ SV200 )
| ~ ( ord_less_eq_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SY1527 )
| ( ( sK35_SY1245 @ SV453 @ SV200 )
= SY1527 ) ) )
= $true )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3951]) ).
thf(4115,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 ) )
= $false )
| ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3952]) ).
thf(4116,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV208: nat] :
( ( ( ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) )
= $false )
| ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3952]) ).
thf(4117,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) ) ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3953]) ).
thf(4118,plain,
! [SV615: nat > $o,SV462: nat,SV830: nat,SV210: nat] :
( ( ( ~ ( dist_a @ c @ SV210 @ SV830 @ SV462 )
| ( ord_less_eq_nat @ ( sK36_SY1400 @ SV615 @ SV462 @ SV210 ) @ SV830 ) )
= $true )
| ( ( SV615 @ ( min_dist_a @ c @ SV210 @ SV462 ) )
= $true )
| ( ( connected_a @ c @ SV210 @ SV462 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3954]) ).
thf(4119,plain,
! [SV466: nat,SV215: nat] :
( ( ( dist_b @ c2 @ SV215 @ ( sK53_SY1258 @ SV466 @ SV215 ) @ SV466 )
= $true )
| ( ( connected_b @ c2 @ SV215 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3955]) ).
thf(4120,plain,
! [SV816: nat,SV466: nat,SV215: nat] :
( ( ( connected_b @ c2 @ SV215 @ SV466 )
= $true )
| ( ( dist_b @ c2 @ SV215 @ SV816 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3956]) ).
thf(4121,plain,
! [SV816: nat,SV466: nat,SV215: nat] :
( ( ( ~ ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) )
= $true )
| ( ( dist_b @ c2 @ SV215 @ SV816 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3957]) ).
thf(4122,plain,
! [SV469: set_nat > $o,SV219: set_nat,SV825: set_nat] :
( ( ( ~ ( ord_less_set_nat @ SV825 @ ( sK22_SY1261 @ SV219 @ SV469 ) ) )
= $true )
| ( ( SV469 @ SV825 )
= $true )
| ( ( SV469 @ SV219 )
= $true )
| ( ( finite_finite_nat @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3958]) ).
thf(4123,plain,
! [SV222: nat > $o,SV472: nat,SV826: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV826 @ ( sK24_SY974 @ SV472 @ SV222 ) )
| ~ ~ ( SV222 @ SV826 ) ) )
= $false )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3966]) ).
thf(4124,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 ) )
= $false )
| ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3971]) ).
thf(4125,plain,
! [SV620: nat,SV229: nat,SV478: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $false )
| ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3971]) ).
thf(4126,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
| ~ ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) )
= $false )
| ( ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV478 )
= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3972]) ).
thf(4127,plain,
! [SV621: nat,SV481: nat,SV233: product_prod_nat_nat > a] :
( ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
= zero_zero_nat )
= $true )
| ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
= zero_zero_nat )
= $false )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3973]) ).
thf(4128,plain,
! [SV233: product_prod_nat_nat > a,SV481: nat,SV621: nat] :
( ( ( SV621 = SV481 )
= $true )
| ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
= zero_zero_nat )
= $false )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3974]) ).
thf(4129,plain,
! [SV621: nat,SV481: nat,SV233: product_prod_nat_nat > a] :
( ( ( ( min_dist_a @ SV233 @ SV481 @ SV621 )
= zero_zero_nat )
= $true )
| ( ( SV621 = SV481 )
= $false )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3975]) ).
thf(4130,plain,
! [SV233: product_prod_nat_nat > a,SV481: nat,SV621: nat] :
( ( ( SV621 = SV481 )
= $true )
| ( ( SV621 = SV481 )
= $false )
| ( ( connected_a @ SV233 @ SV481 @ SV621 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3976]) ).
thf(4131,plain,
! [SV484: nat,SV237: nat] :
( ( ( isPath_b @ c2 @ SV237 @ ( sK54_SY1277 @ SV484 @ SV237 ) @ SV484 )
= $true )
| ( ( connected_b @ c2 @ SV237 @ SV484 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3977]) ).
thf(4132,plain,
! [SV817: list_P559422087at_nat,SV484: nat,SV237: nat] :
( ( ( connected_b @ c2 @ SV237 @ SV484 )
= $true )
| ( ( isPath_b @ c2 @ SV237 @ SV817 @ SV484 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3978]) ).
thf(4133,plain,
! [SV817: list_P559422087at_nat,SV484: nat,SV237: nat] :
( ( ( ~ ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) )
= $true )
| ( ( isPath_b @ c2 @ SV237 @ SV817 @ SV484 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3979]) ).
thf(4134,plain,
! [SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $false )
| ( ( ~ ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3980]) ).
thf(4135,plain,
! [SV776: nat,SV818: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3980]) ).
thf(4136,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 ) )
= $false )
| ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3981]) ).
thf(4137,plain,
! [SV626: nat,SV248: nat,SV489: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $false )
| ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3981]) ).
thf(4138,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
| ~ ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) )
= $false )
| ( ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV489 )
= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3982]) ).
thf(4139,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV491 @ SV713 @ SV777 ) )
= $false )
| ( ( connected_b @ SV491 @ SV713 @ SV777 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3983]) ).
thf(4140,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ~ ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) )
= $false )
| ( ( connected_b @ SV491 @ SV713 @ SV777 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3983]) ).
thf(4141,plain,
! [SV777: nat,SV831: list_P559422087at_nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV491 @ SV713 @ SV831 @ SV777 ) )
= $true )
| ( ( ~ ( ~ ( connected_b @ SV491 @ SV713 @ SV777 )
| ~ ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3984]) ).
thf(4142,plain,
! [SV494: nat,SV254: product_prod_nat_nat > b,SV629: nat] :
( ( ( member_nat @ SV629 @ ( v_b @ SV254 ) )
= $true )
| ( ( member_nat @ SV629 @ ( v_b @ SV254 ) )
= $false )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3985]) ).
thf(4143,plain,
! [SV629: nat,SV254: product_prod_nat_nat > b,SV494: nat] :
( ( ( member_nat @ SV494 @ ( v_b @ SV254 ) )
= $true )
| ( ( member_nat @ SV629 @ ( v_b @ SV254 ) )
= $false )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3986]) ).
thf(4144,plain,
! [SV494: nat,SV254: product_prod_nat_nat > b,SV629: nat] :
( ( ( member_nat @ SV629 @ ( v_b @ SV254 ) )
= $true )
| ( ( member_nat @ SV494 @ ( v_b @ SV254 ) )
= $false )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3987]) ).
thf(4145,plain,
! [SV629: nat,SV254: product_prod_nat_nat > b,SV494: nat] :
( ( ( member_nat @ SV494 @ ( v_b @ SV254 ) )
= $true )
| ( ( member_nat @ SV494 @ ( v_b @ SV254 ) )
= $false )
| ( ( connected_b @ SV254 @ SV494 @ SV629 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3988]) ).
thf(4146,plain,
! [SV630: nat,SV495: nat,SV255: product_prod_nat_nat > b] :
( ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
= zero_zero_nat )
= $true )
| ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
= zero_zero_nat )
= $false )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3989]) ).
thf(4147,plain,
! [SV255: product_prod_nat_nat > b,SV495: nat,SV630: nat] :
( ( ( SV630 = SV495 )
= $true )
| ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
= zero_zero_nat )
= $false )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3990]) ).
thf(4148,plain,
! [SV630: nat,SV495: nat,SV255: product_prod_nat_nat > b] :
( ( ( ( min_dist_b @ SV255 @ SV495 @ SV630 )
= zero_zero_nat )
= $true )
| ( ( SV630 = SV495 )
= $false )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3991]) ).
thf(4149,plain,
! [SV255: product_prod_nat_nat > b,SV495: nat,SV630: nat] :
( ( ( SV630 = SV495 )
= $true )
| ( ( SV630 = SV495 )
= $false )
| ( ( connected_b @ SV255 @ SV495 @ SV630 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3992]) ).
thf(4150,plain,
! [SV498: product_prod_nat_nat > $o,SV823: product_prod_nat_nat,SV259: product_prod_nat_nat > $o] :
( ( ( SV259 @ SV823 )
= $false )
| ( ( SV498 @ SV823 )
= $true )
| ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3993]) ).
thf(4151,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ SV259 ) @ ( collec7649004at_nat @ SV498 ) )
= $true )
| ( ( SV259 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3994]) ).
thf(4152,plain,
! [SV498: product_prod_nat_nat > $o,SV259: product_prod_nat_nat > $o] :
( ( ( ! [SY1292: product_prod_nat_nat] :
( ~ ( SV259 @ SY1292 )
| ( SV498 @ SY1292 ) ) )
= $true )
| ( ( SV259 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3995]) ).
thf(4153,plain,
! [SV498: product_prod_nat_nat > $o,SV832: product_prod_nat_nat,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ( SV259 @ SV832 )
| ( SV498 @ SV832 ) )
= $true )
| ( ( SV498 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3997]) ).
thf(4154,plain,
! [SV714: nat,SV632: nat,SV499: nat,SV260: nat] :
( ( ( ~ ~ ( ~ ( connected_a @ c @ SV260 @ ( sK61_SY1466 @ SV499 @ SV632 @ SV714 @ SV260 ) )
| ( ( min_dist_a @ c @ SV260 @ ( sK61_SY1466 @ SV499 @ SV632 @ SV714 @ SV260 ) )
!= SV714 ) ) )
= $false )
| ( ( ord_less_nat @ SV714 @ SV632 )
= $false )
| ( ( ( min_dist_a @ c @ SV260 @ SV499 )
= SV632 )
= $false )
| ( ( connected_a @ c @ SV260 @ SV499 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3998]) ).
thf(4155,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ~ ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3999]) ).
thf(4156,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ~ ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3999]) ).
thf(4157,plain,
! [SV634: nat,SV502: nat,SV264: nat] :
( ( ( ~ ( connected_a @ c @ SV264 @ ( sK47_SY1417 @ SV502 @ SV634 @ SV264 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV634 @ ( min_dist_a @ c @ SV264 @ SV502 ) )
= $false )
| ( ( connected_a @ c @ SV264 @ SV502 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4000]) ).
thf(4158,plain,
! [SV634: nat,SV502: nat,SV264: nat] :
( ( ( ( min_dist_a @ c @ SV264 @ ( sK47_SY1417 @ SV502 @ SV634 @ SV264 ) )
!= SV634 )
= $false )
| ( ( ord_less_eq_nat @ SV634 @ ( min_dist_a @ c @ SV264 @ SV502 ) )
= $false )
| ( ( connected_a @ c @ SV264 @ SV502 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4000]) ).
thf(4159,plain,
! [SV635: nat,SV716: nat,SV750: nat,SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ( ! [SY1494: nat] :
~ ~ ( ~ ( connected_b @ SV265 @ SV503 @ SY1494 )
| ( ( min_dist_b @ SV265 @ SV503 @ SY1494 )
!= SV750 ) ) )
= $false )
| ( ( ord_less_nat @ SV750 @ SV716 )
= $false )
| ( ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
= SV716 )
= $false )
| ( ( connected_b @ SV265 @ SV503 @ SV635 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4001]) ).
thf(4160,plain,
! [SV508: nat,SV270: set_nat] :
( ( ( ~ ( finite_finite_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) )
| ( ( finite_card_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) )
!= SV508 ) )
= $false )
| ( ( finite_finite_nat @ SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4002]) ).
thf(4161,plain,
! [SV273: set_set_nat,SV509: set_nat] :
( ( ( ~ ( ~ ( member_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV273 )
| ~ ( ord_less_eq_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV509 ) ) )
= $true )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4004]) ).
thf(4162,plain,
! [SV509: set_nat,SV273: set_set_nat] :
( ( ( ! [SY1530: set_nat] :
( ~ ( member_set_nat @ SY1530 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SY1530 @ ( sK37_SY1310 @ SV509 @ SV273 ) )
| ( ( sK37_SY1310 @ SV509 @ SV273 )
= SY1530 ) ) )
= $true )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4005]) ).
thf(4163,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV519 @ SV719 @ SV779 ) )
= $false )
| ( ( connected_b @ SV519 @ SV719 @ SV779 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4007]) ).
thf(4164,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ~ ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) )
= $false )
| ( ( connected_b @ SV519 @ SV719 @ SV779 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4007]) ).
thf(4165,plain,
! [SV779: nat,SV833: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV519 @ SV719 @ SV833 @ SV779 ) )
= $true )
| ( ( ~ ( ~ ( connected_b @ SV519 @ SV719 @ SV779 )
| ~ ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4008]) ).
thf(4166,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4009]) ).
thf(4167,plain,
! [SV648: nat,SV293: nat,SV525: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $false )
| ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4009]) ).
thf(4168,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ~ ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) )
= $false )
| ( ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV525 )
= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4010]) ).
thf(4169,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) )
= $false )
| ( ( ord_less_nat @ SV530 @ SV721 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4012]) ).
thf(4170,plain,
! [SV721: nat,SV530: nat] :
( ( ( SV530 != SV721 )
= $false )
| ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV530 @ SV721 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4013]) ).
thf(4171,plain,
! [SV653: nat > $o,SV533: nat,SV834: nat,SV304: nat] :
( ( ( ~ ( dist_b @ c2 @ SV304 @ SV834 @ SV533 )
| ( ord_less_eq_nat @ ( sK40_SY1428 @ SV653 @ SV533 @ SV304 ) @ SV834 ) )
= $true )
| ( ( SV653 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) )
= $true )
| ( ( connected_b @ c2 @ SV304 @ SV533 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4014]) ).
thf(4172,plain,
! [SV660: nat,SV323: nat] :
( ( ( ord_less_nat @ SV323 @ SV660 )
= $true )
| ( ( SV323 = SV660 )
= $true )
| ( ( ord_less_nat @ SV323 @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4017]) ).
thf(4173,plain,
! [SV660: nat,SV323: nat] :
( ( ( ord_less_nat @ SV323 @ SV660 )
= $true )
| ( ( SV323 = SV660 )
= $true )
| ( ( SV323 = SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4019]) ).
thf(4174,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
| ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) )
= $false )
| ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4020]) ).
thf(4175,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
| ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) )
= $false )
| ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4021]) ).
thf(4176,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
| ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) )
= $false )
| ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4022]) ).
thf(4177,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
| ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) )
= $false )
| ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4023]) ).
thf(4178,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $true )
| ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4024]) ).
thf(4179,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $true )
| ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4025]) ).
thf(4180,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $true )
| ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4026]) ).
thf(4181,plain,
! [SV760: nat,SV665: nat,SV330: product_prod_nat_nat > b] :
( ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $true )
| ( ( connected_b @ SV330 @ SV665 @ SV760 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4027]) ).
thf(4182,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $true )
| ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4028]) ).
thf(4183,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $true )
| ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4029]) ).
thf(4184,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $true )
| ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4030]) ).
thf(4185,plain,
! [SV761: nat,SV666: nat,SV331: product_prod_nat_nat > a] :
( ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $true )
| ( ( connected_a @ SV331 @ SV666 @ SV761 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4031]) ).
thf(4186,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
| ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) )
= $false )
| ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4032]) ).
thf(4187,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
| ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) )
= $false )
| ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4033]) ).
thf(4188,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
| ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) )
= $false )
| ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4034]) ).
thf(4189,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
| ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) )
= $false )
| ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4035]) ).
thf(4190,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
| ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) )
= $false )
| ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4036]) ).
thf(4191,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
| ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) )
= $false )
| ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4037]) ).
thf(4192,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
| ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) )
= $false )
| ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4038]) ).
thf(4193,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
| ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) )
= $false )
| ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4039]) ).
thf(4194,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
| ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) )
= $false )
| ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4040]) ).
thf(4195,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
| ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) )
= $false )
| ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4041]) ).
thf(4196,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
| ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) )
= $false )
| ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4042]) ).
thf(4197,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
| ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) )
= $false )
| ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4043]) ).
thf(4198,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ~ ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) )
= $false )
| ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4044]) ).
thf(4199,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ~ ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4045]) ).
thf(4200,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $true )
| ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4046]) ).
thf(4201,plain,
! [SV566: nat,SV97: nat,SV367: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV367 )
= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $true )
| ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4047]) ).
thf(4202,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 ) )
= $false )
| ( ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4048]) ).
thf(4203,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4048]) ).
thf(4204,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 ) )
= $false )
| ( ( SV372 = SV683 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4049]) ).
thf(4205,plain,
! [SV372: set_nat,SV683: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) )
= $false )
| ( ( SV372 = SV683 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4049]) ).
thf(4206,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ( SV372 != SV683 )
| ~ ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV372 @ SV683 )
= $false )
| ( ( ord_less_eq_set_nat @ SV683 @ SV372 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4050]) ).
thf(4207,plain,
! [SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) )
= $false )
| ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4055]) ).
thf(4208,plain,
! [SV769: nat,SV806: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4056]) ).
thf(4209,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) )
= $false )
| ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4057]) ).
thf(4210,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4058]) ).
thf(4211,plain,
! [SV576: nat,SV384: nat,SV118: nat] :
( ( ( ~ ( ~ ( isPath_a @ c @ SV118 @ ( sK55_SY1353 @ SV384 @ SV576 @ SV118 ) @ SV576 )
| ( ( size_s1990949619at_nat @ ( sK55_SY1353 @ SV384 @ SV576 @ SV118 ) )
!= SV384 ) ) )
= $true )
| ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4059]) ).
thf(4212,plain,
! [SV384: nat,SV576: nat,SV820: list_P559422087at_nat,SV118: nat] :
( ( ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV820 )
!= SV384 )
= $true )
| ( ( ~ ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4060]) ).
thf(4213,plain,
! [SV741: nat,SV689: nat,SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ( ~ ~ ( ~ ( connected_a @ SV120 @ SV386 @ ( sK62_SY1479 @ SV577 @ SV689 @ SV741 @ SV386 @ SV120 ) )
| ( ( min_dist_a @ SV120 @ SV386 @ ( sK62_SY1479 @ SV577 @ SV689 @ SV741 @ SV386 @ SV120 ) )
!= SV741 ) ) )
= $false )
| ( ( ord_less_nat @ SV741 @ SV689 )
= $false )
| ( ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
= SV689 )
= $false )
| ( ( connected_a @ SV120 @ SV386 @ SV577 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4061]) ).
thf(4214,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( connected_a @ SV387 @ SV690 @ SV771 )
= $true )
| ( ( connected_a @ SV387 @ SV690 @ SV771 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4062]) ).
thf(4215,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) )
= $true )
| ( ( connected_a @ SV387 @ SV690 @ SV771 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4063]) ).
thf(4216,plain,
! [SV771: nat,SV827: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( dist_a @ SV387 @ SV690 @ SV827 @ SV771 )
= $false )
| ( ( ~ ( ~ ( connected_a @ SV387 @ SV690 @ SV771 )
| ~ ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4064]) ).
thf(4217,plain,
! [SV691: nat,SV581: nat,SV391: nat,SV128: nat] :
( ( ( ~ ( ~ ( connected_b @ c2 @ SV128 @ ( sK56_SY1443 @ SV391 @ SV581 @ SV691 @ SV128 ) )
| ( ( min_dist_b @ c2 @ SV128 @ ( sK56_SY1443 @ SV391 @ SV581 @ SV691 @ SV128 ) )
!= SV691 ) ) )
= $true )
| ( ( ord_less_nat @ SV691 @ SV581 )
= $false )
| ( ( ( min_dist_b @ c2 @ SV128 @ SV391 )
= SV581 )
= $false )
| ( ( connected_b @ c2 @ SV128 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4065]) ).
thf(4218,plain,
! [SV692: nat > $o,SV582: nat,SV835: nat,SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV129 @ SV392 @ SV835 @ SV582 )
| ( ord_less_eq_nat @ ( sK42_SY1444 @ SV692 @ SV582 @ SV392 @ SV129 ) @ SV835 ) )
= $true )
| ( ( SV692 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) )
= $true )
| ( ( connected_a @ SV129 @ SV392 @ SV582 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4066]) ).
thf(4219,plain,
! [SV693: nat,SV583: nat,SV396: nat,SV134: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV134 @ SV396 @ ( sK48_SY1446 @ SV583 @ SV693 @ SV396 @ SV134 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV693 @ ( min_dist_b @ SV134 @ SV396 @ SV583 ) )
= $false )
| ( ( connected_b @ SV134 @ SV396 @ SV583 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4067]) ).
thf(4220,plain,
! [SV693: nat,SV583: nat,SV396: nat,SV134: product_prod_nat_nat > b] :
( ( ( ( min_dist_b @ SV134 @ SV396 @ ( sK48_SY1446 @ SV583 @ SV693 @ SV396 @ SV134 ) )
!= SV693 )
= $false )
| ( ( ord_less_eq_nat @ SV693 @ ( min_dist_b @ SV134 @ SV396 @ SV583 ) )
= $false )
| ( ( connected_b @ SV134 @ SV396 @ SV583 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4067]) ).
thf(4221,plain,
! [SV808: list_P559422087at_nat,SV398: nat,SV136: nat] :
( ( ( ! [SY1164: list_P559422087at_nat] :
~ ( isPath_a @ c @ SV136 @ SY1164 @ SV398 ) )
= $false )
| ( ( isPath_a @ c @ SV136 @ SV808 @ SV398 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4070]) ).
thf(4222,plain,
! [SV137: set_nat,SV399: nat] :
( ( ( ~ ( member_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV137 )
| ~ ( ord_less_eq_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV399 ) )
= $false )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4071]) ).
thf(4223,plain,
! [SV399: nat,SV137: set_nat,SV836: nat] :
( ( ( ~ ( member_nat @ SV836 @ SV137 )
| ~ ( ord_less_eq_nat @ SV836 @ ( sK29_SY1165 @ SV399 @ SV137 ) )
| ( ( sK29_SY1165 @ SV399 @ SV137 )
= SV836 ) )
= $true )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4072]) ).
