%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP059^1 : 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 : n014.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 08:55:13 AM UTC 2026
% Result : Theorem 13.34s 3.13s
% Output : Refutation 13.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 18
% Syntax : Number of formulae : 168 ( 162 unt; 0 typ; 0 def)
% Number of atoms : 604 ( 257 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 1163 ( 45 ~; 19 |; 0 &;1000 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 38 usr; 19 con; 0-4 aty)
% ( 64 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 221 ( 103 ^; 116 !; 2 ?; 221 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
config256849571t_unit: $tType ).
thf(type_def_6,type,
message_p_v: $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(type_def_9,type,
p: $tType ).
thf(type_def_10,type,
list_c1059388851t_unit: $tType ).
thf(type_def_11,type,
list_message_p_v: $tType ).
thf(type_def_12,type,
set_message_p_v: $tType ).
thf(func_def_0,type,
list_c1059388851t_unit: $tType ).
thf(func_def_1,type,
config256849571t_unit: $tType ).
thf(func_def_2,type,
list_message_p_v: $tType ).
thf(func_def_3,type,
set_message_p_v: $tType ).
thf(func_def_4,type,
message_p_v: $tType ).
thf(func_def_5,type,
nat: $tType ).
thf(func_def_6,type,
p: $tType ).
thf(func_def_7,type,
msgs_p1029620568t_unit: config256849571t_unit > message_p_v > nat ).
thf(func_def_8,type,
enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
thf(func_def_9,type,
isReceiverOf_p_v: p > message_p_v > $o ).
thf(func_def_10,type,
firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
thf(func_def_11,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_12,type,
one_one_nat: nat ).
thf(func_def_13,type,
zero_zero_nat: nat ).
thf(func_def_14,type,
prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
thf(func_def_15,type,
prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
thf(func_def_16,type,
last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_17,type,
last_message_p_v: list_message_p_v > message_p_v ).
thf(func_def_18,type,
nil_co1338500125t_unit: list_c1059388851t_unit ).
thf(func_def_19,type,
nil_message_p_v: list_message_p_v ).
thf(func_def_20,type,
nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
thf(func_def_21,type,
nth_message_p_v: list_message_p_v > nat > message_p_v ).
thf(func_def_22,type,
suc: nat > nat ).
thf(func_def_23,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(func_def_24,type,
size_s1168481041ge_p_v: list_message_p_v > nat ).
thf(func_def_25,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_26,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_27,type,
member_message_p_v: message_p_v > set_message_p_v > $o ).
thf(func_def_28,type,
fe: nat > list_c1059388851t_unit ).
thf(func_def_29,type,
firstOccSet: nat > set_message_p_v ).
thf(func_def_30,type,
ft: nat > list_message_p_v ).
thf(func_def_31,type,
index: nat ).
thf(func_def_32,type,
msgInSet: message_p_v ).
thf(func_def_33,type,
msg: message_p_v ).
thf(func_def_34,type,
n0: nat ).
thf(func_def_35,type,
n1: nat ).
thf(func_def_36,type,
nMsg: nat ).
thf(func_def_37,type,
n: nat ).
thf(func_def_38,type,
p2: p ).
thf(func_def_61,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_62,type,
sK2: p ).
thf(func_def_63,type,
sK3: p ).
thf(func_def_64,type,
sK4: nat > list_message_p_v ).
thf(func_def_65,type,
sK5: nat > list_c1059388851t_unit ).
thf(func_def_66,type,
sK6: nat ).
thf(f13703,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f13702]) ).
thf(f13702,plain,
$true = $false,
inference(boolean_simplification,[status(thm)],[f13701]) ).
thf(f13701,plain,
( ( ~ $false ) = $false ),
inference(forward_demodulation,[status(thm)],[f13700,f5274]) ).
thf(f5274,plain,
( ( ord_less_nat @ nMsg @ sK6 )
= $false ),
inference(superposition,[status(thm)],[f1730,f5246]) ).
thf(f5246,plain,
( nMsg
= ( suc @ sK6 ) ),
inference(equality_proxy_clausification,[status(thm)],[f5214]) ).
thf(f5214,plain,
( $true
= ( ( suc @ sK6 )
= nMsg ) ),
inference(beta_eta_normalization,[status(thm)],[f5211]) ).
thf(f5211,plain,
( ( ^ [Y0: nat] :
( ( suc @ Y0 )
= nMsg )
@ sK6 )
= $true ),
inference(sigma_clausification,[status(thm)],[f2486]) ).
thf(f2486,plain,
( $true
= ( ?? @ nat
@ ^ [Y0: nat] :
( ( suc @ Y0 )
= nMsg ) ) ),
inference(boolean_simplification,[status(thm)],[f2461]) ).
thf(f2461,plain,
( $true
= ( $true
=> ( ?? @ nat
@ ^ [Y0: nat] :
( ( suc @ Y0 )
= nMsg ) ) ) ),
inference(superposition,[status(thm)],[f2456,f1234]) ).
thf(f1234,plain,
( ( ord_less_nat @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) @ nMsg )
= $true ),
inference(forward_demodulation,[status(thm)],[f1087,f1107]) ).
thf(f1107,plain,
( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
= ( size_s1168481041ge_p_v @ nil_message_p_v ) ),
inference(definition_unfolding,[status(thm)],[f939,f909]) ).
thf(f909,plain,
( zero_zero_nat
= ( size_s1168481041ge_p_v @ nil_message_p_v ) ),
inference(cnf_transformation,[status(thm)],[f556]) ).
thf(f556,plain,
( zero_zero_nat
= ( size_s1168481041ge_p_v @ nil_message_p_v ) ),
inference(fool_elimination,[status(thm)],[f223]) ).
thf(f223,axiom,
( zero_zero_nat
= ( size_s1168481041ge_p_v @ nil_message_p_v ) ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_222_list_Osize_I3_J) ).
thf(f939,plain,
( zero_zero_nat
= ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ),
inference(cnf_transformation,[status(thm)],[f555]) ).
thf(f555,plain,
( zero_zero_nat
= ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ),
inference(fool_elimination,[status(thm)],[f222]) ).
thf(f222,axiom,
( zero_zero_nat
= ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_221_list_Osize_I3_J) ).
thf(f1087,plain,
( $true
= ( ord_less_nat @ ( size_s1168481041ge_p_v @ nil_message_p_v ) @ nMsg ) ),
inference(definition_unfolding,[status(thm)],[f908,f909]) ).
thf(f908,plain,
( ( ord_less_nat @ zero_zero_nat @ nMsg )
= $true ),
inference(cnf_transformation,[status(thm)],[f494]) ).
thf(f494,plain,
( ( ord_less_nat @ zero_zero_nat @ nMsg )
= $true ),
inference(fool_elimination,[status(thm)],[f493]) ).
thf(f493,plain,
ord_less_nat @ zero_zero_nat @ nMsg,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
ord_less_nat @ zero_zero_nat @ nMsg,
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_0_AssumpOcc6_I1_J) ).
thf(f2456,plain,
! [X1: nat] :
( ( ( ord_less_nat @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) @ X1 )
=> ( ?? @ nat
@ ^ [Y0: nat] :
( ( suc @ Y0 )
= X1 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2455,f1107]) ).
thf(f2455,plain,
! [X1: nat] :
( $true
= ( ( ord_less_nat @ ( size_s1168481041ge_p_v @ nil_message_p_v ) @ X1 )
=> ( ?? @ nat
@ ^ [Y0: nat] :
( ( suc @ Y0 )
= X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2454]) ).
thf(f2454,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( ( ord_less_nat @ ( size_s1168481041ge_p_v @ nil_message_p_v ) @ Y0 )
=> ( ?? @ nat
@ ^ [Y1: nat] :
( ( suc @ Y1 )
= Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1028]) ).
thf(f1028,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( ord_less_nat @ ( size_s1168481041ge_p_v @ nil_message_p_v ) @ Y0 )
=> ( ?? @ nat
@ ^ [Y1: nat] :
( ( suc @ Y1 )
= Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f810,f909]) ).
thf(f810,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( ord_less_nat @ zero_zero_nat @ Y0 )
=> ( ?? @ nat
@ ^ [Y1: nat] :
( ( suc @ Y1 )
= Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f402]) ).
thf(f402,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( ord_less_nat @ zero_zero_nat @ Y0 )
=> ( ?? @ nat
@ ^ [Y1: nat] :
( ( suc @ Y1 )
= Y0 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f401]) ).
