%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP048^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n022.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 08:55:08 AM UTC 2026
% Result : Theorem 50.63s 8.53s
% Output : Refutation 50.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 60 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 269 ( 98 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 743 ( 18 ~; 10 |; 37 &; 644 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 108 ( 104 usr; 16 con; 0-5 aty)
% ( 0 !!; 28 ??; 0 @@+; 0 @@-)
% Number of variables : 203 ( 173 ^; 28 !; 2 ?; 203 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
product_prod_nat_nat: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_8,type,
nat: $tType ).
thf(type_def_9,type,
capacity: $tType ).
thf(type_def_10,type,
list_P559422087at_nat: $tType ).
thf(type_def_11,type,
set_nat: $tType ).
thf(func_def_0,type,
list_P559422087at_nat: $tType ).
thf(func_def_1,type,
product_prod_nat_nat: $tType ).
thf(func_def_2,type,
set_nat: $tType ).
thf(func_def_3,type,
capacity: $tType ).
thf(func_def_4,type,
nat: $tType ).
thf(func_def_5,type,
a: $tType ).
thf(func_def_6,type,
connected_a: ( product_prod_nat_nat > a ) > nat > nat > $o ).
thf(func_def_7,type,
connected_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > $o ).
thf(func_def_8,type,
dist_a: ( product_prod_nat_nat > a ) > nat > nat > nat > $o ).
thf(func_def_9,type,
dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat > $o ).
thf(func_def_10,type,
isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_11,type,
isPath_capacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_12,type,
isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_13,type,
isShor1936442771pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_14,type,
isSimplePath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_15,type,
isSimp1359852763pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_16,type,
min_dist_a: ( product_prod_nat_nat > a ) > nat > nat > nat ).
thf(func_def_17,type,
min_dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat ).
thf(func_def_18,type,
reachableNodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
thf(func_def_19,type,
reacha1693770334pacity: ( product_prod_nat_nat > capacity ) > nat > set_nat ).
thf(func_def_20,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_21,type,
size_s1990949619at_nat: list_P559422087at_nat > nat ).
thf(func_def_22,type,
ord_Least_nat: ( nat > $o ) > nat ).
thf(func_def_23,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_24,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_25,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_26,type,
member_nat: nat > set_nat > $o ).
thf(func_def_27,type,
c: product_prod_nat_nat > capacity ).
thf(func_def_28,type,
c2: product_prod_nat_nat > a ).
thf(func_def_29,type,
p: list_P559422087at_nat ).
thf(func_def_30,type,
p1: list_P559422087at_nat ).
thf(func_def_31,type,
p1a: list_P559422087at_nat ).
thf(func_def_32,type,
p2: list_P559422087at_nat ).
thf(func_def_33,type,
p2_a: list_P559422087at_nat ).
thf(func_def_34,type,
p3: list_P559422087at_nat ).
thf(func_def_35,type,
s: nat ).
thf(func_def_36,type,
t: nat ).
thf(func_def_37,type,
u: nat ).
thf(func_def_38,type,
ua: nat ).
thf(func_def_39,type,
v: nat ).
thf(func_def_40,type,
va: nat ).
thf(func_def_57,type,
sK0: nat > nat > ( product_prod_nat_nat > capacity ) > nat ).
thf(func_def_58,type,
sK1: ( product_prod_nat_nat > capacity ) > nat > nat > list_P559422087at_nat ).
thf(func_def_59,type,
sK2: nat > nat > ( product_prod_nat_nat > a ) > list_P559422087at_nat ).
thf(func_def_60,type,
sK3: nat > ( product_prod_nat_nat > capacity ) > nat > nat > nat ).
thf(func_def_61,type,
sK4: ( nat > $o ) > nat ).
thf(func_def_62,type,
sK5: nat > nat > nat ).
thf(func_def_63,type,
sK6: ( nat > nat ) > nat ).
thf(func_def_64,type,
sK7: ( nat > nat ) > nat ).
thf(func_def_65,type,
sK8: ( nat > nat ) > nat ).
thf(func_def_66,type,
sK9: ( nat > nat ) > nat ).
thf(func_def_67,type,
sK10: ( nat > $o ) > nat ).
thf(func_def_68,type,
sK11: nat > nat > nat ).
thf(func_def_69,type,
sK12: ( nat > nat ) > nat ).
thf(func_def_70,type,
sK13: ( nat > nat ) > nat ).
thf(func_def_71,type,
sK14: nat > nat ).
thf(func_def_72,type,
sK15: nat > ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat ).
thf(func_def_73,type,
sK16: ( nat > nat ) > nat ).
thf(func_def_74,type,
sK17: ( nat > nat ) > nat ).
thf(func_def_75,type,
sK18: nat > nat > list_P559422087at_nat ).
thf(func_def_76,type,
sK19: nat > nat > ( product_prod_nat_nat > a ) > list_P559422087at_nat ).
thf(func_def_77,type,
sK20: ( nat > nat ) > nat ).
thf(func_def_78,type,
sK21: ( nat > nat ) > nat ).
thf(func_def_79,type,
sK22: nat > nat > nat ).
thf(func_def_80,type,
sK23: nat > nat > nat ).
thf(func_def_81,type,
sK24: nat > nat > list_P559422087at_nat ).
thf(func_def_82,type,
sK25: nat > nat > nat > nat ).
thf(func_def_83,type,
sK26: nat > nat > list_P559422087at_nat ).
thf(func_def_84,type,
sK27: ( nat > nat ) > nat ).
thf(func_def_85,type,
sK28: ( nat > nat ) > nat ).
thf(func_def_86,type,
sK29: ( nat > nat > $o ) > nat ).
thf(func_def_87,type,
sK30: ( nat > nat > $o ) > nat ).
thf(func_def_88,type,
sK31: ( nat > nat > $o ) > nat ).
thf(func_def_89,type,
sK32: ( nat > nat > $o ) > nat ).
thf(func_def_90,type,
sK33: ( nat > nat > $o ) > nat ).
thf(func_def_91,type,
sK34: ( product_prod_nat_nat > capacity ) > ( nat > $o ) > nat > nat > nat ).
thf(func_def_92,type,
sK35: nat > ( product_prod_nat_nat > capacity ) > nat > nat ).
thf(func_def_93,type,
sK36: nat > nat > list_P559422087at_nat ).
thf(func_def_94,type,
sK37: ( nat > $o ) > nat ).
thf(func_def_95,type,
sK38: nat > nat > ( nat > $o ) > nat ).
thf(func_def_97,type,
sK40: nat > nat > nat > ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat ).
thf(func_def_98,type,
sK41: nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat ).
thf(func_def_99,type,
sK42: nat > list_P559422087at_nat > ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat ).
thf(func_def_100,type,
sK43: nat > list_P559422087at_nat ).
thf(func_def_101,type,
sK44: nat > list_P559422087at_nat > nat > list_P559422087at_nat ).
thf(func_def_102,type,
sK45: nat > nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat ).
thf(func_def_103,type,
sK46: nat > nat > list_P559422087at_nat ).
thf(func_def_104,type,
sK47: ( product_prod_nat_nat > capacity ) > nat > nat > list_P559422087at_nat ).
thf(func_def_109,type,
sK48: nat > nat > nat ).
thf(func_def_110,type,
sK49: nat > nat > list_P559422087at_nat ).
thf(func_def_111,type,
sK50: nat > nat > list_P559422087at_nat ).
thf(func_def_112,type,
sK51: ( product_prod_nat_nat > capacity ) > nat > nat > list_P559422087at_nat ).
thf(func_def_113,type,
sK52: list_P559422087at_nat ).
thf(func_def_114,type,
sK53: nat > ( nat > $o ) > ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat ).
thf(func_def_115,type,
sK54: nat > nat > list_P559422087at_nat > list_P559422087at_nat ).
thf(func_def_116,type,
sK55: nat > nat > nat > list_P559422087at_nat ).
thf(func_def_117,type,
sK56: nat > nat > nat > list_P559422087at_nat ).
thf(func_def_118,type,
sK57: nat > nat > nat > nat > list_P559422087at_nat ).
thf(func_def_119,type,
sK58: nat > nat > nat > list_P559422087at_nat ).
thf(func_def_120,type,
sK59: nat > nat > list_P559422087at_nat ).
thf(func_def_121,type,
sK60: nat > nat > list_P559422087at_nat ).
thf(func_def_122,type,
sK61: nat > nat > list_P559422087at_nat ).
thf(func_def_123,type,
sK62: ( product_prod_nat_nat > a ) > nat > nat > list_P559422087at_nat > list_P559422087at_nat ).
thf(func_def_124,type,
sK63: list_P559422087at_nat > nat > nat > list_P559422087at_nat ).
thf(func_def_125,type,
sK64: nat > ( product_prod_nat_nat > capacity ) > nat > nat > list_P559422087at_nat ).
thf(func_def_126,type,
sK65: nat > nat > list_P559422087at_nat > list_P559422087at_nat ).
thf(func_def_127,type,
sK66: nat > nat > list_P559422087at_nat > list_P559422087at_nat ).
thf(func_def_128,type,
sK67: nat > ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat ).
thf(func_def_129,type,
sK68: nat > nat > ( nat > $o ) > list_P559422087at_nat ).
thf(func_def_130,type,
ph69:
!>[X0: $tType] : X0 ).
thf(f7103,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f7102,f5677]) ).
thf(f5677,plain,
( ( ord_less_nat @ ( size_s1990949619at_nat @ p ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) )
!= $true ),
inference(backward_demodulation,[status(thm)],[f1389,f1462]) ).
thf(f1462,plain,
( ( size_s1990949619at_nat @ p )
= ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ s @ Y1 @ t ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f1461]) ).
thf(f1461,plain,
( ( ( size_s1990949619at_nat @ p )
= ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ s @ Y1 @ t ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f1459]) ).
thf(f1459,plain,
( ( ( ( size_s1990949619at_nat @ p )
= ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ s @ Y1 @ t ) ) ) ) )
& ( isSimp1359852763pacity @ c @ s @ p @ t ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1237]) ).
thf(f1237,plain,
( ( ^ [Y0: product_prod_nat_nat > capacity,Y1: nat,Y2: list_P559422087at_nat,Y3: nat] :
( ( ( size_s1990949619at_nat @ Y2 )
= ( ^ [Y4: product_prod_nat_nat > capacity,Y5: nat,Y6: nat] :
( ord_Least_nat
@ ^ [Y7: nat] :
( ^ [Y8: product_prod_nat_nat > capacity,Y9: nat,Y10: nat,Y11: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y12: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y12 )
= Y10 )
& ( isPath_capacity @ Y8 @ Y9 @ Y12 @ Y11 ) ) )
@ Y4
@ Y5
@ Y7
@ Y6 ) )
@ Y0
@ Y1
@ Y3 ) )
& ( isSimp1359852763pacity @ Y0 @ Y1 @ Y2 @ Y3 ) )
@ c
@ s
@ p
@ t )
= $true ),
inference(definition_unfolding,[status(thm)],[f1043,f1227]) ).
thf(f1227,plain,
( isShor1936442771pacity
= ( ^ [Y0: product_prod_nat_nat > capacity,Y1: nat,Y2: list_P559422087at_nat,Y3: nat] :
( ( ( size_s1990949619at_nat @ Y2 )
= ( ^ [Y4: product_prod_nat_nat > capacity,Y5: nat,Y6: nat] :
( ord_Least_nat
@ ^ [Y7: nat] :
( ^ [Y8: product_prod_nat_nat > capacity,Y9: nat,Y10: nat,Y11: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y12: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y12 )
= Y10 )
& ( isPath_capacity @ Y8 @ Y9 @ Y12 @ Y11 ) ) )
@ Y4
@ Y5
@ Y7
@ Y6 ) )
@ Y0
@ Y1
@ Y3 ) )
& ( isSimp1359852763pacity @ Y0 @ Y1 @ Y2 @ Y3 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1078,f1226]) ).
thf(f1226,plain,
( min_dist_capacity
= ( ^ [Y0: product_prod_nat_nat > capacity,Y1: nat,Y2: nat] :
( ord_Least_nat
@ ^ [Y3: nat] :
( ^ [Y4: product_prod_nat_nat > capacity,Y5: nat,Y6: nat,Y7: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y8: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y8 )
= Y6 )
& ( isPath_capacity @ Y4 @ Y5 @ Y8 @ Y7 ) ) )
@ Y0
@ Y1
@ Y3
@ Y2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1060,f1069]) ).
thf(f1069,plain,
( dist_capacity
= ( ^ [Y0: product_prod_nat_nat > capacity,Y1: nat,Y2: nat,Y3: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y4: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y4 )
= Y2 )
& ( isPath_capacity @ Y0 @ Y1 @ Y4 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f736]) ).
thf(f736,plain,
( dist_capacity
= ( ^ [Y0: product_prod_nat_nat > capacity,Y1: nat,Y2: nat,Y3: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y4: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y4 )
= Y2 )
& ( isPath_capacity @ Y0 @ Y1 @ Y4 @ Y3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f735]) ).
thf(f735,plain,
( dist_capacity
= ( ^ [X0: product_prod_nat_nat > capacity,X1: nat,X2: nat,X3: nat] :
? [X4: list_P559422087at_nat] :
( ( isPath_capacity @ X0 @ X1 @ X4 @ X3 )
& ( ( size_s1990949619at_nat @ X4 )
= X2 ) ) ) ),
inference(rectify,[status(thm)],[f121]) ).
thf(f121,axiom,
( dist_capacity
= ( ^ [X33: product_prod_nat_nat > capacity,X53: nat,X18: nat,X54: nat] :
? [X15: list_P559422087at_nat] :
( ( isPath_capacity @ X33 @ X53 @ X15 @ X54 )
& ( ( size_s1990949619at_nat @ X15 )
= X18 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_120_Graph_Odist__def) ).
thf(f1060,plain,
( min_dist_capacity
= ( ^ [Y0: product_prod_nat_nat > capacity,Y1: nat,Y2: nat] :
( ord_Least_nat
@ ^ [Y3: nat] : ( dist_capacity @ Y0 @ Y1 @ Y3 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f440]) ).
thf(f440,plain,
( min_dist_capacity
= ( ^ [Y0: product_prod_nat_nat > capacity,Y1: nat,Y2: nat] :
( ord_Least_nat
@ ^ [Y3: nat] : ( dist_capacity @ Y0 @ Y1 @ Y3 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f439]) ).
thf(f439,plain,
( min_dist_capacity
= ( ^ [X0: product_prod_nat_nat > capacity,X1: nat,X2: nat] :
( ord_Least_nat
@ ^ [X3: nat] : ( dist_capacity @ X0 @ X1 @ X3 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f141]) ).
thf(f141,axiom,
( min_dist_capacity
= ( ^ [X33: product_prod_nat_nat > capacity,X53: nat,X54: nat] :
( ord_Least_nat
@ ^ [X18: nat] : ( dist_capacity @ X33 @ X53 @ X18 @ X54 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_140_Graph_Omin__dist__def) ).
thf(f1078,plain,
( isShor1936442771pacity
= ( ^ [Y0: product_prod_nat_nat > capacity,Y1: nat,Y2: list_P559422087at_nat,Y3: nat] :
( ( ( size_s1990949619at_nat @ Y2 )
= ( min_dist_capacity @ Y0 @ Y1 @ Y3 ) )
& ( isSimp1359852763pacity @ Y0 @ Y1 @ Y2 @ Y3 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f632]) ).
thf(f632,plain,
( isShor1936442771pacity
= ( ^ [Y0: product_prod_nat_nat > capacity,Y1: nat,Y2: list_P559422087at_nat,Y3: nat] :
( ( ( size_s1990949619at_nat @ Y2 )
= ( min_dist_capacity @ Y0 @ Y1 @ Y3 ) )
& ( isSimp1359852763pacity @ Y0 @ Y1 @ Y2 @ Y3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f631]) ).
thf(f631,plain,
( isShor1936442771pacity
= ( ^ [X0: product_prod_nat_nat > capacity,X1: nat,X2: list_P559422087at_nat,X3: nat] :
( ( isSimp1359852763pacity @ X0 @ X1 @ X2 @ X3 )
& ( ( size_s1990949619at_nat @ X2 )
= ( min_dist_capacity @ X0 @ X1 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f143]) ).
thf(f143,axiom,
( isShor1936442771pacity
= ( ^ [X33: product_prod_nat_nat > capacity,X52: nat,X15: list_P559422087at_nat,X53: nat] :
( ( isSimp1359852763pacity @ X33 @ X52 @ X15 @ X53 )
& ( ( size_s1990949619at_nat @ X15 )
= ( min_dist_capacity @ X33 @ X52 @ X53 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_142_Graph_OisShortestPath__alt) ).
thf(f1043,plain,
( ( isShor1936442771pacity @ c @ s @ p @ t )
= $true ),
inference(cnf_transformation,[status(thm)],[f716]) ).
thf(f716,plain,
( ( isShor1936442771pacity @ c @ s @ p @ t )
= $true ),
inference(fool_elimination,[status(thm)],[f715]) ).
thf(f715,plain,
isShor1936442771pacity @ c @ s @ p @ t,
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
isShor1936442771pacity @ c @ s @ p @ t,
file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_7_SP) ).
thf(f1389,plain,
( ( ord_less_nat
@ ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ s @ Y1 @ t ) ) ) )
@ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f1239]) ).
thf(f1239,plain,
( ( ord_less_nat
@ ( ^ [Y0: product_prod_nat_nat > capacity,Y1: nat,Y2: nat] :
( ord_Least_nat
@ ^ [Y3: nat] :
( ^ [Y4: product_prod_nat_nat > capacity,Y5: nat,Y6: nat,Y7: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y8: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y8 )
= Y6 )
& ( isPath_capacity @ Y4 @ Y5 @ Y8 @ Y7 ) ) )
@ Y0
@ Y1
@ Y3
@ Y2 ) )
@ c
@ s
@ t )
@ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f1046,f1226]) ).
thf(f1046,plain,
( ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f757]) ).
thf(f757,plain,
( ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) )
!= $true ),
inference(flattening,[status(thm)],[f606]) ).
thf(f606,plain,
( ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f605]) ).
thf(f605,plain,
~ ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) ),
inference(rectify,[status(thm)],[f275]) ).
thf(f275,negated_conjecture,
~ ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) ),
inference(negated_conjecture,[status(cth)],[f274]) ).
thf(f274,conjecture,
ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ),
file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',conj_0) ).
thf(f7102,plain,
( ( ord_less_nat @ ( size_s1990949619at_nat @ p ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f7097,f5676]) ).
thf(f5676,plain,
( ( plus_plus_nat
@ ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ s @ Y1 @ ua ) ) ) )
@ ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ ua @ Y1 @ t ) ) ) ) )
= ( size_s1990949619at_nat @ p ) ),
inference(backward_demodulation,[status(thm)],[f1593,f1462]) ).
thf(f1593,plain,
( ( plus_plus_nat
@ ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ s @ Y1 @ ua ) ) ) )
@ ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ ua @ Y1 @ t ) ) ) ) )
= ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ s @ Y1 @ t ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1264]) ).
thf(f1264,plain,
( ( ^ [Y0: product_prod_nat_nat > capacity,Y1: nat,Y2: nat] :
( ord_Least_nat
@ ^ [Y3: nat] :
( ^ [Y4: product_prod_nat_nat > capacity,Y5: nat,Y6: nat,Y7: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y8: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y8 )
= Y6 )
& ( isPath_capacity @ Y4 @ Y5 @ Y8 @ Y7 ) ) )
@ Y0
@ Y1
@ Y3
@ Y2 ) )
@ c
@ s
@ t )
= ( plus_plus_nat
@ ( ^ [Y0: product_prod_nat_nat > capacity,Y1: nat,Y2: nat] :
( ord_Least_nat
@ ^ [Y3: nat] :
( ^ [Y4: product_prod_nat_nat > capacity,Y5: nat,Y6: nat,Y7: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y8: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y8 )
= Y6 )
& ( isPath_capacity @ Y4 @ Y5 @ Y8 @ Y7 ) ) )
@ Y0
@ Y1
@ Y3
@ Y2 ) )
@ c
@ s
@ ua )
@ ( ^ [Y0: product_prod_nat_nat > capacity,Y1: nat,Y2: nat] :
( ord_Least_nat
@ ^ [Y3: nat] :
( ^ [Y4: product_prod_nat_nat > capacity,Y5: nat,Y6: nat,Y7: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y8: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y8 )
= Y6 )
& ( isPath_capacity @ Y4 @ Y5 @ Y8 @ Y7 ) ) )
@ Y0
@ Y1
@ Y3
@ Y2 ) )
@ c
@ ua
@ t ) ) ),
inference(definition_unfolding,[status(thm)],[f1130,f1226,f1226,f1226]) ).
thf(f1130,plain,
( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( min_dist_capacity @ c @ ua @ t ) ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( min_dist_capacity @ c @ ua @ t ) ) ),
file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062) ).
thf(f7097,plain,
( ( ord_less_nat
@ ( plus_plus_nat
@ ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ s @ Y1 @ ua ) ) ) )
@ ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ ua @ Y1 @ t ) ) ) ) )
@ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f7088]) ).
thf(f7088,plain,
( ( ( ord_less_nat
@ ( plus_plus_nat
@ ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ s @ Y1 @ ua ) ) ) )
@ ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ ua @ Y1 @ t ) ) ) ) )
@ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f2276,f1469]) ).
thf(f1469,plain,
( ( ord_less_eq_nat
@ ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ ua @ Y1 @ t ) ) ) )
@ ( size_s1990949619at_nat @ p2_a ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1243]) ).
thf(f1243,plain,
( ( ord_less_eq_nat
@ ( ^ [Y0: product_prod_nat_nat > capacity,Y1: nat,Y2: nat] :
( ord_Least_nat
@ ^ [Y3: nat] :
( ^ [Y4: product_prod_nat_nat > capacity,Y5: nat,Y6: nat,Y7: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y8: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y8 )
= Y6 )
& ( isPath_capacity @ Y4 @ Y5 @ Y8 @ Y7 ) ) )
@ Y0
@ Y1
@ Y3
@ Y2 ) )
@ c
@ ua
@ t )
@ ( size_s1990949619at_nat @ p2_a ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f1073,f1226]) ).
thf(f1073,plain,
( ( ord_less_eq_nat @ ( min_dist_capacity @ c @ ua @ t ) @ ( size_s1990949619at_nat @ p2_a ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f554]) ).
thf(f554,plain,
( ( ord_less_eq_nat @ ( min_dist_capacity @ c @ ua @ t ) @ ( size_s1990949619at_nat @ p2_a ) )
= $true ),
inference(fool_elimination,[status(thm)],[f553]) ).
thf(f553,plain,
ord_less_eq_nat @ ( min_dist_capacity @ c @ ua @ t ) @ ( size_s1990949619at_nat @ p2_a ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
ord_less_eq_nat @ ( min_dist_capacity @ c @ ua @ t ) @ ( size_s1990949619at_nat @ p2_a ),
file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062) ).
thf(f2276,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( ord_less_eq_nat @ X0 @ X1 ) )
| ( ( ord_less_nat
@ ( plus_plus_nat
@ ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ s @ Y1 @ ua ) ) ) )
@ X0 )
@ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2271]) ).
thf(f2271,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat
@ ( plus_plus_nat
@ ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ s @ Y1 @ ua ) ) ) )
@ X0 )
@ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ X1 ) )
= $true )
| ( $true
!= ( ord_less_eq_nat @ X0 @ X1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1177,f1388]) ).
thf(f1388,plain,
( ( ord_less_nat
@ ( ord_Least_nat
@ ^ [Y0: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y1 )
= Y0 )
& ( isPath_capacity @ c @ s @ Y1 @ ua ) ) ) )
@ ( size_s1990949619at_nat @ p1a ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1261]) ).
thf(f1261,plain,
( ( ord_less_nat
@ ( ^ [Y0: product_prod_nat_nat > capacity,Y1: nat,Y2: nat] :
( ord_Least_nat
@ ^ [Y3: nat] :
( ^ [Y4: product_prod_nat_nat > capacity,Y5: nat,Y6: nat,Y7: nat] :
( ?? @ list_P559422087at_nat
@ ^ [Y8: list_P559422087at_nat] :
( ( ( size_s1990949619at_nat @ Y8 )
= Y6 )
& ( isPath_capacity @ Y4 @ Y5 @ Y8 @ Y7 ) ) )
@ Y0
@ Y1
@ Y3
@ Y2 ) )
@ c
@ s
@ ua )
@ ( size_s1990949619at_nat @ p1a ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f1125,f1226]) ).
thf(f1125,plain,
( ( ord_less_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( size_s1990949619at_nat @ p1a ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f752]) ).
thf(f752,plain,
( ( ord_less_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( size_s1990949619at_nat @ p1a ) )
= $true ),
inference(fool_elimination,[status(thm)],[f751]) ).
thf(f751,plain,
ord_less_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( size_s1990949619at_nat @ p1a ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
ord_less_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( size_s1990949619at_nat @ p1a ),
file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062) ).
thf(f1177,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true
!= ( ord_less_nat @ X1 @ X3 ) )
| ( ( ord_less_nat @ ( plus_plus_nat @ X1 @ X0 ) @ ( plus_plus_nat @ X3 @ X2 ) )
= $true )
| ( ( ord_less_eq_nat @ X0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f826]) ).
thf(f826,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
!= ( ord_less_nat @ X1 @ X3 ) )
| ( ( ord_less_eq_nat @ X0 @ X2 )
!= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ X1 @ X0 ) @ ( plus_plus_nat @ X3 @ X2 ) )
= $true ) ),
inference(flattening,[status(thm)],[f825]) ).
thf(f825,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ X1 @ X0 ) @ ( plus_plus_nat @ X3 @ X2 ) )
= $true )
| ( ( ord_less_eq_nat @ X0 @ X2 )
!= $true )
| ( $true
!= ( ord_less_nat @ X1 @ X3 ) ) ),
inference(ennf_transformation,[status(thm)],[f408]) ).
thf(f408,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
= ( ord_less_nat @ X1 @ X3 ) )
=> ( ( ( ord_less_eq_nat @ X0 @ X2 )
= $true )
=> ( ( ord_less_nat @ ( plus_plus_nat @ X1 @ X0 ) @ ( plus_plus_nat @ X3 @ X2 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f407]) ).
thf(f407,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ord_less_nat @ X1 @ X3 )
=> ( ( ord_less_eq_nat @ X0 @ X2 )
=> ( ord_less_nat @ ( plus_plus_nat @ X1 @ X0 ) @ ( plus_plus_nat @ X3 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f91]) ).
thf(f91,axiom,
! [X3: nat,X4: nat,X12: nat,X5: nat] :
( ( ord_less_nat @ X4 @ X5 )
=> ( ( ord_less_eq_nat @ X3 @ X12 )
=> ( ord_less_nat @ ( plus_plus_nat @ X4 @ X3 ) @ ( plus_plus_nat @ X5 @ X12 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_90_add__less__le__mono) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP048^1 : TPTP v9.2.1. Released v7.5.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n022.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 08:24:36 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.46 ---- Original DTF file ---
% 0.21/0.46 thf(spec,logic,$$dhol).
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 % File : ITP048^1 : TPTP v9.2.1. Released v7.5.0.
% 0.21/0.46 % Domain : Interactive Theorem Proving
% 0.21/0.46 % Problem : Sledgehammer EdmondsKarp_Termination_Abstract problem prob_146__7582994_1
% 0.21/0.46 % Version : Especial.
% 0.21/0.46 % English :
% 0.21/0.46
% 0.21/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.21/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.21/0.46 % Source : [Des21]
% 0.21/0.46 % Names : EdmondsKarp_Termination_Abstract/prob_146__7582994_1 [Des21]
% 0.21/0.46
% 0.21/0.46 % Status : Theorem
% 0.21/0.46 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.50 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0
% 0.21/0.46 % Syntax : Number of formulae : 315 ( 110 unt; 41 typ; 0 def)
% 0.21/0.46 % Number of atoms : 715 ( 188 equ; 0 cnn)
% 0.21/0.46 % Maximal formula atoms : 12 ( 2 avg)
% 0.21/0.46 % Number of connectives : 2319 ( 60 ~; 10 |; 41 &;1894 @)
% 0.21/0.46 % ( 0 <=>; 314 =>; 0 <=; 0 <~>)
% 0.21/0.46 % Maximal formula depth : 16 ( 7 avg)
% 0.21/0.46 % Number of types : 7 ( 6 usr)
% 0.21/0.46 % Number of type conns : 160 ( 160 >; 0 *; 0 +; 0 <<)
% 0.21/0.46 % Number of symbols : 36 ( 35 usr; 12 con; 0-4 aty)
% 0.21/0.46 % Number of variables : 826 ( 87 ^; 705 !; 34 ?; 826 :)
% 0.21/0.46 % SPC : TH0_THM_EQU_NAR
% 0.21/0.46
% 0.21/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:24.947
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 % Could-be-implicit typings (6)
% 0.21/0.46 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.21/0.46 list_P559422087at_nat: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.21/0.46 product_prod_nat_nat: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.21/0.46 set_nat: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_n_tf__capacity,type,
% 0.21/0.46 capacity: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_n_t__Nat__Onat,type,
% 0.21/0.46 nat: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_n_tf__a,type,
% 0.21/0.46 a: $tType ).
% 0.21/0.46
% 0.21/0.46 % Explicit typings (35)
% 0.21/0.46 thf(sy_c_Graph_OGraph_Oconnected_001tf__a,type,
% 0.21/0.46 connected_a: ( product_prod_nat_nat > a ) > nat > nat > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Graph_OGraph_Oconnected_001tf__capacity,type,
% 0.21/0.46 connected_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Graph_OGraph_Odist_001tf__a,type,
% 0.21/0.46 dist_a: ( product_prod_nat_nat > a ) > nat > nat > nat > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Graph_OGraph_Odist_001tf__capacity,type,
% 0.21/0.46 dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Graph_OGraph_OisPath_001tf__a,type,
% 0.21/0.46 isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Graph_OGraph_OisPath_001tf__capacity,type,
% 0.21/0.46 isPath_capacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Graph_OGraph_OisShortestPath_001tf__a,type,
% 0.21/0.46 isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Graph_OGraph_OisShortestPath_001tf__capacity,type,
% 0.21/0.46 isShor1936442771pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Graph_OGraph_OisSimplePath_001tf__a,type,
% 0.21/0.46 isSimplePath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Graph_OGraph_OisSimplePath_001tf__capacity,type,
% 0.21/0.46 isSimp1359852763pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Graph_OGraph_Omin__dist_001tf__a,type,
% 0.21/0.46 min_dist_a: ( product_prod_nat_nat > a ) > nat > nat > nat ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Graph_OGraph_Omin__dist_001tf__capacity,type,
% 0.21/0.46 min_dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Graph_OGraph_OreachableNodes_001tf__a,type,
% 0.21/0.46 reachableNodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Graph_OGraph_OreachableNodes_001tf__capacity,type,
% 0.21/0.46 reacha1693770334pacity: ( product_prod_nat_nat > capacity ) > nat > set_nat ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 0.21/0.46 plus_plus_nat: nat > nat > nat ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.21/0.47 size_s1990949619at_nat: list_P559422087at_nat > nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Oord__class_OLeast_001t__Nat__Onat,type,
% 0.21/0.47 ord_Least_nat: ( nat > $o ) > nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.21/0.47 ord_less_nat: nat > nat > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.21/0.47 ord_less_eq_nat: nat > nat > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.21/0.47 collect_nat: ( nat > $o ) > set_nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_member_001t__Nat__Onat,type,
% 0.21/0.47 member_nat: nat > set_nat > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_c,type,
% 0.21/0.47 c: product_prod_nat_nat > capacity ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_c_H,type,
% 0.21/0.47 c2: product_prod_nat_nat > a ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_p,type,
% 0.21/0.47 p: list_P559422087at_nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_p1____,type,
% 0.21/0.47 p1: list_P559422087at_nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_p1a____,type,
% 0.21/0.47 p1a: list_P559422087at_nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_p2_H____,type,
% 0.21/0.47 p2: list_P559422087at_nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_p2_Ha____,type,
% 0.21/0.47 p2_a: list_P559422087at_nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_p_H,type,
% 0.21/0.47 p3: list_P559422087at_nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_s,type,
% 0.21/0.47 s: nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_t,type,
% 0.21/0.47 t: nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_u____,type,
% 0.21/0.47 u: nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_ua____,type,
% 0.21/0.47 ua: nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_v____,type,
% 0.21/0.47 v: nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_va____,type,
% 0.21/0.47 va: nat ).
% 0.21/0.47
% 0.21/0.47 % Relevant facts (273)
% 0.21/0.47 thf(fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062,axiom,
% 0.21/0.47 ( ( min_dist_capacity @ c @ s @ t )
% 0.21/0.47 = ( plus_plus_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( min_dist_capacity @ c @ ua @ t ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % \<open>min_dist s t = min_dist s u + min_dist u t\<close>
% 0.21/0.47 thf(fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062,axiom,
% 0.21/0.47 ord_less_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( size_s1990949619at_nat @ p1a ) ).
% 0.21/0.47
% 0.21/0.47 % \<open>min_dist s u < length p1\<close>
% 0.21/0.47 thf(fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062,axiom,
% 0.21/0.47 ord_less_eq_nat @ ( min_dist_capacity @ c @ ua @ t ) @ ( size_s1990949619at_nat @ p2_a ) ).
% 0.21/0.47
% 0.21/0.47 % \<open>min_dist u t \<le> length p2'\<close>
% 0.21/0.47 thf(fact_3_nat__add__left__cancel__less,axiom,
% 0.21/0.47 ! [K: nat,M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.21/0.47 = ( ord_less_nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat_add_left_cancel_less
% 0.21/0.47 thf(fact_4_add__less__cancel__left,axiom,
% 0.21/0.47 ! [C: nat,A: nat,B: nat] :
% 0.21/0.47 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.21/0.47 = ( ord_less_nat @ A @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_less_cancel_left
% 0.21/0.47 thf(fact_5_add__less__cancel__right,axiom,
% 0.21/0.47 ! [A: nat,C: nat,B: nat] :
% 0.21/0.47 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.21/0.47 = ( ord_less_nat @ A @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_less_cancel_right
% 0.21/0.47 thf(fact_6__C1_Oprems_C_I2_J,axiom,
% 0.21/0.47 isPath_capacity @ c @ s @ p1a @ va ).
% 0.21/0.47
% 0.21/0.47 % "1.prems"(2)
% 0.21/0.47 thf(fact_7_SP,axiom,
% 0.21/0.47 isShor1936442771pacity @ c @ s @ p @ t ).
% 0.21/0.47
% 0.21/0.47 % SP
% 0.21/0.47 thf(fact_8_min__dist__split_I2_J,axiom,
% 0.21/0.47 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.21/0.47 ( ( dist_capacity @ c @ U @ D1 @ W )
% 0.21/0.47 => ( ( dist_capacity @ c @ W @ D2 @ V )
% 0.21/0.47 => ( ( ( min_dist_capacity @ c @ U @ V )
% 0.21/0.47 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.21/0.47 => ( ( min_dist_capacity @ c @ W @ V )
% 0.21/0.47 = D2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % min_dist_split(2)
% 0.21/0.47 thf(fact_9_min__dist__split_I1_J,axiom,
% 0.21/0.47 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.21/0.47 ( ( dist_capacity @ c @ U @ D1 @ W )
% 0.21/0.47 => ( ( dist_capacity @ c @ W @ D2 @ V )
% 0.21/0.47 => ( ( ( min_dist_capacity @ c @ U @ V )
% 0.21/0.47 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.21/0.47 => ( ( min_dist_capacity @ c @ U @ W )
% 0.21/0.47 = D1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % min_dist_split(1)
% 0.21/0.47 thf(fact_10_min__dist__less,axiom,
% 0.21/0.47 ! [Src: nat,V: nat,D: nat,D3: nat] :
% 0.21/0.47 ( ( connected_capacity @ c @ Src @ V )
% 0.21/0.47 => ( ( ( min_dist_capacity @ c @ Src @ V )
% 0.21/0.47 = D )
% 0.21/0.47 => ( ( ord_less_nat @ D3 @ D )
% 0.21/0.47 => ? [V2: nat] :
% 0.21/0.47 ( ( connected_capacity @ c @ Src @ V2 )
% 0.21/0.47 & ( ( min_dist_capacity @ c @ Src @ V2 )
% 0.21/0.47 = D3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % min_dist_less
% 0.21/0.47 thf(fact_11_add__left__cancel,axiom,
% 0.21/0.47 ! [A: nat,B: nat,C: nat] :
% 0.21/0.47 ( ( ( plus_plus_nat @ A @ B )
% 0.21/0.47 = ( plus_plus_nat @ A @ C ) )
% 0.21/0.47 = ( B = C ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_left_cancel
% 0.21/0.47 thf(fact_12_add__right__cancel,axiom,
% 0.21/0.47 ! [B: nat,A: nat,C: nat] :
% 0.21/0.47 ( ( ( plus_plus_nat @ B @ A )
% 0.21/0.47 = ( plus_plus_nat @ C @ A ) )
% 0.21/0.47 = ( B = C ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_right_cancel
% 0.21/0.47 thf(fact_13__092_060open_062isPath_Au_Ap2_H_At_092_060close_062,axiom,
% 0.21/0.47 isPath_capacity @ c @ ua @ p2_a @ t ).
% 0.21/0.47
% 0.21/0.47 % \<open>isPath u p2' t\<close>
% 0.21/0.47 thf(fact_14_dist__trans,axiom,
% 0.21/0.47 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.21/0.47 ( ( dist_capacity @ c @ U @ D1 @ W )
% 0.21/0.47 => ( ( dist_capacity @ c @ W @ D2 @ V )
% 0.21/0.47 => ( dist_capacity @ c @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dist_trans
% 0.21/0.47 thf(fact_15_connected__def,axiom,
% 0.21/0.47 ! [U: nat,V: nat] :
% 0.21/0.47 ( ( connected_capacity @ c @ U @ V )
% 0.21/0.47 = ( ? [P: list_P559422087at_nat] : ( isPath_capacity @ c @ U @ P @ V ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % connected_def
% 0.21/0.47 thf(fact_16_shortestPath__is__path,axiom,
% 0.21/0.47 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.21/0.47 ( ( isShor1936442771pacity @ c @ U @ P2 @ V )
% 0.21/0.47 => ( isPath_capacity @ c @ U @ P2 @ V ) ) ).
% 0.21/0.47
% 0.21/0.47 % shortestPath_is_path
% 0.21/0.47 thf(fact_17_connected__by__dist,axiom,
% 0.21/0.47 ! [V: nat,V3: nat] :
% 0.21/0.47 ( ( connected_capacity @ c @ V @ V3 )
% 0.21/0.47 = ( ? [D4: nat] : ( dist_capacity @ c @ V @ D4 @ V3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % connected_by_dist
% 0.21/0.47 thf(fact_18_obtain__shortest__path,axiom,
% 0.21/0.47 ! [U: nat,V: nat] :
% 0.21/0.47 ( ( connected_capacity @ c @ U @ V )
% 0.21/0.47 => ~ ! [P3: list_P559422087at_nat] :
% 0.21/0.47 ~ ( isShor1936442771pacity @ c @ U @ P3 @ V ) ) ).
% 0.21/0.47
% 0.21/0.47 % obtain_shortest_path
% 0.21/0.47 thf(fact_19_min__dist__le,axiom,
% 0.21/0.47 ! [Src: nat,V: nat,D3: nat] :
% 0.21/0.47 ( ( connected_capacity @ c @ Src @ V )
% 0.21/0.47 => ( ( ord_less_eq_nat @ D3 @ ( min_dist_capacity @ c @ Src @ V ) )
% 0.21/0.47 => ? [V2: nat] :
% 0.21/0.47 ( ( connected_capacity @ c @ Src @ V2 )
% 0.21/0.47 & ( ( min_dist_capacity @ c @ Src @ V2 )
% 0.21/0.47 = D3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % min_dist_le
% 0.21/0.47 thf(fact_20_min__dist__minD,axiom,
% 0.21/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.21/0.47 ( ( dist_capacity @ c @ V @ D @ V3 )
% 0.21/0.47 => ( ord_less_eq_nat @ ( min_dist_capacity @ c @ V @ V3 ) @ D ) ) ).
% 0.21/0.47
% 0.21/0.47 % min_dist_minD
% 0.21/0.47 thf(fact_21_min__distI__eq,axiom,
% 0.21/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.21/0.47 ( ( dist_capacity @ c @ V @ D @ V3 )
% 0.21/0.47 => ( ! [D5: nat] :
% 0.21/0.47 ( ( dist_capacity @ c @ V @ D5 @ V3 )
% 0.21/0.47 => ( ord_less_eq_nat @ D @ D5 ) )
% 0.21/0.47 => ( ( min_dist_capacity @ c @ V @ V3 )
% 0.21/0.47 = D ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % min_distI_eq
% 0.21/0.47 thf(fact_22_isPath__distD,axiom,
% 0.21/0.47 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.21/0.47 ( ( isPath_capacity @ c @ U @ P2 @ V )
% 0.21/0.47 => ( dist_capacity @ c @ U @ ( size_s1990949619at_nat @ P2 ) @ V ) ) ).
% 0.21/0.47
% 0.21/0.47 % isPath_distD
% 0.21/0.47 thf(fact_23_dist__def,axiom,
% 0.21/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.21/0.47 ( ( dist_capacity @ c @ V @ D @ V3 )
% 0.21/0.47 = ( ? [P: list_P559422087at_nat] :
% 0.21/0.47 ( ( isPath_capacity @ c @ V @ P @ V3 )
% 0.21/0.47 & ( ( size_s1990949619at_nat @ P )
% 0.21/0.47 = D ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dist_def
% 0.21/0.47 thf(fact_24__092_060open_062isPath_As_Ap1_____Av_____092_060close_062,axiom,
% 0.21/0.47 isPath_capacity @ c @ s @ p1 @ v ).
% 0.21/0.47
% 0.21/0.47 % \<open>isPath s p1__ v__\<close>
% 0.21/0.47 thf(fact_25_min__dist__is__dist,axiom,
% 0.21/0.47 ! [V: nat,V3: nat] :
% 0.21/0.47 ( ( connected_capacity @ c @ V @ V3 )
% 0.21/0.47 => ( dist_capacity @ c @ V @ ( min_dist_capacity @ c @ V @ V3 ) @ V3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % min_dist_is_dist
% 0.21/0.47 thf(fact_26_isShortestPath__def,axiom,
% 0.21/0.47 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.21/0.47 ( ( isShor1936442771pacity @ c @ U @ P2 @ V )
% 0.21/0.47 = ( ( isPath_capacity @ c @ U @ P2 @ V )
% 0.21/0.47 & ! [P4: list_P559422087at_nat] :
% 0.21/0.47 ( ( isPath_capacity @ c @ U @ P4 @ V )
% 0.21/0.47 => ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P2 ) @ ( size_s1990949619at_nat @ P4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % isShortestPath_def
% 0.21/0.47 thf(fact_27_min__distI2,axiom,
% 0.21/0.47 ! [V: nat,V3: nat,Q: nat > $o] :
% 0.21/0.47 ( ( connected_capacity @ c @ V @ V3 )
% 0.21/0.47 => ( ! [D6: nat] :
% 0.21/0.47 ( ( dist_capacity @ c @ V @ D6 @ V3 )
% 0.21/0.47 => ( ! [D7: nat] :
% 0.21/0.47 ( ( dist_capacity @ c @ V @ D7 @ V3 )
% 0.21/0.47 => ( ord_less_eq_nat @ D6 @ D7 ) )
% 0.21/0.47 => ( Q @ D6 ) ) )
% 0.21/0.47 => ( Q @ ( min_dist_capacity @ c @ V @ V3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % min_distI2
% 0.21/0.47 thf(fact_28_isShortestPath__min__dist__def,axiom,
% 0.21/0.47 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.21/0.47 ( ( isShor1936442771pacity @ c @ U @ P2 @ V )
% 0.21/0.47 = ( ( isPath_capacity @ c @ U @ P2 @ V )
% 0.21/0.47 & ( ( size_s1990949619at_nat @ P2 )
% 0.21/0.47 = ( min_dist_capacity @ c @ U @ V ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % isShortestPath_min_dist_def
% 0.21/0.47 thf(fact_29__092_060open_062connected_As_Au_092_060close_062,axiom,
% 0.21/0.47 connected_capacity @ c @ s @ ua ).
% 0.21/0.47
% 0.21/0.47 % \<open>connected s u\<close>
% 0.21/0.47 thf(fact_30_add__le__cancel__right,axiom,
% 0.21/0.47 ! [A: nat,C: nat,B: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.21/0.47 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_le_cancel_right
% 0.21/0.47 thf(fact_31_add__le__cancel__left,axiom,
% 0.21/0.47 ! [C: nat,A: nat,B: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.21/0.47 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_le_cancel_left
% 0.21/0.47 thf(fact_32_nat__add__left__cancel__le,axiom,
% 0.21/0.47 ! [K: nat,M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.21/0.47 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat_add_left_cancel_le
% 0.21/0.47 thf(fact_33_P1,axiom,
% 0.21/0.47 isPath_capacity @ c @ s @ p1a @ va ).
% 0.21/0.47
% 0.21/0.47 % P1
% 0.21/0.47 thf(fact_34_connected__refl,axiom,
% 0.21/0.47 ! [V: nat] : ( connected_capacity @ c @ V @ V ) ).
