%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP053^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 10:23:51 AM UTC 2026
% Result : Theorem 25.56s 4.52s
% Output : CNFRefutation 25.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 118
% Syntax : Number of formulae : 1757 ( 811 unt; 0 typ; 0 def)
% Number of atoms : 10919 (4331 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 24462 (3525 ~;2696 |; 63 &;17851 @)
% ( 0 <=>; 327 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 12 ( 11 usr)
% Number of type conns : 437 ( 437 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 64 usr; 12 con; 0-5 aty)
% Number of variables : 6099 ( 193 ^;5870 !; 36 ?;6099 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_capacity,type,
capacity: $tType ).
thf(tp_list_P559422087at_nat,type,
list_P559422087at_nat: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_produc1190591575at_nat,type,
produc1190591575at_nat: $tType ).
thf(tp_produc1271302400at_nat,type,
produc1271302400at_nat: $tType ).
thf(tp_produc1695820582at_nat,type,
produc1695820582at_nat: $tType ).
thf(tp_produc1864880952at_nat,type,
produc1864880952at_nat: $tType ).
thf(tp_produc2082277813at_nat,type,
produc2082277813at_nat: $tType ).
thf(tp_produc787001653at_nat,type,
produc787001653at_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_c,type,
c: product_prod_nat_nat > capacity ).
thf(tp_collec7649004at_nat,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(tp_connected_capacity,type,
connected_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > $o ).
thf(tp_dist_capacity,type,
dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat > $o ).
thf(tp_isPath_capacity,type,
isPath_capacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(tp_isShor1936442771pacity,type,
isShor1936442771pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(tp_isSimp1359852763pacity,type,
isSimp1359852763pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(tp_member701585322at_nat,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(tp_min_dist_capacity,type,
min_dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat ).
thf(tp_nil_Pr1308055047at_nat,type,
nil_Pr1308055047at_nat: list_P559422087at_nat ).
thf(tp_one_one_nat,type,
one_one_nat: nat ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(tp_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(tp_p,type,
p: list_P559422087at_nat ).
thf(tp_p1,type,
p1: list_P559422087at_nat ).
thf(tp_p2,type,
p2: list_P559422087at_nat ).
thf(tp_p3,type,
p3: list_P559422087at_nat ).
thf(tp_plus_plus_nat,type,
plus_plus_nat: nat > nat > nat ).
thf(tp_produc1682925677at_nat,type,
produc1682925677at_nat: ( nat > nat > nat ) > produc1695820582at_nat > produc2082277813at_nat ).
thf(tp_produc1728816653at_nat,type,
produc1728816653at_nat: produc2082277813at_nat > produc787001653at_nat ).
thf(tp_produc1933845336at_nat,type,
produc1933845336at_nat: nat > product_prod_nat_nat > produc1695820582at_nat ).
thf(tp_produc2019146714at_nat,type,
produc2019146714at_nat: produc1271302400at_nat > produc1695820582at_nat ).
thf(tp_produc365964781at_nat,type,
produc365964781at_nat: produc1695820582at_nat > ( nat > nat > nat ) > produc787001653at_nat ).
thf(tp_produc411855757at_nat,type,
produc411855757at_nat: produc787001653at_nat > produc2082277813at_nat ).
thf(tp_produc696256106at_nat,type,
produc696256106at_nat: ( nat > product_prod_nat_nat > product_prod_nat_nat ) > produc1190591575at_nat > produc1864880952at_nat ).
thf(tp_produc857968056at_nat,type,
produc857968056at_nat: produc1695820582at_nat > produc1271302400at_nat ).
thf(tp_produc869658639at_nat,type,
produc869658639at_nat: nat > produc1695820582at_nat > produc1190591575at_nat ).
thf(tp_produc947540346at_nat,type,
produc947540346at_nat: product_prod_nat_nat > nat > produc1271302400at_nat ).
thf(tp_product_Pair_nat_nat,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(tp_product_swap_nat_nat,type,
product_swap_nat_nat: product_prod_nat_nat > product_prod_nat_nat ).
thf(tp_s,type,
s: nat ).
thf(tp_sK10_SY841,type,
sK10_SY841: ( nat > $o ) > nat > nat > ( product_prod_nat_nat > capacity ) > nat ).
thf(tp_sK11_SY850,type,
sK11_SY850: nat > nat > nat > ( product_prod_nat_nat > capacity ) > nat ).
thf(tp_sK12_SY849,type,
sK12_SY849: nat > nat > nat > ( product_prod_nat_nat > capacity ) > nat ).
thf(tp_sK13_SY709,type,
sK13_SY709: nat > nat > list_P559422087at_nat ).
thf(tp_sK14_SY732,type,
sK14_SY732: nat > nat > nat ).
thf(tp_sK15_SY802,type,
sK15_SY802: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).
thf(tp_sK16_SY845,type,
sK16_SY845: nat > nat > nat > nat > nat ).
thf(tp_sK17_SY813,type,
sK17_SY813: nat > nat > nat > list_P559422087at_nat ).
thf(tp_sK18_SY856,type,
sK18_SY856: nat > nat > nat > nat > ( product_prod_nat_nat > capacity ) > nat ).
thf(tp_sK19_SY836,type,
sK19_SY836: nat > nat > nat ).
thf(tp_sK1_SY395,type,
sK1_SY395: nat > nat > ( nat > nat ) > nat ).
thf(tp_sK20_SY844,type,
sK20_SY844: nat > nat > nat ).
thf(tp_sK21_SY709,type,
sK21_SY709: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).
thf(tp_sK22_SY732,type,
sK22_SY732: nat > nat > nat > nat ).
thf(tp_sK23_SY836,type,
sK23_SY836: nat > nat > nat > nat ).
thf(tp_sK24_SY844,type,
sK24_SY844: nat > nat > nat > nat ).
thf(tp_sK25_SY873,type,
sK25_SY873: nat > nat > nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat ).
thf(tp_sK26_SY875,type,
sK26_SY875: list_P559422087at_nat > nat > nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat ).
thf(tp_sK27_SY813,type,
sK27_SY813: list_P559422087at_nat > nat > nat > nat > list_P559422087at_nat ).
thf(tp_sK28_SY873,type,
sK28_SY873: list_P559422087at_nat > nat > nat > nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat ).
thf(tp_sK2_SY688,type,
sK2_SY688: nat > nat > nat ).
thf(tp_sK3_SY722,type,
sK3_SY722: nat > nat > list_P559422087at_nat ).
thf(tp_sK4_SY738,type,
sK4_SY738: nat > nat > nat ).
thf(tp_sK5_SY866,type,
sK5_SY866: ( nat > nat ) > nat > nat > nat ).
thf(tp_sK6_SY799,type,
sK6_SY799: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).
thf(tp_sK7_SY768,type,
sK7_SY768: nat > nat > nat > nat ).
thf(tp_sK8_SY788,type,
sK8_SY788: ( nat > $o ) > nat > nat > nat ).
thf(tp_sK9_SY782,type,
sK9_SY782: nat > nat > nat > 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_u,type,
u: nat ).
thf(tp_v,type,
v: nat ).
thf(39,axiom,
! [S: nat,P: list_P559422087at_nat] :
( ( isSimp1359852763pacity @ c @ S @ P @ S )
= ( P = nil_Pr1308055047at_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_simplePath__same__conv) ).
thf(40,axiom,
! [S: nat,T: nat] :
( ( isSimp1359852763pacity @ c @ S @ nil_Pr1308055047at_nat @ T )
= ( S = T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_simplePath__empty__conv) ).
thf(42,axiom,
! [U: nat,V: nat] :
( ( isPath_capacity @ c @ U @ nil_Pr1308055047at_nat @ V )
= ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_isPath_Osimps_I1_J) ).
thf(43,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_add__mono1) ).
thf(44,axiom,
! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_less__add__one) ).
thf(55,axiom,
( ord_less_nat
= ( ^ [A2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_discrete) ).
thf(57,axiom,
! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ~ ( ( ord_less_eq_nat @ M @ N )
=> ~ ( ord_less_eq_nat @ K @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_add__leE) ).
thf(58,axiom,
! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_le__add1) ).
thf(59,axiom,
! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_le__add2) ).
thf(60,axiom,
! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_add__leD1) ).
thf(61,axiom,
! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ( ord_less_eq_nat @ K @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_add__leD2) ).
thf(62,axiom,
! [K: nat,L: nat] :
( ( ord_less_eq_nat @ K @ L )
=> ? [N3: nat] :
( L
= ( plus_plus_nat @ K @ N3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_le__Suc__ex) ).
thf(63,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_less_eq_nat @ K @ L )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_add__le__mono) ).
thf(64,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_add__le__mono1) ).
thf(65,axiom,
! [I: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_trans__le__add1) ).
thf(66,axiom,
! [I: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_trans__le__add2) ).
thf(67,axiom,
( ord_less_eq_nat
= ( ^ [M2: nat,N2: nat] :
? [K2: nat] :
( N2
= ( plus_plus_nat @ M2 @ K2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_nat__le__iff__add) ).
thf(68,axiom,
( isShor1936442771pacity
= ( ^ [C2: product_prod_nat_nat > capacity,U3: nat,P2: list_P559422087at_nat,V3: nat] :
( ( isSimp1359852763pacity @ C2 @ U3 @ P2 @ V3 )
& ( ( size_s1990949619at_nat @ P2 )
= ( min_dist_capacity @ C2 @ U3 @ V3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_Graph_OisShortestPath__alt) ).
thf(75,axiom,
! [X: list_P559422087at_nat,Y: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ X )
!= ( size_s1990949619at_nat @ Y ) )
=> ( X != Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_size__neq__size__imp__neq) ).
thf(100,axiom,
! [C: product_prod_nat_nat > capacity,Src: nat,V: nat,D: nat,D5: nat] :
( ( connected_capacity @ C @ Src @ V )
=> ( ( ( min_dist_capacity @ C @ Src @ V )
= D )
=> ( ( ord_less_nat @ D5 @ D )
=> ? [V5: nat] :
( ( connected_capacity @ C @ Src @ V5 )
& ( ( min_dist_capacity @ C @ Src @ V5 )
= D5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_Graph_Omin__dist__less) ).
thf(101,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_add__less__le__mono) ).
thf(102,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_add__le__less__mono) ).
thf(103,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I @ J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_add__mono__thms__linordered__field_I3_J) ).
thf(104,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_add__mono__thms__linordered__field_I4_J) ).
thf(107,axiom,
! [F: nat > nat,M: nat,K: nat] :
( ! [M4: nat,N3: nat] :
( ( ord_less_nat @ M4 @ N3 )
=> ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_mono__nat__linear__lb) ).
thf(108,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I @ J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_add__mono__thms__linordered__field_I5_J) ).
thf(109,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( I = J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_add__mono__thms__linordered__field_I2_J) ).
thf(110,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I @ J )
& ( K = L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_add__mono__thms__linordered__field_I1_J) ).
thf(111,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_add__strict__mono) ).
thf(112,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_add__strict__left__mono) ).
thf(113,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_add__strict__right__mono) ).
thf(114,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_add__less__imp__less__left) ).
thf(115,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_add__less__imp__less__right) ).
thf(124,axiom,
! [K: nat,L: nat,M: nat,N: nat] :
( ( ord_less_nat @ K @ L )
=> ( ( ( plus_plus_nat @ M @ L )
= ( plus_plus_nat @ K @ N ) )
=> ( ord_less_nat @ M @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_less__add__eq__less) ).
thf(125,axiom,
! [I: nat,J: nat,M: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_trans__less__add2) ).
thf(126,axiom,
! [I: nat,J: nat,M: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_trans__less__add1) ).
thf(127,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_add__less__mono1) ).
thf(128,axiom,
! [J: nat,I: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_not__add__less2) ).
thf(129,axiom,
! [I: nat,J: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_not__add__less1) ).
thf(130,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( ord_less_nat @ K @ L )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_add__less__mono) ).
thf(131,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
=> ( ord_less_nat @ I @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_add__lessD1) ).
thf(139,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_nat @ M @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_nat__add__left__cancel__less) ).
thf(140,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_add__less__cancel__left) ).
thf(141,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_add__less__cancel__right) ).
thf(142,axiom,
! [S: nat,P: list_P559422087at_nat,T: nat] :
( ( isShor1936442771pacity @ c @ S @ P @ T )
=> ( isSimp1359852763pacity @ c @ S @ P @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_shortestPath__is__simple) ).
thf(143,axiom,
! [S: nat,P: list_P559422087at_nat,T: nat] :
( ( isPath_capacity @ c @ S @ P @ T )
=> ? [P6: list_P559422087at_nat] : ( isSimp1359852763pacity @ c @ S @ P6 @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_isSPath__pathLE) ).
thf(153,axiom,
! [Src: nat,V: nat,D: nat,D5: nat] :
( ( connected_capacity @ c @ Src @ V )
=> ( ( ( min_dist_capacity @ c @ Src @ V )
= D )
=> ( ( ord_less_nat @ D5 @ D )
=> ? [V5: nat] :
( ( connected_capacity @ c @ Src @ V5 )
& ( ( min_dist_capacity @ c @ Src @ V5 )
= D5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_min__dist__less) ).
thf(154,axiom,
! [U: nat,P: list_P559422087at_nat,V: nat] :
( ( isShor1936442771pacity @ c @ U @ P @ V )
= ( ( isSimp1359852763pacity @ c @ U @ P @ V )
& ( ( size_s1990949619at_nat @ P )
= ( min_dist_capacity @ c @ U @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_isShortestPath__alt) ).
thf(155,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_nat__add__left__cancel__le) ).
thf(156,axiom,
! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ C @ U @ D1 @ W )
=> ( ( dist_capacity @ C @ W @ D2 @ V )
=> ( dist_capacity @ C @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Graph_Odist__trans) ).
thf(158,axiom,
min_dist_capacity = min_dist_capacity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Graph_Omin__dist_Ocong) ).
thf(160,axiom,
( isShor1936442771pacity
= ( ^ [C2: product_prod_nat_nat > capacity,U3: nat,P2: list_P559422087at_nat,V3: nat] :
( ( isPath_capacity @ C2 @ U3 @ P2 @ V3 )
& ( ( size_s1990949619at_nat @ P2 )
= ( min_dist_capacity @ C2 @ U3 @ V3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Graph_OisShortestPath__min__dist__def) ).
thf(161,axiom,
! [C: product_prod_nat_nat > capacity,V: nat,V2: nat] :
( ( connected_capacity @ C @ V @ V2 )
=> ( dist_capacity @ C @ V @ ( min_dist_capacity @ C @ V @ V2 ) @ V2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Graph_Omin__dist__is__dist) ).
thf(162,axiom,
! [C: product_prod_nat_nat > capacity,V: nat,D: nat,V2: nat] :
( ( dist_capacity @ C @ V @ D @ V2 )
=> ( ! [D4: nat] :
( ( dist_capacity @ C @ V @ D4 @ V2 )
=> ( ord_less_eq_nat @ D @ D4 ) )
=> ( ( min_dist_capacity @ C @ V @ V2 )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Graph_Omin__distI__eq) ).
thf(163,axiom,
! [C: product_prod_nat_nat > capacity,V: nat,D: nat,V2: nat] :
( ( dist_capacity @ C @ V @ D @ V2 )
=> ( ord_less_eq_nat @ ( min_dist_capacity @ C @ V @ V2 ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_Graph_Omin__dist__minD) ).
thf(164,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add__le__imp__le__right) ).
thf(165,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_add__le__imp__le__left) ).
thf(166,axiom,
( ord_less_eq_nat
= ( ^ [A2: nat,B2: nat] :
? [C2: nat] :
( B2
= ( plus_plus_nat @ A2 @ C2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_le__iff__add) ).
thf(167,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add__right__mono) ).
thf(168,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ! [C3: nat] :
( B
!= ( plus_plus_nat @ A @ C3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_less__eqE) ).
thf(169,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add__left__mono) ).
thf(170,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__mono) ).
thf(171,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_add__mono__thms__linordered__semiring_I1_J) ).
thf(172,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( I = J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_add__mono__thms__linordered__semiring_I2_J) ).
thf(173,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( K = L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add__mono__thms__linordered__semiring_I3_J) ).
thf(174,axiom,
( isShor1936442771pacity
= ( ^ [C2: product_prod_nat_nat > capacity,U3: nat,P2: list_P559422087at_nat,V3: nat] :
( ( isPath_capacity @ C2 @ U3 @ P2 @ V3 )
& ! [P5: list_P559422087at_nat] :
( ( isPath_capacity @ C2 @ U3 @ P5 @ V3 )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P2 ) @ ( size_s1990949619at_nat @ P5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Graph_OisShortestPath__def) ).
thf(175,axiom,
! [C: product_prod_nat_nat > capacity,V: nat,V2: nat,Q: nat > $o] :
( ( connected_capacity @ C @ V @ V2 )
=> ( ! [D6: nat] :
( ( dist_capacity @ C @ V @ D6 @ V2 )
=> ( ! [D7: nat] :
( ( dist_capacity @ C @ V @ D7 @ V2 )
=> ( ord_less_eq_nat @ D6 @ D7 ) )
=> ( Q @ D6 ) ) )
=> ( Q @ ( min_dist_capacity @ C @ V @ V2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Graph_Omin__distI2) ).
thf(186,axiom,
! [C: product_prod_nat_nat > capacity,Src: nat,V: nat,D5: nat] :
( ( connected_capacity @ C @ Src @ V )
=> ( ( ord_less_eq_nat @ D5 @ ( min_dist_capacity @ C @ Src @ V ) )
=> ? [V5: nat] :
( ( connected_capacity @ C @ Src @ V5 )
& ( ( min_dist_capacity @ C @ Src @ V5 )
= D5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Graph_Omin__dist__le) ).
thf(193,axiom,
! [V: nat,D: nat,V2: nat] :
( ( dist_capacity @ c @ V @ D @ V2 )
=> ( connected_capacity @ c @ V @ V2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_connected__distI) ).
thf(194,axiom,
! [V: nat] : ( connected_capacity @ c @ V @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_connected__refl) ).
thf(198,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_add__le__cancel__right) ).
thf(199,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_add__le__cancel__left) ).
thf(203,axiom,
! [U: nat,P: list_P559422087at_nat,V: nat] :
( ( isShor1936442771pacity @ c @ U @ P @ V )
= ( ( isPath_capacity @ c @ U @ P @ V )
& ! [P5: list_P559422087at_nat] :
( ( isPath_capacity @ c @ U @ P5 @ V )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P ) @ ( size_s1990949619at_nat @ P5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_isShortestPath__def) ).
thf(204,axiom,
! [V: nat,V2: nat,Q: nat > $o] :
( ( connected_capacity @ c @ V @ V2 )
=> ( ! [D6: nat] :
( ( dist_capacity @ c @ V @ D6 @ V2 )
=> ( ! [D7: nat] :
( ( dist_capacity @ c @ V @ D7 @ V2 )
=> ( ord_less_eq_nat @ D6 @ D7 ) )
=> ( Q @ D6 ) ) )
=> ( Q @ ( min_dist_capacity @ c @ V @ V2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_min__distI2) ).
thf(205,axiom,
! [Src: nat,V: nat,D5: nat] :
( ( connected_capacity @ c @ Src @ V )
=> ( ( ord_less_eq_nat @ D5 @ ( min_dist_capacity @ c @ Src @ V ) )
=> ? [V5: nat] :
( ( connected_capacity @ c @ Src @ V5 )
& ( ( min_dist_capacity @ c @ Src @ V5 )
= D5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_min__dist__le) ).
thf(209,axiom,
! [U: nat,V: nat] :
( ( connected_capacity @ c @ U @ V )
=> ~ ! [P4: list_P559422087at_nat] :
~ ( isShor1936442771pacity @ c @ U @ P4 @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_obtain__shortest__path) ).
thf(213,axiom,
! [V: nat,V2: nat] :
( ( connected_capacity @ c @ V @ V2 )
= ( ? [D3: nat] : ( dist_capacity @ c @ V @ D3 @ V2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_connected__by__dist) ).
thf(214,axiom,
! [U: nat,V: nat] :
( ( connected_capacity @ c @ U @ V )
= ( ? [P2: list_P559422087at_nat] : ( isPath_capacity @ c @ U @ P2 @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_connected__def) ).
thf(216,axiom,
! [U: nat,P: list_P559422087at_nat,V: nat] :
( ( isShor1936442771pacity @ c @ U @ P @ V )
=> ( isPath_capacity @ c @ U @ P @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_shortestPath__is__path) ).
thf(217,axiom,
! [V: nat,V2: nat] :
( ( connected_capacity @ c @ V @ V2 )
=> ( dist_capacity @ c @ V @ ( min_dist_capacity @ c @ V @ V2 ) @ V2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_min__dist__is__dist) ).
thf(218,axiom,
! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ C @ U @ D1 @ W )
=> ( ( dist_capacity @ C @ W @ D2 @ V )
=> ( ( ( min_dist_capacity @ C @ U @ V )
= ( plus_plus_nat @ D1 @ D2 ) )
=> ( ( min_dist_capacity @ C @ W @ V )
= D2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Graph_Omin__dist__split_I2_J) ).
thf(219,axiom,
! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ C @ U @ D1 @ W )
=> ( ( dist_capacity @ C @ W @ D2 @ V )
=> ( ( ( min_dist_capacity @ C @ U @ V )
= ( plus_plus_nat @ D1 @ D2 ) )
=> ( ( min_dist_capacity @ C @ U @ W )
= D1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_Graph_Omin__dist__split_I1_J) ).
thf(220,axiom,
! [V: nat,D: nat,V2: nat] :
( ( dist_capacity @ c @ V @ D @ V2 )
=> ( ! [D4: nat] :
( ( dist_capacity @ c @ V @ D4 @ V2 )
=> ( ord_less_eq_nat @ D @ D4 ) )
=> ( ( min_dist_capacity @ c @ V @ V2 )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_min__distI__eq) ).
thf(221,axiom,
! [V: nat,D: nat,V2: nat] :
( ( dist_capacity @ c @ V @ D @ V2 )
=> ( ord_less_eq_nat @ ( min_dist_capacity @ c @ V @ V2 ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_min__dist__minD) ).
thf(222,axiom,
( dist_capacity
= ( ^ [C2: product_prod_nat_nat > capacity,V3: nat,D3: nat,V4: nat] :
? [P2: list_P559422087at_nat] :
( ( isPath_capacity @ C2 @ V3 @ P2 @ V4 )
& ( ( size_s1990949619at_nat @ P2 )
= D3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_Graph_Odist__def) ).
thf(223,axiom,
! [C: product_prod_nat_nat > capacity,U: nat,P: list_P559422087at_nat,V: nat] :
( ( isPath_capacity @ C @ U @ P @ V )
=> ( dist_capacity @ C @ U @ ( size_s1990949619at_nat @ P ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Graph_OisPath__distD) ).
thf(224,axiom,
! [U: nat,P: list_P559422087at_nat,V: nat] :
( ( isShor1936442771pacity @ c @ U @ P @ V )
= ( ( isPath_capacity @ c @ U @ P @ V )
& ( ( size_s1990949619at_nat @ P )
= ( min_dist_capacity @ c @ U @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_isShortestPath__min__dist__def) ).
thf(225,axiom,
! [X: nat] :
( ( one_one_nat = X )
= ( X = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_one__reorient) ).
thf(226,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(227,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( I = J )
& ( K = L ) )
=> ( ( plus_plus_nat @ I @ K )
= ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_add__mono__thms__linordered__semiring_I4_J) ).
thf(228,axiom,
! [A3: nat,K: nat,A: nat,B: nat] :
( ( A3
= ( plus_plus_nat @ K @ A ) )
=> ( ( plus_plus_nat @ A3 @ B )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_group__cancel_Oadd1) ).
thf(229,axiom,
! [B3: nat,K: nat,B: nat,A: nat] :
( ( B3
= ( plus_plus_nat @ K @ B ) )
=> ( ( plus_plus_nat @ A @ B3 )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_group__cancel_Oadd2) ).
thf(230,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_add_Oassoc) ).
thf(231,axiom,
( plus_plus_nat
= ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_add_Ocommute) ).
thf(232,axiom,
! [B: nat,A: nat,C: nat] :
( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_add_Oleft__commute) ).
thf(233,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_add__left__imp__eq) ).
thf(234,axiom,
! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_add__right__imp__eq) ).
thf(235,axiom,
isShor1936442771pacity @ c @ s @ p @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_assms_I1_J) ).
thf(236,axiom,
dist_capacity @ c @ v @ ( size_s1990949619at_nat @ p2 ) @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_DISTS_I3_J) ).
thf(237,axiom,
isPath_capacity @ c @ s @ p @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_P) ).
thf(238,axiom,
dist_capacity @ c @ u @ one_one_nat @ v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_DISTS_I2_J) ).
thf(239,axiom,
! [V: nat,D: nat,V2: nat] :
( ( dist_capacity @ c @ V @ D @ V2 )
= ( ? [P2: list_P559422087at_nat] :
( ( isPath_capacity @ c @ V @ P2 @ V2 )
& ( ( size_s1990949619at_nat @ P2 )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_dist__def) ).
thf(240,axiom,
! [U: nat,P: list_P559422087at_nat,V: nat] :
( ( isPath_capacity @ c @ U @ P @ V )
=> ( dist_capacity @ c @ U @ ( size_s1990949619at_nat @ P ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_isPath__distD) ).
thf(241,axiom,
dist_capacity @ c @ s @ ( size_s1990949619at_nat @ p1 ) @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_DISTS_I1_J) ).
thf(242,axiom,
isPath_capacity @ c @ s @ p3 @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_assms_I3_J) ).
thf(243,axiom,
! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ c @ U @ D1 @ W )
=> ( ( dist_capacity @ c @ W @ D2 @ V )
=> ( dist_capacity @ c @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_dist__trans) ).
thf(244,axiom,
! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_add__right__cancel) ).
thf(245,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_add__left__cancel) ).
thf(246,axiom,
! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ c @ U @ D1 @ W )
=> ( ( dist_capacity @ c @ W @ D2 @ V )
=> ( ( ( min_dist_capacity @ c @ U @ V )
= ( plus_plus_nat @ D1 @ D2 ) )
=> ( ( min_dist_capacity @ c @ U @ W )
= D1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_min__dist__split_I1_J) ).
thf(247,axiom,
! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ c @ U @ D1 @ W )
=> ( ( dist_capacity @ c @ W @ D2 @ V )
=> ( ( ( min_dist_capacity @ c @ U @ V )
= ( plus_plus_nat @ D1 @ D2 ) )
=> ( ( min_dist_capacity @ c @ W @ V )
= D2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_min__dist__split_I2_J) ).
thf(248,axiom,
( ( min_dist_capacity @ c @ s @ v )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_MDSV) ).
thf(249,axiom,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062u_A_092_060noteq_062_Av_092_060close_062) ).
thf(250,axiom,
( ( min_dist_capacity @ c @ s @ t )
= ( size_s1990949619at_nat @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_MIN) ).
thf(251,axiom,
( ( min_dist_capacity @ c @ v @ t )
= ( size_s1990949619at_nat @ p2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062min__dist_Av_At_A_061_Alength_Ap2_092_060close_062) ).
thf(252,axiom,
( ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
=> ( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062min__dist_As_At_A_061_Alength_Ap1_A_L_A_I1_A_L_Alength_Ap2_J_A_092_060Longrightarrow_062_Amin__dist_Au_At_A_061_A1_A_L_Alength_Ap2_092_060close_062) ).
thf(253,axiom,
( ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
=> ( ( min_dist_capacity @ c @ s @ u )
= ( size_s1990949619at_nat @ p1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062min__dist_As_At_A_061_Alength_Ap1_A_L_A_I1_A_L_Alength_Ap2_J_A_092_060Longrightarrow_062_Amin__dist_As_Au_A_061_Alength_Ap1_092_060close_062) ).
thf(254,axiom,
( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ one_one_nat ) @ ( size_s1990949619at_nat @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_MIN_H) ).
thf(255,conjecture,
( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(256,negated_conjecture,
( ( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[255]) ).
thf(257,plain,
( ( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[256]) ).
thf(258,plain,
( ( ! [S: nat,P: list_P559422087at_nat] :
( ( isSimp1359852763pacity @ c @ S @ P @ S )
= ( P = nil_Pr1308055047at_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(259,plain,
( ( ! [S: nat,T: nat] :
( ( isSimp1359852763pacity @ c @ S @ nil_Pr1308055047at_nat @ T )
= ( S = T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(260,plain,
( ( ! [U: nat,V: nat] :
( ( isPath_capacity @ c @ U @ nil_Pr1308055047at_nat @ V )
= ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(261,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(262,plain,
( ( ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(263,plain,
( ( ord_less_nat
= ( ^ [A2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(264,plain,
( ( ! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ~ ( ( ord_less_eq_nat @ M @ N )
=> ~ ( ord_less_eq_nat @ K @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(265,plain,
( ( ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(266,plain,
( ( ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(267,plain,
( ( ! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(268,plain,
( ( ! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ( ord_less_eq_nat @ K @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(269,plain,
( ( ! [K: nat,L: nat] :
( ( ord_less_eq_nat @ K @ L )
=> ? [N3: nat] :
( L
= ( plus_plus_nat @ K @ N3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(270,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_less_eq_nat @ K @ L )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(271,plain,
( ( ! [I: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(272,plain,
( ( ! [I: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(273,plain,
( ( ! [I: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(274,plain,
( ( ord_less_eq_nat
= ( ^ [M2: nat,N2: nat] :
? [K2: nat] :
( N2
= ( plus_plus_nat @ M2 @ K2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(275,plain,
( ( isShor1936442771pacity
= ( ^ [C2: product_prod_nat_nat > capacity,U3: nat,P2: list_P559422087at_nat,V3: nat] :
( ( isSimp1359852763pacity @ C2 @ U3 @ P2 @ V3 )
& ( ( size_s1990949619at_nat @ P2 )
= ( min_dist_capacity @ C2 @ U3 @ V3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(276,plain,
( ( ! [X: list_P559422087at_nat,Y: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ X )
!= ( size_s1990949619at_nat @ Y ) )
=> ( X != Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(277,plain,
( ( ! [C: product_prod_nat_nat > capacity,Src: nat,V: nat,D: nat,D5: nat] :
( ( connected_capacity @ C @ Src @ V )
=> ( ( ( min_dist_capacity @ C @ Src @ V )
= D )
=> ( ( ord_less_nat @ D5 @ D )
=> ? [V5: nat] :
( ( connected_capacity @ C @ Src @ V5 )
& ( ( min_dist_capacity @ C @ Src @ V5 )
= D5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(278,plain,
( ( ! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(279,plain,
( ( ! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(280,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I @ J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(281,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(282,plain,
( ( ! [F: nat > nat,M: nat,K: nat] :
( ! [M4: nat,N3: nat] :
( ( ord_less_nat @ M4 @ N3 )
=> ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(283,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I @ J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(284,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( I = J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(285,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I @ J )
& ( K = L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(286,plain,
( ( ! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(287,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(288,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(289,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(290,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
=> ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(291,plain,
( ( ! [K: nat,L: nat,M: nat,N: nat] :
( ( ord_less_nat @ K @ L )
=> ( ( ( plus_plus_nat @ M @ L )
= ( plus_plus_nat @ K @ N ) )
=> ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(292,plain,
( ( ! [I: nat,J: nat,M: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(293,plain,
( ( ! [I: nat,J: nat,M: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(294,plain,
( ( ! [I: nat,J: nat,K: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(295,plain,
( ( ! [J: nat,I: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(296,plain,
( ( ! [I: nat,J: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(297,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( ord_less_nat @ K @ L )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(298,plain,
( ( ! [I: nat,J: nat,K: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
=> ( ord_less_nat @ I @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(299,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(300,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(301,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(302,plain,
( ( ! [S: nat,P: list_P559422087at_nat,T: nat] :
( ( isShor1936442771pacity @ c @ S @ P @ T )
=> ( isSimp1359852763pacity @ c @ S @ P @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(303,plain,
( ( ! [S: nat,P: list_P559422087at_nat,T: nat] :
( ( isPath_capacity @ c @ S @ P @ T )
=> ? [P6: list_P559422087at_nat] : ( isSimp1359852763pacity @ c @ S @ P6 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(304,plain,
( ( ! [Src: nat,V: nat,D: nat,D5: nat] :
( ( connected_capacity @ c @ Src @ V )
=> ( ( ( min_dist_capacity @ c @ Src @ V )
= D )
=> ( ( ord_less_nat @ D5 @ D )
=> ? [V5: nat] :
( ( connected_capacity @ c @ Src @ V5 )
& ( ( min_dist_capacity @ c @ Src @ V5 )
= D5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(305,plain,
( ( ! [U: nat,P: list_P559422087at_nat,V: nat] :
( ( isShor1936442771pacity @ c @ U @ P @ V )
= ( ( isSimp1359852763pacity @ c @ U @ P @ V )
& ( ( size_s1990949619at_nat @ P )
= ( min_dist_capacity @ c @ U @ V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(306,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(307,plain,
( ( ! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ C @ U @ D1 @ W )
=> ( ( dist_capacity @ C @ W @ D2 @ V )
=> ( dist_capacity @ C @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(308,plain,
( ( min_dist_capacity = min_dist_capacity )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(309,plain,
( ( isShor1936442771pacity
= ( ^ [C2: product_prod_nat_nat > capacity,U3: nat,P2: list_P559422087at_nat,V3: nat] :
( ( isPath_capacity @ C2 @ U3 @ P2 @ V3 )
& ( ( size_s1990949619at_nat @ P2 )
= ( min_dist_capacity @ C2 @ U3 @ V3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(310,plain,
( ( ! [C: product_prod_nat_nat > capacity,V: nat,V2: nat] :
( ( connected_capacity @ C @ V @ V2 )
=> ( dist_capacity @ C @ V @ ( min_dist_capacity @ C @ V @ V2 ) @ V2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(311,plain,
( ( ! [C: product_prod_nat_nat > capacity,V: nat,D: nat,V2: nat] :
( ( dist_capacity @ C @ V @ D @ V2 )
=> ( ! [D4: nat] :
( ( dist_capacity @ C @ V @ D4 @ V2 )
=> ( ord_less_eq_nat @ D @ D4 ) )
=> ( ( min_dist_capacity @ C @ V @ V2 )
= D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(312,plain,
( ( ! [C: product_prod_nat_nat > capacity,V: nat,D: nat,V2: nat] :
( ( dist_capacity @ C @ V @ D @ V2 )
=> ( ord_less_eq_nat @ ( min_dist_capacity @ C @ V @ V2 ) @ D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(313,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
=> ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(314,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(315,plain,
( ( ord_less_eq_nat
= ( ^ [A2: nat,B2: nat] :
? [C2: nat] :
( B2
= ( plus_plus_nat @ A2 @ C2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(316,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(317,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ! [C3: nat] :
( B
!= ( plus_plus_nat @ A @ C3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(318,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(319,plain,
( ( ! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(320,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(321,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( I = J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(322,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( K = L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(323,plain,
( ( isShor1936442771pacity
= ( ^ [C2: product_prod_nat_nat > capacity,U3: nat,P2: list_P559422087at_nat,V3: nat] :
( ( isPath_capacity @ C2 @ U3 @ P2 @ V3 )
& ! [P5: list_P559422087at_nat] :
( ( isPath_capacity @ C2 @ U3 @ P5 @ V3 )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P2 ) @ ( size_s1990949619at_nat @ P5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(324,plain,
( ( ! [C: product_prod_nat_nat > capacity,V: nat,V2: nat,Q: nat > $o] :
( ( connected_capacity @ C @ V @ V2 )
=> ( ! [D6: nat] :
( ( dist_capacity @ C @ V @ D6 @ V2 )
=> ( ! [D7: nat] :
( ( dist_capacity @ C @ V @ D7 @ V2 )
=> ( ord_less_eq_nat @ D6 @ D7 ) )
=> ( Q @ D6 ) ) )
=> ( Q @ ( min_dist_capacity @ C @ V @ V2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(325,plain,
( ( ! [C: product_prod_nat_nat > capacity,Src: nat,V: nat,D5: nat] :
( ( connected_capacity @ C @ Src @ V )
=> ( ( ord_less_eq_nat @ D5 @ ( min_dist_capacity @ C @ Src @ V ) )
=> ? [V5: nat] :
( ( connected_capacity @ C @ Src @ V5 )
& ( ( min_dist_capacity @ C @ Src @ V5 )
= D5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(326,plain,
( ( ! [V: nat,D: nat,V2: nat] :
( ( dist_capacity @ c @ V @ D @ V2 )
=> ( connected_capacity @ c @ V @ V2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(327,plain,
( ( ! [V: nat] : ( connected_capacity @ c @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(328,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(329,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(330,plain,
( ( ! [U: nat,P: list_P559422087at_nat,V: nat] :
( ( isShor1936442771pacity @ c @ U @ P @ V )
= ( ( isPath_capacity @ c @ U @ P @ V )
& ! [P5: list_P559422087at_nat] :
( ( isPath_capacity @ c @ U @ P5 @ V )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P ) @ ( size_s1990949619at_nat @ P5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(331,plain,
( ( ! [V: nat,V2: nat,Q: nat > $o] :
( ( connected_capacity @ c @ V @ V2 )
=> ( ! [D6: nat] :
( ( dist_capacity @ c @ V @ D6 @ V2 )
=> ( ! [D7: nat] :
( ( dist_capacity @ c @ V @ D7 @ V2 )
=> ( ord_less_eq_nat @ D6 @ D7 ) )
=> ( Q @ D6 ) ) )
=> ( Q @ ( min_dist_capacity @ c @ V @ V2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(332,plain,
( ( ! [Src: nat,V: nat,D5: nat] :
( ( connected_capacity @ c @ Src @ V )
=> ( ( ord_less_eq_nat @ D5 @ ( min_dist_capacity @ c @ Src @ V ) )
=> ? [V5: nat] :
( ( connected_capacity @ c @ Src @ V5 )
& ( ( min_dist_capacity @ c @ Src @ V5 )
= D5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(333,plain,
( ( ! [U: nat,V: nat] :
( ( connected_capacity @ c @ U @ V )
=> ~ ! [P4: list_P559422087at_nat] :
~ ( isShor1936442771pacity @ c @ U @ P4 @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(334,plain,
( ( ! [V: nat,V2: nat] :
( ( connected_capacity @ c @ V @ V2 )
= ( ? [D3: nat] : ( dist_capacity @ c @ V @ D3 @ V2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(335,plain,
( ( ! [U: nat,V: nat] :
( ( connected_capacity @ c @ U @ V )
= ( ? [P2: list_P559422087at_nat] : ( isPath_capacity @ c @ U @ P2 @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(336,plain,
( ( ! [U: nat,P: list_P559422087at_nat,V: nat] :
( ( isShor1936442771pacity @ c @ U @ P @ V )
=> ( isPath_capacity @ c @ U @ P @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(337,plain,
( ( ! [V: nat,V2: nat] :
( ( connected_capacity @ c @ V @ V2 )
=> ( dist_capacity @ c @ V @ ( min_dist_capacity @ c @ V @ V2 ) @ V2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(338,plain,
( ( ! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ C @ U @ D1 @ W )
=> ( ( dist_capacity @ C @ W @ D2 @ V )
=> ( ( ( min_dist_capacity @ C @ U @ V )
= ( plus_plus_nat @ D1 @ D2 ) )
=> ( ( min_dist_capacity @ C @ W @ V )
= D2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(339,plain,
( ( ! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ C @ U @ D1 @ W )
=> ( ( dist_capacity @ C @ W @ D2 @ V )
=> ( ( ( min_dist_capacity @ C @ U @ V )
= ( plus_plus_nat @ D1 @ D2 ) )
=> ( ( min_dist_capacity @ C @ U @ W )
= D1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(340,plain,
( ( ! [V: nat,D: nat,V2: nat] :
( ( dist_capacity @ c @ V @ D @ V2 )
=> ( ! [D4: nat] :
( ( dist_capacity @ c @ V @ D4 @ V2 )
=> ( ord_less_eq_nat @ D @ D4 ) )
=> ( ( min_dist_capacity @ c @ V @ V2 )
= D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(341,plain,
( ( ! [V: nat,D: nat,V2: nat] :
( ( dist_capacity @ c @ V @ D @ V2 )
=> ( ord_less_eq_nat @ ( min_dist_capacity @ c @ V @ V2 ) @ D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(342,plain,
( ( dist_capacity
= ( ^ [C2: product_prod_nat_nat > capacity,V3: nat,D3: nat,V4: nat] :
? [P2: list_P559422087at_nat] :
( ( isPath_capacity @ C2 @ V3 @ P2 @ V4 )
& ( ( size_s1990949619at_nat @ P2 )
= D3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(343,plain,
( ( ! [C: product_prod_nat_nat > capacity,U: nat,P: list_P559422087at_nat,V: nat] :
( ( isPath_capacity @ C @ U @ P @ V )
=> ( dist_capacity @ C @ U @ ( size_s1990949619at_nat @ P ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(344,plain,
( ( ! [U: nat,P: list_P559422087at_nat,V: nat] :
( ( isShor1936442771pacity @ c @ U @ P @ V )
= ( ( isPath_capacity @ c @ U @ P @ V )
& ( ( size_s1990949619at_nat @ P )
= ( min_dist_capacity @ c @ U @ V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(345,plain,
( ( ! [X: nat] :
( ( one_one_nat = X )
= ( X = one_one_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(346,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(347,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( I = J )
& ( K = L ) )
=> ( ( plus_plus_nat @ I @ K )
= ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(348,plain,
( ( ! [A3: nat,K: nat,A: nat,B: nat] :
( ( A3
= ( plus_plus_nat @ K @ A ) )
=> ( ( plus_plus_nat @ A3 @ B )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(349,plain,
( ( ! [B3: nat,K: nat,B: nat,A: nat] :
( ( B3
= ( plus_plus_nat @ K @ B ) )
=> ( ( plus_plus_nat @ A @ B3 )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(350,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(351,plain,
( ( plus_plus_nat
= ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(352,plain,
( ( ! [B: nat,A: nat,C: nat] :
( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(353,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(354,plain,
( ( ! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(355,plain,
( ( isShor1936442771pacity @ c @ s @ p @ t )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(356,plain,
( ( dist_capacity @ c @ v @ ( size_s1990949619at_nat @ p2 ) @ t )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(357,plain,
( ( isPath_capacity @ c @ s @ p @ t )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(358,plain,
( ( dist_capacity @ c @ u @ one_one_nat @ v )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(359,plain,
( ( ! [V: nat,D: nat,V2: nat] :
( ( dist_capacity @ c @ V @ D @ V2 )
= ( ? [P2: list_P559422087at_nat] :
( ( isPath_capacity @ c @ V @ P2 @ V2 )
& ( ( size_s1990949619at_nat @ P2 )
= D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(360,plain,
( ( ! [U: nat,P: list_P559422087at_nat,V: nat] :
( ( isPath_capacity @ c @ U @ P @ V )
=> ( dist_capacity @ c @ U @ ( size_s1990949619at_nat @ P ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(361,plain,
( ( dist_capacity @ c @ s @ ( size_s1990949619at_nat @ p1 ) @ u )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(362,plain,
( ( isPath_capacity @ c @ s @ p3 @ t )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(363,plain,
( ( ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ c @ U @ D1 @ W )
=> ( ( dist_capacity @ c @ W @ D2 @ V )
=> ( dist_capacity @ c @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(364,plain,
( ( ! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
= ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(365,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(366,plain,
( ( ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ c @ U @ D1 @ W )
=> ( ( dist_capacity @ c @ W @ D2 @ V )
=> ( ( ( min_dist_capacity @ c @ U @ V )
= ( plus_plus_nat @ D1 @ D2 ) )
=> ( ( min_dist_capacity @ c @ U @ W )
= D1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(367,plain,
( ( ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ c @ U @ D1 @ W )
=> ( ( dist_capacity @ c @ W @ D2 @ V )
=> ( ( ( min_dist_capacity @ c @ U @ V )
= ( plus_plus_nat @ D1 @ D2 ) )
=> ( ( min_dist_capacity @ c @ W @ V )
= D2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(368,plain,
( ( ( min_dist_capacity @ c @ s @ v )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ one_one_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(369,plain,
( ( u != v )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(370,plain,
( ( ( min_dist_capacity @ c @ s @ t )
= ( size_s1990949619at_nat @ p ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(371,plain,
( ( ( min_dist_capacity @ c @ v @ t )
= ( size_s1990949619at_nat @ p2 ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(372,plain,
( ( ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
=> ( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(373,plain,
( ( ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
=> ( ( min_dist_capacity @ c @ s @ u )
= ( size_s1990949619at_nat @ p1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(374,plain,
( ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ one_one_nat ) @ ( size_s1990949619at_nat @ p2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(375,plain,
( ( ( min_dist_capacity @ c @ u @ t )
!= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[257]) ).