thf(f401,plain,
! [X0: nat] :
( ( ord_less_nat @ zero_zero_nat @ X0 )
=> ? [X1: nat] :
( ( suc @ X1 )
= X0 ) ),
inference(rectify,[status(thm)],[f94]) ).
thf(f94,axiom,
! [X15: nat] :
( ( ord_less_nat @ zero_zero_nat @ X15 )
=> ? [X32: nat] :
( ( suc @ X32 )
= X15 ) ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_93_gr0__implies__Suc) ).
thf(f1730,plain,
! [X1: nat] :
( ( ord_less_nat @ ( suc @ X1 ) @ X1 )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f1729]) ).
thf(f1729,plain,
! [X1: nat] :
( $true
= ( ~ ( ord_less_nat @ ( suc @ X1 ) @ X1 ) ) ),
inference(boolean_simplification,[status(thm)],[f1728]) ).
thf(f1728,plain,
! [X1: nat] :
( ( ~ ( ( ord_less_nat @ ( suc @ X1 ) @ X1 )
| $false ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1727,f1276]) ).
thf(f1276,plain,
! [X1: nat] :
( ( ( suc @ X1 )
= X1 )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f1275]) ).
thf(f1275,plain,
! [X1: nat] :
( ( ( suc @ X1 )
!= X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1274]) ).
thf(f1274,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( ( suc @ Y0 )
!= Y0 )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f749]) ).
thf(f749,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( suc @ Y0 )
!= Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f264]) ).
thf(f264,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( suc @ Y0 )
!= Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f263]) ).
thf(f263,plain,
! [X0: nat] :
( ( suc @ X0 )
!= X0 ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,axiom,
! [X15: nat] :
( ( suc @ X15 )
!= X15 ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_31_n__not__Suc__n) ).
thf(f1727,plain,
! [X1: nat] :
( $true
= ( ~ ( ( ord_less_nat @ ( suc @ X1 ) @ X1 )
| ( ( suc @ X1 )
= X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1726]) ).
thf(f1726,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
~ ( ( ord_less_nat @ ( suc @ Y0 ) @ Y0 )
| ( ( suc @ Y0 )
= Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1158]) ).
thf(f1158,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
~ ( ( ord_less_nat @ ( suc @ Y0 ) @ Y0 )
| ( ( suc @ Y0 )
= Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1088]) ).
thf(f1088,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
~ ( ^ [Y1: nat,Y2: nat] :
( ( ord_less_nat @ Y1 @ Y2 )
| ( Y1 = Y2 ) )
@ ( suc @ Y0 )
@ Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f910,f967]) ).
thf(f967,plain,
( ord_less_eq_nat
= ( ^ [Y0: nat,Y1: nat] :
( ( ord_less_nat @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f324]) ).
thf(f324,plain,
( ord_less_eq_nat
= ( ^ [Y0: nat,Y1: nat] :
( ( ord_less_nat @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f323]) ).
thf(f323,plain,
( ( ^ [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( ord_less_nat @ X0 @ X1 ) ) )
= ord_less_eq_nat ),
inference(rectify,[status(thm)],[f167]) ).
thf(f167,axiom,
( ( ^ [X45: nat,X63: nat] :
( ( X45 = X63 )
| ( ord_less_nat @ X45 @ X63 ) ) )
= ord_less_eq_nat ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_166_le__eq__less__or__eq) ).
thf(f910,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
~ ( ord_less_eq_nat @ ( suc @ Y0 ) @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f256]) ).
thf(f256,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
~ ( ord_less_eq_nat @ ( suc @ Y0 ) @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f255]) ).
thf(f255,plain,
! [X0: nat] :
~ ( ord_less_eq_nat @ ( suc @ X0 ) @ X0 ),
inference(rectify,[status(thm)],[f156]) ).
thf(f156,axiom,
! [X15: nat] :
~ ( ord_less_eq_nat @ ( suc @ X15 ) @ X15 ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_155_Suc__n__not__le__n) ).
thf(f13700,plain,
( ( ~ ( ord_less_nat @ nMsg @ sK6 ) )
= $false ),
inference(forward_demodulation,[status(thm)],[f13699,f5293]) ).
thf(f5293,plain,
( $false
= ( sK6 = nMsg ) ),
inference(superposition,[status(thm)],[f3712,f5246]) ).
thf(f3712,plain,
! [X0: nat] :
( ( X0
= ( suc @ X0 ) )
= $false ),
inference(superposition,[status(thm)],[f1276,f3612]) ).
thf(f3612,plain,
! [X2: nat,X1: nat] :
( ( ( suc @ X1 )
= ( suc @ X2 ) )
= ( X2 = X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f3603]) ).
thf(f3603,plain,
! [X2: nat,X1: nat] :
( $true
= ( ( ( suc @ X1 )
= ( suc @ X2 ) )
= ( X2 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3602]) ).
thf(f3602,plain,
! [X2: nat,X1: nat] :
( $true
= ( ^ [Y0: nat] :
( ( ( suc @ X1 )
= ( suc @ Y0 ) )
= ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f3596]) ).
thf(f3596,plain,
! [X1: nat] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( ( suc @ X1 )
= ( suc @ Y0 ) )
= ( Y0 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3595]) ).
thf(f3595,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ( suc @ Y0 )
= ( suc @ Y1 ) )
= ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f957]) ).
thf(f957,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ( suc @ Y0 )
= ( suc @ Y1 ) )
= ( Y1 = Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f392]) ).
thf(f392,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ( suc @ Y0 )
= ( suc @ Y1 ) )
= ( Y1 = Y0 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f391]) ).
thf(f391,plain,
! [X0: nat,X1: nat] :
( ( ( suc @ X1 )
= ( suc @ X0 ) )
= ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,axiom,
! [X20: nat,X21: nat] :
( ( ( suc @ X20 )
= ( suc @ X21 ) )
= ( X20 = X21 ) ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_18_nat_Oinject) ).
thf(f13699,plain,
( ( ~ ( ord_less_nat @ nMsg @ sK6 ) )
= ( sK6 = nMsg ) ),
inference(forward_demodulation,[status(thm)],[f13660,f1340]) ).
thf(f1340,plain,
! [X1: nat] :
( ( minus_minus_nat @ ( suc @ X1 ) @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f1339]) ).
thf(f1339,plain,
! [X1: nat] :
( ( ( minus_minus_nat @ ( suc @ X1 ) @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) )
= X1 )
= $true ),
inference(forward_demodulation,[status(thm)],[f1338,f1107]) ).
thf(f1338,plain,
! [X1: nat] :
( $true
= ( ( minus_minus_nat @ ( suc @ X1 ) @ ( suc @ ( size_s1168481041ge_p_v @ nil_message_p_v ) ) )
= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f1337]) ).
thf(f1337,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( ( minus_minus_nat @ ( suc @ Y0 ) @ ( suc @ ( size_s1168481041ge_p_v @ nil_message_p_v ) ) )
= Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1057]) ).
thf(f1057,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( minus_minus_nat @ ( suc @ Y0 ) @ ( suc @ ( size_s1168481041ge_p_v @ nil_message_p_v ) ) )
= Y0 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f852,f975]) ).
thf(f975,plain,
( one_one_nat
= ( suc @ ( size_s1168481041ge_p_v @ nil_message_p_v ) ) ),
inference(definition_unfolding,[status(thm)],[f771,f909]) ).
thf(f771,plain,
( ( suc @ zero_zero_nat )
= one_one_nat ),
inference(cnf_transformation,[status(thm)],[f290]) ).
thf(f290,plain,
( ( suc @ zero_zero_nat )
= one_one_nat ),
inference(fool_elimination,[status(thm)],[f194]) ).
thf(f194,axiom,
( ( suc @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_193_One__nat__def) ).
thf(f852,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( minus_minus_nat @ ( suc @ Y0 ) @ one_one_nat )
= Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f338]) ).
thf(f338,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( minus_minus_nat @ ( suc @ Y0 ) @ one_one_nat )
= Y0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f337]) ).
thf(f337,plain,
! [X0: nat] :
( ( minus_minus_nat @ ( suc @ X0 ) @ one_one_nat )
= X0 ),
inference(rectify,[status(thm)],[f128]) ).
thf(f128,axiom,
! [X15: nat] :
( ( minus_minus_nat @ ( suc @ X15 ) @ one_one_nat )
= X15 ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_127_diff__Suc__1) ).
