%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP052^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:10 AM UTC 2026
% Result : Theorem 6.53s 2.44s
% Output : Refutation 6.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 21 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 146 ( 9 ~; 3 |; 0 &; 131 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 120 ( 117 usr; 11 con; 0-5 aty)
% Number of variables : 29 ( 0 ^; 29 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
product_prod_nat_nat: $tType ).
thf(type_def_6,type,
capacity: $tType ).
thf(type_def_8,type,
list_P559422087at_nat: $tType ).
thf(type_def_9,type,
nat: $tType ).
thf(type_def_10,type,
set_Pr1986765409at_nat: $tType ).
thf(type_def_11,type,
set_nat: $tType ).
thf(func_def_0,type,
list_P559422087at_nat: $tType ).
thf(func_def_1,type,
set_Pr1986765409at_nat: $tType ).
thf(func_def_2,type,
product_prod_nat_nat: $tType ).
thf(func_def_3,type,
set_nat: $tType ).
thf(func_def_4,type,
capacity: $tType ).
thf(func_def_5,type,
nat: $tType ).
thf(func_def_6,type,
augmen887209518pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
thf(func_def_7,type,
augmen72931474pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > product_prod_nat_nat > capacity ).
thf(func_def_8,type,
augmen1090971539pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > $o ).
thf(func_def_9,type,
augmen68920357pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > capacity ).
thf(func_def_10,type,
finite217307323pacity: ( product_prod_nat_nat > capacity ) > $o ).
thf(func_def_11,type,
isShor1936442771pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_12,type,
isSimp1359852763pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_13,type,
plus_plus_capacity: capacity > capacity > capacity ).
thf(func_def_14,type,
zero_zero_capacity: capacity ).
thf(func_def_15,type,
inf_in2138576462_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
thf(func_def_16,type,
inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_17,type,
set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
thf(func_def_18,type,
finite1387368318pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(func_def_19,type,
flow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(func_def_20,type,
val_capacity: ( product_prod_nat_nat > capacity ) > nat > ( product_prod_nat_nat > capacity ) > capacity ).
thf(func_def_21,type,
nCut_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > set_nat > $o ).
thf(func_def_22,type,
cap_capacity: ( product_prod_nat_nat > capacity ) > set_nat > capacity ).
thf(func_def_23,type,
nFlow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(func_def_24,type,
nPreflow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(func_def_25,type,
network_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > $o ).
thf(func_def_26,type,
excess_capacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > nat > capacity ).
thf(func_def_27,type,
isMaxFlow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(func_def_28,type,
is_max2144541363pacity: ( product_prod_nat_nat > capacity ) > nat > nat > capacity > $o ).
thf(func_def_29,type,
preflow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(func_def_30,type,
isMinCut_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > set_nat > $o ).
thf(func_def_31,type,
bot_bot_nat_o: nat > $o ).
thf(func_def_32,type,
bot_bo513358416_nat_o: product_prod_nat_nat > $o ).
thf(func_def_34,type,
bot_bot_set_nat: set_nat ).
thf(func_def_35,type,
bot_bo2130386637at_nat: set_Pr1986765409at_nat ).
thf(func_def_36,type,
ord_le1015898640_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
thf(func_def_37,type,
ord_le116442893at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_38,type,
ord_less_capacity: capacity > capacity > $o ).
thf(func_def_39,type,
ord_le1039616028_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
thf(func_def_40,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_41,type,
ord_less_eq_capacity: capacity > capacity > $o ).
thf(func_def_42,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_43,type,
product_swap_nat_nat: product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_44,type,
converse_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_45,type,
residu1549650759pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
thf(func_def_46,type,
residu800046103pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(func_def_47,type,
residu164581374pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(func_def_48,type,
residu203630698pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
thf(func_def_49,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_50,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(func_def_51,type,
member_nat: nat > set_nat > $o ).
thf(func_def_52,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_53,type,
c: product_prod_nat_nat > capacity ).
thf(func_def_54,type,
f: product_prod_nat_nat > capacity ).
thf(func_def_55,type,
p: list_P559422087at_nat ).
thf(func_def_56,type,
s: nat ).
thf(func_def_57,type,
t: nat ).
thf(func_def_74,type,
sK0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > nat ).
thf(func_def_75,type,
sK1: set_Pr1986765409at_nat > set_Pr1986765409at_nat > nat ).
thf(func_def_76,type,
sK2: set_Pr1986765409at_nat > ( nat > nat > $o ) > nat ).
thf(func_def_77,type,
sK3: set_Pr1986765409at_nat > ( nat > nat > $o ) > nat ).
thf(func_def_78,type,
sK4: ( capacity > capacity > $o ) > capacity ).
thf(func_def_79,type,
sK5: ( capacity > capacity > $o ) > capacity ).
thf(func_def_80,type,
sK6: ( capacity > capacity > $o ) > capacity ).
thf(func_def_81,type,
sK7: ( capacity > capacity > $o ) > capacity ).
thf(func_def_82,type,
sK8: ( set_Pr1986765409at_nat > capacity ) > set_Pr1986765409at_nat ).
thf(func_def_83,type,
sK9: ( set_Pr1986765409at_nat > capacity ) > set_Pr1986765409at_nat ).
thf(func_def_84,type,
sK10: ( capacity > set_Pr1986765409at_nat ) > capacity ).
thf(func_def_85,type,
sK11: ( capacity > set_Pr1986765409at_nat ) > capacity ).
thf(func_def_86,type,
sK12: ( set_Pr1986765409at_nat > capacity ) > set_Pr1986765409at_nat ).
thf(func_def_87,type,
sK13: ( set_Pr1986765409at_nat > capacity ) > set_Pr1986765409at_nat ).
thf(func_def_88,type,
sK14: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_89,type,
sK15: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_90,type,
sK16: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_91,type,
sK17: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_92,type,
sK18: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_93,type,
sK19: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_94,type,
sK20: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_95,type,
sK21: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_96,type,
sK22: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_97,type,
sK23: ( capacity > capacity ) > capacity ).
thf(func_def_98,type,
sK24: ( capacity > capacity ) > capacity ).
thf(func_def_99,type,
sK25: ( set_Pr1986765409at_nat > capacity ) > set_Pr1986765409at_nat ).
thf(func_def_100,type,
sK26: ( set_Pr1986765409at_nat > capacity ) > set_Pr1986765409at_nat ).
thf(func_def_101,type,
sK27: list_P559422087at_nat ).
thf(func_def_102,type,
sK28: set_nat ).
thf(func_def_103,type,
sK29: ( capacity > capacity ) > capacity ).
thf(func_def_104,type,
sK30: ( capacity > capacity ) > capacity ).
thf(func_def_105,type,
sK31: ( capacity > capacity ) > capacity ).
thf(func_def_106,type,
sK32: ( capacity > capacity ) > capacity ).
thf(func_def_107,type,
sK33: nat > nat > ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
thf(func_def_108,type,
sK34: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_109,type,
sK35: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_110,type,
sK36: product_prod_nat_nat > nat ).
thf(func_def_111,type,
sK37: product_prod_nat_nat > nat ).
thf(func_def_112,type,
sK38: nat > nat > ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > set_nat ).
thf(func_def_113,type,
sK39: nat > nat > ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat ).
thf(func_def_114,type,
sK40: ( capacity > set_Pr1986765409at_nat ) > capacity ).
thf(func_def_115,type,
sK41: ( capacity > set_Pr1986765409at_nat ) > capacity ).
thf(func_def_116,type,
sK42: ( capacity > capacity ) > capacity ).
thf(func_def_117,type,
sK43: ( capacity > capacity ) > capacity ).
thf(func_def_118,type,
sK44: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_119,type,
sK45: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_120,type,
sK46: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_121,type,
sK47: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_122,type,
sK48: ( capacity > set_Pr1986765409at_nat ) > capacity ).
thf(func_def_123,type,
sK49: ( capacity > set_Pr1986765409at_nat ) > capacity ).
thf(func_def_124,type,
sK50: ( product_prod_nat_nat > capacity ) > nat > ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat ).
thf(func_def_125,type,
sK51: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_126,type,
sK52: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_127,type,
sK53: set_Pr1986765409at_nat > product_prod_nat_nat > nat ).
thf(func_def_128,type,
sK54: set_Pr1986765409at_nat > product_prod_nat_nat > nat ).
thf(func_def_129,type,
sK55: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > nat > nat > product_prod_nat_nat > capacity ).
thf(func_def_130,type,
sK56: ( set_Pr1986765409at_nat > capacity ) > set_Pr1986765409at_nat ).
thf(func_def_131,type,
sK57: ( set_Pr1986765409at_nat > capacity ) > set_Pr1986765409at_nat ).
thf(func_def_132,type,
sK58: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_133,type,
sK59: ( set_Pr1986765409at_nat > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat ).
thf(func_def_134,type,
sK60: list_P559422087at_nat ).
thf(func_def_135,type,
sK61: ( capacity > set_Pr1986765409at_nat ) > capacity ).
thf(func_def_136,type,
sK62: ( capacity > set_Pr1986765409at_nat ) > capacity ).
thf(func_def_137,type,
sK63: product_prod_nat_nat > nat ).
thf(func_def_138,type,
sK64: product_prod_nat_nat > nat ).
thf(func_def_140,type,
ph66:
!>[X0: $tType] : X0 ).
thf(f1983,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1974,f1203]) ).
thf(f1203,plain,
( ( augmen1090971539pacity @ c @ s @ t @ f @ p )
= $true ),
inference(cnf_transformation,[status(thm)],[f316]) ).
thf(f316,plain,
( ( augmen1090971539pacity @ c @ s @ t @ f @ p )
= $true ),
inference(fool_elimination,[status(thm)],[f315]) ).
thf(f315,plain,
augmen1090971539pacity @ c @ s @ t @ f @ p,
inference(rectify,[status(thm)],[f279]) ).
thf(f279,axiom,
augmen1090971539pacity @ c @ s @ t @ f @ p,
file('/export/starexec/sandbox2/tmp/tmp.VKYVsEMyde/DTF2THF_13121.p',conj_0) ).
thf(f1974,plain,
( ( augmen1090971539pacity @ c @ s @ t @ f @ p )
!= $true ),
inference(superposition,[status(thm)],[f1847,f1437]) ).
thf(f1437,plain,
! [X0: list_P559422087at_nat] :
( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ s @ X0 @ t )
= ( augmen1090971539pacity @ c @ s @ t @ f @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f746]) ).
thf(f746,plain,
! [X0: list_P559422087at_nat] :
( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ s @ X0 @ t )
= ( augmen1090971539pacity @ c @ s @ t @ f @ X0 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X1: list_P559422087at_nat] :
( ( augmen1090971539pacity @ c @ s @ t @ f @ X1 )
= ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ s @ X1 @ t ) ),
file('/export/starexec/sandbox2/tmp/tmp.VKYVsEMyde/DTF2THF_13121.p',fact_5_isAugmentingPath__def) ).
thf(f1847,plain,
! [X2: nat,X0: product_prod_nat_nat > capacity,X1: nat] :
( $true
!= ( isSimp1359852763pacity @ X0 @ X1 @ p @ X2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1835]) ).
thf(f1835,plain,
! [X2: nat,X0: product_prod_nat_nat > capacity,X1: nat] :
( ( $true
!= ( isSimp1359852763pacity @ X0 @ X1 @ p @ X2 ) )
| ( bot_bo2130386637at_nat != bot_bo2130386637at_nat ) ),
inference(superposition,[status(thm)],[f1431,f1201]) ).
thf(f1201,plain,
! [X2: list_P559422087at_nat,X3: nat,X0: nat,X1: product_prod_nat_nat > capacity] :
( ( bot_bo2130386637at_nat
= ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ X2 ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ X2 ) ) ) )
| ( ( isSimp1359852763pacity @ X1 @ X0 @ X2 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f910]) ).
thf(f910,plain,
! [X0: nat,X1: product_prod_nat_nat > capacity,X2: list_P559422087at_nat,X3: nat] :
( ( bot_bo2130386637at_nat
= ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ X2 ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ X2 ) ) ) )
| ( ( isSimp1359852763pacity @ X1 @ X0 @ X2 @ X3 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f454]) ).
thf(f454,plain,
! [X0: nat,X1: product_prod_nat_nat > capacity,X2: list_P559422087at_nat,X3: nat] :
( ( ( isSimp1359852763pacity @ X1 @ X0 @ X2 @ X3 )
= $true )
=> ( bot_bo2130386637at_nat
= ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ X2 ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f453]) ).
thf(f453,plain,
! [X0: nat,X1: product_prod_nat_nat > capacity,X2: list_P559422087at_nat,X3: nat] :
( ( isSimp1359852763pacity @ X1 @ X0 @ X2 @ X3 )
=> ( bot_bo2130386637at_nat
= ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ X2 ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f58]) ).
thf(f58,axiom,
! [X0: nat,X14: product_prod_nat_nat > capacity,X1: list_P559422087at_nat,X2: nat] :
( ( isSimp1359852763pacity @ X14 @ X0 @ X1 @ X2 )
=> ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ X1 ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ X1 ) ) )
= bot_bo2130386637at_nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.VKYVsEMyde/DTF2THF_13121.p',fact_57_Graph_OisSPath__nt__parallel__pf) ).
thf(f1431,plain,
( bot_bo2130386637at_nat
!= ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(cnf_transformation,[status(thm)],[f745]) ).
thf(f745,plain,
( bot_bo2130386637at_nat
!= ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(flattening,[status(thm)],[f281]) ).
thf(f281,negated_conjecture,
( bot_bo2130386637at_nat
!= ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f280]) ).
thf(f280,conjecture,
( bot_bo2130386637at_nat
= ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VKYVsEMyde/DTF2THF_13121.p',conj_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP052^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n028.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 08:24:42 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.49 ---- Original DTF file ---
% 0.29/0.49 thf(spec,logic,$$dhol).
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 % File : ITP052^1 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.49 % Domain : Interactive Theorem Proving
% 0.29/0.49 % Problem : Sledgehammer EdmondsKarp_Termination_Abstract problem prob_430__7598256_1
% 0.29/0.49 % Version : Especial.
% 0.29/0.49 % English :
% 0.29/0.49
% 0.29/0.49 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.49 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.49 % Source : [Des21]
% 0.29/0.49 % Names : EdmondsKarp_Termination_Abstract/prob_430__7598256_1 [Des21]
% 0.29/0.49
% 0.29/0.49 % Status : Theorem
% 0.29/0.49 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.29/0.49 % Syntax : Number of formulae : 338 ( 114 unt; 58 typ; 0 def)
% 0.29/0.49 % Number of atoms : 729 ( 198 equ; 0 cnn)
% 0.29/0.49 % Maximal formula atoms : 12 ( 2 avg)
% 0.29/0.49 % Number of connectives : 2470 ( 62 ~; 2 |; 35 &;2075 @)
% 0.29/0.49 % ( 0 <=>; 296 =>; 0 <=; 0 <~>)
% 0.29/0.49 % Maximal formula depth : 17 ( 7 avg)
% 0.29/0.49 % Number of types : 7 ( 6 usr)
% 0.29/0.49 % Number of type conns : 332 ( 332 >; 0 *; 0 +; 0 <<)
% 0.29/0.49 % Number of symbols : 53 ( 52 usr; 7 con; 0-5 aty)
% 0.29/0.49 % Number of variables : 813 ( 62 ^; 725 !; 26 ?; 813 :)
% 0.29/0.49 % SPC : TH0_THM_EQU_NAR
% 0.29/0.49
% 0.29/0.49 % Comments : This file was generated by Sledgehammer 2021-02-23 15:32:13.019
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 % Could-be-implicit typings (6)
% 0.29/0.49 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.29/0.49 list_P559422087at_nat: $tType ).
% 0.29/0.49
% 0.29/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.29/0.49 set_Pr1986765409at_nat: $tType ).
% 0.29/0.49
% 0.29/0.49 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49 product_prod_nat_nat: $tType ).
% 0.29/0.49
% 0.29/0.49 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.49 set_nat: $tType ).
% 0.29/0.49
% 0.29/0.49 thf(ty_n_tf__capacity,type,
% 0.29/0.49 capacity: $tType ).
% 0.29/0.49
% 0.29/0.49 thf(ty_n_t__Nat__Onat,type,
% 0.29/0.49 nat: $tType ).
% 0.29/0.49
% 0.29/0.49 % Explicit typings (52)
% 0.29/0.49 thf(sy_c_Augmenting__Flow_ONFlow_Oaugment_001tf__capacity,type,
% 0.29/0.49 augmen887209518pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Augmenting__Path_ONPreflow_OaugmentingFlow_001tf__capacity,type,
% 0.29/0.49 augmen72931474pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > product_prod_nat_nat > capacity ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Augmenting__Path_ONPreflow_OisAugmentingPath_001tf__capacity,type,
% 0.29/0.49 augmen1090971539pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Augmenting__Path_ONPreflow_OresCap_001tf__capacity,type,
% 0.29/0.49 augmen68920357pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > capacity ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Graph_OFinite__Graph_001tf__capacity,type,
% 0.29/0.49 finite217307323pacity: ( product_prod_nat_nat > capacity ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Graph_OGraph_OisShortestPath_001tf__capacity,type,
% 0.29/0.49 isShor1936442771pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Graph_OGraph_OisSimplePath_001tf__capacity,type,
% 0.29/0.49 isSimp1359852763pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Groups_Oplus__class_Oplus_001tf__capacity,type,
% 0.29/0.49 plus_plus_capacity: capacity > capacity > capacity ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Groups_Ozero__class_Ozero_001tf__capacity,type,
% 0.29/0.49 zero_zero_capacity: capacity ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.29/0.49 inf_in2138576462_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.29/0.49 inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49 set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Network_OFinite__Preflow_001tf__capacity,type,
% 0.29/0.49 finite1387368318pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Network_OFlow_001tf__capacity,type,
% 0.29/0.49 flow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Network_OFlow_Oval_001tf__capacity,type,
% 0.29/0.49 val_capacity: ( product_prod_nat_nat > capacity ) > nat > ( product_prod_nat_nat > capacity ) > capacity ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Network_ONCut_001tf__capacity,type,
% 0.29/0.49 nCut_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > set_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Network_ONCut_Ocap_001tf__capacity,type,
% 0.29/0.49 cap_capacity: ( product_prod_nat_nat > capacity ) > set_nat > capacity ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Network_ONFlow_001tf__capacity,type,
% 0.29/0.49 nFlow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Network_ONPreflow_001tf__capacity,type,
% 0.29/0.49 nPreflow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Network_ONetwork_001tf__capacity,type,
% 0.29/0.49 network_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Network_ONetwork_Oexcess_001tf__capacity,type,
% 0.29/0.49 excess_capacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > nat > capacity ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Network_ONetwork_OisMaxFlow_001tf__capacity,type,
% 0.29/0.49 isMaxFlow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Network_ONetwork_Ois__max__flow__val_001tf__capacity,type,
% 0.29/0.49 is_max2144541363pacity: ( product_prod_nat_nat > capacity ) > nat > nat > capacity > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Network_OPreflow_001tf__capacity,type,
% 0.29/0.49 preflow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Network_OisMinCut_001tf__capacity,type,
% 0.29/0.49 isMinCut_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > set_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.29/0.49 bot_bot_nat_o: nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.29/0.49 bot_bo513358416_nat_o: product_prod_nat_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
% 0.29/0.49 bot_bot_o: $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.49 bot_bot_set_nat: set_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.29/0.49 bot_bo2130386637at_nat: set_Pr1986765409at_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Orderings_Oord__class_Oless_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.29/0.49 ord_le1015898640_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.29/0.49 ord_le116442893at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Orderings_Oord__class_Oless_001tf__capacity,type,
% 0.29/0.49 ord_less_capacity: capacity > capacity > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.29/0.49 ord_le1039616028_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.29/0.49 ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001tf__capacity,type,
% 0.29/0.49 ord_less_eq_capacity: capacity > capacity > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Product__Type_Oprod_Oswap_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 product_swap_nat_nat: product_prod_nat_nat > product_prod_nat_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Relation_Oconverse_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.49 converse_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Residual__Graph_ONetwork_Oflow__of__cf_001tf__capacity,type,
% 0.29/0.49 residu1549650759pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Residual__Graph_ORGraph_001tf__capacity,type,
% 0.29/0.49 residu800046103pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Residual__Graph_ORPreGraph_001tf__capacity,type,
% 0.29/0.49 residu164581374pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Residual__Graph_OresidualGraph_001tf__capacity,type,
% 0.29/0.49 residu203630698pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.29/0.49 collect_nat: ( nat > $o ) > set_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49 collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_member_001t__Nat__Onat,type,
% 0.29/0.49 member_nat: nat > set_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.49 member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_v_c,type,
% 0.29/0.49 c: product_prod_nat_nat > capacity ).
% 0.29/0.49
% 0.29/0.49 thf(sy_v_f,type,
% 0.29/0.49 f: product_prod_nat_nat > capacity ).
% 0.29/0.49
% 0.29/0.49 thf(sy_v_p,type,
% 0.29/0.49 p: list_P559422087at_nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_v_s,type,
% 0.29/0.49 s: nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_v_t,type,
% 0.29/0.49 t: nat ).
% 0.29/0.49
% 0.29/0.49 % Relevant facts (278)
% 0.29/0.49 thf(fact_0_t__not__s,axiom,
% 0.29/0.49 t != s ).
% 0.29/0.49
% 0.29/0.49 % t_not_s
% 0.29/0.49 thf(fact_1_cf_OisSPath__nt__parallel__pf,axiom,
% 0.29/0.49 ! [S: nat,P: list_P559422087at_nat,T: nat] :
% 0.29/0.49 ( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ S @ P @ T )
% 0.29/0.49 => ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ P ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ P ) ) )
% 0.29/0.49 = bot_bo2130386637at_nat ) ) ).
% 0.29/0.49
% 0.29/0.49 % cf.isSPath_nt_parallel_pf
% 0.29/0.49 thf(fact_2_isSPath__nt__parallel__pf,axiom,
% 0.29/0.49 ! [S: nat,P: list_P559422087at_nat,T: nat] :
% 0.29/0.49 ( ( isSimp1359852763pacity @ c @ S @ P @ T )
% 0.29/0.49 => ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ P ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ P ) ) )
% 0.29/0.49 = bot_bo2130386637at_nat ) ) ).
% 0.29/0.49
% 0.29/0.49 % isSPath_nt_parallel_pf
% 0.29/0.49 thf(fact_3_NFlow__axioms,axiom,
% 0.29/0.49 nFlow_capacity @ c @ s @ t @ f ).
% 0.29/0.49
% 0.29/0.49 % NFlow_axioms
% 0.29/0.49 thf(fact_4_max__flow__val__unique,axiom,
% 0.29/0.49 ! [Fv1: capacity,Fv2: capacity] :
% 0.29/0.49 ( ( is_max2144541363pacity @ c @ s @ t @ Fv1 )
% 0.29/0.49 => ( ( is_max2144541363pacity @ c @ s @ t @ Fv2 )
% 0.29/0.49 => ( Fv1 = Fv2 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % max_flow_val_unique
% 0.29/0.49 thf(fact_5_isAugmentingPath__def,axiom,
% 0.29/0.49 ! [P: list_P559422087at_nat] :
% 0.29/0.49 ( ( augmen1090971539pacity @ c @ s @ t @ f @ P )
% 0.29/0.49 = ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ s @ P @ t ) ) ).
% 0.29/0.49
% 0.29/0.49 % isAugmentingPath_def
% 0.29/0.49 thf(fact_6_Finite__Preflow__axioms,axiom,
% 0.29/0.49 finite1387368318pacity @ c @ s @ t @ f ).
% 0.29/0.49
% 0.29/0.49 % Finite_Preflow_axioms
% 0.29/0.49 thf(fact_7_fofu__I__II,axiom,
% 0.29/0.49 ( ( isMaxFlow_capacity @ c @ s @ t @ f )
% 0.29/0.49 => ~ ? [X_1: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ X_1 ) ) ).
% 0.29/0.49
% 0.29/0.49 % fofu_I_II
% 0.29/0.49 thf(fact_8_noAugPath__iff__maxFlow,axiom,
% 0.29/0.49 ( ( ~ ? [X: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ X ) )
% 0.29/0.49 = ( isMaxFlow_capacity @ c @ s @ t @ f ) ) ).
% 0.29/0.49
% 0.29/0.49 % noAugPath_iff_maxFlow
% 0.29/0.49 thf(fact_9_Preflow__axioms,axiom,
% 0.29/0.49 preflow_capacity @ c @ s @ t @ f ).
% 0.29/0.49
% 0.29/0.49 % Preflow_axioms
% 0.29/0.49 thf(fact_10_is__RGraph,axiom,
% 0.29/0.49 residu800046103pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ) ).
% 0.29/0.49
% 0.29/0.49 % is_RGraph
% 0.29/0.49 thf(fact_11_Flow__axioms,axiom,
% 0.29/0.49 flow_capacity @ c @ s @ t @ f ).
% 0.29/0.49
% 0.29/0.49 % Flow_axioms
% 0.29/0.49 thf(fact_12_NPreflow__axioms,axiom,
% 0.29/0.49 nPreflow_capacity @ c @ s @ t @ f ).
% 0.29/0.49
% 0.29/0.49 % NPreflow_axioms
% 0.29/0.49 thf(fact_13_converse__empty,axiom,
% 0.29/0.49 ( ( converse_nat_nat @ bot_bo2130386637at_nat )
% 0.29/0.49 = bot_bo2130386637at_nat ) ).
% 0.29/0.49
% 0.29/0.49 % converse_empty
% 0.29/0.49 thf(fact_14_inf__bot__left,axiom,
% 0.29/0.49 ! [X2: product_prod_nat_nat > $o] :
% 0.29/0.49 ( ( inf_in2138576462_nat_o @ bot_bo513358416_nat_o @ X2 )
% 0.29/0.49 = bot_bo513358416_nat_o ) ).
% 0.29/0.49
% 0.29/0.49 % inf_bot_left
% 0.29/0.49 thf(fact_15_inf__bot__left,axiom,
% 0.29/0.49 ! [X2: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( inf_in586391887at_nat @ bot_bo2130386637at_nat @ X2 )
% 0.29/0.49 = bot_bo2130386637at_nat ) ).
% 0.29/0.49
% 0.29/0.49 % inf_bot_left
% 0.29/0.49 thf(fact_16_inf__bot__right,axiom,
% 0.29/0.49 ! [X2: product_prod_nat_nat > $o] :
% 0.29/0.49 ( ( inf_in2138576462_nat_o @ X2 @ bot_bo513358416_nat_o )
% 0.29/0.49 = bot_bo513358416_nat_o ) ).
% 0.29/0.49
% 0.29/0.49 % inf_bot_right
% 0.29/0.49 thf(fact_17_inf__bot__right,axiom,
% 0.29/0.49 ! [X2: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( inf_in586391887at_nat @ X2 @ bot_bo2130386637at_nat )
% 0.29/0.49 = bot_bo2130386637at_nat ) ).
% 0.29/0.49
% 0.29/0.49 % inf_bot_right
% 0.29/0.49 thf(fact_18_is__RPreGraph,axiom,
% 0.29/0.49 residu164581374pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ) ).
% 0.29/0.49
% 0.29/0.49 % is_RPreGraph
% 0.29/0.49 thf(fact_19_Network__axioms,axiom,
% 0.29/0.49 network_capacity @ c @ s @ t ).
% 0.29/0.49
% 0.29/0.49 % Network_axioms
% 0.29/0.49 thf(fact_20_fo__rg__inv,axiom,
% 0.29/0.49 ( ( residu1549650759pacity @ c @ ( residu203630698pacity @ c @ f ) )
% 0.29/0.49 = f ) ).
% 0.29/0.49
% 0.29/0.49 % fo_rg_inv
% 0.29/0.49 thf(fact_21_inf__right__idem,axiom,
% 0.29/0.49 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ X2 @ Y ) @ Y )
% 0.29/0.49 = ( inf_in586391887at_nat @ X2 @ Y ) ) ).
% 0.29/0.49
% 0.29/0.49 % inf_right_idem
% 0.29/0.49 thf(fact_22_inf_Oright__idem,axiom,
% 0.29/0.49 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B )
% 0.29/0.49 = ( inf_in586391887at_nat @ A @ B ) ) ).
% 0.29/0.49
% 0.29/0.49 % inf.right_idem
% 0.29/0.49 thf(fact_23_inf__left__idem,axiom,
% 0.29/0.49 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( inf_in586391887at_nat @ X2 @ ( inf_in586391887at_nat @ X2 @ Y ) )
% 0.29/0.49 = ( inf_in586391887at_nat @ X2 @ Y ) ) ).
% 0.29/0.49
% 0.29/0.49 % inf_left_idem
% 0.29/0.49 thf(fact_24_inf_Oleft__idem,axiom,
% 0.29/0.49 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ A @ B ) )
% 0.29/0.49 = ( inf_in586391887at_nat @ A @ B ) ) ).
% 0.29/0.49
% 0.29/0.49 % inf.left_idem
% 0.29/0.49 thf(fact_25_inf__idem,axiom,
% 0.29/0.49 ! [X2: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( inf_in586391887at_nat @ X2 @ X2 )
% 0.29/0.49 = X2 ) ).
% 0.29/0.49
% 0.29/0.49 % inf_idem
% 0.29/0.49 thf(fact_26_inf_Oidem,axiom,
% 0.29/0.49 ! [A: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( inf_in586391887at_nat @ A @ A )
% 0.29/0.49 = A ) ).
% 0.29/0.49
% 0.29/0.49 % inf.idem
% 0.29/0.49 thf(fact_27_converse__converse,axiom,
% 0.29/0.49 ! [R: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( converse_nat_nat @ ( converse_nat_nat @ R ) )
% 0.29/0.49 = R ) ).
% 0.29/0.49
% 0.29/0.49 % converse_converse
% 0.29/0.49 thf(fact_28_converse__inject,axiom,
% 0.29/0.49 ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( ( converse_nat_nat @ R )
% 0.29/0.49 = ( converse_nat_nat @ S ) )
% 0.29/0.49 = ( R = S ) ) ).
% 0.29/0.49
% 0.29/0.49 % converse_inject
% 0.29/0.49 thf(fact_29_augFlow__resFlow,axiom,
% 0.29/0.49 ! [P: list_P559422087at_nat] :
% 0.29/0.49 ( ( augmen1090971539pacity @ c @ s @ t @ f @ P )
% 0.29/0.49 => ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ ( augmen72931474pacity @ c @ f @ P ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % augFlow_resFlow
% 0.29/0.49 thf(fact_30_bot__empty__eq,axiom,
% 0.29/0.49 ( bot_bot_nat_o
% 0.29/0.49 = ( ^ [X3: nat] : ( member_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % bot_empty_eq
% 0.29/0.49 thf(fact_31_bot__empty__eq,axiom,
% 0.29/0.49 ( bot_bo513358416_nat_o
% 0.29/0.49 = ( ^ [X3: product_prod_nat_nat] : ( member701585322at_nat @ X3 @ bot_bo2130386637at_nat ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % bot_empty_eq
% 0.29/0.49 thf(fact_32_inf__left__commute,axiom,
% 0.29/0.49 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( inf_in586391887at_nat @ X2 @ ( inf_in586391887at_nat @ Y @ Z ) )
% 0.29/0.49 = ( inf_in586391887at_nat @ Y @ ( inf_in586391887at_nat @ X2 @ Z ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % inf_left_commute
% 0.29/0.49 thf(fact_33_inf_Oleft__commute,axiom,
% 0.29/0.49 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( inf_in586391887at_nat @ B @ ( inf_in586391887at_nat @ A @ C ) )
% 0.29/0.49 = ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % inf.left_commute
% 0.29/0.49 thf(fact_34_inf__commute,axiom,
% 0.29/0.49 ( inf_in586391887at_nat
% 0.29/0.49 = ( ^ [X3: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] : ( inf_in586391887at_nat @ Y2 @ X3 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % inf_commute
% 0.29/0.49 thf(fact_35_inf_Ocommute,axiom,
% 0.29/0.49 ( inf_in586391887at_nat
% 0.29/0.49 = ( ^ [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] : ( inf_in586391887at_nat @ B2 @ A2 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % inf.commute
% 0.29/0.49 thf(fact_36_inf__assoc,axiom,
% 0.29/0.49 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ X2 @ Y ) @ Z )
% 0.29/0.49 = ( inf_in586391887at_nat @ X2 @ ( inf_in586391887at_nat @ Y @ Z ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % inf_assoc
% 0.29/0.49 thf(fact_37_inf_Oassoc,axiom,
% 0.29/0.49 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C )
% 0.29/0.49 = ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % inf.assoc
% 0.29/0.49 thf(fact_38_boolean__algebra__cancel_Oinf2,axiom,
% 0.29/0.49 ! [B3: set_Pr1986765409at_nat,K: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( B3
% 0.29/0.49 = ( inf_in586391887at_nat @ K @ B ) )
% 0.29/0.49 => ( ( inf_in586391887at_nat @ A @ B3 )
% 0.29/0.49 = ( inf_in586391887at_nat @ K @ ( inf_in586391887at_nat @ A @ B ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % boolean_algebra_cancel.inf2
% 0.29/0.49 thf(fact_39_boolean__algebra__cancel_Oinf1,axiom,
% 0.29/0.49 ! [A3: set_Pr1986765409at_nat,K: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( A3
% 0.29/0.49 = ( inf_in586391887at_nat @ K @ A ) )
% 0.29/0.49 => ( ( inf_in586391887at_nat @ A3 @ B )
% 0.29/0.49 = ( inf_in586391887at_nat @ K @ ( inf_in586391887at_nat @ A @ B ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % boolean_algebra_cancel.inf1
% 0.29/0.49 thf(fact_40_inf__sup__aci_I1_J,axiom,
% 0.29/0.49 ( inf_in586391887at_nat
% 0.29/0.49 = ( ^ [X3: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] : ( inf_in586391887at_nat @ Y2 @ X3 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % inf_sup_aci(1)
% 0.29/0.49 thf(fact_41_inf__sup__aci_I2_J,axiom,
% 0.29/0.49 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ X2 @ Y ) @ Z )
% 0.29/0.49 = ( inf_in586391887at_nat @ X2 @ ( inf_in586391887at_nat @ Y @ Z ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % inf_sup_aci(2)
% 0.29/0.49 thf(fact_42_inf__sup__aci_I3_J,axiom,
% 0.29/0.49 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( inf_in586391887at_nat @ X2 @ ( inf_in586391887at_nat @ Y @ Z ) )
% 0.29/0.49 = ( inf_in586391887at_nat @ Y @ ( inf_in586391887at_nat @ X2 @ Z ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % inf_sup_aci(3)
% 0.29/0.49 thf(fact_43_inf__sup__aci_I4_J,axiom,
% 0.29/0.49 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( inf_in586391887at_nat @ X2 @ ( inf_in586391887at_nat @ X2 @ Y ) )
% 0.29/0.49 = ( inf_in586391887at_nat @ X2 @ Y ) ) ).