thf(376,plain,
( ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ one_one_nat ) @ ( size_s1990949619at_nat @ p2 ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(377,plain,
( ( ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
=> ( ( min_dist_capacity @ c @ s @ u )
= ( size_s1990949619at_nat @ p1 ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(378,plain,
( ( ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
=> ( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(379,plain,
( ( ( min_dist_capacity @ c @ v @ t )
= ( size_s1990949619at_nat @ p2 ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(380,plain,
( ( ( min_dist_capacity @ c @ s @ t )
= ( size_s1990949619at_nat @ p ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(381,plain,
( ( u != v )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(382,plain,
( ( ( min_dist_capacity @ c @ s @ v )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ one_one_nat ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(383,plain,
( ( ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ c @ U @ D1 @ W )
=> ( ( dist_capacity @ c @ W @ D2 @ V )
=> ( ( ( min_dist_capacity @ c @ U @ V )
= ( plus_plus_nat @ D1 @ D2 ) )
=> ( ( min_dist_capacity @ c @ W @ V )
= D2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(384,plain,
( ( ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ c @ U @ D1 @ W )
=> ( ( dist_capacity @ c @ W @ D2 @ V )
=> ( ( ( min_dist_capacity @ c @ U @ V )
= ( plus_plus_nat @ D1 @ D2 ) )
=> ( ( min_dist_capacity @ c @ U @ W )
= D1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(385,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(386,plain,
( ( ! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
= ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(387,plain,
( ( ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ c @ U @ D1 @ W )
=> ( ( dist_capacity @ c @ W @ D2 @ V )
=> ( dist_capacity @ c @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(388,plain,
( ( isPath_capacity @ c @ s @ p3 @ t )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(389,plain,
( ( dist_capacity @ c @ s @ ( size_s1990949619at_nat @ p1 ) @ u )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(390,plain,
( ( ! [U: nat,P: list_P559422087at_nat,V: nat] :
( ( isPath_capacity @ c @ U @ P @ V )
=> ( dist_capacity @ c @ U @ ( size_s1990949619at_nat @ P ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(391,plain,
( ( ! [V: nat,D: nat,V2: nat] :
( ( dist_capacity @ c @ V @ D @ V2 )
= ( ? [P2: list_P559422087at_nat] :
( ( isPath_capacity @ c @ V @ P2 @ V2 )
& ( ( size_s1990949619at_nat @ P2 )
= D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(392,plain,
( ( dist_capacity @ c @ u @ one_one_nat @ v )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(393,plain,
( ( isPath_capacity @ c @ s @ p @ t )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(394,plain,
( ( dist_capacity @ c @ v @ ( size_s1990949619at_nat @ p2 ) @ t )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(395,plain,
( ( isShor1936442771pacity @ c @ s @ p @ t )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(396,plain,
( ( ! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
=> ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(397,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(398,plain,
( ( ! [B: nat,A: nat,C: nat] :
( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(399,plain,
( ( plus_plus_nat
= ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(400,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(401,plain,
( ( ! [B3: nat,K: nat,B: nat,A: nat] :
( ( B3
= ( plus_plus_nat @ K @ B ) )
=> ( ( plus_plus_nat @ A @ B3 )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(402,plain,
( ( ! [A3: nat,K: nat,A: nat,B: nat] :
( ( A3
= ( plus_plus_nat @ K @ A ) )
=> ( ( plus_plus_nat @ A3 @ B )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(403,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( I = J )
& ( K = L ) )
=> ( ( plus_plus_nat @ I @ K )
= ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(404,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(405,plain,
( ( ! [X: nat] :
( ( one_one_nat = X )
= ( X = one_one_nat ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(406,plain,
( ( ! [U: nat,P: list_P559422087at_nat,V: nat] :
( ( isShor1936442771pacity @ c @ U @ P @ V )
= ( ( isPath_capacity @ c @ U @ P @ V )
& ( ( size_s1990949619at_nat @ P )
= ( min_dist_capacity @ c @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(407,plain,
( ( ! [C: product_prod_nat_nat > capacity,U: nat,P: list_P559422087at_nat,V: nat] :
( ( isPath_capacity @ C @ U @ P @ V )
=> ( dist_capacity @ C @ U @ ( size_s1990949619at_nat @ P ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(408,plain,
( ( dist_capacity
= ( ^ [C2: product_prod_nat_nat > capacity,V3: nat,D3: nat,V4: nat] :
? [P2: list_P559422087at_nat] :
( ( isPath_capacity @ C2 @ V3 @ P2 @ V4 )
& ( ( size_s1990949619at_nat @ P2 )
= D3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(409,plain,
( ( ! [V: nat,D: nat,V2: nat] :
( ( dist_capacity @ c @ V @ D @ V2 )
=> ( ord_less_eq_nat @ ( min_dist_capacity @ c @ V @ V2 ) @ D ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(410,plain,
( ( ! [V: nat,D: nat,V2: nat] :
( ( dist_capacity @ c @ V @ D @ V2 )
=> ( ! [D4: nat] :
( ( dist_capacity @ c @ V @ D4 @ V2 )
=> ( ord_less_eq_nat @ D @ D4 ) )
=> ( ( min_dist_capacity @ c @ V @ V2 )
= D ) ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(411,plain,
( ( ! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ C @ U @ D1 @ W )
=> ( ( dist_capacity @ C @ W @ D2 @ V )
=> ( ( ( min_dist_capacity @ C @ U @ V )
= ( plus_plus_nat @ D1 @ D2 ) )
=> ( ( min_dist_capacity @ C @ U @ W )
= D1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(412,plain,
( ( ! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ C @ U @ D1 @ W )
=> ( ( dist_capacity @ C @ W @ D2 @ V )
=> ( ( ( min_dist_capacity @ C @ U @ V )
= ( plus_plus_nat @ D1 @ D2 ) )
=> ( ( min_dist_capacity @ C @ W @ V )
= D2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(413,plain,
( ( ! [V: nat,V2: nat] :
( ( connected_capacity @ c @ V @ V2 )
=> ( dist_capacity @ c @ V @ ( min_dist_capacity @ c @ V @ V2 ) @ V2 ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(414,plain,
( ( ! [U: nat,P: list_P559422087at_nat,V: nat] :
( ( isShor1936442771pacity @ c @ U @ P @ V )
=> ( isPath_capacity @ c @ U @ P @ V ) ) )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(415,plain,
( ( ! [U: nat,V: nat] :
( ( connected_capacity @ c @ U @ V )
= ( ? [P2: list_P559422087at_nat] : ( isPath_capacity @ c @ U @ P2 @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(416,plain,
( ( ! [V: nat,V2: nat] :
( ( connected_capacity @ c @ V @ V2 )
= ( ? [D3: nat] : ( dist_capacity @ c @ V @ D3 @ V2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(417,plain,
( ( ! [U: nat,V: nat] :
( ( connected_capacity @ c @ U @ V )
=> ~ ! [P4: list_P559422087at_nat] :
~ ( isShor1936442771pacity @ c @ U @ P4 @ V ) ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(418,plain,
( ( ! [Src: nat,V: nat,D5: nat] :
( ( connected_capacity @ c @ Src @ V )
=> ( ( ord_less_eq_nat @ D5 @ ( min_dist_capacity @ c @ Src @ V ) )
=> ? [V5: nat] :
( ( connected_capacity @ c @ Src @ V5 )
& ( ( min_dist_capacity @ c @ Src @ V5 )
= D5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(419,plain,
( ( ! [V: nat,V2: nat,Q: nat > $o] :
( ( connected_capacity @ c @ V @ V2 )
=> ( ! [D6: nat] :
( ( dist_capacity @ c @ V @ D6 @ V2 )
=> ( ! [D7: nat] :
( ( dist_capacity @ c @ V @ D7 @ V2 )
=> ( ord_less_eq_nat @ D6 @ D7 ) )
=> ( Q @ D6 ) ) )
=> ( Q @ ( min_dist_capacity @ c @ V @ V2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(420,plain,
( ( ! [U: nat,P: list_P559422087at_nat,V: nat] :
( ( isShor1936442771pacity @ c @ U @ P @ V )
= ( ( isPath_capacity @ c @ U @ P @ V )
& ! [P5: list_P559422087at_nat] :
( ( isPath_capacity @ c @ U @ P5 @ V )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P ) @ ( size_s1990949619at_nat @ P5 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(421,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(422,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(423,plain,
( ( ! [V: nat] : ( connected_capacity @ c @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(424,plain,
( ( ! [V: nat,D: nat,V2: nat] :
( ( dist_capacity @ c @ V @ D @ V2 )
=> ( connected_capacity @ c @ V @ V2 ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(425,plain,
( ( ! [C: product_prod_nat_nat > capacity,Src: nat,V: nat,D5: nat] :
( ( connected_capacity @ C @ Src @ V )
=> ( ( ord_less_eq_nat @ D5 @ ( min_dist_capacity @ C @ Src @ V ) )
=> ? [V5: nat] :
( ( connected_capacity @ C @ Src @ V5 )
& ( ( min_dist_capacity @ C @ Src @ V5 )
= D5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(426,plain,
( ( ! [C: product_prod_nat_nat > capacity,V: nat,V2: nat,Q: nat > $o] :
( ( connected_capacity @ C @ V @ V2 )
=> ( ! [D6: nat] :
( ( dist_capacity @ C @ V @ D6 @ V2 )
=> ( ! [D7: nat] :
( ( dist_capacity @ C @ V @ D7 @ V2 )
=> ( ord_less_eq_nat @ D6 @ D7 ) )
=> ( Q @ D6 ) ) )
=> ( Q @ ( min_dist_capacity @ C @ V @ V2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(427,plain,
( ( isShor1936442771pacity
= ( ^ [C2: product_prod_nat_nat > capacity,U3: nat,P2: list_P559422087at_nat,V3: nat] :
( ( isPath_capacity @ C2 @ U3 @ P2 @ V3 )
& ! [P5: list_P559422087at_nat] :
( ( isPath_capacity @ C2 @ U3 @ P5 @ V3 )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P2 ) @ ( size_s1990949619at_nat @ P5 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(428,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( K = L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(429,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( I = J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(430,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(431,plain,
( ( ! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(432,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(433,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ! [C3: nat] :
( B
!= ( plus_plus_nat @ A @ C3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(434,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(435,plain,
( ( ord_less_eq_nat
= ( ^ [A2: nat,B2: nat] :
? [C2: nat] :
( B2
= ( plus_plus_nat @ A2 @ C2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(436,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(437,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
=> ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(438,plain,
( ( ! [C: product_prod_nat_nat > capacity,V: nat,D: nat,V2: nat] :
( ( dist_capacity @ C @ V @ D @ V2 )
=> ( ord_less_eq_nat @ ( min_dist_capacity @ C @ V @ V2 ) @ D ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(439,plain,
( ( ! [C: product_prod_nat_nat > capacity,V: nat,D: nat,V2: nat] :
( ( dist_capacity @ C @ V @ D @ V2 )
=> ( ! [D4: nat] :
( ( dist_capacity @ C @ V @ D4 @ V2 )
=> ( ord_less_eq_nat @ D @ D4 ) )
=> ( ( min_dist_capacity @ C @ V @ V2 )
= D ) ) ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(440,plain,
( ( ! [C: product_prod_nat_nat > capacity,V: nat,V2: nat] :
( ( connected_capacity @ C @ V @ V2 )
=> ( dist_capacity @ C @ V @ ( min_dist_capacity @ C @ V @ V2 ) @ V2 ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(441,plain,
( ( isShor1936442771pacity
= ( ^ [C2: product_prod_nat_nat > capacity,U3: nat,P2: list_P559422087at_nat,V3: nat] :
( ( isPath_capacity @ C2 @ U3 @ P2 @ V3 )
& ( ( size_s1990949619at_nat @ P2 )
= ( min_dist_capacity @ C2 @ U3 @ V3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(442,plain,
( ( min_dist_capacity = min_dist_capacity )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(443,plain,
( ( ! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
( ( dist_capacity @ C @ U @ D1 @ W )
=> ( ( dist_capacity @ C @ W @ D2 @ V )
=> ( dist_capacity @ C @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(444,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(445,plain,
( ( ! [U: nat,P: list_P559422087at_nat,V: nat] :
( ( isShor1936442771pacity @ c @ U @ P @ V )
= ( ( isSimp1359852763pacity @ c @ U @ P @ V )
& ( ( size_s1990949619at_nat @ P )
= ( min_dist_capacity @ c @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(446,plain,
( ( ! [Src: nat,V: nat,D: nat,D5: nat] :
( ( connected_capacity @ c @ Src @ V )
=> ( ( ( min_dist_capacity @ c @ Src @ V )
= D )
=> ( ( ord_less_nat @ D5 @ D )
=> ? [V5: nat] :
( ( connected_capacity @ c @ Src @ V5 )
& ( ( min_dist_capacity @ c @ Src @ V5 )
= D5 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(447,plain,
( ( ! [S: nat,P: list_P559422087at_nat,T: nat] :
( ( isPath_capacity @ c @ S @ P @ T )
=> ? [P6: list_P559422087at_nat] : ( isSimp1359852763pacity @ c @ S @ P6 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(448,plain,
( ( ! [S: nat,P: list_P559422087at_nat,T: nat] :
( ( isShor1936442771pacity @ c @ S @ P @ T )
=> ( isSimp1359852763pacity @ c @ S @ P @ T ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(449,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(450,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(451,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(452,plain,
( ( ! [I: nat,J: nat,K: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
=> ( ord_less_nat @ I @ K ) ) )
= $true ),
inference(copy,[status(thm)],[298]) ).
thf(453,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( ord_less_nat @ K @ L )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(454,plain,
( ( ! [I: nat,J: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(455,plain,
( ( ! [J: nat,I: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(456,plain,
( ( ! [I: nat,J: nat,K: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(457,plain,
( ( ! [I: nat,J: nat,M: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(458,plain,
( ( ! [I: nat,J: nat,M: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(459,plain,
( ( ! [K: nat,L: nat,M: nat,N: nat] :
( ( ord_less_nat @ K @ L )
=> ( ( ( plus_plus_nat @ M @ L )
= ( plus_plus_nat @ K @ N ) )
=> ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(460,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
=> ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(461,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[289]) ).
thf(462,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(463,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(464,plain,
( ( ! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(465,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I @ J )
& ( K = L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(466,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( I = J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(467,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I @ J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(468,plain,
( ( ! [F: nat > nat,M: nat,K: nat] :
( ! [M4: nat,N3: nat] :
( ( ord_less_nat @ M4 @ N3 )
=> ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(469,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(470,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I @ J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(471,plain,
( ( ! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(472,plain,
( ( ! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(473,plain,
( ( ! [C: product_prod_nat_nat > capacity,Src: nat,V: nat,D: nat,D5: nat] :
( ( connected_capacity @ C @ Src @ V )
=> ( ( ( min_dist_capacity @ C @ Src @ V )
= D )
=> ( ( ord_less_nat @ D5 @ D )
=> ? [V5: nat] :
( ( connected_capacity @ C @ Src @ V5 )
& ( ( min_dist_capacity @ C @ Src @ V5 )
= D5 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(474,plain,
( ( ! [X: list_P559422087at_nat,Y: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ X )
!= ( size_s1990949619at_nat @ Y ) )
=> ( X != Y ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(475,plain,
( ( isShor1936442771pacity
= ( ^ [C2: product_prod_nat_nat > capacity,U3: nat,P2: list_P559422087at_nat,V3: nat] :
( ( isSimp1359852763pacity @ C2 @ U3 @ P2 @ V3 )
& ( ( size_s1990949619at_nat @ P2 )
= ( min_dist_capacity @ C2 @ U3 @ V3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(476,plain,
( ( ord_less_eq_nat
= ( ^ [M2: nat,N2: nat] :
? [K2: nat] :
( N2
= ( plus_plus_nat @ M2 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(477,plain,
( ( ! [I: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(478,plain,
( ( ! [I: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(479,plain,
( ( ! [I: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(480,plain,
( ( ! [I: nat,J: nat,K: nat,L: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_less_eq_nat @ K @ L )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(481,plain,
( ( ! [K: nat,L: nat] :
( ( ord_less_eq_nat @ K @ L )
=> ? [N3: nat] :
( L
= ( plus_plus_nat @ K @ N3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(482,plain,
( ( ! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ( ord_less_eq_nat @ K @ N ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(483,plain,
( ( ! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(484,plain,
( ( ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(485,plain,
( ( ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(486,plain,
( ( ! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ~ ( ( ord_less_eq_nat @ M @ N )
=> ~ ( ord_less_eq_nat @ K @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(487,plain,
( ( ord_less_nat
= ( ^ [A2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(488,plain,
( ( ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(489,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(490,plain,
( ( ! [U: nat,V: nat] :
( ( isPath_capacity @ c @ U @ nil_Pr1308055047at_nat @ V )
= ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(491,plain,
( ( ! [S: nat,T: nat] :
( ( isSimp1359852763pacity @ c @ S @ nil_Pr1308055047at_nat @ T )
= ( S = T ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(492,plain,
( ( ! [S: nat,P: list_P559422087at_nat] :
( ( isSimp1359852763pacity @ c @ S @ P @ S )
= ( P = nil_Pr1308055047at_nat ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(493,plain,
( ( ( min_dist_capacity @ c @ u @ t )
!= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(494,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX2 @ SX3 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(495,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ SX2 )
| ~ ( ~ ( ord_less_eq_nat @ SX0 @ SX2 )
| ~ ( ord_less_eq_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(496,plain,
( ( dist_capacity
= ( ^ [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: nat,SX3: nat] :
~ ! [SX4: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SX0 @ SX1 @ SX4 @ SX3 )
| ( ( size_s1990949619at_nat @ SX4 )
!= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(497,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(498,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 @ ( plus_plus_nat @ ( SX0 @ SX1 ) @ SX2 ) @ ( SX0 @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(499,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX2 @ SX3 )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(500,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(501,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ( isShor1936442771pacity @ c @ SX0 @ SX1 @ SX2 )
= ( ~ ( ~ ( isPath_capacity @ c @ SX0 @ SX1 @ SX2 )
| ( ( size_s1990949619at_nat @ SX1 )
!= ( min_dist_capacity @ c @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(502,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX2 @ SX3 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(503,plain,
( ( ! [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( dist_capacity @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ord_less_eq_nat @ ( min_dist_capacity @ SX0 @ SX1 @ SX3 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(504,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( dist_capacity @ c @ SX0 @ SX1 @ SX2 )
| ~ ! [SX3: nat] :
( ~ ( dist_capacity @ c @ SX0 @ SX3 @ SX2 )
| ( ord_less_eq_nat @ SX1 @ SX3 ) )
| ( ( min_dist_capacity @ c @ SX0 @ SX2 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(505,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
( ~ ( dist_capacity @ c @ SX0 @ SX1 @ SX2 )
| ~ ( dist_capacity @ c @ SX2 @ SX3 @ SX4 )
| ( ( min_dist_capacity @ c @ SX0 @ SX4 )
!= ( plus_plus_nat @ SX1 @ SX3 ) )
| ( ( min_dist_capacity @ c @ SX2 @ SX4 )
= SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(506,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ( SX0
!= ( plus_plus_nat @ SX1 @ SX2 ) )
| ( ( plus_plus_nat @ SX3 @ SX0 )
= ( plus_plus_nat @ SX1 @ ( plus_plus_nat @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(507,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ( SX0 != SX1 )
| ~ ( ord_less_nat @ SX2 @ SX3 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(508,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ( isShor1936442771pacity @ c @ SX0 @ SX1 @ SX2 )
= ( ~ ( ~ ( isSimp1359852763pacity @ c @ SX0 @ SX1 @ SX2 )
| ( ( size_s1990949619at_nat @ SX1 )
!= ( min_dist_capacity @ c @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(509,plain,
( ( ! [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
( ~ ( connected_capacity @ SX0 @ SX1 @ SX2 )
| ( ( min_dist_capacity @ SX0 @ SX1 @ SX2 )
!= SX3 )
| ~ ( ord_less_nat @ SX4 @ SX3 )
| ~ ! [SX5: nat] :
~ ~ ( ~ ( connected_capacity @ SX0 @ SX1 @ SX5 )
| ( ( min_dist_capacity @ SX0 @ SX1 @ SX5 )
!= SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(510,plain,
( ( ! [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: nat,SX3: nat,SX4: nat,SX5: nat] :
( ~ ( dist_capacity @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ( dist_capacity @ SX0 @ SX3 @ SX4 @ SX5 )
| ( ( min_dist_capacity @ SX0 @ SX1 @ SX5 )
!= ( plus_plus_nat @ SX2 @ SX4 ) )
| ( ( min_dist_capacity @ SX0 @ SX1 @ SX3 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(511,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( ( plus_plus_nat @ SX0 @ SX1 )
!= ( plus_plus_nat @ SX2 @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(512,plain,
( ( ! [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: nat,SX3: nat,SX4: nat,SX5: nat] :
( ~ ( dist_capacity @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ( dist_capacity @ SX0 @ SX3 @ SX4 @ SX5 )
| ( dist_capacity @ SX0 @ SX1 @ ( plus_plus_nat @ SX2 @ SX4 ) @ SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(513,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ ( plus_plus_nat @ SX0 @ SX2 ) )
| ( ord_less_eq_nat @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(514,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(515,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( ( plus_plus_nat @ SX0 @ SX1 )
!= ( plus_plus_nat @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(516,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( dist_capacity @ c @ SX0 @ SX1 @ SX2 )
| ( ord_less_eq_nat @ ( min_dist_capacity @ c @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(517,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(518,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( dist_capacity @ c @ SX0 @ SX1 @ SX2 )
| ( connected_capacity @ c @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(519,plain,
( ( ! [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: nat] :
( ~ ( connected_capacity @ SX0 @ SX1 @ SX2 )
| ( dist_capacity @ SX0 @ SX1 @ ( min_dist_capacity @ SX0 @ SX1 @ SX2 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(520,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( connected_capacity @ c @ SX0 @ SX1 )
| ( dist_capacity @ c @ SX0 @ ( min_dist_capacity @ c @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(521,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( connected_capacity @ c @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ ( min_dist_capacity @ c @ SX0 @ SX1 ) )
| ~ ! [SX3: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SX0 @ SX3 )
| ( ( min_dist_capacity @ c @ SX0 @ SX3 )
!= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(522,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ ( plus_plus_nat @ SX2 @ SX0 ) @ ( plus_plus_nat @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(523,plain,
( ( ord_less_eq_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ! [SX2: nat] :
( SX1
!= ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(524,plain,
( ( ! [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: nat,SX3: nat,SX4: nat,SX5: nat] :
( ~ ( dist_capacity @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ( dist_capacity @ SX0 @ SX3 @ SX4 @ SX5 )
| ( ( min_dist_capacity @ SX0 @ SX1 @ SX5 )
!= ( plus_plus_nat @ SX2 @ SX4 ) )
| ( ( min_dist_capacity @ SX0 @ SX3 @ SX5 )
= SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(525,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ( SX0
!= ( plus_plus_nat @ SX1 @ SX2 ) )
| ( ( plus_plus_nat @ SX0 @ SX3 )
= ( plus_plus_nat @ SX1 @ ( plus_plus_nat @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(526,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat > $o] :
( ~ ( connected_capacity @ c @ SX0 @ SX1 )
| ~ ! [SX3: nat] :
( ~ ( dist_capacity @ c @ SX0 @ SX3 @ SX1 )
| ~ ! [SX4: nat] :
( ~ ( dist_capacity @ c @ SX0 @ SX4 @ SX1 )
| ( ord_less_eq_nat @ SX3 @ SX4 ) )
| ( SX2 @ SX3 ) )
| ( SX2 @ ( min_dist_capacity @ c @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(527,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( isShor1936442771pacity @ c @ SX0 @ SX1 @ SX2 )
| ( isSimp1359852763pacity @ c @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(528,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)],[474]) ).
thf(529,plain,
( ( isShor1936442771pacity
= ( ^ [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isSimp1359852763pacity @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ( size_s1990949619at_nat @ SX2 )
!= ( min_dist_capacity @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(530,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(531,plain,
( ( ! [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: nat,SX3: nat > $o] :
( ~ ( connected_capacity @ SX0 @ SX1 @ SX2 )
| ~ ! [SX4: nat] :
( ~ ( dist_capacity @ SX0 @ SX1 @ SX4 @ SX2 )
| ~ ! [SX5: nat] :
( ~ ( dist_capacity @ SX0 @ SX1 @ SX5 @ SX2 )
| ( ord_less_eq_nat @ SX4 @ SX5 ) )
| ( SX3 @ SX4 ) )
| ( SX3 @ ( min_dist_capacity @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(532,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ one_one_nat ) @ ( plus_plus_nat @ SX1 @ one_one_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(533,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( isShor1936442771pacity @ c @ SX0 @ SX1 @ SX2 )
| ( isPath_capacity @ c @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(534,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ! [SX2: nat] :
( SX1
!= ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(535,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( SX2 != SX3 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(536,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX0 @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(537,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX0 @ ( plus_plus_nat @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(538,plain,
( ( ( ( min_dist_capacity @ c @ s @ t )
!= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
| ( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(539,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX2 @ SX3 )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(540,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ SX2 )
| ( ord_less_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(541,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX2 @ SX3 )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(542,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( isPath_capacity @ c @ SX0 @ SX1 @ SX2 )
| ~ ! [SX3: list_P559422087at_nat] :
~ ( isSimp1359852763pacity @ c @ SX0 @ SX3 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(543,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ ( plus_plus_nat @ SX0 @ SX2 ) )
| ( ord_less_nat @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(544,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
( ~ ( dist_capacity @ c @ SX0 @ SX1 @ SX2 )
| ~ ( dist_capacity @ c @ SX2 @ SX3 @ SX4 )
| ( ( min_dist_capacity @ c @ SX0 @ SX4 )
!= ( plus_plus_nat @ SX1 @ SX3 ) )
| ( ( min_dist_capacity @ c @ SX0 @ SX2 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(545,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ SX2 )
| ( ord_less_eq_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(546,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ SX0 @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(547,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ~ ( isPath_capacity @ c @ SX0 @ SX1 @ SX2 )
| ( dist_capacity @ c @ SX0 @ ( size_s1990949619at_nat @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(548,plain,
( ( ! [SX0: nat,SX1: list_P559422087at_nat,SX2: nat] :
( ( isShor1936442771pacity @ c @ SX0 @ SX1 @ SX2 )
= ( ~ ( ~ ( isPath_capacity @ c @ SX0 @ SX1 @ SX2 )
| ~ ! [SX3: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SX0 @ SX3 @ SX2 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SX1 ) @ ( size_s1990949619at_nat @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(549,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( connected_capacity @ c @ SX0 @ SX1 )
= ( ~ ! [SX2: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(550,plain,
( ( ! [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
( ~ ( isPath_capacity @ SX0 @ SX1 @ SX2 @ SX3 )
| ( dist_capacity @ SX0 @ SX1 @ ( size_s1990949619at_nat @ SX2 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(551,plain,
( ( ord_less_eq_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ! [SX2: nat] :
( SX1
!= ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(552,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(553,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( connected_capacity @ c @ SX0 @ SX1 )
| ( ( min_dist_capacity @ c @ SX0 @ SX1 )
!= SX2 )
| ~ ( ord_less_nat @ SX3 @ SX2 )
| ~ ! [SX4: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SX0 @ SX4 )
| ( ( min_dist_capacity @ c @ SX0 @ SX4 )
!= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(554,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
( ~ ( dist_capacity @ c @ SX0 @ SX1 @ SX2 )
| ~ ( dist_capacity @ c @ SX2 @ SX3 @ SX4 )
| ( dist_capacity @ c @ SX0 @ ( plus_plus_nat @ SX1 @ SX3 ) @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(555,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( connected_capacity @ c @ SX0 @ SX1 )
| ~ ! [SX2: list_P559422087at_nat] :
~ ( isShor1936442771pacity @ c @ SX0 @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(556,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ SX2 )
| ( ord_less_eq_nat @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(557,plain,
( ( isShor1936442771pacity
= ( ^ [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isPath_capacity @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ( size_s1990949619at_nat @ SX2 )
!= ( min_dist_capacity @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(558,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ SX0 @ ( plus_plus_nat @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(559,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(560,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX2 @ SX0 ) @ ( plus_plus_nat @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(561,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ ( plus_plus_nat @ SX2 @ SX1 ) )
| ( ord_less_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(562,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( connected_capacity @ c @ SX0 @ SX1 )
= ( ~ ! [SX2: nat] :
~ ( dist_capacity @ c @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(563,plain,
( ( u != v )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(564,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(565,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( dist_capacity @ c @ SX0 @ SX1 @ SX2 )
= ( ~ ! [SX3: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SX0 @ SX3 @ SX2 )
| ( ( size_s1990949619at_nat @ SX3 )
!= SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(566,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(567,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ! [SX2: nat] :
( SX1
!= ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(568,plain,
( ( ( ( min_dist_capacity @ c @ s @ t )
!= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
| ( ( min_dist_capacity @ c @ s @ u )
= ( size_s1990949619at_nat @ p1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(569,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ( SX0 != SX1 )
| ( SX2 != SX3 ) )
| ( ( plus_plus_nat @ SX0 @ SX2 )
= ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(570,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ ( plus_plus_nat @ SX2 @ SX1 ) )
| ( ord_less_eq_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(571,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ( SX0 != SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(572,plain,
( ( ! [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( connected_capacity @ SX0 @ SX1 @ SX2 )
| ~ ( ord_less_eq_nat @ SX3 @ ( min_dist_capacity @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX4: nat] :
~ ~ ( ~ ( connected_capacity @ SX0 @ SX1 @ SX4 )
| ( ( min_dist_capacity @ SX0 @ SX1 @ SX4 )
!= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(573,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX2 != SX3 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(574,plain,
( ( ! [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( dist_capacity @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ! [SX4: nat] :
( ~ ( dist_capacity @ SX0 @ SX1 @ SX4 @ SX3 )
| ( ord_less_eq_nat @ SX2 @ SX4 ) )
| ( ( min_dist_capacity @ SX0 @ SX1 @ SX3 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(575,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ( plus_plus_nat @ SX2 @ SX1 )
!= ( plus_plus_nat @ SX0 @ SX3 ) )
| ( ord_less_nat @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(576,plain,
( ( isShor1936442771pacity
= ( ^ [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isPath_capacity @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ! [SX4: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SX0 @ SX1 @ SX4 @ SX3 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SX2 ) @ ( size_s1990949619at_nat @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(577,plain,
! [SV1: nat] :
( ( ! [SY352: nat,SY353: nat] :
( ( ( plus_plus_nat @ SV1 @ SY352 )
= ( plus_plus_nat @ SV1 @ SY353 ) )
= ( SY352 = SY353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(578,plain,
! [SV2: nat] :
( ( ! [SY354: nat,SY355: nat] :
( ( ( plus_plus_nat @ SV2 @ SY354 )
= ( plus_plus_nat @ SY355 @ SY354 ) )
= ( SV2 = SY355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(579,plain,
! [SV3: nat] :
( ( ! [SY356: nat,SY357: nat] :
( ( plus_plus_nat @ SV3 @ ( plus_plus_nat @ SY356 @ SY357 ) )
= ( plus_plus_nat @ SY356 @ ( plus_plus_nat @ SV3 @ SY357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(580,plain,
( ( ! [SV4: nat] :
( ( plus_plus_nat @ SV4 )
= ( ^ [SY358: nat] : ( plus_plus_nat @ SY358 @ SV4 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[399]) ).
thf(581,plain,
( ( plus_plus_nat
= ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[399]) ).
thf(582,plain,
! [SV5: nat] :
( ( ! [SY359: nat,SY360: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ SV5 @ SY359 ) @ SY360 )
= ( plus_plus_nat @ SV5 @ ( plus_plus_nat @ SY359 @ SY360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(583,plain,
! [SV6: nat] :
( ( ! [SY361: nat,SY362: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ SV6 @ SY361 ) @ SY362 )
= ( plus_plus_nat @ SV6 @ ( plus_plus_nat @ SY361 @ SY362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(584,plain,
! [SV7: nat] :
( ( ( one_one_nat = SV7 )
= ( SV7 = one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(585,plain,
! [SV8: nat] :
( ( ! [SY363: nat,SY364: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SY363 ) @ ( plus_plus_nat @ SV8 @ SY364 ) )
= ( ord_less_eq_nat @ SY363 @ SY364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(586,plain,
! [SV9: nat] :
( ( ! [SY365: nat,SY366: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SY365 ) @ ( plus_plus_nat @ SY366 @ SY365 ) )
= ( ord_less_eq_nat @ SV9 @ SY366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(587,plain,
! [SV10: nat] :
( ( connected_capacity @ c @ SV10 @ SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(588,plain,
( ( ! [SV11: product_prod_nat_nat > capacity] :
( ( min_dist_capacity @ SV11 )
= ( min_dist_capacity @ SV11 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[442]) ).
thf(589,plain,
( ( min_dist_capacity = min_dist_capacity )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[442]) ).
thf(590,plain,
! [SV12: nat] :
( ( ! [SY367: nat,SY368: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SY367 ) @ ( plus_plus_nat @ SV12 @ SY368 ) )
= ( ord_less_eq_nat @ SY367 @ SY368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(591,plain,
! [SV13: nat] :
( ( ! [SY369: nat,SY370: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SY369 ) @ ( plus_plus_nat @ SY370 @ SY369 ) )
= ( ord_less_nat @ SV13 @ SY370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(592,plain,
! [SV14: nat] :
( ( ! [SY371: nat,SY372: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SY371 ) @ ( plus_plus_nat @ SV14 @ SY372 ) )
= ( ord_less_nat @ SY371 @ SY372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(593,plain,
! [SV15: nat] :
( ( ! [SY373: nat,SY374: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SY373 ) @ ( plus_plus_nat @ SV15 @ SY374 ) )
= ( ord_less_nat @ SY373 @ SY374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(594,plain,
! [SV16: nat] :
( ( ! [SY375: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ SV16 @ SY375 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(595,plain,
! [SV17: nat] :
( ( ! [SY376: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ SV17 @ SY376 ) @ SY376 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(596,plain,
! [SV18: nat] :
( ( ! [SY377: nat] : ( ord_less_eq_nat @ SV18 @ ( plus_plus_nat @ SY377 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(597,plain,
! [SV19: nat] :
( ( ! [SY378: nat] : ( ord_less_eq_nat @ SV19 @ ( plus_plus_nat @ SV19 @ SY378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(598,plain,
( ( ! [SV20: nat] :
( ( ord_less_nat @ SV20 )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SV20 @ one_one_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[487]) ).
thf(599,plain,
( ( ord_less_nat
= ( ^ [A2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[487]) ).
thf(600,plain,
! [SV21: nat] :
( ( ord_less_nat @ SV21 @ ( plus_plus_nat @ SV21 @ one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(601,plain,
! [SV22: nat] :
( ( ! [SY379: nat] :
( ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SY379 )
= ( SV22 = SY379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(602,plain,
! [SV23: nat] :
( ( ! [SY380: nat] :
( ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SY380 )
= ( SV23 = SY380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(603,plain,
! [SV24: nat] :
( ( ! [SY381: list_P559422087at_nat] :
( ( isSimp1359852763pacity @ c @ SV24 @ SY381 @ SV24 )
= ( SY381 = nil_Pr1308055047at_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(604,plain,
( ( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(605,plain,
! [SV25: nat] :
( ( ! [SY382: nat,SY383: nat,SY384: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SV25 @ SY382 )
| ~ ( ord_less_nat @ SY383 @ SY384 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV25 @ SY383 ) @ ( plus_plus_nat @ SY382 @ SY384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(606,plain,
! [SV26: nat] :
( ( ! [SY385: nat,SY386: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV26 @ SY385 ) @ SY386 )
| ~ ( ~ ( ord_less_eq_nat @ SV26 @ SY386 )
| ~ ( ord_less_eq_nat @ SY385 @ SY386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(607,plain,
( ( ! [SV27: product_prod_nat_nat > capacity] :
( ( dist_capacity @ SV27 )
= ( ^ [SY387: nat,SY388: nat,SY389: nat] :
~ ! [SY390: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV27 @ SY387 @ SY390 @ SY389 )
| ( ( size_s1990949619at_nat @ SY390 )
!= SY388 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[496]) ).
thf(608,plain,
( ( dist_capacity
= ( ^ [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: nat,SX3: nat] :
~ ! [SX4: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SX0 @ SX1 @ SX4 @ SX3 )
| ( ( size_s1990949619at_nat @ SX4 )
!= SX2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[496]) ).
thf(609,plain,
! [SV28: nat] :
( ( ! [SY391: nat,SY392: nat] :
( ~ ( ord_less_nat @ SV28 @ SY391 )
| ( ord_less_nat @ ( plus_plus_nat @ SV28 @ SY392 ) @ ( plus_plus_nat @ SY391 @ SY392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(610,plain,
! [SV29: nat > nat] :
( ( ! [SY393: nat,SY394: nat] :
( ~ ! [SY395: nat,SY396: nat] :
( ~ ( ord_less_nat @ SY395 @ SY396 )
| ( ord_less_nat @ ( SV29 @ SY395 ) @ ( SV29 @ SY396 ) ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ ( SV29 @ SY393 ) @ SY394 ) @ ( SV29 @ ( plus_plus_nat @ SY393 @ SY394 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(611,plain,
! [SV30: nat] :
( ( ! [SY397: nat,SY398: nat,SY399: nat] :
( ~ ( ord_less_eq_nat @ SV30 @ SY397 )
| ~ ( ord_less_nat @ SY398 @ SY399 )
| ( ord_less_nat @ ( plus_plus_nat @ SV30 @ SY398 ) @ ( plus_plus_nat @ SY397 @ SY399 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(612,plain,
! [SV31: nat] :
( ( ! [SY400: nat,SY401: nat,SY402: nat] :
( ~ ( ord_less_nat @ SV31 @ SY400 )
| ~ ( ord_less_eq_nat @ SY401 @ SY402 )
| ( ord_less_nat @ ( plus_plus_nat @ SV31 @ SY401 ) @ ( plus_plus_nat @ SY400 @ SY402 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(613,plain,
! [SV32: nat] :
( ( ! [SY403: list_P559422087at_nat,SY404: nat] :
( ( isShor1936442771pacity @ c @ SV32 @ SY403 @ SY404 )
= ( ~ ( ~ ( isPath_capacity @ c @ SV32 @ SY403 @ SY404 )
| ( ( size_s1990949619at_nat @ SY403 )
!= ( min_dist_capacity @ c @ SV32 @ SY404 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(614,plain,
! [SV33: nat] :
( ( ! [SY405: nat,SY406: nat,SY407: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SV33 @ SY405 )
| ~ ( ord_less_nat @ SY406 @ SY407 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV33 @ SY406 ) @ ( plus_plus_nat @ SY405 @ SY407 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(615,plain,
! [SV34: product_prod_nat_nat > capacity] :
( ( ! [SY408: nat,SY409: nat,SY410: nat] :
( ~ ( dist_capacity @ SV34 @ SY408 @ SY409 @ SY410 )
| ( ord_less_eq_nat @ ( min_dist_capacity @ SV34 @ SY408 @ SY410 ) @ SY409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(616,plain,
! [SV35: nat] :
( ( ! [SY411: nat,SY412: nat] :
( ~ ( dist_capacity @ c @ SV35 @ SY411 @ SY412 )
| ~ ! [SY413: nat] :
( ~ ( dist_capacity @ c @ SV35 @ SY413 @ SY412 )
| ( ord_less_eq_nat @ SY411 @ SY413 ) )
| ( ( min_dist_capacity @ c @ SV35 @ SY412 )
= SY411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(617,plain,
! [SV36: nat] :
( ( ! [SY414: nat,SY415: nat,SY416: nat,SY417: nat] :
( ~ ( dist_capacity @ c @ SV36 @ SY414 @ SY415 )
| ~ ( dist_capacity @ c @ SY415 @ SY416 @ SY417 )
| ( ( min_dist_capacity @ c @ SV36 @ SY417 )
!= ( plus_plus_nat @ SY414 @ SY416 ) )
| ( ( min_dist_capacity @ c @ SY415 @ SY417 )
= SY416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(618,plain,
! [SV37: nat] :
( ( ! [SY418: nat,SY419: nat,SY420: nat] :
( ( SV37
!= ( plus_plus_nat @ SY418 @ SY419 ) )
| ( ( plus_plus_nat @ SY420 @ SV37 )
= ( plus_plus_nat @ SY418 @ ( plus_plus_nat @ SY420 @ SY419 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(619,plain,
! [SV38: nat] :
( ( ! [SY421: nat,SY422: nat,SY423: nat] :
( ~ ~ ( ( SV38 != SY421 )
| ~ ( ord_less_nat @ SY422 @ SY423 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV38 @ SY422 ) @ ( plus_plus_nat @ SY421 @ SY423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(620,plain,
! [SV39: nat] :
( ( ! [SY424: list_P559422087at_nat,SY425: nat] :
( ( isShor1936442771pacity @ c @ SV39 @ SY424 @ SY425 )
= ( ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SY424 @ SY425 )
| ( ( size_s1990949619at_nat @ SY424 )
!= ( min_dist_capacity @ c @ SV39 @ SY425 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(621,plain,
! [SV40: product_prod_nat_nat > capacity] :
( ( ! [SY426: nat,SY427: nat,SY428: nat,SY429: nat] :
( ~ ( connected_capacity @ SV40 @ SY426 @ SY427 )
| ( ( min_dist_capacity @ SV40 @ SY426 @ SY427 )
!= SY428 )
| ~ ( ord_less_nat @ SY429 @ SY428 )
| ~ ! [SY430: nat] :
~ ~ ( ~ ( connected_capacity @ SV40 @ SY426 @ SY430 )
| ( ( min_dist_capacity @ SV40 @ SY426 @ SY430 )
!= SY429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(622,plain,
! [SV41: product_prod_nat_nat > capacity] :
( ( ! [SY431: nat,SY432: nat,SY433: nat,SY434: nat,SY435: nat] :
( ~ ( dist_capacity @ SV41 @ SY431 @ SY432 @ SY433 )
| ~ ( dist_capacity @ SV41 @ SY433 @ SY434 @ SY435 )
| ( ( min_dist_capacity @ SV41 @ SY431 @ SY435 )
!= ( plus_plus_nat @ SY432 @ SY434 ) )
| ( ( min_dist_capacity @ SV41 @ SY431 @ SY433 )
= SY432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(623,plain,
! [SV42: nat] :
( ( ! [SY436: nat,SY437: nat] :
( ( ( plus_plus_nat @ SV42 @ SY436 )
!= ( plus_plus_nat @ SY437 @ SY436 ) )
| ( SV42 = SY437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(624,plain,
! [SV43: product_prod_nat_nat > capacity] :
( ( ! [SY438: nat,SY439: nat,SY440: nat,SY441: nat,SY442: nat] :
( ~ ( dist_capacity @ SV43 @ SY438 @ SY439 @ SY440 )
| ~ ( dist_capacity @ SV43 @ SY440 @ SY441 @ SY442 )
| ( dist_capacity @ SV43 @ SY438 @ ( plus_plus_nat @ SY439 @ SY441 ) @ SY442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(625,plain,
! [SV44: nat] :
( ( ! [SY443: nat,SY444: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SY443 ) @ ( plus_plus_nat @ SV44 @ SY444 ) )
| ( ord_less_eq_nat @ SY443 @ SY444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(626,plain,
! [SV45: nat] :
( ( ! [SY445: nat,SY446: nat] :
( ~ ( ord_less_eq_nat @ SV45 @ SY445 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV45 @ SY446 ) @ ( plus_plus_nat @ SY445 @ SY446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(627,plain,
! [SV46: nat] :
( ( ! [SY447: nat,SY448: nat] :
( ( ( plus_plus_nat @ SV46 @ SY447 )
!= ( plus_plus_nat @ SV46 @ SY448 ) )
| ( SY447 = SY448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(628,plain,
! [SV47: nat] :
( ( ! [SY449: nat,SY450: nat] :
( ~ ( dist_capacity @ c @ SV47 @ SY449 @ SY450 )
| ( ord_less_eq_nat @ ( min_dist_capacity @ c @ SV47 @ SY450 ) @ SY449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(629,plain,
! [SV48: nat] :
( ( ! [SY451: nat,SY452: nat] :
( ~ ( ord_less_nat @ SV48 @ SY451 )
| ( ord_less_nat @ ( plus_plus_nat @ SV48 @ SY452 ) @ ( plus_plus_nat @ SY451 @ SY452 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(630,plain,
! [SV49: nat] :
( ( ! [SY453: nat,SY454: nat] :
( ~ ( dist_capacity @ c @ SV49 @ SY453 @ SY454 )
| ( connected_capacity @ c @ SV49 @ SY454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(631,plain,
! [SV50: product_prod_nat_nat > capacity] :
( ( ! [SY455: nat,SY456: nat] :
( ~ ( connected_capacity @ SV50 @ SY455 @ SY456 )
| ( dist_capacity @ SV50 @ SY455 @ ( min_dist_capacity @ SV50 @ SY455 @ SY456 ) @ SY456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(632,plain,
! [SV51: nat] :
( ( ! [SY457: nat] :
( ~ ( connected_capacity @ c @ SV51 @ SY457 )
| ( dist_capacity @ c @ SV51 @ ( min_dist_capacity @ c @ SV51 @ SY457 ) @ SY457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(633,plain,
! [SV52: nat] :
( ( ! [SY458: nat,SY459: nat] :
( ~ ( connected_capacity @ c @ SV52 @ SY458 )
| ~ ( ord_less_eq_nat @ SY459 @ ( min_dist_capacity @ c @ SV52 @ SY458 ) )
| ~ ! [SY460: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV52 @ SY460 )
| ( ( min_dist_capacity @ c @ SV52 @ SY460 )
!= SY459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(634,plain,
! [SV53: nat] :
( ( ! [SY461: nat,SY462: nat] :
( ~ ( ord_less_nat @ SV53 @ SY461 )
| ( ord_less_nat @ ( plus_plus_nat @ SY462 @ SV53 ) @ ( plus_plus_nat @ SY462 @ SY461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(635,plain,
( ( ! [SV54: nat] :
( ( ord_less_eq_nat @ SV54 )
= ( ^ [SY463: nat] :
~ ! [SY464: nat] :
( SY463
!= ( plus_plus_nat @ SV54 @ SY464 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[523]) ).
thf(636,plain,
( ( ord_less_eq_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ! [SX2: nat] :
( SX1
!= ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[523]) ).
thf(637,plain,
! [SV55: product_prod_nat_nat > capacity] :
( ( ! [SY465: nat,SY466: nat,SY467: nat,SY468: nat,SY469: nat] :
( ~ ( dist_capacity @ SV55 @ SY465 @ SY466 @ SY467 )
| ~ ( dist_capacity @ SV55 @ SY467 @ SY468 @ SY469 )
| ( ( min_dist_capacity @ SV55 @ SY465 @ SY469 )
!= ( plus_plus_nat @ SY466 @ SY468 ) )
| ( ( min_dist_capacity @ SV55 @ SY467 @ SY469 )
= SY468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(638,plain,
! [SV56: nat] :
( ( ! [SY470: nat,SY471: nat,SY472: nat] :
( ( SV56
!= ( plus_plus_nat @ SY470 @ SY471 ) )
| ( ( plus_plus_nat @ SV56 @ SY472 )
= ( plus_plus_nat @ SY470 @ ( plus_plus_nat @ SY471 @ SY472 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(639,plain,
! [SV57: nat] :
( ( ! [SY473: nat,SY474: nat > $o] :
( ~ ( connected_capacity @ c @ SV57 @ SY473 )
| ~ ! [SY475: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY475 @ SY473 )
| ~ ! [SY476: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY476 @ SY473 )
| ( ord_less_eq_nat @ SY475 @ SY476 ) )
| ( SY474 @ SY475 ) )
| ( SY474 @ ( min_dist_capacity @ c @ SV57 @ SY473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(640,plain,
! [SV58: nat] :
( ( ! [SY477: list_P559422087at_nat,SY478: nat] :
( ~ ( isShor1936442771pacity @ c @ SV58 @ SY477 @ SY478 )
| ( isSimp1359852763pacity @ c @ SV58 @ SY477 @ SY478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(641,plain,
! [SV59: list_P559422087at_nat] :
( ( ! [SY479: list_P559422087at_nat] :
( ~ ( ( ( size_s1990949619at_nat @ SV59 )
!= ( size_s1990949619at_nat @ SY479 ) ) )
| ( SV59 != SY479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(642,plain,
( ( ! [SV60: product_prod_nat_nat > capacity] :
( ( isShor1936442771pacity @ SV60 )
= ( ^ [SY480: nat,SY481: list_P559422087at_nat,SY482: nat] :
~ ( ~ ( isSimp1359852763pacity @ SV60 @ SY480 @ SY481 @ SY482 )
| ( ( size_s1990949619at_nat @ SY481 )
!= ( min_dist_capacity @ SV60 @ SY480 @ SY482 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[529]) ).
thf(643,plain,
( ( isShor1936442771pacity
= ( ^ [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isSimp1359852763pacity @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ( size_s1990949619at_nat @ SX2 )
!= ( min_dist_capacity @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[529]) ).
thf(644,plain,
! [SV61: nat] :
( ( ! [SY483: nat,SY484: nat,SY485: nat] :
( ~ ( ord_less_eq_nat @ SV61 @ SY483 )
| ~ ( ord_less_eq_nat @ SY484 @ SY485 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV61 @ SY484 ) @ ( plus_plus_nat @ SY483 @ SY485 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(645,plain,
! [SV62: product_prod_nat_nat > capacity] :
( ( ! [SY486: nat,SY487: nat,SY488: nat > $o] :
( ~ ( connected_capacity @ SV62 @ SY486 @ SY487 )
| ~ ! [SY489: nat] :
( ~ ( dist_capacity @ SV62 @ SY486 @ SY489 @ SY487 )
| ~ ! [SY490: nat] :
( ~ ( dist_capacity @ SV62 @ SY486 @ SY490 @ SY487 )
| ( ord_less_eq_nat @ SY489 @ SY490 ) )
| ( SY488 @ SY489 ) )
| ( SY488 @ ( min_dist_capacity @ SV62 @ SY486 @ SY487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(646,plain,
! [SV63: nat] :
( ( ! [SY491: nat] :
( ~ ( ord_less_nat @ SV63 @ SY491 )
| ( ord_less_nat @ ( plus_plus_nat @ SV63 @ one_one_nat ) @ ( plus_plus_nat @ SY491 @ one_one_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(647,plain,
! [SV64: nat] :
( ( ! [SY492: list_P559422087at_nat,SY493: nat] :
( ~ ( isShor1936442771pacity @ c @ SV64 @ SY492 @ SY493 )
| ( isPath_capacity @ c @ SV64 @ SY492 @ SY493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(648,plain,
! [SV65: nat] :
( ( ! [SY494: nat] :
( ~ ( ord_less_eq_nat @ SV65 @ SY494 )
| ~ ! [SY495: nat] :
( SY494
!= ( plus_plus_nat @ SV65 @ SY495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(649,plain,
! [SV66: nat] :
( ( ! [SY496: nat,SY497: nat,SY498: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SV66 @ SY496 )
| ( SY497 != SY498 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV66 @ SY497 ) @ ( plus_plus_nat @ SY496 @ SY498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(650,plain,
! [SV67: nat] :
( ( ! [SY499: nat,SY500: nat] :
( ~ ( ord_less_eq_nat @ SV67 @ SY499 )
| ( ord_less_eq_nat @ SV67 @ ( plus_plus_nat @ SY499 @ SY500 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(651,plain,
! [SV68: nat] :
( ( ! [SY501: nat,SY502: nat] :
( ~ ( ord_less_eq_nat @ SV68 @ SY501 )
| ( ord_less_eq_nat @ SV68 @ ( plus_plus_nat @ SY502 @ SY501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(652,plain,
( ( ( ( min_dist_capacity @ c @ s @ t )
!= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
= $true )
| ( ( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(653,plain,
! [SV69: nat] :
( ( ! [SY503: nat,SY504: nat,SY505: nat] :
( ~ ( ord_less_nat @ SV69 @ SY503 )
| ~ ( ord_less_nat @ SY504 @ SY505 )
| ( ord_less_nat @ ( plus_plus_nat @ SV69 @ SY504 ) @ ( plus_plus_nat @ SY503 @ SY505 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(654,plain,
! [SV70: nat] :
( ( ! [SY506: nat,SY507: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SV70 @ SY506 ) @ SY507 )
| ( ord_less_nat @ SV70 @ SY507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(655,plain,
! [SV71: nat] :
( ( ! [SY508: nat,SY509: nat,SY510: nat] :
( ~ ( ord_less_nat @ SV71 @ SY508 )
| ~ ( ord_less_nat @ SY509 @ SY510 )
| ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SY509 ) @ ( plus_plus_nat @ SY508 @ SY510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(656,plain,
! [SV72: nat] :
( ( ! [SY511: list_P559422087at_nat,SY512: nat] :
( ~ ( isPath_capacity @ c @ SV72 @ SY511 @ SY512 )
| ~ ! [SY513: list_P559422087at_nat] :
~ ( isSimp1359852763pacity @ c @ SV72 @ SY513 @ SY512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(657,plain,
! [SV73: nat] :
( ( ! [SY514: nat,SY515: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SV73 @ SY514 ) @ ( plus_plus_nat @ SV73 @ SY515 ) )
| ( ord_less_nat @ SY514 @ SY515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(658,plain,
! [SV74: nat] :
( ( ! [SY516: nat,SY517: nat,SY518: nat,SY519: nat] :
( ~ ( dist_capacity @ c @ SV74 @ SY516 @ SY517 )
| ~ ( dist_capacity @ c @ SY517 @ SY518 @ SY519 )
| ( ( min_dist_capacity @ c @ SV74 @ SY519 )
!= ( plus_plus_nat @ SY516 @ SY518 ) )
| ( ( min_dist_capacity @ c @ SV74 @ SY517 )
= SY516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(659,plain,
! [SV75: nat] :
( ( ! [SY520: nat,SY521: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV75 @ SY520 ) @ SY521 )
| ( ord_less_eq_nat @ SV75 @ SY521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(660,plain,
! [SV76: nat] :
( ( ! [SY522: nat,SY523: nat] :
( ~ ( ord_less_nat @ SV76 @ SY522 )
| ( ord_less_nat @ SV76 @ ( plus_plus_nat @ SY522 @ SY523 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(661,plain,
! [SV77: nat] :
( ( ! [SY524: list_P559422087at_nat,SY525: nat] :
( ~ ( isPath_capacity @ c @ SV77 @ SY524 @ SY525 )
| ( dist_capacity @ c @ SV77 @ ( size_s1990949619at_nat @ SY524 ) @ SY525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(662,plain,
! [SV78: nat] :
( ( ! [SY526: list_P559422087at_nat,SY527: nat] :
( ( isShor1936442771pacity @ c @ SV78 @ SY526 @ SY527 )
= ( ~ ( ~ ( isPath_capacity @ c @ SV78 @ SY526 @ SY527 )
| ~ ! [SY528: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY528 @ SY527 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY526 ) @ ( size_s1990949619at_nat @ SY528 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(663,plain,
! [SV79: nat] :
( ( ! [SY529: nat] :
( ( connected_capacity @ c @ SV79 @ SY529 )
= ( ~ ! [SY530: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY530 @ SY529 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(664,plain,
! [SV80: product_prod_nat_nat > capacity] :
( ( ! [SY531: nat,SY532: list_P559422087at_nat,SY533: nat] :
( ~ ( isPath_capacity @ SV80 @ SY531 @ SY532 @ SY533 )
| ( dist_capacity @ SV80 @ SY531 @ ( size_s1990949619at_nat @ SY532 ) @ SY533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(665,plain,
( ( ! [SV81: nat] :
( ( ord_less_eq_nat @ SV81 )
= ( ^ [SY534: nat] :
~ ! [SY535: nat] :
( SY534
!= ( plus_plus_nat @ SV81 @ SY535 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[551]) ).
thf(666,plain,
( ( ord_less_eq_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ! [SX2: nat] :
( SX1
!= ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[551]) ).