thf(4224,plain,
! [SV586: nat,SV403: nat,SV142: nat] :
( ( ( connected_b @ c2 @ SV142 @ ( sK43_SY1370 @ SV403 @ SV586 @ SV142 ) )
= $true )
| ( ( ord_less_eq_nat @ SV586 @ ( min_dist_b @ c2 @ SV142 @ SV403 ) )
= $false )
| ( ( connected_b @ c2 @ SV142 @ SV403 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4073]) ).
thf(4225,plain,
! [SV586: nat,SV403: nat,SV142: nat] :
( ( ( ( min_dist_b @ c2 @ SV142 @ ( sK43_SY1370 @ SV403 @ SV586 @ SV142 ) )
= SV586 )
= $true )
| ( ( ord_less_eq_nat @ SV586 @ ( min_dist_b @ c2 @ SV142 @ SV403 ) )
= $false )
| ( ( connected_b @ c2 @ SV142 @ SV403 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4074]) ).
thf(4226,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ( ~ ( finite772653738at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) ) )
= $false )
| ( ( finite772653738at_nat @ SV143 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4075]) ).
thf(4227,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ( ( finite447719721at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) )
!= SV404 )
= $false )
| ( ( finite772653738at_nat @ SV143 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4075]) ).
thf(4228,plain,
! [SV809: nat,SV407: nat,SV146: nat] :
( ( ( ! [SY1177: nat] :
~ ( dist_a @ c @ SV146 @ SY1177 @ SV407 ) )
= $false )
| ( ( dist_a @ c @ SV146 @ SV809 @ SV407 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4078]) ).
thf(4229,plain,
! [SV699: nat,SV591: nat,SV411: nat,SV151: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV151 @ SV411 @ ( sK49_SY1449 @ SV591 @ SV699 @ SV411 @ SV151 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV699 @ ( min_dist_a @ SV151 @ SV411 @ SV591 ) )
= $false )
| ( ( connected_a @ SV151 @ SV411 @ SV591 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4079]) ).
thf(4230,plain,
! [SV699: nat,SV591: nat,SV411: nat,SV151: product_prod_nat_nat > a] :
( ( ( ( min_dist_a @ SV151 @ SV411 @ ( sK49_SY1449 @ SV591 @ SV699 @ SV411 @ SV151 ) )
!= SV699 )
= $false )
| ( ( ord_less_eq_nat @ SV699 @ ( min_dist_a @ SV151 @ SV411 @ SV591 ) )
= $false )
| ( ( connected_a @ SV151 @ SV411 @ SV591 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4079]) ).
thf(4231,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $true )
| ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4080]) ).
thf(4232,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV158: nat] :
( ( ( ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) )
= $true )
| ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4081]) ).
thf(4233,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4082]) ).
thf(4234,plain,
! [SV158: nat,SV593: nat,SV416: list_P559422087at_nat] :
( ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4082]) ).
thf(4235,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( ~ ( ~ ( SV159 @ ( sK58_SY852 @ SV594 @ SV417 @ SV159 ) )
| ~ ! [SY1536: nat] :
( ~ ( SV159 @ SY1536 )
| ( ord_less_eq_nat @ SY1536 @ ( sK58_SY852 @ SV594 @ SV417 @ SV159 ) ) ) ) )
= $true )
| ( ( SV159 @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4083]) ).
thf(4236,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( ~ ( SV159 @ ( sK52_SY852 @ SV594 @ SV417 @ SV159 ) )
| ~ ! [SY1535: nat] :
( ~ ( SV159 @ SY1535 )
| ( ord_less_eq_nat @ SY1535 @ ( sK52_SY852 @ SV594 @ SV417 @ SV159 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) @ SV594 )
= $false )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4084]) ).
thf(4237,plain,
! [SV597: nat,SV421: nat,SV163: nat] :
( ( ( ~ ( ~ ( isPath_b @ c2 @ SV163 @ ( sK59_SY1382 @ SV421 @ SV597 @ SV163 ) @ SV597 )
| ( ( size_s1990949619at_nat @ ( sK59_SY1382 @ SV421 @ SV597 @ SV163 ) )
!= SV421 ) ) )
= $true )
| ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4085]) ).
thf(4238,plain,
! [SV421: nat,SV597: nat,SV821: list_P559422087at_nat,SV163: nat] :
( ( ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV821 )
!= SV421 )
= $true )
| ( ( ~ ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4086]) ).
thf(4239,plain,
! [SV164: set_set_nat,SV422: set_nat] :
( ( ( ~ ( member_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SV164 )
| ~ ( ord_less_eq_set_nat @ SV422 @ ( sK32_SY1199 @ SV422 @ SV164 ) ) )
= $false )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4087]) ).
thf(4240,plain,
! [SV422: set_nat,SV164: set_set_nat,SV837: set_nat] :
( ( ( ~ ( member_set_nat @ SV837 @ SV164 )
| ~ ( ord_less_eq_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SV837 )
| ( ( sK32_SY1199 @ SV422 @ SV164 )
= SV837 ) )
= $true )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4088]) ).
thf(4241,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) )
= $false )
| ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4089]) ).
thf(4242,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4090]) ).
thf(4243,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ~ ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) )
= $false )
| ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4091]) ).
thf(4244,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ~ ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4092]) ).
thf(4245,plain,
! [SV427: nat,SV812: nat,SV171: nat > $o] :
( ( ( ~ ( SV171 @ SV812 ) )
= $false )
| ( ( ord_less_nat @ SV812 @ ( sK5_SY879 @ SV427 @ SV171 ) )
= $false )
| ( ( SV171 @ SV427 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4093]) ).
thf(4246,plain,
! [SV173: set_se1612935105at_nat,SV428: set_Pr1986765409at_nat] :
( ( ( ~ ( member298845450at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV173 )
| ~ ( ord_le841296385at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV428 ) )
= $false )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4094]) ).
thf(4247,plain,
! [SV428: set_Pr1986765409at_nat,SV173: set_se1612935105at_nat,SV838: set_Pr1986765409at_nat] :
( ( ( ~ ( member298845450at_nat @ SV838 @ SV173 )
| ~ ( ord_le841296385at_nat @ SV838 @ ( sK33_SY1214 @ SV428 @ SV173 ) )
| ( ( sK33_SY1214 @ SV428 @ SV173 )
= SV838 ) )
= $true )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4095]) ).
thf(4248,plain,
! [SV703: nat > $o,SV603: nat,SV839: nat,SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV176 @ SV431 @ SV839 @ SV603 )
| ( ord_less_eq_nat @ ( sK45_SY1455 @ SV703 @ SV603 @ SV431 @ SV176 ) @ SV839 ) )
= $true )
| ( ( SV703 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) )
= $true )
| ( ( connected_b @ SV176 @ SV431 @ SV603 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4096]) ).
thf(4249,plain,
! [SV177: set_se1612935105at_nat,SV432: set_Pr1986765409at_nat] :
( ( ( ~ ( member298845450at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SV177 )
| ~ ( ord_le841296385at_nat @ SV432 @ ( sK34_SY1223 @ SV432 @ SV177 ) ) )
= $false )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4097]) ).
thf(4250,plain,
! [SV432: set_Pr1986765409at_nat,SV177: set_se1612935105at_nat,SV840: set_Pr1986765409at_nat] :
( ( ( ~ ( member298845450at_nat @ SV840 @ SV177 )
| ~ ( ord_le841296385at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SV840 )
| ( ( sK34_SY1223 @ SV432 @ SV177 )
= SV840 ) )
= $true )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4098]) ).
thf(4251,plain,
! [SV436: nat > $o,SV841: nat,SV182: nat > $o] :
( ( ( ~ ( SV182 @ SV841 )
| ( SV436 @ SV841 ) )
= $true )
| ( ( SV182 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4101]) ).
thf(4252,plain,
! [SV436: nat > $o,SV828: nat,SV182: nat > $o] :
( ( ( ~ ( SV182 @ SV828 ) )
= $true )
| ( ( SV436 @ SV828 )
= $true )
| ( ( SV436 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4102]) ).
thf(4253,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 ) )
= $false )
| ( ( SV437 = SV704 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4103]) ).
thf(4254,plain,
! [SV437: set_Pr1986765409at_nat,SV704: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) )
= $false )
| ( ( SV437 = SV704 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4103]) ).
thf(4255,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ( SV437 != SV704 )
| ~ ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) )
= $false )
| ( ( ord_le841296385at_nat @ SV437 @ SV704 )
= $false )
| ( ( ord_le841296385at_nat @ SV704 @ SV437 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4104]) ).
thf(4256,plain,
! [SV438: set_Pr1986765409at_nat > $o,SV184: set_Pr1986765409at_nat,SV824: set_Pr1986765409at_nat] :
( ( ( ord_le116442893at_nat @ SV824 @ ( sK20_SY1230 @ SV184 @ SV438 ) )
= $false )
| ( ( SV438 @ SV824 )
= $true )
| ( ( SV438 @ SV184 )
= $true )
| ( ( finite772653738at_nat @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4105]) ).
thf(4257,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ~ ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) )
= $false )
| ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4106]) ).
thf(4258,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ~ ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4107]) ).
thf(4259,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( connected_a @ SV442 @ SV706 @ SV775 )
= $true )
| ( ( connected_a @ SV442 @ SV706 @ SV775 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4108]) ).
thf(4260,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) )
= $true )
| ( ( connected_a @ SV442 @ SV706 @ SV775 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4109]) ).
thf(4261,plain,
! [SV775: nat,SV829: list_P559422087at_nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV442 @ SV706 @ SV829 @ SV775 )
= $false )
| ( ( ~ ( ~ ( connected_a @ SV442 @ SV706 @ SV775 )
| ~ ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4110]) ).
thf(4262,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ ( sK46_SY1241 @ SV196 @ SV449 ) @ SV449 )
| ~ ! [SY1534: nat] :
( ~ ( ord_less_nat @ SY1534 @ ( sK46_SY1241 @ SV196 @ SV449 ) )
| ~ ( SV196 @ SY1534 ) ) ) )
= $true )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4111]) ).
thf(4263,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( SV196 @ ( sK46_SY1241 @ SV196 @ SV449 ) )
= $true )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4112]) ).
thf(4264,plain,
! [SV200: set_nat,SV453: nat] :
( ( ( ~ ( member_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SV200 )
| ~ ( ord_less_eq_nat @ SV453 @ ( sK35_SY1245 @ SV453 @ SV200 ) ) )
= $false )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4113]) ).
thf(4265,plain,
! [SV453: nat,SV200: set_nat,SV842: nat] :
( ( ( ~ ( member_nat @ SV842 @ SV200 )
| ~ ( ord_less_eq_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SV842 )
| ( ( sK35_SY1245 @ SV453 @ SV200 )
= SV842 ) )
= $true )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4114]) ).
thf(4266,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $true )
| ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4115]) ).
thf(4267,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV208: nat] :
( ( ( ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) )
= $true )
| ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4116]) ).
thf(4268,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4117]) ).
thf(4269,plain,
! [SV208: nat,SV614: nat,SV460: list_P559422087at_nat] :
( ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4117]) ).
thf(4270,plain,
! [SV615: nat > $o,SV462: nat,SV830: nat,SV210: nat] :
( ( ( ~ ( dist_a @ c @ SV210 @ SV830 @ SV462 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK36_SY1400 @ SV615 @ SV462 @ SV210 ) @ SV830 )
= $true )
| ( ( SV615 @ ( min_dist_a @ c @ SV210 @ SV462 ) )
= $true )
| ( ( connected_a @ c @ SV210 @ SV462 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4118]) ).
thf(4271,plain,
! [SV816: nat,SV466: nat,SV215: nat] :
( ( ( ! [SY1258: nat] :
~ ( dist_b @ c2 @ SV215 @ SY1258 @ SV466 ) )
= $false )
| ( ( dist_b @ c2 @ SV215 @ SV816 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4121]) ).
thf(4272,plain,
! [SV469: set_nat > $o,SV219: set_nat,SV825: set_nat] :
( ( ( ord_less_set_nat @ SV825 @ ( sK22_SY1261 @ SV219 @ SV469 ) )
= $false )
| ( ( SV469 @ SV825 )
= $true )
| ( ( SV469 @ SV219 )
= $true )
| ( ( finite_finite_nat @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4122]) ).
thf(4273,plain,
! [SV222: nat > $o,SV472: nat,SV826: nat] :
( ( ( ~ ( ord_less_nat @ SV826 @ ( sK24_SY974 @ SV472 @ SV222 ) )
| ~ ~ ( SV222 @ SV826 ) )
= $true )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4123]) ).
thf(4274,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
= $true )
| ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4124]) ).
thf(4275,plain,
! [SV620: nat,SV229: nat,SV478: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV478 )
= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $true )
| ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4125]) ).
thf(4276,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 ) )
= $false )
| ( ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV478 )
= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4126]) ).
thf(4277,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) )
= $false )
| ( ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV478 )
= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4126]) ).
thf(4278,plain,
! [SV817: list_P559422087at_nat,SV484: nat,SV237: nat] :
( ( ( ! [SY1277: list_P559422087at_nat] :
~ ( isPath_b @ c2 @ SV237 @ SY1277 @ SV484 ) )
= $false )
| ( ( isPath_b @ c2 @ SV237 @ SV817 @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4133]) ).
thf(4279,plain,
! [SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) )
= $false )
| ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4134]) ).
thf(4280,plain,
! [SV776: nat,SV818: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4135]) ).
thf(4281,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
= $true )
| ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4136]) ).
thf(4282,plain,
! [SV626: nat,SV248: nat,SV489: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV489 )
= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $true )
| ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4137]) ).
thf(4283,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 ) )
= $false )
| ( ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV489 )
= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4138]) ).
thf(4284,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) )
= $false )
| ( ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV489 )
= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4138]) ).
thf(4285,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( connected_b @ SV491 @ SV713 @ SV777 )
= $true )
| ( ( connected_b @ SV491 @ SV713 @ SV777 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4139]) ).
thf(4286,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) )
= $true )
| ( ( connected_b @ SV491 @ SV713 @ SV777 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4140]) ).
thf(4287,plain,
! [SV777: nat,SV831: list_P559422087at_nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV491 @ SV713 @ SV831 @ SV777 )
= $false )
| ( ( ~ ( ~ ( connected_b @ SV491 @ SV713 @ SV777 )
| ~ ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4141]) ).
thf(4288,plain,
! [SV498: product_prod_nat_nat > $o,SV843: product_prod_nat_nat,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ( SV259 @ SV843 )
| ( SV498 @ SV843 ) )
= $true )
| ( ( SV259 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4152]) ).
thf(4289,plain,
! [SV498: product_prod_nat_nat > $o,SV832: product_prod_nat_nat,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ( SV259 @ SV832 ) )
= $true )
| ( ( SV498 @ SV832 )
= $true )
| ( ( SV498 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4153]) ).
thf(4290,plain,
! [SV714: nat,SV632: nat,SV499: nat,SV260: nat] :
( ( ( ~ ( ~ ( connected_a @ c @ SV260 @ ( sK61_SY1466 @ SV499 @ SV632 @ SV714 @ SV260 ) )
| ( ( min_dist_a @ c @ SV260 @ ( sK61_SY1466 @ SV499 @ SV632 @ SV714 @ SV260 ) )
!= SV714 ) ) )
= $true )
| ( ( ord_less_nat @ SV714 @ SV632 )
= $false )
| ( ( ( min_dist_a @ c @ SV260 @ SV499 )
= SV632 )
= $false )
| ( ( connected_a @ c @ SV260 @ SV499 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4154]) ).
thf(4291,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ~ ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) )
= $false )
| ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4155]) ).
thf(4292,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ~ ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4156]) ).
thf(4293,plain,
! [SV634: nat,SV502: nat,SV264: nat] :
( ( ( connected_a @ c @ SV264 @ ( sK47_SY1417 @ SV502 @ SV634 @ SV264 ) )
= $true )
| ( ( ord_less_eq_nat @ SV634 @ ( min_dist_a @ c @ SV264 @ SV502 ) )
= $false )
| ( ( connected_a @ c @ SV264 @ SV502 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4157]) ).
thf(4294,plain,
! [SV634: nat,SV502: nat,SV264: nat] :
( ( ( ( min_dist_a @ c @ SV264 @ ( sK47_SY1417 @ SV502 @ SV634 @ SV264 ) )
= SV634 )
= $true )
| ( ( ord_less_eq_nat @ SV634 @ ( min_dist_a @ c @ SV264 @ SV502 ) )
= $false )
| ( ( connected_a @ c @ SV264 @ SV502 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4158]) ).
thf(4295,plain,
! [SV750: nat,SV716: nat,SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ( ~ ~ ( ~ ( connected_b @ SV265 @ SV503 @ ( sK63_SY1494 @ SV635 @ SV716 @ SV750 @ SV503 @ SV265 ) )
| ( ( min_dist_b @ SV265 @ SV503 @ ( sK63_SY1494 @ SV635 @ SV716 @ SV750 @ SV503 @ SV265 ) )
!= SV750 ) ) )
= $false )
| ( ( ord_less_nat @ SV750 @ SV716 )
= $false )
| ( ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
= SV716 )
= $false )
| ( ( connected_b @ SV265 @ SV503 @ SV635 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4159]) ).
thf(4296,plain,
! [SV508: nat,SV270: set_nat] :
( ( ( ~ ( finite_finite_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) ) )
= $false )
| ( ( finite_finite_nat @ SV270 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4160]) ).
thf(4297,plain,
! [SV508: nat,SV270: set_nat] :
( ( ( ( finite_card_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) )
!= SV508 )
= $false )
| ( ( finite_finite_nat @ SV270 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4160]) ).
thf(4298,plain,
! [SV273: set_set_nat,SV509: set_nat] :
( ( ( ~ ( member_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV273 )
| ~ ( ord_less_eq_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV509 ) )
= $false )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4161]) ).
thf(4299,plain,
! [SV509: set_nat,SV273: set_set_nat,SV844: set_nat] :
( ( ( ~ ( member_set_nat @ SV844 @ SV273 )
| ~ ( ord_less_eq_set_nat @ SV844 @ ( sK37_SY1310 @ SV509 @ SV273 ) )
| ( ( sK37_SY1310 @ SV509 @ SV273 )
= SV844 ) )
= $true )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4162]) ).
thf(4300,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( connected_b @ SV519 @ SV719 @ SV779 )
= $true )
| ( ( connected_b @ SV519 @ SV719 @ SV779 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4163]) ).
thf(4301,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) )
= $true )
| ( ( connected_b @ SV519 @ SV719 @ SV779 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4164]) ).
thf(4302,plain,
! [SV779: nat,SV833: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( dist_b @ SV519 @ SV719 @ SV833 @ SV779 )
= $false )
| ( ( ~ ( ~ ( connected_b @ SV519 @ SV719 @ SV779 )
| ~ ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4165]) ).
thf(4303,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $true )
| ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4166]) ).
thf(4304,plain,
! [SV648: nat,SV293: nat,SV525: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV525 )
= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $true )
| ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4167]) ).
thf(4305,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 ) )
= $false )
| ( ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV525 )
= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4168]) ).
thf(4306,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) )
= $false )
| ( ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV525 )
= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4168]) ).
thf(4307,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV530 @ SV721 ) )
= $false )
| ( ( ord_less_nat @ SV530 @ SV721 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4169]) ).
thf(4308,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ( SV530 != SV721 ) ) )
= $false )
| ( ( ord_less_nat @ SV530 @ SV721 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4169]) ).
thf(4309,plain,
! [SV721: nat,SV530: nat] :
( ( ( SV530 = SV721 )
= $true )
| ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV530 @ SV721 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4170]) ).
thf(4310,plain,
! [SV653: nat > $o,SV533: nat,SV834: nat,SV304: nat] :
( ( ( ~ ( dist_b @ c2 @ SV304 @ SV834 @ SV533 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK40_SY1428 @ SV653 @ SV533 @ SV304 ) @ SV834 )
= $true )
| ( ( SV653 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) )
= $true )
| ( ( connected_b @ c2 @ SV304 @ SV533 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4171]) ).
thf(4311,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) )
= $false )
| ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4174]) ).
thf(4312,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) )
= $false )
| ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4174]) ).
thf(4313,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) )
= $false )
| ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4175]) ).
thf(4314,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 ) )
= $false )
| ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4175]) ).
thf(4315,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) )
= $false )
| ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4176]) ).
thf(4316,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) )
= $false )
| ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4176]) ).
thf(4317,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) )
= $false )
| ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4177]) ).
thf(4318,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 ) )
= $false )
| ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4177]) ).
thf(4319,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) )
= $false )
| ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4186]) ).
thf(4320,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) )
= $false )
| ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4186]) ).
thf(4321,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) )
= $false )
| ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4187]) ).
thf(4322,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 ) )
= $false )
| ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4187]) ).
thf(4323,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) )
= $false )
| ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4188]) ).
thf(4324,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) )
= $false )
| ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4188]) ).
thf(4325,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) )
= $false )
| ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4189]) ).
thf(4326,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 ) )
= $false )
| ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4189]) ).
thf(4327,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) )
= $false )
| ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4190]) ).
thf(4328,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) )
= $false )
| ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4190]) ).
thf(4329,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) )
= $false )
| ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4191]) ).
thf(4330,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 ) )
= $false )
| ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4191]) ).
thf(4331,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) )
= $false )
| ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4192]) ).
thf(4332,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) )
= $false )
| ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4192]) ).
thf(4333,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) )
= $false )
| ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4193]) ).
thf(4334,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 ) )
= $false )
| ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4193]) ).