% 0.21/0.47
% 0.21/0.47 % connected_refl
% 0.21/0.47 thf(fact_35_connected__distI,axiom,
% 0.21/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.21/0.47 ( ( dist_capacity @ c @ V @ D @ V3 )
% 0.21/0.47 => ( connected_capacity @ c @ V @ V3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % connected_distI
% 0.21/0.47 thf(fact_36_le__refl,axiom,
% 0.21/0.47 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.21/0.47
% 0.21/0.47 % le_refl
% 0.21/0.47 thf(fact_37_le__trans,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.21/0.47 => ( ( ord_less_eq_nat @ J @ K )
% 0.21/0.47 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_trans
% 0.21/0.47 thf(fact_38_eq__imp__le,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( M = N )
% 0.21/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % eq_imp_le
% 0.21/0.47 thf(fact_39_le__antisym,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.21/0.47 => ( ( ord_less_eq_nat @ N @ M )
% 0.21/0.47 => ( M = N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_antisym
% 0.21/0.47 thf(fact_40_nat__le__linear,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.21/0.47 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat_le_linear
% 0.21/0.47 thf(fact_41_Nat_Oex__has__greatest__nat,axiom,
% 0.21/0.47 ! [P5: nat > $o,K: nat,B: nat] :
% 0.21/0.47 ( ( P5 @ K )
% 0.21/0.47 => ( ! [Y: nat] :
% 0.21/0.47 ( ( P5 @ Y )
% 0.21/0.47 => ( ord_less_eq_nat @ Y @ B ) )
% 0.21/0.47 => ? [X: nat] :
% 0.21/0.47 ( ( P5 @ X )
% 0.21/0.47 & ! [Y2: nat] :
% 0.21/0.47 ( ( P5 @ Y2 )
% 0.21/0.47 => ( ord_less_eq_nat @ Y2 @ X ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Nat.ex_has_greatest_nat
% 0.21/0.47 thf(fact_42_add__le__imp__le__right,axiom,
% 0.21/0.47 ! [A: nat,C: nat,B: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.21/0.47 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_le_imp_le_right
% 0.21/0.47 thf(fact_43_add__le__imp__le__left,axiom,
% 0.21/0.47 ! [C: nat,A: nat,B: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.21/0.47 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_le_imp_le_left
% 0.21/0.47 thf(fact_44_le__iff__add,axiom,
% 0.21/0.47 ( ord_less_eq_nat
% 0.21/0.47 = ( ^ [A2: nat,B2: nat] :
% 0.21/0.47 ? [C2: nat] :
% 0.21/0.47 ( B2
% 0.21/0.47 = ( plus_plus_nat @ A2 @ C2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_iff_add
% 0.21/0.47 thf(fact_45_mem__Collect__eq,axiom,
% 0.21/0.47 ! [A: nat,P5: nat > $o] :
% 0.21/0.47 ( ( member_nat @ A @ ( collect_nat @ P5 ) )
% 0.21/0.47 = ( P5 @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 % mem_Collect_eq
% 0.21/0.47 thf(fact_46_Collect__mem__eq,axiom,
% 0.21/0.47 ! [A3: set_nat] :
% 0.21/0.47 ( ( collect_nat
% 0.21/0.47 @ ^ [X2: nat] : ( member_nat @ X2 @ A3 ) )
% 0.21/0.47 = A3 ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mem_eq
% 0.21/0.47 thf(fact_47_Collect__cong,axiom,
% 0.21/0.47 ! [P5: nat > $o,Q: nat > $o] :
% 0.21/0.47 ( ! [X: nat] :
% 0.21/0.47 ( ( P5 @ X )
% 0.21/0.47 = ( Q @ X ) )
% 0.21/0.47 => ( ( collect_nat @ P5 )
% 0.21/0.47 = ( collect_nat @ Q ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_cong
% 0.21/0.47 thf(fact_48_add__right__mono,axiom,
% 0.21/0.47 ! [A: nat,B: nat,C: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.21/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_right_mono
% 0.21/0.47 thf(fact_49_less__eqE,axiom,
% 0.21/0.47 ! [A: nat,B: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.21/0.47 => ~ ! [C3: nat] :
% 0.21/0.47 ( B
% 0.21/0.47 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_eqE
% 0.21/0.47 thf(fact_50_add__left__mono,axiom,
% 0.21/0.47 ! [A: nat,B: nat,C: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.21/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_left_mono
% 0.21/0.47 thf(fact_51_add__mono,axiom,
% 0.21/0.47 ! [A: nat,B: nat,C: nat,D: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.21/0.47 => ( ( ord_less_eq_nat @ C @ D )
% 0.21/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_mono
% 0.21/0.47 thf(fact_52_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.21/0.47 ( ( ( ord_less_eq_nat @ I @ J )
% 0.21/0.47 & ( ord_less_eq_nat @ K @ L ) )
% 0.21/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_mono_thms_linordered_semiring(1)
% 0.21/0.47 thf(fact_53_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.21/0.47 ( ( ( I = J )
% 0.21/0.47 & ( ord_less_eq_nat @ K @ L ) )
% 0.21/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_mono_thms_linordered_semiring(2)
% 0.21/0.47 thf(fact_54_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.21/0.47 ( ( ( ord_less_eq_nat @ I @ J )
% 0.21/0.47 & ( K = L ) )
% 0.21/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_mono_thms_linordered_semiring(3)
% 0.21/0.47 thf(fact_55_less__mono__imp__le__mono,axiom,
% 0.21/0.47 ! [F: nat > nat,I: nat,J: nat] :
% 0.21/0.47 ( ! [I2: nat,J2: nat] :
% 0.21/0.47 ( ( ord_less_nat @ I2 @ J2 )
% 0.21/0.47 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 0.21/0.47 => ( ( ord_less_eq_nat @ I @ J )
% 0.21/0.47 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_mono_imp_le_mono
% 0.21/0.47 thf(fact_56_le__neq__implies__less,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.21/0.47 => ( ( M != N )
% 0.21/0.47 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_neq_implies_less
% 0.21/0.47 thf(fact_57_less__or__eq__imp__le,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ( ord_less_nat @ M @ N )
% 0.21/0.47 | ( M = N ) )
% 0.21/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_or_eq_imp_le
% 0.21/0.47 thf(fact_58_le__eq__less__or__eq,axiom,
% 0.21/0.47 ( ord_less_eq_nat
% 0.21/0.47 = ( ^ [M2: nat,N2: nat] :
% 0.21/0.47 ( ( ord_less_nat @ M2 @ N2 )
% 0.21/0.47 | ( M2 = N2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_eq_less_or_eq
% 0.21/0.47 thf(fact_59_less__imp__le__nat,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_nat @ M @ N )
% 0.21/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_imp_le_nat
% 0.21/0.47 thf(fact_60_nat__less__le,axiom,
% 0.21/0.47 ( ord_less_nat
% 0.21/0.47 = ( ^ [M2: nat,N2: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.21/0.47 & ( M2 != N2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat_less_le
% 0.21/0.47 thf(fact_61_nat__le__iff__add,axiom,
% 0.21/0.47 ( ord_less_eq_nat
% 0.21/0.47 = ( ^ [M2: nat,N2: nat] :
% 0.21/0.47 ? [K2: nat] :
% 0.21/0.47 ( N2
% 0.21/0.47 = ( plus_plus_nat @ M2 @ K2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat_le_iff_add
% 0.21/0.47 thf(fact_62_trans__le__add2,axiom,
% 0.21/0.47 ! [I: nat,J: nat,M: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.21/0.47 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % trans_le_add2
% 0.21/0.47 thf(fact_63_trans__le__add1,axiom,
% 0.21/0.47 ! [I: nat,J: nat,M: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.21/0.47 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % trans_le_add1
% 0.21/0.47 thf(fact_64_add__le__mono1,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.21/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_le_mono1
% 0.21/0.47 thf(fact_65_add__le__mono,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.21/0.47 => ( ( ord_less_eq_nat @ K @ L )
% 0.21/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_le_mono
% 0.21/0.47 thf(fact_66_le__Suc__ex,axiom,
% 0.21/0.47 ! [K: nat,L: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ K @ L )
% 0.21/0.47 => ? [N3: nat] :
% 0.21/0.47 ( L
% 0.21/0.47 = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_Suc_ex
% 0.21/0.47 thf(fact_67_add__leD2,axiom,
% 0.21/0.47 ! [M: nat,K: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.21/0.47 => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_leD2
% 0.21/0.47 thf(fact_68_add__leD1,axiom,
% 0.21/0.47 ! [M: nat,K: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.21/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_leD1
% 0.21/0.47 thf(fact_69_le__add2,axiom,
% 0.21/0.47 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_add2
% 0.21/0.47 thf(fact_70_le__add1,axiom,
% 0.21/0.47 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_add1
% 0.21/0.47 thf(fact_71_add__leE,axiom,
% 0.21/0.47 ! [M: nat,K: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.21/0.47 => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.21/0.47 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_leE
% 0.21/0.47 thf(fact_72_add__right__imp__eq,axiom,
% 0.21/0.47 ! [B: nat,A: nat,C: nat] :
% 0.21/0.47 ( ( ( plus_plus_nat @ B @ A )
% 0.21/0.47 = ( plus_plus_nat @ C @ A ) )
% 0.21/0.47 => ( B = C ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_right_imp_eq
% 0.21/0.47 thf(fact_73_add__left__imp__eq,axiom,
% 0.21/0.47 ! [A: nat,B: nat,C: nat] :
% 0.21/0.47 ( ( ( plus_plus_nat @ A @ B )
% 0.21/0.47 = ( plus_plus_nat @ A @ C ) )
% 0.21/0.47 => ( B = C ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_left_imp_eq
% 0.21/0.47 thf(fact_74_add_Oleft__commute,axiom,
% 0.21/0.47 ! [B: nat,A: nat,C: nat] :
% 0.21/0.47 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 0.21/0.47 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add.left_commute
% 0.21/0.47 thf(fact_75_add_Ocommute,axiom,
% 0.21/0.47 ( plus_plus_nat
% 0.21/0.47 = ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add.commute
% 0.21/0.47 thf(fact_76_add_Oassoc,axiom,
% 0.21/0.47 ! [A: nat,B: nat,C: nat] :
% 0.21/0.47 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.21/0.47 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add.assoc
% 0.21/0.47 thf(fact_77_group__cancel_Oadd2,axiom,
% 0.21/0.47 ! [B3: nat,K: nat,B: nat,A: nat] :
% 0.21/0.47 ( ( B3
% 0.21/0.47 = ( plus_plus_nat @ K @ B ) )
% 0.21/0.47 => ( ( plus_plus_nat @ A @ B3 )
% 0.21/0.47 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % group_cancel.add2
% 0.21/0.47 thf(fact_78_group__cancel_Oadd1,axiom,
% 0.21/0.47 ! [A3: nat,K: nat,A: nat,B: nat] :
% 0.21/0.47 ( ( A3
% 0.21/0.47 = ( plus_plus_nat @ K @ A ) )
% 0.21/0.47 => ( ( plus_plus_nat @ A3 @ B )
% 0.21/0.47 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % group_cancel.add1
% 0.21/0.47 thf(fact_79_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.21/0.47 ( ( ( I = J )
% 0.21/0.47 & ( K = L ) )
% 0.21/0.47 => ( ( plus_plus_nat @ I @ K )
% 0.21/0.47 = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_mono_thms_linordered_semiring(4)
% 0.21/0.47 thf(fact_80_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.21/0.47 ! [A: nat,B: nat,C: nat] :
% 0.21/0.47 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.21/0.47 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ab_semigroup_add_class.add_ac(1)
% 0.21/0.47 thf(fact_81_linorder__neqE__nat,axiom,
% 0.21/0.47 ! [X3: nat,Y3: nat] :
% 0.21/0.47 ( ( X3 != Y3 )
% 0.21/0.47 => ( ~ ( ord_less_nat @ X3 @ Y3 )
% 0.21/0.47 => ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % linorder_neqE_nat
% 0.21/0.47 thf(fact_82_infinite__descent,axiom,
% 0.21/0.47 ! [P5: nat > $o,N: nat] :
% 0.21/0.47 ( ! [N3: nat] :
% 0.21/0.47 ( ~ ( P5 @ N3 )
% 0.21/0.47 => ? [M3: nat] :
% 0.21/0.47 ( ( ord_less_nat @ M3 @ N3 )
% 0.21/0.47 & ~ ( P5 @ M3 ) ) )
% 0.21/0.47 => ( P5 @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % infinite_descent
% 0.21/0.47 thf(fact_83_nat__less__induct,axiom,
% 0.21/0.47 ! [P5: nat > $o,N: nat] :
% 0.21/0.47 ( ! [N3: nat] :
% 0.21/0.47 ( ! [M3: nat] :
% 0.21/0.47 ( ( ord_less_nat @ M3 @ N3 )
% 0.21/0.47 => ( P5 @ M3 ) )
% 0.21/0.47 => ( P5 @ N3 ) )
% 0.21/0.47 => ( P5 @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat_less_induct
% 0.21/0.47 thf(fact_84_less__irrefl__nat,axiom,
% 0.21/0.47 ! [N: nat] :
% 0.21/0.47 ~ ( ord_less_nat @ N @ N ) ).
% 0.21/0.47
% 0.21/0.47 % less_irrefl_nat
% 0.21/0.47 thf(fact_85_less__not__refl3,axiom,
% 0.21/0.47 ! [S: nat,T: nat] :
% 0.21/0.47 ( ( ord_less_nat @ S @ T )
% 0.21/0.47 => ( S != T ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_not_refl3
% 0.21/0.47 thf(fact_86_less__not__refl2,axiom,
% 0.21/0.47 ! [N: nat,M: nat] :
% 0.21/0.47 ( ( ord_less_nat @ N @ M )
% 0.21/0.47 => ( M != N ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_not_refl2
% 0.21/0.47 thf(fact_87_less__not__refl,axiom,
% 0.21/0.47 ! [N: nat] :
% 0.21/0.47 ~ ( ord_less_nat @ N @ N ) ).
% 0.21/0.47
% 0.21/0.47 % less_not_refl
% 0.21/0.47 thf(fact_88_nat__neq__iff,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( M != N )
% 0.21/0.47 = ( ( ord_less_nat @ M @ N )
% 0.21/0.47 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat_neq_iff
% 0.21/0.47 thf(fact_89_size__neq__size__imp__neq,axiom,
% 0.21/0.47 ! [X3: list_P559422087at_nat,Y3: list_P559422087at_nat] :
% 0.21/0.47 ( ( ( size_s1990949619at_nat @ X3 )
% 0.21/0.47 != ( size_s1990949619at_nat @ Y3 ) )
% 0.21/0.47 => ( X3 != Y3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % size_neq_size_imp_neq
% 0.21/0.47 thf(fact_90_add__less__le__mono,axiom,
% 0.21/0.47 ! [A: nat,B: nat,C: nat,D: nat] :
% 0.21/0.47 ( ( ord_less_nat @ A @ B )
% 0.21/0.47 => ( ( ord_less_eq_nat @ C @ D )
% 0.21/0.47 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_less_le_mono
% 0.21/0.47 thf(fact_91_add__le__less__mono,axiom,
% 0.21/0.47 ! [A: nat,B: nat,C: nat,D: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.21/0.47 => ( ( ord_less_nat @ C @ D )
% 0.21/0.47 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_le_less_mono
% 0.21/0.47 thf(fact_92_add__mono__thms__linordered__field_I3_J,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.21/0.47 ( ( ( ord_less_nat @ I @ J )
% 0.21/0.47 & ( ord_less_eq_nat @ K @ L ) )
% 0.21/0.47 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_mono_thms_linordered_field(3)
% 0.21/0.47 thf(fact_93_add__mono__thms__linordered__field_I4_J,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.21/0.47 ( ( ( ord_less_eq_nat @ I @ J )
% 0.21/0.47 & ( ord_less_nat @ K @ L ) )
% 0.21/0.47 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_mono_thms_linordered_field(4)
% 0.21/0.47 thf(fact_94_mono__nat__linear__lb,axiom,
% 0.21/0.47 ! [F: nat > nat,M: nat,K: nat] :
% 0.21/0.47 ( ! [M4: nat,N3: nat] :
% 0.21/0.47 ( ( ord_less_nat @ M4 @ N3 )
% 0.21/0.47 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 0.21/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % mono_nat_linear_lb
% 0.21/0.47 thf(fact_95_add__less__imp__less__right,axiom,
% 0.21/0.47 ! [A: nat,C: nat,B: nat] :
% 0.21/0.47 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.21/0.47 => ( ord_less_nat @ A @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_less_imp_less_right
% 0.21/0.47 thf(fact_96_add__less__imp__less__left,axiom,
% 0.21/0.47 ! [C: nat,A: nat,B: nat] :
% 0.21/0.47 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.21/0.47 => ( ord_less_nat @ A @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_less_imp_less_left
% 0.21/0.47 thf(fact_97_add__strict__right__mono,axiom,
% 0.21/0.47 ! [A: nat,B: nat,C: nat] :
% 0.21/0.47 ( ( ord_less_nat @ A @ B )
% 0.21/0.47 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_strict_right_mono
% 0.21/0.47 thf(fact_98_add__strict__left__mono,axiom,
% 0.21/0.47 ! [A: nat,B: nat,C: nat] :
% 0.21/0.47 ( ( ord_less_nat @ A @ B )
% 0.21/0.47 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_strict_left_mono
% 0.21/0.47 thf(fact_99_add__strict__mono,axiom,
% 0.21/0.47 ! [A: nat,B: nat,C: nat,D: nat] :
% 0.21/0.47 ( ( ord_less_nat @ A @ B )
% 0.21/0.47 => ( ( ord_less_nat @ C @ D )
% 0.21/0.47 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_strict_mono
% 0.21/0.47 thf(fact_100_add__mono__thms__linordered__field_I1_J,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.21/0.47 ( ( ( ord_less_nat @ I @ J )
% 0.21/0.47 & ( K = L ) )
% 0.21/0.47 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_mono_thms_linordered_field(1)
% 0.21/0.47 thf(fact_101_add__mono__thms__linordered__field_I2_J,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.21/0.47 ( ( ( I = J )
% 0.21/0.47 & ( ord_less_nat @ K @ L ) )
% 0.21/0.47 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_mono_thms_linordered_field(2)
% 0.21/0.47 thf(fact_102_add__mono__thms__linordered__field_I5_J,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.21/0.47 ( ( ( ord_less_nat @ I @ J )
% 0.21/0.47 & ( ord_less_nat @ K @ L ) )
% 0.21/0.47 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_mono_thms_linordered_field(5)
% 0.21/0.47 thf(fact_103_less__add__eq__less,axiom,
% 0.21/0.47 ! [K: nat,L: nat,M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_nat @ K @ L )
% 0.21/0.47 => ( ( ( plus_plus_nat @ M @ L )
% 0.21/0.47 = ( plus_plus_nat @ K @ N ) )
% 0.21/0.47 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_add_eq_less
% 0.21/0.47 thf(fact_104_trans__less__add2,axiom,
% 0.21/0.47 ! [I: nat,J: nat,M: nat] :
% 0.21/0.47 ( ( ord_less_nat @ I @ J )
% 0.21/0.47 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % trans_less_add2
% 0.21/0.47 thf(fact_105_trans__less__add1,axiom,
% 0.21/0.47 ! [I: nat,J: nat,M: nat] :
% 0.21/0.47 ( ( ord_less_nat @ I @ J )
% 0.21/0.47 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % trans_less_add1
% 0.21/0.47 thf(fact_106_add__less__mono1,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat] :
% 0.21/0.47 ( ( ord_less_nat @ I @ J )
% 0.21/0.47 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_less_mono1
% 0.21/0.47 thf(fact_107_not__add__less2,axiom,
% 0.21/0.47 ! [J: nat,I: nat] :
% 0.21/0.47 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 0.21/0.47
% 0.21/0.47 % not_add_less2
% 0.21/0.47 thf(fact_108_not__add__less1,axiom,
% 0.21/0.47 ! [I: nat,J: nat] :
% 0.21/0.47 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 0.21/0.47
% 0.21/0.47 % not_add_less1
% 0.21/0.47 thf(fact_109_add__less__mono,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.21/0.47 ( ( ord_less_nat @ I @ J )
% 0.21/0.47 => ( ( ord_less_nat @ K @ L )
% 0.21/0.47 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_less_mono
% 0.21/0.47 thf(fact_110_add__lessD1,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat] :
% 0.21/0.47 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.21/0.47 => ( ord_less_nat @ I @ K ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_lessD1
% 0.21/0.47 thf(fact_111_reachableNodes__def,axiom,
% 0.21/0.47 ! [U: nat] :
% 0.21/0.47 ( ( reacha1693770334pacity @ c @ U )
% 0.21/0.47 = ( collect_nat @ ( connected_capacity @ c @ U ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % reachableNodes_def
% 0.21/0.47 thf(fact_112_min__dist__def,axiom,
% 0.21/0.47 ! [V: nat,V3: nat] :
% 0.21/0.47 ( ( min_dist_capacity @ c @ V @ V3 )
% 0.21/0.47 = ( ord_Least_nat
% 0.21/0.47 @ ^ [D4: nat] : ( dist_capacity @ c @ V @ D4 @ V3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % min_dist_def
% 0.21/0.47 thf(fact_113_Graph_OisShortestPath__min__dist__def,axiom,
% 0.21/0.47 ( isShor1936442771pacity
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > capacity,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 0.21/0.47 ( ( isPath_capacity @ C2 @ U2 @ P @ V4 )
% 0.21/0.47 & ( ( size_s1990949619at_nat @ P )
% 0.21/0.47 = ( min_dist_capacity @ C2 @ U2 @ V4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.isShortestPath_min_dist_def
% 0.21/0.47 thf(fact_114_Graph_OisShortestPath__min__dist__def,axiom,
% 0.21/0.47 ( isShortestPath_a
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 0.21/0.47 ( ( isPath_a @ C2 @ U2 @ P @ V4 )
% 0.21/0.47 & ( ( size_s1990949619at_nat @ P )
% 0.21/0.47 = ( min_dist_a @ C2 @ U2 @ V4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.isShortestPath_min_dist_def
% 0.21/0.47 thf(fact_115_Graph_OisShortestPath__def,axiom,
% 0.21/0.47 ( isShor1936442771pacity
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > capacity,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 0.21/0.47 ( ( isPath_capacity @ C2 @ U2 @ P @ V4 )
% 0.21/0.47 & ! [P4: list_P559422087at_nat] :
% 0.21/0.47 ( ( isPath_capacity @ C2 @ U2 @ P4 @ V4 )
% 0.21/0.47 => ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P ) @ ( size_s1990949619at_nat @ P4 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.isShortestPath_def
% 0.21/0.47 thf(fact_116_Graph_OisShortestPath__def,axiom,
% 0.21/0.47 ( isShortestPath_a
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 0.21/0.47 ( ( isPath_a @ C2 @ U2 @ P @ V4 )
% 0.21/0.47 & ! [P4: list_P559422087at_nat] :
% 0.21/0.47 ( ( isPath_a @ C2 @ U2 @ P4 @ V4 )
% 0.21/0.47 => ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P ) @ ( size_s1990949619at_nat @ P4 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.isShortestPath_def
% 0.21/0.47 thf(fact_117_Graph_Omin__distI2,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,V: nat,V3: nat,Q: nat > $o] :
% 0.21/0.47 ( ( connected_capacity @ C @ V @ V3 )
% 0.21/0.47 => ( ! [D6: nat] :
% 0.21/0.47 ( ( dist_capacity @ C @ V @ D6 @ V3 )
% 0.21/0.47 => ( ! [D7: nat] :
% 0.21/0.47 ( ( dist_capacity @ C @ V @ D7 @ V3 )
% 0.21/0.47 => ( ord_less_eq_nat @ D6 @ D7 ) )
% 0.21/0.47 => ( Q @ D6 ) ) )
% 0.21/0.47 => ( Q @ ( min_dist_capacity @ C @ V @ V3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_distI2
% 0.21/0.47 thf(fact_118_Graph_Omin__distI2,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,V: nat,V3: nat,Q: nat > $o] :
% 0.21/0.47 ( ( connected_a @ C @ V @ V3 )
% 0.21/0.47 => ( ! [D6: nat] :
% 0.21/0.47 ( ( dist_a @ C @ V @ D6 @ V3 )
% 0.21/0.47 => ( ! [D7: nat] :
% 0.21/0.47 ( ( dist_a @ C @ V @ D7 @ V3 )
% 0.21/0.47 => ( ord_less_eq_nat @ D6 @ D7 ) )
% 0.21/0.47 => ( Q @ D6 ) ) )
% 0.21/0.47 => ( Q @ ( min_dist_a @ C @ V @ V3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_distI2
% 0.21/0.47 thf(fact_119_isShortestPath__alt,axiom,
% 0.21/0.47 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.21/0.47 ( ( isShor1936442771pacity @ c @ U @ P2 @ V )
% 0.21/0.47 = ( ( isSimp1359852763pacity @ c @ U @ P2 @ V )
% 0.21/0.47 & ( ( size_s1990949619at_nat @ P2 )
% 0.21/0.47 = ( min_dist_capacity @ c @ U @ V ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % isShortestPath_alt
% 0.21/0.47 thf(fact_120_Graph_Odist__def,axiom,
% 0.21/0.47 ( dist_capacity
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > capacity,V4: nat,D4: nat,V5: nat] :
% 0.21/0.47 ? [P: list_P559422087at_nat] :
% 0.21/0.47 ( ( isPath_capacity @ C2 @ V4 @ P @ V5 )
% 0.21/0.47 & ( ( size_s1990949619at_nat @ P )
% 0.21/0.47 = D4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.dist_def
% 0.21/0.47 thf(fact_121_Graph_Odist__def,axiom,
% 0.21/0.47 ( dist_a
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > a,V4: nat,D4: nat,V5: nat] :
% 0.21/0.47 ? [P: list_P559422087at_nat] :
% 0.21/0.47 ( ( isPath_a @ C2 @ V4 @ P @ V5 )
% 0.21/0.47 & ( ( size_s1990949619at_nat @ P )
% 0.21/0.47 = D4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.dist_def
% 0.21/0.47 thf(fact_122_Graph_OisPath__distD,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.21/0.47 ( ( isPath_capacity @ C @ U @ P2 @ V )
% 0.21/0.47 => ( dist_capacity @ C @ U @ ( size_s1990949619at_nat @ P2 ) @ V ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.isPath_distD
% 0.21/0.47 thf(fact_123_Graph_OisPath__distD,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.21/0.47 ( ( isPath_a @ C @ U @ P2 @ V )
% 0.21/0.47 => ( dist_a @ C @ U @ ( size_s1990949619at_nat @ P2 ) @ V ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.isPath_distD
% 0.21/0.47 thf(fact_124_Graph_Omin__dist__is__dist,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,V: nat,V3: nat] :
% 0.21/0.47 ( ( connected_capacity @ C @ V @ V3 )
% 0.21/0.47 => ( dist_capacity @ C @ V @ ( min_dist_capacity @ C @ V @ V3 ) @ V3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist_is_dist
% 0.21/0.47 thf(fact_125_Graph_Omin__dist__is__dist,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,V: nat,V3: nat] :
% 0.21/0.47 ( ( connected_a @ C @ V @ V3 )
% 0.21/0.47 => ( dist_a @ C @ V @ ( min_dist_a @ C @ V @ V3 ) @ V3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist_is_dist
% 0.21/0.47 thf(fact_126_Graph_Omin__dist__split_I1_J,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.21/0.47 ( ( dist_capacity @ C @ U @ D1 @ W )
% 0.21/0.47 => ( ( dist_capacity @ C @ W @ D2 @ V )
% 0.21/0.47 => ( ( ( min_dist_capacity @ C @ U @ V )
% 0.21/0.47 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.21/0.47 => ( ( min_dist_capacity @ C @ U @ W )
% 0.21/0.47 = D1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist_split(1)
% 0.21/0.47 thf(fact_127_Graph_Omin__dist__split_I1_J,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.21/0.47 ( ( dist_a @ C @ U @ D1 @ W )
% 0.21/0.47 => ( ( dist_a @ C @ W @ D2 @ V )
% 0.21/0.47 => ( ( ( min_dist_a @ C @ U @ V )
% 0.21/0.47 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.21/0.47 => ( ( min_dist_a @ C @ U @ W )
% 0.21/0.47 = D1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist_split(1)
% 0.21/0.47 thf(fact_128_isSPath__pathLE,axiom,
% 0.21/0.47 ! [S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.21/0.47 ( ( isPath_capacity @ c @ S @ P2 @ T )
% 0.21/0.47 => ? [P6: list_P559422087at_nat] : ( isSimp1359852763pacity @ c @ S @ P6 @ T ) ) ).
% 0.21/0.47
% 0.21/0.47 % isSPath_pathLE
% 0.21/0.47 thf(fact_129_shortestPath__is__simple,axiom,
% 0.21/0.47 ! [S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.21/0.47 ( ( isShor1936442771pacity @ c @ S @ P2 @ T )
% 0.21/0.47 => ( isSimp1359852763pacity @ c @ S @ P2 @ T ) ) ).
% 0.21/0.47
% 0.21/0.47 % shortestPath_is_simple
% 0.21/0.47 thf(fact_130_Graph_OreachableNodes_Ocong,axiom,
% 0.21/0.47 reacha1693770334pacity = reacha1693770334pacity ).
% 0.21/0.47
% 0.21/0.47 % Graph.reachableNodes.cong
% 0.21/0.47 thf(fact_131_Graph_OreachableNodes_Ocong,axiom,
% 0.21/0.47 reachableNodes_a = reachableNodes_a ).
% 0.21/0.47
% 0.21/0.47 % Graph.reachableNodes.cong
% 0.21/0.47 thf(fact_132_Graph_OisSimplePath_Ocong,axiom,
% 0.21/0.47 isSimp1359852763pacity = isSimp1359852763pacity ).
% 0.21/0.47
% 0.21/0.47 % Graph.isSimplePath.cong
% 0.21/0.47 thf(fact_133_Graph_OisSimplePath_Ocong,axiom,
% 0.21/0.47 isSimplePath_a = isSimplePath_a ).
% 0.21/0.47
% 0.21/0.47 % Graph.isSimplePath.cong
% 0.21/0.47 thf(fact_134_Graph_OisSPath__pathLE,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.21/0.47 ( ( isPath_capacity @ C @ S @ P2 @ T )
% 0.21/0.47 => ? [P6: list_P559422087at_nat] : ( isSimp1359852763pacity @ C @ S @ P6 @ T ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.isSPath_pathLE
% 0.21/0.47 thf(fact_135_Graph_OisSPath__pathLE,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.21/0.47 ( ( isPath_a @ C @ S @ P2 @ T )
% 0.21/0.47 => ? [P6: list_P559422087at_nat] : ( isSimplePath_a @ C @ S @ P6 @ T ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.isSPath_pathLE
% 0.21/0.47 thf(fact_136_Graph_OshortestPath__is__simple,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.21/0.47 ( ( isShor1936442771pacity @ C @ S @ P2 @ T )
% 0.21/0.47 => ( isSimp1359852763pacity @ C @ S @ P2 @ T ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.shortestPath_is_simple
% 0.21/0.47 thf(fact_137_Graph_OshortestPath__is__simple,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.21/0.47 ( ( isShortestPath_a @ C @ S @ P2 @ T )
% 0.21/0.47 => ( isSimplePath_a @ C @ S @ P2 @ T ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.shortestPath_is_simple
% 0.21/0.47 thf(fact_138_Graph_OreachableNodes__def,axiom,
% 0.21/0.47 ( reacha1693770334pacity
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > capacity,U2: nat] : ( collect_nat @ ( connected_capacity @ C2 @ U2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.reachableNodes_def
% 0.21/0.47 thf(fact_139_Graph_OreachableNodes__def,axiom,
% 0.21/0.47 ( reachableNodes_a
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > a,U2: nat] : ( collect_nat @ ( connected_a @ C2 @ U2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.reachableNodes_def
% 0.21/0.47 thf(fact_140_Graph_Omin__dist__def,axiom,
% 0.21/0.47 ( min_dist_capacity
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > capacity,V4: nat,V5: nat] :
% 0.21/0.47 ( ord_Least_nat
% 0.21/0.47 @ ^ [D4: nat] : ( dist_capacity @ C2 @ V4 @ D4 @ V5 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist_def
% 0.21/0.47 thf(fact_141_Graph_Omin__dist__def,axiom,
% 0.21/0.47 ( min_dist_a
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > a,V4: nat,V5: nat] :
% 0.21/0.47 ( ord_Least_nat
% 0.21/0.47 @ ^ [D4: nat] : ( dist_a @ C2 @ V4 @ D4 @ V5 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist_def
% 0.21/0.47 thf(fact_142_Graph_OisShortestPath__alt,axiom,
% 0.21/0.47 ( isShor1936442771pacity
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > capacity,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 0.21/0.47 ( ( isSimp1359852763pacity @ C2 @ U2 @ P @ V4 )
% 0.21/0.47 & ( ( size_s1990949619at_nat @ P )
% 0.21/0.47 = ( min_dist_capacity @ C2 @ U2 @ V4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.isShortestPath_alt
% 0.21/0.47 thf(fact_143_Graph_OisShortestPath__alt,axiom,
% 0.21/0.47 ( isShortestPath_a
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 0.21/0.47 ( ( isSimplePath_a @ C2 @ U2 @ P @ V4 )
% 0.21/0.47 & ( ( size_s1990949619at_nat @ P )
% 0.21/0.47 = ( min_dist_a @ C2 @ U2 @ V4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.isShortestPath_alt
% 0.21/0.47 thf(fact_144_Graph_OisPath_Ocong,axiom,
% 0.21/0.47 isPath_capacity = isPath_capacity ).
% 0.21/0.47
% 0.21/0.47 % Graph.isPath.cong
% 0.21/0.47 thf(fact_145_Graph_OisPath_Ocong,axiom,
% 0.21/0.47 isPath_a = isPath_a ).
% 0.21/0.47
% 0.21/0.47 % Graph.isPath.cong
% 0.21/0.47 thf(fact_146_Graph_Omin__dist_Ocong,axiom,
% 0.21/0.47 min_dist_capacity = min_dist_capacity ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist.cong
% 0.21/0.47 thf(fact_147_Graph_Omin__dist_Ocong,axiom,
% 0.21/0.47 min_dist_a = min_dist_a ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist.cong
% 0.21/0.47 thf(fact_148_Graph_Oconnected__refl,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,V: nat] : ( connected_capacity @ C @ V @ V ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.connected_refl
% 0.21/0.47 thf(fact_149_Graph_Oconnected__refl,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,V: nat] : ( connected_a @ C @ V @ V ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.connected_refl
% 0.21/0.47 thf(fact_150_Graph_Oconnected_Ocong,axiom,
% 0.21/0.47 connected_capacity = connected_capacity ).
% 0.21/0.47
% 0.21/0.47 % Graph.connected.cong
% 0.21/0.47 thf(fact_151_Graph_Oconnected_Ocong,axiom,
% 0.21/0.47 connected_a = connected_a ).
% 0.21/0.47
% 0.21/0.47 % Graph.connected.cong
% 0.21/0.47 thf(fact_152_Graph_Odist_Ocong,axiom,
% 0.21/0.47 dist_capacity = dist_capacity ).
% 0.21/0.47
% 0.21/0.47 % Graph.dist.cong
% 0.21/0.47 thf(fact_153_Graph_Odist_Ocong,axiom,
% 0.21/0.47 dist_a = dist_a ).
% 0.21/0.47
% 0.21/0.47 % Graph.dist.cong
% 0.21/0.47 thf(fact_154_Graph_OisShortestPath_Ocong,axiom,
% 0.21/0.47 isShor1936442771pacity = isShor1936442771pacity ).
% 0.21/0.47
% 0.21/0.47 % Graph.isShortestPath.cong
% 0.21/0.47 thf(fact_155_Graph_OisShortestPath_Ocong,axiom,
% 0.21/0.47 isShortestPath_a = isShortestPath_a ).
% 0.21/0.47
% 0.21/0.47 % Graph.isShortestPath.cong
% 0.21/0.47 thf(fact_156_Graph_Odist__trans,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.21/0.47 ( ( dist_capacity @ C @ U @ D1 @ W )
% 0.21/0.47 => ( ( dist_capacity @ C @ W @ D2 @ V )
% 0.21/0.47 => ( dist_capacity @ C @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.dist_trans
% 0.21/0.47 thf(fact_157_Graph_Odist__trans,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.21/0.47 ( ( dist_a @ C @ U @ D1 @ W )
% 0.21/0.47 => ( ( dist_a @ C @ W @ D2 @ V )
% 0.21/0.47 => ( dist_a @ C @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.dist_trans
% 0.21/0.47 thf(fact_158_Graph_Oconnected__def,axiom,
% 0.21/0.47 ( connected_capacity
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > capacity,U2: nat,V4: nat] :
% 0.21/0.47 ? [P: list_P559422087at_nat] : ( isPath_capacity @ C2 @ U2 @ P @ V4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.connected_def
% 0.21/0.47 thf(fact_159_Graph_Oconnected__def,axiom,
% 0.21/0.47 ( connected_a
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > a,U2: nat,V4: nat] :
% 0.21/0.47 ? [P: list_P559422087at_nat] : ( isPath_a @ C2 @ U2 @ P @ V4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.connected_def
% 0.21/0.47 thf(fact_160_Graph_OshortestPath__is__path,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.21/0.47 ( ( isShor1936442771pacity @ C @ U @ P2 @ V )
% 0.21/0.47 => ( isPath_capacity @ C @ U @ P2 @ V ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.shortestPath_is_path
% 0.21/0.47 thf(fact_161_Graph_OshortestPath__is__path,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.21/0.47 ( ( isShortestPath_a @ C @ U @ P2 @ V )
% 0.21/0.47 => ( isPath_a @ C @ U @ P2 @ V ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.shortestPath_is_path
% 0.21/0.47 thf(fact_162_Graph_Oconnected__by__dist,axiom,
% 0.21/0.47 ( connected_capacity
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > capacity,V4: nat,V5: nat] :
% 0.21/0.47 ? [D4: nat] : ( dist_capacity @ C2 @ V4 @ D4 @ V5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.connected_by_dist
% 0.21/0.47 thf(fact_163_Graph_Oconnected__by__dist,axiom,
% 0.21/0.47 ( connected_a
% 0.21/0.47 = ( ^ [C2: product_prod_nat_nat > a,V4: nat,V5: nat] :
% 0.21/0.47 ? [D4: nat] : ( dist_a @ C2 @ V4 @ D4 @ V5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.connected_by_dist
% 0.21/0.47 thf(fact_164_Graph_Oconnected__distI,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,V: nat,D: nat,V3: nat] :
% 0.21/0.47 ( ( dist_capacity @ C @ V @ D @ V3 )
% 0.21/0.47 => ( connected_capacity @ C @ V @ V3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.connected_distI
% 0.21/0.47 thf(fact_165_Graph_Oconnected__distI,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
% 0.21/0.47 ( ( dist_a @ C @ V @ D @ V3 )
% 0.21/0.47 => ( connected_a @ C @ V @ V3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.connected_distI
% 0.21/0.47 thf(fact_166_Graph_Oobtain__shortest__path,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,U: nat,V: nat] :
% 0.21/0.47 ( ( connected_capacity @ C @ U @ V )
% 0.21/0.47 => ~ ! [P3: list_P559422087at_nat] :
% 0.21/0.47 ~ ( isShor1936442771pacity @ C @ U @ P3 @ V ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.obtain_shortest_path
% 0.21/0.47 thf(fact_167_Graph_Oobtain__shortest__path,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,U: nat,V: nat] :
% 0.21/0.47 ( ( connected_a @ C @ U @ V )
% 0.21/0.47 => ~ ! [P3: list_P559422087at_nat] :
% 0.21/0.47 ~ ( isShortestPath_a @ C @ U @ P3 @ V ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.obtain_shortest_path
% 0.21/0.47 thf(fact_168_Graph_Omin__dist__less,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,Src: nat,V: nat,D: nat,D3: nat] :
% 0.21/0.47 ( ( connected_capacity @ C @ Src @ V )
% 0.21/0.47 => ( ( ( min_dist_capacity @ C @ Src @ V )
% 0.21/0.47 = D )
% 0.21/0.47 => ( ( ord_less_nat @ D3 @ D )
% 0.21/0.47 => ? [V2: nat] :
% 0.21/0.47 ( ( connected_capacity @ C @ Src @ V2 )
% 0.21/0.47 & ( ( min_dist_capacity @ C @ Src @ V2 )
% 0.21/0.47 = D3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist_less
% 0.21/0.47 thf(fact_169_Graph_Omin__dist__less,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,Src: nat,V: nat,D: nat,D3: nat] :
% 0.21/0.47 ( ( connected_a @ C @ Src @ V )
% 0.21/0.47 => ( ( ( min_dist_a @ C @ Src @ V )
% 0.21/0.47 = D )
% 0.21/0.47 => ( ( ord_less_nat @ D3 @ D )
% 0.21/0.47 => ? [V2: nat] :
% 0.21/0.47 ( ( connected_a @ C @ Src @ V2 )
% 0.21/0.47 & ( ( min_dist_a @ C @ Src @ V2 )
% 0.21/0.47 = D3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist_less
% 0.21/0.47 thf(fact_170_Graph_Omin__dist__le,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,Src: nat,V: nat,D3: nat] :
% 0.21/0.47 ( ( connected_capacity @ C @ Src @ V )
% 0.21/0.47 => ( ( ord_less_eq_nat @ D3 @ ( min_dist_capacity @ C @ Src @ V ) )
% 0.21/0.47 => ? [V2: nat] :
% 0.21/0.47 ( ( connected_capacity @ C @ Src @ V2 )
% 0.21/0.47 & ( ( min_dist_capacity @ C @ Src @ V2 )
% 0.21/0.47 = D3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist_le
% 0.21/0.47 thf(fact_171_Graph_Omin__dist__le,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,Src: nat,V: nat,D3: nat] :
% 0.21/0.47 ( ( connected_a @ C @ Src @ V )
% 0.21/0.47 => ( ( ord_less_eq_nat @ D3 @ ( min_dist_a @ C @ Src @ V ) )
% 0.21/0.47 => ? [V2: nat] :
% 0.21/0.47 ( ( connected_a @ C @ Src @ V2 )
% 0.21/0.47 & ( ( min_dist_a @ C @ Src @ V2 )
% 0.21/0.47 = D3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist_le
% 0.21/0.47 thf(fact_172_Graph_Omin__distI__eq,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,V: nat,D: nat,V3: nat] :
% 0.21/0.47 ( ( dist_capacity @ C @ V @ D @ V3 )
% 0.21/0.47 => ( ! [D5: nat] :
% 0.21/0.47 ( ( dist_capacity @ C @ V @ D5 @ V3 )
% 0.21/0.47 => ( ord_less_eq_nat @ D @ D5 ) )
% 0.21/0.47 => ( ( min_dist_capacity @ C @ V @ V3 )
% 0.21/0.47 = D ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_distI_eq
% 0.21/0.47 thf(fact_173_Graph_Omin__distI__eq,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
% 0.21/0.47 ( ( dist_a @ C @ V @ D @ V3 )
% 0.21/0.47 => ( ! [D5: nat] :
% 0.21/0.47 ( ( dist_a @ C @ V @ D5 @ V3 )
% 0.21/0.47 => ( ord_less_eq_nat @ D @ D5 ) )
% 0.21/0.47 => ( ( min_dist_a @ C @ V @ V3 )
% 0.21/0.47 = D ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_distI_eq
% 0.21/0.47 thf(fact_174_Graph_Omin__dist__minD,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,V: nat,D: nat,V3: nat] :
% 0.21/0.47 ( ( dist_capacity @ C @ V @ D @ V3 )
% 0.21/0.47 => ( ord_less_eq_nat @ ( min_dist_capacity @ C @ V @ V3 ) @ D ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist_minD
% 0.21/0.47 thf(fact_175_Graph_Omin__dist__minD,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
% 0.21/0.47 ( ( dist_a @ C @ V @ D @ V3 )
% 0.21/0.47 => ( ord_less_eq_nat @ ( min_dist_a @ C @ V @ V3 ) @ D ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist_minD
% 0.21/0.47 thf(fact_176_Graph_Omin__dist__split_I2_J,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.21/0.47 ( ( dist_capacity @ C @ U @ D1 @ W )
% 0.21/0.47 => ( ( dist_capacity @ C @ W @ D2 @ V )
% 0.21/0.47 => ( ( ( min_dist_capacity @ C @ U @ V )
% 0.21/0.47 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.21/0.47 => ( ( min_dist_capacity @ C @ W @ V )
% 0.21/0.47 = D2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist_split(2)
% 0.21/0.47 thf(fact_177_Graph_Omin__dist__split_I2_J,axiom,
% 0.21/0.47 ! [C: product_prod_nat_nat > a,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.21/0.47 ( ( dist_a @ C @ U @ D1 @ W )
% 0.21/0.47 => ( ( dist_a @ C @ W @ D2 @ V )
% 0.21/0.47 => ( ( ( min_dist_a @ C @ U @ V )
% 0.21/0.47 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.21/0.47 => ( ( min_dist_a @ C @ W @ V )
% 0.21/0.47 = D2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Graph.min_dist_split(2)
% 0.21/0.47 thf(fact_178__C1_Oprems_C_I3_J,axiom,
% 0.21/0.47 isPath_a @ c2 @ ua @ p2_a @ t ).
% 0.21/0.47
% 0.21/0.47 % "1.prems"(3)
% 0.21/0.47 thf(fact_179_not__less__Least,axiom,
% 0.21/0.47 ! [K: nat,P5: nat > $o] :
% 0.21/0.47 ( ( ord_less_nat @ K @ ( ord_Least_nat @ P5 ) )
% 0.21/0.47 => ~ ( P5 @ K ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_less_Least
% 0.21/0.47 thf(fact_180_Least__le,axiom,
% 0.21/0.47 ! [P5: nat > $o,K: nat] :
% 0.21/0.47 ( ( P5 @ K )
% 0.21/0.47 => ( ord_less_eq_nat @ ( ord_Least_nat @ P5 ) @ K ) ) ).