thf(667,plain,
! [SV82: nat] :
( ( ! [SY536: nat,SY537: nat,SY538: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SV82 @ SY536 )
| ~ ( ord_less_eq_nat @ SY537 @ SY538 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV82 @ SY537 ) @ ( plus_plus_nat @ SY536 @ SY538 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(668,plain,
! [SV83: nat] :
( ( ! [SY539: nat,SY540: nat,SY541: nat] :
( ~ ( connected_capacity @ c @ SV83 @ SY539 )
| ( ( min_dist_capacity @ c @ SV83 @ SY539 )
!= SY540 )
| ~ ( ord_less_nat @ SY541 @ SY540 )
| ~ ! [SY542: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV83 @ SY542 )
| ( ( min_dist_capacity @ c @ SV83 @ SY542 )
!= SY541 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(669,plain,
! [SV84: nat] :
( ( ! [SY543: nat,SY544: nat,SY545: nat,SY546: nat] :
( ~ ( dist_capacity @ c @ SV84 @ SY543 @ SY544 )
| ~ ( dist_capacity @ c @ SY544 @ SY545 @ SY546 )
| ( dist_capacity @ c @ SV84 @ ( plus_plus_nat @ SY543 @ SY545 ) @ SY546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(670,plain,
! [SV85: nat] :
( ( ! [SY547: nat] :
( ~ ( connected_capacity @ c @ SV85 @ SY547 )
| ~ ! [SY548: list_P559422087at_nat] :
~ ( isShor1936442771pacity @ c @ SV85 @ SY548 @ SY547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(671,plain,
! [SV86: nat] :
( ( ! [SY549: nat,SY550: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV86 @ SY549 ) @ SY550 )
| ( ord_less_eq_nat @ SY549 @ SY550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(672,plain,
( ( ! [SV87: product_prod_nat_nat > capacity] :
( ( isShor1936442771pacity @ SV87 )
= ( ^ [SY551: nat,SY552: list_P559422087at_nat,SY553: nat] :
~ ( ~ ( isPath_capacity @ SV87 @ SY551 @ SY552 @ SY553 )
| ( ( size_s1990949619at_nat @ SY552 )
!= ( min_dist_capacity @ SV87 @ SY551 @ SY553 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[557]) ).
thf(673,plain,
( ( isShor1936442771pacity
= ( ^ [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isPath_capacity @ SX0 @ SX1 @ SX2 @ SX3 )
| ( ( size_s1990949619at_nat @ SX2 )
!= ( min_dist_capacity @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[557]) ).
thf(674,plain,
! [SV88: nat] :
( ( ! [SY554: nat,SY555: nat] :
( ~ ( ord_less_nat @ SV88 @ SY554 )
| ( ord_less_nat @ SV88 @ ( plus_plus_nat @ SY555 @ SY554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(675,plain,
! [SV89: nat] :
( ( ! [SY556: nat,SY557: nat,SY558: nat] :
( ~ ( ord_less_eq_nat @ SV89 @ SY556 )
| ~ ( ord_less_eq_nat @ SY557 @ SY558 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV89 @ SY557 ) @ ( plus_plus_nat @ SY556 @ SY558 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(676,plain,
! [SV90: nat] :
( ( ! [SY559: nat,SY560: nat] :
( ~ ( ord_less_eq_nat @ SV90 @ SY559 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SY560 @ SV90 ) @ ( plus_plus_nat @ SY560 @ SY559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(677,plain,
! [SV91: nat] :
( ( ! [SY561: nat,SY562: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SV91 @ SY561 ) @ ( plus_plus_nat @ SY562 @ SY561 ) )
| ( ord_less_nat @ SV91 @ SY562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(678,plain,
! [SV92: nat] :
( ( ! [SY563: nat] :
( ( connected_capacity @ c @ SV92 @ SY563 )
= ( ~ ! [SY564: nat] :
~ ( dist_capacity @ c @ SV92 @ SY564 @ SY563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(679,plain,
( ( u = v )
= $false ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(680,plain,
! [SV93: nat] :
( ( ! [SY565: nat,SY566: nat] :
( ~ ( ord_less_eq_nat @ SV93 @ SY565 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV93 @ SY566 ) @ ( plus_plus_nat @ SY565 @ SY566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(681,plain,
! [SV94: nat] :
( ( ! [SY567: nat,SY568: nat] :
( ( dist_capacity @ c @ SV94 @ SY567 @ SY568 )
= ( ~ ! [SY569: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY569 @ SY568 )
| ( ( size_s1990949619at_nat @ SY569 )
!= SY567 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(682,plain,
! [SV95: nat] :
( ( ! [SY570: nat,SY571: nat,SY572: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SV95 @ SY570 )
| ~ ( ord_less_eq_nat @ SY571 @ SY572 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV95 @ SY571 ) @ ( plus_plus_nat @ SY570 @ SY572 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(683,plain,
! [SV96: nat] :
( ( ! [SY573: nat] :
( ~ ( ord_less_eq_nat @ SV96 @ SY573 )
| ~ ! [SY574: nat] :
( SY573
!= ( plus_plus_nat @ SV96 @ SY574 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(684,plain,
( ( ( ( min_dist_capacity @ c @ s @ t )
!= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
= $true )
| ( ( ( min_dist_capacity @ c @ s @ u )
= ( size_s1990949619at_nat @ p1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(685,plain,
! [SV97: nat] :
( ( ! [SY575: nat,SY576: nat,SY577: nat] :
( ~ ~ ( ( SV97 != SY575 )
| ( SY576 != SY577 ) )
| ( ( plus_plus_nat @ SV97 @ SY576 )
= ( plus_plus_nat @ SY575 @ SY577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(686,plain,
! [SV98: nat] :
( ( ! [SY578: nat,SY579: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV98 @ SY578 ) @ ( plus_plus_nat @ SY579 @ SY578 ) )
| ( ord_less_eq_nat @ SV98 @ SY579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(687,plain,
! [SV99: nat] :
( ( ! [SY580: nat,SY581: nat,SY582: nat] :
( ~ ~ ( ( SV99 != SY580 )
| ~ ( ord_less_eq_nat @ SY581 @ SY582 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV99 @ SY581 ) @ ( plus_plus_nat @ SY580 @ SY582 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(688,plain,
! [SV100: product_prod_nat_nat > capacity] :
( ( ! [SY583: nat,SY584: nat,SY585: nat] :
( ~ ( connected_capacity @ SV100 @ SY583 @ SY584 )
| ~ ( ord_less_eq_nat @ SY585 @ ( min_dist_capacity @ SV100 @ SY583 @ SY584 ) )
| ~ ! [SY586: nat] :
~ ~ ( ~ ( connected_capacity @ SV100 @ SY583 @ SY586 )
| ( ( min_dist_capacity @ SV100 @ SY583 @ SY586 )
!= SY585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(689,plain,
! [SV101: nat] :
( ( ! [SY587: nat,SY588: nat,SY589: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SV101 @ SY587 )
| ( SY588 != SY589 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV101 @ SY588 ) @ ( plus_plus_nat @ SY587 @ SY589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(690,plain,
! [SV102: product_prod_nat_nat > capacity] :
( ( ! [SY590: nat,SY591: nat,SY592: nat] :
( ~ ( dist_capacity @ SV102 @ SY590 @ SY591 @ SY592 )
| ~ ! [SY593: nat] :
( ~ ( dist_capacity @ SV102 @ SY590 @ SY593 @ SY592 )
| ( ord_less_eq_nat @ SY591 @ SY593 ) )
| ( ( min_dist_capacity @ SV102 @ SY590 @ SY592 )
= SY591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(691,plain,
! [SV103: nat] :
( ( ! [SY594: nat,SY595: nat,SY596: nat] :
( ~ ( ord_less_nat @ SV103 @ SY594 )
| ( ( plus_plus_nat @ SY595 @ SY594 )
!= ( plus_plus_nat @ SV103 @ SY596 ) )
| ( ord_less_nat @ SY595 @ SY596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(692,plain,
( ( ! [SV104: product_prod_nat_nat > capacity] :
( ( isShor1936442771pacity @ SV104 )
= ( ^ [SY597: nat,SY598: list_P559422087at_nat,SY599: nat] :
~ ( ~ ( isPath_capacity @ SV104 @ SY597 @ SY598 @ SY599 )
| ~ ! [SY600: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV104 @ SY597 @ SY600 @ SY599 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY598 ) @ ( size_s1990949619at_nat @ SY600 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[576]) ).
thf(693,plain,
( ( isShor1936442771pacity
= ( ^ [SX0: product_prod_nat_nat > capacity,SX1: nat,SX2: list_P559422087at_nat,SX3: nat] :
~ ( ~ ( isPath_capacity @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ! [SX4: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SX0 @ SX1 @ SX4 @ SX3 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SX2 ) @ ( size_s1990949619at_nat @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[576]) ).
thf(694,plain,
! [SV105: nat,SV1: nat] :
( ( ! [SY601: nat] :
( ( ( plus_plus_nat @ SV1 @ SV105 )
= ( plus_plus_nat @ SV1 @ SY601 ) )
= ( SV105 = SY601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(695,plain,
! [SV106: nat,SV2: nat] :
( ( ! [SY602: nat] :
( ( ( plus_plus_nat @ SV2 @ SV106 )
= ( plus_plus_nat @ SY602 @ SV106 ) )
= ( SV2 = SY602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(696,plain,
! [SV107: nat,SV3: nat] :
( ( ! [SY603: nat] :
( ( plus_plus_nat @ SV3 @ ( plus_plus_nat @ SV107 @ SY603 ) )
= ( plus_plus_nat @ SV107 @ ( plus_plus_nat @ SV3 @ SY603 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(697,plain,
! [SV108: nat] :
( ( ( plus_plus_nat @ SV108 )
= ( ^ [SY604: nat] : ( plus_plus_nat @ SY604 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(698,plain,
! [SV109: nat,SV5: nat] :
( ( ! [SY605: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ SV5 @ SV109 ) @ SY605 )
= ( plus_plus_nat @ SV5 @ ( plus_plus_nat @ SV109 @ SY605 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(699,plain,
! [SV110: nat,SV6: nat] :
( ( ! [SY606: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ SV6 @ SV110 ) @ SY606 )
= ( plus_plus_nat @ SV6 @ ( plus_plus_nat @ SV110 @ SY606 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(700,plain,
! [SV7: nat] :
( ( ~ ( ( one_one_nat = SV7 )
| ( SV7 = one_one_nat ) )
| ~ ( ( one_one_nat != SV7 )
| ( SV7 != one_one_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[584]) ).
thf(701,plain,
! [SV7: nat] :
( ( ( one_one_nat = SV7 )
= ( SV7 = one_one_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[584]) ).
thf(702,plain,
! [SV111: nat,SV8: nat] :
( ( ! [SY607: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SY607 ) )
= ( ord_less_eq_nat @ SV111 @ SY607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(703,plain,
! [SV112: nat,SV9: nat] :
( ( ! [SY608: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SY608 @ SV112 ) )
= ( ord_less_eq_nat @ SV9 @ SY608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(704,plain,
! [SV113: product_prod_nat_nat > capacity] :
( ( ( min_dist_capacity @ SV113 )
= ( min_dist_capacity @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(705,plain,
! [SV114: nat,SV12: nat] :
( ( ! [SY609: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SY609 ) )
= ( ord_less_eq_nat @ SV114 @ SY609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(706,plain,
! [SV115: nat,SV13: nat] :
( ( ! [SY610: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SY610 @ SV115 ) )
= ( ord_less_nat @ SV13 @ SY610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(707,plain,
! [SV116: nat,SV14: nat] :
( ( ! [SY611: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SY611 ) )
= ( ord_less_nat @ SV116 @ SY611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(708,plain,
! [SV117: nat,SV15: nat] :
( ( ! [SY612: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SY612 ) )
= ( ord_less_nat @ SV117 @ SY612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(709,plain,
! [SV118: nat,SV16: nat] :
( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV16 @ SV118 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(710,plain,
! [SV119: nat,SV17: nat] :
( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV17 @ SV119 ) @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(711,plain,
! [SV120: nat,SV18: nat] :
( ( ord_less_eq_nat @ SV18 @ ( plus_plus_nat @ SV120 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(712,plain,
! [SV121: nat,SV19: nat] :
( ( ord_less_eq_nat @ SV19 @ ( plus_plus_nat @ SV19 @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(713,plain,
! [SV122: nat] :
( ( ( ord_less_nat @ SV122 )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(714,plain,
! [SV123: nat,SV22: nat] :
( ( ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
= ( SV22 = SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(715,plain,
! [SV124: nat,SV23: nat] :
( ( ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
= ( SV23 = SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(716,plain,
! [SV125: list_P559422087at_nat,SV24: nat] :
( ( ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
= ( SV125 = nil_Pr1308055047at_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(717,plain,
! [SV126: nat,SV25: nat] :
( ( ! [SY613: nat,SY614: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SV25 @ SV126 )
| ~ ( ord_less_nat @ SY613 @ SY614 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV25 @ SY613 ) @ ( plus_plus_nat @ SV126 @ SY614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(718,plain,
! [SV127: nat,SV26: nat] :
( ( ! [SY615: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV26 @ SV127 ) @ SY615 )
| ~ ( ~ ( ord_less_eq_nat @ SV26 @ SY615 )
| ~ ( ord_less_eq_nat @ SV127 @ SY615 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(719,plain,
! [SV128: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV128 )
= ( ^ [SY616: nat,SY617: nat,SY618: nat] :
~ ! [SY619: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SY616 @ SY619 @ SY618 )
| ( ( size_s1990949619at_nat @ SY619 )
!= SY617 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(720,plain,
! [SV129: nat,SV28: nat] :
( ( ! [SY620: nat] :
( ~ ( ord_less_nat @ SV28 @ SV129 )
| ( ord_less_nat @ ( plus_plus_nat @ SV28 @ SY620 ) @ ( plus_plus_nat @ SV129 @ SY620 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(721,plain,
! [SV130: nat,SV29: nat > nat] :
( ( ! [SY621: nat] :
( ~ ! [SY395: nat,SY396: nat] :
( ~ ( ord_less_nat @ SY395 @ SY396 )
| ( ord_less_nat @ ( SV29 @ SY395 ) @ ( SV29 @ SY396 ) ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ ( SV29 @ SV130 ) @ SY621 ) @ ( SV29 @ ( plus_plus_nat @ SV130 @ SY621 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(722,plain,
! [SV131: nat,SV30: nat] :
( ( ! [SY624: nat,SY625: nat] :
( ~ ( ord_less_eq_nat @ SV30 @ SV131 )
| ~ ( ord_less_nat @ SY624 @ SY625 )
| ( ord_less_nat @ ( plus_plus_nat @ SV30 @ SY624 ) @ ( plus_plus_nat @ SV131 @ SY625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(723,plain,
! [SV132: nat,SV31: nat] :
( ( ! [SY626: nat,SY627: nat] :
( ~ ( ord_less_nat @ SV31 @ SV132 )
| ~ ( ord_less_eq_nat @ SY626 @ SY627 )
| ( ord_less_nat @ ( plus_plus_nat @ SV31 @ SY626 ) @ ( plus_plus_nat @ SV132 @ SY627 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(724,plain,
! [SV133: list_P559422087at_nat,SV32: nat] :
( ( ! [SY628: nat] :
( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SY628 )
= ( ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SY628 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SY628 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(725,plain,
! [SV134: nat,SV33: nat] :
( ( ! [SY629: nat,SY630: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SV33 @ SV134 )
| ~ ( ord_less_nat @ SY629 @ SY630 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV33 @ SY629 ) @ ( plus_plus_nat @ SV134 @ SY630 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(726,plain,
! [SV135: nat,SV34: product_prod_nat_nat > capacity] :
( ( ! [SY631: nat,SY632: nat] :
( ~ ( dist_capacity @ SV34 @ SV135 @ SY631 @ SY632 )
| ( ord_less_eq_nat @ ( min_dist_capacity @ SV34 @ SV135 @ SY632 ) @ SY631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(727,plain,
! [SV136: nat,SV35: nat] :
( ( ! [SY633: nat] :
( ~ ( dist_capacity @ c @ SV35 @ SV136 @ SY633 )
| ~ ! [SY634: nat] :
( ~ ( dist_capacity @ c @ SV35 @ SY634 @ SY633 )
| ( ord_less_eq_nat @ SV136 @ SY634 ) )
| ( ( min_dist_capacity @ c @ SV35 @ SY633 )
= SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(728,plain,
! [SV137: nat,SV36: nat] :
( ( ! [SY635: nat,SY636: nat,SY637: nat] :
( ~ ( dist_capacity @ c @ SV36 @ SV137 @ SY635 )
| ~ ( dist_capacity @ c @ SY635 @ SY636 @ SY637 )
| ( ( min_dist_capacity @ c @ SV36 @ SY637 )
!= ( plus_plus_nat @ SV137 @ SY636 ) )
| ( ( min_dist_capacity @ c @ SY635 @ SY637 )
= SY636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(729,plain,
! [SV138: nat,SV37: nat] :
( ( ! [SY638: nat,SY639: nat] :
( ( SV37
!= ( plus_plus_nat @ SV138 @ SY638 ) )
| ( ( plus_plus_nat @ SY639 @ SV37 )
= ( plus_plus_nat @ SV138 @ ( plus_plus_nat @ SY639 @ SY638 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(730,plain,
! [SV139: nat,SV38: nat] :
( ( ! [SY640: nat,SY641: nat] :
( ~ ~ ( ( SV38 != SV139 )
| ~ ( ord_less_nat @ SY640 @ SY641 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV38 @ SY640 ) @ ( plus_plus_nat @ SV139 @ SY641 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(731,plain,
! [SV140: list_P559422087at_nat,SV39: nat] :
( ( ! [SY642: nat] :
( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SY642 )
= ( ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SY642 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SY642 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(732,plain,
! [SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ! [SY643: nat,SY644: nat,SY645: nat] :
( ~ ( connected_capacity @ SV40 @ SV141 @ SY643 )
| ( ( min_dist_capacity @ SV40 @ SV141 @ SY643 )
!= SY644 )
| ~ ( ord_less_nat @ SY645 @ SY644 )
| ~ ! [SY646: nat] :
~ ~ ( ~ ( connected_capacity @ SV40 @ SV141 @ SY646 )
| ( ( min_dist_capacity @ SV40 @ SV141 @ SY646 )
!= SY645 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(733,plain,
! [SV142: nat,SV41: product_prod_nat_nat > capacity] :
( ( ! [SY647: nat,SY648: nat,SY649: nat,SY650: nat] :
( ~ ( dist_capacity @ SV41 @ SV142 @ SY647 @ SY648 )
| ~ ( dist_capacity @ SV41 @ SY648 @ SY649 @ SY650 )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SY650 )
!= ( plus_plus_nat @ SY647 @ SY649 ) )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SY648 )
= SY647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(734,plain,
! [SV143: nat,SV42: nat] :
( ( ! [SY651: nat] :
( ( ( plus_plus_nat @ SV42 @ SV143 )
!= ( plus_plus_nat @ SY651 @ SV143 ) )
| ( SV42 = SY651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(735,plain,
! [SV144: nat,SV43: product_prod_nat_nat > capacity] :
( ( ! [SY652: nat,SY653: nat,SY654: nat,SY655: nat] :
( ~ ( dist_capacity @ SV43 @ SV144 @ SY652 @ SY653 )
| ~ ( dist_capacity @ SV43 @ SY653 @ SY654 @ SY655 )
| ( dist_capacity @ SV43 @ SV144 @ ( plus_plus_nat @ SY652 @ SY654 ) @ SY655 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(736,plain,
! [SV145: nat,SV44: nat] :
( ( ! [SY656: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV145 ) @ ( plus_plus_nat @ SV44 @ SY656 ) )
| ( ord_less_eq_nat @ SV145 @ SY656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(737,plain,
! [SV146: nat,SV45: nat] :
( ( ! [SY657: nat] :
( ~ ( ord_less_eq_nat @ SV45 @ SV146 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV45 @ SY657 ) @ ( plus_plus_nat @ SV146 @ SY657 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(738,plain,
! [SV147: nat,SV46: nat] :
( ( ! [SY658: nat] :
( ( ( plus_plus_nat @ SV46 @ SV147 )
!= ( plus_plus_nat @ SV46 @ SY658 ) )
| ( SV147 = SY658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(739,plain,
! [SV148: nat,SV47: nat] :
( ( ! [SY659: nat] :
( ~ ( dist_capacity @ c @ SV47 @ SV148 @ SY659 )
| ( ord_less_eq_nat @ ( min_dist_capacity @ c @ SV47 @ SY659 ) @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(740,plain,
! [SV149: nat,SV48: nat] :
( ( ! [SY660: nat] :
( ~ ( ord_less_nat @ SV48 @ SV149 )
| ( ord_less_nat @ ( plus_plus_nat @ SV48 @ SY660 ) @ ( plus_plus_nat @ SV149 @ SY660 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(741,plain,
! [SV150: nat,SV49: nat] :
( ( ! [SY661: nat] :
( ~ ( dist_capacity @ c @ SV49 @ SV150 @ SY661 )
| ( connected_capacity @ c @ SV49 @ SY661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(742,plain,
! [SV151: nat,SV50: product_prod_nat_nat > capacity] :
( ( ! [SY662: nat] :
( ~ ( connected_capacity @ SV50 @ SV151 @ SY662 )
| ( dist_capacity @ SV50 @ SV151 @ ( min_dist_capacity @ SV50 @ SV151 @ SY662 ) @ SY662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(743,plain,
! [SV152: nat,SV51: nat] :
( ( ~ ( connected_capacity @ c @ SV51 @ SV152 )
| ( dist_capacity @ c @ SV51 @ ( min_dist_capacity @ c @ SV51 @ SV152 ) @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(744,plain,
! [SV153: nat,SV52: nat] :
( ( ! [SY663: nat] :
( ~ ( connected_capacity @ c @ SV52 @ SV153 )
| ~ ( ord_less_eq_nat @ SY663 @ ( min_dist_capacity @ c @ SV52 @ SV153 ) )
| ~ ! [SY460: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV52 @ SY460 )
| ( ( min_dist_capacity @ c @ SV52 @ SY460 )
!= SY663 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(745,plain,
! [SV154: nat,SV53: nat] :
( ( ! [SY665: nat] :
( ~ ( ord_less_nat @ SV53 @ SV154 )
| ( ord_less_nat @ ( plus_plus_nat @ SY665 @ SV53 ) @ ( plus_plus_nat @ SY665 @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(746,plain,
! [SV155: nat] :
( ( ( ord_less_eq_nat @ SV155 )
= ( ^ [SY666: nat] :
~ ! [SY667: nat] :
( SY666
!= ( plus_plus_nat @ SV155 @ SY667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(747,plain,
! [SV156: nat,SV55: product_prod_nat_nat > capacity] :
( ( ! [SY668: nat,SY669: nat,SY670: nat,SY671: nat] :
( ~ ( dist_capacity @ SV55 @ SV156 @ SY668 @ SY669 )
| ~ ( dist_capacity @ SV55 @ SY669 @ SY670 @ SY671 )
| ( ( min_dist_capacity @ SV55 @ SV156 @ SY671 )
!= ( plus_plus_nat @ SY668 @ SY670 ) )
| ( ( min_dist_capacity @ SV55 @ SY669 @ SY671 )
= SY670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(748,plain,
! [SV157: nat,SV56: nat] :
( ( ! [SY672: nat,SY673: nat] :
( ( SV56
!= ( plus_plus_nat @ SV157 @ SY672 ) )
| ( ( plus_plus_nat @ SV56 @ SY673 )
= ( plus_plus_nat @ SV157 @ ( plus_plus_nat @ SY672 @ SY673 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(749,plain,
! [SV158: nat,SV57: nat] :
( ( ! [SY674: nat > $o] :
( ~ ( connected_capacity @ c @ SV57 @ SV158 )
| ~ ! [SY675: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY675 @ SV158 )
| ~ ! [SY676: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY676 @ SV158 )
| ( ord_less_eq_nat @ SY675 @ SY676 ) )
| ( SY674 @ SY675 ) )
| ( SY674 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(750,plain,
! [SV159: list_P559422087at_nat,SV58: nat] :
( ( ! [SY677: nat] :
( ~ ( isShor1936442771pacity @ c @ SV58 @ SV159 @ SY677 )
| ( isSimp1359852763pacity @ c @ SV58 @ SV159 @ SY677 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(751,plain,
! [SV160: list_P559422087at_nat,SV59: list_P559422087at_nat] :
( ( ~ ( ( ( size_s1990949619at_nat @ SV59 )
!= ( size_s1990949619at_nat @ SV160 ) ) )
| ( SV59 != SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(752,plain,
! [SV161: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV161 )
= ( ^ [SY678: nat,SY679: list_P559422087at_nat,SY680: nat] :
~ ( ~ ( isSimp1359852763pacity @ SV161 @ SY678 @ SY679 @ SY680 )
| ( ( size_s1990949619at_nat @ SY679 )
!= ( min_dist_capacity @ SV161 @ SY678 @ SY680 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(753,plain,
! [SV162: nat,SV61: nat] :
( ( ! [SY681: nat,SY682: nat] :
( ~ ( ord_less_eq_nat @ SV61 @ SV162 )
| ~ ( ord_less_eq_nat @ SY681 @ SY682 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV61 @ SY681 ) @ ( plus_plus_nat @ SV162 @ SY682 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(754,plain,
! [SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ! [SY683: nat,SY684: nat > $o] :
( ~ ( connected_capacity @ SV62 @ SV163 @ SY683 )
| ~ ! [SY685: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY685 @ SY683 )
| ~ ! [SY686: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY686 @ SY683 )
| ( ord_less_eq_nat @ SY685 @ SY686 ) )
| ( SY684 @ SY685 ) )
| ( SY684 @ ( min_dist_capacity @ SV62 @ SV163 @ SY683 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(755,plain,
! [SV164: nat,SV63: nat] :
( ( ~ ( ord_less_nat @ SV63 @ SV164 )
| ( ord_less_nat @ ( plus_plus_nat @ SV63 @ one_one_nat ) @ ( plus_plus_nat @ SV164 @ one_one_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(756,plain,
! [SV165: list_P559422087at_nat,SV64: nat] :
( ( ! [SY687: nat] :
( ~ ( isShor1936442771pacity @ c @ SV64 @ SV165 @ SY687 )
| ( isPath_capacity @ c @ SV64 @ SV165 @ SY687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(757,plain,
! [SV166: nat,SV65: nat] :
( ( ~ ( ord_less_eq_nat @ SV65 @ SV166 )
| ~ ! [SY688: nat] :
( SV166
!= ( plus_plus_nat @ SV65 @ SY688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(758,plain,
! [SV167: nat,SV66: nat] :
( ( ! [SY689: nat,SY690: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SV66 @ SV167 )
| ( SY689 != SY690 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV66 @ SY689 ) @ ( plus_plus_nat @ SV167 @ SY690 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(759,plain,
! [SV168: nat,SV67: nat] :
( ( ! [SY691: nat] :
( ~ ( ord_less_eq_nat @ SV67 @ SV168 )
| ( ord_less_eq_nat @ SV67 @ ( plus_plus_nat @ SV168 @ SY691 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(760,plain,
! [SV169: nat,SV68: nat] :
( ( ! [SY692: nat] :
( ~ ( ord_less_eq_nat @ SV68 @ SV169 )
| ( ord_less_eq_nat @ SV68 @ ( plus_plus_nat @ SY692 @ SV169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(761,plain,
( ( ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
= $false )
| ( ( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(762,plain,
! [SV170: nat,SV69: nat] :
( ( ! [SY693: nat,SY694: nat] :
( ~ ( ord_less_nat @ SV69 @ SV170 )
| ~ ( ord_less_nat @ SY693 @ SY694 )
| ( ord_less_nat @ ( plus_plus_nat @ SV69 @ SY693 ) @ ( plus_plus_nat @ SV170 @ SY694 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(763,plain,
! [SV171: nat,SV70: nat] :
( ( ! [SY695: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SV70 @ SV171 ) @ SY695 )
| ( ord_less_nat @ SV70 @ SY695 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(764,plain,
! [SV172: nat,SV71: nat] :
( ( ! [SY696: nat,SY697: nat] :
( ~ ( ord_less_nat @ SV71 @ SV172 )
| ~ ( ord_less_nat @ SY696 @ SY697 )
| ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SY696 ) @ ( plus_plus_nat @ SV172 @ SY697 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(765,plain,
! [SV173: list_P559422087at_nat,SV72: nat] :
( ( ! [SY698: nat] :
( ~ ( isPath_capacity @ c @ SV72 @ SV173 @ SY698 )
| ~ ! [SY513: list_P559422087at_nat] :
~ ( isSimp1359852763pacity @ c @ SV72 @ SY513 @ SY698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(766,plain,
! [SV174: nat,SV73: nat] :
( ( ! [SY700: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SV73 @ SV174 ) @ ( plus_plus_nat @ SV73 @ SY700 ) )
| ( ord_less_nat @ SV174 @ SY700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(767,plain,
! [SV175: nat,SV74: nat] :
( ( ! [SY701: nat,SY702: nat,SY703: nat] :
( ~ ( dist_capacity @ c @ SV74 @ SV175 @ SY701 )
| ~ ( dist_capacity @ c @ SY701 @ SY702 @ SY703 )
| ( ( min_dist_capacity @ c @ SV74 @ SY703 )
!= ( plus_plus_nat @ SV175 @ SY702 ) )
| ( ( min_dist_capacity @ c @ SV74 @ SY701 )
= SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(768,plain,
! [SV176: nat,SV75: nat] :
( ( ! [SY704: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV75 @ SV176 ) @ SY704 )
| ( ord_less_eq_nat @ SV75 @ SY704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(769,plain,
! [SV177: nat,SV76: nat] :
( ( ! [SY705: nat] :
( ~ ( ord_less_nat @ SV76 @ SV177 )
| ( ord_less_nat @ SV76 @ ( plus_plus_nat @ SV177 @ SY705 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(770,plain,
! [SV178: list_P559422087at_nat,SV77: nat] :
( ( ! [SY706: nat] :
( ~ ( isPath_capacity @ c @ SV77 @ SV178 @ SY706 )
| ( dist_capacity @ c @ SV77 @ ( size_s1990949619at_nat @ SV178 ) @ SY706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(771,plain,
! [SV179: list_P559422087at_nat,SV78: nat] :
( ( ! [SY707: nat] :
( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SY707 )
= ( ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SY707 )
| ~ ! [SY708: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY708 @ SY707 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY708 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(772,plain,
! [SV180: nat,SV79: nat] :
( ( ( connected_capacity @ c @ SV79 @ SV180 )
= ( ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(773,plain,
! [SV181: nat,SV80: product_prod_nat_nat > capacity] :
( ( ! [SY710: list_P559422087at_nat,SY711: nat] :
( ~ ( isPath_capacity @ SV80 @ SV181 @ SY710 @ SY711 )
| ( dist_capacity @ SV80 @ SV181 @ ( size_s1990949619at_nat @ SY710 ) @ SY711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(774,plain,
! [SV182: nat] :
( ( ( ord_less_eq_nat @ SV182 )
= ( ^ [SY712: nat] :
~ ! [SY713: nat] :
( SY712
!= ( plus_plus_nat @ SV182 @ SY713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(775,plain,
! [SV183: nat,SV82: nat] :
( ( ! [SY714: nat,SY715: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SV82 @ SV183 )
| ~ ( ord_less_eq_nat @ SY714 @ SY715 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV82 @ SY714 ) @ ( plus_plus_nat @ SV183 @ SY715 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(776,plain,
! [SV184: nat,SV83: nat] :
( ( ! [SY716: nat,SY717: nat] :
( ~ ( connected_capacity @ c @ SV83 @ SV184 )
| ( ( min_dist_capacity @ c @ SV83 @ SV184 )
!= SY716 )
| ~ ( ord_less_nat @ SY717 @ SY716 )
| ~ ! [SY542: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV83 @ SY542 )
| ( ( min_dist_capacity @ c @ SV83 @ SY542 )
!= SY717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(777,plain,
! [SV185: nat,SV84: nat] :
( ( ! [SY719: nat,SY720: nat,SY721: nat] :
( ~ ( dist_capacity @ c @ SV84 @ SV185 @ SY719 )
| ~ ( dist_capacity @ c @ SY719 @ SY720 @ SY721 )
| ( dist_capacity @ c @ SV84 @ ( plus_plus_nat @ SV185 @ SY720 ) @ SY721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(778,plain,
! [SV186: nat,SV85: nat] :
( ( ~ ( connected_capacity @ c @ SV85 @ SV186 )
| ~ ! [SY722: list_P559422087at_nat] :
~ ( isShor1936442771pacity @ c @ SV85 @ SY722 @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(779,plain,
! [SV187: nat,SV86: nat] :
( ( ! [SY723: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV86 @ SV187 ) @ SY723 )
| ( ord_less_eq_nat @ SV187 @ SY723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(780,plain,
! [SV188: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV188 )
= ( ^ [SY724: nat,SY725: list_P559422087at_nat,SY726: nat] :
~ ( ~ ( isPath_capacity @ SV188 @ SY724 @ SY725 @ SY726 )
| ( ( size_s1990949619at_nat @ SY725 )
!= ( min_dist_capacity @ SV188 @ SY724 @ SY726 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(781,plain,
! [SV189: nat,SV88: nat] :
( ( ! [SY727: nat] :
( ~ ( ord_less_nat @ SV88 @ SV189 )
| ( ord_less_nat @ SV88 @ ( plus_plus_nat @ SY727 @ SV189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(782,plain,
! [SV190: nat,SV89: nat] :
( ( ! [SY728: nat,SY729: nat] :
( ~ ( ord_less_eq_nat @ SV89 @ SV190 )
| ~ ( ord_less_eq_nat @ SY728 @ SY729 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV89 @ SY728 ) @ ( plus_plus_nat @ SV190 @ SY729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(783,plain,
! [SV191: nat,SV90: nat] :
( ( ! [SY730: nat] :
( ~ ( ord_less_eq_nat @ SV90 @ SV191 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SY730 @ SV90 ) @ ( plus_plus_nat @ SY730 @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(784,plain,
! [SV192: nat,SV91: nat] :
( ( ! [SY731: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SV91 @ SV192 ) @ ( plus_plus_nat @ SY731 @ SV192 ) )
| ( ord_less_nat @ SV91 @ SY731 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(785,plain,
! [SV193: nat,SV92: nat] :
( ( ( connected_capacity @ c @ SV92 @ SV193 )
= ( ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(786,plain,
! [SV194: nat,SV93: nat] :
( ( ! [SY733: nat] :
( ~ ( ord_less_eq_nat @ SV93 @ SV194 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV93 @ SY733 ) @ ( plus_plus_nat @ SV194 @ SY733 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(787,plain,
! [SV195: nat,SV94: nat] :
( ( ! [SY734: nat] :
( ( dist_capacity @ c @ SV94 @ SV195 @ SY734 )
= ( ~ ! [SY735: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY735 @ SY734 )
| ( ( size_s1990949619at_nat @ SY735 )
!= SV195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(788,plain,
! [SV196: nat,SV95: nat] :
( ( ! [SY736: nat,SY737: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SV95 @ SV196 )
| ~ ( ord_less_eq_nat @ SY736 @ SY737 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV95 @ SY736 ) @ ( plus_plus_nat @ SV196 @ SY737 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(789,plain,
! [SV197: nat,SV96: nat] :
( ( ~ ( ord_less_eq_nat @ SV96 @ SV197 )
| ~ ! [SY738: nat] :
( SV197
!= ( plus_plus_nat @ SV96 @ SY738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(790,plain,
( ( ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
= $false )
| ( ( ( min_dist_capacity @ c @ s @ u )
= ( size_s1990949619at_nat @ p1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(791,plain,
! [SV198: nat,SV97: nat] :
( ( ! [SY739: nat,SY740: nat] :
( ~ ~ ( ( SV97 != SV198 )
| ( SY739 != SY740 ) )
| ( ( plus_plus_nat @ SV97 @ SY739 )
= ( plus_plus_nat @ SV198 @ SY740 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(792,plain,
! [SV199: nat,SV98: nat] :
( ( ! [SY741: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV98 @ SV199 ) @ ( plus_plus_nat @ SY741 @ SV199 ) )
| ( ord_less_eq_nat @ SV98 @ SY741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(793,plain,
! [SV200: nat,SV99: nat] :
( ( ! [SY742: nat,SY743: nat] :
( ~ ~ ( ( SV99 != SV200 )
| ~ ( ord_less_eq_nat @ SY742 @ SY743 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV99 @ SY742 ) @ ( plus_plus_nat @ SV200 @ SY743 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(794,plain,
! [SV201: nat,SV100: product_prod_nat_nat > capacity] :
( ( ! [SY744: nat,SY745: nat] :
( ~ ( connected_capacity @ SV100 @ SV201 @ SY744 )
| ~ ( ord_less_eq_nat @ SY745 @ ( min_dist_capacity @ SV100 @ SV201 @ SY744 ) )
| ~ ! [SY746: nat] :
~ ~ ( ~ ( connected_capacity @ SV100 @ SV201 @ SY746 )
| ( ( min_dist_capacity @ SV100 @ SV201 @ SY746 )
!= SY745 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(795,plain,
! [SV202: nat,SV101: nat] :
( ( ! [SY747: nat,SY748: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SV101 @ SV202 )
| ( SY747 != SY748 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV101 @ SY747 ) @ ( plus_plus_nat @ SV202 @ SY748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(796,plain,
! [SV203: nat,SV102: product_prod_nat_nat > capacity] :
( ( ! [SY749: nat,SY750: nat] :
( ~ ( dist_capacity @ SV102 @ SV203 @ SY749 @ SY750 )
| ~ ! [SY751: nat] :
( ~ ( dist_capacity @ SV102 @ SV203 @ SY751 @ SY750 )
| ( ord_less_eq_nat @ SY749 @ SY751 ) )
| ( ( min_dist_capacity @ SV102 @ SV203 @ SY750 )
= SY749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(797,plain,
! [SV204: nat,SV103: nat] :
( ( ! [SY752: nat,SY753: nat] :
( ~ ( ord_less_nat @ SV103 @ SV204 )
| ( ( plus_plus_nat @ SY752 @ SV204 )
!= ( plus_plus_nat @ SV103 @ SY753 ) )
| ( ord_less_nat @ SY752 @ SY753 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(798,plain,
! [SV205: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV205 )
= ( ^ [SY754: nat,SY755: list_P559422087at_nat,SY756: nat] :
~ ( ~ ( isPath_capacity @ SV205 @ SY754 @ SY755 @ SY756 )
| ~ ! [SY757: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SY754 @ SY757 @ SY756 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY755 ) @ ( size_s1990949619at_nat @ SY757 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(799,plain,
! [SV206: nat,SV105: nat,SV1: nat] :
( ( ( ( plus_plus_nat @ SV1 @ SV105 )
= ( plus_plus_nat @ SV1 @ SV206 ) )
= ( SV105 = SV206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(800,plain,
! [SV207: nat,SV106: nat,SV2: nat] :
( ( ( ( plus_plus_nat @ SV2 @ SV106 )
= ( plus_plus_nat @ SV207 @ SV106 ) )
= ( SV2 = SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(801,plain,
! [SV208: nat,SV107: nat,SV3: nat] :
( ( ( plus_plus_nat @ SV3 @ ( plus_plus_nat @ SV107 @ SV208 ) )
= ( plus_plus_nat @ SV107 @ ( plus_plus_nat @ SV3 @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(802,plain,
! [SV108: nat] :
( ( ! [SV209: nat] :
( ( plus_plus_nat @ SV108 @ SV209 )
= ( plus_plus_nat @ SV209 @ SV108 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[697]) ).
thf(803,plain,
! [SV108: nat] :
( ( ( plus_plus_nat @ SV108 )
= ( ^ [SY604: nat] : ( plus_plus_nat @ SY604 @ SV108 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[697]) ).
thf(804,plain,
! [SV210: nat,SV109: nat,SV5: nat] :
( ( ( plus_plus_nat @ ( plus_plus_nat @ SV5 @ SV109 ) @ SV210 )
= ( plus_plus_nat @ SV5 @ ( plus_plus_nat @ SV109 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(805,plain,
! [SV211: nat,SV110: nat,SV6: nat] :
( ( ( plus_plus_nat @ ( plus_plus_nat @ SV6 @ SV110 ) @ SV211 )
= ( plus_plus_nat @ SV6 @ ( plus_plus_nat @ SV110 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(806,plain,
! [SV7: nat] :
( ( ( ~ ( ( one_one_nat = SV7 )
| ( SV7 = one_one_nat ) ) )
= $true )
| ( ( ~ ( ( one_one_nat != SV7 )
| ( SV7 != one_one_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[700]) ).
thf(807,plain,
! [SV212: nat,SV111: nat,SV8: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
= ( ord_less_eq_nat @ SV111 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(808,plain,
! [SV213: nat,SV112: nat,SV9: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
= ( ord_less_eq_nat @ SV9 @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(809,plain,
! [SV113: product_prod_nat_nat > capacity] :
( ( ! [SV214: nat] :
( ( min_dist_capacity @ SV113 @ SV214 )
= ( min_dist_capacity @ SV113 @ SV214 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[704]) ).
thf(810,plain,
! [SV113: product_prod_nat_nat > capacity] :
( ( ( min_dist_capacity @ SV113 )
= ( min_dist_capacity @ SV113 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[704]) ).
thf(811,plain,
! [SV215: nat,SV114: nat,SV12: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
= ( ord_less_eq_nat @ SV114 @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(812,plain,
! [SV216: nat,SV115: nat,SV13: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
= ( ord_less_nat @ SV13 @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(813,plain,
! [SV217: nat,SV116: nat,SV14: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
= ( ord_less_nat @ SV116 @ SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(814,plain,
! [SV218: nat,SV117: nat,SV15: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
= ( ord_less_nat @ SV117 @ SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(815,plain,
! [SV118: nat,SV16: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV16 @ SV118 ) @ SV16 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(816,plain,
! [SV119: nat,SV17: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV17 @ SV119 ) @ SV119 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(817,plain,
! [SV122: nat] :
( ( ! [SV219: nat] :
( ( ord_less_nat @ SV122 @ SV219 )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV219 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[713]) ).
thf(818,plain,
! [SV122: nat] :
( ( ( ord_less_nat @ SV122 )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[713]) ).
thf(819,plain,
! [SV123: nat,SV22: nat] :
( ( ~ ( ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
| ( SV22 = SV123 ) )
| ~ ( ~ ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
| ( SV22 != SV123 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[714]) ).
thf(820,plain,
! [SV123: nat,SV22: nat] :
( ( ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
= ( SV22 = SV123 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[714]) ).
thf(821,plain,
! [SV124: nat,SV23: nat] :
( ( ~ ( ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
| ( SV23 = SV124 ) )
| ~ ( ~ ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
| ( SV23 != SV124 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[715]) ).
thf(822,plain,
! [SV124: nat,SV23: nat] :
( ( ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
= ( SV23 = SV124 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[715]) ).
thf(823,plain,
! [SV125: list_P559422087at_nat,SV24: nat] :
( ( ~ ( ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
| ( SV125 = nil_Pr1308055047at_nat ) )
| ~ ( ~ ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
| ( SV125 != nil_Pr1308055047at_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[716]) ).
thf(824,plain,
! [SV125: list_P559422087at_nat,SV24: nat] :
( ( ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
= ( SV125 = nil_Pr1308055047at_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[716]) ).
thf(825,plain,
! [SV220: nat,SV126: nat,SV25: nat] :
( ( ! [SY758: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SV25 @ SV126 )
| ~ ( ord_less_nat @ SV220 @ SY758 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV25 @ SV220 ) @ ( plus_plus_nat @ SV126 @ SY758 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(826,plain,
! [SV221: nat,SV127: nat,SV26: nat] :
( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV26 @ SV127 ) @ SV221 )
| ~ ( ~ ( ord_less_eq_nat @ SV26 @ SV221 )
| ~ ( ord_less_eq_nat @ SV127 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(827,plain,
! [SV128: product_prod_nat_nat > capacity] :
( ( ! [SV222: nat] :
( ( dist_capacity @ SV128 @ SV222 )
= ( ^ [SY759: nat,SY760: nat] :
~ ! [SY761: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV222 @ SY761 @ SY760 )
| ( ( size_s1990949619at_nat @ SY761 )
!= SY759 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[719]) ).
thf(828,plain,
! [SV128: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV128 )
= ( ^ [SY616: nat,SY617: nat,SY618: nat] :
~ ! [SY619: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SY616 @ SY619 @ SY618 )
| ( ( size_s1990949619at_nat @ SY619 )
!= SY617 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[719]) ).
thf(829,plain,
! [SV223: nat,SV129: nat,SV28: nat] :
( ( ~ ( ord_less_nat @ SV28 @ SV129 )
| ( ord_less_nat @ ( plus_plus_nat @ SV28 @ SV223 ) @ ( plus_plus_nat @ SV129 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(830,plain,
! [SV224: nat,SV130: nat,SV29: nat > nat] :
( ( ~ ! [SY395: nat,SY396: nat] :
( ~ ( ord_less_nat @ SY395 @ SY396 )
| ( ord_less_nat @ ( SV29 @ SY395 ) @ ( SV29 @ SY396 ) ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ ( SV29 @ SV130 ) @ SV224 ) @ ( SV29 @ ( plus_plus_nat @ SV130 @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(831,plain,
! [SV225: nat,SV131: nat,SV30: nat] :
( ( ! [SY764: nat] :
( ~ ( ord_less_eq_nat @ SV30 @ SV131 )
| ~ ( ord_less_nat @ SV225 @ SY764 )
| ( ord_less_nat @ ( plus_plus_nat @ SV30 @ SV225 ) @ ( plus_plus_nat @ SV131 @ SY764 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(832,plain,
! [SV226: nat,SV132: nat,SV31: nat] :
( ( ! [SY765: nat] :
( ~ ( ord_less_nat @ SV31 @ SV132 )
| ~ ( ord_less_eq_nat @ SV226 @ SY765 )
| ( ord_less_nat @ ( plus_plus_nat @ SV31 @ SV226 ) @ ( plus_plus_nat @ SV132 @ SY765 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(833,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
= ( ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(834,plain,
! [SV228: nat,SV134: nat,SV33: nat] :
( ( ! [SY766: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SV33 @ SV134 )
| ~ ( ord_less_nat @ SV228 @ SY766 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV33 @ SV228 ) @ ( plus_plus_nat @ SV134 @ SY766 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(835,plain,
! [SV229: nat,SV135: nat,SV34: product_prod_nat_nat > capacity] :
( ( ! [SY767: nat] :
( ~ ( dist_capacity @ SV34 @ SV135 @ SV229 @ SY767 )
| ( ord_less_eq_nat @ ( min_dist_capacity @ SV34 @ SV135 @ SY767 ) @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(836,plain,
! [SV230: nat,SV136: nat,SV35: nat] :
( ( ~ ( dist_capacity @ c @ SV35 @ SV136 @ SV230 )
| ~ ! [SY768: nat] :
( ~ ( dist_capacity @ c @ SV35 @ SY768 @ SV230 )
| ( ord_less_eq_nat @ SV136 @ SY768 ) )
| ( ( min_dist_capacity @ c @ SV35 @ SV230 )
= SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(837,plain,
! [SV231: nat,SV137: nat,SV36: nat] :
( ( ! [SY769: nat,SY770: nat] :
( ~ ( dist_capacity @ c @ SV36 @ SV137 @ SV231 )
| ~ ( dist_capacity @ c @ SV231 @ SY769 @ SY770 )
| ( ( min_dist_capacity @ c @ SV36 @ SY770 )
!= ( plus_plus_nat @ SV137 @ SY769 ) )
| ( ( min_dist_capacity @ c @ SV231 @ SY770 )
= SY769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(838,plain,
! [SV232: nat,SV138: nat,SV37: nat] :
( ( ! [SY771: nat] :
( ( SV37
!= ( plus_plus_nat @ SV138 @ SV232 ) )
| ( ( plus_plus_nat @ SY771 @ SV37 )
= ( plus_plus_nat @ SV138 @ ( plus_plus_nat @ SY771 @ SV232 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(839,plain,
! [SV233: nat,SV139: nat,SV38: nat] :
( ( ! [SY772: nat] :
( ~ ~ ( ( SV38 != SV139 )
| ~ ( ord_less_nat @ SV233 @ SY772 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV38 @ SV233 ) @ ( plus_plus_nat @ SV139 @ SY772 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(840,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
= ( ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(841,plain,
! [SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ! [SY773: nat,SY774: nat] :
( ~ ( connected_capacity @ SV40 @ SV141 @ SV235 )
| ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
!= SY773 )
| ~ ( ord_less_nat @ SY774 @ SY773 )
| ~ ! [SY646: nat] :
~ ~ ( ~ ( connected_capacity @ SV40 @ SV141 @ SY646 )
| ( ( min_dist_capacity @ SV40 @ SV141 @ SY646 )
!= SY774 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(842,plain,
! [SV236: nat,SV142: nat,SV41: product_prod_nat_nat > capacity] :
( ( ! [SY776: nat,SY777: nat,SY778: nat] :
( ~ ( dist_capacity @ SV41 @ SV142 @ SV236 @ SY776 )
| ~ ( dist_capacity @ SV41 @ SY776 @ SY777 @ SY778 )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SY778 )
!= ( plus_plus_nat @ SV236 @ SY777 ) )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SY776 )
= SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(843,plain,
! [SV237: nat,SV143: nat,SV42: nat] :
( ( ( ( plus_plus_nat @ SV42 @ SV143 )
!= ( plus_plus_nat @ SV237 @ SV143 ) )
| ( SV42 = SV237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(844,plain,
! [SV238: nat,SV144: nat,SV43: product_prod_nat_nat > capacity] :
( ( ! [SY779: nat,SY780: nat,SY781: nat] :
( ~ ( dist_capacity @ SV43 @ SV144 @ SV238 @ SY779 )
| ~ ( dist_capacity @ SV43 @ SY779 @ SY780 @ SY781 )
| ( dist_capacity @ SV43 @ SV144 @ ( plus_plus_nat @ SV238 @ SY780 ) @ SY781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(845,plain,
! [SV239: nat,SV145: nat,SV44: nat] :
( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV145 ) @ ( plus_plus_nat @ SV44 @ SV239 ) )
| ( ord_less_eq_nat @ SV145 @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(846,plain,
! [SV240: nat,SV146: nat,SV45: nat] :
( ( ~ ( ord_less_eq_nat @ SV45 @ SV146 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV45 @ SV240 ) @ ( plus_plus_nat @ SV146 @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(847,plain,
! [SV241: nat,SV147: nat,SV46: nat] :
( ( ( ( plus_plus_nat @ SV46 @ SV147 )
!= ( plus_plus_nat @ SV46 @ SV241 ) )
| ( SV147 = SV241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(848,plain,
! [SV242: nat,SV148: nat,SV47: nat] :
( ( ~ ( dist_capacity @ c @ SV47 @ SV148 @ SV242 )
| ( ord_less_eq_nat @ ( min_dist_capacity @ c @ SV47 @ SV242 ) @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(849,plain,
! [SV243: nat,SV149: nat,SV48: nat] :
( ( ~ ( ord_less_nat @ SV48 @ SV149 )
| ( ord_less_nat @ ( plus_plus_nat @ SV48 @ SV243 ) @ ( plus_plus_nat @ SV149 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(850,plain,
! [SV244: nat,SV150: nat,SV49: nat] :
( ( ~ ( dist_capacity @ c @ SV49 @ SV150 @ SV244 )
| ( connected_capacity @ c @ SV49 @ SV244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(851,plain,
! [SV245: nat,SV151: nat,SV50: product_prod_nat_nat > capacity] :
( ( ~ ( connected_capacity @ SV50 @ SV151 @ SV245 )
| ( dist_capacity @ SV50 @ SV151 @ ( min_dist_capacity @ SV50 @ SV151 @ SV245 ) @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(852,plain,
! [SV152: nat,SV51: nat] :
( ( ( ~ ( connected_capacity @ c @ SV51 @ SV152 ) )
= $true )
| ( ( dist_capacity @ c @ SV51 @ ( min_dist_capacity @ c @ SV51 @ SV152 ) @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(853,plain,
! [SV246: nat,SV153: nat,SV52: nat] :
( ( ~ ( connected_capacity @ c @ SV52 @ SV153 )
| ~ ( ord_less_eq_nat @ SV246 @ ( min_dist_capacity @ c @ SV52 @ SV153 ) )
| ~ ! [SY782: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV52 @ SY782 )
| ( ( min_dist_capacity @ c @ SV52 @ SY782 )
!= SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(854,plain,
! [SV247: nat,SV154: nat,SV53: nat] :
( ( ~ ( ord_less_nat @ SV53 @ SV154 )
| ( ord_less_nat @ ( plus_plus_nat @ SV247 @ SV53 ) @ ( plus_plus_nat @ SV247 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(855,plain,
! [SV155: nat] :
( ( ! [SV248: nat] :
( ( ord_less_eq_nat @ SV155 @ SV248 )
= ( ~ ! [SY783: nat] :
( SV248
!= ( plus_plus_nat @ SV155 @ SY783 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[746]) ).