% 0.29/0.49
% 0.29/0.49 % inf_sup_aci(4)
% 0.29/0.49 thf(fact_44_converse__Int,axiom,
% 0.29/0.49 ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 0.29/0.49 ( ( converse_nat_nat @ ( inf_in586391887at_nat @ R @ S ) )
% 0.29/0.49 = ( inf_in586391887at_nat @ ( converse_nat_nat @ R ) @ ( converse_nat_nat @ S ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % converse_Int
% 0.29/0.49 thf(fact_45_augment__flow__presv,axiom,
% 0.29/0.49 ! [F: product_prod_nat_nat > capacity] :
% 0.29/0.49 ( ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ F )
% 0.29/0.49 => ( flow_capacity @ c @ s @ t @ ( augmen887209518pacity @ c @ f @ F ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % augment_flow_presv
% 0.29/0.50 thf(fact_46_mem__Collect__eq,axiom,
% 0.29/0.50 ! [A: nat,P2: nat > $o] :
% 0.29/0.50 ( ( member_nat @ A @ ( collect_nat @ P2 ) )
% 0.29/0.50 = ( P2 @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 % mem_Collect_eq
% 0.29/0.50 thf(fact_47_mem__Collect__eq,axiom,
% 0.29/0.50 ! [A: product_prod_nat_nat,P2: product_prod_nat_nat > $o] :
% 0.29/0.50 ( ( member701585322at_nat @ A @ ( collec7649004at_nat @ P2 ) )
% 0.29/0.50 = ( P2 @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 % mem_Collect_eq
% 0.29/0.50 thf(fact_48_Collect__mem__eq,axiom,
% 0.29/0.50 ! [A3: set_nat] :
% 0.29/0.50 ( ( collect_nat
% 0.29/0.50 @ ^ [X3: nat] : ( member_nat @ X3 @ A3 ) )
% 0.29/0.50 = A3 ) ).
% 0.29/0.50
% 0.29/0.50 % Collect_mem_eq
% 0.29/0.50 thf(fact_49_Collect__mem__eq,axiom,
% 0.29/0.50 ! [A3: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( collec7649004at_nat
% 0.29/0.50 @ ^ [X3: product_prod_nat_nat] : ( member701585322at_nat @ X3 @ A3 ) )
% 0.29/0.50 = A3 ) ).
% 0.29/0.50
% 0.29/0.50 % Collect_mem_eq
% 0.29/0.50 thf(fact_50_Collect__cong,axiom,
% 0.29/0.50 ! [P2: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 0.29/0.50 ( ! [X4: product_prod_nat_nat] :
% 0.29/0.50 ( ( P2 @ X4 )
% 0.29/0.50 = ( Q @ X4 ) )
% 0.29/0.50 => ( ( collec7649004at_nat @ P2 )
% 0.29/0.50 = ( collec7649004at_nat @ Q ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Collect_cong
% 0.29/0.50 thf(fact_51_cf_OisSPath__nt__parallel,axiom,
% 0.29/0.50 ! [S: nat,P: list_P559422087at_nat,T: nat,E: product_prod_nat_nat] :
% 0.29/0.50 ( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ S @ P @ T )
% 0.29/0.50 => ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ P ) )
% 0.29/0.50 => ~ ( member701585322at_nat @ ( product_swap_nat_nat @ E ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % cf.isSPath_nt_parallel
% 0.29/0.50 thf(fact_52_is__max__flow__val__def,axiom,
% 0.29/0.50 ! [Fv: capacity] :
% 0.29/0.50 ( ( is_max2144541363pacity @ c @ s @ t @ Fv )
% 0.29/0.50 = ( ? [F2: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( isMaxFlow_capacity @ c @ s @ t @ F2 )
% 0.29/0.50 & ( Fv
% 0.29/0.50 = ( val_capacity @ c @ s @ F2 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % is_max_flow_val_def
% 0.29/0.50 thf(fact_53_cf_OFinite__Graph__axioms,axiom,
% 0.29/0.50 finite217307323pacity @ ( residu203630698pacity @ c @ f ) ).
% 0.29/0.50
% 0.29/0.50 % cf.Finite_Graph_axioms
% 0.29/0.50 thf(fact_54_ford__fulkerson_I1_J,axiom,
% 0.29/0.50 ( ( isMaxFlow_capacity @ c @ s @ t @ f )
% 0.29/0.50 = ( ~ ? [X: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ X ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ford_fulkerson(1)
% 0.29/0.50 thf(fact_55_shortest__is__augmenting,axiom,
% 0.29/0.50 ! [P: list_P559422087at_nat] :
% 0.29/0.50 ( ( isShor1936442771pacity @ ( residu203630698pacity @ c @ f ) @ s @ P @ t )
% 0.29/0.50 => ( augmen1090971539pacity @ c @ s @ t @ f @ P ) ) ).
% 0.29/0.50
% 0.29/0.50 % shortest_is_augmenting
% 0.29/0.50 thf(fact_56_augmenting__path__imp__shortest,axiom,
% 0.29/0.50 ! [P: list_P559422087at_nat] :
% 0.29/0.50 ( ( augmen1090971539pacity @ c @ s @ t @ f @ P )
% 0.29/0.50 => ? [P3: list_P559422087at_nat] : ( isShor1936442771pacity @ ( residu203630698pacity @ c @ f ) @ s @ P3 @ t ) ) ).
% 0.29/0.50
% 0.29/0.50 % augmenting_path_imp_shortest
% 0.29/0.50 thf(fact_57_Graph_OisSPath__nt__parallel__pf,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,P: list_P559422087at_nat,T: nat] :
% 0.29/0.50 ( ( isSimp1359852763pacity @ C @ S @ P @ T )
% 0.29/0.50 => ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ P ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ P ) ) )
% 0.29/0.50 = bot_bo2130386637at_nat ) ) ).
% 0.29/0.50
% 0.29/0.50 % Graph.isSPath_nt_parallel_pf
% 0.29/0.50 thf(fact_58_RPreGraph_Omaxflow__imp__rgraph,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( residu164581374pacity @ C @ S @ T @ Cf )
% 0.29/0.50 => ( ( isMaxFlow_capacity @ C @ S @ T @ ( residu1549650759pacity @ C @ Cf ) )
% 0.29/0.50 => ( residu800046103pacity @ C @ S @ T @ Cf ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % RPreGraph.maxflow_imp_rgraph
% 0.29/0.50 thf(fact_59_isSPath__nt__parallel,axiom,
% 0.29/0.50 ! [S: nat,P: list_P559422087at_nat,T: nat,E: product_prod_nat_nat] :
% 0.29/0.50 ( ( isSimp1359852763pacity @ c @ S @ P @ T )
% 0.29/0.50 => ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ P ) )
% 0.29/0.50 => ~ ( member701585322at_nat @ ( product_swap_nat_nat @ E ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % isSPath_nt_parallel
% 0.29/0.50 thf(fact_60_Finite__Graph__axioms,axiom,
% 0.29/0.50 finite217307323pacity @ c ).
% 0.29/0.50
% 0.29/0.50 % Finite_Graph_axioms
% 0.29/0.50 thf(fact_61_shortestPath__is__simple,axiom,
% 0.29/0.50 ! [S: nat,P: list_P559422087at_nat,T: nat] :
% 0.29/0.50 ( ( isShor1936442771pacity @ c @ S @ P @ T )
% 0.29/0.50 => ( isSimp1359852763pacity @ c @ S @ P @ T ) ) ).
% 0.29/0.50
% 0.29/0.50 % shortestPath_is_simple
% 0.29/0.50 thf(fact_62_cf_OshortestPath__is__simple,axiom,
% 0.29/0.50 ! [S: nat,P: list_P559422087at_nat,T: nat] :
% 0.29/0.50 ( ( isShor1936442771pacity @ ( residu203630698pacity @ c @ f ) @ S @ P @ T )
% 0.29/0.50 => ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ S @ P @ T ) ) ).
% 0.29/0.50
% 0.29/0.50 % cf.shortestPath_is_simple
% 0.29/0.50 thf(fact_63_Graph_OisShortestPath_Ocong,axiom,
% 0.29/0.50 isShor1936442771pacity = isShor1936442771pacity ).
% 0.29/0.50
% 0.29/0.50 % Graph.isShortestPath.cong
% 0.29/0.50 thf(fact_64_Graph_OshortestPath__is__simple,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,P: list_P559422087at_nat,T: nat] :
% 0.29/0.50 ( ( isShor1936442771pacity @ C @ S @ P @ T )
% 0.29/0.50 => ( isSimp1359852763pacity @ C @ S @ P @ T ) ) ).
% 0.29/0.50
% 0.29/0.50 % Graph.shortestPath_is_simple
% 0.29/0.50 thf(fact_65_Graph_OisSPath__nt__parallel,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,P: list_P559422087at_nat,T: nat,E: product_prod_nat_nat] :
% 0.29/0.50 ( ( isSimp1359852763pacity @ C @ S @ P @ T )
% 0.29/0.50 => ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ P ) )
% 0.29/0.50 => ~ ( member701585322at_nat @ ( product_swap_nat_nat @ E ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Graph.isSPath_nt_parallel
% 0.29/0.50 thf(fact_66_Graph_OisSimplePath_Ocong,axiom,
% 0.29/0.50 isSimp1359852763pacity = isSimp1359852763pacity ).
% 0.29/0.50
% 0.29/0.50 % Graph.isSimplePath.cong
% 0.29/0.50 thf(fact_67_RPreGraph_Othis__loc__rpg,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( residu164581374pacity @ C @ S @ T @ Cf )
% 0.29/0.50 => ( residu164581374pacity @ C @ S @ T @ Cf ) ) ).
% 0.29/0.50
% 0.29/0.50 % RPreGraph.this_loc_rpg
% 0.29/0.50 thf(fact_68_NFlow_Oshortest__is__augmenting,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,P: list_P559422087at_nat] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( isShor1936442771pacity @ ( residu203630698pacity @ C @ F3 ) @ S @ P @ T )
% 0.29/0.50 => ( augmen1090971539pacity @ C @ S @ T @ F3 @ P ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow.shortest_is_augmenting
% 0.29/0.50 thf(fact_69_NFlow_Oaugmenting__path__imp__shortest,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,P: list_P559422087at_nat] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( augmen1090971539pacity @ C @ S @ T @ F3 @ P )
% 0.29/0.50 => ? [P3: list_P559422087at_nat] : ( isShor1936442771pacity @ ( residu203630698pacity @ C @ F3 ) @ S @ P3 @ T ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow.augmenting_path_imp_shortest
% 0.29/0.50 thf(fact_70_RGraph_Othis__loc,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( residu800046103pacity @ C @ S @ T @ Cf )
% 0.29/0.50 => ( residu800046103pacity @ C @ S @ T @ Cf ) ) ).
% 0.29/0.50
% 0.29/0.50 % RGraph.this_loc
% 0.29/0.50 thf(fact_71_Network_Oflow__of__cf_Ocong,axiom,
% 0.29/0.50 residu1549650759pacity = residu1549650759pacity ).
% 0.29/0.50
% 0.29/0.50 % Network.flow_of_cf.cong
% 0.29/0.50 thf(fact_72_RPreGraph_Oaxioms_I1_J,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( residu164581374pacity @ C @ S @ T @ Cf )
% 0.29/0.50 => ( network_capacity @ C @ S @ T ) ) ).
% 0.29/0.50
% 0.29/0.50 % RPreGraph.axioms(1)
% 0.29/0.50 thf(fact_73_RGraph_Oaxioms_I1_J,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( residu800046103pacity @ C @ S @ T @ Cf )
% 0.29/0.50 => ( network_capacity @ C @ S @ T ) ) ).
% 0.29/0.50
% 0.29/0.50 % RGraph.axioms(1)
% 0.29/0.50 thf(fact_74_RGraph_Othis__loc__rpg,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( residu800046103pacity @ C @ S @ T @ Cf )
% 0.29/0.50 => ( residu164581374pacity @ C @ S @ T @ Cf ) ) ).
% 0.29/0.50
% 0.29/0.50 % RGraph.this_loc_rpg
% 0.29/0.50 thf(fact_75_NPreflow_Ois__RPreGraph,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( residu164581374pacity @ C @ S @ T @ ( residu203630698pacity @ C @ F3 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NPreflow.is_RPreGraph
% 0.29/0.50 thf(fact_76_RPreGraph_OEX__RPG,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( residu164581374pacity @ C @ S @ T @ Cf )
% 0.29/0.50 => ? [F4: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nPreflow_capacity @ C @ S @ T @ F4 )
% 0.29/0.50 & ( Cf
% 0.29/0.50 = ( residu203630698pacity @ C @ F4 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % RPreGraph.EX_RPG
% 0.29/0.50 thf(fact_77_NFlow_Ois__RGraph,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( residu800046103pacity @ C @ S @ T @ ( residu203630698pacity @ C @ F3 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow.is_RGraph
% 0.29/0.50 thf(fact_78_RGraph_OEX__RG,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( residu800046103pacity @ C @ S @ T @ Cf )
% 0.29/0.50 => ? [F4: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F4 )
% 0.29/0.50 & ( Cf
% 0.29/0.50 = ( residu203630698pacity @ C @ F4 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % RGraph.EX_RG
% 0.29/0.50 thf(fact_79_NPreflow_Ofo__rg__inv,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( residu1549650759pacity @ C @ ( residu203630698pacity @ C @ F3 ) )
% 0.29/0.50 = F3 ) ) ).
% 0.29/0.50
% 0.29/0.50 % NPreflow.fo_rg_inv
% 0.29/0.50 thf(fact_80_RPreGraph_Org__fo__inv,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( residu164581374pacity @ C @ S @ T @ Cf )
% 0.29/0.50 => ( ( residu203630698pacity @ C @ ( residu1549650759pacity @ C @ Cf ) )
% 0.29/0.50 = Cf ) ) ).
% 0.29/0.50
% 0.29/0.50 % RPreGraph.rg_fo_inv
% 0.29/0.50 thf(fact_81_RPreGraph_Ois__NPreflow,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( residu164581374pacity @ C @ S @ T @ Cf )
% 0.29/0.50 => ( nPreflow_capacity @ C @ S @ T @ ( residu1549650759pacity @ C @ Cf ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % RPreGraph.is_NPreflow
% 0.29/0.50 thf(fact_82_RGraph_Ois__NFlow,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( residu800046103pacity @ C @ S @ T @ Cf )
% 0.29/0.50 => ( nFlow_capacity @ C @ S @ T @ ( residu1549650759pacity @ C @ Cf ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % RGraph.is_NFlow
% 0.29/0.50 thf(fact_83_augFlow__val,axiom,
% 0.29/0.50 ! [P: list_P559422087at_nat] :
% 0.29/0.50 ( ( augmen1090971539pacity @ c @ s @ t @ f @ P )
% 0.29/0.50 => ( ( val_capacity @ ( residu203630698pacity @ c @ f ) @ s @ ( augmen72931474pacity @ c @ f @ P ) )
% 0.29/0.50 = ( augmen68920357pacity @ c @ f @ P ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % augFlow_val
% 0.29/0.50 thf(fact_84_augment__flow__value,axiom,
% 0.29/0.50 ! [F: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ F )
% 0.29/0.50 => ( ( val_capacity @ c @ s @ ( augmen887209518pacity @ c @ f @ F ) )
% 0.29/0.50 = ( plus_plus_capacity @ ( val_capacity @ c @ s @ f ) @ ( val_capacity @ ( residu203630698pacity @ c @ f ) @ s @ F ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % augment_flow_value
% 0.29/0.50 thf(fact_85_isMaxFlow__alt,axiom,
% 0.29/0.50 ! [F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( isMaxFlow_capacity @ c @ s @ t @ F3 )
% 0.29/0.50 = ( ( nFlow_capacity @ c @ s @ t @ F3 )
% 0.29/0.50 & ! [F5: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nFlow_capacity @ c @ s @ t @ F5 )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( val_capacity @ c @ s @ F5 ) @ ( val_capacity @ c @ s @ F3 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % isMaxFlow_alt
% 0.29/0.50 thf(fact_86_isMaxFlow__def,axiom,
% 0.29/0.50 ! [F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( isMaxFlow_capacity @ c @ s @ t @ F3 )
% 0.29/0.50 = ( ( flow_capacity @ c @ s @ t @ F3 )
% 0.29/0.50 & ! [F5: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( flow_capacity @ c @ s @ t @ F5 )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( val_capacity @ c @ s @ F5 ) @ ( val_capacity @ c @ s @ F3 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % isMaxFlow_def
% 0.29/0.50 thf(fact_87_NPreflow_OaugFlow__resFlow,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,P: list_P559422087at_nat] :
% 0.29/0.50 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( augmen1090971539pacity @ C @ S @ T @ F3 @ P )
% 0.29/0.50 => ( flow_capacity @ ( residu203630698pacity @ C @ F3 ) @ S @ T @ ( augmen72931474pacity @ C @ F3 @ P ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NPreflow.augFlow_resFlow
% 0.29/0.50 thf(fact_88_bot__apply,axiom,
% 0.29/0.50 ( bot_bo513358416_nat_o
% 0.29/0.50 = ( ^ [X3: product_prod_nat_nat] : bot_bot_o ) ) ).
% 0.29/0.50
% 0.29/0.50 % bot_apply
% 0.29/0.50 thf(fact_89_maxFlow__minCut,axiom,
% 0.29/0.50 ! [F3: product_prod_nat_nat > capacity,K: set_nat] :
% 0.29/0.50 ( ( isMaxFlow_capacity @ c @ s @ t @ F3 )
% 0.29/0.50 => ( ( isMinCut_capacity @ c @ s @ t @ K )
% 0.29/0.50 => ( ( val_capacity @ c @ s @ F3 )
% 0.29/0.50 = ( cap_capacity @ c @ K ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % maxFlow_minCut
% 0.29/0.50 thf(fact_90_order__refl,axiom,
% 0.29/0.50 ! [X2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ X2 @ X2 ) ).
% 0.29/0.50
% 0.29/0.50 % order_refl
% 0.29/0.50 thf(fact_91_order__refl,axiom,
% 0.29/0.50 ! [X2: capacity] : ( ord_less_eq_capacity @ X2 @ X2 ) ).
% 0.29/0.50
% 0.29/0.50 % order_refl
% 0.29/0.50 thf(fact_92_inf_Obounded__iff,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
% 0.29/0.50 = ( ( ord_le841296385at_nat @ A @ B )
% 0.29/0.50 & ( ord_le841296385at_nat @ A @ C ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.bounded_iff
% 0.29/0.50 thf(fact_93_le__inf__iff,axiom,
% 0.29/0.50 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ Y @ Z ) )
% 0.29/0.50 = ( ( ord_le841296385at_nat @ X2 @ Y )
% 0.29/0.50 & ( ord_le841296385at_nat @ X2 @ Z ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_inf_iff
% 0.29/0.50 thf(fact_94_bot_Oextremum,axiom,
% 0.29/0.50 ! [A: product_prod_nat_nat > $o] : ( ord_le1039616028_nat_o @ bot_bo513358416_nat_o @ A ) ).
% 0.29/0.50
% 0.29/0.50 % bot.extremum
% 0.29/0.50 thf(fact_95_bot_Oextremum,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ bot_bo2130386637at_nat @ A ) ).
% 0.29/0.50
% 0.29/0.50 % bot.extremum
% 0.29/0.50 thf(fact_96_bot_Oextremum__unique,axiom,
% 0.29/0.50 ! [A: product_prod_nat_nat > $o] :
% 0.29/0.50 ( ( ord_le1039616028_nat_o @ A @ bot_bo513358416_nat_o )
% 0.29/0.50 = ( A = bot_bo513358416_nat_o ) ) ).
% 0.29/0.50
% 0.29/0.50 % bot.extremum_unique
% 0.29/0.50 thf(fact_97_bot_Oextremum__unique,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ bot_bo2130386637at_nat )
% 0.29/0.50 = ( A = bot_bo2130386637at_nat ) ) ).
% 0.29/0.50
% 0.29/0.50 % bot.extremum_unique
% 0.29/0.50 thf(fact_98_bot_Oextremum__uniqueI,axiom,
% 0.29/0.50 ! [A: product_prod_nat_nat > $o] :
% 0.29/0.50 ( ( ord_le1039616028_nat_o @ A @ bot_bo513358416_nat_o )
% 0.29/0.50 => ( A = bot_bo513358416_nat_o ) ) ).
% 0.29/0.50
% 0.29/0.50 % bot.extremum_uniqueI
% 0.29/0.50 thf(fact_99_bot_Oextremum__uniqueI,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ bot_bo2130386637at_nat )
% 0.29/0.50 => ( A = bot_bo2130386637at_nat ) ) ).
% 0.29/0.50
% 0.29/0.50 % bot.extremum_uniqueI
% 0.29/0.50 thf(fact_100_order__subst1,axiom,
% 0.29/0.50 ! [A: capacity,F3: set_Pr1986765409at_nat > capacity,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ A @ ( F3 @ B ) )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ B @ C )
% 0.29/0.50 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_less_eq_capacity @ A @ ( F3 @ C ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_subst1
% 0.29/0.50 thf(fact_101_order__subst1,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,F3: capacity > set_Pr1986765409at_nat,B: capacity,C: capacity] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ ( F3 @ B ) )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ B @ C )
% 0.29/0.50 => ( ! [X4: capacity,Y3: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_le841296385at_nat @ A @ ( F3 @ C ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_subst1
% 0.29/0.50 thf(fact_102_order__subst1,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,F3: set_Pr1986765409at_nat > set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ ( F3 @ B ) )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ B @ C )
% 0.29/0.50 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_le841296385at_nat @ A @ ( F3 @ C ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_subst1
% 0.29/0.50 thf(fact_103_order__subst1,axiom,
% 0.29/0.50 ! [A: capacity,F3: capacity > capacity,B: capacity,C: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ A @ ( F3 @ B ) )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ B @ C )
% 0.29/0.50 => ( ! [X4: capacity,Y3: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_less_eq_capacity @ A @ ( F3 @ C ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_subst1
% 0.29/0.50 thf(fact_104_order__subst2,axiom,
% 0.29/0.50 ! [A: capacity,B: capacity,F3: capacity > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ A @ B )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ ( F3 @ B ) @ C )
% 0.29/0.50 => ( ! [X4: capacity,Y3: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( F3 @ A ) @ C ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_subst2
% 0.29/0.50 thf(fact_105_order__subst2,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,F3: set_Pr1986765409at_nat > capacity,C: capacity] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ B )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ ( F3 @ B ) @ C )
% 0.29/0.50 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( F3 @ A ) @ C ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_subst2
% 0.29/0.50 thf(fact_106_order__subst2,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,F3: set_Pr1986765409at_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ B )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ ( F3 @ B ) @ C )
% 0.29/0.50 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( F3 @ A ) @ C ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_subst2
% 0.29/0.50 thf(fact_107_order__subst2,axiom,
% 0.29/0.50 ! [A: capacity,B: capacity,F3: capacity > capacity,C: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ A @ B )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ ( F3 @ B ) @ C )
% 0.29/0.50 => ( ! [X4: capacity,Y3: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( F3 @ A ) @ C ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_subst2
% 0.29/0.50 thf(fact_108_ord__eq__le__subst,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,F3: capacity > set_Pr1986765409at_nat,B: capacity,C: capacity] :
% 0.29/0.50 ( ( A
% 0.29/0.50 = ( F3 @ B ) )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ B @ C )
% 0.29/0.50 => ( ! [X4: capacity,Y3: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_le841296385at_nat @ A @ ( F3 @ C ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord_eq_le_subst
% 0.29/0.50 thf(fact_109_ord__eq__le__subst,axiom,
% 0.29/0.50 ! [A: capacity,F3: set_Pr1986765409at_nat > capacity,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( A
% 0.29/0.50 = ( F3 @ B ) )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ B @ C )
% 0.29/0.50 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_less_eq_capacity @ A @ ( F3 @ C ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord_eq_le_subst
% 0.29/0.50 thf(fact_110_ord__eq__le__subst,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,F3: set_Pr1986765409at_nat > set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( A
% 0.29/0.50 = ( F3 @ B ) )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ B @ C )
% 0.29/0.50 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_le841296385at_nat @ A @ ( F3 @ C ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord_eq_le_subst
% 0.29/0.50 thf(fact_111_ord__eq__le__subst,axiom,
% 0.29/0.50 ! [A: capacity,F3: capacity > capacity,B: capacity,C: capacity] :
% 0.29/0.50 ( ( A
% 0.29/0.50 = ( F3 @ B ) )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ B @ C )
% 0.29/0.50 => ( ! [X4: capacity,Y3: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_less_eq_capacity @ A @ ( F3 @ C ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord_eq_le_subst
% 0.29/0.50 thf(fact_112_ord__le__eq__subst,axiom,
% 0.29/0.50 ! [A: capacity,B: capacity,F3: capacity > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ A @ B )
% 0.29/0.50 => ( ( ( F3 @ B )
% 0.29/0.50 = C )
% 0.29/0.50 => ( ! [X4: capacity,Y3: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( F3 @ A ) @ C ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord_le_eq_subst
% 0.29/0.50 thf(fact_113_ord__le__eq__subst,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,F3: set_Pr1986765409at_nat > capacity,C: capacity] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ B )
% 0.29/0.50 => ( ( ( F3 @ B )
% 0.29/0.50 = C )
% 0.29/0.50 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( F3 @ A ) @ C ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord_le_eq_subst
% 0.29/0.50 thf(fact_114_ord__le__eq__subst,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,F3: set_Pr1986765409at_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ B )
% 0.29/0.50 => ( ( ( F3 @ B )
% 0.29/0.50 = C )
% 0.29/0.50 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( F3 @ A ) @ C ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord_le_eq_subst
% 0.29/0.50 thf(fact_115_ord__le__eq__subst,axiom,
% 0.29/0.50 ! [A: capacity,B: capacity,F3: capacity > capacity,C: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ A @ B )
% 0.29/0.50 => ( ( ( F3 @ B )
% 0.29/0.50 = C )
% 0.29/0.50 => ( ! [X4: capacity,Y3: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( F3 @ A ) @ C ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord_le_eq_subst
% 0.29/0.50 thf(fact_116_eq__iff,axiom,
% 0.29/0.50 ( ( ^ [Y4: set_Pr1986765409at_nat,Z2: set_Pr1986765409at_nat] : ( Y4 = Z2 ) )
% 0.29/0.50 = ( ^ [X3: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X3 @ Y2 )
% 0.29/0.50 & ( ord_le841296385at_nat @ Y2 @ X3 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % eq_iff
% 0.29/0.50 thf(fact_117_eq__iff,axiom,
% 0.29/0.50 ( ( ^ [Y4: capacity,Z2: capacity] : ( Y4 = Z2 ) )
% 0.29/0.50 = ( ^ [X3: capacity,Y2: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ X3 @ Y2 )
% 0.29/0.50 & ( ord_less_eq_capacity @ Y2 @ X3 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % eq_iff
% 0.29/0.50 thf(fact_118_antisym,axiom,
% 0.29/0.50 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X2 @ Y )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ Y @ X2 )
% 0.29/0.50 => ( X2 = Y ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % antisym
% 0.29/0.50 thf(fact_119_antisym,axiom,
% 0.29/0.50 ! [X2: capacity,Y: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ X2 @ Y )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ Y @ X2 )
% 0.29/0.50 => ( X2 = Y ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % antisym
% 0.29/0.50 thf(fact_120_linear,axiom,
% 0.29/0.50 ! [X2: capacity,Y: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ X2 @ Y )
% 0.29/0.50 | ( ord_less_eq_capacity @ Y @ X2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % linear
% 0.29/0.50 thf(fact_121_eq__refl,axiom,
% 0.29/0.50 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( X2 = Y )
% 0.29/0.50 => ( ord_le841296385at_nat @ X2 @ Y ) ) ).
% 0.29/0.50
% 0.29/0.50 % eq_refl
% 0.29/0.50 thf(fact_122_eq__refl,axiom,
% 0.29/0.50 ! [X2: capacity,Y: capacity] :
% 0.29/0.50 ( ( X2 = Y )
% 0.29/0.50 => ( ord_less_eq_capacity @ X2 @ Y ) ) ).