thf(f13660,plain,
( ( sK6
= ( minus_minus_nat @ ( suc @ nMsg ) @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) )
= ( ~ ( ord_less_nat @ ( minus_minus_nat @ ( suc @ nMsg ) @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) @ sK6 ) ) ),
inference(backward_demodulation,[status(thm)],[f10770,f13626]) ).
thf(f13626,plain,
( ( size_s1406904903t_unit @ ( fe @ index ) )
= ( suc @ nMsg ) ),
inference(equality_proxy_clausification,[status(thm)],[f11283]) ).
thf(f11283,plain,
( $true
= ( ( suc @ nMsg )
= ( size_s1406904903t_unit @ ( fe @ index ) ) ) ),
inference(backward_demodulation,[status(thm)],[f10904,f11280]) ).
thf(f11280,plain,
( $true
= ( ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ),
inference(boolean_simplification,[status(thm)],[f11274]) ).
thf(f11274,plain,
( $true
= ( $true
=> ( ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ) ),
inference(superposition,[status(thm)],[f11225,f945]) ).
thf(f945,plain,
( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg )
= $true ),
inference(cnf_transformation,[status(thm)],[f653]) ).
thf(f653,plain,
( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg )
= $true ),
inference(fool_elimination,[status(thm)],[f652]) ).
thf(f652,plain,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg,
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg,
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_3_AssumptionSubset_I3_J) ).
thf(f11225,plain,
! [X1: nat] :
( $true
= ( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ X1 )
=> ( ord_less_nat @ X1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f11224]) ).
thf(f11224,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ Y0 )
=> ( ord_less_nat @ Y0 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f740]) ).
thf(f740,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ Y0 )
=> ( ord_less_nat @ Y0 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f698]) ).
thf(f698,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ Y0 )
=> ( ord_less_nat @ Y0 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f697]) ).
thf(f697,plain,
! [X0: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ X0 )
=> ( ord_less_nat @ X0 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X14: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ X14 )
=> ( ord_less_nat @ X14 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_4_SmallIndex) ).
thf(f10904,plain,
( ( ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
= ( ( suc @ nMsg )
= ( size_s1406904903t_unit @ ( fe @ index ) ) ) ),
inference(boolean_simplification,[status(thm)],[f10903]) ).
thf(f10903,plain,
( ( ( suc @ nMsg )
= ( size_s1406904903t_unit @ ( fe @ index ) ) )
= ( ~ ~ ( ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f10759,f2797]) ).
thf(f2797,plain,
! [X2: nat,X1: nat] :
( ( ord_less_nat @ X1 @ ( suc @ X2 ) )
= ( ~ ( ord_less_nat @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f2792]) ).
thf(f2792,plain,
! [X2: nat,X1: nat] :
( ( ( ord_less_nat @ X1 @ ( suc @ X2 ) )
= ( ~ ( ord_less_nat @ X2 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2791]) ).
thf(f2791,plain,
! [X2: nat,X1: nat] :
( ( ^ [Y0: nat] :
( ( ord_less_nat @ X1 @ ( suc @ Y0 ) )
= ( ~ ( ord_less_nat @ Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f2783]) ).
thf(f2783,plain,
! [X1: nat] :
( ( !! @ nat
@ ^ [Y0: nat] :
( ( ord_less_nat @ X1 @ ( suc @ Y0 ) )
= ( ~ ( ord_less_nat @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2782]) ).
thf(f2782,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ord_less_nat @ Y0 @ ( suc @ Y1 ) )
= ( ~ ( ord_less_nat @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f961]) ).
thf(f961,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ord_less_nat @ Y0 @ ( suc @ Y1 ) )
= ( ~ ( ord_less_nat @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f700]) ).
thf(f700,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ord_less_nat @ Y0 @ ( suc @ Y1 ) )
= ( ~ ( ord_less_nat @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f699]) ).
thf(f699,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ X1 @ ( suc @ X0 ) )
= ( ~ ( ord_less_nat @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f70]) ).
thf(f70,axiom,
! [X16: nat,X15: nat] :
( ( ord_less_nat @ X15 @ ( suc @ X16 ) )
= ( ~ ( ord_less_nat @ X16 @ X15 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_69_not__less__eq) ).
thf(f10759,plain,
( ( ~ ( ord_less_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ nMsg ) ) )
= ( ( suc @ nMsg )
= ( size_s1406904903t_unit @ ( fe @ index ) ) ) ),
inference(boolean_simplification,[status(thm)],[f10666]) ).
thf(f10666,plain,
( ( $false
| ( ( suc @ nMsg )
= ( size_s1406904903t_unit @ ( fe @ index ) ) ) )
= ( ~ ( ord_less_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ nMsg ) ) ) ),
inference(superposition,[status(thm)],[f9402,f4896]) ).
thf(f4896,plain,
( ( ord_less_nat @ ( suc @ nMsg ) @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f4886]) ).
thf(f4886,plain,
( $true
= ( ~ ( ord_less_nat @ ( suc @ nMsg ) @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f4625,f4885]) ).
thf(f4885,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ ( suc @ X1 ) @ X0 )
= ( ord_less_nat @ X1 @ ( minus_minus_nat @ X0 @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f4876,f3838]) ).
thf(f3838,plain,
! [X2: nat,X1: nat] :
( ( ord_less_nat @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) @ ( minus_minus_nat @ X2 @ X1 ) )
= ( ord_less_nat @ X1 @ X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f3837]) ).
thf(f3837,plain,
! [X2: nat,X1: nat] :
( ( ( ord_less_nat @ X1 @ X2 )
= ( ord_less_nat @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) @ ( minus_minus_nat @ X2 @ X1 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f3836,f1107]) ).
thf(f3836,plain,
! [X2: nat,X1: nat] :
( ( ( ord_less_nat @ X1 @ X2 )
= ( ord_less_nat @ ( size_s1168481041ge_p_v @ nil_message_p_v ) @ ( minus_minus_nat @ X2 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f3835]) ).
thf(f3835,plain,
! [X2: nat,X1: nat] :
( ( ^ [Y0: nat] :
( ( ord_less_nat @ X1 @ Y0 )
= ( ord_less_nat @ ( size_s1168481041ge_p_v @ nil_message_p_v ) @ ( minus_minus_nat @ Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f3824]) ).
thf(f3824,plain,
! [X1: nat] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( ord_less_nat @ X1 @ Y0 )
= ( ord_less_nat @ ( size_s1168481041ge_p_v @ nil_message_p_v ) @ ( minus_minus_nat @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3823]) ).
thf(f3823,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ord_less_nat @ Y0 @ Y1 )
= ( ord_less_nat @ ( size_s1168481041ge_p_v @ nil_message_p_v ) @ ( minus_minus_nat @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1035]) ).
thf(f1035,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ord_less_nat @ Y0 @ Y1 )
= ( ord_less_nat @ ( size_s1168481041ge_p_v @ nil_message_p_v ) @ ( minus_minus_nat @ Y1 @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f822,f909]) ).
thf(f822,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ord_less_nat @ Y0 @ Y1 )
= ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f452]) ).
thf(f452,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ord_less_nat @ Y0 @ Y1 )
= ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f451]) ).
thf(f451,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ X1 @ X0 )
= ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X15: nat,X16: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ X15 @ X16 ) )
= ( ord_less_nat @ X16 @ X15 ) ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_8_zero__less__diff) ).
thf(f4876,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) @ ( minus_minus_nat @ X0 @ ( suc @ X1 ) ) )
= ( ord_less_nat @ X1 @ ( minus_minus_nat @ X0 @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) ) ),
inference(superposition,[status(thm)],[f3838,f4818]) ).
thf(f4818,plain,
! [X2: nat,X1: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ X2 @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) @ X1 )
= ( minus_minus_nat @ X2 @ ( suc @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f4806]) ).
thf(f4806,plain,
! [X2: nat,X1: nat] :
( $true
= ( ( minus_minus_nat @ ( minus_minus_nat @ X2 @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) @ X1 )
= ( minus_minus_nat @ X2 @ ( suc @ X1 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f4805,f1107]) ).
thf(f4805,plain,
! [X2: nat,X1: nat] :
( ( ( minus_minus_nat @ ( minus_minus_nat @ X2 @ ( suc @ ( size_s1168481041ge_p_v @ nil_message_p_v ) ) ) @ X1 )
= ( minus_minus_nat @ X2 @ ( suc @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f4804]) ).
thf(f4804,plain,
! [X2: nat,X1: nat] :
( ( ^ [Y0: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ Y0 @ ( suc @ ( size_s1168481041ge_p_v @ nil_message_p_v ) ) ) @ X1 )
= ( minus_minus_nat @ Y0 @ ( suc @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f4788]) ).