thf(856,plain,
! [SV155: nat] :
( ( ( ord_less_eq_nat @ SV155 )
= ( ^ [SY666: nat] :
~ ! [SY667: nat] :
( SY666
!= ( plus_plus_nat @ SV155 @ SY667 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[746]) ).
thf(857,plain,
! [SV249: nat,SV156: nat,SV55: product_prod_nat_nat > capacity] :
( ( ! [SY784: nat,SY785: nat,SY786: nat] :
( ~ ( dist_capacity @ SV55 @ SV156 @ SV249 @ SY784 )
| ~ ( dist_capacity @ SV55 @ SY784 @ SY785 @ SY786 )
| ( ( min_dist_capacity @ SV55 @ SV156 @ SY786 )
!= ( plus_plus_nat @ SV249 @ SY785 ) )
| ( ( min_dist_capacity @ SV55 @ SY784 @ SY786 )
= SY785 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(858,plain,
! [SV250: nat,SV157: nat,SV56: nat] :
( ( ! [SY787: nat] :
( ( SV56
!= ( plus_plus_nat @ SV157 @ SV250 ) )
| ( ( plus_plus_nat @ SV56 @ SY787 )
= ( plus_plus_nat @ SV157 @ ( plus_plus_nat @ SV250 @ SY787 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(859,plain,
! [SV251: nat > $o,SV158: nat,SV57: nat] :
( ( ~ ( connected_capacity @ c @ SV57 @ SV158 )
| ~ ! [SY788: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY788 @ SV158 )
| ~ ! [SY676: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY676 @ SV158 )
| ( ord_less_eq_nat @ SY788 @ SY676 ) )
| ( SV251 @ SY788 ) )
| ( SV251 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(860,plain,
! [SV252: nat,SV159: list_P559422087at_nat,SV58: nat] :
( ( ~ ( isShor1936442771pacity @ c @ SV58 @ SV159 @ SV252 )
| ( isSimp1359852763pacity @ c @ SV58 @ SV159 @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(861,plain,
! [SV160: list_P559422087at_nat,SV59: list_P559422087at_nat] :
( ( ( ~ ( ( ( size_s1990949619at_nat @ SV59 )
!= ( size_s1990949619at_nat @ SV160 ) ) ) )
= $true )
| ( ( SV59 != SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(862,plain,
! [SV161: product_prod_nat_nat > capacity] :
( ( ! [SV253: nat] :
( ( isShor1936442771pacity @ SV161 @ SV253 )
= ( ^ [SY790: list_P559422087at_nat,SY791: nat] :
~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV253 @ SY790 @ SY791 )
| ( ( size_s1990949619at_nat @ SY790 )
!= ( min_dist_capacity @ SV161 @ SV253 @ SY791 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[752]) ).
thf(863,plain,
! [SV161: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV161 )
= ( ^ [SY678: nat,SY679: list_P559422087at_nat,SY680: nat] :
~ ( ~ ( isSimp1359852763pacity @ SV161 @ SY678 @ SY679 @ SY680 )
| ( ( size_s1990949619at_nat @ SY679 )
!= ( min_dist_capacity @ SV161 @ SY678 @ SY680 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[752]) ).
thf(864,plain,
! [SV254: nat,SV162: nat,SV61: nat] :
( ( ! [SY792: nat] :
( ~ ( ord_less_eq_nat @ SV61 @ SV162 )
| ~ ( ord_less_eq_nat @ SV254 @ SY792 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV61 @ SV254 ) @ ( plus_plus_nat @ SV162 @ SY792 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(865,plain,
! [SV255: nat,SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ! [SY793: nat > $o] :
( ~ ( connected_capacity @ SV62 @ SV163 @ SV255 )
| ~ ! [SY794: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY794 @ SV255 )
| ~ ! [SY795: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY795 @ SV255 )
| ( ord_less_eq_nat @ SY794 @ SY795 ) )
| ( SY793 @ SY794 ) )
| ( SY793 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(866,plain,
! [SV164: nat,SV63: nat] :
( ( ( ~ ( ord_less_nat @ SV63 @ SV164 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV63 @ one_one_nat ) @ ( plus_plus_nat @ SV164 @ one_one_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(867,plain,
! [SV256: nat,SV165: list_P559422087at_nat,SV64: nat] :
( ( ~ ( isShor1936442771pacity @ c @ SV64 @ SV165 @ SV256 )
| ( isPath_capacity @ c @ SV64 @ SV165 @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(868,plain,
! [SV166: nat,SV65: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV65 @ SV166 ) )
= $true )
| ( ( ~ ! [SY688: nat] :
( SV166
!= ( plus_plus_nat @ SV65 @ SY688 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(869,plain,
! [SV257: nat,SV167: nat,SV66: nat] :
( ( ! [SY796: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SV66 @ SV167 )
| ( SV257 != SY796 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV66 @ SV257 ) @ ( plus_plus_nat @ SV167 @ SY796 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(870,plain,
! [SV258: nat,SV168: nat,SV67: nat] :
( ( ~ ( ord_less_eq_nat @ SV67 @ SV168 )
| ( ord_less_eq_nat @ SV67 @ ( plus_plus_nat @ SV168 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(871,plain,
! [SV259: nat,SV169: nat,SV68: nat] :
( ( ~ ( ord_less_eq_nat @ SV68 @ SV169 )
| ( ord_less_eq_nat @ SV68 @ ( plus_plus_nat @ SV259 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(872,plain,
! [SV260: nat,SV170: nat,SV69: nat] :
( ( ! [SY797: nat] :
( ~ ( ord_less_nat @ SV69 @ SV170 )
| ~ ( ord_less_nat @ SV260 @ SY797 )
| ( ord_less_nat @ ( plus_plus_nat @ SV69 @ SV260 ) @ ( plus_plus_nat @ SV170 @ SY797 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(873,plain,
! [SV261: nat,SV171: nat,SV70: nat] :
( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV70 @ SV171 ) @ SV261 )
| ( ord_less_nat @ SV70 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(874,plain,
! [SV262: nat,SV172: nat,SV71: nat] :
( ( ! [SY798: nat] :
( ~ ( ord_less_nat @ SV71 @ SV172 )
| ~ ( ord_less_nat @ SV262 @ SY798 )
| ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV262 ) @ ( plus_plus_nat @ SV172 @ SY798 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(875,plain,
! [SV263: nat,SV173: list_P559422087at_nat,SV72: nat] :
( ( ~ ( isPath_capacity @ c @ SV72 @ SV173 @ SV263 )
| ~ ! [SY799: list_P559422087at_nat] :
~ ( isSimp1359852763pacity @ c @ SV72 @ SY799 @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(876,plain,
! [SV264: nat,SV174: nat,SV73: nat] :
( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV73 @ SV174 ) @ ( plus_plus_nat @ SV73 @ SV264 ) )
| ( ord_less_nat @ SV174 @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(877,plain,
! [SV265: nat,SV175: nat,SV74: nat] :
( ( ! [SY800: nat,SY801: nat] :
( ~ ( dist_capacity @ c @ SV74 @ SV175 @ SV265 )
| ~ ( dist_capacity @ c @ SV265 @ SY800 @ SY801 )
| ( ( min_dist_capacity @ c @ SV74 @ SY801 )
!= ( plus_plus_nat @ SV175 @ SY800 ) )
| ( ( min_dist_capacity @ c @ SV74 @ SV265 )
= SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(878,plain,
! [SV266: nat,SV176: nat,SV75: nat] :
( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV75 @ SV176 ) @ SV266 )
| ( ord_less_eq_nat @ SV75 @ SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(879,plain,
! [SV267: nat,SV177: nat,SV76: nat] :
( ( ~ ( ord_less_nat @ SV76 @ SV177 )
| ( ord_less_nat @ SV76 @ ( plus_plus_nat @ SV177 @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(880,plain,
! [SV268: nat,SV178: list_P559422087at_nat,SV77: nat] :
( ( ~ ( isPath_capacity @ c @ SV77 @ SV178 @ SV268 )
| ( dist_capacity @ c @ SV77 @ ( size_s1990949619at_nat @ SV178 ) @ SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(881,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= ( ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(882,plain,
! [SV180: nat,SV79: nat] :
( ( ~ ( ( connected_capacity @ c @ SV79 @ SV180 )
| ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) )
| ~ ( ~ ( connected_capacity @ c @ SV79 @ SV180 )
| ~ ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[772]) ).
thf(883,plain,
! [SV180: nat,SV79: nat] :
( ( ( connected_capacity @ c @ SV79 @ SV180 )
= ( ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[772]) ).
thf(884,plain,
! [SV270: list_P559422087at_nat,SV181: nat,SV80: product_prod_nat_nat > capacity] :
( ( ! [SY803: nat] :
( ~ ( isPath_capacity @ SV80 @ SV181 @ SV270 @ SY803 )
| ( dist_capacity @ SV80 @ SV181 @ ( size_s1990949619at_nat @ SV270 ) @ SY803 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(885,plain,
! [SV182: nat] :
( ( ! [SV271: nat] :
( ( ord_less_eq_nat @ SV182 @ SV271 )
= ( ~ ! [SY804: nat] :
( SV271
!= ( plus_plus_nat @ SV182 @ SY804 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[774]) ).
thf(886,plain,
! [SV182: nat] :
( ( ( ord_less_eq_nat @ SV182 )
= ( ^ [SY712: nat] :
~ ! [SY713: nat] :
( SY712
!= ( plus_plus_nat @ SV182 @ SY713 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[774]) ).
thf(887,plain,
! [SV272: nat,SV183: nat,SV82: nat] :
( ( ! [SY805: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SV82 @ SV183 )
| ~ ( ord_less_eq_nat @ SV272 @ SY805 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV82 @ SV272 ) @ ( plus_plus_nat @ SV183 @ SY805 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(888,plain,
! [SV273: nat,SV184: nat,SV83: nat] :
( ( ! [SY806: nat] :
( ~ ( connected_capacity @ c @ SV83 @ SV184 )
| ( ( min_dist_capacity @ c @ SV83 @ SV184 )
!= SV273 )
| ~ ( ord_less_nat @ SY806 @ SV273 )
| ~ ! [SY542: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV83 @ SY542 )
| ( ( min_dist_capacity @ c @ SV83 @ SY542 )
!= SY806 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(889,plain,
! [SV274: nat,SV185: nat,SV84: nat] :
( ( ! [SY808: nat,SY809: nat] :
( ~ ( dist_capacity @ c @ SV84 @ SV185 @ SV274 )
| ~ ( dist_capacity @ c @ SV274 @ SY808 @ SY809 )
| ( dist_capacity @ c @ SV84 @ ( plus_plus_nat @ SV185 @ SY808 ) @ SY809 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(890,plain,
! [SV186: nat,SV85: nat] :
( ( ( ~ ( connected_capacity @ c @ SV85 @ SV186 ) )
= $true )
| ( ( ~ ! [SY722: list_P559422087at_nat] :
~ ( isShor1936442771pacity @ c @ SV85 @ SY722 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(891,plain,
! [SV275: nat,SV187: nat,SV86: nat] :
( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV86 @ SV187 ) @ SV275 )
| ( ord_less_eq_nat @ SV187 @ SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(892,plain,
! [SV188: product_prod_nat_nat > capacity] :
( ( ! [SV276: nat] :
( ( isShor1936442771pacity @ SV188 @ SV276 )
= ( ^ [SY810: list_P559422087at_nat,SY811: nat] :
~ ( ~ ( isPath_capacity @ SV188 @ SV276 @ SY810 @ SY811 )
| ( ( size_s1990949619at_nat @ SY810 )
!= ( min_dist_capacity @ SV188 @ SV276 @ SY811 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[780]) ).
thf(893,plain,
! [SV188: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV188 )
= ( ^ [SY724: nat,SY725: list_P559422087at_nat,SY726: nat] :
~ ( ~ ( isPath_capacity @ SV188 @ SY724 @ SY725 @ SY726 )
| ( ( size_s1990949619at_nat @ SY725 )
!= ( min_dist_capacity @ SV188 @ SY724 @ SY726 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[780]) ).
thf(894,plain,
! [SV277: nat,SV189: nat,SV88: nat] :
( ( ~ ( ord_less_nat @ SV88 @ SV189 )
| ( ord_less_nat @ SV88 @ ( plus_plus_nat @ SV277 @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(895,plain,
! [SV278: nat,SV190: nat,SV89: nat] :
( ( ! [SY812: nat] :
( ~ ( ord_less_eq_nat @ SV89 @ SV190 )
| ~ ( ord_less_eq_nat @ SV278 @ SY812 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV89 @ SV278 ) @ ( plus_plus_nat @ SV190 @ SY812 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(896,plain,
! [SV279: nat,SV191: nat,SV90: nat] :
( ( ~ ( ord_less_eq_nat @ SV90 @ SV191 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV279 @ SV90 ) @ ( plus_plus_nat @ SV279 @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(897,plain,
! [SV280: nat,SV192: nat,SV91: nat] :
( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV91 @ SV192 ) @ ( plus_plus_nat @ SV280 @ SV192 ) )
| ( ord_less_nat @ SV91 @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(898,plain,
! [SV193: nat,SV92: nat] :
( ( ~ ( ( connected_capacity @ c @ SV92 @ SV193 )
| ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) )
| ~ ( ~ ( connected_capacity @ c @ SV92 @ SV193 )
| ~ ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[785]) ).
thf(899,plain,
! [SV193: nat,SV92: nat] :
( ( ( connected_capacity @ c @ SV92 @ SV193 )
= ( ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[785]) ).
thf(900,plain,
! [SV281: nat,SV194: nat,SV93: nat] :
( ( ~ ( ord_less_eq_nat @ SV93 @ SV194 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV93 @ SV281 ) @ ( plus_plus_nat @ SV194 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(901,plain,
! [SV282: nat,SV195: nat,SV94: nat] :
( ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= ( ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(902,plain,
! [SV283: nat,SV196: nat,SV95: nat] :
( ( ! [SY814: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SV95 @ SV196 )
| ~ ( ord_less_eq_nat @ SV283 @ SY814 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV95 @ SV283 ) @ ( plus_plus_nat @ SV196 @ SY814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(903,plain,
! [SV197: nat,SV96: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV96 @ SV197 ) )
= $true )
| ( ( ~ ! [SY738: nat] :
( SV197
!= ( plus_plus_nat @ SV96 @ SY738 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(904,plain,
! [SV284: nat,SV198: nat,SV97: nat] :
( ( ! [SY815: nat] :
( ~ ~ ( ( SV97 != SV198 )
| ( SV284 != SY815 ) )
| ( ( plus_plus_nat @ SV97 @ SV284 )
= ( plus_plus_nat @ SV198 @ SY815 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(905,plain,
! [SV285: nat,SV199: nat,SV98: nat] :
( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV98 @ SV199 ) @ ( plus_plus_nat @ SV285 @ SV199 ) )
| ( ord_less_eq_nat @ SV98 @ SV285 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(906,plain,
! [SV286: nat,SV200: nat,SV99: nat] :
( ( ! [SY816: nat] :
( ~ ~ ( ( SV99 != SV200 )
| ~ ( ord_less_eq_nat @ SV286 @ SY816 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV99 @ SV286 ) @ ( plus_plus_nat @ SV200 @ SY816 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(907,plain,
! [SV287: nat,SV201: nat,SV100: product_prod_nat_nat > capacity] :
( ( ! [SY817: nat] :
( ~ ( connected_capacity @ SV100 @ SV201 @ SV287 )
| ~ ( ord_less_eq_nat @ SY817 @ ( min_dist_capacity @ SV100 @ SV201 @ SV287 ) )
| ~ ! [SY746: nat] :
~ ~ ( ~ ( connected_capacity @ SV100 @ SV201 @ SY746 )
| ( ( min_dist_capacity @ SV100 @ SV201 @ SY746 )
!= SY817 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(908,plain,
! [SV288: nat,SV202: nat,SV101: nat] :
( ( ! [SY819: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SV101 @ SV202 )
| ( SV288 != SY819 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV101 @ SV288 ) @ ( plus_plus_nat @ SV202 @ SY819 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(909,plain,
! [SV289: nat,SV203: nat,SV102: product_prod_nat_nat > capacity] :
( ( ! [SY820: nat] :
( ~ ( dist_capacity @ SV102 @ SV203 @ SV289 @ SY820 )
| ~ ! [SY821: nat] :
( ~ ( dist_capacity @ SV102 @ SV203 @ SY821 @ SY820 )
| ( ord_less_eq_nat @ SV289 @ SY821 ) )
| ( ( min_dist_capacity @ SV102 @ SV203 @ SY820 )
= SV289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(910,plain,
! [SV290: nat,SV204: nat,SV103: nat] :
( ( ! [SY822: nat] :
( ~ ( ord_less_nat @ SV103 @ SV204 )
| ( ( plus_plus_nat @ SV290 @ SV204 )
!= ( plus_plus_nat @ SV103 @ SY822 ) )
| ( ord_less_nat @ SV290 @ SY822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(911,plain,
! [SV205: product_prod_nat_nat > capacity] :
( ( ! [SV291: nat] :
( ( isShor1936442771pacity @ SV205 @ SV291 )
= ( ^ [SY823: list_P559422087at_nat,SY824: nat] :
~ ( ~ ( isPath_capacity @ SV205 @ SV291 @ SY823 @ SY824 )
| ~ ! [SY825: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV291 @ SY825 @ SY824 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY823 ) @ ( size_s1990949619at_nat @ SY825 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[798]) ).
thf(912,plain,
! [SV205: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV205 )
= ( ^ [SY754: nat,SY755: list_P559422087at_nat,SY756: nat] :
~ ( ~ ( isPath_capacity @ SV205 @ SY754 @ SY755 @ SY756 )
| ~ ! [SY757: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SY754 @ SY757 @ SY756 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY755 ) @ ( size_s1990949619at_nat @ SY757 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[798]) ).
thf(913,plain,
! [SV206: nat,SV105: nat,SV1: nat] :
( ( ~ ( ( ( plus_plus_nat @ SV1 @ SV105 )
= ( plus_plus_nat @ SV1 @ SV206 ) )
| ( SV105 = SV206 ) )
| ~ ( ( ( plus_plus_nat @ SV1 @ SV105 )
!= ( plus_plus_nat @ SV1 @ SV206 ) )
| ( SV105 != SV206 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[799]) ).
thf(914,plain,
! [SV206: nat,SV105: nat,SV1: nat] :
( ( ( ( plus_plus_nat @ SV1 @ SV105 )
= ( plus_plus_nat @ SV1 @ SV206 ) )
= ( SV105 = SV206 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[799]) ).
thf(915,plain,
! [SV207: nat,SV106: nat,SV2: nat] :
( ( ~ ( ( ( plus_plus_nat @ SV2 @ SV106 )
= ( plus_plus_nat @ SV207 @ SV106 ) )
| ( SV2 = SV207 ) )
| ~ ( ( ( plus_plus_nat @ SV2 @ SV106 )
!= ( plus_plus_nat @ SV207 @ SV106 ) )
| ( SV2 != SV207 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[800]) ).
thf(916,plain,
! [SV207: nat,SV106: nat,SV2: nat] :
( ( ( ( plus_plus_nat @ SV2 @ SV106 )
= ( plus_plus_nat @ SV207 @ SV106 ) )
= ( SV2 = SV207 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[800]) ).
thf(917,plain,
! [SV292: nat,SV108: nat] :
( ( ( plus_plus_nat @ SV108 @ SV292 )
= ( plus_plus_nat @ SV292 @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(918,plain,
! [SV7: nat] :
( ( ( ( one_one_nat = SV7 )
| ( SV7 = one_one_nat ) )
= $false )
| ( ( ~ ( ( one_one_nat != SV7 )
| ( SV7 != one_one_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(919,plain,
! [SV212: nat,SV111: nat,SV8: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
| ( ord_less_eq_nat @ SV111 @ SV212 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
| ~ ( ord_less_eq_nat @ SV111 @ SV212 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[807]) ).
thf(920,plain,
! [SV212: nat,SV111: nat,SV8: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
= ( ord_less_eq_nat @ SV111 @ SV212 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[807]) ).
thf(921,plain,
! [SV213: nat,SV112: nat,SV9: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
| ( ord_less_eq_nat @ SV9 @ SV213 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
| ~ ( ord_less_eq_nat @ SV9 @ SV213 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[808]) ).
thf(922,plain,
! [SV213: nat,SV112: nat,SV9: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
= ( ord_less_eq_nat @ SV9 @ SV213 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[808]) ).
thf(923,plain,
! [SV293: nat,SV113: product_prod_nat_nat > capacity] :
( ( ( min_dist_capacity @ SV113 @ SV293 )
= ( min_dist_capacity @ SV113 @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(924,plain,
! [SV215: nat,SV114: nat,SV12: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
| ( ord_less_eq_nat @ SV114 @ SV215 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
| ~ ( ord_less_eq_nat @ SV114 @ SV215 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[811]) ).
thf(925,plain,
! [SV215: nat,SV114: nat,SV12: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
= ( ord_less_eq_nat @ SV114 @ SV215 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[811]) ).
thf(926,plain,
! [SV216: nat,SV115: nat,SV13: nat] :
( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
| ( ord_less_nat @ SV13 @ SV216 ) )
| ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
| ~ ( ord_less_nat @ SV13 @ SV216 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[812]) ).
thf(927,plain,
! [SV216: nat,SV115: nat,SV13: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
= ( ord_less_nat @ SV13 @ SV216 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[812]) ).
thf(928,plain,
! [SV217: nat,SV116: nat,SV14: nat] :
( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
| ( ord_less_nat @ SV116 @ SV217 ) )
| ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
| ~ ( ord_less_nat @ SV116 @ SV217 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[813]) ).
thf(929,plain,
! [SV217: nat,SV116: nat,SV14: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
= ( ord_less_nat @ SV116 @ SV217 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[813]) ).
thf(930,plain,
! [SV218: nat,SV117: nat,SV15: nat] :
( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
| ( ord_less_nat @ SV117 @ SV218 ) )
| ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
| ~ ( ord_less_nat @ SV117 @ SV218 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[814]) ).
thf(931,plain,
! [SV218: nat,SV117: nat,SV15: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
= ( ord_less_nat @ SV117 @ SV218 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[814]) ).
thf(932,plain,
! [SV294: nat,SV122: nat] :
( ( ( ord_less_nat @ SV122 @ SV294 )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(933,plain,
! [SV123: nat,SV22: nat] :
( ( ( ~ ( ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
| ( SV22 = SV123 ) ) )
= $true )
| ( ( ~ ( ~ ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
| ( SV22 != SV123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(934,plain,
! [SV124: nat,SV23: nat] :
( ( ( ~ ( ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
| ( SV23 = SV124 ) ) )
= $true )
| ( ( ~ ( ~ ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
| ( SV23 != SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(935,plain,
! [SV125: list_P559422087at_nat,SV24: nat] :
( ( ( ~ ( ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
| ( SV125 = nil_Pr1308055047at_nat ) ) )
= $true )
| ( ( ~ ( ~ ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
| ( SV125 != nil_Pr1308055047at_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(936,plain,
! [SV295: nat,SV220: nat,SV126: nat,SV25: nat] :
( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV25 @ SV126 )
| ~ ( ord_less_nat @ SV220 @ SV295 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV25 @ SV220 ) @ ( plus_plus_nat @ SV126 @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(937,plain,
! [SV221: nat,SV127: nat,SV26: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV26 @ SV127 ) @ SV221 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV26 @ SV221 )
| ~ ( ord_less_eq_nat @ SV127 @ SV221 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(938,plain,
! [SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV128 @ SV296 )
= ( ^ [SY826: nat,SY827: nat] :
~ ! [SY828: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY828 @ SY827 )
| ( ( size_s1990949619at_nat @ SY828 )
!= SY826 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(939,plain,
! [SV223: nat,SV129: nat,SV28: nat] :
( ( ( ~ ( ord_less_nat @ SV28 @ SV129 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV28 @ SV223 ) @ ( plus_plus_nat @ SV129 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(940,plain,
! [SV224: nat,SV130: nat,SV29: nat > nat] :
( ( ( ~ ! [SY395: nat,SY396: nat] :
( ~ ( ord_less_nat @ SY395 @ SY396 )
| ( ord_less_nat @ ( SV29 @ SY395 ) @ ( SV29 @ SY396 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( SV29 @ SV130 ) @ SV224 ) @ ( SV29 @ ( plus_plus_nat @ SV130 @ SV224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[830]) ).
thf(941,plain,
! [SV297: nat,SV225: nat,SV131: nat,SV30: nat] :
( ( ~ ( ord_less_eq_nat @ SV30 @ SV131 )
| ~ ( ord_less_nat @ SV225 @ SV297 )
| ( ord_less_nat @ ( plus_plus_nat @ SV30 @ SV225 ) @ ( plus_plus_nat @ SV131 @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(942,plain,
! [SV298: nat,SV226: nat,SV132: nat,SV31: nat] :
( ( ~ ( ord_less_nat @ SV31 @ SV132 )
| ~ ( ord_less_eq_nat @ SV226 @ SV298 )
| ( ord_less_nat @ ( plus_plus_nat @ SV31 @ SV226 ) @ ( plus_plus_nat @ SV132 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(943,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ~ ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
| ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) )
| ~ ( ~ ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[833]) ).
thf(944,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
= ( ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[833]) ).
thf(945,plain,
! [SV299: nat,SV228: nat,SV134: nat,SV33: nat] :
( ( ~ ~ ( ~ ( ord_less_nat @ SV33 @ SV134 )
| ~ ( ord_less_nat @ SV228 @ SV299 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV33 @ SV228 ) @ ( plus_plus_nat @ SV134 @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(946,plain,
! [SV300: nat,SV229: nat,SV135: nat,SV34: product_prod_nat_nat > capacity] :
( ( ~ ( dist_capacity @ SV34 @ SV135 @ SV229 @ SV300 )
| ( ord_less_eq_nat @ ( min_dist_capacity @ SV34 @ SV135 @ SV300 ) @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(947,plain,
! [SV230: nat,SV136: nat,SV35: nat] :
( ( ( ~ ( dist_capacity @ c @ SV35 @ SV136 @ SV230 ) )
= $true )
| ( ( ~ ! [SY768: nat] :
( ~ ( dist_capacity @ c @ SV35 @ SY768 @ SV230 )
| ( ord_less_eq_nat @ SV136 @ SY768 ) )
| ( ( min_dist_capacity @ c @ SV35 @ SV230 )
= SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(948,plain,
! [SV301: nat,SV231: nat,SV137: nat,SV36: nat] :
( ( ! [SY829: nat] :
( ~ ( dist_capacity @ c @ SV36 @ SV137 @ SV231 )
| ~ ( dist_capacity @ c @ SV231 @ SV301 @ SY829 )
| ( ( min_dist_capacity @ c @ SV36 @ SY829 )
!= ( plus_plus_nat @ SV137 @ SV301 ) )
| ( ( min_dist_capacity @ c @ SV231 @ SY829 )
= SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(949,plain,
! [SV302: nat,SV232: nat,SV138: nat,SV37: nat] :
( ( ( SV37
!= ( plus_plus_nat @ SV138 @ SV232 ) )
| ( ( plus_plus_nat @ SV302 @ SV37 )
= ( plus_plus_nat @ SV138 @ ( plus_plus_nat @ SV302 @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(950,plain,
! [SV303: nat,SV233: nat,SV139: nat,SV38: nat] :
( ( ~ ~ ( ( SV38 != SV139 )
| ~ ( ord_less_nat @ SV233 @ SV303 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV38 @ SV233 ) @ ( plus_plus_nat @ SV139 @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(951,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ~ ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
| ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) )
| ~ ( ~ ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[840]) ).
thf(952,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
= ( ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[840]) ).
thf(953,plain,
! [SV304: nat,SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ! [SY830: nat] :
( ~ ( connected_capacity @ SV40 @ SV141 @ SV235 )
| ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
!= SV304 )
| ~ ( ord_less_nat @ SY830 @ SV304 )
| ~ ! [SY646: nat] :
~ ~ ( ~ ( connected_capacity @ SV40 @ SV141 @ SY646 )
| ( ( min_dist_capacity @ SV40 @ SV141 @ SY646 )
!= SY830 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(954,plain,
! [SV305: nat,SV236: nat,SV142: nat,SV41: product_prod_nat_nat > capacity] :
( ( ! [SY832: nat,SY833: nat] :
( ~ ( dist_capacity @ SV41 @ SV142 @ SV236 @ SV305 )
| ~ ( dist_capacity @ SV41 @ SV305 @ SY832 @ SY833 )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SY833 )
!= ( plus_plus_nat @ SV236 @ SY832 ) )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SV305 )
= SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(955,plain,
! [SV237: nat,SV143: nat,SV42: nat] :
( ( ( ( plus_plus_nat @ SV42 @ SV143 )
!= ( plus_plus_nat @ SV237 @ SV143 ) )
= $true )
| ( ( SV42 = SV237 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(956,plain,
! [SV306: nat,SV238: nat,SV144: nat,SV43: product_prod_nat_nat > capacity] :
( ( ! [SY834: nat,SY835: nat] :
( ~ ( dist_capacity @ SV43 @ SV144 @ SV238 @ SV306 )
| ~ ( dist_capacity @ SV43 @ SV306 @ SY834 @ SY835 )
| ( dist_capacity @ SV43 @ SV144 @ ( plus_plus_nat @ SV238 @ SY834 ) @ SY835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(957,plain,
! [SV239: nat,SV145: nat,SV44: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV145 ) @ ( plus_plus_nat @ SV44 @ SV239 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV145 @ SV239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[845]) ).
thf(958,plain,
! [SV240: nat,SV146: nat,SV45: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV45 @ SV146 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV45 @ SV240 ) @ ( plus_plus_nat @ SV146 @ SV240 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[846]) ).
thf(959,plain,
! [SV241: nat,SV147: nat,SV46: nat] :
( ( ( ( plus_plus_nat @ SV46 @ SV147 )
!= ( plus_plus_nat @ SV46 @ SV241 ) )
= $true )
| ( ( SV147 = SV241 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(960,plain,
! [SV242: nat,SV148: nat,SV47: nat] :
( ( ( ~ ( dist_capacity @ c @ SV47 @ SV148 @ SV242 ) )
= $true )
| ( ( ord_less_eq_nat @ ( min_dist_capacity @ c @ SV47 @ SV242 ) @ SV148 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(961,plain,
! [SV243: nat,SV149: nat,SV48: nat] :
( ( ( ~ ( ord_less_nat @ SV48 @ SV149 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV48 @ SV243 ) @ ( plus_plus_nat @ SV149 @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(962,plain,
! [SV244: nat,SV150: nat,SV49: nat] :
( ( ( ~ ( dist_capacity @ c @ SV49 @ SV150 @ SV244 ) )
= $true )
| ( ( connected_capacity @ c @ SV49 @ SV244 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(963,plain,
! [SV245: nat,SV151: nat,SV50: product_prod_nat_nat > capacity] :
( ( ( ~ ( connected_capacity @ SV50 @ SV151 @ SV245 ) )
= $true )
| ( ( dist_capacity @ SV50 @ SV151 @ ( min_dist_capacity @ SV50 @ SV151 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(964,plain,
! [SV152: nat,SV51: nat] :
( ( ( connected_capacity @ c @ SV51 @ SV152 )
= $false )
| ( ( dist_capacity @ c @ SV51 @ ( min_dist_capacity @ c @ SV51 @ SV152 ) @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(965,plain,
! [SV246: nat,SV153: nat,SV52: nat] :
( ( ( ~ ( connected_capacity @ c @ SV52 @ SV153 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV246 @ ( min_dist_capacity @ c @ SV52 @ SV153 ) )
| ~ ! [SY782: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV52 @ SY782 )
| ( ( min_dist_capacity @ c @ SV52 @ SY782 )
!= SV246 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(966,plain,
! [SV247: nat,SV154: nat,SV53: nat] :
( ( ( ~ ( ord_less_nat @ SV53 @ SV154 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV247 @ SV53 ) @ ( plus_plus_nat @ SV247 @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[854]) ).
thf(967,plain,
! [SV307: nat,SV155: nat] :
( ( ( ord_less_eq_nat @ SV155 @ SV307 )
= ( ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(968,plain,
! [SV308: nat,SV249: nat,SV156: nat,SV55: product_prod_nat_nat > capacity] :
( ( ! [SY837: nat,SY838: nat] :
( ~ ( dist_capacity @ SV55 @ SV156 @ SV249 @ SV308 )
| ~ ( dist_capacity @ SV55 @ SV308 @ SY837 @ SY838 )
| ( ( min_dist_capacity @ SV55 @ SV156 @ SY838 )
!= ( plus_plus_nat @ SV249 @ SY837 ) )
| ( ( min_dist_capacity @ SV55 @ SV308 @ SY838 )
= SY837 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(969,plain,
! [SV309: nat,SV250: nat,SV157: nat,SV56: nat] :
( ( ( SV56
!= ( plus_plus_nat @ SV157 @ SV250 ) )
| ( ( plus_plus_nat @ SV56 @ SV309 )
= ( plus_plus_nat @ SV157 @ ( plus_plus_nat @ SV250 @ SV309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(970,plain,
! [SV251: nat > $o,SV158: nat,SV57: nat] :
( ( ( ~ ( connected_capacity @ c @ SV57 @ SV158 ) )
= $true )
| ( ( ~ ! [SY788: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY788 @ SV158 )
| ~ ! [SY676: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY676 @ SV158 )
| ( ord_less_eq_nat @ SY788 @ SY676 ) )
| ( SV251 @ SY788 ) )
| ( SV251 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(971,plain,
! [SV252: nat,SV159: list_P559422087at_nat,SV58: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV58 @ SV159 @ SV252 ) )
= $true )
| ( ( isSimp1359852763pacity @ c @ SV58 @ SV159 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(972,plain,
! [SV160: list_P559422087at_nat,SV59: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV59 )
!= ( size_s1990949619at_nat @ SV160 ) )
= $false )
| ( ( SV59 != SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(973,plain,
! [SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV161 @ SV310 )
= ( ^ [SY839: list_P559422087at_nat,SY840: nat] :
~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SY839 @ SY840 )
| ( ( size_s1990949619at_nat @ SY839 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SY840 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(974,plain,
! [SV311: nat,SV254: nat,SV162: nat,SV61: nat] :
( ( ~ ( ord_less_eq_nat @ SV61 @ SV162 )
| ~ ( ord_less_eq_nat @ SV254 @ SV311 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV61 @ SV254 ) @ ( plus_plus_nat @ SV162 @ SV311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(975,plain,
! [SV312: nat > $o,SV255: nat,SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ~ ( connected_capacity @ SV62 @ SV163 @ SV255 )
| ~ ! [SY841: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY841 @ SV255 )
| ~ ! [SY795: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY795 @ SV255 )
| ( ord_less_eq_nat @ SY841 @ SY795 ) )
| ( SV312 @ SY841 ) )
| ( SV312 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(976,plain,
! [SV164: nat,SV63: nat] :
( ( ( ord_less_nat @ SV63 @ SV164 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV63 @ one_one_nat ) @ ( plus_plus_nat @ SV164 @ one_one_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(977,plain,
! [SV256: nat,SV165: list_P559422087at_nat,SV64: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV64 @ SV165 @ SV256 ) )
= $true )
| ( ( isPath_capacity @ c @ SV64 @ SV165 @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(978,plain,
! [SV166: nat,SV65: nat] :
( ( ( ord_less_eq_nat @ SV65 @ SV166 )
= $false )
| ( ( ~ ! [SY688: nat] :
( SV166
!= ( plus_plus_nat @ SV65 @ SY688 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(979,plain,
! [SV313: nat,SV257: nat,SV167: nat,SV66: nat] :
( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV66 @ SV167 )
| ( SV257 != SV313 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV66 @ SV257 ) @ ( plus_plus_nat @ SV167 @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(980,plain,
! [SV258: nat,SV168: nat,SV67: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV67 @ SV168 ) )
= $true )
| ( ( ord_less_eq_nat @ SV67 @ ( plus_plus_nat @ SV168 @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(981,plain,
! [SV259: nat,SV169: nat,SV68: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV68 @ SV169 ) )
= $true )
| ( ( ord_less_eq_nat @ SV68 @ ( plus_plus_nat @ SV259 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(982,plain,
! [SV314: nat,SV260: nat,SV170: nat,SV69: nat] :
( ( ~ ( ord_less_nat @ SV69 @ SV170 )
| ~ ( ord_less_nat @ SV260 @ SV314 )
| ( ord_less_nat @ ( plus_plus_nat @ SV69 @ SV260 ) @ ( plus_plus_nat @ SV170 @ SV314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(983,plain,
! [SV261: nat,SV171: nat,SV70: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV70 @ SV171 ) @ SV261 ) )
= $true )
| ( ( ord_less_nat @ SV70 @ SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(984,plain,
! [SV315: nat,SV262: nat,SV172: nat,SV71: nat] :
( ( ~ ( ord_less_nat @ SV71 @ SV172 )
| ~ ( ord_less_nat @ SV262 @ SV315 )
| ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV262 ) @ ( plus_plus_nat @ SV172 @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(985,plain,
! [SV263: nat,SV173: list_P559422087at_nat,SV72: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV72 @ SV173 @ SV263 ) )
= $true )
| ( ( ~ ! [SY799: list_P559422087at_nat] :
~ ( isSimp1359852763pacity @ c @ SV72 @ SY799 @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(986,plain,
! [SV264: nat,SV174: nat,SV73: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV73 @ SV174 ) @ ( plus_plus_nat @ SV73 @ SV264 ) ) )
= $true )
| ( ( ord_less_nat @ SV174 @ SV264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(987,plain,
! [SV316: nat,SV265: nat,SV175: nat,SV74: nat] :
( ( ! [SY843: nat] :
( ~ ( dist_capacity @ c @ SV74 @ SV175 @ SV265 )
| ~ ( dist_capacity @ c @ SV265 @ SV316 @ SY843 )
| ( ( min_dist_capacity @ c @ SV74 @ SY843 )
!= ( plus_plus_nat @ SV175 @ SV316 ) )
| ( ( min_dist_capacity @ c @ SV74 @ SV265 )
= SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(988,plain,
! [SV266: nat,SV176: nat,SV75: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV75 @ SV176 ) @ SV266 ) )
= $true )
| ( ( ord_less_eq_nat @ SV75 @ SV266 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(989,plain,
! [SV267: nat,SV177: nat,SV76: nat] :
( ( ( ~ ( ord_less_nat @ SV76 @ SV177 ) )
= $true )
| ( ( ord_less_nat @ SV76 @ ( plus_plus_nat @ SV177 @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(990,plain,
! [SV268: nat,SV178: list_P559422087at_nat,SV77: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV77 @ SV178 @ SV268 ) )
= $true )
| ( ( dist_capacity @ c @ SV77 @ ( size_s1990949619at_nat @ SV178 ) @ SV268 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(991,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ~ ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) )
| ~ ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[881]) ).
thf(992,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= ( ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[881]) ).
thf(993,plain,
! [SV180: nat,SV79: nat] :
( ( ( ~ ( ( connected_capacity @ c @ SV79 @ SV180 )
| ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) ) )
= $true )
| ( ( ~ ( ~ ( connected_capacity @ c @ SV79 @ SV180 )
| ~ ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(994,plain,
! [SV317: nat,SV270: list_P559422087at_nat,SV181: nat,SV80: product_prod_nat_nat > capacity] :
( ( ~ ( isPath_capacity @ SV80 @ SV181 @ SV270 @ SV317 )
| ( dist_capacity @ SV80 @ SV181 @ ( size_s1990949619at_nat @ SV270 ) @ SV317 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(995,plain,
! [SV318: nat,SV182: nat] :
( ( ( ord_less_eq_nat @ SV182 @ SV318 )
= ( ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(996,plain,
! [SV319: nat,SV272: nat,SV183: nat,SV82: nat] :
( ( ~ ~ ( ~ ( ord_less_nat @ SV82 @ SV183 )
| ~ ( ord_less_eq_nat @ SV272 @ SV319 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV82 @ SV272 ) @ ( plus_plus_nat @ SV183 @ SV319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(997,plain,
! [SV320: nat,SV273: nat,SV184: nat,SV83: nat] :
( ( ~ ( connected_capacity @ c @ SV83 @ SV184 )
| ( ( min_dist_capacity @ c @ SV83 @ SV184 )
!= SV273 )
| ~ ( ord_less_nat @ SV320 @ SV273 )
| ~ ! [SY845: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV83 @ SY845 )
| ( ( min_dist_capacity @ c @ SV83 @ SY845 )
!= SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(998,plain,
! [SV321: nat,SV274: nat,SV185: nat,SV84: nat] :
( ( ! [SY846: nat] :
( ~ ( dist_capacity @ c @ SV84 @ SV185 @ SV274 )
| ~ ( dist_capacity @ c @ SV274 @ SV321 @ SY846 )
| ( dist_capacity @ c @ SV84 @ ( plus_plus_nat @ SV185 @ SV321 ) @ SY846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(999,plain,
! [SV186: nat,SV85: nat] :
( ( ( connected_capacity @ c @ SV85 @ SV186 )
= $false )
| ( ( ~ ! [SY722: list_P559422087at_nat] :
~ ( isShor1936442771pacity @ c @ SV85 @ SY722 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(1000,plain,
! [SV275: nat,SV187: nat,SV86: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV86 @ SV187 ) @ SV275 ) )
= $true )
| ( ( ord_less_eq_nat @ SV187 @ SV275 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(1001,plain,
! [SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV188 @ SV322 )
= ( ^ [SY847: list_P559422087at_nat,SY848: nat] :
~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SY847 @ SY848 )
| ( ( size_s1990949619at_nat @ SY847 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SY848 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1002,plain,
! [SV277: nat,SV189: nat,SV88: nat] :
( ( ( ~ ( ord_less_nat @ SV88 @ SV189 ) )
= $true )
| ( ( ord_less_nat @ SV88 @ ( plus_plus_nat @ SV277 @ SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(1003,plain,
! [SV323: nat,SV278: nat,SV190: nat,SV89: nat] :
( ( ~ ( ord_less_eq_nat @ SV89 @ SV190 )
| ~ ( ord_less_eq_nat @ SV278 @ SV323 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV89 @ SV278 ) @ ( plus_plus_nat @ SV190 @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1004,plain,
! [SV279: nat,SV191: nat,SV90: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV90 @ SV191 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV279 @ SV90 ) @ ( plus_plus_nat @ SV279 @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(1005,plain,
! [SV280: nat,SV192: nat,SV91: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV91 @ SV192 ) @ ( plus_plus_nat @ SV280 @ SV192 ) ) )
= $true )
| ( ( ord_less_nat @ SV91 @ SV280 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(1006,plain,
! [SV193: nat,SV92: nat] :
( ( ( ~ ( ( connected_capacity @ c @ SV92 @ SV193 )
| ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) ) )
= $true )
| ( ( ~ ( ~ ( connected_capacity @ c @ SV92 @ SV193 )
| ~ ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(1007,plain,
! [SV281: nat,SV194: nat,SV93: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV93 @ SV194 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV93 @ SV281 ) @ ( plus_plus_nat @ SV194 @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(1008,plain,
! [SV282: nat,SV195: nat,SV94: nat] :
( ( ~ ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) )
| ~ ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[901]) ).
thf(1009,plain,
! [SV282: nat,SV195: nat,SV94: nat] :
( ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= ( ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[901]) ).
thf(1010,plain,
! [SV324: nat,SV283: nat,SV196: nat,SV95: nat] :
( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV95 @ SV196 )
| ~ ( ord_less_eq_nat @ SV283 @ SV324 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV95 @ SV283 ) @ ( plus_plus_nat @ SV196 @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1011,plain,
! [SV197: nat,SV96: nat] :
( ( ( ord_less_eq_nat @ SV96 @ SV197 )
= $false )
| ( ( ~ ! [SY738: nat] :
( SV197
!= ( plus_plus_nat @ SV96 @ SY738 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(1012,plain,
! [SV325: nat,SV284: nat,SV198: nat,SV97: nat] :
( ( ~ ~ ( ( SV97 != SV198 )
| ( SV284 != SV325 ) )
| ( ( plus_plus_nat @ SV97 @ SV284 )
= ( plus_plus_nat @ SV198 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1013,plain,
! [SV285: nat,SV199: nat,SV98: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV98 @ SV199 ) @ ( plus_plus_nat @ SV285 @ SV199 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV98 @ SV285 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(1014,plain,
! [SV326: nat,SV286: nat,SV200: nat,SV99: nat] :
( ( ~ ~ ( ( SV99 != SV200 )
| ~ ( ord_less_eq_nat @ SV286 @ SV326 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV99 @ SV286 ) @ ( plus_plus_nat @ SV200 @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1015,plain,
! [SV327: nat,SV287: nat,SV201: nat,SV100: product_prod_nat_nat > capacity] :
( ( ~ ( connected_capacity @ SV100 @ SV201 @ SV287 )
| ~ ( ord_less_eq_nat @ SV327 @ ( min_dist_capacity @ SV100 @ SV201 @ SV287 ) )
| ~ ! [SY849: nat] :
~ ~ ( ~ ( connected_capacity @ SV100 @ SV201 @ SY849 )
| ( ( min_dist_capacity @ SV100 @ SV201 @ SY849 )
!= SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1016,plain,
! [SV328: nat,SV288: nat,SV202: nat,SV101: nat] :
( ( ~ ~ ( ~ ( ord_less_nat @ SV101 @ SV202 )
| ( SV288 != SV328 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV101 @ SV288 ) @ ( plus_plus_nat @ SV202 @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1017,plain,
! [SV329: nat,SV289: nat,SV203: nat,SV102: product_prod_nat_nat > capacity] :
( ( ~ ( dist_capacity @ SV102 @ SV203 @ SV289 @ SV329 )
| ~ ! [SY850: nat] :
( ~ ( dist_capacity @ SV102 @ SV203 @ SY850 @ SV329 )
| ( ord_less_eq_nat @ SV289 @ SY850 ) )
| ( ( min_dist_capacity @ SV102 @ SV203 @ SV329 )
= SV289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1018,plain,
! [SV330: nat,SV290: nat,SV204: nat,SV103: nat] :
( ( ~ ( ord_less_nat @ SV103 @ SV204 )
| ( ( plus_plus_nat @ SV290 @ SV204 )
!= ( plus_plus_nat @ SV103 @ SV330 ) )
| ( ord_less_nat @ SV290 @ SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1019,plain,
! [SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV205 @ SV331 )
= ( ^ [SY851: list_P559422087at_nat,SY852: nat] :
~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SY851 @ SY852 )
| ~ ! [SY853: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY853 @ SY852 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY851 ) @ ( size_s1990949619at_nat @ SY853 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1020,plain,
! [SV206: nat,SV105: nat,SV1: nat] :
( ( ( ~ ( ( ( plus_plus_nat @ SV1 @ SV105 )
= ( plus_plus_nat @ SV1 @ SV206 ) )
| ( SV105 = SV206 ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ SV1 @ SV105 )
!= ( plus_plus_nat @ SV1 @ SV206 ) )
| ( SV105 != SV206 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(1021,plain,
! [SV207: nat,SV106: nat,SV2: nat] :
( ( ( ~ ( ( ( plus_plus_nat @ SV2 @ SV106 )
= ( plus_plus_nat @ SV207 @ SV106 ) )
| ( SV2 = SV207 ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ SV2 @ SV106 )
!= ( plus_plus_nat @ SV207 @ SV106 ) )
| ( SV2 != SV207 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(1022,plain,
! [SV7: nat] :
( ( ( one_one_nat = SV7 )
= $false )
| ( ( ~ ( ( one_one_nat != SV7 )
| ( SV7 != one_one_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[918]) ).
thf(1023,plain,
! [SV7: nat] :
( ( ( SV7 = one_one_nat )
= $false )
| ( ( ~ ( ( one_one_nat != SV7 )
| ( SV7 != one_one_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[918]) ).
thf(1024,plain,
! [SV212: nat,SV111: nat,SV8: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
| ( ord_less_eq_nat @ SV111 @ SV212 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
| ~ ( ord_less_eq_nat @ SV111 @ SV212 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(1025,plain,
! [SV213: nat,SV112: nat,SV9: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
| ( ord_less_eq_nat @ SV9 @ SV213 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
| ~ ( ord_less_eq_nat @ SV9 @ SV213 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(1026,plain,
! [SV293: nat,SV113: product_prod_nat_nat > capacity] :
( ( ! [SV332: nat] :
( ( min_dist_capacity @ SV113 @ SV293 @ SV332 )
= ( min_dist_capacity @ SV113 @ SV293 @ SV332 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[923]) ).
thf(1027,plain,
! [SV293: nat,SV113: product_prod_nat_nat > capacity] :
( ( ( min_dist_capacity @ SV113 @ SV293 )
= ( min_dist_capacity @ SV113 @ SV293 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[923]) ).