% 0.29/0.50
% 0.29/0.50 % eq_refl
% 0.29/0.50 thf(fact_123_le__cases,axiom,
% 0.29/0.50 ! [X2: capacity,Y: capacity] :
% 0.29/0.50 ( ~ ( ord_less_eq_capacity @ X2 @ Y )
% 0.29/0.50 => ( ord_less_eq_capacity @ Y @ X2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_cases
% 0.29/0.50 thf(fact_124_order_Otrans,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ B )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ B @ C )
% 0.29/0.50 => ( ord_le841296385at_nat @ A @ C ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order.trans
% 0.29/0.50 thf(fact_125_order_Otrans,axiom,
% 0.29/0.50 ! [A: capacity,B: capacity,C: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ A @ B )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ B @ C )
% 0.29/0.50 => ( ord_less_eq_capacity @ A @ C ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order.trans
% 0.29/0.50 thf(fact_126_le__cases3,axiom,
% 0.29/0.50 ! [X2: capacity,Y: capacity,Z: capacity] :
% 0.29/0.50 ( ( ( ord_less_eq_capacity @ X2 @ Y )
% 0.29/0.50 => ~ ( ord_less_eq_capacity @ Y @ Z ) )
% 0.29/0.50 => ( ( ( ord_less_eq_capacity @ Y @ X2 )
% 0.29/0.50 => ~ ( ord_less_eq_capacity @ X2 @ Z ) )
% 0.29/0.50 => ( ( ( ord_less_eq_capacity @ X2 @ Z )
% 0.29/0.50 => ~ ( ord_less_eq_capacity @ Z @ Y ) )
% 0.29/0.50 => ( ( ( ord_less_eq_capacity @ Z @ Y )
% 0.29/0.50 => ~ ( ord_less_eq_capacity @ Y @ X2 ) )
% 0.29/0.50 => ( ( ( ord_less_eq_capacity @ Y @ Z )
% 0.29/0.50 => ~ ( ord_less_eq_capacity @ Z @ X2 ) )
% 0.29/0.50 => ~ ( ( ord_less_eq_capacity @ Z @ X2 )
% 0.29/0.50 => ~ ( ord_less_eq_capacity @ X2 @ Y ) ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_cases3
% 0.29/0.50 thf(fact_127_antisym__conv,axiom,
% 0.29/0.50 ! [Y: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ Y @ X2 )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ X2 @ Y )
% 0.29/0.50 = ( X2 = Y ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % antisym_conv
% 0.29/0.50 thf(fact_128_antisym__conv,axiom,
% 0.29/0.50 ! [Y: capacity,X2: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ Y @ X2 )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ X2 @ Y )
% 0.29/0.50 = ( X2 = Y ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % antisym_conv
% 0.29/0.50 thf(fact_129_order__class_Oorder_Oeq__iff,axiom,
% 0.29/0.50 ( ( ^ [Y4: set_Pr1986765409at_nat,Z2: set_Pr1986765409at_nat] : ( Y4 = Z2 ) )
% 0.29/0.50 = ( ^ [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.29/0.50 & ( ord_le841296385at_nat @ B2 @ A2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_class.order.eq_iff
% 0.29/0.50 thf(fact_130_order__class_Oorder_Oeq__iff,axiom,
% 0.29/0.50 ( ( ^ [Y4: capacity,Z2: capacity] : ( Y4 = Z2 ) )
% 0.29/0.50 = ( ^ [A2: capacity,B2: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ A2 @ B2 )
% 0.29/0.50 & ( ord_less_eq_capacity @ B2 @ A2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_class.order.eq_iff
% 0.29/0.50 thf(fact_131_ord__eq__le__trans,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( A = B )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ B @ C )
% 0.29/0.50 => ( ord_le841296385at_nat @ A @ C ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord_eq_le_trans
% 0.29/0.50 thf(fact_132_ord__eq__le__trans,axiom,
% 0.29/0.50 ! [A: capacity,B: capacity,C: capacity] :
% 0.29/0.50 ( ( A = B )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ B @ C )
% 0.29/0.50 => ( ord_less_eq_capacity @ A @ C ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord_eq_le_trans
% 0.29/0.50 thf(fact_133_ord__le__eq__trans,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ B )
% 0.29/0.50 => ( ( B = C )
% 0.29/0.50 => ( ord_le841296385at_nat @ A @ C ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord_le_eq_trans
% 0.29/0.50 thf(fact_134_ord__le__eq__trans,axiom,
% 0.29/0.50 ! [A: capacity,B: capacity,C: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ A @ B )
% 0.29/0.50 => ( ( B = C )
% 0.29/0.50 => ( ord_less_eq_capacity @ A @ C ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord_le_eq_trans
% 0.29/0.50 thf(fact_135_order__class_Oorder_Oantisym,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ B )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ B @ A )
% 0.29/0.50 => ( A = B ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_class.order.antisym
% 0.29/0.50 thf(fact_136_order__class_Oorder_Oantisym,axiom,
% 0.29/0.50 ! [A: capacity,B: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ A @ B )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ B @ A )
% 0.29/0.50 => ( A = B ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_class.order.antisym
% 0.29/0.50 thf(fact_137_NPreflow_OresCap_Ocong,axiom,
% 0.29/0.50 augmen68920357pacity = augmen68920357pacity ).
% 0.29/0.50
% 0.29/0.50 % NPreflow.resCap.cong
% 0.29/0.50 thf(fact_138_order__trans,axiom,
% 0.29/0.50 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X2 @ Y )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ Y @ Z )
% 0.29/0.50 => ( ord_le841296385at_nat @ X2 @ Z ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_trans
% 0.29/0.50 thf(fact_139_order__trans,axiom,
% 0.29/0.50 ! [X2: capacity,Y: capacity,Z: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ X2 @ Y )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ Y @ Z )
% 0.29/0.50 => ( ord_less_eq_capacity @ X2 @ Z ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_trans
% 0.29/0.50 thf(fact_140_dual__order_Orefl,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ) ).
% 0.29/0.50
% 0.29/0.50 % dual_order.refl
% 0.29/0.50 thf(fact_141_dual__order_Orefl,axiom,
% 0.29/0.50 ! [A: capacity] : ( ord_less_eq_capacity @ A @ A ) ).
% 0.29/0.50
% 0.29/0.50 % dual_order.refl
% 0.29/0.50 thf(fact_142_linorder__wlog,axiom,
% 0.29/0.50 ! [P2: capacity > capacity > $o,A: capacity,B: capacity] :
% 0.29/0.50 ( ! [A4: capacity,B4: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ A4 @ B4 )
% 0.29/0.50 => ( P2 @ A4 @ B4 ) )
% 0.29/0.50 => ( ! [A4: capacity,B4: capacity] :
% 0.29/0.50 ( ( P2 @ B4 @ A4 )
% 0.29/0.50 => ( P2 @ A4 @ B4 ) )
% 0.29/0.50 => ( P2 @ A @ B ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % linorder_wlog
% 0.29/0.50 thf(fact_143_dual__order_Otrans,axiom,
% 0.29/0.50 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ B @ A )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ C @ B )
% 0.29/0.50 => ( ord_le841296385at_nat @ C @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % dual_order.trans
% 0.29/0.50 thf(fact_144_dual__order_Otrans,axiom,
% 0.29/0.50 ! [B: capacity,A: capacity,C: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ B @ A )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ C @ B )
% 0.29/0.50 => ( ord_less_eq_capacity @ C @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % dual_order.trans
% 0.29/0.50 thf(fact_145_dual__order_Oeq__iff,axiom,
% 0.29/0.50 ( ( ^ [Y4: set_Pr1986765409at_nat,Z2: set_Pr1986765409at_nat] : ( Y4 = Z2 ) )
% 0.29/0.50 = ( ^ [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ B2 @ A2 )
% 0.29/0.50 & ( ord_le841296385at_nat @ A2 @ B2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % dual_order.eq_iff
% 0.29/0.50 thf(fact_146_dual__order_Oeq__iff,axiom,
% 0.29/0.50 ( ( ^ [Y4: capacity,Z2: capacity] : ( Y4 = Z2 ) )
% 0.29/0.50 = ( ^ [A2: capacity,B2: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ B2 @ A2 )
% 0.29/0.50 & ( ord_less_eq_capacity @ A2 @ B2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % dual_order.eq_iff
% 0.29/0.50 thf(fact_147_dual__order_Oantisym,axiom,
% 0.29/0.50 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ B @ A )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ A @ B )
% 0.29/0.50 => ( A = B ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % dual_order.antisym
% 0.29/0.50 thf(fact_148_dual__order_Oantisym,axiom,
% 0.29/0.50 ! [B: capacity,A: capacity] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ B @ A )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ A @ B )
% 0.29/0.50 => ( A = B ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % dual_order.antisym
% 0.29/0.50 thf(fact_149_inf_OcoboundedI2,axiom,
% 0.29/0.50 ! [B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ B @ C )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.coboundedI2
% 0.29/0.50 thf(fact_150_inf_OcoboundedI1,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ C )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.coboundedI1
% 0.29/0.50 thf(fact_151_inf_Oabsorb__iff2,axiom,
% 0.29/0.50 ( ord_le841296385at_nat
% 0.29/0.50 = ( ^ [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( inf_in586391887at_nat @ A2 @ B2 )
% 0.29/0.50 = B2 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.absorb_iff2
% 0.29/0.50 thf(fact_152_inf_Oabsorb__iff1,axiom,
% 0.29/0.50 ( ord_le841296385at_nat
% 0.29/0.50 = ( ^ [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( inf_in586391887at_nat @ A2 @ B2 )
% 0.29/0.50 = A2 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.absorb_iff1
% 0.29/0.50 thf(fact_153_inf_Ocobounded2,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B ) ).
% 0.29/0.50
% 0.29/0.50 % inf.cobounded2
% 0.29/0.50 thf(fact_154_inf_Ocobounded1,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ A ) ).
% 0.29/0.50
% 0.29/0.50 % inf.cobounded1
% 0.29/0.50 thf(fact_155_inf_Oorder__iff,axiom,
% 0.29/0.50 ( ord_le841296385at_nat
% 0.29/0.50 = ( ^ [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 0.29/0.50 ( A2
% 0.29/0.50 = ( inf_in586391887at_nat @ A2 @ B2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.order_iff
% 0.29/0.50 thf(fact_156_inf__greatest,axiom,
% 0.29/0.50 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X2 @ Y )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ X2 @ Z )
% 0.29/0.50 => ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ Y @ Z ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf_greatest
% 0.29/0.50 thf(fact_157_inf_OboundedI,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ B )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ A @ C )
% 0.29/0.50 => ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.boundedI
% 0.29/0.50 thf(fact_158_inf_OboundedE,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
% 0.29/0.50 => ~ ( ( ord_le841296385at_nat @ A @ B )
% 0.29/0.50 => ~ ( ord_le841296385at_nat @ A @ C ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.boundedE
% 0.29/0.50 thf(fact_159_inf__absorb2,axiom,
% 0.29/0.50 ! [Y: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ Y @ X2 )
% 0.29/0.50 => ( ( inf_in586391887at_nat @ X2 @ Y )
% 0.29/0.50 = Y ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf_absorb2
% 0.29/0.50 thf(fact_160_inf__absorb1,axiom,
% 0.29/0.50 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X2 @ Y )
% 0.29/0.50 => ( ( inf_in586391887at_nat @ X2 @ Y )
% 0.29/0.50 = X2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf_absorb1
% 0.29/0.50 thf(fact_161_inf_Oabsorb2,axiom,
% 0.29/0.50 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ B @ A )
% 0.29/0.50 => ( ( inf_in586391887at_nat @ A @ B )
% 0.29/0.50 = B ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.absorb2
% 0.29/0.50 thf(fact_162_inf_Oabsorb1,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ B )
% 0.29/0.50 => ( ( inf_in586391887at_nat @ A @ B )
% 0.29/0.50 = A ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.absorb1
% 0.29/0.50 thf(fact_163_le__iff__inf,axiom,
% 0.29/0.50 ( ord_le841296385at_nat
% 0.29/0.50 = ( ^ [X3: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( inf_in586391887at_nat @ X3 @ Y2 )
% 0.29/0.50 = X3 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_iff_inf
% 0.29/0.50 thf(fact_164_inf__unique,axiom,
% 0.29/0.50 ! [F3: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( F3 @ X4 @ Y3 ) @ X4 )
% 0.29/0.50 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( F3 @ X4 @ Y3 ) @ Y3 )
% 0.29/0.50 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat,Z3: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ X4 @ Z3 )
% 0.29/0.50 => ( ord_le841296385at_nat @ X4 @ ( F3 @ Y3 @ Z3 ) ) ) )
% 0.29/0.50 => ( ( inf_in586391887at_nat @ X2 @ Y )
% 0.29/0.50 = ( F3 @ X2 @ Y ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf_unique
% 0.29/0.50 thf(fact_165_inf_OorderI,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( A
% 0.29/0.50 = ( inf_in586391887at_nat @ A @ B ) )
% 0.29/0.50 => ( ord_le841296385at_nat @ A @ B ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.orderI
% 0.29/0.50 thf(fact_166_inf_OorderE,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ B )
% 0.29/0.50 => ( A
% 0.29/0.50 = ( inf_in586391887at_nat @ A @ B ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.orderE
% 0.29/0.50 thf(fact_167_le__infI2,axiom,
% 0.29/0.50 ! [B: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ B @ X2 )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ X2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_infI2
% 0.29/0.50 thf(fact_168_le__infI1,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ X2 )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ X2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_infI1
% 0.29/0.50 thf(fact_169_inf__mono,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ A @ C )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ B @ D )
% 0.29/0.50 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ ( inf_in586391887at_nat @ C @ D ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf_mono
% 0.29/0.50 thf(fact_170_le__infI,axiom,
% 0.29/0.50 ! [X2: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X2 @ A )
% 0.29/0.50 => ( ( ord_le841296385at_nat @ X2 @ B )
% 0.29/0.50 => ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ A @ B ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_infI
% 0.29/0.50 thf(fact_171_le__infE,axiom,
% 0.29/0.50 ! [X2: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ A @ B ) )
% 0.29/0.50 => ~ ( ( ord_le841296385at_nat @ X2 @ A )
% 0.29/0.50 => ~ ( ord_le841296385at_nat @ X2 @ B ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_infE
% 0.29/0.50 thf(fact_172_inf__le2,axiom,
% 0.29/0.50 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y ) @ Y ) ).
% 0.29/0.50
% 0.29/0.50 % inf_le2
% 0.29/0.50 thf(fact_173_inf__le1,axiom,
% 0.29/0.50 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y ) @ X2 ) ).
% 0.29/0.50
% 0.29/0.50 % inf_le1
% 0.29/0.50 thf(fact_174_inf__sup__ord_I1_J,axiom,
% 0.29/0.50 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y ) @ X2 ) ).
% 0.29/0.50
% 0.29/0.50 % inf_sup_ord(1)
% 0.29/0.50 thf(fact_175_inf__sup__ord_I2_J,axiom,
% 0.29/0.50 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y ) @ Y ) ).
% 0.29/0.50
% 0.29/0.50 % inf_sup_ord(2)
% 0.29/0.50 thf(fact_176_NPreflow_OisAugmentingPath_Ocong,axiom,
% 0.29/0.50 augmen1090971539pacity = augmen1090971539pacity ).
% 0.29/0.50
% 0.29/0.50 % NPreflow.isAugmentingPath.cong
% 0.29/0.50 thf(fact_177_NPreflow_OaugmentingFlow_Ocong,axiom,
% 0.29/0.50 augmen72931474pacity = augmen72931474pacity ).
% 0.29/0.50
% 0.29/0.50 % NPreflow.augmentingFlow.cong
% 0.29/0.50 thf(fact_178_NPreflow_OaugFlow__val,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,P: list_P559422087at_nat] :
% 0.29/0.50 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( augmen1090971539pacity @ C @ S @ T @ F3 @ P )
% 0.29/0.50 => ( ( val_capacity @ ( residu203630698pacity @ C @ F3 ) @ S @ ( augmen72931474pacity @ C @ F3 @ P ) )
% 0.29/0.50 = ( augmen68920357pacity @ C @ F3 @ P ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NPreflow.augFlow_val
% 0.29/0.50 thf(fact_179_bot__fun__def,axiom,
% 0.29/0.50 ( bot_bo513358416_nat_o
% 0.29/0.50 = ( ^ [X3: product_prod_nat_nat] : bot_bot_o ) ) ).
% 0.29/0.50
% 0.29/0.50 % bot_fun_def
% 0.29/0.50 thf(fact_180_NPreflow_OisAugmentingPath__def,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,P: list_P559422087at_nat] :
% 0.29/0.50 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( augmen1090971539pacity @ C @ S @ T @ F3 @ P )
% 0.29/0.50 = ( isSimp1359852763pacity @ ( residu203630698pacity @ C @ F3 ) @ S @ P @ T ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NPreflow.isAugmentingPath_def
% 0.29/0.50 thf(fact_181_ford__fulkerson_I2_J,axiom,
% 0.29/0.50 ( ( ~ ? [X: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ X ) )
% 0.29/0.50 = ( ? [K2: set_nat] :
% 0.29/0.50 ( ( nCut_capacity @ c @ s @ t @ K2 )
% 0.29/0.50 & ( ( val_capacity @ c @ s @ f )
% 0.29/0.50 = ( cap_capacity @ c @ K2 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ford_fulkerson(2)
% 0.29/0.50 thf(fact_182_fofu__III__I,axiom,
% 0.29/0.50 ( ? [K3: set_nat] :
% 0.29/0.50 ( ( nCut_capacity @ c @ s @ t @ K3 )
% 0.29/0.50 & ( ( val_capacity @ c @ s @ f )
% 0.29/0.50 = ( cap_capacity @ c @ K3 ) ) )
% 0.29/0.50 => ( isMaxFlow_capacity @ c @ s @ t @ f ) ) ).
% 0.29/0.50
% 0.29/0.50 % fofu_III_I
% 0.29/0.50 thf(fact_183_fofu__II__III,axiom,
% 0.29/0.50 ( ~ ? [X_12: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ X_12 )
% 0.29/0.50 => ? [K4: set_nat] :
% 0.29/0.50 ( ( nCut_capacity @ c @ s @ t @ K4 )
% 0.29/0.50 & ( ( val_capacity @ c @ s @ f )
% 0.29/0.50 = ( cap_capacity @ c @ K4 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % fofu_II_III
% 0.29/0.50 thf(fact_184_NFlow_Oaugment__flow__value,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,F: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( flow_capacity @ ( residu203630698pacity @ C @ F3 ) @ S @ T @ F )
% 0.29/0.50 => ( ( val_capacity @ C @ S @ ( augmen887209518pacity @ C @ F3 @ F ) )
% 0.29/0.50 = ( plus_plus_capacity @ ( val_capacity @ C @ S @ F3 ) @ ( val_capacity @ ( residu203630698pacity @ C @ F3 ) @ S @ F ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow.augment_flow_value
% 0.29/0.50 thf(fact_185_Network_OmaxFlow__minCut,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,K: set_nat] :
% 0.29/0.50 ( ( network_capacity @ C @ S @ T )
% 0.29/0.50 => ( ( isMaxFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( isMinCut_capacity @ C @ S @ T @ K )
% 0.29/0.50 => ( ( val_capacity @ C @ S @ F3 )
% 0.29/0.50 = ( cap_capacity @ C @ K ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Network.maxFlow_minCut
% 0.29/0.50 thf(fact_186_Network_OisMaxFlow__alt,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( network_capacity @ C @ S @ T )
% 0.29/0.50 => ( ( isMaxFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 = ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 & ! [F5: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F5 )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( val_capacity @ C @ S @ F5 ) @ ( val_capacity @ C @ S @ F3 ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Network.isMaxFlow_alt
% 0.29/0.50 thf(fact_187_converse__mono,axiom,
% 0.29/0.50 ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ ( converse_nat_nat @ R ) @ ( converse_nat_nat @ S ) )
% 0.29/0.50 = ( ord_le841296385at_nat @ R @ S ) ) ).
% 0.29/0.50
% 0.29/0.50 % converse_mono
% 0.29/0.50 thf(fact_188_NCut_Oaxioms_I1_J,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,K: set_nat] :
% 0.29/0.50 ( ( nCut_capacity @ C @ S @ T @ K )
% 0.29/0.50 => ( network_capacity @ C @ S @ T ) ) ).
% 0.29/0.50
% 0.29/0.50 % NCut.axioms(1)
% 0.29/0.50 thf(fact_189_NCut_Ot__ni__cut,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,K: set_nat] :
% 0.29/0.50 ( ( nCut_capacity @ C @ S @ T @ K )
% 0.29/0.50 => ~ ( member_nat @ T @ K ) ) ).
% 0.29/0.50
% 0.29/0.50 % NCut.t_ni_cut
% 0.29/0.50 thf(fact_190_NCut_Os__in__cut,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,K: set_nat] :
% 0.29/0.50 ( ( nCut_capacity @ C @ S @ T @ K )
% 0.29/0.50 => ( member_nat @ S @ K ) ) ).
% 0.29/0.50
% 0.29/0.50 % NCut.s_in_cut
% 0.29/0.50 thf(fact_191_converse__subset__swap,axiom,
% 0.29/0.50 ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le841296385at_nat @ R @ ( converse_nat_nat @ S ) )
% 0.29/0.50 = ( ord_le841296385at_nat @ ( converse_nat_nat @ R ) @ S ) ) ).
% 0.29/0.50
% 0.29/0.50 % converse_subset_swap
% 0.29/0.50 thf(fact_192_isMinCut__def,axiom,
% 0.29/0.50 ( isMinCut_capacity
% 0.29/0.50 = ( ^ [C2: product_prod_nat_nat > capacity,S2: nat,T2: nat,K2: set_nat] :
% 0.29/0.50 ( ( nCut_capacity @ C2 @ S2 @ T2 @ K2 )
% 0.29/0.50 & ! [K5: set_nat] :
% 0.29/0.50 ( ( nCut_capacity @ C2 @ S2 @ T2 @ K5 )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( cap_capacity @ C2 @ K2 ) @ ( cap_capacity @ C2 @ K5 ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % isMinCut_def
% 0.29/0.50 thf(fact_193_Network_Ot__not__s,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat] :
% 0.29/0.50 ( ( network_capacity @ C @ S @ T )
% 0.29/0.50 => ( T != S ) ) ).
% 0.29/0.50
% 0.29/0.50 % Network.t_not_s
% 0.29/0.50 thf(fact_194_Network_Os__not__t,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat] :
% 0.29/0.50 ( ( network_capacity @ C @ S @ T )
% 0.29/0.50 => ( S != T ) ) ).
% 0.29/0.50
% 0.29/0.50 % Network.s_not_t
% 0.29/0.50 thf(fact_195_Flow_Oval_Ocong,axiom,
% 0.29/0.50 val_capacity = val_capacity ).
% 0.29/0.50
% 0.29/0.50 % Flow.val.cong
% 0.29/0.50 thf(fact_196_Network_OisMaxFlow_Ocong,axiom,
% 0.29/0.50 isMaxFlow_capacity = isMaxFlow_capacity ).
% 0.29/0.50
% 0.29/0.50 % Network.isMaxFlow.cong
% 0.29/0.50 thf(fact_197_NFlow_Oaugment_Ocong,axiom,
% 0.29/0.50 augmen887209518pacity = augmen887209518pacity ).
% 0.29/0.50
% 0.29/0.50 % NFlow.augment.cong
% 0.29/0.50 thf(fact_198_NCut_Ocap_Ocong,axiom,
% 0.29/0.50 cap_capacity = cap_capacity ).
% 0.29/0.50
% 0.29/0.50 % NCut.cap.cong
% 0.29/0.50 thf(fact_199_NFlow_Ofofu__II__III,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ~ ? [X_12: list_P559422087at_nat] : ( augmen1090971539pacity @ C @ S @ T @ F3 @ X_12 )
% 0.29/0.50 => ? [K4: set_nat] :
% 0.29/0.50 ( ( nCut_capacity @ C @ S @ T @ K4 )
% 0.29/0.50 & ( ( val_capacity @ C @ S @ F3 )
% 0.29/0.50 = ( cap_capacity @ C @ K4 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow.fofu_II_III
% 0.29/0.50 thf(fact_200_NFlow_Ofofu__III__I,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ? [K3: set_nat] :
% 0.29/0.50 ( ( nCut_capacity @ C @ S @ T @ K3 )
% 0.29/0.50 & ( ( val_capacity @ C @ S @ F3 )
% 0.29/0.50 = ( cap_capacity @ C @ K3 ) ) )
% 0.29/0.50 => ( isMaxFlow_capacity @ C @ S @ T @ F3 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow.fofu_III_I
% 0.29/0.50 thf(fact_201_Network_Ois__max__flow__val_Ocong,axiom,
% 0.29/0.50 is_max2144541363pacity = is_max2144541363pacity ).
% 0.29/0.50
% 0.29/0.50 % Network.is_max_flow_val.cong
% 0.29/0.50 thf(fact_202_NFlow_Oford__fulkerson_I2_J,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( ~ ? [X: list_P559422087at_nat] : ( augmen1090971539pacity @ C @ S @ T @ F3 @ X ) )
% 0.29/0.50 = ( ? [K2: set_nat] :
% 0.29/0.50 ( ( nCut_capacity @ C @ S @ T @ K2 )
% 0.29/0.50 & ( ( val_capacity @ C @ S @ F3 )
% 0.29/0.50 = ( cap_capacity @ C @ K2 ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow.ford_fulkerson(2)
% 0.29/0.50 thf(fact_203_NPreflow_Oaxioms_I1_J,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( network_capacity @ C @ S @ T ) ) ).
% 0.29/0.50
% 0.29/0.50 % NPreflow.axioms(1)
% 0.29/0.50 thf(fact_204_NFlow_Oaxioms_I1_J,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( nPreflow_capacity @ C @ S @ T @ F3 ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow.axioms(1)
% 0.29/0.50 thf(fact_205_NFlow_Oaxioms_I2_J,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( flow_capacity @ C @ S @ T @ F3 ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow.axioms(2)
% 0.29/0.50 thf(fact_206_NPreflow_Oaxioms_I2_J,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( preflow_capacity @ C @ S @ T @ F3 ) ) ).
% 0.29/0.50
% 0.29/0.50 % NPreflow.axioms(2)
% 0.29/0.50 thf(fact_207_Flow_Oaxioms_I1_J,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( flow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( preflow_capacity @ C @ S @ T @ F3 ) ) ).
% 0.29/0.50
% 0.29/0.50 % Flow.axioms(1)
% 0.29/0.50 thf(fact_208_Network_Omax__flow__val__unique,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Fv1: capacity,Fv2: capacity] :
% 0.29/0.50 ( ( network_capacity @ C @ S @ T )
% 0.29/0.50 => ( ( is_max2144541363pacity @ C @ S @ T @ Fv1 )
% 0.29/0.50 => ( ( is_max2144541363pacity @ C @ S @ T @ Fv2 )
% 0.29/0.50 => ( Fv1 = Fv2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Network.max_flow_val_unique
% 0.29/0.50 thf(fact_209_Finite__Preflow_Oaxioms_I2_J,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( finite1387368318pacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( finite217307323pacity @ C ) ) ).
% 0.29/0.50
% 0.29/0.50 % Finite_Preflow.axioms(2)
% 0.29/0.50 thf(fact_210_Finite__Preflow_Oaxioms_I1_J,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( finite1387368318pacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( preflow_capacity @ C @ S @ T @ F3 ) ) ).
% 0.29/0.50
% 0.29/0.50 % Finite_Preflow.axioms(1)
% 0.29/0.50 thf(fact_211_NFlow_Ointro,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( flow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( nFlow_capacity @ C @ S @ T @ F3 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow.intro
% 0.29/0.50 thf(fact_212_NFlow__def,axiom,
% 0.29/0.50 ( nFlow_capacity
% 0.29/0.50 = ( ^ [C2: product_prod_nat_nat > capacity,S2: nat,T2: nat,F2: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nPreflow_capacity @ C2 @ S2 @ T2 @ F2 )
% 0.29/0.50 & ( flow_capacity @ C2 @ S2 @ T2 @ F2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow_def
% 0.29/0.50 thf(fact_213_NPreflow_Ointro,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( network_capacity @ C @ S @ T )
% 0.29/0.50 => ( ( preflow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( nPreflow_capacity @ C @ S @ T @ F3 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NPreflow.intro
% 0.29/0.50 thf(fact_214_NPreflow__def,axiom,
% 0.29/0.50 ( nPreflow_capacity
% 0.29/0.50 = ( ^ [C2: product_prod_nat_nat > capacity,S2: nat,T2: nat,F2: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( network_capacity @ C2 @ S2 @ T2 )
% 0.29/0.50 & ( preflow_capacity @ C2 @ S2 @ T2 @ F2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NPreflow_def
% 0.29/0.50 thf(fact_215_NFlow_Ofofu__I__II,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( isMaxFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ~ ? [X_1: list_P559422087at_nat] : ( augmen1090971539pacity @ C @ S @ T @ F3 @ X_1 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow.fofu_I_II
% 0.29/0.50 thf(fact_216_NFlow_OnoAugPath__iff__maxFlow,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( ~ ? [X: list_P559422087at_nat] : ( augmen1090971539pacity @ C @ S @ T @ F3 @ X ) )
% 0.29/0.50 = ( isMaxFlow_capacity @ C @ S @ T @ F3 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow.noAugPath_iff_maxFlow
% 0.29/0.50 thf(fact_217_Finite__Preflow_Ointro,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( preflow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( finite217307323pacity @ C )
% 0.29/0.50 => ( finite1387368318pacity @ C @ S @ T @ F3 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Finite_Preflow.intro
% 0.29/0.50 thf(fact_218_Finite__Preflow__def,axiom,
% 0.29/0.50 ( finite1387368318pacity
% 0.29/0.50 = ( ^ [C2: product_prod_nat_nat > capacity,S2: nat,T2: nat,F2: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( preflow_capacity @ C2 @ S2 @ T2 @ F2 )
% 0.29/0.50 & ( finite217307323pacity @ C2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Finite_Preflow_def
% 0.29/0.50 thf(fact_219_NFlow_Oaugment__flow__presv,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,F: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( flow_capacity @ ( residu203630698pacity @ C @ F3 ) @ S @ T @ F )
% 0.29/0.50 => ( flow_capacity @ C @ S @ T @ ( augmen887209518pacity @ C @ F3 @ F ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow.augment_flow_presv
% 0.29/0.50 thf(fact_220_NFlow_Oford__fulkerson_I1_J,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( isMaxFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 = ( ~ ? [X: list_P559422087at_nat] : ( augmen1090971539pacity @ C @ S @ T @ F3 @ X ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow.ford_fulkerson(1)
% 0.29/0.50 thf(fact_221_Network_Ois__max__flow__val__def,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Fv: capacity] :
% 0.29/0.50 ( ( network_capacity @ C @ S @ T )
% 0.29/0.50 => ( ( is_max2144541363pacity @ C @ S @ T @ Fv )
% 0.29/0.50 = ( ? [F2: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( isMaxFlow_capacity @ C @ S @ T @ F2 )
% 0.29/0.50 & ( Fv
% 0.29/0.50 = ( val_capacity @ C @ S @ F2 ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Network.is_max_flow_val_def
% 0.29/0.50 thf(fact_222_Network_OisMaxFlow__def,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( network_capacity @ C @ S @ T )
% 0.29/0.50 => ( ( isMaxFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 = ( ( flow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 & ! [F5: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( flow_capacity @ C @ S @ T @ F5 )
% 0.29/0.50 => ( ord_less_eq_capacity @ ( val_capacity @ C @ S @ F5 ) @ ( val_capacity @ C @ S @ F3 ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Network.isMaxFlow_def
% 0.29/0.50 thf(fact_223_cf_OisSPath__no__selfloop,axiom,
% 0.29/0.50 ! [U: nat,P: list_P559422087at_nat,V: nat,U1: nat] :
% 0.29/0.50 ( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ U @ P @ V )
% 0.29/0.50 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ U1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % cf.isSPath_no_selfloop
% 0.29/0.50 thf(fact_224_cf_OisSPath__sg__incoming,axiom,
% 0.29/0.50 ! [U: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat,U2: nat] :
% 0.29/0.50 ( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ U @ P @ V )
% 0.29/0.50 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 0.29/0.50 => ( ( U1 != U2 )
% 0.29/0.50 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U2 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % cf.isSPath_sg_incoming
% 0.29/0.50 thf(fact_225_cf_OisSPath__sg__outgoing,axiom,
% 0.29/0.50 ! [U: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat,V2: nat] :
% 0.29/0.50 ( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ U @ P @ V )
% 0.29/0.50 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 0.29/0.50 => ( ( V1 != V2 )
% 0.29/0.50 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V2 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % cf.isSPath_sg_outgoing
% 0.29/0.50 thf(fact_226_isSPath__sg__outgoing,axiom,
% 0.29/0.50 ! [U: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat,V2: nat] :
% 0.29/0.50 ( ( isSimp1359852763pacity @ c @ U @ P @ V )
% 0.29/0.50 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 0.29/0.50 => ( ( V1 != V2 )
% 0.29/0.50 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V2 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % isSPath_sg_outgoing
% 0.29/0.50 thf(fact_227_isSPath__sg__incoming,axiom,
% 0.29/0.50 ! [U: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat,U2: nat] :
% 0.29/0.50 ( ( isSimp1359852763pacity @ c @ U @ P @ V )
% 0.29/0.50 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 0.29/0.50 => ( ( U1 != U2 )
% 0.29/0.50 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U2 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % isSPath_sg_incoming
% 0.29/0.50 thf(fact_228_isSPath__no__selfloop,axiom,
% 0.29/0.50 ! [U: nat,P: list_P559422087at_nat,V: nat,U1: nat] :
% 0.29/0.50 ( ( isSimp1359852763pacity @ c @ U @ P @ V )
% 0.29/0.50 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ U1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % isSPath_no_selfloop
% 0.29/0.50 thf(fact_229_converse__iff,axiom,
% 0.29/0.50 ! [A: nat,B: nat,R: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( converse_nat_nat @ R ) )
% 0.29/0.50 = ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ A ) @ R ) ) ).
% 0.29/0.50
% 0.29/0.50 % converse_iff
% 0.29/0.50 thf(fact_230_subrelI,axiom,
% 0.29/0.50 ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ! [X4: nat,Y3: nat] :
% 0.29/0.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y3 ) @ R )
% 0.29/0.50 => ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y3 ) @ S ) )
% 0.29/0.50 => ( ord_le841296385at_nat @ R @ S ) ) ).
% 0.29/0.50
% 0.29/0.50 % subrelI
% 0.29/0.50 thf(fact_231_converseD,axiom,
% 0.29/0.50 ! [A: nat,B: nat,R: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( converse_nat_nat @ R ) )
% 0.29/0.50 => ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ A ) @ R ) ) ).
% 0.29/0.50
% 0.29/0.50 % converseD
% 0.29/0.50 thf(fact_232_converseE,axiom,
% 0.29/0.50 ! [Yx: product_prod_nat_nat,R: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( member701585322at_nat @ Yx @ ( converse_nat_nat @ R ) )
% 0.29/0.50 => ~ ! [X4: nat,Y3: nat] :
% 0.29/0.50 ( ( Yx
% 0.29/0.50 = ( product_Pair_nat_nat @ Y3 @ X4 ) )
% 0.29/0.50 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y3 ) @ R ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % converseE
% 0.29/0.50 thf(fact_233_converse_Ocases,axiom,
% 0.29/0.50 ! [A1: nat,A22: nat,R: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( converse_nat_nat @ R ) )
% 0.29/0.50 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A22 @ A1 ) @ R ) ) ).
