%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP050^1 : 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 : n001.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 08:55:09 AM UTC 2026
% Result : Theorem 16.03s 3.79s
% Output : Refutation 16.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 78 ( 72 unt; 0 typ; 0 def)
% Number of atoms : 311 ( 72 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 615 ( 6 ~; 0 |; 0 &; 498 @)
% ( 0 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 61 usr; 14 con; 0-4 aty)
% ( 42 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 132 ( 71 ^; 59 !; 2 ?; 132 :)
% 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,
set_Pr1986765409at_nat: $tType ).
thf(type_def_10,type,
set_nat: $tType ).
thf(type_def_11,type,
set_set_nat: $tType ).
thf(type_def_12,type,
set_se1612935105at_nat: $tType ).
thf(type_def_13,type,
list_P559422087at_nat: $tType ).
thf(type_def_14,type,
list_nat: $tType ).
thf(func_def_0,type,
set_se1612935105at_nat: $tType ).
thf(func_def_1,type,
list_P559422087at_nat: $tType ).
thf(func_def_2,type,
set_Pr1986765409at_nat: $tType ).
thf(func_def_3,type,
product_prod_nat_nat: $tType ).
thf(func_def_4,type,
set_set_nat: $tType ).
thf(func_def_5,type,
list_nat: $tType ).
thf(func_def_6,type,
set_nat: $tType ).
thf(func_def_7,type,
nat: $tType ).
thf(func_def_8,type,
a: $tType ).
thf(func_def_9,type,
edmond1517640972ysis_a: ( product_prod_nat_nat > a ) > $o ).
thf(func_def_10,type,
edmond475474835dges_a: ( product_prod_nat_nat > a ) > nat > nat > set_Pr1986765409at_nat ).
thf(func_def_11,type,
edmond771116670s_uE_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
thf(func_def_12,type,
finite_card_nat: set_nat > nat ).
thf(func_def_13,type,
finite447719721at_nat: set_Pr1986765409at_nat > nat ).
thf(func_def_14,type,
finite_finite_nat: set_nat > $o ).
thf(func_def_15,type,
finite772653738at_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_16,type,
finite2012248349et_nat: set_set_nat > $o ).
thf(func_def_17,type,
finite1457549322at_nat: set_se1612935105at_nat > $o ).
thf(func_def_18,type,
finite_Graph_a: ( product_prod_nat_nat > a ) > $o ).
thf(func_def_19,type,
e_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
thf(func_def_20,type,
v_a: ( product_prod_nat_nat > a ) > set_nat ).
thf(func_def_21,type,
adjacent_nodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
thf(func_def_22,type,
incoming_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
thf(func_def_23,type,
incoming_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
thf(func_def_24,type,
isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_25,type,
isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(func_def_26,type,
outgoing_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
thf(func_def_27,type,
outgoing_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
thf(func_def_28,type,
pathVertices: nat > list_P559422087at_nat > list_nat ).
thf(func_def_29,type,
reachableNodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
thf(func_def_30,type,
inf_inf_nat: nat > nat > nat ).
thf(func_def_31,type,
inf_inf_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_32,type,
inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_33,type,
cons_nat: nat > list_nat > list_nat ).
thf(func_def_34,type,
cons_P66992567at_nat: product_prod_nat_nat > list_P559422087at_nat > list_P559422087at_nat ).
thf(func_def_35,type,
nil_Pr1308055047at_nat: list_P559422087at_nat ).
thf(func_def_36,type,
set_nat2: list_nat > set_nat ).
thf(func_def_37,type,
set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
thf(func_def_38,type,
size_s1990949619at_nat: list_P559422087at_nat > nat ).
thf(func_def_39,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_40,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_41,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_42,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_43,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_44,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(func_def_45,type,
member_nat: nat > set_nat > $o ).
thf(func_def_46,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_47,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(func_def_48,type,
member298845450at_nat: set_Pr1986765409at_nat > set_se1612935105at_nat > $o ).
thf(func_def_49,type,
c: product_prod_nat_nat > a ).
thf(func_def_50,type,
edges: set_Pr1986765409at_nat ).
thf(func_def_51,type,
p: list_P559422087at_nat ).
thf(func_def_52,type,
s: nat ).
thf(func_def_53,type,
t: nat ).
thf(func_def_74,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_75,type,
sK2: product_prod_nat_nat ).
thf(func_def_76,type,
sK3: list_P559422087at_nat > list_P559422087at_nat ).
thf(func_def_77,type,
sK4: list_P559422087at_nat ).
thf(func_def_78,type,
sK5: list_P559422087at_nat ).
thf(func_def_79,type,
sK6: nat > list_P559422087at_nat ).
thf(func_def_80,type,
sK7: set_nat > list_P559422087at_nat ).
thf(func_def_81,type,
sK8: nat ).
thf(func_def_82,type,
sK9: nat > list_P559422087at_nat ).
thf(func_def_83,type,
sK10: set_nat > list_P559422087at_nat ).
thf(func_def_84,type,
sK11: set_Pr1986765409at_nat > list_P559422087at_nat ).
thf(func_def_85,type,
sK12: list_nat > nat ).
thf(func_def_86,type,
sK13: nat > nat ).
thf(func_def_87,type,
sK14: list_nat > list_nat ).
thf(func_def_88,type,
sK15: list_nat ).
thf(func_def_89,type,
sK16: nat > list_nat ).
thf(f15212,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f15211]) ).
thf(f15211,plain,
$false = $true,
inference(forward_demodulation,[status(thm)],[f15210,f2147]) ).
thf(f2147,plain,
( $false
= ( member701585322at_nat @ sK2 @ ( set_Pr2131844118at_nat @ sK5 ) ) ),
inference(backward_demodulation,[status(thm)],[f2079,f2142]) ).
thf(f2142,plain,
( ( e_a @ c )
= ( set_Pr2131844118at_nat @ sK5 ) ),
inference(equality_proxy_clausification,[status(thm)],[f2138]) ).
thf(f2138,plain,
( ( ( set_Pr2131844118at_nat @ sK5 )
= ( e_a @ c ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2136]) ).
thf(f2136,plain,
( ( ^ [Y0: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ Y0 )
= ( e_a @ c ) )
@ sK5 )
= $true ),
inference(sigma_clausification,[status(thm)],[f2100]) ).
thf(f2100,plain,
( $true
= ( ?? @ list_P559422087at_nat
@ ^ [Y0: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ Y0 )
= ( e_a @ c ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2088]) ).
thf(f2088,plain,
( $true
= ( $true
=> ( ?? @ list_P559422087at_nat
@ ^ [Y0: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ Y0 )
= ( e_a @ c ) ) ) ) ),
inference(superposition,[status(thm)],[f2083,f1248]) ).
thf(f1248,plain,
( ( finite772653738at_nat @ ( e_a @ c ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f989]) ).
thf(f989,plain,
( ( finite772653738at_nat @ ( e_a @ c ) )
= $true ),
inference(fool_elimination,[status(thm)],[f988]) ).
thf(f988,plain,
finite772653738at_nat @ ( e_a @ c ),
inference(rectify,[status(thm)],[f157]) ).
thf(f157,axiom,
finite772653738at_nat @ ( e_a @ c ),
file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',fact_156_finite__E) ).
thf(f2083,plain,
! [X1: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ X1 )
=> ( ?? @ list_P559422087at_nat
@ ^ [Y0: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ Y0 )
= X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2082]) ).
thf(f2082,plain,
! [X1: set_Pr1986765409at_nat] :
( ( ^ [Y0: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ Y0 )
=> ( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ Y1 )
= Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1067]) ).
thf(f1067,plain,
( $true
= ( !! @ set_Pr1986765409at_nat
@ ^ [Y0: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ Y0 )
=> ( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ Y1 )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f993]) ).
thf(f993,plain,
( $true
= ( !! @ set_Pr1986765409at_nat
@ ^ [Y0: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ Y0 )
=> ( ?? @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ Y1 )
= Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f992]) ).
thf(f992,plain,
! [X0: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ X0 )
=> ? [X1: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ X1 )
= X0 ) ),
inference(rectify,[status(thm)],[f327]) ).
thf(f327,axiom,
! [X2: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ X2 )
=> ? [X47: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ X47 )
= X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',fact_326_finite__list) ).
thf(f2079,plain,
( $false
= ( member701585322at_nat @ sK2 @ ( e_a @ c ) ) ),
inference(boolean_simplification,[status(thm)],[f2078]) ).
thf(f2078,plain,
( $false
= ( $true
=> ( member701585322at_nat @ sK2 @ ( e_a @ c ) ) ) ),
inference(backward_demodulation,[status(thm)],[f2075,f2077]) ).
thf(f2077,plain,
( ( member701585322at_nat @ sK2 @ edges )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2075]) ).
thf(f2075,plain,
( $false
= ( ( member701585322at_nat @ sK2 @ edges )
=> ( member701585322at_nat @ sK2 @ ( e_a @ c ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2074]) ).
thf(f2074,plain,
( $false
= ( ^ [Y0: product_prod_nat_nat] :
( ( member701585322at_nat @ Y0 @ edges )
=> ( member701585322at_nat @ Y0 @ ( e_a @ c ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f2071]) ).
thf(f2071,plain,
( $false
= ( !! @ product_prod_nat_nat
@ ^ [Y0: product_prod_nat_nat] :
( ( member701585322at_nat @ Y0 @ edges )
=> ( member701585322at_nat @ Y0 @ ( e_a @ c ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1889]) ).
thf(f1889,plain,
( ( ~ ( !! @ product_prod_nat_nat
@ ^ [Y0: product_prod_nat_nat] :
( ( member701585322at_nat @ Y0 @ edges )
=> ( member701585322at_nat @ Y0 @ ( e_a @ c ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1523]) ).
thf(f1523,plain,
( ( ~ ( ^ [Y0: set_Pr1986765409at_nat,Y1: set_Pr1986765409at_nat] :
( !! @ product_prod_nat_nat
@ ^ [Y2: product_prod_nat_nat] :
( ( member701585322at_nat @ Y2 @ Y0 )
=> ( member701585322at_nat @ Y2 @ Y1 ) ) )
@ edges
@ ( e_a @ c ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f1196,f1083]) ).
thf(f1083,plain,
( ord_le841296385at_nat
= ( ^ [Y0: set_Pr1986765409at_nat,Y1: set_Pr1986765409at_nat] :
( !! @ product_prod_nat_nat
@ ^ [Y2: product_prod_nat_nat] :
( ( member701585322at_nat @ Y2 @ Y0 )
=> ( member701585322at_nat @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f917]) ).
thf(f917,plain,
( ord_le841296385at_nat
= ( ^ [Y0: set_Pr1986765409at_nat,Y1: set_Pr1986765409at_nat] :
( !! @ product_prod_nat_nat
@ ^ [Y2: product_prod_nat_nat] :
( ( member701585322at_nat @ Y2 @ Y0 )
=> ( member701585322at_nat @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f916]) ).
thf(f916,plain,
( ( ^ [X0: set_Pr1986765409at_nat,X1: set_Pr1986765409at_nat] :
! [X2: product_prod_nat_nat] :
( ( member701585322at_nat @ X2 @ X0 )
=> ( member701585322at_nat @ X2 @ X1 ) ) )
= ord_le841296385at_nat ),
inference(rectify,[status(thm)],[f125]) ).
thf(f125,axiom,
( ( ^ [X28: set_Pr1986765409at_nat,X29: set_Pr1986765409at_nat] :
! [X31: product_prod_nat_nat] :
( ( member701585322at_nat @ X31 @ X28 )
=> ( member701585322at_nat @ X31 @ X29 ) ) )
= ord_le841296385at_nat ),
file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',fact_124_subset__iff) ).
thf(f1196,plain,
( ( ~ ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f799]) ).
thf(f799,plain,
( ( ~ ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f798]) ).
thf(f798,plain,
~ ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ),
inference(rectify,[status(thm)],[f355]) ).
thf(f355,negated_conjecture,
~ ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ),
inference(negated_conjecture,[status(cth)],[f354]) ).
thf(f354,conjecture,
ord_le841296385at_nat @ edges @ ( e_a @ c ),
file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',conj_0) ).
thf(f15210,plain,
( $true
= ( member701585322at_nat @ sK2 @ ( set_Pr2131844118at_nat @ sK5 ) ) ),
inference(boolean_simplification,[status(thm)],[f15204]) ).
thf(f15204,plain,
( ( $true
=> ( member701585322at_nat @ sK2 @ ( set_Pr2131844118at_nat @ sK5 ) ) )
= $true ),
inference(superposition,[status(thm)],[f15199,f2081]) ).
thf(f2081,plain,
( $true
= ( member701585322at_nat @ sK2 @ ( set_Pr2131844118at_nat @ p ) ) ),
inference(boolean_simplification,[status(thm)],[f2080]) ).
thf(f2080,plain,
( ( $true
=> ( member701585322at_nat @ sK2 @ ( set_Pr2131844118at_nat @ p ) ) )
= $true ),
inference(superposition,[status(thm)],[f2069,f2077]) ).
thf(f2069,plain,
! [X1: product_prod_nat_nat] :
( ( ( member701585322at_nat @ X1 @ edges )
=> ( member701585322at_nat @ X1 @ ( set_Pr2131844118at_nat @ p ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2068]) ).
thf(f2068,plain,
! [X1: product_prod_nat_nat] :
( $true
= ( ^ [Y0: product_prod_nat_nat] :
( ( member701585322at_nat @ Y0 @ edges )
=> ( member701585322at_nat @ Y0 @ ( set_Pr2131844118at_nat @ p ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1791]) ).
thf(f1791,plain,
( ( !! @ product_prod_nat_nat
@ ^ [Y0: product_prod_nat_nat] :
( ( member701585322at_nat @ Y0 @ edges )
=> ( member701585322at_nat @ Y0 @ ( set_Pr2131844118at_nat @ p ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1424]) ).
thf(f1424,plain,
( $true
= ( ^ [Y0: set_Pr1986765409at_nat,Y1: set_Pr1986765409at_nat] :
( !! @ product_prod_nat_nat
@ ^ [Y2: product_prod_nat_nat] :
( ( member701585322at_nat @ Y2 @ Y0 )
=> ( member701585322at_nat @ Y2 @ Y1 ) ) )
@ edges
@ ( set_Pr2131844118at_nat @ p ) ) ),
inference(definition_unfolding,[status(thm)],[f1073,f1083]) ).
thf(f1073,plain,
( ( ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f438]) ).
thf(f438,plain,
( ( ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ) )
= $true ),
inference(fool_elimination,[status(thm)],[f437]) ).
thf(f437,plain,
ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ),
file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',fact_1_SP__EDGES) ).
thf(f15199,plain,
! [X0: product_prod_nat_nat] :
( ( ( member701585322at_nat @ X0 @ ( set_Pr2131844118at_nat @ p ) )
=> ( member701585322at_nat @ X0 @ ( set_Pr2131844118at_nat @ sK5 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f15196]) ).
thf(f15196,plain,
! [X0: product_prod_nat_nat] :
( ( $true
=> ( ( member701585322at_nat @ X0 @ ( set_Pr2131844118at_nat @ p ) )
=> ( member701585322at_nat @ X0 @ ( set_Pr2131844118at_nat @ sK5 ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f15164,f10520]) ).
thf(f10520,plain,
( $true
= ( isPath_a @ c @ s @ p @ t ) ),
inference(boolean_simplification,[status(thm)],[f10519]) ).
thf(f10519,plain,
( ( $true
=> ( isPath_a @ c @ s @ p @ t ) )
= $true ),
inference(superposition,[status(thm)],[f10468,f1310]) ).
thf(f1310,plain,
( ( isShortestPath_a @ c @ s @ p @ t )
= $true ),
inference(cnf_transformation,[status(thm)],[f848]) ).
thf(f848,plain,
( ( isShortestPath_a @ c @ s @ p @ t )
= $true ),
inference(fool_elimination,[status(thm)],[f847]) ).
thf(f847,plain,
isShortestPath_a @ c @ s @ p @ t,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
isShortestPath_a @ c @ s @ p @ t,
file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',fact_0_SP) ).
thf(f10468,plain,
! [X2: nat,X3: list_P559422087at_nat,X1: nat] :
( ( ( isShortestPath_a @ c @ X1 @ X3 @ X2 )
=> ( isPath_a @ c @ X1 @ X3 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f10467]) ).
thf(f10467,plain,
! [X2: nat,X3: list_P559422087at_nat,X1: nat] :
( ( ^ [Y0: list_P559422087at_nat] :
( ( isShortestPath_a @ c @ X1 @ Y0 @ X2 )
=> ( isPath_a @ c @ X1 @ Y0 @ X2 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f10452]) ).
thf(f10452,plain,
! [X2: nat,X1: nat] :
( ( !! @ list_P559422087at_nat
@ ^ [Y0: list_P559422087at_nat] :
( ( isShortestPath_a @ c @ X1 @ Y0 @ X2 )
=> ( isPath_a @ c @ X1 @ Y0 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f10451]) ).
thf(f10451,plain,
! [X2: nat,X1: nat] :
( ( ^ [Y0: nat] :
( !! @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( isShortestPath_a @ c @ X1 @ Y1 @ Y0 )
=> ( isPath_a @ c @ X1 @ Y1 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f10431]) ).
thf(f10431,plain,
! [X1: nat] :
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( ( isShortestPath_a @ c @ X1 @ Y1 @ Y0 )
=> ( isPath_a @ c @ X1 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f10430]) ).
thf(f10430,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list_P559422087at_nat
@ ^ [Y2: list_P559422087at_nat] :
( ( isShortestPath_a @ c @ Y0 @ Y2 @ Y1 )
=> ( isPath_a @ c @ Y0 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1115]) ).
thf(f1115,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list_P559422087at_nat
@ ^ [Y2: list_P559422087at_nat] :
( ( isShortestPath_a @ c @ Y0 @ Y2 @ Y1 )
=> ( isPath_a @ c @ Y0 @ Y2 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f943]) ).
thf(f943,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list_P559422087at_nat
@ ^ [Y2: list_P559422087at_nat] :
( ( isShortestPath_a @ c @ Y0 @ Y2 @ Y1 )
=> ( isPath_a @ c @ Y0 @ Y2 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f942]) ).
thf(f942,plain,
! [X0: list_P559422087at_nat,X1: nat,X2: nat] :
( ( isShortestPath_a @ c @ X2 @ X0 @ X1 )
=> ( isPath_a @ c @ X2 @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,axiom,
! [X6: list_P559422087at_nat,X7: nat,X1: nat] :
( ( isShortestPath_a @ c @ X1 @ X6 @ X7 )
=> ( isPath_a @ c @ X1 @ X6 @ X7 ) ),
file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',fact_19_shortestPath__is__path) ).
thf(f15164,plain,
! [X2: list_P559422087at_nat,X3: product_prod_nat_nat,X1: nat,X4: nat] :
( ( ( isPath_a @ c @ X4 @ X2 @ X1 )
=> ( ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ X2 ) )
=> ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ sK5 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f15163]) ).
thf(f15163,plain,
! [X2: list_P559422087at_nat,X3: product_prod_nat_nat,X1: nat,X4: nat] :
( ( ^ [Y0: nat] :
( ( isPath_a @ c @ Y0 @ X2 @ X1 )
=> ( ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ X2 ) )
=> ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ sK5 ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f15136]) ).
thf(f15136,plain,
! [X2: list_P559422087at_nat,X3: product_prod_nat_nat,X1: nat] :
( ( !! @ nat
@ ^ [Y0: nat] :
( ( isPath_a @ c @ Y0 @ X2 @ X1 )
=> ( ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ X2 ) )
=> ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ sK5 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f15135,f2142]) ).
thf(f15135,plain,
! [X2: list_P559422087at_nat,X3: product_prod_nat_nat,X1: nat] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( isPath_a @ c @ Y0 @ X2 @ X1 )
=> ( ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ X2 ) )
=> ( member701585322at_nat @ X3 @ ( e_a @ c ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15134]) ).
thf(f15134,plain,
! [X2: list_P559422087at_nat,X3: product_prod_nat_nat,X1: nat] :
( $true
= ( ^ [Y0: product_prod_nat_nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( isPath_a @ c @ Y1 @ X2 @ X1 )
=> ( ( member701585322at_nat @ Y0 @ ( set_Pr2131844118at_nat @ X2 ) )
=> ( member701585322at_nat @ Y0 @ ( e_a @ c ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f15107]) ).
thf(f15107,plain,
! [X2: list_P559422087at_nat,X1: nat] :
( $true
= ( !! @ product_prod_nat_nat
@ ^ [Y0: product_prod_nat_nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( isPath_a @ c @ Y1 @ X2 @ X1 )
=> ( ( member701585322at_nat @ Y0 @ ( set_Pr2131844118at_nat @ X2 ) )
=> ( member701585322at_nat @ Y0 @ ( e_a @ c ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15106]) ).
thf(f15106,plain,
! [X2: list_P559422087at_nat,X1: nat] :
( ( ^ [Y0: list_P559422087at_nat] :
( !! @ product_prod_nat_nat
@ ^ [Y1: product_prod_nat_nat] :
( !! @ nat
@ ^ [Y2: nat] :
( ( isPath_a @ c @ Y2 @ Y0 @ X1 )
=> ( ( member701585322at_nat @ Y1 @ ( set_Pr2131844118at_nat @ Y0 ) )
=> ( member701585322at_nat @ Y1 @ ( e_a @ c ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f15079]) ).
thf(f15079,plain,
! [X1: nat] :
( ( !! @ list_P559422087at_nat
@ ^ [Y0: list_P559422087at_nat] :
( !! @ product_prod_nat_nat
@ ^ [Y1: product_prod_nat_nat] :
( !! @ nat
@ ^ [Y2: nat] :
( ( isPath_a @ c @ Y2 @ Y0 @ X1 )
=> ( ( member701585322at_nat @ Y1 @ ( set_Pr2131844118at_nat @ Y0 ) )
=> ( member701585322at_nat @ Y1 @ ( e_a @ c ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f15078]) ).
thf(f15078,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( !! @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( !! @ product_prod_nat_nat
@ ^ [Y2: product_prod_nat_nat] :
( !! @ nat
@ ^ [Y3: nat] :
( ( isPath_a @ c @ Y3 @ Y1 @ Y0 )
=> ( ( member701585322at_nat @ Y2 @ ( set_Pr2131844118at_nat @ Y1 ) )
=> ( member701585322at_nat @ Y2 @ ( e_a @ c ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1372]) ).
thf(f1372,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( !! @ product_prod_nat_nat
@ ^ [Y2: product_prod_nat_nat] :
( !! @ nat
@ ^ [Y3: nat] :
( ( isPath_a @ c @ Y3 @ Y1 @ Y0 )
=> ( ( member701585322at_nat @ Y2 @ ( set_Pr2131844118at_nat @ Y1 ) )
=> ( member701585322at_nat @ Y2 @ ( e_a @ c ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f533]) ).
thf(f533,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ list_P559422087at_nat
@ ^ [Y1: list_P559422087at_nat] :
( !! @ product_prod_nat_nat
@ ^ [Y2: product_prod_nat_nat] :
( !! @ nat
@ ^ [Y3: nat] :
( ( isPath_a @ c @ Y3 @ Y1 @ Y0 )
=> ( ( member701585322at_nat @ Y2 @ ( set_Pr2131844118at_nat @ Y1 ) )
=> ( member701585322at_nat @ Y2 @ ( e_a @ c ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f532]) ).
thf(f532,plain,
! [X0: nat,X1: product_prod_nat_nat,X2: list_P559422087at_nat,X3: nat] :
( ( isPath_a @ c @ X0 @ X2 @ X3 )
=> ( ( member701585322at_nat @ X1 @ ( set_Pr2131844118at_nat @ X2 ) )
=> ( member701585322at_nat @ X1 @ ( e_a @ c ) ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,axiom,
! [X1: nat,X8: product_prod_nat_nat,X6: list_P559422087at_nat,X7: nat] :
( ( isPath_a @ c @ X1 @ X6 @ X7 )
=> ( ( member701585322at_nat @ X8 @ ( set_Pr2131844118at_nat @ X6 ) )
=> ( member701585322at_nat @ X8 @ ( e_a @ c ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',fact_18_isPath__edgeset) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP050^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Feb 24 08:25:20 EST 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.47 ---- Original DTF file ---
% 0.32/0.47 thf(spec,logic,$$dhol).
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 % File : ITP050^1 : TPTP v9.2.1. Released v7.5.0.
% 0.32/0.47 % Domain : Interactive Theorem Proving
% 0.32/0.47 % Problem : Sledgehammer EdmondsKarp_Termination_Abstract problem prob_276__7590636_1
% 0.32/0.47 % Version : Especial.
% 0.32/0.47 % English :
% 0.32/0.47
% 0.32/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.32/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.32/0.47 % Source : [Des21]
% 0.32/0.47 % Names : EdmondsKarp_Termination_Abstract/prob_276__7590636_1 [Des21]
% 0.32/0.47
% 0.32/0.47 % Status : Theorem
% 0.32/0.47 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0
% 0.32/0.47 % Syntax : Number of formulae : 408 ( 123 unt; 54 typ; 0 def)
% 0.32/0.47 % Number of atoms : 1021 ( 212 equ; 0 cnn)
% 0.32/0.47 % Maximal formula atoms : 12 ( 2 avg)
% 0.32/0.47 % Number of connectives : 2902 ( 62 ~; 3 |; 49 &;2262 @)
% 0.32/0.47 % ( 0 <=>; 526 =>; 0 <=; 0 <~>)
% 0.32/0.47 % Maximal formula depth : 19 ( 7 avg)
% 0.32/0.47 % Number of types : 10 ( 9 usr)
% 0.32/0.47 % Number of type conns : 179 ( 179 >; 0 *; 0 +; 0 <<)
% 0.32/0.47 % Number of symbols : 46 ( 45 usr; 5 con; 0-4 aty)
% 0.32/0.47 % Number of variables : 1010 ( 80 ^; 915 !; 15 ?;1010 :)
% 0.32/0.47 % SPC : TH0_THM_EQU_NAR
% 0.32/0.47
% 0.32/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:31:07.662
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 % Could-be-implicit typings (9)
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.32/0.47 set_se1612935105at_nat: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.32/0.47 list_P559422087at_nat: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.32/0.47 set_Pr1986765409at_nat: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.32/0.47 product_prod_nat_nat: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.32/0.47 set_set_nat: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.32/0.47 list_nat: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.32/0.47 set_nat: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Nat__Onat,type,
% 0.32/0.47 nat: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_tf__a,type,
% 0.32/0.47 a: $tType ).
% 0.32/0.47
% 0.32/0.47 % Explicit typings (45)
% 0.32/0.47 thf(sy_c_EdmondsKarp__Termination__Abstract__Mirabelle__pndqeoznpl_Oek__analysis_001tf__a,type,
% 0.32/0.47 edmond1517640972ysis_a: ( product_prod_nat_nat > a ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_EdmondsKarp__Termination__Abstract__Mirabelle__pndqeoznpl_Oek__analysis__defs_OspEdges_001tf__a,type,
% 0.32/0.47 edmond475474835dges_a: ( product_prod_nat_nat > a ) > nat > nat > set_Pr1986765409at_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_EdmondsKarp__Termination__Abstract__Mirabelle__pndqeoznpl_Oek__analysis__defs_OuE_001tf__a,type,
% 0.32/0.47 edmond771116670s_uE_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 0.32/0.47 finite_card_nat: set_nat > nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.32/0.47 finite447719721at_nat: set_Pr1986765409at_nat > nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 0.32/0.47 finite_finite_nat: set_nat > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.32/0.47 finite772653738at_nat: set_Pr1986765409at_nat > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.32/0.47 finite2012248349et_nat: set_set_nat > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.32/0.47 finite1457549322at_nat: set_se1612935105at_nat > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Graph_OFinite__Graph_001tf__a,type,
% 0.32/0.47 finite_Graph_a: ( product_prod_nat_nat > a ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Graph_OGraph_OE_001tf__a,type,
% 0.32/0.47 e_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Graph_OGraph_OV_001tf__a,type,
% 0.32/0.47 v_a: ( product_prod_nat_nat > a ) > set_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Graph_OGraph_Oadjacent__nodes_001tf__a,type,
% 0.32/0.47 adjacent_nodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Graph_OGraph_Oincoming_001tf__a,type,
% 0.32/0.47 incoming_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Graph_OGraph_Oincoming_H_001tf__a,type,
% 0.32/0.47 incoming_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Graph_OGraph_OisPath_001tf__a,type,
% 0.32/0.47 isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Graph_OGraph_OisShortestPath_001tf__a,type,
% 0.32/0.47 isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Graph_OGraph_Ooutgoing_001tf__a,type,
% 0.32/0.47 outgoing_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Graph_OGraph_Ooutgoing_H_001tf__a,type,
% 0.32/0.47 outgoing_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Graph_OGraph_OpathVertices,type,
% 0.32/0.47 pathVertices: nat > list_P559422087at_nat > list_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Graph_OGraph_OreachableNodes_001tf__a,type,
% 0.32/0.47 reachableNodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 0.32/0.47 inf_inf_nat: nat > nat > nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.32/0.47 inf_inf_set_nat: set_nat > set_nat > set_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.32/0.47 inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 0.32/0.47 cons_nat: nat > list_nat > list_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.32/0.47 cons_P66992567at_nat: product_prod_nat_nat > list_P559422087at_nat > list_P559422087at_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.32/0.47 nil_Pr1308055047at_nat: list_P559422087at_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 0.32/0.47 set_nat2: list_nat > set_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.32/0.47 set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.32/0.47 size_s1990949619at_nat: list_P559422087at_nat > nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.32/0.47 ord_less_eq_nat: nat > nat > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.32/0.47 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.32/0.47 ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.32/0.47 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.32/0.47 collect_nat: ( nat > $o ) > set_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.32/0.47 collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_member_001t__Nat__Onat,type,
% 0.32/0.47 member_nat: nat > set_nat > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.32/0.47 member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.32/0.47 member_set_nat: set_nat > set_set_nat > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.32/0.47 member298845450at_nat: set_Pr1986765409at_nat > set_se1612935105at_nat > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v_c,type,
% 0.32/0.47 c: product_prod_nat_nat > a ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v_edges,type,
% 0.32/0.47 edges: set_Pr1986765409at_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v_p,type,
% 0.32/0.47 p: list_P559422087at_nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v_s,type,
% 0.32/0.47 s: nat ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v_t,type,
% 0.32/0.47 t: nat ).
% 0.32/0.47
% 0.32/0.47 % Relevant facts (353)
% 0.32/0.47 thf(fact_0_SP,axiom,
% 0.32/0.47 isShortestPath_a @ c @ s @ p @ t ).
% 0.32/0.47
% 0.32/0.47 % SP
% 0.32/0.47 thf(fact_1_SP__EDGES,axiom,
% 0.32/0.47 ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ) ).
% 0.32/0.47
% 0.32/0.47 % SP_EDGES
% 0.32/0.47 thf(fact_2_ek__analysis__axioms,axiom,
% 0.32/0.47 edmond1517640972ysis_a @ c ).
% 0.32/0.47
% 0.32/0.47 % ek_analysis_axioms
% 0.32/0.47 thf(fact_3_incoming_H__edges,axiom,
% 0.32/0.47 ! [U: set_nat] : ( ord_le841296385at_nat @ ( incoming_a2 @ c @ U ) @ ( e_a @ c ) ) ).
% 0.32/0.47
% 0.32/0.47 % incoming'_edges
% 0.32/0.47 thf(fact_4_outgoing_H__edges,axiom,
% 0.32/0.47 ! [U: set_nat] : ( ord_le841296385at_nat @ ( outgoing_a2 @ c @ U ) @ ( e_a @ c ) ) ).
% 0.32/0.47
% 0.32/0.47 % outgoing'_edges
% 0.32/0.47 thf(fact_5_E__ss__uE,axiom,
% 0.32/0.47 ord_le841296385at_nat @ ( e_a @ c ) @ ( edmond771116670s_uE_a @ c ) ).
% 0.32/0.47
% 0.32/0.47 % E_ss_uE
% 0.32/0.47 thf(fact_6_incoming__edges,axiom,
% 0.32/0.47 ! [U2: nat] : ( ord_le841296385at_nat @ ( incoming_a @ c @ U2 ) @ ( e_a @ c ) ) ).
% 0.32/0.47
% 0.32/0.47 % incoming_edges
% 0.32/0.47 thf(fact_7_outgoing__edges,axiom,
% 0.32/0.47 ! [U2: nat] : ( ord_le841296385at_nat @ ( outgoing_a @ c @ U2 ) @ ( e_a @ c ) ) ).
% 0.32/0.47
% 0.32/0.47 % outgoing_edges
% 0.32/0.47 thf(fact_8_Finite__Graph__axioms,axiom,
% 0.32/0.47 finite_Graph_a @ c ).
% 0.32/0.47
% 0.32/0.47 % Finite_Graph_axioms
% 0.32/0.47 thf(fact_9_subsetI,axiom,
% 0.32/0.47 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ! [X: product_prod_nat_nat] :
% 0.32/0.47 ( ( member701585322at_nat @ X @ A )
% 0.32/0.47 => ( member701585322at_nat @ X @ B ) )
% 0.32/0.47 => ( ord_le841296385at_nat @ A @ B ) ) ).
% 0.32/0.47
% 0.32/0.47 % subsetI
% 0.32/0.47 thf(fact_10_subsetI,axiom,
% 0.32/0.47 ! [A: set_nat,B: set_nat] :
% 0.32/0.47 ( ! [X: nat] :
% 0.32/0.47 ( ( member_nat @ X @ A )
% 0.32/0.47 => ( member_nat @ X @ B ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 0.32/0.47
% 0.32/0.47 % subsetI
% 0.32/0.47 thf(fact_11_subset__antisym,axiom,
% 0.32/0.47 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A @ B )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ B @ A )
% 0.32/0.47 => ( A = B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_antisym
% 0.32/0.47 thf(fact_12_subset__antisym,axiom,
% 0.32/0.47 ! [A: set_nat,B: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ B @ A )
% 0.32/0.47 => ( A = B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_antisym
% 0.32/0.47 thf(fact_13_order__refl,axiom,
% 0.32/0.47 ! [X2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ X2 @ X2 ) ).
% 0.32/0.47
% 0.32/0.47 % order_refl
% 0.32/0.47 thf(fact_14_order__refl,axiom,
% 0.32/0.47 ! [X2: set_nat] : ( ord_less_eq_set_nat @ X2 @ X2 ) ).
% 0.32/0.47
% 0.32/0.47 % order_refl
% 0.32/0.47 thf(fact_15_order__refl,axiom,
% 0.32/0.47 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 0.32/0.47
% 0.32/0.47 % order_refl
% 0.32/0.47 thf(fact_16_SV,axiom,
% 0.32/0.47 member_nat @ s @ ( v_a @ c ) ).
% 0.32/0.47
% 0.32/0.47 % SV
% 0.32/0.47 thf(fact_17_spEdges__ss__E,axiom,
% 0.32/0.47 ord_le841296385at_nat @ ( edmond475474835dges_a @ c @ s @ t ) @ ( e_a @ c ) ).
% 0.32/0.47
% 0.32/0.47 % spEdges_ss_E
% 0.32/0.47 thf(fact_18_isPath__edgeset,axiom,
% 0.32/0.47 ! [U2: nat,P: list_P559422087at_nat,V: nat,E: product_prod_nat_nat] :
% 0.32/0.47 ( ( isPath_a @ c @ U2 @ P @ V )
% 0.32/0.47 => ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ P ) )
% 0.32/0.47 => ( member701585322at_nat @ E @ ( e_a @ c ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % isPath_edgeset
% 0.32/0.47 thf(fact_19_shortestPath__is__path,axiom,
% 0.32/0.47 ! [U2: nat,P: list_P559422087at_nat,V: nat] :
% 0.32/0.47 ( ( isShortestPath_a @ c @ U2 @ P @ V )
% 0.32/0.47 => ( isPath_a @ c @ U2 @ P @ V ) ) ).
% 0.32/0.47
% 0.32/0.47 % shortestPath_is_path
% 0.32/0.47 thf(fact_20_adjacent__nodes__ss__V,axiom,
% 0.32/0.47 ! [U2: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ c @ U2 ) @ ( v_a @ c ) ) ).
% 0.32/0.47
% 0.32/0.47 % adjacent_nodes_ss_V
% 0.32/0.47 thf(fact_21_ek__analysis__def,axiom,
% 0.32/0.47 edmond1517640972ysis_a = finite_Graph_a ).
% 0.32/0.47
% 0.32/0.47 % ek_analysis_def
% 0.32/0.47 thf(fact_22_ek__analysis_Ointro,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a] :
% 0.32/0.47 ( ( finite_Graph_a @ C )
% 0.32/0.47 => ( edmond1517640972ysis_a @ C ) ) ).
% 0.32/0.47
% 0.32/0.47 % ek_analysis.intro
% 0.32/0.47 thf(fact_23_ek__analysis_Oaxioms,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a] :
% 0.32/0.47 ( ( edmond1517640972ysis_a @ C )
% 0.32/0.47 => ( finite_Graph_a @ C ) ) ).
% 0.32/0.47
% 0.32/0.47 % ek_analysis.axioms
% 0.32/0.47 thf(fact_24_ek__analysis__defs_OspEdges_Ocong,axiom,
% 0.32/0.47 edmond475474835dges_a = edmond475474835dges_a ).
% 0.32/0.47
% 0.32/0.47 % ek_analysis_defs.spEdges.cong
% 0.32/0.47 thf(fact_25_ek__analysis__defs_OuE_Ocong,axiom,
% 0.32/0.47 edmond771116670s_uE_a = edmond771116670s_uE_a ).