thf(1028,plain,
! [SV215: nat,SV114: nat,SV12: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
| ( ord_less_eq_nat @ SV114 @ SV215 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
| ~ ( ord_less_eq_nat @ SV114 @ SV215 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(1029,plain,
! [SV216: nat,SV115: nat,SV13: nat] :
( ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
| ( ord_less_nat @ SV13 @ SV216 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
| ~ ( ord_less_nat @ SV13 @ SV216 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(1030,plain,
! [SV217: nat,SV116: nat,SV14: nat] :
( ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
| ( ord_less_nat @ SV116 @ SV217 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
| ~ ( ord_less_nat @ SV116 @ SV217 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(1031,plain,
! [SV218: nat,SV117: nat,SV15: nat] :
( ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
| ( ord_less_nat @ SV117 @ SV218 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
| ~ ( ord_less_nat @ SV117 @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(1032,plain,
! [SV294: nat,SV122: nat] :
( ( ~ ( ( ord_less_nat @ SV122 @ SV294 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 ) )
| ~ ( ~ ( ord_less_nat @ SV122 @ SV294 )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[932]) ).
thf(1033,plain,
! [SV294: nat,SV122: nat] :
( ( ( ord_less_nat @ SV122 @ SV294 )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[932]) ).
thf(1034,plain,
! [SV123: nat,SV22: nat] :
( ( ( ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
| ( SV22 = SV123 ) )
= $false )
| ( ( ~ ( ~ ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
| ( SV22 != SV123 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(1035,plain,
! [SV124: nat,SV23: nat] :
( ( ( ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
| ( SV23 = SV124 ) )
= $false )
| ( ( ~ ( ~ ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
| ( SV23 != SV124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1036,plain,
! [SV125: list_P559422087at_nat,SV24: nat] :
( ( ( ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
| ( SV125 = nil_Pr1308055047at_nat ) )
= $false )
| ( ( ~ ( ~ ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
| ( SV125 != nil_Pr1308055047at_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(1037,plain,
! [SV295: nat,SV220: nat,SV126: nat,SV25: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV25 @ SV126 )
| ~ ( ord_less_nat @ SV220 @ SV295 ) ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV25 @ SV220 ) @ ( plus_plus_nat @ SV126 @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(1038,plain,
! [SV221: nat,SV127: nat,SV26: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV26 @ SV127 ) @ SV221 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV26 @ SV221 )
| ~ ( ord_less_eq_nat @ SV127 @ SV221 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(1039,plain,
! [SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ! [SV333: nat] :
( ( dist_capacity @ SV128 @ SV296 @ SV333 )
= ( ^ [SY854: nat] :
~ ! [SY855: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY855 @ SY854 )
| ( ( size_s1990949619at_nat @ SY855 )
!= SV333 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[938]) ).
thf(1040,plain,
! [SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV128 @ SV296 )
= ( ^ [SY826: nat,SY827: nat] :
~ ! [SY828: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY828 @ SY827 )
| ( ( size_s1990949619at_nat @ SY828 )
!= SY826 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[938]) ).
thf(1041,plain,
! [SV223: nat,SV129: nat,SV28: nat] :
( ( ( ord_less_nat @ SV28 @ SV129 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV28 @ SV223 ) @ ( plus_plus_nat @ SV129 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(1042,plain,
! [SV224: nat,SV130: nat,SV29: nat > nat] :
( ( ( ! [SY395: nat,SY396: nat] :
( ~ ( ord_less_nat @ SY395 @ SY396 )
| ( ord_less_nat @ ( SV29 @ SY395 ) @ ( SV29 @ SY396 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( SV29 @ SV130 ) @ SV224 ) @ ( SV29 @ ( plus_plus_nat @ SV130 @ SV224 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1043,plain,
! [SV297: nat,SV225: nat,SV131: nat,SV30: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV30 @ SV131 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV225 @ SV297 )
| ( ord_less_nat @ ( plus_plus_nat @ SV30 @ SV225 ) @ ( plus_plus_nat @ SV131 @ SV297 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(1044,plain,
! [SV298: nat,SV226: nat,SV132: nat,SV31: nat] :
( ( ( ~ ( ord_less_nat @ SV31 @ SV132 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV226 @ SV298 )
| ( ord_less_nat @ ( plus_plus_nat @ SV31 @ SV226 ) @ ( plus_plus_nat @ SV132 @ SV298 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1045,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
| ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[943]) ).
thf(1046,plain,
! [SV299: nat,SV228: nat,SV134: nat,SV33: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV33 @ SV134 )
| ~ ( ord_less_nat @ SV228 @ SV299 ) ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV33 @ SV228 ) @ ( plus_plus_nat @ SV134 @ SV299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(1047,plain,
! [SV300: nat,SV229: nat,SV135: nat,SV34: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV34 @ SV135 @ SV229 @ SV300 ) )
= $true )
| ( ( ord_less_eq_nat @ ( min_dist_capacity @ SV34 @ SV135 @ SV300 ) @ SV229 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[946]) ).
thf(1048,plain,
! [SV230: nat,SV136: nat,SV35: nat] :
( ( ( dist_capacity @ c @ SV35 @ SV136 @ SV230 )
= $false )
| ( ( ~ ! [SY768: nat] :
( ~ ( dist_capacity @ c @ SV35 @ SY768 @ SV230 )
| ( ord_less_eq_nat @ SV136 @ SY768 ) )
| ( ( min_dist_capacity @ c @ SV35 @ SV230 )
= SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1049,plain,
! [SV334: nat,SV301: nat,SV231: nat,SV137: nat,SV36: nat] :
( ( ~ ( dist_capacity @ c @ SV36 @ SV137 @ SV231 )
| ~ ( dist_capacity @ c @ SV231 @ SV301 @ SV334 )
| ( ( min_dist_capacity @ c @ SV36 @ SV334 )
!= ( plus_plus_nat @ SV137 @ SV301 ) )
| ( ( min_dist_capacity @ c @ SV231 @ SV334 )
= SV301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1050,plain,
! [SV302: nat,SV232: nat,SV138: nat,SV37: nat] :
( ( ( SV37
!= ( plus_plus_nat @ SV138 @ SV232 ) )
= $true )
| ( ( ( plus_plus_nat @ SV302 @ SV37 )
= ( plus_plus_nat @ SV138 @ ( plus_plus_nat @ SV302 @ SV232 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1051,plain,
! [SV303: nat,SV233: nat,SV139: nat,SV38: nat] :
( ( ( ~ ~ ( ( SV38 != SV139 )
| ~ ( ord_less_nat @ SV233 @ SV303 ) ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV38 @ SV233 ) @ ( plus_plus_nat @ SV139 @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(1052,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
| ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[951]) ).
thf(1053,plain,
! [SV335: nat,SV304: nat,SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ~ ( connected_capacity @ SV40 @ SV141 @ SV235 )
| ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
!= SV304 )
| ~ ( ord_less_nat @ SV335 @ SV304 )
| ~ ! [SY856: nat] :
~ ~ ( ~ ( connected_capacity @ SV40 @ SV141 @ SY856 )
| ( ( min_dist_capacity @ SV40 @ SV141 @ SY856 )
!= SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1054,plain,
! [SV336: nat,SV305: nat,SV236: nat,SV142: nat,SV41: product_prod_nat_nat > capacity] :
( ( ! [SY857: nat] :
( ~ ( dist_capacity @ SV41 @ SV142 @ SV236 @ SV305 )
| ~ ( dist_capacity @ SV41 @ SV305 @ SV336 @ SY857 )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SY857 )
!= ( plus_plus_nat @ SV236 @ SV336 ) )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SV305 )
= SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1055,plain,
! [SV237: nat,SV143: nat,SV42: nat] :
( ( ( ( plus_plus_nat @ SV42 @ SV143 )
= ( plus_plus_nat @ SV237 @ SV143 ) )
= $false )
| ( ( SV42 = SV237 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1056,plain,
! [SV337: nat,SV306: nat,SV238: nat,SV144: nat,SV43: product_prod_nat_nat > capacity] :
( ( ! [SY858: nat] :
( ~ ( dist_capacity @ SV43 @ SV144 @ SV238 @ SV306 )
| ~ ( dist_capacity @ SV43 @ SV306 @ SV337 @ SY858 )
| ( dist_capacity @ SV43 @ SV144 @ ( plus_plus_nat @ SV238 @ SV337 ) @ SY858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1057,plain,
! [SV239: nat,SV145: nat,SV44: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV145 ) @ ( plus_plus_nat @ SV44 @ SV239 ) )
= $false )
| ( ( ord_less_eq_nat @ SV145 @ SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(1058,plain,
! [SV240: nat,SV146: nat,SV45: nat] :
( ( ( ord_less_eq_nat @ SV45 @ SV146 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV45 @ SV240 ) @ ( plus_plus_nat @ SV146 @ SV240 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(1059,plain,
! [SV241: nat,SV147: nat,SV46: nat] :
( ( ( ( plus_plus_nat @ SV46 @ SV147 )
= ( plus_plus_nat @ SV46 @ SV241 ) )
= $false )
| ( ( SV147 = SV241 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1060,plain,
! [SV242: nat,SV148: nat,SV47: nat] :
( ( ( dist_capacity @ c @ SV47 @ SV148 @ SV242 )
= $false )
| ( ( ord_less_eq_nat @ ( min_dist_capacity @ c @ SV47 @ SV242 ) @ SV148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1061,plain,
! [SV243: nat,SV149: nat,SV48: nat] :
( ( ( ord_less_nat @ SV48 @ SV149 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV48 @ SV243 ) @ ( plus_plus_nat @ SV149 @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1062,plain,
! [SV244: nat,SV150: nat,SV49: nat] :
( ( ( dist_capacity @ c @ SV49 @ SV150 @ SV244 )
= $false )
| ( ( connected_capacity @ c @ SV49 @ SV244 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1063,plain,
! [SV245: nat,SV151: nat,SV50: product_prod_nat_nat > capacity] :
( ( ( connected_capacity @ SV50 @ SV151 @ SV245 )
= $false )
| ( ( dist_capacity @ SV50 @ SV151 @ ( min_dist_capacity @ SV50 @ SV151 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1064,plain,
! [SV246: nat,SV153: nat,SV52: nat] :
( ( ( connected_capacity @ c @ SV52 @ SV153 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV246 @ ( min_dist_capacity @ c @ SV52 @ SV153 ) )
| ~ ! [SY782: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV52 @ SY782 )
| ( ( min_dist_capacity @ c @ SV52 @ SY782 )
!= SV246 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1065,plain,
! [SV247: nat,SV154: nat,SV53: nat] :
( ( ( ord_less_nat @ SV53 @ SV154 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV247 @ SV53 ) @ ( plus_plus_nat @ SV247 @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1066,plain,
! [SV307: nat,SV155: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV155 @ SV307 )
| ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) )
| ~ ( ~ ( ord_less_eq_nat @ SV155 @ SV307 )
| ~ ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[967]) ).
thf(1067,plain,
! [SV307: nat,SV155: nat] :
( ( ( ord_less_eq_nat @ SV155 @ SV307 )
= ( ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[967]) ).
thf(1068,plain,
! [SV338: nat,SV308: nat,SV249: nat,SV156: nat,SV55: product_prod_nat_nat > capacity] :
( ( ! [SY859: nat] :
( ~ ( dist_capacity @ SV55 @ SV156 @ SV249 @ SV308 )
| ~ ( dist_capacity @ SV55 @ SV308 @ SV338 @ SY859 )
| ( ( min_dist_capacity @ SV55 @ SV156 @ SY859 )
!= ( plus_plus_nat @ SV249 @ SV338 ) )
| ( ( min_dist_capacity @ SV55 @ SV308 @ SY859 )
= SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1069,plain,
! [SV309: nat,SV250: nat,SV157: nat,SV56: nat] :
( ( ( SV56
!= ( plus_plus_nat @ SV157 @ SV250 ) )
= $true )
| ( ( ( plus_plus_nat @ SV56 @ SV309 )
= ( plus_plus_nat @ SV157 @ ( plus_plus_nat @ SV250 @ SV309 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1070,plain,
! [SV251: nat > $o,SV158: nat,SV57: nat] :
( ( ( connected_capacity @ c @ SV57 @ SV158 )
= $false )
| ( ( ~ ! [SY788: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY788 @ SV158 )
| ~ ! [SY676: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY676 @ SV158 )
| ( ord_less_eq_nat @ SY788 @ SY676 ) )
| ( SV251 @ SY788 ) )
| ( SV251 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(1071,plain,
! [SV252: nat,SV159: list_P559422087at_nat,SV58: nat] :
( ( ( isShor1936442771pacity @ c @ SV58 @ SV159 @ SV252 )
= $false )
| ( ( isSimp1359852763pacity @ c @ SV58 @ SV159 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1072,plain,
! [SV160: list_P559422087at_nat,SV59: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV59 )
= ( size_s1990949619at_nat @ SV160 ) )
= $true )
| ( ( SV59 != SV160 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(1073,plain,
! [SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ! [SV339: list_P559422087at_nat] :
( ( isShor1936442771pacity @ SV161 @ SV310 @ SV339 )
= ( ^ [SY860: nat] :
~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV339 @ SY860 )
| ( ( size_s1990949619at_nat @ SV339 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SY860 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[973]) ).
thf(1074,plain,
! [SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV161 @ SV310 )
= ( ^ [SY839: list_P559422087at_nat,SY840: nat] :
~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SY839 @ SY840 )
| ( ( size_s1990949619at_nat @ SY839 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SY840 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[973]) ).
thf(1075,plain,
! [SV311: nat,SV254: nat,SV162: nat,SV61: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV61 @ SV162 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV254 @ SV311 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV61 @ SV254 ) @ ( plus_plus_nat @ SV162 @ SV311 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(1076,plain,
! [SV312: nat > $o,SV255: nat,SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ( ~ ( connected_capacity @ SV62 @ SV163 @ SV255 ) )
= $true )
| ( ( ~ ! [SY841: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY841 @ SV255 )
| ~ ! [SY795: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY795 @ SV255 )
| ( ord_less_eq_nat @ SY841 @ SY795 ) )
| ( SV312 @ SY841 ) )
| ( SV312 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1077,plain,
! [SV256: nat,SV165: list_P559422087at_nat,SV64: nat] :
( ( ( isShor1936442771pacity @ c @ SV64 @ SV165 @ SV256 )
= $false )
| ( ( isPath_capacity @ c @ SV64 @ SV165 @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1078,plain,
! [SV65: nat,SV166: nat] :
( ( ( ! [SY688: nat] :
( SV166
!= ( plus_plus_nat @ SV65 @ SY688 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV65 @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1079,plain,
! [SV313: nat,SV257: nat,SV167: nat,SV66: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV66 @ SV167 )
| ( SV257 != SV313 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV66 @ SV257 ) @ ( plus_plus_nat @ SV167 @ SV313 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1080,plain,
! [SV258: nat,SV168: nat,SV67: nat] :
( ( ( ord_less_eq_nat @ SV67 @ SV168 )
= $false )
| ( ( ord_less_eq_nat @ SV67 @ ( plus_plus_nat @ SV168 @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1081,plain,
! [SV259: nat,SV169: nat,SV68: nat] :
( ( ( ord_less_eq_nat @ SV68 @ SV169 )
= $false )
| ( ( ord_less_eq_nat @ SV68 @ ( plus_plus_nat @ SV259 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1082,plain,
! [SV314: nat,SV260: nat,SV170: nat,SV69: nat] :
( ( ( ~ ( ord_less_nat @ SV69 @ SV170 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV260 @ SV314 )
| ( ord_less_nat @ ( plus_plus_nat @ SV69 @ SV260 ) @ ( plus_plus_nat @ SV170 @ SV314 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(1083,plain,
! [SV261: nat,SV171: nat,SV70: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV70 @ SV171 ) @ SV261 )
= $false )
| ( ( ord_less_nat @ SV70 @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1084,plain,
! [SV315: nat,SV262: nat,SV172: nat,SV71: nat] :
( ( ( ~ ( ord_less_nat @ SV71 @ SV172 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV262 @ SV315 )
| ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV262 ) @ ( plus_plus_nat @ SV172 @ SV315 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[984]) ).
thf(1085,plain,
! [SV263: nat,SV173: list_P559422087at_nat,SV72: nat] :
( ( ( isPath_capacity @ c @ SV72 @ SV173 @ SV263 )
= $false )
| ( ( ~ ! [SY799: list_P559422087at_nat] :
~ ( isSimp1359852763pacity @ c @ SV72 @ SY799 @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1086,plain,
! [SV264: nat,SV174: nat,SV73: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV73 @ SV174 ) @ ( plus_plus_nat @ SV73 @ SV264 ) )
= $false )
| ( ( ord_less_nat @ SV174 @ SV264 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1087,plain,
! [SV340: nat,SV316: nat,SV265: nat,SV175: nat,SV74: nat] :
( ( ~ ( dist_capacity @ c @ SV74 @ SV175 @ SV265 )
| ~ ( dist_capacity @ c @ SV265 @ SV316 @ SV340 )
| ( ( min_dist_capacity @ c @ SV74 @ SV340 )
!= ( plus_plus_nat @ SV175 @ SV316 ) )
| ( ( min_dist_capacity @ c @ SV74 @ SV265 )
= SV175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1088,plain,
! [SV266: nat,SV176: nat,SV75: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV75 @ SV176 ) @ SV266 )
= $false )
| ( ( ord_less_eq_nat @ SV75 @ SV266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1089,plain,
! [SV267: nat,SV177: nat,SV76: nat] :
( ( ( ord_less_nat @ SV76 @ SV177 )
= $false )
| ( ( ord_less_nat @ SV76 @ ( plus_plus_nat @ SV177 @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1090,plain,
! [SV268: nat,SV178: list_P559422087at_nat,SV77: nat] :
( ( ( isPath_capacity @ c @ SV77 @ SV178 @ SV268 )
= $false )
| ( ( dist_capacity @ c @ SV77 @ ( size_s1990949619at_nat @ SV178 ) @ SV268 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1091,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[991]) ).
thf(1092,plain,
! [SV180: nat,SV79: nat] :
( ( ( ( connected_capacity @ c @ SV79 @ SV180 )
| ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) )
= $false )
| ( ( ~ ( ~ ( connected_capacity @ c @ SV79 @ SV180 )
| ~ ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1093,plain,
! [SV317: nat,SV270: list_P559422087at_nat,SV181: nat,SV80: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV80 @ SV181 @ SV270 @ SV317 ) )
= $true )
| ( ( dist_capacity @ SV80 @ SV181 @ ( size_s1990949619at_nat @ SV270 ) @ SV317 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1094,plain,
! [SV318: nat,SV182: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV182 @ SV318 )
| ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) )
| ~ ( ~ ( ord_less_eq_nat @ SV182 @ SV318 )
| ~ ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[995]) ).
thf(1095,plain,
! [SV318: nat,SV182: nat] :
( ( ( ord_less_eq_nat @ SV182 @ SV318 )
= ( ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[995]) ).
thf(1096,plain,
! [SV319: nat,SV272: nat,SV183: nat,SV82: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV82 @ SV183 )
| ~ ( ord_less_eq_nat @ SV272 @ SV319 ) ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV82 @ SV272 ) @ ( plus_plus_nat @ SV183 @ SV319 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[996]) ).
thf(1097,plain,
! [SV320: nat,SV273: nat,SV184: nat,SV83: nat] :
( ( ( ~ ( connected_capacity @ c @ SV83 @ SV184 ) )
= $true )
| ( ( ( ( min_dist_capacity @ c @ SV83 @ SV184 )
!= SV273 )
| ~ ( ord_less_nat @ SV320 @ SV273 )
| ~ ! [SY845: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV83 @ SY845 )
| ( ( min_dist_capacity @ c @ SV83 @ SY845 )
!= SV320 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1098,plain,
! [SV341: nat,SV321: nat,SV274: nat,SV185: nat,SV84: nat] :
( ( ~ ( dist_capacity @ c @ SV84 @ SV185 @ SV274 )
| ~ ( dist_capacity @ c @ SV274 @ SV321 @ SV341 )
| ( dist_capacity @ c @ SV84 @ ( plus_plus_nat @ SV185 @ SV321 ) @ SV341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1099,plain,
! [SV186: nat,SV85: nat] :
( ( ( ! [SY722: list_P559422087at_nat] :
~ ( isShor1936442771pacity @ c @ SV85 @ SY722 @ SV186 ) )
= $false )
| ( ( connected_capacity @ c @ SV85 @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1100,plain,
! [SV275: nat,SV187: nat,SV86: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV86 @ SV187 ) @ SV275 )
= $false )
| ( ( ord_less_eq_nat @ SV187 @ SV275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1101,plain,
! [SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ! [SV342: list_P559422087at_nat] :
( ( isShor1936442771pacity @ SV188 @ SV322 @ SV342 )
= ( ^ [SY861: nat] :
~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV342 @ SY861 )
| ( ( size_s1990949619at_nat @ SV342 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SY861 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1001]) ).
thf(1102,plain,
! [SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV188 @ SV322 )
= ( ^ [SY847: list_P559422087at_nat,SY848: nat] :
~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SY847 @ SY848 )
| ( ( size_s1990949619at_nat @ SY847 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SY848 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1001]) ).
thf(1103,plain,
! [SV277: nat,SV189: nat,SV88: nat] :
( ( ( ord_less_nat @ SV88 @ SV189 )
= $false )
| ( ( ord_less_nat @ SV88 @ ( plus_plus_nat @ SV277 @ SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1104,plain,
! [SV323: nat,SV278: nat,SV190: nat,SV89: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV89 @ SV190 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV278 @ SV323 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV89 @ SV278 ) @ ( plus_plus_nat @ SV190 @ SV323 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1105,plain,
! [SV279: nat,SV191: nat,SV90: nat] :
( ( ( ord_less_eq_nat @ SV90 @ SV191 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV279 @ SV90 ) @ ( plus_plus_nat @ SV279 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1106,plain,
! [SV280: nat,SV192: nat,SV91: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV91 @ SV192 ) @ ( plus_plus_nat @ SV280 @ SV192 ) )
= $false )
| ( ( ord_less_nat @ SV91 @ SV280 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1005]) ).
thf(1107,plain,
! [SV193: nat,SV92: nat] :
( ( ( ( connected_capacity @ c @ SV92 @ SV193 )
| ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) )
= $false )
| ( ( ~ ( ~ ( connected_capacity @ c @ SV92 @ SV193 )
| ~ ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1108,plain,
! [SV281: nat,SV194: nat,SV93: nat] :
( ( ( ord_less_eq_nat @ SV93 @ SV194 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV93 @ SV281 ) @ ( plus_plus_nat @ SV194 @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1109,plain,
! [SV282: nat,SV195: nat,SV94: nat] :
( ( ( ~ ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) ) )
= $true )
| ( ( ~ ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1110,plain,
! [SV324: nat,SV283: nat,SV196: nat,SV95: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV95 @ SV196 )
| ~ ( ord_less_eq_nat @ SV283 @ SV324 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV95 @ SV283 ) @ ( plus_plus_nat @ SV196 @ SV324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1111,plain,
! [SV96: nat,SV197: nat] :
( ( ( ! [SY738: nat] :
( SV197
!= ( plus_plus_nat @ SV96 @ SY738 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV96 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1112,plain,
! [SV325: nat,SV284: nat,SV198: nat,SV97: nat] :
( ( ( ~ ~ ( ( SV97 != SV198 )
| ( SV284 != SV325 ) ) )
= $true )
| ( ( ( plus_plus_nat @ SV97 @ SV284 )
= ( plus_plus_nat @ SV198 @ SV325 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1113,plain,
! [SV285: nat,SV199: nat,SV98: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV98 @ SV199 ) @ ( plus_plus_nat @ SV285 @ SV199 ) )
= $false )
| ( ( ord_less_eq_nat @ SV98 @ SV285 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1114,plain,
! [SV326: nat,SV286: nat,SV200: nat,SV99: nat] :
( ( ( ~ ~ ( ( SV99 != SV200 )
| ~ ( ord_less_eq_nat @ SV286 @ SV326 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV99 @ SV286 ) @ ( plus_plus_nat @ SV200 @ SV326 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1115,plain,
! [SV327: nat,SV287: nat,SV201: nat,SV100: product_prod_nat_nat > capacity] :
( ( ( ~ ( connected_capacity @ SV100 @ SV201 @ SV287 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV327 @ ( min_dist_capacity @ SV100 @ SV201 @ SV287 ) )
| ~ ! [SY849: nat] :
~ ~ ( ~ ( connected_capacity @ SV100 @ SV201 @ SY849 )
| ( ( min_dist_capacity @ SV100 @ SV201 @ SY849 )
!= SV327 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1116,plain,
! [SV328: nat,SV288: nat,SV202: nat,SV101: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV101 @ SV202 )
| ( SV288 != SV328 ) ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV101 @ SV288 ) @ ( plus_plus_nat @ SV202 @ SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1117,plain,
! [SV329: nat,SV289: nat,SV203: nat,SV102: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV102 @ SV203 @ SV289 @ SV329 ) )
= $true )
| ( ( ~ ! [SY850: nat] :
( ~ ( dist_capacity @ SV102 @ SV203 @ SY850 @ SV329 )
| ( ord_less_eq_nat @ SV289 @ SY850 ) )
| ( ( min_dist_capacity @ SV102 @ SV203 @ SV329 )
= SV289 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1118,plain,
! [SV330: nat,SV290: nat,SV204: nat,SV103: nat] :
( ( ( ~ ( ord_less_nat @ SV103 @ SV204 ) )
= $true )
| ( ( ( ( plus_plus_nat @ SV290 @ SV204 )
!= ( plus_plus_nat @ SV103 @ SV330 ) )
| ( ord_less_nat @ SV290 @ SV330 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1018]) ).
thf(1119,plain,
! [SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ! [SV343: list_P559422087at_nat] :
( ( isShor1936442771pacity @ SV205 @ SV331 @ SV343 )
= ( ^ [SY862: nat] :
~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV343 @ SY862 )
| ~ ! [SY863: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY863 @ SY862 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV343 ) @ ( size_s1990949619at_nat @ SY863 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1019]) ).
thf(1120,plain,
! [SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV205 @ SV331 )
= ( ^ [SY851: list_P559422087at_nat,SY852: nat] :
~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SY851 @ SY852 )
| ~ ! [SY853: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY853 @ SY852 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SY851 ) @ ( size_s1990949619at_nat @ SY853 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1019]) ).
thf(1121,plain,
! [SV206: nat,SV105: nat,SV1: nat] :
( ( ( ( ( plus_plus_nat @ SV1 @ SV105 )
= ( plus_plus_nat @ SV1 @ SV206 ) )
| ( SV105 = SV206 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV1 @ SV105 )
!= ( plus_plus_nat @ SV1 @ SV206 ) )
| ( SV105 != SV206 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1122,plain,
! [SV207: nat,SV106: nat,SV2: nat] :
( ( ( ( ( plus_plus_nat @ SV2 @ SV106 )
= ( plus_plus_nat @ SV207 @ SV106 ) )
| ( SV2 = SV207 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV2 @ SV106 )
!= ( plus_plus_nat @ SV207 @ SV106 ) )
| ( SV2 != SV207 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1123,plain,
! [SV7: nat] :
( ( ( ( one_one_nat != SV7 )
| ( SV7 != one_one_nat ) )
= $false )
| ( ( one_one_nat = SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1124,plain,
! [SV7: nat] :
( ( ( ( one_one_nat != SV7 )
| ( SV7 != one_one_nat ) )
= $false )
| ( ( SV7 = one_one_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1125,plain,
! [SV212: nat,SV111: nat,SV8: nat] :
( ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
| ( ord_less_eq_nat @ SV111 @ SV212 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
| ~ ( ord_less_eq_nat @ SV111 @ SV212 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1126,plain,
! [SV213: nat,SV112: nat,SV9: nat] :
( ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
| ( ord_less_eq_nat @ SV9 @ SV213 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
| ~ ( ord_less_eq_nat @ SV9 @ SV213 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1127,plain,
! [SV344: nat,SV293: nat,SV113: product_prod_nat_nat > capacity] :
( ( ( min_dist_capacity @ SV113 @ SV293 @ SV344 )
= ( min_dist_capacity @ SV113 @ SV293 @ SV344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1128,plain,
! [SV215: nat,SV114: nat,SV12: nat] :
( ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
| ( ord_less_eq_nat @ SV114 @ SV215 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
| ~ ( ord_less_eq_nat @ SV114 @ SV215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1129,plain,
! [SV216: nat,SV115: nat,SV13: nat] :
( ( ( ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
| ( ord_less_nat @ SV13 @ SV216 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
| ~ ( ord_less_nat @ SV13 @ SV216 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1130,plain,
! [SV217: nat,SV116: nat,SV14: nat] :
( ( ( ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
| ( ord_less_nat @ SV116 @ SV217 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
| ~ ( ord_less_nat @ SV116 @ SV217 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1131,plain,
! [SV218: nat,SV117: nat,SV15: nat] :
( ( ( ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
| ( ord_less_nat @ SV117 @ SV218 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
| ~ ( ord_less_nat @ SV117 @ SV218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1132,plain,
! [SV294: nat,SV122: nat] :
( ( ( ~ ( ( ord_less_nat @ SV122 @ SV294 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV122 @ SV294 )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1133,plain,
! [SV123: nat,SV22: nat] :
( ( ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
= $false )
| ( ( ~ ( ~ ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
| ( SV22 != SV123 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1034]) ).
thf(1134,plain,
! [SV123: nat,SV22: nat] :
( ( ( SV22 = SV123 )
= $false )
| ( ( ~ ( ~ ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
| ( SV22 != SV123 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1034]) ).
thf(1135,plain,
! [SV124: nat,SV23: nat] :
( ( ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
= $false )
| ( ( ~ ( ~ ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
| ( SV23 != SV124 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1035]) ).
thf(1136,plain,
! [SV124: nat,SV23: nat] :
( ( ( SV23 = SV124 )
= $false )
| ( ( ~ ( ~ ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
| ( SV23 != SV124 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1035]) ).
thf(1137,plain,
! [SV125: list_P559422087at_nat,SV24: nat] :
( ( ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
= $false )
| ( ( ~ ( ~ ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
| ( SV125 != nil_Pr1308055047at_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1138,plain,
! [SV24: nat,SV125: list_P559422087at_nat] :
( ( ( SV125 = nil_Pr1308055047at_nat )
= $false )
| ( ( ~ ( ~ ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
| ( SV125 != nil_Pr1308055047at_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1139,plain,
! [SV295: nat,SV220: nat,SV126: nat,SV25: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV25 @ SV126 )
| ~ ( ord_less_nat @ SV220 @ SV295 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV25 @ SV220 ) @ ( plus_plus_nat @ SV126 @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1140,plain,
! [SV127: nat,SV221: nat,SV26: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV26 @ SV221 )
| ~ ( ord_less_eq_nat @ SV127 @ SV221 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV26 @ SV127 ) @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1141,plain,
! [SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV128 @ SV296 @ SV345 )
= ( ^ [SY864: nat] :
~ ! [SY865: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY865 @ SY864 )
| ( ( size_s1990949619at_nat @ SY865 )
!= SV345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1142,plain,
! [SV29: nat > nat,SV130: nat,SV224: nat] :
( ( ( ! [SY866: nat] :
( ~ ( ord_less_nat @ ( sK1_SY395 @ SV224 @ SV130 @ SV29 ) @ SY866 )
| ( ord_less_nat @ ( SV29 @ ( sK1_SY395 @ SV224 @ SV130 @ SV29 ) ) @ ( SV29 @ SY866 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( SV29 @ SV130 ) @ SV224 ) @ ( SV29 @ ( plus_plus_nat @ SV130 @ SV224 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1042]) ).
thf(1143,plain,
! [SV297: nat,SV225: nat,SV131: nat,SV30: nat] :
( ( ( ord_less_eq_nat @ SV30 @ SV131 )
= $false )
| ( ( ~ ( ord_less_nat @ SV225 @ SV297 )
| ( ord_less_nat @ ( plus_plus_nat @ SV30 @ SV225 ) @ ( plus_plus_nat @ SV131 @ SV297 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1144,plain,
! [SV298: nat,SV226: nat,SV132: nat,SV31: nat] :
( ( ( ord_less_nat @ SV31 @ SV132 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV226 @ SV298 )
| ( ord_less_nat @ ( plus_plus_nat @ SV31 @ SV226 ) @ ( plus_plus_nat @ SV132 @ SV298 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1145,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
| ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1146,plain,
! [SV299: nat,SV228: nat,SV134: nat,SV33: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV33 @ SV134 )
| ~ ( ord_less_nat @ SV228 @ SV299 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV33 @ SV228 ) @ ( plus_plus_nat @ SV134 @ SV299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1147,plain,
! [SV300: nat,SV229: nat,SV135: nat,SV34: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV34 @ SV135 @ SV229 @ SV300 )
= $false )
| ( ( ord_less_eq_nat @ ( min_dist_capacity @ SV34 @ SV135 @ SV300 ) @ SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1148,plain,
! [SV136: nat,SV230: nat,SV35: nat] :
( ( ( ~ ! [SY768: nat] :
( ~ ( dist_capacity @ c @ SV35 @ SY768 @ SV230 )
| ( ord_less_eq_nat @ SV136 @ SY768 ) ) )
= $true )
| ( ( ( min_dist_capacity @ c @ SV35 @ SV230 )
= SV136 )
= $true )
| ( ( dist_capacity @ c @ SV35 @ SV136 @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1149,plain,
! [SV334: nat,SV301: nat,SV231: nat,SV137: nat,SV36: nat] :
( ( ( ~ ( dist_capacity @ c @ SV36 @ SV137 @ SV231 ) )
= $true )
| ( ( ~ ( dist_capacity @ c @ SV231 @ SV301 @ SV334 )
| ( ( min_dist_capacity @ c @ SV36 @ SV334 )
!= ( plus_plus_nat @ SV137 @ SV301 ) )
| ( ( min_dist_capacity @ c @ SV231 @ SV334 )
= SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1150,plain,
! [SV302: nat,SV232: nat,SV138: nat,SV37: nat] :
( ( ( SV37
= ( plus_plus_nat @ SV138 @ SV232 ) )
= $false )
| ( ( ( plus_plus_nat @ SV302 @ SV37 )
= ( plus_plus_nat @ SV138 @ ( plus_plus_nat @ SV302 @ SV232 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1151,plain,
! [SV303: nat,SV233: nat,SV139: nat,SV38: nat] :
( ( ( ~ ( ( SV38 != SV139 )
| ~ ( ord_less_nat @ SV233 @ SV303 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV38 @ SV233 ) @ ( plus_plus_nat @ SV139 @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1152,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
| ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1153,plain,
! [SV335: nat,SV304: nat,SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ( ~ ( connected_capacity @ SV40 @ SV141 @ SV235 ) )
= $true )
| ( ( ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
!= SV304 )
| ~ ( ord_less_nat @ SV335 @ SV304 )
| ~ ! [SY856: nat] :
~ ~ ( ~ ( connected_capacity @ SV40 @ SV141 @ SY856 )
| ( ( min_dist_capacity @ SV40 @ SV141 @ SY856 )
!= SV335 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1154,plain,
! [SV346: nat,SV336: nat,SV305: nat,SV236: nat,SV142: nat,SV41: product_prod_nat_nat > capacity] :
( ( ~ ( dist_capacity @ SV41 @ SV142 @ SV236 @ SV305 )
| ~ ( dist_capacity @ SV41 @ SV305 @ SV336 @ SV346 )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SV346 )
!= ( plus_plus_nat @ SV236 @ SV336 ) )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SV305 )
= SV236 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1155,plain,
! [SV347: nat,SV337: nat,SV306: nat,SV238: nat,SV144: nat,SV43: product_prod_nat_nat > capacity] :
( ( ~ ( dist_capacity @ SV43 @ SV144 @ SV238 @ SV306 )
| ~ ( dist_capacity @ SV43 @ SV306 @ SV337 @ SV347 )
| ( dist_capacity @ SV43 @ SV144 @ ( plus_plus_nat @ SV238 @ SV337 ) @ SV347 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1156,plain,
! [SV153: nat,SV52: nat,SV246: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV246 @ ( min_dist_capacity @ c @ SV52 @ SV153 ) ) )
= $true )
| ( ( ~ ! [SY782: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV52 @ SY782 )
| ( ( min_dist_capacity @ c @ SV52 @ SY782 )
!= SV246 ) ) )
= $true )
| ( ( connected_capacity @ c @ SV52 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1157,plain,
! [SV307: nat,SV155: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV155 @ SV307 )
| ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV155 @ SV307 )
| ~ ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1158,plain,
! [SV348: nat,SV338: nat,SV308: nat,SV249: nat,SV156: nat,SV55: product_prod_nat_nat > capacity] :
( ( ~ ( dist_capacity @ SV55 @ SV156 @ SV249 @ SV308 )
| ~ ( dist_capacity @ SV55 @ SV308 @ SV338 @ SV348 )
| ( ( min_dist_capacity @ SV55 @ SV156 @ SV348 )
!= ( plus_plus_nat @ SV249 @ SV338 ) )
| ( ( min_dist_capacity @ SV55 @ SV308 @ SV348 )
= SV338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1159,plain,
! [SV309: nat,SV250: nat,SV157: nat,SV56: nat] :
( ( ( SV56
= ( plus_plus_nat @ SV157 @ SV250 ) )
= $false )
| ( ( ( plus_plus_nat @ SV56 @ SV309 )
= ( plus_plus_nat @ SV157 @ ( plus_plus_nat @ SV250 @ SV309 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1160,plain,
! [SV251: nat > $o,SV158: nat,SV57: nat] :
( ( ( ~ ! [SY788: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY788 @ SV158 )
| ~ ! [SY676: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY676 @ SV158 )
| ( ord_less_eq_nat @ SY788 @ SY676 ) )
| ( SV251 @ SY788 ) ) )
= $true )
| ( ( SV251 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) )
= $true )
| ( ( connected_capacity @ c @ SV57 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1161,plain,
! [SV160: list_P559422087at_nat,SV59: list_P559422087at_nat] :
( ( ( SV59 = SV160 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV59 )
= ( size_s1990949619at_nat @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1162,plain,
! [SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 )
= ( ^ [SY867: nat] :
~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SY867 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SY867 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1163,plain,
! [SV311: nat,SV254: nat,SV162: nat,SV61: nat] :
( ( ( ord_less_eq_nat @ SV61 @ SV162 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV254 @ SV311 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV61 @ SV254 ) @ ( plus_plus_nat @ SV162 @ SV311 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1164,plain,
! [SV312: nat > $o,SV255: nat,SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ( connected_capacity @ SV62 @ SV163 @ SV255 )
= $false )
| ( ( ~ ! [SY841: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY841 @ SV255 )
| ~ ! [SY795: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY795 @ SV255 )
| ( ord_less_eq_nat @ SY841 @ SY795 ) )
| ( SV312 @ SY841 ) )
| ( SV312 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1165,plain,
! [SV65: nat,SV166: nat] :
( ( ( SV166
!= ( plus_plus_nat @ SV65 @ ( sK2_SY688 @ SV65 @ SV166 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV65 @ SV166 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1078]) ).
thf(1166,plain,
! [SV313: nat,SV257: nat,SV167: nat,SV66: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV66 @ SV167 )
| ( SV257 != SV313 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV66 @ SV257 ) @ ( plus_plus_nat @ SV167 @ SV313 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1167,plain,
! [SV314: nat,SV260: nat,SV170: nat,SV69: nat] :
( ( ( ord_less_nat @ SV69 @ SV170 )
= $false )
| ( ( ~ ( ord_less_nat @ SV260 @ SV314 )
| ( ord_less_nat @ ( plus_plus_nat @ SV69 @ SV260 ) @ ( plus_plus_nat @ SV170 @ SV314 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1168,plain,
! [SV315: nat,SV262: nat,SV172: nat,SV71: nat] :
( ( ( ord_less_nat @ SV71 @ SV172 )
= $false )
| ( ( ~ ( ord_less_nat @ SV262 @ SV315 )
| ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV262 ) @ ( plus_plus_nat @ SV172 @ SV315 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1169,plain,
! [SV173: list_P559422087at_nat,SV263: nat,SV72: nat] :
( ( ( ! [SY799: list_P559422087at_nat] :
~ ( isSimp1359852763pacity @ c @ SV72 @ SY799 @ SV263 ) )
= $false )
| ( ( isPath_capacity @ c @ SV72 @ SV173 @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1170,plain,
! [SV340: nat,SV316: nat,SV265: nat,SV175: nat,SV74: nat] :
( ( ( ~ ( dist_capacity @ c @ SV74 @ SV175 @ SV265 ) )
= $true )
| ( ( ~ ( dist_capacity @ c @ SV265 @ SV316 @ SV340 )
| ( ( min_dist_capacity @ c @ SV74 @ SV340 )
!= ( plus_plus_nat @ SV175 @ SV316 ) )
| ( ( min_dist_capacity @ c @ SV74 @ SV265 )
= SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1171,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1172,plain,
! [SV180: nat,SV79: nat] :
( ( ( connected_capacity @ c @ SV79 @ SV180 )
= $false )
| ( ( ~ ( ~ ( connected_capacity @ c @ SV79 @ SV180 )
| ~ ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1092]) ).
thf(1173,plain,
! [SV180: nat,SV79: nat] :
( ( ( ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) )
= $false )
| ( ( ~ ( ~ ( connected_capacity @ c @ SV79 @ SV180 )
| ~ ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1092]) ).
thf(1174,plain,
! [SV317: nat,SV270: list_P559422087at_nat,SV181: nat,SV80: product_prod_nat_nat > capacity] :
( ( ( isPath_capacity @ SV80 @ SV181 @ SV270 @ SV317 )
= $false )
| ( ( dist_capacity @ SV80 @ SV181 @ ( size_s1990949619at_nat @ SV270 ) @ SV317 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1175,plain,
! [SV318: nat,SV182: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV182 @ SV318 )
| ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV182 @ SV318 )
| ~ ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1094]) ).
thf(1176,plain,
! [SV319: nat,SV272: nat,SV183: nat,SV82: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV82 @ SV183 )
| ~ ( ord_less_eq_nat @ SV272 @ SV319 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV82 @ SV272 ) @ ( plus_plus_nat @ SV183 @ SV319 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1177,plain,
! [SV320: nat,SV273: nat,SV184: nat,SV83: nat] :
( ( ( connected_capacity @ c @ SV83 @ SV184 )
= $false )
| ( ( ( ( min_dist_capacity @ c @ SV83 @ SV184 )
!= SV273 )
| ~ ( ord_less_nat @ SV320 @ SV273 )
| ~ ! [SY845: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV83 @ SY845 )
| ( ( min_dist_capacity @ c @ SV83 @ SY845 )
!= SV320 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1178,plain,
! [SV341: nat,SV321: nat,SV274: nat,SV185: nat,SV84: nat] :
( ( ( ~ ( dist_capacity @ c @ SV84 @ SV185 @ SV274 ) )
= $true )
| ( ( ~ ( dist_capacity @ c @ SV274 @ SV321 @ SV341 )
| ( dist_capacity @ c @ SV84 @ ( plus_plus_nat @ SV185 @ SV321 ) @ SV341 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1179,plain,
! [SV186: nat,SV85: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV85 @ ( sK3_SY722 @ SV186 @ SV85 ) @ SV186 ) )
= $false )
| ( ( connected_capacity @ c @ SV85 @ SV186 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1099]) ).
thf(1180,plain,
! [SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 )
= ( ^ [SY868: nat] :
~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SY868 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SY868 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1181,plain,
! [SV323: nat,SV278: nat,SV190: nat,SV89: nat] :
( ( ( ord_less_eq_nat @ SV89 @ SV190 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV278 @ SV323 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV89 @ SV278 ) @ ( plus_plus_nat @ SV190 @ SV323 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1182,plain,
! [SV193: nat,SV92: nat] :
( ( ( connected_capacity @ c @ SV92 @ SV193 )
= $false )
| ( ( ~ ( ~ ( connected_capacity @ c @ SV92 @ SV193 )
| ~ ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1183,plain,
! [SV193: nat,SV92: nat] :
( ( ( ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) )
= $false )
| ( ( ~ ( ~ ( connected_capacity @ c @ SV92 @ SV193 )
| ~ ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1184,plain,
! [SV282: nat,SV195: nat,SV94: nat] :
( ( ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1185,plain,
! [SV324: nat,SV283: nat,SV196: nat,SV95: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV95 @ SV196 )
| ~ ( ord_less_eq_nat @ SV283 @ SV324 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV95 @ SV283 ) @ ( plus_plus_nat @ SV196 @ SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1186,plain,
! [SV96: nat,SV197: nat] :
( ( ( SV197
!= ( plus_plus_nat @ SV96 @ ( sK4_SY738 @ SV96 @ SV197 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV96 @ SV197 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1111]) ).
thf(1187,plain,
! [SV325: nat,SV284: nat,SV198: nat,SV97: nat] :
( ( ( ~ ( ( SV97 != SV198 )
| ( SV284 != SV325 ) ) )
= $false )
| ( ( ( plus_plus_nat @ SV97 @ SV284 )
= ( plus_plus_nat @ SV198 @ SV325 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1188,plain,
! [SV326: nat,SV286: nat,SV200: nat,SV99: nat] :
( ( ( ~ ( ( SV99 != SV200 )
| ~ ( ord_less_eq_nat @ SV286 @ SV326 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV99 @ SV286 ) @ ( plus_plus_nat @ SV200 @ SV326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1189,plain,
! [SV327: nat,SV287: nat,SV201: nat,SV100: product_prod_nat_nat > capacity] :
( ( ( connected_capacity @ SV100 @ SV201 @ SV287 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV327 @ ( min_dist_capacity @ SV100 @ SV201 @ SV287 ) )
| ~ ! [SY849: nat] :
~ ~ ( ~ ( connected_capacity @ SV100 @ SV201 @ SY849 )
| ( ( min_dist_capacity @ SV100 @ SV201 @ SY849 )
!= SV327 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1190,plain,
! [SV328: nat,SV288: nat,SV202: nat,SV101: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV101 @ SV202 )
| ( SV288 != SV328 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV101 @ SV288 ) @ ( plus_plus_nat @ SV202 @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1191,plain,
! [SV329: nat,SV289: nat,SV203: nat,SV102: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV102 @ SV203 @ SV289 @ SV329 )
= $false )
| ( ( ~ ! [SY850: nat] :
( ~ ( dist_capacity @ SV102 @ SV203 @ SY850 @ SV329 )
| ( ord_less_eq_nat @ SV289 @ SY850 ) )
| ( ( min_dist_capacity @ SV102 @ SV203 @ SV329 )
= SV289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1192,plain,
! [SV330: nat,SV290: nat,SV204: nat,SV103: nat] :
( ( ( ord_less_nat @ SV103 @ SV204 )
= $false )
| ( ( ( ( plus_plus_nat @ SV290 @ SV204 )
!= ( plus_plus_nat @ SV103 @ SV330 ) )
| ( ord_less_nat @ SV290 @ SV330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1193,plain,
! [SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 )
= ( ^ [SY869: nat] :
~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SY869 )
| ~ ! [SY870: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY870 @ SY869 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY870 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1194,plain,
! [SV206: nat,SV105: nat,SV1: nat] :
( ( ( ( plus_plus_nat @ SV1 @ SV105 )
= ( plus_plus_nat @ SV1 @ SV206 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV1 @ SV105 )
!= ( plus_plus_nat @ SV1 @ SV206 ) )
| ( SV105 != SV206 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1121]) ).
thf(1195,plain,
! [SV1: nat,SV206: nat,SV105: nat] :
( ( ( SV105 = SV206 )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV1 @ SV105 )
!= ( plus_plus_nat @ SV1 @ SV206 ) )
| ( SV105 != SV206 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1121]) ).
thf(1196,plain,
! [SV207: nat,SV106: nat,SV2: nat] :
( ( ( ( plus_plus_nat @ SV2 @ SV106 )
= ( plus_plus_nat @ SV207 @ SV106 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV2 @ SV106 )
!= ( plus_plus_nat @ SV207 @ SV106 ) )
| ( SV2 != SV207 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1197,plain,
! [SV106: nat,SV207: nat,SV2: nat] :
( ( ( SV2 = SV207 )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV2 @ SV106 )
!= ( plus_plus_nat @ SV207 @ SV106 ) )
| ( SV2 != SV207 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1198,plain,
! [SV7: nat] :
( ( ( one_one_nat != SV7 )
= $false )
| ( ( one_one_nat = SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1123]) ).
thf(1199,plain,
! [SV7: nat] :
( ( ( SV7 != one_one_nat )
= $false )
| ( ( one_one_nat = SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1123]) ).
thf(1200,plain,
! [SV7: nat] :
( ( ( one_one_nat != SV7 )
= $false )
| ( ( SV7 = one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1124]) ).
thf(1201,plain,
! [SV7: nat] :
( ( ( SV7 != one_one_nat )
= $false )
| ( ( SV7 = one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1124]) ).
thf(1202,plain,
! [SV212: nat,SV111: nat,SV8: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
| ~ ( ord_less_eq_nat @ SV111 @ SV212 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1203,plain,
! [SV8: nat,SV212: nat,SV111: nat] :
( ( ( ord_less_eq_nat @ SV111 @ SV212 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
| ~ ( ord_less_eq_nat @ SV111 @ SV212 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1204,plain,
! [SV213: nat,SV112: nat,SV9: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
| ~ ( ord_less_eq_nat @ SV9 @ SV213 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1126]) ).
thf(1205,plain,
! [SV112: nat,SV213: nat,SV9: nat] :
( ( ( ord_less_eq_nat @ SV9 @ SV213 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
| ~ ( ord_less_eq_nat @ SV9 @ SV213 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1126]) ).
thf(1206,plain,
! [SV215: nat,SV114: nat,SV12: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
| ~ ( ord_less_eq_nat @ SV114 @ SV215 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1207,plain,
! [SV12: nat,SV215: nat,SV114: nat] :
( ( ( ord_less_eq_nat @ SV114 @ SV215 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
| ~ ( ord_less_eq_nat @ SV114 @ SV215 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1208,plain,
! [SV216: nat,SV115: nat,SV13: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
| ~ ( ord_less_nat @ SV13 @ SV216 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1129]) ).
thf(1209,plain,
! [SV115: nat,SV216: nat,SV13: nat] :
( ( ( ord_less_nat @ SV13 @ SV216 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
| ~ ( ord_less_nat @ SV13 @ SV216 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1129]) ).