% 0.29/0.50
% 0.29/0.50 % converse.cases
% 0.29/0.50 thf(fact_234_converse_Osimps,axiom,
% 0.29/0.50 ! [A1: nat,A22: nat,R: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( converse_nat_nat @ R ) )
% 0.29/0.50 = ( ? [A2: nat,B2: nat] :
% 0.29/0.50 ( ( A1 = B2 )
% 0.29/0.50 & ( A22 = A2 )
% 0.29/0.50 & ( member701585322at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ R ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % converse.simps
% 0.29/0.50 thf(fact_235_converse_Ointros,axiom,
% 0.29/0.50 ! [A: nat,B: nat,R: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.29/0.50 => ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ A ) @ ( converse_nat_nat @ R ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % converse.intros
% 0.29/0.50 thf(fact_236_converse_Oinducts,axiom,
% 0.29/0.50 ! [X1: nat,X22: nat,R: set_Pr1986765409at_nat,P2: nat > nat > $o] :
% 0.29/0.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) @ ( converse_nat_nat @ R ) )
% 0.29/0.50 => ( ! [A4: nat,B4: nat] :
% 0.29/0.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A4 @ B4 ) @ R )
% 0.29/0.50 => ( P2 @ B4 @ A4 ) )
% 0.29/0.50 => ( P2 @ X1 @ X22 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % converse.inducts
% 0.29/0.50 thf(fact_237_Graph_OisSPath__sg__outgoing,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,U: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat,V2: nat] :
% 0.29/0.50 ( ( isSimp1359852763pacity @ C @ U @ P @ V )
% 0.29/0.50 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 0.29/0.50 => ( ( V1 != V2 )
% 0.29/0.50 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V2 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Graph.isSPath_sg_outgoing
% 0.29/0.50 thf(fact_238_Graph_OisSPath__sg__incoming,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,U: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat,U2: nat] :
% 0.29/0.50 ( ( isSimp1359852763pacity @ C @ U @ P @ V )
% 0.29/0.50 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 0.29/0.50 => ( ( U1 != U2 )
% 0.29/0.50 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U2 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Graph.isSPath_sg_incoming
% 0.29/0.50 thf(fact_239_Graph_OisSPath__no__selfloop,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,U: nat,P: list_P559422087at_nat,V: nat,U1: nat] :
% 0.29/0.50 ( ( isSimp1359852763pacity @ C @ U @ P @ V )
% 0.29/0.50 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ U1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Graph.isSPath_no_selfloop
% 0.29/0.50 thf(fact_240_augment__flow__presv__cap,axiom,
% 0.29/0.50 ! [F: product_prod_nat_nat > capacity,U: nat,V: nat] :
% 0.29/0.50 ( ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ F )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ zero_zero_capacity @ ( augmen887209518pacity @ c @ f @ F @ ( product_Pair_nat_nat @ U @ V ) ) )
% 0.29/0.50 & ( ord_less_eq_capacity @ ( augmen887209518pacity @ c @ f @ F @ ( product_Pair_nat_nat @ U @ V ) ) @ ( c @ ( product_Pair_nat_nat @ U @ V ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % augment_flow_presv_cap
% 0.29/0.50 thf(fact_241_swap__simp,axiom,
% 0.29/0.50 ! [X2: nat,Y: nat] :
% 0.29/0.50 ( ( product_swap_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y ) )
% 0.29/0.50 = ( product_Pair_nat_nat @ Y @ X2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % swap_simp
% 0.29/0.50 thf(fact_242_f__non__negative,axiom,
% 0.29/0.50 ! [E: product_prod_nat_nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( f @ E ) ) ).
% 0.29/0.50
% 0.29/0.50 % f_non_negative
% 0.29/0.50 thf(fact_243_old_Oprod_Oinject,axiom,
% 0.29/0.50 ! [A: nat,B: nat,A5: nat,B5: nat] :
% 0.29/0.50 ( ( ( product_Pair_nat_nat @ A @ B )
% 0.29/0.50 = ( product_Pair_nat_nat @ A5 @ B5 ) )
% 0.29/0.50 = ( ( A = A5 )
% 0.29/0.50 & ( B = B5 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % old.prod.inject
% 0.29/0.50 thf(fact_244_prod_Oinject,axiom,
% 0.29/0.50 ! [X1: nat,X22: nat,Y1: nat,Y22: nat] :
% 0.29/0.50 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 0.29/0.50 = ( product_Pair_nat_nat @ Y1 @ Y22 ) )
% 0.29/0.50 = ( ( X1 = Y1 )
% 0.29/0.50 & ( X22 = Y22 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % prod.inject
% 0.29/0.50 thf(fact_245_cap__non__negative,axiom,
% 0.29/0.50 ! [U3: nat,V3: nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( c @ ( product_Pair_nat_nat @ U3 @ V3 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % cap_non_negative
% 0.29/0.50 thf(fact_246_capacity__const,axiom,
% 0.29/0.50 ! [E2: product_prod_nat_nat] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ zero_zero_capacity @ ( f @ E2 ) )
% 0.29/0.50 & ( ord_less_eq_capacity @ ( f @ E2 ) @ ( c @ E2 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % capacity_const
% 0.29/0.50 thf(fact_247_swap__swap,axiom,
% 0.29/0.50 ! [P: product_prod_nat_nat] :
% 0.29/0.50 ( ( product_swap_nat_nat @ ( product_swap_nat_nat @ P ) )
% 0.29/0.50 = P ) ).
% 0.29/0.50
% 0.29/0.50 % swap_swap
% 0.29/0.50 thf(fact_248_resE__nonNegative,axiom,
% 0.29/0.50 ! [E: product_prod_nat_nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( residu203630698pacity @ c @ f @ E ) ) ).
% 0.29/0.50
% 0.29/0.50 % resE_nonNegative
% 0.29/0.50 thf(fact_249_RPreGraph_OresE__nonNegative,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity,E: product_prod_nat_nat] :
% 0.29/0.50 ( ( residu164581374pacity @ C @ S @ T @ Cf )
% 0.29/0.50 => ( ord_less_eq_capacity @ zero_zero_capacity @ ( Cf @ E ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % RPreGraph.resE_nonNegative
% 0.29/0.50 thf(fact_250_Preflow_Ocapacity__const,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 0.29/0.50 ( ( preflow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ! [E2: product_prod_nat_nat] :
% 0.29/0.50 ( ( ord_less_eq_capacity @ zero_zero_capacity @ ( F3 @ E2 ) )
% 0.29/0.50 & ( ord_less_eq_capacity @ ( F3 @ E2 ) @ ( C @ E2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Preflow.capacity_const
% 0.29/0.50 thf(fact_251_Preflow_Of__non__negative,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,E: product_prod_nat_nat] :
% 0.29/0.50 ( ( preflow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ord_less_eq_capacity @ zero_zero_capacity @ ( F3 @ E ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Preflow.f_non_negative
% 0.29/0.50 thf(fact_252_old_Oprod_Oinducts,axiom,
% 0.29/0.50 ! [P2: product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 0.29/0.50 ( ! [A4: nat,B4: nat] : ( P2 @ ( product_Pair_nat_nat @ A4 @ B4 ) )
% 0.29/0.50 => ( P2 @ Prod ) ) ).
% 0.29/0.50
% 0.29/0.50 % old.prod.inducts
% 0.29/0.50 thf(fact_253_old_Oprod_Oexhaust,axiom,
% 0.29/0.50 ! [Y: product_prod_nat_nat] :
% 0.29/0.50 ~ ! [A4: nat,B4: nat] :
% 0.29/0.50 ( Y
% 0.29/0.50 != ( product_Pair_nat_nat @ A4 @ B4 ) ) ).
% 0.29/0.50
% 0.29/0.50 % old.prod.exhaust
% 0.29/0.50 thf(fact_254_Pair__inject,axiom,
% 0.29/0.50 ! [A: nat,B: nat,A5: nat,B5: nat] :
% 0.29/0.50 ( ( ( product_Pair_nat_nat @ A @ B )
% 0.29/0.50 = ( product_Pair_nat_nat @ A5 @ B5 ) )
% 0.29/0.50 => ~ ( ( A = A5 )
% 0.29/0.50 => ( B != B5 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Pair_inject
% 0.29/0.50 thf(fact_255_prod__cases,axiom,
% 0.29/0.50 ! [P2: product_prod_nat_nat > $o,P: product_prod_nat_nat] :
% 0.29/0.50 ( ! [A4: nat,B4: nat] : ( P2 @ ( product_Pair_nat_nat @ A4 @ B4 ) )
% 0.29/0.50 => ( P2 @ P ) ) ).
% 0.29/0.50
% 0.29/0.50 % prod_cases
% 0.29/0.50 thf(fact_256_surj__pair,axiom,
% 0.29/0.50 ! [P: product_prod_nat_nat] :
% 0.29/0.50 ? [X4: nat,Y3: nat] :
% 0.29/0.50 ( P
% 0.29/0.50 = ( product_Pair_nat_nat @ X4 @ Y3 ) ) ).
% 0.29/0.50
% 0.29/0.50 % surj_pair
% 0.29/0.50 thf(fact_257_Network_Ocap__non__negative,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat] :
% 0.29/0.50 ( ( network_capacity @ C @ S @ T )
% 0.29/0.50 => ! [U3: nat,V3: nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( C @ ( product_Pair_nat_nat @ U3 @ V3 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Network.cap_non_negative
% 0.29/0.50 thf(fact_258_NPreflow_OresE__nonNegative,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,E: product_prod_nat_nat] :
% 0.29/0.50 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ord_less_eq_capacity @ zero_zero_capacity @ ( residu203630698pacity @ C @ F3 @ E ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NPreflow.resE_nonNegative
% 0.29/0.50 thf(fact_259_NFlow_Oaugment__flow__presv__cap,axiom,
% 0.29/0.50 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,F: product_prod_nat_nat > capacity,U: nat,V: nat] :
% 0.29/0.50 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 0.29/0.50 => ( ( flow_capacity @ ( residu203630698pacity @ C @ F3 ) @ S @ T @ F )
% 0.29/0.50 => ( ( ord_less_eq_capacity @ zero_zero_capacity @ ( augmen887209518pacity @ C @ F3 @ F @ ( product_Pair_nat_nat @ U @ V ) ) )
% 0.29/0.50 & ( ord_less_eq_capacity @ ( augmen887209518pacity @ C @ F3 @ F @ ( product_Pair_nat_nat @ U @ V ) ) @ ( C @ ( product_Pair_nat_nat @ U @ V ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NFlow.augment_flow_presv_cap
% 0.29/0.50 thf(fact_260_excess__s__non__pos,axiom,
% 0.29/0.50 ord_less_eq_capacity @ ( excess_capacity @ c @ f @ s ) @ zero_zero_capacity ).
% 0.29/0.50
% 0.29/0.50 % excess_s_non_pos
% 0.29/0.50 thf(fact_261_resCap__gzero,axiom,
% 0.29/0.50 ! [P: list_P559422087at_nat] :
% 0.29/0.50 ( ( augmen1090971539pacity @ c @ s @ t @ f @ P )
% 0.29/0.50 => ( ord_less_capacity @ zero_zero_capacity @ ( augmen68920357pacity @ c @ f @ P ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % resCap_gzero
% 0.29/0.50 thf(fact_262_Network_Oexcess_Ocong,axiom,
% 0.29/0.50 excess_capacity = excess_capacity ).
% 0.29/0.50
% 0.29/0.50 % Network.excess.cong
% 0.29/0.50 thf(fact_263_bot_Onot__eq__extremum,axiom,
% 0.29/0.50 ! [A: product_prod_nat_nat > $o] :
% 0.29/0.50 ( ( A != bot_bo513358416_nat_o )
% 0.29/0.50 = ( ord_le1015898640_nat_o @ bot_bo513358416_nat_o @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 % bot.not_eq_extremum
% 0.29/0.50 thf(fact_264_bot_Onot__eq__extremum,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( A != bot_bo2130386637at_nat )
% 0.29/0.50 = ( ord_le116442893at_nat @ bot_bo2130386637at_nat @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 % bot.not_eq_extremum
% 0.29/0.50 thf(fact_265_bot_Oextremum__strict,axiom,
% 0.29/0.50 ! [A: product_prod_nat_nat > $o] :
% 0.29/0.50 ~ ( ord_le1015898640_nat_o @ A @ bot_bo513358416_nat_o ) ).
% 0.29/0.50
% 0.29/0.50 % bot.extremum_strict
% 0.29/0.50 thf(fact_266_bot_Oextremum__strict,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat] :
% 0.29/0.50 ~ ( ord_le116442893at_nat @ A @ bot_bo2130386637at_nat ) ).
% 0.29/0.50
% 0.29/0.50 % bot.extremum_strict
% 0.29/0.50 thf(fact_267_less__infI1,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le116442893at_nat @ A @ X2 )
% 0.29/0.50 => ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ A @ B ) @ X2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % less_infI1
% 0.29/0.50 thf(fact_268_less__infI2,axiom,
% 0.29/0.50 ! [B: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le116442893at_nat @ B @ X2 )
% 0.29/0.50 => ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ A @ B ) @ X2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % less_infI2
% 0.29/0.50 thf(fact_269_inf_Ostrict__boundedE,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le116442893at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
% 0.29/0.50 => ~ ( ( ord_le116442893at_nat @ A @ B )
% 0.29/0.50 => ~ ( ord_le116442893at_nat @ A @ C ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.strict_boundedE
% 0.29/0.50 thf(fact_270_inf_Ostrict__order__iff,axiom,
% 0.29/0.50 ( ord_le116442893at_nat
% 0.29/0.50 = ( ^ [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( A2
% 0.29/0.50 = ( inf_in586391887at_nat @ A2 @ B2 ) )
% 0.29/0.50 & ( A2 != B2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.strict_order_iff
% 0.29/0.50 thf(fact_271_inf_Ostrict__coboundedI1,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le116442893at_nat @ A @ C )
% 0.29/0.50 => ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.strict_coboundedI1
% 0.29/0.50 thf(fact_272_inf_Ostrict__coboundedI2,axiom,
% 0.29/0.50 ! [B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le116442893at_nat @ B @ C )
% 0.29/0.50 => ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C ) ) ).
% 0.29/0.50
% 0.29/0.50 % inf.strict_coboundedI2
% 0.29/0.50 thf(fact_273_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.50 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le116442893at_nat @ B @ A )
% 0.29/0.50 => ( A != B ) ) ).
% 0.29/0.50
% 0.29/0.50 % dual_order.strict_implies_not_eq
% 0.29/0.50 thf(fact_274_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.50 ! [B: capacity,A: capacity] :
% 0.29/0.50 ( ( ord_less_capacity @ B @ A )
% 0.29/0.50 => ( A != B ) ) ).
% 0.29/0.50
% 0.29/0.50 % dual_order.strict_implies_not_eq
% 0.29/0.50 thf(fact_275_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.50 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.29/0.50 ( ( ord_le116442893at_nat @ A @ B )
% 0.29/0.50 => ( A != B ) ) ).
% 0.29/0.50
% 0.29/0.50 % order.strict_implies_not_eq
% 0.29/0.50 thf(fact_276_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.50 ! [A: capacity,B: capacity] :
% 0.29/0.50 ( ( ord_less_capacity @ A @ B )
% 0.29/0.50 => ( A != B ) ) ).
% 0.29/0.50
% 0.29/0.50 % order.strict_implies_not_eq
% 0.29/0.50 thf(fact_277_not__less__iff__gr__or__eq,axiom,
% 0.29/0.50 ! [X2: capacity,Y: capacity] :
% 0.29/0.50 ( ( ~ ( ord_less_capacity @ X2 @ Y ) )
% 0.29/0.50 = ( ( ord_less_capacity @ Y @ X2 )
% 0.29/0.50 | ( X2 = Y ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % not_less_iff_gr_or_eq
% 0.29/0.50
% 0.29/0.50 % Conjectures (2)
% 0.29/0.50 thf(conj_0,hypothesis,
% 0.29/0.50 augmen1090971539pacity @ c @ s @ t @ f @ p ).
% 0.29/0.50
% 0.29/0.50 thf(conj_1,conjecture,
% 0.29/0.50 ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
% 0.29/0.50 = bot_bo2130386637at_nat ) ).
% 0.29/0.50
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 ------------------------
% 2.76/1.72 ---- Embedded in THF ---
% 2.76/1.73 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.76/1.73 %%% Generated on Tue Feb 24 08:24:43 EST 2026
% 2.76/1.73 %%% using '$$dhol' embedding, version 1.3.0.
% 2.76/1.73 %%% Logic specification used:
% 2.76/1.73 %%% thf(spec, logic, $$dhol).
% 2.76/1.73
% 2.76/1.73 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.VKYVsEMyde/DTF2DTF13121.p
% See solution above
% 2.76/1.73 ------------------------
% 2.76/1.75 ---- Cleaned THF ---
% 2.76/1.75 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.76/1.75 list_P559422087at_nat: $tType ).
% 2.76/1.75
% 2.76/1.75 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.76/1.75 set_Pr1986765409at_nat: $tType ).
% 2.76/1.75
% 2.76/1.75 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.76/1.75 product_prod_nat_nat: $tType ).
% 2.76/1.75
% 2.76/1.75 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 2.76/1.75 set_nat: $tType ).
% 2.76/1.75
% 2.76/1.75 thf(ty_n_tf__capacity,type,
% 2.76/1.75 capacity: $tType ).
% 2.76/1.75
% 2.76/1.75 thf(ty_n_t__Nat__Onat,type,
% 2.76/1.75 nat: $tType ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Augmenting__Flow_ONFlow_Oaugment_001tf__capacity,type,
% 2.76/1.75 augmen887209518pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Augmenting__Path_ONPreflow_OaugmentingFlow_001tf__capacity,type,
% 2.76/1.75 augmen72931474pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > product_prod_nat_nat > capacity ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Augmenting__Path_ONPreflow_OisAugmentingPath_001tf__capacity,type,
% 2.76/1.75 augmen1090971539pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Augmenting__Path_ONPreflow_OresCap_001tf__capacity,type,
% 2.76/1.75 augmen68920357pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > capacity ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Graph_OFinite__Graph_001tf__capacity,type,
% 2.76/1.75 finite217307323pacity: ( product_prod_nat_nat > capacity ) > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Graph_OGraph_OisShortestPath_001tf__capacity,type,
% 2.76/1.75 isShor1936442771pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Graph_OGraph_OisSimplePath_001tf__capacity,type,
% 2.76/1.75 isSimp1359852763pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Groups_Oplus__class_Oplus_001tf__capacity,type,
% 2.76/1.75 plus_plus_capacity: capacity > capacity > capacity ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Groups_Ozero__class_Ozero_001tf__capacity,type,
% 2.76/1.75 zero_zero_capacity: capacity ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 2.76/1.75 inf_in2138576462_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.76/1.75 inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.76/1.75 set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Network_OFinite__Preflow_001tf__capacity,type,
% 2.76/1.75 finite1387368318pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Network_OFlow_001tf__capacity,type,
% 2.76/1.75 flow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Network_OFlow_Oval_001tf__capacity,type,
% 2.76/1.75 val_capacity: ( product_prod_nat_nat > capacity ) > nat > ( product_prod_nat_nat > capacity ) > capacity ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Network_ONCut_001tf__capacity,type,
% 2.76/1.75 nCut_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > set_nat > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Network_ONCut_Ocap_001tf__capacity,type,
% 2.76/1.75 cap_capacity: ( product_prod_nat_nat > capacity ) > set_nat > capacity ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Network_ONFlow_001tf__capacity,type,
% 2.76/1.75 nFlow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Network_ONPreflow_001tf__capacity,type,
% 2.76/1.75 nPreflow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Network_ONetwork_001tf__capacity,type,
% 2.76/1.75 network_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Network_ONetwork_Oexcess_001tf__capacity,type,
% 2.76/1.75 excess_capacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > nat > capacity ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Network_ONetwork_OisMaxFlow_001tf__capacity,type,
% 2.76/1.75 isMaxFlow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Network_ONetwork_Ois__max__flow__val_001tf__capacity,type,
% 2.76/1.75 is_max2144541363pacity: ( product_prod_nat_nat > capacity ) > nat > nat > capacity > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Network_OPreflow_001tf__capacity,type,
% 2.76/1.75 preflow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Network_OisMinCut_001tf__capacity,type,
% 2.76/1.75 isMinCut_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > set_nat > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_Eo_J,type,
% 2.76/1.75 bot_bot_nat_o: nat > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 2.76/1.75 bot_bo513358416_nat_o: product_prod_nat_nat > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
% 2.76/1.75 bot_bot_o: $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.76/1.75 bot_bot_set_nat: set_nat ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.76/1.75 bot_bo2130386637at_nat: set_Pr1986765409at_nat ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Orderings_Oord__class_Oless_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 2.76/1.75 ord_le1015898640_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.76/1.75 ord_le116442893at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Orderings_Oord__class_Oless_001tf__capacity,type,
% 2.76/1.75 ord_less_capacity: capacity > capacity > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 2.76/1.75 ord_le1039616028_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.76/1.75 ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Orderings_Oord__class_Oless__eq_001tf__capacity,type,
% 2.76/1.75 ord_less_eq_capacity: capacity > capacity > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.76/1.75 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Product__Type_Oprod_Oswap_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.76/1.75 product_swap_nat_nat: product_prod_nat_nat > product_prod_nat_nat ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Relation_Oconverse_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.76/1.75 converse_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Residual__Graph_ONetwork_Oflow__of__cf_001tf__capacity,type,
% 2.76/1.75 residu1549650759pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Residual__Graph_ORGraph_001tf__capacity,type,
% 2.76/1.75 residu800046103pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Residual__Graph_ORPreGraph_001tf__capacity,type,
% 2.76/1.75 residu164581374pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Residual__Graph_OresidualGraph_001tf__capacity,type,
% 2.76/1.75 residu203630698pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 2.76/1.75 collect_nat: ( nat > $o ) > set_nat ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.76/1.75 collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_member_001t__Nat__Onat,type,
% 2.76/1.75 member_nat: nat > set_nat > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.76/1.75 member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 2.76/1.75
% 2.76/1.75 thf(sy_v_c,type,
% 2.76/1.75 c: product_prod_nat_nat > capacity ).
% 2.76/1.75
% 2.76/1.75 thf(sy_v_f,type,
% 2.76/1.75 f: product_prod_nat_nat > capacity ).
% 2.76/1.75
% 2.76/1.75 thf(sy_v_p,type,
% 2.76/1.75 p: list_P559422087at_nat ).
% 2.76/1.75
% 2.76/1.75 thf(sy_v_s,type,
% 2.76/1.75 s: nat ).
% 2.76/1.75
% 2.76/1.75 thf(sy_v_t,type,
% 2.76/1.75 t: nat ).
% 2.76/1.75
% 2.76/1.75 thf(fact_0_t__not__s,axiom,
% 2.76/1.75 t != s ).
% 2.76/1.75
% 2.76/1.75 thf(fact_1_cf_OisSPath__nt__parallel__pf,axiom,
% 2.76/1.75 ! [S: nat,P: list_P559422087at_nat,T: nat] :
% 2.76/1.75 ( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ S @ P @ T )
% 2.76/1.75 => ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ P ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ P ) ) )
% 2.76/1.75 = bot_bo2130386637at_nat ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_2_isSPath__nt__parallel__pf,axiom,
% 2.76/1.75 ! [S: nat,P: list_P559422087at_nat,T: nat] :
% 2.76/1.75 ( ( isSimp1359852763pacity @ c @ S @ P @ T )
% 2.76/1.75 => ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ P ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ P ) ) )
% 2.76/1.75 = bot_bo2130386637at_nat ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_3_NFlow__axioms,axiom,
% 2.76/1.75 nFlow_capacity @ c @ s @ t @ f ).
% 2.76/1.75
% 2.76/1.75 thf(fact_4_max__flow__val__unique,axiom,
% 2.76/1.75 ! [Fv1: capacity,Fv2: capacity] :
% 2.76/1.75 ( ( is_max2144541363pacity @ c @ s @ t @ Fv1 )
% 2.76/1.75 => ( ( is_max2144541363pacity @ c @ s @ t @ Fv2 )
% 2.76/1.75 => ( Fv1 = Fv2 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_5_isAugmentingPath__def,axiom,
% 2.76/1.75 ! [P: list_P559422087at_nat] :
% 2.76/1.75 ( ( augmen1090971539pacity @ c @ s @ t @ f @ P )
% 2.76/1.75 = ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ s @ P @ t ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_6_Finite__Preflow__axioms,axiom,
% 2.76/1.75 finite1387368318pacity @ c @ s @ t @ f ).
% 2.76/1.75
% 2.76/1.75 thf(fact_7_fofu__I__II,axiom,
% 2.76/1.75 ( ( isMaxFlow_capacity @ c @ s @ t @ f )
% 2.76/1.75 => ~ ? [X_1: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ X_1 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_8_noAugPath__iff__maxFlow,axiom,
% 2.76/1.75 ( ( ~ ? [X: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ X ) )
% 2.76/1.75 = ( isMaxFlow_capacity @ c @ s @ t @ f ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_9_Preflow__axioms,axiom,
% 2.76/1.75 preflow_capacity @ c @ s @ t @ f ).
% 2.76/1.75
% 2.76/1.75 thf(fact_10_is__RGraph,axiom,
% 2.76/1.75 residu800046103pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_11_Flow__axioms,axiom,
% 2.76/1.75 flow_capacity @ c @ s @ t @ f ).
% 2.76/1.75
% 2.76/1.75 thf(fact_12_NPreflow__axioms,axiom,
% 2.76/1.75 nPreflow_capacity @ c @ s @ t @ f ).
% 2.76/1.75
% 2.76/1.75 thf(fact_13_converse__empty,axiom,
% 2.76/1.75 ( ( converse_nat_nat @ bot_bo2130386637at_nat )
% 2.76/1.75 = bot_bo2130386637at_nat ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_14_inf__bot__left,axiom,
% 2.76/1.75 ! [X2: product_prod_nat_nat > $o] :
% 2.76/1.75 ( ( inf_in2138576462_nat_o @ bot_bo513358416_nat_o @ X2 )
% 2.76/1.75 = bot_bo513358416_nat_o ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_15_inf__bot__left,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ bot_bo2130386637at_nat @ X2 )
% 2.76/1.75 = bot_bo2130386637at_nat ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_16_inf__bot__right,axiom,
% 2.76/1.75 ! [X2: product_prod_nat_nat > $o] :
% 2.76/1.75 ( ( inf_in2138576462_nat_o @ X2 @ bot_bo513358416_nat_o )
% 2.76/1.75 = bot_bo513358416_nat_o ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_17_inf__bot__right,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ X2 @ bot_bo2130386637at_nat )
% 2.76/1.75 = bot_bo2130386637at_nat ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_18_is__RPreGraph,axiom,
% 2.76/1.75 residu164581374pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_19_Network__axioms,axiom,
% 2.76/1.75 network_capacity @ c @ s @ t ).
% 2.76/1.75
% 2.76/1.75 thf(fact_20_fo__rg__inv,axiom,
% 2.76/1.75 ( ( residu1549650759pacity @ c @ ( residu203630698pacity @ c @ f ) )
% 2.76/1.75 = f ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_21_inf__right__idem,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ X2 @ Y ) @ Y )
% 2.76/1.75 = ( inf_in586391887at_nat @ X2 @ Y ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_22_inf_Oright__idem,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B )
% 2.76/1.75 = ( inf_in586391887at_nat @ A @ B ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_23_inf__left__idem,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ X2 @ ( inf_in586391887at_nat @ X2 @ Y ) )
% 2.76/1.75 = ( inf_in586391887at_nat @ X2 @ Y ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_24_inf_Oleft__idem,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ A @ B ) )
% 2.76/1.75 = ( inf_in586391887at_nat @ A @ B ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_25_inf__idem,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ X2 @ X2 )
% 2.76/1.75 = X2 ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_26_inf_Oidem,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ A @ A )
% 2.76/1.75 = A ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_27_converse__converse,axiom,
% 2.76/1.75 ! [R: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( converse_nat_nat @ ( converse_nat_nat @ R ) )
% 2.76/1.75 = R ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_28_converse__inject,axiom,
% 2.76/1.75 ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ( converse_nat_nat @ R )
% 2.76/1.75 = ( converse_nat_nat @ S ) )
% 2.76/1.75 = ( R = S ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_29_augFlow__resFlow,axiom,
% 2.76/1.75 ! [P: list_P559422087at_nat] :
% 2.76/1.75 ( ( augmen1090971539pacity @ c @ s @ t @ f @ P )
% 2.76/1.75 => ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ ( augmen72931474pacity @ c @ f @ P ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_30_bot__empty__eq,axiom,
% 2.76/1.75 ( bot_bot_nat_o
% 2.76/1.75 = ( ^ [X3: nat] : ( member_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_31_bot__empty__eq,axiom,
% 2.76/1.75 ( bot_bo513358416_nat_o
% 2.76/1.75 = ( ^ [X3: product_prod_nat_nat] : ( member701585322at_nat @ X3 @ bot_bo2130386637at_nat ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_32_inf__left__commute,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ X2 @ ( inf_in586391887at_nat @ Y @ Z ) )
% 2.76/1.75 = ( inf_in586391887at_nat @ Y @ ( inf_in586391887at_nat @ X2 @ Z ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_33_inf_Oleft__commute,axiom,
% 2.76/1.75 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ B @ ( inf_in586391887at_nat @ A @ C ) )
% 2.76/1.75 = ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_34_inf__commute,axiom,
% 2.76/1.75 ( inf_in586391887at_nat
% 2.76/1.75 = ( ^ [X3: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] : ( inf_in586391887at_nat @ Y2 @ X3 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_35_inf_Ocommute,axiom,
% 2.76/1.75 ( inf_in586391887at_nat
% 2.76/1.75 = ( ^ [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] : ( inf_in586391887at_nat @ B2 @ A2 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_36_inf__assoc,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ X2 @ Y ) @ Z )
% 2.76/1.75 = ( inf_in586391887at_nat @ X2 @ ( inf_in586391887at_nat @ Y @ Z ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_37_inf_Oassoc,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C )
% 2.76/1.75 = ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_38_boolean__algebra__cancel_Oinf2,axiom,
% 2.76/1.75 ! [B3: set_Pr1986765409at_nat,K: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( B3
% 2.76/1.75 = ( inf_in586391887at_nat @ K @ B ) )
% 2.76/1.75 => ( ( inf_in586391887at_nat @ A @ B3 )
% 2.76/1.75 = ( inf_in586391887at_nat @ K @ ( inf_in586391887at_nat @ A @ B ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_39_boolean__algebra__cancel_Oinf1,axiom,
% 2.76/1.75 ! [A3: set_Pr1986765409at_nat,K: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( A3
% 2.76/1.75 = ( inf_in586391887at_nat @ K @ A ) )
% 2.76/1.75 => ( ( inf_in586391887at_nat @ A3 @ B )
% 2.76/1.75 = ( inf_in586391887at_nat @ K @ ( inf_in586391887at_nat @ A @ B ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_40_inf__sup__aci_I1_J,axiom,
% 2.76/1.75 ( inf_in586391887at_nat
% 2.76/1.75 = ( ^ [X3: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] : ( inf_in586391887at_nat @ Y2 @ X3 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_41_inf__sup__aci_I2_J,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ X2 @ Y ) @ Z )
% 2.76/1.75 = ( inf_in586391887at_nat @ X2 @ ( inf_in586391887at_nat @ Y @ Z ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_42_inf__sup__aci_I3_J,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ X2 @ ( inf_in586391887at_nat @ Y @ Z ) )
% 2.76/1.75 = ( inf_in586391887at_nat @ Y @ ( inf_in586391887at_nat @ X2 @ Z ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_43_inf__sup__aci_I4_J,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ X2 @ ( inf_in586391887at_nat @ X2 @ Y ) )
% 2.76/1.75 = ( inf_in586391887at_nat @ X2 @ Y ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_44_converse__Int,axiom,
% 2.76/1.75 ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( converse_nat_nat @ ( inf_in586391887at_nat @ R @ S ) )
% 2.76/1.75 = ( inf_in586391887at_nat @ ( converse_nat_nat @ R ) @ ( converse_nat_nat @ S ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_45_augment__flow__presv,axiom,
% 2.76/1.75 ! [F: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ F )
% 2.76/1.75 => ( flow_capacity @ c @ s @ t @ ( augmen887209518pacity @ c @ f @ F ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_46_mem__Collect__eq,axiom,
% 2.76/1.75 ! [A: nat,P2: nat > $o] :
% 2.76/1.75 ( ( member_nat @ A @ ( collect_nat @ P2 ) )
% 2.76/1.75 = ( P2 @ A ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_47_mem__Collect__eq,axiom,
% 2.76/1.75 ! [A: product_prod_nat_nat,P2: product_prod_nat_nat > $o] :
% 2.76/1.75 ( ( member701585322at_nat @ A @ ( collec7649004at_nat @ P2 ) )
% 2.76/1.75 = ( P2 @ A ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_48_Collect__mem__eq,axiom,
% 2.76/1.75 ! [A3: set_nat] :
% 2.76/1.75 ( ( collect_nat
% 2.76/1.75 @ ^ [X3: nat] : ( member_nat @ X3 @ A3 ) )
% 2.76/1.75 = A3 ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_49_Collect__mem__eq,axiom,
% 2.76/1.75 ! [A3: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( collec7649004at_nat
% 2.76/1.75 @ ^ [X3: product_prod_nat_nat] : ( member701585322at_nat @ X3 @ A3 ) )
% 2.76/1.75 = A3 ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_50_Collect__cong,axiom,
% 2.76/1.75 ! [P2: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 2.76/1.75 ( ! [X4: product_prod_nat_nat] :
% 2.76/1.75 ( ( P2 @ X4 )
% 2.76/1.75 = ( Q @ X4 ) )
% 2.76/1.75 => ( ( collec7649004at_nat @ P2 )
% 2.76/1.75 = ( collec7649004at_nat @ Q ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_51_cf_OisSPath__nt__parallel,axiom,
% 2.76/1.75 ! [S: nat,P: list_P559422087at_nat,T: nat,E: product_prod_nat_nat] :
% 2.76/1.75 ( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ S @ P @ T )
% 2.76/1.75 => ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ P ) )
% 2.76/1.75 => ~ ( member701585322at_nat @ ( product_swap_nat_nat @ E ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_52_is__max__flow__val__def,axiom,
% 2.76/1.75 ! [Fv: capacity] :
% 2.76/1.75 ( ( is_max2144541363pacity @ c @ s @ t @ Fv )
% 2.76/1.75 = ( ? [F2: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( isMaxFlow_capacity @ c @ s @ t @ F2 )
% 2.76/1.75 & ( Fv
% 2.76/1.75 = ( val_capacity @ c @ s @ F2 ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_53_cf_OFinite__Graph__axioms,axiom,
% 2.76/1.75 finite217307323pacity @ ( residu203630698pacity @ c @ f ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_54_ford__fulkerson_I1_J,axiom,
% 2.76/1.75 ( ( isMaxFlow_capacity @ c @ s @ t @ f )
% 2.76/1.75 = ( ~ ? [X: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ X ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_55_shortest__is__augmenting,axiom,
% 2.76/1.75 ! [P: list_P559422087at_nat] :
% 2.76/1.75 ( ( isShor1936442771pacity @ ( residu203630698pacity @ c @ f ) @ s @ P @ t )
% 2.76/1.75 => ( augmen1090971539pacity @ c @ s @ t @ f @ P ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_56_augmenting__path__imp__shortest,axiom,
% 2.76/1.75 ! [P: list_P559422087at_nat] :
% 2.76/1.75 ( ( augmen1090971539pacity @ c @ s @ t @ f @ P )
% 2.76/1.75 => ? [P3: list_P559422087at_nat] : ( isShor1936442771pacity @ ( residu203630698pacity @ c @ f ) @ s @ P3 @ t ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_57_Graph_OisSPath__nt__parallel__pf,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,P: list_P559422087at_nat,T: nat] :
% 2.76/1.75 ( ( isSimp1359852763pacity @ C @ S @ P @ T )
% 2.76/1.75 => ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ P ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ P ) ) )
% 2.76/1.75 = bot_bo2130386637at_nat ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_58_RPreGraph_Omaxflow__imp__rgraph,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( residu164581374pacity @ C @ S @ T @ Cf )
% 2.76/1.75 => ( ( isMaxFlow_capacity @ C @ S @ T @ ( residu1549650759pacity @ C @ Cf ) )
% 2.76/1.75 => ( residu800046103pacity @ C @ S @ T @ Cf ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_59_isSPath__nt__parallel,axiom,
% 2.76/1.75 ! [S: nat,P: list_P559422087at_nat,T: nat,E: product_prod_nat_nat] :
% 2.76/1.75 ( ( isSimp1359852763pacity @ c @ S @ P @ T )
% 2.76/1.75 => ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ P ) )
% 2.76/1.75 => ~ ( member701585322at_nat @ ( product_swap_nat_nat @ E ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_60_Finite__Graph__axioms,axiom,
% 2.76/1.75 finite217307323pacity @ c ).