% 0.32/0.47
% 0.32/0.47 % ek_analysis_defs.uE.cong
% 0.32/0.47 thf(fact_26_ek__analysis_OspEdges__ss__E,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,S: nat,T: nat] :
% 0.32/0.47 ( ( edmond1517640972ysis_a @ C )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( edmond475474835dges_a @ C @ S @ T ) @ ( e_a @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ek_analysis.spEdges_ss_E
% 0.32/0.47 thf(fact_27_ek__analysis_OE__ss__uE,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a] :
% 0.32/0.47 ( ( edmond1517640972ysis_a @ C )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( e_a @ C ) @ ( edmond771116670s_uE_a @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ek_analysis.E_ss_uE
% 0.32/0.47 thf(fact_28_dual__order_Oantisym,axiom,
% 0.32/0.47 ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ B2 @ A2 )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.32/0.47 => ( A2 = B2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.antisym
% 0.32/0.47 thf(fact_29_dual__order_Oantisym,axiom,
% 0.32/0.47 ! [B2: set_nat,A2: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.47 => ( A2 = B2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.antisym
% 0.32/0.47 thf(fact_30_dual__order_Oantisym,axiom,
% 0.32/0.47 ! [B2: nat,A2: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.32/0.47 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.47 => ( A2 = B2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.antisym
% 0.32/0.47 thf(fact_31_dual__order_Oeq__iff,axiom,
% 0.32/0.47 ( ( ^ [Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] : ( Y = Z ) )
% 0.32/0.47 = ( ^ [A3: set_Pr1986765409at_nat,B3: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ B3 @ A3 )
% 0.32/0.47 & ( ord_le841296385at_nat @ A3 @ B3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.eq_iff
% 0.32/0.47 thf(fact_32_dual__order_Oeq__iff,axiom,
% 0.32/0.47 ( ( ^ [Y: set_nat,Z: set_nat] : ( Y = Z ) )
% 0.32/0.47 = ( ^ [A3: set_nat,B3: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 0.32/0.47 & ( ord_less_eq_set_nat @ A3 @ B3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.eq_iff
% 0.32/0.47 thf(fact_33_dual__order_Oeq__iff,axiom,
% 0.32/0.47 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.32/0.47 = ( ^ [A3: nat,B3: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ B3 @ A3 )
% 0.32/0.47 & ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.eq_iff
% 0.32/0.47 thf(fact_34_dual__order_Otrans,axiom,
% 0.32/0.47 ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ B2 @ A2 )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ C @ B2 )
% 0.32/0.47 => ( ord_le841296385at_nat @ C @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.trans
% 0.32/0.47 thf(fact_35_dual__order_Otrans,axiom,
% 0.32/0.47 ! [B2: set_nat,A2: set_nat,C: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ C @ B2 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ C @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.trans
% 0.32/0.47 thf(fact_36_dual__order_Otrans,axiom,
% 0.32/0.47 ! [B2: nat,A2: nat,C: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.32/0.47 => ( ( ord_less_eq_nat @ C @ B2 )
% 0.32/0.47 => ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.trans
% 0.32/0.47 thf(fact_37_linorder__wlog,axiom,
% 0.32/0.47 ! [P2: nat > nat > $o,A2: nat,B2: nat] :
% 0.32/0.47 ( ! [A4: nat,B4: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A4 @ B4 )
% 0.32/0.47 => ( P2 @ A4 @ B4 ) )
% 0.32/0.47 => ( ! [A4: nat,B4: nat] :
% 0.32/0.47 ( ( P2 @ B4 @ A4 )
% 0.32/0.47 => ( P2 @ A4 @ B4 ) )
% 0.32/0.47 => ( P2 @ A2 @ B2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % linorder_wlog
% 0.32/0.47 thf(fact_38_dual__order_Orefl,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A2 @ A2 ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.refl
% 0.32/0.47 thf(fact_39_dual__order_Orefl,axiom,
% 0.32/0.47 ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ A2 ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.refl
% 0.32/0.47 thf(fact_40_dual__order_Orefl,axiom,
% 0.32/0.47 ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.refl
% 0.32/0.47 thf(fact_41_order__trans,axiom,
% 0.32/0.47 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat,Z2: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X2 @ Y2 )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ Y2 @ Z2 )
% 0.32/0.47 => ( ord_le841296385at_nat @ X2 @ Z2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_trans
% 0.32/0.47 thf(fact_42_order__trans,axiom,
% 0.32/0.47 ! [X2: set_nat,Y2: set_nat,Z2: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ Y2 @ Z2 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ X2 @ Z2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_trans
% 0.32/0.47 thf(fact_43_order__trans,axiom,
% 0.32/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.32/0.47 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.32/0.47 => ( ord_less_eq_nat @ X2 @ Z2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_trans
% 0.32/0.47 thf(fact_44_order__class_Oorder_Oantisym,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ B2 @ A2 )
% 0.32/0.47 => ( A2 = B2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_class.order.antisym
% 0.32/0.47 thf(fact_45_order__class_Oorder_Oantisym,axiom,
% 0.32/0.47 ! [A2: set_nat,B2: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.32/0.47 => ( A2 = B2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_class.order.antisym
% 0.32/0.47 thf(fact_46_order__class_Oorder_Oantisym,axiom,
% 0.32/0.47 ! [A2: nat,B2: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.32/0.47 => ( A2 = B2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_class.order.antisym
% 0.32/0.47 thf(fact_47_ord__le__eq__trans,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( B2 = C )
% 0.32/0.47 => ( ord_le841296385at_nat @ A2 @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_trans
% 0.32/0.47 thf(fact_48_ord__le__eq__trans,axiom,
% 0.32/0.47 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( B2 = C )
% 0.32/0.47 => ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_trans
% 0.32/0.47 thf(fact_49_ord__le__eq__trans,axiom,
% 0.32/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( B2 = C )
% 0.32/0.47 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_trans
% 0.32/0.47 thf(fact_50_ord__eq__le__trans,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( A2 = B2 )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ B2 @ C )
% 0.32/0.47 => ( ord_le841296385at_nat @ A2 @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_trans
% 0.32/0.47 thf(fact_51_ord__eq__le__trans,axiom,
% 0.32/0.47 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 0.32/0.47 ( ( A2 = B2 )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 0.32/0.47 => ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_trans
% 0.32/0.47 thf(fact_52_ord__eq__le__trans,axiom,
% 0.32/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.32/0.47 ( ( A2 = B2 )
% 0.32/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.32/0.47 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_trans
% 0.32/0.47 thf(fact_53_order__class_Oorder_Oeq__iff,axiom,
% 0.32/0.47 ( ( ^ [Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] : ( Y = Z ) )
% 0.32/0.47 = ( ^ [A3: set_Pr1986765409at_nat,B3: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A3 @ B3 )
% 0.32/0.47 & ( ord_le841296385at_nat @ B3 @ A3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_class.order.eq_iff
% 0.32/0.47 thf(fact_54_order__class_Oorder_Oeq__iff,axiom,
% 0.32/0.47 ( ( ^ [Y: set_nat,Z: set_nat] : ( Y = Z ) )
% 0.32/0.47 = ( ^ [A3: set_nat,B3: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 0.32/0.47 & ( ord_less_eq_set_nat @ B3 @ A3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_class.order.eq_iff
% 0.32/0.47 thf(fact_55_order__class_Oorder_Oeq__iff,axiom,
% 0.32/0.47 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.32/0.47 = ( ^ [A3: nat,B3: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.32/0.47 & ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_class.order.eq_iff
% 0.32/0.47 thf(fact_56_antisym__conv,axiom,
% 0.32/0.47 ! [Y2: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ Y2 @ X2 )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ X2 @ Y2 )
% 0.32/0.47 = ( X2 = Y2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % antisym_conv
% 0.32/0.47 thf(fact_57_antisym__conv,axiom,
% 0.32/0.47 ! [Y2: set_nat,X2: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ Y2 @ X2 )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 0.32/0.47 = ( X2 = Y2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % antisym_conv
% 0.32/0.47 thf(fact_58_antisym__conv,axiom,
% 0.32/0.47 ! [Y2: nat,X2: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.32/0.47 => ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.32/0.47 = ( X2 = Y2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % antisym_conv
% 0.32/0.47 thf(fact_59_le__cases3,axiom,
% 0.32/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.32/0.47 ( ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.32/0.47 => ~ ( ord_less_eq_nat @ Y2 @ Z2 ) )
% 0.32/0.47 => ( ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.32/0.47 => ~ ( ord_less_eq_nat @ X2 @ Z2 ) )
% 0.32/0.47 => ( ( ( ord_less_eq_nat @ X2 @ Z2 )
% 0.32/0.47 => ~ ( ord_less_eq_nat @ Z2 @ Y2 ) )
% 0.32/0.47 => ( ( ( ord_less_eq_nat @ Z2 @ Y2 )
% 0.32/0.47 => ~ ( ord_less_eq_nat @ Y2 @ X2 ) )
% 0.32/0.47 => ( ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.32/0.47 => ~ ( ord_less_eq_nat @ Z2 @ X2 ) )
% 0.32/0.47 => ~ ( ( ord_less_eq_nat @ Z2 @ X2 )
% 0.32/0.47 => ~ ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % le_cases3
% 0.32/0.47 thf(fact_60_order_Otrans,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ B2 @ C )
% 0.32/0.47 => ( ord_le841296385at_nat @ A2 @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order.trans
% 0.32/0.47 thf(fact_61_order_Otrans,axiom,
% 0.32/0.47 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 0.32/0.47 => ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order.trans
% 0.32/0.47 thf(fact_62_order_Otrans,axiom,
% 0.32/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.32/0.47 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order.trans
% 0.32/0.47 thf(fact_63_le__cases,axiom,
% 0.32/0.47 ! [X2: nat,Y2: nat] :
% 0.32/0.47 ( ~ ( ord_less_eq_nat @ X2 @ Y2 )
% 0.32/0.47 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % le_cases
% 0.32/0.47 thf(fact_64_eq__refl,axiom,
% 0.32/0.47 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( X2 = Y2 )
% 0.32/0.47 => ( ord_le841296385at_nat @ X2 @ Y2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_refl
% 0.32/0.47 thf(fact_65_eq__refl,axiom,
% 0.32/0.47 ! [X2: set_nat,Y2: set_nat] :
% 0.32/0.47 ( ( X2 = Y2 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ X2 @ Y2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_refl
% 0.32/0.47 thf(fact_66_eq__refl,axiom,
% 0.32/0.47 ! [X2: nat,Y2: nat] :
% 0.32/0.47 ( ( X2 = Y2 )
% 0.32/0.47 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_refl
% 0.32/0.47 thf(fact_67_linear,axiom,
% 0.32/0.47 ! [X2: nat,Y2: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.32/0.47 | ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % linear
% 0.32/0.47 thf(fact_68_antisym,axiom,
% 0.32/0.47 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X2 @ Y2 )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ Y2 @ X2 )
% 0.32/0.47 => ( X2 = Y2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % antisym
% 0.32/0.47 thf(fact_69_antisym,axiom,
% 0.32/0.47 ! [X2: set_nat,Y2: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ Y2 @ X2 )
% 0.32/0.47 => ( X2 = Y2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % antisym
% 0.32/0.47 thf(fact_70_antisym,axiom,
% 0.32/0.47 ! [X2: nat,Y2: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.32/0.47 => ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.32/0.47 => ( X2 = Y2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % antisym
% 0.32/0.47 thf(fact_71_eq__iff,axiom,
% 0.32/0.47 ( ( ^ [Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] : ( Y = Z ) )
% 0.32/0.47 = ( ^ [X3: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X3 @ Y3 )
% 0.32/0.47 & ( ord_le841296385at_nat @ Y3 @ X3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_iff
% 0.32/0.47 thf(fact_72_eq__iff,axiom,
% 0.32/0.47 ( ( ^ [Y: set_nat,Z: set_nat] : ( Y = Z ) )
% 0.32/0.47 = ( ^ [X3: set_nat,Y3: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 0.32/0.47 & ( ord_less_eq_set_nat @ Y3 @ X3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_iff
% 0.32/0.47 thf(fact_73_eq__iff,axiom,
% 0.32/0.47 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.32/0.47 = ( ^ [X3: nat,Y3: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.32/0.47 & ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_iff
% 0.32/0.47 thf(fact_74_ord__le__eq__subst,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ( F @ B2 )
% 0.32/0.47 = C )
% 0.32/0.47 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_subst
% 0.32/0.47 thf(fact_75_ord__le__eq__subst,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > set_nat,C: set_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ( F @ B2 )
% 0.32/0.47 = C )
% 0.32/0.47 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_subst
% 0.32/0.47 thf(fact_76_ord__le__eq__subst,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > nat,C: nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ( F @ B2 )
% 0.32/0.47 = C )
% 0.32/0.47 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_subst
% 0.32/0.47 thf(fact_77_ord__le__eq__subst,axiom,
% 0.32/0.47 ! [A2: set_nat,B2: set_nat,F: set_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ( F @ B2 )
% 0.32/0.47 = C )
% 0.32/0.47 => ( ! [X: set_nat,Y4: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_subst
% 0.32/0.47 thf(fact_78_ord__le__eq__subst,axiom,
% 0.32/0.47 ! [A2: set_nat,B2: set_nat,F: set_nat > set_nat,C: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ( F @ B2 )
% 0.32/0.47 = C )
% 0.32/0.47 => ( ! [X: set_nat,Y4: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_subst
% 0.32/0.47 thf(fact_79_ord__le__eq__subst,axiom,
% 0.32/0.47 ! [A2: set_nat,B2: set_nat,F: set_nat > nat,C: nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ( F @ B2 )
% 0.32/0.47 = C )
% 0.32/0.47 => ( ! [X: set_nat,Y4: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_subst
% 0.32/0.47 thf(fact_80_ord__le__eq__subst,axiom,
% 0.32/0.47 ! [A2: nat,B2: nat,F: nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ( F @ B2 )
% 0.32/0.47 = C )
% 0.32/0.47 => ( ! [X: nat,Y4: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_subst
% 0.32/0.47 thf(fact_81_ord__le__eq__subst,axiom,
% 0.32/0.47 ! [A2: nat,B2: nat,F: nat > set_nat,C: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ( F @ B2 )
% 0.32/0.47 = C )
% 0.32/0.47 => ( ! [X: nat,Y4: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_subst
% 0.32/0.47 thf(fact_82_ord__le__eq__subst,axiom,
% 0.32/0.47 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ( F @ B2 )
% 0.32/0.47 = C )
% 0.32/0.47 => ( ! [X: nat,Y4: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_subst
% 0.32/0.47 thf(fact_83_ord__eq__le__subst,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( A2
% 0.32/0.47 = ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le841296385at_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_subst
% 0.32/0.47 thf(fact_84_ord__eq__le__subst,axiom,
% 0.32/0.47 ! [A2: set_nat,F: set_Pr1986765409at_nat > set_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( A2
% 0.32/0.47 = ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_subst
% 0.32/0.47 thf(fact_85_ord__eq__le__subst,axiom,
% 0.32/0.47 ! [A2: nat,F: set_Pr1986765409at_nat > nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( A2
% 0.32/0.47 = ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_subst
% 0.32/0.47 thf(fact_86_ord__eq__le__subst,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,F: set_nat > set_Pr1986765409at_nat,B2: set_nat,C: set_nat] :
% 0.32/0.47 ( ( A2
% 0.32/0.47 = ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: set_nat,Y4: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le841296385at_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_subst
% 0.32/0.47 thf(fact_87_ord__eq__le__subst,axiom,
% 0.32/0.47 ! [A2: set_nat,F: set_nat > set_nat,B2: set_nat,C: set_nat] :
% 0.32/0.47 ( ( A2
% 0.32/0.47 = ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: set_nat,Y4: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_subst
% 0.32/0.47 thf(fact_88_ord__eq__le__subst,axiom,
% 0.32/0.47 ! [A2: nat,F: set_nat > nat,B2: set_nat,C: set_nat] :
% 0.32/0.47 ( ( A2
% 0.32/0.47 = ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: set_nat,Y4: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_subst
% 0.32/0.47 thf(fact_89_ord__eq__le__subst,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,F: nat > set_Pr1986765409at_nat,B2: nat,C: nat] :
% 0.32/0.47 ( ( A2
% 0.32/0.47 = ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: nat,Y4: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le841296385at_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_subst
% 0.32/0.47 thf(fact_90_ord__eq__le__subst,axiom,
% 0.32/0.47 ! [A2: set_nat,F: nat > set_nat,B2: nat,C: nat] :
% 0.32/0.47 ( ( A2
% 0.32/0.47 = ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: nat,Y4: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_subst
% 0.32/0.47 thf(fact_91_ord__eq__le__subst,axiom,
% 0.32/0.47 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 0.32/0.47 ( ( A2
% 0.32/0.47 = ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: nat,Y4: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_subst
% 0.32/0.47 thf(fact_92_order__subst2,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ ( F @ B2 ) @ C )
% 0.32/0.47 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst2
% 0.32/0.47 thf(fact_93_order__subst2,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > set_nat,C: set_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ ( F @ B2 ) @ C )
% 0.32/0.47 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst2
% 0.32/0.47 thf(fact_94_order__subst2,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > nat,C: nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 0.32/0.47 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst2
% 0.32/0.47 thf(fact_95_order__subst2,axiom,
% 0.32/0.47 ! [A2: set_nat,B2: set_nat,F: set_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ ( F @ B2 ) @ C )
% 0.32/0.47 => ( ! [X: set_nat,Y4: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst2
% 0.32/0.47 thf(fact_96_order__subst2,axiom,
% 0.32/0.47 ! [A2: set_nat,B2: set_nat,F: set_nat > set_nat,C: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ ( F @ B2 ) @ C )
% 0.32/0.47 => ( ! [X: set_nat,Y4: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst2
% 0.32/0.47 thf(fact_97_order__subst2,axiom,
% 0.32/0.47 ! [A2: set_nat,B2: set_nat,F: set_nat > nat,C: nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 0.32/0.47 => ( ! [X: set_nat,Y4: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst2
% 0.32/0.47 thf(fact_98_order__subst2,axiom,
% 0.32/0.47 ! [A2: nat,B2: nat,F: nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ ( F @ B2 ) @ C )
% 0.32/0.47 => ( ! [X: nat,Y4: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst2
% 0.32/0.47 thf(fact_99_order__subst2,axiom,
% 0.32/0.47 ! [A2: nat,B2: nat,F: nat > set_nat,C: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ ( F @ B2 ) @ C )
% 0.32/0.47 => ( ! [X: nat,Y4: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst2
% 0.32/0.47 thf(fact_100_order__subst2,axiom,
% 0.32/0.47 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 0.32/0.47 => ( ! [X: nat,Y4: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst2
% 0.32/0.47 thf(fact_101_mem__Collect__eq,axiom,
% 0.32/0.47 ! [A2: nat,P2: nat > $o] :
% 0.32/0.47 ( ( member_nat @ A2 @ ( collect_nat @ P2 ) )
% 0.32/0.47 = ( P2 @ A2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % mem_Collect_eq
% 0.32/0.47 thf(fact_102_mem__Collect__eq,axiom,
% 0.32/0.47 ! [A2: product_prod_nat_nat,P2: product_prod_nat_nat > $o] :
% 0.32/0.47 ( ( member701585322at_nat @ A2 @ ( collec7649004at_nat @ P2 ) )
% 0.32/0.47 = ( P2 @ A2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % mem_Collect_eq
% 0.32/0.47 thf(fact_103_Collect__mem__eq,axiom,
% 0.32/0.47 ! [A: set_nat] :
% 0.32/0.47 ( ( collect_nat
% 0.32/0.47 @ ^ [X3: nat] : ( member_nat @ X3 @ A ) )
% 0.32/0.47 = A ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mem_eq
% 0.32/0.47 thf(fact_104_Collect__mem__eq,axiom,
% 0.32/0.47 ! [A: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( collec7649004at_nat
% 0.32/0.47 @ ^ [X3: product_prod_nat_nat] : ( member701585322at_nat @ X3 @ A ) )
% 0.32/0.47 = A ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mem_eq
% 0.32/0.47 thf(fact_105_order__subst1,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A2 @ ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le841296385at_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst1
% 0.32/0.47 thf(fact_106_order__subst1,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,F: set_nat > set_Pr1986765409at_nat,B2: set_nat,C: set_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A2 @ ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: set_nat,Y4: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le841296385at_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst1
% 0.32/0.47 thf(fact_107_order__subst1,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,F: nat > set_Pr1986765409at_nat,B2: nat,C: nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A2 @ ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: nat,Y4: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le841296385at_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst1
% 0.32/0.47 thf(fact_108_order__subst1,axiom,
% 0.32/0.47 ! [A2: set_nat,F: set_Pr1986765409at_nat > set_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A2 @ ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst1
% 0.32/0.47 thf(fact_109_order__subst1,axiom,
% 0.32/0.47 ! [A2: set_nat,F: set_nat > set_nat,B2: set_nat,C: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A2 @ ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: set_nat,Y4: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst1
% 0.32/0.47 thf(fact_110_order__subst1,axiom,
% 0.32/0.47 ! [A2: set_nat,F: nat > set_nat,B2: nat,C: nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A2 @ ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: nat,Y4: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst1
% 0.32/0.47 thf(fact_111_order__subst1,axiom,
% 0.32/0.47 ! [A2: nat,F: set_Pr1986765409at_nat > nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A2 @ ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst1
% 0.32/0.47 thf(fact_112_order__subst1,axiom,
% 0.32/0.47 ! [A2: nat,F: set_nat > nat,B2: set_nat,C: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A2 @ ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: set_nat,Y4: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst1
% 0.32/0.47 thf(fact_113_order__subst1,axiom,
% 0.32/0.47 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A2 @ ( F @ B2 ) )
% 0.32/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.32/0.47 => ( ! [X: nat,Y4: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst1
% 0.32/0.47 thf(fact_114_Collect__mono__iff,axiom,
% 0.32/0.47 ! [P2: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ P2 ) @ ( collec7649004at_nat @ Q ) )
% 0.32/0.47 = ( ! [X3: product_prod_nat_nat] :
% 0.32/0.47 ( ( P2 @ X3 )
% 0.32/0.47 => ( Q @ X3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mono_iff
% 0.32/0.47 thf(fact_115_Collect__mono__iff,axiom,
% 0.32/0.47 ! [P2: nat > $o,Q: nat > $o] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q ) )
% 0.32/0.47 = ( ! [X3: nat] :
% 0.32/0.47 ( ( P2 @ X3 )
% 0.32/0.47 => ( Q @ X3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mono_iff
% 0.32/0.47 thf(fact_116_set__eq__subset,axiom,
% 0.32/0.47 ( ( ^ [Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] : ( Y = Z ) )
% 0.32/0.47 = ( ^ [A5: set_Pr1986765409at_nat,B5: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A5 @ B5 )
% 0.32/0.47 & ( ord_le841296385at_nat @ B5 @ A5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % set_eq_subset
% 0.32/0.47 thf(fact_117_set__eq__subset,axiom,
% 0.32/0.47 ( ( ^ [Y: set_nat,Z: set_nat] : ( Y = Z ) )
% 0.32/0.47 = ( ^ [A5: set_nat,B5: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A5 @ B5 )
% 0.32/0.47 & ( ord_less_eq_set_nat @ B5 @ A5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % set_eq_subset
% 0.32/0.47 thf(fact_118_subset__trans,axiom,
% 0.32/0.47 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C2: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A @ B )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ B @ C2 )
% 0.32/0.47 => ( ord_le841296385at_nat @ A @ C2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_trans
% 0.32/0.47 thf(fact_119_subset__trans,axiom,
% 0.32/0.47 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_trans
% 0.32/0.47 thf(fact_120_Collect__mono,axiom,
% 0.32/0.47 ! [P2: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 0.32/0.47 ( ! [X: product_prod_nat_nat] :
% 0.32/0.47 ( ( P2 @ X )
% 0.32/0.47 => ( Q @ X ) )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( collec7649004at_nat @ P2 ) @ ( collec7649004at_nat @ Q ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mono
% 0.32/0.47 thf(fact_121_Collect__mono,axiom,
% 0.32/0.47 ! [P2: nat > $o,Q: nat > $o] :
% 0.32/0.47 ( ! [X: nat] :
% 0.32/0.47 ( ( P2 @ X )
% 0.32/0.47 => ( Q @ X ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mono
% 0.32/0.47 thf(fact_122_subset__refl,axiom,
% 0.32/0.47 ! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ) ).
% 0.32/0.47
% 0.32/0.47 % subset_refl
% 0.32/0.47 thf(fact_123_subset__refl,axiom,
% 0.32/0.47 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 0.32/0.47
% 0.32/0.47 % subset_refl
% 0.32/0.47 thf(fact_124_subset__iff,axiom,
% 0.32/0.47 ( ord_le841296385at_nat
% 0.32/0.47 = ( ^ [A5: set_Pr1986765409at_nat,B5: set_Pr1986765409at_nat] :
% 0.32/0.47 ! [T2: product_prod_nat_nat] :
% 0.32/0.47 ( ( member701585322at_nat @ T2 @ A5 )
% 0.32/0.47 => ( member701585322at_nat @ T2 @ B5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_iff
% 0.32/0.47 thf(fact_125_subset__iff,axiom,
% 0.32/0.47 ( ord_less_eq_set_nat
% 0.32/0.47 = ( ^ [A5: set_nat,B5: set_nat] :
% 0.32/0.47 ! [T2: nat] :
% 0.32/0.47 ( ( member_nat @ T2 @ A5 )
% 0.32/0.47 => ( member_nat @ T2 @ B5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_iff
% 0.32/0.47 thf(fact_126_equalityD2,axiom,
% 0.32/0.47 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( A = B )
% 0.32/0.47 => ( ord_le841296385at_nat @ B @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % equalityD2
% 0.32/0.47 thf(fact_127_equalityD2,axiom,
% 0.32/0.47 ! [A: set_nat,B: set_nat] :
% 0.32/0.47 ( ( A = B )
% 0.32/0.47 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % equalityD2
% 0.32/0.47 thf(fact_128_equalityD1,axiom,
% 0.32/0.47 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( A = B )
% 0.32/0.47 => ( ord_le841296385at_nat @ A @ B ) ) ).
% 0.32/0.47
% 0.32/0.47 % equalityD1
% 0.32/0.47 thf(fact_129_equalityD1,axiom,
% 0.32/0.47 ! [A: set_nat,B: set_nat] :
% 0.32/0.47 ( ( A = B )
% 0.32/0.47 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 0.32/0.47
% 0.32/0.47 % equalityD1
% 0.32/0.47 thf(fact_130_subset__eq,axiom,
% 0.32/0.47 ( ord_le841296385at_nat
% 0.32/0.47 = ( ^ [A5: set_Pr1986765409at_nat,B5: set_Pr1986765409at_nat] :
% 0.32/0.47 ! [X3: product_prod_nat_nat] :
% 0.32/0.47 ( ( member701585322at_nat @ X3 @ A5 )
% 0.32/0.47 => ( member701585322at_nat @ X3 @ B5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_eq
% 0.32/0.47 thf(fact_131_subset__eq,axiom,
% 0.32/0.47 ( ord_less_eq_set_nat
% 0.32/0.47 = ( ^ [A5: set_nat,B5: set_nat] :
% 0.32/0.47 ! [X3: nat] :
% 0.32/0.47 ( ( member_nat @ X3 @ A5 )
% 0.32/0.47 => ( member_nat @ X3 @ B5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_eq
% 0.32/0.47 thf(fact_132_equalityE,axiom,
% 0.32/0.47 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( A = B )
% 0.32/0.47 => ~ ( ( ord_le841296385at_nat @ A @ B )
% 0.32/0.47 => ~ ( ord_le841296385at_nat @ B @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % equalityE
% 0.32/0.47 thf(fact_133_equalityE,axiom,
% 0.32/0.47 ! [A: set_nat,B: set_nat] :
% 0.32/0.47 ( ( A = B )
% 0.32/0.47 => ~ ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.47 => ~ ( ord_less_eq_set_nat @ B @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % equalityE
% 0.32/0.47 thf(fact_134_subsetD,axiom,
% 0.32/0.47 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A @ B )
% 0.32/0.47 => ( ( member701585322at_nat @ C @ A )
% 0.32/0.47 => ( member701585322at_nat @ C @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subsetD
% 0.32/0.47 thf(fact_135_subsetD,axiom,
% 0.32/0.47 ! [A: set_nat,B: set_nat,C: nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.47 => ( ( member_nat @ C @ A )
% 0.32/0.47 => ( member_nat @ C @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subsetD
% 0.32/0.47 thf(fact_136_in__mono,axiom,
% 0.32/0.47 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,X2: product_prod_nat_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A @ B )
% 0.32/0.47 => ( ( member701585322at_nat @ X2 @ A )
% 0.32/0.47 => ( member701585322at_nat @ X2 @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % in_mono
% 0.32/0.47 thf(fact_137_in__mono,axiom,
% 0.32/0.47 ! [A: set_nat,B: set_nat,X2: nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.47 => ( ( member_nat @ X2 @ A )
% 0.32/0.47 => ( member_nat @ X2 @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % in_mono
% 0.32/0.47 thf(fact_138_reachable__ss__V,axiom,
% 0.32/0.47 ! [S: nat] :
% 0.32/0.47 ( ( member_nat @ S @ ( v_a @ c ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( reachableNodes_a @ c @ S ) @ ( v_a @ c ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % reachable_ss_V
% 0.32/0.47 thf(fact_139_transfer__path,axiom,
% 0.32/0.47 ! [P: list_P559422087at_nat,C3: product_prod_nat_nat > a,U2: nat,V: nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ P ) @ ( e_a @ c ) ) @ ( e_a @ C3 ) )
% 0.32/0.47 => ( ( isPath_a @ c @ U2 @ P @ V )
% 0.32/0.47 => ( isPath_a @ C3 @ U2 @ P @ V ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % transfer_path
% 0.32/0.47 thf(fact_140_card__spEdges__le,axiom,
% 0.32/0.47 ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ c ) ) ).
% 0.32/0.47
% 0.32/0.47 % card_spEdges_le
% 0.32/0.47 thf(fact_141_Finite__Graph__EI,axiom,
% 0.32/0.47 ( ( finite772653738at_nat @ ( e_a @ c ) )
% 0.32/0.47 => ( finite_Graph_a @ c ) ) ).
% 0.32/0.47
% 0.32/0.47 % Finite_Graph_EI
% 0.32/0.47 thf(fact_142_Graph_Oincoming_H__edges,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,U: set_nat] : ( ord_le841296385at_nat @ ( incoming_a2 @ C @ U ) @ ( e_a @ C ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.incoming'_edges
% 0.32/0.47 thf(fact_143_Graph_Ooutgoing_H__edges,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,U: set_nat] : ( ord_le841296385at_nat @ ( outgoing_a2 @ C @ U ) @ ( e_a @ C ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.outgoing'_edges
% 0.32/0.47 thf(fact_144_Graph_Oincoming__edges,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,U2: nat] : ( ord_le841296385at_nat @ ( incoming_a @ C @ U2 ) @ ( e_a @ C ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.incoming_edges
% 0.32/0.47 thf(fact_145_Graph_Ooutgoing__edges,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,U2: nat] : ( ord_le841296385at_nat @ ( outgoing_a @ C @ U2 ) @ ( e_a @ C ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.outgoing_edges
% 0.32/0.47 thf(fact_146_Graph_OisPath__edgeset,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V: nat,E: product_prod_nat_nat] :
% 0.32/0.47 ( ( isPath_a @ C @ U2 @ P @ V )
% 0.32/0.47 => ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ P ) )
% 0.32/0.47 => ( member701585322at_nat @ E @ ( e_a @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.isPath_edgeset
% 0.32/0.47 thf(fact_147_isPath__ex__edge2,axiom,
% 0.32/0.47 ! [U2: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat] :
% 0.32/0.47 ( ( isPath_a @ c @ U2 @ P @ V )
% 0.32/0.47 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 0.32/0.47 => ( ( V1 != V )
% 0.32/0.47 => ? [V2: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ V1 @ V2 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % isPath_ex_edge2
% 0.32/0.47 thf(fact_148_IntI,axiom,
% 0.32/0.47 ! [C: nat,A: set_nat,B: set_nat] :
% 0.32/0.47 ( ( member_nat @ C @ A )
% 0.32/0.47 => ( ( member_nat @ C @ B )
% 0.32/0.47 => ( member_nat @ C @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % IntI
% 0.32/0.47 thf(fact_149_IntI,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( member701585322at_nat @ C @ A )
% 0.32/0.47 => ( ( member701585322at_nat @ C @ B )
% 0.32/0.47 => ( member701585322at_nat @ C @ ( inf_in586391887at_nat @ A @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % IntI
% 0.32/0.47 thf(fact_150_Int__iff,axiom,
% 0.32/0.47 ! [C: nat,A: set_nat,B: set_nat] :
% 0.32/0.47 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B ) )
% 0.32/0.47 = ( ( member_nat @ C @ A )
% 0.32/0.47 & ( member_nat @ C @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_iff
% 0.32/0.47 thf(fact_151_Int__iff,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( member701585322at_nat @ C @ ( inf_in586391887at_nat @ A @ B ) )
% 0.32/0.47 = ( ( member701585322at_nat @ C @ A )
% 0.32/0.47 & ( member701585322at_nat @ C @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_iff
% 0.32/0.47 thf(fact_152_isPath__ex__edge1,axiom,
% 0.32/0.47 ! [U2: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat] :
% 0.32/0.47 ( ( isPath_a @ c @ U2 @ P @ V )
% 0.32/0.47 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 0.32/0.47 => ( ( U1 != U2 )
% 0.32/0.47 => ? [U22: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ U22 @ U1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % isPath_ex_edge1
% 0.32/0.47 thf(fact_153_reachableNodes__append__edge,axiom,
% 0.32/0.47 ! [U2: nat,S: nat,V: nat] :
% 0.32/0.47 ( ( member_nat @ U2 @ ( reachableNodes_a @ c @ S ) )
% 0.32/0.47 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U2 @ V ) @ ( e_a @ c ) )
% 0.32/0.47 => ( member_nat @ V @ ( reachableNodes_a @ c @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % reachableNodes_append_edge
% 0.32/0.47 thf(fact_154_Int__subset__iff,axiom,
% 0.32/0.47 ! [C2: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ C2 @ ( inf_in586391887at_nat @ A @ B ) )
% 0.32/0.47 = ( ( ord_le841296385at_nat @ C2 @ A )
% 0.32/0.47 & ( ord_le841296385at_nat @ C2 @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_subset_iff
% 0.32/0.47 thf(fact_155_Int__subset__iff,axiom,
% 0.32/0.47 ! [C2: set_nat,A: set_nat,B: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ C2 @ ( inf_inf_set_nat @ A @ B ) )
% 0.32/0.47 = ( ( ord_less_eq_set_nat @ C2 @ A )
% 0.32/0.47 & ( ord_less_eq_set_nat @ C2 @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_subset_iff
% 0.32/0.47 thf(fact_156_finite__E,axiom,
% 0.32/0.47 finite772653738at_nat @ ( e_a @ c ) ).
% 0.32/0.47
% 0.32/0.47 % finite_E
% 0.32/0.47 thf(fact_157_finite__uE,axiom,
% 0.32/0.47 finite772653738at_nat @ ( edmond771116670s_uE_a @ c ) ).
% 0.32/0.47
% 0.32/0.47 % finite_uE
% 0.32/0.47 thf(fact_158_finite__spEdges,axiom,
% 0.32/0.47 finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ).
% 0.32/0.47
% 0.32/0.47 % finite_spEdges
% 0.32/0.47 thf(fact_159_IntE,axiom,
% 0.32/0.47 ! [C: nat,A: set_nat,B: set_nat] :
% 0.32/0.47 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B ) )
% 0.32/0.47 => ~ ( ( member_nat @ C @ A )
% 0.32/0.47 => ~ ( member_nat @ C @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % IntE
% 0.32/0.47 thf(fact_160_IntE,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( member701585322at_nat @ C @ ( inf_in586391887at_nat @ A @ B ) )
% 0.32/0.47 => ~ ( ( member701585322at_nat @ C @ A )
% 0.32/0.47 => ~ ( member701585322at_nat @ C @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % IntE
% 0.32/0.47 thf(fact_161_IntD1,axiom,
% 0.32/0.47 ! [C: nat,A: set_nat,B: set_nat] :
% 0.32/0.47 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B ) )
% 0.32/0.47 => ( member_nat @ C @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % IntD1
% 0.32/0.47 thf(fact_162_IntD1,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( member701585322at_nat @ C @ ( inf_in586391887at_nat @ A @ B ) )
% 0.32/0.47 => ( member701585322at_nat @ C @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % IntD1
% 0.32/0.47 thf(fact_163_IntD2,axiom,
% 0.32/0.47 ! [C: nat,A: set_nat,B: set_nat] :
% 0.32/0.47 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B ) )
% 0.32/0.47 => ( member_nat @ C @ B ) ) ).
% 0.32/0.47
% 0.32/0.47 % IntD2
% 0.32/0.47 thf(fact_164_IntD2,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( member701585322at_nat @ C @ ( inf_in586391887at_nat @ A @ B ) )
% 0.32/0.47 => ( member701585322at_nat @ C @ B ) ) ).
% 0.32/0.47
% 0.32/0.47 % IntD2
% 0.32/0.47 thf(fact_165_Graph_OreachableNodes__append__edge,axiom,
% 0.32/0.47 ! [U2: nat,C: product_prod_nat_nat > a,S: nat,V: nat] :
% 0.32/0.47 ( ( member_nat @ U2 @ ( reachableNodes_a @ C @ S ) )
% 0.32/0.47 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U2 @ V ) @ ( e_a @ C ) )
% 0.32/0.47 => ( member_nat @ V @ ( reachableNodes_a @ C @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.reachableNodes_append_edge
% 0.32/0.47 thf(fact_166_Graph_OreachableNodes_Ocong,axiom,
% 0.32/0.47 reachableNodes_a = reachableNodes_a ).
% 0.32/0.47
% 0.32/0.47 % Graph.reachableNodes.cong
% 0.32/0.47 thf(fact_167_Graph_Oadjacent__nodes_Ocong,axiom,
% 0.32/0.47 adjacent_nodes_a = adjacent_nodes_a ).
% 0.32/0.47
% 0.32/0.47 % Graph.adjacent_nodes.cong
% 0.32/0.47 thf(fact_168_Graph_Oreachable__ss__V,axiom,
% 0.32/0.47 ! [S: nat,C: product_prod_nat_nat > a] :
% 0.32/0.47 ( ( member_nat @ S @ ( v_a @ C ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( reachableNodes_a @ C @ S ) @ ( v_a @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.reachable_ss_V
% 0.32/0.47 thf(fact_169_Int__mono,axiom,
% 0.32/0.47 ! [A: set_Pr1986765409at_nat,C2: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A @ C2 )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ B @ D )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ ( inf_in586391887at_nat @ C2 @ D ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_mono
% 0.32/0.47 thf(fact_170_Int__mono,axiom,
% 0.32/0.47 ! [A: set_nat,C2: set_nat,B: set_nat,D: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A @ C2 )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ B @ D )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ ( inf_inf_set_nat @ C2 @ D ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_mono
% 0.32/0.47 thf(fact_171_Int__lower1,axiom,
% 0.32/0.47 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ A ) ).
% 0.32/0.47
% 0.32/0.47 % Int_lower1
% 0.32/0.47 thf(fact_172_Int__lower1,axiom,
% 0.32/0.47 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ A ) ).
% 0.32/0.47
% 0.32/0.47 % Int_lower1
% 0.32/0.47 thf(fact_173_Int__lower2,axiom,
% 0.32/0.47 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B ) ).
% 0.32/0.47
% 0.32/0.47 % Int_lower2
% 0.32/0.47 thf(fact_174_Int__lower2,axiom,
% 0.32/0.47 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ B ) ).
% 0.32/0.47
% 0.32/0.47 % Int_lower2
% 0.32/0.47 thf(fact_175_Int__absorb1,axiom,
% 0.32/0.47 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ B @ A )
% 0.32/0.47 => ( ( inf_in586391887at_nat @ A @ B )
% 0.32/0.47 = B ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_absorb1
% 0.32/0.47 thf(fact_176_Int__absorb1,axiom,
% 0.32/0.47 ! [B: set_nat,A: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ B @ A )
% 0.32/0.47 => ( ( inf_inf_set_nat @ A @ B )
% 0.32/0.47 = B ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_absorb1
% 0.32/0.47 thf(fact_177_Int__absorb2,axiom,
% 0.32/0.47 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A @ B )
% 0.32/0.47 => ( ( inf_in586391887at_nat @ A @ B )
% 0.32/0.47 = A ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_absorb2
% 0.32/0.47 thf(fact_178_Int__absorb2,axiom,
% 0.32/0.47 ! [A: set_nat,B: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.47 => ( ( inf_inf_set_nat @ A @ B )
% 0.32/0.47 = A ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_absorb2
% 0.32/0.47 thf(fact_179_Int__greatest,axiom,
% 0.32/0.47 ! [C2: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ C2 @ A )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ C2 @ B )
% 0.32/0.47 => ( ord_le841296385at_nat @ C2 @ ( inf_in586391887at_nat @ A @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_greatest
% 0.32/0.47 thf(fact_180_Int__greatest,axiom,
% 0.32/0.47 ! [C2: set_nat,A: set_nat,B: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ C2 @ A )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ C2 @ B )
% 0.32/0.47 => ( ord_less_eq_set_nat @ C2 @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_greatest
% 0.32/0.47 thf(fact_181_Int__Collect__mono,axiom,
% 0.32/0.47 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,P2: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A @ B )
% 0.32/0.47 => ( ! [X: product_prod_nat_nat] :
% 0.32/0.47 ( ( member701585322at_nat @ X @ A )
% 0.32/0.47 => ( ( P2 @ X )
% 0.32/0.47 => ( Q @ X ) ) )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ ( collec7649004at_nat @ P2 ) ) @ ( inf_in586391887at_nat @ B @ ( collec7649004at_nat @ Q ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_Collect_mono
% 0.32/0.47 thf(fact_182_Int__Collect__mono,axiom,
% 0.32/0.47 ! [A: set_nat,B: set_nat,P2: nat > $o,Q: nat > $o] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.47 => ( ! [X: nat] :
% 0.32/0.47 ( ( member_nat @ X @ A )
% 0.32/0.47 => ( ( P2 @ X )
% 0.32/0.47 => ( Q @ X ) ) )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ ( collect_nat @ P2 ) ) @ ( inf_inf_set_nat @ B @ ( collect_nat @ Q ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_Collect_mono
% 0.32/0.47 thf(fact_183_Graph_Oadjacent__nodes__ss__V,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,U2: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ C @ U2 ) @ ( v_a @ C ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.adjacent_nodes_ss_V
% 0.32/0.47 thf(fact_184_Graph_OisPath__ex__edge2,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat] :
% 0.32/0.47 ( ( isPath_a @ C @ U2 @ P @ V )
% 0.32/0.47 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 0.32/0.47 => ( ( V1 != V )
% 0.32/0.47 => ? [V2: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ V1 @ V2 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.isPath_ex_edge2
% 0.32/0.47 thf(fact_185_Graph_OisPath__ex__edge1,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat] :
% 0.32/0.47 ( ( isPath_a @ C @ U2 @ P @ V )
% 0.32/0.47 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 0.32/0.47 => ( ( U1 != U2 )
% 0.32/0.47 => ? [U22: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ U22 @ U1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.isPath_ex_edge1
% 0.32/0.47 thf(fact_186_Graph_OFinite__Graph__EI,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a] :
% 0.32/0.47 ( ( finite772653738at_nat @ ( e_a @ C ) )
% 0.32/0.47 => ( finite_Graph_a @ C ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.Finite_Graph_EI
% 0.32/0.47 thf(fact_187_Finite__Graph_Ofinite__E,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a] :
% 0.32/0.47 ( ( finite_Graph_a @ C )
% 0.32/0.47 => ( finite772653738at_nat @ ( e_a @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Finite_Graph.finite_E
% 0.32/0.47 thf(fact_188_ek__analysis_Ofinite__spEdges,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,S: nat,T: nat] :
% 0.32/0.47 ( ( edmond1517640972ysis_a @ C )
% 0.32/0.47 => ( finite772653738at_nat @ ( edmond475474835dges_a @ C @ S @ T ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ek_analysis.finite_spEdges
% 0.32/0.47 thf(fact_189_ek__analysis_Ofinite__uE,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a] :
% 0.32/0.47 ( ( edmond1517640972ysis_a @ C )
% 0.32/0.47 => ( finite772653738at_nat @ ( edmond771116670s_uE_a @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ek_analysis.finite_uE
% 0.32/0.47 thf(fact_190_Graph_Otransfer__path,axiom,
% 0.32/0.47 ! [P: list_P559422087at_nat,C: product_prod_nat_nat > a,C3: product_prod_nat_nat > a,U2: nat,V: nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ P ) @ ( e_a @ C ) ) @ ( e_a @ C3 ) )
% 0.32/0.47 => ( ( isPath_a @ C @ U2 @ P @ V )
% 0.32/0.47 => ( isPath_a @ C3 @ U2 @ P @ V ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.transfer_path
% 0.32/0.47 thf(fact_191_Graph_OE_Ocong,axiom,
% 0.32/0.47 e_a = e_a ).
% 0.32/0.47
% 0.32/0.47 % Graph.E.cong
% 0.32/0.47 thf(fact_192_Graph_OisPath_Ocong,axiom,
% 0.32/0.47 isPath_a = isPath_a ).
% 0.32/0.47
% 0.32/0.47 % Graph.isPath.cong
% 0.32/0.47 thf(fact_193_Graph_OV_Ocong,axiom,
% 0.32/0.47 v_a = v_a ).
% 0.32/0.47
% 0.32/0.47 % Graph.V.cong
% 0.32/0.47 thf(fact_194_ek__analysis_Ocard__spEdges__le,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,S: nat,T: nat] :
% 0.32/0.47 ( ( edmond1517640972ysis_a @ C )
% 0.32/0.47 => ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ C @ S @ T ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ek_analysis.card_spEdges_le
% 0.32/0.47 thf(fact_195_Graph_OisShortestPath_Ocong,axiom,
% 0.32/0.47 isShortestPath_a = isShortestPath_a ).
% 0.32/0.47
% 0.32/0.47 % Graph.isShortestPath.cong
% 0.32/0.47 thf(fact_196_Graph_Ooutgoing_Ocong,axiom,
% 0.32/0.47 outgoing_a = outgoing_a ).
% 0.32/0.47
% 0.32/0.47 % Graph.outgoing.cong
% 0.32/0.47 thf(fact_197_Graph_Oincoming_Ocong,axiom,
% 0.32/0.47 incoming_a = incoming_a ).
% 0.32/0.47
% 0.32/0.47 % Graph.incoming.cong
% 0.32/0.47 thf(fact_198_Graph_Ooutgoing_H_Ocong,axiom,
% 0.32/0.47 outgoing_a2 = outgoing_a2 ).
% 0.32/0.47
% 0.32/0.47 % Graph.outgoing'.cong
% 0.32/0.47 thf(fact_199_Graph_Oincoming_H_Ocong,axiom,
% 0.32/0.47 incoming_a2 = incoming_a2 ).
% 0.32/0.47
% 0.32/0.47 % Graph.incoming'.cong
% 0.32/0.47 thf(fact_200_Graph_OshortestPath__is__path,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V: nat] :
% 0.32/0.47 ( ( isShortestPath_a @ C @ U2 @ P @ V )
% 0.32/0.47 => ( isPath_a @ C @ U2 @ P @ V ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.shortestPath_is_path
% 0.32/0.47 thf(fact_201_finite__Int,axiom,
% 0.32/0.47 ! [F2: set_Pr1986765409at_nat,G: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ( finite772653738at_nat @ F2 )
% 0.32/0.47 | ( finite772653738at_nat @ G ) )
% 0.32/0.47 => ( finite772653738at_nat @ ( inf_in586391887at_nat @ F2 @ G ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Int
% 0.32/0.47 thf(fact_202_finite__Int,axiom,
% 0.32/0.47 ! [F2: set_nat,G: set_nat] :
% 0.32/0.47 ( ( ( finite_finite_nat @ F2 )
% 0.32/0.47 | ( finite_finite_nat @ G ) )
% 0.32/0.47 => ( finite_finite_nat @ ( inf_inf_set_nat @ F2 @ G ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Int
% 0.32/0.47 thf(fact_203_List_Ofinite__set,axiom,
% 0.32/0.47 ! [Xs: list_P559422087at_nat] : ( finite772653738at_nat @ ( set_Pr2131844118at_nat @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % List.finite_set
% 0.32/0.47 thf(fact_204_List_Ofinite__set,axiom,
% 0.32/0.47 ! [Xs: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % List.finite_set
% 0.32/0.47 thf(fact_205_le__inf__iff,axiom,
% 0.32/0.47 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat,Z2: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ Y2 @ Z2 ) )
% 0.32/0.47 = ( ( ord_le841296385at_nat @ X2 @ Y2 )
% 0.32/0.47 & ( ord_le841296385at_nat @ X2 @ Z2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % le_inf_iff
% 0.32/0.47 thf(fact_206_le__inf__iff,axiom,
% 0.32/0.47 ! [X2: set_nat,Y2: set_nat,Z2: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X2 @ ( inf_inf_set_nat @ Y2 @ Z2 ) )
% 0.32/0.47 = ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 0.32/0.47 & ( ord_less_eq_set_nat @ X2 @ Z2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % le_inf_iff
% 0.32/0.47 thf(fact_207_le__inf__iff,axiom,
% 0.32/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X2 @ ( inf_inf_nat @ Y2 @ Z2 ) )
% 0.32/0.47 = ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.32/0.47 & ( ord_less_eq_nat @ X2 @ Z2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % le_inf_iff
% 0.32/0.47 thf(fact_208_inf_Obounded__iff,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A2 @ ( inf_in586391887at_nat @ B2 @ C ) )
% 0.32/0.47 = ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.32/0.47 & ( ord_le841296385at_nat @ A2 @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.bounded_iff
% 0.32/0.47 thf(fact_209_inf_Obounded__iff,axiom,
% 0.32/0.47 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C ) )
% 0.32/0.47 = ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.47 & ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.bounded_iff
% 0.32/0.47 thf(fact_210_inf_Obounded__iff,axiom,
% 0.32/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A2 @ ( inf_inf_nat @ B2 @ C ) )
% 0.32/0.47 = ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.47 & ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.bounded_iff
% 0.32/0.47 thf(fact_211_card__mono,axiom,
% 0.32/0.47 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( finite772653738at_nat @ B )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ A @ B )
% 0.32/0.47 => ( ord_less_eq_nat @ ( finite447719721at_nat @ A ) @ ( finite447719721at_nat @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % card_mono
% 0.32/0.47 thf(fact_212_card__mono,axiom,
% 0.32/0.47 ! [B: set_nat,A: set_nat] :
% 0.32/0.47 ( ( finite_finite_nat @ B )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.47 => ( ord_less_eq_nat @ ( finite_card_nat @ A ) @ ( finite_card_nat @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % card_mono
% 0.32/0.47 thf(fact_213_card__seteq,axiom,
% 0.32/0.47 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( finite772653738at_nat @ B )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ A @ B )
% 0.32/0.47 => ( ( ord_less_eq_nat @ ( finite447719721at_nat @ B ) @ ( finite447719721at_nat @ A ) )
% 0.32/0.47 => ( A = B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % card_seteq
% 0.32/0.47 thf(fact_214_card__seteq,axiom,
% 0.32/0.47 ! [B: set_nat,A: set_nat] :
% 0.32/0.47 ( ( finite_finite_nat @ B )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.47 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B ) @ ( finite_card_nat @ A ) )
% 0.32/0.47 => ( A = B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % card_seteq
% 0.32/0.47 thf(fact_215_Efin__imp__Vfin,axiom,
% 0.32/0.47 ( ( finite772653738at_nat @ ( e_a @ c ) )
% 0.32/0.47 => ( finite_finite_nat @ ( v_a @ c ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Efin_imp_Vfin
% 0.32/0.47 thf(fact_216_finite__V,axiom,
% 0.32/0.47 finite_finite_nat @ ( v_a @ c ) ).