thf(1210,plain,
! [SV217: nat,SV116: nat,SV14: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
| ~ ( ord_less_nat @ SV116 @ SV217 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1211,plain,
! [SV14: nat,SV217: nat,SV116: nat] :
( ( ( ord_less_nat @ SV116 @ SV217 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
| ~ ( ord_less_nat @ SV116 @ SV217 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1212,plain,
! [SV218: nat,SV117: nat,SV15: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
| ~ ( ord_less_nat @ SV117 @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1213,plain,
! [SV15: nat,SV218: nat,SV117: nat] :
( ( ( ord_less_nat @ SV117 @ SV218 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
| ~ ( ord_less_nat @ SV117 @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1214,plain,
! [SV294: nat,SV122: nat] :
( ( ( ( ord_less_nat @ SV122 @ SV294 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV122 @ SV294 )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1215,plain,
! [SV123: nat,SV22: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
| ( SV22 != SV123 ) )
= $false )
| ( ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1216,plain,
! [SV123: nat,SV22: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
| ( SV22 != SV123 ) )
= $false )
| ( ( SV22 = SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1217,plain,
! [SV124: nat,SV23: nat] :
( ( ( ~ ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
| ( SV23 != SV124 ) )
= $false )
| ( ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1218,plain,
! [SV124: nat,SV23: nat] :
( ( ( ~ ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
| ( SV23 != SV124 ) )
= $false )
| ( ( SV23 = SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1219,plain,
! [SV125: list_P559422087at_nat,SV24: nat] :
( ( ( ~ ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
| ( SV125 != nil_Pr1308055047at_nat ) )
= $false )
| ( ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1220,plain,
! [SV125: list_P559422087at_nat,SV24: nat] :
( ( ( ~ ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
| ( SV125 != nil_Pr1308055047at_nat ) )
= $false )
| ( ( SV125 = nil_Pr1308055047at_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1221,plain,
! [SV295: nat,SV220: nat,SV126: nat,SV25: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV25 @ SV126 )
| ~ ( ord_less_nat @ SV220 @ SV295 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV25 @ SV220 ) @ ( plus_plus_nat @ SV126 @ SV295 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1139]) ).
thf(1222,plain,
! [SV127: nat,SV221: nat,SV26: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV26 @ SV221 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV26 @ SV127 ) @ SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1140]) ).
thf(1223,plain,
! [SV26: nat,SV221: nat,SV127: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV127 @ SV221 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV26 @ SV127 ) @ SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1140]) ).
thf(1224,plain,
! [SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ! [SV352: nat] :
( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV352 )
= ( ~ ! [SY871: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY871 @ SV352 )
| ( ( size_s1990949619at_nat @ SY871 )
!= SV345 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1141]) ).
thf(1225,plain,
! [SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV128 @ SV296 @ SV345 )
= ( ^ [SY864: nat] :
~ ! [SY865: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY865 @ SY864 )
| ( ( size_s1990949619at_nat @ SY865 )
!= SV345 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1141]) ).
thf(1226,plain,
! [SV29: nat > nat,SV130: nat,SV224: nat] :
( ( ( ~ ( ord_less_nat @ ( sK1_SY395 @ SV224 @ SV130 @ SV29 ) @ ( sK5_SY866 @ SV29 @ SV130 @ SV224 ) )
| ( ord_less_nat @ ( SV29 @ ( sK1_SY395 @ SV224 @ SV130 @ SV29 ) ) @ ( SV29 @ ( sK5_SY866 @ SV29 @ SV130 @ SV224 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( SV29 @ SV130 ) @ SV224 ) @ ( SV29 @ ( plus_plus_nat @ SV130 @ SV224 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1142]) ).
thf(1227,plain,
! [SV131: nat,SV30: nat,SV297: nat,SV225: nat] :
( ( ( ~ ( ord_less_nat @ SV225 @ SV297 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV30 @ SV225 ) @ ( plus_plus_nat @ SV131 @ SV297 ) )
= $true )
| ( ( ord_less_eq_nat @ SV30 @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1228,plain,
! [SV132: nat,SV31: nat,SV298: nat,SV226: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV226 @ SV298 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV31 @ SV226 ) @ ( plus_plus_nat @ SV132 @ SV298 ) )
= $true )
| ( ( ord_less_nat @ SV31 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1229,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1145]) ).
thf(1230,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1145]) ).
thf(1231,plain,
! [SV299: nat,SV228: nat,SV134: nat,SV33: nat] :
( ( ( ~ ( ord_less_nat @ SV33 @ SV134 )
| ~ ( ord_less_nat @ SV228 @ SV299 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV33 @ SV228 ) @ ( plus_plus_nat @ SV134 @ SV299 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1146]) ).
thf(1232,plain,
! [SV136: nat,SV230: nat,SV35: nat] :
( ( ( ! [SY768: nat] :
( ~ ( dist_capacity @ c @ SV35 @ SY768 @ SV230 )
| ( ord_less_eq_nat @ SV136 @ SY768 ) ) )
= $false )
| ( ( ( min_dist_capacity @ c @ SV35 @ SV230 )
= SV136 )
= $true )
| ( ( dist_capacity @ c @ SV35 @ SV136 @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1233,plain,
! [SV334: nat,SV301: nat,SV231: nat,SV137: nat,SV36: nat] :
( ( ( dist_capacity @ c @ SV36 @ SV137 @ SV231 )
= $false )
| ( ( ~ ( dist_capacity @ c @ SV231 @ SV301 @ SV334 )
| ( ( min_dist_capacity @ c @ SV36 @ SV334 )
!= ( plus_plus_nat @ SV137 @ SV301 ) )
| ( ( min_dist_capacity @ c @ SV231 @ SV334 )
= SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1234,plain,
! [SV303: nat,SV233: nat,SV139: nat,SV38: nat] :
( ( ( ( SV38 != SV139 )
| ~ ( ord_less_nat @ SV233 @ SV303 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV38 @ SV233 ) @ ( plus_plus_nat @ SV139 @ SV303 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1235,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1152]) ).
thf(1236,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1152]) ).
thf(1237,plain,
! [SV335: nat,SV304: nat,SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ( connected_capacity @ SV40 @ SV141 @ SV235 )
= $false )
| ( ( ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
!= SV304 )
| ~ ( ord_less_nat @ SV335 @ SV304 )
| ~ ! [SY856: nat] :
~ ~ ( ~ ( connected_capacity @ SV40 @ SV141 @ SY856 )
| ( ( min_dist_capacity @ SV40 @ SV141 @ SY856 )
!= SV335 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1238,plain,
! [SV346: nat,SV336: nat,SV305: nat,SV236: nat,SV142: nat,SV41: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV41 @ SV142 @ SV236 @ SV305 ) )
= $true )
| ( ( ~ ( dist_capacity @ SV41 @ SV305 @ SV336 @ SV346 )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SV346 )
!= ( plus_plus_nat @ SV236 @ SV336 ) )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SV305 )
= SV236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1239,plain,
! [SV347: nat,SV337: nat,SV306: nat,SV238: nat,SV144: nat,SV43: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV43 @ SV144 @ SV238 @ SV306 ) )
= $true )
| ( ( ~ ( dist_capacity @ SV43 @ SV306 @ SV337 @ SV347 )
| ( dist_capacity @ SV43 @ SV144 @ ( plus_plus_nat @ SV238 @ SV337 ) @ SV347 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1240,plain,
! [SV153: nat,SV52: nat,SV246: nat] :
( ( ( ord_less_eq_nat @ SV246 @ ( min_dist_capacity @ c @ SV52 @ SV153 ) )
= $false )
| ( ( ~ ! [SY782: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV52 @ SY782 )
| ( ( min_dist_capacity @ c @ SV52 @ SY782 )
!= SV246 ) ) )
= $true )
| ( ( connected_capacity @ c @ SV52 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1241,plain,
! [SV307: nat,SV155: nat] :
( ( ( ( ord_less_eq_nat @ SV155 @ SV307 )
| ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV155 @ SV307 )
| ~ ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1242,plain,
! [SV348: nat,SV338: nat,SV308: nat,SV249: nat,SV156: nat,SV55: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV55 @ SV156 @ SV249 @ SV308 ) )
= $true )
| ( ( ~ ( dist_capacity @ SV55 @ SV308 @ SV338 @ SV348 )
| ( ( min_dist_capacity @ SV55 @ SV156 @ SV348 )
!= ( plus_plus_nat @ SV249 @ SV338 ) )
| ( ( min_dist_capacity @ SV55 @ SV308 @ SV348 )
= SV338 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1243,plain,
! [SV251: nat > $o,SV158: nat,SV57: nat] :
( ( ( ! [SY788: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY788 @ SV158 )
| ~ ! [SY676: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY676 @ SV158 )
| ( ord_less_eq_nat @ SY788 @ SY676 ) )
| ( SV251 @ SY788 ) ) )
= $false )
| ( ( SV251 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) )
= $true )
| ( ( connected_capacity @ c @ SV57 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1244,plain,
! [SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ! [SV353: nat] :
( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV353 )
= ( ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV353 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV353 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1162]) ).
thf(1245,plain,
! [SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 )
= ( ^ [SY867: nat] :
~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SY867 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SY867 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1162]) ).
thf(1246,plain,
! [SV162: nat,SV61: nat,SV311: nat,SV254: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV254 @ SV311 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV61 @ SV254 ) @ ( plus_plus_nat @ SV162 @ SV311 ) )
= $true )
| ( ( ord_less_eq_nat @ SV61 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1163]) ).
thf(1247,plain,
! [SV312: nat > $o,SV255: nat,SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ( ~ ! [SY841: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY841 @ SV255 )
| ~ ! [SY795: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY795 @ SV255 )
| ( ord_less_eq_nat @ SY841 @ SY795 ) )
| ( SV312 @ SY841 ) ) )
= $true )
| ( ( SV312 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) )
= $true )
| ( ( connected_capacity @ SV62 @ SV163 @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1164]) ).
thf(1248,plain,
! [SV65: nat,SV166: nat] :
( ( ( SV166
= ( plus_plus_nat @ SV65 @ ( sK2_SY688 @ SV65 @ SV166 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV65 @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1165]) ).
thf(1249,plain,
! [SV313: nat,SV257: nat,SV167: nat,SV66: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV66 @ SV167 )
| ( SV257 != SV313 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV66 @ SV257 ) @ ( plus_plus_nat @ SV167 @ SV313 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1166]) ).
thf(1250,plain,
! [SV170: nat,SV69: nat,SV314: nat,SV260: nat] :
( ( ( ~ ( ord_less_nat @ SV260 @ SV314 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV69 @ SV260 ) @ ( plus_plus_nat @ SV170 @ SV314 ) )
= $true )
| ( ( ord_less_nat @ SV69 @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1251,plain,
! [SV172: nat,SV71: nat,SV315: nat,SV262: nat] :
( ( ( ~ ( ord_less_nat @ SV262 @ SV315 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV262 ) @ ( plus_plus_nat @ SV172 @ SV315 ) )
= $true )
| ( ( ord_less_nat @ SV71 @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1252,plain,
! [SV263: nat,SV173: list_P559422087at_nat,SV72: nat] :
( ( ( ~ ( isSimp1359852763pacity @ c @ SV72 @ ( sK6_SY799 @ SV173 @ SV263 @ SV72 ) @ SV263 ) )
= $false )
| ( ( isPath_capacity @ c @ SV72 @ SV173 @ SV263 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1169]) ).
thf(1253,plain,
! [SV340: nat,SV316: nat,SV265: nat,SV175: nat,SV74: nat] :
( ( ( dist_capacity @ c @ SV74 @ SV175 @ SV265 )
= $false )
| ( ( ~ ( dist_capacity @ c @ SV265 @ SV316 @ SV340 )
| ( ( min_dist_capacity @ c @ SV74 @ SV340 )
!= ( plus_plus_nat @ SV175 @ SV316 ) )
| ( ( min_dist_capacity @ c @ SV74 @ SV265 )
= SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1254,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1255,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1256,plain,
! [SV180: nat,SV79: nat] :
( ( ( ~ ( connected_capacity @ c @ SV79 @ SV180 )
| ~ ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) )
= $false )
| ( ( connected_capacity @ c @ SV79 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1257,plain,
! [SV180: nat,SV79: nat] :
( ( ( ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) )
= $true )
| ( ( ~ ( ~ ( connected_capacity @ c @ SV79 @ SV180 )
| ~ ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1173]) ).
thf(1258,plain,
! [SV318: nat,SV182: nat] :
( ( ( ( ord_less_eq_nat @ SV182 @ SV318 )
| ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV182 @ SV318 )
| ~ ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1259,plain,
! [SV319: nat,SV272: nat,SV183: nat,SV82: nat] :
( ( ( ~ ( ord_less_nat @ SV82 @ SV183 )
| ~ ( ord_less_eq_nat @ SV272 @ SV319 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV82 @ SV272 ) @ ( plus_plus_nat @ SV183 @ SV319 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1260,plain,
! [SV320: nat,SV273: nat,SV184: nat,SV83: nat] :
( ( ( ( min_dist_capacity @ c @ SV83 @ SV184 )
!= SV273 )
= $true )
| ( ( ~ ( ord_less_nat @ SV320 @ SV273 )
| ~ ! [SY845: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV83 @ SY845 )
| ( ( min_dist_capacity @ c @ SV83 @ SY845 )
!= SV320 ) ) )
= $true )
| ( ( connected_capacity @ c @ SV83 @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1261,plain,
! [SV341: nat,SV321: nat,SV274: nat,SV185: nat,SV84: nat] :
( ( ( dist_capacity @ c @ SV84 @ SV185 @ SV274 )
= $false )
| ( ( ~ ( dist_capacity @ c @ SV274 @ SV321 @ SV341 )
| ( dist_capacity @ c @ SV84 @ ( plus_plus_nat @ SV185 @ SV321 ) @ SV341 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1262,plain,
! [SV186: nat,SV85: nat] :
( ( ( isShor1936442771pacity @ c @ SV85 @ ( sK3_SY722 @ SV186 @ SV85 ) @ SV186 )
= $true )
| ( ( connected_capacity @ c @ SV85 @ SV186 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1179]) ).
thf(1263,plain,
! [SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ! [SV354: nat] :
( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV354 )
= ( ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV354 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV354 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1180]) ).
thf(1264,plain,
! [SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 )
= ( ^ [SY868: nat] :
~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SY868 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SY868 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1180]) ).
thf(1265,plain,
! [SV190: nat,SV89: nat,SV323: nat,SV278: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV278 @ SV323 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV89 @ SV278 ) @ ( plus_plus_nat @ SV190 @ SV323 ) )
= $true )
| ( ( ord_less_eq_nat @ SV89 @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1266,plain,
! [SV193: nat,SV92: nat] :
( ( ( ~ ( connected_capacity @ c @ SV92 @ SV193 )
| ~ ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) )
= $false )
| ( ( connected_capacity @ c @ SV92 @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1267,plain,
! [SV193: nat,SV92: nat] :
( ( ( ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ( connected_capacity @ c @ SV92 @ SV193 )
| ~ ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1183]) ).
thf(1268,plain,
! [SV282: nat,SV195: nat,SV94: nat] :
( ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $false )
| ( ( ~ ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1184]) ).
thf(1269,plain,
! [SV195: nat,SV282: nat,SV94: nat] :
( ( ( ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1184]) ).
thf(1270,plain,
! [SV324: nat,SV283: nat,SV196: nat,SV95: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV95 @ SV196 )
| ~ ( ord_less_eq_nat @ SV283 @ SV324 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV95 @ SV283 ) @ ( plus_plus_nat @ SV196 @ SV324 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1185]) ).
thf(1271,plain,
! [SV96: nat,SV197: nat] :
( ( ( SV197
= ( plus_plus_nat @ SV96 @ ( sK4_SY738 @ SV96 @ SV197 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV96 @ SV197 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1186]) ).
thf(1272,plain,
! [SV325: nat,SV284: nat,SV198: nat,SV97: nat] :
( ( ( ( SV97 != SV198 )
| ( SV284 != SV325 ) )
= $true )
| ( ( ( plus_plus_nat @ SV97 @ SV284 )
= ( plus_plus_nat @ SV198 @ SV325 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1273,plain,
! [SV326: nat,SV286: nat,SV200: nat,SV99: nat] :
( ( ( ( SV99 != SV200 )
| ~ ( ord_less_eq_nat @ SV286 @ SV326 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV99 @ SV286 ) @ ( plus_plus_nat @ SV200 @ SV326 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1188]) ).
thf(1274,plain,
! [SV287: nat,SV201: nat,SV100: product_prod_nat_nat > capacity,SV327: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV327 @ ( min_dist_capacity @ SV100 @ SV201 @ SV287 ) ) )
= $true )
| ( ( ~ ! [SY849: nat] :
~ ~ ( ~ ( connected_capacity @ SV100 @ SV201 @ SY849 )
| ( ( min_dist_capacity @ SV100 @ SV201 @ SY849 )
!= SV327 ) ) )
= $true )
| ( ( connected_capacity @ SV100 @ SV201 @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1275,plain,
! [SV328: nat,SV288: nat,SV202: nat,SV101: nat] :
( ( ( ~ ( ord_less_nat @ SV101 @ SV202 )
| ( SV288 != SV328 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV101 @ SV288 ) @ ( plus_plus_nat @ SV202 @ SV328 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1276,plain,
! [SV289: nat,SV329: nat,SV203: nat,SV102: product_prod_nat_nat > capacity] :
( ( ( ~ ! [SY850: nat] :
( ~ ( dist_capacity @ SV102 @ SV203 @ SY850 @ SV329 )
| ( ord_less_eq_nat @ SV289 @ SY850 ) ) )
= $true )
| ( ( ( min_dist_capacity @ SV102 @ SV203 @ SV329 )
= SV289 )
= $true )
| ( ( dist_capacity @ SV102 @ SV203 @ SV289 @ SV329 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1277,plain,
! [SV330: nat,SV103: nat,SV204: nat,SV290: nat] :
( ( ( ( plus_plus_nat @ SV290 @ SV204 )
!= ( plus_plus_nat @ SV103 @ SV330 ) )
= $true )
| ( ( ord_less_nat @ SV290 @ SV330 )
= $true )
| ( ( ord_less_nat @ SV103 @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1278,plain,
! [SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ! [SV355: nat] :
( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV355 )
= ( ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV355 )
| ~ ! [SY872: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY872 @ SV355 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY872 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1193]) ).
thf(1279,plain,
! [SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 )
= ( ^ [SY869: nat] :
~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SY869 )
| ~ ! [SY870: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY870 @ SY869 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY870 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1193]) ).
thf(1280,plain,
! [SV206: nat,SV105: nat,SV1: nat] :
( ( ( ( ( plus_plus_nat @ SV1 @ SV105 )
!= ( plus_plus_nat @ SV1 @ SV206 ) )
| ( SV105 != SV206 ) )
= $false )
| ( ( ( plus_plus_nat @ SV1 @ SV105 )
= ( plus_plus_nat @ SV1 @ SV206 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1281,plain,
! [SV206: nat,SV105: nat,SV1: nat] :
( ( ( ( ( plus_plus_nat @ SV1 @ SV105 )
!= ( plus_plus_nat @ SV1 @ SV206 ) )
| ( SV105 != SV206 ) )
= $false )
| ( ( SV105 = SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1282,plain,
! [SV207: nat,SV106: nat,SV2: nat] :
( ( ( ( ( plus_plus_nat @ SV2 @ SV106 )
!= ( plus_plus_nat @ SV207 @ SV106 ) )
| ( SV2 != SV207 ) )
= $false )
| ( ( ( plus_plus_nat @ SV2 @ SV106 )
= ( plus_plus_nat @ SV207 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1283,plain,
! [SV207: nat,SV106: nat,SV2: nat] :
( ( ( ( ( plus_plus_nat @ SV2 @ SV106 )
!= ( plus_plus_nat @ SV207 @ SV106 ) )
| ( SV2 != SV207 ) )
= $false )
| ( ( SV2 = SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1284,plain,
! [SV7: nat] :
( ( ( one_one_nat = SV7 )
= $true )
| ( ( one_one_nat = SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1198]) ).
thf(1285,plain,
! [SV7: nat] :
( ( ( SV7 = one_one_nat )
= $true )
| ( ( one_one_nat = SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1199]) ).
thf(1286,plain,
! [SV7: nat] :
( ( ( one_one_nat = SV7 )
= $true )
| ( ( SV7 = one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1287,plain,
! [SV7: nat] :
( ( ( SV7 = one_one_nat )
= $true )
| ( ( SV7 = one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1201]) ).
thf(1288,plain,
! [SV212: nat,SV111: nat,SV8: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
| ~ ( ord_less_eq_nat @ SV111 @ SV212 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1289,plain,
! [SV212: nat,SV111: nat,SV8: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
| ~ ( ord_less_eq_nat @ SV111 @ SV212 ) )
= $false )
| ( ( ord_less_eq_nat @ SV111 @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1290,plain,
! [SV213: nat,SV112: nat,SV9: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
| ~ ( ord_less_eq_nat @ SV9 @ SV213 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1291,plain,
! [SV213: nat,SV112: nat,SV9: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
| ~ ( ord_less_eq_nat @ SV9 @ SV213 ) )
= $false )
| ( ( ord_less_eq_nat @ SV9 @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1292,plain,
! [SV215: nat,SV114: nat,SV12: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
| ~ ( ord_less_eq_nat @ SV114 @ SV215 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1293,plain,
! [SV215: nat,SV114: nat,SV12: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
| ~ ( ord_less_eq_nat @ SV114 @ SV215 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV215 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1294,plain,
! [SV216: nat,SV115: nat,SV13: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
| ~ ( ord_less_nat @ SV13 @ SV216 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1295,plain,
! [SV216: nat,SV115: nat,SV13: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
| ~ ( ord_less_nat @ SV13 @ SV216 ) )
= $false )
| ( ( ord_less_nat @ SV13 @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1296,plain,
! [SV217: nat,SV116: nat,SV14: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
| ~ ( ord_less_nat @ SV116 @ SV217 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1297,plain,
! [SV217: nat,SV116: nat,SV14: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
| ~ ( ord_less_nat @ SV116 @ SV217 ) )
= $false )
| ( ( ord_less_nat @ SV116 @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1298,plain,
! [SV218: nat,SV117: nat,SV15: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
| ~ ( ord_less_nat @ SV117 @ SV218 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1299,plain,
! [SV218: nat,SV117: nat,SV15: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
| ~ ( ord_less_nat @ SV117 @ SV218 ) )
= $false )
| ( ( ord_less_nat @ SV117 @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1300,plain,
! [SV294: nat,SV122: nat] :
( ( ( ord_less_nat @ SV122 @ SV294 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV122 @ SV294 )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1214]) ).
thf(1301,plain,
! [SV294: nat,SV122: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV122 @ SV294 )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1214]) ).
thf(1302,plain,
! [SV123: nat,SV22: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 ) )
= $false )
| ( ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1215]) ).
thf(1303,plain,
! [SV123: nat,SV22: nat] :
( ( ( SV22 != SV123 )
= $false )
| ( ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1215]) ).
thf(1304,plain,
! [SV123: nat,SV22: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 ) )
= $false )
| ( ( SV22 = SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1216]) ).
thf(1305,plain,
! [SV123: nat,SV22: nat] :
( ( ( SV22 != SV123 )
= $false )
| ( ( SV22 = SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1216]) ).
thf(1306,plain,
! [SV124: nat,SV23: nat] :
( ( ( ~ ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 ) )
= $false )
| ( ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1217]) ).
thf(1307,plain,
! [SV124: nat,SV23: nat] :
( ( ( SV23 != SV124 )
= $false )
| ( ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1217]) ).
thf(1308,plain,
! [SV124: nat,SV23: nat] :
( ( ( ~ ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 ) )
= $false )
| ( ( SV23 = SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1218]) ).
thf(1309,plain,
! [SV124: nat,SV23: nat] :
( ( ( SV23 != SV124 )
= $false )
| ( ( SV23 = SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1218]) ).
thf(1310,plain,
! [SV125: list_P559422087at_nat,SV24: nat] :
( ( ( ~ ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 ) )
= $false )
| ( ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1219]) ).
thf(1311,plain,
! [SV24: nat,SV125: list_P559422087at_nat] :
( ( ( SV125 != nil_Pr1308055047at_nat )
= $false )
| ( ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1219]) ).
thf(1312,plain,
! [SV125: list_P559422087at_nat,SV24: nat] :
( ( ( ~ ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 ) )
= $false )
| ( ( SV125 = nil_Pr1308055047at_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1220]) ).
thf(1313,plain,
! [SV125: list_P559422087at_nat] :
( ( ( SV125 != nil_Pr1308055047at_nat )
= $false )
| ( ( SV125 = nil_Pr1308055047at_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1220]) ).
thf(1314,plain,
! [SV295: nat,SV220: nat,SV126: nat,SV25: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV25 @ SV126 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV220 @ SV295 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV25 @ SV220 ) @ ( plus_plus_nat @ SV126 @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1315,plain,
! [SV127: nat,SV221: nat,SV26: nat] :
( ( ( ord_less_eq_nat @ SV26 @ SV221 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV26 @ SV127 ) @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1222]) ).
thf(1316,plain,
! [SV26: nat,SV221: nat,SV127: nat] :
( ( ( ord_less_eq_nat @ SV127 @ SV221 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV26 @ SV127 ) @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1223]) ).
thf(1317,plain,
! [SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= ( ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1318,plain,
! [SV29: nat > nat,SV130: nat,SV224: nat] :
( ( ( ~ ( ord_less_nat @ ( sK1_SY395 @ SV224 @ SV130 @ SV29 ) @ ( sK5_SY866 @ SV29 @ SV130 @ SV224 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( SV29 @ SV130 ) @ SV224 ) @ ( SV29 @ ( plus_plus_nat @ SV130 @ SV224 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1319,plain,
! [SV130: nat,SV224: nat,SV29: nat > nat] :
( ( ( ord_less_nat @ ( SV29 @ ( sK1_SY395 @ SV224 @ SV130 @ SV29 ) ) @ ( SV29 @ ( sK5_SY866 @ SV29 @ SV130 @ SV224 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( SV29 @ SV130 ) @ SV224 ) @ ( SV29 @ ( plus_plus_nat @ SV130 @ SV224 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1320,plain,
! [SV131: nat,SV30: nat,SV297: nat,SV225: nat] :
( ( ( ord_less_nat @ SV225 @ SV297 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV30 @ SV225 ) @ ( plus_plus_nat @ SV131 @ SV297 ) )
= $true )
| ( ( ord_less_eq_nat @ SV30 @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1321,plain,
! [SV132: nat,SV31: nat,SV298: nat,SV226: nat] :
( ( ( ord_less_eq_nat @ SV226 @ SV298 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV31 @ SV226 ) @ ( plus_plus_nat @ SV132 @ SV298 ) )
= $true )
| ( ( ord_less_nat @ SV31 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1322,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1323,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1230]) ).
thf(1324,plain,
! [SV299: nat,SV228: nat,SV134: nat,SV33: nat] :
( ( ( ~ ( ord_less_nat @ SV33 @ SV134 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV228 @ SV299 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV33 @ SV228 ) @ ( plus_plus_nat @ SV134 @ SV299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1231]) ).
thf(1325,plain,
! [SV230: nat,SV136: nat,SV35: nat] :
( ( ( ~ ( dist_capacity @ c @ SV35 @ ( sK7_SY768 @ SV136 @ SV230 @ SV35 ) @ SV230 )
| ( ord_less_eq_nat @ SV136 @ ( sK7_SY768 @ SV136 @ SV230 @ SV35 ) ) )
= $false )
| ( ( ( min_dist_capacity @ c @ SV35 @ SV230 )
= SV136 )
= $true )
| ( ( dist_capacity @ c @ SV35 @ SV136 @ SV230 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1232]) ).
thf(1326,plain,
! [SV137: nat,SV36: nat,SV334: nat,SV301: nat,SV231: nat] :
( ( ( ~ ( dist_capacity @ c @ SV231 @ SV301 @ SV334 ) )
= $true )
| ( ( ( ( min_dist_capacity @ c @ SV36 @ SV334 )
!= ( plus_plus_nat @ SV137 @ SV301 ) )
| ( ( min_dist_capacity @ c @ SV231 @ SV334 )
= SV301 ) )
= $true )
| ( ( dist_capacity @ c @ SV36 @ SV137 @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1327,plain,
! [SV303: nat,SV233: nat,SV139: nat,SV38: nat] :
( ( ( SV38 != SV139 )
= $true )
| ( ( ~ ( ord_less_nat @ SV233 @ SV303 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV38 @ SV233 ) @ ( plus_plus_nat @ SV139 @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1328,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1329,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1236]) ).
thf(1330,plain,
! [SV335: nat,SV304: nat,SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
!= SV304 )
= $true )
| ( ( ~ ( ord_less_nat @ SV335 @ SV304 )
| ~ ! [SY856: nat] :
~ ~ ( ~ ( connected_capacity @ SV40 @ SV141 @ SY856 )
| ( ( min_dist_capacity @ SV40 @ SV141 @ SY856 )
!= SV335 ) ) )
= $true )
| ( ( connected_capacity @ SV40 @ SV141 @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1331,plain,
! [SV346: nat,SV336: nat,SV305: nat,SV236: nat,SV142: nat,SV41: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV41 @ SV142 @ SV236 @ SV305 )
= $false )
| ( ( ~ ( dist_capacity @ SV41 @ SV305 @ SV336 @ SV346 )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SV346 )
!= ( plus_plus_nat @ SV236 @ SV336 ) )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SV305 )
= SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1332,plain,
! [SV347: nat,SV337: nat,SV306: nat,SV238: nat,SV144: nat,SV43: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV43 @ SV144 @ SV238 @ SV306 )
= $false )
| ( ( ~ ( dist_capacity @ SV43 @ SV306 @ SV337 @ SV347 )
| ( dist_capacity @ SV43 @ SV144 @ ( plus_plus_nat @ SV238 @ SV337 ) @ SV347 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1333,plain,
! [SV153: nat,SV246: nat,SV52: nat] :
( ( ( ! [SY782: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV52 @ SY782 )
| ( ( min_dist_capacity @ c @ SV52 @ SY782 )
!= SV246 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV246 @ ( min_dist_capacity @ c @ SV52 @ SV153 ) )
= $false )
| ( ( connected_capacity @ c @ SV52 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1334,plain,
! [SV307: nat,SV155: nat] :
( ( ( ord_less_eq_nat @ SV155 @ SV307 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV155 @ SV307 )
| ~ ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1335,plain,
! [SV155: nat,SV307: nat] :
( ( ( ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV155 @ SV307 )
| ~ ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1336,plain,
! [SV348: nat,SV338: nat,SV308: nat,SV249: nat,SV156: nat,SV55: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV55 @ SV156 @ SV249 @ SV308 )
= $false )
| ( ( ~ ( dist_capacity @ SV55 @ SV308 @ SV338 @ SV348 )
| ( ( min_dist_capacity @ SV55 @ SV156 @ SV348 )
!= ( plus_plus_nat @ SV249 @ SV338 ) )
| ( ( min_dist_capacity @ SV55 @ SV308 @ SV348 )
= SV338 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1337,plain,
! [SV158: nat,SV251: nat > $o,SV57: nat] :
( ( ( ~ ( dist_capacity @ c @ SV57 @ ( sK8_SY788 @ SV251 @ SV158 @ SV57 ) @ SV158 )
| ~ ! [SY874: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY874 @ SV158 )
| ( ord_less_eq_nat @ ( sK8_SY788 @ SV251 @ SV158 @ SV57 ) @ SY874 ) )
| ( SV251 @ ( sK8_SY788 @ SV251 @ SV158 @ SV57 ) ) )
= $false )
| ( ( SV251 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) )
= $true )
| ( ( connected_capacity @ c @ SV57 @ SV158 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1243]) ).
thf(1338,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= ( ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1339,plain,
! [SV162: nat,SV61: nat,SV311: nat,SV254: nat] :
( ( ( ord_less_eq_nat @ SV254 @ SV311 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV61 @ SV254 ) @ ( plus_plus_nat @ SV162 @ SV311 ) )
= $true )
| ( ( ord_less_eq_nat @ SV61 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1340,plain,
! [SV312: nat > $o,SV255: nat,SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ( ! [SY841: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY841 @ SV255 )
| ~ ! [SY795: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY795 @ SV255 )
| ( ord_less_eq_nat @ SY841 @ SY795 ) )
| ( SV312 @ SY841 ) ) )
= $false )
| ( ( SV312 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) )
= $true )
| ( ( connected_capacity @ SV62 @ SV163 @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1341,plain,
! [SV313: nat,SV257: nat,SV167: nat,SV66: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV66 @ SV167 ) )
= $true )
| ( ( SV257 != SV313 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV66 @ SV257 ) @ ( plus_plus_nat @ SV167 @ SV313 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1342,plain,
! [SV170: nat,SV69: nat,SV314: nat,SV260: nat] :
( ( ( ord_less_nat @ SV260 @ SV314 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV69 @ SV260 ) @ ( plus_plus_nat @ SV170 @ SV314 ) )
= $true )
| ( ( ord_less_nat @ SV69 @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1343,plain,
! [SV172: nat,SV71: nat,SV315: nat,SV262: nat] :
( ( ( ord_less_nat @ SV262 @ SV315 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV262 ) @ ( plus_plus_nat @ SV172 @ SV315 ) )
= $true )
| ( ( ord_less_nat @ SV71 @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1344,plain,
! [SV263: nat,SV173: list_P559422087at_nat,SV72: nat] :
( ( ( isSimp1359852763pacity @ c @ SV72 @ ( sK6_SY799 @ SV173 @ SV263 @ SV72 ) @ SV263 )
= $true )
| ( ( isPath_capacity @ c @ SV72 @ SV173 @ SV263 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1252]) ).
thf(1345,plain,
! [SV175: nat,SV74: nat,SV340: nat,SV316: nat,SV265: nat] :
( ( ( ~ ( dist_capacity @ c @ SV265 @ SV316 @ SV340 ) )
= $true )
| ( ( ( ( min_dist_capacity @ c @ SV74 @ SV340 )
!= ( plus_plus_nat @ SV175 @ SV316 ) )
| ( ( min_dist_capacity @ c @ SV74 @ SV265 )
= SV175 ) )
= $true )
| ( ( dist_capacity @ c @ SV74 @ SV175 @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1253]) ).
thf(1346,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1347,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1255]) ).
thf(1348,plain,
! [SV180: nat,SV79: nat] :
( ( ( ~ ( connected_capacity @ c @ SV79 @ SV180 ) )
= $false )
| ( ( connected_capacity @ c @ SV79 @ SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1256]) ).
thf(1349,plain,
! [SV180: nat,SV79: nat] :
( ( ( ~ ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) )
= $false )
| ( ( connected_capacity @ c @ SV79 @ SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1256]) ).
thf(1350,plain,
! [SV180: nat,SV358: list_P559422087at_nat,SV79: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV79 @ SV358 @ SV180 ) )
= $true )
| ( ( ~ ( ~ ( connected_capacity @ c @ SV79 @ SV180 )
| ~ ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1351,plain,
! [SV318: nat,SV182: nat] :
( ( ( ord_less_eq_nat @ SV182 @ SV318 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV182 @ SV318 )
| ~ ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1258]) ).
thf(1352,plain,
! [SV182: nat,SV318: nat] :
( ( ( ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV182 @ SV318 )
| ~ ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1258]) ).
thf(1353,plain,
! [SV319: nat,SV272: nat,SV183: nat,SV82: nat] :
( ( ( ~ ( ord_less_nat @ SV82 @ SV183 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV272 @ SV319 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV82 @ SV272 ) @ ( plus_plus_nat @ SV183 @ SV319 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1259]) ).
thf(1354,plain,
! [SV320: nat,SV273: nat,SV184: nat,SV83: nat] :
( ( ( ( min_dist_capacity @ c @ SV83 @ SV184 )
= SV273 )
= $false )
| ( ( ~ ( ord_less_nat @ SV320 @ SV273 )
| ~ ! [SY845: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV83 @ SY845 )
| ( ( min_dist_capacity @ c @ SV83 @ SY845 )
!= SV320 ) ) )
= $true )
| ( ( connected_capacity @ c @ SV83 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1355,plain,
! [SV185: nat,SV84: nat,SV341: nat,SV321: nat,SV274: nat] :
( ( ( ~ ( dist_capacity @ c @ SV274 @ SV321 @ SV341 ) )
= $true )
| ( ( dist_capacity @ c @ SV84 @ ( plus_plus_nat @ SV185 @ SV321 ) @ SV341 )
= $true )
| ( ( dist_capacity @ c @ SV84 @ SV185 @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1261]) ).
thf(1356,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
= ( ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1357,plain,
! [SV190: nat,SV89: nat,SV323: nat,SV278: nat] :
( ( ( ord_less_eq_nat @ SV278 @ SV323 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV89 @ SV278 ) @ ( plus_plus_nat @ SV190 @ SV323 ) )
= $true )
| ( ( ord_less_eq_nat @ SV89 @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1358,plain,
! [SV193: nat,SV92: nat] :
( ( ( ~ ( connected_capacity @ c @ SV92 @ SV193 ) )
= $false )
| ( ( connected_capacity @ c @ SV92 @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1266]) ).
thf(1359,plain,
! [SV193: nat,SV92: nat] :
( ( ( ~ ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) )
= $false )
| ( ( connected_capacity @ c @ SV92 @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1266]) ).
thf(1360,plain,
! [SV193: nat,SV360: nat,SV92: nat] :
( ( ( ~ ( dist_capacity @ c @ SV92 @ SV360 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ( connected_capacity @ c @ SV92 @ SV193 )
| ~ ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1361,plain,
! [SV282: nat,SV195: nat,SV94: nat] :
( ( ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) )
= $false )
| ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1362,plain,
! [SV195: nat,SV282: nat,SV94: nat] :
( ( ( ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1269]) ).
thf(1363,plain,
! [SV324: nat,SV283: nat,SV196: nat,SV95: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV95 @ SV196 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV283 @ SV324 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV95 @ SV283 ) @ ( plus_plus_nat @ SV196 @ SV324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1270]) ).
thf(1364,plain,
! [SV325: nat,SV284: nat,SV198: nat,SV97: nat] :
( ( ( SV97 != SV198 )
= $true )
| ( ( SV284 != SV325 )
= $true )
| ( ( ( plus_plus_nat @ SV97 @ SV284 )
= ( plus_plus_nat @ SV198 @ SV325 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1365,plain,
! [SV326: nat,SV286: nat,SV200: nat,SV99: nat] :
( ( ( SV99 != SV200 )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV286 @ SV326 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV99 @ SV286 ) @ ( plus_plus_nat @ SV200 @ SV326 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1366,plain,
! [SV287: nat,SV201: nat,SV100: product_prod_nat_nat > capacity,SV327: nat] :
( ( ( ord_less_eq_nat @ SV327 @ ( min_dist_capacity @ SV100 @ SV201 @ SV287 ) )
= $false )
| ( ( ~ ! [SY849: nat] :
~ ~ ( ~ ( connected_capacity @ SV100 @ SV201 @ SY849 )
| ( ( min_dist_capacity @ SV100 @ SV201 @ SY849 )
!= SV327 ) ) )
= $true )
| ( ( connected_capacity @ SV100 @ SV201 @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1367,plain,
! [SV328: nat,SV288: nat,SV202: nat,SV101: nat] :
( ( ( ~ ( ord_less_nat @ SV101 @ SV202 ) )
= $true )
| ( ( SV288 != SV328 )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV101 @ SV288 ) @ ( plus_plus_nat @ SV202 @ SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1368,plain,
! [SV289: nat,SV329: nat,SV203: nat,SV102: product_prod_nat_nat > capacity] :
( ( ( ! [SY850: nat] :
( ~ ( dist_capacity @ SV102 @ SV203 @ SY850 @ SV329 )
| ( ord_less_eq_nat @ SV289 @ SY850 ) ) )
= $false )
| ( ( ( min_dist_capacity @ SV102 @ SV203 @ SV329 )
= SV289 )
= $true )
| ( ( dist_capacity @ SV102 @ SV203 @ SV289 @ SV329 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1369,plain,
! [SV330: nat,SV103: nat,SV204: nat,SV290: nat] :
( ( ( ( plus_plus_nat @ SV290 @ SV204 )
= ( plus_plus_nat @ SV103 @ SV330 ) )
= $false )
| ( ( ord_less_nat @ SV290 @ SV330 )
= $true )
| ( ( ord_less_nat @ SV103 @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1370,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= ( ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1371,plain,
! [SV206: nat,SV105: nat,SV1: nat] :
( ( ( ( plus_plus_nat @ SV1 @ SV105 )
!= ( plus_plus_nat @ SV1 @ SV206 ) )
= $false )
| ( ( ( plus_plus_nat @ SV1 @ SV105 )
= ( plus_plus_nat @ SV1 @ SV206 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1280]) ).
thf(1372,plain,
! [SV1: nat,SV206: nat,SV105: nat] :
( ( ( SV105 != SV206 )
= $false )
| ( ( ( plus_plus_nat @ SV1 @ SV105 )
= ( plus_plus_nat @ SV1 @ SV206 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1280]) ).
thf(1373,plain,
! [SV206: nat,SV105: nat,SV1: nat] :
( ( ( ( plus_plus_nat @ SV1 @ SV105 )
!= ( plus_plus_nat @ SV1 @ SV206 ) )
= $false )
| ( ( SV105 = SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1281]) ).
thf(1374,plain,
! [SV206: nat,SV105: nat] :
( ( ( SV105 != SV206 )
= $false )
| ( ( SV105 = SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1281]) ).
thf(1375,plain,
! [SV207: nat,SV106: nat,SV2: nat] :
( ( ( ( plus_plus_nat @ SV2 @ SV106 )
!= ( plus_plus_nat @ SV207 @ SV106 ) )
= $false )
| ( ( ( plus_plus_nat @ SV2 @ SV106 )
= ( plus_plus_nat @ SV207 @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1282]) ).
thf(1376,plain,
! [SV106: nat,SV207: nat,SV2: nat] :
( ( ( SV2 != SV207 )
= $false )
| ( ( ( plus_plus_nat @ SV2 @ SV106 )
= ( plus_plus_nat @ SV207 @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1282]) ).
thf(1377,plain,
! [SV207: nat,SV106: nat,SV2: nat] :
( ( ( ( plus_plus_nat @ SV2 @ SV106 )
!= ( plus_plus_nat @ SV207 @ SV106 ) )
= $false )
| ( ( SV2 = SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1378,plain,
! [SV207: nat,SV2: nat] :
( ( ( SV2 != SV207 )
= $false )
| ( ( SV2 = SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1379,plain,
! [SV212: nat,SV111: nat,SV8: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1288]) ).
thf(1380,plain,
! [SV8: nat,SV212: nat,SV111: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV111 @ SV212 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1288]) ).
thf(1381,plain,
! [SV212: nat,SV111: nat,SV8: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV111 @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1289]) ).
thf(1382,plain,
! [SV212: nat,SV111: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV111 @ SV212 ) )
= $false )
| ( ( ord_less_eq_nat @ SV111 @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1289]) ).
thf(1383,plain,
! [SV213: nat,SV112: nat,SV9: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1384,plain,
! [SV112: nat,SV213: nat,SV9: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV9 @ SV213 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1385,plain,
! [SV213: nat,SV112: nat,SV9: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV9 @ SV213 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1386,plain,
! [SV213: nat,SV9: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV9 @ SV213 ) )
= $false )
| ( ( ord_less_eq_nat @ SV9 @ SV213 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1387,plain,
! [SV215: nat,SV114: nat,SV12: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1292]) ).
thf(1388,plain,
! [SV12: nat,SV215: nat,SV114: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV114 @ SV215 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1292]) ).
thf(1389,plain,
! [SV215: nat,SV114: nat,SV12: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV215 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1390,plain,
! [SV215: nat,SV114: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV114 @ SV215 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV215 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1391,plain,
! [SV216: nat,SV115: nat,SV13: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1294]) ).
thf(1392,plain,
! [SV115: nat,SV216: nat,SV13: nat] :
( ( ( ~ ( ord_less_nat @ SV13 @ SV216 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1294]) ).
thf(1393,plain,
! [SV216: nat,SV115: nat,SV13: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) ) )
= $false )
| ( ( ord_less_nat @ SV13 @ SV216 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1394,plain,
! [SV216: nat,SV13: nat] :
( ( ( ~ ( ord_less_nat @ SV13 @ SV216 ) )
= $false )
| ( ( ord_less_nat @ SV13 @ SV216 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1395,plain,
! [SV217: nat,SV116: nat,SV14: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1296]) ).
thf(1396,plain,
! [SV14: nat,SV217: nat,SV116: nat] :
( ( ( ~ ( ord_less_nat @ SV116 @ SV217 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1296]) ).
thf(1397,plain,
! [SV217: nat,SV116: nat,SV14: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) ) )
= $false )
| ( ( ord_less_nat @ SV116 @ SV217 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1297]) ).
thf(1398,plain,
! [SV217: nat,SV116: nat] :
( ( ( ~ ( ord_less_nat @ SV116 @ SV217 ) )
= $false )
| ( ( ord_less_nat @ SV116 @ SV217 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1297]) ).
thf(1399,plain,
! [SV218: nat,SV117: nat,SV15: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1298]) ).
thf(1400,plain,
! [SV15: nat,SV218: nat,SV117: nat] :
( ( ( ~ ( ord_less_nat @ SV117 @ SV218 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1298]) ).
thf(1401,plain,
! [SV218: nat,SV117: nat,SV15: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) ) )
= $false )
| ( ( ord_less_nat @ SV117 @ SV218 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1299]) ).
thf(1402,plain,
! [SV218: nat,SV117: nat] :
( ( ( ~ ( ord_less_nat @ SV117 @ SV218 ) )
= $false )
| ( ( ord_less_nat @ SV117 @ SV218 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1299]) ).
thf(1403,plain,
! [SV294: nat,SV122: nat] :
( ( ( ~ ( ord_less_nat @ SV122 @ SV294 )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 ) )
= $false )
| ( ( ord_less_nat @ SV122 @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1404,plain,
! [SV294: nat,SV122: nat] :
( ( ( ~ ( ord_less_nat @ SV122 @ SV294 )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1405,plain,
! [SV123: nat,SV22: nat] :
( ( ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
= $true )
| ( ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1302]) ).
thf(1406,plain,
! [SV123: nat,SV22: nat] :
( ( ( SV22 = SV123 )
= $true )
| ( ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1303]) ).
thf(1407,plain,
! [SV123: nat,SV22: nat] :
( ( ( isPath_capacity @ c @ SV22 @ nil_Pr1308055047at_nat @ SV123 )
= $true )
| ( ( SV22 = SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1304]) ).
thf(1408,plain,
! [SV123: nat,SV22: nat] :
( ( ( SV22 = SV123 )
= $true )
| ( ( SV22 = SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1305]) ).
thf(1409,plain,
! [SV124: nat,SV23: nat] :
( ( ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
= $true )
| ( ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1306]) ).
thf(1410,plain,
! [SV124: nat,SV23: nat] :
( ( ( SV23 = SV124 )
= $true )
| ( ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1307]) ).
thf(1411,plain,
! [SV124: nat,SV23: nat] :
( ( ( isSimp1359852763pacity @ c @ SV23 @ nil_Pr1308055047at_nat @ SV124 )
= $true )
| ( ( SV23 = SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1308]) ).
thf(1412,plain,
! [SV124: nat,SV23: nat] :
( ( ( SV23 = SV124 )
= $true )
| ( ( SV23 = SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1309]) ).
thf(1413,plain,
! [SV125: list_P559422087at_nat,SV24: nat] :
( ( ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
= $true )
| ( ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1310]) ).
thf(1414,plain,
! [SV24: nat,SV125: list_P559422087at_nat] :
( ( ( SV125 = nil_Pr1308055047at_nat )
= $true )
| ( ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1311]) ).
thf(1415,plain,
! [SV125: list_P559422087at_nat,SV24: nat] :
( ( ( isSimp1359852763pacity @ c @ SV24 @ SV125 @ SV24 )
= $true )
| ( ( SV125 = nil_Pr1308055047at_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1312]) ).
thf(1416,plain,
! [SV125: list_P559422087at_nat] :
( ( ( SV125 = nil_Pr1308055047at_nat )
= $true )
| ( ( SV125 = nil_Pr1308055047at_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1417,plain,
! [SV295: nat,SV220: nat,SV126: nat,SV25: nat] :
( ( ( ord_less_eq_nat @ SV25 @ SV126 )
= $false )
| ( ( ~ ( ord_less_nat @ SV220 @ SV295 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV25 @ SV220 ) @ ( plus_plus_nat @ SV126 @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1418,plain,
! [SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ~ ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) )
| ~ ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1317]) ).
thf(1419,plain,
! [SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= ( ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1317]) ).
thf(1420,plain,
! [SV29: nat > nat,SV130: nat,SV224: nat] :
( ( ( ord_less_nat @ ( sK1_SY395 @ SV224 @ SV130 @ SV29 ) @ ( sK5_SY866 @ SV29 @ SV130 @ SV224 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( SV29 @ SV130 ) @ SV224 ) @ ( SV29 @ ( plus_plus_nat @ SV130 @ SV224 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1318]) ).
thf(1421,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1322]) ).
thf(1422,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1322]) ).
thf(1423,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1424,plain,
! [SV299: nat,SV228: nat,SV134: nat,SV33: nat] :
( ( ( ord_less_nat @ SV33 @ SV134 )
= $false )
| ( ( ~ ( ord_less_nat @ SV228 @ SV299 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV33 @ SV228 ) @ ( plus_plus_nat @ SV134 @ SV299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1425,plain,
! [SV230: nat,SV136: nat,SV35: nat] :
( ( ( ~ ( dist_capacity @ c @ SV35 @ ( sK7_SY768 @ SV136 @ SV230 @ SV35 ) @ SV230 ) )
= $false )
| ( ( ( min_dist_capacity @ c @ SV35 @ SV230 )
= SV136 )
= $true )
| ( ( dist_capacity @ c @ SV35 @ SV136 @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1325]) ).
thf(1426,plain,
! [SV35: nat,SV230: nat,SV136: nat] :
( ( ( ord_less_eq_nat @ SV136 @ ( sK7_SY768 @ SV136 @ SV230 @ SV35 ) )
= $false )
| ( ( ( min_dist_capacity @ c @ SV35 @ SV230 )
= SV136 )
= $true )
| ( ( dist_capacity @ c @ SV35 @ SV136 @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1325]) ).
thf(1427,plain,
! [SV137: nat,SV36: nat,SV334: nat,SV301: nat,SV231: nat] :
( ( ( dist_capacity @ c @ SV231 @ SV301 @ SV334 )
= $false )
| ( ( ( ( min_dist_capacity @ c @ SV36 @ SV334 )
!= ( plus_plus_nat @ SV137 @ SV301 ) )
| ( ( min_dist_capacity @ c @ SV231 @ SV334 )
= SV301 ) )
= $true )
| ( ( dist_capacity @ c @ SV36 @ SV137 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1428,plain,
! [SV303: nat,SV233: nat,SV139: nat,SV38: nat] :
( ( ( SV38 = SV139 )
= $false )
| ( ( ~ ( ord_less_nat @ SV233 @ SV303 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV38 @ SV233 ) @ ( plus_plus_nat @ SV139 @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1429,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1328]) ).