thf(f4788,plain,
! [X1: nat] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ Y0 @ ( suc @ ( size_s1168481041ge_p_v @ nil_message_p_v ) ) ) @ X1 )
= ( minus_minus_nat @ Y0 @ ( suc @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f4787]) ).
thf(f4787,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ Y1 @ ( suc @ ( size_s1168481041ge_p_v @ nil_message_p_v ) ) ) @ Y0 )
= ( minus_minus_nat @ Y1 @ ( suc @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1102]) ).
thf(f1102,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ Y1 @ ( suc @ ( size_s1168481041ge_p_v @ nil_message_p_v ) ) ) @ Y0 )
= ( minus_minus_nat @ Y1 @ ( suc @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f927,f975]) ).
thf(f927,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ Y1 @ one_one_nat ) @ Y0 )
= ( minus_minus_nat @ Y1 @ ( suc @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f356]) ).
thf(f356,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ Y1 @ one_one_nat ) @ Y0 )
= ( minus_minus_nat @ Y1 @ ( suc @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f355]) ).
thf(f355,plain,
! [X0: nat,X1: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ X0 @ one_one_nat ) @ X1 )
= ( minus_minus_nat @ X0 @ ( suc @ X1 ) ) ),
inference(rectify,[status(thm)],[f195]) ).
thf(f195,axiom,
! [X16: nat,X15: nat] :
( ( minus_minus_nat @ X16 @ ( suc @ X15 ) )
= ( minus_minus_nat @ ( minus_minus_nat @ X16 @ one_one_nat ) @ X15 ) ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_194_diff__Suc__eq__diff__pred) ).
thf(f4625,plain,
( $true
= ( ~ ( ord_less_nat @ nMsg @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f4568]) ).
thf(f4568,plain,
( $true
= ( ( ord_less_nat @ nMsg @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) )
=> $false ) ),
inference(superposition,[status(thm)],[f4547,f1740]) ).
thf(f1740,plain,
( ( ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f1224]) ).
thf(f1224,plain,
( ( ~ ( ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1094,f1107]) ).
thf(f1094,plain,
( $true
= ( ~ ( ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ ( size_s1168481041ge_p_v @ nil_message_p_v ) ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ ( size_s1168481041ge_p_v @ nil_message_p_v ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f918,f909,f909]) ).
thf(f918,plain,
( $true
= ( ~ ( ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f318]) ).
thf(f318,plain,
( $true
= ( ~ ( ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f317]) ).
thf(f317,plain,
~ ( ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ),
inference(rectify,[status(thm)],[f246]) ).
thf(f246,negated_conjecture,
~ ( ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ),
inference(negated_conjecture,[status(cth)],[f245]) ).
thf(f245,conjecture,
ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',conj_0) ).
thf(f4547,plain,
! [X2: nat,X3: nat,X1: nat] :
( $true
= ( ( ord_less_nat @ X2 @ X1 )
=> ( ord_less_nat @ ( minus_minus_nat @ X2 @ X3 ) @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f4546]) ).
thf(f4546,plain,
! [X2: nat,X3: nat,X1: nat] :
( $true
= ( ^ [Y0: nat] :
( ( ord_less_nat @ X2 @ X1 )
=> ( ord_less_nat @ ( minus_minus_nat @ X2 @ Y0 ) @ X1 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f4540]) ).
thf(f4540,plain,
! [X2: nat,X1: nat] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( ord_less_nat @ X2 @ X1 )
=> ( ord_less_nat @ ( minus_minus_nat @ X2 @ Y0 ) @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f4539]) ).
thf(f4539,plain,
! [X2: nat,X1: nat] :
( $true
= ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ord_less_nat @ Y0 @ X1 )
=> ( ord_less_nat @ ( minus_minus_nat @ Y0 @ Y1 ) @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f4443]) ).
thf(f4443,plain,
! [X1: nat] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ord_less_nat @ Y0 @ X1 )
=> ( ord_less_nat @ ( minus_minus_nat @ Y0 @ Y1 ) @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f4442]) ).
thf(f4442,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ nat
@ ^ [Y2: nat] :
( ( ord_less_nat @ Y1 @ Y0 )
=> ( ord_less_nat @ ( minus_minus_nat @ Y1 @ Y2 ) @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f849]) ).
thf(f849,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ nat
@ ^ [Y2: nat] :
( ( ord_less_nat @ Y1 @ Y0 )
=> ( ord_less_nat @ ( minus_minus_nat @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f627]) ).
thf(f627,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ nat
@ ^ [Y2: nat] :
( ( ord_less_nat @ Y1 @ Y0 )
=> ( ord_less_nat @ ( minus_minus_nat @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f626]) ).
thf(f626,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ord_less_nat @ X1 @ X2 )
=> ( ord_less_nat @ ( minus_minus_nat @ X1 @ X0 ) @ X2 ) ),
inference(rectify,[status(thm)],[f89]) ).
thf(f89,axiom,
! [X15: nat,X31: nat,X17: nat] :
( ( ord_less_nat @ X31 @ X17 )
=> ( ord_less_nat @ ( minus_minus_nat @ X31 @ X15 ) @ X17 ) ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_88_less__imp__diff__less) ).
thf(f9402,plain,
! [X2: nat,X1: nat] :
( ( ~ ( ord_less_nat @ X1 @ X2 ) )
= ( ( ord_less_nat @ X2 @ X1 )
| ( X2 = X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f9364]) ).
thf(f9364,plain,
! [X2: nat,X1: nat] :
( ( ( ( ord_less_nat @ X2 @ X1 )
| ( X2 = X1 ) )
= ( ~ ( ord_less_nat @ X1 @ X2 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f9363,f2797]) ).
thf(f9363,plain,
! [X2: nat,X1: nat] :
( $true
= ( ( ( ord_less_nat @ X2 @ X1 )
| ( X2 = X1 ) )
= ( ord_less_nat @ X2 @ ( suc @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f9362]) ).
thf(f9362,plain,
! [X2: nat,X1: nat] :
( ( ^ [Y0: nat] :
( ( ( ord_less_nat @ Y0 @ X1 )
| ( Y0 = X1 ) )
= ( ord_less_nat @ Y0 @ ( suc @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f9360]) ).
thf(f9360,plain,
! [X1: nat] :
( ( !! @ nat
@ ^ [Y0: nat] :
( ( ( ord_less_nat @ Y0 @ X1 )
| ( Y0 = X1 ) )
= ( ord_less_nat @ Y0 @ ( suc @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f9359]) ).
thf(f9359,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ( ord_less_nat @ Y1 @ Y0 )
| ( Y1 = Y0 ) )
= ( ord_less_nat @ Y1 @ ( suc @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1206]) ).
thf(f1206,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ( ord_less_nat @ Y1 @ Y0 )
| ( Y1 = Y0 ) )
= ( ord_less_nat @ Y1 @ ( suc @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1024]) ).
thf(f1024,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ^ [Y2: nat,Y3: nat] :
( ( ord_less_nat @ Y2 @ Y3 )
| ( Y2 = Y3 ) )
@ Y1
@ Y0 )
= ( ord_less_nat @ Y1 @ ( suc @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f803,f967]) ).
thf(f803,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ord_less_eq_nat @ Y1 @ Y0 )
= ( ord_less_nat @ Y1 @ ( suc @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f554]) ).
thf(f554,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ord_less_eq_nat @ Y1 @ Y0 )
= ( ord_less_nat @ Y1 @ ( suc @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f553]) ).
thf(f553,plain,
! [X0: nat,X1: nat] :
( ( ord_less_eq_nat @ X0 @ X1 )
= ( ord_less_nat @ X0 @ ( suc @ X1 ) ) ),
inference(rectify,[status(thm)],[f187]) ).
thf(f187,axiom,
! [X16: nat,X15: nat] :
( ( ord_less_nat @ X16 @ ( suc @ X15 ) )
= ( ord_less_eq_nat @ X16 @ X15 ) ),
file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_186_less__Suc__eq__le) ).
thf(f10770,plain,
( ( ~ ( ord_less_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) @ sK6 ) )
= ( sK6
= ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f10699]) ).
thf(f10699,plain,
( ( $false
| ( sK6
= ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) ) )
= ( ~ ( ord_less_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) @ sK6 ) ) ),
inference(superposition,[status(thm)],[f9402,f5301]) ).
thf(f5301,plain,
( ( ord_less_nat @ sK6 @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f1740,f5271]) ).
thf(f5271,plain,
( ( minus_minus_nat @ nMsg @ ( suc @ ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) )
= sK6 ),
inference(superposition,[status(thm)],[f1340,f5246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP059^1 : 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
% 0.15/0.33 % Computer : n014.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 08:24:57 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : ITP059^1 : TPTP v9.2.1. Released v7.5.0.