% 0.32/0.47
% 0.32/0.47 % finite_V
% 0.32/0.47 thf(fact_217_adjacent__nodes__finite,axiom,
% 0.32/0.47 ! [U2: nat] : ( finite_finite_nat @ ( adjacent_nodes_a @ c @ U2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % adjacent_nodes_finite
% 0.32/0.47 thf(fact_218_Vfin__imp__Efin,axiom,
% 0.32/0.47 ( ( finite_finite_nat @ ( v_a @ c ) )
% 0.32/0.47 => ( finite772653738at_nat @ ( e_a @ c ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Vfin_imp_Efin
% 0.32/0.47 thf(fact_219_finite__incoming,axiom,
% 0.32/0.47 ! [U2: nat] :
% 0.32/0.47 ( ( finite_finite_nat @ ( v_a @ c ) )
% 0.32/0.47 => ( finite772653738at_nat @ ( incoming_a @ c @ U2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_incoming
% 0.32/0.47 thf(fact_220_finite__outgoing,axiom,
% 0.32/0.47 ! [U2: nat] :
% 0.32/0.47 ( ( finite_finite_nat @ ( v_a @ c ) )
% 0.32/0.47 => ( finite772653738at_nat @ ( outgoing_a @ c @ U2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_outgoing
% 0.32/0.47 thf(fact_221_finite__incoming_H,axiom,
% 0.32/0.47 ! [U: set_nat] :
% 0.32/0.47 ( ( finite_finite_nat @ ( v_a @ c ) )
% 0.32/0.47 => ( finite772653738at_nat @ ( incoming_a2 @ c @ U ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_incoming'
% 0.32/0.47 thf(fact_222_finite__outgoing_H,axiom,
% 0.32/0.47 ! [U: set_nat] :
% 0.32/0.47 ( ( finite_finite_nat @ ( v_a @ c ) )
% 0.32/0.47 => ( finite772653738at_nat @ ( outgoing_a2 @ c @ U ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_outgoing'
% 0.32/0.47 thf(fact_223_Finite__Graph__def,axiom,
% 0.32/0.47 ( finite_Graph_a
% 0.32/0.47 = ( ^ [C4: product_prod_nat_nat > a] : ( finite_finite_nat @ ( v_a @ C4 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Finite_Graph_def
% 0.32/0.47 thf(fact_224_Finite__Graph_Ointro,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a] :
% 0.32/0.47 ( ( finite_finite_nat @ ( v_a @ C ) )
% 0.32/0.47 => ( finite_Graph_a @ C ) ) ).
% 0.32/0.47
% 0.32/0.47 % Finite_Graph.intro
% 0.32/0.47 thf(fact_225_Finite__Graph_Ofinite__V,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a] :
% 0.32/0.47 ( ( finite_Graph_a @ C )
% 0.32/0.47 => ( finite_finite_nat @ ( v_a @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Finite_Graph.finite_V
% 0.32/0.47 thf(fact_226_Finite__Graph_Oadjacent__nodes__finite,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,U2: nat] :
% 0.32/0.47 ( ( finite_Graph_a @ C )
% 0.32/0.47 => ( finite_finite_nat @ ( adjacent_nodes_a @ C @ U2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Finite_Graph.adjacent_nodes_finite
% 0.32/0.47 thf(fact_227_Graph_OEfin__imp__Vfin,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a] :
% 0.32/0.47 ( ( finite772653738at_nat @ ( e_a @ C ) )
% 0.32/0.47 => ( finite_finite_nat @ ( v_a @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.Efin_imp_Vfin
% 0.32/0.47 thf(fact_228_Graph_OVfin__imp__Efin,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a] :
% 0.32/0.47 ( ( finite_finite_nat @ ( v_a @ C ) )
% 0.32/0.47 => ( finite772653738at_nat @ ( e_a @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.Vfin_imp_Efin
% 0.32/0.47 thf(fact_229_Graph_Ofinite__outgoing,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,U2: nat] :
% 0.32/0.47 ( ( finite_finite_nat @ ( v_a @ C ) )
% 0.32/0.47 => ( finite772653738at_nat @ ( outgoing_a @ C @ U2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.finite_outgoing
% 0.32/0.47 thf(fact_230_Graph_Ofinite__incoming,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,U2: nat] :
% 0.32/0.47 ( ( finite_finite_nat @ ( v_a @ C ) )
% 0.32/0.47 => ( finite772653738at_nat @ ( incoming_a @ C @ U2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.finite_incoming
% 0.32/0.47 thf(fact_231_Graph_Ofinite__outgoing_H,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,U: set_nat] :
% 0.32/0.47 ( ( finite_finite_nat @ ( v_a @ C ) )
% 0.32/0.47 => ( finite772653738at_nat @ ( outgoing_a2 @ C @ U ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.finite_outgoing'
% 0.32/0.47 thf(fact_232_Graph_Ofinite__incoming_H,axiom,
% 0.32/0.47 ! [C: product_prod_nat_nat > a,U: set_nat] :
% 0.32/0.47 ( ( finite_finite_nat @ ( v_a @ C ) )
% 0.32/0.47 => ( finite772653738at_nat @ ( incoming_a2 @ C @ U ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Graph.finite_incoming'
% 0.32/0.47 thf(fact_233_finite__has__minimal2,axiom,
% 0.32/0.47 ! [A: set_se1612935105at_nat,A2: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( finite1457549322at_nat @ A )
% 0.32/0.47 => ( ( member298845450at_nat @ A2 @ A )
% 0.32/0.47 => ? [X: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( member298845450at_nat @ X @ A )
% 0.32/0.47 & ( ord_le841296385at_nat @ X @ A2 )
% 0.32/0.47 & ! [Xa: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( member298845450at_nat @ Xa @ A )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ Xa @ X )
% 0.32/0.47 => ( X = Xa ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_has_minimal2
% 0.32/0.47 thf(fact_234_finite__has__minimal2,axiom,
% 0.32/0.47 ! [A: set_set_nat,A2: set_nat] :
% 0.32/0.47 ( ( finite2012248349et_nat @ A )
% 0.32/0.47 => ( ( member_set_nat @ A2 @ A )
% 0.32/0.47 => ? [X: set_nat] :
% 0.32/0.47 ( ( member_set_nat @ X @ A )
% 0.32/0.47 & ( ord_less_eq_set_nat @ X @ A2 )
% 0.32/0.47 & ! [Xa: set_nat] :
% 0.32/0.47 ( ( member_set_nat @ Xa @ A )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ Xa @ X )
% 0.32/0.47 => ( X = Xa ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_has_minimal2
% 0.32/0.47 thf(fact_235_finite__has__minimal2,axiom,
% 0.32/0.47 ! [A: set_nat,A2: nat] :
% 0.32/0.47 ( ( finite_finite_nat @ A )
% 0.32/0.47 => ( ( member_nat @ A2 @ A )
% 0.32/0.47 => ? [X: nat] :
% 0.32/0.47 ( ( member_nat @ X @ A )
% 0.32/0.47 & ( ord_less_eq_nat @ X @ A2 )
% 0.32/0.47 & ! [Xa: nat] :
% 0.32/0.47 ( ( member_nat @ Xa @ A )
% 0.32/0.47 => ( ( ord_less_eq_nat @ Xa @ X )
% 0.32/0.47 => ( X = Xa ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_has_minimal2
% 0.32/0.47 thf(fact_236_finite__has__maximal2,axiom,
% 0.32/0.47 ! [A: set_se1612935105at_nat,A2: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( finite1457549322at_nat @ A )
% 0.32/0.47 => ( ( member298845450at_nat @ A2 @ A )
% 0.32/0.47 => ? [X: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( member298845450at_nat @ X @ A )
% 0.32/0.47 & ( ord_le841296385at_nat @ A2 @ X )
% 0.32/0.47 & ! [Xa: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( member298845450at_nat @ Xa @ A )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ X @ Xa )
% 0.32/0.47 => ( X = Xa ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_has_maximal2
% 0.32/0.47 thf(fact_237_finite__has__maximal2,axiom,
% 0.32/0.47 ! [A: set_set_nat,A2: set_nat] :
% 0.32/0.47 ( ( finite2012248349et_nat @ A )
% 0.32/0.47 => ( ( member_set_nat @ A2 @ A )
% 0.32/0.47 => ? [X: set_nat] :
% 0.32/0.47 ( ( member_set_nat @ X @ A )
% 0.32/0.47 & ( ord_less_eq_set_nat @ A2 @ X )
% 0.32/0.47 & ! [Xa: set_nat] :
% 0.32/0.47 ( ( member_set_nat @ Xa @ A )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ X @ Xa )
% 0.32/0.47 => ( X = Xa ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_has_maximal2
% 0.32/0.47 thf(fact_238_finite__has__maximal2,axiom,
% 0.32/0.47 ! [A: set_nat,A2: nat] :
% 0.32/0.47 ( ( finite_finite_nat @ A )
% 0.32/0.47 => ( ( member_nat @ A2 @ A )
% 0.32/0.47 => ? [X: nat] :
% 0.32/0.47 ( ( member_nat @ X @ A )
% 0.32/0.47 & ( ord_less_eq_nat @ A2 @ X )
% 0.32/0.47 & ! [Xa: nat] :
% 0.32/0.47 ( ( member_nat @ Xa @ A )
% 0.32/0.47 => ( ( ord_less_eq_nat @ X @ Xa )
% 0.32/0.47 => ( X = Xa ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_has_maximal2
% 0.32/0.47 thf(fact_239_inf_OcoboundedI2,axiom,
% 0.32/0.47 ! [B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ B2 @ C )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A2 @ B2 ) @ C ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.coboundedI2
% 0.32/0.47 thf(fact_240_inf_OcoboundedI2,axiom,
% 0.32/0.47 ! [B2: set_nat,C: set_nat,A2: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ B2 @ C )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ C ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.coboundedI2
% 0.32/0.47 thf(fact_241_inf_OcoboundedI2,axiom,
% 0.32/0.47 ! [B2: nat,C: nat,A2: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ B2 @ C )
% 0.32/0.47 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ C ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.coboundedI2
% 0.32/0.47 thf(fact_242_inf_OcoboundedI1,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A2 @ C )
% 0.32/0.47 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A2 @ B2 ) @ C ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.coboundedI1
% 0.32/0.47 thf(fact_243_inf_OcoboundedI1,axiom,
% 0.32/0.47 ! [A2: set_nat,C: set_nat,B2: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A2 @ C )
% 0.32/0.47 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ C ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.coboundedI1
% 0.32/0.47 thf(fact_244_inf_OcoboundedI1,axiom,
% 0.32/0.47 ! [A2: nat,C: nat,B2: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A2 @ C )
% 0.32/0.47 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ C ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.coboundedI1
% 0.32/0.47 thf(fact_245_inf_Oabsorb__iff2,axiom,
% 0.32/0.47 ( ord_le841296385at_nat
% 0.32/0.47 = ( ^ [B3: set_Pr1986765409at_nat,A3: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( inf_in586391887at_nat @ A3 @ B3 )
% 0.32/0.47 = B3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.absorb_iff2
% 0.32/0.47 thf(fact_246_inf_Oabsorb__iff2,axiom,
% 0.32/0.47 ( ord_less_eq_set_nat
% 0.32/0.47 = ( ^ [B3: set_nat,A3: set_nat] :
% 0.32/0.47 ( ( inf_inf_set_nat @ A3 @ B3 )
% 0.32/0.47 = B3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.absorb_iff2
% 0.32/0.47 thf(fact_247_inf_Oabsorb__iff2,axiom,
% 0.32/0.47 ( ord_less_eq_nat
% 0.32/0.47 = ( ^ [B3: nat,A3: nat] :
% 0.32/0.47 ( ( inf_inf_nat @ A3 @ B3 )
% 0.32/0.47 = B3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.absorb_iff2
% 0.32/0.47 thf(fact_248_inf_Oabsorb__iff1,axiom,
% 0.32/0.47 ( ord_le841296385at_nat
% 0.32/0.47 = ( ^ [A3: set_Pr1986765409at_nat,B3: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( inf_in586391887at_nat @ A3 @ B3 )
% 0.32/0.47 = A3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.absorb_iff1
% 0.32/0.47 thf(fact_249_inf_Oabsorb__iff1,axiom,
% 0.32/0.47 ( ord_less_eq_set_nat
% 0.32/0.47 = ( ^ [A3: set_nat,B3: set_nat] :
% 0.32/0.47 ( ( inf_inf_set_nat @ A3 @ B3 )
% 0.32/0.47 = A3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.absorb_iff1
% 0.32/0.47 thf(fact_250_inf_Oabsorb__iff1,axiom,
% 0.32/0.47 ( ord_less_eq_nat
% 0.32/0.47 = ( ^ [A3: nat,B3: nat] :
% 0.32/0.47 ( ( inf_inf_nat @ A3 @ B3 )
% 0.32/0.47 = A3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.absorb_iff1
% 0.32/0.47 thf(fact_251_inf_Ocobounded2,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A2 @ B2 ) @ B2 ) ).
% 0.32/0.47
% 0.32/0.47 % inf.cobounded2
% 0.32/0.47 thf(fact_252_inf_Ocobounded2,axiom,
% 0.32/0.47 ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ B2 ) ).
% 0.32/0.47
% 0.32/0.47 % inf.cobounded2
% 0.32/0.47 thf(fact_253_inf_Ocobounded2,axiom,
% 0.32/0.47 ! [A2: nat,B2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ B2 ) ).
% 0.32/0.47
% 0.32/0.47 % inf.cobounded2
% 0.32/0.47 thf(fact_254_inf_Ocobounded1,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A2 @ B2 ) @ A2 ) ).
% 0.32/0.47
% 0.32/0.47 % inf.cobounded1
% 0.32/0.47 thf(fact_255_inf_Ocobounded1,axiom,
% 0.32/0.47 ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ A2 ) ).
% 0.32/0.47
% 0.32/0.47 % inf.cobounded1
% 0.32/0.47 thf(fact_256_inf_Ocobounded1,axiom,
% 0.32/0.47 ! [A2: nat,B2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ A2 ) ).
% 0.32/0.47
% 0.32/0.47 % inf.cobounded1
% 0.32/0.47 thf(fact_257_inf_Oorder__iff,axiom,
% 0.32/0.47 ( ord_le841296385at_nat
% 0.32/0.47 = ( ^ [A3: set_Pr1986765409at_nat,B3: set_Pr1986765409at_nat] :
% 0.32/0.47 ( A3
% 0.32/0.47 = ( inf_in586391887at_nat @ A3 @ B3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.order_iff
% 0.32/0.47 thf(fact_258_inf_Oorder__iff,axiom,
% 0.32/0.47 ( ord_less_eq_set_nat
% 0.32/0.47 = ( ^ [A3: set_nat,B3: set_nat] :
% 0.32/0.47 ( A3
% 0.32/0.47 = ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.order_iff
% 0.32/0.47 thf(fact_259_inf_Oorder__iff,axiom,
% 0.32/0.47 ( ord_less_eq_nat
% 0.32/0.47 = ( ^ [A3: nat,B3: nat] :
% 0.32/0.47 ( A3
% 0.32/0.47 = ( inf_inf_nat @ A3 @ B3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.order_iff
% 0.32/0.47 thf(fact_260_inf__greatest,axiom,
% 0.32/0.47 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat,Z2: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ X2 @ Y2 )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ X2 @ Z2 )
% 0.32/0.47 => ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ Y2 @ Z2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf_greatest
% 0.32/0.47 thf(fact_261_inf__greatest,axiom,
% 0.32/0.47 ! [X2: set_nat,Y2: set_nat,Z2: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ X2 @ Z2 )
% 0.32/0.47 => ( ord_less_eq_set_nat @ X2 @ ( inf_inf_set_nat @ Y2 @ Z2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf_greatest
% 0.32/0.47 thf(fact_262_inf__greatest,axiom,
% 0.32/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.32/0.47 => ( ( ord_less_eq_nat @ X2 @ Z2 )
% 0.32/0.47 => ( ord_less_eq_nat @ X2 @ ( inf_inf_nat @ Y2 @ Z2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf_greatest
% 0.32/0.47 thf(fact_263_inf_OboundedI,axiom,
% 0.32/0.47 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.47 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_le841296385at_nat @ A2 @ C )
% 0.32/0.47 => ( ord_le841296385at_nat @ A2 @ ( inf_in586391887at_nat @ B2 @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.boundedI
% 0.32/0.47 thf(fact_264_inf_OboundedI,axiom,
% 0.32/0.47 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 0.32/0.47 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.47 => ( ( ord_less_eq_set_nat @ A2 @ C )
% 0.32/0.47 => ( ord_less_eq_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.boundedI
% 0.32/0.47 thf(fact_265_inf_OboundedI,axiom,
% 0.32/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.32/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.48 => ( ( ord_less_eq_nat @ A2 @ C )
% 0.32/0.48 => ( ord_less_eq_nat @ A2 @ ( inf_inf_nat @ B2 @ C ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.boundedI
% 0.32/0.48 thf(fact_266_inf_OboundedE,axiom,
% 0.32/0.48 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ A2 @ ( inf_in586391887at_nat @ B2 @ C ) )
% 0.32/0.48 => ~ ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.32/0.48 => ~ ( ord_le841296385at_nat @ A2 @ C ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.boundedE
% 0.32/0.48 thf(fact_267_inf_OboundedE,axiom,
% 0.32/0.48 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C ) )
% 0.32/0.48 => ~ ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.48 => ~ ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.boundedE
% 0.32/0.48 thf(fact_268_inf_OboundedE,axiom,
% 0.32/0.48 ! [A2: nat,B2: nat,C: nat] :
% 0.32/0.48 ( ( ord_less_eq_nat @ A2 @ ( inf_inf_nat @ B2 @ C ) )
% 0.32/0.48 => ~ ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.48 => ~ ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.boundedE
% 0.32/0.48 thf(fact_269_inf__absorb2,axiom,
% 0.32/0.48 ! [Y2: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ Y2 @ X2 )
% 0.32/0.48 => ( ( inf_in586391887at_nat @ X2 @ Y2 )
% 0.32/0.48 = Y2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_absorb2
% 0.32/0.48 thf(fact_270_inf__absorb2,axiom,
% 0.32/0.48 ! [Y2: set_nat,X2: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ Y2 @ X2 )
% 0.32/0.48 => ( ( inf_inf_set_nat @ X2 @ Y2 )
% 0.32/0.48 = Y2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_absorb2
% 0.32/0.48 thf(fact_271_inf__absorb2,axiom,
% 0.32/0.48 ! [Y2: nat,X2: nat] :
% 0.32/0.48 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.32/0.48 => ( ( inf_inf_nat @ X2 @ Y2 )
% 0.32/0.48 = Y2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_absorb2
% 0.32/0.48 thf(fact_272_inf__absorb1,axiom,
% 0.32/0.48 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ X2 @ Y2 )
% 0.32/0.48 => ( ( inf_in586391887at_nat @ X2 @ Y2 )
% 0.32/0.48 = X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_absorb1
% 0.32/0.48 thf(fact_273_inf__absorb1,axiom,
% 0.32/0.48 ! [X2: set_nat,Y2: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 0.32/0.48 => ( ( inf_inf_set_nat @ X2 @ Y2 )
% 0.32/0.48 = X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_absorb1
% 0.32/0.48 thf(fact_274_inf__absorb1,axiom,
% 0.32/0.48 ! [X2: nat,Y2: nat] :
% 0.32/0.48 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.32/0.48 => ( ( inf_inf_nat @ X2 @ Y2 )
% 0.32/0.48 = X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_absorb1
% 0.32/0.48 thf(fact_275_inf_Oabsorb2,axiom,
% 0.32/0.48 ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ B2 @ A2 )
% 0.32/0.48 => ( ( inf_in586391887at_nat @ A2 @ B2 )
% 0.32/0.48 = B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.absorb2
% 0.32/0.48 thf(fact_276_inf_Oabsorb2,axiom,
% 0.32/0.48 ! [B2: set_nat,A2: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.32/0.48 => ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.32/0.48 = B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.absorb2
% 0.32/0.48 thf(fact_277_inf_Oabsorb2,axiom,
% 0.32/0.48 ! [B2: nat,A2: nat] :
% 0.32/0.48 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.32/0.48 => ( ( inf_inf_nat @ A2 @ B2 )
% 0.32/0.48 = B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.absorb2
% 0.32/0.48 thf(fact_278_inf_Oabsorb1,axiom,
% 0.32/0.48 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.32/0.48 => ( ( inf_in586391887at_nat @ A2 @ B2 )
% 0.32/0.48 = A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.absorb1
% 0.32/0.48 thf(fact_279_inf_Oabsorb1,axiom,
% 0.32/0.48 ! [A2: set_nat,B2: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.48 => ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.32/0.48 = A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.absorb1
% 0.32/0.48 thf(fact_280_inf_Oabsorb1,axiom,
% 0.32/0.48 ! [A2: nat,B2: nat] :
% 0.32/0.48 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.48 => ( ( inf_inf_nat @ A2 @ B2 )
% 0.32/0.48 = A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.absorb1
% 0.32/0.48 thf(fact_281_le__iff__inf,axiom,
% 0.32/0.48 ( ord_le841296385at_nat
% 0.32/0.48 = ( ^ [X3: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( inf_in586391887at_nat @ X3 @ Y3 )
% 0.32/0.48 = X3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_iff_inf
% 0.32/0.48 thf(fact_282_le__iff__inf,axiom,
% 0.32/0.48 ( ord_less_eq_set_nat
% 0.32/0.48 = ( ^ [X3: set_nat,Y3: set_nat] :
% 0.32/0.48 ( ( inf_inf_set_nat @ X3 @ Y3 )
% 0.32/0.48 = X3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_iff_inf
% 0.32/0.48 thf(fact_283_le__iff__inf,axiom,
% 0.32/0.48 ( ord_less_eq_nat
% 0.32/0.48 = ( ^ [X3: nat,Y3: nat] :
% 0.32/0.48 ( ( inf_inf_nat @ X3 @ Y3 )
% 0.32/0.48 = X3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_iff_inf
% 0.32/0.48 thf(fact_284_inf__unique,axiom,
% 0.32/0.48 ! [F: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( F @ X @ Y4 ) @ X )
% 0.32/0.48 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( F @ X @ Y4 ) @ Y4 )
% 0.32/0.48 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat,Z3: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ X @ Y4 )
% 0.32/0.48 => ( ( ord_le841296385at_nat @ X @ Z3 )
% 0.32/0.48 => ( ord_le841296385at_nat @ X @ ( F @ Y4 @ Z3 ) ) ) )
% 0.32/0.48 => ( ( inf_in586391887at_nat @ X2 @ Y2 )
% 0.32/0.48 = ( F @ X2 @ Y2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_unique
% 0.32/0.48 thf(fact_285_inf__unique,axiom,
% 0.32/0.48 ! [F: set_nat > set_nat > set_nat,X2: set_nat,Y2: set_nat] :
% 0.32/0.48 ( ! [X: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ ( F @ X @ Y4 ) @ X )
% 0.32/0.48 => ( ! [X: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ ( F @ X @ Y4 ) @ Y4 )
% 0.32/0.48 => ( ! [X: set_nat,Y4: set_nat,Z3: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 0.32/0.48 => ( ( ord_less_eq_set_nat @ X @ Z3 )
% 0.32/0.48 => ( ord_less_eq_set_nat @ X @ ( F @ Y4 @ Z3 ) ) ) )
% 0.32/0.48 => ( ( inf_inf_set_nat @ X2 @ Y2 )
% 0.32/0.48 = ( F @ X2 @ Y2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_unique
% 0.32/0.48 thf(fact_286_inf__unique,axiom,
% 0.32/0.48 ! [F: nat > nat > nat,X2: nat,Y2: nat] :
% 0.32/0.48 ( ! [X: nat,Y4: nat] : ( ord_less_eq_nat @ ( F @ X @ Y4 ) @ X )
% 0.32/0.48 => ( ! [X: nat,Y4: nat] : ( ord_less_eq_nat @ ( F @ X @ Y4 ) @ Y4 )
% 0.32/0.48 => ( ! [X: nat,Y4: nat,Z3: nat] :
% 0.32/0.48 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.32/0.48 => ( ( ord_less_eq_nat @ X @ Z3 )
% 0.32/0.48 => ( ord_less_eq_nat @ X @ ( F @ Y4 @ Z3 ) ) ) )
% 0.32/0.48 => ( ( inf_inf_nat @ X2 @ Y2 )
% 0.32/0.48 = ( F @ X2 @ Y2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_unique
% 0.32/0.48 thf(fact_287_inf_OorderI,axiom,
% 0.32/0.48 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( A2
% 0.32/0.48 = ( inf_in586391887at_nat @ A2 @ B2 ) )
% 0.32/0.48 => ( ord_le841296385at_nat @ A2 @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.orderI
% 0.32/0.48 thf(fact_288_inf_OorderI,axiom,
% 0.32/0.48 ! [A2: set_nat,B2: set_nat] :
% 0.32/0.48 ( ( A2
% 0.32/0.48 = ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.32/0.48 => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.orderI
% 0.32/0.48 thf(fact_289_inf_OorderI,axiom,
% 0.32/0.48 ! [A2: nat,B2: nat] :
% 0.32/0.48 ( ( A2
% 0.32/0.48 = ( inf_inf_nat @ A2 @ B2 ) )
% 0.32/0.48 => ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.orderI
% 0.32/0.48 thf(fact_290_inf_OorderE,axiom,
% 0.32/0.48 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 0.32/0.48 => ( A2
% 0.32/0.48 = ( inf_in586391887at_nat @ A2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.orderE
% 0.32/0.48 thf(fact_291_inf_OorderE,axiom,
% 0.32/0.48 ! [A2: set_nat,B2: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.32/0.48 => ( A2
% 0.32/0.48 = ( inf_inf_set_nat @ A2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.orderE
% 0.32/0.48 thf(fact_292_inf_OorderE,axiom,
% 0.32/0.48 ! [A2: nat,B2: nat] :
% 0.32/0.48 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.32/0.48 => ( A2
% 0.32/0.48 = ( inf_inf_nat @ A2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf.orderE
% 0.32/0.48 thf(fact_293_le__infI2,axiom,
% 0.32/0.48 ! [B2: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ B2 @ X2 )
% 0.32/0.48 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A2 @ B2 ) @ X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_infI2
% 0.32/0.48 thf(fact_294_le__infI2,axiom,
% 0.32/0.48 ! [B2: set_nat,X2: set_nat,A2: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ B2 @ X2 )
% 0.32/0.48 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_infI2
% 0.32/0.48 thf(fact_295_le__infI2,axiom,
% 0.32/0.48 ! [B2: nat,X2: nat,A2: nat] :
% 0.32/0.48 ( ( ord_less_eq_nat @ B2 @ X2 )
% 0.32/0.48 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_infI2
% 0.32/0.48 thf(fact_296_le__infI1,axiom,
% 0.32/0.48 ! [A2: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ A2 @ X2 )
% 0.32/0.48 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A2 @ B2 ) @ X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_infI1
% 0.32/0.48 thf(fact_297_le__infI1,axiom,
% 0.32/0.48 ! [A2: set_nat,X2: set_nat,B2: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ A2 @ X2 )
% 0.32/0.48 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_infI1
% 0.32/0.48 thf(fact_298_le__infI1,axiom,
% 0.32/0.48 ! [A2: nat,X2: nat,B2: nat] :
% 0.32/0.48 ( ( ord_less_eq_nat @ A2 @ X2 )
% 0.32/0.48 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_infI1
% 0.32/0.48 thf(fact_299_inf__mono,axiom,
% 0.32/0.48 ! [A2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,D2: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ A2 @ C )
% 0.32/0.48 => ( ( ord_le841296385at_nat @ B2 @ D2 )
% 0.32/0.48 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A2 @ B2 ) @ ( inf_in586391887at_nat @ C @ D2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_mono
% 0.32/0.48 thf(fact_300_inf__mono,axiom,
% 0.32/0.48 ! [A2: set_nat,C: set_nat,B2: set_nat,D2: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ A2 @ C )
% 0.32/0.48 => ( ( ord_less_eq_set_nat @ B2 @ D2 )
% 0.32/0.48 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ ( inf_inf_set_nat @ C @ D2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_mono
% 0.32/0.48 thf(fact_301_inf__mono,axiom,
% 0.32/0.48 ! [A2: nat,C: nat,B2: nat,D2: nat] :
% 0.32/0.48 ( ( ord_less_eq_nat @ A2 @ C )
% 0.32/0.48 => ( ( ord_less_eq_nat @ B2 @ D2 )
% 0.32/0.48 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ ( inf_inf_nat @ C @ D2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_mono
% 0.32/0.48 thf(fact_302_le__infI,axiom,
% 0.32/0.48 ! [X2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ X2 @ A2 )
% 0.32/0.48 => ( ( ord_le841296385at_nat @ X2 @ B2 )
% 0.32/0.48 => ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ A2 @ B2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_infI
% 0.32/0.48 thf(fact_303_le__infI,axiom,
% 0.32/0.48 ! [X2: set_nat,A2: set_nat,B2: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ X2 @ A2 )
% 0.32/0.48 => ( ( ord_less_eq_set_nat @ X2 @ B2 )
% 0.32/0.48 => ( ord_less_eq_set_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_infI
% 0.32/0.48 thf(fact_304_le__infI,axiom,
% 0.32/0.48 ! [X2: nat,A2: nat,B2: nat] :
% 0.32/0.48 ( ( ord_less_eq_nat @ X2 @ A2 )
% 0.32/0.48 => ( ( ord_less_eq_nat @ X2 @ B2 )
% 0.32/0.48 => ( ord_less_eq_nat @ X2 @ ( inf_inf_nat @ A2 @ B2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_infI
% 0.32/0.48 thf(fact_305_le__infE,axiom,
% 0.32/0.48 ! [X2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ A2 @ B2 ) )
% 0.32/0.48 => ~ ( ( ord_le841296385at_nat @ X2 @ A2 )
% 0.32/0.48 => ~ ( ord_le841296385at_nat @ X2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_infE
% 0.32/0.48 thf(fact_306_le__infE,axiom,
% 0.32/0.48 ! [X2: set_nat,A2: set_nat,B2: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.32/0.48 => ~ ( ( ord_less_eq_set_nat @ X2 @ A2 )
% 0.32/0.48 => ~ ( ord_less_eq_set_nat @ X2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_infE
% 0.32/0.48 thf(fact_307_le__infE,axiom,
% 0.32/0.48 ! [X2: nat,A2: nat,B2: nat] :
% 0.32/0.48 ( ( ord_less_eq_nat @ X2 @ ( inf_inf_nat @ A2 @ B2 ) )
% 0.32/0.48 => ~ ( ( ord_less_eq_nat @ X2 @ A2 )
% 0.32/0.48 => ~ ( ord_less_eq_nat @ X2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_infE
% 0.32/0.48 thf(fact_308_inf__le2,axiom,
% 0.32/0.48 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y2 ) @ Y2 ) ).
% 0.32/0.48
% 0.32/0.48 % inf_le2
% 0.32/0.48 thf(fact_309_inf__le2,axiom,
% 0.32/0.48 ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X2 @ Y2 ) @ Y2 ) ).
% 0.32/0.48
% 0.32/0.48 % inf_le2
% 0.32/0.48 thf(fact_310_inf__le2,axiom,
% 0.32/0.48 ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X2 @ Y2 ) @ Y2 ) ).
% 0.32/0.48
% 0.32/0.48 % inf_le2
% 0.32/0.48 thf(fact_311_inf__le1,axiom,
% 0.32/0.48 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y2 ) @ X2 ) ).
% 0.32/0.48
% 0.32/0.48 % inf_le1
% 0.32/0.48 thf(fact_312_inf__le1,axiom,
% 0.32/0.48 ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X2 @ Y2 ) @ X2 ) ).
% 0.32/0.48
% 0.32/0.48 % inf_le1
% 0.32/0.48 thf(fact_313_inf__le1,axiom,
% 0.32/0.48 ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X2 @ Y2 ) @ X2 ) ).
% 0.32/0.48
% 0.32/0.48 % inf_le1
% 0.32/0.48 thf(fact_314_inf__sup__ord_I1_J,axiom,
% 0.32/0.48 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y2 ) @ X2 ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_ord(1)
% 0.32/0.48 thf(fact_315_inf__sup__ord_I1_J,axiom,
% 0.32/0.48 ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X2 @ Y2 ) @ X2 ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_ord(1)
% 0.32/0.48 thf(fact_316_inf__sup__ord_I1_J,axiom,
% 0.32/0.48 ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X2 @ Y2 ) @ X2 ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_ord(1)
% 0.32/0.48 thf(fact_317_inf__sup__ord_I2_J,axiom,
% 0.32/0.48 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y2 ) @ Y2 ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_ord(2)
% 0.32/0.48 thf(fact_318_inf__sup__ord_I2_J,axiom,
% 0.32/0.48 ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X2 @ Y2 ) @ Y2 ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_ord(2)
% 0.32/0.48 thf(fact_319_inf__sup__ord_I2_J,axiom,
% 0.32/0.48 ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X2 @ Y2 ) @ Y2 ) ).
% 0.32/0.48
% 0.32/0.48 % inf_sup_ord(2)
% 0.32/0.48 thf(fact_320_rev__finite__subset,axiom,
% 0.32/0.48 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( finite772653738at_nat @ B )
% 0.32/0.48 => ( ( ord_le841296385at_nat @ A @ B )
% 0.32/0.48 => ( finite772653738at_nat @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rev_finite_subset
% 0.32/0.48 thf(fact_321_rev__finite__subset,axiom,
% 0.32/0.48 ! [B: set_nat,A: set_nat] :
% 0.32/0.48 ( ( finite_finite_nat @ B )
% 0.32/0.48 => ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.48 => ( finite_finite_nat @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rev_finite_subset
% 0.32/0.48 thf(fact_322_infinite__super,axiom,
% 0.32/0.48 ! [S2: set_Pr1986765409at_nat,T3: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ S2 @ T3 )
% 0.32/0.48 => ( ~ ( finite772653738at_nat @ S2 )
% 0.32/0.48 => ~ ( finite772653738at_nat @ T3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % infinite_super
% 0.32/0.48 thf(fact_323_infinite__super,axiom,
% 0.32/0.48 ! [S2: set_nat,T3: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.32/0.48 => ( ~ ( finite_finite_nat @ S2 )
% 0.32/0.48 => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % infinite_super
% 0.32/0.48 thf(fact_324_finite__subset,axiom,
% 0.32/0.48 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ A @ B )
% 0.32/0.48 => ( ( finite772653738at_nat @ B )
% 0.32/0.48 => ( finite772653738at_nat @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_subset
% 0.32/0.48 thf(fact_325_finite__subset,axiom,
% 0.32/0.48 ! [A: set_nat,B: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.48 => ( ( finite_finite_nat @ B )
% 0.32/0.48 => ( finite_finite_nat @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_subset
% 0.32/0.48 thf(fact_326_finite__list,axiom,
% 0.32/0.48 ! [A: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( finite772653738at_nat @ A )
% 0.32/0.48 => ? [Xs2: list_P559422087at_nat] :
% 0.32/0.48 ( ( set_Pr2131844118at_nat @ Xs2 )
% 0.32/0.48 = A ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_list
% 0.32/0.48 thf(fact_327_finite__list,axiom,
% 0.32/0.48 ! [A: set_nat] :
% 0.32/0.48 ( ( finite_finite_nat @ A )
% 0.32/0.48 => ? [Xs2: list_nat] :
% 0.32/0.48 ( ( set_nat2 @ Xs2 )
% 0.32/0.48 = A ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_list
% 0.32/0.48 thf(fact_328_subset__code_I1_J,axiom,
% 0.32/0.48 ! [Xs: list_P559422087at_nat,B: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ ( set_Pr2131844118at_nat @ Xs ) @ B )
% 0.32/0.48 = ( ! [X3: product_prod_nat_nat] :
% 0.32/0.48 ( ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ Xs ) )
% 0.32/0.48 => ( member701585322at_nat @ X3 @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subset_code(1)
% 0.32/0.48 thf(fact_329_subset__code_I1_J,axiom,
% 0.32/0.48 ! [Xs: list_nat,B: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B )
% 0.32/0.48 = ( ! [X3: nat] :
% 0.32/0.48 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.32/0.48 => ( member_nat @ X3 @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subset_code(1)
% 0.32/0.48 thf(fact_330_infinite__arbitrarily__large,axiom,
% 0.32/0.48 ! [A: set_Pr1986765409at_nat,N: nat] :
% 0.32/0.48 ( ~ ( finite772653738at_nat @ A )
% 0.32/0.48 => ? [B6: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( finite772653738at_nat @ B6 )
% 0.32/0.48 & ( ( finite447719721at_nat @ B6 )
% 0.32/0.48 = N )
% 0.32/0.48 & ( ord_le841296385at_nat @ B6 @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % infinite_arbitrarily_large
% 0.32/0.48 thf(fact_331_infinite__arbitrarily__large,axiom,
% 0.32/0.48 ! [A: set_nat,N: nat] :
% 0.32/0.48 ( ~ ( finite_finite_nat @ A )
% 0.32/0.48 => ? [B6: set_nat] :
% 0.32/0.48 ( ( finite_finite_nat @ B6 )
% 0.32/0.48 & ( ( finite_card_nat @ B6 )
% 0.32/0.48 = N )
% 0.32/0.48 & ( ord_less_eq_set_nat @ B6 @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % infinite_arbitrarily_large
% 0.32/0.48 thf(fact_332_card__subset__eq,axiom,
% 0.32/0.48 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( finite772653738at_nat @ B )
% 0.32/0.48 => ( ( ord_le841296385at_nat @ A @ B )
% 0.32/0.48 => ( ( ( finite447719721at_nat @ A )
% 0.32/0.48 = ( finite447719721at_nat @ B ) )
% 0.32/0.48 => ( A = B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % card_subset_eq
% 0.32/0.48 thf(fact_333_card__subset__eq,axiom,
% 0.32/0.48 ! [B: set_nat,A: set_nat] :
% 0.32/0.48 ( ( finite_finite_nat @ B )
% 0.32/0.48 => ( ( ord_less_eq_set_nat @ A @ B )
% 0.32/0.48 => ( ( ( finite_card_nat @ A )
% 0.32/0.48 = ( finite_card_nat @ B ) )
% 0.32/0.48 => ( A = B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % card_subset_eq
% 0.32/0.48 thf(fact_334_finite__if__finite__subsets__card__bdd,axiom,
% 0.32/0.48 ! [F2: set_Pr1986765409at_nat,C2: nat] :
% 0.32/0.48 ( ! [G2: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ G2 @ F2 )
% 0.32/0.48 => ( ( finite772653738at_nat @ G2 )
% 0.32/0.48 => ( ord_less_eq_nat @ ( finite447719721at_nat @ G2 ) @ C2 ) ) )
% 0.32/0.48 => ( ( finite772653738at_nat @ F2 )
% 0.32/0.48 & ( ord_less_eq_nat @ ( finite447719721at_nat @ F2 ) @ C2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_if_finite_subsets_card_bdd
% 0.32/0.48 thf(fact_335_finite__if__finite__subsets__card__bdd,axiom,
% 0.32/0.48 ! [F2: set_nat,C2: nat] :
% 0.32/0.48 ( ! [G2: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ G2 @ F2 )
% 0.32/0.48 => ( ( finite_finite_nat @ G2 )
% 0.32/0.48 => ( ord_less_eq_nat @ ( finite_card_nat @ G2 ) @ C2 ) ) )
% 0.32/0.48 => ( ( finite_finite_nat @ F2 )
% 0.32/0.48 & ( ord_less_eq_nat @ ( finite_card_nat @ F2 ) @ C2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_if_finite_subsets_card_bdd
% 0.32/0.48 thf(fact_336_pathVertices__edgeset,axiom,
% 0.32/0.48 ! [U2: nat,P: list_P559422087at_nat,V: nat] :
% 0.32/0.48 ( ( member_nat @ U2 @ ( v_a @ c ) )
% 0.32/0.48 => ( ( isPath_a @ c @ U2 @ P @ V )
% 0.32/0.48 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( pathVertices @ U2 @ P ) ) @ ( v_a @ c ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % pathVertices_edgeset
% 0.32/0.48 thf(fact_337_obtain__subset__with__card__n,axiom,
% 0.32/0.48 ! [N: nat,S2: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_less_eq_nat @ N @ ( finite447719721at_nat @ S2 ) )
% 0.32/0.48 => ~ ! [T4: set_Pr1986765409at_nat] :
% 0.32/0.48 ( ( ord_le841296385at_nat @ T4 @ S2 )
% 0.32/0.48 => ( ( ( finite447719721at_nat @ T4 )
% 0.32/0.48 = N )
% 0.32/0.48 => ~ ( finite772653738at_nat @ T4 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % obtain_subset_with_card_n
% 0.32/0.48 thf(fact_338_obtain__subset__with__card__n,axiom,
% 0.32/0.48 ! [N: nat,S2: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_nat @ N @ ( finite_card_nat @ S2 ) )
% 0.32/0.48 => ~ ! [T4: set_nat] :
% 0.32/0.48 ( ( ord_less_eq_set_nat @ T4 @ S2 )
% 0.32/0.48 => ( ( ( finite_card_nat @ T4 )
% 0.32/0.48 = N )
% 0.32/0.48 => ~ ( finite_finite_nat @ T4 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % obtain_subset_with_card_n
% 0.32/0.48 thf(fact_339_isPath_Osimps_I2_J,axiom,
% 0.32/0.48 ! [U2: nat,X2: nat,Y2: nat,P: list_P559422087at_nat,V: nat] :
% 0.32/0.48 ( ( isPath_a @ c @ U2 @ ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ P ) @ V )
% 0.32/0.48 = ( ( U2 = X2 )
% 0.32/0.48 & ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ ( e_a @ c ) )
% 0.32/0.48 & ( isPath_a @ c @ Y2 @ P @ V ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % isPath.simps(2)
% 0.32/0.48 thf(fact_340_isShortestPath__def,axiom,
% 0.32/0.48 ! [U2: nat,P: list_P559422087at_nat,V: nat] :
% 0.32/0.48 ( ( isShortestPath_a @ c @ U2 @ P @ V )
% 0.32/0.48 = ( ( isPath_a @ c @ U2 @ P @ V )
% 0.32/0.48 & ! [P3: list_P559422087at_nat] :
% 0.32/0.48 ( ( isPath_a @ c @ U2 @ P3 @ V )
% 0.32/0.48 => ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P ) @ ( size_s1990949619at_nat @ P3 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % isShortestPath_def
% 0.32/0.48 thf(fact_341_list_Oinject,axiom,
% 0.32/0.48 ! [X21: product_prod_nat_nat,X22: list_P559422087at_nat,Y21: product_prod_nat_nat,Y22: list_P559422087at_nat] :
% 0.32/0.48 ( ( ( cons_P66992567at_nat @ X21 @ X22 )
% 0.32/0.48 = ( cons_P66992567at_nat @ Y21 @ Y22 ) )
% 0.32/0.48 = ( ( X21 = Y21 )
% 0.32/0.48 & ( X22 = Y22 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % list.inject
% 0.32/0.48 thf(fact_342_impossible__Cons,axiom,
% 0.32/0.48 ! [Xs: list_P559422087at_nat,Ys: list_P559422087at_nat,X2: product_prod_nat_nat] :
% 0.32/0.48 ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ Xs ) @ ( size_s1990949619at_nat @ Ys ) )
% 0.32/0.48 => ( Xs
% 0.32/0.48 != ( cons_P66992567at_nat @ X2 @ Ys ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % impossible_Cons
% 0.32/0.48 thf(fact_343_list_Oset__cases,axiom,
% 0.32/0.48 ! [E: nat,A2: list_nat] :
% 0.32/0.48 ( ( member_nat @ E @ ( set_nat2 @ A2 ) )
% 0.32/0.48 => ( ! [Z22: list_nat] :
% 0.32/0.48 ( A2
% 0.32/0.48 != ( cons_nat @ E @ Z22 ) )
% 0.32/0.48 => ~ ! [Z1: nat,Z22: list_nat] :
% 0.32/0.48 ( ( A2
% 0.32/0.48 = ( cons_nat @ Z1 @ Z22 ) )
% 0.32/0.48 => ~ ( member_nat @ E @ ( set_nat2 @ Z22 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % list.set_cases
% 0.32/0.48 thf(fact_344_list_Oset__cases,axiom,
% 0.32/0.48 ! [E: product_prod_nat_nat,A2: list_P559422087at_nat] :
% 0.32/0.48 ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ A2 ) )
% 0.32/0.48 => ( ! [Z22: list_P559422087at_nat] :
% 0.32/0.48 ( A2
% 0.32/0.48 != ( cons_P66992567at_nat @ E @ Z22 ) )
% 0.32/0.48 => ~ ! [Z1: product_prod_nat_nat,Z22: list_P559422087at_nat] :
% 0.32/0.48 ( ( A2
% 0.32/0.48 = ( cons_P66992567at_nat @ Z1 @ Z22 ) )
% 0.32/0.48 => ~ ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ Z22 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % list.set_cases
% 0.32/0.48 thf(fact_345_bounded__Max__nat,axiom,
% 0.32/0.48 ! [P2: nat > $o,X2: nat,M: nat] :
% 0.32/0.48 ( ( P2 @ X2 )
% 0.32/0.48 => ( ! [X: nat] :
% 0.32/0.48 ( ( P2 @ X )
% 0.32/0.48 => ( ord_less_eq_nat @ X @ M ) )
% 0.32/0.48 => ~ ! [M2: nat] :
% 0.32/0.48 ( ( P2 @ M2 )
% 0.32/0.48 => ~ ! [X4: nat] :
% 0.32/0.48 ( ( P2 @ X4 )
% 0.32/0.48 => ( ord_less_eq_nat @ X4 @ M2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bounded_Max_nat
% 0.32/0.48 thf(fact_346_finite__nat__set__iff__bounded__le,axiom,
% 0.32/0.48 ( finite_finite_nat
% 0.32/0.48 = ( ^ [N2: set_nat] :
% 0.32/0.48 ? [M3: nat] :
% 0.32/0.48 ! [X3: nat] :
% 0.32/0.48 ( ( member_nat @ X3 @ N2 )
% 0.32/0.48 => ( ord_less_eq_nat @ X3 @ M3 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_nat_set_iff_bounded_le
% 0.32/0.48 thf(fact_347_isPath_Oelims_I3_J,axiom,
% 0.32/0.48 ! [X2: nat,Xa2: list_P559422087at_nat,Xb: nat] :
% 0.32/0.48 ( ~ ( isPath_a @ c @ X2 @ Xa2 @ Xb )
% 0.32/0.48 => ( ( ( Xa2 = nil_Pr1308055047at_nat )
% 0.32/0.48 => ( X2 = Xb ) )
% 0.32/0.48 => ~ ! [X: nat,Y4: nat,P4: list_P559422087at_nat] :
% 0.32/0.48 ( ( Xa2
% 0.32/0.48 = ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ P4 ) )
% 0.32/0.48 => ( ( X2 = X )
% 0.32/0.48 & ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ ( e_a @ c ) )
% 0.32/0.48 & ( isPath_a @ c @ Y4 @ P4 @ Xb ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % isPath.elims(3)
% 0.32/0.48 thf(fact_348_isPath_Oelims_I2_J,axiom,
% 0.32/0.48 ! [X2: nat,Xa2: list_P559422087at_nat,Xb: nat] :
% 0.32/0.48 ( ( isPath_a @ c @ X2 @ Xa2 @ Xb )
% 0.32/0.48 => ( ( ( Xa2 = nil_Pr1308055047at_nat )
% 0.32/0.48 => ( X2 != Xb ) )
% 0.32/0.48 => ~ ! [X: nat,Y4: nat,P4: list_P559422087at_nat] :
% 0.32/0.48 ( ( Xa2
% 0.32/0.48 = ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ P4 ) )
% 0.32/0.48 => ~ ( ( X2 = X )
% 0.32/0.48 & ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ ( e_a @ c ) )
% 0.32/0.48 & ( isPath_a @ c @ Y4 @ P4 @ Xb ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % isPath.elims(2)
% 0.32/0.48 thf(fact_349_isPath_Osimps_I1_J,axiom,
% 0.32/0.48 ! [U2: nat,V: nat] :
% 0.32/0.48 ( ( isPath_a @ c @ U2 @ nil_Pr1308055047at_nat @ V )
% 0.32/0.48 = ( U2 = V ) ) ).