thf(1430,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1328]) ).
thf(1431,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1329]) ).
thf(1432,plain,
! [SV335: nat,SV304: nat,SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
= SV304 )
= $false )
| ( ( ~ ( ord_less_nat @ SV335 @ SV304 )
| ~ ! [SY856: nat] :
~ ~ ( ~ ( connected_capacity @ SV40 @ SV141 @ SY856 )
| ( ( min_dist_capacity @ SV40 @ SV141 @ SY856 )
!= SV335 ) ) )
= $true )
| ( ( connected_capacity @ SV40 @ SV141 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1433,plain,
! [SV236: nat,SV142: nat,SV346: nat,SV336: nat,SV305: nat,SV41: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV41 @ SV305 @ SV336 @ SV346 ) )
= $true )
| ( ( ( ( min_dist_capacity @ SV41 @ SV142 @ SV346 )
!= ( plus_plus_nat @ SV236 @ SV336 ) )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SV305 )
= SV236 ) )
= $true )
| ( ( dist_capacity @ SV41 @ SV142 @ SV236 @ SV305 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1434,plain,
! [SV238: nat,SV144: nat,SV347: nat,SV337: nat,SV306: nat,SV43: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV43 @ SV306 @ SV337 @ SV347 ) )
= $true )
| ( ( dist_capacity @ SV43 @ SV144 @ ( plus_plus_nat @ SV238 @ SV337 ) @ SV347 )
= $true )
| ( ( dist_capacity @ SV43 @ SV144 @ SV238 @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1435,plain,
! [SV246: nat,SV153: nat,SV52: nat] :
( ( ( ~ ~ ( ~ ( connected_capacity @ c @ SV52 @ ( sK9_SY782 @ SV153 @ SV246 @ SV52 ) )
| ( ( min_dist_capacity @ c @ SV52 @ ( sK9_SY782 @ SV153 @ SV246 @ SV52 ) )
!= SV246 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV246 @ ( min_dist_capacity @ c @ SV52 @ SV153 ) )
= $false )
| ( ( connected_capacity @ c @ SV52 @ SV153 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1333]) ).
thf(1436,plain,
! [SV307: nat,SV155: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV155 @ SV307 )
| ~ ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV155 @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1334]) ).
thf(1437,plain,
! [SV155: nat,SV307: nat] :
( ( ( ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV155 @ SV307 )
| ~ ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1335]) ).
thf(1438,plain,
! [SV249: nat,SV156: nat,SV348: nat,SV338: nat,SV308: nat,SV55: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV55 @ SV308 @ SV338 @ SV348 ) )
= $true )
| ( ( ( ( min_dist_capacity @ SV55 @ SV156 @ SV348 )
!= ( plus_plus_nat @ SV249 @ SV338 ) )
| ( ( min_dist_capacity @ SV55 @ SV308 @ SV348 )
= SV338 ) )
= $true )
| ( ( dist_capacity @ SV55 @ SV156 @ SV249 @ SV308 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1336]) ).
thf(1439,plain,
! [SV158: nat,SV251: nat > $o,SV57: nat] :
( ( ( ~ ( dist_capacity @ c @ SV57 @ ( sK8_SY788 @ SV251 @ SV158 @ SV57 ) @ SV158 ) )
= $false )
| ( ( SV251 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) )
= $true )
| ( ( connected_capacity @ c @ SV57 @ SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1337]) ).
thf(1440,plain,
! [SV251: nat > $o,SV158: nat,SV57: nat] :
( ( ( ~ ! [SY874: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY874 @ SV158 )
| ( ord_less_eq_nat @ ( sK8_SY788 @ SV251 @ SV158 @ SV57 ) @ SY874 ) )
| ( SV251 @ ( sK8_SY788 @ SV251 @ SV158 @ SV57 ) ) )
= $false )
| ( ( SV251 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) )
= $true )
| ( ( connected_capacity @ c @ SV57 @ SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1337]) ).
thf(1441,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ~ ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) )
| ~ ( ~ ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1338]) ).
thf(1442,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= ( ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1338]) ).
thf(1443,plain,
! [SV255: nat,SV312: nat > $o,SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV62 @ SV163 @ ( sK10_SY841 @ SV312 @ SV255 @ SV163 @ SV62 ) @ SV255 )
| ~ ! [SY876: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY876 @ SV255 )
| ( ord_less_eq_nat @ ( sK10_SY841 @ SV312 @ SV255 @ SV163 @ SV62 ) @ SY876 ) )
| ( SV312 @ ( sK10_SY841 @ SV312 @ SV255 @ SV163 @ SV62 ) ) )
= $false )
| ( ( SV312 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) )
= $true )
| ( ( connected_capacity @ SV62 @ SV163 @ SV255 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1340]) ).
thf(1444,plain,
! [SV313: nat,SV257: nat,SV167: nat,SV66: nat] :
( ( ( ord_less_eq_nat @ SV66 @ SV167 )
= $false )
| ( ( SV257 != SV313 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV66 @ SV257 ) @ ( plus_plus_nat @ SV167 @ SV313 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1445,plain,
! [SV175: nat,SV74: nat,SV340: nat,SV316: nat,SV265: nat] :
( ( ( dist_capacity @ c @ SV265 @ SV316 @ SV340 )
= $false )
| ( ( ( ( min_dist_capacity @ c @ SV74 @ SV340 )
!= ( plus_plus_nat @ SV175 @ SV316 ) )
| ( ( min_dist_capacity @ c @ SV74 @ SV265 )
= SV175 ) )
= $true )
| ( ( dist_capacity @ c @ SV74 @ SV175 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1446,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1447,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1448,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 ) )
= $true )
| ( ( ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1449,plain,
! [SV180: nat,SV79: nat] :
( ( ( connected_capacity @ c @ SV79 @ SV180 )
= $true )
| ( ( connected_capacity @ c @ SV79 @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1348]) ).
thf(1450,plain,
! [SV180: nat,SV79: nat] :
( ( ( ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) )
= $true )
| ( ( connected_capacity @ c @ SV79 @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1349]) ).
thf(1451,plain,
! [SV180: nat,SV358: list_P559422087at_nat,SV79: nat] :
( ( ( isPath_capacity @ c @ SV79 @ SV358 @ SV180 )
= $false )
| ( ( ~ ( ~ ( connected_capacity @ c @ SV79 @ SV180 )
| ~ ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1452,plain,
! [SV318: nat,SV182: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV182 @ SV318 )
| ~ ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1453,plain,
! [SV182: nat,SV318: nat] :
( ( ( ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV182 @ SV318 )
| ~ ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1352]) ).
thf(1454,plain,
! [SV319: nat,SV272: nat,SV183: nat,SV82: nat] :
( ( ( ord_less_nat @ SV82 @ SV183 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV272 @ SV319 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV82 @ SV272 ) @ ( plus_plus_nat @ SV183 @ SV319 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1455,plain,
! [SV184: nat,SV83: nat,SV273: nat,SV320: nat] :
( ( ( ~ ( ord_less_nat @ SV320 @ SV273 ) )
= $true )
| ( ( ~ ! [SY845: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV83 @ SY845 )
| ( ( min_dist_capacity @ c @ SV83 @ SY845 )
!= SV320 ) ) )
= $true )
| ( ( ( min_dist_capacity @ c @ SV83 @ SV184 )
= SV273 )
= $false )
| ( ( connected_capacity @ c @ SV83 @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1354]) ).
thf(1456,plain,
! [SV185: nat,SV84: nat,SV341: nat,SV321: nat,SV274: nat] :
( ( ( dist_capacity @ c @ SV274 @ SV321 @ SV341 )
= $false )
| ( ( dist_capacity @ c @ SV84 @ ( plus_plus_nat @ SV185 @ SV321 ) @ SV341 )
= $true )
| ( ( dist_capacity @ c @ SV84 @ SV185 @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1457,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ~ ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) )
| ~ ( ~ ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ~ ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1356]) ).
thf(1458,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
= ( ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1356]) ).
thf(1459,plain,
! [SV193: nat,SV92: nat] :
( ( ( connected_capacity @ c @ SV92 @ SV193 )
= $true )
| ( ( connected_capacity @ c @ SV92 @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1358]) ).
thf(1460,plain,
! [SV193: nat,SV92: nat] :
( ( ( ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) )
= $true )
| ( ( connected_capacity @ c @ SV92 @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1359]) ).
thf(1461,plain,
! [SV193: nat,SV360: nat,SV92: nat] :
( ( ( dist_capacity @ c @ SV92 @ SV360 @ SV193 )
= $false )
| ( ( ~ ( ~ ( connected_capacity @ c @ SV92 @ SV193 )
| ~ ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1462,plain,
! [SV282: nat,SV195: nat,SV94: nat] :
( ( ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 ) )
= $false )
| ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1361]) ).
thf(1463,plain,
! [SV195: nat,SV282: nat,SV94: nat] :
( ( ( ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) )
= $false )
| ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1361]) ).
thf(1464,plain,
! [SV195: nat,SV282: nat,SV362: list_P559422087at_nat,SV94: nat] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
| ( ( size_s1990949619at_nat @ SV362 )
!= SV195 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1465,plain,
! [SV324: nat,SV283: nat,SV196: nat,SV95: nat] :
( ( ( ord_less_eq_nat @ SV95 @ SV196 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV283 @ SV324 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV95 @ SV283 ) @ ( plus_plus_nat @ SV196 @ SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1466,plain,
! [SV325: nat,SV284: nat,SV198: nat,SV97: nat] :
( ( ( SV97 = SV198 )
= $false )
| ( ( SV284 != SV325 )
= $true )
| ( ( ( plus_plus_nat @ SV97 @ SV284 )
= ( plus_plus_nat @ SV198 @ SV325 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1467,plain,
! [SV326: nat,SV286: nat,SV200: nat,SV99: nat] :
( ( ( SV99 = SV200 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV286 @ SV326 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV99 @ SV286 ) @ ( plus_plus_nat @ SV200 @ SV326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1468,plain,
! [SV287: nat,SV327: nat,SV201: nat,SV100: product_prod_nat_nat > capacity] :
( ( ( ! [SY849: nat] :
~ ~ ( ~ ( connected_capacity @ SV100 @ SV201 @ SY849 )
| ( ( min_dist_capacity @ SV100 @ SV201 @ SY849 )
!= SV327 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV327 @ ( min_dist_capacity @ SV100 @ SV201 @ SV287 ) )
= $false )
| ( ( connected_capacity @ SV100 @ SV201 @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1366]) ).
thf(1469,plain,
! [SV328: nat,SV288: nat,SV202: nat,SV101: nat] :
( ( ( ord_less_nat @ SV101 @ SV202 )
= $false )
| ( ( SV288 != SV328 )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV101 @ SV288 ) @ ( plus_plus_nat @ SV202 @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1470,plain,
! [SV329: nat,SV289: nat,SV203: nat,SV102: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV102 @ SV203 @ ( sK11_SY850 @ SV289 @ SV329 @ SV203 @ SV102 ) @ SV329 )
| ( ord_less_eq_nat @ SV289 @ ( sK11_SY850 @ SV289 @ SV329 @ SV203 @ SV102 ) ) )
= $false )
| ( ( ( min_dist_capacity @ SV102 @ SV203 @ SV329 )
= SV289 )
= $true )
| ( ( dist_capacity @ SV102 @ SV203 @ SV289 @ SV329 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1368]) ).
thf(1471,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ~ ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) )
| ~ ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1370]) ).
thf(1472,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= ( ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1370]) ).
thf(1473,plain,
! [SV206: nat,SV105: nat,SV1: nat] :
( ( ( ( plus_plus_nat @ SV1 @ SV105 )
= ( plus_plus_nat @ SV1 @ SV206 ) )
= $true )
| ( ( ( plus_plus_nat @ SV1 @ SV105 )
= ( plus_plus_nat @ SV1 @ SV206 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1371]) ).
thf(1474,plain,
! [SV1: nat,SV206: nat,SV105: nat] :
( ( ( SV105 = SV206 )
= $true )
| ( ( ( plus_plus_nat @ SV1 @ SV105 )
= ( plus_plus_nat @ SV1 @ SV206 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1372]) ).
thf(1475,plain,
! [SV206: nat,SV105: nat,SV1: nat] :
( ( ( ( plus_plus_nat @ SV1 @ SV105 )
= ( plus_plus_nat @ SV1 @ SV206 ) )
= $true )
| ( ( SV105 = SV206 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1373]) ).
thf(1476,plain,
! [SV206: nat,SV105: nat] :
( ( ( SV105 = SV206 )
= $true )
| ( ( SV105 = SV206 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1374]) ).
thf(1477,plain,
! [SV207: nat,SV106: nat,SV2: nat] :
( ( ( ( plus_plus_nat @ SV2 @ SV106 )
= ( plus_plus_nat @ SV207 @ SV106 ) )
= $true )
| ( ( ( plus_plus_nat @ SV2 @ SV106 )
= ( plus_plus_nat @ SV207 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1375]) ).
thf(1478,plain,
! [SV106: nat,SV207: nat,SV2: nat] :
( ( ( SV2 = SV207 )
= $true )
| ( ( ( plus_plus_nat @ SV2 @ SV106 )
= ( plus_plus_nat @ SV207 @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1376]) ).
thf(1479,plain,
! [SV207: nat,SV106: nat,SV2: nat] :
( ( ( ( plus_plus_nat @ SV2 @ SV106 )
= ( plus_plus_nat @ SV207 @ SV106 ) )
= $true )
| ( ( SV2 = SV207 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1377]) ).
thf(1480,plain,
! [SV207: nat,SV2: nat] :
( ( ( SV2 = SV207 )
= $true )
| ( ( SV2 = SV207 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1378]) ).
thf(1481,plain,
! [SV212: nat,SV111: nat,SV8: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1379]) ).
thf(1482,plain,
! [SV8: nat,SV212: nat,SV111: nat] :
( ( ( ord_less_eq_nat @ SV111 @ SV212 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1380]) ).
thf(1483,plain,
! [SV212: nat,SV111: nat,SV8: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV8 @ SV111 ) @ ( plus_plus_nat @ SV8 @ SV212 ) )
= $true )
| ( ( ord_less_eq_nat @ SV111 @ SV212 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1381]) ).
thf(1484,plain,
! [SV212: nat,SV111: nat] :
( ( ( ord_less_eq_nat @ SV111 @ SV212 )
= $true )
| ( ( ord_less_eq_nat @ SV111 @ SV212 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1382]) ).
thf(1485,plain,
! [SV213: nat,SV112: nat,SV9: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1383]) ).
thf(1486,plain,
! [SV112: nat,SV213: nat,SV9: nat] :
( ( ( ord_less_eq_nat @ SV9 @ SV213 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1384]) ).
thf(1487,plain,
! [SV213: nat,SV112: nat,SV9: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV9 @ SV112 ) @ ( plus_plus_nat @ SV213 @ SV112 ) )
= $true )
| ( ( ord_less_eq_nat @ SV9 @ SV213 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1385]) ).
thf(1488,plain,
! [SV213: nat,SV9: nat] :
( ( ( ord_less_eq_nat @ SV9 @ SV213 )
= $true )
| ( ( ord_less_eq_nat @ SV9 @ SV213 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1386]) ).
thf(1489,plain,
! [SV215: nat,SV114: nat,SV12: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1387]) ).
thf(1490,plain,
! [SV12: nat,SV215: nat,SV114: nat] :
( ( ( ord_less_eq_nat @ SV114 @ SV215 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1388]) ).
thf(1491,plain,
! [SV215: nat,SV114: nat,SV12: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV114 ) @ ( plus_plus_nat @ SV12 @ SV215 ) )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV215 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1389]) ).
thf(1492,plain,
! [SV215: nat,SV114: nat] :
( ( ( ord_less_eq_nat @ SV114 @ SV215 )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV215 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1390]) ).
thf(1493,plain,
! [SV216: nat,SV115: nat,SV13: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1391]) ).
thf(1494,plain,
! [SV115: nat,SV216: nat,SV13: nat] :
( ( ( ord_less_nat @ SV13 @ SV216 )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1392]) ).
thf(1495,plain,
! [SV216: nat,SV115: nat,SV13: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV13 @ SV115 ) @ ( plus_plus_nat @ SV216 @ SV115 ) )
= $true )
| ( ( ord_less_nat @ SV13 @ SV216 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1393]) ).
thf(1496,plain,
! [SV216: nat,SV13: nat] :
( ( ( ord_less_nat @ SV13 @ SV216 )
= $true )
| ( ( ord_less_nat @ SV13 @ SV216 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1394]) ).
thf(1497,plain,
! [SV217: nat,SV116: nat,SV14: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1395]) ).
thf(1498,plain,
! [SV14: nat,SV217: nat,SV116: nat] :
( ( ( ord_less_nat @ SV116 @ SV217 )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1396]) ).
thf(1499,plain,
! [SV217: nat,SV116: nat,SV14: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV14 @ SV116 ) @ ( plus_plus_nat @ SV14 @ SV217 ) )
= $true )
| ( ( ord_less_nat @ SV116 @ SV217 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1397]) ).
thf(1500,plain,
! [SV217: nat,SV116: nat] :
( ( ( ord_less_nat @ SV116 @ SV217 )
= $true )
| ( ( ord_less_nat @ SV116 @ SV217 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1398]) ).
thf(1501,plain,
! [SV218: nat,SV117: nat,SV15: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1399]) ).
thf(1502,plain,
! [SV15: nat,SV218: nat,SV117: nat] :
( ( ( ord_less_nat @ SV117 @ SV218 )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1400]) ).
thf(1503,plain,
! [SV218: nat,SV117: nat,SV15: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV15 @ SV117 ) @ ( plus_plus_nat @ SV15 @ SV218 ) )
= $true )
| ( ( ord_less_nat @ SV117 @ SV218 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1401]) ).
thf(1504,plain,
! [SV218: nat,SV117: nat] :
( ( ( ord_less_nat @ SV117 @ SV218 )
= $true )
| ( ( ord_less_nat @ SV117 @ SV218 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1402]) ).
thf(1505,plain,
! [SV294: nat,SV122: nat] :
( ( ( ~ ( ord_less_nat @ SV122 @ SV294 ) )
= $false )
| ( ( ord_less_nat @ SV122 @ SV294 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1403]) ).
thf(1506,plain,
! [SV294: nat,SV122: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 ) )
= $false )
| ( ( ord_less_nat @ SV122 @ SV294 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1403]) ).
thf(1507,plain,
! [SV294: nat,SV122: nat] :
( ( ( ~ ( ord_less_nat @ SV122 @ SV294 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1404]) ).
thf(1508,plain,
! [SV294: nat,SV122: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1404]) ).
thf(1509,plain,
! [SV126: nat,SV25: nat,SV295: nat,SV220: nat] :
( ( ( ord_less_nat @ SV220 @ SV295 )
= $false )
| ( ( ord_less_eq_nat @ SV25 @ SV126 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV25 @ SV220 ) @ ( plus_plus_nat @ SV126 @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1417]) ).
thf(1510,plain,
! [SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) ) )
= $true )
| ( ( ~ ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1511,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
= $true )
| ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1421]) ).
thf(1512,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) )
= $true )
| ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1422]) ).
thf(1513,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1514,plain,
! [SV134: nat,SV33: nat,SV299: nat,SV228: nat] :
( ( ( ord_less_nat @ SV228 @ SV299 )
= $false )
| ( ( ord_less_nat @ SV33 @ SV134 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV33 @ SV228 ) @ ( plus_plus_nat @ SV134 @ SV299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1515,plain,
! [SV230: nat,SV136: nat,SV35: nat] :
( ( ( dist_capacity @ c @ SV35 @ ( sK7_SY768 @ SV136 @ SV230 @ SV35 ) @ SV230 )
= $true )
| ( ( ( min_dist_capacity @ c @ SV35 @ SV230 )
= SV136 )
= $true )
| ( ( dist_capacity @ c @ SV35 @ SV136 @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1425]) ).
thf(1516,plain,
! [SV231: nat,SV301: nat,SV137: nat,SV334: nat,SV36: nat] :
( ( ( ( min_dist_capacity @ c @ SV36 @ SV334 )
!= ( plus_plus_nat @ SV137 @ SV301 ) )
= $true )
| ( ( ( min_dist_capacity @ c @ SV231 @ SV334 )
= SV301 )
= $true )
| ( ( dist_capacity @ c @ SV231 @ SV301 @ SV334 )
= $false )
| ( ( dist_capacity @ c @ SV36 @ SV137 @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1517,plain,
! [SV139: nat,SV38: nat,SV303: nat,SV233: nat] :
( ( ( ord_less_nat @ SV233 @ SV303 )
= $false )
| ( ( SV38 = SV139 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV38 @ SV233 ) @ ( plus_plus_nat @ SV139 @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1518,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
= $true )
| ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1429]) ).
thf(1519,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) )
= $true )
| ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1430]) ).
thf(1520,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1521,plain,
! [SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity,SV304: nat,SV335: nat] :
( ( ( ~ ( ord_less_nat @ SV335 @ SV304 ) )
= $true )
| ( ( ~ ! [SY856: nat] :
~ ~ ( ~ ( connected_capacity @ SV40 @ SV141 @ SY856 )
| ( ( min_dist_capacity @ SV40 @ SV141 @ SY856 )
!= SV335 ) ) )
= $true )
| ( ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
= SV304 )
= $false )
| ( ( connected_capacity @ SV40 @ SV141 @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1432]) ).
thf(1522,plain,
! [SV236: nat,SV142: nat,SV346: nat,SV336: nat,SV305: nat,SV41: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV41 @ SV305 @ SV336 @ SV346 )
= $false )
| ( ( ( ( min_dist_capacity @ SV41 @ SV142 @ SV346 )
!= ( plus_plus_nat @ SV236 @ SV336 ) )
| ( ( min_dist_capacity @ SV41 @ SV142 @ SV305 )
= SV236 ) )
= $true )
| ( ( dist_capacity @ SV41 @ SV142 @ SV236 @ SV305 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1523,plain,
! [SV238: nat,SV144: nat,SV347: nat,SV337: nat,SV306: nat,SV43: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV43 @ SV306 @ SV337 @ SV347 )
= $false )
| ( ( dist_capacity @ SV43 @ SV144 @ ( plus_plus_nat @ SV238 @ SV337 ) @ SV347 )
= $true )
| ( ( dist_capacity @ SV43 @ SV144 @ SV238 @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1434]) ).
thf(1524,plain,
! [SV246: nat,SV153: nat,SV52: nat] :
( ( ( ~ ( ~ ( connected_capacity @ c @ SV52 @ ( sK9_SY782 @ SV153 @ SV246 @ SV52 ) )
| ( ( min_dist_capacity @ c @ SV52 @ ( sK9_SY782 @ SV153 @ SV246 @ SV52 ) )
!= SV246 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV246 @ ( min_dist_capacity @ c @ SV52 @ SV153 ) )
= $false )
| ( ( connected_capacity @ c @ SV52 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1525,plain,
! [SV307: nat,SV155: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV155 @ SV307 ) )
= $false )
| ( ( ord_less_eq_nat @ SV155 @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1526,plain,
! [SV155: nat,SV307: nat] :
( ( ( ~ ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV155 @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1527,plain,
! [SV363: nat,SV155: nat,SV307: nat] :
( ( ( SV307
!= ( plus_plus_nat @ SV155 @ SV363 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV155 @ SV307 )
| ~ ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1528,plain,
! [SV249: nat,SV156: nat,SV348: nat,SV338: nat,SV308: nat,SV55: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV55 @ SV308 @ SV338 @ SV348 )
= $false )
| ( ( ( ( min_dist_capacity @ SV55 @ SV156 @ SV348 )
!= ( plus_plus_nat @ SV249 @ SV338 ) )
| ( ( min_dist_capacity @ SV55 @ SV308 @ SV348 )
= SV338 ) )
= $true )
| ( ( dist_capacity @ SV55 @ SV156 @ SV249 @ SV308 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1529,plain,
! [SV158: nat,SV251: nat > $o,SV57: nat] :
( ( ( dist_capacity @ c @ SV57 @ ( sK8_SY788 @ SV251 @ SV158 @ SV57 ) @ SV158 )
= $true )
| ( ( SV251 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) )
= $true )
| ( ( connected_capacity @ c @ SV57 @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1530,plain,
! [SV251: nat > $o,SV158: nat,SV57: nat] :
( ( ( ~ ! [SY874: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY874 @ SV158 )
| ( ord_less_eq_nat @ ( sK8_SY788 @ SV251 @ SV158 @ SV57 ) @ SY874 ) ) )
= $false )
| ( ( SV251 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) )
= $true )
| ( ( connected_capacity @ c @ SV57 @ SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1531,plain,
! [SV57: nat,SV158: nat,SV251: nat > $o] :
( ( ( SV251 @ ( sK8_SY788 @ SV251 @ SV158 @ SV57 ) )
= $false )
| ( ( SV251 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) )
= $true )
| ( ( connected_capacity @ c @ SV57 @ SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1532,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1441]) ).
thf(1533,plain,
! [SV255: nat,SV312: nat > $o,SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV62 @ SV163 @ ( sK10_SY841 @ SV312 @ SV255 @ SV163 @ SV62 ) @ SV255 ) )
= $false )
| ( ( SV312 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) )
= $true )
| ( ( connected_capacity @ SV62 @ SV163 @ SV255 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1534,plain,
! [SV312: nat > $o,SV255: nat,SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ( ~ ! [SY876: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY876 @ SV255 )
| ( ord_less_eq_nat @ ( sK10_SY841 @ SV312 @ SV255 @ SV163 @ SV62 ) @ SY876 ) )
| ( SV312 @ ( sK10_SY841 @ SV312 @ SV255 @ SV163 @ SV62 ) ) )
= $false )
| ( ( SV312 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) )
= $true )
| ( ( connected_capacity @ SV62 @ SV163 @ SV255 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1535,plain,
! [SV167: nat,SV66: nat,SV313: nat,SV257: nat] :
( ( ( SV257 = SV313 )
= $false )
| ( ( ord_less_eq_nat @ SV66 @ SV167 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV66 @ SV257 ) @ ( plus_plus_nat @ SV167 @ SV313 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1536,plain,
! [SV265: nat,SV316: nat,SV175: nat,SV340: nat,SV74: nat] :
( ( ( ( min_dist_capacity @ c @ SV74 @ SV340 )
!= ( plus_plus_nat @ SV175 @ SV316 ) )
= $true )
| ( ( ( min_dist_capacity @ c @ SV74 @ SV265 )
= SV175 )
= $true )
| ( ( dist_capacity @ c @ SV265 @ SV316 @ SV340 )
= $false )
| ( ( dist_capacity @ c @ SV74 @ SV175 @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1445]) ).
thf(1537,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $true )
| ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1446]) ).
thf(1538,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) )
= $true )
| ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1447]) ).
thf(1539,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1540,plain,
! [SV180: nat,SV79: nat] :
( ( ( ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) )
= $false )
| ( ( connected_capacity @ c @ SV79 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1450]) ).
thf(1541,plain,
! [SV358: list_P559422087at_nat,SV180: nat,SV79: nat] :
( ( ( ~ ( connected_capacity @ c @ SV79 @ SV180 )
| ~ ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) )
= $false )
| ( ( isPath_capacity @ c @ SV79 @ SV358 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1542,plain,
! [SV318: nat,SV182: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV182 @ SV318 ) )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1543,plain,
! [SV182: nat,SV318: nat] :
( ( ( ~ ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1544,plain,
! [SV364: nat,SV182: nat,SV318: nat] :
( ( ( SV318
!= ( plus_plus_nat @ SV182 @ SV364 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV182 @ SV318 )
| ~ ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1545,plain,
! [SV183: nat,SV82: nat,SV319: nat,SV272: nat] :
( ( ( ord_less_eq_nat @ SV272 @ SV319 )
= $false )
| ( ( ord_less_nat @ SV82 @ SV183 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV82 @ SV272 ) @ ( plus_plus_nat @ SV183 @ SV319 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1454]) ).
thf(1546,plain,
! [SV184: nat,SV83: nat,SV273: nat,SV320: nat] :
( ( ( ord_less_nat @ SV320 @ SV273 )
= $false )
| ( ( ~ ! [SY845: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV83 @ SY845 )
| ( ( min_dist_capacity @ c @ SV83 @ SY845 )
!= SV320 ) ) )
= $true )
| ( ( ( min_dist_capacity @ c @ SV83 @ SV184 )
= SV273 )
= $false )
| ( ( connected_capacity @ c @ SV83 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1547,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ~ ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1457]) ).
thf(1548,plain,
! [SV193: nat,SV92: nat] :
( ( ( ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) )
= $false )
| ( ( connected_capacity @ c @ SV92 @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1549,plain,
! [SV360: nat,SV193: nat,SV92: nat] :
( ( ( ~ ( connected_capacity @ c @ SV92 @ SV193 )
| ~ ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) )
= $false )
| ( ( dist_capacity @ c @ SV92 @ SV360 @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1550,plain,
! [SV282: nat,SV195: nat,SV94: nat] :
( ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $true )
| ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1462]) ).
thf(1551,plain,
! [SV195: nat,SV282: nat,SV94: nat] :
( ( ( ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) )
= $true )
| ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1463]) ).
thf(1552,plain,
! [SV195: nat,SV282: nat,SV362: list_P559422087at_nat,SV94: nat] :
( ( ( ~ ( ~ ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
| ( ( size_s1990949619at_nat @ SV362 )
!= SV195 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1553,plain,
! [SV196: nat,SV95: nat,SV324: nat,SV283: nat] :
( ( ( ord_less_eq_nat @ SV283 @ SV324 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV196 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV95 @ SV283 ) @ ( plus_plus_nat @ SV196 @ SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1554,plain,
! [SV198: nat,SV97: nat,SV325: nat,SV284: nat] :
( ( ( SV284 = SV325 )
= $false )
| ( ( SV97 = SV198 )
= $false )
| ( ( ( plus_plus_nat @ SV97 @ SV284 )
= ( plus_plus_nat @ SV198 @ SV325 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1555,plain,
! [SV200: nat,SV99: nat,SV326: nat,SV286: nat] :
( ( ( ord_less_eq_nat @ SV286 @ SV326 )
= $false )
| ( ( SV99 = SV200 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV99 @ SV286 ) @ ( plus_plus_nat @ SV200 @ SV326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1556,plain,
! [SV327: nat,SV287: nat,SV201: nat,SV100: product_prod_nat_nat > capacity] :
( ( ( ~ ~ ( ~ ( connected_capacity @ SV100 @ SV201 @ ( sK12_SY849 @ SV287 @ SV327 @ SV201 @ SV100 ) )
| ( ( min_dist_capacity @ SV100 @ SV201 @ ( sK12_SY849 @ SV287 @ SV327 @ SV201 @ SV100 ) )
!= SV327 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV327 @ ( min_dist_capacity @ SV100 @ SV201 @ SV287 ) )
= $false )
| ( ( connected_capacity @ SV100 @ SV201 @ SV287 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1468]) ).
thf(1557,plain,
! [SV202: nat,SV101: nat,SV328: nat,SV288: nat] :
( ( ( SV288 = SV328 )
= $false )
| ( ( ord_less_nat @ SV101 @ SV202 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV101 @ SV288 ) @ ( plus_plus_nat @ SV202 @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1558,plain,
! [SV329: nat,SV289: nat,SV203: nat,SV102: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV102 @ SV203 @ ( sK11_SY850 @ SV289 @ SV329 @ SV203 @ SV102 ) @ SV329 ) )
= $false )
| ( ( ( min_dist_capacity @ SV102 @ SV203 @ SV329 )
= SV289 )
= $true )
| ( ( dist_capacity @ SV102 @ SV203 @ SV289 @ SV329 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1470]) ).
thf(1559,plain,
! [SV102: product_prod_nat_nat > capacity,SV203: nat,SV329: nat,SV289: nat] :
( ( ( ord_less_eq_nat @ SV289 @ ( sK11_SY850 @ SV289 @ SV329 @ SV203 @ SV102 ) )
= $false )
| ( ( ( min_dist_capacity @ SV102 @ SV203 @ SV329 )
= SV289 )
= $true )
| ( ( dist_capacity @ SV102 @ SV203 @ SV289 @ SV329 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1470]) ).
thf(1560,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1471]) ).
thf(1561,plain,
! [SV294: nat,SV122: nat] :
( ( ( ord_less_nat @ SV122 @ SV294 )
= $true )
| ( ( ord_less_nat @ SV122 @ SV294 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1505]) ).
thf(1562,plain,
! [SV294: nat,SV122: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 )
= $true )
| ( ( ord_less_nat @ SV122 @ SV294 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1506]) ).
thf(1563,plain,
! [SV294: nat,SV122: nat] :
( ( ( ord_less_nat @ SV122 @ SV294 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1507]) ).
thf(1564,plain,
! [SV294: nat,SV122: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ one_one_nat ) @ SV294 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1508]) ).
thf(1565,plain,
! [SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1566,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1567,plain,
! [SV227: nat,SV32: nat,SV133: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV133 )
= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $false )
| ( ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1513]) ).
thf(1568,plain,
! [SV231: nat,SV301: nat,SV137: nat,SV334: nat,SV36: nat] :
( ( ( ( min_dist_capacity @ c @ SV36 @ SV334 )
= ( plus_plus_nat @ SV137 @ SV301 ) )
= $false )
| ( ( ( min_dist_capacity @ c @ SV231 @ SV334 )
= SV301 )
= $true )
| ( ( dist_capacity @ c @ SV231 @ SV301 @ SV334 )
= $false )
| ( ( dist_capacity @ c @ SV36 @ SV137 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1569,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1570,plain,
! [SV234: nat,SV39: nat,SV140: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV140 )
= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $false )
| ( ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1571,plain,
! [SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity,SV304: nat,SV335: nat] :
( ( ( ord_less_nat @ SV335 @ SV304 )
= $false )
| ( ( ~ ! [SY856: nat] :
~ ~ ( ~ ( connected_capacity @ SV40 @ SV141 @ SY856 )
| ( ( min_dist_capacity @ SV40 @ SV141 @ SY856 )
!= SV335 ) ) )
= $true )
| ( ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
= SV304 )
= $false )
| ( ( connected_capacity @ SV40 @ SV141 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1572,plain,
! [SV305: nat,SV336: nat,SV236: nat,SV346: nat,SV142: nat,SV41: product_prod_nat_nat > capacity] :
( ( ( ( min_dist_capacity @ SV41 @ SV142 @ SV346 )
!= ( plus_plus_nat @ SV236 @ SV336 ) )
= $true )
| ( ( ( min_dist_capacity @ SV41 @ SV142 @ SV305 )
= SV236 )
= $true )
| ( ( dist_capacity @ SV41 @ SV305 @ SV336 @ SV346 )
= $false )
| ( ( dist_capacity @ SV41 @ SV142 @ SV236 @ SV305 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1573,plain,
! [SV246: nat,SV153: nat,SV52: nat] :
( ( ( ~ ( connected_capacity @ c @ SV52 @ ( sK9_SY782 @ SV153 @ SV246 @ SV52 ) )
| ( ( min_dist_capacity @ c @ SV52 @ ( sK9_SY782 @ SV153 @ SV246 @ SV52 ) )
!= SV246 ) )
= $false )
| ( ( ord_less_eq_nat @ SV246 @ ( min_dist_capacity @ c @ SV52 @ SV153 ) )
= $false )
| ( ( connected_capacity @ c @ SV52 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1574,plain,
! [SV307: nat,SV155: nat] :
( ( ( ord_less_eq_nat @ SV155 @ SV307 )
= $true )
| ( ( ord_less_eq_nat @ SV155 @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1525]) ).
thf(1575,plain,
! [SV155: nat,SV307: nat] :
( ( ( ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV155 @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1526]) ).
thf(1576,plain,
! [SV363: nat,SV155: nat,SV307: nat] :
( ( ( SV307
= ( plus_plus_nat @ SV155 @ SV363 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV155 @ SV307 )
| ~ ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1577,plain,
! [SV308: nat,SV338: nat,SV249: nat,SV348: nat,SV156: nat,SV55: product_prod_nat_nat > capacity] :
( ( ( ( min_dist_capacity @ SV55 @ SV156 @ SV348 )
!= ( plus_plus_nat @ SV249 @ SV338 ) )
= $true )
| ( ( ( min_dist_capacity @ SV55 @ SV308 @ SV348 )
= SV338 )
= $true )
| ( ( dist_capacity @ SV55 @ SV308 @ SV338 @ SV348 )
= $false )
| ( ( dist_capacity @ SV55 @ SV156 @ SV249 @ SV308 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1528]) ).
thf(1578,plain,
! [SV251: nat > $o,SV158: nat,SV57: nat] :
( ( ( ! [SY874: nat] :
( ~ ( dist_capacity @ c @ SV57 @ SY874 @ SV158 )
| ( ord_less_eq_nat @ ( sK8_SY788 @ SV251 @ SV158 @ SV57 ) @ SY874 ) ) )
= $true )
| ( ( SV251 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) )
= $true )
| ( ( connected_capacity @ c @ SV57 @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1530]) ).
thf(1579,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1532]) ).
thf(1580,plain,
! [SV255: nat,SV312: nat > $o,SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV62 @ SV163 @ ( sK10_SY841 @ SV312 @ SV255 @ SV163 @ SV62 ) @ SV255 )
= $true )
| ( ( SV312 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) )
= $true )
| ( ( connected_capacity @ SV62 @ SV163 @ SV255 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1533]) ).
thf(1581,plain,
! [SV312: nat > $o,SV255: nat,SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ( ~ ! [SY876: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY876 @ SV255 )
| ( ord_less_eq_nat @ ( sK10_SY841 @ SV312 @ SV255 @ SV163 @ SV62 ) @ SY876 ) ) )
= $false )
| ( ( SV312 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) )
= $true )
| ( ( connected_capacity @ SV62 @ SV163 @ SV255 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1534]) ).
thf(1582,plain,
! [SV62: product_prod_nat_nat > capacity,SV163: nat,SV255: nat,SV312: nat > $o] :
( ( ( SV312 @ ( sK10_SY841 @ SV312 @ SV255 @ SV163 @ SV62 ) )
= $false )
| ( ( SV312 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) )
= $true )
| ( ( connected_capacity @ SV62 @ SV163 @ SV255 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1534]) ).
thf(1583,plain,
! [SV265: nat,SV316: nat,SV175: nat,SV340: nat,SV74: nat] :
( ( ( ( min_dist_capacity @ c @ SV74 @ SV340 )
= ( plus_plus_nat @ SV175 @ SV316 ) )
= $false )
| ( ( ( min_dist_capacity @ c @ SV74 @ SV265 )
= SV175 )
= $true )
| ( ( dist_capacity @ c @ SV265 @ SV316 @ SV340 )
= $false )
| ( ( dist_capacity @ c @ SV74 @ SV175 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1584,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1585,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV78: nat] :
( ( ( ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1586,plain,
! [SV180: nat,SV79: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV79 @ ( sK13_SY709 @ SV180 @ SV79 ) @ SV180 ) )
= $false )
| ( ( connected_capacity @ c @ SV79 @ SV180 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1540]) ).
thf(1587,plain,
! [SV358: list_P559422087at_nat,SV180: nat,SV79: nat] :
( ( ( ~ ( connected_capacity @ c @ SV79 @ SV180 ) )
= $false )
| ( ( isPath_capacity @ c @ SV79 @ SV358 @ SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1541]) ).
thf(1588,plain,
! [SV358: list_P559422087at_nat,SV180: nat,SV79: nat] :
( ( ( ~ ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) )
= $false )
| ( ( isPath_capacity @ c @ SV79 @ SV358 @ SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1541]) ).
thf(1589,plain,
! [SV318: nat,SV182: nat] :
( ( ( ord_less_eq_nat @ SV182 @ SV318 )
= $true )
| ( ( ord_less_eq_nat @ SV182 @ SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1542]) ).
thf(1590,plain,
! [SV182: nat,SV318: nat] :
( ( ( ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV182 @ SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1543]) ).
thf(1591,plain,
! [SV364: nat,SV182: nat,SV318: nat] :
( ( ( SV318
= ( plus_plus_nat @ SV182 @ SV364 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV182 @ SV318 )
| ~ ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1592,plain,
! [SV184: nat,SV273: nat,SV320: nat,SV83: nat] :
( ( ( ! [SY845: nat] :
~ ~ ( ~ ( connected_capacity @ c @ SV83 @ SY845 )
| ( ( min_dist_capacity @ c @ SV83 @ SY845 )
!= SV320 ) ) )
= $false )
| ( ( ord_less_nat @ SV320 @ SV273 )
= $false )
| ( ( ( min_dist_capacity @ c @ SV83 @ SV184 )
= SV273 )
= $false )
| ( ( connected_capacity @ c @ SV83 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1593,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ~ ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1594,plain,
! [SV193: nat,SV92: nat] :
( ( ( ~ ( dist_capacity @ c @ SV92 @ ( sK14_SY732 @ SV193 @ SV92 ) @ SV193 ) )
= $false )
| ( ( connected_capacity @ c @ SV92 @ SV193 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1548]) ).
thf(1595,plain,
! [SV360: nat,SV193: nat,SV92: nat] :
( ( ( ~ ( connected_capacity @ c @ SV92 @ SV193 ) )
= $false )
| ( ( dist_capacity @ c @ SV92 @ SV360 @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1549]) ).
thf(1596,plain,
! [SV360: nat,SV193: nat,SV92: nat] :
( ( ( ~ ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) )
= $false )
| ( ( dist_capacity @ c @ SV92 @ SV360 @ SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1549]) ).
thf(1597,plain,
! [SV195: nat,SV282: nat,SV94: nat] :
( ( ( ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) )
= $false )
| ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1598,plain,
! [SV195: nat,SV282: nat,SV362: list_P559422087at_nat,SV94: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
| ( ( size_s1990949619at_nat @ SV362 )
!= SV195 ) )
= $true )
| ( ( ~ ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1552]) ).
thf(1599,plain,
! [SV327: nat,SV287: nat,SV201: nat,SV100: product_prod_nat_nat > capacity] :
( ( ( ~ ( ~ ( connected_capacity @ SV100 @ SV201 @ ( sK12_SY849 @ SV287 @ SV327 @ SV201 @ SV100 ) )
| ( ( min_dist_capacity @ SV100 @ SV201 @ ( sK12_SY849 @ SV287 @ SV327 @ SV201 @ SV100 ) )
!= SV327 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV327 @ ( min_dist_capacity @ SV100 @ SV201 @ SV287 ) )
= $false )
| ( ( connected_capacity @ SV100 @ SV201 @ SV287 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1556]) ).
thf(1600,plain,
! [SV329: nat,SV289: nat,SV203: nat,SV102: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV102 @ SV203 @ ( sK11_SY850 @ SV289 @ SV329 @ SV203 @ SV102 ) @ SV329 )
= $true )
| ( ( ( min_dist_capacity @ SV102 @ SV203 @ SV329 )
= SV289 )
= $true )
| ( ( dist_capacity @ SV102 @ SV203 @ SV289 @ SV329 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1558]) ).
thf(1601,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1602,plain,
! [SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $false )
| ( ( ~ ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1565]) ).
thf(1603,plain,
! [SV345: nat,SV356: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1565]) ).
thf(1604,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1605,plain,
! [SV227: nat,SV32: nat,SV133: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1606,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV133 )
= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1607,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1608,plain,
! [SV234: nat,SV39: nat,SV140: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1609,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) )
= $false )
| ( ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV140 )
= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1610,plain,
! [SV235: nat,SV304: nat,SV335: nat,SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ( ! [SY856: nat] :
~ ~ ( ~ ( connected_capacity @ SV40 @ SV141 @ SY856 )
| ( ( min_dist_capacity @ SV40 @ SV141 @ SY856 )
!= SV335 ) ) )
= $false )
| ( ( ord_less_nat @ SV335 @ SV304 )
= $false )
| ( ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
= SV304 )
= $false )
| ( ( connected_capacity @ SV40 @ SV141 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1611,plain,
! [SV305: nat,SV336: nat,SV236: nat,SV346: nat,SV142: nat,SV41: product_prod_nat_nat > capacity] :
( ( ( ( min_dist_capacity @ SV41 @ SV142 @ SV346 )
= ( plus_plus_nat @ SV236 @ SV336 ) )
= $false )
| ( ( ( min_dist_capacity @ SV41 @ SV142 @ SV305 )
= SV236 )
= $true )
| ( ( dist_capacity @ SV41 @ SV305 @ SV336 @ SV346 )
= $false )
| ( ( dist_capacity @ SV41 @ SV142 @ SV236 @ SV305 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1612,plain,
! [SV246: nat,SV153: nat,SV52: nat] :
( ( ( ~ ( connected_capacity @ c @ SV52 @ ( sK9_SY782 @ SV153 @ SV246 @ SV52 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV246 @ ( min_dist_capacity @ c @ SV52 @ SV153 ) )
= $false )
| ( ( connected_capacity @ c @ SV52 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1613,plain,
! [SV246: nat,SV153: nat,SV52: nat] :
( ( ( ( min_dist_capacity @ c @ SV52 @ ( sK9_SY782 @ SV153 @ SV246 @ SV52 ) )
!= SV246 )
= $false )
| ( ( ord_less_eq_nat @ SV246 @ ( min_dist_capacity @ c @ SV52 @ SV153 ) )
= $false )
| ( ( connected_capacity @ c @ SV52 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1614,plain,
! [SV155: nat,SV307: nat] :
( ( ( ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV155 @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1575]) ).
thf(1615,plain,
! [SV363: nat,SV307: nat,SV155: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV155 @ SV307 )
| ~ ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) )
= $false )
| ( ( SV307
= ( plus_plus_nat @ SV155 @ SV363 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1616,plain,
! [SV308: nat,SV338: nat,SV249: nat,SV348: nat,SV156: nat,SV55: product_prod_nat_nat > capacity] :
( ( ( ( min_dist_capacity @ SV55 @ SV156 @ SV348 )
= ( plus_plus_nat @ SV249 @ SV338 ) )
= $false )
| ( ( ( min_dist_capacity @ SV55 @ SV308 @ SV348 )
= SV338 )
= $true )
| ( ( dist_capacity @ SV55 @ SV308 @ SV338 @ SV348 )
= $false )
| ( ( dist_capacity @ SV55 @ SV156 @ SV249 @ SV308 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1617,plain,
! [SV251: nat > $o,SV158: nat,SV365: nat,SV57: nat] :
( ( ( ~ ( dist_capacity @ c @ SV57 @ SV365 @ SV158 )
| ( ord_less_eq_nat @ ( sK8_SY788 @ SV251 @ SV158 @ SV57 ) @ SV365 ) )
= $true )
| ( ( SV251 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) )
= $true )
| ( ( connected_capacity @ c @ SV57 @ SV158 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1618,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1579]) ).
thf(1619,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1579]) ).
thf(1620,plain,
! [SV312: nat > $o,SV255: nat,SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ( ! [SY876: nat] :
( ~ ( dist_capacity @ SV62 @ SV163 @ SY876 @ SV255 )
| ( ord_less_eq_nat @ ( sK10_SY841 @ SV312 @ SV255 @ SV163 @ SV62 ) @ SY876 ) ) )
= $true )
| ( ( SV312 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) )
= $true )
| ( ( connected_capacity @ SV62 @ SV163 @ SV255 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1581]) ).
thf(1621,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1584]) ).
thf(1622,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV78: nat] :
( ( ( ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1584]) ).
thf(1623,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1585]) ).
thf(1624,plain,
! [SV180: nat,SV79: nat] :
( ( ( isPath_capacity @ c @ SV79 @ ( sK13_SY709 @ SV180 @ SV79 ) @ SV180 )
= $true )
| ( ( connected_capacity @ c @ SV79 @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1586]) ).
thf(1625,plain,
! [SV358: list_P559422087at_nat,SV180: nat,SV79: nat] :
( ( ( connected_capacity @ c @ SV79 @ SV180 )
= $true )
| ( ( isPath_capacity @ c @ SV79 @ SV358 @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1587]) ).
thf(1626,plain,
! [SV358: list_P559422087at_nat,SV180: nat,SV79: nat] :
( ( ( ~ ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) )
= $true )
| ( ( isPath_capacity @ c @ SV79 @ SV358 @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1588]) ).
thf(1627,plain,
! [SV182: nat,SV318: nat] :
( ( ( ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1628,plain,
! [SV364: nat,SV318: nat,SV182: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV182 @ SV318 )
| ~ ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) )
= $false )
| ( ( SV318
= ( plus_plus_nat @ SV182 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1629,plain,
! [SV320: nat,SV273: nat,SV184: nat,SV83: nat] :
( ( ( ~ ~ ( ~ ( connected_capacity @ c @ SV83 @ ( sK16_SY845 @ SV184 @ SV273 @ SV320 @ SV83 ) )
| ( ( min_dist_capacity @ c @ SV83 @ ( sK16_SY845 @ SV184 @ SV273 @ SV320 @ SV83 ) )
!= SV320 ) ) )
= $false )
| ( ( ord_less_nat @ SV320 @ SV273 )
= $false )
| ( ( ( min_dist_capacity @ c @ SV83 @ SV184 )
= SV273 )
= $false )
| ( ( connected_capacity @ c @ SV83 @ SV184 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1592]) ).
thf(1630,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ~ ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1593]) ).
thf(1631,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ~ ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1593]) ).
thf(1632,plain,
! [SV193: nat,SV92: nat] :
( ( ( dist_capacity @ c @ SV92 @ ( sK14_SY732 @ SV193 @ SV92 ) @ SV193 )
= $true )
| ( ( connected_capacity @ c @ SV92 @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1594]) ).
thf(1633,plain,
! [SV360: nat,SV193: nat,SV92: nat] :
( ( ( connected_capacity @ c @ SV92 @ SV193 )
= $true )
| ( ( dist_capacity @ c @ SV92 @ SV360 @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1595]) ).
thf(1634,plain,
! [SV360: nat,SV193: nat,SV92: nat] :
( ( ( ~ ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) )
= $true )
| ( ( dist_capacity @ c @ SV92 @ SV360 @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1596]) ).
thf(1635,plain,
! [SV282: nat,SV195: nat,SV94: nat] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ ( sK17_SY813 @ SV195 @ SV282 @ SV94 ) @ SV282 )
| ( ( size_s1990949619at_nat @ ( sK17_SY813 @ SV195 @ SV282 @ SV94 ) )
!= SV195 ) ) )
= $false )
| ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1597]) ).