% 2.76/1.75
% 2.76/1.75 thf(fact_61_shortestPath__is__simple,axiom,
% 2.76/1.75 ! [S: nat,P: list_P559422087at_nat,T: nat] :
% 2.76/1.75 ( ( isShor1936442771pacity @ c @ S @ P @ T )
% 2.76/1.75 => ( isSimp1359852763pacity @ c @ S @ P @ T ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_62_cf_OshortestPath__is__simple,axiom,
% 2.76/1.75 ! [S: nat,P: list_P559422087at_nat,T: nat] :
% 2.76/1.75 ( ( isShor1936442771pacity @ ( residu203630698pacity @ c @ f ) @ S @ P @ T )
% 2.76/1.75 => ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ S @ P @ T ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_63_Graph_OisShortestPath_Ocong,axiom,
% 2.76/1.75 isShor1936442771pacity = isShor1936442771pacity ).
% 2.76/1.75
% 2.76/1.75 thf(fact_64_Graph_OshortestPath__is__simple,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,P: list_P559422087at_nat,T: nat] :
% 2.76/1.75 ( ( isShor1936442771pacity @ C @ S @ P @ T )
% 2.76/1.75 => ( isSimp1359852763pacity @ C @ S @ P @ T ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_65_Graph_OisSPath__nt__parallel,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,P: list_P559422087at_nat,T: nat,E: product_prod_nat_nat] :
% 2.76/1.75 ( ( isSimp1359852763pacity @ C @ S @ P @ T )
% 2.76/1.75 => ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ P ) )
% 2.76/1.75 => ~ ( member701585322at_nat @ ( product_swap_nat_nat @ E ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_66_Graph_OisSimplePath_Ocong,axiom,
% 2.76/1.75 isSimp1359852763pacity = isSimp1359852763pacity ).
% 2.76/1.75
% 2.76/1.75 thf(fact_67_RPreGraph_Othis__loc__rpg,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( residu164581374pacity @ C @ S @ T @ Cf )
% 2.76/1.75 => ( residu164581374pacity @ C @ S @ T @ Cf ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_68_NFlow_Oshortest__is__augmenting,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,P: list_P559422087at_nat] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( isShor1936442771pacity @ ( residu203630698pacity @ C @ F3 ) @ S @ P @ T )
% 2.76/1.75 => ( augmen1090971539pacity @ C @ S @ T @ F3 @ P ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_69_NFlow_Oaugmenting__path__imp__shortest,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,P: list_P559422087at_nat] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( augmen1090971539pacity @ C @ S @ T @ F3 @ P )
% 2.76/1.75 => ? [P3: list_P559422087at_nat] : ( isShor1936442771pacity @ ( residu203630698pacity @ C @ F3 ) @ S @ P3 @ T ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_70_RGraph_Othis__loc,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( residu800046103pacity @ C @ S @ T @ Cf )
% 2.76/1.75 => ( residu800046103pacity @ C @ S @ T @ Cf ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_71_Network_Oflow__of__cf_Ocong,axiom,
% 2.76/1.75 residu1549650759pacity = residu1549650759pacity ).
% 2.76/1.75
% 2.76/1.75 thf(fact_72_RPreGraph_Oaxioms_I1_J,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( residu164581374pacity @ C @ S @ T @ Cf )
% 2.76/1.75 => ( network_capacity @ C @ S @ T ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_73_RGraph_Oaxioms_I1_J,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( residu800046103pacity @ C @ S @ T @ Cf )
% 2.76/1.75 => ( network_capacity @ C @ S @ T ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_74_RGraph_Othis__loc__rpg,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( residu800046103pacity @ C @ S @ T @ Cf )
% 2.76/1.75 => ( residu164581374pacity @ C @ S @ T @ Cf ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_75_NPreflow_Ois__RPreGraph,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( residu164581374pacity @ C @ S @ T @ ( residu203630698pacity @ C @ F3 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_76_RPreGraph_OEX__RPG,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( residu164581374pacity @ C @ S @ T @ Cf )
% 2.76/1.75 => ? [F4: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nPreflow_capacity @ C @ S @ T @ F4 )
% 2.76/1.75 & ( Cf
% 2.76/1.75 = ( residu203630698pacity @ C @ F4 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_77_NFlow_Ois__RGraph,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( residu800046103pacity @ C @ S @ T @ ( residu203630698pacity @ C @ F3 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_78_RGraph_OEX__RG,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( residu800046103pacity @ C @ S @ T @ Cf )
% 2.76/1.75 => ? [F4: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F4 )
% 2.76/1.75 & ( Cf
% 2.76/1.75 = ( residu203630698pacity @ C @ F4 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_79_NPreflow_Ofo__rg__inv,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( residu1549650759pacity @ C @ ( residu203630698pacity @ C @ F3 ) )
% 2.76/1.75 = F3 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_80_RPreGraph_Org__fo__inv,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( residu164581374pacity @ C @ S @ T @ Cf )
% 2.76/1.75 => ( ( residu203630698pacity @ C @ ( residu1549650759pacity @ C @ Cf ) )
% 2.76/1.75 = Cf ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_81_RPreGraph_Ois__NPreflow,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( residu164581374pacity @ C @ S @ T @ Cf )
% 2.76/1.75 => ( nPreflow_capacity @ C @ S @ T @ ( residu1549650759pacity @ C @ Cf ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_82_RGraph_Ois__NFlow,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( residu800046103pacity @ C @ S @ T @ Cf )
% 2.76/1.75 => ( nFlow_capacity @ C @ S @ T @ ( residu1549650759pacity @ C @ Cf ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_83_augFlow__val,axiom,
% 2.76/1.75 ! [P: list_P559422087at_nat] :
% 2.76/1.75 ( ( augmen1090971539pacity @ c @ s @ t @ f @ P )
% 2.76/1.75 => ( ( val_capacity @ ( residu203630698pacity @ c @ f ) @ s @ ( augmen72931474pacity @ c @ f @ P ) )
% 2.76/1.75 = ( augmen68920357pacity @ c @ f @ P ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_84_augment__flow__value,axiom,
% 2.76/1.75 ! [F: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ F )
% 2.76/1.75 => ( ( val_capacity @ c @ s @ ( augmen887209518pacity @ c @ f @ F ) )
% 2.76/1.75 = ( plus_plus_capacity @ ( val_capacity @ c @ s @ f ) @ ( val_capacity @ ( residu203630698pacity @ c @ f ) @ s @ F ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_85_isMaxFlow__alt,axiom,
% 2.76/1.75 ! [F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( isMaxFlow_capacity @ c @ s @ t @ F3 )
% 2.76/1.75 = ( ( nFlow_capacity @ c @ s @ t @ F3 )
% 2.76/1.75 & ! [F5: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nFlow_capacity @ c @ s @ t @ F5 )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( val_capacity @ c @ s @ F5 ) @ ( val_capacity @ c @ s @ F3 ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_86_isMaxFlow__def,axiom,
% 2.76/1.75 ! [F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( isMaxFlow_capacity @ c @ s @ t @ F3 )
% 2.76/1.75 = ( ( flow_capacity @ c @ s @ t @ F3 )
% 2.76/1.75 & ! [F5: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( flow_capacity @ c @ s @ t @ F5 )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( val_capacity @ c @ s @ F5 ) @ ( val_capacity @ c @ s @ F3 ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_87_NPreflow_OaugFlow__resFlow,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,P: list_P559422087at_nat] :
% 2.76/1.75 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( augmen1090971539pacity @ C @ S @ T @ F3 @ P )
% 2.76/1.75 => ( flow_capacity @ ( residu203630698pacity @ C @ F3 ) @ S @ T @ ( augmen72931474pacity @ C @ F3 @ P ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_88_bot__apply,axiom,
% 2.76/1.75 ( bot_bo513358416_nat_o
% 2.76/1.75 = ( ^ [X3: product_prod_nat_nat] : bot_bot_o ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_89_maxFlow__minCut,axiom,
% 2.76/1.75 ! [F3: product_prod_nat_nat > capacity,K: set_nat] :
% 2.76/1.75 ( ( isMaxFlow_capacity @ c @ s @ t @ F3 )
% 2.76/1.75 => ( ( isMinCut_capacity @ c @ s @ t @ K )
% 2.76/1.75 => ( ( val_capacity @ c @ s @ F3 )
% 2.76/1.75 = ( cap_capacity @ c @ K ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_90_order__refl,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ X2 @ X2 ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_91_order__refl,axiom,
% 2.76/1.75 ! [X2: capacity] : ( ord_less_eq_capacity @ X2 @ X2 ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_92_inf_Obounded__iff,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
% 2.76/1.75 = ( ( ord_le841296385at_nat @ A @ B )
% 2.76/1.75 & ( ord_le841296385at_nat @ A @ C ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_93_le__inf__iff,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ Y @ Z ) )
% 2.76/1.75 = ( ( ord_le841296385at_nat @ X2 @ Y )
% 2.76/1.75 & ( ord_le841296385at_nat @ X2 @ Z ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_94_bot_Oextremum,axiom,
% 2.76/1.75 ! [A: product_prod_nat_nat > $o] : ( ord_le1039616028_nat_o @ bot_bo513358416_nat_o @ A ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_95_bot_Oextremum,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ bot_bo2130386637at_nat @ A ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_96_bot_Oextremum__unique,axiom,
% 2.76/1.75 ! [A: product_prod_nat_nat > $o] :
% 2.76/1.75 ( ( ord_le1039616028_nat_o @ A @ bot_bo513358416_nat_o )
% 2.76/1.75 = ( A = bot_bo513358416_nat_o ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_97_bot_Oextremum__unique,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ bot_bo2130386637at_nat )
% 2.76/1.75 = ( A = bot_bo2130386637at_nat ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_98_bot_Oextremum__uniqueI,axiom,
% 2.76/1.75 ! [A: product_prod_nat_nat > $o] :
% 2.76/1.75 ( ( ord_le1039616028_nat_o @ A @ bot_bo513358416_nat_o )
% 2.76/1.75 => ( A = bot_bo513358416_nat_o ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_99_bot_Oextremum__uniqueI,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ bot_bo2130386637at_nat )
% 2.76/1.75 => ( A = bot_bo2130386637at_nat ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_100_order__subst1,axiom,
% 2.76/1.75 ! [A: capacity,F3: set_Pr1986765409at_nat > capacity,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ A @ ( F3 @ B ) )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ B @ C )
% 2.76/1.75 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_less_eq_capacity @ A @ ( F3 @ C ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_101_order__subst1,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,F3: capacity > set_Pr1986765409at_nat,B: capacity,C: capacity] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ ( F3 @ B ) )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ B @ C )
% 2.76/1.75 => ( ! [X4: capacity,Y3: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_le841296385at_nat @ A @ ( F3 @ C ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_102_order__subst1,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,F3: set_Pr1986765409at_nat > set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ ( F3 @ B ) )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ B @ C )
% 2.76/1.75 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_le841296385at_nat @ A @ ( F3 @ C ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_103_order__subst1,axiom,
% 2.76/1.75 ! [A: capacity,F3: capacity > capacity,B: capacity,C: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ A @ ( F3 @ B ) )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ B @ C )
% 2.76/1.75 => ( ! [X4: capacity,Y3: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_less_eq_capacity @ A @ ( F3 @ C ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_104_order__subst2,axiom,
% 2.76/1.75 ! [A: capacity,B: capacity,F3: capacity > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ A @ B )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ ( F3 @ B ) @ C )
% 2.76/1.75 => ( ! [X4: capacity,Y3: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( F3 @ A ) @ C ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_105_order__subst2,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,F3: set_Pr1986765409at_nat > capacity,C: capacity] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ B )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ ( F3 @ B ) @ C )
% 2.76/1.75 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( F3 @ A ) @ C ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_106_order__subst2,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,F3: set_Pr1986765409at_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ B )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ ( F3 @ B ) @ C )
% 2.76/1.75 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( F3 @ A ) @ C ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_107_order__subst2,axiom,
% 2.76/1.75 ! [A: capacity,B: capacity,F3: capacity > capacity,C: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ A @ B )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ ( F3 @ B ) @ C )
% 2.76/1.75 => ( ! [X4: capacity,Y3: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( F3 @ A ) @ C ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_108_ord__eq__le__subst,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,F3: capacity > set_Pr1986765409at_nat,B: capacity,C: capacity] :
% 2.76/1.75 ( ( A
% 2.76/1.75 = ( F3 @ B ) )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ B @ C )
% 2.76/1.75 => ( ! [X4: capacity,Y3: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_le841296385at_nat @ A @ ( F3 @ C ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_109_ord__eq__le__subst,axiom,
% 2.76/1.75 ! [A: capacity,F3: set_Pr1986765409at_nat > capacity,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( A
% 2.76/1.75 = ( F3 @ B ) )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ B @ C )
% 2.76/1.75 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_less_eq_capacity @ A @ ( F3 @ C ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_110_ord__eq__le__subst,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,F3: set_Pr1986765409at_nat > set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( A
% 2.76/1.75 = ( F3 @ B ) )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ B @ C )
% 2.76/1.75 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_le841296385at_nat @ A @ ( F3 @ C ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_111_ord__eq__le__subst,axiom,
% 2.76/1.75 ! [A: capacity,F3: capacity > capacity,B: capacity,C: capacity] :
% 2.76/1.75 ( ( A
% 2.76/1.75 = ( F3 @ B ) )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ B @ C )
% 2.76/1.75 => ( ! [X4: capacity,Y3: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_less_eq_capacity @ A @ ( F3 @ C ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_112_ord__le__eq__subst,axiom,
% 2.76/1.75 ! [A: capacity,B: capacity,F3: capacity > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ A @ B )
% 2.76/1.75 => ( ( ( F3 @ B )
% 2.76/1.75 = C )
% 2.76/1.75 => ( ! [X4: capacity,Y3: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( F3 @ A ) @ C ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_113_ord__le__eq__subst,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,F3: set_Pr1986765409at_nat > capacity,C: capacity] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ B )
% 2.76/1.75 => ( ( ( F3 @ B )
% 2.76/1.75 = C )
% 2.76/1.75 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( F3 @ A ) @ C ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_114_ord__le__eq__subst,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,F3: set_Pr1986765409at_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ B )
% 2.76/1.75 => ( ( ( F3 @ B )
% 2.76/1.75 = C )
% 2.76/1.75 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( F3 @ A ) @ C ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_115_ord__le__eq__subst,axiom,
% 2.76/1.75 ! [A: capacity,B: capacity,F3: capacity > capacity,C: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ A @ B )
% 2.76/1.75 => ( ( ( F3 @ B )
% 2.76/1.75 = C )
% 2.76/1.75 => ( ! [X4: capacity,Y3: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ X4 @ Y3 )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( F3 @ X4 ) @ ( F3 @ Y3 ) ) )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( F3 @ A ) @ C ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_116_eq__iff,axiom,
% 2.76/1.75 ( ( ^ [Y4: set_Pr1986765409at_nat,Z2: set_Pr1986765409at_nat] : ( Y4 = Z2 ) )
% 2.76/1.75 = ( ^ [X3: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X3 @ Y2 )
% 2.76/1.75 & ( ord_le841296385at_nat @ Y2 @ X3 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_117_eq__iff,axiom,
% 2.76/1.75 ( ( ^ [Y4: capacity,Z2: capacity] : ( Y4 = Z2 ) )
% 2.76/1.75 = ( ^ [X3: capacity,Y2: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ X3 @ Y2 )
% 2.76/1.75 & ( ord_less_eq_capacity @ Y2 @ X3 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_118_antisym,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X2 @ Y )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ Y @ X2 )
% 2.76/1.75 => ( X2 = Y ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_119_antisym,axiom,
% 2.76/1.75 ! [X2: capacity,Y: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ X2 @ Y )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ Y @ X2 )
% 2.76/1.75 => ( X2 = Y ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_120_linear,axiom,
% 2.76/1.75 ! [X2: capacity,Y: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ X2 @ Y )
% 2.76/1.75 | ( ord_less_eq_capacity @ Y @ X2 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_121_eq__refl,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( X2 = Y )
% 2.76/1.75 => ( ord_le841296385at_nat @ X2 @ Y ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_122_eq__refl,axiom,
% 2.76/1.75 ! [X2: capacity,Y: capacity] :
% 2.76/1.75 ( ( X2 = Y )
% 2.76/1.75 => ( ord_less_eq_capacity @ X2 @ Y ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_123_le__cases,axiom,
% 2.76/1.75 ! [X2: capacity,Y: capacity] :
% 2.76/1.75 ( ~ ( ord_less_eq_capacity @ X2 @ Y )
% 2.76/1.75 => ( ord_less_eq_capacity @ Y @ X2 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_124_order_Otrans,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ B )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ B @ C )
% 2.76/1.75 => ( ord_le841296385at_nat @ A @ C ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_125_order_Otrans,axiom,
% 2.76/1.75 ! [A: capacity,B: capacity,C: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ A @ B )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ B @ C )
% 2.76/1.75 => ( ord_less_eq_capacity @ A @ C ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_126_le__cases3,axiom,
% 2.76/1.75 ! [X2: capacity,Y: capacity,Z: capacity] :
% 2.76/1.75 ( ( ( ord_less_eq_capacity @ X2 @ Y )
% 2.76/1.75 => ~ ( ord_less_eq_capacity @ Y @ Z ) )
% 2.76/1.75 => ( ( ( ord_less_eq_capacity @ Y @ X2 )
% 2.76/1.75 => ~ ( ord_less_eq_capacity @ X2 @ Z ) )
% 2.76/1.75 => ( ( ( ord_less_eq_capacity @ X2 @ Z )
% 2.76/1.75 => ~ ( ord_less_eq_capacity @ Z @ Y ) )
% 2.76/1.75 => ( ( ( ord_less_eq_capacity @ Z @ Y )
% 2.76/1.75 => ~ ( ord_less_eq_capacity @ Y @ X2 ) )
% 2.76/1.75 => ( ( ( ord_less_eq_capacity @ Y @ Z )
% 2.76/1.75 => ~ ( ord_less_eq_capacity @ Z @ X2 ) )
% 2.76/1.75 => ~ ( ( ord_less_eq_capacity @ Z @ X2 )
% 2.76/1.75 => ~ ( ord_less_eq_capacity @ X2 @ Y ) ) ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_127_antisym__conv,axiom,
% 2.76/1.75 ! [Y: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ Y @ X2 )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ X2 @ Y )
% 2.76/1.75 = ( X2 = Y ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_128_antisym__conv,axiom,
% 2.76/1.75 ! [Y: capacity,X2: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ Y @ X2 )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ X2 @ Y )
% 2.76/1.75 = ( X2 = Y ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_129_order__class_Oorder_Oeq__iff,axiom,
% 2.76/1.75 ( ( ^ [Y4: set_Pr1986765409at_nat,Z2: set_Pr1986765409at_nat] : ( Y4 = Z2 ) )
% 2.76/1.75 = ( ^ [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.76/1.75 & ( ord_le841296385at_nat @ B2 @ A2 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_130_order__class_Oorder_Oeq__iff,axiom,
% 2.76/1.75 ( ( ^ [Y4: capacity,Z2: capacity] : ( Y4 = Z2 ) )
% 2.76/1.75 = ( ^ [A2: capacity,B2: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ A2 @ B2 )
% 2.76/1.75 & ( ord_less_eq_capacity @ B2 @ A2 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_131_ord__eq__le__trans,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( A = B )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ B @ C )
% 2.76/1.75 => ( ord_le841296385at_nat @ A @ C ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_132_ord__eq__le__trans,axiom,
% 2.76/1.75 ! [A: capacity,B: capacity,C: capacity] :
% 2.76/1.75 ( ( A = B )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ B @ C )
% 2.76/1.75 => ( ord_less_eq_capacity @ A @ C ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_133_ord__le__eq__trans,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ B )
% 2.76/1.75 => ( ( B = C )
% 2.76/1.75 => ( ord_le841296385at_nat @ A @ C ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_134_ord__le__eq__trans,axiom,
% 2.76/1.75 ! [A: capacity,B: capacity,C: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ A @ B )
% 2.76/1.75 => ( ( B = C )
% 2.76/1.75 => ( ord_less_eq_capacity @ A @ C ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_135_order__class_Oorder_Oantisym,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ B )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ B @ A )
% 2.76/1.75 => ( A = B ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_136_order__class_Oorder_Oantisym,axiom,
% 2.76/1.75 ! [A: capacity,B: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ A @ B )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ B @ A )
% 2.76/1.75 => ( A = B ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_137_NPreflow_OresCap_Ocong,axiom,
% 2.76/1.75 augmen68920357pacity = augmen68920357pacity ).
% 2.76/1.75
% 2.76/1.75 thf(fact_138_order__trans,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X2 @ Y )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ Y @ Z )
% 2.76/1.75 => ( ord_le841296385at_nat @ X2 @ Z ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_139_order__trans,axiom,
% 2.76/1.75 ! [X2: capacity,Y: capacity,Z: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ X2 @ Y )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ Y @ Z )
% 2.76/1.75 => ( ord_less_eq_capacity @ X2 @ Z ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_140_dual__order_Orefl,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_141_dual__order_Orefl,axiom,
% 2.76/1.75 ! [A: capacity] : ( ord_less_eq_capacity @ A @ A ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_142_linorder__wlog,axiom,
% 2.76/1.75 ! [P2: capacity > capacity > $o,A: capacity,B: capacity] :
% 2.76/1.75 ( ! [A4: capacity,B4: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ A4 @ B4 )
% 2.76/1.75 => ( P2 @ A4 @ B4 ) )
% 2.76/1.75 => ( ! [A4: capacity,B4: capacity] :
% 2.76/1.75 ( ( P2 @ B4 @ A4 )
% 2.76/1.75 => ( P2 @ A4 @ B4 ) )
% 2.76/1.75 => ( P2 @ A @ B ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_143_dual__order_Otrans,axiom,
% 2.76/1.75 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ B @ A )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ C @ B )
% 2.76/1.75 => ( ord_le841296385at_nat @ C @ A ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_144_dual__order_Otrans,axiom,
% 2.76/1.75 ! [B: capacity,A: capacity,C: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ B @ A )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ C @ B )
% 2.76/1.75 => ( ord_less_eq_capacity @ C @ A ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_145_dual__order_Oeq__iff,axiom,
% 2.76/1.75 ( ( ^ [Y4: set_Pr1986765409at_nat,Z2: set_Pr1986765409at_nat] : ( Y4 = Z2 ) )
% 2.76/1.75 = ( ^ [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ B2 @ A2 )
% 2.76/1.75 & ( ord_le841296385at_nat @ A2 @ B2 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_146_dual__order_Oeq__iff,axiom,
% 2.76/1.75 ( ( ^ [Y4: capacity,Z2: capacity] : ( Y4 = Z2 ) )
% 2.76/1.75 = ( ^ [A2: capacity,B2: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ B2 @ A2 )
% 2.76/1.75 & ( ord_less_eq_capacity @ A2 @ B2 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_147_dual__order_Oantisym,axiom,
% 2.76/1.75 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ B @ A )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ A @ B )
% 2.76/1.75 => ( A = B ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_148_dual__order_Oantisym,axiom,
% 2.76/1.75 ! [B: capacity,A: capacity] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ B @ A )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ A @ B )
% 2.76/1.75 => ( A = B ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_149_inf_OcoboundedI2,axiom,
% 2.76/1.75 ! [B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ B @ C )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_150_inf_OcoboundedI1,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ C )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_151_inf_Oabsorb__iff2,axiom,
% 2.76/1.75 ( ord_le841296385at_nat
% 2.76/1.75 = ( ^ [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ A2 @ B2 )
% 2.76/1.75 = B2 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_152_inf_Oabsorb__iff1,axiom,
% 2.76/1.75 ( ord_le841296385at_nat
% 2.76/1.75 = ( ^ [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ A2 @ B2 )
% 2.76/1.75 = A2 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_153_inf_Ocobounded2,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_154_inf_Ocobounded1,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ A ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_155_inf_Oorder__iff,axiom,
% 2.76/1.75 ( ord_le841296385at_nat
% 2.76/1.75 = ( ^ [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 2.76/1.75 ( A2
% 2.76/1.75 = ( inf_in586391887at_nat @ A2 @ B2 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_156_inf__greatest,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X2 @ Y )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ X2 @ Z )
% 2.76/1.75 => ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ Y @ Z ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_157_inf_OboundedI,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ B )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ A @ C )
% 2.76/1.75 => ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_158_inf_OboundedE,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
% 2.76/1.75 => ~ ( ( ord_le841296385at_nat @ A @ B )
% 2.76/1.75 => ~ ( ord_le841296385at_nat @ A @ C ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_159_inf__absorb2,axiom,
% 2.76/1.75 ! [Y: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ Y @ X2 )
% 2.76/1.75 => ( ( inf_in586391887at_nat @ X2 @ Y )
% 2.76/1.75 = Y ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_160_inf__absorb1,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X2 @ Y )
% 2.76/1.75 => ( ( inf_in586391887at_nat @ X2 @ Y )
% 2.76/1.75 = X2 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_161_inf_Oabsorb2,axiom,
% 2.76/1.75 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ B @ A )
% 2.76/1.75 => ( ( inf_in586391887at_nat @ A @ B )
% 2.76/1.75 = B ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_162_inf_Oabsorb1,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ B )
% 2.76/1.75 => ( ( inf_in586391887at_nat @ A @ B )
% 2.76/1.75 = A ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_163_le__iff__inf,axiom,
% 2.76/1.75 ( ord_le841296385at_nat
% 2.76/1.75 = ( ^ [X3: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( inf_in586391887at_nat @ X3 @ Y2 )
% 2.76/1.75 = X3 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_164_inf__unique,axiom,
% 2.76/1.75 ! [F3: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( F3 @ X4 @ Y3 ) @ X4 )
% 2.76/1.75 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( F3 @ X4 @ Y3 ) @ Y3 )
% 2.76/1.75 => ( ! [X4: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat,Z3: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X4 @ Y3 )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ X4 @ Z3 )
% 2.76/1.75 => ( ord_le841296385at_nat @ X4 @ ( F3 @ Y3 @ Z3 ) ) ) )
% 2.76/1.75 => ( ( inf_in586391887at_nat @ X2 @ Y )
% 2.76/1.75 = ( F3 @ X2 @ Y ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_165_inf_OorderI,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( A
% 2.76/1.75 = ( inf_in586391887at_nat @ A @ B ) )
% 2.76/1.75 => ( ord_le841296385at_nat @ A @ B ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_166_inf_OorderE,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ B )
% 2.76/1.75 => ( A
% 2.76/1.75 = ( inf_in586391887at_nat @ A @ B ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_167_le__infI2,axiom,
% 2.76/1.75 ! [B: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ B @ X2 )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ X2 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_168_le__infI1,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ X2 )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ X2 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_169_inf__mono,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ A @ C )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ B @ D )
% 2.76/1.75 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ ( inf_in586391887at_nat @ C @ D ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_170_le__infI,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X2 @ A )
% 2.76/1.75 => ( ( ord_le841296385at_nat @ X2 @ B )
% 2.76/1.75 => ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ A @ B ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_171_le__infE,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ A @ B ) )
% 2.76/1.75 => ~ ( ( ord_le841296385at_nat @ X2 @ A )
% 2.76/1.75 => ~ ( ord_le841296385at_nat @ X2 @ B ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_172_inf__le2,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y ) @ Y ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_173_inf__le1,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y ) @ X2 ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_174_inf__sup__ord_I1_J,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y ) @ X2 ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_175_inf__sup__ord_I2_J,axiom,
% 2.76/1.75 ! [X2: set_Pr1986765409at_nat,Y: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y ) @ Y ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_176_NPreflow_OisAugmentingPath_Ocong,axiom,
% 2.76/1.75 augmen1090971539pacity = augmen1090971539pacity ).
% 2.76/1.75
% 2.76/1.75 thf(fact_177_NPreflow_OaugmentingFlow_Ocong,axiom,
% 2.76/1.75 augmen72931474pacity = augmen72931474pacity ).