% 0.32/0.48
% 0.32/0.48 % isPath.simps(1)
% 0.32/0.48 thf(fact_350_isPath__fwd__cases,axiom,
% 0.32/0.48 ! [S: nat,P: list_P559422087at_nat,T: nat] :
% 0.32/0.48 ( ( isPath_a @ c @ S @ P @ T )
% 0.32/0.48 => ( ( ( P = nil_Pr1308055047at_nat )
% 0.32/0.48 => ( T != S ) )
% 0.32/0.48 => ~ ! [P5: list_P559422087at_nat,U3: nat] :
% 0.32/0.48 ( ( P
% 0.32/0.48 = ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ S @ U3 ) @ P5 ) )
% 0.32/0.48 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ S @ U3 ) @ ( e_a @ c ) )
% 0.32/0.48 => ~ ( isPath_a @ c @ U3 @ P5 @ T ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % isPath_fwd_cases
% 0.32/0.48 thf(fact_351_isPath_Oelims_I1_J,axiom,
% 0.32/0.48 ! [X2: nat,Xa2: list_P559422087at_nat,Xb: nat,Y2: $o] :
% 0.32/0.48 ( ( ( isPath_a @ c @ X2 @ Xa2 @ Xb )
% 0.32/0.48 = Y2 )
% 0.32/0.48 => ( ( ( Xa2 = nil_Pr1308055047at_nat )
% 0.32/0.48 => ( Y2
% 0.32/0.48 = ( X2 != Xb ) ) )
% 0.32/0.48 => ~ ! [X: nat,Y4: nat,P4: list_P559422087at_nat] :
% 0.32/0.48 ( ( Xa2
% 0.32/0.48 = ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ P4 ) )
% 0.32/0.48 => ( Y2
% 0.32/0.48 = ( ~ ( ( X2 = X )
% 0.32/0.48 & ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ ( e_a @ c ) )
% 0.32/0.48 & ( isPath_a @ c @ Y4 @ P4 @ Xb ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % isPath.elims(1)
% 0.32/0.48 thf(fact_352_Graph_OisPath_Oinduct,axiom,
% 0.32/0.48 ! [P2: nat > list_P559422087at_nat > nat > $o,A0: nat,A1: list_P559422087at_nat,A22: nat] :
% 0.32/0.48 ( ! [U3: nat,X_1: nat] : ( P2 @ U3 @ nil_Pr1308055047at_nat @ X_1 )
% 0.32/0.48 => ( ! [U3: nat,X: nat,Y4: nat,P4: list_P559422087at_nat,V3: nat] :
% 0.32/0.48 ( ( P2 @ Y4 @ P4 @ V3 )
% 0.32/0.48 => ( P2 @ U3 @ ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ P4 ) @ V3 ) )
% 0.32/0.48 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Graph.isPath.induct
% 0.32/0.48
% 0.32/0.48 % Conjectures (1)
% 0.32/0.48 thf(conj_0,conjecture,
% 0.32/0.48 ord_le841296385at_nat @ edges @ ( e_a @ c ) ).
% 0.32/0.48
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 ------------------------
% 2.42/1.59 ---- Embedded in THF ---
% 2.42/1.59 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.42/1.59 %%% Generated on Tue Feb 24 08:25:21 EST 2026
% 2.42/1.59 %%% using '$$dhol' embedding, version 1.3.0.
% 2.42/1.59 %%% Logic specification used:
% 2.42/1.59 %%% thf(spec, logic, $$dhol).
% 2.42/1.59
% 2.42/1.59 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2DTF8264.p
% See solution above
% 2.42/1.59 ------------------------
% 2.64/1.63 ---- Cleaned THF ---
% 2.64/1.63 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.64/1.63 set_se1612935105at_nat: $tType ).
% 2.64/1.63
% 2.64/1.63 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.64/1.63 list_P559422087at_nat: $tType ).
% 2.64/1.63
% 2.64/1.63 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.64/1.63 set_Pr1986765409at_nat: $tType ).
% 2.64/1.63
% 2.64/1.63 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.64/1.63 product_prod_nat_nat: $tType ).
% 2.64/1.63
% 2.64/1.63 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 2.64/1.63 set_set_nat: $tType ).
% 2.64/1.63
% 2.64/1.63 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 2.64/1.63 list_nat: $tType ).
% 2.64/1.63
% 2.64/1.63 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 2.64/1.63 set_nat: $tType ).
% 2.64/1.63
% 2.64/1.63 thf(ty_n_t__Nat__Onat,type,
% 2.64/1.63 nat: $tType ).
% 2.64/1.63
% 2.64/1.63 thf(ty_n_tf__a,type,
% 2.64/1.63 a: $tType ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_EdmondsKarp__Termination__Abstract__Mirabelle__pndqeoznpl_Oek__analysis_001tf__a,type,
% 2.64/1.63 edmond1517640972ysis_a: ( product_prod_nat_nat > a ) > $o ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_EdmondsKarp__Termination__Abstract__Mirabelle__pndqeoznpl_Oek__analysis__defs_OspEdges_001tf__a,type,
% 2.64/1.63 edmond475474835dges_a: ( product_prod_nat_nat > a ) > nat > nat > set_Pr1986765409at_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_EdmondsKarp__Termination__Abstract__Mirabelle__pndqeoznpl_Oek__analysis__defs_OuE_001tf__a,type,
% 2.64/1.63 edmond771116670s_uE_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 2.64/1.63 finite_card_nat: set_nat > nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.64/1.63 finite447719721at_nat: set_Pr1986765409at_nat > nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 2.64/1.63 finite_finite_nat: set_nat > $o ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.64/1.63 finite772653738at_nat: set_Pr1986765409at_nat > $o ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.64/1.63 finite2012248349et_nat: set_set_nat > $o ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.64/1.63 finite1457549322at_nat: set_se1612935105at_nat > $o ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Graph_OFinite__Graph_001tf__a,type,
% 2.64/1.63 finite_Graph_a: ( product_prod_nat_nat > a ) > $o ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Graph_OGraph_OE_001tf__a,type,
% 2.64/1.63 e_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Graph_OGraph_OV_001tf__a,type,
% 2.64/1.63 v_a: ( product_prod_nat_nat > a ) > set_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Graph_OGraph_Oadjacent__nodes_001tf__a,type,
% 2.64/1.63 adjacent_nodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Graph_OGraph_Oincoming_001tf__a,type,
% 2.64/1.63 incoming_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Graph_OGraph_Oincoming_H_001tf__a,type,
% 2.64/1.63 incoming_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Graph_OGraph_OisPath_001tf__a,type,
% 2.64/1.63 isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Graph_OGraph_OisShortestPath_001tf__a,type,
% 2.64/1.63 isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Graph_OGraph_Ooutgoing_001tf__a,type,
% 2.64/1.63 outgoing_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Graph_OGraph_Ooutgoing_H_001tf__a,type,
% 2.64/1.63 outgoing_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Graph_OGraph_OpathVertices,type,
% 2.64/1.63 pathVertices: nat > list_P559422087at_nat > list_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Graph_OGraph_OreachableNodes_001tf__a,type,
% 2.64/1.63 reachableNodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 2.64/1.63 inf_inf_nat: nat > nat > nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.64/1.63 inf_inf_set_nat: set_nat > set_nat > set_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.64/1.63 inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 2.64/1.63 cons_nat: nat > list_nat > list_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.64/1.63 cons_P66992567at_nat: product_prod_nat_nat > list_P559422087at_nat > list_P559422087at_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.64/1.63 nil_Pr1308055047at_nat: list_P559422087at_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 2.64/1.63 set_nat2: list_nat > set_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.64/1.63 set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.64/1.63 size_s1990949619at_nat: list_P559422087at_nat > nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 2.64/1.63 ord_less_eq_nat: nat > nat > $o ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.64/1.63 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.64/1.63 ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.64/1.63 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 2.64/1.63 collect_nat: ( nat > $o ) > set_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.64/1.63 collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_member_001t__Nat__Onat,type,
% 2.64/1.63 member_nat: nat > set_nat > $o ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.64/1.63 member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.64/1.63 member_set_nat: set_nat > set_set_nat > $o ).
% 2.64/1.63
% 2.64/1.63 thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.64/1.63 member298845450at_nat: set_Pr1986765409at_nat > set_se1612935105at_nat > $o ).
% 2.64/1.63
% 2.64/1.63 thf(sy_v_c,type,
% 2.64/1.63 c: product_prod_nat_nat > a ).
% 2.64/1.63
% 2.64/1.63 thf(sy_v_edges,type,
% 2.64/1.63 edges: set_Pr1986765409at_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_v_p,type,
% 2.64/1.63 p: list_P559422087at_nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_v_s,type,
% 2.64/1.63 s: nat ).
% 2.64/1.63
% 2.64/1.63 thf(sy_v_t,type,
% 2.64/1.63 t: nat ).
% 2.64/1.63
% 2.64/1.63 thf(fact_0_SP,axiom,
% 2.64/1.63 isShortestPath_a @ c @ s @ p @ t ).
% 2.64/1.63
% 2.64/1.63 thf(fact_1_SP__EDGES,axiom,
% 2.64/1.63 ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_2_ek__analysis__axioms,axiom,
% 2.64/1.63 edmond1517640972ysis_a @ c ).
% 2.64/1.63
% 2.64/1.63 thf(fact_3_incoming_H__edges,axiom,
% 2.64/1.63 ! [U: set_nat] : ( ord_le841296385at_nat @ ( incoming_a2 @ c @ U ) @ ( e_a @ c ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_4_outgoing_H__edges,axiom,
% 2.64/1.63 ! [U: set_nat] : ( ord_le841296385at_nat @ ( outgoing_a2 @ c @ U ) @ ( e_a @ c ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_5_E__ss__uE,axiom,
% 2.64/1.63 ord_le841296385at_nat @ ( e_a @ c ) @ ( edmond771116670s_uE_a @ c ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_6_incoming__edges,axiom,
% 2.64/1.63 ! [U2: nat] : ( ord_le841296385at_nat @ ( incoming_a @ c @ U2 ) @ ( e_a @ c ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_7_outgoing__edges,axiom,
% 2.64/1.63 ! [U2: nat] : ( ord_le841296385at_nat @ ( outgoing_a @ c @ U2 ) @ ( e_a @ c ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_8_Finite__Graph__axioms,axiom,
% 2.64/1.63 finite_Graph_a @ c ).
% 2.64/1.63
% 2.64/1.63 thf(fact_9_subsetI,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ! [X: product_prod_nat_nat] :
% 2.64/1.63 ( ( member701585322at_nat @ X @ A )
% 2.64/1.63 => ( member701585322at_nat @ X @ B ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ A @ B ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_10_subsetI,axiom,
% 2.64/1.63 ! [A: set_nat,B: set_nat] :
% 2.64/1.63 ( ! [X: nat] :
% 2.64/1.63 ( ( member_nat @ X @ A )
% 2.64/1.63 => ( member_nat @ X @ B ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_11_subset__antisym,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A @ B )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ B @ A )
% 2.64/1.63 => ( A = B ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_12_subset__antisym,axiom,
% 2.64/1.63 ! [A: set_nat,B: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A @ B )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ B @ A )
% 2.64/1.63 => ( A = B ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_13_order__refl,axiom,
% 2.64/1.63 ! [X2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ X2 @ X2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_14_order__refl,axiom,
% 2.64/1.63 ! [X2: set_nat] : ( ord_less_eq_set_nat @ X2 @ X2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_15_order__refl,axiom,
% 2.64/1.63 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_16_SV,axiom,
% 2.64/1.63 member_nat @ s @ ( v_a @ c ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_17_spEdges__ss__E,axiom,
% 2.64/1.63 ord_le841296385at_nat @ ( edmond475474835dges_a @ c @ s @ t ) @ ( e_a @ c ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_18_isPath__edgeset,axiom,
% 2.64/1.63 ! [U2: nat,P: list_P559422087at_nat,V: nat,E: product_prod_nat_nat] :
% 2.64/1.63 ( ( isPath_a @ c @ U2 @ P @ V )
% 2.64/1.63 => ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ P ) )
% 2.64/1.63 => ( member701585322at_nat @ E @ ( e_a @ c ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_19_shortestPath__is__path,axiom,
% 2.64/1.63 ! [U2: nat,P: list_P559422087at_nat,V: nat] :
% 2.64/1.63 ( ( isShortestPath_a @ c @ U2 @ P @ V )
% 2.64/1.63 => ( isPath_a @ c @ U2 @ P @ V ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_20_adjacent__nodes__ss__V,axiom,
% 2.64/1.63 ! [U2: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ c @ U2 ) @ ( v_a @ c ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_21_ek__analysis__def,axiom,
% 2.64/1.63 edmond1517640972ysis_a = finite_Graph_a ).
% 2.64/1.63
% 2.64/1.63 thf(fact_22_ek__analysis_Ointro,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a] :
% 2.64/1.63 ( ( finite_Graph_a @ C )
% 2.64/1.63 => ( edmond1517640972ysis_a @ C ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_23_ek__analysis_Oaxioms,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a] :
% 2.64/1.63 ( ( edmond1517640972ysis_a @ C )
% 2.64/1.63 => ( finite_Graph_a @ C ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_24_ek__analysis__defs_OspEdges_Ocong,axiom,
% 2.64/1.63 edmond475474835dges_a = edmond475474835dges_a ).
% 2.64/1.63
% 2.64/1.63 thf(fact_25_ek__analysis__defs_OuE_Ocong,axiom,
% 2.64/1.63 edmond771116670s_uE_a = edmond771116670s_uE_a ).
% 2.64/1.63
% 2.64/1.63 thf(fact_26_ek__analysis_OspEdges__ss__E,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,S: nat,T: nat] :
% 2.64/1.63 ( ( edmond1517640972ysis_a @ C )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( edmond475474835dges_a @ C @ S @ T ) @ ( e_a @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_27_ek__analysis_OE__ss__uE,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a] :
% 2.64/1.63 ( ( edmond1517640972ysis_a @ C )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( e_a @ C ) @ ( edmond771116670s_uE_a @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_28_dual__order_Oantisym,axiom,
% 2.64/1.63 ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ B2 @ A2 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.64/1.63 => ( A2 = B2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_29_dual__order_Oantisym,axiom,
% 2.64/1.63 ! [B2: set_nat,A2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.64/1.63 => ( A2 = B2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_30_dual__order_Oantisym,axiom,
% 2.64/1.63 ! [B2: nat,A2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.64/1.63 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.64/1.63 => ( A2 = B2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_31_dual__order_Oeq__iff,axiom,
% 2.64/1.63 ( ( ^ [Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] : ( Y = Z ) )
% 2.64/1.63 = ( ^ [A3: set_Pr1986765409at_nat,B3: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ B3 @ A3 )
% 2.64/1.63 & ( ord_le841296385at_nat @ A3 @ B3 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_32_dual__order_Oeq__iff,axiom,
% 2.64/1.63 ( ( ^ [Y: set_nat,Z: set_nat] : ( Y = Z ) )
% 2.64/1.63 = ( ^ [A3: set_nat,B3: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 2.64/1.63 & ( ord_less_eq_set_nat @ A3 @ B3 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_33_dual__order_Oeq__iff,axiom,
% 2.64/1.63 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 2.64/1.63 = ( ^ [A3: nat,B3: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ B3 @ A3 )
% 2.64/1.63 & ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_34_dual__order_Otrans,axiom,
% 2.64/1.63 ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ B2 @ A2 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ C @ B2 )
% 2.64/1.63 => ( ord_le841296385at_nat @ C @ A2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_35_dual__order_Otrans,axiom,
% 2.64/1.63 ! [B2: set_nat,A2: set_nat,C: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ C @ B2 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ C @ A2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_36_dual__order_Otrans,axiom,
% 2.64/1.63 ! [B2: nat,A2: nat,C: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.64/1.63 => ( ( ord_less_eq_nat @ C @ B2 )
% 2.64/1.63 => ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_37_linorder__wlog,axiom,
% 2.64/1.63 ! [P2: nat > nat > $o,A2: nat,B2: nat] :
% 2.64/1.63 ( ! [A4: nat,B4: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A4 @ B4 )
% 2.64/1.63 => ( P2 @ A4 @ B4 ) )
% 2.64/1.63 => ( ! [A4: nat,B4: nat] :
% 2.64/1.63 ( ( P2 @ B4 @ A4 )
% 2.64/1.63 => ( P2 @ A4 @ B4 ) )
% 2.64/1.63 => ( P2 @ A2 @ B2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_38_dual__order_Orefl,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A2 @ A2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_39_dual__order_Orefl,axiom,
% 2.64/1.63 ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ A2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_40_dual__order_Orefl,axiom,
% 2.64/1.63 ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_41_order__trans,axiom,
% 2.64/1.63 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat,Z2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X2 @ Y2 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ Y2 @ Z2 )
% 2.64/1.63 => ( ord_le841296385at_nat @ X2 @ Z2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_42_order__trans,axiom,
% 2.64/1.63 ! [X2: set_nat,Y2: set_nat,Z2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ Y2 @ Z2 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ X2 @ Z2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_43_order__trans,axiom,
% 2.64/1.63 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.64/1.63 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 2.64/1.63 => ( ord_less_eq_nat @ X2 @ Z2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_44_order__class_Oorder_Oantisym,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ B2 @ A2 )
% 2.64/1.63 => ( A2 = B2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_45_order__class_Oorder_Oantisym,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 2.64/1.63 => ( A2 = B2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_46_order__class_Oorder_Oantisym,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.64/1.63 => ( A2 = B2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_47_ord__le__eq__trans,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( B2 = C )
% 2.64/1.63 => ( ord_le841296385at_nat @ A2 @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_48_ord__le__eq__trans,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( B2 = C )
% 2.64/1.63 => ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_49_ord__le__eq__trans,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat,C: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( B2 = C )
% 2.64/1.63 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_50_ord__eq__le__trans,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( A2 = B2 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ B2 @ C )
% 2.64/1.63 => ( ord_le841296385at_nat @ A2 @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_51_ord__eq__le__trans,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.64/1.63 ( ( A2 = B2 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 2.64/1.63 => ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_52_ord__eq__le__trans,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat,C: nat] :
% 2.64/1.63 ( ( A2 = B2 )
% 2.64/1.63 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.64/1.63 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_53_order__class_Oorder_Oeq__iff,axiom,
% 2.64/1.63 ( ( ^ [Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] : ( Y = Z ) )
% 2.64/1.63 = ( ^ [A3: set_Pr1986765409at_nat,B3: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A3 @ B3 )
% 2.64/1.63 & ( ord_le841296385at_nat @ B3 @ A3 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_54_order__class_Oorder_Oeq__iff,axiom,
% 2.64/1.63 ( ( ^ [Y: set_nat,Z: set_nat] : ( Y = Z ) )
% 2.64/1.63 = ( ^ [A3: set_nat,B3: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 2.64/1.63 & ( ord_less_eq_set_nat @ B3 @ A3 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_55_order__class_Oorder_Oeq__iff,axiom,
% 2.64/1.63 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 2.64/1.63 = ( ^ [A3: nat,B3: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A3 @ B3 )
% 2.64/1.63 & ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_56_antisym__conv,axiom,
% 2.64/1.63 ! [Y2: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ Y2 @ X2 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ X2 @ Y2 )
% 2.64/1.63 = ( X2 = Y2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_57_antisym__conv,axiom,
% 2.64/1.63 ! [Y2: set_nat,X2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ Y2 @ X2 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 2.64/1.63 = ( X2 = Y2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_58_antisym__conv,axiom,
% 2.64/1.63 ! [Y2: nat,X2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 2.64/1.63 => ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.64/1.63 = ( X2 = Y2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_59_le__cases3,axiom,
% 2.64/1.63 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.64/1.63 ( ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.64/1.63 => ~ ( ord_less_eq_nat @ Y2 @ Z2 ) )
% 2.64/1.63 => ( ( ( ord_less_eq_nat @ Y2 @ X2 )
% 2.64/1.63 => ~ ( ord_less_eq_nat @ X2 @ Z2 ) )
% 2.64/1.63 => ( ( ( ord_less_eq_nat @ X2 @ Z2 )
% 2.64/1.63 => ~ ( ord_less_eq_nat @ Z2 @ Y2 ) )
% 2.64/1.63 => ( ( ( ord_less_eq_nat @ Z2 @ Y2 )
% 2.64/1.63 => ~ ( ord_less_eq_nat @ Y2 @ X2 ) )
% 2.64/1.63 => ( ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 2.64/1.63 => ~ ( ord_less_eq_nat @ Z2 @ X2 ) )
% 2.64/1.63 => ~ ( ( ord_less_eq_nat @ Z2 @ X2 )
% 2.64/1.63 => ~ ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_60_order_Otrans,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ B2 @ C )
% 2.64/1.63 => ( ord_le841296385at_nat @ A2 @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_61_order_Otrans,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 2.64/1.63 => ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_62_order_Otrans,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat,C: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.64/1.63 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_63_le__cases,axiom,
% 2.64/1.63 ! [X2: nat,Y2: nat] :
% 2.64/1.63 ( ~ ( ord_less_eq_nat @ X2 @ Y2 )
% 2.64/1.63 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_64_eq__refl,axiom,
% 2.64/1.63 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( X2 = Y2 )
% 2.64/1.63 => ( ord_le841296385at_nat @ X2 @ Y2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_65_eq__refl,axiom,
% 2.64/1.63 ! [X2: set_nat,Y2: set_nat] :
% 2.64/1.63 ( ( X2 = Y2 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ X2 @ Y2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_66_eq__refl,axiom,
% 2.64/1.63 ! [X2: nat,Y2: nat] :
% 2.64/1.63 ( ( X2 = Y2 )
% 2.64/1.63 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_67_linear,axiom,
% 2.64/1.63 ! [X2: nat,Y2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.64/1.63 | ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_68_antisym,axiom,
% 2.64/1.63 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X2 @ Y2 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ Y2 @ X2 )
% 2.64/1.63 => ( X2 = Y2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_69_antisym,axiom,
% 2.64/1.63 ! [X2: set_nat,Y2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ Y2 @ X2 )
% 2.64/1.63 => ( X2 = Y2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_70_antisym,axiom,
% 2.64/1.63 ! [X2: nat,Y2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.64/1.63 => ( ( ord_less_eq_nat @ Y2 @ X2 )
% 2.64/1.63 => ( X2 = Y2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_71_eq__iff,axiom,
% 2.64/1.63 ( ( ^ [Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] : ( Y = Z ) )
% 2.64/1.63 = ( ^ [X3: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X3 @ Y3 )
% 2.64/1.63 & ( ord_le841296385at_nat @ Y3 @ X3 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_72_eq__iff,axiom,
% 2.64/1.63 ( ( ^ [Y: set_nat,Z: set_nat] : ( Y = Z ) )
% 2.64/1.63 = ( ^ [X3: set_nat,Y3: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 2.64/1.63 & ( ord_less_eq_set_nat @ Y3 @ X3 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_73_eq__iff,axiom,
% 2.64/1.63 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 2.64/1.63 = ( ^ [X3: nat,Y3: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.64/1.63 & ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_74_ord__le__eq__subst,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ( F @ B2 )
% 2.64/1.63 = C )
% 2.64/1.63 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_75_ord__le__eq__subst,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > set_nat,C: set_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ( F @ B2 )
% 2.64/1.63 = C )
% 2.64/1.63 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_76_ord__le__eq__subst,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > nat,C: nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ( F @ B2 )
% 2.64/1.63 = C )
% 2.64/1.63 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_77_ord__le__eq__subst,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat,F: set_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ( F @ B2 )
% 2.64/1.63 = C )
% 2.64/1.63 => ( ! [X: set_nat,Y4: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_78_ord__le__eq__subst,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat,F: set_nat > set_nat,C: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ( F @ B2 )
% 2.64/1.63 = C )
% 2.64/1.63 => ( ! [X: set_nat,Y4: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_79_ord__le__eq__subst,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat,F: set_nat > nat,C: nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ( F @ B2 )
% 2.64/1.63 = C )
% 2.64/1.63 => ( ! [X: set_nat,Y4: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_80_ord__le__eq__subst,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat,F: nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ( F @ B2 )
% 2.64/1.63 = C )
% 2.64/1.63 => ( ! [X: nat,Y4: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_81_ord__le__eq__subst,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat,F: nat > set_nat,C: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ( F @ B2 )
% 2.64/1.63 = C )
% 2.64/1.63 => ( ! [X: nat,Y4: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_82_ord__le__eq__subst,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ( F @ B2 )
% 2.64/1.63 = C )
% 2.64/1.63 => ( ! [X: nat,Y4: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_83_ord__eq__le__subst,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( A2
% 2.64/1.63 = ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_84_ord__eq__le__subst,axiom,
% 2.64/1.63 ! [A2: set_nat,F: set_Pr1986765409at_nat > set_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( A2
% 2.64/1.63 = ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_85_ord__eq__le__subst,axiom,
% 2.64/1.63 ! [A2: nat,F: set_Pr1986765409at_nat > nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( A2
% 2.64/1.63 = ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_86_ord__eq__le__subst,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,F: set_nat > set_Pr1986765409at_nat,B2: set_nat,C: set_nat] :
% 2.64/1.63 ( ( A2
% 2.64/1.63 = ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: set_nat,Y4: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_87_ord__eq__le__subst,axiom,
% 2.64/1.63 ! [A2: set_nat,F: set_nat > set_nat,B2: set_nat,C: set_nat] :
% 2.64/1.63 ( ( A2
% 2.64/1.63 = ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: set_nat,Y4: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_88_ord__eq__le__subst,axiom,
% 2.64/1.63 ! [A2: nat,F: set_nat > nat,B2: set_nat,C: set_nat] :
% 2.64/1.63 ( ( A2
% 2.64/1.63 = ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: set_nat,Y4: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_89_ord__eq__le__subst,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,F: nat > set_Pr1986765409at_nat,B2: nat,C: nat] :
% 2.64/1.63 ( ( A2
% 2.64/1.63 = ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: nat,Y4: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_90_ord__eq__le__subst,axiom,
% 2.64/1.63 ! [A2: set_nat,F: nat > set_nat,B2: nat,C: nat] :
% 2.64/1.63 ( ( A2
% 2.64/1.63 = ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: nat,Y4: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_91_ord__eq__le__subst,axiom,
% 2.64/1.63 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 2.64/1.63 ( ( A2
% 2.64/1.63 = ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: nat,Y4: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_92_order__subst2,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ ( F @ B2 ) @ C )
% 2.64/1.63 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_93_order__subst2,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > set_nat,C: set_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ ( F @ B2 ) @ C )
% 2.64/1.63 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_94_order__subst2,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > nat,C: nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 2.64/1.63 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_95_order__subst2,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat,F: set_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ ( F @ B2 ) @ C )
% 2.64/1.63 => ( ! [X: set_nat,Y4: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_96_order__subst2,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat,F: set_nat > set_nat,C: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ ( F @ B2 ) @ C )
% 2.64/1.63 => ( ! [X: set_nat,Y4: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_97_order__subst2,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat,F: set_nat > nat,C: nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 2.64/1.63 => ( ! [X: set_nat,Y4: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_98_order__subst2,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat,F: nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ ( F @ B2 ) @ C )
% 2.64/1.63 => ( ! [X: nat,Y4: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_99_order__subst2,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat,F: nat > set_nat,C: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ ( F @ B2 ) @ C )
% 2.64/1.63 => ( ! [X: nat,Y4: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_100_order__subst2,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 2.64/1.63 => ( ! [X: nat,Y4: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_101_mem__Collect__eq,axiom,
% 2.64/1.63 ! [A2: nat,P2: nat > $o] :
% 2.64/1.63 ( ( member_nat @ A2 @ ( collect_nat @ P2 ) )
% 2.64/1.63 = ( P2 @ A2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_102_mem__Collect__eq,axiom,
% 2.64/1.63 ! [A2: product_prod_nat_nat,P2: product_prod_nat_nat > $o] :
% 2.64/1.63 ( ( member701585322at_nat @ A2 @ ( collec7649004at_nat @ P2 ) )
% 2.64/1.63 = ( P2 @ A2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_103_Collect__mem__eq,axiom,
% 2.64/1.63 ! [A: set_nat] :
% 2.64/1.63 ( ( collect_nat
% 2.64/1.63 @ ^ [X3: nat] : ( member_nat @ X3 @ A ) )
% 2.64/1.63 = A ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_104_Collect__mem__eq,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( collec7649004at_nat
% 2.64/1.63 @ ^ [X3: product_prod_nat_nat] : ( member701585322at_nat @ X3 @ A ) )
% 2.64/1.63 = A ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_105_order__subst1,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat > set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_106_order__subst1,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,F: set_nat > set_Pr1986765409at_nat,B2: set_nat,C: set_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: set_nat,Y4: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_107_order__subst1,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,F: nat > set_Pr1986765409at_nat,B2: nat,C: nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: nat,Y4: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_108_order__subst1,axiom,
% 2.64/1.63 ! [A2: set_nat,F: set_Pr1986765409at_nat > set_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_109_order__subst1,axiom,
% 2.64/1.63 ! [A2: set_nat,F: set_nat > set_nat,B2: set_nat,C: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: set_nat,Y4: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_110_order__subst1,axiom,
% 2.64/1.63 ! [A2: set_nat,F: nat > set_nat,B2: nat,C: nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: nat,Y4: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_111_order__subst1,axiom,
% 2.64/1.63 ! [A2: nat,F: set_Pr1986765409at_nat > nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_112_order__subst1,axiom,
% 2.64/1.63 ! [A2: nat,F: set_nat > nat,B2: set_nat,C: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: set_nat,Y4: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_113_order__subst1,axiom,
% 2.64/1.63 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ ( F @ B2 ) )
% 2.64/1.63 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.64/1.63 => ( ! [X: nat,Y4: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.64/1.63 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_114_Collect__mono__iff,axiom,
% 2.64/1.63 ! [P2: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ ( collec7649004at_nat @ P2 ) @ ( collec7649004at_nat @ Q ) )
% 2.64/1.63 = ( ! [X3: product_prod_nat_nat] :
% 2.64/1.63 ( ( P2 @ X3 )
% 2.64/1.63 => ( Q @ X3 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_115_Collect__mono__iff,axiom,
% 2.64/1.63 ! [P2: nat > $o,Q: nat > $o] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q ) )
% 2.64/1.63 = ( ! [X3: nat] :
% 2.64/1.63 ( ( P2 @ X3 )
% 2.64/1.63 => ( Q @ X3 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_116_set__eq__subset,axiom,
% 2.64/1.63 ( ( ^ [Y: set_Pr1986765409at_nat,Z: set_Pr1986765409at_nat] : ( Y = Z ) )
% 2.64/1.63 = ( ^ [A5: set_Pr1986765409at_nat,B5: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A5 @ B5 )
% 2.64/1.63 & ( ord_le841296385at_nat @ B5 @ A5 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_117_set__eq__subset,axiom,
% 2.64/1.63 ( ( ^ [Y: set_nat,Z: set_nat] : ( Y = Z ) )
% 2.64/1.63 = ( ^ [A5: set_nat,B5: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A5 @ B5 )
% 2.64/1.63 & ( ord_less_eq_set_nat @ B5 @ A5 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_118_subset__trans,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A @ B )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ B @ C2 )
% 2.64/1.63 => ( ord_le841296385at_nat @ A @ C2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_119_subset__trans,axiom,
% 2.64/1.63 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A @ B )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_120_Collect__mono,axiom,
% 2.64/1.63 ! [P2: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 2.64/1.63 ( ! [X: product_prod_nat_nat] :
% 2.64/1.63 ( ( P2 @ X )
% 2.64/1.63 => ( Q @ X ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( collec7649004at_nat @ P2 ) @ ( collec7649004at_nat @ Q ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_121_Collect__mono,axiom,
% 2.64/1.63 ! [P2: nat > $o,Q: nat > $o] :
% 2.64/1.63 ( ! [X: nat] :
% 2.64/1.63 ( ( P2 @ X )
% 2.64/1.63 => ( Q @ X ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_122_subset__refl,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_123_subset__refl,axiom,
% 2.64/1.63 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_124_subset__iff,axiom,
% 2.64/1.63 ( ord_le841296385at_nat
% 2.64/1.63 = ( ^ [A5: set_Pr1986765409at_nat,B5: set_Pr1986765409at_nat] :
% 2.64/1.63 ! [T2: product_prod_nat_nat] :
% 2.64/1.63 ( ( member701585322at_nat @ T2 @ A5 )
% 2.64/1.63 => ( member701585322at_nat @ T2 @ B5 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_125_subset__iff,axiom,
% 2.64/1.63 ( ord_less_eq_set_nat
% 2.64/1.63 = ( ^ [A5: set_nat,B5: set_nat] :
% 2.64/1.63 ! [T2: nat] :
% 2.64/1.63 ( ( member_nat @ T2 @ A5 )
% 2.64/1.63 => ( member_nat @ T2 @ B5 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_126_equalityD2,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( A = B )
% 2.64/1.63 => ( ord_le841296385at_nat @ B @ A ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_127_equalityD2,axiom,
% 2.64/1.63 ! [A: set_nat,B: set_nat] :
% 2.64/1.63 ( ( A = B )
% 2.64/1.63 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_128_equalityD1,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( A = B )
% 2.64/1.63 => ( ord_le841296385at_nat @ A @ B ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_129_equalityD1,axiom,
% 2.64/1.63 ! [A: set_nat,B: set_nat] :
% 2.64/1.63 ( ( A = B )
% 2.64/1.63 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_130_subset__eq,axiom,
% 2.64/1.63 ( ord_le841296385at_nat
% 2.64/1.63 = ( ^ [A5: set_Pr1986765409at_nat,B5: set_Pr1986765409at_nat] :
% 2.64/1.63 ! [X3: product_prod_nat_nat] :
% 2.64/1.63 ( ( member701585322at_nat @ X3 @ A5 )
% 2.64/1.63 => ( member701585322at_nat @ X3 @ B5 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_131_subset__eq,axiom,
% 2.64/1.63 ( ord_less_eq_set_nat
% 2.64/1.63 = ( ^ [A5: set_nat,B5: set_nat] :
% 2.64/1.63 ! [X3: nat] :
% 2.64/1.63 ( ( member_nat @ X3 @ A5 )
% 2.64/1.63 => ( member_nat @ X3 @ B5 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_132_equalityE,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( A = B )
% 2.64/1.63 => ~ ( ( ord_le841296385at_nat @ A @ B )
% 2.64/1.63 => ~ ( ord_le841296385at_nat @ B @ A ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_133_equalityE,axiom,
% 2.64/1.63 ! [A: set_nat,B: set_nat] :
% 2.64/1.63 ( ( A = B )
% 2.64/1.63 => ~ ( ( ord_less_eq_set_nat @ A @ B )
% 2.64/1.63 => ~ ( ord_less_eq_set_nat @ B @ A ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_134_subsetD,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A @ B )
% 2.64/1.63 => ( ( member701585322at_nat @ C @ A )
% 2.64/1.63 => ( member701585322at_nat @ C @ B ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_135_subsetD,axiom,
% 2.64/1.63 ! [A: set_nat,B: set_nat,C: nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A @ B )
% 2.64/1.63 => ( ( member_nat @ C @ A )
% 2.64/1.63 => ( member_nat @ C @ B ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_136_in__mono,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,X2: product_prod_nat_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A @ B )
% 2.64/1.63 => ( ( member701585322at_nat @ X2 @ A )
% 2.64/1.63 => ( member701585322at_nat @ X2 @ B ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_137_in__mono,axiom,
% 2.64/1.63 ! [A: set_nat,B: set_nat,X2: nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A @ B )
% 2.64/1.63 => ( ( member_nat @ X2 @ A )
% 2.64/1.63 => ( member_nat @ X2 @ B ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_138_reachable__ss__V,axiom,
% 2.64/1.63 ! [S: nat] :
% 2.64/1.63 ( ( member_nat @ S @ ( v_a @ c ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( reachableNodes_a @ c @ S ) @ ( v_a @ c ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_139_transfer__path,axiom,
% 2.64/1.63 ! [P: list_P559422087at_nat,C3: product_prod_nat_nat > a,U2: nat,V: nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ P ) @ ( e_a @ c ) ) @ ( e_a @ C3 ) )
% 2.64/1.63 => ( ( isPath_a @ c @ U2 @ P @ V )
% 2.64/1.63 => ( isPath_a @ C3 @ U2 @ P @ V ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_140_card__spEdges__le,axiom,
% 2.64/1.63 ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ c ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_141_Finite__Graph__EI,axiom,
% 2.64/1.63 ( ( finite772653738at_nat @ ( e_a @ c ) )
% 2.64/1.63 => ( finite_Graph_a @ c ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_142_Graph_Oincoming_H__edges,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,U: set_nat] : ( ord_le841296385at_nat @ ( incoming_a2 @ C @ U ) @ ( e_a @ C ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_143_Graph_Ooutgoing_H__edges,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,U: set_nat] : ( ord_le841296385at_nat @ ( outgoing_a2 @ C @ U ) @ ( e_a @ C ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_144_Graph_Oincoming__edges,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,U2: nat] : ( ord_le841296385at_nat @ ( incoming_a @ C @ U2 ) @ ( e_a @ C ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_145_Graph_Ooutgoing__edges,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,U2: nat] : ( ord_le841296385at_nat @ ( outgoing_a @ C @ U2 ) @ ( e_a @ C ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_146_Graph_OisPath__edgeset,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V: nat,E: product_prod_nat_nat] :
% 2.64/1.63 ( ( isPath_a @ C @ U2 @ P @ V )
% 2.64/1.63 => ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ P ) )
% 2.64/1.63 => ( member701585322at_nat @ E @ ( e_a @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_147_isPath__ex__edge2,axiom,
% 2.64/1.63 ! [U2: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat] :
% 2.64/1.63 ( ( isPath_a @ c @ U2 @ P @ V )
% 2.64/1.63 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 2.64/1.63 => ( ( V1 != V )
% 2.64/1.63 => ? [V2: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ V1 @ V2 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_148_IntI,axiom,
% 2.64/1.63 ! [C: nat,A: set_nat,B: set_nat] :
% 2.64/1.63 ( ( member_nat @ C @ A )
% 2.64/1.63 => ( ( member_nat @ C @ B )
% 2.64/1.63 => ( member_nat @ C @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_149_IntI,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( member701585322at_nat @ C @ A )
% 2.64/1.63 => ( ( member701585322at_nat @ C @ B )
% 2.64/1.63 => ( member701585322at_nat @ C @ ( inf_in586391887at_nat @ A @ B ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_150_Int__iff,axiom,
% 2.64/1.63 ! [C: nat,A: set_nat,B: set_nat] :
% 2.64/1.63 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B ) )
% 2.64/1.63 = ( ( member_nat @ C @ A )
% 2.64/1.63 & ( member_nat @ C @ B ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_151_Int__iff,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( member701585322at_nat @ C @ ( inf_in586391887at_nat @ A @ B ) )
% 2.64/1.63 = ( ( member701585322at_nat @ C @ A )
% 2.64/1.63 & ( member701585322at_nat @ C @ B ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_152_isPath__ex__edge1,axiom,
% 2.64/1.63 ! [U2: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat] :
% 2.64/1.63 ( ( isPath_a @ c @ U2 @ P @ V )
% 2.64/1.63 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 2.64/1.63 => ( ( U1 != U2 )
% 2.64/1.63 => ? [U22: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ U22 @ U1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_153_reachableNodes__append__edge,axiom,
% 2.64/1.63 ! [U2: nat,S: nat,V: nat] :
% 2.64/1.63 ( ( member_nat @ U2 @ ( reachableNodes_a @ c @ S ) )
% 2.64/1.63 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U2 @ V ) @ ( e_a @ c ) )
% 2.64/1.63 => ( member_nat @ V @ ( reachableNodes_a @ c @ S ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_154_Int__subset__iff,axiom,
% 2.64/1.63 ! [C2: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ C2 @ ( inf_in586391887at_nat @ A @ B ) )
% 2.64/1.63 = ( ( ord_le841296385at_nat @ C2 @ A )
% 2.64/1.63 & ( ord_le841296385at_nat @ C2 @ B ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_155_Int__subset__iff,axiom,
% 2.64/1.63 ! [C2: set_nat,A: set_nat,B: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ C2 @ ( inf_inf_set_nat @ A @ B ) )
% 2.64/1.63 = ( ( ord_less_eq_set_nat @ C2 @ A )
% 2.64/1.63 & ( ord_less_eq_set_nat @ C2 @ B ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_156_finite__E,axiom,
% 2.64/1.63 finite772653738at_nat @ ( e_a @ c ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_157_finite__uE,axiom,
% 2.64/1.63 finite772653738at_nat @ ( edmond771116670s_uE_a @ c ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_158_finite__spEdges,axiom,
% 2.64/1.63 finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_159_IntE,axiom,
% 2.64/1.63 ! [C: nat,A: set_nat,B: set_nat] :
% 2.64/1.63 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B ) )
% 2.64/1.63 => ~ ( ( member_nat @ C @ A )
% 2.64/1.63 => ~ ( member_nat @ C @ B ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_160_IntE,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( member701585322at_nat @ C @ ( inf_in586391887at_nat @ A @ B ) )
% 2.64/1.63 => ~ ( ( member701585322at_nat @ C @ A )
% 2.64/1.63 => ~ ( member701585322at_nat @ C @ B ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_161_IntD1,axiom,
% 2.64/1.63 ! [C: nat,A: set_nat,B: set_nat] :
% 2.64/1.63 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B ) )
% 2.64/1.63 => ( member_nat @ C @ A ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_162_IntD1,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( member701585322at_nat @ C @ ( inf_in586391887at_nat @ A @ B ) )
% 2.64/1.63 => ( member701585322at_nat @ C @ A ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_163_IntD2,axiom,
% 2.64/1.63 ! [C: nat,A: set_nat,B: set_nat] :
% 2.64/1.63 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B ) )
% 2.64/1.63 => ( member_nat @ C @ B ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_164_IntD2,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( member701585322at_nat @ C @ ( inf_in586391887at_nat @ A @ B ) )
% 2.64/1.63 => ( member701585322at_nat @ C @ B ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_165_Graph_OreachableNodes__append__edge,axiom,
% 2.64/1.63 ! [U2: nat,C: product_prod_nat_nat > a,S: nat,V: nat] :
% 2.64/1.63 ( ( member_nat @ U2 @ ( reachableNodes_a @ C @ S ) )
% 2.64/1.63 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U2 @ V ) @ ( e_a @ C ) )
% 2.64/1.63 => ( member_nat @ V @ ( reachableNodes_a @ C @ S ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_166_Graph_OreachableNodes_Ocong,axiom,
% 2.64/1.63 reachableNodes_a = reachableNodes_a ).