thf(1636,plain,
! [SV195: nat,SV282: nat,SV362: list_P559422087at_nat,SV94: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV362 )
!= SV195 )
= $true )
| ( ( ~ ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1598]) ).
thf(1637,plain,
! [SV327: nat,SV287: nat,SV201: nat,SV100: product_prod_nat_nat > capacity] :
( ( ( ~ ( connected_capacity @ SV100 @ SV201 @ ( sK12_SY849 @ SV287 @ SV327 @ SV201 @ SV100 ) )
| ( ( min_dist_capacity @ SV100 @ SV201 @ ( sK12_SY849 @ SV287 @ SV327 @ SV201 @ SV100 ) )
!= SV327 ) )
= $false )
| ( ( ord_less_eq_nat @ SV327 @ ( min_dist_capacity @ SV100 @ SV201 @ SV287 ) )
= $false )
| ( ( connected_capacity @ SV100 @ SV201 @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1638,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1601]) ).
thf(1639,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1601]) ).
thf(1640,plain,
! [SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) )
= $false )
| ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1641,plain,
! [SV345: nat,SV356: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1603]) ).
thf(1642,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
= $true )
| ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1604]) ).
thf(1643,plain,
! [SV227: nat,SV32: nat,SV133: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV133 )
= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $true )
| ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1605]) ).
thf(1644,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 ) )
= $false )
| ( ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV133 )
= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1606]) ).
thf(1645,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV133 )
= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1606]) ).
thf(1646,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
= $true )
| ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1647,plain,
! [SV234: nat,SV39: nat,SV140: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV140 )
= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $true )
| ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1608]) ).
thf(1648,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 ) )
= $false )
| ( ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV140 )
= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1649,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) )
= $false )
| ( ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV140 )
= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1650,plain,
! [SV335: nat,SV304: nat,SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ( ~ ~ ( ~ ( connected_capacity @ SV40 @ SV141 @ ( sK18_SY856 @ SV235 @ SV304 @ SV335 @ SV141 @ SV40 ) )
| ( ( min_dist_capacity @ SV40 @ SV141 @ ( sK18_SY856 @ SV235 @ SV304 @ SV335 @ SV141 @ SV40 ) )
!= SV335 ) ) )
= $false )
| ( ( ord_less_nat @ SV335 @ SV304 )
= $false )
| ( ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
= SV304 )
= $false )
| ( ( connected_capacity @ SV40 @ SV141 @ SV235 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1610]) ).
thf(1651,plain,
! [SV246: nat,SV153: nat,SV52: nat] :
( ( ( connected_capacity @ c @ SV52 @ ( sK9_SY782 @ SV153 @ SV246 @ SV52 ) )
= $true )
| ( ( ord_less_eq_nat @ SV246 @ ( min_dist_capacity @ c @ SV52 @ SV153 ) )
= $false )
| ( ( connected_capacity @ c @ SV52 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1612]) ).
thf(1652,plain,
! [SV246: nat,SV153: nat,SV52: nat] :
( ( ( ( min_dist_capacity @ c @ SV52 @ ( sK9_SY782 @ SV153 @ SV246 @ SV52 ) )
= SV246 )
= $true )
| ( ( ord_less_eq_nat @ SV246 @ ( min_dist_capacity @ c @ SV52 @ SV153 ) )
= $false )
| ( ( connected_capacity @ c @ SV52 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1613]) ).
thf(1653,plain,
! [SV155: nat,SV307: nat] :
( ( ( SV307
!= ( plus_plus_nat @ SV155 @ ( sK19_SY836 @ SV155 @ SV307 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV155 @ SV307 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1614]) ).
thf(1654,plain,
! [SV363: nat,SV307: nat,SV155: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV155 @ SV307 ) )
= $false )
| ( ( SV307
= ( plus_plus_nat @ SV155 @ SV363 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1615]) ).
thf(1655,plain,
! [SV363: nat,SV155: nat,SV307: nat] :
( ( ( ~ ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) )
= $false )
| ( ( SV307
= ( plus_plus_nat @ SV155 @ SV363 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1615]) ).
thf(1656,plain,
! [SV251: nat > $o,SV158: nat,SV365: nat,SV57: nat] :
( ( ( ~ ( dist_capacity @ c @ SV57 @ SV365 @ SV158 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK8_SY788 @ SV251 @ SV158 @ SV57 ) @ SV365 )
= $true )
| ( ( SV251 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) )
= $true )
| ( ( connected_capacity @ c @ SV57 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1617]) ).
thf(1657,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1658,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1659,plain,
! [SV312: nat > $o,SV255: nat,SV366: nat,SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV62 @ SV163 @ SV366 @ SV255 )
| ( ord_less_eq_nat @ ( sK10_SY841 @ SV312 @ SV255 @ SV163 @ SV62 ) @ SV366 ) )
= $true )
| ( ( SV312 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) )
= $true )
| ( ( connected_capacity @ SV62 @ SV163 @ SV255 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1660,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $true )
| ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1621]) ).
thf(1661,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV78: nat] :
( ( ( ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) )
= $true )
| ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1622]) ).
thf(1662,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1623]) ).
thf(1663,plain,
! [SV78: nat,SV269: nat,SV179: list_P559422087at_nat] :
( ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1623]) ).
thf(1664,plain,
! [SV358: list_P559422087at_nat,SV180: nat,SV79: nat] :
( ( ( ! [SY709: list_P559422087at_nat] :
~ ( isPath_capacity @ c @ SV79 @ SY709 @ SV180 ) )
= $false )
| ( ( isPath_capacity @ c @ SV79 @ SV358 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1626]) ).
thf(1665,plain,
! [SV182: nat,SV318: nat] :
( ( ( SV318
!= ( plus_plus_nat @ SV182 @ ( sK20_SY844 @ SV182 @ SV318 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV318 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1627]) ).
thf(1666,plain,
! [SV364: nat,SV318: nat,SV182: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV182 @ SV318 ) )
= $false )
| ( ( SV318
= ( plus_plus_nat @ SV182 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1667,plain,
! [SV364: nat,SV182: nat,SV318: nat] :
( ( ( ~ ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) )
= $false )
| ( ( SV318
= ( plus_plus_nat @ SV182 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1668,plain,
! [SV320: nat,SV273: nat,SV184: nat,SV83: nat] :
( ( ( ~ ( ~ ( connected_capacity @ c @ SV83 @ ( sK16_SY845 @ SV184 @ SV273 @ SV320 @ SV83 ) )
| ( ( min_dist_capacity @ c @ SV83 @ ( sK16_SY845 @ SV184 @ SV273 @ SV320 @ SV83 ) )
!= SV320 ) ) )
= $true )
| ( ( ord_less_nat @ SV320 @ SV273 )
= $false )
| ( ( ( min_dist_capacity @ c @ SV83 @ SV184 )
= SV273 )
= $false )
| ( ( connected_capacity @ c @ SV83 @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1629]) ).
thf(1669,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ~ ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1670,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ~ ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1671,plain,
! [SV360: nat,SV193: nat,SV92: nat] :
( ( ( ! [SY732: nat] :
~ ( dist_capacity @ c @ SV92 @ SY732 @ SV193 ) )
= $false )
| ( ( dist_capacity @ c @ SV92 @ SV360 @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1634]) ).
thf(1672,plain,
! [SV282: nat,SV195: nat,SV94: nat] :
( ( ( ~ ( ~ ( isPath_capacity @ c @ SV94 @ ( sK17_SY813 @ SV195 @ SV282 @ SV94 ) @ SV282 )
| ( ( size_s1990949619at_nat @ ( sK17_SY813 @ SV195 @ SV282 @ SV94 ) )
!= SV195 ) ) )
= $true )
| ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1635]) ).
thf(1673,plain,
! [SV195: nat,SV282: nat,SV362: list_P559422087at_nat,SV94: nat] :
( ( ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV362 )
!= SV195 )
= $true )
| ( ( ~ ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1674,plain,
! [SV327: nat,SV287: nat,SV201: nat,SV100: product_prod_nat_nat > capacity] :
( ( ( ~ ( connected_capacity @ SV100 @ SV201 @ ( sK12_SY849 @ SV287 @ SV327 @ SV201 @ SV100 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV327 @ ( min_dist_capacity @ SV100 @ SV201 @ SV287 ) )
= $false )
| ( ( connected_capacity @ SV100 @ SV201 @ SV287 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1637]) ).
thf(1675,plain,
! [SV327: nat,SV287: nat,SV201: nat,SV100: product_prod_nat_nat > capacity] :
( ( ( ( min_dist_capacity @ SV100 @ SV201 @ ( sK12_SY849 @ SV287 @ SV327 @ SV201 @ SV100 ) )
!= SV327 )
= $false )
| ( ( ord_less_eq_nat @ SV327 @ ( min_dist_capacity @ SV100 @ SV201 @ SV287 ) )
= $false )
| ( ( connected_capacity @ SV100 @ SV201 @ SV287 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1637]) ).
thf(1676,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1677,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1639]) ).
thf(1678,plain,
! [SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 ) )
= $false )
| ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1679,plain,
! [SV345: nat,SV356: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) )
= $false )
| ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1680,plain,
! [SV345: nat,SV356: nat,SV367: list_P559422087at_nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
| ( ( size_s1990949619at_nat @ SV367 )
!= SV345 ) ) )
= $true )
| ( ( ~ ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(1681,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( isShor1936442771pacity @ c @ SV32 @ SV133 @ SV227 )
= $true )
| ( ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV133 )
= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1644]) ).
thf(1682,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) ) )
= $true )
| ( ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV133 )
= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1645]) ).
thf(1683,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( isShor1936442771pacity @ c @ SV39 @ SV140 @ SV234 )
= $true )
| ( ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV140 )
= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1648]) ).
thf(1684,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) ) )
= $true )
| ( ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV140 )
= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1649]) ).
thf(1685,plain,
! [SV335: nat,SV304: nat,SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ( ~ ( ~ ( connected_capacity @ SV40 @ SV141 @ ( sK18_SY856 @ SV235 @ SV304 @ SV335 @ SV141 @ SV40 ) )
| ( ( min_dist_capacity @ SV40 @ SV141 @ ( sK18_SY856 @ SV235 @ SV304 @ SV335 @ SV141 @ SV40 ) )
!= SV335 ) ) )
= $true )
| ( ( ord_less_nat @ SV335 @ SV304 )
= $false )
| ( ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
= SV304 )
= $false )
| ( ( connected_capacity @ SV40 @ SV141 @ SV235 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1686,plain,
! [SV155: nat,SV307: nat] :
( ( ( SV307
= ( plus_plus_nat @ SV155 @ ( sK19_SY836 @ SV155 @ SV307 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV155 @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1653]) ).
thf(1687,plain,
! [SV363: nat,SV307: nat,SV155: nat] :
( ( ( ord_less_eq_nat @ SV155 @ SV307 )
= $true )
| ( ( SV307
= ( plus_plus_nat @ SV155 @ SV363 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1654]) ).
thf(1688,plain,
! [SV363: nat,SV155: nat,SV307: nat] :
( ( ( ~ ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) )
= $true )
| ( ( SV307
= ( plus_plus_nat @ SV155 @ SV363 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1655]) ).
thf(1689,plain,
! [SV251: nat > $o,SV158: nat,SV365: nat,SV57: nat] :
( ( ( dist_capacity @ c @ SV57 @ SV365 @ SV158 )
= $false )
| ( ( ord_less_eq_nat @ ( sK8_SY788 @ SV251 @ SV158 @ SV57 ) @ SV365 )
= $true )
| ( ( SV251 @ ( min_dist_capacity @ c @ SV57 @ SV158 ) )
= $true )
| ( ( connected_capacity @ c @ SV57 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1656]) ).
thf(1690,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 ) )
= $false )
| ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1691,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1692,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1658]) ).
thf(1693,plain,
! [SV312: nat > $o,SV255: nat,SV366: nat,SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV62 @ SV163 @ SV366 @ SV255 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK10_SY841 @ SV312 @ SV255 @ SV163 @ SV62 ) @ SV366 )
= $true )
| ( ( SV312 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) )
= $true )
| ( ( connected_capacity @ SV62 @ SV163 @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1659]) ).
thf(1694,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV368: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ SV368 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SV368 ) ) )
= $true )
| ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(1695,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 )
= $true )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1662]) ).
thf(1696,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1697,plain,
! [SV180: nat,SV358: list_P559422087at_nat,SV79: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV79 @ ( sK21_SY709 @ SV358 @ SV180 @ SV79 ) @ SV180 ) )
= $false )
| ( ( isPath_capacity @ c @ SV79 @ SV358 @ SV180 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1664]) ).
thf(1698,plain,
! [SV182: nat,SV318: nat] :
( ( ( SV318
= ( plus_plus_nat @ SV182 @ ( sK20_SY844 @ SV182 @ SV318 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV182 @ SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1665]) ).
thf(1699,plain,
! [SV364: nat,SV318: nat,SV182: nat] :
( ( ( ord_less_eq_nat @ SV182 @ SV318 )
= $true )
| ( ( SV318
= ( plus_plus_nat @ SV182 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1666]) ).
thf(1700,plain,
! [SV364: nat,SV182: nat,SV318: nat] :
( ( ( ~ ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) )
= $true )
| ( ( SV318
= ( plus_plus_nat @ SV182 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1667]) ).
thf(1701,plain,
! [SV320: nat,SV273: nat,SV184: nat,SV83: nat] :
( ( ( ~ ( connected_capacity @ c @ SV83 @ ( sK16_SY845 @ SV184 @ SV273 @ SV320 @ SV83 ) )
| ( ( min_dist_capacity @ c @ SV83 @ ( sK16_SY845 @ SV184 @ SV273 @ SV320 @ SV83 ) )
!= SV320 ) )
= $false )
| ( ( ord_less_nat @ SV320 @ SV273 )
= $false )
| ( ( ( min_dist_capacity @ c @ SV83 @ SV184 )
= SV273 )
= $false )
| ( ( connected_capacity @ c @ SV83 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1702,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 ) )
= $false )
| ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1703,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1704,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ~ ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1670]) ).
thf(1705,plain,
! [SV193: nat,SV360: nat,SV92: nat] :
( ( ( ~ ( dist_capacity @ c @ SV92 @ ( sK22_SY732 @ SV360 @ SV193 @ SV92 ) @ SV193 ) )
= $false )
| ( ( dist_capacity @ c @ SV92 @ SV360 @ SV193 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1671]) ).
thf(1706,plain,
! [SV282: nat,SV195: nat,SV94: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV94 @ ( sK17_SY813 @ SV195 @ SV282 @ SV94 ) @ SV282 )
| ( ( size_s1990949619at_nat @ ( sK17_SY813 @ SV195 @ SV282 @ SV94 ) )
!= SV195 ) )
= $false )
| ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1672]) ).
thf(1707,plain,
! [SV282: nat,SV94: nat,SV195: nat,SV362: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV362 )
= SV195 )
= $false )
| ( ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
= $false )
| ( ( ~ ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1708,plain,
! [SV327: nat,SV287: nat,SV201: nat,SV100: product_prod_nat_nat > capacity] :
( ( ( connected_capacity @ SV100 @ SV201 @ ( sK12_SY849 @ SV287 @ SV327 @ SV201 @ SV100 ) )
= $true )
| ( ( ord_less_eq_nat @ SV327 @ ( min_dist_capacity @ SV100 @ SV201 @ SV287 ) )
= $false )
| ( ( connected_capacity @ SV100 @ SV201 @ SV287 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1709,plain,
! [SV327: nat,SV287: nat,SV201: nat,SV100: product_prod_nat_nat > capacity] :
( ( ( ( min_dist_capacity @ SV100 @ SV201 @ ( sK12_SY849 @ SV287 @ SV327 @ SV201 @ SV100 ) )
= SV327 )
= $true )
| ( ( ord_less_eq_nat @ SV327 @ ( min_dist_capacity @ SV100 @ SV201 @ SV287 ) )
= $false )
| ( ( connected_capacity @ SV100 @ SV201 @ SV287 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1675]) ).
thf(1710,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 ) )
= $false )
| ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1676]) ).
thf(1711,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1676]) ).
thf(1712,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 ) )
= $true )
| ( ( ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1677]) ).
thf(1713,plain,
! [SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $true )
| ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1678]) ).
thf(1714,plain,
! [SV345: nat,SV356: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) )
= $true )
| ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1715,plain,
! [SV345: nat,SV356: nat,SV367: list_P559422087at_nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
| ( ( size_s1990949619at_nat @ SV367 )
!= SV345 ) ) )
= $false )
| ( ( ~ ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1680]) ).
thf(1716,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
| ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV133 )
= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1682]) ).
thf(1717,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
| ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) ) )
= $false )
| ( ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV140 )
= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1718,plain,
! [SV335: nat,SV304: nat,SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ( ~ ( connected_capacity @ SV40 @ SV141 @ ( sK18_SY856 @ SV235 @ SV304 @ SV335 @ SV141 @ SV40 ) )
| ( ( min_dist_capacity @ SV40 @ SV141 @ ( sK18_SY856 @ SV235 @ SV304 @ SV335 @ SV141 @ SV40 ) )
!= SV335 ) )
= $false )
| ( ( ord_less_nat @ SV335 @ SV304 )
= $false )
| ( ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
= SV304 )
= $false )
| ( ( connected_capacity @ SV40 @ SV141 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1719,plain,
! [SV363: nat,SV155: nat,SV307: nat] :
( ( ( ! [SY836: nat] :
( SV307
!= ( plus_plus_nat @ SV155 @ SY836 ) ) )
= $false )
| ( ( SV307
= ( plus_plus_nat @ SV155 @ SV363 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1720,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $true )
| ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1690]) ).
thf(1721,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) )
= $true )
| ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1691]) ).
thf(1722,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1692]) ).
thf(1723,plain,
! [SV312: nat > $o,SV255: nat,SV366: nat,SV163: nat,SV62: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV62 @ SV163 @ SV366 @ SV255 )
= $false )
| ( ( ord_less_eq_nat @ ( sK10_SY841 @ SV312 @ SV255 @ SV163 @ SV62 ) @ SV366 )
= $true )
| ( ( SV312 @ ( min_dist_capacity @ SV62 @ SV163 @ SV255 ) )
= $true )
| ( ( connected_capacity @ SV62 @ SV163 @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1724,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV368: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ SV368 @ SV269 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SV368 ) )
= $true )
| ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1694]) ).
thf(1725,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1726,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(1727,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(1728,plain,
! [SV180: nat,SV358: list_P559422087at_nat,SV79: nat] :
( ( ( isPath_capacity @ c @ SV79 @ ( sK21_SY709 @ SV358 @ SV180 @ SV79 ) @ SV180 )
= $true )
| ( ( isPath_capacity @ c @ SV79 @ SV358 @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1697]) ).
thf(1729,plain,
! [SV364: nat,SV182: nat,SV318: nat] :
( ( ( ! [SY844: nat] :
( SV318
!= ( plus_plus_nat @ SV182 @ SY844 ) ) )
= $false )
| ( ( SV318
= ( plus_plus_nat @ SV182 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1730,plain,
! [SV320: nat,SV273: nat,SV184: nat,SV83: nat] :
( ( ( ~ ( connected_capacity @ c @ SV83 @ ( sK16_SY845 @ SV184 @ SV273 @ SV320 @ SV83 ) ) )
= $false )
| ( ( ord_less_nat @ SV320 @ SV273 )
= $false )
| ( ( ( min_dist_capacity @ c @ SV83 @ SV184 )
= SV273 )
= $false )
| ( ( connected_capacity @ c @ SV83 @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1701]) ).
thf(1731,plain,
! [SV320: nat,SV273: nat,SV184: nat,SV83: nat] :
( ( ( ( min_dist_capacity @ c @ SV83 @ ( sK16_SY845 @ SV184 @ SV273 @ SV320 @ SV83 ) )
!= SV320 )
= $false )
| ( ( ord_less_nat @ SV320 @ SV273 )
= $false )
| ( ( ( min_dist_capacity @ c @ SV83 @ SV184 )
= SV273 )
= $false )
| ( ( connected_capacity @ c @ SV83 @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1701]) ).
thf(1732,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $true )
| ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1733,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) )
= $true )
| ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1703]) ).
thf(1734,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ~ ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(1735,plain,
! [SV193: nat,SV360: nat,SV92: nat] :
( ( ( dist_capacity @ c @ SV92 @ ( sK22_SY732 @ SV360 @ SV193 @ SV92 ) @ SV193 )
= $true )
| ( ( dist_capacity @ c @ SV92 @ SV360 @ SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1705]) ).
thf(1736,plain,
! [SV282: nat,SV195: nat,SV94: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV94 @ ( sK17_SY813 @ SV195 @ SV282 @ SV94 ) @ SV282 ) )
= $false )
| ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1706]) ).
thf(1737,plain,
! [SV94: nat,SV282: nat,SV195: nat] :
( ( ( ( size_s1990949619at_nat @ ( sK17_SY813 @ SV195 @ SV282 @ SV94 ) )
!= SV195 )
= $false )
| ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1706]) ).
thf(1738,plain,
! [SV362: list_P559422087at_nat,SV282: nat,SV195: nat,SV94: nat] :
( ( ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
| ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV362 )
= SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1739,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $true )
| ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1710]) ).
thf(1740,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) )
= $true )
| ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1711]) ).
thf(1741,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) )
= $true )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1742,plain,
! [SV345: nat,SV356: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) )
= $false )
| ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(1743,plain,
! [SV345: nat,SV356: nat,SV367: list_P559422087at_nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
| ( ( size_s1990949619at_nat @ SV367 )
!= SV345 ) )
= $true )
| ( ( ~ ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1715]) ).
thf(1744,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 ) )
= $false )
| ( ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV133 )
= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1716]) ).
thf(1745,plain,
! [SV227: nat,SV32: nat,SV133: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV133 )
!= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $false )
| ( ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV133 )
= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1716]) ).
thf(1746,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( ~ ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 ) )
= $false )
| ( ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV140 )
= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1717]) ).
thf(1747,plain,
! [SV234: nat,SV39: nat,SV140: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV140 )
!= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $false )
| ( ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV140 )
= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1717]) ).
thf(1748,plain,
! [SV335: nat,SV304: nat,SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ( ~ ( connected_capacity @ SV40 @ SV141 @ ( sK18_SY856 @ SV235 @ SV304 @ SV335 @ SV141 @ SV40 ) ) )
= $false )
| ( ( ord_less_nat @ SV335 @ SV304 )
= $false )
| ( ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
= SV304 )
= $false )
| ( ( connected_capacity @ SV40 @ SV141 @ SV235 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1718]) ).
thf(1749,plain,
! [SV335: nat,SV304: nat,SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ( ( min_dist_capacity @ SV40 @ SV141 @ ( sK18_SY856 @ SV235 @ SV304 @ SV335 @ SV141 @ SV40 ) )
!= SV335 )
= $false )
| ( ( ord_less_nat @ SV335 @ SV304 )
= $false )
| ( ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
= SV304 )
= $false )
| ( ( connected_capacity @ SV40 @ SV141 @ SV235 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1718]) ).
thf(1750,plain,
! [SV363: nat,SV155: nat,SV307: nat] :
( ( ( SV307
!= ( plus_plus_nat @ SV155 @ ( sK23_SY836 @ SV363 @ SV155 @ SV307 ) ) )
= $false )
| ( ( SV307
= ( plus_plus_nat @ SV155 @ SV363 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1719]) ).
thf(1751,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) )
= $false )
| ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1752,plain,
! [SV357: nat,SV310: nat,SV161: product_prod_nat_nat > capacity,SV349: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV349 )
= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $false )
| ( ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1753,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV368: list_P559422087at_nat,SV78: nat] :
( ( ( isPath_capacity @ c @ SV78 @ SV368 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SV368 ) )
= $true )
| ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1754,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1725]) ).
thf(1755,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1725]) ).
thf(1756,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $true )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1757,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) )
= $true )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1727]) ).
thf(1758,plain,
! [SV364: nat,SV182: nat,SV318: nat] :
( ( ( SV318
!= ( plus_plus_nat @ SV182 @ ( sK24_SY844 @ SV364 @ SV182 @ SV318 ) ) )
= $false )
| ( ( SV318
= ( plus_plus_nat @ SV182 @ SV364 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1729]) ).
thf(1759,plain,
! [SV320: nat,SV273: nat,SV184: nat,SV83: nat] :
( ( ( connected_capacity @ c @ SV83 @ ( sK16_SY845 @ SV184 @ SV273 @ SV320 @ SV83 ) )
= $true )
| ( ( ord_less_nat @ SV320 @ SV273 )
= $false )
| ( ( ( min_dist_capacity @ c @ SV83 @ SV184 )
= SV273 )
= $false )
| ( ( connected_capacity @ c @ SV83 @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1730]) ).
thf(1760,plain,
! [SV320: nat,SV273: nat,SV184: nat,SV83: nat] :
( ( ( ( min_dist_capacity @ c @ SV83 @ ( sK16_SY845 @ SV184 @ SV273 @ SV320 @ SV83 ) )
= SV320 )
= $true )
| ( ( ord_less_nat @ SV320 @ SV273 )
= $false )
| ( ( ( min_dist_capacity @ c @ SV83 @ SV184 )
= SV273 )
= $false )
| ( ( connected_capacity @ c @ SV83 @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1731]) ).
thf(1761,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) )
= $false )
| ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(1762,plain,
! [SV359: nat,SV322: nat,SV188: product_prod_nat_nat > capacity,SV350: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV350 )
= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $false )
| ( ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ~ ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(1763,plain,
! [SV282: nat,SV195: nat,SV94: nat] :
( ( ( isPath_capacity @ c @ SV94 @ ( sK17_SY813 @ SV195 @ SV282 @ SV94 ) @ SV282 )
= $true )
| ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1736]) ).
thf(1764,plain,
! [SV94: nat,SV282: nat,SV195: nat] :
( ( ( ( size_s1990949619at_nat @ ( sK17_SY813 @ SV195 @ SV282 @ SV94 ) )
= SV195 )
= $true )
| ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1737]) ).
thf(1765,plain,
! [SV362: list_P559422087at_nat,SV282: nat,SV195: nat,SV94: nat] :
( ( ( ~ ( dist_capacity @ c @ SV94 @ SV195 @ SV282 ) )
= $false )
| ( ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV362 )
= SV195 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1738]) ).
thf(1766,plain,
! [SV362: list_P559422087at_nat,SV195: nat,SV282: nat,SV94: nat] :
( ( ( ~ ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV362 )
= SV195 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1738]) ).
thf(1767,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1768,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1769,plain,
! [SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ ( sK25_SY873 @ SV345 @ SV356 @ SV296 @ SV128 ) @ SV356 )
| ( ( size_s1990949619at_nat @ ( sK25_SY873 @ SV345 @ SV356 @ SV296 @ SV128 ) )
!= SV345 ) ) )
= $false )
| ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1742]) ).
thf(1770,plain,
! [SV345: nat,SV356: nat,SV367: list_P559422087at_nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 ) )
= $true )
| ( ( ( size_s1990949619at_nat @ SV367 )
!= SV345 )
= $true )
| ( ( ~ ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1743]) ).
thf(1771,plain,
! [SV227: nat,SV133: list_P559422087at_nat,SV32: nat] :
( ( ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
= $true )
| ( ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV133 )
= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1744]) ).
thf(1772,plain,
! [SV227: nat,SV32: nat,SV133: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV133 )
= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $true )
| ( ( isPath_capacity @ c @ SV32 @ SV133 @ SV227 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV133 )
= ( min_dist_capacity @ c @ SV32 @ SV227 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1745]) ).
thf(1773,plain,
! [SV234: nat,SV140: list_P559422087at_nat,SV39: nat] :
( ( ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
= $true )
| ( ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV140 )
= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1746]) ).
thf(1774,plain,
! [SV234: nat,SV39: nat,SV140: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV140 )
= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $true )
| ( ( isSimp1359852763pacity @ c @ SV39 @ SV140 @ SV234 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV140 )
= ( min_dist_capacity @ c @ SV39 @ SV234 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1747]) ).
thf(1775,plain,
! [SV335: nat,SV304: nat,SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ( connected_capacity @ SV40 @ SV141 @ ( sK18_SY856 @ SV235 @ SV304 @ SV335 @ SV141 @ SV40 ) )
= $true )
| ( ( ord_less_nat @ SV335 @ SV304 )
= $false )
| ( ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
= SV304 )
= $false )
| ( ( connected_capacity @ SV40 @ SV141 @ SV235 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(1776,plain,
! [SV335: nat,SV304: nat,SV235: nat,SV141: nat,SV40: product_prod_nat_nat > capacity] :
( ( ( ( min_dist_capacity @ SV40 @ SV141 @ ( sK18_SY856 @ SV235 @ SV304 @ SV335 @ SV141 @ SV40 ) )
= SV335 )
= $true )
| ( ( ord_less_nat @ SV335 @ SV304 )
= $false )
| ( ( ( min_dist_capacity @ SV40 @ SV141 @ SV235 )
= SV304 )
= $false )
| ( ( connected_capacity @ SV40 @ SV141 @ SV235 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1749]) ).
thf(1777,plain,
! [SV363: nat,SV155: nat,SV307: nat] :
( ( ( SV307
= ( plus_plus_nat @ SV155 @ ( sK23_SY836 @ SV363 @ SV155 @ SV307 ) ) )
= $true )
| ( ( SV307
= ( plus_plus_nat @ SV155 @ SV363 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1750]) ).
thf(1778,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 ) )
= $false )
| ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1751]) ).
thf(1779,plain,
! [SV357: nat,SV310: nat,SV161: product_prod_nat_nat > capacity,SV349: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $false )
| ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1751]) ).
thf(1780,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ~ ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) )
= $false )
| ( ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV349 )
= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(1781,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( isShor1936442771pacity @ c @ SV78 @ SV179 @ SV269 )
= $true )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1754]) ).
thf(1782,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) ) )
= $true )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1755]) ).
thf(1783,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1784,plain,
! [SV364: nat,SV182: nat,SV318: nat] :
( ( ( SV318
= ( plus_plus_nat @ SV182 @ ( sK24_SY844 @ SV364 @ SV182 @ SV318 ) ) )
= $true )
| ( ( SV318
= ( plus_plus_nat @ SV182 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1758]) ).
thf(1785,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 ) )
= $false )
| ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1761]) ).
thf(1786,plain,
! [SV359: nat,SV322: nat,SV188: product_prod_nat_nat > capacity,SV350: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $false )
| ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1761]) ).
thf(1787,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ~ ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) )
= $false )
| ( ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV350 )
= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1788,plain,
! [SV362: list_P559422087at_nat,SV282: nat,SV195: nat,SV94: nat] :
( ( ( dist_capacity @ c @ SV94 @ SV195 @ SV282 )
= $true )
| ( ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV362 )
= SV195 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1765]) ).
thf(1789,plain,
! [SV362: list_P559422087at_nat,SV195: nat,SV282: nat,SV94: nat] :
( ( ( ~ ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) )
= $true )
| ( ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV362 )
= SV195 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1766]) ).
thf(1790,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 ) )
= $false )
| ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1791,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) )
= $false )
| ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1792,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) ) ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1768]) ).
thf(1793,plain,
! [SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ ( sK25_SY873 @ SV345 @ SV356 @ SV296 @ SV128 ) @ SV356 )
| ( ( size_s1990949619at_nat @ ( sK25_SY873 @ SV345 @ SV356 @ SV296 @ SV128 ) )
!= SV345 ) ) )
= $true )
| ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1769]) ).
thf(1794,plain,
! [SV345: nat,SV356: nat,SV367: list_P559422087at_nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
!= SV345 )
= $true )
| ( ( ~ ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1795,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $true )
| ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1778]) ).
thf(1796,plain,
! [SV357: nat,SV310: nat,SV161: product_prod_nat_nat > capacity,SV349: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV349 )
= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $true )
| ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1779]) ).
thf(1797,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 ) )
= $false )
| ( ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV349 )
= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1780]) ).
thf(1798,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) )
= $false )
| ( ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV349 )
= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1780]) ).
thf(1799,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
| ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1800,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1783]) ).
thf(1801,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV78: nat] :
( ( ( ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1783]) ).
thf(1802,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $true )
| ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1785]) ).
thf(1803,plain,
! [SV359: nat,SV322: nat,SV188: product_prod_nat_nat > capacity,SV350: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV350 )
= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $true )
| ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1804,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 ) )
= $false )
| ( ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV350 )
= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1787]) ).
thf(1805,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) )
= $false )
| ( ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV350 )
= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1787]) ).
thf(1806,plain,
! [SV362: list_P559422087at_nat,SV195: nat,SV282: nat,SV94: nat] :
( ( ( ! [SY813: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ SY813 @ SV282 )
| ( ( size_s1990949619at_nat @ SY813 )
!= SV195 ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV362 )
= SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1807,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $true )
| ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1790]) ).
thf(1808,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) )
= $true )
| ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1791]) ).
thf(1809,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1792]) ).
thf(1810,plain,
! [SV205: product_prod_nat_nat > capacity,SV331: nat,SV361: nat,SV351: list_P559422087at_nat] :
( ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1792]) ).
thf(1811,plain,
! [SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV128 @ SV296 @ ( sK25_SY873 @ SV345 @ SV356 @ SV296 @ SV128 ) @ SV356 )
| ( ( size_s1990949619at_nat @ ( sK25_SY873 @ SV345 @ SV356 @ SV296 @ SV128 ) )
!= SV345 ) )
= $false )
| ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1812,plain,
! [SV356: nat,SV296: nat,SV128: product_prod_nat_nat > capacity,SV345: nat,SV367: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV367 )
= SV345 )
= $false )
| ( ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
= $false )
| ( ( ~ ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1794]) ).
thf(1813,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $true )
| ( ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV349 )
= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1797]) ).
thf(1814,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) ) )
= $true )
| ( ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV349 )
= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1798]) ).
thf(1815,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1799]) ).
thf(1816,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV78: nat] :
( ( ( ~ ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1799]) ).
thf(1817,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $true )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(1818,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV78: nat] :
( ( ( ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) )
= $true )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1819,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $true )
| ( ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV350 )
= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1804]) ).
thf(1820,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) ) )
= $true )
| ( ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV350 )
= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1805]) ).
thf(1821,plain,
! [SV282: nat,SV195: nat,SV362: list_P559422087at_nat,SV94: nat] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ c @ SV94 @ ( sK27_SY813 @ SV362 @ SV195 @ SV282 @ SV94 ) @ SV282 )
| ( ( size_s1990949619at_nat @ ( sK27_SY813 @ SV362 @ SV195 @ SV282 @ SV94 ) )
!= SV195 ) ) )
= $false )
| ( ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV362 )
= SV195 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1806]) ).
thf(1822,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV369: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV369 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SV369 ) ) )
= $true )
| ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(1823,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 )
= $true )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ~ ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1809]) ).
thf(1824,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1810]) ).
thf(1825,plain,
! [SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV128 @ SV296 @ ( sK25_SY873 @ SV345 @ SV356 @ SV296 @ SV128 ) @ SV356 ) )
= $false )
| ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1811]) ).
thf(1826,plain,
! [SV128: product_prod_nat_nat > capacity,SV296: nat,SV356: nat,SV345: nat] :
( ( ( ( size_s1990949619at_nat @ ( sK25_SY873 @ SV345 @ SV356 @ SV296 @ SV128 ) )
!= SV345 )
= $false )
| ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1811]) ).
thf(1827,plain,
! [SV367: list_P559422087at_nat,SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
| ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) )
= $false )
| ( ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1828,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
| ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) ) )
= $false )
| ( ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV349 )
= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1829,plain,
! [SV269: nat,SV179: list_P559422087at_nat,SV78: nat] :
( ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $true )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1815]) ).
thf(1830,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV78: nat] :
( ( ( ! [SY802: list_P559422087at_nat] :
( ~ ( isPath_capacity @ c @ SV78 @ SY802 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SY802 ) ) ) )
= $true )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1816]) ).
thf(1831,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV370: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ SV370 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SV370 ) ) )
= $true )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(1832,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
| ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) ) )
= $false )
| ( ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV350 )
= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(1833,plain,
! [SV282: nat,SV195: nat,SV362: list_P559422087at_nat,SV94: nat] :
( ( ( ~ ( ~ ( isPath_capacity @ c @ SV94 @ ( sK27_SY813 @ SV362 @ SV195 @ SV282 @ SV94 ) @ SV282 )
| ( ( size_s1990949619at_nat @ ( sK27_SY813 @ SV362 @ SV195 @ SV282 @ SV94 ) )
!= SV195 ) ) )
= $true )
| ( ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV362 )
= SV195 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1821]) ).
thf(1834,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV369: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV369 @ SV361 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SV369 ) )
= $true )
| ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1822]) ).
thf(1835,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1836,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1824]) ).
thf(1837,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1824]) ).
thf(1838,plain,
! [SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( isPath_capacity @ SV128 @ SV296 @ ( sK25_SY873 @ SV345 @ SV356 @ SV296 @ SV128 ) @ SV356 )
= $true )
| ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1825]) ).
thf(1839,plain,
! [SV128: product_prod_nat_nat > capacity,SV296: nat,SV356: nat,SV345: nat] :
( ( ( ( size_s1990949619at_nat @ ( sK25_SY873 @ SV345 @ SV356 @ SV296 @ SV128 ) )
= SV345 )
= $true )
| ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1826]) ).
thf(1840,plain,
! [SV367: list_P559422087at_nat,SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 ) )
= $false )
| ( ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1827]) ).
thf(1841,plain,
! [SV367: list_P559422087at_nat,SV345: nat,SV356: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) )
= $false )
| ( ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1827]) ).
thf(1842,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( ~ ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 ) )
= $false )
| ( ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV349 )
= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1828]) ).
thf(1843,plain,
! [SV357: nat,SV310: nat,SV161: product_prod_nat_nat > capacity,SV349: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV349 )
!= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $false )
| ( ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV349 )
= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1828]) ).
thf(1844,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV371: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ SV371 @ SV269 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SV371 ) ) )
= $true )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(1845,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV370: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ SV370 @ SV269 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SV370 ) )
= $true )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1831]) ).
thf(1846,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 ) )
= $false )
| ( ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV350 )
= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1832]) ).
thf(1847,plain,
! [SV359: nat,SV322: nat,SV188: product_prod_nat_nat > capacity,SV350: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV350 )
!= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $false )
| ( ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV350 )
= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1832]) ).
thf(1848,plain,
! [SV282: nat,SV195: nat,SV362: list_P559422087at_nat,SV94: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV94 @ ( sK27_SY813 @ SV362 @ SV195 @ SV282 @ SV94 ) @ SV282 )
| ( ( size_s1990949619at_nat @ ( sK27_SY813 @ SV362 @ SV195 @ SV282 @ SV94 ) )
!= SV195 ) )
= $false )
| ( ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV362 )
= SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(1849,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV369: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isPath_capacity @ SV205 @ SV331 @ SV369 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SV369 ) )
= $true )
| ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(1850,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1835]) ).
thf(1851,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1835]) ).
thf(1852,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $true )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1836]) ).
thf(1853,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) )
= $true )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1837]) ).
thf(1854,plain,
! [SV367: list_P559422087at_nat,SV356: nat,SV345: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( dist_capacity @ SV128 @ SV296 @ SV345 @ SV356 )
= $true )
| ( ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1840]) ).
thf(1855,plain,
! [SV367: list_P559422087at_nat,SV345: nat,SV356: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) )
= $true )
| ( ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1841]) ).
thf(1856,plain,
! [SV357: nat,SV349: list_P559422087at_nat,SV310: nat,SV161: product_prod_nat_nat > capacity] :
( ( ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $true )
| ( ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV349 )
= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1842]) ).
thf(1857,plain,
! [SV357: nat,SV310: nat,SV161: product_prod_nat_nat > capacity,SV349: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV349 )
= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $true )
| ( ( isSimp1359852763pacity @ SV161 @ SV310 @ SV349 @ SV357 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV349 )
= ( min_dist_capacity @ SV161 @ SV310 @ SV357 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1843]) ).
thf(1858,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV371: list_P559422087at_nat,SV78: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV78 @ SV371 @ SV269 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SV371 ) )
= $true )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1844]) ).
thf(1859,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV370: list_P559422087at_nat,SV78: nat] :
( ( ( isPath_capacity @ c @ SV78 @ SV370 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SV370 ) )
= $true )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(1860,plain,
! [SV359: nat,SV350: list_P559422087at_nat,SV322: nat,SV188: product_prod_nat_nat > capacity] :
( ( ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $true )
| ( ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV350 )
= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1846]) ).
thf(1861,plain,
! [SV359: nat,SV322: nat,SV188: product_prod_nat_nat > capacity,SV350: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ SV350 )
= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $true )
| ( ( isPath_capacity @ SV188 @ SV322 @ SV350 @ SV359 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV350 )
= ( min_dist_capacity @ SV188 @ SV322 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1847]) ).
thf(1862,plain,
! [SV282: nat,SV195: nat,SV362: list_P559422087at_nat,SV94: nat] :
( ( ( ~ ( isPath_capacity @ c @ SV94 @ ( sK27_SY813 @ SV362 @ SV195 @ SV282 @ SV94 ) @ SV282 ) )
= $false )
| ( ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV362 )
= SV195 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1848]) ).
thf(1863,plain,
! [SV94: nat,SV282: nat,SV195: nat,SV362: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ ( sK27_SY813 @ SV362 @ SV195 @ SV282 @ SV94 ) )
!= SV195 )
= $false )
| ( ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV362 )
= SV195 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1848]) ).
thf(1864,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isShor1936442771pacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $true )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1850]) ).
thf(1865,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) ) )
= $true )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1851]) ).
thf(1866,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(1867,plain,
! [SV367: list_P559422087at_nat,SV345: nat,SV356: nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ! [SY873: list_P559422087at_nat] :
~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ SY873 @ SV356 )
| ( ( size_s1990949619at_nat @ SY873 )
!= SV345 ) ) )
= $false )
| ( ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1855]) ).
thf(1868,plain,
! [SV179: list_P559422087at_nat,SV269: nat,SV371: list_P559422087at_nat,SV78: nat] :
( ( ( isPath_capacity @ c @ SV78 @ SV371 @ SV269 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV179 ) @ ( size_s1990949619at_nat @ SV371 ) )
= $true )
| ( ( isPath_capacity @ c @ SV78 @ SV179 @ SV269 )
= $false )
| ( ( isPath_capacity @ c @ SV78 @ ( sK15_SY802 @ SV179 @ SV269 @ SV78 ) @ SV269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(1869,plain,
! [SV282: nat,SV195: nat,SV362: list_P559422087at_nat,SV94: nat] :
( ( ( isPath_capacity @ c @ SV94 @ ( sK27_SY813 @ SV362 @ SV195 @ SV282 @ SV94 ) @ SV282 )
= $true )
| ( ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV362 )
= SV195 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1862]) ).
thf(1870,plain,
! [SV94: nat,SV282: nat,SV195: nat,SV362: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ ( sK27_SY813 @ SV362 @ SV195 @ SV282 @ SV94 ) )
= SV195 )
= $true )
| ( ( isPath_capacity @ c @ SV94 @ SV362 @ SV282 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV362 )
= SV195 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1863]) ).
thf(1871,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
| ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(1872,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1866]) ).
thf(1873,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1866]) ).
thf(1874,plain,
! [SV356: nat,SV345: nat,SV367: list_P559422087at_nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ ( sK28_SY873 @ SV367 @ SV345 @ SV356 @ SV296 @ SV128 ) @ SV356 )
| ( ( size_s1990949619at_nat @ ( sK28_SY873 @ SV367 @ SV345 @ SV356 @ SV296 @ SV128 ) )
!= SV345 ) ) )
= $false )
| ( ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= SV345 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1867]) ).
thf(1875,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1871]) ).
thf(1876,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1871]) ).
thf(1877,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $true )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1872]) ).
thf(1878,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) )
= $true )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1873]) ).
thf(1879,plain,
! [SV356: nat,SV345: nat,SV367: list_P559422087at_nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ( ~ ( isPath_capacity @ SV128 @ SV296 @ ( sK28_SY873 @ SV367 @ SV345 @ SV356 @ SV296 @ SV128 ) @ SV356 )
| ( ( size_s1990949619at_nat @ ( sK28_SY873 @ SV367 @ SV345 @ SV356 @ SV296 @ SV128 ) )
!= SV345 ) ) )
= $true )
| ( ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1874]) ).
thf(1880,plain,
! [SV361: nat,SV351: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $true )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1875]) ).
thf(1881,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ! [SY875: list_P559422087at_nat] :
( ~ ( isPath_capacity @ SV205 @ SV331 @ SY875 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SY875 ) ) ) )
= $true )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1876]) ).
thf(1882,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV372: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV372 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SV372 ) ) )
= $true )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(1883,plain,
! [SV356: nat,SV345: nat,SV367: list_P559422087at_nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV128 @ SV296 @ ( sK28_SY873 @ SV367 @ SV345 @ SV356 @ SV296 @ SV128 ) @ SV356 )
| ( ( size_s1990949619at_nat @ ( sK28_SY873 @ SV367 @ SV345 @ SV356 @ SV296 @ SV128 ) )
!= SV345 ) )
= $false )
| ( ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(1884,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV373: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV373 @ SV361 )
| ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SV373 ) ) )
= $true )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(1885,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV372: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV372 @ SV361 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SV372 ) )
= $true )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(1886,plain,
! [SV356: nat,SV345: nat,SV367: list_P559422087at_nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV128 @ SV296 @ ( sK28_SY873 @ SV367 @ SV345 @ SV356 @ SV296 @ SV128 ) @ SV356 ) )
= $false )
| ( ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1883]) ).
thf(1887,plain,
! [SV128: product_prod_nat_nat > capacity,SV296: nat,SV356: nat,SV345: nat,SV367: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ ( sK28_SY873 @ SV367 @ SV345 @ SV356 @ SV296 @ SV128 ) )
!= SV345 )
= $false )
| ( ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1883]) ).
thf(1888,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV373: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( ~ ( isPath_capacity @ SV205 @ SV331 @ SV373 @ SV361 ) )
= $true )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SV373 ) )
= $true )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1884]) ).
thf(1889,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV372: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isPath_capacity @ SV205 @ SV331 @ SV372 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SV372 ) )
= $true )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(1890,plain,
! [SV356: nat,SV345: nat,SV367: list_P559422087at_nat,SV296: nat,SV128: product_prod_nat_nat > capacity] :
( ( ( isPath_capacity @ SV128 @ SV296 @ ( sK28_SY873 @ SV367 @ SV345 @ SV356 @ SV296 @ SV128 ) @ SV356 )
= $true )
| ( ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1886]) ).
thf(1891,plain,
! [SV128: product_prod_nat_nat > capacity,SV296: nat,SV356: nat,SV345: nat,SV367: list_P559422087at_nat] :
( ( ( ( size_s1990949619at_nat @ ( sK28_SY873 @ SV367 @ SV345 @ SV356 @ SV296 @ SV128 ) )
= SV345 )
= $true )
| ( ( isPath_capacity @ SV128 @ SV296 @ SV367 @ SV356 )
= $false )
| ( ( ( size_s1990949619at_nat @ SV367 )
= SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1887]) ).
thf(1892,plain,
! [SV351: list_P559422087at_nat,SV361: nat,SV373: list_P559422087at_nat,SV331: nat,SV205: product_prod_nat_nat > capacity] :
( ( ( isPath_capacity @ SV205 @ SV331 @ SV373 @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ SV351 ) @ ( size_s1990949619at_nat @ SV373 ) )
= $true )
| ( ( isPath_capacity @ SV205 @ SV331 @ SV351 @ SV361 )
= $false )
| ( ( isPath_capacity @ SV205 @ SV331 @ ( sK26_SY875 @ SV351 @ SV361 @ SV331 @ SV205 ) @ SV361 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(1893,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[376,1892,1891,1890,1889,1880,1877,1870,1869,1868,1864,1861,1860,1859,1857,1856,1854,1852,1849,1839,1838,1829,1819,1817,1813,1807,1803,1802,1796,1795,1788,1784,1781,1777,1776,1775,1774,1773,1772,1771,1764,1763,1760,1759,1756,1753,1739,1735,1732,1728,1723,1720,1713,1709,1708,1699,1698,1689,1687,1686,1683,1681,1660,1652,1651,1647,1646,1643,1642,1633,1632,1625,1624,1616,1611,1600,1589,1583,1582,1580,1574,1568,1564,1563,1562,1561,1559,1557,1555,1554,1553,1550,1545,1537,1535,1531,1529,1523,1518,1517,1515,1514,1511,1509,1504,1503,1502,1501,1500,1499,1498,1497,1496,1495,1494,1493,1492,1491,1490,1489,1488,1487,1486,1485,1484,1483,1482,1481,1480,1479,1478,1477,1476,1475,1474,1473,1472,1459,1458,1456,1449,1442,1426,1420,1419,1416,1415,1414,1413,1412,1411,1410,1409,1408,1407,1406,1405,1369,1357,1344,1343,1342,1339,1321,1320,1319,1316,1315,1287,1286,1285,1284,1279,1271,1264,1262,1248,1245,1225,1174,1161,1159,1150,1147,1127,1120,1113,1108,1106,1105,1103,1102,1100,1095,1090,1089,1088,1086,1083,1081,1080,1077,1074,1071,1067,1065,1063,1062,1061,1060,1059,1058,1057,1055,1041,1040,1033,1027,1009,992,976,964,952,944,931,929,927,925,922,920,917,916,914,912,899,893,886,883,863,856,828,824,822,820,818,816,815,810,805,804,803,801,790,761,712,711,701,693,679,673,666,643,636,608,604,600,599,589,587,581,395,394,393,392,389,388,382,380,379]) ).
thf(1894,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1893]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP053^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.16 % Computer : n002.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Oct 6 11:17:57 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.56/4.52 .
% 25.56/4.52
% 25.56/4.52 No.of.Axioms: 117
% 25.56/4.52
% 25.56/4.52 Length.of.Defs: 0
% 25.56/4.52
% 25.56/4.52 Contains.Choice.Funs: false
% 25.56/4.52 .............................................................
% 25.56/4.52
% 25.56/4.52 ********************************
% 25.56/4.52 * All subproblems solved! *
% 25.56/4.52 ********************************
% 25.56/4.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:117,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1893,loop_count:0,foatp_calls:1,translation:fof_full)
% 25.56/4.52
% 25.56/4.52 %**** Beginning of derivation protocol ****
% 25.56/4.52 % SZS output start CNFRefutation
% See solution above
% 25.56/4.54
% 25.56/4.54 %**** End of derivation protocol ****
% 25.56/4.54 %**** no. of clauses in derivation: 1757 ****
% 25.56/4.54 %**** clause counter: 1893 ****
% 25.56/4.54
% 25.56/4.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:117,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1893,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------