% 0.21/0.47
% 0.21/0.47 % Least_le
% 0.21/0.47 thf(fact_181_g_H_Oconnected__by__dist,axiom,
% 0.21/0.47 ! [V: nat,V3: nat] :
% 0.21/0.47 ( ( connected_a @ c2 @ V @ V3 )
% 0.21/0.47 = ( ? [D4: nat] : ( dist_a @ c2 @ V @ D4 @ V3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.connected_by_dist
% 0.21/0.47 thf(fact_182_g_H_Omin__dist__is__dist,axiom,
% 0.21/0.47 ! [V: nat,V3: nat] :
% 0.21/0.47 ( ( connected_a @ c2 @ V @ V3 )
% 0.21/0.47 => ( dist_a @ c2 @ V @ ( min_dist_a @ c2 @ V @ V3 ) @ V3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.min_dist_is_dist
% 0.21/0.47 thf(fact_183_g_H_Oobtain__shortest__path,axiom,
% 0.21/0.47 ! [U: nat,V: nat] :
% 0.21/0.47 ( ( connected_a @ c2 @ U @ V )
% 0.21/0.47 => ~ ! [P3: list_P559422087at_nat] :
% 0.21/0.47 ~ ( isShortestPath_a @ c2 @ U @ P3 @ V ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.obtain_shortest_path
% 0.21/0.47 thf(fact_184_g_H_OshortestPath__is__simple,axiom,
% 0.21/0.47 ! [S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.21/0.47 ( ( isShortestPath_a @ c2 @ S @ P2 @ T )
% 0.21/0.47 => ( isSimplePath_a @ c2 @ S @ P2 @ T ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.shortestPath_is_simple
% 0.21/0.47 thf(fact_185_g_H_OreachableNodes__def,axiom,
% 0.21/0.47 ! [U: nat] :
% 0.21/0.47 ( ( reachableNodes_a @ c2 @ U )
% 0.21/0.47 = ( collect_nat @ ( connected_a @ c2 @ U ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.reachableNodes_def
% 0.21/0.47 thf(fact_186_g_H_Omin__dist__less,axiom,
% 0.21/0.47 ! [Src: nat,V: nat,D: nat,D3: nat] :
% 0.21/0.47 ( ( connected_a @ c2 @ Src @ V )
% 0.21/0.47 => ( ( ( min_dist_a @ c2 @ Src @ V )
% 0.21/0.47 = D )
% 0.21/0.47 => ( ( ord_less_nat @ D3 @ D )
% 0.21/0.47 => ? [V2: nat] :
% 0.21/0.47 ( ( connected_a @ c2 @ Src @ V2 )
% 0.21/0.47 & ( ( min_dist_a @ c2 @ Src @ V2 )
% 0.21/0.47 = D3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.min_dist_less
% 0.21/0.47 thf(fact_187_g_H_Omin__distI2,axiom,
% 0.21/0.47 ! [V: nat,V3: nat,Q: nat > $o] :
% 0.21/0.47 ( ( connected_a @ c2 @ V @ V3 )
% 0.21/0.47 => ( ! [D6: nat] :
% 0.21/0.47 ( ( dist_a @ c2 @ V @ D6 @ V3 )
% 0.21/0.47 => ( ! [D7: nat] :
% 0.21/0.47 ( ( dist_a @ c2 @ V @ D7 @ V3 )
% 0.21/0.47 => ( ord_less_eq_nat @ D6 @ D7 ) )
% 0.21/0.47 => ( Q @ D6 ) ) )
% 0.21/0.47 => ( Q @ ( min_dist_a @ c2 @ V @ V3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.min_distI2
% 0.21/0.47 thf(fact_188_g_H_Omin__distI__eq,axiom,
% 0.21/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.21/0.47 ( ( dist_a @ c2 @ V @ D @ V3 )
% 0.21/0.47 => ( ! [D5: nat] :
% 0.21/0.47 ( ( dist_a @ c2 @ V @ D5 @ V3 )
% 0.21/0.47 => ( ord_less_eq_nat @ D @ D5 ) )
% 0.21/0.47 => ( ( min_dist_a @ c2 @ V @ V3 )
% 0.21/0.47 = D ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.min_distI_eq
% 0.21/0.47 thf(fact_189_g_H_Omin__dist__le,axiom,
% 0.21/0.47 ! [Src: nat,V: nat,D3: nat] :
% 0.21/0.47 ( ( connected_a @ c2 @ Src @ V )
% 0.21/0.47 => ( ( ord_less_eq_nat @ D3 @ ( min_dist_a @ c2 @ Src @ V ) )
% 0.21/0.47 => ? [V2: nat] :
% 0.21/0.47 ( ( connected_a @ c2 @ Src @ V2 )
% 0.21/0.47 & ( ( min_dist_a @ c2 @ Src @ V2 )
% 0.21/0.47 = D3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.min_dist_le
% 0.21/0.47 thf(fact_190_g_H_Omin__dist__minD,axiom,
% 0.21/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.21/0.47 ( ( dist_a @ c2 @ V @ D @ V3 )
% 0.21/0.47 => ( ord_less_eq_nat @ ( min_dist_a @ c2 @ V @ V3 ) @ D ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.min_dist_minD
% 0.21/0.47 thf(fact_191_g_H_Omin__dist__split_I2_J,axiom,
% 0.21/0.47 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.21/0.47 ( ( dist_a @ c2 @ U @ D1 @ W )
% 0.21/0.47 => ( ( dist_a @ c2 @ W @ D2 @ V )
% 0.21/0.47 => ( ( ( min_dist_a @ c2 @ U @ V )
% 0.21/0.47 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.21/0.47 => ( ( min_dist_a @ c2 @ W @ V )
% 0.21/0.47 = D2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.min_dist_split(2)
% 0.21/0.47 thf(fact_192_g_H_Omin__dist__split_I1_J,axiom,
% 0.21/0.47 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.21/0.47 ( ( dist_a @ c2 @ U @ D1 @ W )
% 0.21/0.47 => ( ( dist_a @ c2 @ W @ D2 @ V )
% 0.21/0.47 => ( ( ( min_dist_a @ c2 @ U @ V )
% 0.21/0.47 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.21/0.47 => ( ( min_dist_a @ c2 @ U @ W )
% 0.21/0.47 = D1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.min_dist_split(1)
% 0.21/0.47 thf(fact_193_g_H_Odist__trans,axiom,
% 0.21/0.47 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.21/0.47 ( ( dist_a @ c2 @ U @ D1 @ W )
% 0.21/0.47 => ( ( dist_a @ c2 @ W @ D2 @ V )
% 0.21/0.47 => ( dist_a @ c2 @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.dist_trans
% 0.21/0.47 thf(fact_194_g_H_Oconnected__def,axiom,
% 0.21/0.47 ! [U: nat,V: nat] :
% 0.21/0.47 ( ( connected_a @ c2 @ U @ V )
% 0.21/0.47 = ( ? [P: list_P559422087at_nat] : ( isPath_a @ c2 @ U @ P @ V ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.connected_def
% 0.21/0.47 thf(fact_195_g_H_OisSPath__pathLE,axiom,
% 0.21/0.47 ! [S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.21/0.47 ( ( isPath_a @ c2 @ S @ P2 @ T )
% 0.21/0.47 => ? [P6: list_P559422087at_nat] : ( isSimplePath_a @ c2 @ S @ P6 @ T ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.isSPath_pathLE
% 0.21/0.47 thf(fact_196_g_H_OshortestPath__is__path,axiom,
% 0.21/0.47 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.21/0.47 ( ( isShortestPath_a @ c2 @ U @ P2 @ V )
% 0.21/0.47 => ( isPath_a @ c2 @ U @ P2 @ V ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.shortestPath_is_path
% 0.21/0.47 thf(fact_197_g_H_OisShortestPath__alt,axiom,
% 0.21/0.47 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.21/0.47 ( ( isShortestPath_a @ c2 @ U @ P2 @ V )
% 0.21/0.47 = ( ( isSimplePath_a @ c2 @ U @ P2 @ V )
% 0.21/0.47 & ( ( size_s1990949619at_nat @ P2 )
% 0.21/0.47 = ( min_dist_a @ c2 @ U @ V ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.isShortestPath_alt
% 0.21/0.47 thf(fact_198_g_H_Omin__dist__def,axiom,
% 0.21/0.47 ! [V: nat,V3: nat] :
% 0.21/0.47 ( ( min_dist_a @ c2 @ V @ V3 )
% 0.21/0.47 = ( ord_Least_nat
% 0.21/0.47 @ ^ [D4: nat] : ( dist_a @ c2 @ V @ D4 @ V3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.min_dist_def
% 0.21/0.47 thf(fact_199_g_H_Odist__def,axiom,
% 0.21/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.21/0.47 ( ( dist_a @ c2 @ V @ D @ V3 )
% 0.21/0.47 = ( ? [P: list_P559422087at_nat] :
% 0.21/0.47 ( ( isPath_a @ c2 @ V @ P @ V3 )
% 0.21/0.47 & ( ( size_s1990949619at_nat @ P )
% 0.21/0.47 = D ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.dist_def
% 0.21/0.47 thf(fact_200_g_H_OisPath__distD,axiom,
% 0.21/0.47 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.21/0.47 ( ( isPath_a @ c2 @ U @ P2 @ V )
% 0.21/0.47 => ( dist_a @ c2 @ U @ ( size_s1990949619at_nat @ P2 ) @ V ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.isPath_distD
% 0.21/0.47 thf(fact_201_g_H_OisShortestPath__min__dist__def,axiom,
% 0.21/0.47 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.21/0.47 ( ( isShortestPath_a @ c2 @ U @ P2 @ V )
% 0.21/0.47 = ( ( isPath_a @ c2 @ U @ P2 @ V )
% 0.21/0.47 & ( ( size_s1990949619at_nat @ P2 )
% 0.21/0.47 = ( min_dist_a @ c2 @ U @ V ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.isShortestPath_min_dist_def
% 0.21/0.47 thf(fact_202_order__refl,axiom,
% 0.21/0.47 ! [X3: nat] : ( ord_less_eq_nat @ X3 @ X3 ) ).
% 0.21/0.47
% 0.21/0.47 % order_refl
% 0.21/0.47 thf(fact_203_g_H_OisShortestPath__def,axiom,
% 0.21/0.47 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.21/0.47 ( ( isShortestPath_a @ c2 @ U @ P2 @ V )
% 0.21/0.47 = ( ( isPath_a @ c2 @ U @ P2 @ V )
% 0.21/0.47 & ! [P4: list_P559422087at_nat] :
% 0.21/0.47 ( ( isPath_a @ c2 @ U @ P4 @ V )
% 0.21/0.47 => ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P2 ) @ ( size_s1990949619at_nat @ P4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.isShortestPath_def
% 0.21/0.47 thf(fact_204_assms_I5_J,axiom,
% 0.21/0.47 isPath_a @ c2 @ s @ p3 @ t ).
% 0.21/0.47
% 0.21/0.47 % assms(5)
% 0.21/0.47 thf(fact_205__092_060open_062g_H_OisPath_Au_____Ap2_H_____At_092_060close_062,axiom,
% 0.21/0.47 isPath_a @ c2 @ u @ p2 @ t ).
% 0.21/0.47
% 0.21/0.47 % \<open>g'.isPath u__ p2'__ t\<close>
% 0.21/0.47 thf(fact_206_g_H_Oconnected__distI,axiom,
% 0.21/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.21/0.47 ( ( dist_a @ c2 @ V @ D @ V3 )
% 0.21/0.47 => ( connected_a @ c2 @ V @ V3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % g'.connected_distI
% 0.21/0.47 thf(fact_207_g_H_Oconnected__refl,axiom,
% 0.21/0.47 ! [V: nat] : ( connected_a @ c2 @ V @ V ) ).
% 0.21/0.47
% 0.21/0.47 % g'.connected_refl
% 0.21/0.47 thf(fact_208_P2_H,axiom,
% 0.21/0.47 isPath_a @ c2 @ ua @ p2_a @ t ).
% 0.21/0.47
% 0.21/0.47 % P2'
% 0.21/0.47 thf(fact_209_order__subst1,axiom,
% 0.21/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.21/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.21/0.47 => ( ! [X: nat,Y: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.21/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.21/0.47 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_subst1
% 0.21/0.47 thf(fact_210_order__subst2,axiom,
% 0.21/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.21/0.47 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.21/0.47 => ( ! [X: nat,Y: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.21/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.21/0.47 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_subst2
% 0.21/0.47 thf(fact_211_ord__eq__le__subst,axiom,
% 0.21/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.21/0.47 ( ( A
% 0.21/0.47 = ( F @ B ) )
% 0.21/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.21/0.47 => ( ! [X: nat,Y: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.21/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.21/0.47 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_eq_le_subst
% 0.21/0.47 thf(fact_212_ord__le__eq__subst,axiom,
% 0.21/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.21/0.47 => ( ( ( F @ B )
% 0.21/0.47 = C )
% 0.21/0.47 => ( ! [X: nat,Y: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.21/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.21/0.47 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_le_eq_subst
% 0.21/0.47 thf(fact_213_eq__iff,axiom,
% 0.21/0.47 ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 0.21/0.47 = ( ^ [X2: nat,Y5: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ X2 @ Y5 )
% 0.21/0.47 & ( ord_less_eq_nat @ Y5 @ X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eq_iff
% 0.21/0.47 thf(fact_214_antisym,axiom,
% 0.21/0.47 ! [X3: nat,Y3: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.21/0.47 => ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.21/0.47 => ( X3 = Y3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % antisym
% 0.21/0.47 thf(fact_215_linear,axiom,
% 0.21/0.47 ! [X3: nat,Y3: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.21/0.47 | ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % linear
% 0.21/0.47 thf(fact_216_eq__refl,axiom,
% 0.21/0.47 ! [X3: nat,Y3: nat] :
% 0.21/0.47 ( ( X3 = Y3 )
% 0.21/0.47 => ( ord_less_eq_nat @ X3 @ Y3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % eq_refl
% 0.21/0.47 thf(fact_217_le__cases,axiom,
% 0.21/0.47 ! [X3: nat,Y3: nat] :
% 0.21/0.47 ( ~ ( ord_less_eq_nat @ X3 @ Y3 )
% 0.21/0.47 => ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_cases
% 0.21/0.47 thf(fact_218_order_Otrans,axiom,
% 0.21/0.47 ! [A: nat,B: nat,C: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.21/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.21/0.47 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.trans
% 0.21/0.47 thf(fact_219_le__cases3,axiom,
% 0.21/0.47 ! [X3: nat,Y3: nat,Z2: nat] :
% 0.21/0.47 ( ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.21/0.47 => ~ ( ord_less_eq_nat @ Y3 @ Z2 ) )
% 0.21/0.47 => ( ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.21/0.47 => ~ ( ord_less_eq_nat @ X3 @ Z2 ) )
% 0.21/0.47 => ( ( ( ord_less_eq_nat @ X3 @ Z2 )
% 0.21/0.47 => ~ ( ord_less_eq_nat @ Z2 @ Y3 ) )
% 0.21/0.47 => ( ( ( ord_less_eq_nat @ Z2 @ Y3 )
% 0.21/0.47 => ~ ( ord_less_eq_nat @ Y3 @ X3 ) )
% 0.21/0.47 => ( ( ( ord_less_eq_nat @ Y3 @ Z2 )
% 0.21/0.47 => ~ ( ord_less_eq_nat @ Z2 @ X3 ) )
% 0.21/0.47 => ~ ( ( ord_less_eq_nat @ Z2 @ X3 )
% 0.21/0.47 => ~ ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_cases3
% 0.21/0.47 thf(fact_220_antisym__conv,axiom,
% 0.21/0.47 ! [Y3: nat,X3: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.21/0.47 => ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.21/0.47 = ( X3 = Y3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % antisym_conv
% 0.21/0.47 thf(fact_221_order__class_Oorder_Oeq__iff,axiom,
% 0.21/0.47 ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 0.21/0.47 = ( ^ [A2: nat,B2: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.21/0.47 & ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_class.order.eq_iff
% 0.21/0.47 thf(fact_222_ord__eq__le__trans,axiom,
% 0.21/0.47 ! [A: nat,B: nat,C: nat] :
% 0.21/0.47 ( ( A = B )
% 0.21/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.21/0.47 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_eq_le_trans
% 0.21/0.47 thf(fact_223_ord__le__eq__trans,axiom,
% 0.21/0.47 ! [A: nat,B: nat,C: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.21/0.47 => ( ( B = C )
% 0.21/0.47 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_le_eq_trans
% 0.21/0.47 thf(fact_224_order__class_Oorder_Oantisym,axiom,
% 0.21/0.47 ! [A: nat,B: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.21/0.47 => ( ( ord_less_eq_nat @ B @ A )
% 0.21/0.47 => ( A = B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_class.order.antisym
% 0.21/0.47 thf(fact_225_order__trans,axiom,
% 0.21/0.47 ! [X3: nat,Y3: nat,Z2: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.21/0.47 => ( ( ord_less_eq_nat @ Y3 @ Z2 )
% 0.21/0.47 => ( ord_less_eq_nat @ X3 @ Z2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_trans
% 0.21/0.47 thf(fact_226_dual__order_Orefl,axiom,
% 0.21/0.47 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.refl
% 0.21/0.47 thf(fact_227_linorder__wlog,axiom,
% 0.21/0.47 ! [P5: nat > nat > $o,A: nat,B: nat] :
% 0.21/0.47 ( ! [A4: nat,B4: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ A4 @ B4 )
% 0.21/0.47 => ( P5 @ A4 @ B4 ) )
% 0.21/0.47 => ( ! [A4: nat,B4: nat] :
% 0.21/0.47 ( ( P5 @ B4 @ A4 )
% 0.21/0.47 => ( P5 @ A4 @ B4 ) )
% 0.21/0.47 => ( P5 @ A @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % linorder_wlog
% 0.21/0.47 thf(fact_228_dual__order_Otrans,axiom,
% 0.21/0.47 ! [B: nat,A: nat,C: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ B @ A )
% 0.21/0.47 => ( ( ord_less_eq_nat @ C @ B )
% 0.21/0.47 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.trans
% 0.21/0.47 thf(fact_229_dual__order_Oeq__iff,axiom,
% 0.21/0.47 ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 0.21/0.47 = ( ^ [A2: nat,B2: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.21/0.47 & ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.eq_iff
% 0.21/0.47 thf(fact_230_dual__order_Oantisym,axiom,
% 0.21/0.47 ! [B: nat,A: nat] :
% 0.21/0.47 ( ( ord_less_eq_nat @ B @ A )
% 0.21/0.47 => ( ( ord_less_eq_nat @ A @ B )
% 0.21/0.47 => ( A = B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.antisym
% 0.21/0.47 thf(fact_231_dual__order_Ostrict__implies__not__eq,axiom,
% 0.21/0.47 ! [B: nat,A: nat] :
% 0.21/0.47 ( ( ord_less_nat @ B @ A )
% 0.21/0.47 => ( A != B ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.strict_implies_not_eq
% 0.21/0.47 thf(fact_232_order_Ostrict__implies__not__eq,axiom,
% 0.21/0.47 ! [A: nat,B: nat] :
% 0.21/0.47 ( ( ord_less_nat @ A @ B )
% 0.21/0.47 => ( A != B ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.strict_implies_not_eq
% 0.21/0.47 thf(fact_233_not__less__iff__gr__or__eq,axiom,
% 0.21/0.47 ! [X3: nat,Y3: nat] :
% 0.21/0.47 ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
% 0.21/0.47 = ( ( ord_less_nat @ Y3 @ X3 )
% 0.21/0.47 | ( X3 = Y3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_less_iff_gr_or_eq
% 0.21/0.47 thf(fact_234_dual__order_Ostrict__trans,axiom,
% 0.21/0.47 ! [B: nat,A: nat,C: nat] :
% 0.21/0.47 ( ( ord_less_nat @ B @ A )
% 0.21/0.47 => ( ( ord_less_nat @ C @ B )
% 0.21/0.47 => ( ord_less_nat @ C @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.strict_trans
% 0.21/0.47 thf(fact_235_linorder__less__wlog,axiom,
% 0.21/0.47 ! [P5: nat > nat > $o,A: nat,B: nat] :
% 0.21/0.47 ( ! [A4: nat,B4: nat] :
% 0.21/0.47 ( ( ord_less_nat @ A4 @ B4 )
% 0.21/0.47 => ( P5 @ A4 @ B4 ) )
% 0.21/0.47 => ( ! [A4: nat] : ( P5 @ A4 @ A4 )
% 0.21/0.47 => ( ! [A4: nat,B4: nat] :
% 0.21/0.47 ( ( P5 @ B4 @ A4 )
% 0.21/0.47 => ( P5 @ A4 @ B4 ) )
% 0.21/0.47 => ( P5 @ A @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % linorder_less_wlog
% 0.32/0.47 thf(fact_236_exists__least__iff,axiom,
% 0.32/0.47 ( ( ^ [P7: nat > $o] :
% 0.32/0.47 ? [X4: nat] : ( P7 @ X4 ) )
% 0.32/0.47 = ( ^ [P8: nat > $o] :
% 0.32/0.47 ? [N2: nat] :
% 0.32/0.47 ( ( P8 @ N2 )
% 0.32/0.47 & ! [M2: nat] :
% 0.32/0.47 ( ( ord_less_nat @ M2 @ N2 )
% 0.32/0.47 => ~ ( P8 @ M2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % exists_least_iff
% 0.32/0.47 thf(fact_237_less__imp__not__less,axiom,
% 0.32/0.47 ! [X3: nat,Y3: nat] :
% 0.32/0.47 ( ( ord_less_nat @ X3 @ Y3 )
% 0.32/0.47 => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_imp_not_less
% 0.32/0.47 thf(fact_238_order_Ostrict__trans,axiom,
% 0.32/0.47 ! [A: nat,B: nat,C: nat] :
% 0.32/0.47 ( ( ord_less_nat @ A @ B )
% 0.32/0.47 => ( ( ord_less_nat @ B @ C )
% 0.32/0.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order.strict_trans
% 0.32/0.47 thf(fact_239_dual__order_Oirrefl,axiom,
% 0.32/0.47 ! [A: nat] :
% 0.32/0.47 ~ ( ord_less_nat @ A @ A ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.irrefl
% 0.32/0.47 thf(fact_240_linorder__cases,axiom,
% 0.32/0.47 ! [X3: nat,Y3: nat] :
% 0.32/0.47 ( ~ ( ord_less_nat @ X3 @ Y3 )
% 0.32/0.47 => ( ( X3 != Y3 )
% 0.32/0.47 => ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % linorder_cases
% 0.32/0.47 thf(fact_241_less__imp__triv,axiom,
% 0.32/0.47 ! [X3: nat,Y3: nat,P5: $o] :
% 0.32/0.47 ( ( ord_less_nat @ X3 @ Y3 )
% 0.32/0.47 => ( ( ord_less_nat @ Y3 @ X3 )
% 0.32/0.47 => P5 ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_imp_triv
% 0.32/0.47 thf(fact_242_less__imp__not__eq2,axiom,
% 0.32/0.47 ! [X3: nat,Y3: nat] :
% 0.32/0.47 ( ( ord_less_nat @ X3 @ Y3 )
% 0.32/0.47 => ( Y3 != X3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_imp_not_eq2
% 0.32/0.47 thf(fact_243_antisym__conv3,axiom,
% 0.32/0.47 ! [Y3: nat,X3: nat] :
% 0.32/0.47 ( ~ ( ord_less_nat @ Y3 @ X3 )
% 0.32/0.47 => ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
% 0.32/0.47 = ( X3 = Y3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % antisym_conv3
% 0.32/0.47 thf(fact_244_less__induct,axiom,
% 0.32/0.47 ! [P5: nat > $o,A: nat] :
% 0.32/0.47 ( ! [X: nat] :
% 0.32/0.47 ( ! [Y2: nat] :
% 0.32/0.47 ( ( ord_less_nat @ Y2 @ X )
% 0.32/0.47 => ( P5 @ Y2 ) )
% 0.32/0.47 => ( P5 @ X ) )
% 0.32/0.47 => ( P5 @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_induct
% 0.32/0.47 thf(fact_245_less__not__sym,axiom,
% 0.32/0.47 ! [X3: nat,Y3: nat] :
% 0.32/0.47 ( ( ord_less_nat @ X3 @ Y3 )
% 0.32/0.47 => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_not_sym
% 0.32/0.47 thf(fact_246_less__imp__not__eq,axiom,
% 0.32/0.47 ! [X3: nat,Y3: nat] :
% 0.32/0.47 ( ( ord_less_nat @ X3 @ Y3 )
% 0.32/0.47 => ( X3 != Y3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_imp_not_eq
% 0.32/0.47 thf(fact_247_dual__order_Oasym,axiom,
% 0.32/0.47 ! [B: nat,A: nat] :
% 0.32/0.47 ( ( ord_less_nat @ B @ A )
% 0.32/0.47 => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.asym
% 0.32/0.47 thf(fact_248_ord__less__eq__trans,axiom,
% 0.32/0.47 ! [A: nat,B: nat,C: nat] :
% 0.32/0.47 ( ( ord_less_nat @ A @ B )
% 0.32/0.47 => ( ( B = C )
% 0.32/0.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_less_eq_trans
% 0.32/0.47 thf(fact_249_ord__eq__less__trans,axiom,
% 0.32/0.47 ! [A: nat,B: nat,C: nat] :
% 0.32/0.47 ( ( A = B )
% 0.32/0.47 => ( ( ord_less_nat @ B @ C )
% 0.32/0.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_less_trans
% 0.32/0.47 thf(fact_250_less__irrefl,axiom,
% 0.32/0.47 ! [X3: nat] :
% 0.32/0.47 ~ ( ord_less_nat @ X3 @ X3 ) ).
% 0.32/0.47
% 0.32/0.47 % less_irrefl
% 0.32/0.47 thf(fact_251_less__linear,axiom,
% 0.32/0.47 ! [X3: nat,Y3: nat] :
% 0.32/0.47 ( ( ord_less_nat @ X3 @ Y3 )
% 0.32/0.47 | ( X3 = Y3 )
% 0.32/0.47 | ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_linear
% 0.32/0.47 thf(fact_252_less__trans,axiom,
% 0.32/0.47 ! [X3: nat,Y3: nat,Z2: nat] :
% 0.32/0.47 ( ( ord_less_nat @ X3 @ Y3 )
% 0.32/0.47 => ( ( ord_less_nat @ Y3 @ Z2 )
% 0.32/0.47 => ( ord_less_nat @ X3 @ Z2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_trans
% 0.32/0.47 thf(fact_253_less__asym_H,axiom,
% 0.32/0.47 ! [A: nat,B: nat] :
% 0.32/0.47 ( ( ord_less_nat @ A @ B )
% 0.32/0.47 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_asym'
% 0.32/0.47 thf(fact_254_less__asym,axiom,
% 0.32/0.47 ! [X3: nat,Y3: nat] :
% 0.32/0.47 ( ( ord_less_nat @ X3 @ Y3 )
% 0.32/0.47 => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_asym
% 0.32/0.47 thf(fact_255_less__imp__neq,axiom,
% 0.32/0.47 ! [X3: nat,Y3: nat] :
% 0.32/0.47 ( ( ord_less_nat @ X3 @ Y3 )
% 0.32/0.47 => ( X3 != Y3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_imp_neq
% 0.32/0.47 thf(fact_256_order_Oasym,axiom,
% 0.32/0.47 ! [A: nat,B: nat] :
% 0.32/0.47 ( ( ord_less_nat @ A @ B )
% 0.32/0.47 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % order.asym
% 0.32/0.47 thf(fact_257_neq__iff,axiom,
% 0.32/0.47 ! [X3: nat,Y3: nat] :
% 0.32/0.47 ( ( X3 != Y3 )
% 0.32/0.47 = ( ( ord_less_nat @ X3 @ Y3 )
% 0.32/0.47 | ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % neq_iff
% 0.32/0.47 thf(fact_258_neqE,axiom,
% 0.32/0.47 ! [X3: nat,Y3: nat] :
% 0.32/0.47 ( ( X3 != Y3 )
% 0.32/0.47 => ( ~ ( ord_less_nat @ X3 @ Y3 )
% 0.32/0.47 => ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % neqE
% 0.32/0.47 thf(fact_259_gt__ex,axiom,
% 0.32/0.47 ! [X3: nat] :
% 0.32/0.47 ? [X_1: nat] : ( ord_less_nat @ X3 @ X_1 ) ).
% 0.32/0.47
% 0.32/0.47 % gt_ex
% 0.32/0.47 thf(fact_260_order__less__subst2,axiom,
% 0.32/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.32/0.47 ( ( ord_less_nat @ A @ B )
% 0.32/0.47 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.32/0.47 => ( ! [X: nat,Y: nat] :
% 0.32/0.47 ( ( ord_less_nat @ X @ Y )
% 0.32/0.47 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.32/0.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_less_subst2
% 0.32/0.47 thf(fact_261_order__less__subst1,axiom,
% 0.32/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.32/0.47 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.32/0.47 => ( ( ord_less_nat @ B @ C )
% 0.32/0.47 => ( ! [X: nat,Y: nat] :
% 0.32/0.47 ( ( ord_less_nat @ X @ Y )
% 0.32/0.47 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.32/0.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_less_subst1
% 0.32/0.47 thf(fact_262_ord__less__eq__subst,axiom,
% 0.32/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.32/0.47 ( ( ord_less_nat @ A @ B )
% 0.32/0.47 => ( ( ( F @ B )
% 0.32/0.47 = C )
% 0.32/0.47 => ( ! [X: nat,Y: nat] :
% 0.32/0.47 ( ( ord_less_nat @ X @ Y )
% 0.32/0.47 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.32/0.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_less_eq_subst
% 0.32/0.47 thf(fact_263_ord__eq__less__subst,axiom,
% 0.32/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.32/0.47 ( ( A
% 0.32/0.47 = ( F @ B ) )
% 0.32/0.47 => ( ( ord_less_nat @ B @ C )
% 0.32/0.47 => ( ! [X: nat,Y: nat] :
% 0.32/0.47 ( ( ord_less_nat @ X @ Y )
% 0.32/0.47 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.32/0.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_less_subst
% 0.32/0.47 thf(fact_264_LeastI2,axiom,
% 0.32/0.47 ! [P5: nat > $o,A: nat,Q: nat > $o] :
% 0.32/0.47 ( ( P5 @ A )
% 0.32/0.47 => ( ! [X: nat] :
% 0.32/0.47 ( ( P5 @ X )
% 0.32/0.47 => ( Q @ X ) )
% 0.32/0.47 => ( Q @ ( ord_Least_nat @ P5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % LeastI2
% 0.32/0.47 thf(fact_265_LeastI__ex,axiom,
% 0.32/0.47 ! [P5: nat > $o] :
% 0.32/0.47 ( ? [X_12: nat] : ( P5 @ X_12 )
% 0.32/0.47 => ( P5 @ ( ord_Least_nat @ P5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % LeastI_ex
% 0.32/0.47 thf(fact_266_LeastI2__ex,axiom,
% 0.32/0.47 ! [P5: nat > $o,Q: nat > $o] :
% 0.32/0.47 ( ? [X_12: nat] : ( P5 @ X_12 )
% 0.32/0.47 => ( ! [X: nat] :
% 0.32/0.47 ( ( P5 @ X )
% 0.32/0.47 => ( Q @ X ) )
% 0.32/0.47 => ( Q @ ( ord_Least_nat @ P5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % LeastI2_ex
% 0.32/0.47 thf(fact_267_LeastI,axiom,
% 0.32/0.47 ! [P5: nat > $o,K: nat] :
% 0.32/0.47 ( ( P5 @ K )
% 0.32/0.47 => ( P5 @ ( ord_Least_nat @ P5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % LeastI
% 0.32/0.47 thf(fact_268_order_Onot__eq__order__implies__strict,axiom,
% 0.32/0.47 ! [A: nat,B: nat] :
% 0.32/0.47 ( ( A != B )
% 0.32/0.47 => ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.47 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order.not_eq_order_implies_strict
% 0.32/0.47 thf(fact_269_dual__order_Ostrict__implies__order,axiom,
% 0.32/0.47 ! [B: nat,A: nat] :
% 0.32/0.47 ( ( ord_less_nat @ B @ A )
% 0.32/0.47 => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.strict_implies_order
% 0.32/0.47 thf(fact_270_dual__order_Ostrict__iff__order,axiom,
% 0.32/0.47 ( ord_less_nat
% 0.32/0.47 = ( ^ [B2: nat,A2: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.32/0.47 & ( A2 != B2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.strict_iff_order
% 0.32/0.47 thf(fact_271_dual__order_Oorder__iff__strict,axiom,
% 0.32/0.47 ( ord_less_eq_nat
% 0.32/0.47 = ( ^ [B2: nat,A2: nat] :
% 0.32/0.47 ( ( ord_less_nat @ B2 @ A2 )
% 0.32/0.47 | ( A2 = B2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.order_iff_strict
% 0.32/0.47 thf(fact_272_order_Ostrict__implies__order,axiom,
% 0.32/0.47 ! [A: nat,B: nat] :
% 0.32/0.47 ( ( ord_less_nat @ A @ B )
% 0.32/0.47 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.32/0.47
% 0.32/0.47 % order.strict_implies_order
% 0.32/0.47
% 0.32/0.47 % Conjectures (1)
% 0.32/0.47 thf(conj_0,conjecture,
% 0.32/0.47 ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) ).
% 0.32/0.47
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 ------------------------
% 2.38/1.46 ---- Embedded in THF ---
% 2.38/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.38/1.46 %%% Generated on Tue Feb 24 08:24:37 EST 2026
% 2.38/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 2.38/1.46 %%% Logic specification used:
% 2.38/1.46 %%% thf(spec, logic, $$dhol).
% 2.38/1.46
% 2.38/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2DTF16520.p
% See solution above
% 2.38/1.46 ------------------------
% 2.55/1.50 ---- Cleaned THF ---
% 2.55/1.50 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.55/1.50 list_P559422087at_nat: $tType ).
% 2.55/1.50
% 2.55/1.50 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.55/1.50 product_prod_nat_nat: $tType ).
% 2.55/1.50
% 2.55/1.50 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 2.55/1.50 set_nat: $tType ).
% 2.55/1.50
% 2.55/1.50 thf(ty_n_tf__capacity,type,
% 2.55/1.50 capacity: $tType ).
% 2.55/1.50
% 2.55/1.50 thf(ty_n_t__Nat__Onat,type,
% 2.55/1.50 nat: $tType ).
% 2.55/1.50
% 2.55/1.50 thf(ty_n_tf__a,type,
% 2.55/1.50 a: $tType ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Graph_OGraph_Oconnected_001tf__a,type,
% 2.55/1.50 connected_a: ( product_prod_nat_nat > a ) > nat > nat > $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Graph_OGraph_Oconnected_001tf__capacity,type,
% 2.55/1.50 connected_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Graph_OGraph_Odist_001tf__a,type,
% 2.55/1.50 dist_a: ( product_prod_nat_nat > a ) > nat > nat > nat > $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Graph_OGraph_Odist_001tf__capacity,type,
% 2.55/1.50 dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat > $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Graph_OGraph_OisPath_001tf__a,type,
% 2.55/1.50 isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Graph_OGraph_OisPath_001tf__capacity,type,
% 2.55/1.50 isPath_capacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Graph_OGraph_OisShortestPath_001tf__a,type,
% 2.55/1.50 isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Graph_OGraph_OisShortestPath_001tf__capacity,type,
% 2.55/1.50 isShor1936442771pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Graph_OGraph_OisSimplePath_001tf__a,type,
% 2.55/1.50 isSimplePath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Graph_OGraph_OisSimplePath_001tf__capacity,type,
% 2.55/1.50 isSimp1359852763pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Graph_OGraph_Omin__dist_001tf__a,type,
% 2.55/1.50 min_dist_a: ( product_prod_nat_nat > a ) > nat > nat > nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Graph_OGraph_Omin__dist_001tf__capacity,type,
% 2.55/1.50 min_dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Graph_OGraph_OreachableNodes_001tf__a,type,
% 2.55/1.50 reachableNodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Graph_OGraph_OreachableNodes_001tf__capacity,type,
% 2.55/1.50 reacha1693770334pacity: ( product_prod_nat_nat > capacity ) > nat > set_nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 2.55/1.50 plus_plus_nat: nat > nat > nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.55/1.50 size_s1990949619at_nat: list_P559422087at_nat > nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Orderings_Oord__class_OLeast_001t__Nat__Onat,type,
% 2.55/1.50 ord_Least_nat: ( nat > $o ) > nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 2.55/1.50 ord_less_nat: nat > nat > $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 2.55/1.50 ord_less_eq_nat: nat > nat > $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 2.55/1.50 collect_nat: ( nat > $o ) > set_nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_c_member_001t__Nat__Onat,type,
% 2.55/1.50 member_nat: nat > set_nat > $o ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_c,type,
% 2.55/1.50 c: product_prod_nat_nat > capacity ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_c_H,type,
% 2.55/1.50 c2: product_prod_nat_nat > a ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_p,type,
% 2.55/1.50 p: list_P559422087at_nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_p1____,type,
% 2.55/1.50 p1: list_P559422087at_nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_p1a____,type,
% 2.55/1.50 p1a: list_P559422087at_nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_p2_H____,type,
% 2.55/1.50 p2: list_P559422087at_nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_p2_Ha____,type,
% 2.55/1.50 p2_a: list_P559422087at_nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_p_H,type,
% 2.55/1.50 p3: list_P559422087at_nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_s,type,
% 2.55/1.50 s: nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_t,type,
% 2.55/1.50 t: nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_u____,type,
% 2.55/1.50 u: nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_ua____,type,
% 2.55/1.50 ua: nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_v____,type,
% 2.55/1.50 v: nat ).
% 2.55/1.50
% 2.55/1.50 thf(sy_v_va____,type,
% 2.55/1.50 va: nat ).
% 2.55/1.50
% 2.55/1.50 thf(fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062,axiom,
% 2.55/1.50 ( ( min_dist_capacity @ c @ s @ t )
% 2.55/1.50 = ( plus_plus_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( min_dist_capacity @ c @ ua @ t ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062,axiom,
% 2.55/1.50 ord_less_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( size_s1990949619at_nat @ p1a ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062,axiom,
% 2.55/1.50 ord_less_eq_nat @ ( min_dist_capacity @ c @ ua @ t ) @ ( size_s1990949619at_nat @ p2_a ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_3_nat__add__left__cancel__less,axiom,
% 2.55/1.50 ! [K: nat,M: nat,N: nat] :
% 2.55/1.50 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 2.55/1.50 = ( ord_less_nat @ M @ N ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_4_add__less__cancel__left,axiom,
% 2.55/1.50 ! [C: nat,A: nat,B: nat] :
% 2.55/1.50 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.55/1.50 = ( ord_less_nat @ A @ B ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_5_add__less__cancel__right,axiom,
% 2.55/1.50 ! [A: nat,C: nat,B: nat] :
% 2.55/1.50 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.55/1.50 = ( ord_less_nat @ A @ B ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_6__C1_Oprems_C_I2_J,axiom,
% 2.55/1.50 isPath_capacity @ c @ s @ p1a @ va ).
% 2.55/1.50
% 2.55/1.50 thf(fact_7_SP,axiom,
% 2.55/1.50 isShor1936442771pacity @ c @ s @ p @ t ).
% 2.55/1.50
% 2.55/1.50 thf(fact_8_min__dist__split_I2_J,axiom,
% 2.55/1.50 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.55/1.50 ( ( dist_capacity @ c @ U @ D1 @ W )
% 2.55/1.50 => ( ( dist_capacity @ c @ W @ D2 @ V )
% 2.55/1.50 => ( ( ( min_dist_capacity @ c @ U @ V )
% 2.55/1.50 = ( plus_plus_nat @ D1 @ D2 ) )
% 2.55/1.50 => ( ( min_dist_capacity @ c @ W @ V )
% 2.55/1.50 = D2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_9_min__dist__split_I1_J,axiom,
% 2.55/1.50 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.55/1.50 ( ( dist_capacity @ c @ U @ D1 @ W )
% 2.55/1.50 => ( ( dist_capacity @ c @ W @ D2 @ V )
% 2.55/1.50 => ( ( ( min_dist_capacity @ c @ U @ V )
% 2.55/1.50 = ( plus_plus_nat @ D1 @ D2 ) )
% 2.55/1.50 => ( ( min_dist_capacity @ c @ U @ W )
% 2.55/1.50 = D1 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_10_min__dist__less,axiom,
% 2.55/1.50 ! [Src: nat,V: nat,D: nat,D3: nat] :
% 2.55/1.50 ( ( connected_capacity @ c @ Src @ V )
% 2.55/1.50 => ( ( ( min_dist_capacity @ c @ Src @ V )
% 2.55/1.50 = D )
% 2.55/1.50 => ( ( ord_less_nat @ D3 @ D )
% 2.55/1.50 => ? [V2: nat] :
% 2.55/1.50 ( ( connected_capacity @ c @ Src @ V2 )
% 2.55/1.50 & ( ( min_dist_capacity @ c @ Src @ V2 )
% 2.55/1.50 = D3 ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_11_add__left__cancel,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat] :
% 2.55/1.50 ( ( ( plus_plus_nat @ A @ B )
% 2.55/1.50 = ( plus_plus_nat @ A @ C ) )
% 2.55/1.50 = ( B = C ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_12_add__right__cancel,axiom,
% 2.55/1.50 ! [B: nat,A: nat,C: nat] :
% 2.55/1.50 ( ( ( plus_plus_nat @ B @ A )
% 2.55/1.50 = ( plus_plus_nat @ C @ A ) )
% 2.55/1.50 = ( B = C ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_13__092_060open_062isPath_Au_Ap2_H_At_092_060close_062,axiom,
% 2.55/1.50 isPath_capacity @ c @ ua @ p2_a @ t ).
% 2.55/1.50
% 2.55/1.50 thf(fact_14_dist__trans,axiom,
% 2.55/1.50 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.55/1.50 ( ( dist_capacity @ c @ U @ D1 @ W )
% 2.55/1.50 => ( ( dist_capacity @ c @ W @ D2 @ V )
% 2.55/1.50 => ( dist_capacity @ c @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_15_connected__def,axiom,
% 2.55/1.50 ! [U: nat,V: nat] :
% 2.55/1.50 ( ( connected_capacity @ c @ U @ V )
% 2.55/1.50 = ( ? [P: list_P559422087at_nat] : ( isPath_capacity @ c @ U @ P @ V ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_16_shortestPath__is__path,axiom,
% 2.55/1.50 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 2.55/1.50 ( ( isShor1936442771pacity @ c @ U @ P2 @ V )
% 2.55/1.50 => ( isPath_capacity @ c @ U @ P2 @ V ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_17_connected__by__dist,axiom,
% 2.55/1.50 ! [V: nat,V3: nat] :
% 2.55/1.50 ( ( connected_capacity @ c @ V @ V3 )
% 2.55/1.50 = ( ? [D4: nat] : ( dist_capacity @ c @ V @ D4 @ V3 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_18_obtain__shortest__path,axiom,
% 2.55/1.50 ! [U: nat,V: nat] :
% 2.55/1.50 ( ( connected_capacity @ c @ U @ V )
% 2.55/1.50 => ~ ! [P3: list_P559422087at_nat] :
% 2.55/1.50 ~ ( isShor1936442771pacity @ c @ U @ P3 @ V ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_19_min__dist__le,axiom,
% 2.55/1.50 ! [Src: nat,V: nat,D3: nat] :
% 2.55/1.50 ( ( connected_capacity @ c @ Src @ V )
% 2.55/1.50 => ( ( ord_less_eq_nat @ D3 @ ( min_dist_capacity @ c @ Src @ V ) )
% 2.55/1.50 => ? [V2: nat] :
% 2.55/1.50 ( ( connected_capacity @ c @ Src @ V2 )
% 2.55/1.50 & ( ( min_dist_capacity @ c @ Src @ V2 )
% 2.55/1.50 = D3 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_20_min__dist__minD,axiom,
% 2.55/1.50 ! [V: nat,D: nat,V3: nat] :
% 2.55/1.50 ( ( dist_capacity @ c @ V @ D @ V3 )
% 2.55/1.50 => ( ord_less_eq_nat @ ( min_dist_capacity @ c @ V @ V3 ) @ D ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_21_min__distI__eq,axiom,
% 2.55/1.50 ! [V: nat,D: nat,V3: nat] :
% 2.55/1.50 ( ( dist_capacity @ c @ V @ D @ V3 )
% 2.55/1.50 => ( ! [D5: nat] :
% 2.55/1.50 ( ( dist_capacity @ c @ V @ D5 @ V3 )
% 2.55/1.50 => ( ord_less_eq_nat @ D @ D5 ) )
% 2.55/1.50 => ( ( min_dist_capacity @ c @ V @ V3 )
% 2.55/1.50 = D ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_22_isPath__distD,axiom,
% 2.55/1.50 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 2.55/1.50 ( ( isPath_capacity @ c @ U @ P2 @ V )
% 2.55/1.50 => ( dist_capacity @ c @ U @ ( size_s1990949619at_nat @ P2 ) @ V ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_23_dist__def,axiom,
% 2.55/1.50 ! [V: nat,D: nat,V3: nat] :
% 2.55/1.50 ( ( dist_capacity @ c @ V @ D @ V3 )
% 2.55/1.50 = ( ? [P: list_P559422087at_nat] :
% 2.55/1.50 ( ( isPath_capacity @ c @ V @ P @ V3 )
% 2.55/1.50 & ( ( size_s1990949619at_nat @ P )
% 2.55/1.50 = D ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_24__092_060open_062isPath_As_Ap1_____Av_____092_060close_062,axiom,
% 2.55/1.50 isPath_capacity @ c @ s @ p1 @ v ).
% 2.55/1.50
% 2.55/1.50 thf(fact_25_min__dist__is__dist,axiom,
% 2.55/1.50 ! [V: nat,V3: nat] :
% 2.55/1.50 ( ( connected_capacity @ c @ V @ V3 )
% 2.55/1.50 => ( dist_capacity @ c @ V @ ( min_dist_capacity @ c @ V @ V3 ) @ V3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_26_isShortestPath__def,axiom,
% 2.55/1.50 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 2.55/1.50 ( ( isShor1936442771pacity @ c @ U @ P2 @ V )
% 2.55/1.50 = ( ( isPath_capacity @ c @ U @ P2 @ V )
% 2.55/1.50 & ! [P4: list_P559422087at_nat] :
% 2.55/1.50 ( ( isPath_capacity @ c @ U @ P4 @ V )
% 2.55/1.50 => ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P2 ) @ ( size_s1990949619at_nat @ P4 ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_27_min__distI2,axiom,
% 2.55/1.50 ! [V: nat,V3: nat,Q: nat > $o] :
% 2.55/1.50 ( ( connected_capacity @ c @ V @ V3 )
% 2.55/1.50 => ( ! [D6: nat] :
% 2.55/1.50 ( ( dist_capacity @ c @ V @ D6 @ V3 )
% 2.55/1.50 => ( ! [D7: nat] :
% 2.55/1.50 ( ( dist_capacity @ c @ V @ D7 @ V3 )
% 2.55/1.50 => ( ord_less_eq_nat @ D6 @ D7 ) )
% 2.55/1.50 => ( Q @ D6 ) ) )
% 2.55/1.50 => ( Q @ ( min_dist_capacity @ c @ V @ V3 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_28_isShortestPath__min__dist__def,axiom,
% 2.55/1.50 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 2.55/1.50 ( ( isShor1936442771pacity @ c @ U @ P2 @ V )
% 2.55/1.50 = ( ( isPath_capacity @ c @ U @ P2 @ V )
% 2.55/1.50 & ( ( size_s1990949619at_nat @ P2 )
% 2.55/1.50 = ( min_dist_capacity @ c @ U @ V ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_29__092_060open_062connected_As_Au_092_060close_062,axiom,
% 2.55/1.50 connected_capacity @ c @ s @ ua ).
% 2.55/1.50
% 2.55/1.50 thf(fact_30_add__le__cancel__right,axiom,
% 2.55/1.50 ! [A: nat,C: nat,B: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.55/1.50 = ( ord_less_eq_nat @ A @ B ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_31_add__le__cancel__left,axiom,
% 2.55/1.50 ! [C: nat,A: nat,B: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.55/1.50 = ( ord_less_eq_nat @ A @ B ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_32_nat__add__left__cancel__le,axiom,
% 2.55/1.50 ! [K: nat,M: nat,N: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 2.55/1.50 = ( ord_less_eq_nat @ M @ N ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_33_P1,axiom,
% 2.55/1.50 isPath_capacity @ c @ s @ p1a @ va ).