% 0.18/0.45 % Domain : Interactive Theorem Proving
% 0.18/0.45 % Problem : Sledgehammer FLPTheorem problem prob_747__3300826_1
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.18/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Des21]
% 0.18/0.45 % Names : FLPTheorem/prob_747__3300826_1 [Des21]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.18/0.45 % Syntax : Number of formulae : 284 ( 127 unt; 39 typ; 0 def)
% 0.18/0.45 % Number of atoms : 528 ( 207 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 7 ( 2 avg)
% 0.18/0.45 % Number of connectives : 1888 ( 87 ~; 15 |; 42 &;1486 @)
% 0.18/0.45 % ( 0 <=>; 258 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 21 ( 6 avg)
% 0.18/0.45 % Number of types : 8 ( 7 usr)
% 0.18/0.45 % Number of type conns : 148 ( 148 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 33 ( 32 usr; 12 con; 0-4 aty)
% 0.18/0.45 % Number of variables : 505 ( 13 ^; 456 !; 36 ?; 505 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 15:31:23.474
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % Could-be-implicit typings (7)
% 0.18/0.45 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.18/0.45 list_c1059388851t_unit: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.18/0.45 config256849571t_unit: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.18/0.45 list_message_p_v: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Set__Oset_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.18/0.45 set_message_p_v: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.18/0.45 message_p_v: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Nat__Onat,type,
% 0.18/0.45 nat: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_tf__p,type,
% 0.18/0.45 p: $tType ).
% 0.18/0.45
% 0.18/0.45 % Explicit typings (32)
% 0.18/0.45 thf(sy_c_AsynchronousSystem_Oconfiguration_Omsgs_001tf__p_001tf__v_001tf__s_001t__Product____Type__Ounit,type,
% 0.18/0.45 msgs_p1029620568t_unit: config256849571t_unit > message_p_v > nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_AsynchronousSystem_Oenabled_001tf__p_001tf__v_001tf__s,type,
% 0.18/0.45 enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_AsynchronousSystem_OisReceiverOf_001tf__p_001tf__v,type,
% 0.18/0.45 isReceiverOf_p_v: p > message_p_v > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Execution_Oexecution_OfirstOccurrence_001tf__p_001tf__v_001tf__s,type,
% 0.18/0.45 firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 0.18/0.45 minus_minus_nat: nat > nat > nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.18/0.45 one_one_nat: nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.18/0.45 zero_zero_nat: nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.18/0.45 prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.18/0.45 prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olast_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.18/0.45 last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olast_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.18/0.45 last_message_p_v: list_message_p_v > message_p_v ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.18/0.45 nil_co1338500125t_unit: list_c1059388851t_unit ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.18/0.45 nil_message_p_v: list_message_p_v ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Onth_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.18/0.45 nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Onth_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.18/0.45 nth_message_p_v: list_message_p_v > nat > message_p_v ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Nat_OSuc,type,
% 0.18/0.45 suc: nat > nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.18/0.45 size_s1406904903t_unit: list_c1059388851t_unit > nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.18/0.45 size_s1168481041ge_p_v: list_message_p_v > nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.18/0.45 ord_less_nat: nat > nat > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.18/0.45 ord_less_eq_nat: nat > nat > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_member_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.18/0.45 member_message_p_v: message_p_v > set_message_p_v > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_fe____,type,
% 0.18/0.45 fe: nat > list_c1059388851t_unit ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_firstOccSet____,type,
% 0.18/0.45 firstOccSet: nat > set_message_p_v ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_ft____,type,
% 0.18/0.45 ft: nat > list_message_p_v ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_index____,type,
% 0.18/0.45 index: nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_msgInSet____,type,
% 0.18/0.45 msgInSet: message_p_v ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_msg____,type,
% 0.18/0.45 msg: message_p_v ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_n0____,type,
% 0.18/0.45 n0: nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_n1____,type,
% 0.18/0.45 n1: nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_nMsg____,type,
% 0.18/0.45 nMsg: nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_n____,type,
% 0.18/0.45 n: nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_p____,type,
% 0.18/0.45 p2: p ).
% 0.18/0.45
% 0.18/0.45 % Relevant facts (244)
% 0.18/0.45 thf(fact_0_AssumpOcc6_I1_J,axiom,
% 0.18/0.45 ord_less_nat @ zero_zero_nat @ nMsg ).
% 0.18/0.45
% 0.18/0.45 % AssumpOcc6(1)
% 0.18/0.45 thf(fact_1_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 0.18/0.45 ! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A4: config256849571t_unit,A5: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A6: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A7: nat] :
% 0.18/0.46 ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.18/0.46 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.18/0.46 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.18/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.18/0.46 => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.18/0.46 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.18/0.46 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.18/0.46 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.18/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.18/0.46 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.18/0.46 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % infiniteExecutionCfg_infiniteExecutionMsg.induct(2)
% 0.18/0.46 thf(fact_2_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 0.18/0.46 ! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A0: config256849571t_unit,A1: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A3: nat] :
% 0.18/0.46 ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.18/0.46 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.18/0.46 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.18/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.18/0.46 => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.18/0.46 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.18/0.46 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.18/0.46 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.18/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.18/0.46 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.18/0.46 => ( P @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % infiniteExecutionCfg_infiniteExecutionMsg.induct(1)
% 0.18/0.46 thf(fact_3_AssumptionSubset_I3_J,axiom,
% 0.18/0.46 firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg ).
% 0.18/0.46
% 0.18/0.46 % AssumptionSubset(3)
% 0.18/0.46 thf(fact_4_SmallIndex,axiom,
% 0.18/0.46 ! [NMsg: nat] :
% 0.18/0.46 ( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ NMsg )
% 0.18/0.46 => ( ord_less_nat @ NMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % SmallIndex
% 0.18/0.46 thf(fact_5_AssumptionSubset3_I3_J,axiom,
% 0.18/0.46 ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % AssumptionSubset3(3)
% 0.18/0.46 thf(fact_6_AssumptionSubset2_I3_J,axiom,
% 0.18/0.46 ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % AssumptionSubset2(3)
% 0.18/0.46 thf(fact_7_Suc__pred,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.46 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 0.18/0.46 = N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_pred
% 0.18/0.46 thf(fact_8_zero__less__diff,axiom,
% 0.18/0.46 ! [N2: nat,M: nat] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) )
% 0.18/0.46 = ( ord_less_nat @ M @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % zero_less_diff
% 0.18/0.46 thf(fact_9_less__Suc0,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.18/0.46 = ( N2 = zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_Suc0
% 0.18/0.46 thf(fact_10_zero__less__Suc,axiom,
% 0.18/0.46 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % zero_less_Suc
% 0.18/0.46 thf(fact_11_diff__0__eq__0,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 0.18/0.46 = zero_zero_nat ) ).
% 0.18/0.46
% 0.18/0.46 % diff_0_eq_0
% 0.18/0.46 thf(fact_12_diff__self__eq__0,axiom,
% 0.18/0.46 ! [M: nat] :
% 0.18/0.46 ( ( minus_minus_nat @ M @ M )
% 0.18/0.46 = zero_zero_nat ) ).
% 0.18/0.46
% 0.18/0.46 % diff_self_eq_0
% 0.18/0.46 thf(fact_13_diff__Suc__Suc,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.18/0.46 = ( minus_minus_nat @ M @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_Suc_Suc
% 0.18/0.46 thf(fact_14_Suc__diff__diff,axiom,
% 0.18/0.46 ! [M: nat,N2: nat,K: nat] :
% 0.18/0.46 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( suc @ K ) )
% 0.18/0.46 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N2 ) @ K ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_diff_diff
% 0.18/0.46 thf(fact_15_neq0__conv,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( N2 != zero_zero_nat )
% 0.18/0.46 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % neq0_conv
% 0.18/0.46 thf(fact_16_less__nat__zero__code,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.18/0.46
% 0.18/0.46 % less_nat_zero_code
% 0.18/0.46 thf(fact_17_old_Onat_Oinject,axiom,
% 0.18/0.46 ! [Nat: nat,Nat2: nat] :
% 0.18/0.46 ( ( ( suc @ Nat )
% 0.18/0.46 = ( suc @ Nat2 ) )
% 0.18/0.46 = ( Nat = Nat2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % old.nat.inject
% 0.18/0.46 thf(fact_18_nat_Oinject,axiom,
% 0.18/0.46 ! [X2: nat,Y2: nat] :
% 0.18/0.46 ( ( ( suc @ X2 )
% 0.18/0.46 = ( suc @ Y2 ) )
% 0.18/0.46 = ( X2 = Y2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % nat.inject
% 0.18/0.46 thf(fact_19_not__gr__zero,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 0.18/0.46 = ( N2 = zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % not_gr_zero
% 0.18/0.46 thf(fact_20_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.18/0.46 ! [A: nat] :
% 0.18/0.46 ( ( minus_minus_nat @ A @ A )
% 0.18/0.46 = zero_zero_nat ) ).