thf(4335,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) )
= $false )
| ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4194]) ).
thf(4336,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) )
= $false )
| ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4194]) ).
thf(4337,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) )
= $false )
| ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4195]) ).
thf(4338,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( ~ ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 ) )
= $false )
| ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4195]) ).
thf(4339,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) )
= $false )
| ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4196]) ).
thf(4340,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) )
= $false )
| ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4196]) ).
thf(4341,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) )
= $false )
| ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4197]) ).
thf(4342,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( ~ ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 ) )
= $false )
| ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4197]) ).
thf(4343,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 ) )
= $false )
| ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4198]) ).
thf(4344,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) )
= $false )
| ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4198]) ).
thf(4345,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ~ ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4199]) ).
thf(4346,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( isShortestPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $true )
| ( ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4202]) ).
thf(4347,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) ) )
= $true )
| ( ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4203]) ).
thf(4348,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ord_less_eq_set_nat @ SV372 @ SV683 )
= $true )
| ( ( SV372 = SV683 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4204]) ).
thf(4349,plain,
! [SV372: set_nat,SV683: set_nat] :
( ( ( ord_less_eq_set_nat @ SV683 @ SV372 )
= $true )
| ( ( SV372 = SV683 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4205]) ).
thf(4350,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( SV372 != SV683 )
= $false )
| ( ( ord_less_eq_set_nat @ SV372 @ SV683 )
= $false )
| ( ( ord_less_eq_set_nat @ SV683 @ SV372 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4206]) ).
thf(4351,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV372 @ SV683 )
= $false )
| ( ( ord_less_eq_set_nat @ SV683 @ SV372 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4206]) ).
thf(4352,plain,
! [SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 ) )
= $false )
| ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4207]) ).
thf(4353,plain,
! [SV769: nat,SV806: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) )
= $false )
| ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4207]) ).
thf(4354,plain,
! [SV769: nat,SV806: nat,SV845: list_P559422087at_nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
| ( ( size_s1990949619at_nat @ SV845 )
!= SV769 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4208]) ).
thf(4355,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 ) )
= $false )
| ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4209]) ).
thf(4356,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) )
= $false )
| ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4209]) ).
thf(4357,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 ) )
= $true )
| ( ( ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4210]) ).
thf(4358,plain,
! [SV576: nat,SV384: nat,SV118: nat] :
( ( ( ~ ( isPath_a @ c @ SV118 @ ( sK55_SY1353 @ SV384 @ SV576 @ SV118 ) @ SV576 )
| ( ( size_s1990949619at_nat @ ( sK55_SY1353 @ SV384 @ SV576 @ SV118 ) )
!= SV384 ) )
= $false )
| ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4211]) ).
thf(4359,plain,
! [SV576: nat,SV118: nat,SV384: nat,SV820: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV820 )
= SV384 )
= $false )
| ( ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
= $false )
| ( ( ~ ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4212]) ).
thf(4360,plain,
! [SV741: nat,SV689: nat,SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ( ~ ( ~ ( connected_a @ SV120 @ SV386 @ ( sK62_SY1479 @ SV577 @ SV689 @ SV741 @ SV386 @ SV120 ) )
| ( ( min_dist_a @ SV120 @ SV386 @ ( sK62_SY1479 @ SV577 @ SV689 @ SV741 @ SV386 @ SV120 ) )
!= SV741 ) ) )
= $true )
| ( ( ord_less_nat @ SV741 @ SV689 )
= $false )
| ( ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
= SV689 )
= $false )
| ( ( connected_a @ SV120 @ SV386 @ SV577 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4213]) ).
thf(4361,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) )
= $false )
| ( ( connected_a @ SV387 @ SV690 @ SV771 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4215]) ).
thf(4362,plain,
! [SV827: nat,SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV387 @ SV690 @ SV771 )
| ~ ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) )
= $false )
| ( ( dist_a @ SV387 @ SV690 @ SV827 @ SV771 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4216]) ).
thf(4363,plain,
! [SV691: nat,SV581: nat,SV391: nat,SV128: nat] :
( ( ( ~ ( connected_b @ c2 @ SV128 @ ( sK56_SY1443 @ SV391 @ SV581 @ SV691 @ SV128 ) )
| ( ( min_dist_b @ c2 @ SV128 @ ( sK56_SY1443 @ SV391 @ SV581 @ SV691 @ SV128 ) )
!= SV691 ) )
= $false )
| ( ( ord_less_nat @ SV691 @ SV581 )
= $false )
| ( ( ( min_dist_b @ c2 @ SV128 @ SV391 )
= SV581 )
= $false )
| ( ( connected_b @ c2 @ SV128 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4217]) ).
thf(4364,plain,
! [SV692: nat > $o,SV582: nat,SV835: nat,SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV129 @ SV392 @ SV835 @ SV582 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK42_SY1444 @ SV692 @ SV582 @ SV392 @ SV129 ) @ SV835 )
= $true )
| ( ( SV692 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) )
= $true )
| ( ( connected_a @ SV129 @ SV392 @ SV582 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4218]) ).
thf(4365,plain,
! [SV693: nat,SV583: nat,SV396: nat,SV134: product_prod_nat_nat > b] :
( ( ( connected_b @ SV134 @ SV396 @ ( sK48_SY1446 @ SV583 @ SV693 @ SV396 @ SV134 ) )
= $true )
| ( ( ord_less_eq_nat @ SV693 @ ( min_dist_b @ SV134 @ SV396 @ SV583 ) )
= $false )
| ( ( connected_b @ SV134 @ SV396 @ SV583 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4219]) ).
thf(4366,plain,
! [SV693: nat,SV583: nat,SV396: nat,SV134: product_prod_nat_nat > b] :
( ( ( ( min_dist_b @ SV134 @ SV396 @ ( sK48_SY1446 @ SV583 @ SV693 @ SV396 @ SV134 ) )
= SV693 )
= $true )
| ( ( ord_less_eq_nat @ SV693 @ ( min_dist_b @ SV134 @ SV396 @ SV583 ) )
= $false )
| ( ( connected_b @ SV134 @ SV396 @ SV583 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4220]) ).
thf(4367,plain,
! [SV398: nat,SV808: list_P559422087at_nat,SV136: nat] :
( ( ( ~ ( isPath_a @ c @ SV136 @ ( sK64_SY1164 @ SV808 @ SV398 @ SV136 ) @ SV398 ) )
= $false )
| ( ( isPath_a @ c @ SV136 @ SV808 @ SV398 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4221]) ).
thf(4368,plain,
! [SV137: set_nat,SV399: nat] :
( ( ( ~ ( member_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV137 ) )
= $false )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4222]) ).
thf(4369,plain,
! [SV137: set_nat,SV399: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV399 ) )
= $false )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4222]) ).
thf(4370,plain,
! [SV399: nat,SV137: set_nat,SV836: nat] :
( ( ( ~ ( member_nat @ SV836 @ SV137 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV836 @ ( sK29_SY1165 @ SV399 @ SV137 ) )
| ( ( sK29_SY1165 @ SV399 @ SV137 )
= SV836 ) )
= $true )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4223]) ).
thf(4371,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) )
= $true )
| ( ( finite772653738at_nat @ SV143 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4226]) ).
thf(4372,plain,
! [SV404: nat,SV143: set_Pr1986765409at_nat] :
( ( ( ( finite447719721at_nat @ ( sK17_SY1174 @ SV143 @ SV404 ) )
= SV404 )
= $true )
| ( ( finite772653738at_nat @ SV143 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4227]) ).
thf(4373,plain,
! [SV407: nat,SV809: nat,SV146: nat] :
( ( ( ~ ( dist_a @ c @ SV146 @ ( sK65_SY1177 @ SV809 @ SV407 @ SV146 ) @ SV407 ) )
= $false )
| ( ( dist_a @ c @ SV146 @ SV809 @ SV407 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4228]) ).
thf(4374,plain,
! [SV699: nat,SV591: nat,SV411: nat,SV151: product_prod_nat_nat > a] :
( ( ( connected_a @ SV151 @ SV411 @ ( sK49_SY1449 @ SV591 @ SV699 @ SV411 @ SV151 ) )
= $true )
| ( ( ord_less_eq_nat @ SV699 @ ( min_dist_a @ SV151 @ SV411 @ SV591 ) )
= $false )
| ( ( connected_a @ SV151 @ SV411 @ SV591 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4229]) ).
thf(4375,plain,
! [SV699: nat,SV591: nat,SV411: nat,SV151: product_prod_nat_nat > a] :
( ( ( ( min_dist_a @ SV151 @ SV411 @ ( sK49_SY1449 @ SV591 @ SV699 @ SV411 @ SV151 ) )
= SV699 )
= $true )
| ( ( ord_less_eq_nat @ SV699 @ ( min_dist_a @ SV151 @ SV411 @ SV591 ) )
= $false )
| ( ( connected_a @ SV151 @ SV411 @ SV591 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4230]) ).
thf(4376,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV846: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ SV846 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SV846 ) ) )
= $true )
| ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4232]) ).
thf(4377,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 )
= $true )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4233]) ).
thf(4378,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4234]) ).
thf(4379,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( ~ ( SV159 @ ( sK58_SY852 @ SV594 @ SV417 @ SV159 ) )
| ~ ! [SY1536: nat] :
( ~ ( SV159 @ SY1536 )
| ( ord_less_eq_nat @ SY1536 @ ( sK58_SY852 @ SV594 @ SV417 @ SV159 ) ) ) )
= $false )
| ( ( SV159 @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4235]) ).
thf(4380,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( ~ ( SV159 @ ( sK52_SY852 @ SV594 @ SV417 @ SV159 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) @ SV594 )
= $false )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4236]) ).
thf(4381,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( ~ ! [SY1535: nat] :
( ~ ( SV159 @ SY1535 )
| ( ord_less_eq_nat @ SY1535 @ ( sK52_SY852 @ SV594 @ SV417 @ SV159 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) @ SV594 )
= $false )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4236]) ).
thf(4382,plain,
! [SV597: nat,SV421: nat,SV163: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV163 @ ( sK59_SY1382 @ SV421 @ SV597 @ SV163 ) @ SV597 )
| ( ( size_s1990949619at_nat @ ( sK59_SY1382 @ SV421 @ SV597 @ SV163 ) )
!= SV421 ) )
= $false )
| ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4237]) ).
thf(4383,plain,
! [SV597: nat,SV163: nat,SV421: nat,SV821: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV821 )
= SV421 )
= $false )
| ( ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
= $false )
| ( ( ~ ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4238]) ).
thf(4384,plain,
! [SV164: set_set_nat,SV422: set_nat] :
( ( ( ~ ( member_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SV164 ) )
= $false )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4239]) ).
thf(4385,plain,
! [SV164: set_set_nat,SV422: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV422 @ ( sK32_SY1199 @ SV422 @ SV164 ) ) )
= $false )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4239]) ).
thf(4386,plain,
! [SV422: set_nat,SV164: set_set_nat,SV837: set_nat] :
( ( ( ~ ( member_set_nat @ SV837 @ SV164 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SV837 )
| ( ( sK32_SY1199 @ SV422 @ SV164 )
= SV837 ) )
= $true )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4240]) ).
thf(4387,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 ) )
= $false )
| ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4241]) ).
thf(4388,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) )
= $false )
| ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4241]) ).
thf(4389,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 ) )
= $true )
| ( ( ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4242]) ).
thf(4390,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 ) )
= $false )
| ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4243]) ).
thf(4391,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) )
= $false )
| ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4243]) ).
thf(4392,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ~ ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4244]) ).
thf(4393,plain,
! [SV427: nat,SV812: nat,SV171: nat > $o] :
( ( ( SV171 @ SV812 )
= $true )
| ( ( ord_less_nat @ SV812 @ ( sK5_SY879 @ SV427 @ SV171 ) )
= $false )
| ( ( SV171 @ SV427 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4245]) ).
thf(4394,plain,
! [SV173: set_se1612935105at_nat,SV428: set_Pr1986765409at_nat] :
( ( ( ~ ( member298845450at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV173 ) )
= $false )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4246]) ).
thf(4395,plain,
! [SV173: set_se1612935105at_nat,SV428: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV428 ) )
= $false )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4246]) ).
thf(4396,plain,
! [SV428: set_Pr1986765409at_nat,SV173: set_se1612935105at_nat,SV838: set_Pr1986765409at_nat] :
( ( ( ~ ( member298845450at_nat @ SV838 @ SV173 ) )
= $true )
| ( ( ~ ( ord_le841296385at_nat @ SV838 @ ( sK33_SY1214 @ SV428 @ SV173 ) )
| ( ( sK33_SY1214 @ SV428 @ SV173 )
= SV838 ) )
= $true )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4247]) ).
thf(4397,plain,
! [SV703: nat > $o,SV603: nat,SV839: nat,SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV176 @ SV431 @ SV839 @ SV603 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK45_SY1455 @ SV703 @ SV603 @ SV431 @ SV176 ) @ SV839 )
= $true )
| ( ( SV703 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) )
= $true )
| ( ( connected_b @ SV176 @ SV431 @ SV603 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4248]) ).
thf(4398,plain,
! [SV177: set_se1612935105at_nat,SV432: set_Pr1986765409at_nat] :
( ( ( ~ ( member298845450at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SV177 ) )
= $false )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4249]) ).
thf(4399,plain,
! [SV177: set_se1612935105at_nat,SV432: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV432 @ ( sK34_SY1223 @ SV432 @ SV177 ) ) )
= $false )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4249]) ).
thf(4400,plain,
! [SV432: set_Pr1986765409at_nat,SV177: set_se1612935105at_nat,SV840: set_Pr1986765409at_nat] :
( ( ( ~ ( member298845450at_nat @ SV840 @ SV177 ) )
= $true )
| ( ( ~ ( ord_le841296385at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SV840 )
| ( ( sK34_SY1223 @ SV432 @ SV177 )
= SV840 ) )
= $true )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4250]) ).
thf(4401,plain,
! [SV436: nat > $o,SV841: nat,SV182: nat > $o] :
( ( ( ~ ( SV182 @ SV841 ) )
= $true )
| ( ( SV436 @ SV841 )
= $true )
| ( ( SV182 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4251]) ).
thf(4402,plain,
! [SV436: nat > $o,SV828: nat,SV182: nat > $o] :
( ( ( SV182 @ SV828 )
= $false )
| ( ( SV436 @ SV828 )
= $true )
| ( ( SV436 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4252]) ).
thf(4403,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV437 @ SV704 )
= $true )
| ( ( SV437 = SV704 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4253]) ).
thf(4404,plain,
! [SV437: set_Pr1986765409at_nat,SV704: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV704 @ SV437 )
= $true )
| ( ( SV437 = SV704 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4254]) ).
thf(4405,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( SV437 != SV704 )
= $false )
| ( ( ord_le841296385at_nat @ SV437 @ SV704 )
= $false )
| ( ( ord_le841296385at_nat @ SV704 @ SV437 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4255]) ).
thf(4406,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ~ ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) )
= $false )
| ( ( ord_le841296385at_nat @ SV437 @ SV704 )
= $false )
| ( ( ord_le841296385at_nat @ SV704 @ SV437 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4255]) ).
thf(4407,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 ) )
= $false )
| ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4257]) ).
thf(4408,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) )
= $false )
| ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4257]) ).
thf(4409,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ~ ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4258]) ).
thf(4410,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) )
= $false )
| ( ( connected_a @ SV442 @ SV706 @ SV775 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4260]) ).
thf(4411,plain,
! [SV829: list_P559422087at_nat,SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV442 @ SV706 @ SV775 )
| ~ ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) )
= $false )
| ( ( isPath_a @ SV442 @ SV706 @ SV829 @ SV775 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4261]) ).
thf(4412,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( ~ ( ord_less_eq_nat @ ( sK46_SY1241 @ SV196 @ SV449 ) @ SV449 )
| ~ ! [SY1534: nat] :
( ~ ( ord_less_nat @ SY1534 @ ( sK46_SY1241 @ SV196 @ SV449 ) )
| ~ ( SV196 @ SY1534 ) ) )
= $false )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4262]) ).
thf(4413,plain,
! [SV200: set_nat,SV453: nat] :
( ( ( ~ ( member_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SV200 ) )
= $false )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4264]) ).
thf(4414,plain,
! [SV200: set_nat,SV453: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV453 @ ( sK35_SY1245 @ SV453 @ SV200 ) ) )
= $false )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4264]) ).
thf(4415,plain,
! [SV453: nat,SV200: set_nat,SV842: nat] :
( ( ( ~ ( member_nat @ SV842 @ SV200 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SV842 )
| ( ( sK35_SY1245 @ SV453 @ SV200 )
= SV842 ) )
= $true )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4265]) ).
thf(4416,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV847: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ SV847 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SV847 ) ) )
= $true )
| ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4267]) ).
thf(4417,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 )
= $true )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4268]) ).
thf(4418,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4269]) ).
thf(4419,plain,
! [SV615: nat > $o,SV462: nat,SV830: nat,SV210: nat] :
( ( ( dist_a @ c @ SV210 @ SV830 @ SV462 )
= $false )
| ( ( ord_less_eq_nat @ ( sK36_SY1400 @ SV615 @ SV462 @ SV210 ) @ SV830 )
= $true )
| ( ( SV615 @ ( min_dist_a @ c @ SV210 @ SV462 ) )
= $true )
| ( ( connected_a @ c @ SV210 @ SV462 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4270]) ).
thf(4420,plain,
! [SV466: nat,SV816: nat,SV215: nat] :
( ( ( ~ ( dist_b @ c2 @ SV215 @ ( sK66_SY1258 @ SV816 @ SV466 @ SV215 ) @ SV466 ) )
= $false )
| ( ( dist_b @ c2 @ SV215 @ SV816 @ SV466 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4271]) ).
thf(4421,plain,
! [SV222: nat > $o,SV472: nat,SV826: nat] :
( ( ( ~ ( ord_less_nat @ SV826 @ ( sK24_SY974 @ SV472 @ SV222 ) ) )
= $true )
| ( ( ~ ~ ( SV222 @ SV826 ) )
= $true )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4273]) ).
thf(4422,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( isShortestPath_a @ c @ SV229 @ SV478 @ SV620 )
= $true )
| ( ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV478 )
= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4276]) ).
thf(4423,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) ) )
= $true )
| ( ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV478 )
= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4277]) ).
thf(4424,plain,
! [SV484: nat,SV817: list_P559422087at_nat,SV237: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV237 @ ( sK67_SY1277 @ SV817 @ SV484 @ SV237 ) @ SV484 ) )
= $false )
| ( ( isPath_b @ c2 @ SV237 @ SV817 @ SV484 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4278]) ).
thf(4425,plain,
! [SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 ) )
= $false )
| ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4279]) ).
thf(4426,plain,
! [SV776: nat,SV818: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) )
= $false )
| ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4279]) ).
thf(4427,plain,
! [SV776: nat,SV818: nat,SV848: list_P559422087at_nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
| ( ( size_s1990949619at_nat @ SV848 )
!= SV776 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4280]) ).
thf(4428,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( isShortestPath_a @ c @ SV248 @ SV489 @ SV626 )
= $true )
| ( ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV489 )
= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4283]) ).
thf(4429,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) ) )
= $true )
| ( ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV489 )
= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4284]) ).
thf(4430,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) )
= $false )
| ( ( connected_b @ SV491 @ SV713 @ SV777 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4286]) ).
thf(4431,plain,
! [SV831: list_P559422087at_nat,SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV491 @ SV713 @ SV777 )
| ~ ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) )
= $false )
| ( ( isPath_b @ SV491 @ SV713 @ SV831 @ SV777 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4287]) ).
thf(4432,plain,
! [SV498: product_prod_nat_nat > $o,SV843: product_prod_nat_nat,SV259: product_prod_nat_nat > $o] :
( ( ( ~ ( SV259 @ SV843 ) )
= $true )
| ( ( SV498 @ SV843 )
= $true )
| ( ( SV259 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4288]) ).
thf(4433,plain,
! [SV498: product_prod_nat_nat > $o,SV832: product_prod_nat_nat,SV259: product_prod_nat_nat > $o] :
( ( ( SV259 @ SV832 )
= $false )
| ( ( SV498 @ SV832 )
= $true )
| ( ( SV498 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4289]) ).
thf(4434,plain,
! [SV714: nat,SV632: nat,SV499: nat,SV260: nat] :
( ( ( ~ ( connected_a @ c @ SV260 @ ( sK61_SY1466 @ SV499 @ SV632 @ SV714 @ SV260 ) )
| ( ( min_dist_a @ c @ SV260 @ ( sK61_SY1466 @ SV499 @ SV632 @ SV714 @ SV260 ) )
!= SV714 ) )
= $false )
| ( ( ord_less_nat @ SV714 @ SV632 )
= $false )
| ( ( ( min_dist_a @ c @ SV260 @ SV499 )
= SV632 )
= $false )
| ( ( connected_a @ c @ SV260 @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4290]) ).
thf(4435,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 ) )
= $false )
| ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4291]) ).
thf(4436,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) )
= $false )
| ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4291]) ).
thf(4437,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ~ ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4292]) ).
thf(4438,plain,
! [SV750: nat,SV716: nat,SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ( ~ ( ~ ( connected_b @ SV265 @ SV503 @ ( sK63_SY1494 @ SV635 @ SV716 @ SV750 @ SV503 @ SV265 ) )
| ( ( min_dist_b @ SV265 @ SV503 @ ( sK63_SY1494 @ SV635 @ SV716 @ SV750 @ SV503 @ SV265 ) )
!= SV750 ) ) )
= $true )
| ( ( ord_less_nat @ SV750 @ SV716 )
= $false )
| ( ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
= SV716 )
= $false )
| ( ( connected_b @ SV265 @ SV503 @ SV635 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4295]) ).