% 2.55/1.50
% 2.55/1.50 thf(fact_34_connected__refl,axiom,
% 2.55/1.50 ! [V: nat] : ( connected_capacity @ c @ V @ V ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_35_connected__distI,axiom,
% 2.55/1.50 ! [V: nat,D: nat,V3: nat] :
% 2.55/1.50 ( ( dist_capacity @ c @ V @ D @ V3 )
% 2.55/1.50 => ( connected_capacity @ c @ V @ V3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_36_le__refl,axiom,
% 2.55/1.50 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_37_le__trans,axiom,
% 2.55/1.50 ! [I: nat,J: nat,K: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.55/1.50 => ( ( ord_less_eq_nat @ J @ K )
% 2.55/1.50 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_38_eq__imp__le,axiom,
% 2.55/1.50 ! [M: nat,N: nat] :
% 2.55/1.50 ( ( M = N )
% 2.55/1.50 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_39_le__antisym,axiom,
% 2.55/1.50 ! [M: nat,N: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.55/1.50 => ( ( ord_less_eq_nat @ N @ M )
% 2.55/1.50 => ( M = N ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_40_nat__le__linear,axiom,
% 2.55/1.50 ! [M: nat,N: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.55/1.50 | ( ord_less_eq_nat @ N @ M ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_41_Nat_Oex__has__greatest__nat,axiom,
% 2.55/1.50 ! [P5: nat > $o,K: nat,B: nat] :
% 2.55/1.50 ( ( P5 @ K )
% 2.55/1.50 => ( ! [Y: nat] :
% 2.55/1.50 ( ( P5 @ Y )
% 2.55/1.50 => ( ord_less_eq_nat @ Y @ B ) )
% 2.55/1.50 => ? [X: nat] :
% 2.55/1.50 ( ( P5 @ X )
% 2.55/1.50 & ! [Y2: nat] :
% 2.55/1.50 ( ( P5 @ Y2 )
% 2.55/1.50 => ( ord_less_eq_nat @ Y2 @ X ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_42_add__le__imp__le__right,axiom,
% 2.55/1.50 ! [A: nat,C: nat,B: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.55/1.50 => ( ord_less_eq_nat @ A @ B ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_43_add__le__imp__le__left,axiom,
% 2.55/1.50 ! [C: nat,A: nat,B: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.55/1.50 => ( ord_less_eq_nat @ A @ B ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_44_le__iff__add,axiom,
% 2.55/1.50 ( ord_less_eq_nat
% 2.55/1.50 = ( ^ [A2: nat,B2: nat] :
% 2.55/1.50 ? [C2: nat] :
% 2.55/1.50 ( B2
% 2.55/1.50 = ( plus_plus_nat @ A2 @ C2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_45_mem__Collect__eq,axiom,
% 2.55/1.50 ! [A: nat,P5: nat > $o] :
% 2.55/1.50 ( ( member_nat @ A @ ( collect_nat @ P5 ) )
% 2.55/1.50 = ( P5 @ A ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_46_Collect__mem__eq,axiom,
% 2.55/1.50 ! [A3: set_nat] :
% 2.55/1.50 ( ( collect_nat
% 2.55/1.50 @ ^ [X2: nat] : ( member_nat @ X2 @ A3 ) )
% 2.55/1.50 = A3 ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_47_Collect__cong,axiom,
% 2.55/1.50 ! [P5: nat > $o,Q: nat > $o] :
% 2.55/1.50 ( ! [X: nat] :
% 2.55/1.50 ( ( P5 @ X )
% 2.55/1.50 = ( Q @ X ) )
% 2.55/1.50 => ( ( collect_nat @ P5 )
% 2.55/1.50 = ( collect_nat @ Q ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_48_add__right__mono,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.55/1.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_49_less__eqE,axiom,
% 2.55/1.50 ! [A: nat,B: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.55/1.50 => ~ ! [C3: nat] :
% 2.55/1.50 ( B
% 2.55/1.50 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_50_add__left__mono,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.55/1.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_51_add__mono,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat,D: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.55/1.50 => ( ( ord_less_eq_nat @ C @ D )
% 2.55/1.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_52_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.55/1.50 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.55/1.50 ( ( ( ord_less_eq_nat @ I @ J )
% 2.55/1.50 & ( ord_less_eq_nat @ K @ L ) )
% 2.55/1.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_53_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.55/1.50 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.55/1.50 ( ( ( I = J )
% 2.55/1.50 & ( ord_less_eq_nat @ K @ L ) )
% 2.55/1.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_54_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.55/1.50 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.55/1.50 ( ( ( ord_less_eq_nat @ I @ J )
% 2.55/1.50 & ( K = L ) )
% 2.55/1.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_55_less__mono__imp__le__mono,axiom,
% 2.55/1.50 ! [F: nat > nat,I: nat,J: nat] :
% 2.55/1.50 ( ! [I2: nat,J2: nat] :
% 2.55/1.50 ( ( ord_less_nat @ I2 @ J2 )
% 2.55/1.50 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 2.55/1.50 => ( ( ord_less_eq_nat @ I @ J )
% 2.55/1.50 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_56_le__neq__implies__less,axiom,
% 2.55/1.50 ! [M: nat,N: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.55/1.50 => ( ( M != N )
% 2.55/1.50 => ( ord_less_nat @ M @ N ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_57_less__or__eq__imp__le,axiom,
% 2.55/1.50 ! [M: nat,N: nat] :
% 2.55/1.50 ( ( ( ord_less_nat @ M @ N )
% 2.55/1.50 | ( M = N ) )
% 2.55/1.50 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_58_le__eq__less__or__eq,axiom,
% 2.55/1.50 ( ord_less_eq_nat
% 2.55/1.50 = ( ^ [M2: nat,N2: nat] :
% 2.55/1.50 ( ( ord_less_nat @ M2 @ N2 )
% 2.55/1.50 | ( M2 = N2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_59_less__imp__le__nat,axiom,
% 2.55/1.50 ! [M: nat,N: nat] :
% 2.55/1.50 ( ( ord_less_nat @ M @ N )
% 2.55/1.50 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_60_nat__less__le,axiom,
% 2.55/1.50 ( ord_less_nat
% 2.55/1.50 = ( ^ [M2: nat,N2: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ M2 @ N2 )
% 2.55/1.50 & ( M2 != N2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_61_nat__le__iff__add,axiom,
% 2.55/1.50 ( ord_less_eq_nat
% 2.55/1.50 = ( ^ [M2: nat,N2: nat] :
% 2.55/1.50 ? [K2: nat] :
% 2.55/1.50 ( N2
% 2.55/1.50 = ( plus_plus_nat @ M2 @ K2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_62_trans__le__add2,axiom,
% 2.55/1.50 ! [I: nat,J: nat,M: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.55/1.50 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_63_trans__le__add1,axiom,
% 2.55/1.50 ! [I: nat,J: nat,M: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.55/1.50 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_64_add__le__mono1,axiom,
% 2.55/1.50 ! [I: nat,J: nat,K: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.55/1.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_65_add__le__mono,axiom,
% 2.55/1.50 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.55/1.50 => ( ( ord_less_eq_nat @ K @ L )
% 2.55/1.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_66_le__Suc__ex,axiom,
% 2.55/1.50 ! [K: nat,L: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ K @ L )
% 2.55/1.50 => ? [N3: nat] :
% 2.55/1.50 ( L
% 2.55/1.50 = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_67_add__leD2,axiom,
% 2.55/1.50 ! [M: nat,K: nat,N: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 2.55/1.50 => ( ord_less_eq_nat @ K @ N ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_68_add__leD1,axiom,
% 2.55/1.50 ! [M: nat,K: nat,N: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 2.55/1.50 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_69_le__add2,axiom,
% 2.55/1.50 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_70_le__add1,axiom,
% 2.55/1.50 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_71_add__leE,axiom,
% 2.55/1.50 ! [M: nat,K: nat,N: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 2.55/1.50 => ~ ( ( ord_less_eq_nat @ M @ N )
% 2.55/1.50 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_72_add__right__imp__eq,axiom,
% 2.55/1.50 ! [B: nat,A: nat,C: nat] :
% 2.55/1.50 ( ( ( plus_plus_nat @ B @ A )
% 2.55/1.50 = ( plus_plus_nat @ C @ A ) )
% 2.55/1.50 => ( B = C ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_73_add__left__imp__eq,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat] :
% 2.55/1.50 ( ( ( plus_plus_nat @ A @ B )
% 2.55/1.50 = ( plus_plus_nat @ A @ C ) )
% 2.55/1.50 => ( B = C ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_74_add_Oleft__commute,axiom,
% 2.55/1.50 ! [B: nat,A: nat,C: nat] :
% 2.55/1.50 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 2.55/1.50 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_75_add_Ocommute,axiom,
% 2.55/1.50 ( plus_plus_nat
% 2.55/1.50 = ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_76_add_Oassoc,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat] :
% 2.55/1.50 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.55/1.50 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_77_group__cancel_Oadd2,axiom,
% 2.55/1.50 ! [B3: nat,K: nat,B: nat,A: nat] :
% 2.55/1.50 ( ( B3
% 2.55/1.50 = ( plus_plus_nat @ K @ B ) )
% 2.55/1.50 => ( ( plus_plus_nat @ A @ B3 )
% 2.55/1.50 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_78_group__cancel_Oadd1,axiom,
% 2.55/1.50 ! [A3: nat,K: nat,A: nat,B: nat] :
% 2.55/1.50 ( ( A3
% 2.55/1.50 = ( plus_plus_nat @ K @ A ) )
% 2.55/1.50 => ( ( plus_plus_nat @ A3 @ B )
% 2.55/1.50 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_79_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.55/1.50 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.55/1.50 ( ( ( I = J )
% 2.55/1.50 & ( K = L ) )
% 2.55/1.50 => ( ( plus_plus_nat @ I @ K )
% 2.55/1.50 = ( plus_plus_nat @ J @ L ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_80_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat] :
% 2.55/1.50 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.55/1.50 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_81_linorder__neqE__nat,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ( X3 != Y3 )
% 2.55/1.50 => ( ~ ( ord_less_nat @ X3 @ Y3 )
% 2.55/1.50 => ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_82_infinite__descent,axiom,
% 2.55/1.50 ! [P5: nat > $o,N: nat] :
% 2.55/1.50 ( ! [N3: nat] :
% 2.55/1.50 ( ~ ( P5 @ N3 )
% 2.55/1.50 => ? [M3: nat] :
% 2.55/1.50 ( ( ord_less_nat @ M3 @ N3 )
% 2.55/1.50 & ~ ( P5 @ M3 ) ) )
% 2.55/1.50 => ( P5 @ N ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_83_nat__less__induct,axiom,
% 2.55/1.50 ! [P5: nat > $o,N: nat] :
% 2.55/1.50 ( ! [N3: nat] :
% 2.55/1.50 ( ! [M3: nat] :
% 2.55/1.50 ( ( ord_less_nat @ M3 @ N3 )
% 2.55/1.50 => ( P5 @ M3 ) )
% 2.55/1.50 => ( P5 @ N3 ) )
% 2.55/1.50 => ( P5 @ N ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_84_less__irrefl__nat,axiom,
% 2.55/1.50 ! [N: nat] :
% 2.55/1.50 ~ ( ord_less_nat @ N @ N ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_85_less__not__refl3,axiom,
% 2.55/1.50 ! [S: nat,T: nat] :
% 2.55/1.50 ( ( ord_less_nat @ S @ T )
% 2.55/1.50 => ( S != T ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_86_less__not__refl2,axiom,
% 2.55/1.50 ! [N: nat,M: nat] :
% 2.55/1.50 ( ( ord_less_nat @ N @ M )
% 2.55/1.50 => ( M != N ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_87_less__not__refl,axiom,
% 2.55/1.50 ! [N: nat] :
% 2.55/1.50 ~ ( ord_less_nat @ N @ N ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_88_nat__neq__iff,axiom,
% 2.55/1.50 ! [M: nat,N: nat] :
% 2.55/1.50 ( ( M != N )
% 2.55/1.50 = ( ( ord_less_nat @ M @ N )
% 2.55/1.50 | ( ord_less_nat @ N @ M ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_89_size__neq__size__imp__neq,axiom,
% 2.55/1.50 ! [X3: list_P559422087at_nat,Y3: list_P559422087at_nat] :
% 2.55/1.50 ( ( ( size_s1990949619at_nat @ X3 )
% 2.55/1.50 != ( size_s1990949619at_nat @ Y3 ) )
% 2.55/1.50 => ( X3 != Y3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_90_add__less__le__mono,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat,D: nat] :
% 2.55/1.50 ( ( ord_less_nat @ A @ B )
% 2.55/1.50 => ( ( ord_less_eq_nat @ C @ D )
% 2.55/1.50 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_91_add__le__less__mono,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat,D: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.55/1.50 => ( ( ord_less_nat @ C @ D )
% 2.55/1.50 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_92_add__mono__thms__linordered__field_I3_J,axiom,
% 2.55/1.50 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.55/1.50 ( ( ( ord_less_nat @ I @ J )
% 2.55/1.50 & ( ord_less_eq_nat @ K @ L ) )
% 2.55/1.50 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_93_add__mono__thms__linordered__field_I4_J,axiom,
% 2.55/1.50 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.55/1.50 ( ( ( ord_less_eq_nat @ I @ J )
% 2.55/1.50 & ( ord_less_nat @ K @ L ) )
% 2.55/1.50 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_94_mono__nat__linear__lb,axiom,
% 2.55/1.50 ! [F: nat > nat,M: nat,K: nat] :
% 2.55/1.50 ( ! [M4: nat,N3: nat] :
% 2.55/1.50 ( ( ord_less_nat @ M4 @ N3 )
% 2.55/1.50 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 2.55/1.50 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_95_add__less__imp__less__right,axiom,
% 2.55/1.50 ! [A: nat,C: nat,B: nat] :
% 2.55/1.50 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.55/1.50 => ( ord_less_nat @ A @ B ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_96_add__less__imp__less__left,axiom,
% 2.55/1.50 ! [C: nat,A: nat,B: nat] :
% 2.55/1.50 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.55/1.50 => ( ord_less_nat @ A @ B ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_97_add__strict__right__mono,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat] :
% 2.55/1.50 ( ( ord_less_nat @ A @ B )
% 2.55/1.50 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_98_add__strict__left__mono,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat] :
% 2.55/1.50 ( ( ord_less_nat @ A @ B )
% 2.55/1.50 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_99_add__strict__mono,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat,D: nat] :
% 2.55/1.50 ( ( ord_less_nat @ A @ B )
% 2.55/1.50 => ( ( ord_less_nat @ C @ D )
% 2.55/1.50 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_100_add__mono__thms__linordered__field_I1_J,axiom,
% 2.55/1.50 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.55/1.50 ( ( ( ord_less_nat @ I @ J )
% 2.55/1.50 & ( K = L ) )
% 2.55/1.50 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_101_add__mono__thms__linordered__field_I2_J,axiom,
% 2.55/1.50 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.55/1.50 ( ( ( I = J )
% 2.55/1.50 & ( ord_less_nat @ K @ L ) )
% 2.55/1.50 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_102_add__mono__thms__linordered__field_I5_J,axiom,
% 2.55/1.50 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.55/1.50 ( ( ( ord_less_nat @ I @ J )
% 2.55/1.50 & ( ord_less_nat @ K @ L ) )
% 2.55/1.50 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_103_less__add__eq__less,axiom,
% 2.55/1.50 ! [K: nat,L: nat,M: nat,N: nat] :
% 2.55/1.50 ( ( ord_less_nat @ K @ L )
% 2.55/1.50 => ( ( ( plus_plus_nat @ M @ L )
% 2.55/1.50 = ( plus_plus_nat @ K @ N ) )
% 2.55/1.50 => ( ord_less_nat @ M @ N ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_104_trans__less__add2,axiom,
% 2.55/1.50 ! [I: nat,J: nat,M: nat] :
% 2.55/1.50 ( ( ord_less_nat @ I @ J )
% 2.55/1.50 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_105_trans__less__add1,axiom,
% 2.55/1.50 ! [I: nat,J: nat,M: nat] :
% 2.55/1.50 ( ( ord_less_nat @ I @ J )
% 2.55/1.50 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_106_add__less__mono1,axiom,
% 2.55/1.50 ! [I: nat,J: nat,K: nat] :
% 2.55/1.50 ( ( ord_less_nat @ I @ J )
% 2.55/1.50 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_107_not__add__less2,axiom,
% 2.55/1.50 ! [J: nat,I: nat] :
% 2.55/1.50 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_108_not__add__less1,axiom,
% 2.55/1.50 ! [I: nat,J: nat] :
% 2.55/1.50 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_109_add__less__mono,axiom,
% 2.55/1.50 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.55/1.50 ( ( ord_less_nat @ I @ J )
% 2.55/1.50 => ( ( ord_less_nat @ K @ L )
% 2.55/1.50 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_110_add__lessD1,axiom,
% 2.55/1.50 ! [I: nat,J: nat,K: nat] :
% 2.55/1.50 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 2.55/1.50 => ( ord_less_nat @ I @ K ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_111_reachableNodes__def,axiom,
% 2.55/1.50 ! [U: nat] :
% 2.55/1.50 ( ( reacha1693770334pacity @ c @ U )
% 2.55/1.50 = ( collect_nat @ ( connected_capacity @ c @ U ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_112_min__dist__def,axiom,
% 2.55/1.50 ! [V: nat,V3: nat] :
% 2.55/1.50 ( ( min_dist_capacity @ c @ V @ V3 )
% 2.55/1.50 = ( ord_Least_nat
% 2.55/1.50 @ ^ [D4: nat] : ( dist_capacity @ c @ V @ D4 @ V3 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_113_Graph_OisShortestPath__min__dist__def,axiom,
% 2.55/1.50 ( isShor1936442771pacity
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > capacity,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 2.55/1.50 ( ( isPath_capacity @ C2 @ U2 @ P @ V4 )
% 2.55/1.50 & ( ( size_s1990949619at_nat @ P )
% 2.55/1.50 = ( min_dist_capacity @ C2 @ U2 @ V4 ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_114_Graph_OisShortestPath__min__dist__def,axiom,
% 2.55/1.50 ( isShortestPath_a
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 2.55/1.50 ( ( isPath_a @ C2 @ U2 @ P @ V4 )
% 2.55/1.50 & ( ( size_s1990949619at_nat @ P )
% 2.55/1.50 = ( min_dist_a @ C2 @ U2 @ V4 ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_115_Graph_OisShortestPath__def,axiom,
% 2.55/1.50 ( isShor1936442771pacity
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > capacity,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 2.55/1.50 ( ( isPath_capacity @ C2 @ U2 @ P @ V4 )
% 2.55/1.50 & ! [P4: list_P559422087at_nat] :
% 2.55/1.50 ( ( isPath_capacity @ C2 @ U2 @ P4 @ V4 )
% 2.55/1.50 => ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P ) @ ( size_s1990949619at_nat @ P4 ) ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_116_Graph_OisShortestPath__def,axiom,
% 2.55/1.50 ( isShortestPath_a
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 2.55/1.50 ( ( isPath_a @ C2 @ U2 @ P @ V4 )
% 2.55/1.50 & ! [P4: list_P559422087at_nat] :
% 2.55/1.50 ( ( isPath_a @ C2 @ U2 @ P4 @ V4 )
% 2.55/1.50 => ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P ) @ ( size_s1990949619at_nat @ P4 ) ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_117_Graph_Omin__distI2,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,V: nat,V3: nat,Q: nat > $o] :
% 2.55/1.50 ( ( connected_capacity @ C @ V @ V3 )
% 2.55/1.50 => ( ! [D6: nat] :
% 2.55/1.50 ( ( dist_capacity @ C @ V @ D6 @ V3 )
% 2.55/1.50 => ( ! [D7: nat] :
% 2.55/1.50 ( ( dist_capacity @ C @ V @ D7 @ V3 )
% 2.55/1.50 => ( ord_less_eq_nat @ D6 @ D7 ) )
% 2.55/1.50 => ( Q @ D6 ) ) )
% 2.55/1.50 => ( Q @ ( min_dist_capacity @ C @ V @ V3 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_118_Graph_Omin__distI2,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,V: nat,V3: nat,Q: nat > $o] :
% 2.55/1.50 ( ( connected_a @ C @ V @ V3 )
% 2.55/1.50 => ( ! [D6: nat] :
% 2.55/1.50 ( ( dist_a @ C @ V @ D6 @ V3 )
% 2.55/1.50 => ( ! [D7: nat] :
% 2.55/1.50 ( ( dist_a @ C @ V @ D7 @ V3 )
% 2.55/1.50 => ( ord_less_eq_nat @ D6 @ D7 ) )
% 2.55/1.50 => ( Q @ D6 ) ) )
% 2.55/1.50 => ( Q @ ( min_dist_a @ C @ V @ V3 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_119_isShortestPath__alt,axiom,
% 2.55/1.50 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 2.55/1.50 ( ( isShor1936442771pacity @ c @ U @ P2 @ V )
% 2.55/1.50 = ( ( isSimp1359852763pacity @ c @ U @ P2 @ V )
% 2.55/1.50 & ( ( size_s1990949619at_nat @ P2 )
% 2.55/1.50 = ( min_dist_capacity @ c @ U @ V ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_120_Graph_Odist__def,axiom,
% 2.55/1.50 ( dist_capacity
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > capacity,V4: nat,D4: nat,V5: nat] :
% 2.55/1.50 ? [P: list_P559422087at_nat] :
% 2.55/1.50 ( ( isPath_capacity @ C2 @ V4 @ P @ V5 )
% 2.55/1.50 & ( ( size_s1990949619at_nat @ P )
% 2.55/1.50 = D4 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_121_Graph_Odist__def,axiom,
% 2.55/1.50 ( dist_a
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > a,V4: nat,D4: nat,V5: nat] :
% 2.55/1.50 ? [P: list_P559422087at_nat] :
% 2.55/1.50 ( ( isPath_a @ C2 @ V4 @ P @ V5 )
% 2.55/1.50 & ( ( size_s1990949619at_nat @ P )
% 2.55/1.50 = D4 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_122_Graph_OisPath__distD,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,U: nat,P2: list_P559422087at_nat,V: nat] :
% 2.55/1.50 ( ( isPath_capacity @ C @ U @ P2 @ V )
% 2.55/1.50 => ( dist_capacity @ C @ U @ ( size_s1990949619at_nat @ P2 ) @ V ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_123_Graph_OisPath__distD,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,U: nat,P2: list_P559422087at_nat,V: nat] :
% 2.55/1.50 ( ( isPath_a @ C @ U @ P2 @ V )
% 2.55/1.50 => ( dist_a @ C @ U @ ( size_s1990949619at_nat @ P2 ) @ V ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_124_Graph_Omin__dist__is__dist,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,V: nat,V3: nat] :
% 2.55/1.50 ( ( connected_capacity @ C @ V @ V3 )
% 2.55/1.50 => ( dist_capacity @ C @ V @ ( min_dist_capacity @ C @ V @ V3 ) @ V3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_125_Graph_Omin__dist__is__dist,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,V: nat,V3: nat] :
% 2.55/1.50 ( ( connected_a @ C @ V @ V3 )
% 2.55/1.50 => ( dist_a @ C @ V @ ( min_dist_a @ C @ V @ V3 ) @ V3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_126_Graph_Omin__dist__split_I1_J,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.55/1.50 ( ( dist_capacity @ C @ U @ D1 @ W )
% 2.55/1.50 => ( ( dist_capacity @ C @ W @ D2 @ V )
% 2.55/1.50 => ( ( ( min_dist_capacity @ C @ U @ V )
% 2.55/1.50 = ( plus_plus_nat @ D1 @ D2 ) )
% 2.55/1.50 => ( ( min_dist_capacity @ C @ U @ W )
% 2.55/1.50 = D1 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_127_Graph_Omin__dist__split_I1_J,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.55/1.50 ( ( dist_a @ C @ U @ D1 @ W )
% 2.55/1.50 => ( ( dist_a @ C @ W @ D2 @ V )
% 2.55/1.50 => ( ( ( min_dist_a @ C @ U @ V )
% 2.55/1.50 = ( plus_plus_nat @ D1 @ D2 ) )
% 2.55/1.50 => ( ( min_dist_a @ C @ U @ W )
% 2.55/1.50 = D1 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_128_isSPath__pathLE,axiom,
% 2.55/1.50 ! [S: nat,P2: list_P559422087at_nat,T: nat] :
% 2.55/1.50 ( ( isPath_capacity @ c @ S @ P2 @ T )
% 2.55/1.50 => ? [P6: list_P559422087at_nat] : ( isSimp1359852763pacity @ c @ S @ P6 @ T ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_129_shortestPath__is__simple,axiom,
% 2.55/1.50 ! [S: nat,P2: list_P559422087at_nat,T: nat] :
% 2.55/1.50 ( ( isShor1936442771pacity @ c @ S @ P2 @ T )
% 2.55/1.50 => ( isSimp1359852763pacity @ c @ S @ P2 @ T ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_130_Graph_OreachableNodes_Ocong,axiom,
% 2.55/1.50 reacha1693770334pacity = reacha1693770334pacity ).
% 2.55/1.50
% 2.55/1.50 thf(fact_131_Graph_OreachableNodes_Ocong,axiom,
% 2.55/1.50 reachableNodes_a = reachableNodes_a ).
% 2.55/1.50
% 2.55/1.50 thf(fact_132_Graph_OisSimplePath_Ocong,axiom,
% 2.55/1.50 isSimp1359852763pacity = isSimp1359852763pacity ).
% 2.55/1.50
% 2.55/1.50 thf(fact_133_Graph_OisSimplePath_Ocong,axiom,
% 2.55/1.50 isSimplePath_a = isSimplePath_a ).
% 2.55/1.50
% 2.55/1.50 thf(fact_134_Graph_OisSPath__pathLE,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,S: nat,P2: list_P559422087at_nat,T: nat] :
% 2.55/1.50 ( ( isPath_capacity @ C @ S @ P2 @ T )
% 2.55/1.50 => ? [P6: list_P559422087at_nat] : ( isSimp1359852763pacity @ C @ S @ P6 @ T ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_135_Graph_OisSPath__pathLE,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,S: nat,P2: list_P559422087at_nat,T: nat] :
% 2.55/1.50 ( ( isPath_a @ C @ S @ P2 @ T )
% 2.55/1.50 => ? [P6: list_P559422087at_nat] : ( isSimplePath_a @ C @ S @ P6 @ T ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_136_Graph_OshortestPath__is__simple,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,S: nat,P2: list_P559422087at_nat,T: nat] :
% 2.55/1.50 ( ( isShor1936442771pacity @ C @ S @ P2 @ T )
% 2.55/1.50 => ( isSimp1359852763pacity @ C @ S @ P2 @ T ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_137_Graph_OshortestPath__is__simple,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,S: nat,P2: list_P559422087at_nat,T: nat] :
% 2.55/1.50 ( ( isShortestPath_a @ C @ S @ P2 @ T )
% 2.55/1.50 => ( isSimplePath_a @ C @ S @ P2 @ T ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_138_Graph_OreachableNodes__def,axiom,
% 2.55/1.50 ( reacha1693770334pacity
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > capacity,U2: nat] : ( collect_nat @ ( connected_capacity @ C2 @ U2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_139_Graph_OreachableNodes__def,axiom,
% 2.55/1.50 ( reachableNodes_a
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > a,U2: nat] : ( collect_nat @ ( connected_a @ C2 @ U2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_140_Graph_Omin__dist__def,axiom,
% 2.55/1.50 ( min_dist_capacity
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > capacity,V4: nat,V5: nat] :
% 2.55/1.50 ( ord_Least_nat
% 2.55/1.50 @ ^ [D4: nat] : ( dist_capacity @ C2 @ V4 @ D4 @ V5 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_141_Graph_Omin__dist__def,axiom,
% 2.55/1.50 ( min_dist_a
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > a,V4: nat,V5: nat] :
% 2.55/1.50 ( ord_Least_nat
% 2.55/1.50 @ ^ [D4: nat] : ( dist_a @ C2 @ V4 @ D4 @ V5 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_142_Graph_OisShortestPath__alt,axiom,
% 2.55/1.50 ( isShor1936442771pacity
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > capacity,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 2.55/1.50 ( ( isSimp1359852763pacity @ C2 @ U2 @ P @ V4 )
% 2.55/1.50 & ( ( size_s1990949619at_nat @ P )
% 2.55/1.50 = ( min_dist_capacity @ C2 @ U2 @ V4 ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_143_Graph_OisShortestPath__alt,axiom,
% 2.55/1.50 ( isShortestPath_a
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 2.55/1.50 ( ( isSimplePath_a @ C2 @ U2 @ P @ V4 )
% 2.55/1.50 & ( ( size_s1990949619at_nat @ P )
% 2.55/1.50 = ( min_dist_a @ C2 @ U2 @ V4 ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_144_Graph_OisPath_Ocong,axiom,
% 2.55/1.50 isPath_capacity = isPath_capacity ).
% 2.55/1.50
% 2.55/1.50 thf(fact_145_Graph_OisPath_Ocong,axiom,
% 2.55/1.50 isPath_a = isPath_a ).
% 2.55/1.50
% 2.55/1.50 thf(fact_146_Graph_Omin__dist_Ocong,axiom,
% 2.55/1.50 min_dist_capacity = min_dist_capacity ).
% 2.55/1.50
% 2.55/1.50 thf(fact_147_Graph_Omin__dist_Ocong,axiom,
% 2.55/1.50 min_dist_a = min_dist_a ).
% 2.55/1.50
% 2.55/1.50 thf(fact_148_Graph_Oconnected__refl,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,V: nat] : ( connected_capacity @ C @ V @ V ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_149_Graph_Oconnected__refl,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,V: nat] : ( connected_a @ C @ V @ V ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_150_Graph_Oconnected_Ocong,axiom,
% 2.55/1.50 connected_capacity = connected_capacity ).
% 2.55/1.50
% 2.55/1.50 thf(fact_151_Graph_Oconnected_Ocong,axiom,
% 2.55/1.50 connected_a = connected_a ).
% 2.55/1.50
% 2.55/1.50 thf(fact_152_Graph_Odist_Ocong,axiom,
% 2.55/1.50 dist_capacity = dist_capacity ).
% 2.55/1.50
% 2.55/1.50 thf(fact_153_Graph_Odist_Ocong,axiom,
% 2.55/1.50 dist_a = dist_a ).
% 2.55/1.50
% 2.55/1.50 thf(fact_154_Graph_OisShortestPath_Ocong,axiom,
% 2.55/1.50 isShor1936442771pacity = isShor1936442771pacity ).
% 2.55/1.50
% 2.55/1.50 thf(fact_155_Graph_OisShortestPath_Ocong,axiom,
% 2.55/1.50 isShortestPath_a = isShortestPath_a ).
% 2.55/1.50
% 2.55/1.50 thf(fact_156_Graph_Odist__trans,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.55/1.50 ( ( dist_capacity @ C @ U @ D1 @ W )
% 2.55/1.50 => ( ( dist_capacity @ C @ W @ D2 @ V )
% 2.55/1.50 => ( dist_capacity @ C @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_157_Graph_Odist__trans,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.55/1.50 ( ( dist_a @ C @ U @ D1 @ W )
% 2.55/1.50 => ( ( dist_a @ C @ W @ D2 @ V )
% 2.55/1.50 => ( dist_a @ C @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_158_Graph_Oconnected__def,axiom,
% 2.55/1.50 ( connected_capacity
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > capacity,U2: nat,V4: nat] :
% 2.55/1.50 ? [P: list_P559422087at_nat] : ( isPath_capacity @ C2 @ U2 @ P @ V4 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_159_Graph_Oconnected__def,axiom,
% 2.55/1.50 ( connected_a
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > a,U2: nat,V4: nat] :
% 2.55/1.50 ? [P: list_P559422087at_nat] : ( isPath_a @ C2 @ U2 @ P @ V4 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_160_Graph_OshortestPath__is__path,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,U: nat,P2: list_P559422087at_nat,V: nat] :
% 2.55/1.50 ( ( isShor1936442771pacity @ C @ U @ P2 @ V )
% 2.55/1.50 => ( isPath_capacity @ C @ U @ P2 @ V ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_161_Graph_OshortestPath__is__path,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,U: nat,P2: list_P559422087at_nat,V: nat] :
% 2.55/1.50 ( ( isShortestPath_a @ C @ U @ P2 @ V )
% 2.55/1.50 => ( isPath_a @ C @ U @ P2 @ V ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_162_Graph_Oconnected__by__dist,axiom,
% 2.55/1.50 ( connected_capacity
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > capacity,V4: nat,V5: nat] :
% 2.55/1.50 ? [D4: nat] : ( dist_capacity @ C2 @ V4 @ D4 @ V5 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_163_Graph_Oconnected__by__dist,axiom,
% 2.55/1.50 ( connected_a
% 2.55/1.50 = ( ^ [C2: product_prod_nat_nat > a,V4: nat,V5: nat] :
% 2.55/1.50 ? [D4: nat] : ( dist_a @ C2 @ V4 @ D4 @ V5 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_164_Graph_Oconnected__distI,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,V: nat,D: nat,V3: nat] :
% 2.55/1.50 ( ( dist_capacity @ C @ V @ D @ V3 )
% 2.55/1.50 => ( connected_capacity @ C @ V @ V3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_165_Graph_Oconnected__distI,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
% 2.55/1.50 ( ( dist_a @ C @ V @ D @ V3 )
% 2.55/1.50 => ( connected_a @ C @ V @ V3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_166_Graph_Oobtain__shortest__path,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,U: nat,V: nat] :
% 2.55/1.50 ( ( connected_capacity @ C @ U @ V )
% 2.55/1.50 => ~ ! [P3: list_P559422087at_nat] :
% 2.55/1.50 ~ ( isShor1936442771pacity @ C @ U @ P3 @ V ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_167_Graph_Oobtain__shortest__path,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,U: nat,V: nat] :
% 2.55/1.50 ( ( connected_a @ C @ U @ V )
% 2.55/1.50 => ~ ! [P3: list_P559422087at_nat] :
% 2.55/1.50 ~ ( isShortestPath_a @ C @ U @ P3 @ V ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_168_Graph_Omin__dist__less,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,Src: nat,V: nat,D: nat,D3: nat] :
% 2.55/1.50 ( ( connected_capacity @ C @ Src @ V )
% 2.55/1.50 => ( ( ( min_dist_capacity @ C @ Src @ V )
% 2.55/1.50 = D )
% 2.55/1.50 => ( ( ord_less_nat @ D3 @ D )
% 2.55/1.50 => ? [V2: nat] :
% 2.55/1.50 ( ( connected_capacity @ C @ Src @ V2 )
% 2.55/1.50 & ( ( min_dist_capacity @ C @ Src @ V2 )
% 2.55/1.50 = D3 ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_169_Graph_Omin__dist__less,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,Src: nat,V: nat,D: nat,D3: nat] :
% 2.55/1.50 ( ( connected_a @ C @ Src @ V )
% 2.55/1.50 => ( ( ( min_dist_a @ C @ Src @ V )
% 2.55/1.50 = D )
% 2.55/1.50 => ( ( ord_less_nat @ D3 @ D )
% 2.55/1.50 => ? [V2: nat] :
% 2.55/1.50 ( ( connected_a @ C @ Src @ V2 )
% 2.55/1.50 & ( ( min_dist_a @ C @ Src @ V2 )
% 2.55/1.50 = D3 ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_170_Graph_Omin__dist__le,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,Src: nat,V: nat,D3: nat] :
% 2.55/1.50 ( ( connected_capacity @ C @ Src @ V )
% 2.55/1.50 => ( ( ord_less_eq_nat @ D3 @ ( min_dist_capacity @ C @ Src @ V ) )
% 2.55/1.50 => ? [V2: nat] :
% 2.55/1.50 ( ( connected_capacity @ C @ Src @ V2 )
% 2.55/1.50 & ( ( min_dist_capacity @ C @ Src @ V2 )
% 2.55/1.50 = D3 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_171_Graph_Omin__dist__le,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,Src: nat,V: nat,D3: nat] :
% 2.55/1.50 ( ( connected_a @ C @ Src @ V )
% 2.55/1.50 => ( ( ord_less_eq_nat @ D3 @ ( min_dist_a @ C @ Src @ V ) )
% 2.55/1.50 => ? [V2: nat] :
% 2.55/1.50 ( ( connected_a @ C @ Src @ V2 )
% 2.55/1.50 & ( ( min_dist_a @ C @ Src @ V2 )
% 2.55/1.50 = D3 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_172_Graph_Omin__distI__eq,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,V: nat,D: nat,V3: nat] :
% 2.55/1.50 ( ( dist_capacity @ C @ V @ D @ V3 )
% 2.55/1.50 => ( ! [D5: nat] :
% 2.55/1.50 ( ( dist_capacity @ C @ V @ D5 @ V3 )
% 2.55/1.50 => ( ord_less_eq_nat @ D @ D5 ) )
% 2.55/1.50 => ( ( min_dist_capacity @ C @ V @ V3 )
% 2.55/1.50 = D ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_173_Graph_Omin__distI__eq,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
% 2.55/1.50 ( ( dist_a @ C @ V @ D @ V3 )
% 2.55/1.50 => ( ! [D5: nat] :
% 2.55/1.50 ( ( dist_a @ C @ V @ D5 @ V3 )
% 2.55/1.50 => ( ord_less_eq_nat @ D @ D5 ) )
% 2.55/1.50 => ( ( min_dist_a @ C @ V @ V3 )
% 2.55/1.50 = D ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_174_Graph_Omin__dist__minD,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,V: nat,D: nat,V3: nat] :
% 2.55/1.50 ( ( dist_capacity @ C @ V @ D @ V3 )
% 2.55/1.50 => ( ord_less_eq_nat @ ( min_dist_capacity @ C @ V @ V3 ) @ D ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_175_Graph_Omin__dist__minD,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
% 2.55/1.50 ( ( dist_a @ C @ V @ D @ V3 )
% 2.55/1.50 => ( ord_less_eq_nat @ ( min_dist_a @ C @ V @ V3 ) @ D ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_176_Graph_Omin__dist__split_I2_J,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.55/1.50 ( ( dist_capacity @ C @ U @ D1 @ W )
% 2.55/1.50 => ( ( dist_capacity @ C @ W @ D2 @ V )
% 2.55/1.50 => ( ( ( min_dist_capacity @ C @ U @ V )
% 2.55/1.50 = ( plus_plus_nat @ D1 @ D2 ) )
% 2.55/1.50 => ( ( min_dist_capacity @ C @ W @ V )
% 2.55/1.50 = D2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_177_Graph_Omin__dist__split_I2_J,axiom,
% 2.55/1.50 ! [C: product_prod_nat_nat > a,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.55/1.50 ( ( dist_a @ C @ U @ D1 @ W )
% 2.55/1.50 => ( ( dist_a @ C @ W @ D2 @ V )
% 2.55/1.50 => ( ( ( min_dist_a @ C @ U @ V )
% 2.55/1.50 = ( plus_plus_nat @ D1 @ D2 ) )
% 2.55/1.50 => ( ( min_dist_a @ C @ W @ V )
% 2.55/1.50 = D2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_178__C1_Oprems_C_I3_J,axiom,
% 2.55/1.50 isPath_a @ c2 @ ua @ p2_a @ t ).
% 2.55/1.50
% 2.55/1.50 thf(fact_179_not__less__Least,axiom,
% 2.55/1.50 ! [K: nat,P5: nat > $o] :
% 2.55/1.50 ( ( ord_less_nat @ K @ ( ord_Least_nat @ P5 ) )
% 2.55/1.50 => ~ ( P5 @ K ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_180_Least__le,axiom,
% 2.55/1.50 ! [P5: nat > $o,K: nat] :
% 2.55/1.50 ( ( P5 @ K )
% 2.55/1.50 => ( ord_less_eq_nat @ ( ord_Least_nat @ P5 ) @ K ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_181_g_H_Oconnected__by__dist,axiom,
% 2.55/1.50 ! [V: nat,V3: nat] :
% 2.55/1.50 ( ( connected_a @ c2 @ V @ V3 )
% 2.55/1.50 = ( ? [D4: nat] : ( dist_a @ c2 @ V @ D4 @ V3 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_182_g_H_Omin__dist__is__dist,axiom,
% 2.55/1.50 ! [V: nat,V3: nat] :
% 2.55/1.50 ( ( connected_a @ c2 @ V @ V3 )
% 2.55/1.50 => ( dist_a @ c2 @ V @ ( min_dist_a @ c2 @ V @ V3 ) @ V3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_183_g_H_Oobtain__shortest__path,axiom,
% 2.55/1.50 ! [U: nat,V: nat] :
% 2.55/1.50 ( ( connected_a @ c2 @ U @ V )
% 2.55/1.50 => ~ ! [P3: list_P559422087at_nat] :
% 2.55/1.50 ~ ( isShortestPath_a @ c2 @ U @ P3 @ V ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_184_g_H_OshortestPath__is__simple,axiom,
% 2.55/1.50 ! [S: nat,P2: list_P559422087at_nat,T: nat] :
% 2.55/1.50 ( ( isShortestPath_a @ c2 @ S @ P2 @ T )
% 2.55/1.50 => ( isSimplePath_a @ c2 @ S @ P2 @ T ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_185_g_H_OreachableNodes__def,axiom,
% 2.55/1.50 ! [U: nat] :
% 2.55/1.50 ( ( reachableNodes_a @ c2 @ U )
% 2.55/1.50 = ( collect_nat @ ( connected_a @ c2 @ U ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_186_g_H_Omin__dist__less,axiom,
% 2.55/1.50 ! [Src: nat,V: nat,D: nat,D3: nat] :
% 2.55/1.50 ( ( connected_a @ c2 @ Src @ V )
% 2.55/1.50 => ( ( ( min_dist_a @ c2 @ Src @ V )
% 2.55/1.50 = D )
% 2.55/1.50 => ( ( ord_less_nat @ D3 @ D )
% 2.55/1.50 => ? [V2: nat] :
% 2.55/1.50 ( ( connected_a @ c2 @ Src @ V2 )
% 2.55/1.50 & ( ( min_dist_a @ c2 @ Src @ V2 )
% 2.55/1.50 = D3 ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_187_g_H_Omin__distI2,axiom,
% 2.55/1.50 ! [V: nat,V3: nat,Q: nat > $o] :
% 2.55/1.50 ( ( connected_a @ c2 @ V @ V3 )
% 2.55/1.50 => ( ! [D6: nat] :
% 2.55/1.50 ( ( dist_a @ c2 @ V @ D6 @ V3 )
% 2.55/1.50 => ( ! [D7: nat] :
% 2.55/1.50 ( ( dist_a @ c2 @ V @ D7 @ V3 )
% 2.55/1.50 => ( ord_less_eq_nat @ D6 @ D7 ) )
% 2.55/1.50 => ( Q @ D6 ) ) )
% 2.55/1.50 => ( Q @ ( min_dist_a @ c2 @ V @ V3 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_188_g_H_Omin__distI__eq,axiom,
% 2.55/1.50 ! [V: nat,D: nat,V3: nat] :
% 2.55/1.50 ( ( dist_a @ c2 @ V @ D @ V3 )
% 2.55/1.50 => ( ! [D5: nat] :
% 2.55/1.50 ( ( dist_a @ c2 @ V @ D5 @ V3 )
% 2.55/1.50 => ( ord_less_eq_nat @ D @ D5 ) )
% 2.55/1.50 => ( ( min_dist_a @ c2 @ V @ V3 )
% 2.55/1.50 = D ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_189_g_H_Omin__dist__le,axiom,
% 2.55/1.50 ! [Src: nat,V: nat,D3: nat] :
% 2.55/1.50 ( ( connected_a @ c2 @ Src @ V )
% 2.55/1.50 => ( ( ord_less_eq_nat @ D3 @ ( min_dist_a @ c2 @ Src @ V ) )
% 2.55/1.50 => ? [V2: nat] :
% 2.55/1.50 ( ( connected_a @ c2 @ Src @ V2 )
% 2.55/1.50 & ( ( min_dist_a @ c2 @ Src @ V2 )
% 2.55/1.50 = D3 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_190_g_H_Omin__dist__minD,axiom,
% 2.55/1.50 ! [V: nat,D: nat,V3: nat] :
% 2.55/1.50 ( ( dist_a @ c2 @ V @ D @ V3 )
% 2.55/1.50 => ( ord_less_eq_nat @ ( min_dist_a @ c2 @ V @ V3 ) @ D ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_191_g_H_Omin__dist__split_I2_J,axiom,
% 2.55/1.50 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.55/1.50 ( ( dist_a @ c2 @ U @ D1 @ W )
% 2.55/1.50 => ( ( dist_a @ c2 @ W @ D2 @ V )
% 2.55/1.50 => ( ( ( min_dist_a @ c2 @ U @ V )
% 2.55/1.50 = ( plus_plus_nat @ D1 @ D2 ) )
% 2.55/1.50 => ( ( min_dist_a @ c2 @ W @ V )
% 2.55/1.50 = D2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_192_g_H_Omin__dist__split_I1_J,axiom,
% 2.55/1.50 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.55/1.50 ( ( dist_a @ c2 @ U @ D1 @ W )
% 2.55/1.50 => ( ( dist_a @ c2 @ W @ D2 @ V )
% 2.55/1.50 => ( ( ( min_dist_a @ c2 @ U @ V )
% 2.55/1.50 = ( plus_plus_nat @ D1 @ D2 ) )
% 2.55/1.50 => ( ( min_dist_a @ c2 @ U @ W )
% 2.55/1.50 = D1 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_193_g_H_Odist__trans,axiom,
% 2.55/1.50 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.55/1.50 ( ( dist_a @ c2 @ U @ D1 @ W )
% 2.55/1.50 => ( ( dist_a @ c2 @ W @ D2 @ V )
% 2.55/1.50 => ( dist_a @ c2 @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_194_g_H_Oconnected__def,axiom,
% 2.55/1.50 ! [U: nat,V: nat] :
% 2.55/1.50 ( ( connected_a @ c2 @ U @ V )
% 2.55/1.50 = ( ? [P: list_P559422087at_nat] : ( isPath_a @ c2 @ U @ P @ V ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_195_g_H_OisSPath__pathLE,axiom,
% 2.55/1.50 ! [S: nat,P2: list_P559422087at_nat,T: nat] :
% 2.55/1.50 ( ( isPath_a @ c2 @ S @ P2 @ T )
% 2.55/1.50 => ? [P6: list_P559422087at_nat] : ( isSimplePath_a @ c2 @ S @ P6 @ T ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_196_g_H_OshortestPath__is__path,axiom,
% 2.55/1.50 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 2.55/1.50 ( ( isShortestPath_a @ c2 @ U @ P2 @ V )
% 2.55/1.50 => ( isPath_a @ c2 @ U @ P2 @ V ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_197_g_H_OisShortestPath__alt,axiom,
% 2.55/1.50 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 2.55/1.50 ( ( isShortestPath_a @ c2 @ U @ P2 @ V )
% 2.55/1.50 = ( ( isSimplePath_a @ c2 @ U @ P2 @ V )
% 2.55/1.50 & ( ( size_s1990949619at_nat @ P2 )
% 2.55/1.50 = ( min_dist_a @ c2 @ U @ V ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_198_g_H_Omin__dist__def,axiom,
% 2.55/1.50 ! [V: nat,V3: nat] :
% 2.55/1.50 ( ( min_dist_a @ c2 @ V @ V3 )
% 2.55/1.50 = ( ord_Least_nat
% 2.55/1.50 @ ^ [D4: nat] : ( dist_a @ c2 @ V @ D4 @ V3 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_199_g_H_Odist__def,axiom,
% 2.55/1.50 ! [V: nat,D: nat,V3: nat] :
% 2.55/1.50 ( ( dist_a @ c2 @ V @ D @ V3 )
% 2.55/1.50 = ( ? [P: list_P559422087at_nat] :
% 2.55/1.50 ( ( isPath_a @ c2 @ V @ P @ V3 )
% 2.55/1.50 & ( ( size_s1990949619at_nat @ P )
% 2.55/1.50 = D ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_200_g_H_OisPath__distD,axiom,
% 2.55/1.50 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 2.55/1.50 ( ( isPath_a @ c2 @ U @ P2 @ V )
% 2.55/1.50 => ( dist_a @ c2 @ U @ ( size_s1990949619at_nat @ P2 ) @ V ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_201_g_H_OisShortestPath__min__dist__def,axiom,
% 2.55/1.50 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 2.55/1.50 ( ( isShortestPath_a @ c2 @ U @ P2 @ V )
% 2.55/1.50 = ( ( isPath_a @ c2 @ U @ P2 @ V )
% 2.55/1.50 & ( ( size_s1990949619at_nat @ P2 )
% 2.55/1.50 = ( min_dist_a @ c2 @ U @ V ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_202_order__refl,axiom,
% 2.55/1.50 ! [X3: nat] : ( ord_less_eq_nat @ X3 @ X3 ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_203_g_H_OisShortestPath__def,axiom,
% 2.55/1.50 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 2.55/1.50 ( ( isShortestPath_a @ c2 @ U @ P2 @ V )
% 2.55/1.50 = ( ( isPath_a @ c2 @ U @ P2 @ V )
% 2.55/1.50 & ! [P4: list_P559422087at_nat] :
% 2.55/1.50 ( ( isPath_a @ c2 @ U @ P4 @ V )
% 2.55/1.50 => ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P2 ) @ ( size_s1990949619at_nat @ P4 ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_204_assms_I5_J,axiom,
% 2.55/1.50 isPath_a @ c2 @ s @ p3 @ t ).
% 2.55/1.50
% 2.55/1.50 thf(fact_205__092_060open_062g_H_OisPath_Au_____Ap2_H_____At_092_060close_062,axiom,
% 2.55/1.50 isPath_a @ c2 @ u @ p2 @ t ).
% 2.55/1.50
% 2.55/1.50 thf(fact_206_g_H_Oconnected__distI,axiom,
% 2.55/1.50 ! [V: nat,D: nat,V3: nat] :
% 2.55/1.50 ( ( dist_a @ c2 @ V @ D @ V3 )
% 2.55/1.50 => ( connected_a @ c2 @ V @ V3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_207_g_H_Oconnected__refl,axiom,
% 2.55/1.50 ! [V: nat] : ( connected_a @ c2 @ V @ V ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_208_P2_H,axiom,
% 2.55/1.50 isPath_a @ c2 @ ua @ p2_a @ t ).