% 2.64/1.63
% 2.64/1.63 thf(fact_167_Graph_Oadjacent__nodes_Ocong,axiom,
% 2.64/1.63 adjacent_nodes_a = adjacent_nodes_a ).
% 2.64/1.63
% 2.64/1.63 thf(fact_168_Graph_Oreachable__ss__V,axiom,
% 2.64/1.63 ! [S: nat,C: product_prod_nat_nat > a] :
% 2.64/1.63 ( ( member_nat @ S @ ( v_a @ C ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( reachableNodes_a @ C @ S ) @ ( v_a @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_169_Int__mono,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat,C2: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A @ C2 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ B @ D )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ ( inf_in586391887at_nat @ C2 @ D ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_170_Int__mono,axiom,
% 2.64/1.63 ! [A: set_nat,C2: set_nat,B: set_nat,D: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A @ C2 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ B @ D )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ ( inf_inf_set_nat @ C2 @ D ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_171_Int__lower1,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ A ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_172_Int__lower1,axiom,
% 2.64/1.63 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ A ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_173_Int__lower2,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_174_Int__lower2,axiom,
% 2.64/1.63 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ B ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_175_Int__absorb1,axiom,
% 2.64/1.63 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ B @ A )
% 2.64/1.63 => ( ( inf_in586391887at_nat @ A @ B )
% 2.64/1.63 = B ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_176_Int__absorb1,axiom,
% 2.64/1.63 ! [B: set_nat,A: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ B @ A )
% 2.64/1.63 => ( ( inf_inf_set_nat @ A @ B )
% 2.64/1.63 = B ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_177_Int__absorb2,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A @ B )
% 2.64/1.63 => ( ( inf_in586391887at_nat @ A @ B )
% 2.64/1.63 = A ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_178_Int__absorb2,axiom,
% 2.64/1.63 ! [A: set_nat,B: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A @ B )
% 2.64/1.63 => ( ( inf_inf_set_nat @ A @ B )
% 2.64/1.63 = A ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_179_Int__greatest,axiom,
% 2.64/1.63 ! [C2: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ C2 @ A )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ C2 @ B )
% 2.64/1.63 => ( ord_le841296385at_nat @ C2 @ ( inf_in586391887at_nat @ A @ B ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_180_Int__greatest,axiom,
% 2.64/1.63 ! [C2: set_nat,A: set_nat,B: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ C2 @ A )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ C2 @ B )
% 2.64/1.63 => ( ord_less_eq_set_nat @ C2 @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_181_Int__Collect__mono,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,P2: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A @ B )
% 2.64/1.63 => ( ! [X: product_prod_nat_nat] :
% 2.64/1.63 ( ( member701585322at_nat @ X @ A )
% 2.64/1.63 => ( ( P2 @ X )
% 2.64/1.63 => ( Q @ X ) ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ ( collec7649004at_nat @ P2 ) ) @ ( inf_in586391887at_nat @ B @ ( collec7649004at_nat @ Q ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_182_Int__Collect__mono,axiom,
% 2.64/1.63 ! [A: set_nat,B: set_nat,P2: nat > $o,Q: nat > $o] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A @ B )
% 2.64/1.63 => ( ! [X: nat] :
% 2.64/1.63 ( ( member_nat @ X @ A )
% 2.64/1.63 => ( ( P2 @ X )
% 2.64/1.63 => ( Q @ X ) ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ ( collect_nat @ P2 ) ) @ ( inf_inf_set_nat @ B @ ( collect_nat @ Q ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_183_Graph_Oadjacent__nodes__ss__V,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,U2: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ C @ U2 ) @ ( v_a @ C ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_184_Graph_OisPath__ex__edge2,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat] :
% 2.64/1.63 ( ( isPath_a @ C @ U2 @ P @ V )
% 2.64/1.63 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 2.64/1.63 => ( ( V1 != V )
% 2.64/1.63 => ? [V2: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ V1 @ V2 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_185_Graph_OisPath__ex__edge1,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V: nat,U1: nat,V1: nat] :
% 2.64/1.63 ( ( isPath_a @ C @ U2 @ P @ V )
% 2.64/1.63 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ U1 @ V1 ) @ ( set_Pr2131844118at_nat @ P ) )
% 2.64/1.63 => ( ( U1 != U2 )
% 2.64/1.63 => ? [U22: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ U22 @ U1 ) @ ( set_Pr2131844118at_nat @ P ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_186_Graph_OFinite__Graph__EI,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a] :
% 2.64/1.63 ( ( finite772653738at_nat @ ( e_a @ C ) )
% 2.64/1.63 => ( finite_Graph_a @ C ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_187_Finite__Graph_Ofinite__E,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a] :
% 2.64/1.63 ( ( finite_Graph_a @ C )
% 2.64/1.63 => ( finite772653738at_nat @ ( e_a @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_188_ek__analysis_Ofinite__spEdges,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,S: nat,T: nat] :
% 2.64/1.63 ( ( edmond1517640972ysis_a @ C )
% 2.64/1.63 => ( finite772653738at_nat @ ( edmond475474835dges_a @ C @ S @ T ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_189_ek__analysis_Ofinite__uE,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a] :
% 2.64/1.63 ( ( edmond1517640972ysis_a @ C )
% 2.64/1.63 => ( finite772653738at_nat @ ( edmond771116670s_uE_a @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_190_Graph_Otransfer__path,axiom,
% 2.64/1.63 ! [P: list_P559422087at_nat,C: product_prod_nat_nat > a,C3: product_prod_nat_nat > a,U2: nat,V: nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ P ) @ ( e_a @ C ) ) @ ( e_a @ C3 ) )
% 2.64/1.63 => ( ( isPath_a @ C @ U2 @ P @ V )
% 2.64/1.63 => ( isPath_a @ C3 @ U2 @ P @ V ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_191_Graph_OE_Ocong,axiom,
% 2.64/1.63 e_a = e_a ).
% 2.64/1.63
% 2.64/1.63 thf(fact_192_Graph_OisPath_Ocong,axiom,
% 2.64/1.63 isPath_a = isPath_a ).
% 2.64/1.63
% 2.64/1.63 thf(fact_193_Graph_OV_Ocong,axiom,
% 2.64/1.63 v_a = v_a ).
% 2.64/1.63
% 2.64/1.63 thf(fact_194_ek__analysis_Ocard__spEdges__le,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,S: nat,T: nat] :
% 2.64/1.63 ( ( edmond1517640972ysis_a @ C )
% 2.64/1.63 => ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ C @ S @ T ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_195_Graph_OisShortestPath_Ocong,axiom,
% 2.64/1.63 isShortestPath_a = isShortestPath_a ).
% 2.64/1.63
% 2.64/1.63 thf(fact_196_Graph_Ooutgoing_Ocong,axiom,
% 2.64/1.63 outgoing_a = outgoing_a ).
% 2.64/1.63
% 2.64/1.63 thf(fact_197_Graph_Oincoming_Ocong,axiom,
% 2.64/1.63 incoming_a = incoming_a ).
% 2.64/1.63
% 2.64/1.63 thf(fact_198_Graph_Ooutgoing_H_Ocong,axiom,
% 2.64/1.63 outgoing_a2 = outgoing_a2 ).
% 2.64/1.63
% 2.64/1.63 thf(fact_199_Graph_Oincoming_H_Ocong,axiom,
% 2.64/1.63 incoming_a2 = incoming_a2 ).
% 2.64/1.63
% 2.64/1.63 thf(fact_200_Graph_OshortestPath__is__path,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V: nat] :
% 2.64/1.63 ( ( isShortestPath_a @ C @ U2 @ P @ V )
% 2.64/1.63 => ( isPath_a @ C @ U2 @ P @ V ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_201_finite__Int,axiom,
% 2.64/1.63 ! [F2: set_Pr1986765409at_nat,G: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ( finite772653738at_nat @ F2 )
% 2.64/1.63 | ( finite772653738at_nat @ G ) )
% 2.64/1.63 => ( finite772653738at_nat @ ( inf_in586391887at_nat @ F2 @ G ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_202_finite__Int,axiom,
% 2.64/1.63 ! [F2: set_nat,G: set_nat] :
% 2.64/1.63 ( ( ( finite_finite_nat @ F2 )
% 2.64/1.63 | ( finite_finite_nat @ G ) )
% 2.64/1.63 => ( finite_finite_nat @ ( inf_inf_set_nat @ F2 @ G ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_203_List_Ofinite__set,axiom,
% 2.64/1.63 ! [Xs: list_P559422087at_nat] : ( finite772653738at_nat @ ( set_Pr2131844118at_nat @ Xs ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_204_List_Ofinite__set,axiom,
% 2.64/1.63 ! [Xs: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_205_le__inf__iff,axiom,
% 2.64/1.63 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat,Z2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ Y2 @ Z2 ) )
% 2.64/1.63 = ( ( ord_le841296385at_nat @ X2 @ Y2 )
% 2.64/1.63 & ( ord_le841296385at_nat @ X2 @ Z2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_206_le__inf__iff,axiom,
% 2.64/1.63 ! [X2: set_nat,Y2: set_nat,Z2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X2 @ ( inf_inf_set_nat @ Y2 @ Z2 ) )
% 2.64/1.63 = ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 2.64/1.63 & ( ord_less_eq_set_nat @ X2 @ Z2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_207_le__inf__iff,axiom,
% 2.64/1.63 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X2 @ ( inf_inf_nat @ Y2 @ Z2 ) )
% 2.64/1.63 = ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.64/1.63 & ( ord_less_eq_nat @ X2 @ Z2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_208_inf_Obounded__iff,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ ( inf_in586391887at_nat @ B2 @ C ) )
% 2.64/1.63 = ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.64/1.63 & ( ord_le841296385at_nat @ A2 @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_209_inf_Obounded__iff,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C ) )
% 2.64/1.63 = ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.64/1.63 & ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_210_inf_Obounded__iff,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat,C: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ ( inf_inf_nat @ B2 @ C ) )
% 2.64/1.63 = ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.64/1.63 & ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_211_card__mono,axiom,
% 2.64/1.63 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( finite772653738at_nat @ B )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ A @ B )
% 2.64/1.63 => ( ord_less_eq_nat @ ( finite447719721at_nat @ A ) @ ( finite447719721at_nat @ B ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_212_card__mono,axiom,
% 2.64/1.63 ! [B: set_nat,A: set_nat] :
% 2.64/1.63 ( ( finite_finite_nat @ B )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ A @ B )
% 2.64/1.63 => ( ord_less_eq_nat @ ( finite_card_nat @ A ) @ ( finite_card_nat @ B ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_213_card__seteq,axiom,
% 2.64/1.63 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( finite772653738at_nat @ B )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ A @ B )
% 2.64/1.63 => ( ( ord_less_eq_nat @ ( finite447719721at_nat @ B ) @ ( finite447719721at_nat @ A ) )
% 2.64/1.63 => ( A = B ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_214_card__seteq,axiom,
% 2.64/1.63 ! [B: set_nat,A: set_nat] :
% 2.64/1.63 ( ( finite_finite_nat @ B )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ A @ B )
% 2.64/1.63 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B ) @ ( finite_card_nat @ A ) )
% 2.64/1.63 => ( A = B ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_215_Efin__imp__Vfin,axiom,
% 2.64/1.63 ( ( finite772653738at_nat @ ( e_a @ c ) )
% 2.64/1.63 => ( finite_finite_nat @ ( v_a @ c ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_216_finite__V,axiom,
% 2.64/1.63 finite_finite_nat @ ( v_a @ c ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_217_adjacent__nodes__finite,axiom,
% 2.64/1.63 ! [U2: nat] : ( finite_finite_nat @ ( adjacent_nodes_a @ c @ U2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_218_Vfin__imp__Efin,axiom,
% 2.64/1.63 ( ( finite_finite_nat @ ( v_a @ c ) )
% 2.64/1.63 => ( finite772653738at_nat @ ( e_a @ c ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_219_finite__incoming,axiom,
% 2.64/1.63 ! [U2: nat] :
% 2.64/1.63 ( ( finite_finite_nat @ ( v_a @ c ) )
% 2.64/1.63 => ( finite772653738at_nat @ ( incoming_a @ c @ U2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_220_finite__outgoing,axiom,
% 2.64/1.63 ! [U2: nat] :
% 2.64/1.63 ( ( finite_finite_nat @ ( v_a @ c ) )
% 2.64/1.63 => ( finite772653738at_nat @ ( outgoing_a @ c @ U2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_221_finite__incoming_H,axiom,
% 2.64/1.63 ! [U: set_nat] :
% 2.64/1.63 ( ( finite_finite_nat @ ( v_a @ c ) )
% 2.64/1.63 => ( finite772653738at_nat @ ( incoming_a2 @ c @ U ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_222_finite__outgoing_H,axiom,
% 2.64/1.63 ! [U: set_nat] :
% 2.64/1.63 ( ( finite_finite_nat @ ( v_a @ c ) )
% 2.64/1.63 => ( finite772653738at_nat @ ( outgoing_a2 @ c @ U ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_223_Finite__Graph__def,axiom,
% 2.64/1.63 ( finite_Graph_a
% 2.64/1.63 = ( ^ [C4: product_prod_nat_nat > a] : ( finite_finite_nat @ ( v_a @ C4 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_224_Finite__Graph_Ointro,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a] :
% 2.64/1.63 ( ( finite_finite_nat @ ( v_a @ C ) )
% 2.64/1.63 => ( finite_Graph_a @ C ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_225_Finite__Graph_Ofinite__V,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a] :
% 2.64/1.63 ( ( finite_Graph_a @ C )
% 2.64/1.63 => ( finite_finite_nat @ ( v_a @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_226_Finite__Graph_Oadjacent__nodes__finite,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,U2: nat] :
% 2.64/1.63 ( ( finite_Graph_a @ C )
% 2.64/1.63 => ( finite_finite_nat @ ( adjacent_nodes_a @ C @ U2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_227_Graph_OEfin__imp__Vfin,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a] :
% 2.64/1.63 ( ( finite772653738at_nat @ ( e_a @ C ) )
% 2.64/1.63 => ( finite_finite_nat @ ( v_a @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_228_Graph_OVfin__imp__Efin,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a] :
% 2.64/1.63 ( ( finite_finite_nat @ ( v_a @ C ) )
% 2.64/1.63 => ( finite772653738at_nat @ ( e_a @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_229_Graph_Ofinite__outgoing,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,U2: nat] :
% 2.64/1.63 ( ( finite_finite_nat @ ( v_a @ C ) )
% 2.64/1.63 => ( finite772653738at_nat @ ( outgoing_a @ C @ U2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_230_Graph_Ofinite__incoming,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,U2: nat] :
% 2.64/1.63 ( ( finite_finite_nat @ ( v_a @ C ) )
% 2.64/1.63 => ( finite772653738at_nat @ ( incoming_a @ C @ U2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_231_Graph_Ofinite__outgoing_H,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,U: set_nat] :
% 2.64/1.63 ( ( finite_finite_nat @ ( v_a @ C ) )
% 2.64/1.63 => ( finite772653738at_nat @ ( outgoing_a2 @ C @ U ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_232_Graph_Ofinite__incoming_H,axiom,
% 2.64/1.63 ! [C: product_prod_nat_nat > a,U: set_nat] :
% 2.64/1.63 ( ( finite_finite_nat @ ( v_a @ C ) )
% 2.64/1.63 => ( finite772653738at_nat @ ( incoming_a2 @ C @ U ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_233_finite__has__minimal2,axiom,
% 2.64/1.63 ! [A: set_se1612935105at_nat,A2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( finite1457549322at_nat @ A )
% 2.64/1.63 => ( ( member298845450at_nat @ A2 @ A )
% 2.64/1.63 => ? [X: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( member298845450at_nat @ X @ A )
% 2.64/1.63 & ( ord_le841296385at_nat @ X @ A2 )
% 2.64/1.63 & ! [Xa: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( member298845450at_nat @ Xa @ A )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ Xa @ X )
% 2.64/1.63 => ( X = Xa ) ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_234_finite__has__minimal2,axiom,
% 2.64/1.63 ! [A: set_set_nat,A2: set_nat] :
% 2.64/1.63 ( ( finite2012248349et_nat @ A )
% 2.64/1.63 => ( ( member_set_nat @ A2 @ A )
% 2.64/1.63 => ? [X: set_nat] :
% 2.64/1.63 ( ( member_set_nat @ X @ A )
% 2.64/1.63 & ( ord_less_eq_set_nat @ X @ A2 )
% 2.64/1.63 & ! [Xa: set_nat] :
% 2.64/1.63 ( ( member_set_nat @ Xa @ A )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ Xa @ X )
% 2.64/1.63 => ( X = Xa ) ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_235_finite__has__minimal2,axiom,
% 2.64/1.63 ! [A: set_nat,A2: nat] :
% 2.64/1.63 ( ( finite_finite_nat @ A )
% 2.64/1.63 => ( ( member_nat @ A2 @ A )
% 2.64/1.63 => ? [X: nat] :
% 2.64/1.63 ( ( member_nat @ X @ A )
% 2.64/1.63 & ( ord_less_eq_nat @ X @ A2 )
% 2.64/1.63 & ! [Xa: nat] :
% 2.64/1.63 ( ( member_nat @ Xa @ A )
% 2.64/1.63 => ( ( ord_less_eq_nat @ Xa @ X )
% 2.64/1.63 => ( X = Xa ) ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_236_finite__has__maximal2,axiom,
% 2.64/1.63 ! [A: set_se1612935105at_nat,A2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( finite1457549322at_nat @ A )
% 2.64/1.63 => ( ( member298845450at_nat @ A2 @ A )
% 2.64/1.63 => ? [X: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( member298845450at_nat @ X @ A )
% 2.64/1.63 & ( ord_le841296385at_nat @ A2 @ X )
% 2.64/1.63 & ! [Xa: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( member298845450at_nat @ Xa @ A )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ X @ Xa )
% 2.64/1.63 => ( X = Xa ) ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_237_finite__has__maximal2,axiom,
% 2.64/1.63 ! [A: set_set_nat,A2: set_nat] :
% 2.64/1.63 ( ( finite2012248349et_nat @ A )
% 2.64/1.63 => ( ( member_set_nat @ A2 @ A )
% 2.64/1.63 => ? [X: set_nat] :
% 2.64/1.63 ( ( member_set_nat @ X @ A )
% 2.64/1.63 & ( ord_less_eq_set_nat @ A2 @ X )
% 2.64/1.63 & ! [Xa: set_nat] :
% 2.64/1.63 ( ( member_set_nat @ Xa @ A )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ X @ Xa )
% 2.64/1.63 => ( X = Xa ) ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_238_finite__has__maximal2,axiom,
% 2.64/1.63 ! [A: set_nat,A2: nat] :
% 2.64/1.63 ( ( finite_finite_nat @ A )
% 2.64/1.63 => ( ( member_nat @ A2 @ A )
% 2.64/1.63 => ? [X: nat] :
% 2.64/1.63 ( ( member_nat @ X @ A )
% 2.64/1.63 & ( ord_less_eq_nat @ A2 @ X )
% 2.64/1.63 & ! [Xa: nat] :
% 2.64/1.63 ( ( member_nat @ Xa @ A )
% 2.64/1.63 => ( ( ord_less_eq_nat @ X @ Xa )
% 2.64/1.63 => ( X = Xa ) ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_239_inf_OcoboundedI2,axiom,
% 2.64/1.63 ! [B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ B2 @ C )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A2 @ B2 ) @ C ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_240_inf_OcoboundedI2,axiom,
% 2.64/1.63 ! [B2: set_nat,C: set_nat,A2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ B2 @ C )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ C ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_241_inf_OcoboundedI2,axiom,
% 2.64/1.63 ! [B2: nat,C: nat,A2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ B2 @ C )
% 2.64/1.63 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ C ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_242_inf_OcoboundedI1,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ C )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A2 @ B2 ) @ C ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_243_inf_OcoboundedI1,axiom,
% 2.64/1.63 ! [A2: set_nat,C: set_nat,B2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ C )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ C ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_244_inf_OcoboundedI1,axiom,
% 2.64/1.63 ! [A2: nat,C: nat,B2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ C )
% 2.64/1.63 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ C ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_245_inf_Oabsorb__iff2,axiom,
% 2.64/1.63 ( ord_le841296385at_nat
% 2.64/1.63 = ( ^ [B3: set_Pr1986765409at_nat,A3: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( inf_in586391887at_nat @ A3 @ B3 )
% 2.64/1.63 = B3 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_246_inf_Oabsorb__iff2,axiom,
% 2.64/1.63 ( ord_less_eq_set_nat
% 2.64/1.63 = ( ^ [B3: set_nat,A3: set_nat] :
% 2.64/1.63 ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.64/1.63 = B3 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_247_inf_Oabsorb__iff2,axiom,
% 2.64/1.63 ( ord_less_eq_nat
% 2.64/1.63 = ( ^ [B3: nat,A3: nat] :
% 2.64/1.63 ( ( inf_inf_nat @ A3 @ B3 )
% 2.64/1.63 = B3 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_248_inf_Oabsorb__iff1,axiom,
% 2.64/1.63 ( ord_le841296385at_nat
% 2.64/1.63 = ( ^ [A3: set_Pr1986765409at_nat,B3: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( inf_in586391887at_nat @ A3 @ B3 )
% 2.64/1.63 = A3 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_249_inf_Oabsorb__iff1,axiom,
% 2.64/1.63 ( ord_less_eq_set_nat
% 2.64/1.63 = ( ^ [A3: set_nat,B3: set_nat] :
% 2.64/1.63 ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.64/1.63 = A3 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_250_inf_Oabsorb__iff1,axiom,
% 2.64/1.63 ( ord_less_eq_nat
% 2.64/1.63 = ( ^ [A3: nat,B3: nat] :
% 2.64/1.63 ( ( inf_inf_nat @ A3 @ B3 )
% 2.64/1.63 = A3 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_251_inf_Ocobounded2,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A2 @ B2 ) @ B2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_252_inf_Ocobounded2,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ B2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_253_inf_Ocobounded2,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ B2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_254_inf_Ocobounded1,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A2 @ B2 ) @ A2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_255_inf_Ocobounded1,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ A2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_256_inf_Ocobounded1,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ A2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_257_inf_Oorder__iff,axiom,
% 2.64/1.63 ( ord_le841296385at_nat
% 2.64/1.63 = ( ^ [A3: set_Pr1986765409at_nat,B3: set_Pr1986765409at_nat] :
% 2.64/1.63 ( A3
% 2.64/1.63 = ( inf_in586391887at_nat @ A3 @ B3 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_258_inf_Oorder__iff,axiom,
% 2.64/1.63 ( ord_less_eq_set_nat
% 2.64/1.63 = ( ^ [A3: set_nat,B3: set_nat] :
% 2.64/1.63 ( A3
% 2.64/1.63 = ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_259_inf_Oorder__iff,axiom,
% 2.64/1.63 ( ord_less_eq_nat
% 2.64/1.63 = ( ^ [A3: nat,B3: nat] :
% 2.64/1.63 ( A3
% 2.64/1.63 = ( inf_inf_nat @ A3 @ B3 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_260_inf__greatest,axiom,
% 2.64/1.63 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat,Z2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X2 @ Y2 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ X2 @ Z2 )
% 2.64/1.63 => ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ Y2 @ Z2 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_261_inf__greatest,axiom,
% 2.64/1.63 ! [X2: set_nat,Y2: set_nat,Z2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ X2 @ Z2 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ X2 @ ( inf_inf_set_nat @ Y2 @ Z2 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_262_inf__greatest,axiom,
% 2.64/1.63 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.64/1.63 => ( ( ord_less_eq_nat @ X2 @ Z2 )
% 2.64/1.63 => ( ord_less_eq_nat @ X2 @ ( inf_inf_nat @ Y2 @ Z2 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_263_inf_OboundedI,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ A2 @ C )
% 2.64/1.63 => ( ord_le841296385at_nat @ A2 @ ( inf_in586391887at_nat @ B2 @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_264_inf_OboundedI,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ A2 @ C )
% 2.64/1.63 => ( ord_less_eq_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_265_inf_OboundedI,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat,C: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( ord_less_eq_nat @ A2 @ C )
% 2.64/1.63 => ( ord_less_eq_nat @ A2 @ ( inf_inf_nat @ B2 @ C ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_266_inf_OboundedE,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ ( inf_in586391887at_nat @ B2 @ C ) )
% 2.64/1.63 => ~ ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.64/1.63 => ~ ( ord_le841296385at_nat @ A2 @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_267_inf_OboundedE,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C ) )
% 2.64/1.63 => ~ ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.64/1.63 => ~ ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_268_inf_OboundedE,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat,C: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ ( inf_inf_nat @ B2 @ C ) )
% 2.64/1.63 => ~ ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.64/1.63 => ~ ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_269_inf__absorb2,axiom,
% 2.64/1.63 ! [Y2: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ Y2 @ X2 )
% 2.64/1.63 => ( ( inf_in586391887at_nat @ X2 @ Y2 )
% 2.64/1.63 = Y2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_270_inf__absorb2,axiom,
% 2.64/1.63 ! [Y2: set_nat,X2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ Y2 @ X2 )
% 2.64/1.63 => ( ( inf_inf_set_nat @ X2 @ Y2 )
% 2.64/1.63 = Y2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_271_inf__absorb2,axiom,
% 2.64/1.63 ! [Y2: nat,X2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 2.64/1.63 => ( ( inf_inf_nat @ X2 @ Y2 )
% 2.64/1.63 = Y2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_272_inf__absorb1,axiom,
% 2.64/1.63 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X2 @ Y2 )
% 2.64/1.63 => ( ( inf_in586391887at_nat @ X2 @ Y2 )
% 2.64/1.63 = X2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_273_inf__absorb1,axiom,
% 2.64/1.63 ! [X2: set_nat,Y2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 2.64/1.63 => ( ( inf_inf_set_nat @ X2 @ Y2 )
% 2.64/1.63 = X2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_274_inf__absorb1,axiom,
% 2.64/1.63 ! [X2: nat,Y2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.64/1.63 => ( ( inf_inf_nat @ X2 @ Y2 )
% 2.64/1.63 = X2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_275_inf_Oabsorb2,axiom,
% 2.64/1.63 ! [B2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ B2 @ A2 )
% 2.64/1.63 => ( ( inf_in586391887at_nat @ A2 @ B2 )
% 2.64/1.63 = B2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_276_inf_Oabsorb2,axiom,
% 2.64/1.63 ! [B2: set_nat,A2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 2.64/1.63 => ( ( inf_inf_set_nat @ A2 @ B2 )
% 2.64/1.63 = B2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_277_inf_Oabsorb2,axiom,
% 2.64/1.63 ! [B2: nat,A2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.64/1.63 => ( ( inf_inf_nat @ A2 @ B2 )
% 2.64/1.63 = B2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_278_inf_Oabsorb1,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( inf_in586391887at_nat @ A2 @ B2 )
% 2.64/1.63 = A2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_279_inf_Oabsorb1,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( inf_inf_set_nat @ A2 @ B2 )
% 2.64/1.63 = A2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_280_inf_Oabsorb1,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.64/1.63 => ( ( inf_inf_nat @ A2 @ B2 )
% 2.64/1.63 = A2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_281_le__iff__inf,axiom,
% 2.64/1.63 ( ord_le841296385at_nat
% 2.64/1.63 = ( ^ [X3: set_Pr1986765409at_nat,Y3: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( inf_in586391887at_nat @ X3 @ Y3 )
% 2.64/1.63 = X3 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_282_le__iff__inf,axiom,
% 2.64/1.63 ( ord_less_eq_set_nat
% 2.64/1.63 = ( ^ [X3: set_nat,Y3: set_nat] :
% 2.64/1.63 ( ( inf_inf_set_nat @ X3 @ Y3 )
% 2.64/1.63 = X3 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_283_le__iff__inf,axiom,
% 2.64/1.63 ( ord_less_eq_nat
% 2.64/1.63 = ( ^ [X3: nat,Y3: nat] :
% 2.64/1.63 ( ( inf_inf_nat @ X3 @ Y3 )
% 2.64/1.63 = X3 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_284_inf__unique,axiom,
% 2.64/1.63 ! [F: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( F @ X @ Y4 ) @ X )
% 2.64/1.63 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( F @ X @ Y4 ) @ Y4 )
% 2.64/1.63 => ( ! [X: set_Pr1986765409at_nat,Y4: set_Pr1986765409at_nat,Z3: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X @ Y4 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ X @ Z3 )
% 2.64/1.63 => ( ord_le841296385at_nat @ X @ ( F @ Y4 @ Z3 ) ) ) )
% 2.64/1.63 => ( ( inf_in586391887at_nat @ X2 @ Y2 )
% 2.64/1.63 = ( F @ X2 @ Y2 ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_285_inf__unique,axiom,
% 2.64/1.63 ! [F: set_nat > set_nat > set_nat,X2: set_nat,Y2: set_nat] :
% 2.64/1.63 ( ! [X: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ ( F @ X @ Y4 ) @ X )
% 2.64/1.63 => ( ! [X: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ ( F @ X @ Y4 ) @ Y4 )
% 2.64/1.63 => ( ! [X: set_nat,Y4: set_nat,Z3: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X @ Y4 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ X @ Z3 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ X @ ( F @ Y4 @ Z3 ) ) ) )
% 2.64/1.63 => ( ( inf_inf_set_nat @ X2 @ Y2 )
% 2.64/1.63 = ( F @ X2 @ Y2 ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_286_inf__unique,axiom,
% 2.64/1.63 ! [F: nat > nat > nat,X2: nat,Y2: nat] :
% 2.64/1.63 ( ! [X: nat,Y4: nat] : ( ord_less_eq_nat @ ( F @ X @ Y4 ) @ X )
% 2.64/1.63 => ( ! [X: nat,Y4: nat] : ( ord_less_eq_nat @ ( F @ X @ Y4 ) @ Y4 )
% 2.64/1.63 => ( ! [X: nat,Y4: nat,Z3: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.64/1.63 => ( ( ord_less_eq_nat @ X @ Z3 )
% 2.64/1.63 => ( ord_less_eq_nat @ X @ ( F @ Y4 @ Z3 ) ) ) )
% 2.64/1.63 => ( ( inf_inf_nat @ X2 @ Y2 )
% 2.64/1.63 = ( F @ X2 @ Y2 ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_287_inf_OorderI,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( A2
% 2.64/1.63 = ( inf_in586391887at_nat @ A2 @ B2 ) )
% 2.64/1.63 => ( ord_le841296385at_nat @ A2 @ B2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_288_inf_OorderI,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat] :
% 2.64/1.63 ( ( A2
% 2.64/1.63 = ( inf_inf_set_nat @ A2 @ B2 ) )
% 2.64/1.63 => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_289_inf_OorderI,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat] :
% 2.64/1.63 ( ( A2
% 2.64/1.63 = ( inf_inf_nat @ A2 @ B2 ) )
% 2.64/1.63 => ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_290_inf_OorderE,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ B2 )
% 2.64/1.63 => ( A2
% 2.64/1.63 = ( inf_in586391887at_nat @ A2 @ B2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_291_inf_OorderE,axiom,
% 2.64/1.63 ! [A2: set_nat,B2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.64/1.63 => ( A2
% 2.64/1.63 = ( inf_inf_set_nat @ A2 @ B2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_292_inf_OorderE,axiom,
% 2.64/1.63 ! [A2: nat,B2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.64/1.63 => ( A2
% 2.64/1.63 = ( inf_inf_nat @ A2 @ B2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_293_le__infI2,axiom,
% 2.64/1.63 ! [B2: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ B2 @ X2 )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A2 @ B2 ) @ X2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_294_le__infI2,axiom,
% 2.64/1.63 ! [B2: set_nat,X2: set_nat,A2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ B2 @ X2 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ X2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_295_le__infI2,axiom,
% 2.64/1.63 ! [B2: nat,X2: nat,A2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ B2 @ X2 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ X2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_296_le__infI1,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,X2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ X2 )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A2 @ B2 ) @ X2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_297_le__infI1,axiom,
% 2.64/1.63 ! [A2: set_nat,X2: set_nat,B2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ X2 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ X2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_298_le__infI1,axiom,
% 2.64/1.63 ! [A2: nat,X2: nat,B2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ X2 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ X2 ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_299_inf__mono,axiom,
% 2.64/1.63 ! [A2: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat,D2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A2 @ C )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ B2 @ D2 )
% 2.64/1.63 => ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A2 @ B2 ) @ ( inf_in586391887at_nat @ C @ D2 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_300_inf__mono,axiom,
% 2.64/1.63 ! [A2: set_nat,C: set_nat,B2: set_nat,D2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A2 @ C )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ B2 @ D2 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ ( inf_inf_set_nat @ C @ D2 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_301_inf__mono,axiom,
% 2.64/1.63 ! [A2: nat,C: nat,B2: nat,D2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ A2 @ C )
% 2.64/1.63 => ( ( ord_less_eq_nat @ B2 @ D2 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ ( inf_inf_nat @ C @ D2 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_302_le__infI,axiom,
% 2.64/1.63 ! [X2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X2 @ A2 )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ X2 @ B2 )
% 2.64/1.63 => ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ A2 @ B2 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_303_le__infI,axiom,
% 2.64/1.63 ! [X2: set_nat,A2: set_nat,B2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X2 @ A2 )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ X2 @ B2 )
% 2.64/1.63 => ( ord_less_eq_set_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_304_le__infI,axiom,
% 2.64/1.63 ! [X2: nat,A2: nat,B2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X2 @ A2 )
% 2.64/1.63 => ( ( ord_less_eq_nat @ X2 @ B2 )
% 2.64/1.63 => ( ord_less_eq_nat @ X2 @ ( inf_inf_nat @ A2 @ B2 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_305_le__infE,axiom,
% 2.64/1.63 ! [X2: set_Pr1986765409at_nat,A2: set_Pr1986765409at_nat,B2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ X2 @ ( inf_in586391887at_nat @ A2 @ B2 ) )
% 2.64/1.63 => ~ ( ( ord_le841296385at_nat @ X2 @ A2 )
% 2.64/1.63 => ~ ( ord_le841296385at_nat @ X2 @ B2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_306_le__infE,axiom,
% 2.64/1.63 ! [X2: set_nat,A2: set_nat,B2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 2.64/1.63 => ~ ( ( ord_less_eq_set_nat @ X2 @ A2 )
% 2.64/1.63 => ~ ( ord_less_eq_set_nat @ X2 @ B2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_307_le__infE,axiom,
% 2.64/1.63 ! [X2: nat,A2: nat,B2: nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ X2 @ ( inf_inf_nat @ A2 @ B2 ) )
% 2.64/1.63 => ~ ( ( ord_less_eq_nat @ X2 @ A2 )
% 2.64/1.63 => ~ ( ord_less_eq_nat @ X2 @ B2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_308_inf__le2,axiom,
% 2.64/1.63 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y2 ) @ Y2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_309_inf__le2,axiom,
% 2.64/1.63 ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X2 @ Y2 ) @ Y2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_310_inf__le2,axiom,
% 2.64/1.63 ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X2 @ Y2 ) @ Y2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_311_inf__le1,axiom,
% 2.64/1.63 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y2 ) @ X2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_312_inf__le1,axiom,
% 2.64/1.63 ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X2 @ Y2 ) @ X2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_313_inf__le1,axiom,
% 2.64/1.63 ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X2 @ Y2 ) @ X2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_314_inf__sup__ord_I1_J,axiom,
% 2.64/1.63 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y2 ) @ X2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_315_inf__sup__ord_I1_J,axiom,
% 2.64/1.63 ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X2 @ Y2 ) @ X2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_316_inf__sup__ord_I1_J,axiom,
% 2.64/1.63 ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X2 @ Y2 ) @ X2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_317_inf__sup__ord_I2_J,axiom,
% 2.64/1.63 ! [X2: set_Pr1986765409at_nat,Y2: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ X2 @ Y2 ) @ Y2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_318_inf__sup__ord_I2_J,axiom,
% 2.64/1.63 ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X2 @ Y2 ) @ Y2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_319_inf__sup__ord_I2_J,axiom,
% 2.64/1.63 ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X2 @ Y2 ) @ Y2 ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_320_rev__finite__subset,axiom,
% 2.64/1.63 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( finite772653738at_nat @ B )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ A @ B )
% 2.64/1.63 => ( finite772653738at_nat @ A ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_321_rev__finite__subset,axiom,
% 2.64/1.63 ! [B: set_nat,A: set_nat] :
% 2.64/1.63 ( ( finite_finite_nat @ B )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ A @ B )
% 2.64/1.63 => ( finite_finite_nat @ A ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_322_infinite__super,axiom,
% 2.64/1.63 ! [S2: set_Pr1986765409at_nat,T3: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ S2 @ T3 )
% 2.64/1.63 => ( ~ ( finite772653738at_nat @ S2 )
% 2.64/1.63 => ~ ( finite772653738at_nat @ T3 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_323_infinite__super,axiom,
% 2.64/1.63 ! [S2: set_nat,T3: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 2.64/1.63 => ( ~ ( finite_finite_nat @ S2 )
% 2.64/1.63 => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_324_finite__subset,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ A @ B )
% 2.64/1.63 => ( ( finite772653738at_nat @ B )
% 2.64/1.63 => ( finite772653738at_nat @ A ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_325_finite__subset,axiom,
% 2.64/1.63 ! [A: set_nat,B: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ A @ B )
% 2.64/1.63 => ( ( finite_finite_nat @ B )
% 2.64/1.63 => ( finite_finite_nat @ A ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_326_finite__list,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( finite772653738at_nat @ A )