thf(4439,plain,
! [SV508: nat,SV270: set_nat] :
( ( ( finite_finite_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) )
= $true )
| ( ( finite_finite_nat @ SV270 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4296]) ).
thf(4440,plain,
! [SV508: nat,SV270: set_nat] :
( ( ( ( finite_card_nat @ ( sK27_SY1309 @ SV270 @ SV508 ) )
= SV508 )
= $true )
| ( ( finite_finite_nat @ SV270 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4297]) ).
thf(4441,plain,
! [SV273: set_set_nat,SV509: set_nat] :
( ( ( ~ ( member_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV273 ) )
= $false )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4298]) ).
thf(4442,plain,
! [SV273: set_set_nat,SV509: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV509 ) )
= $false )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4298]) ).
thf(4443,plain,
! [SV509: set_nat,SV273: set_set_nat,SV844: set_nat] :
( ( ( ~ ( member_set_nat @ SV844 @ SV273 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_nat @ SV844 @ ( sK37_SY1310 @ SV509 @ SV273 ) )
| ( ( sK37_SY1310 @ SV509 @ SV273 )
= SV844 ) )
= $true )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4299]) ).
thf(4444,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) )
= $false )
| ( ( connected_b @ SV519 @ SV719 @ SV779 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4301]) ).
thf(4445,plain,
! [SV833: nat,SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV519 @ SV719 @ SV779 )
| ~ ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) )
= $false )
| ( ( dist_b @ SV519 @ SV719 @ SV833 @ SV779 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4302]) ).
thf(4446,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( isShortestPath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $true )
| ( ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV525 )
= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4305]) ).
thf(4447,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) ) )
= $true )
| ( ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV525 )
= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4306]) ).
thf(4448,plain,
! [SV721: nat,SV530: nat] :
( ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $true )
| ( ( ord_less_nat @ SV530 @ SV721 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4307]) ).
thf(4449,plain,
! [SV721: nat,SV530: nat] :
( ( ( SV530 != SV721 )
= $true )
| ( ( ord_less_nat @ SV530 @ SV721 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4308]) ).
thf(4450,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ord_less_nat @ SV530 @ SV721 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $false )
| ( ( SV530 = SV721 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4309]) ).
thf(4451,plain,
! [SV653: nat > $o,SV533: nat,SV834: nat,SV304: nat] :
( ( ( dist_b @ c2 @ SV304 @ SV834 @ SV533 )
= $false )
| ( ( ord_less_eq_nat @ ( sK40_SY1428 @ SV653 @ SV533 @ SV304 ) @ SV834 )
= $true )
| ( ( SV653 @ ( min_dist_b @ c2 @ SV304 @ SV533 ) )
= $true )
| ( ( connected_b @ c2 @ SV304 @ SV533 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4310]) ).
thf(4452,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $true )
| ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4311]) ).
thf(4453,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $true )
| ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4312]) ).
thf(4454,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $true )
| ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4313]) ).
thf(4455,plain,
! [SV797: nat,SV756: list_P559422087at_nat,SV661: nat,SV324: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $true )
| ( ( isPath_b @ SV324 @ SV661 @ SV756 @ SV797 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4314]) ).
thf(4456,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $true )
| ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4315]) ).
thf(4457,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $true )
| ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4316]) ).
thf(4458,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $true )
| ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4317]) ).
thf(4459,plain,
! [SV798: nat,SV757: list_P559422087at_nat,SV662: nat,SV325: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $true )
| ( ( isPath_a @ SV325 @ SV662 @ SV757 @ SV798 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4318]) ).
thf(4460,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $true )
| ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4319]) ).
thf(4461,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $true )
| ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4320]) ).
thf(4462,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $true )
| ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4321]) ).
thf(4463,plain,
! [SV799: nat,SV762: nat,SV667: nat,SV334: product_prod_nat_nat > b] :
( ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $true )
| ( ( dist_b @ SV334 @ SV667 @ SV762 @ SV799 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4322]) ).
thf(4464,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $true )
| ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4323]) ).
thf(4465,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $true )
| ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4324]) ).
thf(4466,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $true )
| ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4325]) ).
thf(4467,plain,
! [SV800: nat,SV763: nat,SV668: nat,SV335: product_prod_nat_nat > a] :
( ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $true )
| ( ( dist_a @ SV335 @ SV668 @ SV763 @ SV800 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4326]) ).
thf(4468,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $true )
| ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4327]) ).
thf(4469,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $true )
| ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4328]) ).
thf(4470,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $true )
| ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4329]) ).
thf(4471,plain,
! [SV801: nat,SV764: list_P559422087at_nat,SV669: nat,SV336: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $true )
| ( ( isShortestPath_a @ SV336 @ SV669 @ SV764 @ SV801 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4330]) ).
thf(4472,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $true )
| ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4331]) ).
thf(4473,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $true )
| ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4332]) ).
thf(4474,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $true )
| ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4333]) ).
thf(4475,plain,
! [SV802: nat,SV765: list_P559422087at_nat,SV670: nat,SV337: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $true )
| ( ( isShortestPath_b @ SV337 @ SV670 @ SV765 @ SV802 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4334]) ).
thf(4476,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $true )
| ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4335]) ).
thf(4477,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $true )
| ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4336]) ).
thf(4478,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $true )
| ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4337]) ).
thf(4479,plain,
! [SV803: nat,SV766: list_P559422087at_nat,SV671: nat,SV345: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $true )
| ( ( isSimplePath_a @ SV345 @ SV671 @ SV766 @ SV803 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4338]) ).
thf(4480,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $true )
| ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4339]) ).
thf(4481,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $true )
| ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4340]) ).
thf(4482,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $true )
| ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4341]) ).
thf(4483,plain,
! [SV804: nat,SV767: list_P559422087at_nat,SV672: nat,SV346: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $true )
| ( ( isSimplePath_b @ SV346 @ SV672 @ SV767 @ SV804 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4342]) ).
thf(4484,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $true )
| ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4343]) ).
thf(4485,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) )
= $true )
| ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4344]) ).
thf(4486,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ~ ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4345]) ).
thf(4487,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
| ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4347]) ).
thf(4488,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( SV372 = SV683 )
= $true )
| ( ( ord_less_eq_set_nat @ SV372 @ SV683 )
= $false )
| ( ( ord_less_eq_set_nat @ SV683 @ SV372 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4350]) ).
thf(4489,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ~ ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV372 @ SV683 )
= $false )
| ( ( ord_less_eq_set_nat @ SV683 @ SV372 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4351]) ).
thf(4490,plain,
! [SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $true )
| ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4352]) ).
thf(4491,plain,
! [SV769: nat,SV806: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) )
= $true )
| ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4353]) ).
thf(4492,plain,
! [SV769: nat,SV806: nat,SV845: list_P559422087at_nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
| ( ( size_s1990949619at_nat @ SV845 )
!= SV769 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4354]) ).
thf(4493,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $true )
| ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4355]) ).
thf(4494,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) )
= $true )
| ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4356]) ).
thf(4495,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4357]) ).
thf(4496,plain,
! [SV576: nat,SV384: nat,SV118: nat] :
( ( ( ~ ( isPath_a @ c @ SV118 @ ( sK55_SY1353 @ SV384 @ SV576 @ SV118 ) @ SV576 ) )
= $false )
| ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4358]) ).
thf(4497,plain,
! [SV118: nat,SV576: nat,SV384: nat] :
( ( ( ( size_s1990949619at_nat @ ( sK55_SY1353 @ SV384 @ SV576 @ SV118 ) )
!= SV384 )
= $false )
| ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4358]) ).
thf(4498,plain,
! [SV820: list_P559422087at_nat,SV576: nat,SV384: nat,SV118: nat] :
( ( ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 )
| ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) )
= $false )
| ( ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV820 )
= SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4359]) ).
thf(4499,plain,
! [SV741: nat,SV689: nat,SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV120 @ SV386 @ ( sK62_SY1479 @ SV577 @ SV689 @ SV741 @ SV386 @ SV120 ) )
| ( ( min_dist_a @ SV120 @ SV386 @ ( sK62_SY1479 @ SV577 @ SV689 @ SV741 @ SV386 @ SV120 ) )
!= SV741 ) )
= $false )
| ( ( ord_less_nat @ SV741 @ SV689 )
= $false )
| ( ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
= SV689 )
= $false )
| ( ( connected_a @ SV120 @ SV386 @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4360]) ).
thf(4500,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV387 @ SV690 @ ( sK68_SY1501 @ SV771 @ SV690 @ SV387 ) @ SV771 ) )
= $false )
| ( ( connected_a @ SV387 @ SV690 @ SV771 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4361]) ).
thf(4501,plain,
! [SV827: nat,SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV387 @ SV690 @ SV771 ) )
= $false )
| ( ( dist_a @ SV387 @ SV690 @ SV827 @ SV771 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4362]) ).
thf(4502,plain,
! [SV827: nat,SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ~ ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) )
= $false )
| ( ( dist_a @ SV387 @ SV690 @ SV827 @ SV771 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4362]) ).
thf(4503,plain,
! [SV691: nat,SV581: nat,SV391: nat,SV128: nat] :
( ( ( ~ ( connected_b @ c2 @ SV128 @ ( sK56_SY1443 @ SV391 @ SV581 @ SV691 @ SV128 ) ) )
= $false )
| ( ( ord_less_nat @ SV691 @ SV581 )
= $false )
| ( ( ( min_dist_b @ c2 @ SV128 @ SV391 )
= SV581 )
= $false )
| ( ( connected_b @ c2 @ SV128 @ SV391 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4363]) ).
thf(4504,plain,
! [SV691: nat,SV581: nat,SV391: nat,SV128: nat] :
( ( ( ( min_dist_b @ c2 @ SV128 @ ( sK56_SY1443 @ SV391 @ SV581 @ SV691 @ SV128 ) )
!= SV691 )
= $false )
| ( ( ord_less_nat @ SV691 @ SV581 )
= $false )
| ( ( ( min_dist_b @ c2 @ SV128 @ SV391 )
= SV581 )
= $false )
| ( ( connected_b @ c2 @ SV128 @ SV391 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4363]) ).
thf(4505,plain,
! [SV692: nat > $o,SV582: nat,SV835: nat,SV392: nat,SV129: product_prod_nat_nat > a] :
( ( ( dist_a @ SV129 @ SV392 @ SV835 @ SV582 )
= $false )
| ( ( ord_less_eq_nat @ ( sK42_SY1444 @ SV692 @ SV582 @ SV392 @ SV129 ) @ SV835 )
= $true )
| ( ( SV692 @ ( min_dist_a @ SV129 @ SV392 @ SV582 ) )
= $true )
| ( ( connected_a @ SV129 @ SV392 @ SV582 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4364]) ).
thf(4506,plain,
! [SV398: nat,SV808: list_P559422087at_nat,SV136: nat] :
( ( ( isPath_a @ c @ SV136 @ ( sK64_SY1164 @ SV808 @ SV398 @ SV136 ) @ SV398 )
= $true )
| ( ( isPath_a @ c @ SV136 @ SV808 @ SV398 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4367]) ).
thf(4507,plain,
! [SV137: set_nat,SV399: nat] :
( ( ( member_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV137 )
= $true )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4368]) ).
thf(4508,plain,
! [SV137: set_nat,SV399: nat] :
( ( ( ord_less_eq_nat @ ( sK29_SY1165 @ SV399 @ SV137 ) @ SV399 )
= $true )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4369]) ).
thf(4509,plain,
! [SV399: nat,SV137: set_nat,SV836: nat] :
( ( ( member_nat @ SV836 @ SV137 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV836 @ ( sK29_SY1165 @ SV399 @ SV137 ) )
| ( ( sK29_SY1165 @ SV399 @ SV137 )
= SV836 ) )
= $true )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4370]) ).
thf(4510,plain,
! [SV407: nat,SV809: nat,SV146: nat] :
( ( ( dist_a @ c @ SV146 @ ( sK65_SY1177 @ SV809 @ SV407 @ SV146 ) @ SV407 )
= $true )
| ( ( dist_a @ c @ SV146 @ SV809 @ SV407 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4373]) ).
thf(4511,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV846: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ SV846 @ SV593 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SV846 ) )
= $true )
| ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4376]) ).
thf(4512,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4377]) ).
thf(4513,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4378]) ).
thf(4514,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4378]) ).
thf(4515,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( ~ ( SV159 @ ( sK58_SY852 @ SV594 @ SV417 @ SV159 ) ) )
= $false )
| ( ( SV159 @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4379]) ).
thf(4516,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( ~ ! [SY1536: nat] :
( ~ ( SV159 @ SY1536 )
| ( ord_less_eq_nat @ SY1536 @ ( sK58_SY852 @ SV594 @ SV417 @ SV159 ) ) ) )
= $false )
| ( ( SV159 @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4379]) ).
thf(4517,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( SV159 @ ( sK52_SY852 @ SV594 @ SV417 @ SV159 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) @ SV594 )
= $false )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4380]) ).
thf(4518,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( ! [SY1535: nat] :
( ~ ( SV159 @ SY1535 )
| ( ord_less_eq_nat @ SY1535 @ ( sK52_SY852 @ SV594 @ SV417 @ SV159 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) @ SV594 )
= $false )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4381]) ).
thf(4519,plain,
! [SV597: nat,SV421: nat,SV163: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV163 @ ( sK59_SY1382 @ SV421 @ SV597 @ SV163 ) @ SV597 ) )
= $false )
| ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4382]) ).
thf(4520,plain,
! [SV163: nat,SV597: nat,SV421: nat] :
( ( ( ( size_s1990949619at_nat @ ( sK59_SY1382 @ SV421 @ SV597 @ SV163 ) )
!= SV421 )
= $false )
| ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4382]) ).
thf(4521,plain,
! [SV821: list_P559422087at_nat,SV597: nat,SV421: nat,SV163: nat] :
( ( ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
| ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV821 )
= SV421 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4383]) ).
thf(4522,plain,
! [SV164: set_set_nat,SV422: set_nat] :
( ( ( member_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SV164 )
= $true )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4384]) ).
thf(4523,plain,
! [SV164: set_set_nat,SV422: set_nat] :
( ( ( ord_less_eq_set_nat @ SV422 @ ( sK32_SY1199 @ SV422 @ SV164 ) )
= $true )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4385]) ).
thf(4524,plain,
! [SV422: set_nat,SV164: set_set_nat,SV837: set_nat] :
( ( ( member_set_nat @ SV837 @ SV164 )
= $false )
| ( ( ~ ( ord_less_eq_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SV837 )
| ( ( sK32_SY1199 @ SV422 @ SV164 )
= SV837 ) )
= $true )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4386]) ).
thf(4525,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $true )
| ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4387]) ).
thf(4526,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) )
= $true )
| ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4388]) ).
thf(4527,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4389]) ).
thf(4528,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $true )
| ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4390]) ).
thf(4529,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) )
= $true )
| ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4391]) ).
thf(4530,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ~ ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4392]) ).
thf(4531,plain,
! [SV173: set_se1612935105at_nat,SV428: set_Pr1986765409at_nat] :
( ( ( member298845450at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV173 )
= $true )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4394]) ).
thf(4532,plain,
! [SV173: set_se1612935105at_nat,SV428: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ ( sK33_SY1214 @ SV428 @ SV173 ) @ SV428 )
= $true )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4395]) ).
thf(4533,plain,
! [SV428: set_Pr1986765409at_nat,SV173: set_se1612935105at_nat,SV838: set_Pr1986765409at_nat] :
( ( ( member298845450at_nat @ SV838 @ SV173 )
= $false )
| ( ( ~ ( ord_le841296385at_nat @ SV838 @ ( sK33_SY1214 @ SV428 @ SV173 ) )
| ( ( sK33_SY1214 @ SV428 @ SV173 )
= SV838 ) )
= $true )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4396]) ).
thf(4534,plain,
! [SV703: nat > $o,SV603: nat,SV839: nat,SV431: nat,SV176: product_prod_nat_nat > b] :
( ( ( dist_b @ SV176 @ SV431 @ SV839 @ SV603 )
= $false )
| ( ( ord_less_eq_nat @ ( sK45_SY1455 @ SV703 @ SV603 @ SV431 @ SV176 ) @ SV839 )
= $true )
| ( ( SV703 @ ( min_dist_b @ SV176 @ SV431 @ SV603 ) )
= $true )
| ( ( connected_b @ SV176 @ SV431 @ SV603 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4397]) ).
thf(4535,plain,
! [SV177: set_se1612935105at_nat,SV432: set_Pr1986765409at_nat] :
( ( ( member298845450at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SV177 )
= $true )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4398]) ).
thf(4536,plain,
! [SV177: set_se1612935105at_nat,SV432: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV432 @ ( sK34_SY1223 @ SV432 @ SV177 ) )
= $true )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4399]) ).
thf(4537,plain,
! [SV432: set_Pr1986765409at_nat,SV177: set_se1612935105at_nat,SV840: set_Pr1986765409at_nat] :
( ( ( member298845450at_nat @ SV840 @ SV177 )
= $false )
| ( ( ~ ( ord_le841296385at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SV840 )
| ( ( sK34_SY1223 @ SV432 @ SV177 )
= SV840 ) )
= $true )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4400]) ).
thf(4538,plain,
! [SV436: nat > $o,SV841: nat,SV182: nat > $o] :
( ( ( SV182 @ SV841 )
= $false )
| ( ( SV436 @ SV841 )
= $true )
| ( ( SV182 @ ( sK19_SY1227 @ SV436 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4401]) ).
thf(4539,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( SV437 = SV704 )
= $true )
| ( ( ord_le841296385at_nat @ SV437 @ SV704 )
= $false )
| ( ( ord_le841296385at_nat @ SV704 @ SV437 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4405]) ).
thf(4540,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ~ ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) ) )
= $true )
| ( ( ord_le841296385at_nat @ SV437 @ SV704 )
= $false )
| ( ( ord_le841296385at_nat @ SV704 @ SV437 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4406]) ).
thf(4541,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $true )
| ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4407]) ).
thf(4542,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) )
= $true )
| ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4408]) ).
thf(4543,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ~ ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4409]) ).
thf(4544,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV442 @ SV706 @ ( sK69_SY1507 @ SV775 @ SV706 @ SV442 ) @ SV775 ) )
= $false )
| ( ( connected_a @ SV442 @ SV706 @ SV775 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4410]) ).
thf(4545,plain,
! [SV829: list_P559422087at_nat,SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV442 @ SV706 @ SV775 ) )
= $false )
| ( ( isPath_a @ SV442 @ SV706 @ SV829 @ SV775 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4411]) ).
thf(4546,plain,
! [SV829: list_P559422087at_nat,SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ~ ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) )
= $false )
| ( ( isPath_a @ SV442 @ SV706 @ SV829 @ SV775 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4411]) ).
thf(4547,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( ~ ( ord_less_eq_nat @ ( sK46_SY1241 @ SV196 @ SV449 ) @ SV449 ) )
= $false )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4412]) ).
thf(4548,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( ~ ! [SY1534: nat] :
( ~ ( ord_less_nat @ SY1534 @ ( sK46_SY1241 @ SV196 @ SV449 ) )
| ~ ( SV196 @ SY1534 ) ) )
= $false )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4412]) ).
thf(4549,plain,
! [SV200: set_nat,SV453: nat] :
( ( ( member_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SV200 )
= $true )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4413]) ).
thf(4550,plain,
! [SV200: set_nat,SV453: nat] :
( ( ( ord_less_eq_nat @ SV453 @ ( sK35_SY1245 @ SV453 @ SV200 ) )
= $true )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4414]) ).
thf(4551,plain,
! [SV453: nat,SV200: set_nat,SV842: nat] :
( ( ( member_nat @ SV842 @ SV200 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SV842 )
| ( ( sK35_SY1245 @ SV453 @ SV200 )
= SV842 ) )
= $true )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4415]) ).
thf(4552,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV847: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ SV847 @ SV614 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SV847 ) )
= $true )
| ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4416]) ).
thf(4553,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4417]) ).
thf(4554,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4418]) ).
thf(4555,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4418]) ).
thf(4556,plain,
! [SV466: nat,SV816: nat,SV215: nat] :
( ( ( dist_b @ c2 @ SV215 @ ( sK66_SY1258 @ SV816 @ SV466 @ SV215 ) @ SV466 )
= $true )
| ( ( dist_b @ c2 @ SV215 @ SV816 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4420]) ).
thf(4557,plain,
! [SV222: nat > $o,SV472: nat,SV826: nat] :
( ( ( ord_less_nat @ SV826 @ ( sK24_SY974 @ SV472 @ SV222 ) )
= $false )
| ( ( ~ ~ ( SV222 @ SV826 ) )
= $true )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4421]) ).
thf(4558,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
| ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) ) )
= $false )
| ( ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV478 )
= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4423]) ).
thf(4559,plain,
! [SV484: nat,SV817: list_P559422087at_nat,SV237: nat] :
( ( ( isPath_b @ c2 @ SV237 @ ( sK67_SY1277 @ SV817 @ SV484 @ SV237 ) @ SV484 )
= $true )
| ( ( isPath_b @ c2 @ SV237 @ SV817 @ SV484 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4424]) ).
thf(4560,plain,
! [SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $true )
| ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4425]) ).
thf(4561,plain,
! [SV776: nat,SV818: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) )
= $true )
| ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4426]) ).
thf(4562,plain,
! [SV776: nat,SV818: nat,SV848: list_P559422087at_nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
| ( ( size_s1990949619at_nat @ SV848 )
!= SV776 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4427]) ).
thf(4563,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
| ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) ) )
= $false )
| ( ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV489 )
= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4429]) ).