% 2.55/1.50
% 2.55/1.50 thf(fact_209_order__subst1,axiom,
% 2.55/1.50 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 2.55/1.50 => ( ( ord_less_eq_nat @ B @ C )
% 2.55/1.50 => ( ! [X: nat,Y: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ X @ Y )
% 2.55/1.50 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 2.55/1.50 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_210_order__subst2,axiom,
% 2.55/1.50 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.55/1.50 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 2.55/1.50 => ( ! [X: nat,Y: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ X @ Y )
% 2.55/1.50 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 2.55/1.50 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_211_ord__eq__le__subst,axiom,
% 2.55/1.50 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.55/1.50 ( ( A
% 2.55/1.50 = ( F @ B ) )
% 2.55/1.50 => ( ( ord_less_eq_nat @ B @ C )
% 2.55/1.50 => ( ! [X: nat,Y: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ X @ Y )
% 2.55/1.50 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 2.55/1.50 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_212_ord__le__eq__subst,axiom,
% 2.55/1.50 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.55/1.50 => ( ( ( F @ B )
% 2.55/1.50 = C )
% 2.55/1.50 => ( ! [X: nat,Y: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ X @ Y )
% 2.55/1.50 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 2.55/1.50 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_213_eq__iff,axiom,
% 2.55/1.50 ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 2.55/1.50 = ( ^ [X2: nat,Y5: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ X2 @ Y5 )
% 2.55/1.50 & ( ord_less_eq_nat @ Y5 @ X2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_214_antisym,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.55/1.50 => ( ( ord_less_eq_nat @ Y3 @ X3 )
% 2.55/1.50 => ( X3 = Y3 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_215_linear,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.55/1.50 | ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_216_eq__refl,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ( X3 = Y3 )
% 2.55/1.50 => ( ord_less_eq_nat @ X3 @ Y3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_217_le__cases,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ~ ( ord_less_eq_nat @ X3 @ Y3 )
% 2.55/1.50 => ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_218_order_Otrans,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.55/1.50 => ( ( ord_less_eq_nat @ B @ C )
% 2.55/1.50 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_219_le__cases3,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat,Z2: nat] :
% 2.55/1.50 ( ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.55/1.50 => ~ ( ord_less_eq_nat @ Y3 @ Z2 ) )
% 2.55/1.50 => ( ( ( ord_less_eq_nat @ Y3 @ X3 )
% 2.55/1.50 => ~ ( ord_less_eq_nat @ X3 @ Z2 ) )
% 2.55/1.50 => ( ( ( ord_less_eq_nat @ X3 @ Z2 )
% 2.55/1.50 => ~ ( ord_less_eq_nat @ Z2 @ Y3 ) )
% 2.55/1.50 => ( ( ( ord_less_eq_nat @ Z2 @ Y3 )
% 2.55/1.50 => ~ ( ord_less_eq_nat @ Y3 @ X3 ) )
% 2.55/1.50 => ( ( ( ord_less_eq_nat @ Y3 @ Z2 )
% 2.55/1.50 => ~ ( ord_less_eq_nat @ Z2 @ X3 ) )
% 2.55/1.50 => ~ ( ( ord_less_eq_nat @ Z2 @ X3 )
% 2.55/1.50 => ~ ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_220_antisym__conv,axiom,
% 2.55/1.50 ! [Y3: nat,X3: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ Y3 @ X3 )
% 2.55/1.50 => ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.55/1.50 = ( X3 = Y3 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_221_order__class_Oorder_Oeq__iff,axiom,
% 2.55/1.50 ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 2.55/1.50 = ( ^ [A2: nat,B2: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.55/1.50 & ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_222_ord__eq__le__trans,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat] :
% 2.55/1.50 ( ( A = B )
% 2.55/1.50 => ( ( ord_less_eq_nat @ B @ C )
% 2.55/1.50 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_223_ord__le__eq__trans,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.55/1.50 => ( ( B = C )
% 2.55/1.50 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_224_order__class_Oorder_Oantisym,axiom,
% 2.55/1.50 ! [A: nat,B: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.55/1.50 => ( ( ord_less_eq_nat @ B @ A )
% 2.55/1.50 => ( A = B ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_225_order__trans,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat,Z2: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.55/1.50 => ( ( ord_less_eq_nat @ Y3 @ Z2 )
% 2.55/1.50 => ( ord_less_eq_nat @ X3 @ Z2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_226_dual__order_Orefl,axiom,
% 2.55/1.50 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_227_linorder__wlog,axiom,
% 2.55/1.50 ! [P5: nat > nat > $o,A: nat,B: nat] :
% 2.55/1.50 ( ! [A4: nat,B4: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ A4 @ B4 )
% 2.55/1.50 => ( P5 @ A4 @ B4 ) )
% 2.55/1.50 => ( ! [A4: nat,B4: nat] :
% 2.55/1.50 ( ( P5 @ B4 @ A4 )
% 2.55/1.50 => ( P5 @ A4 @ B4 ) )
% 2.55/1.50 => ( P5 @ A @ B ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_228_dual__order_Otrans,axiom,
% 2.55/1.50 ! [B: nat,A: nat,C: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ B @ A )
% 2.55/1.50 => ( ( ord_less_eq_nat @ C @ B )
% 2.55/1.50 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_229_dual__order_Oeq__iff,axiom,
% 2.55/1.50 ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 2.55/1.50 = ( ^ [A2: nat,B2: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.55/1.50 & ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_230_dual__order_Oantisym,axiom,
% 2.55/1.50 ! [B: nat,A: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ B @ A )
% 2.55/1.50 => ( ( ord_less_eq_nat @ A @ B )
% 2.55/1.50 => ( A = B ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_231_dual__order_Ostrict__implies__not__eq,axiom,
% 2.55/1.50 ! [B: nat,A: nat] :
% 2.55/1.50 ( ( ord_less_nat @ B @ A )
% 2.55/1.50 => ( A != B ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_232_order_Ostrict__implies__not__eq,axiom,
% 2.55/1.50 ! [A: nat,B: nat] :
% 2.55/1.50 ( ( ord_less_nat @ A @ B )
% 2.55/1.50 => ( A != B ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_233_not__less__iff__gr__or__eq,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
% 2.55/1.50 = ( ( ord_less_nat @ Y3 @ X3 )
% 2.55/1.50 | ( X3 = Y3 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_234_dual__order_Ostrict__trans,axiom,
% 2.55/1.50 ! [B: nat,A: nat,C: nat] :
% 2.55/1.50 ( ( ord_less_nat @ B @ A )
% 2.55/1.50 => ( ( ord_less_nat @ C @ B )
% 2.55/1.50 => ( ord_less_nat @ C @ A ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_235_linorder__less__wlog,axiom,
% 2.55/1.50 ! [P5: nat > nat > $o,A: nat,B: nat] :
% 2.55/1.50 ( ! [A4: nat,B4: nat] :
% 2.55/1.50 ( ( ord_less_nat @ A4 @ B4 )
% 2.55/1.50 => ( P5 @ A4 @ B4 ) )
% 2.55/1.50 => ( ! [A4: nat] : ( P5 @ A4 @ A4 )
% 2.55/1.50 => ( ! [A4: nat,B4: nat] :
% 2.55/1.50 ( ( P5 @ B4 @ A4 )
% 2.55/1.50 => ( P5 @ A4 @ B4 ) )
% 2.55/1.50 => ( P5 @ A @ B ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_236_exists__least__iff,axiom,
% 2.55/1.50 ( ( ^ [P7: nat > $o] :
% 2.55/1.50 ? [X4: nat] : ( P7 @ X4 ) )
% 2.55/1.50 = ( ^ [P8: nat > $o] :
% 2.55/1.50 ? [N2: nat] :
% 2.55/1.50 ( ( P8 @ N2 )
% 2.55/1.50 & ! [M2: nat] :
% 2.55/1.50 ( ( ord_less_nat @ M2 @ N2 )
% 2.55/1.50 => ~ ( P8 @ M2 ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_237_less__imp__not__less,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ( ord_less_nat @ X3 @ Y3 )
% 2.55/1.50 => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_238_order_Ostrict__trans,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat] :
% 2.55/1.50 ( ( ord_less_nat @ A @ B )
% 2.55/1.50 => ( ( ord_less_nat @ B @ C )
% 2.55/1.50 => ( ord_less_nat @ A @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_239_dual__order_Oirrefl,axiom,
% 2.55/1.50 ! [A: nat] :
% 2.55/1.50 ~ ( ord_less_nat @ A @ A ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_240_linorder__cases,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ~ ( ord_less_nat @ X3 @ Y3 )
% 2.55/1.50 => ( ( X3 != Y3 )
% 2.55/1.50 => ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_241_less__imp__triv,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat,P5: $o] :
% 2.55/1.50 ( ( ord_less_nat @ X3 @ Y3 )
% 2.55/1.50 => ( ( ord_less_nat @ Y3 @ X3 )
% 2.55/1.50 => P5 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_242_less__imp__not__eq2,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ( ord_less_nat @ X3 @ Y3 )
% 2.55/1.50 => ( Y3 != X3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_243_antisym__conv3,axiom,
% 2.55/1.50 ! [Y3: nat,X3: nat] :
% 2.55/1.50 ( ~ ( ord_less_nat @ Y3 @ X3 )
% 2.55/1.50 => ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
% 2.55/1.50 = ( X3 = Y3 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_244_less__induct,axiom,
% 2.55/1.50 ! [P5: nat > $o,A: nat] :
% 2.55/1.50 ( ! [X: nat] :
% 2.55/1.50 ( ! [Y2: nat] :
% 2.55/1.50 ( ( ord_less_nat @ Y2 @ X )
% 2.55/1.50 => ( P5 @ Y2 ) )
% 2.55/1.50 => ( P5 @ X ) )
% 2.55/1.50 => ( P5 @ A ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_245_less__not__sym,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ( ord_less_nat @ X3 @ Y3 )
% 2.55/1.50 => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_246_less__imp__not__eq,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ( ord_less_nat @ X3 @ Y3 )
% 2.55/1.50 => ( X3 != Y3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_247_dual__order_Oasym,axiom,
% 2.55/1.50 ! [B: nat,A: nat] :
% 2.55/1.50 ( ( ord_less_nat @ B @ A )
% 2.55/1.50 => ~ ( ord_less_nat @ A @ B ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_248_ord__less__eq__trans,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat] :
% 2.55/1.50 ( ( ord_less_nat @ A @ B )
% 2.55/1.50 => ( ( B = C )
% 2.55/1.50 => ( ord_less_nat @ A @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_249_ord__eq__less__trans,axiom,
% 2.55/1.50 ! [A: nat,B: nat,C: nat] :
% 2.55/1.50 ( ( A = B )
% 2.55/1.50 => ( ( ord_less_nat @ B @ C )
% 2.55/1.50 => ( ord_less_nat @ A @ C ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_250_less__irrefl,axiom,
% 2.55/1.50 ! [X3: nat] :
% 2.55/1.50 ~ ( ord_less_nat @ X3 @ X3 ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_251_less__linear,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ( ord_less_nat @ X3 @ Y3 )
% 2.55/1.50 | ( X3 = Y3 )
% 2.55/1.50 | ( ord_less_nat @ Y3 @ X3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_252_less__trans,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat,Z2: nat] :
% 2.55/1.50 ( ( ord_less_nat @ X3 @ Y3 )
% 2.55/1.50 => ( ( ord_less_nat @ Y3 @ Z2 )
% 2.55/1.50 => ( ord_less_nat @ X3 @ Z2 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_253_less__asym_H,axiom,
% 2.55/1.50 ! [A: nat,B: nat] :
% 2.55/1.50 ( ( ord_less_nat @ A @ B )
% 2.55/1.50 => ~ ( ord_less_nat @ B @ A ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_254_less__asym,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ( ord_less_nat @ X3 @ Y3 )
% 2.55/1.50 => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_255_less__imp__neq,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ( ord_less_nat @ X3 @ Y3 )
% 2.55/1.50 => ( X3 != Y3 ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_256_order_Oasym,axiom,
% 2.55/1.50 ! [A: nat,B: nat] :
% 2.55/1.50 ( ( ord_less_nat @ A @ B )
% 2.55/1.50 => ~ ( ord_less_nat @ B @ A ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_257_neq__iff,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ( X3 != Y3 )
% 2.55/1.50 = ( ( ord_less_nat @ X3 @ Y3 )
% 2.55/1.50 | ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_258_neqE,axiom,
% 2.55/1.50 ! [X3: nat,Y3: nat] :
% 2.55/1.50 ( ( X3 != Y3 )
% 2.55/1.50 => ( ~ ( ord_less_nat @ X3 @ Y3 )
% 2.55/1.50 => ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_259_gt__ex,axiom,
% 2.55/1.50 ! [X3: nat] :
% 2.55/1.50 ? [X_1: nat] : ( ord_less_nat @ X3 @ X_1 ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_260_order__less__subst2,axiom,
% 2.55/1.50 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.55/1.50 ( ( ord_less_nat @ A @ B )
% 2.55/1.50 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 2.55/1.50 => ( ! [X: nat,Y: nat] :
% 2.55/1.50 ( ( ord_less_nat @ X @ Y )
% 2.55/1.50 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 2.55/1.50 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_261_order__less__subst1,axiom,
% 2.55/1.50 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.55/1.50 ( ( ord_less_nat @ A @ ( F @ B ) )
% 2.55/1.50 => ( ( ord_less_nat @ B @ C )
% 2.55/1.50 => ( ! [X: nat,Y: nat] :
% 2.55/1.50 ( ( ord_less_nat @ X @ Y )
% 2.55/1.50 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 2.55/1.50 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_262_ord__less__eq__subst,axiom,
% 2.55/1.50 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.55/1.50 ( ( ord_less_nat @ A @ B )
% 2.55/1.50 => ( ( ( F @ B )
% 2.55/1.50 = C )
% 2.55/1.50 => ( ! [X: nat,Y: nat] :
% 2.55/1.50 ( ( ord_less_nat @ X @ Y )
% 2.55/1.50 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 2.55/1.50 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_263_ord__eq__less__subst,axiom,
% 2.55/1.50 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.55/1.50 ( ( A
% 2.55/1.50 = ( F @ B ) )
% 2.55/1.50 => ( ( ord_less_nat @ B @ C )
% 2.55/1.50 => ( ! [X: nat,Y: nat] :
% 2.55/1.50 ( ( ord_less_nat @ X @ Y )
% 2.55/1.50 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 2.55/1.50 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_264_LeastI2,axiom,
% 2.55/1.50 ! [P5: nat > $o,A: nat,Q: nat > $o] :
% 2.55/1.50 ( ( P5 @ A )
% 2.55/1.50 => ( ! [X: nat] :
% 2.55/1.50 ( ( P5 @ X )
% 2.55/1.50 => ( Q @ X ) )
% 2.55/1.50 => ( Q @ ( ord_Least_nat @ P5 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_265_LeastI__ex,axiom,
% 2.55/1.50 ! [P5: nat > $o] :
% 2.55/1.50 ( ? [X_12: nat] : ( P5 @ X_12 )
% 2.55/1.50 => ( P5 @ ( ord_Least_nat @ P5 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_266_LeastI2__ex,axiom,
% 2.55/1.50 ! [P5: nat > $o,Q: nat > $o] :
% 2.55/1.50 ( ? [X_12: nat] : ( P5 @ X_12 )
% 2.55/1.50 => ( ! [X: nat] :
% 2.55/1.50 ( ( P5 @ X )
% 2.55/1.50 => ( Q @ X ) )
% 2.55/1.50 => ( Q @ ( ord_Least_nat @ P5 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_267_LeastI,axiom,
% 2.55/1.50 ! [P5: nat > $o,K: nat] :
% 2.55/1.50 ( ( P5 @ K )
% 2.55/1.50 => ( P5 @ ( ord_Least_nat @ P5 ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_268_order_Onot__eq__order__implies__strict,axiom,
% 2.55/1.50 ! [A: nat,B: nat] :
% 2.55/1.50 ( ( A != B )
% 2.55/1.50 => ( ( ord_less_eq_nat @ A @ B )
% 2.55/1.50 => ( ord_less_nat @ A @ B ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_269_dual__order_Ostrict__implies__order,axiom,
% 2.55/1.50 ! [B: nat,A: nat] :
% 2.55/1.50 ( ( ord_less_nat @ B @ A )
% 2.55/1.50 => ( ord_less_eq_nat @ B @ A ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_270_dual__order_Ostrict__iff__order,axiom,
% 2.55/1.50 ( ord_less_nat
% 2.55/1.50 = ( ^ [B2: nat,A2: nat] :
% 2.55/1.50 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.55/1.50 & ( A2 != B2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_271_dual__order_Oorder__iff__strict,axiom,
% 2.55/1.50 ( ord_less_eq_nat
% 2.55/1.50 = ( ^ [B2: nat,A2: nat] :
% 2.55/1.50 ( ( ord_less_nat @ B2 @ A2 )
% 2.55/1.50 | ( A2 = B2 ) ) ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(fact_272_order_Ostrict__implies__order,axiom,
% 2.55/1.50 ! [A: nat,B: nat] :
% 2.55/1.50 ( ( ord_less_nat @ A @ B )
% 2.55/1.50 => ( ord_less_eq_nat @ A @ B ) ) ).
% 2.55/1.50
% 2.55/1.50 thf(conj_0,conjecture,
% 2.55/1.50 ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) ).
% 2.55/1.50 ------------------------
% 2.55/1.53 % (16630)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_16520 for (2999ds/2Mi)
% 2.55/1.53 % (16631)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_16520 for (2999ds/275Mi)
% 2.55/1.53 % (16630)Instruction limit reached!
% 2.55/1.53 % (16630)------------------------------
% 2.55/1.53 % (16630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.53 % (16630)Termination reason: Unknown
% 2.55/1.53 % (16630)Termination phase: shuffling
% 2.55/1.53
% 2.55/1.53 % (16630)Memory used [KB]: 1407
% 2.55/1.53 % (16630)Time elapsed: 0.003 s
% 2.55/1.53 % (16630)Instructions burned: 5 (million)
% 2.55/1.53 % (16630)------------------------------
% 2.55/1.53 % (16630)------------------------------
% 2.55/1.53 % (16632)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16520 for (2999ds/18Mi)
% 2.55/1.53 % (16626)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16520 for (2999ds/183Mi)
% 2.55/1.53 % (16627)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_16520 for (2999ds/4Mi)
% 2.55/1.53 % (16629)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16520 for (2999ds/2Mi)
% 2.55/1.53 % (16628)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_16520 for (2999ds/27Mi)
% 2.55/1.54 % (16629)Instruction limit reached!
% 2.55/1.54 % (16629)------------------------------
% 2.55/1.54 % (16629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.54 % (16629)Termination reason: Unknown
% 2.55/1.54 % (16629)Termination phase: shuffling
% 2.55/1.54
% 2.55/1.54 % (16629)Memory used [KB]: 1279
% 2.55/1.54 % (16629)Time elapsed: 0.004 s
% 2.55/1.54 % (16629)Instructions burned: 3 (million)
% 2.55/1.54 % (16629)------------------------------
% 2.55/1.54 % (16629)------------------------------
% 2.55/1.54 % (16632)Instruction limit reached!
% 2.55/1.54 % (16632)------------------------------
% 2.55/1.54 % (16632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.54 % (16632)Termination reason: Unknown
% 2.55/1.54 % (16632)Termination phase: shuffling
% 2.55/1.54
% 2.55/1.54 % (16632)Memory used [KB]: 1535
% 2.55/1.54 % (16632)Time elapsed: 0.008 s
% 2.55/1.54 % (16632)Instructions burned: 20 (million)
% 2.55/1.54 % (16632)------------------------------
% 2.55/1.54 % (16632)------------------------------
% 2.55/1.54 % (16627)Instruction limit reached!
% 2.55/1.54 % (16627)------------------------------
% 2.55/1.54 % (16627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.54 % (16627)Termination reason: Unknown
% 2.55/1.54 % (16627)Termination phase: shuffling
% 2.55/1.54
% 2.55/1.54 % (16627)Memory used [KB]: 1407
% 2.55/1.54 % (16627)Time elapsed: 0.005 s
% 2.55/1.54 % (16627)Instructions burned: 5 (million)
% 2.55/1.54 % (16627)------------------------------
% 2.55/1.54 % (16627)------------------------------
% 2.55/1.54 % (16633)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16520 for (2999ds/3Mi)
% 2.55/1.54 % (16633)Instruction limit reached!
% 2.55/1.54 % (16633)------------------------------
% 2.55/1.54 % (16633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.54 % (16633)Termination reason: Unknown
% 2.55/1.54 % (16633)Termination phase: shuffling
% 2.55/1.54
% 2.55/1.54 % (16633)Memory used [KB]: 1279
% 2.55/1.54 % (16633)Time elapsed: 0.002 s
% 2.55/1.54 % (16633)Instructions burned: 3 (million)
% 2.55/1.54 % (16633)------------------------------
% 2.55/1.54 % (16633)------------------------------
% 2.55/1.55 % (16635)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_16520 for (2999ds/15Mi)
% 2.55/1.55 % (16628)Instruction limit reached!
% 2.55/1.55 % (16628)------------------------------
% 2.55/1.55 % (16628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.55 % (16628)Termination reason: Unknown
% 2.55/1.55 % (16628)Termination phase: Property scanning
% 2.55/1.55
% 2.55/1.55 % (16628)Memory used [KB]: 1663
% 2.55/1.55 % (16628)Time elapsed: 0.018 s
% 2.55/1.55 % (16628)Instructions burned: 28 (million)
% 2.55/1.55 % (16628)------------------------------
% 2.55/1.55 % (16628)------------------------------
% 2.55/1.55 % (16637)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_16520 for (2999ds/1041Mi)
% 2.55/1.55 % (16635)Instruction limit reached!
% 2.55/1.55 % (16635)------------------------------
% 2.55/1.55 % (16635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.55 % (16635)Termination reason: Unknown
% 2.55/1.55 % (16635)Termination phase: shuffling
% 2.55/1.55
% 2.55/1.55 % (16635)Memory used [KB]: 1535
% 2.55/1.55 % (16635)Time elapsed: 0.007 s
% 2.55/1.55 % (16635)Instructions burned: 15 (million)
% 2.55/1.55 % (16635)------------------------------
% 2.55/1.55 % (16635)------------------------------
% 2.55/1.55 % (16634)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_16520 for (2999ds/37Mi)
% 2.55/1.55 % (16636)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_16520 for (2999ds/3Mi)
% 2.55/1.56 % (16636)Instruction limit reached!
% 2.55/1.56 % (16636)------------------------------
% 2.55/1.56 % (16636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.56 % (16636)Termination reason: Unknown
% 2.55/1.56 % (16636)Termination phase: shuffling
% 2.55/1.56
% 2.55/1.56 % (16636)Memory used [KB]: 1279
% 2.55/1.56 % (16636)Time elapsed: 0.004 s
% 2.55/1.56 % (16636)Instructions burned: 3 (million)
% 2.55/1.56 % (16636)------------------------------
% 2.55/1.56 % (16636)------------------------------
% 2.55/1.56 % (16638)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16520 for (2999ds/7Mi)
% 2.55/1.56 % (16639)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16520 for (2999ds/16Mi)
% 2.55/1.56 % (16638)Instruction limit reached!
% 2.55/1.56 % (16638)------------------------------
% 2.55/1.56 % (16638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.56 % (16638)Termination reason: Unknown
% 2.55/1.56 % (16638)Termination phase: shuffling
% 2.55/1.56
% 2.55/1.56 % (16638)Memory used [KB]: 1407
% 2.55/1.56 % (16638)Time elapsed: 0.004 s
% 2.55/1.56 % (16638)Instructions burned: 8 (million)
% 2.55/1.56 % (16638)------------------------------
% 2.55/1.56 % (16638)------------------------------
% 2.55/1.57 % (16639)Instruction limit reached!
% 2.55/1.57 % (16639)------------------------------
% 2.55/1.57 % (16639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.57 % (16639)Termination reason: Unknown
% 2.55/1.57 % (16639)Termination phase: shuffling
% 2.55/1.57
% 2.55/1.57 % (16639)Memory used [KB]: 1535
% 2.55/1.57 % (16639)Time elapsed: 0.008 s
% 2.55/1.57 % (16639)Instructions burned: 18 (million)
% 2.55/1.57 % (16639)------------------------------
% 2.55/1.57 % (16639)------------------------------
% 2.55/1.57 % (16640)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_16520 for (2999ds/3Mi)
% 2.55/1.57 % (16634)Instruction limit reached!
% 2.55/1.57 % (16634)------------------------------
% 2.55/1.57 % (16634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.57 % (16634)Termination reason: Unknown
% 2.55/1.57 % (16634)Termination phase: shuffling
% 2.55/1.57
% 2.55/1.57 % (16634)Memory used [KB]: 2046
% 2.55/1.57 % (16634)Time elapsed: 0.021 s
% 2.55/1.57 % (16634)Instructions burned: 38 (million)
% 2.55/1.57 % (16634)------------------------------
% 2.55/1.57 % (16634)------------------------------
% 2.55/1.57 % (16640)Instruction limit reached!
% 2.55/1.57 % (16640)------------------------------
% 2.55/1.57 % (16640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.57 % (16640)Termination reason: Unknown
% 2.55/1.57 % (16640)Termination phase: shuffling
% 2.55/1.57
% 2.55/1.57 % (16640)Memory used [KB]: 1279
% 2.55/1.57 % (16640)Time elapsed: 0.003 s
% 2.55/1.57 % (16640)Instructions burned: 3 (million)
% 2.55/1.57 % (16640)------------------------------
% 2.55/1.57 % (16640)------------------------------
% 2.55/1.57 % (16641)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_16520 for (2999ds/3Mi)
% 2.55/1.58 % (16641)Instruction limit reached!
% 2.55/1.58 % (16641)------------------------------
% 2.55/1.58 % (16641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.58 % (16641)Termination reason: Unknown
% 2.55/1.58 % (16641)Termination phase: shuffling
% 2.55/1.58
% 2.55/1.58 % (16641)Memory used [KB]: 1279
% 2.55/1.58 % (16641)Time elapsed: 0.003 s
% 2.55/1.58 % (16641)Instructions burned: 4 (million)
% 2.55/1.58 % (16641)------------------------------
% 2.55/1.58 % (16641)------------------------------
% 2.55/1.58 % (16642)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16520 for (2999ds/7Mi)
% 2.55/1.58 % (16642)Instruction limit reached!
% 2.55/1.58 % (16642)------------------------------
% 2.55/1.58 % (16642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.58 % (16642)Termination reason: Unknown
% 2.55/1.58 % (16642)Termination phase: shuffling
% 2.55/1.58
% 2.55/1.58 % (16642)Memory used [KB]: 1407
% 2.55/1.58 % (16642)Time elapsed: 0.004 s
% 2.55/1.58 % (16642)Instructions burned: 7 (million)
% 2.55/1.58 % (16642)------------------------------
% 2.55/1.58 % (16642)------------------------------
% 2.55/1.58 % (16644)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_16520 for (2999ds/4Mi)
% 2.55/1.59 % (16644)Instruction limit reached!
% 2.55/1.59 % (16644)------------------------------
% 2.55/1.59 % (16644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.59 % (16644)Termination reason: Unknown
% 2.55/1.59 % (16644)Termination phase: shuffling
% 2.55/1.59
% 2.55/1.59 % (16644)Memory used [KB]: 1279
% 2.55/1.59 % (16644)Time elapsed: 0.003 s
% 2.55/1.59 % (16644)Instructions burned: 4 (million)
% 2.55/1.59 % (16644)------------------------------
% 2.55/1.59 % (16644)------------------------------
% 2.55/1.59 % (16645)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_16520 for (2999ds/18Mi)
% 2.55/1.59 % (16643)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_16520 for (2999ds/3Mi)
% 2.55/1.59 % (16646)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_16520 for (2999ds/710Mi)
% 2.55/1.59 % (16643)Instruction limit reached!
% 2.55/1.59 % (16643)------------------------------
% 2.55/1.59 % (16643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.59 % (16643)Termination reason: Unknown
% 2.55/1.59 % (16643)Termination phase: shuffling
% 2.55/1.59
% 2.55/1.59 % (16643)Memory used [KB]: 1279
% 2.55/1.59 % (16643)Time elapsed: 0.004 s
% 2.55/1.59 % (16643)Instructions burned: 3 (million)
% 2.55/1.59 % (16643)------------------------------
% 2.55/1.59 % (16643)------------------------------
% 2.55/1.59 % (16645)Instruction limit reached!
% 2.55/1.59 % (16645)------------------------------
% 2.55/1.59 % (16645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.59 % (16645)Termination reason: Unknown
% 2.55/1.59 % (16645)Termination phase: shuffling
% 2.55/1.59
% 2.55/1.59 % (16645)Memory used [KB]: 1535
% 2.55/1.59 % (16645)Time elapsed: 0.008 s
% 2.55/1.59 % (16645)Instructions burned: 19 (million)
% 2.55/1.59 % (16645)------------------------------
% 2.55/1.59 % (16645)------------------------------
% 2.55/1.59 % (16647)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16520 for (2999ds/6Mi)
% 2.58/1.60 % (16647)Instruction limit reached!
% 2.58/1.60 % (16647)------------------------------
% 2.58/1.60 % (16647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.60 % (16647)Termination reason: Unknown
% 2.58/1.60 % (16647)Termination phase: shuffling
% 2.58/1.60
% 2.58/1.60 % (16647)Memory used [KB]: 1407
% 2.58/1.60 % (16647)Time elapsed: 0.003 s
% 2.58/1.60 % (16647)Instructions burned: 7 (million)
% 2.58/1.60 % (16647)------------------------------
% 2.58/1.60 % (16647)------------------------------
% 2.58/1.60 % (16649)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_16520 for (2999ds/21Mi)
% 2.58/1.61 % (16650)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_16520 for (2999ds/5Mi)
% 2.58/1.61 % (16648)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_16520 for (2999ds/902Mi)
% 2.58/1.61 % (16631)Instruction limit reached!
% 2.58/1.61 % (16631)------------------------------
% 2.58/1.61 % (16631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.61 % (16631)Termination reason: Unknown
% 2.58/1.61 % (16631)Termination phase: Saturation
% 2.58/1.61
% 2.58/1.61 % (16631)Memory used [KB]: 6908
% 2.58/1.61 % (16631)Time elapsed: 0.083 s
% 2.58/1.61 % (16631)Instructions burned: 278 (million)
% 2.58/1.61 % (16631)------------------------------
% 2.58/1.61 % (16631)------------------------------
% 2.58/1.61 % (16650)Instruction limit reached!
% 2.58/1.61 % (16650)------------------------------
% 2.58/1.61 % (16650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.61 % (16650)Termination reason: Unknown
% 2.58/1.61 % (16650)Termination phase: shuffling
% 2.58/1.61
% 2.58/1.61 % (16650)Memory used [KB]: 1407
% 2.58/1.61 % (16650)Time elapsed: 0.003 s
% 2.58/1.61 % (16650)Instructions burned: 7 (million)
% 2.58/1.61 % (16650)------------------------------
% 2.58/1.61 % (16650)------------------------------
% 2.58/1.61 % (16649)Instruction limit reached!
% 2.58/1.61 % (16649)------------------------------
% 2.58/1.61 % (16649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.61 % (16649)Termination reason: Unknown
% 2.58/1.61 % (16649)Termination phase: shuffling
% 2.58/1.61
% 2.58/1.61 % (16649)Memory used [KB]: 1663
% 2.58/1.61 % (16649)Time elapsed: 0.009 s
% 2.58/1.61 % (16649)Instructions burned: 23 (million)
% 2.58/1.61 % (16649)------------------------------
% 2.58/1.61 % (16649)------------------------------
% 2.58/1.61 % (16626)Instruction limit reached!
% 2.58/1.61 % (16626)------------------------------
% 2.58/1.61 % (16626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.61 % (16626)Termination reason: Unknown
% 2.58/1.61 % (16626)Termination phase: Saturation
% 2.58/1.61
% 2.58/1.61 % (16626)Memory used [KB]: 7036
% 2.58/1.61 % (16626)Time elapsed: 0.080 s
% 2.58/1.61 % (16626)Instructions burned: 184 (million)
% 2.58/1.61 % (16626)------------------------------
% 2.58/1.61 % (16626)------------------------------
% 2.58/1.62 % (16651)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_16520 for (2998ds/6Mi)
% 2.58/1.62 % (16652)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_16520 for (2998ds/377Mi)
% 2.58/1.62 % (16651)Instruction limit reached!
% 2.58/1.62 % (16651)------------------------------
% 2.58/1.62 % (16651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.62 % (16651)Termination reason: Unknown
% 2.58/1.62 % (16651)Termination phase: shuffling
% 2.58/1.62
% 2.58/1.62 % (16651)Memory used [KB]: 1407
% 2.58/1.62 % (16651)Time elapsed: 0.003 s
% 2.58/1.62 % (16651)Instructions burned: 8 (million)
% 2.58/1.62 % (16651)------------------------------
% 2.58/1.62 % (16651)------------------------------
% 2.58/1.62 % (16653)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_16520 for (2998ds/779Mi)
% 2.58/1.62 % (16654)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_16520 for (2998ds/19Mi)
% 2.58/1.63 % (16654)Instruction limit reached!
% 2.58/1.63 % (16654)------------------------------
% 2.58/1.63 % (16654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.63 % (16654)Termination reason: Unknown
% 2.58/1.63 % (16654)Termination phase: shuffling
% 2.58/1.63
% 2.58/1.63 % (16654)Memory used [KB]: 1663
% 2.58/1.63 % (16654)Time elapsed: 0.008 s
% 2.58/1.63 % (16654)Instructions burned: 22 (million)
% 2.58/1.63 % (16654)------------------------------
% 2.58/1.63 % (16654)------------------------------
% 2.58/1.63 % (16655)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_16520 for (2998ds/879Mi)
% 2.58/1.64 % (16656)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_16520 for (2998ds/17Mi)
% 2.58/1.64 % (16656)Instruction limit reached!
% 2.58/1.64 % (16656)------------------------------
% 2.58/1.64 % (16656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.64 % (16656)Termination reason: Unknown
% 2.58/1.64 % (16656)Termination phase: shuffling
% 2.58/1.64
% 2.58/1.64 % (16656)Memory used [KB]: 1535
% 2.58/1.64 % (16656)Time elapsed: 0.008 s
% 2.58/1.64 % (16656)Instructions burned: 18 (million)
% 2.58/1.64 % (16656)------------------------------
% 2.58/1.64 % (16656)------------------------------
% 2.58/1.65 % (16657)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_16520 for (2998ds/3Mi)
% 2.58/1.66 % (16657)Instruction limit reached!
% 2.58/1.66 % (16657)------------------------------
% 2.58/1.66 % (16657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.66 % (16657)Termination reason: Unknown
% 2.58/1.66 % (16657)Termination phase: shuffling
% 2.58/1.66
% 2.58/1.66 % (16657)Memory used [KB]: 1279
% 2.58/1.66 % (16657)Time elapsed: 0.003 s
% 2.58/1.66 % (16657)Instructions burned: 3 (million)
% 2.58/1.66 % (16657)------------------------------
% 2.58/1.66 % (16657)------------------------------
% 2.58/1.67 % (16658)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_16520 for (2998ds/30Mi)
% 2.58/1.68 % (16658)Instruction limit reached!
% 2.58/1.68 % (16658)------------------------------
% 2.58/1.68 % (16658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.68 % (16658)Termination reason: Unknown
% 2.58/1.68 % (16658)Termination phase: Property scanning
% 2.58/1.68
% 2.58/1.68 % (16658)Memory used [KB]: 1663
% 2.58/1.68 % (16658)Time elapsed: 0.012 s
% 2.58/1.68 % (16658)Instructions burned: 30 (million)
% 2.58/1.68 % (16658)------------------------------
% 2.58/1.68 % (16658)------------------------------
% 2.58/1.69 % (16659)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_16520 for (2998ds/127Mi)
% 2.58/1.72 % (16652)Instruction limit reached!
% 2.58/1.72 % (16652)------------------------------
% 2.58/1.72 % (16652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.72 % (16652)Termination reason: Unknown
% 2.58/1.72 % (16652)Termination phase: Saturation
% 2.58/1.72
% 2.58/1.72 % (16652)Memory used [KB]: 8315
% 2.58/1.72 % (16652)Time elapsed: 0.106 s
% 2.58/1.72 % (16652)Instructions burned: 377 (million)
% 2.58/1.72 % (16652)------------------------------
% 2.58/1.72 % (16652)------------------------------
% 2.58/1.72 % (16659)Instruction limit reached!
% 2.58/1.72 % (16659)------------------------------
% 2.58/1.72 % (16659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.72 % (16659)Termination reason: Unknown
% 2.58/1.72 % (16659)Termination phase: Saturation
% 2.58/1.72
% 2.58/1.72 % (16659)Memory used [KB]: 6524
% 2.58/1.72 % (16659)Time elapsed: 0.039 s
% 2.58/1.72 % (16659)Instructions burned: 127 (million)
% 2.58/1.72 % (16659)------------------------------
% 2.58/1.72 % (16659)------------------------------
% 2.58/1.73 % (16660)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_16520 for (2997ds/100Mi)
% 2.58/1.73 % (16661)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_16520 for (2997ds/3Mi)
% 2.58/1.74 % (16661)Instruction limit reached!
% 2.58/1.74 % (16661)------------------------------
% 2.58/1.74 % (16661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.74 % (16661)Termination reason: Unknown
% 2.58/1.74 % (16661)Termination phase: shuffling
% 2.58/1.74
% 2.58/1.74 % (16661)Memory used [KB]: 1279
% 2.58/1.74 % (16661)Time elapsed: 0.003 s
% 2.58/1.74 % (16661)Instructions burned: 3 (million)
% 2.58/1.74 % (16661)------------------------------
% 2.58/1.74 % (16661)------------------------------
% 2.58/1.75 % (16662)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_16520 for (2997ds/20Mi)
% 2.58/1.75 % (16662)Instruction limit reached!
% 2.58/1.75 % (16662)------------------------------
% 2.58/1.75 % (16662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.75 % (16662)Termination reason: Unknown
% 2.58/1.75 % (16662)Termination phase: shuffling
% 2.58/1.75
% 2.58/1.75 % (16662)Memory used [KB]: 1535
% 2.58/1.75 % (16662)Time elapsed: 0.009 s
% 2.58/1.75 % (16662)Instructions burned: 21 (million)
% 2.58/1.75 % (16662)------------------------------
% 2.58/1.75 % (16662)------------------------------
% 2.58/1.76 % (16660)Instruction limit reached!
% 2.58/1.76 % (16660)------------------------------
% 2.58/1.76 % (16660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.76 % (16660)Termination reason: Unknown
% 2.58/1.76 % (16660)Termination phase: Function definition elimination
% 2.58/1.76
% 2.58/1.76 % (16660)Memory used [KB]: 2302
% 2.58/1.76 % (16660)Time elapsed: 0.026 s
% 2.58/1.76 % (16660)Instructions burned: 100 (million)
% 2.58/1.76 % (16660)------------------------------
% 2.58/1.76 % (16660)------------------------------
% 2.58/1.76 % (16663)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_16520 for (2997ds/86Mi)
% 2.58/1.77 % (16664)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_16520 for (2997ds/107Mi)
% 2.58/1.79 % (16663)Instruction limit reached!
% 2.58/1.79 % (16663)------------------------------
% 2.58/1.79 % (16663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.79 % (16663)Termination reason: Unknown
% 2.58/1.79 % (16663)Termination phase: Property scanning
% 2.58/1.79
% 2.58/1.79 % (16663)Memory used [KB]: 2046
% 2.58/1.79 % (16663)Time elapsed: 0.028 s
% 2.58/1.79 % (16663)Instructions burned: 89 (million)
% 2.58/1.79 % (16663)------------------------------
% 2.58/1.79 % (16663)------------------------------
% 2.58/1.80 % (16664)Instruction limit reached!
% 2.58/1.80 % (16664)------------------------------
% 2.58/1.80 % (16664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.80 % (16664)Termination reason: Unknown
% 2.58/1.80 % (16664)Termination phase: Property scanning
% 2.58/1.80
% 2.58/1.80 % (16664)Memory used [KB]: 2046
% 2.58/1.80 % (16664)Time elapsed: 0.030 s
% 2.58/1.80 % (16664)Instructions burned: 107 (million)
% 2.58/1.80 % (16664)------------------------------
% 2.58/1.80 % (16664)------------------------------
% 2.58/1.80 % (16665)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_16520 for (2997ds/39Mi)
% 2.58/1.81 % (16666)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_16520 for (2997ds/448Mi)
% 2.58/1.81 % (16665)Instruction limit reached!
% 2.58/1.81 % (16665)------------------------------
% 2.58/1.81 % (16665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.81 % (16665)Termination reason: Unknown
% 2.58/1.81 % (16665)Termination phase: shuffling
% 2.58/1.81
% 2.58/1.81 % (16665)Memory used [KB]: 2046
% 2.58/1.81 % (16665)Time elapsed: 0.013 s
% 2.58/1.81 % (16665)Instructions burned: 39 (million)
% 2.58/1.81 % (16665)------------------------------
% 2.58/1.81 % (16665)------------------------------
% 2.58/1.82 % (16667)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_16520 for (2996ds/46Mi)
% 2.58/1.83 % (16646)Instruction limit reached!
% 2.58/1.83 % (16646)------------------------------
% 2.58/1.83 % (16646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.83 % (16646)Termination reason: Unknown
% 2.58/1.83 % (16646)Termination phase: Saturation
% 2.58/1.83
% 2.58/1.83 % (16646)Memory used [KB]: 7803
% 2.58/1.83 % (16646)Time elapsed: 0.238 s
% 2.58/1.83 % (16646)Instructions burned: 711 (million)
% 2.58/1.83 % (16646)------------------------------
% 2.58/1.83 % (16646)------------------------------
% 2.58/1.84 % (16667)Instruction limit reached!
% 2.58/1.84 % (16667)------------------------------
% 2.58/1.84 % (16667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.84 % (16667)Termination reason: Unknown
% 2.58/1.84 % (16667)Termination phase: Unused predicate definition removal
% 2.58/1.84
% 2.58/1.84 % (16667)Memory used [KB]: 1663
% 2.58/1.84 % (16667)Time elapsed: 0.017 s
% 2.58/1.84 % (16667)Instructions burned: 47 (million)
% 2.58/1.84 % (16667)------------------------------
% 2.58/1.84 % (16667)------------------------------
% 2.58/1.84 % (16668)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_16520 for (2996ds/98Mi)
% 2.58/1.85 % (16669)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_16520 for (2996ds/507Mi)
% 2.58/1.85 % (16637)Instruction limit reached!
% 2.58/1.85 % (16637)------------------------------
% 2.58/1.85 % (16637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.85 % (16637)Termination reason: Unknown
% 2.58/1.85 % (16637)Termination phase: Saturation
% 2.58/1.85
% 2.58/1.85 % (16637)Memory used [KB]: 9594
% 2.58/1.85 % (16637)Time elapsed: 0.324 s
% 2.58/1.85 % (16637)Instructions burned: 1042 (million)
% 2.58/1.85 % (16637)------------------------------
% 2.58/1.85 % (16637)------------------------------
% 2.58/1.86 % (16653)Instruction limit reached!
% 2.58/1.86 % (16653)------------------------------
% 2.58/1.86 % (16653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.86 % (16653)Termination reason: Unknown
% 2.58/1.86 % (16653)Termination phase: Saturation
% 2.58/1.86
% 2.58/1.86 % (16653)Memory used [KB]: 9466
% 2.58/1.86 % (16653)Time elapsed: 0.241 s
% 2.58/1.86 % (16653)Instructions burned: 779 (million)
% 2.58/1.86 % (16653)------------------------------
% 2.58/1.86 % (16653)------------------------------
% 2.58/1.86 % (16670)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_16520 for (2996ds/149Mi)
% 2.58/1.86 % (16668)Instruction limit reached!
% 2.58/1.86 % (16668)------------------------------
% 2.58/1.86 % (16668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.86 % (16668)Termination reason: Unknown
% 2.58/1.86 % (16668)Termination phase: Function definition elimination
% 2.58/1.86
% 2.58/1.86 % (16668)Memory used [KB]: 2302
% 2.58/1.86 % (16668)Time elapsed: 0.028 s
% 2.58/1.86 % (16668)Instructions burned: 100 (million)
% 2.58/1.86 % (16668)------------------------------
% 2.58/1.86 % (16668)------------------------------
% 2.58/1.87 % (16671)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_16520 for (2996ds/39Mi)
% 2.58/1.87 % (16672)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_16520 for (2996ds/6Mi)
% 2.58/1.88 % (16672)Instruction limit reached!
% 2.58/1.88 % (16672)------------------------------
% 2.58/1.88 % (16672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.88 % (16672)Termination reason: Unknown
% 2.58/1.88 % (16672)Termination phase: shuffling
% 2.58/1.88
% 2.58/1.88 % (16672)Memory used [KB]: 1407
% 2.58/1.88 % (16672)Time elapsed: 0.003 s
% 2.58/1.88 % (16672)Instructions burned: 7 (million)
% 2.58/1.88 % (16672)------------------------------
% 2.58/1.88 % (16672)------------------------------
% 2.58/1.88 % (16671)Instruction limit reached!
% 2.58/1.88 % (16671)------------------------------
% 2.58/1.88 % (16671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.88 % (16671)Termination reason: Unknown
% 2.58/1.88 % (16671)Termination phase: Preprocessing 3
% 2.58/1.88
% 2.58/1.88 % (16671)Memory used [KB]: 1791
% 2.58/1.88 % (16671)Time elapsed: 0.015 s
% 2.58/1.88 % (16671)Instructions burned: 41 (million)
% 2.58/1.88 % (16671)------------------------------
% 2.58/1.88 % (16671)------------------------------
% 2.58/1.89 % (16673)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_16520 for (2996ds/1087Mi)
% 2.58/1.89 % (16648)Instruction limit reached!
% 2.58/1.89 % (16648)------------------------------
% 2.58/1.89 % (16648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.89 % (16648)Termination reason: Unknown
% 2.58/1.89 % (16648)Termination phase: Saturation
% 2.58/1.89
% 2.58/1.89 % (16648)Memory used [KB]: 8187
% 2.58/1.89 % (16648)Time elapsed: 0.289 s
% 2.58/1.89 % (16648)Instructions burned: 904 (million)
% 2.58/1.89 % (16648)------------------------------
% 2.58/1.89 % (16648)------------------------------
% 2.58/1.89 % (16674)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_16520 for (2996ds/47Mi)
% 2.58/1.90 % (16655)Instruction limit reached!
% 2.58/1.90 % (16655)------------------------------
% 2.58/1.90 % (16655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.90 % (16655)Termination reason: Unknown
% 2.58/1.90 % (16655)Termination phase: Saturation
% 2.58/1.90
% 2.58/1.90 % (16655)Memory used [KB]: 8187
% 2.58/1.90 % (16655)Time elapsed: 0.268 s
% 2.58/1.90 % (16655)Instructions burned: 879 (million)
% 2.58/1.90 % (16655)------------------------------
% 2.58/1.90 % (16655)------------------------------
% 2.58/1.90 % (16670)Instruction limit reached!
% 2.58/1.90 % (16670)------------------------------
% 2.58/1.90 % (16670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.90 % (16670)Termination reason: Unknown
% 2.58/1.90 % (16670)Termination phase: Saturation
% 2.58/1.90
% 2.58/1.90 % (16670)Memory used [KB]: 6780
% 2.58/1.90 % (16670)Time elapsed: 0.040 s
% 2.58/1.90 % (16670)Instructions burned: 150 (million)
% 2.58/1.90 % (16670)------------------------------
% 2.58/1.90 % (16670)------------------------------
% 2.58/1.90 % (16675)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_16520 for (2996ds/44Mi)
% 2.58/1.91 % (16676)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_16520 for (2996ds/432Mi)
% 2.58/1.91 % (16674)Instruction limit reached!