% 2.76/1.75
% 2.76/1.75 thf(fact_178_NPreflow_OaugFlow__val,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,P: list_P559422087at_nat] :
% 2.76/1.75 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( augmen1090971539pacity @ C @ S @ T @ F3 @ P )
% 2.76/1.75 => ( ( val_capacity @ ( residu203630698pacity @ C @ F3 ) @ S @ ( augmen72931474pacity @ C @ F3 @ P ) )
% 2.76/1.75 = ( augmen68920357pacity @ C @ F3 @ P ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_179_bot__fun__def,axiom,
% 2.76/1.75 ( bot_bo513358416_nat_o
% 2.76/1.75 = ( ^ [X3: product_prod_nat_nat] : bot_bot_o ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_180_NPreflow_OisAugmentingPath__def,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,P: list_P559422087at_nat] :
% 2.76/1.75 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( augmen1090971539pacity @ C @ S @ T @ F3 @ P )
% 2.76/1.75 = ( isSimp1359852763pacity @ ( residu203630698pacity @ C @ F3 ) @ S @ P @ T ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_181_ford__fulkerson_I2_J,axiom,
% 2.76/1.75 ( ( ~ ? [X: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ X ) )
% 2.76/1.75 = ( ? [K2: set_nat] :
% 2.76/1.75 ( ( nCut_capacity @ c @ s @ t @ K2 )
% 2.76/1.75 & ( ( val_capacity @ c @ s @ f )
% 2.76/1.75 = ( cap_capacity @ c @ K2 ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_182_fofu__III__I,axiom,
% 2.76/1.75 ( ? [K3: set_nat] :
% 2.76/1.75 ( ( nCut_capacity @ c @ s @ t @ K3 )
% 2.76/1.75 & ( ( val_capacity @ c @ s @ f )
% 2.76/1.75 = ( cap_capacity @ c @ K3 ) ) )
% 2.76/1.75 => ( isMaxFlow_capacity @ c @ s @ t @ f ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_183_fofu__II__III,axiom,
% 2.76/1.75 ( ~ ? [X_12: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ X_12 )
% 2.76/1.75 => ? [K4: set_nat] :
% 2.76/1.75 ( ( nCut_capacity @ c @ s @ t @ K4 )
% 2.76/1.75 & ( ( val_capacity @ c @ s @ f )
% 2.76/1.75 = ( cap_capacity @ c @ K4 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_184_NFlow_Oaugment__flow__value,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,F: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( flow_capacity @ ( residu203630698pacity @ C @ F3 ) @ S @ T @ F )
% 2.76/1.75 => ( ( val_capacity @ C @ S @ ( augmen887209518pacity @ C @ F3 @ F ) )
% 2.76/1.75 = ( plus_plus_capacity @ ( val_capacity @ C @ S @ F3 ) @ ( val_capacity @ ( residu203630698pacity @ C @ F3 ) @ S @ F ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_185_Network_OmaxFlow__minCut,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,K: set_nat] :
% 2.76/1.75 ( ( network_capacity @ C @ S @ T )
% 2.76/1.75 => ( ( isMaxFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( isMinCut_capacity @ C @ S @ T @ K )
% 2.76/1.75 => ( ( val_capacity @ C @ S @ F3 )
% 2.76/1.75 = ( cap_capacity @ C @ K ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_186_Network_OisMaxFlow__alt,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( network_capacity @ C @ S @ T )
% 2.76/1.75 => ( ( isMaxFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 = ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 & ! [F5: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F5 )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( val_capacity @ C @ S @ F5 ) @ ( val_capacity @ C @ S @ F3 ) ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_187_converse__mono,axiom,
% 2.76/1.75 ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ ( converse_nat_nat @ R ) @ ( converse_nat_nat @ S ) )
% 2.76/1.75 = ( ord_le841296385at_nat @ R @ S ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_188_NCut_Oaxioms_I1_J,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,K: set_nat] :
% 2.76/1.75 ( ( nCut_capacity @ C @ S @ T @ K )
% 2.76/1.75 => ( network_capacity @ C @ S @ T ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_189_NCut_Ot__ni__cut,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,K: set_nat] :
% 2.76/1.75 ( ( nCut_capacity @ C @ S @ T @ K )
% 2.76/1.75 => ~ ( member_nat @ T @ K ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_190_NCut_Os__in__cut,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,K: set_nat] :
% 2.76/1.75 ( ( nCut_capacity @ C @ S @ T @ K )
% 2.76/1.75 => ( member_nat @ S @ K ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_191_converse__subset__swap,axiom,
% 2.76/1.75 ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le841296385at_nat @ R @ ( converse_nat_nat @ S ) )
% 2.76/1.75 = ( ord_le841296385at_nat @ ( converse_nat_nat @ R ) @ S ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_192_isMinCut__def,axiom,
% 2.76/1.75 ( isMinCut_capacity
% 2.76/1.75 = ( ^ [C2: product_prod_nat_nat > capacity,S2: nat,T2: nat,K2: set_nat] :
% 2.76/1.75 ( ( nCut_capacity @ C2 @ S2 @ T2 @ K2 )
% 2.76/1.75 & ! [K5: set_nat] :
% 2.76/1.75 ( ( nCut_capacity @ C2 @ S2 @ T2 @ K5 )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( cap_capacity @ C2 @ K2 ) @ ( cap_capacity @ C2 @ K5 ) ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_193_Network_Ot__not__s,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat] :
% 2.76/1.75 ( ( network_capacity @ C @ S @ T )
% 2.76/1.75 => ( T != S ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_194_Network_Os__not__t,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat] :
% 2.76/1.75 ( ( network_capacity @ C @ S @ T )
% 2.76/1.75 => ( S != T ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_195_Flow_Oval_Ocong,axiom,
% 2.76/1.75 val_capacity = val_capacity ).
% 2.76/1.75
% 2.76/1.75 thf(fact_196_Network_OisMaxFlow_Ocong,axiom,
% 2.76/1.75 isMaxFlow_capacity = isMaxFlow_capacity ).
% 2.76/1.75
% 2.76/1.75 thf(fact_197_NFlow_Oaugment_Ocong,axiom,
% 2.76/1.75 augmen887209518pacity = augmen887209518pacity ).
% 2.76/1.75
% 2.76/1.75 thf(fact_198_NCut_Ocap_Ocong,axiom,
% 2.76/1.75 cap_capacity = cap_capacity ).
% 2.76/1.75
% 2.76/1.75 thf(fact_199_NFlow_Ofofu__II__III,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ~ ? [X_12: list_P559422087at_nat] : ( augmen1090971539pacity @ C @ S @ T @ F3 @ X_12 )
% 2.76/1.75 => ? [K4: set_nat] :
% 2.76/1.75 ( ( nCut_capacity @ C @ S @ T @ K4 )
% 2.76/1.75 & ( ( val_capacity @ C @ S @ F3 )
% 2.76/1.75 = ( cap_capacity @ C @ K4 ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_200_NFlow_Ofofu__III__I,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ? [K3: set_nat] :
% 2.76/1.75 ( ( nCut_capacity @ C @ S @ T @ K3 )
% 2.76/1.75 & ( ( val_capacity @ C @ S @ F3 )
% 2.76/1.75 = ( cap_capacity @ C @ K3 ) ) )
% 2.76/1.75 => ( isMaxFlow_capacity @ C @ S @ T @ F3 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_201_Network_Ois__max__flow__val_Ocong,axiom,
% 2.76/1.75 is_max2144541363pacity = is_max2144541363pacity ).
% 2.76/1.75
% 2.76/1.75 thf(fact_202_NFlow_Oford__fulkerson_I2_J,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( ~ ? [X: list_P559422087at_nat] : ( augmen1090971539pacity @ C @ S @ T @ F3 @ X ) )
% 2.76/1.75 = ( ? [K2: set_nat] :
% 2.76/1.75 ( ( nCut_capacity @ C @ S @ T @ K2 )
% 2.76/1.75 & ( ( val_capacity @ C @ S @ F3 )
% 2.76/1.75 = ( cap_capacity @ C @ K2 ) ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_203_NPreflow_Oaxioms_I1_J,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( network_capacity @ C @ S @ T ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_204_NFlow_Oaxioms_I1_J,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( nPreflow_capacity @ C @ S @ T @ F3 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_205_NFlow_Oaxioms_I2_J,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( flow_capacity @ C @ S @ T @ F3 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_206_NPreflow_Oaxioms_I2_J,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( preflow_capacity @ C @ S @ T @ F3 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_207_Flow_Oaxioms_I1_J,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( flow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( preflow_capacity @ C @ S @ T @ F3 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_208_Network_Omax__flow__val__unique,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Fv1: capacity,Fv2: capacity] :
% 2.76/1.75 ( ( network_capacity @ C @ S @ T )
% 2.76/1.75 => ( ( is_max2144541363pacity @ C @ S @ T @ Fv1 )
% 2.76/1.75 => ( ( is_max2144541363pacity @ C @ S @ T @ Fv2 )
% 2.76/1.75 => ( Fv1 = Fv2 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_209_Finite__Preflow_Oaxioms_I2_J,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( finite1387368318pacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( finite217307323pacity @ C ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_210_Finite__Preflow_Oaxioms_I1_J,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( finite1387368318pacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( preflow_capacity @ C @ S @ T @ F3 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_211_NFlow_Ointro,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( flow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( nFlow_capacity @ C @ S @ T @ F3 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_212_NFlow__def,axiom,
% 2.76/1.75 ( nFlow_capacity
% 2.76/1.75 = ( ^ [C2: product_prod_nat_nat > capacity,S2: nat,T2: nat,F2: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nPreflow_capacity @ C2 @ S2 @ T2 @ F2 )
% 2.76/1.75 & ( flow_capacity @ C2 @ S2 @ T2 @ F2 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_213_NPreflow_Ointro,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( network_capacity @ C @ S @ T )
% 2.76/1.75 => ( ( preflow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( nPreflow_capacity @ C @ S @ T @ F3 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_214_NPreflow__def,axiom,
% 2.76/1.75 ( nPreflow_capacity
% 2.76/1.75 = ( ^ [C2: product_prod_nat_nat > capacity,S2: nat,T2: nat,F2: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( network_capacity @ C2 @ S2 @ T2 )
% 2.76/1.75 & ( preflow_capacity @ C2 @ S2 @ T2 @ F2 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_215_NFlow_Ofofu__I__II,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( isMaxFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ~ ? [X_1: list_P559422087at_nat] : ( augmen1090971539pacity @ C @ S @ T @ F3 @ X_1 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_216_NFlow_OnoAugPath__iff__maxFlow,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( ~ ? [X: list_P559422087at_nat] : ( augmen1090971539pacity @ C @ S @ T @ F3 @ X ) )
% 2.76/1.75 = ( isMaxFlow_capacity @ C @ S @ T @ F3 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_217_Finite__Preflow_Ointro,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( preflow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( finite217307323pacity @ C )
% 2.76/1.75 => ( finite1387368318pacity @ C @ S @ T @ F3 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_218_Finite__Preflow__def,axiom,
% 2.76/1.75 ( finite1387368318pacity
% 2.76/1.75 = ( ^ [C2: product_prod_nat_nat > capacity,S2: nat,T2: nat,F2: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( preflow_capacity @ C2 @ S2 @ T2 @ F2 )
% 2.76/1.75 & ( finite217307323pacity @ C2 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_219_NFlow_Oaugment__flow__presv,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,F: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( flow_capacity @ ( residu203630698pacity @ C @ F3 ) @ S @ T @ F )
% 2.76/1.75 => ( flow_capacity @ C @ S @ T @ ( augmen887209518pacity @ C @ F3 @ F ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_220_NFlow_Oford__fulkerson_I1_J,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( isMaxFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 = ( ~ ? [X: list_P559422087at_nat] : ( augmen1090971539pacity @ C @ S @ T @ F3 @ X ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_221_Network_Ois__max__flow__val__def,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Fv: capacity] :
% 2.76/1.75 ( ( network_capacity @ C @ S @ T )
% 2.76/1.75 => ( ( is_max2144541363pacity @ C @ S @ T @ Fv )
% 2.76/1.75 = ( ? [F2: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( isMaxFlow_capacity @ C @ S @ T @ F2 )
% 2.76/1.75 & ( Fv
% 2.76/1.75 = ( val_capacity @ C @ S @ F2 ) ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_222_Network_OisMaxFlow__def,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( network_capacity @ C @ S @ T )
% 2.76/1.75 => ( ( isMaxFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 = ( ( flow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 & ! [F5: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( flow_capacity @ C @ S @ T @ F5 )
% 2.76/1.75 => ( ord_less_eq_capacity @ ( val_capacity @ C @ S @ F5 ) @ ( val_capacity @ C @ S @ F3 ) ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_223_cf_OisSPath__no__selfloop,axiom,
% 2.76/1.75 ! [U: nat,P: list_P559422087at_nat,V: nat,U1: nat] :
% 2.76/1.75 ( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ U @ P @ V )
% 2.76/1.75 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ U1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_224_cf_OisSPath__sg__incoming,axiom,
% 2.76/1.75 ! [U: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat,U2: nat] :
% 2.76/1.75 ( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ U @ P @ V )
% 2.76/1.75 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 2.76/1.75 => ( ( U1 != U2 )
% 2.76/1.75 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U2 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_225_cf_OisSPath__sg__outgoing,axiom,
% 2.76/1.75 ! [U: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat,V2: nat] :
% 2.76/1.75 ( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ U @ P @ V )
% 2.76/1.75 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 2.76/1.75 => ( ( V1 != V2 )
% 2.76/1.75 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V2 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_226_isSPath__sg__outgoing,axiom,
% 2.76/1.75 ! [U: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat,V2: nat] :
% 2.76/1.75 ( ( isSimp1359852763pacity @ c @ U @ P @ V )
% 2.76/1.75 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 2.76/1.75 => ( ( V1 != V2 )
% 2.76/1.75 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V2 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_227_isSPath__sg__incoming,axiom,
% 2.76/1.75 ! [U: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat,U2: nat] :
% 2.76/1.75 ( ( isSimp1359852763pacity @ c @ U @ P @ V )
% 2.76/1.75 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 2.76/1.75 => ( ( U1 != U2 )
% 2.76/1.75 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U2 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_228_isSPath__no__selfloop,axiom,
% 2.76/1.75 ! [U: nat,P: list_P559422087at_nat,V: nat,U1: nat] :
% 2.76/1.75 ( ( isSimp1359852763pacity @ c @ U @ P @ V )
% 2.76/1.75 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ U1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_229_converse__iff,axiom,
% 2.76/1.75 ! [A: nat,B: nat,R: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( converse_nat_nat @ R ) )
% 2.76/1.75 = ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ A ) @ R ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_230_subrelI,axiom,
% 2.76/1.75 ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ! [X4: nat,Y3: nat] :
% 2.76/1.75 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y3 ) @ R )
% 2.76/1.75 => ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y3 ) @ S ) )
% 2.76/1.75 => ( ord_le841296385at_nat @ R @ S ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_231_converseD,axiom,
% 2.76/1.75 ! [A: nat,B: nat,R: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( converse_nat_nat @ R ) )
% 2.76/1.75 => ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ A ) @ R ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_232_converseE,axiom,
% 2.76/1.75 ! [Yx: product_prod_nat_nat,R: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( member701585322at_nat @ Yx @ ( converse_nat_nat @ R ) )
% 2.76/1.75 => ~ ! [X4: nat,Y3: nat] :
% 2.76/1.75 ( ( Yx
% 2.76/1.75 = ( product_Pair_nat_nat @ Y3 @ X4 ) )
% 2.76/1.75 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y3 ) @ R ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_233_converse_Ocases,axiom,
% 2.76/1.75 ! [A1: nat,A22: nat,R: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( converse_nat_nat @ R ) )
% 2.76/1.75 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A22 @ A1 ) @ R ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_234_converse_Osimps,axiom,
% 2.76/1.75 ! [A1: nat,A22: nat,R: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( converse_nat_nat @ R ) )
% 2.76/1.75 = ( ? [A2: nat,B2: nat] :
% 2.76/1.75 ( ( A1 = B2 )
% 2.76/1.75 & ( A22 = A2 )
% 2.76/1.75 & ( member701585322at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ R ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_235_converse_Ointros,axiom,
% 2.76/1.75 ! [A: nat,B: nat,R: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 2.76/1.75 => ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ A ) @ ( converse_nat_nat @ R ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_236_converse_Oinducts,axiom,
% 2.76/1.75 ! [X1: nat,X22: nat,R: set_Pr1986765409at_nat,P2: nat > nat > $o] :
% 2.76/1.75 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) @ ( converse_nat_nat @ R ) )
% 2.76/1.75 => ( ! [A4: nat,B4: nat] :
% 2.76/1.75 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A4 @ B4 ) @ R )
% 2.76/1.75 => ( P2 @ B4 @ A4 ) )
% 2.76/1.75 => ( P2 @ X1 @ X22 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_237_Graph_OisSPath__sg__outgoing,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,U: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat,V2: nat] :
% 2.76/1.75 ( ( isSimp1359852763pacity @ C @ U @ P @ V )
% 2.76/1.75 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 2.76/1.75 => ( ( V1 != V2 )
% 2.76/1.75 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V2 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_238_Graph_OisSPath__sg__incoming,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,U: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat,U2: nat] :
% 2.76/1.75 ( ( isSimp1359852763pacity @ C @ U @ P @ V )
% 2.76/1.75 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 2.76/1.75 => ( ( U1 != U2 )
% 2.76/1.75 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U2 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_239_Graph_OisSPath__no__selfloop,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,U: nat,P: list_P559422087at_nat,V: nat,U1: nat] :
% 2.76/1.75 ( ( isSimp1359852763pacity @ C @ U @ P @ V )
% 2.76/1.75 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ U1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_240_augment__flow__presv__cap,axiom,
% 2.76/1.75 ! [F: product_prod_nat_nat > capacity,U: nat,V: nat] :
% 2.76/1.75 ( ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ F )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ zero_zero_capacity @ ( augmen887209518pacity @ c @ f @ F @ ( product_Pair_nat_nat @ U @ V ) ) )
% 2.76/1.75 & ( ord_less_eq_capacity @ ( augmen887209518pacity @ c @ f @ F @ ( product_Pair_nat_nat @ U @ V ) ) @ ( c @ ( product_Pair_nat_nat @ U @ V ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_241_swap__simp,axiom,
% 2.76/1.75 ! [X2: nat,Y: nat] :
% 2.76/1.75 ( ( product_swap_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y ) )
% 2.76/1.75 = ( product_Pair_nat_nat @ Y @ X2 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_242_f__non__negative,axiom,
% 2.76/1.75 ! [E: product_prod_nat_nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( f @ E ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_243_old_Oprod_Oinject,axiom,
% 2.76/1.75 ! [A: nat,B: nat,A5: nat,B5: nat] :
% 2.76/1.75 ( ( ( product_Pair_nat_nat @ A @ B )
% 2.76/1.75 = ( product_Pair_nat_nat @ A5 @ B5 ) )
% 2.76/1.75 = ( ( A = A5 )
% 2.76/1.75 & ( B = B5 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_244_prod_Oinject,axiom,
% 2.76/1.75 ! [X1: nat,X22: nat,Y1: nat,Y22: nat] :
% 2.76/1.75 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 2.76/1.75 = ( product_Pair_nat_nat @ Y1 @ Y22 ) )
% 2.76/1.75 = ( ( X1 = Y1 )
% 2.76/1.75 & ( X22 = Y22 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_245_cap__non__negative,axiom,
% 2.76/1.75 ! [U3: nat,V3: nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( c @ ( product_Pair_nat_nat @ U3 @ V3 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_246_capacity__const,axiom,
% 2.76/1.75 ! [E2: product_prod_nat_nat] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ zero_zero_capacity @ ( f @ E2 ) )
% 2.76/1.75 & ( ord_less_eq_capacity @ ( f @ E2 ) @ ( c @ E2 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_247_swap__swap,axiom,
% 2.76/1.75 ! [P: product_prod_nat_nat] :
% 2.76/1.75 ( ( product_swap_nat_nat @ ( product_swap_nat_nat @ P ) )
% 2.76/1.75 = P ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_248_resE__nonNegative,axiom,
% 2.76/1.75 ! [E: product_prod_nat_nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( residu203630698pacity @ c @ f @ E ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_249_RPreGraph_OresE__nonNegative,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,Cf: product_prod_nat_nat > capacity,E: product_prod_nat_nat] :
% 2.76/1.75 ( ( residu164581374pacity @ C @ S @ T @ Cf )
% 2.76/1.75 => ( ord_less_eq_capacity @ zero_zero_capacity @ ( Cf @ E ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_250_Preflow_Ocapacity__const,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity] :
% 2.76/1.75 ( ( preflow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ! [E2: product_prod_nat_nat] :
% 2.76/1.75 ( ( ord_less_eq_capacity @ zero_zero_capacity @ ( F3 @ E2 ) )
% 2.76/1.75 & ( ord_less_eq_capacity @ ( F3 @ E2 ) @ ( C @ E2 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_251_Preflow_Of__non__negative,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,E: product_prod_nat_nat] :
% 2.76/1.75 ( ( preflow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ord_less_eq_capacity @ zero_zero_capacity @ ( F3 @ E ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_252_old_Oprod_Oinducts,axiom,
% 2.76/1.75 ! [P2: product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 2.76/1.75 ( ! [A4: nat,B4: nat] : ( P2 @ ( product_Pair_nat_nat @ A4 @ B4 ) )
% 2.76/1.75 => ( P2 @ Prod ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_253_old_Oprod_Oexhaust,axiom,
% 2.76/1.75 ! [Y: product_prod_nat_nat] :
% 2.76/1.75 ~ ! [A4: nat,B4: nat] :
% 2.76/1.75 ( Y
% 2.76/1.75 != ( product_Pair_nat_nat @ A4 @ B4 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_254_Pair__inject,axiom,
% 2.76/1.75 ! [A: nat,B: nat,A5: nat,B5: nat] :
% 2.76/1.75 ( ( ( product_Pair_nat_nat @ A @ B )
% 2.76/1.75 = ( product_Pair_nat_nat @ A5 @ B5 ) )
% 2.76/1.75 => ~ ( ( A = A5 )
% 2.76/1.75 => ( B != B5 ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_255_prod__cases,axiom,
% 2.76/1.75 ! [P2: product_prod_nat_nat > $o,P: product_prod_nat_nat] :
% 2.76/1.75 ( ! [A4: nat,B4: nat] : ( P2 @ ( product_Pair_nat_nat @ A4 @ B4 ) )
% 2.76/1.75 => ( P2 @ P ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_256_surj__pair,axiom,
% 2.76/1.75 ! [P: product_prod_nat_nat] :
% 2.76/1.75 ? [X4: nat,Y3: nat] :
% 2.76/1.75 ( P
% 2.76/1.75 = ( product_Pair_nat_nat @ X4 @ Y3 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_257_Network_Ocap__non__negative,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat] :
% 2.76/1.75 ( ( network_capacity @ C @ S @ T )
% 2.76/1.75 => ! [U3: nat,V3: nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( C @ ( product_Pair_nat_nat @ U3 @ V3 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_258_NPreflow_OresE__nonNegative,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,E: product_prod_nat_nat] :
% 2.76/1.75 ( ( nPreflow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ord_less_eq_capacity @ zero_zero_capacity @ ( residu203630698pacity @ C @ F3 @ E ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_259_NFlow_Oaugment__flow__presv__cap,axiom,
% 2.76/1.75 ! [C: product_prod_nat_nat > capacity,S: nat,T: nat,F3: product_prod_nat_nat > capacity,F: product_prod_nat_nat > capacity,U: nat,V: nat] :
% 2.76/1.75 ( ( nFlow_capacity @ C @ S @ T @ F3 )
% 2.76/1.75 => ( ( flow_capacity @ ( residu203630698pacity @ C @ F3 ) @ S @ T @ F )
% 2.76/1.75 => ( ( ord_less_eq_capacity @ zero_zero_capacity @ ( augmen887209518pacity @ C @ F3 @ F @ ( product_Pair_nat_nat @ U @ V ) ) )
% 2.76/1.75 & ( ord_less_eq_capacity @ ( augmen887209518pacity @ C @ F3 @ F @ ( product_Pair_nat_nat @ U @ V ) ) @ ( C @ ( product_Pair_nat_nat @ U @ V ) ) ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_260_excess__s__non__pos,axiom,
% 2.76/1.75 ord_less_eq_capacity @ ( excess_capacity @ c @ f @ s ) @ zero_zero_capacity ).
% 2.76/1.75
% 2.76/1.75 thf(fact_261_resCap__gzero,axiom,
% 2.76/1.75 ! [P: list_P559422087at_nat] :
% 2.76/1.75 ( ( augmen1090971539pacity @ c @ s @ t @ f @ P )
% 2.76/1.75 => ( ord_less_capacity @ zero_zero_capacity @ ( augmen68920357pacity @ c @ f @ P ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_262_Network_Oexcess_Ocong,axiom,
% 2.76/1.75 excess_capacity = excess_capacity ).
% 2.76/1.75
% 2.76/1.75 thf(fact_263_bot_Onot__eq__extremum,axiom,
% 2.76/1.75 ! [A: product_prod_nat_nat > $o] :
% 2.76/1.75 ( ( A != bot_bo513358416_nat_o )
% 2.76/1.75 = ( ord_le1015898640_nat_o @ bot_bo513358416_nat_o @ A ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_264_bot_Onot__eq__extremum,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( A != bot_bo2130386637at_nat )
% 2.76/1.75 = ( ord_le116442893at_nat @ bot_bo2130386637at_nat @ A ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_265_bot_Oextremum__strict,axiom,
% 2.76/1.75 ! [A: product_prod_nat_nat > $o] :
% 2.76/1.75 ~ ( ord_le1015898640_nat_o @ A @ bot_bo513358416_nat_o ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_266_bot_Oextremum__strict,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat] :
% 2.76/1.75 ~ ( ord_le116442893at_nat @ A @ bot_bo2130386637at_nat ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_267_less__infI1,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le116442893at_nat @ A @ X2 )
% 2.76/1.75 => ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ A @ B ) @ X2 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_268_less__infI2,axiom,
% 2.76/1.75 ! [B: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le116442893at_nat @ B @ X2 )
% 2.76/1.75 => ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ A @ B ) @ X2 ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_269_inf_Ostrict__boundedE,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le116442893at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
% 2.76/1.75 => ~ ( ( ord_le116442893at_nat @ A @ B )
% 2.76/1.75 => ~ ( ord_le116442893at_nat @ A @ C ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_270_inf_Ostrict__order__iff,axiom,
% 2.76/1.75 ( ord_le116442893at_nat
% 2.76/1.75 = ( ^ [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( A2
% 2.76/1.75 = ( inf_in586391887at_nat @ A2 @ B2 ) )
% 2.76/1.75 & ( A2 != B2 ) ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_271_inf_Ostrict__coboundedI1,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le116442893at_nat @ A @ C )
% 2.76/1.75 => ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_272_inf_Ostrict__coboundedI2,axiom,
% 2.76/1.75 ! [B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le116442893at_nat @ B @ C )
% 2.76/1.75 => ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_273_dual__order_Ostrict__implies__not__eq,axiom,
% 2.76/1.75 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le116442893at_nat @ B @ A )
% 2.76/1.75 => ( A != B ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_274_dual__order_Ostrict__implies__not__eq,axiom,
% 2.76/1.75 ! [B: capacity,A: capacity] :
% 2.76/1.75 ( ( ord_less_capacity @ B @ A )
% 2.76/1.75 => ( A != B ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_275_order_Ostrict__implies__not__eq,axiom,
% 2.76/1.75 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.75 ( ( ord_le116442893at_nat @ A @ B )
% 2.76/1.75 => ( A != B ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_276_order_Ostrict__implies__not__eq,axiom,
% 2.76/1.75 ! [A: capacity,B: capacity] :
% 2.76/1.75 ( ( ord_less_capacity @ A @ B )
% 2.76/1.75 => ( A != B ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(fact_277_not__less__iff__gr__or__eq,axiom,
% 2.76/1.75 ! [X2: capacity,Y: capacity] :
% 2.76/1.75 ( ( ~ ( ord_less_capacity @ X2 @ Y ) )
% 2.76/1.75 = ( ( ord_less_capacity @ Y @ X2 )
% 2.76/1.75 | ( X2 = Y ) ) ) ).
% 2.76/1.75
% 2.76/1.75 thf(conj_0,hypothesis,
% 2.76/1.75 augmen1090971539pacity @ c @ s @ t @ f @ p ).
% 2.76/1.75
% 2.76/1.75 thf(conj_1,conjecture,
% 2.76/1.75 ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
% 2.76/1.75 = bot_bo2130386637at_nat ) ).
% 2.76/1.75 ------------------------
% 2.76/1.78 % (13285)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/4Mi)
% 2.76/1.78 % (13287)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/2Mi)
% 2.76/1.78 % (13286)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/27Mi)
% 2.76/1.78 % (13288)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/2Mi)
% 2.76/1.78 % (13287)Instruction limit reached!
% 2.76/1.78 % (13287)------------------------------
% 2.76/1.78 % (13287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.78 % (13287)Termination reason: Unknown
% 2.76/1.78 % (13287)Termination phase: shuffling
% 2.76/1.78
% 2.76/1.78 % (13287)Memory used [KB]: 1279
% 2.76/1.78 % (13287)Time elapsed: 0.002 s
% 2.76/1.78 % (13287)Instructions burned: 2 (million)
% 2.76/1.78 % (13287)------------------------------
% 2.76/1.78 % (13287)------------------------------
% 2.76/1.78 % (13288)Instruction limit reached!
% 2.76/1.78 % (13288)------------------------------
% 2.76/1.78 % (13288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.78 % (13288)Termination reason: Unknown
% 2.76/1.78 % (13288)Termination phase: shuffling
% 2.76/1.78
% 2.76/1.78 % (13288)Memory used [KB]: 1279
% 2.76/1.78 % (13288)Time elapsed: 0.002 s
% 2.76/1.78 % (13288)Instructions burned: 2 (million)
% 2.76/1.78 % (13288)------------------------------
% 2.76/1.78 % (13288)------------------------------
% 2.76/1.78 % (13285)Instruction limit reached!
% 2.76/1.78 % (13285)------------------------------
% 2.76/1.78 % (13285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.78 % (13285)Termination reason: Unknown
% 2.76/1.78 % (13285)Termination phase: shuffling
% 2.76/1.78
% 2.76/1.78 % (13285)Memory used [KB]: 1407
% 2.76/1.78 % (13285)Time elapsed: 0.003 s
% 2.76/1.78 % (13285)Instructions burned: 6 (million)
% 2.76/1.78 % (13285)------------------------------
% 2.76/1.78 % (13285)------------------------------
% 2.76/1.78 % (13284)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/183Mi)
% 2.76/1.79 % (13289)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/275Mi)
% 2.76/1.79 % (13290)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/18Mi)
% 2.76/1.79 % (13286)Instruction limit reached!
% 2.76/1.79 % (13286)------------------------------
% 2.76/1.79 % (13286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.79 % (13286)Termination reason: Unknown
% 2.76/1.79 % (13286)Termination phase: shuffling
% 2.76/1.79
% 2.76/1.79 % (13286)Memory used [KB]: 1663
% 2.76/1.79 % (13286)Time elapsed: 0.010 s
% 2.76/1.79 % (13286)Instructions burned: 27 (million)
% 2.76/1.79 % (13286)------------------------------
% 2.76/1.79 % (13286)------------------------------
% 2.76/1.79 % (13292)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/3Mi)
% 2.76/1.79 % (13294)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/37Mi)
% 2.76/1.79 % (13295)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/15Mi)
% 2.76/1.79 % (13292)Instruction limit reached!
% 2.76/1.79 % (13292)------------------------------
% 2.76/1.79 % (13292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.79 % (13292)Termination reason: Unknown
% 2.76/1.79 % (13292)Termination phase: shuffling
% 2.76/1.79
% 2.76/1.79 % (13292)Memory used [KB]: 1279
% 2.76/1.79 % (13292)Time elapsed: 0.002 s
% 2.76/1.79 % (13292)Instructions burned: 3 (million)
% 2.76/1.79 % (13292)------------------------------
% 2.76/1.79 % (13292)------------------------------
% 2.76/1.79 % (13295)Instruction limit reached!
% 2.76/1.79 % (13295)------------------------------
% 2.76/1.79 % (13295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.79 % (13295)Termination reason: Unknown
% 2.76/1.79 % (13295)Termination phase: shuffling
% 2.76/1.79
% 2.76/1.79 % (13295)Memory used [KB]: 1535
% 2.76/1.79 % (13295)Time elapsed: 0.006 s
% 2.76/1.79 % (13295)Instructions burned: 16 (million)
% 2.76/1.79 % (13295)------------------------------
% 2.76/1.79 % (13295)------------------------------
% 2.76/1.79 % (13301)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/3Mi)
% 2.76/1.80 % (13301)Instruction limit reached!
% 2.76/1.80 % (13301)------------------------------
% 2.76/1.80 % (13301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.80 % (13301)Termination reason: Unknown
% 2.76/1.80 % (13301)Termination phase: shuffling
% 2.76/1.80
% 2.76/1.80 % (13301)Memory used [KB]: 1279
% 2.76/1.80 % (13290)Instruction limit reached!