thf(4564,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV491 @ SV713 @ ( sK70_SY1510 @ SV777 @ SV713 @ SV491 ) @ SV777 ) )
= $false )
| ( ( connected_b @ SV491 @ SV713 @ SV777 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4430]) ).
thf(4565,plain,
! [SV831: list_P559422087at_nat,SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV491 @ SV713 @ SV777 ) )
= $false )
| ( ( isPath_b @ SV491 @ SV713 @ SV831 @ SV777 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4431]) ).
thf(4566,plain,
! [SV831: list_P559422087at_nat,SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ~ ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) )
= $false )
| ( ( isPath_b @ SV491 @ SV713 @ SV831 @ SV777 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4431]) ).
thf(4567,plain,
! [SV498: product_prod_nat_nat > $o,SV843: product_prod_nat_nat,SV259: product_prod_nat_nat > $o] :
( ( ( SV259 @ SV843 )
= $false )
| ( ( SV498 @ SV843 )
= $true )
| ( ( SV259 @ ( sK26_SY1292 @ SV498 @ SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4432]) ).
thf(4568,plain,
! [SV714: nat,SV632: nat,SV499: nat,SV260: nat] :
( ( ( ~ ( connected_a @ c @ SV260 @ ( sK61_SY1466 @ SV499 @ SV632 @ SV714 @ SV260 ) ) )
= $false )
| ( ( ord_less_nat @ SV714 @ SV632 )
= $false )
| ( ( ( min_dist_a @ c @ SV260 @ SV499 )
= SV632 )
= $false )
| ( ( connected_a @ c @ SV260 @ SV499 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4434]) ).
thf(4569,plain,
! [SV714: nat,SV632: nat,SV499: nat,SV260: nat] :
( ( ( ( min_dist_a @ c @ SV260 @ ( sK61_SY1466 @ SV499 @ SV632 @ SV714 @ SV260 ) )
!= SV714 )
= $false )
| ( ( ord_less_nat @ SV714 @ SV632 )
= $false )
| ( ( ( min_dist_a @ c @ SV260 @ SV499 )
= SV632 )
= $false )
| ( ( connected_a @ c @ SV260 @ SV499 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4434]) ).
thf(4570,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $true )
| ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4435]) ).
thf(4571,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) )
= $true )
| ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4436]) ).
thf(4572,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $true )
| ( ( ~ ( ~ ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ~ ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4437]) ).
thf(4573,plain,
! [SV750: nat,SV716: nat,SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV265 @ SV503 @ ( sK63_SY1494 @ SV635 @ SV716 @ SV750 @ SV503 @ SV265 ) )
| ( ( min_dist_b @ SV265 @ SV503 @ ( sK63_SY1494 @ SV635 @ SV716 @ SV750 @ SV503 @ SV265 ) )
!= SV750 ) )
= $false )
| ( ( ord_less_nat @ SV750 @ SV716 )
= $false )
| ( ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
= SV716 )
= $false )
| ( ( connected_b @ SV265 @ SV503 @ SV635 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4438]) ).
thf(4574,plain,
! [SV273: set_set_nat,SV509: set_nat] :
( ( ( member_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV273 )
= $true )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4441]) ).
thf(4575,plain,
! [SV273: set_set_nat,SV509: set_nat] :
( ( ( ord_less_eq_set_nat @ ( sK37_SY1310 @ SV509 @ SV273 ) @ SV509 )
= $true )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4442]) ).
thf(4576,plain,
! [SV509: set_nat,SV273: set_set_nat,SV844: set_nat] :
( ( ( member_set_nat @ SV844 @ SV273 )
= $false )
| ( ( ~ ( ord_less_eq_set_nat @ SV844 @ ( sK37_SY1310 @ SV509 @ SV273 ) )
| ( ( sK37_SY1310 @ SV509 @ SV273 )
= SV844 ) )
= $true )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4443]) ).
thf(4577,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV519 @ SV719 @ ( sK71_SY1512 @ SV779 @ SV719 @ SV519 ) @ SV779 ) )
= $false )
| ( ( connected_b @ SV519 @ SV719 @ SV779 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4444]) ).
thf(4578,plain,
! [SV833: nat,SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV519 @ SV719 @ SV779 ) )
= $false )
| ( ( dist_b @ SV519 @ SV719 @ SV833 @ SV779 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4445]) ).
thf(4579,plain,
! [SV833: nat,SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ~ ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) )
= $false )
| ( ( dist_b @ SV519 @ SV719 @ SV833 @ SV779 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4445]) ).
thf(4580,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
| ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) ) )
= $false )
| ( ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV525 )
= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4447]) ).
thf(4581,plain,
! [SV721: nat,SV530: nat] :
( ( ( SV530 = SV721 )
= $false )
| ( ( ord_less_nat @ SV530 @ SV721 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4449]) ).
thf(4582,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ord_less_nat @ SV530 @ SV721 ) )
= $false )
| ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $false )
| ( ( SV530 = SV721 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4450]) ).
thf(4583,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $false )
| ( ( SV530 = SV721 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4450]) ).
thf(4584,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) )
= $false )
| ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4485]) ).
thf(4585,plain,
! [SV805: nat,SV681: nat,SV366: product_prod_nat_nat > a,SV768: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV768 )
= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $false )
| ( ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ~ ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4486]) ).
thf(4586,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 ) )
= $false )
| ( ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4487]) ).
thf(4587,plain,
! [SV566: nat,SV97: nat,SV367: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV367 )
!= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $false )
| ( ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4487]) ).
thf(4588,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 )
| ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV372 @ SV683 )
= $false )
| ( ( ord_less_eq_set_nat @ SV683 @ SV372 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4489]) ).
thf(4589,plain,
! [SV769: nat,SV806: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) )
= $false )
| ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4491]) ).
thf(4590,plain,
! [SV769: nat,SV806: nat,SV845: list_P559422087at_nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
| ( ( size_s1990949619at_nat @ SV845 )
!= SV769 ) )
= $true )
| ( ( ~ ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4492]) ).
thf(4591,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) )
= $false )
| ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4494]) ).
thf(4592,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4495]) ).
thf(4593,plain,
! [SV576: nat,SV384: nat,SV118: nat] :
( ( ( isPath_a @ c @ SV118 @ ( sK55_SY1353 @ SV384 @ SV576 @ SV118 ) @ SV576 )
= $true )
| ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4496]) ).
thf(4594,plain,
! [SV118: nat,SV576: nat,SV384: nat] :
( ( ( ( size_s1990949619at_nat @ ( sK55_SY1353 @ SV384 @ SV576 @ SV118 ) )
= SV384 )
= $true )
| ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4497]) ).
thf(4595,plain,
! [SV820: list_P559422087at_nat,SV576: nat,SV384: nat,SV118: nat] :
( ( ( ~ ( dist_a @ c @ SV118 @ SV384 @ SV576 ) )
= $false )
| ( ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV820 )
= SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4498]) ).
thf(4596,plain,
! [SV820: list_P559422087at_nat,SV384: nat,SV576: nat,SV118: nat] :
( ( ( ~ ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) )
= $false )
| ( ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV820 )
= SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4498]) ).
thf(4597,plain,
! [SV741: nat,SV689: nat,SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ( ~ ( connected_a @ SV120 @ SV386 @ ( sK62_SY1479 @ SV577 @ SV689 @ SV741 @ SV386 @ SV120 ) ) )
= $false )
| ( ( ord_less_nat @ SV741 @ SV689 )
= $false )
| ( ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
= SV689 )
= $false )
| ( ( connected_a @ SV120 @ SV386 @ SV577 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4499]) ).
thf(4598,plain,
! [SV741: nat,SV689: nat,SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ( ( min_dist_a @ SV120 @ SV386 @ ( sK62_SY1479 @ SV577 @ SV689 @ SV741 @ SV386 @ SV120 ) )
!= SV741 )
= $false )
| ( ( ord_less_nat @ SV741 @ SV689 )
= $false )
| ( ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
= SV689 )
= $false )
| ( ( connected_a @ SV120 @ SV386 @ SV577 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4499]) ).
thf(4599,plain,
! [SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( dist_a @ SV387 @ SV690 @ ( sK68_SY1501 @ SV771 @ SV690 @ SV387 ) @ SV771 )
= $true )
| ( ( connected_a @ SV387 @ SV690 @ SV771 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4500]) ).
thf(4600,plain,
! [SV827: nat,SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( connected_a @ SV387 @ SV690 @ SV771 )
= $true )
| ( ( dist_a @ SV387 @ SV690 @ SV827 @ SV771 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4501]) ).
thf(4601,plain,
! [SV827: nat,SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) )
= $true )
| ( ( dist_a @ SV387 @ SV690 @ SV827 @ SV771 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4502]) ).
thf(4602,plain,
! [SV691: nat,SV581: nat,SV391: nat,SV128: nat] :
( ( ( connected_b @ c2 @ SV128 @ ( sK56_SY1443 @ SV391 @ SV581 @ SV691 @ SV128 ) )
= $true )
| ( ( ord_less_nat @ SV691 @ SV581 )
= $false )
| ( ( ( min_dist_b @ c2 @ SV128 @ SV391 )
= SV581 )
= $false )
| ( ( connected_b @ c2 @ SV128 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4503]) ).
thf(4603,plain,
! [SV691: nat,SV581: nat,SV391: nat,SV128: nat] :
( ( ( ( min_dist_b @ c2 @ SV128 @ ( sK56_SY1443 @ SV391 @ SV581 @ SV691 @ SV128 ) )
= SV691 )
= $true )
| ( ( ord_less_nat @ SV691 @ SV581 )
= $false )
| ( ( ( min_dist_b @ c2 @ SV128 @ SV391 )
= SV581 )
= $false )
| ( ( connected_b @ c2 @ SV128 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4504]) ).
thf(4604,plain,
! [SV137: set_nat,SV399: nat,SV836: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV836 @ ( sK29_SY1165 @ SV399 @ SV137 ) ) )
= $true )
| ( ( ( sK29_SY1165 @ SV399 @ SV137 )
= SV836 )
= $true )
| ( ( member_nat @ SV836 @ SV137 )
= $false )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4509]) ).
thf(4605,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV846: list_P559422087at_nat,SV158: nat] :
( ( ( isPath_b @ c2 @ SV158 @ SV846 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SV846 ) )
= $true )
| ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4511]) ).
thf(4606,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4512]) ).
thf(4607,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4512]) ).
thf(4608,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $true )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4513]) ).
thf(4609,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) )
= $true )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4514]) ).
thf(4610,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( SV159 @ ( sK58_SY852 @ SV594 @ SV417 @ SV159 ) )
= $true )
| ( ( SV159 @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4515]) ).
thf(4611,plain,
! [SV417: nat,SV594: nat,SV159: nat > $o] :
( ( ( ! [SY1536: nat] :
( ~ ( SV159 @ SY1536 )
| ( ord_less_eq_nat @ SY1536 @ ( sK58_SY852 @ SV594 @ SV417 @ SV159 ) ) ) )
= $true )
| ( ( SV159 @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4516]) ).
thf(4612,plain,
! [SV417: nat,SV594: nat,SV849: nat,SV159: nat > $o] :
( ( ( ~ ( SV159 @ SV849 )
| ( ord_less_eq_nat @ SV849 @ ( sK52_SY852 @ SV594 @ SV417 @ SV159 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) @ SV594 )
= $false )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4518]) ).
thf(4613,plain,
! [SV597: nat,SV421: nat,SV163: nat] :
( ( ( isPath_b @ c2 @ SV163 @ ( sK59_SY1382 @ SV421 @ SV597 @ SV163 ) @ SV597 )
= $true )
| ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4519]) ).
thf(4614,plain,
! [SV163: nat,SV597: nat,SV421: nat] :
( ( ( ( size_s1990949619at_nat @ ( sK59_SY1382 @ SV421 @ SV597 @ SV163 ) )
= SV421 )
= $true )
| ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4520]) ).
thf(4615,plain,
! [SV821: list_P559422087at_nat,SV597: nat,SV421: nat,SV163: nat] :
( ( ( ~ ( dist_b @ c2 @ SV163 @ SV421 @ SV597 ) )
= $false )
| ( ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV821 )
= SV421 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4521]) ).
thf(4616,plain,
! [SV821: list_P559422087at_nat,SV421: nat,SV597: nat,SV163: nat] :
( ( ( ~ ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV821 )
= SV421 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4521]) ).
thf(4617,plain,
! [SV837: set_nat,SV164: set_set_nat,SV422: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SV837 ) )
= $true )
| ( ( ( sK32_SY1199 @ SV422 @ SV164 )
= SV837 )
= $true )
| ( ( member_set_nat @ SV837 @ SV164 )
= $false )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4524]) ).
thf(4618,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) )
= $false )
| ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4526]) ).
thf(4619,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4527]) ).
thf(4620,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) )
= $false )
| ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4529]) ).
thf(4621,plain,
! [SV811: nat,SV702: nat,SV426: product_prod_nat_nat > a,SV773: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV773 )
= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $false )
| ( ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ~ ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4530]) ).
thf(4622,plain,
! [SV173: set_se1612935105at_nat,SV428: set_Pr1986765409at_nat,SV838: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV838 @ ( sK33_SY1214 @ SV428 @ SV173 ) ) )
= $true )
| ( ( ( sK33_SY1214 @ SV428 @ SV173 )
= SV838 )
= $true )
| ( ( member298845450at_nat @ SV838 @ SV173 )
= $false )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4533]) ).
thf(4623,plain,
! [SV840: set_Pr1986765409at_nat,SV177: set_se1612935105at_nat,SV432: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SV840 ) )
= $true )
| ( ( ( sK34_SY1223 @ SV432 @ SV177 )
= SV840 )
= $true )
| ( ( member298845450at_nat @ SV840 @ SV177 )
= $false )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4537]) ).
thf(4624,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 )
| ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) )
= $false )
| ( ( ord_le841296385at_nat @ SV437 @ SV704 )
= $false )
| ( ( ord_le841296385at_nat @ SV704 @ SV437 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4540]) ).
thf(4625,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) )
= $false )
| ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4542]) ).
thf(4626,plain,
! [SV814: nat,SV705: nat,SV439: product_prod_nat_nat > b,SV774: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV774 )
= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $false )
| ( ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ~ ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4543]) ).
thf(4627,plain,
! [SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV442 @ SV706 @ ( sK69_SY1507 @ SV775 @ SV706 @ SV442 ) @ SV775 )
= $true )
| ( ( connected_a @ SV442 @ SV706 @ SV775 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4544]) ).
thf(4628,plain,
! [SV829: list_P559422087at_nat,SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( connected_a @ SV442 @ SV706 @ SV775 )
= $true )
| ( ( isPath_a @ SV442 @ SV706 @ SV829 @ SV775 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4545]) ).
thf(4629,plain,
! [SV829: list_P559422087at_nat,SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) )
= $true )
| ( ( isPath_a @ SV442 @ SV706 @ SV829 @ SV775 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4546]) ).
thf(4630,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( ord_less_eq_nat @ ( sK46_SY1241 @ SV196 @ SV449 ) @ SV449 )
= $true )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4547]) ).
thf(4631,plain,
! [SV449: nat,SV196: nat > $o] :
( ( ( ! [SY1534: nat] :
( ~ ( ord_less_nat @ SY1534 @ ( sK46_SY1241 @ SV196 @ SV449 ) )
| ~ ( SV196 @ SY1534 ) ) )
= $true )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4548]) ).
thf(4632,plain,
! [SV842: nat,SV200: set_nat,SV453: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SV842 ) )
= $true )
| ( ( ( sK35_SY1245 @ SV453 @ SV200 )
= SV842 )
= $true )
| ( ( member_nat @ SV842 @ SV200 )
= $false )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4551]) ).
thf(4633,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV847: list_P559422087at_nat,SV208: nat] :
( ( ( isPath_a @ c @ SV208 @ SV847 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SV847 ) )
= $true )
| ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4552]) ).
thf(4634,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4553]) ).
thf(4635,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4553]) ).
thf(4636,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $true )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4554]) ).
thf(4637,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) )
= $true )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4555]) ).
thf(4638,plain,
! [SV472: nat,SV826: nat,SV222: nat > $o] :
( ( ( ~ ( SV222 @ SV826 ) )
= $false )
| ( ( ord_less_nat @ SV826 @ ( sK24_SY974 @ SV472 @ SV222 ) )
= $false )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4557]) ).
thf(4639,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( ~ ( isPath_a @ c @ SV229 @ SV478 @ SV620 ) )
= $false )
| ( ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV478 )
= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4558]) ).
thf(4640,plain,
! [SV620: nat,SV229: nat,SV478: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV478 )
!= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $false )
| ( ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV478 )
= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4558]) ).
thf(4641,plain,
! [SV776: nat,SV818: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) )
= $false )
| ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4561]) ).
thf(4642,plain,
! [SV776: nat,SV818: nat,SV848: list_P559422087at_nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
| ( ( size_s1990949619at_nat @ SV848 )
!= SV776 ) )
= $true )
| ( ( ~ ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4562]) ).
thf(4643,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( ~ ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 ) )
= $false )
| ( ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV489 )
= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4563]) ).
thf(4644,plain,
! [SV626: nat,SV248: nat,SV489: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV489 )
!= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $false )
| ( ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV489 )
= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4563]) ).
thf(4645,plain,
! [SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV491 @ SV713 @ ( sK70_SY1510 @ SV777 @ SV713 @ SV491 ) @ SV777 )
= $true )
| ( ( connected_b @ SV491 @ SV713 @ SV777 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4564]) ).
thf(4646,plain,
! [SV831: list_P559422087at_nat,SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( connected_b @ SV491 @ SV713 @ SV777 )
= $true )
| ( ( isPath_b @ SV491 @ SV713 @ SV831 @ SV777 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4565]) ).
thf(4647,plain,
! [SV831: list_P559422087at_nat,SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) )
= $true )
| ( ( isPath_b @ SV491 @ SV713 @ SV831 @ SV777 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4566]) ).
thf(4648,plain,
! [SV714: nat,SV632: nat,SV499: nat,SV260: nat] :
( ( ( connected_a @ c @ SV260 @ ( sK61_SY1466 @ SV499 @ SV632 @ SV714 @ SV260 ) )
= $true )
| ( ( ord_less_nat @ SV714 @ SV632 )
= $false )
| ( ( ( min_dist_a @ c @ SV260 @ SV499 )
= SV632 )
= $false )
| ( ( connected_a @ c @ SV260 @ SV499 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4568]) ).
thf(4649,plain,
! [SV714: nat,SV632: nat,SV499: nat,SV260: nat] :
( ( ( ( min_dist_a @ c @ SV260 @ ( sK61_SY1466 @ SV499 @ SV632 @ SV714 @ SV260 ) )
= SV714 )
= $true )
| ( ( ord_less_nat @ SV714 @ SV632 )
= $false )
| ( ( ( min_dist_a @ c @ SV260 @ SV499 )
= SV632 )
= $false )
| ( ( connected_a @ c @ SV260 @ SV499 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4569]) ).
thf(4650,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) )
= $false )
| ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4571]) ).
thf(4651,plain,
! [SV819: nat,SV715: nat,SV501: product_prod_nat_nat > b,SV778: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV778 )
= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $false )
| ( ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ~ ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4572]) ).
thf(4652,plain,
! [SV750: nat,SV716: nat,SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ( ~ ( connected_b @ SV265 @ SV503 @ ( sK63_SY1494 @ SV635 @ SV716 @ SV750 @ SV503 @ SV265 ) ) )
= $false )
| ( ( ord_less_nat @ SV750 @ SV716 )
= $false )
| ( ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
= SV716 )
= $false )
| ( ( connected_b @ SV265 @ SV503 @ SV635 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4573]) ).
thf(4653,plain,
! [SV750: nat,SV716: nat,SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ( ( min_dist_b @ SV265 @ SV503 @ ( sK63_SY1494 @ SV635 @ SV716 @ SV750 @ SV503 @ SV265 ) )
!= SV750 )
= $false )
| ( ( ord_less_nat @ SV750 @ SV716 )
= $false )
| ( ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
= SV716 )
= $false )
| ( ( connected_b @ SV265 @ SV503 @ SV635 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4573]) ).
thf(4654,plain,
! [SV273: set_set_nat,SV509: set_nat,SV844: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV844 @ ( sK37_SY1310 @ SV509 @ SV273 ) ) )
= $true )
| ( ( ( sK37_SY1310 @ SV509 @ SV273 )
= SV844 )
= $true )
| ( ( member_set_nat @ SV844 @ SV273 )
= $false )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4576]) ).
thf(4655,plain,
! [SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( dist_b @ SV519 @ SV719 @ ( sK71_SY1512 @ SV779 @ SV719 @ SV519 ) @ SV779 )
= $true )
| ( ( connected_b @ SV519 @ SV719 @ SV779 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4577]) ).
thf(4656,plain,
! [SV833: nat,SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( connected_b @ SV519 @ SV719 @ SV779 )
= $true )
| ( ( dist_b @ SV519 @ SV719 @ SV833 @ SV779 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4578]) ).
thf(4657,plain,
! [SV833: nat,SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) )
= $true )
| ( ( dist_b @ SV519 @ SV719 @ SV833 @ SV779 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4579]) ).
thf(4658,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( ~ ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 ) )
= $false )
| ( ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV525 )
= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4580]) ).
thf(4659,plain,
! [SV648: nat,SV293: nat,SV525: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV525 )
!= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $false )
| ( ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV525 )
= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4580]) ).
thf(4660,plain,
! [SV721: nat,SV530: nat] :
( ( ( ord_less_nat @ SV530 @ SV721 )
= $true )
| ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $false )
| ( ( SV530 = SV721 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4582]) ).
thf(4661,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $false )
| ( ( SV530 = SV721 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4583]) ).
thf(4662,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 ) )
= $false )
| ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4584]) ).