% 2.58/1.91 % (16674)------------------------------
% 2.58/1.91 % (16674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.91 % (16674)Termination reason: Unknown
% 2.58/1.91 % (16674)Termination phase: Property scanning
% 2.58/1.91
% 2.58/1.91 % (16674)Memory used [KB]: 1918
% 2.58/1.91 % (16674)Time elapsed: 0.017 s
% 2.58/1.91 % (16674)Instructions burned: 48 (million)
% 2.58/1.91 % (16674)------------------------------
% 2.58/1.91 % (16674)------------------------------
% 2.58/1.91 % (16677)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_16520 for (2996ds/62Mi)
% 2.58/1.92 % (16675)Instruction limit reached!
% 2.58/1.92 % (16675)------------------------------
% 2.58/1.92 % (16675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.92 % (16675)Termination reason: Unknown
% 2.58/1.92 % (16675)Termination phase: Property scanning
% 2.58/1.92
% 2.58/1.92 % (16675)Memory used [KB]: 2174
% 2.58/1.92 % (16675)Time elapsed: 0.015 s
% 2.58/1.92 % (16675)Instructions burned: 46 (million)
% 2.58/1.92 % (16675)------------------------------
% 2.58/1.92 % (16675)------------------------------
% 2.58/1.92 % (16678)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_16520 for (2996ds/31Mi)
% 2.58/1.92 % (16666)Instruction limit reached!
% 2.58/1.92 % (16666)------------------------------
% 2.58/1.92 % (16666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.92 % (16666)Termination reason: Unknown
% 2.58/1.92 % (16666)Termination phase: Saturation
% 2.58/1.92
% 2.58/1.92 % (16666)Memory used [KB]: 8571
% 2.58/1.92 % (16666)Time elapsed: 0.120 s
% 2.58/1.92 % (16666)Instructions burned: 450 (million)
% 2.58/1.92 % (16666)------------------------------
% 2.58/1.92 % (16666)------------------------------
% 2.58/1.93 % (16677)Instruction limit reached!
% 2.58/1.93 % (16677)------------------------------
% 2.58/1.93 % (16677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.93 % (16677)Termination reason: Unknown
% 2.58/1.93 % (16677)Termination phase: Property scanning
% 2.58/1.93
% 2.58/1.93 % (16677)Memory used [KB]: 2174
% 2.58/1.93 % (16677)Time elapsed: 0.017 s
% 2.58/1.93 % (16677)Instructions burned: 62 (million)
% 2.58/1.93 % (16677)------------------------------
% 2.58/1.93 % (16677)------------------------------
% 2.58/1.93 % (16679)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_16520 for (2995ds/96Mi)
% 2.58/1.93 % (16678)Instruction limit reached!
% 2.58/1.93 % (16678)------------------------------
% 2.58/1.93 % (16678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.93 % (16678)Termination reason: Unknown
% 2.58/1.93 % (16678)Termination phase: Property scanning
% 2.58/1.93
% 2.58/1.93 % (16678)Memory used [KB]: 1663
% 2.58/1.93 % (16678)Time elapsed: 0.011 s
% 2.58/1.93 % (16678)Instructions burned: 34 (million)
% 2.58/1.93 % (16678)------------------------------
% 2.58/1.93 % (16678)------------------------------
% 2.58/1.93 % (16680)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_16520 for (2995ds/453Mi)
% 2.58/1.94 % (16681)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_16520 for (2995ds/71Mi)
% 2.58/1.94 % (16682)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_16520 for (2995ds/83Mi)
% 2.58/1.95 % (16679)Instruction limit reached!
% 2.58/1.95 % (16679)------------------------------
% 2.58/1.95 % (16679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.95 % (16679)Termination reason: Unknown
% 2.58/1.95 % (16679)Termination phase: Property scanning
% 2.58/1.95
% 2.58/1.95 % (16679)Memory used [KB]: 2046
% 2.58/1.95 % (16679)Time elapsed: 0.029 s
% 2.58/1.95 % (16679)Instructions burned: 98 (million)
% 2.58/1.95 % (16679)------------------------------
% 2.58/1.95 % (16679)------------------------------
% 2.58/1.96 % (16681)Instruction limit reached!
% 2.58/1.96 % (16681)------------------------------
% 2.58/1.96 % (16681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.96 % (16681)Termination reason: Unknown
% 2.58/1.96 % (16681)Termination phase: Function definition elimination
% 2.58/1.96
% 2.58/1.96 % (16681)Memory used [KB]: 2046
% 2.58/1.96 % (16681)Time elapsed: 0.021 s
% 2.58/1.96 % (16681)Instructions burned: 72 (million)
% 2.58/1.96 % (16681)------------------------------
% 2.58/1.96 % (16681)------------------------------
% 2.58/1.96 % (16682)Instruction limit reached!
% 2.58/1.96 % (16682)------------------------------
% 2.58/1.96 % (16682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.96 % (16682)Termination reason: Unknown
% 2.58/1.96 % (16682)Termination phase: Saturation
% 2.58/1.96
% 2.58/1.96 % (16682)Memory used [KB]: 6524
% 2.58/1.96 % (16682)Time elapsed: 0.025 s
% 2.58/1.96 % (16682)Instructions burned: 83 (million)
% 2.58/1.96 % (16682)------------------------------
% 2.58/1.96 % (16682)------------------------------
% 2.58/1.96 % (16683)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_16520 for (2995ds/11Mi)
% 2.58/1.97 % (16684)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_16520 for (2995ds/41Mi)
% 2.58/1.97 % (16683)Instruction limit reached!
% 2.58/1.97 % (16683)------------------------------
% 2.58/1.97 % (16683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.97 % (16683)Termination reason: Unknown
% 2.58/1.97 % (16683)Termination phase: shuffling
% 2.58/1.97
% 2.58/1.97 % (16683)Memory used [KB]: 1535
% 2.58/1.97 % (16683)Time elapsed: 0.004 s
% 2.58/1.97 % (16683)Instructions burned: 11 (million)
% 2.58/1.97 % (16683)------------------------------
% 2.58/1.97 % (16683)------------------------------
% 2.58/1.97 % (16685)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16520 for (2995ds/6Mi)
% 2.58/1.97 % (16685)Instruction limit reached!
% 2.58/1.97 % (16685)------------------------------
% 2.58/1.97 % (16685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.97 % (16685)Termination reason: Unknown
% 2.58/1.97 % (16685)Termination phase: shuffling
% 2.58/1.97
% 2.58/1.97 % (16685)Memory used [KB]: 1407
% 2.58/1.97 % (16685)Time elapsed: 0.003 s
% 2.58/1.97 % (16685)Instructions burned: 7 (million)
% 2.58/1.97 % (16685)------------------------------
% 2.58/1.97 % (16685)------------------------------
% 2.58/1.98 % (16684)Instruction limit reached!
% 2.58/1.98 % (16684)------------------------------
% 2.58/1.98 % (16684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.98 % (16684)Termination reason: Unknown
% 2.58/1.98 % (16684)Termination phase: Property scanning
% 2.58/1.98
% 2.58/1.98 % (16684)Memory used [KB]: 2174
% 2.58/1.98 % (16684)Time elapsed: 0.012 s
% 2.58/1.98 % (16684)Instructions burned: 42 (million)
% 2.58/1.98 % (16684)------------------------------
% 2.58/1.98 % (16684)------------------------------
% 2.58/1.98 % (16686)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_16520 for (2995ds/150Mi)
% 2.58/1.98 % (16687)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_16520 for (2995ds/343Mi)
% 2.58/1.99 % (16688)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_16520 for (2995ds/109Mi)
% 2.58/2.00 % (16669)Instruction limit reached!
% 2.58/2.00 % (16669)------------------------------
% 2.58/2.00 % (16669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/2.00 % (16669)Termination reason: Unknown
% 2.58/2.00 % (16669)Termination phase: Saturation
% 2.58/2.00
% 2.58/2.00 % (16669)Memory used [KB]: 7931
% 2.58/2.00 % (16669)Time elapsed: 0.153 s
% 2.58/2.00 % (16669)Instructions burned: 510 (million)
% 2.58/2.00 % (16669)------------------------------
% 2.58/2.00 % (16669)------------------------------
% 2.58/2.01 % (16689)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_16520 for (2995ds/253Mi)
% 5.98/2.02 % (16688)Instruction limit reached!
% 5.98/2.02 % (16688)------------------------------
% 5.98/2.02 % (16688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.02 % (16688)Termination reason: Unknown
% 5.98/2.02 % (16688)Termination phase: Property scanning
% 5.98/2.02
% 5.98/2.02 % (16688)Memory used [KB]: 2046
% 5.98/2.02 % (16688)Time elapsed: 0.031 s
% 5.98/2.02 % (16688)Instructions burned: 111 (million)
% 5.98/2.02 % (16688)------------------------------
% 5.98/2.02 % (16688)------------------------------
% 5.98/2.02 % (16686)Instruction limit reached!
% 5.98/2.02 % (16686)------------------------------
% 5.98/2.02 % (16686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.02 % (16686)Termination reason: Unknown
% 5.98/2.02 % (16686)Termination phase: Saturation
% 5.98/2.02
% 5.98/2.02 % (16686)Memory used [KB]: 6908
% 5.98/2.02 % (16686)Time elapsed: 0.041 s
% 5.98/2.02 % (16686)Instructions burned: 153 (million)
% 5.98/2.02 % (16686)------------------------------
% 5.98/2.02 % (16686)------------------------------
% 5.98/2.02 % (16676)Instruction limit reached!
% 5.98/2.02 % (16676)------------------------------
% 5.98/2.02 % (16676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.02 % (16676)Termination reason: Unknown
% 5.98/2.02 % (16676)Termination phase: Saturation
% 5.98/2.02
% 5.98/2.02 % (16676)Memory used [KB]: 4477
% 5.98/2.02 % (16676)Time elapsed: 0.140 s
% 5.98/2.02 % (16676)Instructions burned: 435 (million)
% 5.98/2.02 % (16676)------------------------------
% 5.98/2.02 % (16676)------------------------------
% 5.98/2.03 % (16690)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_16520 for (2994ds/140Mi)
% 5.98/2.03 % (16691)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_16520 for (2994ds/614Mi)
% 5.98/2.03 % (16692)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_16520 for (2994ds/202Mi)
% 5.98/2.06 % (16680)Instruction limit reached!
% 5.98/2.06 % (16680)------------------------------
% 5.98/2.06 % (16680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.06 % (16680)Termination reason: Unknown
% 5.98/2.06 % (16680)Termination phase: Saturation
% 5.98/2.06
% 5.98/2.06 % (16680)Memory used [KB]: 7675
% 5.98/2.06 % (16680)Time elapsed: 0.127 s
% 5.98/2.06 % (16680)Instructions burned: 453 (million)
% 5.98/2.06 % (16680)------------------------------
% 5.98/2.06 % (16680)------------------------------
% 5.98/2.07 % (16690)Instruction limit reached!
% 5.98/2.07 % (16690)------------------------------
% 5.98/2.07 % (16690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.07 % (16690)Termination reason: Unknown
% 5.98/2.07 % (16690)Termination phase: Saturation
% 5.98/2.07
% 5.98/2.07 % (16690)Memory used [KB]: 6652
% 5.98/2.07 % (16690)Time elapsed: 0.045 s
% 5.98/2.07 % (16690)Instructions burned: 142 (million)
% 5.98/2.07 % (16690)------------------------------
% 5.98/2.07 % (16690)------------------------------
% 5.98/2.07 % (16693)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_16520 for (2994ds/339Mi)
% 5.98/2.08 % (16694)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_16520 for (2994ds/283Mi)
% 5.98/2.08 % (16689)Instruction limit reached!
% 5.98/2.08 % (16689)------------------------------
% 5.98/2.08 % (16689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.08 % (16689)Termination reason: Unknown
% 5.98/2.08 % (16689)Termination phase: Saturation
% 5.98/2.08
% 5.98/2.08 % (16689)Memory used [KB]: 7547
% 5.98/2.08 % (16689)Time elapsed: 0.076 s
% 5.98/2.08 % (16689)Instructions burned: 255 (million)
% 5.98/2.08 % (16689)------------------------------
% 5.98/2.08 % (16689)------------------------------
% 5.98/2.09 % (16692)Instruction limit reached!
% 5.98/2.09 % (16692)------------------------------
% 5.98/2.09 % (16692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.09 % (16692)Termination reason: Unknown
% 5.98/2.09 % (16692)Termination phase: Saturation
% 5.98/2.09
% 5.98/2.09 % (16692)Memory used [KB]: 6908
% 5.98/2.09 % (16692)Time elapsed: 0.061 s
% 5.98/2.09 % (16692)Instructions burned: 203 (million)
% 5.98/2.09 % (16692)------------------------------
% 5.98/2.09 % (16692)------------------------------
% 5.98/2.09 % (16695)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_16520 for (2994ds/134Mi)
% 5.98/2.10 % (16696)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_16520 for (2994ds/298Mi)
% 5.98/2.10 % (16687)Instruction limit reached!
% 5.98/2.10 % (16687)------------------------------
% 5.98/2.10 % (16687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.10 % (16687)Termination reason: Unknown
% 5.98/2.10 % (16687)Termination phase: Saturation
% 5.98/2.10
% 5.98/2.10 % (16687)Memory used [KB]: 7931
% 5.98/2.10 % (16687)Time elapsed: 0.106 s
% 5.98/2.10 % (16687)Instructions burned: 344 (million)
% 5.98/2.10 % (16687)------------------------------
% 5.98/2.10 % (16687)------------------------------
% 5.98/2.11 % (16697)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_16520 for (2994ds/192Mi)
% 6.46/2.13 % (16695)Instruction limit reached!
% 6.46/2.13 % (16695)------------------------------
% 6.46/2.13 % (16695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.13 % (16695)Termination reason: Unknown
% 6.46/2.13 % (16695)Termination phase: Saturation
% 6.46/2.13
% 6.46/2.13 % (16695)Memory used [KB]: 6780
% 6.46/2.13 % (16695)Time elapsed: 0.037 s
% 6.46/2.13 % (16695)Instructions burned: 135 (million)
% 6.46/2.13 % (16695)------------------------------
% 6.46/2.13 % (16695)------------------------------
% 6.46/2.14 % (16698)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_16520 for (2993ds/258Mi)
% 6.46/2.15 % (16694)Instruction limit reached!
% 6.46/2.15 % (16694)------------------------------
% 6.46/2.15 % (16694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.15 % (16694)Termination reason: Unknown
% 6.46/2.15 % (16694)Termination phase: Saturation
% 6.46/2.15
% 6.46/2.15 % (16694)Memory used [KB]: 7547
% 6.46/2.15 % (16694)Time elapsed: 0.077 s
% 6.46/2.15 % (16694)Instructions burned: 286 (million)
% 6.46/2.15 % (16694)------------------------------
% 6.46/2.15 % (16694)------------------------------
% 6.46/2.16 % (16697)Instruction limit reached!
% 6.46/2.16 % (16697)------------------------------
% 6.46/2.16 % (16697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.16 % (16697)Termination reason: Unknown
% 6.46/2.16 % (16697)Termination phase: Saturation
% 6.46/2.16
% 6.46/2.16 % (16697)Memory used [KB]: 2942
% 6.46/2.16 % (16697)Time elapsed: 0.053 s
% 6.46/2.16 % (16697)Instructions burned: 193 (million)
% 6.46/2.16 % (16697)------------------------------
% 6.46/2.16 % (16697)------------------------------
% 6.46/2.16 % (16699)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_16520 for (2993ds/90Mi)
% 6.46/2.16 % (16693)Instruction limit reached!
% 6.46/2.16 % (16693)------------------------------
% 6.46/2.16 % (16693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.16 % (16693)Termination reason: Unknown
% 6.46/2.16 % (16693)Termination phase: Saturation
% 6.46/2.16
% 6.46/2.16 % (16693)Memory used [KB]: 7419
% 6.46/2.16 % (16693)Time elapsed: 0.096 s
% 6.46/2.16 % (16693)Instructions burned: 341 (million)
% 6.46/2.16 % (16693)------------------------------
% 6.46/2.16 % (16693)------------------------------
% 6.46/2.17 % (16700)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_16520 for (2993ds/231Mi)
% 6.46/2.17 % (16701)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_16520 for (2993ds/458Mi)
% 6.46/2.18 % (16696)Instruction limit reached!
% 6.46/2.18 % (16696)------------------------------
% 6.46/2.18 % (16696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.18 % (16696)Termination reason: Unknown
% 6.46/2.18 % (16696)Termination phase: Saturation
% 6.46/2.18
% 6.46/2.18 % (16696)Memory used [KB]: 8059
% 6.46/2.18 % (16696)Time elapsed: 0.077 s
% 6.46/2.18 % (16696)Instructions burned: 301 (million)
% 6.46/2.18 % (16696)------------------------------
% 6.46/2.18 % (16696)------------------------------
% 6.46/2.19 % (16702)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_16520 for (2993ds/31Mi)
% 6.46/2.19 % (16699)Instruction limit reached!
% 6.46/2.19 % (16699)------------------------------
% 6.46/2.19 % (16699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.19 % (16699)Termination reason: Unknown
% 6.46/2.19 % (16699)Termination phase: Property scanning
% 6.46/2.19
% 6.46/2.19 % (16699)Memory used [KB]: 2046
% 6.46/2.19 % (16699)Time elapsed: 0.026 s
% 6.46/2.19 % (16699)Instructions burned: 92 (million)
% 6.46/2.19 % (16699)------------------------------
% 6.46/2.19 % (16699)------------------------------
% 6.96/2.20 % (16702)Instruction limit reached!
% 6.96/2.20 % (16702)------------------------------
% 6.96/2.20 % (16702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.20 % (16702)Termination reason: Unknown
% 6.96/2.20 % (16702)Termination phase: Property scanning
% 6.96/2.20
% 6.96/2.20 % (16702)Memory used [KB]: 1663
% 6.96/2.20 % (16702)Time elapsed: 0.011 s
% 6.96/2.20 % (16702)Instructions burned: 34 (million)
% 6.96/2.20 % (16702)------------------------------
% 6.96/2.20 % (16702)------------------------------
% 6.96/2.20 % (16691)Instruction limit reached!
% 6.96/2.20 % (16691)------------------------------
% 6.96/2.20 % (16691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.20 % (16691)Termination reason: Unknown
% 6.96/2.20 % (16691)Termination phase: Saturation
% 6.96/2.20
% 6.96/2.20 % (16691)Memory used [KB]: 9594
% 6.96/2.20 % (16691)Time elapsed: 0.173 s
% 6.96/2.20 % (16691)Instructions burned: 617 (million)
% 6.96/2.20 % (16691)------------------------------
% 6.96/2.20 % (16691)------------------------------
% 6.96/2.20 % (16703)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_16520 for (2993ds/297Mi)
% 6.96/2.21 % (16704)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_16520 for (2993ds/987Mi)
% 6.96/2.21 % (16698)Instruction limit reached!
% 6.96/2.21 % (16698)------------------------------
% 6.96/2.21 % (16698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.21 % (16698)Termination reason: Unknown
% 6.96/2.21 % (16698)Termination phase: Saturation
% 6.96/2.21
% 6.96/2.21 % (16698)Memory used [KB]: 3070
% 6.96/2.21 % (16698)Time elapsed: 0.071 s
% 6.96/2.21 % (16698)Instructions burned: 258 (million)
% 6.96/2.21 % (16698)------------------------------
% 6.96/2.21 % (16698)------------------------------
% 6.96/2.21 % (16705)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_16520 for (2993ds/182Mi)
% 6.96/2.22 % (16706)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_16520 for (2993ds/182Mi)
% 6.96/2.22 % (16673)Instruction limit reached!
% 6.96/2.22 % (16673)------------------------------
% 6.96/2.22 % (16673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.22 % (16673)Termination reason: Unknown
% 6.96/2.22 % (16673)Termination phase: Saturation
% 6.96/2.22
% 6.96/2.22 % (16673)Memory used [KB]: 8187
% 6.96/2.22 % (16673)Time elapsed: 0.356 s
% 6.96/2.22 % (16673)Instructions burned: 1087 (million)
% 6.96/2.22 % (16673)------------------------------
% 6.96/2.22 % (16673)------------------------------
% 6.96/2.23 % (16707)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_16520 for (2992ds/154Mi)
% 6.96/2.23 % (16700)Instruction limit reached!
% 6.96/2.23 % (16700)------------------------------
% 6.96/2.23 % (16700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.23 % (16700)Termination reason: Unknown
% 6.96/2.23 % (16700)Termination phase: Saturation
% 6.96/2.23
% 6.96/2.23 % (16700)Memory used [KB]: 7291
% 6.96/2.23 % (16700)Time elapsed: 0.060 s
% 6.96/2.23 % (16700)Instructions burned: 234 (million)
% 6.96/2.23 % (16700)------------------------------
% 6.96/2.23 % (16700)------------------------------
% 6.96/2.24 % (16708)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_16520 for (2992ds/79Mi)
% 6.96/2.26 % (16705)Instruction limit reached!
% 6.96/2.26 % (16705)------------------------------
% 6.96/2.26 % (16705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.26 % (16705)Termination reason: Unknown
% 6.96/2.26 % (16705)Termination phase: Saturation
% 6.96/2.26
% 6.96/2.26 % (16705)Memory used [KB]: 6908
% 6.96/2.26 % (16705)Time elapsed: 0.048 s
% 6.96/2.26 % (16705)Instructions burned: 183 (million)
% 6.96/2.26 % (16705)------------------------------
% 6.96/2.26 % (16705)------------------------------
% 6.96/2.26 % (16708)Instruction limit reached!
% 6.96/2.26 % (16708)------------------------------
% 6.96/2.26 % (16708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.26 % (16708)Termination reason: Unknown
% 6.96/2.26 % (16708)Termination phase: Property scanning
% 6.96/2.26
% 6.96/2.26 % (16708)Memory used [KB]: 2046
% 6.96/2.26 % (16708)Time elapsed: 0.023 s
% 6.96/2.26 % (16708)Instructions burned: 80 (million)
% 6.96/2.26 % (16708)------------------------------
% 6.96/2.26 % (16708)------------------------------
% 6.96/2.26 % (16709)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_16520 for (2992ds/216Mi)
% 6.96/2.27 % (16707)Instruction limit reached!
% 6.96/2.27 % (16707)------------------------------
% 6.96/2.27 % (16707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.27 % (16707)Termination reason: Unknown
% 6.96/2.27 % (16707)Termination phase: Saturation
% 6.96/2.27
% 6.96/2.27 % (16707)Memory used [KB]: 2302
% 6.96/2.27 % (16707)Time elapsed: 0.039 s
% 6.96/2.27 % (16707)Instructions burned: 155 (million)
% 6.96/2.27 % (16707)------------------------------
% 6.96/2.27 % (16707)------------------------------
% 6.96/2.27 % (16706)Instruction limit reached!
% 6.96/2.27 % (16706)------------------------------
% 6.96/2.27 % (16706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.27 % (16706)Termination reason: Unknown
% 6.96/2.27 % (16706)Termination phase: Saturation
% 6.96/2.27
% 6.96/2.27 % (16706)Memory used [KB]: 6780
% 6.96/2.27 % (16706)Time elapsed: 0.056 s
% 6.96/2.27 % (16706)Instructions burned: 184 (million)
% 6.96/2.27 % (16706)------------------------------
% 6.96/2.27 % (16706)------------------------------
% 6.96/2.27 % (16710)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_16520 for (2992ds/114Mi)
% 6.96/2.28 % (16711)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_16520 for (2992ds/922Mi)
% 6.96/2.28 % (16703)Instruction limit reached!
% 6.96/2.28 % (16703)------------------------------
% 6.96/2.28 % (16703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.28 % (16703)Termination reason: Unknown
% 6.96/2.28 % (16703)Termination phase: Saturation
% 6.96/2.28
% 6.96/2.28 % (16703)Memory used [KB]: 7547
% 6.96/2.28 % (16703)Time elapsed: 0.081 s
% 6.96/2.28 % (16703)Instructions burned: 300 (million)
% 6.96/2.28 % (16703)------------------------------
% 6.96/2.28 % (16703)------------------------------
% 6.96/2.28 % (16712)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_16520 for (2992ds/182Mi)
% 6.96/2.29 % (16713)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_16520 for (2992ds/164Mi)
% 7.63/2.30 % (16710)Instruction limit reached!
% 7.63/2.30 % (16710)------------------------------
% 7.63/2.30 % (16710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.30 % (16710)Termination reason: Unknown
% 7.63/2.30 % (16710)Termination phase: Property scanning
% 7.63/2.30
% 7.63/2.30 % (16710)Memory used [KB]: 2046
% 7.63/2.30 % (16710)Time elapsed: 0.031 s
% 7.63/2.30 % (16710)Instructions burned: 115 (million)
% 7.63/2.30 % (16710)------------------------------
% 7.63/2.30 % (16710)------------------------------
% 7.63/2.31 % (16714)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_16520 for (2992ds/50Mi)
% 7.63/2.32 % (16701)Instruction limit reached!
% 7.63/2.32 % (16701)------------------------------
% 7.63/2.32 % (16701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.32 % (16701)Termination reason: Unknown
% 7.63/2.32 % (16701)Termination phase: Saturation
% 7.63/2.32
% 7.63/2.32 % (16701)Memory used [KB]: 8571
% 7.63/2.32 % (16701)Time elapsed: 0.142 s
% 7.63/2.32 % (16701)Instructions burned: 459 (million)
% 7.63/2.32 % (16701)------------------------------
% 7.63/2.32 % (16701)------------------------------
% 7.63/2.32 % (16709)Instruction limit reached!
% 7.63/2.32 % (16709)------------------------------
% 7.63/2.32 % (16709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.32 % (16709)Termination reason: Unknown
% 7.63/2.32 % (16709)Termination phase: Saturation
% 7.63/2.32
% 7.63/2.32 % (16709)Memory used [KB]: 7164
% 7.63/2.32 % (16709)Time elapsed: 0.056 s
% 7.63/2.32 % (16709)Instructions burned: 218 (million)
% 7.63/2.32 % (16709)------------------------------
% 7.63/2.32 % (16709)------------------------------
% 7.63/2.32 % (16714)Instruction limit reached!
% 7.63/2.32 % (16714)------------------------------
% 7.63/2.32 % (16714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.32 % (16714)Termination reason: Unknown
% 7.63/2.32 % (16714)Termination phase: Property scanning
% 7.63/2.32
% 7.63/2.32 % (16714)Memory used [KB]: 2174
% 7.63/2.32 % (16714)Time elapsed: 0.014 s
% 7.63/2.32 % (16714)Instructions burned: 50 (million)
% 7.63/2.32 % (16714)------------------------------
% 7.63/2.32 % (16714)------------------------------
% 7.63/2.32 % (16715)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_16520 for (2991ds/368Mi)
% 7.63/2.33 % (16712)Instruction limit reached!
% 7.63/2.33 % (16712)------------------------------
% 7.63/2.33 % (16712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.33 % (16712)Termination reason: Unknown
% 7.63/2.33 % (16712)Termination phase: Saturation
% 7.63/2.33
% 7.63/2.33 % (16712)Memory used [KB]: 7036
% 7.63/2.33 % (16712)Time elapsed: 0.046 s
% 7.63/2.33 % (16712)Instructions burned: 184 (million)
% 7.63/2.33 % (16712)------------------------------
% 7.63/2.33 % (16712)------------------------------
% 7.63/2.33 % (16716)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_16520 for (2991ds/1021Mi)
% 7.63/2.33 % (16713)Instruction limit reached!
% 7.63/2.33 % (16713)------------------------------
% 7.63/2.33 % (16713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.33 % (16713)Termination reason: Unknown
% 7.63/2.33 % (16713)Termination phase: Saturation
% 7.63/2.33
% 7.63/2.33 % (16713)Memory used [KB]: 2558
% 7.63/2.33 % (16713)Time elapsed: 0.042 s
% 7.63/2.33 % (16713)Instructions burned: 164 (million)
% 7.63/2.33 % (16713)------------------------------
% 7.63/2.33 % (16713)------------------------------
% 7.63/2.33 % (16717)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_16520 for (2991ds/267Mi)
% 7.63/2.34 % (16718)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_16520 for (2991ds/204Mi)
% 7.63/2.34 % (16719)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_16520 for (2991ds/26Mi)
% 7.63/2.35 % (16719)Instruction limit reached!
% 7.63/2.35 % (16719)------------------------------
% 7.63/2.35 % (16719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.35 % (16719)Termination reason: Unknown
% 7.63/2.35 % (16719)Termination phase: shuffling
% 7.63/2.35
% 7.63/2.35 % (16719)Memory used [KB]: 1791
% 7.63/2.35 % (16719)Time elapsed: 0.008 s
% 7.63/2.35 % (16719)Instructions burned: 26 (million)
% 7.63/2.35 % (16719)------------------------------
% 7.63/2.35 % (16719)------------------------------
% 7.63/2.36 % (16720)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_16520 for (2991ds/53Mi)
% 7.63/2.37 % (16720)Instruction limit reached!
% 7.63/2.37 % (16720)------------------------------
% 7.63/2.37 % (16720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.37 % (16720)Termination reason: Unknown
% 7.63/2.37 % (16720)Termination phase: Property scanning
% 7.63/2.37
% 7.63/2.37 % (16720)Memory used [KB]: 2174
% 7.63/2.37 % (16720)Time elapsed: 0.015 s
% 7.63/2.37 % (16720)Instructions burned: 53 (million)
% 7.63/2.37 % (16720)------------------------------
% 7.63/2.37 % (16720)------------------------------
% 7.63/2.38 % (16721)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_16520 for (2991ds/4436Mi)
% 7.63/2.39 % (16718)Instruction limit reached!
% 7.63/2.39 % (16718)------------------------------
% 7.63/2.39 % (16718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.39 % (16718)Termination reason: Unknown
% 7.63/2.39 % (16718)Termination phase: Saturation
% 7.63/2.39
% 7.63/2.39 % (16718)Memory used [KB]: 7036
% 7.63/2.39 % (16718)Time elapsed: 0.056 s
% 7.63/2.39 % (16718)Instructions burned: 207 (million)
% 7.63/2.39 % (16718)------------------------------
% 7.63/2.39 % (16718)------------------------------
% 8.12/2.40 % (16722)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_16520 for (2991ds/1539Mi)
% 8.12/2.40 % (16717)Instruction limit reached!
% 8.12/2.40 % (16717)------------------------------
% 8.12/2.40 % (16717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.40 % (16717)Termination reason: Unknown
% 8.12/2.40 % (16717)Termination phase: Saturation
% 8.12/2.40
% 8.12/2.40 % (16717)Memory used [KB]: 7547
% 8.12/2.40 % (16717)Time elapsed: 0.092 s
% 8.12/2.40 % (16717)Instructions burned: 269 (million)
% 8.12/2.40 % (16717)------------------------------
% 8.12/2.40 % (16717)------------------------------
% 8.12/2.41 % (16723)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_16520 for (2990ds/408Mi)
% 8.12/2.43 % (16715)Instruction limit reached!
% 8.12/2.43 % (16715)------------------------------
% 8.12/2.43 % (16715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.43 % (16715)Termination reason: Unknown
% 8.12/2.43 % (16715)Termination phase: Saturation
% 8.12/2.43
% 8.12/2.43 % (16715)Memory used [KB]: 8315
% 8.12/2.43 % (16715)Time elapsed: 0.107 s
% 8.12/2.43 % (16715)Instructions burned: 371 (million)
% 8.12/2.43 % (16715)------------------------------
% 8.12/2.43 % (16715)------------------------------
% 8.12/2.44 % (16724)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_16520 for (2990ds/5205Mi)
% 8.12/2.49 % (16704)Instruction limit reached!
% 8.12/2.49 % (16704)------------------------------
% 8.12/2.49 % (16704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.49 % (16704)Termination reason: Unknown
% 8.12/2.49 % (16704)Termination phase: Saturation
% 8.12/2.49
% 8.12/2.49 % (16704)Memory used [KB]: 9210
% 8.12/2.49 % (16704)Time elapsed: 0.282 s
% 8.12/2.49 % (16704)Instructions burned: 988 (million)
% 8.12/2.49 % (16704)------------------------------
% 8.12/2.49 % (16704)------------------------------
% 8.60/2.50 % (16725)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_16520 for (2990ds/1913Mi)
% 8.60/2.53 % (16723)Instruction limit reached!
% 8.60/2.53 % (16723)------------------------------
% 8.60/2.53 % (16723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.53 % (16723)Termination reason: Unknown
% 8.60/2.53 % (16723)Termination phase: Saturation
% 8.60/2.53
% 8.60/2.53 % (16723)Memory used [KB]: 7419
% 8.60/2.53 % (16723)Time elapsed: 0.118 s
% 8.60/2.53 % (16723)Instructions burned: 409 (million)
% 8.60/2.53 % (16723)------------------------------
% 8.60/2.53 % (16723)------------------------------
% 8.60/2.54 % (16726)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_16520 for (2989ds/4350Mi)
% 8.60/2.56 % (16711)Instruction limit reached!
% 8.60/2.56 % (16711)------------------------------
% 8.60/2.56 % (16711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.56 % (16711)Termination reason: Unknown
% 8.60/2.56 % (16711)Termination phase: Saturation
% 8.60/2.56
% 8.60/2.56 % (16711)Memory used [KB]: 8187
% 8.60/2.56 % (16711)Time elapsed: 0.283 s
% 8.60/2.56 % (16711)Instructions burned: 923 (million)
% 8.60/2.56 % (16711)------------------------------
% 8.60/2.56 % (16711)------------------------------
% 8.60/2.57 % (16727)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=68:si=on:rtra=on_0 on DTF2THF_16520 for (2989ds/68Mi)
% 8.60/2.59 % (16727)Instruction limit reached!
% 8.60/2.59 % (16727)------------------------------
% 8.60/2.59 % (16727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.59 % (16727)Termination reason: Unknown
% 8.60/2.59 % (16727)Termination phase: Property scanning
% 8.60/2.59
% 8.60/2.59 % (16727)Memory used [KB]: 1918
% 8.60/2.59 % (16727)Time elapsed: 0.021 s
% 8.60/2.59 % (16727)Instructions burned: 69 (million)
% 8.60/2.59 % (16727)------------------------------
% 8.60/2.59 % (16727)------------------------------
% 9.05/2.60 % (16728)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_16520 for (2989ds/358Mi)
% 9.05/2.63 % (16716)Instruction limit reached!
% 9.05/2.63 % (16716)------------------------------
% 9.05/2.63 % (16716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.63 % (16716)Termination reason: Unknown
% 9.05/2.63 % (16716)Termination phase: Saturation
% 9.05/2.63
% 9.05/2.63 % (16716)Memory used [KB]: 8571
% 9.05/2.63 % (16716)Time elapsed: 0.326 s
% 9.05/2.63 % (16716)Instructions burned: 1023 (million)
% 9.05/2.63 % (16716)------------------------------
% 9.05/2.63 % (16716)------------------------------
% 9.05/2.64 % (16729)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_16520 for (2988ds/31Mi)
% 9.05/2.65 % (16729)Instruction limit reached!
% 9.05/2.65 % (16729)------------------------------
% 9.05/2.65 % (16729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.65 % (16729)Termination reason: Unknown
% 9.05/2.65 % (16729)Termination phase: Property scanning
% 9.05/2.65
% 9.05/2.65 % (16729)Memory used [KB]: 1663
% 9.05/2.65 % (16729)Time elapsed: 0.011 s
% 9.05/2.65 % (16729)Instructions burned: 33 (million)
% 9.05/2.65 % (16729)------------------------------
% 9.05/2.65 % (16729)------------------------------
% 9.05/2.66 % (16730)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_16520 for (2988ds/279Mi)
% 9.38/2.70 % (16728)Instruction limit reached!
% 9.38/2.70 % (16728)------------------------------
% 9.38/2.70 % (16728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.38/2.70 % (16728)Termination reason: Unknown
% 9.38/2.70 % (16728)Termination phase: Saturation
% 9.38/2.70
% 9.38/2.70 % (16728)Memory used [KB]: 7675
% 9.38/2.70 % (16728)Time elapsed: 0.108 s
% 9.38/2.70 % (16728)Instructions burned: 361 (million)
% 9.38/2.70 % (16728)------------------------------
% 9.38/2.70 % (16728)------------------------------
% 9.38/2.71 % (16731)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_16520 for (2987ds/258Mi)
% 9.38/2.72 % (16730)Refutation not found, incomplete strategy
% 9.38/2.72 % (16730)------------------------------
% 9.38/2.72 % (16730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.38/2.72 % (16730)Termination reason: Refutation not found, incomplete strategy
% 9.38/2.72
% 9.38/2.72
% 9.38/2.72 % (16730)Memory used [KB]: 7419
% 9.38/2.72 % (16730)Time elapsed: 0.059 s
% 9.38/2.72 % (16730)Instructions burned: 222 (million)
% 9.38/2.72 % (16730)------------------------------
% 9.38/2.72 % (16730)------------------------------
% 9.38/2.73 % (16732)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_16520 for (2987ds/26Mi)
% 9.38/2.74 % (16732)Instruction limit reached!
% 9.38/2.74 % (16732)------------------------------
% 9.38/2.74 % (16732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.38/2.74 % (16732)Termination reason: Unknown
% 9.38/2.74 % (16732)Termination phase: shuffling
% 9.38/2.74
% 9.38/2.74 % (16732)Memory used [KB]: 1791
% 9.38/2.74 % (16732)Time elapsed: 0.008 s
% 9.38/2.74 % (16732)Instructions burned: 26 (million)
% 9.38/2.74 % (16732)------------------------------
% 9.38/2.74 % (16732)------------------------------
% 9.38/2.75 % (16733)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_16520 for (2987ds/995Mi)
% 9.38/2.79 % (16731)Instruction limit reached!
% 9.38/2.79 % (16731)------------------------------
% 9.38/2.79 % (16731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.38/2.79 % (16731)Termination reason: Unknown
% 9.38/2.79 % (16731)Termination phase: Saturation
% 9.38/2.79
% 9.38/2.79 % (16731)Memory used [KB]: 7291
% 9.38/2.79 % (16731)Time elapsed: 0.080 s
% 9.38/2.79 % (16731)Instructions burned: 259 (million)
% 9.38/2.79 % (16731)------------------------------
% 9.38/2.79 % (16731)------------------------------
% 9.68/2.80 % (16734)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_16520 for (2987ds/373Mi)
% 9.68/2.86 % (16722)Instruction limit reached!
% 9.68/2.86 % (16722)------------------------------
% 9.68/2.86 % (16722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.68/2.86 % (16722)Termination reason: Unknown
% 9.68/2.86 % (16722)Termination phase: Saturation
% 9.68/2.86
% 9.68/2.86 % (16722)Memory used [KB]: 9594
% 9.68/2.86 % (16722)Time elapsed: 0.480 s
% 9.68/2.86 % (16722)Instructions burned: 1540 (million)
% 9.68/2.86 % (16722)------------------------------
% 9.68/2.86 % (16722)------------------------------
% 9.68/2.87 % (16735)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_16520 for (2986ds/253Mi)
% 10.15/2.91 % (16734)Instruction limit reached!
% 10.15/2.91 % (16734)------------------------------
% 10.15/2.91 % (16734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.15/2.91 % (16734)Termination reason: Unknown
% 10.15/2.91 % (16734)Termination phase: Saturation
% 10.15/2.91
% 10.15/2.91 % (16734)Memory used [KB]: 8315
% 10.15/2.91 % (16734)Time elapsed: 0.106 s
% 10.15/2.91 % (16734)Instructions burned: 376 (million)
% 10.15/2.91 % (16734)------------------------------
% 10.15/2.91 % (16734)------------------------------
% 10.15/2.92 % (16736)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_16520 for (2985ds/832Mi)
% 10.15/2.93 % (16735)Instruction limit reached!
% 10.15/2.93 % (16735)------------------------------
% 10.15/2.93 % (16735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.15/2.93 % (16735)Termination reason: Unknown
% 10.15/2.93 % (16735)Termination phase: Saturation
% 10.15/2.93
% 10.15/2.93 % (16735)Memory used [KB]: 7675
% 10.15/2.93 % (16735)Time elapsed: 0.067 s
% 10.15/2.93 % (16735)Instructions burned: 255 (million)
% 10.15/2.93 % (16735)------------------------------
% 10.15/2.93 % (16735)------------------------------
% 10.15/2.94 % (16737)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_16520 for (2985ds/668Mi)
% 12.96/3.03 % (16733)Instruction limit reached!
% 12.96/3.03 % (16733)------------------------------
% 12.96/3.03 % (16733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.03 % (16733)Termination reason: Unknown
% 12.96/3.03 % (16733)Termination phase: Saturation
% 12.96/3.03
% 12.96/3.03 % (16733)Memory used [KB]: 9594
% 12.96/3.03 % (16733)Time elapsed: 0.285 s
% 12.96/3.03 % (16733)Instructions burned: 995 (million)
% 12.96/3.03 % (16733)------------------------------
% 12.96/3.03 % (16733)------------------------------
% 12.96/3.04 % (16738)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=40:si=on:rtra=on_0 on DTF2THF_16520 for (2984ds/40Mi)
% 12.96/3.05 % (16738)Instruction limit reached!
% 12.96/3.05 % (16738)------------------------------
% 12.96/3.05 % (16738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.05 % (16738)Termination reason: Unknown
% 12.96/3.05 % (16738)Termination phase: Property scanning
% 12.96/3.05
% 12.96/3.05 % (16738)Memory used [KB]: 2174
% 12.96/3.05 % (16738)Time elapsed: 0.013 s
% 12.96/3.05 % (16738)Instructions burned: 43 (million)
% 12.96/3.05 % (16738)------------------------------
% 12.96/3.05 % (16738)------------------------------
% 12.96/3.05 % (16725)Instruction limit reached!
% 12.96/3.05 % (16725)------------------------------
% 12.96/3.05 % (16725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.05 % (16725)Termination reason: Unknown
% 12.96/3.05 % (16725)Termination phase: Saturation
% 12.96/3.05
% 12.96/3.05 % (16725)Memory used [KB]: 4221
% 12.96/3.05 % (16725)Time elapsed: 0.558 s
% 12.96/3.05 % (16725)Instructions burned: 1916 (million)
% 12.96/3.05 % (16725)------------------------------
% 12.96/3.05 % (16725)------------------------------
% 12.96/3.06 % (16739)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_16520 for (2984ds/294Mi)
% 12.96/3.06 % (16740)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_16520 for (2984ds/187Mi)
% 12.96/3.10 % (16739)Refutation not found, incomplete strategy
% 12.96/3.10 % (16739)------------------------------
% 12.96/3.10 % (16739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.10 % (16739)Termination reason: Refutation not found, incomplete strategy
% 12.96/3.10
% 12.96/3.10
% 12.96/3.10 % (16739)Memory used [KB]: 7164
% 12.96/3.10 % (16739)Time elapsed: 0.038 s
% 12.96/3.10 % (16739)Instructions burned: 145 (million)
% 12.96/3.10 % (16739)------------------------------
% 12.96/3.10 % (16739)------------------------------
% 12.96/3.11 % (16741)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_16520 for (2984ds/371Mi)
% 13.59/3.11 % (16740)Instruction limit reached!
% 13.59/3.11 % (16740)------------------------------
% 13.59/3.11 % (16740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.59/3.11 % (16740)Termination reason: Unknown
% 13.59/3.11 % (16740)Termination phase: Saturation
% 13.59/3.11
% 13.59/3.11 % (16740)Memory used [KB]: 7036
% 13.59/3.11 % (16740)Time elapsed: 0.051 s
% 13.59/3.11 % (16740)Instructions burned: 187 (million)
% 13.59/3.11 % (16740)------------------------------
% 13.59/3.11 % (16740)------------------------------
% 13.59/3.12 % (16742)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_16520 for (2983ds/1827Mi)
% 13.59/3.13 % (16737)Instruction limit reached!
% 13.59/3.13 % (16737)------------------------------
% 13.59/3.13 % (16737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.59/3.13 % (16737)Termination reason: Unknown
% 13.59/3.13 % (16737)Termination phase: Saturation
% 13.59/3.13
% 13.59/3.13 % (16737)Memory used [KB]: 13944
% 13.59/3.13 % (16737)Time elapsed: 0.188 s
% 13.59/3.13 % (16737)Instructions burned: 669 (million)
% 13.59/3.13 % (16737)------------------------------
% 13.59/3.13 % (16737)------------------------------
% 13.59/3.14 % (16743)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_16520 for (2983ds/70Mi)
% 13.59/3.16 % (16736)Instruction limit reached!
% 13.59/3.16 % (16736)------------------------------
% 13.59/3.16 % (16736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.59/3.16 % (16736)Termination reason: Unknown
% 13.59/3.16 % (16736)Termination phase: Saturation
% 13.59/3.16
% 13.59/3.16 % (16736)Memory used [KB]: 7547
% 13.59/3.16 % (16736)Time elapsed: 0.241 s
% 13.59/3.16 % (16736)Instructions burned: 832 (million)
% 13.59/3.16 % (16736)------------------------------
% 13.59/3.16 % (16736)------------------------------
% 13.59/3.16 % (16743)Instruction limit reached!
% 13.59/3.16 % (16743)------------------------------
% 13.59/3.16 % (16743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.59/3.16 % (16743)Termination reason: Unknown
% 13.59/3.16 % (16743)Termination phase: Property scanning
% 13.59/3.16
% 13.59/3.16 % (16743)Memory used [KB]: 2174
% 13.59/3.16 % (16743)Time elapsed: 0.019 s
% 13.59/3.16 % (16743)Instructions burned: 70 (million)
% 13.59/3.16 % (16743)------------------------------
% 13.59/3.16 % (16743)------------------------------
% 13.59/3.17 % (16744)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_16520 for (2983ds/316Mi)
% 13.59/3.17 % (16745)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_16520 for (2983ds/932Mi)
% 14.01/3.22 % (16741)Instruction limit reached!
% 14.01/3.22 % (16741)------------------------------
% 14.01/3.22 % (16741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.01/3.22 % (16741)Termination reason: Unknown
% 14.01/3.22 % (16741)Termination phase: Saturation
% 14.01/3.22
% 14.01/3.22 % (16741)Memory used [KB]: 8187
% 14.01/3.22 % (16741)Time elapsed: 0.114 s
% 14.01/3.22 % (16741)Instructions burned: 373 (million)
% 14.01/3.22 % (16741)------------------------------
% 14.01/3.22 % (16741)------------------------------
% 14.01/3.23 % (16746)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_16520 for (2982ds/4714Mi)
% 14.01/3.24 % (16744)Refutation not found, incomplete strategy
% 14.01/3.24 % (16744)------------------------------
% 14.01/3.24 % (16744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.01/3.24 % (16744)Termination reason: Refutation not found, incomplete strategy
% 14.01/3.24
% 14.01/3.24
% 14.01/3.24 % (16744)Memory used [KB]: 8187
% 14.01/3.24 % (16744)Time elapsed: 0.078 s
% 14.01/3.24 % (16744)Instructions burned: 300 (million)
% 14.01/3.24 % (16744)------------------------------
% 14.01/3.24 % (16744)------------------------------
% 14.01/3.26 % (16747)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_16520 for (2982ds/8250Mi)
% 14.51/3.31 % (16746)Refutation not found, incomplete strategy
% 14.51/3.31 % (16746)------------------------------
% 14.51/3.31 % (16746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.51/3.31 % (16746)Termination reason: Refutation not found, incomplete strategy
% 14.51/3.31
% 14.51/3.31
% 14.51/3.31 % (16746)Memory used [KB]: 7675
% 14.51/3.31 % (16746)Time elapsed: 0.077 s
% 14.51/3.31 % (16746)Instructions burned: 294 (million)
% 14.51/3.31 % (16746)------------------------------
% 14.51/3.31 % (16746)------------------------------
% 14.51/3.32 % (16748)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_16520 for (2981ds/770Mi)
% 14.90/3.44 % (16745)Instruction limit reached!