% 2.64/1.63 => ? [Xs2: list_P559422087at_nat] :
% 2.64/1.63 ( ( set_Pr2131844118at_nat @ Xs2 )
% 2.64/1.63 = A ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_327_finite__list,axiom,
% 2.64/1.63 ! [A: set_nat] :
% 2.64/1.63 ( ( finite_finite_nat @ A )
% 2.64/1.63 => ? [Xs2: list_nat] :
% 2.64/1.63 ( ( set_nat2 @ Xs2 )
% 2.64/1.63 = A ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_328_subset__code_I1_J,axiom,
% 2.64/1.63 ! [Xs: list_P559422087at_nat,B: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ ( set_Pr2131844118at_nat @ Xs ) @ B )
% 2.64/1.63 = ( ! [X3: product_prod_nat_nat] :
% 2.64/1.63 ( ( member701585322at_nat @ X3 @ ( set_Pr2131844118at_nat @ Xs ) )
% 2.64/1.63 => ( member701585322at_nat @ X3 @ B ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_329_subset__code_I1_J,axiom,
% 2.64/1.63 ! [Xs: list_nat,B: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B )
% 2.64/1.63 = ( ! [X3: nat] :
% 2.64/1.63 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 2.64/1.63 => ( member_nat @ X3 @ B ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_330_infinite__arbitrarily__large,axiom,
% 2.64/1.63 ! [A: set_Pr1986765409at_nat,N: nat] :
% 2.64/1.63 ( ~ ( finite772653738at_nat @ A )
% 2.64/1.63 => ? [B6: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( finite772653738at_nat @ B6 )
% 2.64/1.63 & ( ( finite447719721at_nat @ B6 )
% 2.64/1.63 = N )
% 2.64/1.63 & ( ord_le841296385at_nat @ B6 @ A ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_331_infinite__arbitrarily__large,axiom,
% 2.64/1.63 ! [A: set_nat,N: nat] :
% 2.64/1.63 ( ~ ( finite_finite_nat @ A )
% 2.64/1.63 => ? [B6: set_nat] :
% 2.64/1.63 ( ( finite_finite_nat @ B6 )
% 2.64/1.63 & ( ( finite_card_nat @ B6 )
% 2.64/1.63 = N )
% 2.64/1.63 & ( ord_less_eq_set_nat @ B6 @ A ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_332_card__subset__eq,axiom,
% 2.64/1.63 ! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( finite772653738at_nat @ B )
% 2.64/1.63 => ( ( ord_le841296385at_nat @ A @ B )
% 2.64/1.63 => ( ( ( finite447719721at_nat @ A )
% 2.64/1.63 = ( finite447719721at_nat @ B ) )
% 2.64/1.63 => ( A = B ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_333_card__subset__eq,axiom,
% 2.64/1.63 ! [B: set_nat,A: set_nat] :
% 2.64/1.63 ( ( finite_finite_nat @ B )
% 2.64/1.63 => ( ( ord_less_eq_set_nat @ A @ B )
% 2.64/1.63 => ( ( ( finite_card_nat @ A )
% 2.64/1.63 = ( finite_card_nat @ B ) )
% 2.64/1.63 => ( A = B ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_334_finite__if__finite__subsets__card__bdd,axiom,
% 2.64/1.63 ! [F2: set_Pr1986765409at_nat,C2: nat] :
% 2.64/1.63 ( ! [G2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ G2 @ F2 )
% 2.64/1.63 => ( ( finite772653738at_nat @ G2 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( finite447719721at_nat @ G2 ) @ C2 ) ) )
% 2.64/1.63 => ( ( finite772653738at_nat @ F2 )
% 2.64/1.63 & ( ord_less_eq_nat @ ( finite447719721at_nat @ F2 ) @ C2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_335_finite__if__finite__subsets__card__bdd,axiom,
% 2.64/1.63 ! [F2: set_nat,C2: nat] :
% 2.64/1.63 ( ! [G2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ G2 @ F2 )
% 2.64/1.63 => ( ( finite_finite_nat @ G2 )
% 2.64/1.63 => ( ord_less_eq_nat @ ( finite_card_nat @ G2 ) @ C2 ) ) )
% 2.64/1.63 => ( ( finite_finite_nat @ F2 )
% 2.64/1.63 & ( ord_less_eq_nat @ ( finite_card_nat @ F2 ) @ C2 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_336_pathVertices__edgeset,axiom,
% 2.64/1.63 ! [U2: nat,P: list_P559422087at_nat,V: nat] :
% 2.64/1.63 ( ( member_nat @ U2 @ ( v_a @ c ) )
% 2.64/1.63 => ( ( isPath_a @ c @ U2 @ P @ V )
% 2.64/1.63 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( pathVertices @ U2 @ P ) ) @ ( v_a @ c ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_337_obtain__subset__with__card__n,axiom,
% 2.64/1.63 ! [N: nat,S2: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ N @ ( finite447719721at_nat @ S2 ) )
% 2.64/1.63 => ~ ! [T4: set_Pr1986765409at_nat] :
% 2.64/1.63 ( ( ord_le841296385at_nat @ T4 @ S2 )
% 2.64/1.63 => ( ( ( finite447719721at_nat @ T4 )
% 2.64/1.63 = N )
% 2.64/1.63 => ~ ( finite772653738at_nat @ T4 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_338_obtain__subset__with__card__n,axiom,
% 2.64/1.63 ! [N: nat,S2: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ N @ ( finite_card_nat @ S2 ) )
% 2.64/1.63 => ~ ! [T4: set_nat] :
% 2.64/1.63 ( ( ord_less_eq_set_nat @ T4 @ S2 )
% 2.64/1.63 => ( ( ( finite_card_nat @ T4 )
% 2.64/1.63 = N )
% 2.64/1.63 => ~ ( finite_finite_nat @ T4 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_339_isPath_Osimps_I2_J,axiom,
% 2.64/1.63 ! [U2: nat,X2: nat,Y2: nat,P: list_P559422087at_nat,V: nat] :
% 2.64/1.63 ( ( isPath_a @ c @ U2 @ ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ P ) @ V )
% 2.64/1.63 = ( ( U2 = X2 )
% 2.64/1.63 & ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ ( e_a @ c ) )
% 2.64/1.63 & ( isPath_a @ c @ Y2 @ P @ V ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_340_isShortestPath__def,axiom,
% 2.64/1.63 ! [U2: nat,P: list_P559422087at_nat,V: nat] :
% 2.64/1.63 ( ( isShortestPath_a @ c @ U2 @ P @ V )
% 2.64/1.63 = ( ( isPath_a @ c @ U2 @ P @ V )
% 2.64/1.63 & ! [P3: list_P559422087at_nat] :
% 2.64/1.63 ( ( isPath_a @ c @ U2 @ P3 @ V )
% 2.64/1.63 => ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P ) @ ( size_s1990949619at_nat @ P3 ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_341_list_Oinject,axiom,
% 2.64/1.63 ! [X21: product_prod_nat_nat,X22: list_P559422087at_nat,Y21: product_prod_nat_nat,Y22: list_P559422087at_nat] :
% 2.64/1.63 ( ( ( cons_P66992567at_nat @ X21 @ X22 )
% 2.64/1.63 = ( cons_P66992567at_nat @ Y21 @ Y22 ) )
% 2.64/1.63 = ( ( X21 = Y21 )
% 2.64/1.63 & ( X22 = Y22 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_342_impossible__Cons,axiom,
% 2.64/1.63 ! [Xs: list_P559422087at_nat,Ys: list_P559422087at_nat,X2: product_prod_nat_nat] :
% 2.64/1.63 ( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ Xs ) @ ( size_s1990949619at_nat @ Ys ) )
% 2.64/1.63 => ( Xs
% 2.64/1.63 != ( cons_P66992567at_nat @ X2 @ Ys ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_343_list_Oset__cases,axiom,
% 2.64/1.63 ! [E: nat,A2: list_nat] :
% 2.64/1.63 ( ( member_nat @ E @ ( set_nat2 @ A2 ) )
% 2.64/1.63 => ( ! [Z22: list_nat] :
% 2.64/1.63 ( A2
% 2.64/1.63 != ( cons_nat @ E @ Z22 ) )
% 2.64/1.63 => ~ ! [Z1: nat,Z22: list_nat] :
% 2.64/1.63 ( ( A2
% 2.64/1.63 = ( cons_nat @ Z1 @ Z22 ) )
% 2.64/1.63 => ~ ( member_nat @ E @ ( set_nat2 @ Z22 ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_344_list_Oset__cases,axiom,
% 2.64/1.63 ! [E: product_prod_nat_nat,A2: list_P559422087at_nat] :
% 2.64/1.63 ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ A2 ) )
% 2.64/1.63 => ( ! [Z22: list_P559422087at_nat] :
% 2.64/1.63 ( A2
% 2.64/1.63 != ( cons_P66992567at_nat @ E @ Z22 ) )
% 2.64/1.63 => ~ ! [Z1: product_prod_nat_nat,Z22: list_P559422087at_nat] :
% 2.64/1.63 ( ( A2
% 2.64/1.63 = ( cons_P66992567at_nat @ Z1 @ Z22 ) )
% 2.64/1.63 => ~ ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ Z22 ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_345_bounded__Max__nat,axiom,
% 2.64/1.63 ! [P2: nat > $o,X2: nat,M: nat] :
% 2.64/1.63 ( ( P2 @ X2 )
% 2.64/1.63 => ( ! [X: nat] :
% 2.64/1.63 ( ( P2 @ X )
% 2.64/1.63 => ( ord_less_eq_nat @ X @ M ) )
% 2.64/1.63 => ~ ! [M2: nat] :
% 2.64/1.63 ( ( P2 @ M2 )
% 2.64/1.63 => ~ ! [X4: nat] :
% 2.64/1.63 ( ( P2 @ X4 )
% 2.64/1.63 => ( ord_less_eq_nat @ X4 @ M2 ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_346_finite__nat__set__iff__bounded__le,axiom,
% 2.64/1.63 ( finite_finite_nat
% 2.64/1.63 = ( ^ [N2: set_nat] :
% 2.64/1.63 ? [M3: nat] :
% 2.64/1.63 ! [X3: nat] :
% 2.64/1.63 ( ( member_nat @ X3 @ N2 )
% 2.64/1.63 => ( ord_less_eq_nat @ X3 @ M3 ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_347_isPath_Oelims_I3_J,axiom,
% 2.64/1.63 ! [X2: nat,Xa2: list_P559422087at_nat,Xb: nat] :
% 2.64/1.63 ( ~ ( isPath_a @ c @ X2 @ Xa2 @ Xb )
% 2.64/1.63 => ( ( ( Xa2 = nil_Pr1308055047at_nat )
% 2.64/1.63 => ( X2 = Xb ) )
% 2.64/1.63 => ~ ! [X: nat,Y4: nat,P4: list_P559422087at_nat] :
% 2.64/1.63 ( ( Xa2
% 2.64/1.63 = ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ P4 ) )
% 2.64/1.63 => ( ( X2 = X )
% 2.64/1.63 & ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ ( e_a @ c ) )
% 2.64/1.63 & ( isPath_a @ c @ Y4 @ P4 @ Xb ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_348_isPath_Oelims_I2_J,axiom,
% 2.64/1.63 ! [X2: nat,Xa2: list_P559422087at_nat,Xb: nat] :
% 2.64/1.63 ( ( isPath_a @ c @ X2 @ Xa2 @ Xb )
% 2.64/1.63 => ( ( ( Xa2 = nil_Pr1308055047at_nat )
% 2.64/1.63 => ( X2 != Xb ) )
% 2.64/1.63 => ~ ! [X: nat,Y4: nat,P4: list_P559422087at_nat] :
% 2.64/1.63 ( ( Xa2
% 2.64/1.63 = ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ P4 ) )
% 2.64/1.63 => ~ ( ( X2 = X )
% 2.64/1.63 & ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ ( e_a @ c ) )
% 2.64/1.63 & ( isPath_a @ c @ Y4 @ P4 @ Xb ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_349_isPath_Osimps_I1_J,axiom,
% 2.64/1.63 ! [U2: nat,V: nat] :
% 2.64/1.63 ( ( isPath_a @ c @ U2 @ nil_Pr1308055047at_nat @ V )
% 2.64/1.63 = ( U2 = V ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_350_isPath__fwd__cases,axiom,
% 2.64/1.63 ! [S: nat,P: list_P559422087at_nat,T: nat] :
% 2.64/1.63 ( ( isPath_a @ c @ S @ P @ T )
% 2.64/1.63 => ( ( ( P = nil_Pr1308055047at_nat )
% 2.64/1.63 => ( T != S ) )
% 2.64/1.63 => ~ ! [P5: list_P559422087at_nat,U3: nat] :
% 2.64/1.63 ( ( P
% 2.64/1.63 = ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ S @ U3 ) @ P5 ) )
% 2.64/1.63 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ S @ U3 ) @ ( e_a @ c ) )
% 2.64/1.63 => ~ ( isPath_a @ c @ U3 @ P5 @ T ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_351_isPath_Oelims_I1_J,axiom,
% 2.64/1.63 ! [X2: nat,Xa2: list_P559422087at_nat,Xb: nat,Y2: $o] :
% 2.64/1.63 ( ( ( isPath_a @ c @ X2 @ Xa2 @ Xb )
% 2.64/1.63 = Y2 )
% 2.64/1.63 => ( ( ( Xa2 = nil_Pr1308055047at_nat )
% 2.64/1.63 => ( Y2
% 2.64/1.63 = ( X2 != Xb ) ) )
% 2.64/1.63 => ~ ! [X: nat,Y4: nat,P4: list_P559422087at_nat] :
% 2.64/1.63 ( ( Xa2
% 2.64/1.63 = ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ P4 ) )
% 2.64/1.63 => ( Y2
% 2.64/1.63 = ( ~ ( ( X2 = X )
% 2.64/1.63 & ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ ( e_a @ c ) )
% 2.64/1.63 & ( isPath_a @ c @ Y4 @ P4 @ Xb ) ) ) ) ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(fact_352_Graph_OisPath_Oinduct,axiom,
% 2.64/1.63 ! [P2: nat > list_P559422087at_nat > nat > $o,A0: nat,A1: list_P559422087at_nat,A22: nat] :
% 2.64/1.63 ( ! [U3: nat,X_1: nat] : ( P2 @ U3 @ nil_Pr1308055047at_nat @ X_1 )
% 2.64/1.63 => ( ! [U3: nat,X: nat,Y4: nat,P4: list_P559422087at_nat,V3: nat] :
% 2.64/1.63 ( ( P2 @ Y4 @ P4 @ V3 )
% 2.64/1.63 => ( P2 @ U3 @ ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ X @ Y4 ) @ P4 ) @ V3 ) )
% 2.64/1.63 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 2.64/1.63
% 2.64/1.63 thf(conj_0,conjecture,
% 2.64/1.63 ord_le841296385at_nat @ edges @ ( e_a @ c ) ).
% 2.64/1.63 ------------------------
% 2.64/1.67 % (8498)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8264 for (2999ds/183Mi)
% 2.64/1.67 % (8499)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_8264 for (2999ds/4Mi)
% 2.64/1.67 % (8500)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_8264 for (2999ds/27Mi)
% 2.64/1.67 % (8499)Instruction limit reached!
% 2.64/1.67 % (8499)------------------------------
% 2.64/1.67 % (8499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.64/1.67 % (8499)Termination reason: Unknown
% 2.64/1.67 % (8499)Termination phase: shuffling
% 2.64/1.67
% 2.64/1.67 % (8499)Memory used [KB]: 1407
% 2.64/1.67 % (8499)Time elapsed: 0.003 s
% 2.64/1.67 % (8499)Instructions burned: 5 (million)
% 2.64/1.67 % (8499)------------------------------
% 2.64/1.67 % (8499)------------------------------
% 2.64/1.67 % (8501)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8264 for (2999ds/2Mi)
% 2.64/1.67 % (8502)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_8264 for (2999ds/2Mi)
% 2.64/1.67 % (8503)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_8264 for (2999ds/275Mi)
% 2.64/1.68 % (8504)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8264 for (2999ds/18Mi)
% 2.64/1.68 % (8500)Instruction limit reached!
% 2.64/1.68 % (8500)------------------------------
% 2.64/1.68 % (8500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.64/1.68 % (8500)Termination reason: Unknown
% 2.64/1.68 % (8500)Termination phase: Property scanning
% 2.64/1.68
% 2.64/1.68 % (8500)Memory used [KB]: 1918
% 2.64/1.68 % (8500)Time elapsed: 0.011 s
% 2.64/1.68 % (8500)Instructions burned: 29 (million)
% 2.64/1.68 % (8500)------------------------------
% 2.64/1.68 % (8500)------------------------------
% 2.64/1.68 % (8501)Instruction limit reached!
% 2.64/1.68 % (8501)------------------------------
% 2.64/1.68 % (8501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.64/1.68 % (8501)Termination reason: Unknown
% 2.64/1.68 % (8501)Termination phase: shuffling
% 2.64/1.68
% 2.64/1.68 % (8501)Memory used [KB]: 1407
% 2.64/1.68 % (8501)Time elapsed: 0.004 s
% 2.64/1.68 % (8501)Instructions burned: 3 (million)
% 2.64/1.68 % (8501)------------------------------
% 2.64/1.68 % (8501)------------------------------
% 2.64/1.68 % (8502)Instruction limit reached!
% 2.64/1.68 % (8502)------------------------------
% 2.64/1.68 % (8502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.64/1.68 % (8502)Termination reason: Unknown
% 2.64/1.68 % (8502)Termination phase: shuffling
% 2.64/1.68
% 2.64/1.68 % (8502)Memory used [KB]: 1407
% 2.64/1.68 % (8502)Time elapsed: 0.004 s
% 2.64/1.68 % (8502)Instructions burned: 3 (million)
% 2.64/1.68 % (8502)------------------------------
% 2.64/1.68 % (8502)------------------------------
% 2.64/1.68 % (8510)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8264 for (2999ds/3Mi)
% 2.64/1.68 % (8510)Instruction limit reached!
% 2.64/1.68 % (8510)------------------------------
% 2.64/1.68 % (8510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.64/1.68 % (8510)Termination reason: Unknown
% 2.64/1.68 % (8510)Termination phase: shuffling
% 2.64/1.68
% 2.64/1.68 % (8510)Memory used [KB]: 1407
% 2.64/1.68 % (8510)Time elapsed: 0.003 s
% 2.64/1.68 % (8510)Instructions burned: 6 (million)
% 2.64/1.68 % (8510)------------------------------
% 2.64/1.68 % (8510)------------------------------
% 2.64/1.69 % (8504)Instruction limit reached!
% 2.64/1.69 % (8504)------------------------------
% 2.64/1.69 % (8504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.64/1.69 % (8504)Termination reason: Unknown
% 2.64/1.69 % (8504)Termination phase: shuffling
% 2.64/1.69
% 2.64/1.69 % (8504)Memory used [KB]: 1791
% 2.64/1.69 % (8504)Time elapsed: 0.013 s
% 2.64/1.69 % (8504)Instructions burned: 18 (million)
% 2.64/1.69 % (8504)------------------------------
% 2.64/1.69 % (8504)------------------------------
% 2.64/1.69 % (8520)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_8264 for (2999ds/1041Mi)
% 2.64/1.69 % (8515)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_8264 for (2999ds/37Mi)
% 2.64/1.69 % (8517)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_8264 for (2999ds/15Mi)
% 2.64/1.69 % (8518)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_8264 for (2999ds/3Mi)
% 2.64/1.70 % (8518)Instruction limit reached!
% 2.64/1.70 % (8518)------------------------------
% 2.64/1.70 % (8518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.64/1.70 % (8518)Termination reason: Unknown
% 2.64/1.70 % (8518)Termination phase: shuffling
% 2.64/1.70
% 2.64/1.70 % (8518)Memory used [KB]: 1407
% 2.64/1.70 % (8518)Time elapsed: 0.004 s
% 2.64/1.70 % (8518)Instructions burned: 3 (million)
% 2.64/1.70 % (8518)------------------------------
% 2.64/1.70 % (8518)------------------------------
% 2.68/1.70 % (8517)Instruction limit reached!
% 2.68/1.70 % (8517)------------------------------
% 2.68/1.70 % (8517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.70 % (8517)Termination reason: Unknown
% 2.68/1.70 % (8517)Termination phase: shuffling
% 2.68/1.70
% 2.68/1.70 % (8517)Memory used [KB]: 1663
% 2.68/1.70 % (8517)Time elapsed: 0.010 s
% 2.68/1.70 % (8517)Instructions burned: 15 (million)
% 2.68/1.70 % (8517)------------------------------
% 2.68/1.70 % (8517)------------------------------
% 2.68/1.71 % (8523)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8264 for (2999ds/7Mi)
% 2.68/1.71 % (8515)Instruction limit reached!
% 2.68/1.71 % (8515)------------------------------
% 2.68/1.71 % (8515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.71 % (8515)Termination reason: Unknown
% 2.68/1.71 % (8515)Termination phase: shuffling
% 2.68/1.71
% 2.68/1.71 % (8515)Memory used [KB]: 2174
% 2.68/1.71 % (8515)Time elapsed: 0.018 s
% 2.68/1.71 % (8515)Instructions burned: 37 (million)
% 2.68/1.71 % (8515)------------------------------
% 2.68/1.71 % (8515)------------------------------
% 2.68/1.71 % (8523)Instruction limit reached!
% 2.68/1.71 % (8523)------------------------------
% 2.68/1.71 % (8523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.71 % (8523)Termination reason: Unknown
% 2.68/1.71 % (8523)Termination phase: shuffling
% 2.68/1.71
% 2.68/1.71 % (8523)Memory used [KB]: 1407
% 2.68/1.71 % (8523)Time elapsed: 0.006 s
% 2.68/1.71 % (8523)Instructions burned: 7 (million)
% 2.68/1.71 % (8523)------------------------------
% 2.68/1.71 % (8523)------------------------------
% 2.68/1.71 % (8529)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_8264 for (2999ds/3Mi)
% 2.68/1.71 % (8526)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8264 for (2999ds/16Mi)
% 2.68/1.71 % (8529)Instruction limit reached!
% 2.68/1.71 % (8529)------------------------------
% 2.68/1.71 % (8529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.71 % (8529)Termination reason: Unknown
% 2.68/1.71 % (8529)Termination phase: shuffling
% 2.68/1.71
% 2.68/1.71 % (8529)Memory used [KB]: 1407
% 2.68/1.71 % (8529)Time elapsed: 0.003 s
% 2.68/1.71 % (8529)Instructions burned: 5 (million)
% 2.68/1.71 % (8529)------------------------------
% 2.68/1.71 % (8529)------------------------------
% 2.68/1.72 % (8498)Instruction limit reached!
% 2.68/1.72 % (8498)------------------------------
% 2.68/1.72 % (8498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.72 % (8498)Termination reason: Unknown
% 2.68/1.72 % (8498)Termination phase: Saturation
% 2.68/1.72
% 2.68/1.72 % (8498)Memory used [KB]: 7419
% 2.68/1.72 % (8498)Time elapsed: 0.052 s
% 2.68/1.72 % (8498)Instructions burned: 183 (million)
% 2.68/1.72 % (8498)------------------------------
% 2.68/1.72 % (8498)------------------------------
% 2.68/1.72 % (8532)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_8264 for (2999ds/3Mi)
% 2.68/1.72 % (8532)Instruction limit reached!
% 2.68/1.72 % (8532)------------------------------
% 2.68/1.72 % (8532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.72 % (8532)Termination reason: Unknown
% 2.68/1.72 % (8532)Termination phase: shuffling
% 2.68/1.72
% 2.68/1.72 % (8532)Memory used [KB]: 1407
% 2.68/1.72 % (8532)Time elapsed: 0.003 s
% 2.68/1.72 % (8532)Instructions burned: 4 (million)
% 2.68/1.72 % (8532)------------------------------
% 2.68/1.72 % (8532)------------------------------
% 2.68/1.72 % (8526)Instruction limit reached!
% 2.68/1.72 % (8526)------------------------------
% 2.68/1.72 % (8526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.72 % (8526)Termination reason: Unknown
% 2.68/1.72 % (8526)Termination phase: shuffling
% 2.68/1.72
% 2.68/1.72 % (8526)Memory used [KB]: 1663
% 2.68/1.72 % (8526)Time elapsed: 0.012 s
% 2.68/1.72 % (8526)Instructions burned: 16 (million)
% 2.68/1.72 % (8526)------------------------------
% 2.68/1.72 % (8526)------------------------------
% 2.68/1.72 % (8536)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_8264 for (2999ds/3Mi)
% 2.68/1.72 % (8536)Instruction limit reached!
% 2.68/1.72 % (8536)------------------------------
% 2.68/1.72 % (8536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.72 % (8536)Termination reason: Unknown
% 2.68/1.72 % (8536)Termination phase: shuffling
% 2.68/1.72
% 2.68/1.72 % (8536)Memory used [KB]: 1407
% 2.68/1.72 % (8536)Time elapsed: 0.002 s
% 2.68/1.72 % (8536)Instructions burned: 3 (million)
% 2.68/1.72 % (8536)------------------------------
% 2.68/1.72 % (8536)------------------------------
% 2.68/1.73 % (8538)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_8264 for (2999ds/4Mi)
% 2.68/1.73 % (8538)Instruction limit reached!
% 2.68/1.73 % (8538)------------------------------
% 2.68/1.73 % (8538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.73 % (8538)Termination reason: Unknown
% 2.68/1.73 % (8538)Termination phase: shuffling
% 2.68/1.73
% 2.68/1.73 % (8538)Memory used [KB]: 1407
% 2.68/1.73 % (8538)Time elapsed: 0.003 s
% 2.68/1.73 % (8538)Instructions burned: 6 (million)
% 2.68/1.73 % (8538)------------------------------
% 2.68/1.73 % (8538)------------------------------
% 2.68/1.73 % (8534)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_8264 for (2999ds/7Mi)
% 2.68/1.73 % (8541)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_8264 for (2999ds/18Mi)
% 2.68/1.73 % (8534)Instruction limit reached!
% 2.68/1.73 % (8534)------------------------------
% 2.68/1.73 % (8534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.73 % (8534)Termination reason: Unknown
% 2.68/1.73 % (8534)Termination phase: shuffling
% 2.68/1.73
% 2.68/1.73 % (8534)Memory used [KB]: 1535
% 2.68/1.73 % (8534)Time elapsed: 0.007 s
% 2.68/1.73 % (8534)Instructions burned: 7 (million)
% 2.68/1.73 % (8534)------------------------------
% 2.68/1.73 % (8534)------------------------------
% 2.68/1.73 % (8543)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_8264 for (2999ds/6Mi)
% 2.68/1.74 % (8543)Instruction limit reached!
% 2.68/1.74 % (8543)------------------------------
% 2.68/1.74 % (8543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.74 % (8543)Termination reason: Unknown
% 2.68/1.74 % (8543)Termination phase: shuffling
% 2.68/1.74
% 2.68/1.74 % (8543)Memory used [KB]: 1407
% 2.68/1.74 % (8543)Time elapsed: 0.003 s
% 2.68/1.74 % (8543)Instructions burned: 6 (million)
% 2.68/1.74 % (8543)------------------------------
% 2.68/1.74 % (8543)------------------------------
% 2.68/1.74 % (8541)Instruction limit reached!
% 2.68/1.74 % (8541)------------------------------
% 2.68/1.74 % (8541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.74 % (8541)Termination reason: Unknown
% 2.68/1.74 % (8541)Termination phase: shuffling
% 2.68/1.74
% 2.68/1.74 % (8541)Memory used [KB]: 1663
% 2.68/1.74 % (8541)Time elapsed: 0.007 s
% 2.68/1.74 % (8541)Instructions burned: 18 (million)
% 2.68/1.74 % (8541)------------------------------
% 2.68/1.74 % (8541)------------------------------
% 2.68/1.74 % (8546)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_8264 for (2999ds/902Mi)
% 2.68/1.74 % (8542)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_8264 for (2999ds/710Mi)
% 2.68/1.74 % (8549)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_8264 for (2999ds/21Mi)
% 2.68/1.75 % (8551)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_8264 for (2999ds/5Mi)
% 2.68/1.75 % (8552)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_8264 for (2999ds/6Mi)
% 2.68/1.75 % (8551)Instruction limit reached!
% 2.68/1.75 % (8551)------------------------------
% 2.68/1.75 % (8551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.75 % (8551)Termination reason: Unknown
% 2.68/1.75 % (8551)Termination phase: shuffling
% 2.68/1.75
% 2.68/1.75 % (8551)Memory used [KB]: 1407
% 2.68/1.75 % (8551)Time elapsed: 0.003 s
% 2.68/1.75 % (8551)Instructions burned: 7 (million)
% 2.68/1.75 % (8551)------------------------------
% 2.68/1.75 % (8551)------------------------------
% 2.68/1.75 % (8552)Instruction limit reached!
% 2.68/1.75 % (8552)------------------------------
% 2.68/1.75 % (8552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.75 % (8552)Termination reason: Unknown
% 2.68/1.75 % (8552)Termination phase: shuffling
% 2.68/1.75
% 2.68/1.75 % (8552)Memory used [KB]: 1407
% 2.68/1.75 % (8552)Time elapsed: 0.003 s
% 2.68/1.75 % (8552)Instructions burned: 6 (million)
% 2.68/1.75 % (8552)------------------------------
% 2.68/1.75 % (8552)------------------------------
% 2.68/1.75 % (8549)Instruction limit reached!
% 2.68/1.75 % (8549)------------------------------
% 2.68/1.75 % (8549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.75 % (8549)Termination reason: Unknown
% 2.68/1.75 % (8549)Termination phase: shuffling
% 2.68/1.75
% 2.68/1.75 % (8549)Memory used [KB]: 1791
% 2.68/1.75 % (8549)Time elapsed: 0.010 s
% 2.68/1.75 % (8549)Instructions burned: 23 (million)
% 2.68/1.75 % (8549)------------------------------
% 2.68/1.75 % (8549)------------------------------
% 2.68/1.76 % (8557)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_8264 for (2999ds/377Mi)
% 2.68/1.76 % (8558)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_8264 for (2999ds/779Mi)
% 2.68/1.76 % (8503)Instruction limit reached!
% 2.68/1.76 % (8503)------------------------------
% 2.68/1.76 % (8503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.76 % (8503)Termination reason: Unknown
% 2.68/1.76 % (8503)Termination phase: Saturation
% 2.68/1.76
% 2.68/1.76 % (8503)Memory used [KB]: 6524
% 2.68/1.76 % (8503)Time elapsed: 0.088 s
% 2.68/1.76 % (8503)Instructions burned: 275 (million)
% 2.68/1.76 % (8503)------------------------------
% 2.68/1.76 % (8503)------------------------------
% 2.68/1.76 % (8561)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_8264 for (2998ds/19Mi)
% 2.68/1.77 % (8561)Instruction limit reached!
% 2.68/1.77 % (8561)------------------------------
% 2.68/1.77 % (8561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.77 % (8561)Termination reason: Unknown
% 2.68/1.77 % (8561)Termination phase: shuffling
% 2.68/1.77
% 2.68/1.77 % (8561)Memory used [KB]: 1663
% 2.68/1.77 % (8561)Time elapsed: 0.007 s
% 2.68/1.77 % (8561)Instructions burned: 19 (million)
% 2.68/1.77 % (8561)------------------------------
% 2.68/1.77 % (8561)------------------------------
% 2.68/1.77 % (8566)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_8264 for (2998ds/879Mi)
% 2.68/1.78 % (8568)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_8264 for (2998ds/17Mi)
% 2.68/1.78 % (8568)Instruction limit reached!
% 2.68/1.78 % (8568)------------------------------
% 2.68/1.78 % (8568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.78 % (8568)Termination reason: Unknown
% 2.68/1.78 % (8568)Termination phase: shuffling
% 2.68/1.78
% 2.68/1.78 % (8568)Memory used [KB]: 1663
% 2.68/1.78 % (8568)Time elapsed: 0.007 s
% 2.68/1.78 % (8568)Instructions burned: 18 (million)
% 2.68/1.78 % (8568)------------------------------
% 2.68/1.78 % (8568)------------------------------
% 2.68/1.79 % (8573)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_8264 for (2998ds/3Mi)
% 2.68/1.80 % (8573)Instruction limit reached!
% 2.68/1.80 % (8573)------------------------------
% 2.68/1.80 % (8573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.80 % (8573)Termination reason: Unknown
% 2.68/1.80 % (8573)Termination phase: shuffling
% 2.68/1.80
% 2.68/1.80 % (8573)Memory used [KB]: 1407
% 2.68/1.80 % (8573)Time elapsed: 0.003 s
% 2.68/1.80 % (8573)Instructions burned: 5 (million)
% 2.68/1.80 % (8573)------------------------------
% 2.68/1.80 % (8573)------------------------------
% 2.68/1.80 % (8577)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_8264 for (2998ds/30Mi)
% 2.68/1.81 % (8577)Instruction limit reached!
% 2.68/1.81 % (8577)------------------------------
% 2.68/1.81 % (8577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.81 % (8577)Termination reason: Unknown
% 2.68/1.81 % (8577)Termination phase: Property scanning
% 2.68/1.81
% 2.68/1.81 % (8577)Memory used [KB]: 1918
% 2.68/1.81 % (8577)Time elapsed: 0.011 s
% 2.68/1.81 % (8577)Instructions burned: 32 (million)
% 2.68/1.81 % (8577)------------------------------
% 2.68/1.81 % (8577)------------------------------
% 2.68/1.82 % (8580)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_8264 for (2998ds/127Mi)
% 2.68/1.86 % (8580)Instruction limit reached!
% 2.68/1.86 % (8580)------------------------------
% 2.68/1.86 % (8580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.86 % (8580)Termination reason: Unknown
% 2.68/1.86 % (8580)Termination phase: Property scanning
% 2.68/1.86
% 2.68/1.86 % (8580)Memory used [KB]: 2686
% 2.68/1.86 % (8580)Time elapsed: 0.036 s
% 2.68/1.86 % (8580)Instructions burned: 127 (million)
% 2.68/1.86 % (8580)------------------------------
% 2.68/1.86 % (8580)------------------------------
% 2.68/1.87 % (8592)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_8264 for (2997ds/100Mi)
% 2.68/1.87 % (8557)Instruction limit reached!
% 2.68/1.87 % (8557)------------------------------
% 2.68/1.87 % (8557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.87 % (8557)Termination reason: Unknown
% 2.68/1.87 % (8557)Termination phase: Saturation
% 2.68/1.87
% 2.68/1.87 % (8557)Memory used [KB]: 8699
% 2.68/1.87 % (8557)Time elapsed: 0.114 s
% 2.68/1.87 % (8557)Instructions burned: 379 (million)
% 2.68/1.87 % (8557)------------------------------
% 2.68/1.87 % (8557)------------------------------
% 2.68/1.88 % (8594)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_8264 for (2997ds/3Mi)
% 2.68/1.88 % (8594)Instruction limit reached!
% 2.68/1.88 % (8594)------------------------------
% 2.68/1.88 % (8594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.88 % (8594)Termination reason: Unknown
% 2.68/1.88 % (8594)Termination phase: shuffling
% 2.68/1.88
% 2.68/1.88 % (8594)Memory used [KB]: 1407
% 2.68/1.88 % (8594)Time elapsed: 0.002 s
% 2.68/1.88 % (8594)Instructions burned: 3 (million)
% 2.68/1.88 % (8594)------------------------------
% 2.68/1.88 % (8594)------------------------------
% 2.68/1.89 % (8598)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_8264 for (2997ds/20Mi)
% 2.68/1.89 % (8592)Instruction limit reached!
% 2.68/1.89 % (8592)------------------------------
% 2.68/1.89 % (8592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.89 % (8592)Termination reason: Unknown
% 2.68/1.89 % (8592)Termination phase: Property scanning
% 2.68/1.89
% 2.68/1.89 % (8592)Memory used [KB]: 2430
% 2.68/1.89 % (8592)Time elapsed: 0.027 s
% 2.68/1.89 % (8592)Instructions burned: 101 (million)
% 2.68/1.89 % (8592)------------------------------
% 2.68/1.89 % (8592)------------------------------
% 2.68/1.90 % (8598)Instruction limit reached!
% 2.68/1.90 % (8598)------------------------------
% 2.68/1.90 % (8598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.90 % (8598)Termination reason: Unknown
% 2.68/1.90 % (8598)Termination phase: shuffling
% 2.68/1.90
% 2.68/1.90 % (8598)Memory used [KB]: 1791
% 2.68/1.90 % (8598)Time elapsed: 0.008 s
% 2.68/1.90 % (8598)Instructions burned: 21 (million)
% 2.68/1.90 % (8598)------------------------------
% 2.68/1.90 % (8598)------------------------------
% 2.68/1.90 % (8603)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_8264 for (2997ds/86Mi)
% 2.68/1.91 % (8605)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_8264 for (2997ds/107Mi)
% 2.68/1.93 % (8603)Instruction limit reached!
% 2.68/1.93 % (8603)------------------------------
% 2.68/1.93 % (8603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.93 % (8603)Termination reason: Unknown
% 2.68/1.93 % (8603)Termination phase: Function definition elimination
% 2.68/1.93
% 2.68/1.93 % (8603)Memory used [KB]: 2430
% 2.68/1.93 % (8603)Time elapsed: 0.025 s
% 2.68/1.93 % (8603)Instructions burned: 86 (million)
% 2.68/1.93 % (8603)------------------------------
% 2.68/1.93 % (8603)------------------------------
% 2.68/1.94 % (8605)Instruction limit reached!
% 2.68/1.94 % (8605)------------------------------
% 2.68/1.94 % (8605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.94 % (8605)Termination reason: Unknown
% 2.68/1.94 % (8605)Termination phase: Property scanning
% 2.68/1.94
% 2.68/1.94 % (8605)Memory used [KB]: 2558
% 2.68/1.94 % (8605)Time elapsed: 0.032 s
% 2.68/1.94 % (8605)Instructions burned: 110 (million)
% 2.68/1.94 % (8605)------------------------------
% 2.68/1.94 % (8605)------------------------------
% 2.68/1.94 % (8624)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_8264 for (2997ds/39Mi)
% 2.68/1.94 % (8542)Refutation not found, non-redundant clauses discarded% (8542)------------------------------
% 2.68/1.94 % (8542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.94 % (8542)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.68/1.94
% 2.68/1.94 % (8542)Memory used [KB]: 7547
% 2.68/1.94 % (8542)Time elapsed: 0.206 s
% 2.68/1.94 % (8542)Instructions burned: 627 (million)
% 2.68/1.94 % (8542)------------------------------
% 2.68/1.94 % (8542)------------------------------
% 2.68/1.95 % (8630)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_8264 for (2997ds/448Mi)
% 2.68/1.95 % (8624)Instruction limit reached!
% 2.68/1.95 % (8624)------------------------------
% 2.68/1.95 % (8624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.95 % (8624)Termination reason: Unknown
% 2.68/1.95 % (8624)Termination phase: shuffling
% 2.68/1.95
% 2.68/1.95 % (8624)Memory used [KB]: 2174
% 2.68/1.95 % (8624)Time elapsed: 0.012 s
% 2.68/1.95 % (8624)Instructions burned: 39 (million)
% 2.68/1.95 % (8624)------------------------------
% 2.68/1.95 % (8624)------------------------------
% 2.68/1.95 % (8635)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_8264 for (2996ds/46Mi)
% 2.68/1.96 % (8637)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_8264 for (2996ds/98Mi)
% 2.68/1.97 % (8635)Instruction limit reached!
% 2.68/1.97 % (8635)------------------------------
% 2.68/1.97 % (8635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.97 % (8635)Termination reason: Unknown
% 2.68/1.97 % (8635)Termination phase: SInE selection
% 2.68/1.97
% 2.68/1.97 % (8635)Memory used [KB]: 1918
% 2.68/1.97 % (8635)Time elapsed: 0.015 s
% 2.68/1.97 % (8635)Instructions burned: 47 (million)
% 2.68/1.97 % (8635)------------------------------
% 2.68/1.97 % (8635)------------------------------
% 2.68/1.98 % (8644)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_8264 for (2996ds/507Mi)
% 2.68/1.98 % (8558)Instruction limit reached!
% 2.68/1.98 % (8558)------------------------------
% 2.68/1.98 % (8558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.98 % (8558)Termination reason: Unknown
% 2.68/1.98 % (8558)Termination phase: Saturation
% 2.68/1.98
% 2.68/1.98 % (8558)Memory used [KB]: 9722
% 2.68/1.98 % (8558)Time elapsed: 0.248 s
% 2.68/1.98 % (8558)Instructions burned: 781 (million)
% 2.68/1.98 % (8558)------------------------------
% 2.68/1.98 % (8558)------------------------------
% 2.68/1.98 % (8637)Instruction limit reached!
% 2.68/1.98 % (8637)------------------------------
% 2.68/1.98 % (8637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.98 % (8637)Termination reason: Unknown
% 2.68/1.98 % (8637)Termination phase: Property scanning
% 2.68/1.98
% 2.68/1.98 % (8637)Memory used [KB]: 2430
% 2.68/1.98 % (8637)Time elapsed: 0.026 s
% 2.68/1.98 % (8637)Instructions burned: 98 (million)
% 2.68/1.98 % (8637)------------------------------
% 2.68/1.98 % (8637)------------------------------
% 2.68/1.99 % (8520)Instruction limit reached!
% 2.68/1.99 % (8520)------------------------------
% 2.68/1.99 % (8520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.99 % (8520)Termination reason: Unknown
% 2.68/1.99 % (8520)Termination phase: Saturation
% 2.68/1.99
% 2.68/1.99 % (8520)Memory used [KB]: 9978
% 2.68/1.99 % (8520)Time elapsed: 0.301 s
% 2.68/1.99 % (8520)Instructions burned: 1043 (million)
% 2.68/1.99 % (8520)------------------------------
% 2.68/1.99 % (8520)------------------------------
% 2.68/1.99 % (8645)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_8264 for (2996ds/149Mi)
% 2.68/1.99 % (8646)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_8264 for (2996ds/39Mi)
% 2.68/2.00 % (8566)Refutation not found, non-redundant clauses discarded% (8566)------------------------------
% 2.68/2.00 % (8566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/2.00 % (8566)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.68/2.00
% 2.68/2.00 % (8566)Memory used [KB]: 7547
% 2.68/2.00 % (8566)Time elapsed: 0.229 s
% 2.68/2.00 % (8566)Instructions burned: 763 (million)
% 2.68/2.00 % (8566)------------------------------
% 2.68/2.00 % (8566)------------------------------
% 2.68/2.00 % (8647)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_8264 for (2996ds/6Mi)
% 2.68/2.00 % (8546)Instruction limit reached!
% 2.68/2.00 % (8546)------------------------------
% 2.68/2.00 % (8546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/2.00 % (8546)Termination reason: Unknown
% 2.68/2.00 % (8546)Termination phase: Saturation
% 2.68/2.00
% 2.68/2.00 % (8546)Memory used [KB]: 9083
% 2.68/2.00 % (8546)Time elapsed: 0.263 s
% 2.68/2.00 % (8546)Instructions burned: 902 (million)
% 2.68/2.00 % (8546)------------------------------
% 2.68/2.00 % (8546)------------------------------
% 2.68/2.00 % (8647)Instruction limit reached!
% 2.68/2.00 % (8647)------------------------------
% 2.68/2.00 % (8647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/2.00 % (8647)Termination reason: Unknown
% 2.68/2.00 % (8647)Termination phase: shuffling
% 2.68/2.00
% 2.68/2.00 % (8647)Memory used [KB]: 1407
% 2.68/2.00 % (8647)Time elapsed: 0.003 s
% 2.68/2.00 % (8647)Instructions burned: 7 (million)
% 2.68/2.00 % (8647)------------------------------
% 2.68/2.00 % (8647)------------------------------
% 2.68/2.00 % (8646)Instruction limit reached!
% 2.68/2.00 % (8646)------------------------------
% 2.68/2.00 % (8646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/2.00 % (8646)Termination reason: Unknown
% 2.68/2.00 % (8646)Termination phase: Property scanning
% 2.68/2.00
% 2.68/2.00 % (8646)Memory used [KB]: 1918
% 2.68/2.00 % (8646)Time elapsed: 0.013 s
% 2.68/2.00 % (8646)Instructions burned: 40 (million)
% 2.68/2.00 % (8646)------------------------------
% 2.68/2.00 % (8646)------------------------------
% 2.68/2.01 % (8648)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_8264 for (2996ds/1087Mi)
% 2.68/2.01 % (8649)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_8264 for (2996ds/47Mi)
% 2.68/2.01 % (8650)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_8264 for (2996ds/44Mi)
% 2.68/2.01 % (8651)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_8264 for (2996ds/432Mi)
% 2.68/2.02 % (8650)Instruction limit reached!
% 2.68/2.02 % (8650)------------------------------
% 2.68/2.02 % (8650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/2.02 % (8650)Termination reason: Unknown
% 2.68/2.02 % (8650)Termination phase: shuffling
% 2.68/2.02
% 2.68/2.02 % (8650)Memory used [KB]: 2302
% 2.68/2.02 % (8650)Time elapsed: 0.013 s
% 2.68/2.02 % (8650)Instructions burned: 45 (million)
% 2.68/2.02 % (8650)------------------------------
% 2.68/2.02 % (8650)------------------------------
% 2.68/2.02 % (8649)Instruction limit reached!