thf(4663,plain,
! [SV805: nat,SV681: nat,SV366: product_prod_nat_nat > a,SV768: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $false )
| ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4584]) ).
thf(4664,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ~ ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) )
= $false )
| ( ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV768 )
= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4585]) ).
thf(4665,plain,
! [SV566: nat,SV367: list_P559422087at_nat,SV97: nat] :
( ( ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $true )
| ( ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4586]) ).
thf(4666,plain,
! [SV566: nat,SV97: nat,SV367: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV367 )
= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $true )
| ( ( isPath_b @ c2 @ SV97 @ SV367 @ SV566 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= ( min_dist_b @ c2 @ SV97 @ SV566 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4587]) ).
thf(4667,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV372 @ SV683 ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV372 @ SV683 )
= $false )
| ( ( ord_less_eq_set_nat @ SV683 @ SV372 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4588]) ).
thf(4668,plain,
! [SV372: set_nat,SV683: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV683 @ SV372 ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV372 @ SV683 )
= $false )
| ( ( ord_less_eq_set_nat @ SV683 @ SV372 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4588]) ).
thf(4669,plain,
! [SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ ( sK72_SY1520 @ SV769 @ SV806 @ SV686 @ SV380 ) @ SV806 )
| ( ( size_s1990949619at_nat @ ( sK72_SY1520 @ SV769 @ SV806 @ SV686 @ SV380 ) )
!= SV769 ) ) )
= $false )
| ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4589]) ).
thf(4670,plain,
! [SV769: nat,SV806: nat,SV845: list_P559422087at_nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV845 )
!= SV769 )
= $true )
| ( ( ~ ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4590]) ).
thf(4671,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 ) )
= $false )
| ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4591]) ).
thf(4672,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) )
= $false )
| ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4591]) ).
thf(4673,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) ) ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4592]) ).
thf(4674,plain,
! [SV820: list_P559422087at_nat,SV576: nat,SV384: nat,SV118: nat] :
( ( ( dist_a @ c @ SV118 @ SV384 @ SV576 )
= $true )
| ( ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV820 )
= SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4595]) ).
thf(4675,plain,
! [SV820: list_P559422087at_nat,SV384: nat,SV576: nat,SV118: nat] :
( ( ( ~ ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) )
= $true )
| ( ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV820 )
= SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4596]) ).
thf(4676,plain,
! [SV741: nat,SV689: nat,SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ( connected_a @ SV120 @ SV386 @ ( sK62_SY1479 @ SV577 @ SV689 @ SV741 @ SV386 @ SV120 ) )
= $true )
| ( ( ord_less_nat @ SV741 @ SV689 )
= $false )
| ( ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
= SV689 )
= $false )
| ( ( connected_a @ SV120 @ SV386 @ SV577 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4597]) ).
thf(4677,plain,
! [SV741: nat,SV689: nat,SV577: nat,SV386: nat,SV120: product_prod_nat_nat > a] :
( ( ( ( min_dist_a @ SV120 @ SV386 @ ( sK62_SY1479 @ SV577 @ SV689 @ SV741 @ SV386 @ SV120 ) )
= SV741 )
= $true )
| ( ( ord_less_nat @ SV741 @ SV689 )
= $false )
| ( ( ( min_dist_a @ SV120 @ SV386 @ SV577 )
= SV689 )
= $false )
| ( ( connected_a @ SV120 @ SV386 @ SV577 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4598]) ).
thf(4678,plain,
! [SV827: nat,SV771: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ! [SY1501: nat] :
~ ( dist_a @ SV387 @ SV690 @ SY1501 @ SV771 ) )
= $false )
| ( ( dist_a @ SV387 @ SV690 @ SV827 @ SV771 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4601]) ).
thf(4679,plain,
! [SV137: set_nat,SV399: nat,SV836: nat] :
( ( ( ord_less_eq_nat @ SV836 @ ( sK29_SY1165 @ SV399 @ SV137 ) )
= $false )
| ( ( ( sK29_SY1165 @ SV399 @ SV137 )
= SV836 )
= $true )
| ( ( member_nat @ SV836 @ SV137 )
= $false )
| ( ( member_nat @ SV399 @ SV137 )
= $false )
| ( ( finite_finite_nat @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4604]) ).
thf(4680,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( isShortestPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $true )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4606]) ).
thf(4681,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) ) )
= $true )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4607]) ).
thf(4682,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4609]) ).
thf(4683,plain,
! [SV417: nat,SV594: nat,SV850: nat,SV159: nat > $o] :
( ( ( ~ ( SV159 @ SV850 )
| ( ord_less_eq_nat @ SV850 @ ( sK58_SY852 @ SV594 @ SV417 @ SV159 ) ) )
= $true )
| ( ( SV159 @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4611]) ).
thf(4684,plain,
! [SV417: nat,SV594: nat,SV849: nat,SV159: nat > $o] :
( ( ( ~ ( SV159 @ SV849 ) )
= $true )
| ( ( ord_less_eq_nat @ SV849 @ ( sK52_SY852 @ SV594 @ SV417 @ SV159 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) @ SV594 )
= $false )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4612]) ).
thf(4685,plain,
! [SV821: list_P559422087at_nat,SV597: nat,SV421: nat,SV163: nat] :
( ( ( dist_b @ c2 @ SV163 @ SV421 @ SV597 )
= $true )
| ( ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV821 )
= SV421 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4615]) ).
thf(4686,plain,
! [SV821: list_P559422087at_nat,SV421: nat,SV597: nat,SV163: nat] :
( ( ( ~ ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) )
= $true )
| ( ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV821 )
= SV421 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4616]) ).
thf(4687,plain,
! [SV837: set_nat,SV164: set_set_nat,SV422: set_nat] :
( ( ( ord_less_eq_set_nat @ ( sK32_SY1199 @ SV422 @ SV164 ) @ SV837 )
= $false )
| ( ( ( sK32_SY1199 @ SV422 @ SV164 )
= SV837 )
= $true )
| ( ( member_set_nat @ SV837 @ SV164 )
= $false )
| ( ( member_set_nat @ SV422 @ SV164 )
= $false )
| ( ( finite2012248349et_nat @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4617]) ).
thf(4688,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 ) )
= $false )
| ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4618]) ).
thf(4689,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) )
= $false )
| ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4618]) ).
thf(4690,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) ) ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4619]) ).
thf(4691,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 ) )
= $false )
| ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4620]) ).
thf(4692,plain,
! [SV811: nat,SV702: nat,SV426: product_prod_nat_nat > a,SV773: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $false )
| ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4620]) ).
thf(4693,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ~ ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) )
= $false )
| ( ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV773 )
= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4621]) ).
thf(4694,plain,
! [SV173: set_se1612935105at_nat,SV428: set_Pr1986765409at_nat,SV838: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV838 @ ( sK33_SY1214 @ SV428 @ SV173 ) )
= $false )
| ( ( ( sK33_SY1214 @ SV428 @ SV173 )
= SV838 )
= $true )
| ( ( member298845450at_nat @ SV838 @ SV173 )
= $false )
| ( ( member298845450at_nat @ SV428 @ SV173 )
= $false )
| ( ( finite1457549322at_nat @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4622]) ).
thf(4695,plain,
! [SV840: set_Pr1986765409at_nat,SV177: set_se1612935105at_nat,SV432: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ ( sK34_SY1223 @ SV432 @ SV177 ) @ SV840 )
= $false )
| ( ( ( sK34_SY1223 @ SV432 @ SV177 )
= SV840 )
= $true )
| ( ( member298845450at_nat @ SV840 @ SV177 )
= $false )
| ( ( member298845450at_nat @ SV432 @ SV177 )
= $false )
| ( ( finite1457549322at_nat @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4623]) ).
thf(4696,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV437 @ SV704 ) )
= $false )
| ( ( ord_le841296385at_nat @ SV437 @ SV704 )
= $false )
| ( ( ord_le841296385at_nat @ SV704 @ SV437 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4624]) ).
thf(4697,plain,
! [SV437: set_Pr1986765409at_nat,SV704: set_Pr1986765409at_nat] :
( ( ( ~ ( ord_le841296385at_nat @ SV704 @ SV437 ) )
= $false )
| ( ( ord_le841296385at_nat @ SV437 @ SV704 )
= $false )
| ( ( ord_le841296385at_nat @ SV704 @ SV437 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4624]) ).
thf(4698,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 ) )
= $false )
| ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4625]) ).
thf(4699,plain,
! [SV814: nat,SV705: nat,SV439: product_prod_nat_nat > b,SV774: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $false )
| ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4625]) ).
thf(4700,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ~ ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) )
= $false )
| ( ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV774 )
= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4626]) ).
thf(4701,plain,
! [SV829: list_P559422087at_nat,SV775: nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ! [SY1507: list_P559422087at_nat] :
~ ( isPath_a @ SV442 @ SV706 @ SY1507 @ SV775 ) )
= $false )
| ( ( isPath_a @ SV442 @ SV706 @ SV829 @ SV775 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4629]) ).
thf(4702,plain,
! [SV449: nat,SV196: nat > $o,SV851: nat] :
( ( ( ~ ( ord_less_nat @ SV851 @ ( sK46_SY1241 @ SV196 @ SV449 ) )
| ~ ( SV196 @ SV851 ) )
= $true )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4631]) ).
thf(4703,plain,
! [SV842: nat,SV200: set_nat,SV453: nat] :
( ( ( ord_less_eq_nat @ ( sK35_SY1245 @ SV453 @ SV200 ) @ SV842 )
= $false )
| ( ( ( sK35_SY1245 @ SV453 @ SV200 )
= SV842 )
= $true )
| ( ( member_nat @ SV842 @ SV200 )
= $false )
| ( ( member_nat @ SV453 @ SV200 )
= $false )
| ( ( finite_finite_nat @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4632]) ).
thf(4704,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( isShortestPath_a @ c @ SV208 @ SV460 @ SV614 )
= $true )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4634]) ).
thf(4705,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) ) )
= $true )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4635]) ).
thf(4706,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4637]) ).
thf(4707,plain,
! [SV472: nat,SV826: nat,SV222: nat > $o] :
( ( ( SV222 @ SV826 )
= $true )
| ( ( ord_less_nat @ SV826 @ ( sK24_SY974 @ SV472 @ SV222 ) )
= $false )
| ( ( SV222 @ SV472 )
= $true )
| ( ( SV222 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4638]) ).
thf(4708,plain,
! [SV620: nat,SV478: list_P559422087at_nat,SV229: nat] :
( ( ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
= $true )
| ( ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV478 )
= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4639]) ).
thf(4709,plain,
! [SV620: nat,SV229: nat,SV478: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV478 )
= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $true )
| ( ( isPath_a @ c @ SV229 @ SV478 @ SV620 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV478 )
= ( min_dist_a @ c @ SV229 @ SV620 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4640]) ).
thf(4710,plain,
! [SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ ( sK75_SY1529 @ SV776 @ SV818 @ SV712 @ SV488 ) @ SV818 )
| ( ( size_s1990949619at_nat @ ( sK75_SY1529 @ SV776 @ SV818 @ SV712 @ SV488 ) )
!= SV776 ) ) )
= $false )
| ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4641]) ).
thf(4711,plain,
! [SV776: nat,SV818: nat,SV848: list_P559422087at_nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV848 )
!= SV776 )
= $true )
| ( ( ~ ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4642]) ).
thf(4712,plain,
! [SV626: nat,SV489: list_P559422087at_nat,SV248: nat] :
( ( ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
= $true )
| ( ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV489 )
= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4643]) ).
thf(4713,plain,
! [SV626: nat,SV248: nat,SV489: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV489 )
= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $true )
| ( ( isSimplePath_a @ c @ SV248 @ SV489 @ SV626 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV489 )
= ( min_dist_a @ c @ SV248 @ SV626 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4644]) ).
thf(4714,plain,
! [SV831: list_P559422087at_nat,SV777: nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ! [SY1510: list_P559422087at_nat] :
~ ( isPath_b @ SV491 @ SV713 @ SY1510 @ SV777 ) )
= $false )
| ( ( isPath_b @ SV491 @ SV713 @ SV831 @ SV777 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4647]) ).
thf(4715,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 ) )
= $false )
| ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4650]) ).
thf(4716,plain,
! [SV819: nat,SV715: nat,SV501: product_prod_nat_nat > b,SV778: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $false )
| ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4650]) ).
thf(4717,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ~ ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) )
= $false )
| ( ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV778 )
= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4651]) ).
thf(4718,plain,
! [SV750: nat,SV716: nat,SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ( connected_b @ SV265 @ SV503 @ ( sK63_SY1494 @ SV635 @ SV716 @ SV750 @ SV503 @ SV265 ) )
= $true )
| ( ( ord_less_nat @ SV750 @ SV716 )
= $false )
| ( ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
= SV716 )
= $false )
| ( ( connected_b @ SV265 @ SV503 @ SV635 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4652]) ).
thf(4719,plain,
! [SV750: nat,SV716: nat,SV635: nat,SV503: nat,SV265: product_prod_nat_nat > b] :
( ( ( ( min_dist_b @ SV265 @ SV503 @ ( sK63_SY1494 @ SV635 @ SV716 @ SV750 @ SV503 @ SV265 ) )
= SV750 )
= $true )
| ( ( ord_less_nat @ SV750 @ SV716 )
= $false )
| ( ( ( min_dist_b @ SV265 @ SV503 @ SV635 )
= SV716 )
= $false )
| ( ( connected_b @ SV265 @ SV503 @ SV635 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4653]) ).
thf(4720,plain,
! [SV273: set_set_nat,SV509: set_nat,SV844: set_nat] :
( ( ( ord_less_eq_set_nat @ SV844 @ ( sK37_SY1310 @ SV509 @ SV273 ) )
= $false )
| ( ( ( sK37_SY1310 @ SV509 @ SV273 )
= SV844 )
= $true )
| ( ( member_set_nat @ SV844 @ SV273 )
= $false )
| ( ( member_set_nat @ SV509 @ SV273 )
= $false )
| ( ( finite2012248349et_nat @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4654]) ).
thf(4721,plain,
! [SV833: nat,SV779: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ! [SY1512: nat] :
~ ( dist_b @ SV519 @ SV719 @ SY1512 @ SV779 ) )
= $false )
| ( ( dist_b @ SV519 @ SV719 @ SV833 @ SV779 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4657]) ).
thf(4722,plain,
! [SV648: nat,SV525: list_P559422087at_nat,SV293: nat] :
( ( ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $true )
| ( ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV525 )
= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4658]) ).
thf(4723,plain,
! [SV648: nat,SV293: nat,SV525: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV525 )
= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $true )
| ( ( isSimplePath_b @ c2 @ SV293 @ SV525 @ SV648 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV525 )
= ( min_dist_b @ c2 @ SV293 @ SV648 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4659]) ).
thf(4724,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV530 @ SV721 )
| ~ ( ( SV530 != SV721 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $false )
| ( ( SV530 = SV721 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4661]) ).
thf(4725,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $true )
| ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4662]) ).
thf(4726,plain,
! [SV805: nat,SV681: nat,SV366: product_prod_nat_nat > a,SV768: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV768 )
= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $true )
| ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4663]) ).
thf(4727,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 ) )
= $false )
| ( ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV768 )
= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4664]) ).
thf(4728,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) )
= $false )
| ( ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV768 )
= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4664]) ).
thf(4729,plain,
! [SV683: set_nat,SV372: set_nat] :
( ( ( ord_less_eq_set_nat @ SV372 @ SV683 )
= $true )
| ( ( ord_less_eq_set_nat @ SV372 @ SV683 )
= $false )
| ( ( ord_less_eq_set_nat @ SV683 @ SV372 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4667]) ).
thf(4730,plain,
! [SV372: set_nat,SV683: set_nat] :
( ( ( ord_less_eq_set_nat @ SV683 @ SV372 )
= $true )
| ( ( ord_less_eq_set_nat @ SV372 @ SV683 )
= $false )
| ( ( ord_less_eq_set_nat @ SV683 @ SV372 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4668]) ).
thf(4731,plain,
! [SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ( ~ ( isPath_b @ SV380 @ SV686 @ ( sK72_SY1520 @ SV769 @ SV806 @ SV686 @ SV380 ) @ SV806 )
| ( ( size_s1990949619at_nat @ ( sK72_SY1520 @ SV769 @ SV806 @ SV686 @ SV380 ) )
!= SV769 ) ) )
= $true )
| ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4669]) ).
thf(4732,plain,
! [SV769: nat,SV806: nat,SV845: list_P559422087at_nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV845 )
!= SV769 )
= $true )
| ( ( ~ ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4670]) ).
thf(4733,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $true )
| ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4671]) ).
thf(4734,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) )
= $true )
| ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4672]) ).
thf(4735,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4673]) ).
thf(4736,plain,
! [SV381: product_prod_nat_nat > a,SV687: nat,SV807: nat,SV770: list_P559422087at_nat] :
( ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4673]) ).
thf(4737,plain,
! [SV820: list_P559422087at_nat,SV384: nat,SV576: nat,SV118: nat] :
( ( ( ! [SY1353: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ c @ SV118 @ SY1353 @ SV576 )
| ( ( size_s1990949619at_nat @ SY1353 )
!= SV384 ) ) )
= $false )
| ( ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV820 )
= SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4675]) ).
thf(4738,plain,
! [SV771: nat,SV827: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV387 @ SV690 @ ( sK76_SY1501 @ SV827 @ SV771 @ SV690 @ SV387 ) @ SV771 ) )
= $false )
| ( ( dist_a @ SV387 @ SV690 @ SV827 @ SV771 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4678]) ).
thf(4739,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
| ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4681]) ).
thf(4740,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4682]) ).
thf(4741,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV158: nat] :
( ( ( ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4682]) ).
thf(4742,plain,
! [SV417: nat,SV594: nat,SV850: nat,SV159: nat > $o] :
( ( ( ~ ( SV159 @ SV850 ) )
= $true )
| ( ( ord_less_eq_nat @ SV850 @ ( sK58_SY852 @ SV594 @ SV417 @ SV159 ) )
= $true )
| ( ( SV159 @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4683]) ).
thf(4743,plain,
! [SV417: nat,SV594: nat,SV849: nat,SV159: nat > $o] :
( ( ( SV159 @ SV849 )
= $false )
| ( ( ord_less_eq_nat @ SV849 @ ( sK52_SY852 @ SV594 @ SV417 @ SV159 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) @ SV594 )
= $false )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4684]) ).
thf(4744,plain,
! [SV821: list_P559422087at_nat,SV421: nat,SV597: nat,SV163: nat] :
( ( ( ! [SY1382: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ SY1382 @ SV597 )
| ( ( size_s1990949619at_nat @ SY1382 )
!= SV421 ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV821 )
= SV421 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4686]) ).
thf(4745,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $true )
| ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4688]) ).
thf(4746,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) )
= $true )
| ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4689]) ).
thf(4747,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4690]) ).
thf(4748,plain,
! [SV423: product_prod_nat_nat > b,SV701: nat,SV810: nat,SV772: list_P559422087at_nat] :
( ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4690]) ).
thf(4749,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $true )
| ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4691]) ).
thf(4750,plain,
! [SV811: nat,SV702: nat,SV426: product_prod_nat_nat > a,SV773: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV773 )
= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $true )
| ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4692]) ).
thf(4751,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 ) )
= $false )
| ( ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV773 )
= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4693]) ).
thf(4752,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) )
= $false )
| ( ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV773 )
= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4693]) ).
thf(4753,plain,
! [SV704: set_Pr1986765409at_nat,SV437: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV437 @ SV704 )
= $true )
| ( ( ord_le841296385at_nat @ SV437 @ SV704 )
= $false )
| ( ( ord_le841296385at_nat @ SV704 @ SV437 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4696]) ).
thf(4754,plain,
! [SV437: set_Pr1986765409at_nat,SV704: set_Pr1986765409at_nat] :
( ( ( ord_le841296385at_nat @ SV704 @ SV437 )
= $true )
| ( ( ord_le841296385at_nat @ SV437 @ SV704 )
= $false )
| ( ( ord_le841296385at_nat @ SV704 @ SV437 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4697]) ).
thf(4755,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $true )
| ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4698]) ).
thf(4756,plain,
! [SV814: nat,SV705: nat,SV439: product_prod_nat_nat > b,SV774: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV774 )
= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $true )
| ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4699]) ).
thf(4757,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 ) )
= $false )
| ( ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV774 )
= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4700]) ).
thf(4758,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) )
= $false )
| ( ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV774 )
= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4700]) ).
thf(4759,plain,
! [SV775: nat,SV829: list_P559422087at_nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV442 @ SV706 @ ( sK77_SY1507 @ SV829 @ SV775 @ SV706 @ SV442 ) @ SV775 ) )
= $false )
| ( ( isPath_a @ SV442 @ SV706 @ SV829 @ SV775 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4701]) ).
thf(4760,plain,
! [SV449: nat,SV196: nat > $o,SV851: nat] :
( ( ( ~ ( ord_less_nat @ SV851 @ ( sK46_SY1241 @ SV196 @ SV449 ) ) )
= $true )
| ( ( ~ ( SV196 @ SV851 ) )
= $true )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4702]) ).
thf(4761,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
| ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4705]) ).
thf(4762,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4706]) ).
thf(4763,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV208: nat] :
( ( ( ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4706]) ).
thf(4764,plain,
! [SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ( ~ ( isPath_a @ SV488 @ SV712 @ ( sK75_SY1529 @ SV776 @ SV818 @ SV712 @ SV488 ) @ SV818 )
| ( ( size_s1990949619at_nat @ ( sK75_SY1529 @ SV776 @ SV818 @ SV712 @ SV488 ) )
!= SV776 ) ) )
= $true )
| ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4710]) ).