% 14.90/3.44 % (16745)------------------------------
% 14.90/3.44 % (16745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.90/3.44 % (16745)Termination reason: Unknown
% 14.90/3.44 % (16745)Termination phase: Saturation
% 14.90/3.44
% 14.90/3.44 % (16745)Memory used [KB]: 9338
% 14.90/3.44 % (16745)Time elapsed: 0.274 s
% 14.90/3.44 % (16745)Instructions burned: 933 (million)
% 14.90/3.44 % (16745)------------------------------
% 14.90/3.44 % (16745)------------------------------
% 14.90/3.45 % (16749)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_16520 for (2980ds/794Mi)
% 15.49/3.55 % (16748)Instruction limit reached!
% 15.49/3.55 % (16748)------------------------------
% 15.49/3.55 % (16748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.49/3.55 % (16748)Termination reason: Unknown
% 15.49/3.55 % (16748)Termination phase: Saturation
% 15.49/3.55
% 15.49/3.55 % (16748)Memory used [KB]: 7164
% 15.49/3.55 % (16748)Time elapsed: 0.231 s
% 15.49/3.55 % (16748)Instructions burned: 772 (million)
% 15.49/3.55 % (16748)------------------------------
% 15.49/3.55 % (16748)------------------------------
% 15.49/3.56 % (16750)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_16520 for (2979ds/464Mi)
% 16.03/3.68 % (16749)Instruction limit reached!
% 16.03/3.68 % (16749)------------------------------
% 16.03/3.68 % (16749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.03/3.68 % (16749)Termination reason: Unknown
% 16.03/3.68 % (16749)Termination phase: Saturation
% 16.03/3.68
% 16.03/3.68 % (16749)Memory used [KB]: 6140
% 16.03/3.68 % (16749)Time elapsed: 0.233 s
% 16.03/3.68 % (16749)Instructions burned: 796 (million)
% 16.03/3.68 % (16749)------------------------------
% 16.03/3.68 % (16749)------------------------------
% 16.03/3.68 % (16742)Instruction limit reached!
% 16.03/3.68 % (16742)------------------------------
% 16.03/3.68 % (16742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.03/3.68 % (16742)Termination reason: Unknown
% 16.03/3.68 % (16742)Termination phase: Saturation
% 16.03/3.68
% 16.03/3.68 % (16742)Memory used [KB]: 8955
% 16.03/3.68 % (16742)Time elapsed: 0.562 s
% 16.03/3.68 % (16742)Instructions burned: 1828 (million)
% 16.03/3.68 % (16742)------------------------------
% 16.03/3.68 % (16742)------------------------------
% 16.03/3.69 % (16750)Instruction limit reached!
% 16.03/3.69 % (16750)------------------------------
% 16.03/3.69 % (16750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.03/3.69 % (16750)Termination reason: Unknown
% 16.03/3.69 % (16750)Termination phase: Saturation
% 16.03/3.69
% 16.03/3.69 % (16750)Memory used [KB]: 8443
% 16.03/3.69 % (16750)Time elapsed: 0.133 s
% 16.03/3.69 % (16750)Instructions burned: 465 (million)
% 16.03/3.69 % (16750)------------------------------
% 16.03/3.69 % (16750)------------------------------
% 16.03/3.69 % (16751)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_16520 for (2978ds/1376Mi)
% 16.03/3.69 % (16752)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_16520 for (2978ds/906Mi)
% 17.29/3.70 % (16753)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_16520 for (2978ds/434Mi)
% 17.29/3.74 % (16726)Instruction limit reached!
% 17.29/3.74 % (16726)------------------------------
% 17.29/3.74 % (16726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.29/3.74 % (16726)Termination reason: Unknown
% 17.29/3.74 % (16726)Termination phase: Saturation
% 17.29/3.74
% 17.29/3.74 % (16726)Memory used [KB]: 9722
% 17.29/3.74 % (16726)Time elapsed: 1.196 s
% 17.29/3.74 % (16726)Instructions burned: 4350 (million)
% 17.29/3.74 % (16726)------------------------------
% 17.29/3.74 % (16726)------------------------------
% 17.29/3.75 % (16754)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_16520 for (2977ds/865Mi)
% 17.29/3.76 % (16721)Instruction limit reached!
% 17.29/3.76 % (16721)------------------------------
% 17.29/3.76 % (16721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.29/3.76 % (16721)Termination reason: Unknown
% 17.29/3.76 % (16721)Termination phase: Saturation
% 17.29/3.76
% 17.29/3.76 % (16721)Memory used [KB]: 11641
% 17.29/3.76 % (16721)Time elapsed: 1.400 s
% 17.29/3.76 % (16721)Instructions burned: 4438 (million)
% 17.29/3.76 % (16721)------------------------------
% 17.29/3.76 % (16721)------------------------------
% 17.29/3.77 % (16755)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_16520 for (2977ds/593Mi)
% 17.51/3.82 % (16753)Instruction limit reached!
% 17.51/3.82 % (16753)------------------------------
% 17.51/3.82 % (16753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.51/3.82 % (16753)Termination reason: Unknown
% 17.51/3.82 % (16753)Termination phase: Saturation
% 17.51/3.82
% 17.51/3.82 % (16753)Memory used [KB]: 7164
% 17.51/3.82 % (16753)Time elapsed: 0.121 s
% 17.51/3.82 % (16753)Instructions burned: 434 (million)
% 17.51/3.82 % (16753)------------------------------
% 17.51/3.82 % (16753)------------------------------
% 17.51/3.83 % (16756)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_16520 for (2976ds/443Mi)
% 17.74/3.93 % (16755)Instruction limit reached!
% 17.74/3.93 % (16755)------------------------------
% 17.74/3.93 % (16755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.74/3.93 % (16755)Termination reason: Unknown
% 17.74/3.93 % (16755)Termination phase: Saturation
% 17.74/3.93
% 17.74/3.93 % (16755)Memory used [KB]: 9083
% 17.74/3.93 % (16755)Time elapsed: 0.161 s
% 17.74/3.93 % (16755)Instructions burned: 596 (million)
% 17.74/3.93 % (16755)------------------------------
% 17.74/3.93 % (16755)------------------------------
% 17.74/3.94 % (16757)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_16520 for (2975ds/594Mi)
% 17.74/3.95 % (16724)Instruction limit reached!
% 17.74/3.95 % (16724)------------------------------
% 17.74/3.95 % (16724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.74/3.95 % (16724)Termination reason: Unknown
% 17.74/3.95 % (16724)Termination phase: Saturation
% 17.74/3.95
% 17.74/3.95 % (16724)Memory used [KB]: 14583
% 17.74/3.95 % (16724)Time elapsed: 1.508 s
% 17.74/3.95 % (16724)Instructions burned: 5205 (million)
% 17.74/3.95 % (16724)------------------------------
% 17.74/3.95 % (16724)------------------------------
% 17.74/3.96 % (16756)Instruction limit reached!
% 17.74/3.96 % (16756)------------------------------
% 17.74/3.96 % (16756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.74/3.96 % (16756)Termination reason: Unknown
% 17.74/3.96 % (16756)Termination phase: Saturation
% 17.74/3.96
% 17.74/3.96 % (16756)Memory used [KB]: 7803
% 17.74/3.96 % (16756)Time elapsed: 0.132 s
% 17.74/3.96 % (16756)Instructions burned: 443 (million)
% 17.74/3.96 % (16756)------------------------------
% 17.74/3.96 % (16756)------------------------------
% 17.74/3.96 % (16758)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_16520 for (2975ds/327Mi)
% 17.74/3.97 % (16759)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_16520 for (2975ds/5411Mi)
% 17.74/4.00 % (16754)Instruction limit reached!
% 17.74/4.00 % (16754)------------------------------
% 17.74/4.00 % (16754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.74/4.00 % (16754)Termination reason: Unknown
% 17.74/4.00 % (16754)Termination phase: Saturation
% 17.74/4.00
% 17.74/4.00 % (16754)Memory used [KB]: 8827
% 17.74/4.00 % (16754)Time elapsed: 0.248 s
% 17.74/4.00 % (16754)Instructions burned: 867 (million)
% 17.74/4.00 % (16754)------------------------------
% 17.74/4.00 % (16754)------------------------------
% 17.74/4.01 % (16752)Instruction limit reached!
% 17.74/4.01 % (16752)------------------------------
% 17.74/4.01 % (16752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.74/4.01 % (16752)Termination reason: Unknown
% 17.74/4.01 % (16752)Termination phase: Saturation
% 17.74/4.01
% 17.74/4.01 % (16752)Memory used [KB]: 12537
% 17.74/4.01 % (16752)Time elapsed: 0.315 s
% 17.74/4.01 % (16752)Instructions burned: 906 (million)
% 17.74/4.01 % (16752)------------------------------
% 17.74/4.01 % (16752)------------------------------
% 17.74/4.01 % (16760)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_16520 for (2975ds/1762Mi)
% 19.91/4.02 % (16761)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_16520 for (2975ds/96Mi)
% 19.91/4.05 % (16761)Instruction limit reached!
% 19.91/4.05 % (16761)------------------------------
% 19.91/4.05 % (16761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.91/4.05 % (16761)Termination reason: Unknown
% 19.91/4.05 % (16761)Termination phase: Function definition elimination
% 19.91/4.05
% 19.91/4.05 % (16761)Memory used [KB]: 2302
% 19.91/4.05 % (16761)Time elapsed: 0.026 s
% 19.91/4.05 % (16761)Instructions burned: 99 (million)
% 19.91/4.05 % (16761)------------------------------
% 19.91/4.05 % (16761)------------------------------
% 19.91/4.06 % (16762)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_16520 for (2974ds/503Mi)
% 19.91/4.06 % (16758)Instruction limit reached!
% 19.91/4.06 % (16758)------------------------------
% 19.91/4.06 % (16758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.91/4.06 % (16758)Termination reason: Unknown
% 19.91/4.06 % (16758)Termination phase: Saturation
% 19.91/4.06
% 19.91/4.06 % (16758)Memory used [KB]: 7547
% 19.91/4.06 % (16758)Time elapsed: 0.119 s
% 19.91/4.06 % (16758)Instructions burned: 328 (million)
% 19.91/4.06 % (16758)------------------------------
% 19.91/4.06 % (16758)------------------------------
% 19.91/4.07 % (16763)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_16520 for (2974ds/90Mi)
% 19.91/4.08 % (16751)Instruction limit reached!
% 19.91/4.08 % (16751)------------------------------
% 19.91/4.08 % (16751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.91/4.08 % (16751)Termination reason: Unknown
% 19.91/4.08 % (16751)Termination phase: Saturation
% 19.91/4.08
% 19.91/4.08 % (16751)Memory used [KB]: 13560
% 19.91/4.08 % (16751)Time elapsed: 0.389 s
% 19.91/4.08 % (16751)Instructions burned: 1377 (million)
% 19.91/4.08 % (16751)------------------------------
% 19.91/4.08 % (16751)------------------------------
% 19.91/4.09 % (16764)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_16520 for (2974ds/593Mi)
% 19.91/4.10 % (16763)Instruction limit reached!
% 19.91/4.10 % (16763)------------------------------
% 19.91/4.10 % (16763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.91/4.10 % (16763)Termination reason: Unknown
% 19.91/4.10 % (16763)Termination phase: Property scanning
% 19.91/4.10
% 19.91/4.10 % (16763)Memory used [KB]: 2174
% 19.91/4.10 % (16763)Time elapsed: 0.026 s
% 19.91/4.10 % (16763)Instructions burned: 93 (million)
% 19.91/4.10 % (16763)------------------------------
% 19.91/4.10 % (16763)------------------------------
% 19.91/4.10 % (16765)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_16520 for (2974ds/1512Mi)
% 20.44/4.12 % (16757)Instruction limit reached!
% 20.44/4.12 % (16757)------------------------------
% 20.44/4.12 % (16757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.44/4.12 % (16757)Termination reason: Unknown
% 20.44/4.12 % (16757)Termination phase: Saturation
% 20.44/4.12
% 20.44/4.12 % (16757)Memory used [KB]: 8187
% 20.44/4.12 % (16757)Time elapsed: 0.205 s
% 20.44/4.12 % (16757)Instructions burned: 595 (million)
% 20.44/4.12 % (16757)------------------------------
% 20.44/4.12 % (16757)------------------------------
% 20.44/4.13 % (16766)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_16520 for (2973ds/569Mi)
% 20.62/4.21 % (16762)Instruction limit reached!
% 20.62/4.21 % (16762)------------------------------
% 20.62/4.21 % (16762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.62/4.21 % (16762)Termination reason: Unknown
% 20.62/4.21 % (16762)Termination phase: Saturation
% 20.62/4.21
% 20.62/4.21 % (16762)Memory used [KB]: 7547
% 20.62/4.21 % (16762)Time elapsed: 0.174 s
% 20.62/4.21 % (16762)Instructions burned: 504 (million)
% 20.62/4.21 % (16762)------------------------------
% 20.62/4.21 % (16762)------------------------------
% 20.62/4.23 % (16767)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_16520 for (2972ds/501Mi)
% 20.62/4.26 % (16764)Instruction limit reached!
% 20.62/4.26 % (16764)------------------------------
% 20.62/4.26 % (16764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.62/4.26 % (16764)Termination reason: Unknown
% 20.62/4.26 % (16764)Termination phase: Saturation
% 20.62/4.26
% 20.62/4.26 % (16764)Memory used [KB]: 9466
% 20.62/4.26 % (16764)Time elapsed: 0.171 s
% 20.62/4.26 % (16764)Instructions burned: 595 (million)
% 20.62/4.26 % (16764)------------------------------
% 20.62/4.26 % (16764)------------------------------
% 20.62/4.27 % (16768)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_16520 for (2972ds/562Mi)
% 20.62/4.28 % (16766)Instruction limit reached!
% 20.62/4.28 % (16766)------------------------------
% 20.62/4.28 % (16766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.62/4.28 % (16766)Termination reason: Unknown
% 20.62/4.28 % (16766)Termination phase: Saturation
% 20.62/4.28
% 20.62/4.28 % (16766)Memory used [KB]: 8315
% 20.62/4.28 % (16766)Time elapsed: 0.151 s
% 20.62/4.28 % (16766)Instructions burned: 570 (million)
% 20.62/4.28 % (16766)------------------------------
% 20.62/4.28 % (16766)------------------------------
% 20.62/4.29 % (16769)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_16520 for (2972ds/406Mi)
% 21.32/4.36 % (16767)Instruction limit reached!
% 21.32/4.36 % (16767)------------------------------
% 21.32/4.36 % (16767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.32/4.36 % (16767)Termination reason: Unknown
% 21.32/4.36 % (16767)Termination phase: Saturation
% 21.32/4.36
% 21.32/4.36 % (16767)Memory used [KB]: 8699
% 21.32/4.36 % (16767)Time elapsed: 0.141 s
% 21.32/4.36 % (16767)Instructions burned: 502 (million)
% 21.32/4.36 % (16767)------------------------------
% 21.32/4.36 % (16767)------------------------------
% 21.32/4.37 % (16770)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_16520 for (2971ds/582Mi)
% 21.67/4.42 % (16769)Instruction limit reached!
% 21.67/4.42 % (16769)------------------------------
% 21.67/4.42 % (16769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.67/4.42 % (16769)Termination reason: Unknown
% 21.67/4.42 % (16769)Termination phase: Saturation
% 21.67/4.42
% 21.67/4.42 % (16769)Memory used [KB]: 7419
% 21.67/4.42 % (16769)Time elapsed: 0.127 s
% 21.67/4.42 % (16769)Instructions burned: 407 (million)
% 21.67/4.42 % (16769)------------------------------
% 21.67/4.42 % (16769)------------------------------
% 21.67/4.43 % (16768)Instruction limit reached!
% 21.67/4.43 % (16768)------------------------------
% 21.67/4.43 % (16768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.67/4.43 % (16768)Termination reason: Unknown
% 21.67/4.43 % (16768)Termination phase: Saturation
% 21.67/4.43
% 21.67/4.43 % (16768)Memory used [KB]: 8443
% 21.67/4.43 % (16768)Time elapsed: 0.158 s
% 21.67/4.43 % (16768)Instructions burned: 563 (million)
% 21.67/4.43 % (16768)------------------------------
% 21.67/4.43 % (16768)------------------------------
% 21.67/4.43 % (16771)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_16520 for (2970ds/456Mi)
% 21.67/4.44 % (16772)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_16520 for (2970ds/393Mi)
% 21.67/4.48 % (16760)Instruction limit reached!
% 21.67/4.48 % (16760)------------------------------
% 21.67/4.48 % (16760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.67/4.48 % (16760)Termination reason: Unknown
% 21.67/4.48 % (16760)Termination phase: Saturation
% 21.67/4.48
% 21.67/4.48 % (16760)Memory used [KB]: 8827
% 21.67/4.48 % (16760)Time elapsed: 0.494 s
% 21.67/4.48 % (16760)Instructions burned: 1762 (million)
% 21.67/4.48 % (16760)------------------------------
% 21.67/4.48 % (16760)------------------------------
% 21.67/4.49 % (16773)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_16520 for (2970ds/1335Mi)
% 22.65/4.54 % (16772)Instruction limit reached!
% 22.65/4.54 % (16772)------------------------------
% 22.65/4.54 % (16772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.65/4.54 % (16772)Termination reason: Unknown
% 22.65/4.54 % (16772)Termination phase: Saturation
% 22.65/4.54
% 22.65/4.54 % (16772)Memory used [KB]: 8315
% 22.65/4.54 % (16772)Time elapsed: 0.106 s
% 22.65/4.54 % (16772)Instructions burned: 395 (million)
% 22.65/4.54 % (16772)------------------------------
% 22.65/4.54 % (16772)------------------------------
% 22.65/4.54 % (16770)Instruction limit reached!
% 22.65/4.54 % (16770)------------------------------
% 22.65/4.54 % (16770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.65/4.54 % (16770)Termination reason: Unknown
% 22.65/4.54 % (16770)Termination phase: Saturation
% 22.65/4.54
% 22.65/4.54 % (16770)Memory used [KB]: 8571
% 22.65/4.54 % (16770)Time elapsed: 0.170 s
% 22.65/4.54 % (16770)Instructions burned: 582 (million)
% 22.65/4.54 % (16770)------------------------------
% 22.65/4.54 % (16770)------------------------------
% 22.65/4.55 % (16765)Instruction limit reached!
% 22.65/4.55 % (16765)------------------------------
% 22.65/4.55 % (16765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.65/4.55 % (16765)Termination reason: Unknown
% 22.65/4.55 % (16765)Termination phase: Saturation
% 22.65/4.55
% 22.65/4.55 % (16765)Memory used [KB]: 8187
% 22.65/4.55 % (16765)Time elapsed: 0.446 s
% 22.65/4.55 % (16765)Instructions burned: 1514 (million)
% 22.65/4.55 % (16765)------------------------------
% 22.65/4.55 % (16765)------------------------------
% 22.65/4.55 % (16774)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_16520 for (2969ds/3373Mi)
% 22.65/4.55 % (16775)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_16520 for (2969ds/474Mi)
% 22.65/4.55 % (16771)Instruction limit reached!
% 22.65/4.55 % (16771)------------------------------
% 22.65/4.55 % (16771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.65/4.55 % (16771)Termination reason: Unknown
% 22.65/4.55 % (16771)Termination phase: Saturation
% 22.65/4.55
% 22.65/4.55 % (16771)Memory used [KB]: 8059
% 22.65/4.55 % (16771)Time elapsed: 0.125 s
% 22.65/4.55 % (16771)Instructions burned: 458 (million)
% 22.65/4.55 % (16771)------------------------------
% 22.65/4.55 % (16771)------------------------------
% 22.65/4.56 % (16776)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_16520 for (2969ds/157Mi)
% 22.65/4.56 % (16777)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_16520 for (2969ds/590Mi)
% 23.75/4.60 % (16776)Instruction limit reached!
% 23.75/4.60 % (16776)------------------------------
% 23.75/4.60 % (16776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.75/4.60 % (16776)Termination reason: Unknown
% 23.75/4.60 % (16776)Termination phase: Property scanning
% 23.75/4.60
% 23.75/4.60 % (16776)Memory used [KB]: 2302
% 23.75/4.60 % (16776)Time elapsed: 0.040 s
% 23.75/4.60 % (16776)Instructions burned: 160 (million)
% 23.75/4.60 % (16776)------------------------------
% 23.75/4.60 % (16776)------------------------------
% 23.75/4.61 % (16778)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_16520 for (2969ds/104Mi)
% 23.75/4.64 % (16778)Instruction limit reached!
% 23.75/4.64 % (16778)------------------------------
% 23.75/4.64 % (16778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.75/4.64 % (16778)Termination reason: Unknown
% 23.75/4.64 % (16778)Termination phase: Property scanning
% 23.75/4.64
% 23.75/4.64 % (16778)Memory used [KB]: 2046
% 23.75/4.64 % (16778)Time elapsed: 0.029 s
% 23.75/4.64 % (16778)Instructions burned: 104 (million)
% 23.75/4.64 % (16778)------------------------------
% 23.75/4.64 % (16778)------------------------------
% 23.75/4.65 % (16779)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_16520 for (2968ds/414Mi)
% 23.75/4.68 % (16775)Instruction limit reached!
% 23.75/4.68 % (16775)------------------------------
% 23.75/4.68 % (16775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.75/4.68 % (16775)Termination reason: Unknown
% 23.75/4.68 % (16775)Termination phase: Saturation
% 23.75/4.68
% 23.75/4.68 % (16775)Memory used [KB]: 8443
% 23.75/4.68 % (16775)Time elapsed: 0.132 s
% 23.75/4.68 % (16775)Instructions burned: 474 (million)
% 23.75/4.68 % (16775)------------------------------
% 23.75/4.68 % (16775)------------------------------
% 23.75/4.69 % (16780)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_16520 for (2968ds/715Mi)
% 24.17/4.73 % (16777)Instruction limit reached!
% 24.17/4.73 % (16777)------------------------------
% 24.17/4.73 % (16777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.17/4.73 % (16777)Termination reason: Unknown
% 24.17/4.73 % (16777)Termination phase: Saturation
% 24.17/4.73
% 24.17/4.73 % (16777)Memory used [KB]: 8315
% 24.17/4.73 % (16777)Time elapsed: 0.168 s
% 24.17/4.73 % (16777)Instructions burned: 590 (million)
% 24.17/4.73 % (16777)------------------------------
% 24.17/4.73 % (16777)------------------------------
% 24.17/4.74 % (16781)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_16520 for (2967ds/961Mi)
% 24.17/4.76 % (16779)Instruction limit reached!
% 24.17/4.76 % (16779)------------------------------
% 24.17/4.76 % (16779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.17/4.76 % (16779)Termination reason: Unknown
% 24.17/4.76 % (16779)Termination phase: Saturation
% 24.17/4.76
% 24.17/4.76 % (16779)Memory used [KB]: 8315
% 24.17/4.76 % (16779)Time elapsed: 0.112 s
% 24.17/4.76 % (16779)Instructions burned: 414 (million)
% 24.17/4.76 % (16779)------------------------------
% 24.17/4.76 % (16779)------------------------------
% 24.17/4.77 % (16782)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_16520 for (2967ds/1213Mi)
% 24.66/4.86 % (16773)Instruction limit reached!
% 24.66/4.86 % (16773)------------------------------
% 24.66/4.86 % (16773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.66/4.86 % (16773)Termination reason: Unknown
% 24.66/4.86 % (16773)Termination phase: Saturation
% 24.66/4.86
% 24.66/4.86 % (16773)Memory used [KB]: 8955
% 24.66/4.86 % (16773)Time elapsed: 0.375 s
% 24.66/4.86 % (16773)Instructions burned: 1336 (million)
% 24.66/4.86 % (16773)------------------------------
% 24.66/4.86 % (16773)------------------------------
% 24.66/4.87 % (16783)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_16520 for (2966ds/1979Mi)
% 25.24/4.90 % (16780)Instruction limit reached!
% 25.24/4.90 % (16780)------------------------------
% 25.24/4.90 % (16780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.24/4.90 % (16780)Termination reason: Unknown
% 25.24/4.90 % (16780)Termination phase: Saturation
% 25.24/4.90
% 25.24/4.90 % (16780)Memory used [KB]: 5117
% 25.24/4.90 % (16780)Time elapsed: 0.210 s
% 25.24/4.90 % (16780)Instructions burned: 717 (million)
% 25.24/4.90 % (16780)------------------------------
% 25.24/4.90 % (16780)------------------------------
% 25.24/4.91 % (16784)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_16520 for (2966ds/481Mi)
% 26.92/5.03 % (16781)Instruction limit reached!
% 26.92/5.03 % (16781)------------------------------
% 26.92/5.03 % (16781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.92/5.03 % (16781)Termination reason: Unknown
% 26.92/5.03 % (16781)Termination phase: Saturation
% 26.92/5.03
% 26.92/5.03 % (16781)Memory used [KB]: 8699
% 26.92/5.03 % (16781)Time elapsed: 0.288 s
% 26.92/5.03 % (16781)Instructions burned: 962 (million)
% 26.92/5.03 % (16781)------------------------------
% 26.92/5.03 % (16781)------------------------------
% 26.92/5.04 % (16785)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_16520 for (2964ds/783Mi)
% 26.92/5.07 % (16784)Instruction limit reached!
% 26.92/5.07 % (16784)------------------------------
% 26.92/5.07 % (16784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.92/5.07 % (16784)Termination reason: Unknown
% 26.92/5.07 % (16784)Termination phase: Saturation
% 26.92/5.07
% 26.92/5.07 % (16784)Memory used [KB]: 8571
% 26.92/5.07 % (16784)Time elapsed: 0.170 s
% 26.92/5.07 % (16784)Instructions burned: 484 (million)
% 26.92/5.07 % (16784)------------------------------
% 26.92/5.07 % (16784)------------------------------
% 26.92/5.08 % (16786)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_16520 for (2964ds/432Mi)
% 27.50/5.14 % (16782)Instruction limit reached!
% 27.50/5.14 % (16782)------------------------------
% 27.50/5.14 % (16782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.50/5.14 % (16782)Termination reason: Unknown
% 27.50/5.14 % (16782)Termination phase: Saturation
% 27.50/5.14
% 27.50/5.14 % (16782)Memory used [KB]: 8827
% 27.50/5.14 % (16782)Time elapsed: 0.373 s
% 27.50/5.14 % (16782)Instructions burned: 1215 (million)
% 27.50/5.14 % (16782)------------------------------
% 27.50/5.14 % (16782)------------------------------
% 27.50/5.15 % (16787)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_16520 for (2963ds/1670Mi)
% 27.85/5.22 % (16786)Instruction limit reached!
% 27.85/5.22 % (16786)------------------------------
% 27.85/5.22 % (16786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.85/5.22 % (16786)Termination reason: Unknown
% 27.85/5.22 % (16786)Termination phase: Saturation
% 27.85/5.22
% 27.85/5.22 % (16786)Memory used [KB]: 7803
% 27.85/5.22 % (16786)Time elapsed: 0.164 s
% 27.85/5.22 % (16786)Instructions burned: 432 (million)
% 27.85/5.22 % (16786)------------------------------
% 27.85/5.22 % (16786)------------------------------
% 27.85/5.23 % (16788)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_16520 for (2962ds/90Mi)
% 27.85/5.26 % (16788)Instruction limit reached!
% 27.85/5.26 % (16788)------------------------------
% 27.85/5.26 % (16788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.85/5.26 % (16788)Termination reason: Unknown
% 27.85/5.26 % (16788)Termination phase: Property scanning
% 27.85/5.26
% 27.85/5.26 % (16788)Memory used [KB]: 2046
% 27.85/5.26 % (16788)Time elapsed: 0.027 s
% 27.85/5.26 % (16788)Instructions burned: 92 (million)
% 27.85/5.26 % (16788)------------------------------
% 27.85/5.26 % (16788)------------------------------
% 27.85/5.27 % (16789)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_16520 for (2962ds/346Mi)
% 27.85/5.27 % (16785)Instruction limit reached!
% 27.85/5.27 % (16785)------------------------------
% 27.85/5.27 % (16785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.85/5.27 % (16785)Termination reason: Unknown
% 27.85/5.27 % (16785)Termination phase: Saturation
% 27.85/5.27
% 27.85/5.27 % (16785)Memory used [KB]: 8059
% 27.85/5.27 % (16785)Time elapsed: 0.258 s
% 27.85/5.27 % (16785)Instructions burned: 785 (million)
% 27.85/5.27 % (16785)------------------------------
% 27.85/5.27 % (16785)------------------------------
% 27.85/5.28 % (16790)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_16520 for (2962ds/401Mi)
% 28.69/5.36 % (16789)Instruction limit reached!
% 28.69/5.36 % (16789)------------------------------
% 28.69/5.36 % (16789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.69/5.36 % (16789)Termination reason: Unknown
% 28.69/5.36 % (16789)Termination phase: Saturation
% 28.69/5.36
% 28.69/5.36 % (16789)Memory used [KB]: 8315
% 28.69/5.36 % (16789)Time elapsed: 0.118 s
% 28.69/5.36 % (16789)Instructions burned: 348 (million)
% 28.69/5.36 % (16789)------------------------------
% 28.69/5.36 % (16789)------------------------------
% 28.69/5.37 % (16791)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_16520 for (2961ds/6454Mi)
% 28.69/5.39 % (16790)Instruction limit reached!
% 28.69/5.39 % (16790)------------------------------
% 28.69/5.39 % (16790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.69/5.39 % (16790)Termination reason: Unknown
% 28.69/5.39 % (16790)Termination phase: Saturation
% 28.69/5.39
% 28.69/5.39 % (16790)Memory used [KB]: 8443
% 28.69/5.39 % (16790)Time elapsed: 0.107 s
% 28.69/5.39 % (16790)Instructions burned: 403 (million)
% 28.69/5.39 % (16790)------------------------------
% 28.69/5.39 % (16790)------------------------------
% 29.30/5.40 % (16792)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_16520 for (2961ds/283Mi)
% 29.30/5.48 % (16783)Instruction limit reached!
% 29.30/5.48 % (16783)------------------------------
% 29.30/5.48 % (16783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.30/5.48 % (16783)Termination reason: Unknown
% 29.30/5.48 % (16783)Termination phase: Saturation
% 29.30/5.48
% 29.30/5.48 % (16783)Memory used [KB]: 8571
% 29.30/5.48 % (16783)Time elapsed: 0.604 s
% 29.30/5.48 % (16783)Instructions burned: 1981 (million)
% 29.30/5.48 % (16783)------------------------------
% 29.30/5.48 % (16783)------------------------------
% 29.30/5.48 % (16792)Instruction limit reached!
% 29.30/5.48 % (16792)------------------------------
% 29.30/5.48 % (16792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.30/5.48 % (16792)Termination reason: Unknown
% 29.30/5.48 % (16792)Termination phase: Saturation
% 29.30/5.48
% 29.30/5.48 % (16792)Memory used [KB]: 7675
% 29.30/5.48 % (16792)Time elapsed: 0.081 s
% 29.30/5.48 % (16792)Instructions burned: 283 (million)
% 29.30/5.48 % (16792)------------------------------
% 29.30/5.48 % (16792)------------------------------
% 29.30/5.49 % (16793)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_16520 for (2960ds/865Mi)
% 29.30/5.49 % (16794)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_16520 for (2960ds/4528Mi)
% 29.78/5.51 % (16774)Instruction limit reached!
% 29.78/5.51 % (16774)------------------------------
% 29.78/5.51 % (16774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.78/5.51 % (16774)Termination reason: Unknown
% 29.78/5.51 % (16774)Termination phase: Saturation
% 29.78/5.51
% 29.78/5.51 % (16774)Memory used [KB]: 11769
% 29.78/5.51 % (16774)Time elapsed: 0.963 s
% 29.78/5.51 % (16774)Instructions burned: 3375 (million)
% 29.78/5.51 % (16774)------------------------------
% 29.78/5.51 % (16774)------------------------------
% 29.78/5.52 % (16795)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_16520 for (2959ds/1001Mi)
% 29.78/5.53 % (16759)Instruction limit reached!
% 29.78/5.53 % (16759)------------------------------
% 29.78/5.53 % (16759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.78/5.53 % (16759)Termination reason: Unknown
% 29.78/5.53 % (16759)Termination phase: Saturation
% 29.78/5.53
% 29.78/5.53 % (16759)Memory used [KB]: 10362
% 29.78/5.53 % (16759)Time elapsed: 1.583 s
% 29.78/5.53 % (16759)Instructions burned: 5413 (million)
% 29.78/5.53 % (16759)------------------------------
% 29.78/5.53 % (16759)------------------------------
% 29.78/5.54 % (16796)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_16520 for (2959ds/102Mi)
% 29.78/5.57 % (16796)Instruction limit reached!
% 29.78/5.57 % (16796)------------------------------
% 29.78/5.57 % (16796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.78/5.57 % (16796)Termination reason: Unknown
% 29.78/5.57 % (16796)Termination phase: Function definition elimination
% 29.78/5.57
% 29.78/5.57 % (16796)Memory used [KB]: 2302
% 29.78/5.57 % (16796)Time elapsed: 0.028 s
% 29.78/5.57 % (16796)Instructions burned: 105 (million)
% 29.78/5.57 % (16796)------------------------------
% 29.78/5.57 % (16796)------------------------------
% 29.78/5.58 % (16797)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_16520 for (2959ds/952Mi)
% 29.98/5.63 % (16787)Instruction limit reached!
% 29.98/5.63 % (16787)------------------------------
% 29.98/5.63 % (16787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.98/5.63 % (16787)Termination reason: Unknown
% 29.98/5.63 % (16787)Termination phase: Saturation
% 29.98/5.63
% 29.98/5.63 % (16787)Memory used [KB]: 11257
% 29.98/5.63 % (16787)Time elapsed: 0.484 s
% 29.98/5.63 % (16787)Instructions burned: 1671 (million)
% 29.98/5.63 % (16787)------------------------------
% 29.98/5.63 % (16787)------------------------------
% 29.98/5.64 % (16798)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_16520 for (2958ds/578Mi)
% 30.59/5.73 % (16793)Instruction limit reached!
% 30.59/5.73 % (16793)------------------------------
% 30.59/5.73 % (16793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.59/5.73 % (16793)Termination reason: Unknown
% 30.59/5.73 % (16793)Termination phase: Saturation
% 30.59/5.73
% 30.59/5.73 % (16793)Memory used [KB]: 8571
% 30.59/5.73 % (16793)Time elapsed: 0.245 s
% 30.59/5.73 % (16793)Instructions burned: 867 (million)
% 30.59/5.73 % (16793)------------------------------
% 30.59/5.73 % (16793)------------------------------
% 30.59/5.74 % (16799)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_16520 for (2957ds/643Mi)
% 30.94/5.80 % (16798)Instruction limit reached!
% 30.94/5.80 % (16798)------------------------------
% 30.94/5.80 % (16798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.94/5.80 % (16798)Termination reason: Unknown
% 30.94/5.80 % (16798)Termination phase: Saturation
% 30.94/5.80
% 30.94/5.80 % (16798)Memory used [KB]: 7291
% 30.94/5.80 % (16798)Time elapsed: 0.162 s
% 30.94/5.80 % (16798)Instructions burned: 579 (million)
% 30.94/5.80 % (16798)------------------------------
% 30.94/5.80 % (16798)------------------------------
% 30.94/5.81 % (16747)Instruction limit reached!
% 30.94/5.81 % (16747)------------------------------
% 30.94/5.81 % (16747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.94/5.81 % (16747)Termination reason: Unknown
% 30.94/5.81 % (16747)Termination phase: Saturation
% 30.94/5.81
% 30.94/5.81 % (16747)Memory used [KB]: 17398
% 30.94/5.81 % (16747)Time elapsed: 2.553 s
% 30.94/5.81 % (16747)Instructions burned: 8250 (million)
% 30.94/5.81 % (16747)------------------------------
% 30.94/5.81 % (16747)------------------------------
% 30.94/5.81 % (16800)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_16520 for (2956ds/865Mi)
% 30.94/5.82 % (16801)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_16520 for (2956ds/1174Mi)
% 30.94/5.82 % (16795)Instruction limit reached!
% 30.94/5.82 % (16795)------------------------------
% 30.94/5.82 % (16795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.94/5.82 % (16795)Termination reason: Unknown
% 30.94/5.82 % (16795)Termination phase: Saturation
% 30.94/5.82
% 30.94/5.82 % (16795)Memory used [KB]: 9850
% 30.94/5.82 % (16795)Time elapsed: 0.297 s
% 30.94/5.82 % (16795)Instructions burned: 1001 (million)
% 30.94/5.82 % (16795)------------------------------
% 30.94/5.82 % (16795)------------------------------
% 30.94/5.83 % (16802)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_16520 for (2956ds/644Mi)
% 30.94/5.86 % (16797)Instruction limit reached!
% 30.94/5.86 % (16797)------------------------------
% 30.94/5.86 % (16797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.94/5.86 % (16797)Termination reason: Unknown
% 30.94/5.86 % (16797)Termination phase: Saturation
% 30.94/5.86
% 30.94/5.86 % (16797)Memory used [KB]: 10106
% 30.94/5.86 % (16797)Time elapsed: 0.281 s
% 30.94/5.86 % (16797)Instructions burned: 954 (million)
% 30.94/5.86 % (16797)------------------------------
% 30.94/5.86 % (16797)------------------------------
% 30.94/5.87 % (16803)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_16520 for (2956ds/1201Mi)
% 31.73/5.92 % (16799)Instruction limit reached!
% 31.73/5.92 % (16799)------------------------------
% 31.73/5.92 % (16799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.73/5.92 % (16799)Termination reason: Unknown
% 31.73/5.92 % (16799)Termination phase: Saturation
% 31.73/5.92
% 31.73/5.92 % (16799)Memory used [KB]: 9466
% 31.73/5.92 % (16799)Time elapsed: 0.179 s
% 31.73/5.92 % (16799)Instructions burned: 643 (million)
% 31.73/5.92 % (16799)------------------------------
% 31.73/5.92 % (16799)------------------------------
% 31.73/5.93 % (16804)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_16520 for (2955ds/1046Mi)
% 33.87/6.02 % (16802)Instruction limit reached!
% 33.87/6.02 % (16802)------------------------------
% 33.87/6.02 % (16802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.87/6.02 % (16802)Termination reason: Unknown
% 33.87/6.02 % (16802)Termination phase: Saturation
% 33.87/6.02
% 33.87/6.02 % (16802)Memory used [KB]: 8699
% 33.87/6.02 % (16802)Time elapsed: 0.186 s
% 33.87/6.02 % (16802)Instructions burned: 646 (million)
% 33.87/6.02 % (16802)------------------------------
% 33.87/6.02 % (16802)------------------------------
% 33.87/6.03 % (16805)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_16520 for (2954ds/222Mi)
% 33.87/6.06 % (16800)Instruction limit reached!
% 33.87/6.06 % (16800)------------------------------
% 33.87/6.06 % (16800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.87/6.06 % (16800)Termination reason: Unknown
% 33.87/6.06 % (16800)Termination phase: Saturation
% 33.87/6.06
% 33.87/6.06 % (16800)Memory used [KB]: 9210
% 33.87/6.06 % (16800)Time elapsed: 0.254 s
% 33.87/6.06 % (16800)Instructions burned: 866 (million)
% 33.87/6.06 % (16800)------------------------------
% 33.87/6.06 % (16800)------------------------------
% 33.87/6.07 % (16806)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=68:si=on:rtra=on_0 on DTF2THF_16520 for (2954ds/68Mi)
% 33.87/6.09 % (16805)Instruction limit reached!
% 33.87/6.09 % (16805)------------------------------
% 33.87/6.09 % (16805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.87/6.09 % (16805)Termination reason: Unknown
% 33.87/6.09 % (16805)Termination phase: Saturation
% 33.87/6.09
% 33.87/6.09 % (16805)Memory used [KB]: 7291
% 33.87/6.09 % (16805)Time elapsed: 0.057 s
% 33.87/6.09 % (16805)Instructions burned: 223 (million)
% 33.87/6.09 % (16805)------------------------------
% 33.87/6.09 % (16805)------------------------------
% 33.87/6.09 % (16806)Instruction limit reached!
% 33.87/6.09 % (16806)------------------------------
% 33.87/6.09 % (16806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.87/6.09 % (16806)Termination reason: Unknown
% 33.87/6.09 % (16806)Termination phase: Property scanning
% 33.87/6.09
% 33.87/6.09 % (16806)Memory used [KB]: 1918
% 33.87/6.09 % (16806)Time elapsed: 0.021 s
% 33.87/6.09 % (16806)Instructions burned: 69 (million)
% 33.87/6.09 % (16806)------------------------------
% 33.87/6.09 % (16806)------------------------------
% 33.87/6.10 % (16807)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_16520 for (2954ds/454Mi)
% 33.87/6.10 % (16808)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_16520 for (2954ds/360Mi)
% 34.56/6.14 % (16801)Instruction limit reached!
% 34.56/6.14 % (16801)------------------------------
% 34.56/6.14 % (16801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.56/6.14 % (16801)Termination reason: Unknown
% 34.56/6.14 % (16801)Termination phase: Saturation
% 34.56/6.14
% 34.56/6.14 % (16801)Memory used [KB]: 10106
% 34.56/6.14 % (16801)Time elapsed: 0.327 s
% 34.56/6.14 % (16801)Instructions burned: 1175 (million)
% 34.56/6.14 % (16801)------------------------------
% 34.56/6.14 % (16801)------------------------------
% 34.56/6.15 % (16809)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_16520 for (2953ds/157Mi)
% 34.56/6.19 % (16809)Instruction limit reached!
% 34.56/6.19 % (16809)------------------------------
% 34.56/6.19 % (16809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.56/6.19 % (16809)Termination reason: Unknown
% 34.56/6.19 % (16809)Termination phase: Property scanning
% 34.56/6.19
% 34.56/6.19 % (16809)Memory used [KB]: 2558
% 34.56/6.19 % (16809)Time elapsed: 0.041 s
% 34.56/6.19 % (16809)Instructions burned: 159 (million)
% 34.56/6.19 % (16809)------------------------------
% 34.56/6.19 % (16809)------------------------------
% 34.98/6.20 % (16808)Instruction limit reached!
% 34.98/6.20 % (16808)------------------------------
% 34.98/6.20 % (16808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.98/6.20 % (16808)Termination reason: Unknown
% 34.98/6.20 % (16808)Termination phase: Saturation
% 34.98/6.20
% 34.98/6.20 % (16808)Memory used [KB]: 8443
% 34.98/6.20 % (16808)Time elapsed: 0.098 s
% 34.98/6.20 % (16808)Instructions burned: 362 (million)
% 34.98/6.20 % (16808)------------------------------
% 34.98/6.20 % (16808)------------------------------
% 34.98/6.20 % (16810)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_16520 for (2953ds/5061Mi)
% 34.98/6.22 % (16803)Instruction limit reached!
% 34.98/6.22 % (16803)------------------------------
% 34.98/6.22 % (16803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.98/6.22 % (16803)Termination reason: Unknown
% 34.98/6.22 % (16803)Termination phase: Saturation
% 34.98/6.22
% 34.98/6.22 % (16803)Memory used [KB]: 9978
% 34.98/6.22 % (16803)Time elapsed: 0.348 s
% 34.98/6.22 % (16803)Instructions burned: 1203 (million)
% 34.98/6.22 % (16803)------------------------------
% 34.98/6.22 % (16803)------------------------------
% 34.98/6.22 % (16811)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_16520 for (2953ds/2401Mi)
% 34.98/6.22 % (16807)Instruction limit reached!
% 34.98/6.22 % (16807)------------------------------
% 34.98/6.22 % (16807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.98/6.22 % (16807)Termination reason: Unknown
% 34.98/6.22 % (16807)Termination phase: Saturation
% 34.98/6.22
% 34.98/6.22 % (16807)Memory used [KB]: 13176
% 34.98/6.22 % (16807)Time elapsed: 0.124 s
% 34.98/6.22 % (16807)Instructions burned: 455 (million)
% 34.98/6.22 % (16807)------------------------------
% 34.98/6.22 % (16807)------------------------------
% 34.98/6.22 % (16812)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_16520 for (2952ds/5798Mi)
% 34.98/6.23 % (16804)Instruction limit reached!
% 34.98/6.23 % (16804)------------------------------
% 34.98/6.23 % (16804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.98/6.23 % (16804)Termination reason: Unknown
% 34.98/6.23 % (16804)Termination phase: Saturation
% 34.98/6.23
% 34.98/6.23 % (16804)Memory used [KB]: 9594
% 34.98/6.23 % (16804)Time elapsed: 0.302 s
% 34.98/6.23 % (16804)Instructions burned: 1049 (million)
% 34.98/6.23 % (16804)------------------------------
% 34.98/6.23 % (16804)------------------------------
% 34.98/6.23 % (16813)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_16520 for (2952ds/346Mi)
% 34.98/6.24 % (16814)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_16520 for (2952ds/1321Mi)
% 35.49/6.32 % (16813)Instruction limit reached!
% 35.49/6.32 % (16813)------------------------------
% 35.49/6.32 % (16813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.49/6.32 % (16813)Termination reason: Unknown
% 35.49/6.32 % (16813)Termination phase: Saturation
% 35.49/6.32
% 35.49/6.32 % (16813)Memory used [KB]: 8315
% 35.49/6.32 % (16813)Time elapsed: 0.093 s
% 35.49/6.32 % (16813)Instructions burned: 347 (million)
% 35.49/6.32 % (16813)------------------------------
% 35.49/6.32 % (16813)------------------------------
% 35.49/6.33 % (16816)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_16520 for (2951ds/1312Mi)
% 36.18/6.62 % (16814)Instruction limit reached!
% 36.18/6.62 % (16814)------------------------------
% 36.18/6.62 % (16814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.18/6.62 % (16814)Termination reason: Unknown
% 36.18/6.62 % (16814)Termination phase: Saturation
% 36.18/6.62
% 36.18/6.62 % (16814)Memory used [KB]: 3070
% 36.18/6.62 % (16814)Time elapsed: 0.382 s
% 36.18/6.62 % (16814)Instructions burned: 1322 (million)
% 36.18/6.62 % (16814)------------------------------
% 36.18/6.62 % (16814)------------------------------
% 36.18/6.63 % (16817)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_16520 for (2948ds/672Mi)
% 36.77/6.71 % (16816)Instruction limit reached!
% 36.77/6.71 % (16816)------------------------------
% 36.77/6.71 % (16816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.77/6.71 % (16816)Termination reason: Unknown
% 36.77/6.71 % (16816)Termination phase: Saturation
% 36.77/6.71
% 36.77/6.71 % (16816)Memory used [KB]: 9850
% 36.77/6.71 % (16816)Time elapsed: 0.377 s
% 36.77/6.71 % (16816)Instructions burned: 1312 (million)
% 36.77/6.71 % (16816)------------------------------
% 36.77/6.71 % (16816)------------------------------
% 36.77/6.72 % (16818)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_16520 for (2948ds/1897Mi)
% 36.77/6.77 % (16794)Instruction limit reached!