% 0.18/0.46
% 0.18/0.46 % cancel_comm_monoid_add_class.diff_cancel
% 0.18/0.46 thf(fact_21_diff__zero,axiom,
% 0.18/0.46 ! [A: nat] :
% 0.18/0.46 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.18/0.46 = A ) ).
% 0.18/0.46
% 0.18/0.46 % diff_zero
% 0.18/0.46 thf(fact_22_zero__diff,axiom,
% 0.18/0.46 ! [A: nat] :
% 0.18/0.46 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.18/0.46 = zero_zero_nat ) ).
% 0.18/0.46
% 0.18/0.46 % zero_diff
% 0.18/0.46 thf(fact_23_Suc__less__eq,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.18/0.46 = ( ord_less_nat @ M @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_less_eq
% 0.18/0.46 thf(fact_24_Suc__mono,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M @ N2 )
% 0.18/0.46 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_mono
% 0.18/0.46 thf(fact_25_lessI,axiom,
% 0.18/0.46 ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % lessI
% 0.18/0.46 thf(fact_26_bot__nat__0_Onot__eq__extremum,axiom,
% 0.18/0.46 ! [A: nat] :
% 0.18/0.46 ( ( A != zero_zero_nat )
% 0.18/0.46 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.18/0.46
% 0.18/0.46 % bot_nat_0.not_eq_extremum
% 0.18/0.46 thf(fact_27_AssumptionSubset_I2_J,axiom,
% 0.18/0.46 firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msgInSet @ n1 ).
% 0.18/0.46
% 0.18/0.46 % AssumptionSubset(2)
% 0.18/0.46 thf(fact_28_AssumptionSubset_I1_J,axiom,
% 0.18/0.46 ord_less_eq_nat @ n1 @ nMsg ).
% 0.18/0.46
% 0.18/0.46 % AssumptionSubset(1)
% 0.18/0.46 thf(fact_29_zero__reorient,axiom,
% 0.18/0.46 ! [X: nat] :
% 0.18/0.46 ( ( zero_zero_nat = X )
% 0.18/0.46 = ( X = zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % zero_reorient
% 0.18/0.46 thf(fact_30_diff__right__commute,axiom,
% 0.18/0.46 ! [A: nat,C: nat,B: nat] :
% 0.18/0.46 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 0.18/0.46 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_right_commute
% 0.18/0.46 thf(fact_31_n__not__Suc__n,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( N2
% 0.18/0.46 != ( suc @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % n_not_Suc_n
% 0.18/0.46 thf(fact_32_Suc__inject,axiom,
% 0.18/0.46 ! [X: nat,Y: nat] :
% 0.18/0.46 ( ( ( suc @ X )
% 0.18/0.46 = ( suc @ Y ) )
% 0.18/0.46 => ( X = Y ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_inject
% 0.18/0.46 thf(fact_33_linorder__neqE__nat,axiom,
% 0.18/0.46 ! [X: nat,Y: nat] :
% 0.18/0.46 ( ( X != Y )
% 0.18/0.46 => ( ~ ( ord_less_nat @ X @ Y )
% 0.18/0.46 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % linorder_neqE_nat
% 0.18/0.46 thf(fact_34_infinite__descent,axiom,
% 0.18/0.46 ! [P: nat > $o,N2: nat] :
% 0.18/0.46 ( ! [N: nat] :
% 0.18/0.46 ( ~ ( P @ N )
% 0.18/0.46 => ? [M2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M2 @ N )
% 0.18/0.46 & ~ ( P @ M2 ) ) )
% 0.18/0.46 => ( P @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % infinite_descent
% 0.18/0.46 thf(fact_35_nat__less__induct,axiom,
% 0.18/0.46 ! [P: nat > $o,N2: nat] :
% 0.18/0.46 ( ! [N: nat] :
% 0.18/0.46 ( ! [M2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M2 @ N )
% 0.18/0.46 => ( P @ M2 ) )
% 0.18/0.46 => ( P @ N ) )
% 0.18/0.46 => ( P @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % nat_less_induct
% 0.18/0.46 thf(fact_36_less__irrefl__nat,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 0.18/0.46
% 0.18/0.46 % less_irrefl_nat
% 0.18/0.46 thf(fact_37_less__not__refl3,axiom,
% 0.18/0.46 ! [S: nat,T: nat] :
% 0.18/0.46 ( ( ord_less_nat @ S @ T )
% 0.18/0.46 => ( S != T ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_not_refl3
% 0.18/0.46 thf(fact_38_less__not__refl2,axiom,
% 0.18/0.46 ! [N2: nat,M: nat] :
% 0.18/0.46 ( ( ord_less_nat @ N2 @ M )
% 0.18/0.46 => ( M != N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_not_refl2
% 0.18/0.46 thf(fact_39_less__not__refl,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 0.18/0.46
% 0.18/0.46 % less_not_refl
% 0.18/0.46 thf(fact_40_nat__neq__iff,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( M != N2 )
% 0.18/0.46 = ( ( ord_less_nat @ M @ N2 )
% 0.18/0.46 | ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % nat_neq_iff
% 0.18/0.46 thf(fact_41_size__neq__size__imp__neq,axiom,
% 0.18/0.46 ! [X: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 0.18/0.46 ( ( ( size_s1406904903t_unit @ X )
% 0.18/0.46 != ( size_s1406904903t_unit @ Y ) )
% 0.18/0.46 => ( X != Y ) ) ).
% 0.18/0.46
% 0.18/0.46 % size_neq_size_imp_neq
% 0.18/0.46 thf(fact_42_size__neq__size__imp__neq,axiom,
% 0.18/0.46 ! [X: list_message_p_v,Y: list_message_p_v] :
% 0.18/0.46 ( ( ( size_s1168481041ge_p_v @ X )
% 0.18/0.46 != ( size_s1168481041ge_p_v @ Y ) )
% 0.18/0.46 => ( X != Y ) ) ).
% 0.18/0.46
% 0.18/0.46 % size_neq_size_imp_neq
% 0.18/0.46 thf(fact_43_diff__commute,axiom,
% 0.18/0.46 ! [I: nat,J: nat,K: nat] :
% 0.18/0.46 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.18/0.46 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_commute
% 0.18/0.46 thf(fact_44_zero__less__iff__neq__zero,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.46 = ( N2 != zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % zero_less_iff_neq_zero
% 0.18/0.46 thf(fact_45_gr__implies__not__zero,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M @ N2 )
% 0.18/0.46 => ( N2 != zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % gr_implies_not_zero
% 0.18/0.46 thf(fact_46_not__less__zero,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.18/0.46
% 0.18/0.46 % not_less_zero
% 0.18/0.46 thf(fact_47_gr__zeroI,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( N2 != zero_zero_nat )
% 0.18/0.46 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % gr_zeroI
% 0.18/0.46 thf(fact_48_not0__implies__Suc,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( N2 != zero_zero_nat )
% 0.18/0.46 => ? [M3: nat] :
% 0.18/0.46 ( N2
% 0.18/0.46 = ( suc @ M3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % not0_implies_Suc
% 0.18/0.46 thf(fact_49_old_Onat_Oinducts,axiom,
% 0.18/0.46 ! [P: nat > $o,Nat: nat] :
% 0.18/0.46 ( ( P @ zero_zero_nat )
% 0.18/0.46 => ( ! [Nat3: nat] :
% 0.18/0.46 ( ( P @ Nat3 )
% 0.18/0.46 => ( P @ ( suc @ Nat3 ) ) )
% 0.18/0.46 => ( P @ Nat ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % old.nat.inducts
% 0.18/0.46 thf(fact_50_old_Onat_Oexhaust,axiom,
% 0.18/0.46 ! [Y: nat] :
% 0.18/0.46 ( ( Y != zero_zero_nat )
% 0.18/0.46 => ~ ! [Nat3: nat] :
% 0.18/0.46 ( Y
% 0.18/0.46 != ( suc @ Nat3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % old.nat.exhaust
% 0.18/0.46 thf(fact_51_Zero__not__Suc,axiom,
% 0.18/0.46 ! [M: nat] :
% 0.18/0.46 ( zero_zero_nat
% 0.18/0.46 != ( suc @ M ) ) ).