thf(4765,plain,
! [SV776: nat,SV818: nat,SV848: list_P559422087at_nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV848 )
!= SV776 )
= $true )
| ( ( ~ ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4711]) ).
thf(4766,plain,
! [SV777: nat,SV831: list_P559422087at_nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV491 @ SV713 @ ( sK78_SY1510 @ SV831 @ SV777 @ SV713 @ SV491 ) @ SV777 ) )
= $false )
| ( ( isPath_b @ SV491 @ SV713 @ SV831 @ SV777 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4714]) ).
thf(4767,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $true )
| ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4715]) ).
thf(4768,plain,
! [SV819: nat,SV715: nat,SV501: product_prod_nat_nat > b,SV778: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV778 )
= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $true )
| ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4716]) ).
thf(4769,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 ) )
= $false )
| ( ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV778 )
= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4717]) ).
thf(4770,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) )
= $false )
| ( ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV778 )
= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4717]) ).
thf(4771,plain,
! [SV779: nat,SV833: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV519 @ SV719 @ ( sK79_SY1512 @ SV833 @ SV779 @ SV719 @ SV519 ) @ SV779 ) )
= $false )
| ( ( dist_b @ SV519 @ SV719 @ SV833 @ SV779 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4721]) ).
thf(4772,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV530 @ SV721 ) )
= $false )
| ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $false )
| ( ( SV530 = SV721 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4724]) ).
thf(4773,plain,
! [SV721: nat,SV530: nat] :
( ( ( ~ ( ( SV530 != SV721 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $false )
| ( ( SV530 = SV721 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4724]) ).
thf(4774,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $true )
| ( ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV768 )
= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4727]) ).
thf(4775,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) ) )
= $true )
| ( ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV768 )
= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4728]) ).
thf(4776,plain,
! [SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV380 @ SV686 @ ( sK72_SY1520 @ SV769 @ SV806 @ SV686 @ SV380 ) @ SV806 )
| ( ( size_s1990949619at_nat @ ( sK72_SY1520 @ SV769 @ SV806 @ SV686 @ SV380 ) )
!= SV769 ) )
= $false )
| ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4731]) ).
thf(4777,plain,
! [SV806: nat,SV686: nat,SV380: product_prod_nat_nat > b,SV769: nat,SV845: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV845 )
= SV769 )
= $false )
| ( ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
= $false )
| ( ( ~ ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4732]) ).
thf(4778,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV852: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ SV852 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SV852 ) ) )
= $true )
| ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4734]) ).
thf(4779,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 )
= $true )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4735]) ).
thf(4780,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4736]) ).
thf(4781,plain,
! [SV576: nat,SV384: nat,SV820: list_P559422087at_nat,SV118: nat] :
( ( ( ~ ~ ( ~ ( isPath_a @ c @ SV118 @ ( sK80_SY1353 @ SV820 @ SV384 @ SV576 @ SV118 ) @ SV576 )
| ( ( size_s1990949619at_nat @ ( sK80_SY1353 @ SV820 @ SV384 @ SV576 @ SV118 ) )
!= SV384 ) ) )
= $false )
| ( ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV820 )
= SV384 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4737]) ).
thf(4782,plain,
! [SV771: nat,SV827: nat,SV690: nat,SV387: product_prod_nat_nat > a] :
( ( ( dist_a @ SV387 @ SV690 @ ( sK76_SY1501 @ SV827 @ SV771 @ SV690 @ SV387 ) @ SV771 )
= $true )
| ( ( dist_a @ SV387 @ SV690 @ SV827 @ SV771 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4738]) ).
thf(4783,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4739]) ).
thf(4784,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV158: nat] :
( ( ( ~ ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4739]) ).
thf(4785,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $true )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4740]) ).
thf(4786,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV158: nat] :
( ( ( ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) )
= $true )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4741]) ).
thf(4787,plain,
! [SV417: nat,SV594: nat,SV850: nat,SV159: nat > $o] :
( ( ( SV159 @ SV850 )
= $false )
| ( ( ord_less_eq_nat @ SV850 @ ( sK58_SY852 @ SV594 @ SV417 @ SV159 ) )
= $true )
| ( ( SV159 @ ( sK31_SY1379 @ SV417 @ SV594 @ SV159 ) )
= $true )
| ( ( SV159 @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4742]) ).
thf(4788,plain,
! [SV597: nat,SV421: nat,SV821: list_P559422087at_nat,SV163: nat] :
( ( ( ~ ~ ( ~ ( isPath_b @ c2 @ SV163 @ ( sK81_SY1382 @ SV821 @ SV421 @ SV597 @ SV163 ) @ SV597 )
| ( ( size_s1990949619at_nat @ ( sK81_SY1382 @ SV821 @ SV421 @ SV597 @ SV163 ) )
!= SV421 ) ) )
= $false )
| ( ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV821 )
= SV421 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4744]) ).
thf(4789,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV853: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ SV853 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SV853 ) ) )
= $true )
| ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4746]) ).
thf(4790,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 )
= $true )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ~ ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4747]) ).
thf(4791,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4748]) ).
thf(4792,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $true )
| ( ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV773 )
= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4751]) ).
thf(4793,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) ) )
= $true )
| ( ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV773 )
= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4752]) ).
thf(4794,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $true )
| ( ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV774 )
= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4757]) ).
thf(4795,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) ) )
= $true )
| ( ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV774 )
= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4758]) ).
thf(4796,plain,
! [SV775: nat,SV829: list_P559422087at_nat,SV706: nat,SV442: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV442 @ SV706 @ ( sK77_SY1507 @ SV829 @ SV775 @ SV706 @ SV442 ) @ SV775 )
= $true )
| ( ( isPath_a @ SV442 @ SV706 @ SV829 @ SV775 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4759]) ).
thf(4797,plain,
! [SV449: nat,SV196: nat > $o,SV851: nat] :
( ( ( ord_less_nat @ SV851 @ ( sK46_SY1241 @ SV196 @ SV449 ) )
= $false )
| ( ( ~ ( SV196 @ SV851 ) )
= $true )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4760]) ).
thf(4798,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ SV460 @ SV614 ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4761]) ).
thf(4799,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV208: nat] :
( ( ( ~ ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) )
= $false )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4761]) ).
thf(4800,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $true )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4762]) ).
thf(4801,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV208: nat] :
( ( ( ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) )
= $true )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4763]) ).
thf(4802,plain,
! [SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV488 @ SV712 @ ( sK75_SY1529 @ SV776 @ SV818 @ SV712 @ SV488 ) @ SV818 )
| ( ( size_s1990949619at_nat @ ( sK75_SY1529 @ SV776 @ SV818 @ SV712 @ SV488 ) )
!= SV776 ) )
= $false )
| ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4764]) ).
thf(4803,plain,
! [SV818: nat,SV712: nat,SV488: product_prod_nat_nat > a,SV776: nat,SV848: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV848 )
= SV776 )
= $false )
| ( ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
= $false )
| ( ( ~ ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4765]) ).
thf(4804,plain,
! [SV777: nat,SV831: list_P559422087at_nat,SV713: nat,SV491: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV491 @ SV713 @ ( sK78_SY1510 @ SV831 @ SV777 @ SV713 @ SV491 ) @ SV777 )
= $true )
| ( ( isPath_b @ SV491 @ SV713 @ SV831 @ SV777 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4766]) ).
thf(4805,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $true )
| ( ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV778 )
= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4769]) ).
thf(4806,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) ) )
= $true )
| ( ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV778 )
= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4770]) ).
thf(4807,plain,
! [SV779: nat,SV833: nat,SV719: nat,SV519: product_prod_nat_nat > b] :
( ( ( dist_b @ SV519 @ SV719 @ ( sK79_SY1512 @ SV833 @ SV779 @ SV719 @ SV519 ) @ SV779 )
= $true )
| ( ( dist_b @ SV519 @ SV719 @ SV833 @ SV779 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4771]) ).
thf(4808,plain,
! [SV721: nat,SV530: nat] :
( ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $true )
| ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $false )
| ( ( SV530 = SV721 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4772]) ).
thf(4809,plain,
! [SV721: nat,SV530: nat] :
( ( ( SV530 != SV721 )
= $true )
| ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $false )
| ( ( SV530 = SV721 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4773]) ).
thf(4810,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
| ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) ) )
= $false )
| ( ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV768 )
= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4775]) ).
thf(4811,plain,
! [SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV380 @ SV686 @ ( sK72_SY1520 @ SV769 @ SV806 @ SV686 @ SV380 ) @ SV806 ) )
= $false )
| ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4776]) ).
thf(4812,plain,
! [SV380: product_prod_nat_nat > b,SV686: nat,SV806: nat,SV769: nat] :
( ( ( ( size_s1990949619at_nat @ ( sK72_SY1520 @ SV769 @ SV806 @ SV686 @ SV380 ) )
!= SV769 )
= $false )
| ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4776]) ).
thf(4813,plain,
! [SV845: list_P559422087at_nat,SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
| ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) )
= $false )
| ( ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV845 )
= SV769 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4777]) ).
thf(4814,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV852: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ SV852 @ SV807 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SV852 ) )
= $true )
| ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4778]) ).
thf(4815,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4779]) ).
thf(4816,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4780]) ).
thf(4817,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4780]) ).
thf(4818,plain,
! [SV576: nat,SV384: nat,SV820: list_P559422087at_nat,SV118: nat] :
( ( ( ~ ( ~ ( isPath_a @ c @ SV118 @ ( sK80_SY1353 @ SV820 @ SV384 @ SV576 @ SV118 ) @ SV576 )
| ( ( size_s1990949619at_nat @ ( sK80_SY1353 @ SV820 @ SV384 @ SV576 @ SV118 ) )
!= SV384 ) ) )
= $true )
| ( ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV820 )
= SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4781]) ).
thf(4819,plain,
! [SV593: nat,SV416: list_P559422087at_nat,SV158: nat] :
( ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $true )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4783]) ).
thf(4820,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV158: nat] :
( ( ( ! [SY1378: list_P559422087at_nat] :
( ~ ( isPath_b @ c2 @ SV158 @ SY1378 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SY1378 ) ) ) )
= $true )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4784]) ).
thf(4821,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV854: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ SV854 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SV854 ) ) )
= $true )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4786]) ).
thf(4822,plain,
! [SV597: nat,SV421: nat,SV821: list_P559422087at_nat,SV163: nat] :
( ( ( ~ ( ~ ( isPath_b @ c2 @ SV163 @ ( sK81_SY1382 @ SV821 @ SV421 @ SV597 @ SV163 ) @ SV597 )
| ( ( size_s1990949619at_nat @ ( sK81_SY1382 @ SV821 @ SV421 @ SV597 @ SV163 ) )
!= SV421 ) ) )
= $true )
| ( ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV821 )
= SV421 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4788]) ).
thf(4823,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV853: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ SV853 @ SV810 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SV853 ) )
= $true )
| ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4789]) ).
thf(4824,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4790]) ).
thf(4825,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4791]) ).
thf(4826,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4791]) ).
thf(4827,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
| ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) ) )
= $false )
| ( ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV773 )
= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4793]) ).
thf(4828,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
| ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) ) )
= $false )
| ( ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV774 )
= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4795]) ).
thf(4829,plain,
! [SV449: nat,SV851: nat,SV196: nat > $o] :
( ( ( SV196 @ SV851 )
= $false )
| ( ( ord_less_nat @ SV851 @ ( sK46_SY1241 @ SV196 @ SV449 ) )
= $false )
| ( ( SV196 @ zero_zero_nat )
= $true )
| ( ( SV196 @ SV449 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4797]) ).
thf(4830,plain,
! [SV614: nat,SV460: list_P559422087at_nat,SV208: nat] :
( ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $true )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4798]) ).
thf(4831,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV208: nat] :
( ( ( ! [SY1399: list_P559422087at_nat] :
( ~ ( isPath_a @ c @ SV208 @ SY1399 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SY1399 ) ) ) )
= $true )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4799]) ).
thf(4832,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV855: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ SV855 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SV855 ) ) )
= $true )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4801]) ).
thf(4833,plain,
! [SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV488 @ SV712 @ ( sK75_SY1529 @ SV776 @ SV818 @ SV712 @ SV488 ) @ SV818 ) )
= $false )
| ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4802]) ).
thf(4834,plain,
! [SV488: product_prod_nat_nat > a,SV712: nat,SV818: nat,SV776: nat] :
( ( ( ( size_s1990949619at_nat @ ( sK75_SY1529 @ SV776 @ SV818 @ SV712 @ SV488 ) )
!= SV776 )
= $false )
| ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4802]) ).
thf(4835,plain,
! [SV848: list_P559422087at_nat,SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
| ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) )
= $false )
| ( ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV848 )
= SV776 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4803]) ).
thf(4836,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
| ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) ) )
= $false )
| ( ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV778 )
= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4806]) ).
thf(4837,plain,
! [SV721: nat,SV530: nat] :
( ( ( SV530 = SV721 )
= $false )
| ( ( ord_less_eq_nat @ SV530 @ SV721 )
= $false )
| ( ( SV530 = SV721 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4809]) ).
thf(4838,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( ~ ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 ) )
= $false )
| ( ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV768 )
= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4810]) ).
thf(4839,plain,
! [SV805: nat,SV681: nat,SV366: product_prod_nat_nat > a,SV768: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV768 )
!= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $false )
| ( ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV768 )
= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4810]) ).
thf(4840,plain,
! [SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV380 @ SV686 @ ( sK72_SY1520 @ SV769 @ SV806 @ SV686 @ SV380 ) @ SV806 )
= $true )
| ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4811]) ).
thf(4841,plain,
! [SV380: product_prod_nat_nat > b,SV686: nat,SV806: nat,SV769: nat] :
( ( ( ( size_s1990949619at_nat @ ( sK72_SY1520 @ SV769 @ SV806 @ SV686 @ SV380 ) )
= SV769 )
= $true )
| ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4812]) ).
thf(4842,plain,
! [SV845: list_P559422087at_nat,SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 ) )
= $false )
| ( ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV845 )
= SV769 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4813]) ).
thf(4843,plain,
! [SV845: list_P559422087at_nat,SV769: nat,SV806: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) )
= $false )
| ( ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV845 )
= SV769 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4813]) ).
thf(4844,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV852: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV381 @ SV687 @ SV852 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SV852 ) )
= $true )
| ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4814]) ).
thf(4845,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4815]) ).
thf(4846,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4815]) ).
thf(4847,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $true )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4816]) ).
thf(4848,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) )
= $true )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4817]) ).
thf(4849,plain,
! [SV576: nat,SV384: nat,SV820: list_P559422087at_nat,SV118: nat] :
( ( ( ~ ( isPath_a @ c @ SV118 @ ( sK80_SY1353 @ SV820 @ SV384 @ SV576 @ SV118 ) @ SV576 )
| ( ( size_s1990949619at_nat @ ( sK80_SY1353 @ SV820 @ SV384 @ SV576 @ SV118 ) )
!= SV384 ) )
= $false )
| ( ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV820 )
= SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4818]) ).
thf(4850,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV856: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ SV856 @ SV593 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SV856 ) ) )
= $true )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4820]) ).
thf(4851,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV854: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ SV854 @ SV593 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SV854 ) )
= $true )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4821]) ).
thf(4852,plain,
! [SV597: nat,SV421: nat,SV821: list_P559422087at_nat,SV163: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV163 @ ( sK81_SY1382 @ SV821 @ SV421 @ SV597 @ SV163 ) @ SV597 )
| ( ( size_s1990949619at_nat @ ( sK81_SY1382 @ SV821 @ SV421 @ SV597 @ SV163 ) )
!= SV421 ) )
= $false )
| ( ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV821 )
= SV421 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4822]) ).
thf(4853,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV853: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV423 @ SV701 @ SV853 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SV853 ) )
= $true )
| ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4823]) ).
thf(4854,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4824]) ).
thf(4855,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4824]) ).
thf(4856,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $true )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4825]) ).
thf(4857,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) )
= $true )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4826]) ).
thf(4858,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 ) )
= $false )
| ( ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV773 )
= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4827]) ).
thf(4859,plain,
! [SV811: nat,SV702: nat,SV426: product_prod_nat_nat > a,SV773: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV773 )
!= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $false )
| ( ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV773 )
= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4827]) ).
thf(4860,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 ) )
= $false )
| ( ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV774 )
= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4828]) ).
thf(4861,plain,
! [SV814: nat,SV705: nat,SV439: product_prod_nat_nat > b,SV774: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV774 )
!= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $false )
| ( ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV774 )
= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4828]) ).
thf(4862,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV857: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ SV857 @ SV614 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SV857 ) ) )
= $true )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4831]) ).
thf(4863,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV855: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ SV855 @ SV614 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SV855 ) )
= $true )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4832]) ).
thf(4864,plain,
! [SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV488 @ SV712 @ ( sK75_SY1529 @ SV776 @ SV818 @ SV712 @ SV488 ) @ SV818 )
= $true )
| ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4833]) ).
thf(4865,plain,
! [SV488: product_prod_nat_nat > a,SV712: nat,SV818: nat,SV776: nat] :
( ( ( ( size_s1990949619at_nat @ ( sK75_SY1529 @ SV776 @ SV818 @ SV712 @ SV488 ) )
= SV776 )
= $true )
| ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4834]) ).
thf(4866,plain,
! [SV848: list_P559422087at_nat,SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 ) )
= $false )
| ( ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV848 )
= SV776 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4835]) ).
thf(4867,plain,
! [SV848: list_P559422087at_nat,SV776: nat,SV818: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) )
= $false )
| ( ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV848 )
= SV776 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4835]) ).
thf(4868,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( ~ ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 ) )
= $false )
| ( ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV778 )
= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4836]) ).
thf(4869,plain,
! [SV819: nat,SV715: nat,SV501: product_prod_nat_nat > b,SV778: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV778 )
!= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $false )
| ( ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV778 )
= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4836]) ).
thf(4870,plain,
! [SV805: nat,SV768: list_P559422087at_nat,SV681: nat,SV366: product_prod_nat_nat > a] :
( ( ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $true )
| ( ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV768 )
= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4838]) ).
thf(4871,plain,
! [SV805: nat,SV681: nat,SV366: product_prod_nat_nat > a,SV768: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV768 )
= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $true )
| ( ( isSimplePath_a @ SV366 @ SV681 @ SV768 @ SV805 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV768 )
= ( min_dist_a @ SV366 @ SV681 @ SV805 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4839]) ).
thf(4872,plain,
! [SV845: list_P559422087at_nat,SV806: nat,SV769: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( dist_b @ SV380 @ SV686 @ SV769 @ SV806 )
= $true )
| ( ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV845 )
= SV769 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4842]) ).
thf(4873,plain,
! [SV845: list_P559422087at_nat,SV769: nat,SV806: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) )
= $true )
| ( ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV845 )
= SV769 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4843]) ).
thf(4874,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isShortestPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $true )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4845]) ).
thf(4875,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) ) )
= $true )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4846]) ).
thf(4876,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4848]) ).
thf(4877,plain,
! [SV576: nat,SV384: nat,SV820: list_P559422087at_nat,SV118: nat] :
( ( ( ~ ( isPath_a @ c @ SV118 @ ( sK80_SY1353 @ SV820 @ SV384 @ SV576 @ SV118 ) @ SV576 ) )
= $false )
| ( ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV820 )
= SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4849]) ).
thf(4878,plain,
! [SV118: nat,SV576: nat,SV384: nat,SV820: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ ( sK80_SY1353 @ SV820 @ SV384 @ SV576 @ SV118 ) )
!= SV384 )
= $false )
| ( ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV820 )
= SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4849]) ).
thf(4879,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV856: list_P559422087at_nat,SV158: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV158 @ SV856 @ SV593 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SV856 ) )
= $true )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4850]) ).
thf(4880,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV854: list_P559422087at_nat,SV158: nat] :
( ( ( isPath_b @ c2 @ SV158 @ SV854 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SV854 ) )
= $true )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4851]) ).
thf(4881,plain,
! [SV597: nat,SV421: nat,SV821: list_P559422087at_nat,SV163: nat] :
( ( ( ~ ( isPath_b @ c2 @ SV163 @ ( sK81_SY1382 @ SV821 @ SV421 @ SV597 @ SV163 ) @ SV597 ) )
= $false )
| ( ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV821 )
= SV421 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4852]) ).
thf(4882,plain,
! [SV163: nat,SV597: nat,SV421: nat,SV821: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ ( sK81_SY1382 @ SV821 @ SV421 @ SV597 @ SV163 ) )
!= SV421 )
= $false )
| ( ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV821 )
= SV421 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4852]) ).
thf(4883,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isShortestPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $true )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4854]) ).
thf(4884,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) ) )
= $true )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4855]) ).
thf(4885,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4857]) ).
thf(4886,plain,
! [SV811: nat,SV773: list_P559422087at_nat,SV702: nat,SV426: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $true )
| ( ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV773 )
= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4858]) ).
thf(4887,plain,
! [SV811: nat,SV702: nat,SV426: product_prod_nat_nat > a,SV773: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV773 )
= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $true )
| ( ( isPath_a @ SV426 @ SV702 @ SV773 @ SV811 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV773 )
= ( min_dist_a @ SV426 @ SV702 @ SV811 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4859]) ).
thf(4888,plain,
! [SV814: nat,SV774: list_P559422087at_nat,SV705: nat,SV439: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $true )
| ( ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV774 )
= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4860]) ).
thf(4889,plain,
! [SV814: nat,SV705: nat,SV439: product_prod_nat_nat > b,SV774: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV774 )
= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $true )
| ( ( isPath_b @ SV439 @ SV705 @ SV774 @ SV814 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV774 )
= ( min_dist_b @ SV439 @ SV705 @ SV814 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4861]) ).