% 36.77/6.77 % (16794)------------------------------
% 36.77/6.77 % (16794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.77/6.77 % (16794)Termination reason: Unknown
% 36.77/6.77 % (16794)Termination phase: Saturation
% 36.77/6.77
% 36.77/6.77 % (16794)Memory used [KB]: 5245
% 36.77/6.77 % (16794)Time elapsed: 1.285 s
% 36.77/6.77 % (16794)Instructions burned: 4531 (million)
% 36.77/6.77 % (16794)------------------------------
% 36.77/6.77 % (16794)------------------------------
% 36.77/6.78 % (16819)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_16520 for (2947ds/1202Mi)
% 37.35/6.84 % (16817)Instruction limit reached!
% 37.35/6.84 % (16817)------------------------------
% 37.35/6.84 % (16817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.35/6.84 % (16817)Termination reason: Unknown
% 37.35/6.84 % (16817)Termination phase: Saturation
% 37.35/6.84
% 37.35/6.84 % (16817)Memory used [KB]: 8187
% 37.35/6.84 % (16817)Time elapsed: 0.207 s
% 37.35/6.84 % (16817)Instructions burned: 673 (million)
% 37.35/6.84 % (16817)------------------------------
% 37.35/6.84 % (16817)------------------------------
% 37.35/6.85 % (16820)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_16520 for (2946ds/1493Mi)
% 37.35/6.87 % (16811)Instruction limit reached!
% 37.35/6.87 % (16811)------------------------------
% 37.35/6.87 % (16811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.35/6.87 % (16811)Termination reason: Unknown
% 37.35/6.87 % (16811)Termination phase: Saturation
% 37.35/6.87
% 37.35/6.87 % (16811)Memory used [KB]: 4477
% 37.35/6.87 % (16811)Time elapsed: 0.653 s
% 37.35/6.87 % (16811)Instructions burned: 2403 (million)
% 37.35/6.87 % (16811)------------------------------
% 37.35/6.87 % (16811)------------------------------
% 37.35/6.88 % (16821)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_16520 for (2946ds/7679Mi)
% 38.34/6.90 % (16820)Refutation not found, incomplete strategy
% 38.34/6.90 % (16820)------------------------------
% 38.34/6.90 % (16820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.34/6.90 % (16820)Termination reason: Refutation not found, incomplete strategy
% 38.34/6.90
% 38.34/6.90
% 38.34/6.90 % (16820)Memory used [KB]: 7419
% 38.34/6.90 % (16820)Time elapsed: 0.059 s
% 38.34/6.90 % (16820)Instructions burned: 222 (million)
% 38.34/6.90 % (16820)------------------------------
% 38.34/6.90 % (16820)------------------------------
% 38.34/6.91 % (16822)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_16520 for (2946ds/340Mi)
% 38.34/7.01 % (16822)Instruction limit reached!
% 38.34/7.01 % (16822)------------------------------
% 38.34/7.01 % (16822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.34/7.01 % (16822)Termination reason: Unknown
% 38.34/7.01 % (16822)Termination phase: Saturation
% 38.34/7.01
% 38.34/7.01 % (16822)Memory used [KB]: 7036
% 38.34/7.01 % (16822)Time elapsed: 0.096 s
% 38.34/7.01 % (16822)Instructions burned: 342 (million)
% 38.34/7.01 % (16822)------------------------------
% 38.34/7.01 % (16822)------------------------------
% 40.84/7.02 % (16823)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_16520 for (2945ds/3672Mi)
% 41.46/7.13 % (16819)Instruction limit reached!
% 41.46/7.13 % (16819)------------------------------
% 41.46/7.13 % (16819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.46/7.13 % (16819)Termination reason: Unknown
% 41.46/7.13 % (16819)Termination phase: Saturation
% 41.46/7.13
% 41.46/7.13 % (16819)Memory used [KB]: 4093
% 41.46/7.13 % (16819)Time elapsed: 0.348 s
% 41.46/7.13 % (16819)Instructions burned: 1203 (million)
% 41.46/7.13 % (16819)------------------------------
% 41.46/7.13 % (16819)------------------------------
% 41.46/7.14 % (16824)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_16520 for (2943ds/1535Mi)
% 42.39/7.30 % (16818)Instruction limit reached!
% 42.39/7.30 % (16818)------------------------------
% 42.39/7.30 % (16818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.39/7.30 % (16818)Termination reason: Unknown
% 42.39/7.30 % (16818)Termination phase: Saturation
% 42.39/7.30
% 42.39/7.30 % (16818)Memory used [KB]: 9338
% 42.39/7.30 % (16818)Time elapsed: 0.597 s
% 42.39/7.30 % (16818)Instructions burned: 1900 (million)
% 42.39/7.30 % (16818)------------------------------
% 42.39/7.30 % (16818)------------------------------
% 42.39/7.31 % (16825)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_16520 for (2942ds/4637Mi)
% 42.39/7.37 % (16791)Refutation not found, non-redundant clauses discarded% (16791)------------------------------
% 42.39/7.37 % (16791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.39/7.37 % (16791)Termination reason: Refutation not found, non-redundant clauses discarded
% 42.39/7.37
% 42.39/7.37 % (16791)Memory used [KB]: 13688
% 42.39/7.37 % (16791)Time elapsed: 1.988 s
% 42.39/7.37 % (16791)Instructions burned: 6442 (million)
% 42.39/7.37 % (16791)------------------------------
% 42.39/7.37 % (16791)------------------------------
% 42.39/7.38 % (16826)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_16520 for (2941ds/3174Mi)
% 43.08/7.57 % (16824)Instruction limit reached!
% 43.08/7.57 % (16824)------------------------------
% 43.08/7.57 % (16824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.08/7.57 % (16824)Termination reason: Unknown
% 43.08/7.57 % (16824)Termination phase: Saturation
% 43.08/7.57
% 43.08/7.57 % (16824)Memory used [KB]: 12153
% 43.08/7.57 % (16824)Time elapsed: 0.434 s
% 43.08/7.57 % (16824)Instructions burned: 1537 (million)
% 43.08/7.57 % (16824)------------------------------
% 43.08/7.57 % (16824)------------------------------
% 43.08/7.58 % (16827)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_16520 for (2939ds/307Mi)
% 43.83/7.66 % (16827)Instruction limit reached!
% 43.83/7.66 % (16827)------------------------------
% 43.83/7.66 % (16827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.83/7.66 % (16827)Termination reason: Unknown
% 43.83/7.66 % (16827)Termination phase: Saturation
% 43.83/7.66
% 43.83/7.66 % (16827)Memory used [KB]: 7675
% 43.83/7.66 % (16827)Time elapsed: 0.105 s
% 43.83/7.66 % (16827)Instructions burned: 307 (million)
% 43.83/7.66 % (16827)------------------------------
% 43.83/7.66 % (16827)------------------------------
% 43.83/7.67 % (16828)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_16520 for (2938ds/3619Mi)
% 43.83/7.67 % (16810)Instruction limit reached!
% 43.83/7.67 % (16810)------------------------------
% 43.83/7.67 % (16810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.83/7.67 % (16810)Termination reason: Unknown
% 43.83/7.67 % (16810)Termination phase: Saturation
% 43.83/7.67
% 43.83/7.67 % (16810)Memory used [KB]: 12537
% 43.83/7.67 % (16810)Time elapsed: 1.473 s
% 43.83/7.67 % (16810)Instructions burned: 5062 (million)
% 43.83/7.67 % (16810)------------------------------
% 43.83/7.67 % (16810)------------------------------
% 43.83/7.68 % (16829)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_16520 for (2938ds/2325Mi)
% 44.61/7.92 % (16812)Instruction limit reached!
% 44.61/7.92 % (16812)------------------------------
% 44.61/7.92 % (16812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.61/7.92 % (16812)Termination reason: Unknown
% 44.61/7.92 % (16812)Termination phase: Saturation
% 44.61/7.92
% 44.61/7.92 % (16812)Memory used [KB]: 10106
% 44.61/7.92 % (16812)Time elapsed: 1.697 s
% 44.61/7.92 % (16812)Instructions burned: 5798 (million)
% 44.61/7.92 % (16812)------------------------------
% 44.61/7.92 % (16812)------------------------------
% 44.61/7.93 % (16830)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_16520 for (2935ds/2341Mi)
% 48.52/8.15 % (16823)Instruction limit reached!
% 48.52/8.15 % (16823)------------------------------
% 48.52/8.15 % (16823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.52/8.15 % (16823)Termination reason: Unknown
% 48.52/8.15 % (16823)Termination phase: Saturation
% 48.52/8.15
% 48.52/8.15 % (16823)Memory used [KB]: 12537
% 48.52/8.15 % (16823)Time elapsed: 1.151 s
% 48.52/8.15 % (16823)Instructions burned: 3673 (million)
% 48.52/8.15 % (16823)------------------------------
% 48.52/8.15 % (16823)------------------------------
% 48.52/8.17 % (16831)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_16520 for (2933ds/7257Mi)
% 49.67/8.33 % (16826)Instruction limit reached!
% 49.67/8.33 % (16826)------------------------------
% 49.67/8.33 % (16826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.67/8.33 % (16826)Termination reason: Unknown
% 49.67/8.33 % (16826)Termination phase: Saturation
% 49.67/8.33
% 49.67/8.33 % (16826)Memory used [KB]: 10362
% 49.67/8.33 % (16826)Time elapsed: 0.972 s
% 49.67/8.33 % (16826)Instructions burned: 3174 (million)
% 49.67/8.33 % (16826)------------------------------
% 49.67/8.33 % (16826)------------------------------
% 49.67/8.34 % (16832)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_16520 for (2931ds/3710Mi)
% 50.22/8.40 % (16829)Refutation not found, non-redundant clauses discarded% (16829)------------------------------
% 50.22/8.40 % (16829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.22/8.40 % (16829)Termination reason: Refutation not found, non-redundant clauses discarded
% 50.22/8.40
% 50.22/8.40 % (16829)Memory used [KB]: 10234
% 50.22/8.40 % (16829)Time elapsed: 0.714 s
% 50.22/8.40 % (16829)Instructions burned: 2312 (million)
% 50.22/8.40 % (16829)------------------------------
% 50.22/8.40 % (16829)------------------------------
% 50.22/8.41 % (16833)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_16520 for (2930ds/326Mi)
% 50.63/8.51 % (16833)Instruction limit reached!
% 50.63/8.51 % (16833)------------------------------
% 50.63/8.51 % (16833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.63/8.51 % (16833)Termination reason: Unknown
% 50.63/8.51 % (16833)Termination phase: Saturation
% 50.63/8.51
% 50.63/8.51 % (16833)Memory used [KB]: 7547
% 50.63/8.51 % (16833)Time elapsed: 0.103 s
% 50.63/8.51 % (16833)Instructions burned: 326 (million)
% 50.63/8.51 % (16833)------------------------------
% 50.63/8.51 % (16833)------------------------------
% 50.63/8.52 % (16834)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_16520 for (2929ds/1100Mi)
% 50.63/8.53 % (16825)First to succeed.
% 50.63/8.53 % (16825)Refutation found. Thanks to Tanya!
% 50.63/8.53 % SZS status Theorem for DTF2THF_16520
% 50.63/8.53 % SZS output start Proof for DTF2THF_16520
% 50.63/8.53 thf(type_def_5, type, product_prod_nat_nat: $tType).
% 50.63/8.53 thf(type_def_6, type, a: $tType).
% 50.63/8.53 thf(type_def_8, type, nat: $tType).
% 50.63/8.53 thf(type_def_9, type, capacity: $tType).
% 50.63/8.53 thf(type_def_10, type, list_P559422087at_nat: $tType).
% 50.63/8.53 thf(type_def_11, type, set_nat: $tType).
% 50.63/8.53 thf(func_def_0, type, list_P559422087at_nat: $tType).
% 50.63/8.53 thf(func_def_1, type, product_prod_nat_nat: $tType).
% 50.63/8.53 thf(func_def_2, type, set_nat: $tType).
% 50.63/8.53 thf(func_def_3, type, capacity: $tType).
% 50.63/8.53 thf(func_def_4, type, nat: $tType).
% 50.63/8.53 thf(func_def_5, type, a: $tType).
% 50.63/8.53 thf(func_def_6, type, connected_a: (product_prod_nat_nat > a) > nat > nat > $o).
% 50.63/8.53 thf(func_def_7, type, connected_capacity: (product_prod_nat_nat > capacity) > nat > nat > $o).
% 50.63/8.53 thf(func_def_8, type, dist_a: (product_prod_nat_nat > a) > nat > nat > nat > $o).
% 50.63/8.53 thf(func_def_9, type, dist_capacity: (product_prod_nat_nat > capacity) > nat > nat > nat > $o).
% 50.63/8.53 thf(func_def_10, type, isPath_a: (product_prod_nat_nat > a) > nat > list_P559422087at_nat > nat > $o).
% 50.63/8.53 thf(func_def_11, type, isPath_capacity: (product_prod_nat_nat > capacity) > nat > list_P559422087at_nat > nat > $o).
% 50.63/8.53 thf(func_def_12, type, isShortestPath_a: (product_prod_nat_nat > a) > nat > list_P559422087at_nat > nat > $o).
% 50.63/8.53 thf(func_def_13, type, isShor1936442771pacity: (product_prod_nat_nat > capacity) > nat > list_P559422087at_nat > nat > $o).
% 50.63/8.53 thf(func_def_14, type, isSimplePath_a: (product_prod_nat_nat > a) > nat > list_P559422087at_nat > nat > $o).
% 50.63/8.53 thf(func_def_15, type, isSimp1359852763pacity: (product_prod_nat_nat > capacity) > nat > list_P559422087at_nat > nat > $o).
% 50.63/8.53 thf(func_def_16, type, min_dist_a: (product_prod_nat_nat > a) > nat > nat > nat).
% 50.63/8.53 thf(func_def_17, type, min_dist_capacity: (product_prod_nat_nat > capacity) > nat > nat > nat).
% 50.63/8.53 thf(func_def_18, type, reachableNodes_a: (product_prod_nat_nat > a) > nat > set_nat).
% 50.63/8.53 thf(func_def_19, type, reacha1693770334pacity: (product_prod_nat_nat > capacity) > nat > set_nat).
% 50.63/8.53 thf(func_def_20, type, plus_plus_nat: nat > nat > nat).
% 50.63/8.53 thf(func_def_21, type, size_s1990949619at_nat: list_P559422087at_nat > nat).
% 50.63/8.53 thf(func_def_22, type, ord_Least_nat: (nat > $o) > nat).
% 50.63/8.53 thf(func_def_23, type, ord_less_nat: nat > nat > $o).
% 50.63/8.53 thf(func_def_24, type, ord_less_eq_nat: nat > nat > $o).
% 50.63/8.53 thf(func_def_25, type, collect_nat: (nat > $o) > set_nat).
% 50.63/8.53 thf(func_def_26, type, member_nat: nat > set_nat > $o).
% 50.63/8.53 thf(func_def_27, type, c: product_prod_nat_nat > capacity).
% 50.63/8.53 thf(func_def_28, type, c2: product_prod_nat_nat > a).
% 50.63/8.53 thf(func_def_29, type, p: list_P559422087at_nat).
% 50.63/8.53 thf(func_def_30, type, p1: list_P559422087at_nat).
% 50.63/8.53 thf(func_def_31, type, p1a: list_P559422087at_nat).
% 50.63/8.53 thf(func_def_32, type, p2: list_P559422087at_nat).
% 50.63/8.53 thf(func_def_33, type, p2_a: list_P559422087at_nat).
% 50.63/8.53 thf(func_def_34, type, p3: list_P559422087at_nat).
% 50.63/8.53 thf(func_def_35, type, s: nat).
% 50.63/8.53 thf(func_def_36, type, t: nat).
% 50.63/8.53 thf(func_def_37, type, u: nat).
% 50.63/8.53 thf(func_def_38, type, ua: nat).
% 50.63/8.53 thf(func_def_39, type, v: nat).
% 50.63/8.53 thf(func_def_40, type, va: nat).
% 50.63/8.53 thf(func_def_57, type, sK0: nat > nat > (product_prod_nat_nat > capacity) > nat).
% 50.63/8.53 thf(func_def_58, type, sK1: (product_prod_nat_nat > capacity) > nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_59, type, sK2: nat > nat > (product_prod_nat_nat > a) > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_60, type, sK3: nat > (product_prod_nat_nat > capacity) > nat > nat > nat).
% 50.63/8.53 thf(func_def_61, type, sK4: (nat > $o) > nat).
% 50.63/8.53 thf(func_def_62, type, sK5: nat > nat > nat).
% 50.63/8.53 thf(func_def_63, type, sK6: (nat > nat) > nat).
% 50.63/8.53 thf(func_def_64, type, sK7: (nat > nat) > nat).
% 50.63/8.53 thf(func_def_65, type, sK8: (nat > nat) > nat).
% 50.63/8.53 thf(func_def_66, type, sK9: (nat > nat) > nat).
% 50.63/8.53 thf(func_def_67, type, sK10: (nat > $o) > nat).
% 50.63/8.53 thf(func_def_68, type, sK11: nat > nat > nat).
% 50.63/8.53 thf(func_def_69, type, sK12: (nat > nat) > nat).
% 50.63/8.53 thf(func_def_70, type, sK13: (nat > nat) > nat).
% 50.63/8.53 thf(func_def_71, type, sK14: nat > nat).
% 50.63/8.53 thf(func_def_72, type, sK15: nat > (product_prod_nat_nat > capacity) > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_73, type, sK16: (nat > nat) > nat).
% 50.63/8.53 thf(func_def_74, type, sK17: (nat > nat) > nat).
% 50.63/8.53 thf(func_def_75, type, sK18: nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_76, type, sK19: nat > nat > (product_prod_nat_nat > a) > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_77, type, sK20: (nat > nat) > nat).
% 50.63/8.53 thf(func_def_78, type, sK21: (nat > nat) > nat).
% 50.63/8.53 thf(func_def_79, type, sK22: nat > nat > nat).
% 50.63/8.53 thf(func_def_80, type, sK23: nat > nat > nat).
% 50.63/8.53 thf(func_def_81, type, sK24: nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_82, type, sK25: nat > nat > nat > nat).
% 50.63/8.53 thf(func_def_83, type, sK26: nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_84, type, sK27: (nat > nat) > nat).
% 50.63/8.53 thf(func_def_85, type, sK28: (nat > nat) > nat).
% 50.63/8.53 thf(func_def_86, type, sK29: (nat > nat > $o) > nat).
% 50.63/8.53 thf(func_def_87, type, sK30: (nat > nat > $o) > nat).
% 50.63/8.53 thf(func_def_88, type, sK31: (nat > nat > $o) > nat).
% 50.63/8.53 thf(func_def_89, type, sK32: (nat > nat > $o) > nat).
% 50.63/8.53 thf(func_def_90, type, sK33: (nat > nat > $o) > nat).
% 50.63/8.53 thf(func_def_91, type, sK34: (product_prod_nat_nat > capacity) > (nat > $o) > nat > nat > nat).
% 50.63/8.53 thf(func_def_92, type, sK35: nat > (product_prod_nat_nat > capacity) > nat > nat).
% 50.63/8.53 thf(func_def_93, type, sK36: nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_94, type, sK37: (nat > $o) > nat).
% 50.63/8.53 thf(func_def_95, type, sK38: nat > nat > (nat > $o) > nat).
% 50.63/8.53 thf(func_def_97, type, sK40: nat > nat > nat > (product_prod_nat_nat > capacity) > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_98, type, sK41: nat > (product_prod_nat_nat > capacity) > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_99, type, sK42: nat > list_P559422087at_nat > (product_prod_nat_nat > capacity) > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_100, type, sK43: nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_101, type, sK44: nat > list_P559422087at_nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_102, type, sK45: nat > nat > (product_prod_nat_nat > capacity) > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_103, type, sK46: nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_104, type, sK47: (product_prod_nat_nat > capacity) > nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_109, type, sK48: nat > nat > nat).
% 50.63/8.53 thf(func_def_110, type, sK49: nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_111, type, sK50: nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_112, type, sK51: (product_prod_nat_nat > capacity) > nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_113, type, sK52: list_P559422087at_nat).
% 50.63/8.53 thf(func_def_114, type, sK53: nat > (nat > $o) > (product_prod_nat_nat > capacity) > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_115, type, sK54: nat > nat > list_P559422087at_nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_116, type, sK55: nat > nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_117, type, sK56: nat > nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_118, type, sK57: nat > nat > nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_119, type, sK58: nat > nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_120, type, sK59: nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_121, type, sK60: nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_122, type, sK61: nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_123, type, sK62: (product_prod_nat_nat > a) > nat > nat > list_P559422087at_nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_124, type, sK63: list_P559422087at_nat > nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_125, type, sK64: nat > (product_prod_nat_nat > capacity) > nat > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_126, type, sK65: nat > nat > list_P559422087at_nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_127, type, sK66: nat > nat > list_P559422087at_nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_128, type, sK67: nat > (product_prod_nat_nat > capacity) > nat > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_129, type, sK68: nat > nat > (nat > $o) > list_P559422087at_nat).
% 50.63/8.53 thf(func_def_130, type, ph69: !>[X0: $tType]:(X0)).
% 50.63/8.53 thf(f7103,plain,(
% 50.63/8.53 $false),
% 50.63/8.53 inference(subsumption_resolution,[status(thm)],[f7102,f5677])).
% 50.63/8.53 thf(f5677,plain,(
% 50.63/8.53 ((ord_less_nat @ (size_s1990949619at_nat @ p) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ (size_s1990949619at_nat @ p2_a))) != $true)),
% 50.63/8.53 inference(backward_demodulation,[status(thm)],[f1389,f1462])).
% 50.63/8.53 thf(f1462,plain,(
% 50.63/8.53 ((size_s1990949619at_nat @ p) = (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ s @ Y1 @ t)))))))),
% 50.63/8.53 inference(equality_proxy_clausification,[status(thm)],[f1461])).
% 50.63/8.53 thf(f1461,plain,(
% 50.63/8.53 (((size_s1990949619at_nat @ p) = (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ s @ Y1 @ t))))))) = $true)),
% 50.63/8.53 inference(binary_proxy_clausification,[status(thm)],[f1459])).
% 50.63/8.53 thf(f1459,plain,(
% 50.63/8.53 ((((size_s1990949619at_nat @ p) = (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ s @ Y1 @ t))))))) & (isSimp1359852763pacity @ c @ s @ p @ t)) = $true)),
% 50.63/8.53 inference(beta_eta_normalization,[status(thm)],[f1237])).
% 50.63/8.53 thf(f1237,plain,(
% 50.63/8.53 (((^[Y0 : product_prod_nat_nat > capacity]: ((^[Y1 : nat]: ((^[Y2 : list_P559422087at_nat]: ((^[Y3 : nat]: (((size_s1990949619at_nat @ Y2) = ((^[Y4 : product_prod_nat_nat > capacity]: ((^[Y5 : nat]: ((^[Y6 : nat]: (ord_Least_nat @ (^[Y7 : nat]: ((^[Y8 : product_prod_nat_nat > capacity]: ((^[Y9 : nat]: ((^[Y10 : nat]: ((^[Y11 : nat]: (?? @ list_P559422087at_nat @ (^[Y12 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y12) = Y10) & (isPath_capacity @ Y8 @ Y9 @ Y12 @ Y11))))))))))) @ Y4 @ Y5 @ Y7 @ Y6)))))))) @ Y0 @ Y1 @ Y3)) & (isSimp1359852763pacity @ Y0 @ Y1 @ Y2 @ Y3))))))))) @ c @ s @ p @ t) = $true)),
% 50.63/8.53 inference(definition_unfolding,[status(thm)],[f1043,f1227])).
% 50.63/8.53 thf(f1227,plain,(
% 50.63/8.53 (isShor1936442771pacity = (^[Y0 : product_prod_nat_nat > capacity]: ((^[Y1 : nat]: ((^[Y2 : list_P559422087at_nat]: ((^[Y3 : nat]: (((size_s1990949619at_nat @ Y2) = ((^[Y4 : product_prod_nat_nat > capacity]: ((^[Y5 : nat]: ((^[Y6 : nat]: (ord_Least_nat @ (^[Y7 : nat]: ((^[Y8 : product_prod_nat_nat > capacity]: ((^[Y9 : nat]: ((^[Y10 : nat]: ((^[Y11 : nat]: (?? @ list_P559422087at_nat @ (^[Y12 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y12) = Y10) & (isPath_capacity @ Y8 @ Y9 @ Y12 @ Y11))))))))))) @ Y4 @ Y5 @ Y7 @ Y6)))))))) @ Y0 @ Y1 @ Y3)) & (isSimp1359852763pacity @ Y0 @ Y1 @ Y2 @ Y3))))))))))),
% 50.63/8.53 inference(definition_unfolding,[status(thm)],[f1078,f1226])).
% 50.63/8.53 thf(f1226,plain,(
% 50.63/8.53 (min_dist_capacity = (^[Y0 : product_prod_nat_nat > capacity]: ((^[Y1 : nat]: ((^[Y2 : nat]: (ord_Least_nat @ (^[Y3 : nat]: ((^[Y4 : product_prod_nat_nat > capacity]: ((^[Y5 : nat]: ((^[Y6 : nat]: ((^[Y7 : nat]: (?? @ list_P559422087at_nat @ (^[Y8 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y8) = Y6) & (isPath_capacity @ Y4 @ Y5 @ Y8 @ Y7))))))))))) @ Y0 @ Y1 @ Y3 @ Y2)))))))))),
% 50.63/8.53 inference(definition_unfolding,[status(thm)],[f1060,f1069])).
% 50.63/8.53 thf(f1069,plain,(
% 50.63/8.53 (dist_capacity = (^[Y0 : product_prod_nat_nat > capacity]: ((^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: (?? @ list_P559422087at_nat @ (^[Y4 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y4) = Y2) & (isPath_capacity @ Y0 @ Y1 @ Y4 @ Y3))))))))))))),
% 50.63/8.53 inference(cnf_transformation,[status(thm)],[f736])).
% 50.63/8.53 thf(f736,plain,(
% 50.63/8.53 (dist_capacity = (^[Y0 : product_prod_nat_nat > capacity]: ((^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: (?? @ list_P559422087at_nat @ (^[Y4 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y4) = Y2) & (isPath_capacity @ Y0 @ Y1 @ Y4 @ Y3))))))))))))),
% 50.63/8.53 inference(fool_elimination,[status(thm)],[f735])).
% 50.63/8.53 thf(f735,plain,(
% 50.63/8.53 (dist_capacity = (^[X0 : product_prod_nat_nat > capacity, X1 : nat, X2 : nat, X3 : nat] : (? [X4 : list_P559422087at_nat] : ((isPath_capacity @ X0 @ X1 @ X4 @ X3) & ((size_s1990949619at_nat @ X4) = X2)))))),
% 50.63/8.53 inference(rectify,[status(thm)],[f121])).
% 50.63/8.53 thf(f121,axiom,(
% 50.63/8.53 (dist_capacity = (^[X33 : product_prod_nat_nat > capacity, X53 : nat, X18 : nat, X54 : nat] : (? [X15 : list_P559422087at_nat] : ((isPath_capacity @ X33 @ X53 @ X15 @ X54) & ((size_s1990949619at_nat @ X15) = X18)))))),
% 50.63/8.53 file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_120_Graph_Odist__def)).
% 50.63/8.53 thf(f1060,plain,(
% 50.63/8.53 (min_dist_capacity = (^[Y0 : product_prod_nat_nat > capacity]: ((^[Y1 : nat]: ((^[Y2 : nat]: (ord_Least_nat @ (^[Y3 : nat]: (dist_capacity @ Y0 @ Y1 @ Y3 @ Y2)))))))))),
% 50.63/8.53 inference(cnf_transformation,[status(thm)],[f440])).
% 50.63/8.53 thf(f440,plain,(
% 50.63/8.53 (min_dist_capacity = (^[Y0 : product_prod_nat_nat > capacity]: ((^[Y1 : nat]: ((^[Y2 : nat]: (ord_Least_nat @ (^[Y3 : nat]: (dist_capacity @ Y0 @ Y1 @ Y3 @ Y2)))))))))),
% 50.63/8.53 inference(fool_elimination,[status(thm)],[f439])).
% 50.63/8.53 thf(f439,plain,(
% 50.63/8.53 (min_dist_capacity = (^[X0 : product_prod_nat_nat > capacity, X1 : nat, X2 : nat] : (ord_Least_nat @ (^[X3 : nat] : (dist_capacity @ X0 @ X1 @ X3 @ X2)))))),
% 50.63/8.53 inference(rectify,[status(thm)],[f141])).
% 50.63/8.53 thf(f141,axiom,(
% 50.63/8.53 (min_dist_capacity = (^[X33 : product_prod_nat_nat > capacity, X53 : nat, X54 : nat] : (ord_Least_nat @ (^[X18 : nat] : (dist_capacity @ X33 @ X53 @ X18 @ X54)))))),
% 50.63/8.53 file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_140_Graph_Omin__dist__def)).
% 50.63/8.53 thf(f1078,plain,(
% 50.63/8.53 (isShor1936442771pacity = (^[Y0 : product_prod_nat_nat > capacity]: ((^[Y1 : nat]: ((^[Y2 : list_P559422087at_nat]: ((^[Y3 : nat]: (((size_s1990949619at_nat @ Y2) = (min_dist_capacity @ Y0 @ Y1 @ Y3)) & (isSimp1359852763pacity @ Y0 @ Y1 @ Y2 @ Y3))))))))))),
% 50.63/8.53 inference(cnf_transformation,[status(thm)],[f632])).
% 50.63/8.53 thf(f632,plain,(
% 50.63/8.53 (isShor1936442771pacity = (^[Y0 : product_prod_nat_nat > capacity]: ((^[Y1 : nat]: ((^[Y2 : list_P559422087at_nat]: ((^[Y3 : nat]: (((size_s1990949619at_nat @ Y2) = (min_dist_capacity @ Y0 @ Y1 @ Y3)) & (isSimp1359852763pacity @ Y0 @ Y1 @ Y2 @ Y3))))))))))),
% 50.63/8.53 inference(fool_elimination,[status(thm)],[f631])).
% 50.63/8.53 thf(f631,plain,(
% 50.63/8.53 (isShor1936442771pacity = (^[X0 : product_prod_nat_nat > capacity, X1 : nat, X2 : list_P559422087at_nat, X3 : nat] : ((isSimp1359852763pacity @ X0 @ X1 @ X2 @ X3) & ((size_s1990949619at_nat @ X2) = (min_dist_capacity @ X0 @ X1 @ X3)))))),
% 50.63/8.53 inference(rectify,[status(thm)],[f143])).
% 50.63/8.53 thf(f143,axiom,(
% 50.63/8.53 (isShor1936442771pacity = (^[X33 : product_prod_nat_nat > capacity, X52 : nat, X15 : list_P559422087at_nat, X53 : nat] : ((isSimp1359852763pacity @ X33 @ X52 @ X15 @ X53) & ((size_s1990949619at_nat @ X15) = (min_dist_capacity @ X33 @ X52 @ X53)))))),
% 50.63/8.53 file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_142_Graph_OisShortestPath__alt)).
% 50.63/8.53 thf(f1043,plain,(
% 50.63/8.53 ((isShor1936442771pacity @ c @ s @ p @ t) = $true)),
% 50.63/8.53 inference(cnf_transformation,[status(thm)],[f716])).
% 50.63/8.53 thf(f716,plain,(
% 50.63/8.53 ((isShor1936442771pacity @ c @ s @ p @ t) = $true)),
% 50.63/8.53 inference(fool_elimination,[status(thm)],[f715])).
% 50.63/8.53 thf(f715,plain,(
% 50.63/8.53 (isShor1936442771pacity @ c @ s @ p @ t)),
% 50.63/8.53 inference(rectify,[status(thm)],[f8])).
% 50.63/8.53 thf(f8,axiom,(
% 50.63/8.53 (isShor1936442771pacity @ c @ s @ p @ t)),
% 50.63/8.53 file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_7_SP)).
% 50.63/8.53 thf(f1389,plain,(
% 50.63/8.53 ((ord_less_nat @ (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ s @ Y1 @ t)))))) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ (size_s1990949619at_nat @ p2_a))) != $true)),
% 50.63/8.53 inference(beta_eta_normalization,[status(thm)],[f1239])).
% 50.63/8.53 thf(f1239,plain,(
% 50.63/8.53 ((ord_less_nat @ ((^[Y0 : product_prod_nat_nat > capacity]: ((^[Y1 : nat]: ((^[Y2 : nat]: (ord_Least_nat @ (^[Y3 : nat]: ((^[Y4 : product_prod_nat_nat > capacity]: ((^[Y5 : nat]: ((^[Y6 : nat]: ((^[Y7 : nat]: (?? @ list_P559422087at_nat @ (^[Y8 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y8) = Y6) & (isPath_capacity @ Y4 @ Y5 @ Y8 @ Y7))))))))))) @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ c @ s @ t) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ (size_s1990949619at_nat @ p2_a))) != $true)),
% 50.63/8.53 inference(definition_unfolding,[status(thm)],[f1046,f1226])).
% 50.63/8.53 thf(f1046,plain,(
% 50.63/8.53 ((ord_less_nat @ (min_dist_capacity @ c @ s @ t) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ (size_s1990949619at_nat @ p2_a))) != $true)),
% 50.63/8.53 inference(cnf_transformation,[status(thm)],[f757])).
% 50.63/8.53 thf(f757,plain,(
% 50.63/8.53 ((ord_less_nat @ (min_dist_capacity @ c @ s @ t) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ (size_s1990949619at_nat @ p2_a))) != $true)),
% 50.63/8.53 inference(flattening,[status(thm)],[f606])).
% 50.63/8.53 thf(f606,plain,(
% 50.63/8.53 ~((ord_less_nat @ (min_dist_capacity @ c @ s @ t) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ (size_s1990949619at_nat @ p2_a))) = $true)),
% 50.63/8.53 inference(fool_elimination,[status(thm)],[f605])).
% 50.63/8.53 thf(f605,plain,(
% 50.63/8.53 ~(ord_less_nat @ (min_dist_capacity @ c @ s @ t) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ (size_s1990949619at_nat @ p2_a)))),
% 50.63/8.53 inference(rectify,[status(thm)],[f275])).
% 50.63/8.53 thf(f275,negated_conjecture,(
% 50.63/8.53 ~(ord_less_nat @ (min_dist_capacity @ c @ s @ t) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ (size_s1990949619at_nat @ p2_a)))),
% 50.63/8.53 inference(negated_conjecture,[status(cth)],[f274])).
% 50.63/8.53 thf(f274,conjecture,(
% 50.63/8.53 (ord_less_nat @ (min_dist_capacity @ c @ s @ t) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ (size_s1990949619at_nat @ p2_a)))),
% 50.63/8.53 file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',conj_0)).
% 50.63/8.53 thf(f7102,plain,(
% 50.63/8.53 ((ord_less_nat @ (size_s1990949619at_nat @ p) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ (size_s1990949619at_nat @ p2_a))) = $true)),
% 50.63/8.53 inference(forward_demodulation,[status(thm)],[f7097,f5676])).
% 50.63/8.53 thf(f5676,plain,(
% 50.63/8.53 ((plus_plus_nat @ (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ s @ Y1 @ ua)))))) @ (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ ua @ Y1 @ t))))))) = (size_s1990949619at_nat @ p))),
% 50.63/8.53 inference(backward_demodulation,[status(thm)],[f1593,f1462])).
% 50.63/8.53 thf(f1593,plain,(
% 50.63/8.53 ((plus_plus_nat @ (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ s @ Y1 @ ua)))))) @ (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ ua @ Y1 @ t))))))) = (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ s @ Y1 @ t)))))))),
% 50.63/8.53 inference(beta_eta_normalization,[status(thm)],[f1264])).
% 50.63/8.53 thf(f1264,plain,(
% 50.63/8.53 (((^[Y0 : product_prod_nat_nat > capacity]: ((^[Y1 : nat]: ((^[Y2 : nat]: (ord_Least_nat @ (^[Y3 : nat]: ((^[Y4 : product_prod_nat_nat > capacity]: ((^[Y5 : nat]: ((^[Y6 : nat]: ((^[Y7 : nat]: (?? @ list_P559422087at_nat @ (^[Y8 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y8) = Y6) & (isPath_capacity @ Y4 @ Y5 @ Y8 @ Y7))))))))))) @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ c @ s @ t) = (plus_plus_nat @ ((^[Y0 : product_prod_nat_nat > capacity]: ((^[Y1 : nat]: ((^[Y2 : nat]: (ord_Least_nat @ (^[Y3 : nat]: ((^[Y4 : product_prod_nat_nat > capacity]: ((^[Y5 : nat]: ((^[Y6 : nat]: ((^[Y7 : nat]: (?? @ list_P559422087at_nat @ (^[Y8 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y8) = Y6) & (isPath_capacity @ Y4 @ Y5 @ Y8 @ Y7))))))))))) @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ c @ s @ ua) @ ((^[Y0 : product_prod_nat_nat > capacity]: ((^[Y1 : nat]: ((^[Y2 : nat]: (ord_Least_nat @ (^[Y3 : nat]: ((^[Y4 : product_prod_nat_nat > capacity]: ((^[Y5 : nat]: ((^[Y6 : nat]: ((^[Y7 : nat]: (?? @ list_P559422087at_nat @ (^[Y8 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y8) = Y6) & (isPath_capacity @ Y4 @ Y5 @ Y8 @ Y7))))))))))) @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ c @ ua @ t)))),
% 50.63/8.53 inference(definition_unfolding,[status(thm)],[f1130,f1226,f1226,f1226])).
% 50.63/8.53 thf(f1130,plain,(
% 50.63/8.53 ((min_dist_capacity @ c @ s @ t) = (plus_plus_nat @ (min_dist_capacity @ c @ s @ ua) @ (min_dist_capacity @ c @ ua @ t)))),
% 50.63/8.53 inference(cnf_transformation,[status(thm)],[f1])).
% 50.63/8.53 thf(f1,axiom,(
% 50.63/8.53 ((min_dist_capacity @ c @ s @ t) = (plus_plus_nat @ (min_dist_capacity @ c @ s @ ua) @ (min_dist_capacity @ c @ ua @ t)))),
% 50.63/8.53 file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062)).
% 50.63/8.53 thf(f7097,plain,(
% 50.63/8.53 ((ord_less_nat @ (plus_plus_nat @ (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ s @ Y1 @ ua)))))) @ (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ ua @ Y1 @ t))))))) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ (size_s1990949619at_nat @ p2_a))) = $true)),
% 50.63/8.53 inference(trivial_inequality_removal,[status(thm)],[f7088])).
% 50.63/8.53 thf(f7088,plain,(
% 50.63/8.53 ((ord_less_nat @ (plus_plus_nat @ (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ s @ Y1 @ ua)))))) @ (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ ua @ Y1 @ t))))))) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ (size_s1990949619at_nat @ p2_a))) = $true) | ($true != $true)),
% 50.63/8.53 inference(superposition,[status(thm)],[f2276,f1469])).
% 50.63/8.53 thf(f1469,plain,(
% 50.63/8.53 ((ord_less_eq_nat @ (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ ua @ Y1 @ t)))))) @ (size_s1990949619at_nat @ p2_a)) = $true)),
% 50.63/8.53 inference(beta_eta_normalization,[status(thm)],[f1243])).
% 50.63/8.53 thf(f1243,plain,(
% 50.63/8.53 ((ord_less_eq_nat @ ((^[Y0 : product_prod_nat_nat > capacity]: ((^[Y1 : nat]: ((^[Y2 : nat]: (ord_Least_nat @ (^[Y3 : nat]: ((^[Y4 : product_prod_nat_nat > capacity]: ((^[Y5 : nat]: ((^[Y6 : nat]: ((^[Y7 : nat]: (?? @ list_P559422087at_nat @ (^[Y8 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y8) = Y6) & (isPath_capacity @ Y4 @ Y5 @ Y8 @ Y7))))))))))) @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ c @ ua @ t) @ (size_s1990949619at_nat @ p2_a)) = $true)),
% 50.63/8.53 inference(definition_unfolding,[status(thm)],[f1073,f1226])).
% 50.63/8.53 thf(f1073,plain,(
% 50.63/8.53 ((ord_less_eq_nat @ (min_dist_capacity @ c @ ua @ t) @ (size_s1990949619at_nat @ p2_a)) = $true)),
% 50.63/8.53 inference(cnf_transformation,[status(thm)],[f554])).
% 50.63/8.53 thf(f554,plain,(
% 50.63/8.53 ((ord_less_eq_nat @ (min_dist_capacity @ c @ ua @ t) @ (size_s1990949619at_nat @ p2_a)) = $true)),
% 50.63/8.53 inference(fool_elimination,[status(thm)],[f553])).
% 50.63/8.53 thf(f553,plain,(
% 50.63/8.53 (ord_less_eq_nat @ (min_dist_capacity @ c @ ua @ t) @ (size_s1990949619at_nat @ p2_a))),
% 50.63/8.53 inference(rectify,[status(thm)],[f3])).
% 50.63/8.53 thf(f3,axiom,(
% 50.63/8.53 (ord_less_eq_nat @ (min_dist_capacity @ c @ ua @ t) @ (size_s1990949619at_nat @ p2_a))),
% 50.63/8.53 file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062)).
% 50.63/8.53 thf(f2276,plain,(
% 50.63/8.53 ( ! [X0 : nat,X1 : nat] : (($true != (ord_less_eq_nat @ X0 @ X1)) | ((ord_less_nat @ (plus_plus_nat @ (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ s @ Y1 @ ua)))))) @ X0) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ X1)) = $true)) )),
% 50.63/8.53 inference(trivial_inequality_removal,[status(thm)],[f2271])).
% 50.63/8.53 thf(f2271,plain,(
% 50.63/8.53 ( ! [X0 : nat,X1 : nat] : (((ord_less_nat @ (plus_plus_nat @ (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ s @ Y1 @ ua)))))) @ X0) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ X1)) = $true) | ($true != (ord_less_eq_nat @ X0 @ X1)) | ($true != $true)) )),
% 50.63/8.53 inference(superposition,[status(thm)],[f1177,f1388])).
% 50.63/8.53 thf(f1388,plain,(
% 50.63/8.53 ((ord_less_nat @ (ord_Least_nat @ (^[Y0 : nat]: (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y1) = Y0) & (isPath_capacity @ c @ s @ Y1 @ ua)))))) @ (size_s1990949619at_nat @ p1a)) = $true)),
% 50.63/8.53 inference(beta_eta_normalization,[status(thm)],[f1261])).
% 50.63/8.53 thf(f1261,plain,(
% 50.63/8.53 ((ord_less_nat @ ((^[Y0 : product_prod_nat_nat > capacity]: ((^[Y1 : nat]: ((^[Y2 : nat]: (ord_Least_nat @ (^[Y3 : nat]: ((^[Y4 : product_prod_nat_nat > capacity]: ((^[Y5 : nat]: ((^[Y6 : nat]: ((^[Y7 : nat]: (?? @ list_P559422087at_nat @ (^[Y8 : list_P559422087at_nat]: (((size_s1990949619at_nat @ Y8) = Y6) & (isPath_capacity @ Y4 @ Y5 @ Y8 @ Y7))))))))))) @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ c @ s @ ua) @ (size_s1990949619at_nat @ p1a)) = $true)),
% 50.63/8.53 inference(definition_unfolding,[status(thm)],[f1125,f1226])).
% 50.63/8.53 thf(f1125,plain,(
% 50.63/8.53 ((ord_less_nat @ (min_dist_capacity @ c @ s @ ua) @ (size_s1990949619at_nat @ p1a)) = $true)),
% 50.63/8.53 inference(cnf_transformation,[status(thm)],[f752])).
% 50.63/8.53 thf(f752,plain,(
% 50.63/8.53 ((ord_less_nat @ (min_dist_capacity @ c @ s @ ua) @ (size_s1990949619at_nat @ p1a)) = $true)),
% 50.63/8.53 inference(fool_elimination,[status(thm)],[f751])).
% 50.63/8.53 thf(f751,plain,(
% 50.63/8.53 (ord_less_nat @ (min_dist_capacity @ c @ s @ ua) @ (size_s1990949619at_nat @ p1a))),
% 50.63/8.53 inference(rectify,[status(thm)],[f2])).
% 50.63/8.53 thf(f2,axiom,(
% 50.63/8.53 (ord_less_nat @ (min_dist_capacity @ c @ s @ ua) @ (size_s1990949619at_nat @ p1a))),
% 50.63/8.53 file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062)).
% 50.63/8.53 thf(f1177,plain,(
% 50.63/8.53 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != (ord_less_nat @ X1 @ X3)) | ((ord_less_nat @ (plus_plus_nat @ X1 @ X0) @ (plus_plus_nat @ X3 @ X2)) = $true) | ((ord_less_eq_nat @ X0 @ X2) != $true)) )),
% 50.63/8.53 inference(cnf_transformation,[status(thm)],[f826])).
% 50.63/8.53 thf(f826,plain,(
% 50.63/8.53 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true != (ord_less_nat @ X1 @ X3)) | ((ord_less_eq_nat @ X0 @ X2) != $true) | ((ord_less_nat @ (plus_plus_nat @ X1 @ X0) @ (plus_plus_nat @ X3 @ X2)) = $true))),
% 50.63/8.53 inference(flattening,[status(thm)],[f825])).
% 50.63/8.53 thf(f825,plain,(
% 50.63/8.53 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((((ord_less_nat @ (plus_plus_nat @ X1 @ X0) @ (plus_plus_nat @ X3 @ X2)) = $true) | ((ord_less_eq_nat @ X0 @ X2) != $true)) | ($true != (ord_less_nat @ X1 @ X3)))),
% 50.63/8.53 inference(ennf_transformation,[status(thm)],[f408])).
% 50.63/8.53 thf(f408,plain,(
% 50.63/8.53 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = (ord_less_nat @ X1 @ X3)) => (((ord_less_eq_nat @ X0 @ X2) = $true) => ((ord_less_nat @ (plus_plus_nat @ X1 @ X0) @ (plus_plus_nat @ X3 @ X2)) = $true)))),
% 50.63/8.53 inference(fool_elimination,[status(thm)],[f407])).
% 50.63/8.53 thf(f407,plain,(
% 50.63/8.53 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((ord_less_nat @ X1 @ X3) => ((ord_less_eq_nat @ X0 @ X2) => (ord_less_nat @ (plus_plus_nat @ X1 @ X0) @ (plus_plus_nat @ X3 @ X2))))),
% 50.63/8.53 inference(rectify,[status(thm)],[f91])).
% 50.63/8.53 thf(f91,axiom,(
% 50.63/8.53 ! [X3 : nat,X4 : nat,X12 : nat,X5 : nat] : ((ord_less_nat @ X4 @ X5) => ((ord_less_eq_nat @ X3 @ X12) => (ord_less_nat @ (plus_plus_nat @ X4 @ X3) @ (plus_plus_nat @ X5 @ X12))))),
% 50.63/8.53 file('/export/starexec/sandbox/tmp/tmp.z4lpNYM1sy/DTF2THF_16520.p',fact_90_add__less__le__mono)).
% 50.63/8.53 % SZS output end Proof for DTF2THF_16520
% 50.63/8.53 % (16825)------------------------------
% 50.63/8.53 % (16825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.63/8.53 % (16825)Termination reason: Refutation
% 50.63/8.53
% 50.63/8.53 % (16825)Memory used [KB]: 10490
% 50.63/8.53 % (16825)Time elapsed: 1.233 s
% 50.63/8.53 % (16825)Instructions burned: 3993 (million)
% 50.63/8.53 % (16825)------------------------------
% 50.63/8.53 % (16825)------------------------------
% 50.63/8.53 % (16625)Success in time 7.031 s
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