% 0.18/0.46
% 0.18/0.46 % Zero_not_Suc
% 0.18/0.46 thf(fact_52_Zero__neq__Suc,axiom,
% 0.18/0.46 ! [M: nat] :
% 0.18/0.46 ( zero_zero_nat
% 0.18/0.46 != ( suc @ M ) ) ).
% 0.18/0.46
% 0.18/0.46 % Zero_neq_Suc
% 0.18/0.46 thf(fact_53_Suc__neq__Zero,axiom,
% 0.18/0.46 ! [M: nat] :
% 0.18/0.46 ( ( suc @ M )
% 0.18/0.46 != zero_zero_nat ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_neq_Zero
% 0.18/0.46 thf(fact_54_zero__induct,axiom,
% 0.18/0.46 ! [P: nat > $o,K: nat] :
% 0.18/0.46 ( ( P @ K )
% 0.18/0.46 => ( ! [N: nat] :
% 0.18/0.46 ( ( P @ ( suc @ N ) )
% 0.18/0.46 => ( P @ N ) )
% 0.18/0.46 => ( P @ zero_zero_nat ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % zero_induct
% 0.18/0.46 thf(fact_55_diff__induct,axiom,
% 0.18/0.46 ! [P: nat > nat > $o,M: nat,N2: nat] :
% 0.18/0.46 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 0.18/0.46 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 0.18/0.46 => ( ! [X3: nat,Y3: nat] :
% 0.18/0.46 ( ( P @ X3 @ Y3 )
% 0.18/0.46 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 0.18/0.46 => ( P @ M @ N2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_induct
% 0.18/0.46 thf(fact_56_nat__induct,axiom,
% 0.18/0.46 ! [P: nat > $o,N2: nat] :
% 0.18/0.46 ( ( P @ zero_zero_nat )
% 0.18/0.46 => ( ! [N: nat] :
% 0.18/0.46 ( ( P @ N )
% 0.18/0.46 => ( P @ ( suc @ N ) ) )
% 0.18/0.46 => ( P @ N2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % nat_induct
% 0.18/0.46 thf(fact_57_nat_OdiscI,axiom,
% 0.18/0.46 ! [Nat: nat,X2: nat] :
% 0.18/0.46 ( ( Nat
% 0.18/0.46 = ( suc @ X2 ) )
% 0.18/0.46 => ( Nat != zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % nat.discI
% 0.18/0.46 thf(fact_58_old_Onat_Odistinct_I1_J,axiom,
% 0.18/0.46 ! [Nat2: nat] :
% 0.18/0.46 ( zero_zero_nat
% 0.18/0.46 != ( suc @ Nat2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % old.nat.distinct(1)
% 0.18/0.46 thf(fact_59_old_Onat_Odistinct_I2_J,axiom,
% 0.18/0.46 ! [Nat2: nat] :
% 0.18/0.46 ( ( suc @ Nat2 )
% 0.18/0.46 != zero_zero_nat ) ).
% 0.18/0.46
% 0.18/0.46 % old.nat.distinct(2)
% 0.18/0.46 thf(fact_60_nat_Odistinct_I1_J,axiom,
% 0.18/0.46 ! [X2: nat] :
% 0.18/0.46 ( zero_zero_nat
% 0.18/0.46 != ( suc @ X2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % nat.distinct(1)
% 0.18/0.46 thf(fact_61_not__less__less__Suc__eq,axiom,
% 0.18/0.46 ! [N2: nat,M: nat] :
% 0.18/0.46 ( ~ ( ord_less_nat @ N2 @ M )
% 0.18/0.46 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 0.18/0.46 = ( N2 = M ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % not_less_less_Suc_eq
% 0.18/0.46 thf(fact_62_strict__inc__induct,axiom,
% 0.18/0.46 ! [I: nat,J: nat,P: nat > $o] :
% 0.18/0.46 ( ( ord_less_nat @ I @ J )
% 0.18/0.46 => ( ! [I2: nat] :
% 0.18/0.46 ( ( J
% 0.18/0.46 = ( suc @ I2 ) )
% 0.18/0.46 => ( P @ I2 ) )
% 0.18/0.46 => ( ! [I2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I2 @ J )
% 0.18/0.46 => ( ( P @ ( suc @ I2 ) )
% 0.18/0.46 => ( P @ I2 ) ) )
% 0.18/0.46 => ( P @ I ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % strict_inc_induct
% 0.18/0.46 thf(fact_63_less__Suc__induct,axiom,
% 0.18/0.46 ! [I: nat,J: nat,P: nat > nat > $o] :
% 0.18/0.46 ( ( ord_less_nat @ I @ J )
% 0.18/0.46 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 0.18/0.46 => ( ! [I2: nat,J2: nat,K2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I2 @ J2 )
% 0.18/0.46 => ( ( ord_less_nat @ J2 @ K2 )
% 0.18/0.46 => ( ( P @ I2 @ J2 )
% 0.18/0.46 => ( ( P @ J2 @ K2 )
% 0.18/0.46 => ( P @ I2 @ K2 ) ) ) ) )
% 0.18/0.46 => ( P @ I @ J ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_Suc_induct
% 0.18/0.46 thf(fact_64_less__trans__Suc,axiom,
% 0.18/0.46 ! [I: nat,J: nat,K: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I @ J )
% 0.18/0.46 => ( ( ord_less_nat @ J @ K )
% 0.18/0.46 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_trans_Suc
% 0.18/0.46 thf(fact_65_Suc__less__SucD,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.18/0.46 => ( ord_less_nat @ M @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_less_SucD
% 0.18/0.46 thf(fact_66_less__antisym,axiom,
% 0.18/0.46 ! [N2: nat,M: nat] :
% 0.18/0.46 ( ~ ( ord_less_nat @ N2 @ M )
% 0.18/0.46 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 0.18/0.46 => ( M = N2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_antisym
% 0.18/0.46 thf(fact_67_Suc__less__eq2,axiom,
% 0.18/0.46 ! [N2: nat,M: nat] :
% 0.18/0.46 ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.18/0.46 = ( ? [M4: nat] :
% 0.18/0.46 ( ( M
% 0.18/0.46 = ( suc @ M4 ) )
% 0.18/0.46 & ( ord_less_nat @ N2 @ M4 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_less_eq2
% 0.18/0.46 thf(fact_68_All__less__Suc,axiom,
% 0.18/0.46 ! [N2: nat,P: nat > $o] :
% 0.18/0.46 ( ( ! [I3: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 0.18/0.46 => ( P @ I3 ) ) )
% 0.18/0.46 = ( ( P @ N2 )
% 0.18/0.46 & ! [I3: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I3 @ N2 )
% 0.18/0.46 => ( P @ I3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % All_less_Suc
% 0.18/0.46 thf(fact_69_not__less__eq,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ~ ( ord_less_nat @ M @ N2 ) )
% 0.18/0.46 = ( ord_less_nat @ N2 @ ( suc @ M ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % not_less_eq
% 0.18/0.46 thf(fact_70_less__Suc__eq,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.18/0.46 = ( ( ord_less_nat @ M @ N2 )
% 0.18/0.46 | ( M = N2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_Suc_eq
% 0.18/0.46 thf(fact_71_Ex__less__Suc,axiom,
% 0.18/0.46 ! [N2: nat,P: nat > $o] :
% 0.18/0.46 ( ( ? [I3: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 0.18/0.46 & ( P @ I3 ) ) )
% 0.18/0.46 = ( ( P @ N2 )
% 0.18/0.46 | ? [I3: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I3 @ N2 )
% 0.18/0.46 & ( P @ I3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Ex_less_Suc
% 0.18/0.46 thf(fact_72_less__SucI,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M @ N2 )
% 0.18/0.46 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_SucI
% 0.18/0.46 thf(fact_73_less__SucE,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.18/0.46 => ( ~ ( ord_less_nat @ M @ N2 )
% 0.18/0.46 => ( M = N2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_SucE
% 0.18/0.46 thf(fact_74_Suc__lessI,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M @ N2 )
% 0.18/0.46 => ( ( ( suc @ M )
% 0.18/0.46 != N2 )
% 0.18/0.46 => ( ord_less_nat @ ( suc @ M ) @ N2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_lessI
% 0.18/0.46 thf(fact_75_Suc__lessE,axiom,
% 0.18/0.46 ! [I: nat,K: nat] :
% 0.18/0.46 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.18/0.46 => ~ ! [J2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I @ J2 )
% 0.18/0.46 => ( K
% 0.18/0.46 != ( suc @ J2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_lessE
% 0.18/0.46 thf(fact_76_Suc__lessD,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ ( suc @ M ) @ N2 )