thf(4890,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV857: list_P559422087at_nat,SV208: nat] :
( ( ( ~ ( isPath_a @ c @ SV208 @ SV857 @ SV614 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SV857 ) )
= $true )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4862]) ).
thf(4891,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV855: list_P559422087at_nat,SV208: nat] :
( ( ( isPath_a @ c @ SV208 @ SV855 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SV855 ) )
= $true )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4863]) ).
thf(4892,plain,
! [SV848: list_P559422087at_nat,SV818: nat,SV776: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( dist_a @ SV488 @ SV712 @ SV776 @ SV818 )
= $true )
| ( ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV848 )
= SV776 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4866]) ).
thf(4893,plain,
! [SV848: list_P559422087at_nat,SV776: nat,SV818: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) )
= $true )
| ( ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV848 )
= SV776 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4867]) ).
thf(4894,plain,
! [SV819: nat,SV778: list_P559422087at_nat,SV715: nat,SV501: product_prod_nat_nat > b] :
( ( ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $true )
| ( ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV778 )
= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4868]) ).
thf(4895,plain,
! [SV819: nat,SV715: nat,SV501: product_prod_nat_nat > b,SV778: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV778 )
= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $true )
| ( ( isSimplePath_b @ SV501 @ SV715 @ SV778 @ SV819 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV778 )
= ( min_dist_b @ SV501 @ SV715 @ SV819 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4869]) ).
thf(4896,plain,
! [SV845: list_P559422087at_nat,SV769: nat,SV806: nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ! [SY1520: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ SY1520 @ SV806 )
| ( ( size_s1990949619at_nat @ SY1520 )
!= SV769 ) ) )
= $false )
| ( ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV845 )
= SV769 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4873]) ).
thf(4897,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
| ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4875]) ).
thf(4898,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4876]) ).
thf(4899,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4876]) ).
thf(4900,plain,
! [SV576: nat,SV384: nat,SV820: list_P559422087at_nat,SV118: nat] :
( ( ( isPath_a @ c @ SV118 @ ( sK80_SY1353 @ SV820 @ SV384 @ SV576 @ SV118 ) @ SV576 )
= $true )
| ( ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV820 )
= SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4877]) ).
thf(4901,plain,
! [SV118: nat,SV576: nat,SV384: nat,SV820: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ ( sK80_SY1353 @ SV820 @ SV384 @ SV576 @ SV118 ) )
= SV384 )
= $true )
| ( ( isPath_a @ c @ SV118 @ SV820 @ SV576 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV820 )
= SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4878]) ).
thf(4902,plain,
! [SV416: list_P559422087at_nat,SV593: nat,SV856: list_P559422087at_nat,SV158: nat] :
( ( ( isPath_b @ c2 @ SV158 @ SV856 @ SV593 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV416 ) @ ( size_s1990949619at_nat @ SV856 ) )
= $true )
| ( ( isPath_b @ c2 @ SV158 @ SV416 @ SV593 )
= $false )
| ( ( isPath_b @ c2 @ SV158 @ ( sK57_SY1378 @ SV416 @ SV593 @ SV158 ) @ SV593 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4879]) ).
thf(4903,plain,
! [SV597: nat,SV421: nat,SV821: list_P559422087at_nat,SV163: nat] :
( ( ( isPath_b @ c2 @ SV163 @ ( sK81_SY1382 @ SV821 @ SV421 @ SV597 @ SV163 ) @ SV597 )
= $true )
| ( ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV821 )
= SV421 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4881]) ).
thf(4904,plain,
! [SV163: nat,SV597: nat,SV421: nat,SV821: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ ( sK81_SY1382 @ SV821 @ SV421 @ SV597 @ SV163 ) )
= SV421 )
= $true )
| ( ( isPath_b @ c2 @ SV163 @ SV821 @ SV597 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV821 )
= SV421 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4882]) ).
thf(4905,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
| ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4884]) ).
thf(4906,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4885]) ).
thf(4907,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4885]) ).
thf(4908,plain,
! [SV460: list_P559422087at_nat,SV614: nat,SV857: list_P559422087at_nat,SV208: nat] :
( ( ( isPath_a @ c @ SV208 @ SV857 @ SV614 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV460 ) @ ( size_s1990949619at_nat @ SV857 ) )
= $true )
| ( ( isPath_a @ c @ SV208 @ SV460 @ SV614 )
= $false )
| ( ( isPath_a @ c @ SV208 @ ( sK60_SY1399 @ SV460 @ SV614 @ SV208 ) @ SV614 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4890]) ).
thf(4909,plain,
! [SV848: list_P559422087at_nat,SV776: nat,SV818: nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ! [SY1529: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ SY1529 @ SV818 )
| ( ( size_s1990949619at_nat @ SY1529 )
!= SV776 ) ) )
= $false )
| ( ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV848 )
= SV776 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4893]) ).
thf(4910,plain,
! [SV806: nat,SV769: nat,SV845: list_P559422087at_nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ~ ( ~ ( isPath_b @ SV380 @ SV686 @ ( sK82_SY1520 @ SV845 @ SV769 @ SV806 @ SV686 @ SV380 ) @ SV806 )
| ( ( size_s1990949619at_nat @ ( sK82_SY1520 @ SV845 @ SV769 @ SV806 @ SV686 @ SV380 ) )
!= SV769 ) ) )
= $false )
| ( ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV845 )
= SV769 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4896]) ).
thf(4911,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4897]) ).
thf(4912,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4897]) ).
thf(4913,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $true )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4898]) ).
thf(4914,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) )
= $true )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4899]) ).
thf(4915,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4905]) ).
thf(4916,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4905]) ).
thf(4917,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $true )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4906]) ).
thf(4918,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) )
= $true )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4907]) ).
thf(4919,plain,
! [SV818: nat,SV776: nat,SV848: list_P559422087at_nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ~ ( ~ ( isPath_a @ SV488 @ SV712 @ ( sK83_SY1529 @ SV848 @ SV776 @ SV818 @ SV712 @ SV488 ) @ SV818 )
| ( ( size_s1990949619at_nat @ ( sK83_SY1529 @ SV848 @ SV776 @ SV818 @ SV712 @ SV488 ) )
!= SV776 ) ) )
= $false )
| ( ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV848 )
= SV776 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4909]) ).
thf(4920,plain,
! [SV806: nat,SV769: nat,SV845: list_P559422087at_nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ( ~ ( isPath_b @ SV380 @ SV686 @ ( sK82_SY1520 @ SV845 @ SV769 @ SV806 @ SV686 @ SV380 ) @ SV806 )
| ( ( size_s1990949619at_nat @ ( sK82_SY1520 @ SV845 @ SV769 @ SV806 @ SV686 @ SV380 ) )
!= SV769 ) ) )
= $true )
| ( ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV845 )
= SV769 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4910]) ).
thf(4921,plain,
! [SV807: nat,SV770: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $true )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4911]) ).
thf(4922,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ! [SY1521: list_P559422087at_nat] :
( ~ ( isPath_a @ SV381 @ SV687 @ SY1521 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SY1521 ) ) ) )
= $true )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4912]) ).
thf(4923,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV858: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ SV858 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SV858 ) ) )
= $true )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4914]) ).
thf(4924,plain,
! [SV810: nat,SV772: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $true )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4915]) ).
thf(4925,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ! [SY1524: list_P559422087at_nat] :
( ~ ( isPath_b @ SV423 @ SV701 @ SY1524 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SY1524 ) ) ) )
= $true )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4916]) ).
thf(4926,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV859: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ SV859 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SV859 ) ) )
= $true )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4918]) ).
thf(4927,plain,
! [SV818: nat,SV776: nat,SV848: list_P559422087at_nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ( ~ ( isPath_a @ SV488 @ SV712 @ ( sK83_SY1529 @ SV848 @ SV776 @ SV818 @ SV712 @ SV488 ) @ SV818 )
| ( ( size_s1990949619at_nat @ ( sK83_SY1529 @ SV848 @ SV776 @ SV818 @ SV712 @ SV488 ) )
!= SV776 ) ) )
= $true )
| ( ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV848 )
= SV776 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4919]) ).
thf(4928,plain,
! [SV806: nat,SV769: nat,SV845: list_P559422087at_nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV380 @ SV686 @ ( sK82_SY1520 @ SV845 @ SV769 @ SV806 @ SV686 @ SV380 ) @ SV806 )
| ( ( size_s1990949619at_nat @ ( sK82_SY1520 @ SV845 @ SV769 @ SV806 @ SV686 @ SV380 ) )
!= SV769 ) )
= $false )
| ( ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV845 )
= SV769 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4920]) ).
thf(4929,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV860: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ SV860 @ SV807 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SV860 ) ) )
= $true )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4922]) ).
thf(4930,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV858: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ SV858 @ SV807 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SV858 ) )
= $true )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4923]) ).
thf(4931,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV861: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ SV861 @ SV810 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SV861 ) ) )
= $true )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4925]) ).
thf(4932,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV859: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ SV859 @ SV810 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SV859 ) )
= $true )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4926]) ).
thf(4933,plain,
! [SV818: nat,SV776: nat,SV848: list_P559422087at_nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV488 @ SV712 @ ( sK83_SY1529 @ SV848 @ SV776 @ SV818 @ SV712 @ SV488 ) @ SV818 )
| ( ( size_s1990949619at_nat @ ( sK83_SY1529 @ SV848 @ SV776 @ SV818 @ SV712 @ SV488 ) )
!= SV776 ) )
= $false )
| ( ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV848 )
= SV776 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4927]) ).
thf(4934,plain,
! [SV806: nat,SV769: nat,SV845: list_P559422087at_nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV380 @ SV686 @ ( sK82_SY1520 @ SV845 @ SV769 @ SV806 @ SV686 @ SV380 ) @ SV806 ) )
= $false )
| ( ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV845 )
= SV769 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4928]) ).
thf(4935,plain,
! [SV380: product_prod_nat_nat > b,SV686: nat,SV806: nat,SV769: nat,SV845: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ ( sK82_SY1520 @ SV845 @ SV769 @ SV806 @ SV686 @ SV380 ) )
!= SV769 )
= $false )
| ( ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV845 )
= SV769 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4928]) ).
thf(4936,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV860: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV381 @ SV687 @ SV860 @ SV807 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SV860 ) )
= $true )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4929]) ).
thf(4937,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV858: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV381 @ SV687 @ SV858 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SV858 ) )
= $true )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4930]) ).
thf(4938,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV861: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( ~ ( isPath_b @ SV423 @ SV701 @ SV861 @ SV810 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SV861 ) )
= $true )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4931]) ).
thf(4939,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV859: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV423 @ SV701 @ SV859 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SV859 ) )
= $true )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4932]) ).
thf(4940,plain,
! [SV818: nat,SV776: nat,SV848: list_P559422087at_nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( ~ ( isPath_a @ SV488 @ SV712 @ ( sK83_SY1529 @ SV848 @ SV776 @ SV818 @ SV712 @ SV488 ) @ SV818 ) )
= $false )
| ( ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV848 )
= SV776 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4933]) ).
thf(4941,plain,
! [SV488: product_prod_nat_nat > a,SV712: nat,SV818: nat,SV776: nat,SV848: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ ( sK83_SY1529 @ SV848 @ SV776 @ SV818 @ SV712 @ SV488 ) )
!= SV776 )
= $false )
| ( ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV848 )
= SV776 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4933]) ).
thf(4942,plain,
! [SV806: nat,SV769: nat,SV845: list_P559422087at_nat,SV686: nat,SV380: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV380 @ SV686 @ ( sK82_SY1520 @ SV845 @ SV769 @ SV806 @ SV686 @ SV380 ) @ SV806 )
= $true )
| ( ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV845 )
= SV769 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4934]) ).
thf(4943,plain,
! [SV380: product_prod_nat_nat > b,SV686: nat,SV806: nat,SV769: nat,SV845: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ ( sK82_SY1520 @ SV845 @ SV769 @ SV806 @ SV686 @ SV380 ) )
= SV769 )
= $true )
| ( ( isPath_b @ SV380 @ SV686 @ SV845 @ SV806 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV845 )
= SV769 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4935]) ).
thf(4944,plain,
! [SV770: list_P559422087at_nat,SV807: nat,SV860: list_P559422087at_nat,SV687: nat,SV381: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV381 @ SV687 @ SV860 @ SV807 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV770 ) @ ( size_s1990949619at_nat @ SV860 ) )
= $true )
| ( ( isPath_a @ SV381 @ SV687 @ SV770 @ SV807 )
= $false )
| ( ( isPath_a @ SV381 @ SV687 @ ( sK73_SY1521 @ SV770 @ SV807 @ SV687 @ SV381 ) @ SV807 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4936]) ).
thf(4945,plain,
! [SV772: list_P559422087at_nat,SV810: nat,SV861: list_P559422087at_nat,SV701: nat,SV423: product_prod_nat_nat > b] :
( ( ( isPath_b @ SV423 @ SV701 @ SV861 @ SV810 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV772 ) @ ( size_s1990949619at_nat @ SV861 ) )
= $true )
| ( ( isPath_b @ SV423 @ SV701 @ SV772 @ SV810 )
= $false )
| ( ( isPath_b @ SV423 @ SV701 @ ( sK74_SY1524 @ SV772 @ SV810 @ SV701 @ SV423 ) @ SV810 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4938]) ).
thf(4946,plain,
! [SV818: nat,SV776: nat,SV848: list_P559422087at_nat,SV712: nat,SV488: product_prod_nat_nat > a] :
( ( ( isPath_a @ SV488 @ SV712 @ ( sK83_SY1529 @ SV848 @ SV776 @ SV818 @ SV712 @ SV488 ) @ SV818 )
= $true )
| ( ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV848 )
= SV776 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4940]) ).
thf(4947,plain,
! [SV488: product_prod_nat_nat > a,SV712: nat,SV818: nat,SV776: nat,SV848: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ ( sK83_SY1529 @ SV848 @ SV776 @ SV818 @ SV712 @ SV488 ) )
= SV776 )
= $true )
| ( ( isPath_a @ SV488 @ SV712 @ SV848 @ SV818 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV848 )
= SV776 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4941]) ).
thf(4948,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[701,4947,4946,4945,4944,4943,4942,4939,4937,4924,4921,4917,4913,4908,4904,4903,4902,4901,4900,4895,4894,4892,4891,4889,4888,4887,4886,4883,4880,4874,4872,4871,4870,4865,4864,4856,4853,4847,4844,4841,4840,4837,4830,4829,4819,4808,4807,4805,4804,4800,4796,4794,4792,4787,4785,4782,4774,4768,4767,4756,4755,4754,4753,4750,4749,4745,4743,4733,4730,4729,4726,4725,4723,4722,4720,4719,4718,4713,4712,4709,4708,4707,4704,4703,4695,4694,4687,4685,4680,4679,4677,4676,4674,4666,4665,4660,4656,4655,4649,4648,4646,4645,4636,4633,4630,4628,4627,4614,4613,4610,4608,4605,4603,4602,4600,4599,4594,4593,4581,4575,4574,4570,4567,4560,4559,4556,4550,4549,4541,4539,4538,4536,4535,4534,4532,4531,4528,4525,4523,4522,4517,4510,4508,4507,4506,4505,4493,4490,4488,4484,4483,4482,4481,4480,4479,4478,4477,4476,4475,4474,4473,4472,4471,4470,4469,4468,4467,4466,4465,4464,4463,4462,4461,4460,4459,4458,4457,4456,4455,4454,4453,4452,4451,4448,4446,4440,4439,4433,4428,4422,4419,4404,4403,4402,4393,4375,4374,4372,4371,4366,4365,4349,4348,4346,4304,4303,4300,4294,4293,4285,4282,4281,4275,4274,4272,4266,4263,4259,4256,4231,4225,4224,4214,4201,4200,4185,4184,4183,4182,4181,4180,4179,4178,4173,4172,4151,4150,4149,4148,4147,4146,4145,4144,4143,4142,4132,4131,4130,4129,4128,4127,4120,4119,4100,4099,4077,4076,4069,4068,4054,4053,4052,4051,4018,4016,4015,4011,4006,4003,3996,3970,3969,3968,3967,3965,3964,3963,3962,3961,3960,3959,3948,3947,3946,3945,3944,3943,3942,3941,3934,3932,3928,3927,3926,3925,3922,3920,3915,3904,3900,3891,3889,3882,3881,3880,3879,3878,3871,3868,3847,3846,3844,3838,3835,3832,3813,3805,3804,3803,3800,3799,3798,3797,3794,3793,3783,3780,3778,3775,3768,3745,3741,3735,3730,3728,3721,3708,3703,3699,3695,3691,3690,3687,3685,3682,3681,3680,3679,3678,3677,3676,3675,3674,3659,3651,3649,3646,3643,3642,3638,3637,3631,3630,3621,3617,3599,3592,3590,3586,3580,3571,3569,3567,3561,3553,3549,3534,3531,3526,3514,3512,3510,3505,3500,3499,3494,3492,3491,3489,3488,3487,3486,3485,3484,3483,3482,3481,3479,3477,3476,3475,3474,3465,3464,3462,3460,3458,3456,3452,3450,3445,3444,3442,3441,3440,3439,3438,3437,3436,3435,3434,3433,3432,3431,3430,3429,3428,3427,3426,3425,3424,3423,3422,3421,3420,3419,3418,3417,3416,3415,3400,3386,3378,3366,3356,3352,3351,3350,3347,3346,3344,3338,3320,3295,3292,3274,3267,3245,3233,3232,3231,3230,3227,3226,3225,3224,3223,3222,3221,3220,3219,3218,3217,3216,3215,3182,3177,3176,3173,3165,3164,3160,3155,3150,3146,3144,3131,3104,3102,3093,3088,3085,3077,3076,3064,3058,3051,3049,3040,3034,3032,3024,3022,3011,3009,3007,3005,3003,3001,2999,2997,2961,2959,2956,2951,2949,2948,2946,2940,2939,2929,2926,2924,2920,2917,2912,2911,2909,2907,2896,2892,2889,2885,2876,2871,2861,2851,2846,2844,2840,2839,2828,2825,2821,2814,2812,2810,2806,2779,2778,2750,2749,2748,2747,2746,2745,2740,2737,2736,2735,2734,2732,2730,2728,2726,2721,2720,2706,2698,2696,2692,2666,2657,2654,2651,2648,2647,2645,2643,2640,2637,2636,2635,2627,2624,2623,2619,2618,2609,2592,2589,2584,2581,2579,2574,2571,2564,2557,2555,2548,2546,2544,2542,2540,2538,2536,2534,2532,2530,2526,2509,2507,2505,2503,2497,2489,2485,2471,2460,2455,2448,2444,2437,2436,2434,2431,2419,2418,2415,2410,2403,2402,2378,2371,2365,2362,2350,2342,2340,2331,2322,2317,2313,2312,2307,2306,2305,2304,2303,2302,2301,2300,2294,2292,2261,2256,2253,2248,2241,2239,2234,2232,2230,2214,2210,2201,2199,2196,2195,2194,2193,2191,2188,2187,2185,2182,2179,2167,2162,2161,2138,2131,2127,2124,2122,2118,2109,2108,2107,2103,2093,2089,2087,2083,2076,2072,2067,2059,2057,2056,2055,2048,2047,2045,2036,2029,2028,2026,2023,2021,2019,2017,2015,2013,2011,2009,2007,2005,2003,2001,1999,1997,1992,1990,1988,1986,1984,1982,1980,1978,1976,1974,1971,1967,1964,1962,1960,1958,1956,1954,1952,1950,1948,1946,1944,1926,1925,1911,1902,1897,1870,1812,1726,1717,1715,1714,1713,1712,1707,1706,1705,1704,1692,1691,1690,1689,1688,1687,1686,1685,1683,1678,1677,1672,1671,1668,1667,1666,1663,1661,1658,1656,1654,1644,1643,1631,1615,1588,1576,1568,1509,1504,1501,1485,1481,1435,1427,1425,1416,1406,1401,1400,1399,1394,1392,1390,1388,1386,1385,1382,1380,1378,1376,1374,1372,1370,1369,1368,1366,1364,1362,1360,1359,1358,1345,1343,1341,1339,1335,1333,1331,1329,1327,1325,1323,1321,1316,1312,1310,1309,1308,1307,1303,1302,1301,1300,1295,1293,1292,1291,1290,1289,1287,1285,1283,1281,1279,1277,1275,1042,1035,1015,1014,1011,981,978,977,923,919,918,894,893,750,749,734,733,729,727,719,718,717,716,715,714,713,712,707,706,703,702]) ).
thf(4949,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[4948]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP051^1 : TPTP v9.3.1. Released v7.5.0.
% 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
% 0.09/0.17 % Computer : n004.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 11:14:54 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 78.15/13.23 ..
% 78.15/13.23
% 78.15/13.23 No.of.Axioms: 348
% 78.15/13.23
% 78.15/13.23 Length.of.Defs: 0
% 78.15/13.23
% 78.15/13.23 Contains.Choice.Funs: false
% 78.15/13.23 .............................................................................................................................................
% 78.15/13.23
% 78.15/13.23 ********************************
% 78.15/13.23 * All subproblems solved! *
% 78.15/13.23 ********************************
% 78.15/13.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:348,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4948,loop_count:0,foatp_calls:1,translation:fof_full)
% 78.15/13.23
% 78.15/13.23 %**** Beginning of derivation protocol ****
% 78.15/13.23 % SZS output start CNFRefutation
% See solution above
% 78.15/13.27
% 78.15/13.27 %**** End of derivation protocol ****
% 78.15/13.27 %**** no. of clauses in derivation: 4949 ****
% 78.15/13.27 %**** clause counter: 4948 ****
% 78.15/13.27
% 78.15/13.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:348,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4948,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------