% 2.76/1.80 % (13290)------------------------------
% 2.76/1.80 % (13290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.80 % (13290)Termination reason: Unknown
% 2.76/1.80 % (13301)Time elapsed: 0.002 s
% 2.76/1.80 % (13301)Instructions burned: 3 (million)
% 2.76/1.80 % (13301)------------------------------
% 2.76/1.80 % (13301)------------------------------
% 2.76/1.80 % (13290)Termination phase: shuffling
% 2.76/1.80
% 2.76/1.80 % (13290)Memory used [KB]: 1535
% 2.76/1.80 % (13290)Time elapsed: 0.013 s
% 2.76/1.80 % (13290)Instructions burned: 18 (million)
% 2.76/1.80 % (13290)------------------------------
% 2.76/1.80 % (13290)------------------------------
% 2.81/1.80 % (13294)Instruction limit reached!
% 2.81/1.80 % (13294)------------------------------
% 2.81/1.80 % (13294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.80 % (13294)Termination reason: Unknown
% 2.81/1.80 % (13294)Termination phase: shuffling
% 2.81/1.80
% 2.81/1.80 % (13294)Memory used [KB]: 2046
% 2.81/1.80 % (13294)Time elapsed: 0.011 s
% 2.81/1.80 % (13294)Instructions burned: 37 (million)
% 2.81/1.80 % (13294)------------------------------
% 2.81/1.80 % (13294)------------------------------
% 2.81/1.80 % (13303)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/1041Mi)
% 2.81/1.80 % (13305)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/7Mi)
% 2.81/1.81 % (13305)Instruction limit reached!
% 2.81/1.81 % (13305)------------------------------
% 2.81/1.81 % (13305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.81 % (13305)Termination reason: Unknown
% 2.81/1.81 % (13305)Termination phase: shuffling
% 2.81/1.81
% 2.81/1.81 % (13305)Memory used [KB]: 1407
% 2.81/1.81 % (13305)Time elapsed: 0.004 s
% 2.81/1.81 % (13305)Instructions burned: 9 (million)
% 2.81/1.81 % (13305)------------------------------
% 2.81/1.81 % (13305)------------------------------
% 2.81/1.81 % (13306)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/16Mi)
% 2.81/1.81 % (13308)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/3Mi)
% 2.81/1.81 % (13308)Instruction limit reached!
% 2.81/1.81 % (13308)------------------------------
% 2.81/1.81 % (13308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.81 % (13308)Termination reason: Unknown
% 2.81/1.81 % (13308)Termination phase: shuffling
% 2.81/1.81
% 2.81/1.81 % (13308)Memory used [KB]: 1279
% 2.81/1.81 % (13308)Time elapsed: 0.002 s
% 2.81/1.81 % (13308)Instructions burned: 3 (million)
% 2.81/1.81 % (13308)------------------------------
% 2.81/1.81 % (13308)------------------------------
% 2.81/1.81 % (13306)Instruction limit reached!
% 2.81/1.81 % (13306)------------------------------
% 2.81/1.81 % (13306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.81 % (13306)Termination reason: Unknown
% 2.81/1.81 % (13306)Termination phase: shuffling
% 2.81/1.81
% 2.81/1.81 % (13306)Memory used [KB]: 1535
% 2.81/1.81 % (13306)Time elapsed: 0.006 s
% 2.81/1.81 % (13306)Instructions burned: 16 (million)
% 2.81/1.81 % (13306)------------------------------
% 2.81/1.81 % (13306)------------------------------
% 2.81/1.81 % (13307)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/3Mi)
% 2.81/1.81 % (13309)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/7Mi)
% 2.81/1.82 % (13307)Instruction limit reached!
% 2.81/1.82 % (13307)------------------------------
% 2.81/1.82 % (13307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.82 % (13307)Termination reason: Unknown
% 2.81/1.82 % (13307)Termination phase: shuffling
% 2.81/1.82
% 2.81/1.82 % (13307)Memory used [KB]: 1279
% 2.81/1.82 % (13307)Time elapsed: 0.004 s
% 2.81/1.82 % (13307)Instructions burned: 3 (million)
% 2.81/1.82 % (13307)------------------------------
% 2.81/1.82 % (13307)------------------------------
% 2.81/1.82 % (13312)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/3Mi)
% 2.81/1.82 % (13309)Instruction limit reached!
% 2.81/1.82 % (13309)------------------------------
% 2.81/1.82 % (13309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.82 % (13309)Termination reason: Unknown
% 2.81/1.82 % (13309)Termination phase: shuffling
% 2.81/1.82
% 2.81/1.82 % (13309)Memory used [KB]: 1407
% 2.81/1.82 % (13309)Time elapsed: 0.004 s
% 2.81/1.82 % (13309)Instructions burned: 9 (million)
% 2.81/1.82 % (13309)------------------------------
% 2.81/1.82 % (13309)------------------------------
% 2.81/1.82 % (13312)Instruction limit reached!
% 2.81/1.82 % (13312)------------------------------
% 2.81/1.82 % (13312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.82 % (13312)Termination reason: Unknown
% 2.81/1.82 % (13312)Termination phase: shuffling
% 2.81/1.82
% 2.81/1.82 % (13312)Memory used [KB]: 1279
% 2.81/1.82 % (13312)Time elapsed: 0.002 s
% 2.81/1.82 % (13312)Instructions burned: 4 (million)
% 2.81/1.82 % (13312)------------------------------
% 2.81/1.82 % (13312)------------------------------
% 2.81/1.82 % (13316)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/4Mi)
% 2.81/1.82 % (13316)Instruction limit reached!
% 2.81/1.82 % (13316)------------------------------
% 2.81/1.82 % (13316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.82 % (13316)Termination reason: Unknown
% 2.81/1.82 % (13316)Termination phase: shuffling
% 2.81/1.82
% 2.81/1.82 % (13316)Memory used [KB]: 1407
% 2.81/1.82 % (13316)Time elapsed: 0.003 s
% 2.81/1.82 % (13316)Instructions burned: 6 (million)
% 2.81/1.82 % (13316)------------------------------
% 2.81/1.82 % (13316)------------------------------
% 2.81/1.83 % (13324)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/710Mi)
% 2.81/1.83 % (13325)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/6Mi)
% 2.81/1.83 % (13325)Instruction limit reached!
% 2.81/1.83 % (13325)------------------------------
% 2.81/1.83 % (13325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.83 % (13325)Termination reason: Unknown
% 2.81/1.83 % (13325)Termination phase: shuffling
% 2.81/1.83
% 2.81/1.83 % (13325)Memory used [KB]: 1407
% 2.81/1.83 % (13325)Time elapsed: 0.003 s
% 2.81/1.83 % (13325)Instructions burned: 6 (million)
% 2.81/1.83 % (13325)------------------------------
% 2.81/1.83 % (13325)------------------------------
% 2.81/1.83 % (13327)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/902Mi)
% 2.81/1.83 % (13322)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/18Mi)
% 2.81/1.84 % (13334)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/21Mi)
% 2.81/1.84 % (13322)Instruction limit reached!
% 2.81/1.84 % (13322)------------------------------
% 2.81/1.84 % (13322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.84 % (13322)Termination reason: Unknown
% 2.81/1.84 % (13322)Termination phase: shuffling
% 2.81/1.84
% 2.81/1.84 % (13322)Memory used [KB]: 1535
% 2.81/1.84 % (13322)Time elapsed: 0.013 s
% 2.81/1.84 % (13322)Instructions burned: 18 (million)
% 2.81/1.84 % (13322)------------------------------
% 2.81/1.84 % (13322)------------------------------
% 2.81/1.85 % (13334)Instruction limit reached!
% 2.81/1.85 % (13334)------------------------------
% 2.81/1.85 % (13334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.85 % (13334)Termination reason: Unknown
% 2.81/1.85 % (13334)Termination phase: shuffling
% 2.81/1.85
% 2.81/1.85 % (13334)Memory used [KB]: 1663
% 2.81/1.85 % (13334)Time elapsed: 0.008 s
% 2.81/1.85 % (13334)Instructions burned: 22 (million)
% 2.81/1.85 % (13334)------------------------------
% 2.81/1.85 % (13334)------------------------------
% 2.81/1.85 % (13338)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/6Mi)
% 2.81/1.86 % (13338)Instruction limit reached!
% 2.81/1.86 % (13338)------------------------------
% 2.81/1.86 % (13338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.86 % (13338)Termination reason: Unknown
% 2.81/1.86 % (13338)Termination phase: shuffling
% 2.81/1.86
% 2.81/1.86 % (13338)Memory used [KB]: 1407
% 2.81/1.86 % (13338)Time elapsed: 0.003 s
% 2.81/1.86 % (13338)Instructions burned: 7 (million)
% 2.81/1.86 % (13338)------------------------------
% 2.81/1.86 % (13338)------------------------------
% 2.81/1.86 % (13337)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/5Mi)
% 2.81/1.86 % (13284)Instruction limit reached!
% 2.81/1.86 % (13284)------------------------------
% 2.81/1.86 % (13284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.86 % (13284)Termination reason: Unknown
% 2.81/1.86 % (13284)Termination phase: Saturation
% 2.81/1.86
% 2.81/1.86 % (13284)Memory used [KB]: 7164
% 2.81/1.86 % (13284)Time elapsed: 0.076 s
% 2.81/1.86 % (13284)Instructions burned: 186 (million)
% 2.81/1.86 % (13284)------------------------------
% 2.81/1.86 % (13284)------------------------------
% 2.81/1.86 % (13337)Instruction limit reached!
% 2.81/1.86 % (13337)------------------------------
% 2.81/1.86 % (13337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.86 % (13337)Termination reason: Unknown
% 2.81/1.86 % (13337)Termination phase: shuffling
% 2.81/1.86
% 2.81/1.86 % (13337)Memory used [KB]: 1407
% 2.81/1.86 % (13337)Time elapsed: 0.004 s
% 2.81/1.86 % (13337)Instructions burned: 6 (million)
% 2.81/1.86 % (13337)------------------------------
% 2.81/1.86 % (13337)------------------------------
% 2.81/1.87 % (13347)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/377Mi)
% 2.81/1.87 % (13351)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/779Mi)
% 2.81/1.87 % (13353)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_13121 for (2999ds/19Mi)
% 2.81/1.88 % (13353)Instruction limit reached!
% 2.81/1.88 % (13353)------------------------------
% 2.81/1.88 % (13353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.88 % (13353)Termination reason: Unknown
% 2.81/1.88 % (13353)Termination phase: shuffling
% 2.81/1.88
% 2.81/1.88 % (13353)Memory used [KB]: 1663
% 2.81/1.88 % (13353)Time elapsed: 0.007 s
% 2.81/1.88 % (13353)Instructions burned: 20 (million)
% 2.81/1.88 % (13353)------------------------------
% 2.81/1.88 % (13353)------------------------------
% 2.81/1.88 % (13289)Instruction limit reached!
% 2.81/1.88 % (13289)------------------------------
% 2.81/1.88 % (13289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.88 % (13289)Termination reason: Unknown
% 2.81/1.88 % (13289)Termination phase: Saturation
% 2.81/1.88
% 2.81/1.88 % (13289)Memory used [KB]: 6780
% 2.81/1.88 % (13289)Time elapsed: 0.097 s
% 2.81/1.88 % (13289)Instructions burned: 276 (million)
% 2.81/1.88 % (13289)------------------------------
% 2.81/1.88 % (13289)------------------------------
% 2.81/1.89 % (13362)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13121 for (2998ds/879Mi)
% 2.81/1.89 % (13366)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13121 for (2998ds/17Mi)
% 2.81/1.90 % (13366)Instruction limit reached!
% 2.81/1.90 % (13366)------------------------------
% 2.81/1.90 % (13366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.90 % (13366)Termination reason: Unknown
% 2.81/1.90 % (13366)Termination phase: shuffling
% 2.81/1.90
% 2.81/1.90 % (13366)Memory used [KB]: 1535
% 2.81/1.90 % (13366)Time elapsed: 0.007 s
% 2.81/1.90 % (13366)Instructions burned: 19 (million)
% 2.81/1.90 % (13366)------------------------------
% 2.81/1.90 % (13366)------------------------------
% 2.81/1.90 % (13369)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13121 for (2998ds/3Mi)
% 2.81/1.91 % (13369)Instruction limit reached!
% 2.81/1.91 % (13369)------------------------------
% 2.81/1.91 % (13369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.91 % (13369)Termination reason: Unknown
% 2.81/1.91 % (13369)Termination phase: shuffling
% 2.81/1.91
% 2.81/1.91 % (13369)Memory used [KB]: 1279
% 2.81/1.91 % (13369)Time elapsed: 0.002 s
% 2.81/1.91 % (13369)Instructions burned: 3 (million)
% 2.81/1.91 % (13369)------------------------------
% 2.81/1.91 % (13369)------------------------------
% 2.81/1.92 % (13378)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_13121 for (2998ds/30Mi)
% 2.81/1.93 % (13378)Instruction limit reached!
% 2.81/1.93 % (13378)------------------------------
% 2.81/1.93 % (13378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.93 % (13378)Termination reason: Unknown
% 2.81/1.93 % (13378)Termination phase: Property scanning
% 2.81/1.93
% 2.81/1.93 % (13378)Memory used [KB]: 1791
% 2.81/1.93 % (13378)Time elapsed: 0.012 s
% 2.81/1.93 % (13378)Instructions burned: 33 (million)
% 2.81/1.93 % (13378)------------------------------
% 2.81/1.93 % (13378)------------------------------
% 2.81/1.94 % (13387)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_13121 for (2998ds/127Mi)
% 2.81/1.97 % (13387)Instruction limit reached!
% 2.81/1.97 % (13387)------------------------------
% 2.81/1.97 % (13387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.97 % (13387)Termination reason: Unknown
% 2.81/1.97 % (13387)Termination phase: Saturation
% 2.81/1.97
% 2.81/1.97 % (13387)Memory used [KB]: 6780
% 2.81/1.97 % (13387)Time elapsed: 0.038 s
% 2.81/1.97 % (13387)Instructions burned: 128 (million)
% 2.81/1.97 % (13387)------------------------------
% 2.81/1.97 % (13387)------------------------------
% 2.81/1.98 % (13407)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_13121 for (2997ds/100Mi)
% 2.81/1.98 % (13347)Instruction limit reached!
% 2.81/1.98 % (13347)------------------------------
% 2.81/1.98 % (13347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.98 % (13347)Termination reason: Unknown
% 2.81/1.98 % (13347)Termination phase: Saturation
% 2.81/1.98
% 2.81/1.98 % (13347)Memory used [KB]: 7803
% 2.81/1.98 % (13347)Time elapsed: 0.117 s
% 2.81/1.98 % (13347)Instructions burned: 379 (million)
% 2.81/1.98 % (13347)------------------------------
% 2.81/1.98 % (13347)------------------------------
% 2.81/1.99 % (13410)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_13121 for (2997ds/3Mi)
% 2.81/1.99 % (13410)Instruction limit reached!
% 2.81/1.99 % (13410)------------------------------
% 2.81/1.99 % (13410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.99 % (13410)Termination reason: Unknown
% 2.81/1.99 % (13410)Termination phase: shuffling
% 2.81/1.99
% 2.81/1.99 % (13410)Memory used [KB]: 1279
% 2.81/1.99 % (13410)Time elapsed: 0.002 s
% 2.81/1.99 % (13410)Instructions burned: 3 (million)
% 2.81/1.99 % (13410)------------------------------
% 2.81/1.99 % (13410)------------------------------
% 2.81/2.00 % (13415)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_13121 for (2997ds/20Mi)
% 2.81/2.01 % (13407)Instruction limit reached!
% 2.81/2.01 % (13407)------------------------------
% 2.81/2.01 % (13407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/2.01 % (13407)Termination reason: Unknown
% 2.81/2.01 % (13407)Termination phase: Function definition elimination
% 2.81/2.01
% 2.81/2.01 % (13407)Memory used [KB]: 2302
% 2.81/2.01 % (13407)Time elapsed: 0.027 s
% 2.81/2.01 % (13407)Instructions burned: 101 (million)
% 2.81/2.01 % (13407)------------------------------
% 2.81/2.01 % (13407)------------------------------
% 2.81/2.01 % (13415)Instruction limit reached!
% 2.81/2.01 % (13415)------------------------------
% 2.81/2.01 % (13415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/2.01 % (13415)Termination reason: Unknown
% 2.81/2.01 % (13415)Termination phase: shuffling
% 2.81/2.01
% 2.81/2.01 % (13415)Memory used [KB]: 1535
% 2.81/2.01 % (13415)Time elapsed: 0.008 s
% 2.81/2.01 % (13415)Instructions burned: 22 (million)
% 2.81/2.01 % (13415)------------------------------
% 2.81/2.01 % (13415)------------------------------
% 4.46/2.02 % (13422)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_13121 for (2997ds/86Mi)
% 4.46/2.02 % (13424)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_13121 for (2997ds/107Mi)
% 4.46/2.04 % (13422)Instruction limit reached!
% 4.46/2.04 % (13422)------------------------------
% 4.46/2.04 % (13422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.04 % (13422)Termination reason: Unknown
% 4.46/2.04 % (13422)Termination phase: Property scanning
% 4.46/2.04
% 4.46/2.04 % (13422)Memory used [KB]: 2046
% 4.46/2.04 % (13422)Time elapsed: 0.026 s
% 4.46/2.04 % (13422)Instructions burned: 87 (million)
% 4.46/2.04 % (13422)------------------------------
% 4.46/2.04 % (13422)------------------------------
% 4.46/2.05 % (13424)Instruction limit reached!
% 4.46/2.05 % (13424)------------------------------
% 4.46/2.05 % (13424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.05 % (13424)Termination reason: Unknown
% 4.46/2.05 % (13424)Termination phase: Saturation
% 4.46/2.05
% 4.46/2.05 % (13424)Memory used [KB]: 6524
% 4.46/2.05 % (13424)Time elapsed: 0.031 s
% 4.46/2.05 % (13424)Instructions burned: 109 (million)
% 4.46/2.05 % (13424)------------------------------
% 4.46/2.05 % (13424)------------------------------
% 4.46/2.05 % (13436)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_13121 for (2997ds/39Mi)
% 4.46/2.06 % (13438)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_13121 for (2997ds/448Mi)
% 4.46/2.06 % (13436)Instruction limit reached!
% 4.46/2.06 % (13436)------------------------------
% 4.46/2.06 % (13436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.06 % (13436)Termination reason: Unknown
% 4.46/2.06 % (13436)Termination phase: shuffling
% 4.46/2.06
% 4.46/2.06 % (13436)Memory used [KB]: 2174
% 4.46/2.06 % (13436)Time elapsed: 0.012 s
% 4.46/2.06 % (13436)Instructions burned: 41 (million)
% 4.46/2.06 % (13436)------------------------------
% 4.46/2.06 % (13436)------------------------------
% 4.46/2.07 % (13442)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_13121 for (2996ds/46Mi)
% 4.46/2.09 % (13442)Instruction limit reached!
% 4.46/2.09 % (13442)------------------------------
% 4.46/2.09 % (13442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.09 % (13442)Termination reason: Unknown
% 4.46/2.09 % (13442)Termination phase: SInE selection
% 4.46/2.09
% 4.46/2.09 % (13442)Memory used [KB]: 1663
% 4.46/2.09 % (13442)Time elapsed: 0.016 s
% 4.46/2.09 % (13442)Instructions burned: 49 (million)
% 4.46/2.09 % (13442)------------------------------
% 4.46/2.09 % (13442)------------------------------
% 4.46/2.09 % (13324)Instruction limit reached!
% 4.46/2.09 % (13324)------------------------------
% 4.46/2.09 % (13324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.09 % (13324)Termination reason: Unknown
% 4.46/2.09 % (13324)Termination phase: Saturation
% 4.46/2.09
% 4.46/2.09 % (13324)Memory used [KB]: 7164
% 4.46/2.09 % (13324)Time elapsed: 0.262 s
% 4.46/2.09 % (13324)Instructions burned: 712 (million)
% 4.46/2.09 % (13324)------------------------------
% 4.46/2.09 % (13324)------------------------------
% 4.46/2.10 % (13451)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_13121 for (2996ds/98Mi)
% 4.46/2.10 % (13351)Instruction limit reached!
% 4.46/2.10 % (13351)------------------------------
% 4.46/2.10 % (13351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.10 % (13351)Termination reason: Unknown
% 4.46/2.10 % (13351)Termination phase: Saturation
% 4.46/2.10
% 4.46/2.10 % (13351)Memory used [KB]: 8955
% 4.46/2.10 % (13351)Time elapsed: 0.233 s
% 4.46/2.10 % (13351)Instructions burned: 781 (million)
% 4.46/2.10 % (13351)------------------------------
% 4.46/2.10 % (13351)------------------------------
% 4.46/2.10 % (13452)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_13121 for (2996ds/507Mi)
% 4.46/2.10 % (13327)Instruction limit reached!
% 4.46/2.10 % (13327)------------------------------
% 4.46/2.10 % (13327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.10 % (13327)Termination reason: Unknown
% 4.46/2.10 % (13327)Termination phase: Saturation
% 4.46/2.10
% 4.46/2.10 % (13327)Memory used [KB]: 8059
% 4.46/2.10 % (13327)Time elapsed: 0.271 s
% 4.46/2.10 % (13327)Instructions burned: 902 (million)
% 4.46/2.10 % (13327)------------------------------
% 4.46/2.10 % (13327)------------------------------
% 4.46/2.11 % (13303)Instruction limit reached!
% 4.46/2.11 % (13303)------------------------------
% 4.46/2.11 % (13303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.11 % (13303)Termination reason: Unknown
% 4.46/2.11 % (13303)Termination phase: Saturation
% 4.46/2.11
% 4.46/2.11 % (13303)Memory used [KB]: 9338
% 4.46/2.11 % (13303)Time elapsed: 0.310 s
% 4.46/2.11 % (13303)Instructions burned: 1042 (million)
% 4.46/2.11 % (13303)------------------------------
% 4.46/2.11 % (13303)------------------------------
% 4.46/2.11 % (13453)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_13121 for (2996ds/149Mi)
% 4.46/2.11 % (13454)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_13121 for (2996ds/39Mi)
% 5.07/2.12 % (13455)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_13121 for (2996ds/6Mi)
% 5.07/2.12 % (13455)Instruction limit reached!
% 5.07/2.12 % (13455)------------------------------
% 5.07/2.12 % (13455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.07/2.12 % (13455)Termination reason: Unknown
% 5.07/2.12 % (13455)Termination phase: shuffling
% 5.07/2.12
% 5.07/2.12 % (13455)Memory used [KB]: 1535
% 5.07/2.12 % (13455)Time elapsed: 0.004 s
% 5.07/2.12 % (13455)Instructions burned: 9 (million)
% 5.07/2.12 % (13455)------------------------------
% 5.07/2.12 % (13455)------------------------------
% 5.07/2.12 % (13451)Instruction limit reached!
% 5.07/2.12 % (13451)------------------------------
% 5.07/2.12 % (13451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.07/2.12 % (13451)Termination reason: Unknown
% 5.07/2.12 % (13451)Termination phase: Function definition elimination
% 5.07/2.12
% 5.07/2.12 % (13451)Memory used [KB]: 2174
% 5.07/2.12 % (13451)Time elapsed: 0.027 s
% 5.07/2.12 % (13451)Instructions burned: 100 (million)
% 5.07/2.12 % (13451)------------------------------
% 5.07/2.12 % (13451)------------------------------
% 5.07/2.12 % (13454)Instruction limit reached!
% 5.07/2.12 % (13454)------------------------------
% 5.07/2.12 % (13454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.07/2.12 % (13454)Termination reason: Unknown
% 5.07/2.12 % (13454)Termination phase: Preprocessing 1
% 5.07/2.12
% 5.07/2.12 % (13454)Memory used [KB]: 1663
% 5.07/2.12 % (13454)Time elapsed: 0.014 s
% 5.07/2.12 % (13454)Instructions burned: 42 (million)
% 5.07/2.12 % (13454)------------------------------
% 5.07/2.12 % (13454)------------------------------
% 5.07/2.13 % (13461)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_13121 for (2996ds/1087Mi)
% 5.07/2.13 % (13463)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_13121 for (2996ds/47Mi)
% 5.07/2.13 % (13464)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_13121 for (2996ds/44Mi)
% 5.07/2.14 % (13464)Instruction limit reached!
% 5.07/2.14 % (13464)------------------------------
% 5.07/2.14 % (13464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.07/2.14 % (13464)Termination reason: Unknown
% 5.07/2.14 % (13464)Termination phase: Property scanning
% 5.07/2.14
% 5.07/2.14 % (13464)Memory used [KB]: 2174
% 5.07/2.14 % (13464)Time elapsed: 0.013 s
% 5.07/2.14 % (13464)Instructions burned: 44 (million)
% 5.07/2.14 % (13464)------------------------------
% 5.07/2.14 % (13464)------------------------------
% 5.07/2.15 % (13463)Instruction limit reached!
% 5.07/2.15 % (13463)------------------------------
% 5.07/2.15 % (13463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.07/2.15 % (13463)Termination reason: Unknown
% 5.07/2.15 % (13463)Termination phase: Preprocessing 3
% 5.07/2.15
% 5.07/2.15 % (13463)Memory used [KB]: 1918
% 5.07/2.15 % (13463)Time elapsed: 0.015 s
% 5.07/2.15 % (13463)Instructions burned: 47 (million)
% 5.07/2.15 % (13463)------------------------------
% 5.07/2.15 % (13463)------------------------------
% 5.07/2.15 % (13453)Instruction limit reached!
% 5.07/2.15 % (13453)------------------------------
% 5.07/2.15 % (13453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.07/2.15 % (13453)Termination reason: Unknown
% 5.07/2.15 % (13453)Termination phase: Saturation
% 5.07/2.15
% 5.07/2.15 % (13453)Memory used [KB]: 7036
% 5.07/2.15 % (13453)Time elapsed: 0.044 s
% 5.07/2.15 % (13453)Instructions burned: 150 (million)
% 5.07/2.15 % (13453)------------------------------
% 5.07/2.15 % (13453)------------------------------
% 5.07/2.15 % (13469)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_13121 for (2996ds/432Mi)
% 5.07/2.16 % (13471)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_13121 for (2996ds/62Mi)
% 5.07/2.16 % (13362)Instruction limit reached!
% 5.07/2.16 % (13362)------------------------------
% 5.07/2.16 % (13362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.07/2.16 % (13362)Termination reason: Unknown
% 5.07/2.16 % (13362)Termination phase: Saturation
% 5.07/2.16
% 5.07/2.16 % (13362)Memory used [KB]: 7291
% 5.07/2.16 % (13362)Time elapsed: 0.276 s
% 5.07/2.16 % (13362)Instructions burned: 879 (million)
% 5.07/2.16 % (13362)------------------------------
% 5.07/2.16 % (13362)------------------------------
% 5.07/2.16 % (13476)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_13121 for (2996ds/31Mi)
% 5.07/2.17 % (13482)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_13121 for (2995ds/96Mi)
% 5.07/2.17 % (13471)Instruction limit reached!
% 5.07/2.17 % (13471)------------------------------
% 5.07/2.17 % (13471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.07/2.17 % (13471)Termination reason: Unknown
% 5.07/2.17 % (13476)Instruction limit reached!
% 5.07/2.17 % (13476)------------------------------
% 5.07/2.17 % (13476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.07/2.17 % (13476)Termination reason: Unknown
% 5.07/2.17 % (13471)Termination phase: Property scanning
% 5.07/2.17
% 5.07/2.17 % (13471)Memory used [KB]: 2174
% 5.07/2.17 % (13476)Termination phase: Property scanning
% 5.07/2.17 % (13471)Time elapsed: 0.018 s
% 5.07/2.17
% 5.07/2.17 % (13471)Instructions burned: 64 (million)
% 5.07/2.17 % (13476)Memory used [KB]: 1663
% 5.07/2.17 % (13471)------------------------------
% 5.07/2.17 % (13471)------------------------------
% 5.07/2.17 % (13476)Time elapsed: 0.011 s
% 5.07/2.17 % (13476)Instructions burned: 32 (million)
% 5.07/2.17 % (13476)------------------------------
% 5.07/2.17 % (13476)------------------------------
% 5.07/2.18 % (13489)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_13121 for (2995ds/453Mi)
% 5.07/2.18 % (13490)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_13121 for (2995ds/71Mi)
% 5.07/2.19 % (13438)Instruction limit reached!
% 5.07/2.19 % (13438)------------------------------
% 5.07/2.19 % (13438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.07/2.19 % (13438)Termination reason: Unknown
% 5.07/2.19 % (13438)Termination phase: Saturation
% 5.07/2.19
% 5.07/2.19 % (13438)Memory used [KB]: 8955
% 5.07/2.19 % (13438)Time elapsed: 0.129 s
% 5.07/2.19 % (13438)Instructions burned: 448 (million)
% 5.07/2.19 % (13438)------------------------------
% 5.07/2.19 % (13438)------------------------------
% 5.07/2.20 % (13499)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_13121 for (2995ds/83Mi)
% 5.48/2.20 % (13482)Instruction limit reached!
% 5.48/2.20 % (13482)------------------------------
% 5.48/2.20 % (13482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.48/2.20 % (13482)Termination reason: Unknown
% 5.48/2.20 % (13482)Termination phase: Saturation
% 5.48/2.20
% 5.48/2.20 % (13482)Memory used [KB]: 6524
% 5.48/2.20 % (13482)Time elapsed: 0.028 s
% 5.48/2.20 % (13482)Instructions burned: 99 (million)
% 5.48/2.20 % (13482)------------------------------
% 5.48/2.20 % (13482)------------------------------
% 5.48/2.20 % (13490)Instruction limit reached!
% 5.48/2.20 % (13490)------------------------------
% 5.48/2.20 % (13490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.48/2.20 % (13490)Termination reason: Unknown
% 5.48/2.20 % (13490)Termination phase: Function definition elimination
% 5.48/2.20
% 5.48/2.20 % (13490)Memory used [KB]: 2046
% 5.48/2.20 % (13490)Time elapsed: 0.021 s
% 5.48/2.20 % (13490)Instructions burned: 71 (million)
% 5.48/2.20 % (13490)------------------------------
% 5.48/2.20 % (13490)------------------------------
% 5.48/2.21 % (13507)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_13121 for (2995ds/11Mi)
% 5.48/2.21 % (13507)Instruction limit reached!
% 5.48/2.21 % (13507)------------------------------
% 5.48/2.21 % (13507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.48/2.21 % (13507)Termination reason: Unknown
% 5.48/2.21 % (13507)Termination phase: shuffling
% 5.48/2.21
% 5.48/2.21 % (13507)Memory used [KB]: 1663
% 5.48/2.21 % (13507)Time elapsed: 0.005 s
% 5.48/2.21 % (13507)Instructions burned: 14 (million)
% 5.48/2.21 % (13507)------------------------------
% 5.48/2.21 % (13507)------------------------------
% 5.48/2.21 % (13509)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_13121 for (2995ds/41Mi)
% 5.48/2.22 % (13512)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13121 for (2995ds/6Mi)
% 5.48/2.22 % (13499)Instruction limit reached!
% 5.48/2.22 % (13499)------------------------------
% 5.48/2.22 % (13499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.48/2.22 % (13499)Termination reason: Unknown
% 5.48/2.22 % (13499)Termination phase: Saturation
% 5.48/2.22
% 5.48/2.22 % (13499)Memory used [KB]: 6396
% 5.48/2.22 % (13499)Time elapsed: 0.026 s
% 5.48/2.22 % (13499)Instructions burned: 85 (million)
% 5.48/2.22 % (13499)------------------------------
% 5.48/2.22 % (13499)------------------------------
% 5.48/2.22 % (13509)Instruction limit reached!
% 5.48/2.22 % (13509)------------------------------
% 5.48/2.22 % (13509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.48/2.22 % (13509)Termination reason: Unknown
% 5.48/2.22 % (13509)Termination phase: shuffling
% 5.48/2.22
% 5.48/2.22 % (13509)Memory used [KB]: 2174
% 5.48/2.22 % (13509)Time elapsed: 0.012 s
% 5.48/2.22 % (13509)Instructions burned: 41 (million)
% 5.48/2.22 % (13509)------------------------------
% 5.48/2.22 % (13509)------------------------------
% 5.48/2.22 % (13512)Instruction limit reached!