% 2.68/2.02 % (8649)------------------------------
% 2.68/2.02 % (8649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/2.02 % (8649)Termination reason: Unknown
% 2.68/2.02 % (8649)Termination phase: Preprocessing 3
% 2.68/2.02
% 2.68/2.02 % (8649)Memory used [KB]: 2046
% 2.68/2.02 % (8649)Time elapsed: 0.015 s
% 2.68/2.02 % (8649)Instructions burned: 47 (million)
% 2.68/2.02 % (8649)------------------------------
% 2.68/2.02 % (8649)------------------------------
% 5.13/2.03 % (8652)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_8264 for (2996ds/62Mi)
% 5.13/2.03 % (8645)Instruction limit reached!
% 5.13/2.03 % (8645)------------------------------
% 5.13/2.03 % (8645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.13/2.03 % (8645)Termination reason: Unknown
% 5.13/2.03 % (8645)Termination phase: Property scanning
% 5.13/2.03
% 5.13/2.03 % (8645)Memory used [KB]: 2686
% 5.13/2.03 % (8645)Time elapsed: 0.041 s
% 5.13/2.03 % (8645)Instructions burned: 151 (million)
% 5.13/2.03 % (8645)------------------------------
% 5.13/2.03 % (8645)------------------------------
% 5.13/2.03 % (8653)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_8264 for (2996ds/31Mi)
% 5.13/2.04 % (8654)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_8264 for (2996ds/96Mi)
% 5.13/2.04 % (8653)Instruction limit reached!
% 5.13/2.04 % (8653)------------------------------
% 5.13/2.04 % (8653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.13/2.04 % (8653)Termination reason: Unknown
% 5.13/2.04 % (8653)Termination phase: Property scanning
% 5.13/2.04
% 5.13/2.04 % (8653)Memory used [KB]: 1918
% 5.13/2.04 % (8653)Time elapsed: 0.011 s
% 5.13/2.04 % (8653)Instructions burned: 32 (million)
% 5.13/2.04 % (8653)------------------------------
% 5.13/2.04 % (8653)------------------------------
% 5.13/2.05 % (8652)Instruction limit reached!
% 5.13/2.05 % (8652)------------------------------
% 5.13/2.05 % (8652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.13/2.05 % (8652)Termination reason: Unknown
% 5.13/2.05 % (8652)Termination phase: Property scanning
% 5.13/2.05
% 5.13/2.05 % (8652)Memory used [KB]: 2302
% 5.13/2.05 % (8652)Time elapsed: 0.018 s
% 5.13/2.05 % (8652)Instructions burned: 64 (million)
% 5.13/2.05 % (8652)------------------------------
% 5.13/2.05 % (8652)------------------------------
% 5.13/2.05 % (8655)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_8264 for (2996ds/453Mi)
% 5.13/2.06 % (8656)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_8264 for (2995ds/71Mi)
% 5.13/2.07 % (8630)Instruction limit reached!
% 5.13/2.07 % (8630)------------------------------
% 5.13/2.07 % (8630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.13/2.07 % (8630)Termination reason: Unknown
% 5.13/2.07 % (8630)Termination phase: Saturation
% 5.13/2.07
% 5.13/2.07 % (8630)Memory used [KB]: 8827
% 5.13/2.07 % (8630)Time elapsed: 0.120 s
% 5.13/2.07 % (8630)Instructions burned: 448 (million)
% 5.13/2.07 % (8630)------------------------------
% 5.13/2.07 % (8630)------------------------------
% 5.13/2.07 % (8654)Instruction limit reached!
% 5.13/2.07 % (8654)------------------------------
% 5.13/2.07 % (8654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.13/2.07 % (8654)Termination reason: Unknown
% 5.13/2.07 % (8654)Termination phase: Property scanning
% 5.13/2.07
% 5.13/2.07 % (8654)Memory used [KB]: 2558
% 5.13/2.07 % (8654)Time elapsed: 0.029 s
% 5.13/2.07 % (8654)Instructions burned: 100 (million)
% 5.13/2.07 % (8654)------------------------------
% 5.13/2.07 % (8654)------------------------------
% 5.13/2.08 % (8657)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_8264 for (2995ds/83Mi)
% 5.13/2.08 % (8658)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_8264 for (2995ds/11Mi)
% 5.13/2.08 % (8656)Instruction limit reached!
% 5.13/2.08 % (8656)------------------------------
% 5.13/2.08 % (8656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.13/2.08 % (8656)Termination reason: Unknown
% 5.13/2.08 % (8656)Termination phase: Property scanning
% 5.13/2.08
% 5.13/2.08 % (8656)Memory used [KB]: 2302
% 5.13/2.08 % (8656)Time elapsed: 0.022 s
% 5.13/2.08 % (8656)Instructions burned: 73 (million)
% 5.13/2.08 % (8656)------------------------------
% 5.13/2.08 % (8656)------------------------------
% 5.13/2.08 % (8658)Instruction limit reached!
% 5.13/2.08 % (8658)------------------------------
% 5.13/2.08 % (8658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.13/2.08 % (8658)Termination reason: Unknown
% 5.13/2.08 % (8658)Termination phase: shuffling
% 5.13/2.08
% 5.13/2.08 % (8658)Memory used [KB]: 1535
% 5.13/2.08 % (8658)Time elapsed: 0.004 s
% 5.13/2.08 % (8658)Instructions burned: 11 (million)
% 5.13/2.08 % (8658)------------------------------
% 5.13/2.08 % (8658)------------------------------
% 5.13/2.09 % (8659)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_8264 for (2995ds/41Mi)
% 5.13/2.09 % (8660)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_8264 for (2995ds/6Mi)
% 5.13/2.09 % (8660)Instruction limit reached!
% 5.13/2.09 % (8660)------------------------------
% 5.13/2.09 % (8660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.13/2.09 % (8660)Termination reason: Unknown
% 5.13/2.09 % (8660)Termination phase: shuffling
% 5.13/2.09
% 5.13/2.09 % (8660)Memory used [KB]: 1407
% 5.13/2.09 % (8660)Time elapsed: 0.003 s
% 5.13/2.09 % (8660)Instructions burned: 7 (million)
% 5.13/2.09 % (8660)------------------------------
% 5.13/2.09 % (8660)------------------------------
% 5.13/2.10 % (8657)Instruction limit reached!
% 5.13/2.10 % (8657)------------------------------
% 5.13/2.10 % (8657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.13/2.10 % (8657)Termination reason: Unknown
% 5.13/2.10 % (8657)Termination phase: Function definition elimination
% 5.13/2.10
% 5.13/2.10 % (8657)Memory used [KB]: 2174
% 5.13/2.10 % (8657)Time elapsed: 0.025 s
% 5.13/2.10 % (8657)Instructions burned: 83 (million)
% 5.13/2.10 % (8657)------------------------------
% 5.13/2.10 % (8657)------------------------------
% 5.13/2.10 % (8659)Instruction limit reached!
% 5.13/2.10 % (8659)------------------------------
% 5.13/2.10 % (8659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.13/2.10 % (8659)Termination reason: Unknown
% 5.13/2.10 % (8659)Termination phase: shuffling
% 5.13/2.10
% 5.13/2.10 % (8659)Memory used [KB]: 2174
% 5.13/2.10 % (8659)Time elapsed: 0.013 s
% 5.13/2.10 % (8659)Instructions burned: 44 (million)
% 5.13/2.10 % (8659)------------------------------
% 5.13/2.10 % (8659)------------------------------
% 5.13/2.10 % (8661)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_8264 for (2995ds/150Mi)
% 5.13/2.11 % (8662)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_8264 for (2995ds/343Mi)
% 5.13/2.11 % (8663)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_8264 for (2995ds/109Mi)
% 5.13/2.12 % (8644)Instruction limit reached!
% 5.13/2.12 % (8644)------------------------------
% 5.13/2.12 % (8644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.13/2.12 % (8644)Termination reason: Unknown
% 5.13/2.12 % (8644)Termination phase: Saturation
% 5.13/2.12
% 5.13/2.12 % (8644)Memory used [KB]: 8443
% 5.13/2.12 % (8644)Time elapsed: 0.145 s
% 5.13/2.12 % (8644)Instructions burned: 507 (million)
% 5.13/2.12 % (8644)------------------------------
% 5.13/2.12 % (8644)------------------------------
% 5.55/2.13 % (8664)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_8264 for (2995ds/253Mi)
% 5.55/2.13 % (8651)Instruction limit reached!
% 5.55/2.13 % (8651)------------------------------
% 5.55/2.13 % (8651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.13 % (8651)Termination reason: Unknown
% 5.55/2.13 % (8651)Termination phase: Saturation
% 5.55/2.13
% 5.55/2.13 % (8651)Memory used [KB]: 4733
% 5.55/2.13 % (8651)Time elapsed: 0.120 s
% 5.55/2.13 % (8651)Instructions burned: 432 (million)
% 5.55/2.13 % (8651)------------------------------
% 5.55/2.13 % (8651)------------------------------
% 5.55/2.14 % (8663)Instruction limit reached!
% 5.55/2.14 % (8663)------------------------------
% 5.55/2.14 % (8663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.14 % (8663)Termination reason: Unknown
% 5.55/2.14 % (8663)Termination phase: Property scanning
% 5.55/2.14
% 5.55/2.14 % (8663)Memory used [KB]: 2558
% 5.55/2.14 % (8663)Time elapsed: 0.032 s
% 5.55/2.14 % (8663)Instructions burned: 110 (million)
% 5.55/2.14 % (8663)------------------------------
% 5.55/2.14 % (8663)------------------------------
% 5.55/2.14 % (8665)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_8264 for (2994ds/140Mi)
% 5.55/2.14 % (8661)Instruction limit reached!
% 5.55/2.14 % (8661)------------------------------
% 5.55/2.14 % (8661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.14 % (8661)Termination reason: Unknown
% 5.55/2.14 % (8661)Termination phase: Property scanning
% 5.55/2.14
% 5.55/2.14 % (8661)Memory used [KB]: 2686
% 5.55/2.14 % (8661)Time elapsed: 0.043 s
% 5.55/2.14 % (8661)Instructions burned: 153 (million)
% 5.55/2.14 % (8661)------------------------------
% 5.55/2.14 % (8661)------------------------------
% 5.55/2.15 % (8666)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_8264 for (2994ds/614Mi)
% 5.55/2.15 % (8667)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_8264 for (2994ds/202Mi)
% 5.55/2.18 % (8655)Instruction limit reached!
% 5.55/2.18 % (8655)------------------------------
% 5.55/2.18 % (8655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.18 % (8655)Termination reason: Unknown
% 5.55/2.18 % (8655)Termination phase: Saturation
% 5.55/2.18
% 5.55/2.18 % (8655)Memory used [KB]: 8187
% 5.55/2.18 % (8655)Time elapsed: 0.124 s
% 5.55/2.18 % (8655)Instructions burned: 455 (million)
% 5.55/2.18 % (8655)------------------------------
% 5.55/2.18 % (8655)------------------------------
% 5.55/2.18 % (8668)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_8264 for (2994ds/339Mi)
% 5.55/2.19 % (8665)Instruction limit reached!
% 5.55/2.19 % (8665)------------------------------
% 5.55/2.19 % (8665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.19 % (8665)Termination reason: Unknown
% 5.55/2.19 % (8665)Termination phase: Saturation
% 5.55/2.19
% 5.55/2.19 % (8665)Memory used [KB]: 6652
% 5.55/2.19 % (8665)Time elapsed: 0.044 s
% 5.55/2.19 % (8665)Instructions burned: 141 (million)
% 5.55/2.19 % (8665)------------------------------
% 5.55/2.19 % (8665)------------------------------
% 5.55/2.19 % (8669)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_8264 for (2994ds/283Mi)
% 5.96/2.21 % (8664)Instruction limit reached!
% 5.96/2.21 % (8664)------------------------------
% 5.96/2.21 % (8664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.21 % (8664)Termination reason: Unknown
% 5.96/2.21 % (8664)Termination phase: Saturation
% 5.96/2.21
% 5.96/2.21 % (8664)Memory used [KB]: 7803
% 5.96/2.21 % (8664)Time elapsed: 0.077 s
% 5.96/2.21 % (8664)Instructions burned: 253 (million)
% 5.96/2.21 % (8664)------------------------------
% 5.96/2.21 % (8664)------------------------------
% 5.96/2.21 % (8667)Instruction limit reached!
% 5.96/2.21 % (8667)------------------------------
% 5.96/2.21 % (8667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.21 % (8667)Termination reason: Unknown
% 5.96/2.21 % (8667)Termination phase: Saturation
% 5.96/2.21
% 5.96/2.21 % (8667)Memory used [KB]: 6780
% 5.96/2.21 % (8667)Time elapsed: 0.057 s
% 5.96/2.21 % (8667)Instructions burned: 206 (million)
% 5.96/2.21 % (8667)------------------------------
% 5.96/2.21 % (8667)------------------------------
% 5.96/2.21 % (8662)Instruction limit reached!
% 5.96/2.21 % (8662)------------------------------
% 5.96/2.21 % (8662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.21 % (8662)Termination reason: Unknown
% 5.96/2.21 % (8662)Termination phase: Saturation
% 5.96/2.21
% 5.96/2.21 % (8662)Memory used [KB]: 8059
% 5.96/2.21 % (8662)Time elapsed: 0.125 s
% 5.96/2.21 % (8662)Instructions burned: 343 (million)
% 5.96/2.21 % (8662)------------------------------
% 5.96/2.21 % (8662)------------------------------
% 5.96/2.22 % (8670)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_8264 for (2994ds/134Mi)
% 5.96/2.22 % (8671)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_8264 for (2994ds/298Mi)
% 5.96/2.22 % (8672)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_8264 for (2994ds/192Mi)
% 5.96/2.25 % (8670)Instruction limit reached!
% 5.96/2.25 % (8670)------------------------------
% 5.96/2.25 % (8670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.25 % (8670)Termination reason: Unknown
% 5.96/2.25 % (8670)Termination phase: Property scanning
% 5.96/2.25
% 5.96/2.25 % (8670)Memory used [KB]: 2558
% 5.96/2.25 % (8670)Time elapsed: 0.037 s
% 5.96/2.25 % (8670)Instructions burned: 135 (million)
% 5.96/2.25 % (8670)------------------------------
% 5.96/2.25 % (8670)------------------------------
% 5.96/2.26 % (8673)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_8264 for (2993ds/258Mi)
% 5.96/2.27 % (8669)Instruction limit reached!
% 5.96/2.27 % (8669)------------------------------
% 5.96/2.27 % (8669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.27 % (8669)Termination reason: Unknown
% 5.96/2.27 % (8669)Termination phase: Saturation
% 5.96/2.27
% 5.96/2.27 % (8669)Memory used [KB]: 7675
% 5.96/2.27 % (8669)Time elapsed: 0.076 s
% 5.96/2.27 % (8669)Instructions burned: 283 (million)
% 5.96/2.27 % (8669)------------------------------
% 5.96/2.27 % (8669)------------------------------
% 5.96/2.28 % (8672)Instruction limit reached!
% 5.96/2.28 % (8672)------------------------------
% 5.96/2.28 % (8672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.28 % (8672)Termination reason: Unknown
% 5.96/2.28 % (8672)Termination phase: Saturation
% 5.96/2.28
% 5.96/2.28 % (8672)Memory used [KB]: 3582
% 5.96/2.28 % (8672)Time elapsed: 0.056 s
% 5.96/2.28 % (8672)Instructions burned: 194 (million)
% 5.96/2.28 % (8672)------------------------------
% 5.96/2.28 % (8672)------------------------------
% 5.96/2.28 % (8674)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_8264 for (2993ds/90Mi)
% 5.96/2.28 % (8668)Instruction limit reached!
% 5.96/2.28 % (8668)------------------------------
% 5.96/2.28 % (8668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.28 % (8668)Termination reason: Unknown
% 5.96/2.28 % (8668)Termination phase: Saturation
% 5.96/2.28
% 5.96/2.28 % (8668)Memory used [KB]: 8315
% 5.96/2.28 % (8668)Time elapsed: 0.097 s
% 5.96/2.28 % (8668)Instructions burned: 339 (million)
% 5.96/2.28 % (8668)------------------------------
% 5.96/2.28 % (8668)------------------------------
% 5.96/2.28 % (8675)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_8264 for (2993ds/231Mi)
% 5.96/2.29 % (8676)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_8264 for (2993ds/458Mi)
% 6.53/2.30 % (8671)Instruction limit reached!
% 6.53/2.30 % (8671)------------------------------
% 6.53/2.30 % (8671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.30 % (8671)Termination reason: Unknown
% 6.53/2.30 % (8671)Termination phase: Saturation
% 6.53/2.30
% 6.53/2.30 % (8671)Memory used [KB]: 8443
% 6.53/2.30 % (8671)Time elapsed: 0.079 s
% 6.53/2.30 % (8671)Instructions burned: 300 (million)
% 6.53/2.30 % (8671)------------------------------
% 6.53/2.30 % (8671)------------------------------
% 6.53/2.31 % (8674)Instruction limit reached!
% 6.53/2.31 % (8674)------------------------------
% 6.53/2.31 % (8674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.31 % (8674)Termination reason: Unknown
% 6.53/2.31 % (8674)Termination phase: Property scanning
% 6.53/2.31
% 6.53/2.31 % (8674)Memory used [KB]: 2558
% 6.53/2.31 % (8674)Time elapsed: 0.027 s
% 6.53/2.31 % (8674)Instructions burned: 92 (million)
% 6.53/2.31 % (8674)------------------------------
% 6.53/2.31 % (8674)------------------------------
% 6.53/2.31 % (8677)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_8264 for (2993ds/31Mi)
% 6.53/2.31 % (8678)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_8264 for (2993ds/297Mi)
% 6.53/2.32 % (8677)Instruction limit reached!
% 6.53/2.32 % (8677)------------------------------
% 6.53/2.32 % (8677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.32 % (8677)Termination reason: Unknown
% 6.53/2.32 % (8677)Termination phase: Property scanning
% 6.53/2.32
% 6.53/2.32 % (8677)Memory used [KB]: 1918
% 6.53/2.32 % (8677)Time elapsed: 0.011 s
% 6.53/2.32 % (8677)Instructions burned: 33 (million)
% 6.53/2.32 % (8677)------------------------------
% 6.53/2.32 % (8677)------------------------------
% 6.53/2.33 % (8679)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_8264 for (2993ds/987Mi)
% 6.53/2.33 % (8666)Instruction limit reached!
% 6.53/2.33 % (8666)------------------------------
% 6.53/2.33 % (8666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.33 % (8666)Termination reason: Unknown
% 6.53/2.33 % (8666)Termination phase: Saturation
% 6.53/2.33
% 6.53/2.33 % (8666)Memory used [KB]: 9594
% 6.53/2.33 % (8666)Time elapsed: 0.183 s
% 6.53/2.33 % (8666)Instructions burned: 615 (million)
% 6.53/2.33 % (8666)------------------------------
% 6.53/2.33 % (8666)------------------------------
% 6.53/2.34 % (8673)Instruction limit reached!
% 6.53/2.34 % (8673)------------------------------
% 6.53/2.34 % (8673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.34 % (8673)Termination reason: Unknown
% 6.53/2.34 % (8673)Termination phase: Saturation
% 6.53/2.34
% 6.53/2.34 % (8673)Memory used [KB]: 7036
% 6.53/2.34 % (8673)Time elapsed: 0.075 s
% 6.53/2.34 % (8673)Instructions burned: 258 (million)
% 6.53/2.34 % (8673)------------------------------
% 6.53/2.34 % (8673)------------------------------
% 6.53/2.34 % (8648)Instruction limit reached!
% 6.53/2.34 % (8648)------------------------------
% 6.53/2.34 % (8648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.34 % (8648)Termination reason: Unknown
% 6.53/2.34 % (8648)Termination phase: Saturation
% 6.53/2.34
% 6.53/2.34 % (8648)Memory used [KB]: 7931
% 6.53/2.34 % (8648)Time elapsed: 0.333 s
% 6.53/2.34 % (8648)Instructions burned: 1087 (million)
% 6.53/2.34 % (8648)------------------------------
% 6.53/2.34 % (8648)------------------------------
% 6.53/2.34 % (8680)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_8264 for (2993ds/182Mi)
% 6.53/2.34 % (8675)Instruction limit reached!
% 6.53/2.34 % (8675)------------------------------
% 6.53/2.34 % (8675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.34 % (8675)Termination reason: Unknown
% 6.53/2.34 % (8675)Termination phase: Saturation
% 6.53/2.34
% 6.53/2.34 % (8675)Memory used [KB]: 7419
% 6.53/2.34 % (8675)Time elapsed: 0.061 s
% 6.53/2.34 % (8675)Instructions burned: 234 (million)
% 6.53/2.34 % (8675)------------------------------
% 6.53/2.34 % (8675)------------------------------
% 6.53/2.35 % (8681)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_8264 for (2993ds/182Mi)
% 6.53/2.35 % (8682)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_8264 for (2993ds/154Mi)
% 6.53/2.35 % (8683)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_8264 for (2992ds/79Mi)
% 6.53/2.38 % (8683)Instruction limit reached!
% 6.53/2.38 % (8683)------------------------------
% 6.53/2.38 % (8683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.38 % (8683)Termination reason: Unknown
% 6.53/2.38 % (8683)Termination phase: Function definition elimination
% 6.53/2.38
% 6.53/2.38 % (8683)Memory used [KB]: 2302
% 6.53/2.38 % (8683)Time elapsed: 0.024 s
% 6.53/2.38 % (8683)Instructions burned: 81 (million)
% 6.53/2.38 % (8683)------------------------------
% 6.53/2.38 % (8683)------------------------------
% 6.53/2.39 % (8684)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_8264 for (2992ds/216Mi)
% 6.53/2.39 % (8682)Instruction limit reached!
% 6.53/2.39 % (8682)------------------------------
% 6.53/2.39 % (8682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.39 % (8682)Termination reason: Unknown
% 6.53/2.39 % (8682)Termination phase: Property scanning
% 6.53/2.39
% 6.53/2.39 % (8682)Memory used [KB]: 2686
% 6.53/2.39 % (8682)Time elapsed: 0.040 s
% 6.53/2.39 % (8682)Instructions burned: 154 (million)
% 6.53/2.39 % (8682)------------------------------
% 6.53/2.39 % (8682)------------------------------
% 6.53/2.39 % (8680)Instruction limit reached!
% 6.53/2.39 % (8680)------------------------------
% 6.53/2.39 % (8680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.53/2.39 % (8680)Termination reason: Unknown
% 6.53/2.39 % (8680)Termination phase: Saturation
% 6.53/2.39
% 6.53/2.39 % (8680)Memory used [KB]: 7291
% 6.53/2.39 % (8680)Time elapsed: 0.050 s
% 6.53/2.39 % (8680)Instructions burned: 183 (million)
% 6.53/2.39 % (8680)------------------------------
% 6.53/2.39 % (8680)------------------------------
% 7.49/2.40 % (8678)Instruction limit reached!
% 7.49/2.40 % (8678)------------------------------
% 7.49/2.40 % (8678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.40 % (8678)Termination reason: Unknown
% 7.49/2.40 % (8678)Termination phase: Saturation
% 7.49/2.40
% 7.49/2.40 % (8678)Memory used [KB]: 7675
% 7.49/2.40 % (8678)Time elapsed: 0.083 s
% 7.49/2.40 % (8678)Instructions burned: 299 (million)
% 7.49/2.40 % (8678)------------------------------
% 7.49/2.40 % (8678)------------------------------
% 7.49/2.40 % (8685)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_8264 for (2992ds/114Mi)
% 7.49/2.40 % (8686)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_8264 for (2992ds/922Mi)
% 7.49/2.40 % (8681)Instruction limit reached!
% 7.49/2.40 % (8681)------------------------------
% 7.49/2.40 % (8681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.40 % (8681)Termination reason: Unknown
% 7.49/2.40 % (8681)Termination phase: Saturation
% 7.49/2.40
% 7.49/2.40 % (8681)Memory used [KB]: 7419
% 7.49/2.40 % (8681)Time elapsed: 0.056 s
% 7.49/2.40 % (8681)Instructions burned: 183 (million)
% 7.49/2.40 % (8681)------------------------------
% 7.49/2.40 % (8681)------------------------------
% 7.49/2.41 % (8687)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_8264 for (2992ds/182Mi)
% 7.49/2.41 % (8688)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_8264 for (2992ds/164Mi)
% 7.49/2.43 % (8676)Instruction limit reached!
% 7.49/2.43 % (8676)------------------------------
% 7.49/2.43 % (8676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.43 % (8676)Termination reason: Unknown
% 7.49/2.43 % (8676)Termination phase: Saturation
% 7.49/2.43
% 7.49/2.43 % (8676)Memory used [KB]: 8827
% 7.49/2.43 % (8676)Time elapsed: 0.137 s
% 7.49/2.43 % (8676)Instructions burned: 459 (million)
% 7.49/2.43 % (8676)------------------------------
% 7.49/2.43 % (8676)------------------------------
% 7.49/2.43 % (8685)Instruction limit reached!
% 7.49/2.43 % (8685)------------------------------
% 7.49/2.43 % (8685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.43 % (8685)Termination reason: Unknown
% 7.49/2.43 % (8685)Termination phase: Property scanning
% 7.49/2.43
% 7.49/2.43 % (8685)Memory used [KB]: 2686
% 7.49/2.43 % (8685)Time elapsed: 0.034 s
% 7.49/2.43 % (8685)Instructions burned: 116 (million)
% 7.49/2.43 % (8685)------------------------------
% 7.49/2.43 % (8685)------------------------------
% 7.49/2.44 % (8689)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_8264 for (2992ds/50Mi)
% 7.49/2.44 % (8690)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_8264 for (2992ds/368Mi)
% 7.49/2.44 % (8684)Instruction limit reached!
% 7.49/2.44 % (8684)------------------------------
% 7.49/2.44 % (8684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.44 % (8684)Termination reason: Unknown
% 7.49/2.44 % (8684)Termination phase: Saturation
% 7.49/2.44
% 7.49/2.44 % (8684)Memory used [KB]: 7291
% 7.49/2.44 % (8684)Time elapsed: 0.057 s
% 7.49/2.44 % (8684)Instructions burned: 217 (million)
% 7.49/2.44 % (8684)------------------------------
% 7.49/2.44 % (8684)------------------------------
% 7.49/2.45 % (8689)Instruction limit reached!
% 7.49/2.45 % (8689)------------------------------
% 7.49/2.45 % (8689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.45 % (8689)Termination reason: Unknown
% 7.49/2.45 % (8689)Termination phase: Property scanning
% 7.49/2.45
% 7.49/2.45 % (8689)Memory used [KB]: 2302
% 7.49/2.45 % (8689)Time elapsed: 0.015 s
% 7.49/2.45 % (8689)Instructions burned: 52 (million)
% 7.49/2.45 % (8689)------------------------------
% 7.49/2.45 % (8689)------------------------------
% 7.49/2.45 % (8691)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_8264 for (2992ds/1021Mi)
% 7.49/2.45 % (8688)Instruction limit reached!
% 7.49/2.45 % (8688)------------------------------
% 7.49/2.45 % (8688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.45 % (8688)Termination reason: Unknown
% 7.49/2.45 % (8688)Termination phase: Property scanning
% 7.49/2.45
% 7.49/2.45 % (8688)Memory used [KB]: 2686
% 7.49/2.45 % (8688)Time elapsed: 0.044 s
% 7.49/2.45 % (8688)Instructions burned: 164 (million)
% 7.49/2.45 % (8688)------------------------------
% 7.49/2.45 % (8688)------------------------------
% 7.49/2.45 % (8687)Instruction limit reached!
% 7.49/2.45 % (8687)------------------------------
% 7.49/2.45 % (8687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.45 % (8687)Termination reason: Unknown
% 7.49/2.45 % (8687)Termination phase: Property scanning
% 7.49/2.45
% 7.49/2.45 % (8687)Memory used [KB]: 2686
% 7.49/2.45 % (8687)Time elapsed: 0.048 s
% 7.49/2.45 % (8687)Instructions burned: 183 (million)
% 7.49/2.45 % (8687)------------------------------
% 7.49/2.45 % (8687)------------------------------
% 7.49/2.46 % (8692)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_8264 for (2991ds/267Mi)
% 7.49/2.46 % (8693)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_8264 for (2991ds/204Mi)
% 7.49/2.46 % (8694)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_8264 for (2991ds/26Mi)
% 7.49/2.47 % (8694)Instruction limit reached!
% 7.49/2.47 % (8694)------------------------------
% 7.49/2.47 % (8694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.47 % (8694)Termination reason: Unknown
% 7.49/2.47 % (8694)Termination phase: shuffling
% 7.49/2.47
% 7.49/2.47 % (8694)Memory used [KB]: 1918
% 7.49/2.47 % (8694)Time elapsed: 0.008 s
% 7.49/2.47 % (8694)Instructions burned: 26 (million)
% 7.49/2.47 % (8694)------------------------------
% 7.49/2.47 % (8694)------------------------------
% 7.49/2.48 % (8695)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_8264 for (2991ds/53Mi)
% 7.49/2.49 % (8695)Instruction limit reached!
% 7.49/2.49 % (8695)------------------------------
% 7.49/2.49 % (8695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.49 % (8695)Termination reason: Unknown
% 7.49/2.49 % (8695)Termination phase: Property scanning
% 7.49/2.49
% 7.49/2.49 % (8695)Memory used [KB]: 2302
% 7.49/2.49 % (8695)Time elapsed: 0.016 s
% 7.49/2.49 % (8695)Instructions burned: 53 (million)
% 7.49/2.49 % (8695)------------------------------
% 7.49/2.49 % (8695)------------------------------
% 8.09/2.50 % (8696)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_8264 for (2991ds/4436Mi)
% 8.09/2.52 % (8693)Instruction limit reached!
% 8.09/2.52 % (8693)------------------------------
% 8.09/2.52 % (8693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.52 % (8693)Termination reason: Unknown
% 8.09/2.52 % (8693)Termination phase: Saturation
% 8.09/2.52
% 8.09/2.52 % (8693)Memory used [KB]: 7419
% 8.09/2.52 % (8693)Time elapsed: 0.058 s
% 8.09/2.52 % (8693)Instructions burned: 204 (million)
% 8.09/2.52 % (8693)------------------------------
% 8.09/2.52 % (8693)------------------------------
% 8.09/2.53 % (8692)Instruction limit reached!
% 8.09/2.53 % (8692)------------------------------
% 8.09/2.53 % (8692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.53 % (8692)Termination reason: Unknown
% 8.09/2.53 % (8692)Termination phase: Saturation
% 8.09/2.53
% 8.09/2.53 % (8692)Memory used [KB]: 7547
% 8.09/2.53 % (8692)Time elapsed: 0.070 s
% 8.09/2.53 % (8692)Instructions burned: 269 (million)
% 8.09/2.53 % (8692)------------------------------
% 8.09/2.53 % (8692)------------------------------
% 8.09/2.53 % (8697)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_8264 for (2991ds/1539Mi)
% 8.09/2.54 % (8698)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_8264 for (2991ds/408Mi)
% 8.09/2.55 % (8690)Instruction limit reached!
% 8.09/2.55 % (8690)------------------------------
% 8.09/2.55 % (8690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.55 % (8690)Termination reason: Unknown
% 8.09/2.55 % (8690)Termination phase: Saturation
% 8.09/2.55
% 8.09/2.55 % (8690)Memory used [KB]: 8827
% 8.09/2.55 % (8690)Time elapsed: 0.113 s
% 8.09/2.55 % (8690)Instructions burned: 368 (million)
% 8.09/2.55 % (8690)------------------------------
% 8.09/2.55 % (8690)------------------------------
% 8.09/2.56 % (8699)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_8264 for (2990ds/5205Mi)
% 8.35/2.62 % (8679)Instruction limit reached!
% 8.35/2.62 % (8679)------------------------------
% 8.35/2.62 % (8679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.62 % (8679)Termination reason: Unknown
% 8.35/2.62 % (8679)Termination phase: Saturation
% 8.35/2.62
% 8.35/2.62 % (8679)Memory used [KB]: 9978
% 8.35/2.62 % (8679)Time elapsed: 0.293 s
% 8.35/2.62 % (8679)Instructions burned: 987 (million)
% 8.35/2.62 % (8679)------------------------------
% 8.35/2.62 % (8679)------------------------------
% 8.35/2.63 % (8700)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_8264 for (2990ds/1913Mi)
% 8.35/2.66 % (8698)Instruction limit reached!
% 8.35/2.66 % (8698)------------------------------
% 8.35/2.66 % (8698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.66 % (8698)Termination reason: Unknown
% 8.35/2.66 % (8698)Termination phase: Saturation
% 8.35/2.66
% 8.35/2.66 % (8698)Memory used [KB]: 8443
% 8.35/2.66 % (8698)Time elapsed: 0.122 s
% 8.35/2.66 % (8698)Instructions burned: 411 (million)
% 8.35/2.66 % (8698)------------------------------
% 8.35/2.66 % (8698)------------------------------
% 8.35/2.67 % (8701)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_8264 for (2989ds/4350Mi)
% 8.35/2.70 % (8686)Instruction limit reached!
% 8.35/2.70 % (8686)------------------------------
% 8.35/2.70 % (8686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.70 % (8686)Termination reason: Unknown
% 8.35/2.70 % (8686)Termination phase: Saturation
% 8.35/2.70
% 8.35/2.70 % (8686)Memory used [KB]: 8571
% 8.35/2.70 % (8686)Time elapsed: 0.296 s
% 8.35/2.70 % (8686)Instructions burned: 924 (million)
% 8.35/2.70 % (8686)------------------------------
% 8.35/2.70 % (8686)------------------------------
% 9.09/2.71 % (8702)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_8264 for (2989ds/68Mi)
% 9.09/2.73 % (8702)Instruction limit reached!
% 9.09/2.73 % (8702)------------------------------
% 9.09/2.73 % (8702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.73 % (8702)Termination reason: Unknown
% 9.09/2.73 % (8702)Termination phase: Property scanning
% 9.09/2.73
% 9.09/2.73 % (8702)Memory used [KB]: 2302
% 9.09/2.73 % (8702)Time elapsed: 0.023 s
% 9.09/2.73 % (8702)Instructions burned: 70 (million)
% 9.09/2.73 % (8702)------------------------------
% 9.09/2.73 % (8702)------------------------------
% 9.09/2.74 % (8703)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_8264 for (2989ds/358Mi)
% 9.09/2.76 % (8691)Instruction limit reached!
% 9.09/2.76 % (8691)------------------------------
% 9.09/2.76 % (8691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.76 % (8691)Termination reason: Unknown
% 9.09/2.76 % (8691)Termination phase: Saturation
% 9.09/2.76
% 9.09/2.76 % (8691)Memory used [KB]: 9210
% 9.09/2.76 % (8691)Time elapsed: 0.306 s
% 9.09/2.76 % (8691)Instructions burned: 1022 (million)
% 9.09/2.76 % (8691)------------------------------
% 9.09/2.76 % (8691)------------------------------
% 9.09/2.77 % (8704)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_8264 for (2988ds/31Mi)
% 9.09/2.78 % (8704)Instruction limit reached!
% 9.09/2.78 % (8704)------------------------------
% 9.09/2.78 % (8704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.78 % (8704)Termination reason: Unknown
% 9.09/2.78 % (8704)Termination phase: Property scanning
% 9.09/2.78
% 9.09/2.78 % (8704)Memory used [KB]: 1918
% 9.09/2.78 % (8704)Time elapsed: 0.011 s
% 9.09/2.78 % (8704)Instructions burned: 32 (million)
% 9.09/2.78 % (8704)------------------------------
% 9.09/2.78 % (8704)------------------------------
% 9.09/2.79 % (8705)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_8264 for (2988ds/279Mi)
% 9.46/2.84 % (8703)Instruction limit reached!
% 9.46/2.84 % (8703)------------------------------
% 9.46/2.84 % (8703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.46/2.84 % (8703)Termination reason: Unknown
% 9.46/2.84 % (8703)Termination phase: Saturation
% 9.46/2.84
% 9.46/2.84 % (8703)Memory used [KB]: 7931
% 9.46/2.84 % (8703)Time elapsed: 0.109 s
% 9.46/2.84 % (8703)Instructions burned: 358 (million)
% 9.46/2.84 % (8703)------------------------------
% 9.46/2.84 % (8703)------------------------------
% 9.46/2.85 % (8705)Refutation not found, incomplete strategy
% 9.46/2.85 % (8705)------------------------------
% 9.46/2.85 % (8705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.46/2.85 % (8705)Termination reason: Refutation not found, incomplete strategy
% 9.46/2.85
% 9.46/2.85
% 9.46/2.85 % (8705)Memory used [KB]: 7803
% 9.46/2.85 % (8705)Time elapsed: 0.067 s
% 9.46/2.85 % (8705)Instructions burned: 251 (million)
% 9.46/2.85 % (8705)------------------------------
% 9.46/2.85 % (8705)------------------------------
% 9.46/2.85 % (8706)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_8264 for (2987ds/258Mi)
% 9.46/2.86 % (8707)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_8264 for (2987ds/26Mi)
% 9.46/2.87 % (8707)Instruction limit reached!
% 9.46/2.87 % (8707)------------------------------
% 9.46/2.87 % (8707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.46/2.87 % (8707)Termination reason: Unknown
% 9.46/2.87 % (8707)Termination phase: shuffling
% 9.46/2.87
% 9.46/2.87 % (8707)Memory used [KB]: 1918
% 9.46/2.87 % (8707)Time elapsed: 0.008 s
% 9.46/2.87 % (8707)Instructions burned: 26 (million)
% 9.46/2.87 % (8707)------------------------------
% 9.46/2.87 % (8707)------------------------------
% 9.46/2.88 % (8708)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_8264 for (2987ds/995Mi)
% 9.67/2.93 % (8706)Instruction limit reached!
% 9.67/2.93 % (8706)------------------------------
% 9.67/2.93 % (8706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.93 % (8706)Termination reason: Unknown
% 9.67/2.93 % (8706)Termination phase: Saturation
% 9.67/2.93
% 9.67/2.93 % (8706)Memory used [KB]: 7675
% 9.67/2.93 % (8706)Time elapsed: 0.079 s
% 9.67/2.93 % (8706)Instructions burned: 258 (million)
% 9.67/2.93 % (8706)------------------------------
% 9.67/2.93 % (8706)------------------------------
% 9.67/2.94 % (8709)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_8264 for (2987ds/373Mi)
% 9.67/2.99 % (8697)Instruction limit reached!
% 9.67/2.99 % (8697)------------------------------
% 9.67/2.99 % (8697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.99 % (8697)Termination reason: Unknown
% 9.67/2.99 % (8697)Termination phase: Saturation
% 9.67/2.99
% 9.67/2.99 % (8697)Memory used [KB]: 9338
% 9.67/2.99 % (8697)Time elapsed: 0.461 s
% 9.67/2.99 % (8697)Instructions burned: 1541 (million)
% 9.67/2.99 % (8697)------------------------------
% 9.67/2.99 % (8697)------------------------------
% 9.67/3.00 % (8711)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_8264 for (2986ds/253Mi)
% 12.17/3.05 % (8709)Instruction limit reached!
% 12.17/3.05 % (8709)------------------------------
% 12.17/3.05 % (8709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.17/3.05 % (8709)Termination reason: Unknown
% 12.17/3.05 % (8709)Termination phase: Saturation
% 12.17/3.05
% 12.17/3.05 % (8709)Memory used [KB]: 9083
% 12.17/3.05 % (8709)Time elapsed: 0.108 s
% 12.17/3.05 % (8709)Instructions burned: 375 (million)
% 12.17/3.05 % (8709)------------------------------
% 12.17/3.05 % (8709)------------------------------
% 12.17/3.06 % (8712)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_8264 for (2985ds/832Mi)
% 12.17/3.06 % (8711)Instruction limit reached!
% 12.17/3.06 % (8711)------------------------------
% 12.17/3.06 % (8711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.17/3.06 % (8711)Termination reason: Unknown
% 12.17/3.06 % (8711)Termination phase: Saturation
% 12.17/3.06
% 12.17/3.06 % (8711)Memory used [KB]: 7675
% 12.17/3.06 % (8711)Time elapsed: 0.066 s
% 12.17/3.06 % (8711)Instructions burned: 255 (million)
% 12.17/3.06 % (8711)------------------------------
% 12.17/3.06 % (8711)------------------------------
% 12.17/3.07 % (8713)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_8264 for (2985ds/668Mi)
% 12.82/3.16 % (8708)Instruction limit reached!
% 12.82/3.16 % (8708)------------------------------
% 12.82/3.16 % (8708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.82/3.16 % (8708)Termination reason: Unknown
% 12.82/3.16 % (8708)Termination phase: Saturation
% 12.82/3.16
% 12.82/3.16 % (8708)Memory used [KB]: 9850
% 12.82/3.16 % (8708)Time elapsed: 0.287 s
% 12.82/3.16 % (8708)Instructions burned: 996 (million)
% 12.82/3.16 % (8708)------------------------------
% 12.82/3.16 % (8708)------------------------------
% 12.82/3.17 % (8714)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_8264 for (2984ds/40Mi)
% 12.82/3.19 % (8714)Instruction limit reached!
% 12.82/3.19 % (8714)------------------------------
% 12.82/3.19 % (8714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.82/3.19 % (8714)Termination reason: Unknown
% 12.82/3.19 % (8714)Termination phase: shuffling
% 12.82/3.19
% 12.82/3.19 % (8714)Memory used [KB]: 2174
% 12.82/3.19 % (8714)Time elapsed: 0.013 s
% 12.82/3.19 % (8714)Instructions burned: 40 (million)
% 12.82/3.19 % (8714)------------------------------
% 12.82/3.19 % (8714)------------------------------
% 12.82/3.20 % (8715)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_8264 for (2984ds/294Mi)
% 13.18/3.22 % (8700)Instruction limit reached!
% 13.18/3.22 % (8700)------------------------------
% 13.18/3.22 % (8700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.18/3.22 % (8700)Termination reason: Unknown
% 13.18/3.22 % (8700)Termination phase: Saturation
% 13.18/3.22
% 13.18/3.22 % (8700)Memory used [KB]: 4477
% 13.18/3.22 % (8700)Time elapsed: 0.590 s
% 13.18/3.22 % (8700)Instructions burned: 1916 (million)
% 13.18/3.22 % (8700)------------------------------
% 13.18/3.22 % (8700)------------------------------
% 13.18/3.22 % (8715)Refutation not found, incomplete strategy
% 13.18/3.22 % (8715)------------------------------
% 13.18/3.22 % (8715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.18/3.22 % (8715)Termination reason: Refutation not found, incomplete strategy
% 13.18/3.22
% 13.18/3.22
% 13.18/3.22 % (8715)Memory used [KB]: 6908
% 13.18/3.22 % (8715)Time elapsed: 0.027 s
% 13.18/3.22 % (8715)Instructions burned: 101 (million)
% 13.18/3.22 % (8715)------------------------------
% 13.18/3.22 % (8715)------------------------------
% 13.18/3.23 % (8716)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_8264 for (2984ds/187Mi)
% 13.18/3.23 % (8717)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_8264 for (2984ds/371Mi)
% 13.18/3.26 % (8713)Instruction limit reached!
% 13.18/3.26 % (8713)------------------------------
% 13.18/3.26 % (8713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.18/3.26 % (8713)Termination reason: Unknown
% 13.18/3.26 % (8713)Termination phase: Saturation
% 13.18/3.26
% 13.18/3.26 % (8713)Memory used [KB]: 13688
% 13.18/3.26 % (8713)Time elapsed: 0.187 s
% 13.18/3.26 % (8713)Instructions burned: 669 (million)
% 13.18/3.26 % (8713)------------------------------
% 13.18/3.26 % (8713)------------------------------
% 13.18/3.27 % (8718)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_8264 for (2983ds/1827Mi)
% 13.18/3.28 % (8716)Instruction limit reached!
% 13.18/3.28 % (8716)------------------------------
% 13.18/3.28 % (8716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.18/3.28 % (8716)Termination reason: Unknown
% 13.18/3.28 % (8716)Termination phase: Saturation
% 13.18/3.28
% 13.18/3.28 % (8716)Memory used [KB]: 7419
% 13.18/3.28 % (8716)Time elapsed: 0.053 s
% 13.18/3.28 % (8716)Instructions burned: 187 (million)
% 13.18/3.28 % (8716)------------------------------
% 13.18/3.28 % (8716)------------------------------
% 13.18/3.29 % (8719)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_8264 for (2983ds/70Mi)
% 13.80/3.31 % (8719)Instruction limit reached!
% 13.80/3.31 % (8719)------------------------------
% 13.80/3.31 % (8719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.80/3.31 % (8719)Termination reason: Unknown
% 13.80/3.31 % (8719)Termination phase: Property scanning
% 13.80/3.31
% 13.80/3.31 % (8719)Memory used [KB]: 2302
% 13.80/3.31 % (8719)Time elapsed: 0.021 s
% 13.80/3.31 % (8719)Instructions burned: 73 (million)
% 13.80/3.31 % (8719)------------------------------
% 13.80/3.31 % (8719)------------------------------
% 13.80/3.31 % (8712)Instruction limit reached!
% 13.80/3.31 % (8712)------------------------------
% 13.80/3.31 % (8712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.80/3.31 % (8712)Termination reason: Unknown
% 13.80/3.31 % (8712)Termination phase: Saturation
% 13.80/3.31
% 13.80/3.31 % (8712)Memory used [KB]: 8187
% 13.80/3.31 % (8712)Time elapsed: 0.251 s
% 13.80/3.31 % (8712)Instructions burned: 833 (million)
% 13.80/3.31 % (8712)------------------------------
% 13.80/3.31 % (8712)------------------------------
% 13.80/3.32 % (8720)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_8264 for (2983ds/316Mi)
% 13.80/3.32 % (8721)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_8264 for (2983ds/932Mi)
% 13.80/3.35 % (8717)Instruction limit reached!
% 13.80/3.35 % (8717)------------------------------
% 13.80/3.35 % (8717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.80/3.35 % (8717)Termination reason: Unknown
% 13.80/3.35 % (8717)Termination phase: Saturation
% 13.80/3.35
% 13.80/3.35 % (8717)Memory used [KB]: 8187
% 13.80/3.35 % (8717)Time elapsed: 0.116 s
% 13.80/3.35 % (8717)Instructions burned: 371 (million)
% 13.80/3.35 % (8717)------------------------------
% 13.80/3.35 % (8717)------------------------------
% 13.80/3.36 % (8722)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_8264 for (2983ds/4714Mi)
% 13.80/3.39 % (8720)Refutation not found, incomplete strategy
% 13.80/3.39 % (8720)------------------------------
% 13.80/3.39 % (8720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.80/3.39 % (8720)Termination reason: Refutation not found, incomplete strategy
% 13.80/3.39
% 13.80/3.39
% 13.80/3.39 % (8720)Memory used [KB]: 7803
% 13.80/3.39 % (8720)Time elapsed: 0.096 s
% 13.80/3.39 % (8720)Instructions burned: 276 (million)
% 13.80/3.39 % (8720)------------------------------
% 13.80/3.39 % (8720)------------------------------
% 14.59/3.40 % (8723)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_8264 for (2982ds/8250Mi)
% 14.59/3.43 % (8722)Refutation not found, incomplete strategy
% 14.59/3.43 % (8722)------------------------------
% 14.59/3.43 % (8722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.59/3.43 % (8722)Termination reason: Refutation not found, incomplete strategy
% 14.59/3.43
% 14.59/3.43
% 14.59/3.43 % (8722)Memory used [KB]: 7803
% 14.59/3.43 % (8722)Time elapsed: 0.071 s
% 14.59/3.43 % (8722)Instructions burned: 272 (million)
% 14.59/3.43 % (8722)------------------------------
% 14.59/3.43 % (8722)------------------------------
% 14.59/3.44 % (8724)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_8264 for (2982ds/770Mi)
% 14.97/3.58 % (8721)Instruction limit reached!
% 14.97/3.58 % (8721)------------------------------
% 14.97/3.58 % (8721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.97/3.58 % (8721)Termination reason: Unknown
% 14.97/3.58 % (8721)Termination phase: Saturation
% 14.97/3.58
% 14.97/3.58 % (8721)Memory used [KB]: 9850
% 14.97/3.58 % (8721)Time elapsed: 0.283 s
% 14.97/3.58 % (8721)Instructions burned: 935 (million)
% 14.97/3.58 % (8721)------------------------------
% 14.97/3.58 % (8721)------------------------------
% 14.97/3.59 % (8725)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_8264 for (2980ds/794Mi)
% 15.54/3.61 % (8724)Instruction limit reached!
% 15.54/3.61 % (8724)------------------------------
% 15.54/3.61 % (8724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/3.61 % (8724)Termination reason: Unknown
% 15.54/3.61 % (8724)Termination phase: Saturation
% 15.54/3.61
% 15.54/3.61 % (8724)Memory used [KB]: 6652
% 15.54/3.61 % (8724)Time elapsed: 0.172 s
% 15.54/3.61 % (8724)Instructions burned: 771 (million)
% 15.54/3.61 % (8724)------------------------------
% 15.54/3.61 % (8724)------------------------------
% 15.54/3.62 % (8726)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_8264 for (2980ds/464Mi)
% 16.03/3.76 % (8726)Instruction limit reached!
% 16.03/3.76 % (8726)------------------------------
% 16.03/3.76 % (8726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.03/3.76 % (8726)Termination reason: Unknown
% 16.03/3.76 % (8726)Termination phase: Saturation
% 16.03/3.76
% 16.03/3.76 % (8726)Memory used [KB]: 8955
% 16.03/3.76 % (8726)Time elapsed: 0.139 s
% 16.03/3.76 % (8726)Instructions burned: 465 (million)
% 16.03/3.76 % (8726)------------------------------
% 16.03/3.76 % (8726)------------------------------
% 16.03/3.77 % (8727)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_8264 for (2978ds/1376Mi)
% 16.03/3.79 % (8699)First to succeed.
% 16.03/3.79 % (8699)Refutation found. Thanks to Tanya!
% 16.03/3.79 % SZS status Theorem for DTF2THF_8264
% 16.03/3.79 % SZS output start Proof for DTF2THF_8264
% 16.03/3.79 thf(type_def_5, type, product_prod_nat_nat: $tType).
% 16.03/3.79 thf(type_def_6, type, a: $tType).
% 16.03/3.79 thf(type_def_8, type, nat: $tType).
% 16.03/3.79 thf(type_def_9, type, set_Pr1986765409at_nat: $tType).
% 16.03/3.79 thf(type_def_10, type, set_nat: $tType).
% 16.03/3.79 thf(type_def_11, type, set_set_nat: $tType).
% 16.03/3.79 thf(type_def_12, type, set_se1612935105at_nat: $tType).
% 16.03/3.79 thf(type_def_13, type, list_P559422087at_nat: $tType).
% 16.03/3.79 thf(type_def_14, type, list_nat: $tType).
% 16.03/3.79 thf(func_def_0, type, set_se1612935105at_nat: $tType).
% 16.03/3.79 thf(func_def_1, type, list_P559422087at_nat: $tType).
% 16.03/3.79 thf(func_def_2, type, set_Pr1986765409at_nat: $tType).
% 16.03/3.79 thf(func_def_3, type, product_prod_nat_nat: $tType).
% 16.03/3.79 thf(func_def_4, type, set_set_nat: $tType).
% 16.03/3.79 thf(func_def_5, type, list_nat: $tType).
% 16.03/3.79 thf(func_def_6, type, set_nat: $tType).
% 16.03/3.79 thf(func_def_7, type, nat: $tType).
% 16.03/3.79 thf(func_def_8, type, a: $tType).
% 16.03/3.79 thf(func_def_9, type, edmond1517640972ysis_a: (product_prod_nat_nat > a) > $o).
% 16.03/3.79 thf(func_def_10, type, edmond475474835dges_a: (product_prod_nat_nat > a) > nat > nat > set_Pr1986765409at_nat).
% 16.03/3.79 thf(func_def_11, type, edmond771116670s_uE_a: (product_prod_nat_nat > a) > set_Pr1986765409at_nat).
% 16.03/3.79 thf(func_def_12, type, finite_card_nat: set_nat > nat).
% 16.03/3.79 thf(func_def_13, type, finite447719721at_nat: set_Pr1986765409at_nat > nat).
% 16.03/3.79 thf(func_def_14, type, finite_finite_nat: set_nat > $o).
% 16.03/3.79 thf(func_def_15, type, finite772653738at_nat: set_Pr1986765409at_nat > $o).
% 16.03/3.79 thf(func_def_16, type, finite2012248349et_nat: set_set_nat > $o).
% 16.03/3.79 thf(func_def_17, type, finite1457549322at_nat: set_se1612935105at_nat > $o).
% 16.03/3.79 thf(func_def_18, type, finite_Graph_a: (product_prod_nat_nat > a) > $o).
% 16.03/3.79 thf(func_def_19, type, e_a: (product_prod_nat_nat > a) > set_Pr1986765409at_nat).
% 16.03/3.79 thf(func_def_20, type, v_a: (product_prod_nat_nat > a) > set_nat).
% 16.03/3.79 thf(func_def_21, type, adjacent_nodes_a: (product_prod_nat_nat > a) > nat > set_nat).
% 16.03/3.79 thf(func_def_22, type, incoming_a: (product_prod_nat_nat > a) > nat > set_Pr1986765409at_nat).
% 16.03/3.79 thf(func_def_23, type, incoming_a2: (product_prod_nat_nat > a) > set_nat > set_Pr1986765409at_nat).
% 16.03/3.79 thf(func_def_24, type, isPath_a: (product_prod_nat_nat > a) > nat > list_P559422087at_nat > nat > $o).
% 16.03/3.79 thf(func_def_25, type, isShortestPath_a: (product_prod_nat_nat > a) > nat > list_P559422087at_nat > nat > $o).
% 16.03/3.79 thf(func_def_26, type, outgoing_a: (product_prod_nat_nat > a) > nat > set_Pr1986765409at_nat).
% 16.03/3.79 thf(func_def_27, type, outgoing_a2: (product_prod_nat_nat > a) > set_nat > set_Pr1986765409at_nat).
% 16.03/3.79 thf(func_def_28, type, pathVertices: nat > list_P559422087at_nat > list_nat).
% 16.03/3.79 thf(func_def_29, type, reachableNodes_a: (product_prod_nat_nat > a) > nat > set_nat).
% 16.03/3.79 thf(func_def_30, type, inf_inf_nat: nat > nat > nat).
% 16.03/3.79 thf(func_def_31, type, inf_inf_set_nat: set_nat > set_nat > set_nat).
% 16.03/3.79 thf(func_def_32, type, inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat).
% 16.03/3.79 thf(func_def_33, type, cons_nat: nat > list_nat > list_nat).
% 16.03/3.79 thf(func_def_34, type, cons_P66992567at_nat: product_prod_nat_nat > list_P559422087at_nat > list_P559422087at_nat).
% 16.03/3.79 thf(func_def_35, type, nil_Pr1308055047at_nat: list_P559422087at_nat).
% 16.03/3.79 thf(func_def_36, type, set_nat2: list_nat > set_nat).
% 16.03/3.79 thf(func_def_37, type, set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat).
% 16.03/3.79 thf(func_def_38, type, size_s1990949619at_nat: list_P559422087at_nat > nat).
% 16.03/3.79 thf(func_def_39, type, ord_less_eq_nat: nat > nat > $o).
% 16.03/3.79 thf(func_def_40, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 16.03/3.79 thf(func_def_41, type, ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o).
% 16.03/3.79 thf(func_def_42, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 16.03/3.79 thf(func_def_43, type, collect_nat: (nat > $o) > set_nat).
% 16.03/3.79 thf(func_def_44, type, collec7649004at_nat: (product_prod_nat_nat > $o) > set_Pr1986765409at_nat).
% 16.03/3.79 thf(func_def_45, type, member_nat: nat > set_nat > $o).
% 16.03/3.79 thf(func_def_46, type, member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o).
% 16.03/3.79 thf(func_def_47, type, member_set_nat: set_nat > set_set_nat > $o).
% 16.03/3.79 thf(func_def_48, type, member298845450at_nat: set_Pr1986765409at_nat > set_se1612935105at_nat > $o).
% 16.03/3.79 thf(func_def_49, type, c: product_prod_nat_nat > a).
% 16.03/3.79 thf(func_def_50, type, edges: set_Pr1986765409at_nat).
% 16.03/3.79 thf(func_def_51, type, p: list_P559422087at_nat).
% 16.03/3.79 thf(func_def_52, type, s: nat).
% 16.03/3.79 thf(func_def_53, type, t: nat).
% 16.03/3.79 thf(func_def_74, type, ph1: !>[X0: $tType]:(X0)).
% 16.03/3.79 thf(func_def_75, type, sK2: product_prod_nat_nat).
% 16.03/3.79 thf(func_def_76, type, sK3: list_P559422087at_nat > list_P559422087at_nat).
% 16.03/3.79 thf(func_def_77, type, sK4: list_P559422087at_nat).
% 16.03/3.79 thf(func_def_78, type, sK5: list_P559422087at_nat).
% 16.03/3.79 thf(func_def_79, type, sK6: nat > list_P559422087at_nat).
% 16.03/3.79 thf(func_def_80, type, sK7: set_nat > list_P559422087at_nat).
% 16.03/3.79 thf(func_def_81, type, sK8: nat).
% 16.03/3.79 thf(func_def_82, type, sK9: nat > list_P559422087at_nat).
% 16.03/3.79 thf(func_def_83, type, sK10: set_nat > list_P559422087at_nat).
% 16.03/3.79 thf(func_def_84, type, sK11: set_Pr1986765409at_nat > list_P559422087at_nat).
% 16.03/3.79 thf(func_def_85, type, sK12: list_nat > nat).
% 16.03/3.79 thf(func_def_86, type, sK13: nat > nat).
% 16.03/3.79 thf(func_def_87, type, sK14: list_nat > list_nat).
% 16.03/3.79 thf(func_def_88, type, sK15: list_nat).
% 16.03/3.79 thf(func_def_89, type, sK16: nat > list_nat).
% 16.03/3.79 thf(f15212,plain,(
% 16.03/3.79 $false),
% 16.03/3.79 inference(trivial_inequality_removal,[status(thm)],[f15211])).
% 16.03/3.79 thf(f15211,plain,(
% 16.03/3.79 ($false = $true)),
% 16.03/3.79 inference(forward_demodulation,[status(thm)],[f15210,f2147])).
% 16.03/3.79 thf(f2147,plain,(
% 16.03/3.79 ($false = (member701585322at_nat @ sK2 @ (set_Pr2131844118at_nat @ sK5)))),
% 16.03/3.79 inference(backward_demodulation,[status(thm)],[f2079,f2142])).
% 16.03/3.79 thf(f2142,plain,(
% 16.03/3.79 ((e_a @ c) = (set_Pr2131844118at_nat @ sK5))),
% 16.03/3.79 inference(equality_proxy_clausification,[status(thm)],[f2138])).
% 16.03/3.79 thf(f2138,plain,(
% 16.03/3.79 (((set_Pr2131844118at_nat @ sK5) = (e_a @ c)) = $true)),
% 16.03/3.79 inference(beta_eta_normalization,[status(thm)],[f2136])).
% 16.03/3.79 thf(f2136,plain,(
% 16.03/3.79 (((^[Y0 : list_P559422087at_nat]: ((set_Pr2131844118at_nat @ Y0) = (e_a @ c))) @ sK5) = $true)),
% 16.03/3.79 inference(sigma_clausification,[status(thm)],[f2100])).
% 16.03/3.79 thf(f2100,plain,(
% 16.03/3.79 ($true = (?? @ list_P559422087at_nat @ (^[Y0 : list_P559422087at_nat]: ((set_Pr2131844118at_nat @ Y0) = (e_a @ c)))))),
% 16.03/3.79 inference(boolean_simplification,[status(thm)],[f2088])).
% 16.03/3.79 thf(f2088,plain,(
% 16.03/3.79 ($true = ($true => (?? @ list_P559422087at_nat @ (^[Y0 : list_P559422087at_nat]: ((set_Pr2131844118at_nat @ Y0) = (e_a @ c))))))),
% 16.03/3.79 inference(superposition,[status(thm)],[f2083,f1248])).
% 16.03/3.79 thf(f1248,plain,(
% 16.03/3.79 ((finite772653738at_nat @ (e_a @ c)) = $true)),
% 16.03/3.79 inference(cnf_transformation,[status(thm)],[f989])).
% 16.03/3.79 thf(f989,plain,(
% 16.03/3.79 ((finite772653738at_nat @ (e_a @ c)) = $true)),
% 16.03/3.79 inference(fool_elimination,[status(thm)],[f988])).
% 16.03/3.79 thf(f988,plain,(
% 16.03/3.79 (finite772653738at_nat @ (e_a @ c))),
% 16.03/3.79 inference(rectify,[status(thm)],[f157])).
% 16.03/3.79 thf(f157,axiom,(
% 16.03/3.79 (finite772653738at_nat @ (e_a @ c))),
% 16.03/3.79 file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',fact_156_finite__E)).
% 16.03/3.79 thf(f2083,plain,(
% 16.03/3.79 ( ! [X1 : set_Pr1986765409at_nat] : ((((finite772653738at_nat @ X1) => (?? @ list_P559422087at_nat @ (^[Y0 : list_P559422087at_nat]: ((set_Pr2131844118at_nat @ Y0) = X1)))) = $true)) )),
% 16.03/3.79 inference(beta_eta_normalization,[status(thm)],[f2082])).
% 16.03/3.79 thf(f2082,plain,(
% 16.03/3.79 ( ! [X1 : set_Pr1986765409at_nat] : ((((^[Y0 : set_Pr1986765409at_nat]: ((finite772653738at_nat @ Y0) => (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: ((set_Pr2131844118at_nat @ Y1) = Y0))))) @ X1) = $true)) )),
% 16.03/3.79 inference(pi_clausification,[status(thm)],[f1067])).
% 16.03/3.79 thf(f1067,plain,(
% 16.03/3.79 ($true = (!! @ set_Pr1986765409at_nat @ (^[Y0 : set_Pr1986765409at_nat]: ((finite772653738at_nat @ Y0) => (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: ((set_Pr2131844118at_nat @ Y1) = Y0)))))))),
% 16.03/3.79 inference(cnf_transformation,[status(thm)],[f993])).
% 16.03/3.79 thf(f993,plain,(
% 16.03/3.79 ($true = (!! @ set_Pr1986765409at_nat @ (^[Y0 : set_Pr1986765409at_nat]: ((finite772653738at_nat @ Y0) => (?? @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: ((set_Pr2131844118at_nat @ Y1) = Y0)))))))),
% 16.03/3.79 inference(fool_elimination,[status(thm)],[f992])).
% 16.03/3.79 thf(f992,plain,(
% 16.03/3.79 ! [X0 : set_Pr1986765409at_nat] : ((finite772653738at_nat @ X0) => ? [X1 : list_P559422087at_nat] : ((set_Pr2131844118at_nat @ X1) = X0))),
% 16.03/3.79 inference(rectify,[status(thm)],[f327])).
% 16.03/3.79 thf(f327,axiom,(
% 16.03/3.79 ! [X2 : set_Pr1986765409at_nat] : ((finite772653738at_nat @ X2) => ? [X47 : list_P559422087at_nat] : ((set_Pr2131844118at_nat @ X47) = X2))),
% 16.03/3.79 file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',fact_326_finite__list)).
% 16.03/3.79 thf(f2079,plain,(
% 16.03/3.79 ($false = (member701585322at_nat @ sK2 @ (e_a @ c)))),
% 16.03/3.79 inference(boolean_simplification,[status(thm)],[f2078])).
% 16.03/3.79 thf(f2078,plain,(
% 16.03/3.79 ($false = ($true => (member701585322at_nat @ sK2 @ (e_a @ c))))),
% 16.03/3.79 inference(backward_demodulation,[status(thm)],[f2075,f2077])).
% 16.03/3.79 thf(f2077,plain,(
% 16.03/3.79 ((member701585322at_nat @ sK2 @ edges) = $true)),
% 16.03/3.79 inference(binary_proxy_clausification,[status(thm)],[f2075])).
% 16.03/3.79 thf(f2075,plain,(
% 16.03/3.79 ($false = ((member701585322at_nat @ sK2 @ edges) => (member701585322at_nat @ sK2 @ (e_a @ c))))),
% 16.03/3.79 inference(beta_eta_normalization,[status(thm)],[f2074])).
% 16.03/3.79 thf(f2074,plain,(
% 16.03/3.79 ($false = ((^[Y0 : product_prod_nat_nat]: ((member701585322at_nat @ Y0 @ edges) => (member701585322at_nat @ Y0 @ (e_a @ c)))) @ sK2))),
% 16.03/3.79 inference(sigma_clausification,[status(thm)],[f2071])).
% 16.03/3.79 thf(f2071,plain,(
% 16.03/3.79 ($false = (!! @ product_prod_nat_nat @ (^[Y0 : product_prod_nat_nat]: ((member701585322at_nat @ Y0 @ edges) => (member701585322at_nat @ Y0 @ (e_a @ c))))))),
% 16.03/3.79 inference(not_proxy_clausification,[status(thm)],[f1889])).
% 16.03/3.79 thf(f1889,plain,(
% 16.03/3.79 ((~ (!! @ product_prod_nat_nat @ (^[Y0 : product_prod_nat_nat]: ((member701585322at_nat @ Y0 @ edges) => (member701585322at_nat @ Y0 @ (e_a @ c)))))) = $true)),
% 16.03/3.79 inference(beta_eta_normalization,[status(thm)],[f1523])).
% 16.03/3.79 thf(f1523,plain,(
% 16.03/3.79 ((~ ((^[Y0 : set_Pr1986765409at_nat]: ((^[Y1 : set_Pr1986765409at_nat]: (!! @ product_prod_nat_nat @ (^[Y2 : product_prod_nat_nat]: ((member701585322at_nat @ Y2 @ Y0) => (member701585322at_nat @ Y2 @ Y1))))))) @ edges @ (e_a @ c))) = $true)),
% 16.03/3.79 inference(definition_unfolding,[status(thm)],[f1196,f1083])).
% 16.03/3.79 thf(f1083,plain,(
% 16.03/3.79 (ord_le841296385at_nat = (^[Y0 : set_Pr1986765409at_nat]: ((^[Y1 : set_Pr1986765409at_nat]: (!! @ product_prod_nat_nat @ (^[Y2 : product_prod_nat_nat]: ((member701585322at_nat @ Y2 @ Y0) => (member701585322at_nat @ Y2 @ Y1))))))))),
% 16.03/3.79 inference(cnf_transformation,[status(thm)],[f917])).
% 16.03/3.79 thf(f917,plain,(
% 16.03/3.79 (ord_le841296385at_nat = (^[Y0 : set_Pr1986765409at_nat]: ((^[Y1 : set_Pr1986765409at_nat]: (!! @ product_prod_nat_nat @ (^[Y2 : product_prod_nat_nat]: ((member701585322at_nat @ Y2 @ Y0) => (member701585322at_nat @ Y2 @ Y1))))))))),
% 16.03/3.79 inference(fool_elimination,[status(thm)],[f916])).
% 16.03/3.79 thf(f916,plain,(
% 16.03/3.79 ((^[X0 : set_Pr1986765409at_nat, X1 : set_Pr1986765409at_nat] : (! [X2 : product_prod_nat_nat] : ((member701585322at_nat @ X2 @ X0) => (member701585322at_nat @ X2 @ X1)))) = ord_le841296385at_nat)),
% 16.03/3.79 inference(rectify,[status(thm)],[f125])).
% 16.03/3.79 thf(f125,axiom,(
% 16.03/3.79 ((^[X28 : set_Pr1986765409at_nat, X29 : set_Pr1986765409at_nat] : (! [X31 : product_prod_nat_nat] : ((member701585322at_nat @ X31 @ X28) => (member701585322at_nat @ X31 @ X29)))) = ord_le841296385at_nat)),
% 16.03/3.79 file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',fact_124_subset__iff)).
% 16.03/3.79 thf(f1196,plain,(
% 16.03/3.79 ((~ (ord_le841296385at_nat @ edges @ (e_a @ c))) = $true)),
% 16.03/3.79 inference(cnf_transformation,[status(thm)],[f799])).
% 16.03/3.79 thf(f799,plain,(
% 16.03/3.79 ((~ (ord_le841296385at_nat @ edges @ (e_a @ c))) = $true)),
% 16.03/3.79 inference(fool_elimination,[status(thm)],[f798])).
% 16.03/3.79 thf(f798,plain,(
% 16.03/3.79 ~(ord_le841296385at_nat @ edges @ (e_a @ c))),
% 16.03/3.79 inference(rectify,[status(thm)],[f355])).
% 16.03/3.79 thf(f355,negated_conjecture,(
% 16.03/3.79 ~(ord_le841296385at_nat @ edges @ (e_a @ c))),
% 16.03/3.79 inference(negated_conjecture,[status(cth)],[f354])).
% 16.03/3.79 thf(f354,conjecture,(
% 16.03/3.79 (ord_le841296385at_nat @ edges @ (e_a @ c))),
% 16.03/3.79 file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',conj_0)).
% 16.03/3.79 thf(f15210,plain,(
% 16.03/3.79 ($true = (member701585322at_nat @ sK2 @ (set_Pr2131844118at_nat @ sK5)))),
% 16.03/3.79 inference(boolean_simplification,[status(thm)],[f15204])).
% 16.03/3.79 thf(f15204,plain,(
% 16.03/3.79 (($true => (member701585322at_nat @ sK2 @ (set_Pr2131844118at_nat @ sK5))) = $true)),
% 16.03/3.79 inference(superposition,[status(thm)],[f15199,f2081])).
% 16.03/3.79 thf(f2081,plain,(
% 16.03/3.79 ($true = (member701585322at_nat @ sK2 @ (set_Pr2131844118at_nat @ p)))),
% 16.03/3.79 inference(boolean_simplification,[status(thm)],[f2080])).
% 16.03/3.79 thf(f2080,plain,(
% 16.03/3.79 (($true => (member701585322at_nat @ sK2 @ (set_Pr2131844118at_nat @ p))) = $true)),
% 16.03/3.79 inference(superposition,[status(thm)],[f2069,f2077])).
% 16.03/3.79 thf(f2069,plain,(
% 16.03/3.79 ( ! [X1 : product_prod_nat_nat] : ((((member701585322at_nat @ X1 @ edges) => (member701585322at_nat @ X1 @ (set_Pr2131844118at_nat @ p))) = $true)) )),
% 16.03/3.79 inference(beta_eta_normalization,[status(thm)],[f2068])).
% 16.03/3.79 thf(f2068,plain,(
% 16.03/3.79 ( ! [X1 : product_prod_nat_nat] : (($true = ((^[Y0 : product_prod_nat_nat]: ((member701585322at_nat @ Y0 @ edges) => (member701585322at_nat @ Y0 @ (set_Pr2131844118at_nat @ p)))) @ X1))) )),
% 16.03/3.79 inference(pi_clausification,[status(thm)],[f1791])).
% 16.03/3.79 thf(f1791,plain,(
% 16.03/3.79 ((!! @ product_prod_nat_nat @ (^[Y0 : product_prod_nat_nat]: ((member701585322at_nat @ Y0 @ edges) => (member701585322at_nat @ Y0 @ (set_Pr2131844118at_nat @ p))))) = $true)),
% 16.03/3.79 inference(beta_eta_normalization,[status(thm)],[f1424])).
% 16.03/3.79 thf(f1424,plain,(
% 16.03/3.79 ($true = ((^[Y0 : set_Pr1986765409at_nat]: ((^[Y1 : set_Pr1986765409at_nat]: (!! @ product_prod_nat_nat @ (^[Y2 : product_prod_nat_nat]: ((member701585322at_nat @ Y2 @ Y0) => (member701585322at_nat @ Y2 @ Y1))))))) @ edges @ (set_Pr2131844118at_nat @ p)))),
% 16.03/3.79 inference(definition_unfolding,[status(thm)],[f1073,f1083])).
% 16.03/3.79 thf(f1073,plain,(
% 16.03/3.79 ((ord_le841296385at_nat @ edges @ (set_Pr2131844118at_nat @ p)) = $true)),
% 16.03/3.79 inference(cnf_transformation,[status(thm)],[f438])).
% 16.03/3.79 thf(f438,plain,(
% 16.03/3.79 ((ord_le841296385at_nat @ edges @ (set_Pr2131844118at_nat @ p)) = $true)),
% 16.03/3.79 inference(fool_elimination,[status(thm)],[f437])).
% 16.03/3.79 thf(f437,plain,(
% 16.03/3.79 (ord_le841296385at_nat @ edges @ (set_Pr2131844118at_nat @ p))),
% 16.03/3.79 inference(rectify,[status(thm)],[f2])).
% 16.03/3.79 thf(f2,axiom,(
% 16.03/3.79 (ord_le841296385at_nat @ edges @ (set_Pr2131844118at_nat @ p))),
% 16.03/3.79 file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',fact_1_SP__EDGES)).
% 16.03/3.79 thf(f15199,plain,(
% 16.03/3.79 ( ! [X0 : product_prod_nat_nat] : ((((member701585322at_nat @ X0 @ (set_Pr2131844118at_nat @ p)) => (member701585322at_nat @ X0 @ (set_Pr2131844118at_nat @ sK5))) = $true)) )),
% 16.03/3.79 inference(boolean_simplification,[status(thm)],[f15196])).
% 16.03/3.79 thf(f15196,plain,(
% 16.03/3.79 ( ! [X0 : product_prod_nat_nat] : ((($true => ((member701585322at_nat @ X0 @ (set_Pr2131844118at_nat @ p)) => (member701585322at_nat @ X0 @ (set_Pr2131844118at_nat @ sK5)))) = $true)) )),
% 16.03/3.79 inference(superposition,[status(thm)],[f15164,f10520])).
% 16.03/3.79 thf(f10520,plain,(
% 16.03/3.79 ($true = (isPath_a @ c @ s @ p @ t))),
% 16.03/3.79 inference(boolean_simplification,[status(thm)],[f10519])).
% 16.03/3.79 thf(f10519,plain,(
% 16.03/3.79 (($true => (isPath_a @ c @ s @ p @ t)) = $true)),
% 16.03/3.79 inference(superposition,[status(thm)],[f10468,f1310])).
% 16.03/3.79 thf(f1310,plain,(
% 16.03/3.79 ((isShortestPath_a @ c @ s @ p @ t) = $true)),
% 16.03/3.79 inference(cnf_transformation,[status(thm)],[f848])).
% 16.03/3.79 thf(f848,plain,(
% 16.03/3.79 ((isShortestPath_a @ c @ s @ p @ t) = $true)),
% 16.03/3.79 inference(fool_elimination,[status(thm)],[f847])).
% 16.03/3.79 thf(f847,plain,(
% 16.03/3.79 (isShortestPath_a @ c @ s @ p @ t)),
% 16.03/3.79 inference(rectify,[status(thm)],[f1])).
% 16.03/3.79 thf(f1,axiom,(
% 16.03/3.79 (isShortestPath_a @ c @ s @ p @ t)),
% 16.03/3.79 file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',fact_0_SP)).
% 16.03/3.79 thf(f10468,plain,(
% 16.03/3.79 ( ! [X2 : nat,X3 : list_P559422087at_nat,X1 : nat] : ((((isShortestPath_a @ c @ X1 @ X3 @ X2) => (isPath_a @ c @ X1 @ X3 @ X2)) = $true)) )),
% 16.03/3.79 inference(beta_eta_normalization,[status(thm)],[f10467])).
% 16.03/3.79 thf(f10467,plain,(
% 16.03/3.79 ( ! [X2 : nat,X3 : list_P559422087at_nat,X1 : nat] : ((((^[Y0 : list_P559422087at_nat]: ((isShortestPath_a @ c @ X1 @ Y0 @ X2) => (isPath_a @ c @ X1 @ Y0 @ X2))) @ X3) = $true)) )),
% 16.03/3.79 inference(pi_clausification,[status(thm)],[f10452])).
% 16.03/3.79 thf(f10452,plain,(
% 16.03/3.79 ( ! [X2 : nat,X1 : nat] : (((!! @ list_P559422087at_nat @ (^[Y0 : list_P559422087at_nat]: ((isShortestPath_a @ c @ X1 @ Y0 @ X2) => (isPath_a @ c @ X1 @ Y0 @ X2)))) = $true)) )),
% 16.03/3.79 inference(beta_eta_normalization,[status(thm)],[f10451])).
% 16.03/3.79 thf(f10451,plain,(
% 16.03/3.79 ( ! [X2 : nat,X1 : nat] : ((((^[Y0 : nat]: (!! @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: ((isShortestPath_a @ c @ X1 @ Y1 @ Y0) => (isPath_a @ c @ X1 @ Y1 @ Y0))))) @ X2) = $true)) )),
% 16.03/3.79 inference(pi_clausification,[status(thm)],[f10431])).
% 16.03/3.79 thf(f10431,plain,(
% 16.03/3.79 ( ! [X1 : nat] : (((!! @ nat @ (^[Y0 : nat]: (!! @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: ((isShortestPath_a @ c @ X1 @ Y1 @ Y0) => (isPath_a @ c @ X1 @ Y1 @ Y0)))))) = $true)) )),
% 16.03/3.79 inference(beta_eta_normalization,[status(thm)],[f10430])).
% 16.03/3.79 thf(f10430,plain,(
% 16.03/3.79 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (!! @ list_P559422087at_nat @ (^[Y2 : list_P559422087at_nat]: ((isShortestPath_a @ c @ Y0 @ Y2 @ Y1) => (isPath_a @ c @ Y0 @ Y2 @ Y1))))))) @ X1))) )),
% 16.03/3.79 inference(pi_clausification,[status(thm)],[f1115])).
% 16.03/3.79 thf(f1115,plain,(
% 16.03/3.79 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (!! @ list_P559422087at_nat @ (^[Y2 : list_P559422087at_nat]: ((isShortestPath_a @ c @ Y0 @ Y2 @ Y1) => (isPath_a @ c @ Y0 @ Y2 @ Y1)))))))) = $true)),
% 16.03/3.79 inference(cnf_transformation,[status(thm)],[f943])).
% 16.03/3.79 thf(f943,plain,(
% 16.03/3.79 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (!! @ list_P559422087at_nat @ (^[Y2 : list_P559422087at_nat]: ((isShortestPath_a @ c @ Y0 @ Y2 @ Y1) => (isPath_a @ c @ Y0 @ Y2 @ Y1)))))))) = $true)),
% 16.03/3.79 inference(fool_elimination,[status(thm)],[f942])).
% 16.03/3.79 thf(f942,plain,(
% 16.03/3.79 ! [X0 : list_P559422087at_nat,X1 : nat,X2 : nat] : ((isShortestPath_a @ c @ X2 @ X0 @ X1) => (isPath_a @ c @ X2 @ X0 @ X1))),
% 16.03/3.79 inference(rectify,[status(thm)],[f20])).
% 16.03/3.79 thf(f20,axiom,(
% 16.03/3.79 ! [X6 : list_P559422087at_nat,X7 : nat,X1 : nat] : ((isShortestPath_a @ c @ X1 @ X6 @ X7) => (isPath_a @ c @ X1 @ X6 @ X7))),
% 16.03/3.79 file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',fact_19_shortestPath__is__path)).
% 16.03/3.79 thf(f15164,plain,(
% 16.03/3.79 ( ! [X2 : list_P559422087at_nat,X3 : product_prod_nat_nat,X1 : nat,X4 : nat] : ((((isPath_a @ c @ X4 @ X2 @ X1) => ((member701585322at_nat @ X3 @ (set_Pr2131844118at_nat @ X2)) => (member701585322at_nat @ X3 @ (set_Pr2131844118at_nat @ sK5)))) = $true)) )),
% 16.03/3.79 inference(beta_eta_normalization,[status(thm)],[f15163])).
% 16.03/3.79 thf(f15163,plain,(
% 16.03/3.79 ( ! [X2 : list_P559422087at_nat,X3 : product_prod_nat_nat,X1 : nat,X4 : nat] : ((((^[Y0 : nat]: ((isPath_a @ c @ Y0 @ X2 @ X1) => ((member701585322at_nat @ X3 @ (set_Pr2131844118at_nat @ X2)) => (member701585322at_nat @ X3 @ (set_Pr2131844118at_nat @ sK5))))) @ X4) = $true)) )),
% 16.03/3.79 inference(pi_clausification,[status(thm)],[f15136])).
% 16.03/3.79 thf(f15136,plain,(
% 16.03/3.79 ( ! [X2 : list_P559422087at_nat,X3 : product_prod_nat_nat,X1 : nat] : (((!! @ nat @ (^[Y0 : nat]: ((isPath_a @ c @ Y0 @ X2 @ X1) => ((member701585322at_nat @ X3 @ (set_Pr2131844118at_nat @ X2)) => (member701585322at_nat @ X3 @ (set_Pr2131844118at_nat @ sK5)))))) = $true)) )),
% 16.03/3.79 inference(forward_demodulation,[status(thm)],[f15135,f2142])).
% 16.03/3.79 thf(f15135,plain,(
% 16.03/3.79 ( ! [X2 : list_P559422087at_nat,X3 : product_prod_nat_nat,X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((isPath_a @ c @ Y0 @ X2 @ X1) => ((member701585322at_nat @ X3 @ (set_Pr2131844118at_nat @ X2)) => (member701585322at_nat @ X3 @ (e_a @ c)))))))) )),
% 16.03/3.79 inference(beta_eta_normalization,[status(thm)],[f15134])).
% 16.03/3.79 thf(f15134,plain,(
% 16.03/3.79 ( ! [X2 : list_P559422087at_nat,X3 : product_prod_nat_nat,X1 : nat] : (($true = ((^[Y0 : product_prod_nat_nat]: (!! @ nat @ (^[Y1 : nat]: ((isPath_a @ c @ Y1 @ X2 @ X1) => ((member701585322at_nat @ Y0 @ (set_Pr2131844118at_nat @ X2)) => (member701585322at_nat @ Y0 @ (e_a @ c))))))) @ X3))) )),
% 16.03/3.79 inference(pi_clausification,[status(thm)],[f15107])).
% 16.03/3.79 thf(f15107,plain,(
% 16.03/3.79 ( ! [X2 : list_P559422087at_nat,X1 : nat] : (($true = (!! @ product_prod_nat_nat @ (^[Y0 : product_prod_nat_nat]: (!! @ nat @ (^[Y1 : nat]: ((isPath_a @ c @ Y1 @ X2 @ X1) => ((member701585322at_nat @ Y0 @ (set_Pr2131844118at_nat @ X2)) => (member701585322at_nat @ Y0 @ (e_a @ c)))))))))) )),
% 16.03/3.79 inference(beta_eta_normalization,[status(thm)],[f15106])).
% 16.03/3.79 thf(f15106,plain,(
% 16.03/3.79 ( ! [X2 : list_P559422087at_nat,X1 : nat] : ((((^[Y0 : list_P559422087at_nat]: (!! @ product_prod_nat_nat @ (^[Y1 : product_prod_nat_nat]: (!! @ nat @ (^[Y2 : nat]: ((isPath_a @ c @ Y2 @ Y0 @ X1) => ((member701585322at_nat @ Y1 @ (set_Pr2131844118at_nat @ Y0)) => (member701585322at_nat @ Y1 @ (e_a @ c))))))))) @ X2) = $true)) )),
% 16.03/3.79 inference(pi_clausification,[status(thm)],[f15079])).
% 16.03/3.79 thf(f15079,plain,(
% 16.03/3.79 ( ! [X1 : nat] : (((!! @ list_P559422087at_nat @ (^[Y0 : list_P559422087at_nat]: (!! @ product_prod_nat_nat @ (^[Y1 : product_prod_nat_nat]: (!! @ nat @ (^[Y2 : nat]: ((isPath_a @ c @ Y2 @ Y0 @ X1) => ((member701585322at_nat @ Y1 @ (set_Pr2131844118at_nat @ Y0)) => (member701585322at_nat @ Y1 @ (e_a @ c)))))))))) = $true)) )),
% 16.03/3.79 inference(beta_eta_normalization,[status(thm)],[f15078])).
% 16.03/3.79 thf(f15078,plain,(
% 16.03/3.79 ( ! [X1 : nat] : ((((^[Y0 : nat]: (!! @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (!! @ product_prod_nat_nat @ (^[Y2 : product_prod_nat_nat]: (!! @ nat @ (^[Y3 : nat]: ((isPath_a @ c @ Y3 @ Y1 @ Y0) => ((member701585322at_nat @ Y2 @ (set_Pr2131844118at_nat @ Y1)) => (member701585322at_nat @ Y2 @ (e_a @ c))))))))))) @ X1) = $true)) )),
% 16.03/3.79 inference(pi_clausification,[status(thm)],[f1372])).
% 16.03/3.79 thf(f1372,plain,(
% 16.03/3.79 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (!! @ product_prod_nat_nat @ (^[Y2 : product_prod_nat_nat]: (!! @ nat @ (^[Y3 : nat]: ((isPath_a @ c @ Y3 @ Y1 @ Y0) => ((member701585322at_nat @ Y2 @ (set_Pr2131844118at_nat @ Y1)) => (member701585322at_nat @ Y2 @ (e_a @ c)))))))))))))),
% 16.03/3.79 inference(cnf_transformation,[status(thm)],[f533])).
% 16.03/3.79 thf(f533,plain,(
% 16.03/3.79 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ list_P559422087at_nat @ (^[Y1 : list_P559422087at_nat]: (!! @ product_prod_nat_nat @ (^[Y2 : product_prod_nat_nat]: (!! @ nat @ (^[Y3 : nat]: ((isPath_a @ c @ Y3 @ Y1 @ Y0) => ((member701585322at_nat @ Y2 @ (set_Pr2131844118at_nat @ Y1)) => (member701585322at_nat @ Y2 @ (e_a @ c)))))))))))))),
% 16.03/3.79 inference(fool_elimination,[status(thm)],[f532])).
% 16.03/3.79 thf(f532,plain,(
% 16.03/3.79 ! [X0 : nat,X1 : product_prod_nat_nat,X2 : list_P559422087at_nat,X3 : nat] : ((isPath_a @ c @ X0 @ X2 @ X3) => ((member701585322at_nat @ X1 @ (set_Pr2131844118at_nat @ X2)) => (member701585322at_nat @ X1 @ (e_a @ c))))),
% 16.03/3.79 inference(rectify,[status(thm)],[f19])).
% 16.03/3.79 thf(f19,axiom,(
% 16.03/3.79 ! [X1 : nat,X8 : product_prod_nat_nat,X6 : list_P559422087at_nat,X7 : nat] : ((isPath_a @ c @ X1 @ X6 @ X7) => ((member701585322at_nat @ X8 @ (set_Pr2131844118at_nat @ X6)) => (member701585322at_nat @ X8 @ (e_a @ c))))),
% 16.03/3.79 file('/export/starexec/sandbox/tmp/tmp.oskuXxGIob/DTF2THF_8264.p',fact_18_isPath__edgeset)).
% 16.03/3.79 % SZS output end Proof for DTF2THF_8264
% 16.03/3.79 % (8699)------------------------------
% 16.03/3.79 % (8699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.03/3.79 % (8699)Termination reason: Refutation
% 16.03/3.79
% 16.03/3.79 % (8699)Memory used [KB]: 17782
% 16.03/3.79 % (8699)Time elapsed: 1.226 s
% 16.03/3.79 % (8699)Instructions burned: 4042 (million)
% 16.03/3.79 % (8699)------------------------------
% 16.03/3.79 % (8699)------------------------------
% 16.03/3.79 % (8485)Success in time 2.156 s
%------------------------------------------------------------------------------