% 5.48/2.22 % (13512)------------------------------
% 5.48/2.22 % (13512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.48/2.22 % (13512)Termination reason: Unknown
% 5.48/2.22 % (13512)Termination phase: shuffling
% 5.48/2.22
% 5.48/2.22 % (13512)Memory used [KB]: 1407
% 5.48/2.22 % (13512)Time elapsed: 0.003 s
% 5.48/2.22 % (13512)Instructions burned: 6 (million)
% 5.48/2.22 % (13512)------------------------------
% 5.48/2.22 % (13512)------------------------------
% 5.48/2.23 % (13517)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_13121 for (2995ds/150Mi)
% 5.48/2.23 % (13519)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_13121 for (2995ds/109Mi)
% 5.48/2.24 % (13518)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_13121 for (2995ds/343Mi)
% 5.48/2.25 % (13452)Instruction limit reached!
% 5.48/2.25 % (13452)------------------------------
% 5.48/2.25 % (13452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.48/2.25 % (13452)Termination reason: Unknown
% 5.48/2.25 % (13452)Termination phase: Saturation
% 5.48/2.25
% 5.48/2.25 % (13452)Memory used [KB]: 7675
% 5.48/2.25 % (13452)Time elapsed: 0.150 s
% 5.48/2.25 % (13452)Instructions burned: 507 (million)
% 5.48/2.25 % (13452)------------------------------
% 5.48/2.25 % (13452)------------------------------
% 5.48/2.26 % (13520)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_13121 for (2995ds/253Mi)
% 5.48/2.26 % (13519)Instruction limit reached!
% 5.48/2.26 % (13519)------------------------------
% 5.48/2.26 % (13519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.48/2.26 % (13519)Termination reason: Unknown
% 5.48/2.26 % (13519)Termination phase: Saturation
% 5.48/2.26
% 5.48/2.26 % (13519)Memory used [KB]: 6524
% 5.48/2.26 % (13519)Time elapsed: 0.031 s
% 5.48/2.26 % (13519)Instructions burned: 109 (million)
% 5.48/2.26 % (13519)------------------------------
% 5.48/2.26 % (13519)------------------------------
% 5.48/2.27 % (13521)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_13121 for (2995ds/140Mi)
% 5.48/2.27 % (13517)Instruction limit reached!
% 5.48/2.27 % (13517)------------------------------
% 5.48/2.27 % (13517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.48/2.27 % (13517)Termination reason: Unknown
% 5.48/2.27 % (13517)Termination phase: Saturation
% 5.48/2.27
% 5.48/2.27 % (13517)Memory used [KB]: 7164
% 5.48/2.27 % (13517)Time elapsed: 0.045 s
% 5.48/2.27 % (13517)Instructions burned: 152 (million)
% 5.48/2.27 % (13517)------------------------------
% 5.48/2.27 % (13517)------------------------------
% 5.48/2.28 % (13469)Instruction limit reached!
% 5.48/2.28 % (13469)------------------------------
% 5.48/2.28 % (13469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.48/2.28 % (13469)Termination reason: Unknown
% 5.48/2.28 % (13469)Termination phase: Saturation
% 5.48/2.28
% 5.48/2.28 % (13469)Memory used [KB]: 4349
% 5.48/2.28 % (13469)Time elapsed: 0.128 s
% 5.48/2.28 % (13469)Instructions burned: 433 (million)
% 5.48/2.28 % (13469)------------------------------
% 5.48/2.28 % (13469)------------------------------
% 5.48/2.28 % (13522)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_13121 for (2994ds/614Mi)
% 5.48/2.29 % (13523)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_13121 for (2994ds/202Mi)
% 6.02/2.31 % (13489)Instruction limit reached!
% 6.02/2.31 % (13489)------------------------------
% 6.02/2.31 % (13489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.31 % (13489)Termination reason: Unknown
% 6.02/2.31 % (13489)Termination phase: Saturation
% 6.02/2.31
% 6.02/2.31 % (13489)Memory used [KB]: 7675
% 6.02/2.31 % (13489)Time elapsed: 0.131 s
% 6.02/2.31 % (13489)Instructions burned: 454 (million)
% 6.02/2.31 % (13489)------------------------------
% 6.02/2.31 % (13489)------------------------------
% 6.02/2.31 % (13521)Instruction limit reached!
% 6.02/2.31 % (13521)------------------------------
% 6.02/2.31 % (13521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.31 % (13521)Termination reason: Unknown
% 6.02/2.31 % (13521)Termination phase: Saturation
% 6.02/2.31
% 6.02/2.31 % (13521)Memory used [KB]: 6652
% 6.02/2.31 % (13521)Time elapsed: 0.045 s
% 6.02/2.31 % (13521)Instructions burned: 141 (million)
% 6.02/2.31 % (13521)------------------------------
% 6.02/2.31 % (13521)------------------------------
% 6.02/2.32 % (13523)Refutation not found, incomplete strategy
% 6.02/2.32 % (13523)------------------------------
% 6.02/2.32 % (13523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.32 % (13523)Termination reason: Refutation not found, incomplete strategy
% 6.02/2.32
% 6.02/2.32
% 6.02/2.32 % (13523)Memory used [KB]: 6652
% 6.02/2.32 % (13523)Time elapsed: 0.027 s
% 6.02/2.32 % (13523)Instructions burned: 84 (million)
% 6.02/2.32 % (13523)------------------------------
% 6.02/2.32 % (13523)------------------------------
% 6.02/2.32 % (13524)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_13121 for (2994ds/339Mi)
% 6.02/2.32 % (13525)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_13121 for (2994ds/283Mi)
% 6.02/2.33 % (13526)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_13121 for (2994ds/134Mi)
% 6.02/2.34 % (13520)Instruction limit reached!
% 6.02/2.34 % (13520)------------------------------
% 6.02/2.34 % (13520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.34 % (13520)Termination reason: Unknown
% 6.02/2.34 % (13520)Termination phase: Saturation
% 6.02/2.34
% 6.02/2.34 % (13520)Memory used [KB]: 7036
% 6.02/2.34 % (13520)Time elapsed: 0.079 s
% 6.02/2.34 % (13520)Instructions burned: 253 (million)
% 6.02/2.34 % (13520)------------------------------
% 6.02/2.34 % (13520)------------------------------
% 6.02/2.35 % (13527)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_13121 for (2994ds/298Mi)
% 6.02/2.36 % (13518)Instruction limit reached!
% 6.02/2.36 % (13518)------------------------------
% 6.02/2.36 % (13518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.36 % (13518)Termination reason: Unknown
% 6.02/2.36 % (13518)Termination phase: Saturation
% 6.02/2.36
% 6.02/2.36 % (13518)Memory used [KB]: 7291
% 6.02/2.36 % (13518)Time elapsed: 0.120 s
% 6.02/2.36 % (13518)Instructions burned: 344 (million)
% 6.02/2.36 % (13518)------------------------------
% 6.02/2.36 % (13518)------------------------------
% 6.02/2.36 % (13526)Instruction limit reached!
% 6.02/2.36 % (13526)------------------------------
% 6.02/2.36 % (13526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.36 % (13526)Termination reason: Unknown
% 6.02/2.36 % (13526)Termination phase: Saturation
% 6.02/2.36
% 6.02/2.36 % (13526)Memory used [KB]: 6908
% 6.02/2.36 % (13526)Time elapsed: 0.039 s
% 6.02/2.36 % (13526)Instructions burned: 135 (million)
% 6.02/2.36 % (13526)------------------------------
% 6.02/2.36 % (13526)------------------------------
% 6.02/2.37 % (13528)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_13121 for (2994ds/192Mi)
% 6.02/2.37 % (13529)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_13121 for (2994ds/258Mi)
% 6.53/2.41 % (13525)Instruction limit reached!
% 6.53/2.41 % (13525)------------------------------
% 6.53/2.41 % (13525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.41 % (13525)Termination reason: Unknown
% 6.53/2.41 % (13525)Termination phase: Saturation
% 6.53/2.41
% 6.53/2.41 % (13525)Memory used [KB]: 7419
% 6.53/2.41 % (13525)Time elapsed: 0.083 s
% 6.53/2.41 % (13525)Instructions burned: 284 (million)
% 6.53/2.41 % (13525)------------------------------
% 6.53/2.41 % (13525)------------------------------
% 6.53/2.42 % (13524)Instruction limit reached!
% 6.53/2.42 % (13524)------------------------------
% 6.53/2.42 % (13524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.42 % (13524)Termination reason: Unknown
% 6.53/2.42 % (13524)Termination phase: Saturation
% 6.53/2.42
% 6.53/2.42 % (13524)Memory used [KB]: 7291
% 6.53/2.42 % (13524)Time elapsed: 0.096 s
% 6.53/2.42 % (13524)Instructions burned: 341 (million)
% 6.53/2.42 % (13524)------------------------------
% 6.53/2.42 % (13524)------------------------------
% 6.53/2.42 % (13530)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_13121 for (2993ds/90Mi)
% 6.53/2.43 % (13528)Instruction limit reached!
% 6.53/2.43 % (13528)------------------------------
% 6.53/2.43 % (13528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.43 % (13528)Termination reason: Unknown
% 6.53/2.43 % (13528)Termination phase: Saturation
% 6.53/2.43
% 6.53/2.43 % (13528)Memory used [KB]: 7675
% 6.53/2.43 % (13528)Time elapsed: 0.059 s
% 6.53/2.43 % (13528)Instructions burned: 194 (million)
% 6.53/2.43 % (13528)------------------------------
% 6.53/2.43 % (13528)------------------------------
% 6.53/2.43 % (13531)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_13121 for (2993ds/231Mi)
% 6.53/2.43 % (13527)Instruction limit reached!
% 6.53/2.43 % (13527)------------------------------
% 6.53/2.43 % (13527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.43 % (13527)Termination reason: Unknown
% 6.53/2.43 % (13527)Termination phase: Saturation
% 6.53/2.43
% 6.53/2.43 % (13527)Memory used [KB]: 8443
% 6.53/2.43 % (13527)Time elapsed: 0.082 s
% 6.53/2.43 % (13527)Instructions burned: 299 (million)
% 6.53/2.43 % (13527)------------------------------
% 6.53/2.43 % (13527)------------------------------
% 6.53/2.44 % (13532)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_13121 for (2993ds/458Mi)
% 6.53/2.44 % (13533)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_13121 for (2993ds/31Mi)
% 6.53/2.44 % (13529)First to succeed.
% 6.53/2.44 % (13529)Refutation found. Thanks to Tanya!
% 6.53/2.44 % SZS status Theorem for DTF2THF_13121
% 6.53/2.44 % SZS output start Proof for DTF2THF_13121
% 6.53/2.44 thf(type_def_5, type, product_prod_nat_nat: $tType).
% 6.53/2.44 thf(type_def_6, type, capacity: $tType).
% 6.53/2.44 thf(type_def_8, type, list_P559422087at_nat: $tType).
% 6.53/2.44 thf(type_def_9, type, nat: $tType).
% 6.53/2.44 thf(type_def_10, type, set_Pr1986765409at_nat: $tType).
% 6.53/2.44 thf(type_def_11, type, set_nat: $tType).
% 6.53/2.44 thf(func_def_0, type, list_P559422087at_nat: $tType).
% 6.53/2.44 thf(func_def_1, type, set_Pr1986765409at_nat: $tType).
% 6.53/2.44 thf(func_def_2, type, product_prod_nat_nat: $tType).
% 6.53/2.44 thf(func_def_3, type, set_nat: $tType).
% 6.53/2.44 thf(func_def_4, type, capacity: $tType).
% 6.53/2.44 thf(func_def_5, type, nat: $tType).
% 6.53/2.44 thf(func_def_6, type, augmen887209518pacity: (product_prod_nat_nat > capacity) > (product_prod_nat_nat > capacity) > (product_prod_nat_nat > capacity) > product_prod_nat_nat > capacity).
% 6.53/2.44 thf(func_def_7, type, augmen72931474pacity: (product_prod_nat_nat > capacity) > (product_prod_nat_nat > capacity) > list_P559422087at_nat > product_prod_nat_nat > capacity).
% 6.53/2.44 thf(func_def_8, type, augmen1090971539pacity: (product_prod_nat_nat > capacity) > nat > nat > (product_prod_nat_nat > capacity) > list_P559422087at_nat > $o).
% 6.53/2.44 thf(func_def_9, type, augmen68920357pacity: (product_prod_nat_nat > capacity) > (product_prod_nat_nat > capacity) > list_P559422087at_nat > capacity).
% 6.53/2.44 thf(func_def_10, type, finite217307323pacity: (product_prod_nat_nat > capacity) > $o).
% 6.53/2.44 thf(func_def_11, type, isShor1936442771pacity: (product_prod_nat_nat > capacity) > nat > list_P559422087at_nat > nat > $o).
% 6.53/2.44 thf(func_def_12, type, isSimp1359852763pacity: (product_prod_nat_nat > capacity) > nat > list_P559422087at_nat > nat > $o).
% 6.53/2.44 thf(func_def_13, type, plus_plus_capacity: capacity > capacity > capacity).
% 6.53/2.44 thf(func_def_14, type, zero_zero_capacity: capacity).
% 6.53/2.44 thf(func_def_15, type, inf_in2138576462_nat_o: (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > product_prod_nat_nat > $o).
% 6.53/2.44 thf(func_def_16, type, inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_17, type, set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_18, type, finite1387368318pacity: (product_prod_nat_nat > capacity) > nat > nat > (product_prod_nat_nat > capacity) > $o).
% 6.53/2.44 thf(func_def_19, type, flow_capacity: (product_prod_nat_nat > capacity) > nat > nat > (product_prod_nat_nat > capacity) > $o).
% 6.53/2.44 thf(func_def_20, type, val_capacity: (product_prod_nat_nat > capacity) > nat > (product_prod_nat_nat > capacity) > capacity).
% 6.53/2.44 thf(func_def_21, type, nCut_capacity: (product_prod_nat_nat > capacity) > nat > nat > set_nat > $o).
% 6.53/2.44 thf(func_def_22, type, cap_capacity: (product_prod_nat_nat > capacity) > set_nat > capacity).
% 6.53/2.44 thf(func_def_23, type, nFlow_capacity: (product_prod_nat_nat > capacity) > nat > nat > (product_prod_nat_nat > capacity) > $o).
% 6.53/2.44 thf(func_def_24, type, nPreflow_capacity: (product_prod_nat_nat > capacity) > nat > nat > (product_prod_nat_nat > capacity) > $o).
% 6.53/2.44 thf(func_def_25, type, network_capacity: (product_prod_nat_nat > capacity) > nat > nat > $o).
% 6.53/2.44 thf(func_def_26, type, excess_capacity: (product_prod_nat_nat > capacity) > (product_prod_nat_nat > capacity) > nat > capacity).
% 6.53/2.44 thf(func_def_27, type, isMaxFlow_capacity: (product_prod_nat_nat > capacity) > nat > nat > (product_prod_nat_nat > capacity) > $o).
% 6.53/2.44 thf(func_def_28, type, is_max2144541363pacity: (product_prod_nat_nat > capacity) > nat > nat > capacity > $o).
% 6.53/2.44 thf(func_def_29, type, preflow_capacity: (product_prod_nat_nat > capacity) > nat > nat > (product_prod_nat_nat > capacity) > $o).
% 6.53/2.44 thf(func_def_30, type, isMinCut_capacity: (product_prod_nat_nat > capacity) > nat > nat > set_nat > $o).
% 6.53/2.44 thf(func_def_31, type, bot_bot_nat_o: nat > $o).
% 6.53/2.44 thf(func_def_32, type, bot_bo513358416_nat_o: product_prod_nat_nat > $o).
% 6.53/2.44 thf(func_def_34, type, bot_bot_set_nat: set_nat).
% 6.53/2.44 thf(func_def_35, type, bot_bo2130386637at_nat: set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_36, type, ord_le1015898640_nat_o: (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > $o).
% 6.53/2.44 thf(func_def_37, type, ord_le116442893at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o).
% 6.53/2.44 thf(func_def_38, type, ord_less_capacity: capacity > capacity > $o).
% 6.53/2.44 thf(func_def_39, type, ord_le1039616028_nat_o: (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > $o).
% 6.53/2.44 thf(func_def_40, type, ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o).
% 6.53/2.44 thf(func_def_41, type, ord_less_eq_capacity: capacity > capacity > $o).
% 6.53/2.44 thf(func_def_42, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 6.53/2.44 thf(func_def_43, type, product_swap_nat_nat: product_prod_nat_nat > product_prod_nat_nat).
% 6.53/2.44 thf(func_def_44, type, converse_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_45, type, residu1549650759pacity: (product_prod_nat_nat > capacity) > (product_prod_nat_nat > capacity) > product_prod_nat_nat > capacity).
% 6.53/2.44 thf(func_def_46, type, residu800046103pacity: (product_prod_nat_nat > capacity) > nat > nat > (product_prod_nat_nat > capacity) > $o).
% 6.53/2.44 thf(func_def_47, type, residu164581374pacity: (product_prod_nat_nat > capacity) > nat > nat > (product_prod_nat_nat > capacity) > $o).
% 6.53/2.44 thf(func_def_48, type, residu203630698pacity: (product_prod_nat_nat > capacity) > (product_prod_nat_nat > capacity) > product_prod_nat_nat > capacity).
% 6.53/2.44 thf(func_def_49, type, collect_nat: (nat > $o) > set_nat).
% 6.53/2.44 thf(func_def_50, type, collec7649004at_nat: (product_prod_nat_nat > $o) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_51, type, member_nat: nat > set_nat > $o).
% 6.53/2.44 thf(func_def_52, type, member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o).
% 6.53/2.44 thf(func_def_53, type, c: product_prod_nat_nat > capacity).
% 6.53/2.44 thf(func_def_54, type, f: product_prod_nat_nat > capacity).
% 6.53/2.44 thf(func_def_55, type, p: list_P559422087at_nat).
% 6.53/2.44 thf(func_def_56, type, s: nat).
% 6.53/2.44 thf(func_def_57, type, t: nat).
% 6.53/2.44 thf(func_def_74, type, sK0: set_Pr1986765409at_nat > set_Pr1986765409at_nat > nat).
% 6.53/2.44 thf(func_def_75, type, sK1: set_Pr1986765409at_nat > set_Pr1986765409at_nat > nat).
% 6.53/2.44 thf(func_def_76, type, sK2: set_Pr1986765409at_nat > (nat > nat > $o) > nat).
% 6.53/2.44 thf(func_def_77, type, sK3: set_Pr1986765409at_nat > (nat > nat > $o) > nat).
% 6.53/2.44 thf(func_def_78, type, sK4: (capacity > capacity > $o) > capacity).
% 6.53/2.44 thf(func_def_79, type, sK5: (capacity > capacity > $o) > capacity).
% 6.53/2.44 thf(func_def_80, type, sK6: (capacity > capacity > $o) > capacity).
% 6.53/2.44 thf(func_def_81, type, sK7: (capacity > capacity > $o) > capacity).
% 6.53/2.44 thf(func_def_82, type, sK8: (set_Pr1986765409at_nat > capacity) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_83, type, sK9: (set_Pr1986765409at_nat > capacity) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_84, type, sK10: (capacity > set_Pr1986765409at_nat) > capacity).
% 6.53/2.44 thf(func_def_85, type, sK11: (capacity > set_Pr1986765409at_nat) > capacity).
% 6.53/2.44 thf(func_def_86, type, sK12: (set_Pr1986765409at_nat > capacity) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_87, type, sK13: (set_Pr1986765409at_nat > capacity) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_88, type, sK14: (set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_89, type, sK15: (set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_90, type, sK16: (set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_91, type, sK17: (set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_92, type, sK18: (set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_93, type, sK19: (set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_94, type, sK20: (set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_95, type, sK21: (product_prod_nat_nat > $o) > nat).
% 6.53/2.44 thf(func_def_96, type, sK22: (product_prod_nat_nat > $o) > nat).
% 6.53/2.44 thf(func_def_97, type, sK23: (capacity > capacity) > capacity).
% 6.53/2.44 thf(func_def_98, type, sK24: (capacity > capacity) > capacity).
% 6.53/2.44 thf(func_def_99, type, sK25: (set_Pr1986765409at_nat > capacity) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_100, type, sK26: (set_Pr1986765409at_nat > capacity) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_101, type, sK27: list_P559422087at_nat).
% 6.53/2.44 thf(func_def_102, type, sK28: set_nat).
% 6.53/2.44 thf(func_def_103, type, sK29: (capacity > capacity) > capacity).
% 6.53/2.44 thf(func_def_104, type, sK30: (capacity > capacity) > capacity).
% 6.53/2.44 thf(func_def_105, type, sK31: (capacity > capacity) > capacity).
% 6.53/2.44 thf(func_def_106, type, sK32: (capacity > capacity) > capacity).
% 6.53/2.44 thf(func_def_107, type, sK33: nat > nat > (product_prod_nat_nat > capacity) > (product_prod_nat_nat > capacity) > product_prod_nat_nat > capacity).
% 6.53/2.44 thf(func_def_108, type, sK34: (set_Pr1986765409at_nat > set_Pr1986765409at_nat) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_109, type, sK35: (set_Pr1986765409at_nat > set_Pr1986765409at_nat) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_110, type, sK36: product_prod_nat_nat > nat).
% 6.53/2.44 thf(func_def_111, type, sK37: product_prod_nat_nat > nat).
% 6.53/2.44 thf(func_def_112, type, sK38: nat > nat > (product_prod_nat_nat > capacity) > (product_prod_nat_nat > capacity) > set_nat).
% 6.53/2.44 thf(func_def_113, type, sK39: nat > nat > (product_prod_nat_nat > capacity) > (product_prod_nat_nat > capacity) > list_P559422087at_nat).
% 6.53/2.44 thf(func_def_114, type, sK40: (capacity > set_Pr1986765409at_nat) > capacity).
% 6.53/2.44 thf(func_def_115, type, sK41: (capacity > set_Pr1986765409at_nat) > capacity).
% 6.53/2.44 thf(func_def_116, type, sK42: (capacity > capacity) > capacity).
% 6.53/2.44 thf(func_def_117, type, sK43: (capacity > capacity) > capacity).
% 6.53/2.44 thf(func_def_118, type, sK44: (set_Pr1986765409at_nat > set_Pr1986765409at_nat) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_119, type, sK45: (set_Pr1986765409at_nat > set_Pr1986765409at_nat) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_120, type, sK46: (product_prod_nat_nat > $o) > nat).
% 6.53/2.44 thf(func_def_121, type, sK47: (product_prod_nat_nat > $o) > nat).
% 6.53/2.44 thf(func_def_122, type, sK48: (capacity > set_Pr1986765409at_nat) > capacity).
% 6.53/2.44 thf(func_def_123, type, sK49: (capacity > set_Pr1986765409at_nat) > capacity).
% 6.53/2.44 thf(func_def_124, type, sK50: (product_prod_nat_nat > capacity) > nat > (product_prod_nat_nat > capacity) > nat > list_P559422087at_nat).
% 6.53/2.44 thf(func_def_125, type, sK51: (set_Pr1986765409at_nat > set_Pr1986765409at_nat) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_126, type, sK52: (set_Pr1986765409at_nat > set_Pr1986765409at_nat) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_127, type, sK53: set_Pr1986765409at_nat > product_prod_nat_nat > nat).
% 6.53/2.44 thf(func_def_128, type, sK54: set_Pr1986765409at_nat > product_prod_nat_nat > nat).
% 6.53/2.44 thf(func_def_129, type, sK55: (product_prod_nat_nat > capacity) > (product_prod_nat_nat > capacity) > nat > nat > product_prod_nat_nat > capacity).
% 6.53/2.44 thf(func_def_130, type, sK56: (set_Pr1986765409at_nat > capacity) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_131, type, sK57: (set_Pr1986765409at_nat > capacity) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_132, type, sK58: (set_Pr1986765409at_nat > set_Pr1986765409at_nat) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_133, type, sK59: (set_Pr1986765409at_nat > set_Pr1986765409at_nat) > set_Pr1986765409at_nat).
% 6.53/2.44 thf(func_def_134, type, sK60: list_P559422087at_nat).
% 6.53/2.44 thf(func_def_135, type, sK61: (capacity > set_Pr1986765409at_nat) > capacity).
% 6.53/2.44 thf(func_def_136, type, sK62: (capacity > set_Pr1986765409at_nat) > capacity).
% 6.53/2.44 thf(func_def_137, type, sK63: product_prod_nat_nat > nat).
% 6.53/2.44 thf(func_def_138, type, sK64: product_prod_nat_nat > nat).
% 6.53/2.44 thf(func_def_140, type, ph66: !>[X0: $tType]:(X0)).
% 6.53/2.44 thf(f1983,plain,(
% 6.53/2.44 $false),
% 6.53/2.44 inference(subsumption_resolution,[status(thm)],[f1974,f1203])).
% 6.53/2.44 thf(f1203,plain,(
% 6.53/2.44 ((augmen1090971539pacity @ c @ s @ t @ f @ p) = $true)),
% 6.53/2.44 inference(cnf_transformation,[status(thm)],[f316])).
% 6.53/2.44 thf(f316,plain,(
% 6.53/2.44 ((augmen1090971539pacity @ c @ s @ t @ f @ p) = $true)),
% 6.53/2.44 inference(fool_elimination,[status(thm)],[f315])).
% 6.53/2.44 thf(f315,plain,(
% 6.53/2.44 (augmen1090971539pacity @ c @ s @ t @ f @ p)),
% 6.53/2.44 inference(rectify,[status(thm)],[f279])).
% 6.53/2.44 thf(f279,axiom,(
% 6.53/2.44 (augmen1090971539pacity @ c @ s @ t @ f @ p)),
% 6.53/2.44 file('/export/starexec/sandbox2/tmp/tmp.VKYVsEMyde/DTF2THF_13121.p',conj_0)).
% 6.53/2.44 thf(f1974,plain,(
% 6.53/2.44 ((augmen1090971539pacity @ c @ s @ t @ f @ p) != $true)),
% 6.53/2.44 inference(superposition,[status(thm)],[f1847,f1437])).
% 6.53/2.44 thf(f1437,plain,(
% 6.53/2.44 ( ! [X0 : list_P559422087at_nat] : (((isSimp1359852763pacity @ (residu203630698pacity @ c @ f) @ s @ X0 @ t) = (augmen1090971539pacity @ c @ s @ t @ f @ X0))) )),
% 6.53/2.44 inference(cnf_transformation,[status(thm)],[f746])).
% 6.53/2.44 thf(f746,plain,(
% 6.53/2.44 ! [X0 : list_P559422087at_nat] : ((isSimp1359852763pacity @ (residu203630698pacity @ c @ f) @ s @ X0 @ t) = (augmen1090971539pacity @ c @ s @ t @ f @ X0))),
% 6.53/2.44 inference(rectify,[status(thm)],[f6])).
% 6.53/2.44 thf(f6,axiom,(
% 6.53/2.44 ! [X1 : list_P559422087at_nat] : ((augmen1090971539pacity @ c @ s @ t @ f @ X1) = (isSimp1359852763pacity @ (residu203630698pacity @ c @ f) @ s @ X1 @ t))),
% 6.53/2.44 file('/export/starexec/sandbox2/tmp/tmp.VKYVsEMyde/DTF2THF_13121.p',fact_5_isAugmentingPath__def)).
% 6.53/2.44 thf(f1847,plain,(
% 6.53/2.44 ( ! [X2 : nat,X0 : product_prod_nat_nat > capacity,X1 : nat] : (($true != (isSimp1359852763pacity @ X0 @ X1 @ p @ X2))) )),
% 6.53/2.44 inference(trivial_inequality_removal,[status(thm)],[f1835])).
% 6.53/2.44 thf(f1835,plain,(
% 6.53/2.44 ( ! [X2 : nat,X0 : product_prod_nat_nat > capacity,X1 : nat] : (($true != (isSimp1359852763pacity @ X0 @ X1 @ p @ X2)) | (bot_bo2130386637at_nat != bot_bo2130386637at_nat)) )),
% 6.53/2.44 inference(superposition,[status(thm)],[f1431,f1201])).
% 6.53/2.44 thf(f1201,plain,(
% 6.53/2.44 ( ! [X2 : list_P559422087at_nat,X3 : nat,X0 : nat,X1 : product_prod_nat_nat > capacity] : ((bot_bo2130386637at_nat = (inf_in586391887at_nat @ (set_Pr2131844118at_nat @ X2) @ (converse_nat_nat @ (set_Pr2131844118at_nat @ X2)))) | ((isSimp1359852763pacity @ X1 @ X0 @ X2 @ X3) != $true)) )),
% 6.53/2.44 inference(cnf_transformation,[status(thm)],[f910])).
% 6.53/2.44 thf(f910,plain,(
% 6.53/2.44 ! [X0 : nat,X1 : product_prod_nat_nat > capacity,X2 : list_P559422087at_nat,X3 : nat] : ((bot_bo2130386637at_nat = (inf_in586391887at_nat @ (set_Pr2131844118at_nat @ X2) @ (converse_nat_nat @ (set_Pr2131844118at_nat @ X2)))) | ((isSimp1359852763pacity @ X1 @ X0 @ X2 @ X3) != $true))),
% 6.53/2.44 inference(ennf_transformation,[status(thm)],[f454])).
% 6.53/2.44 thf(f454,plain,(
% 6.53/2.44 ! [X0 : nat,X1 : product_prod_nat_nat > capacity,X2 : list_P559422087at_nat,X3 : nat] : (((isSimp1359852763pacity @ X1 @ X0 @ X2 @ X3) = $true) => (bot_bo2130386637at_nat = (inf_in586391887at_nat @ (set_Pr2131844118at_nat @ X2) @ (converse_nat_nat @ (set_Pr2131844118at_nat @ X2)))))),
% 6.53/2.44 inference(fool_elimination,[status(thm)],[f453])).
% 6.53/2.44 thf(f453,plain,(
% 6.53/2.44 ! [X0 : nat,X1 : product_prod_nat_nat > capacity,X2 : list_P559422087at_nat,X3 : nat] : ((isSimp1359852763pacity @ X1 @ X0 @ X2 @ X3) => (bot_bo2130386637at_nat = (inf_in586391887at_nat @ (set_Pr2131844118at_nat @ X2) @ (converse_nat_nat @ (set_Pr2131844118at_nat @ X2)))))),
% 6.53/2.44 inference(rectify,[status(thm)],[f58])).
% 6.53/2.44 thf(f58,axiom,(
% 6.53/2.44 ! [X0 : nat,X14 : product_prod_nat_nat > capacity,X1 : list_P559422087at_nat,X2 : nat] : ((isSimp1359852763pacity @ X14 @ X0 @ X1 @ X2) => ((inf_in586391887at_nat @ (set_Pr2131844118at_nat @ X1) @ (converse_nat_nat @ (set_Pr2131844118at_nat @ X1))) = bot_bo2130386637at_nat))),
% 6.53/2.44 file('/export/starexec/sandbox2/tmp/tmp.VKYVsEMyde/DTF2THF_13121.p',fact_57_Graph_OisSPath__nt__parallel__pf)).
% 6.53/2.44 thf(f1431,plain,(
% 6.53/2.44 (bot_bo2130386637at_nat != (inf_in586391887at_nat @ (set_Pr2131844118at_nat @ p) @ (converse_nat_nat @ (set_Pr2131844118at_nat @ p))))),
% 6.53/2.44 inference(cnf_transformation,[status(thm)],[f745])).
% 6.53/2.44 thf(f745,plain,(
% 6.53/2.44 (bot_bo2130386637at_nat != (inf_in586391887at_nat @ (set_Pr2131844118at_nat @ p) @ (converse_nat_nat @ (set_Pr2131844118at_nat @ p))))),
% 6.53/2.44 inference(flattening,[status(thm)],[f281])).
% 6.53/2.44 thf(f281,negated_conjecture,(
% 6.53/2.44 ~(bot_bo2130386637at_nat = (inf_in586391887at_nat @ (set_Pr2131844118at_nat @ p) @ (converse_nat_nat @ (set_Pr2131844118at_nat @ p))))),
% 6.53/2.44 inference(negated_conjecture,[status(cth)],[f280])).
% 6.53/2.44 thf(f280,conjecture,(
% 6.53/2.44 (bot_bo2130386637at_nat = (inf_in586391887at_nat @ (set_Pr2131844118at_nat @ p) @ (converse_nat_nat @ (set_Pr2131844118at_nat @ p))))),
% 6.53/2.44 file('/export/starexec/sandbox2/tmp/tmp.VKYVsEMyde/DTF2THF_13121.p',conj_1)).
% 6.53/2.44 % SZS output end Proof for DTF2THF_13121
% 6.53/2.44 % (13529)------------------------------
% 6.53/2.44 % (13529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.44 % (13529)Termination reason: Refutation
% 6.53/2.44
% 6.53/2.44 % (13529)Memory used [KB]: 7547
% 6.53/2.44 % (13529)Time elapsed: 0.067 s
% 6.53/2.44 % (13529)Instructions burned: 213 (million)
% 6.53/2.44 % (13529)------------------------------
% 6.53/2.44 % (13529)------------------------------
% 6.53/2.44 % (13277)Success in time 0.669 s
%------------------------------------------------------------------------------