% 0.18/0.46 => ( ord_less_nat @ M @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_lessD
% 0.18/0.46 thf(fact_77_Nat_OlessE,axiom,
% 0.18/0.46 ! [I: nat,K: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I @ K )
% 0.18/0.46 => ( ( K
% 0.18/0.46 != ( suc @ I ) )
% 0.18/0.46 => ~ ! [J2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I @ J2 )
% 0.18/0.46 => ( K
% 0.18/0.46 != ( suc @ J2 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Nat.lessE
% 0.18/0.46 thf(fact_78_bot__nat__0_Oextremum__strict,axiom,
% 0.18/0.46 ! [A: nat] :
% 0.18/0.46 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.18/0.46
% 0.18/0.46 % bot_nat_0.extremum_strict
% 0.18/0.46 thf(fact_79_infinite__descent0,axiom,
% 0.18/0.46 ! [P: nat > $o,N2: nat] :
% 0.18/0.46 ( ( P @ zero_zero_nat )
% 0.18/0.46 => ( ! [N: nat] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.46 => ( ~ ( P @ N )
% 0.18/0.46 => ? [M2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M2 @ N )
% 0.18/0.46 & ~ ( P @ M2 ) ) ) )
% 0.18/0.46 => ( P @ N2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % infinite_descent0
% 0.18/0.46 thf(fact_80_gr__implies__not0,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M @ N2 )
% 0.18/0.46 => ( N2 != zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % gr_implies_not0
% 0.18/0.46 thf(fact_81_less__zeroE,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.18/0.46
% 0.18/0.46 % less_zeroE
% 0.18/0.46 thf(fact_82_not__less0,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.18/0.46
% 0.18/0.46 % not_less0
% 0.18/0.46 thf(fact_83_not__gr0,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 0.18/0.46 = ( N2 = zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % not_gr0
% 0.18/0.46 thf(fact_84_gr0I,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( N2 != zero_zero_nat )
% 0.18/0.46 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % gr0I
% 0.18/0.46 thf(fact_85_zero__induct__lemma,axiom,
% 0.18/0.46 ! [P: nat > $o,K: nat,I: nat] :
% 0.18/0.46 ( ( P @ K )
% 0.18/0.46 => ( ! [N: nat] :
% 0.18/0.46 ( ( P @ ( suc @ N ) )
% 0.18/0.46 => ( P @ N ) )
% 0.18/0.46 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % zero_induct_lemma
% 0.18/0.46 thf(fact_86_minus__nat_Odiff__0,axiom,
% 0.18/0.46 ! [M: nat] :
% 0.18/0.46 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.18/0.46 = M ) ).
% 0.18/0.46
% 0.18/0.46 % minus_nat.diff_0
% 0.18/0.46 thf(fact_87_diffs0__imp__equal,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ( minus_minus_nat @ M @ N2 )
% 0.18/0.46 = zero_zero_nat )
% 0.18/0.46 => ( ( ( minus_minus_nat @ N2 @ M )
% 0.18/0.46 = zero_zero_nat )
% 0.18/0.46 => ( M = N2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % diffs0_imp_equal
% 0.18/0.46 thf(fact_88_less__imp__diff__less,axiom,
% 0.18/0.46 ! [J: nat,K: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ J @ K )
% 0.18/0.46 => ( ord_less_nat @ ( minus_minus_nat @ J @ N2 ) @ K ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_imp_diff_less
% 0.18/0.46 thf(fact_89_diff__less__mono2,axiom,
% 0.18/0.46 ! [M: nat,N2: nat,L: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M @ N2 )
% 0.18/0.46 => ( ( ord_less_nat @ M @ L )
% 0.18/0.46 => ( ord_less_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_less_mono2
% 0.18/0.46 thf(fact_90_lift__Suc__mono__less__iff,axiom,
% 0.18/0.46 ! [F: nat > nat,N2: nat,M: nat] :
% 0.18/0.46 ( ! [N: nat] : ( ord_less_nat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.18/0.46 => ( ( ord_less_nat @ ( F @ N2 ) @ ( F @ M ) )
% 0.18/0.46 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % lift_Suc_mono_less_iff
% 0.18/0.46 thf(fact_91_lift__Suc__mono__less,axiom,
% 0.18/0.46 ! [F: nat > nat,N2: nat,N3: nat] :
% 0.18/0.46 ( ! [N: nat] : ( ord_less_nat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.18/0.46 => ( ( ord_less_nat @ N2 @ N3 )
% 0.18/0.46 => ( ord_less_nat @ ( F @ N2 ) @ ( F @ N3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % lift_Suc_mono_less
% 0.18/0.46 thf(fact_92_less__Suc__eq__0__disj,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.18/0.46 = ( ( M = zero_zero_nat )
% 0.18/0.46 | ? [J3: nat] :
% 0.18/0.46 ( ( M
% 0.18/0.46 = ( suc @ J3 ) )
% 0.18/0.46 & ( ord_less_nat @ J3 @ N2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_Suc_eq_0_disj
% 0.18/0.46 thf(fact_93_gr0__implies__Suc,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.46 => ? [M3: nat] :
% 0.18/0.46 ( N2
% 0.18/0.46 = ( suc @ M3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % gr0_implies_Suc
% 0.18/0.46 thf(fact_94_All__less__Suc2,axiom,
% 0.18/0.46 ! [N2: nat,P: nat > $o] :
% 0.18/0.46 ( ( ! [I3: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 0.18/0.46 => ( P @ I3 ) ) )
% 0.18/0.46 = ( ( P @ zero_zero_nat )
% 0.18/0.46 & ! [I3: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I3 @ N2 )
% 0.18/0.46 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % All_less_Suc2
% 0.18/0.46 thf(fact_95_gr0__conv__Suc,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.46 = ( ? [M5: nat] :
% 0.18/0.46 ( N2
% 0.18/0.46 = ( suc @ M5 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % gr0_conv_Suc
% 0.18/0.46 thf(fact_96_Ex__less__Suc2,axiom,
% 0.18/0.46 ! [N2: nat,P: nat > $o] :
% 0.18/0.46 ( ( ? [I3: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 0.18/0.46 & ( P @ I3 ) ) )
% 0.18/0.46 = ( ( P @ zero_zero_nat )
% 0.18/0.46 | ? [I3: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I3 @ N2 )
% 0.18/0.46 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Ex_less_Suc2
% 0.18/0.46 thf(fact_97_diff__less__Suc,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ ( suc @ M ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_less_Suc
% 0.18/0.46 thf(fact_98_Suc__diff__Suc,axiom,
% 0.18/0.46 ! [N2: nat,M: nat] :
% 0.18/0.46 ( ( ord_less_nat @ N2 @ M )
% 0.18/0.46 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N2 ) ) )
% 0.18/0.46 = ( minus_minus_nat @ M @ N2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_diff_Suc
% 0.18/0.46 thf(fact_99_diff__less,axiom,
% 0.18/0.46 ! [N2: nat,M: nat] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.46 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.18/0.46 => ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_less
% 0.18/0.46 thf(fact_100_diff__Suc__less,axiom,
% 0.18/0.46 ! [N2: nat,I: nat] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.46 => ( ord_less_nat @ ( minus_minus_nat @ N2 @ ( suc @ I ) ) @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_Suc_less
% 0.18/0.46 thf(fact_101_SameCfgOnLow,axiom,
% 0.18/0.46 ! [I4: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I4 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
% 0.18/0.46 => ( ( nth_co1649820636t_unit @ ( fe @ index ) @ I4 )
% 0.18/0.46 = ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % SameCfgOnLow
% 0.18/0.46 thf(fact_102__092_060open_062fe_Aindex_A_B_AnMsg_A_061_Afe_A_ISuc_Aindex_J_A_B_AnMsg_092_060close_062,axiom,
% 0.18/0.46 ( ( nth_co1649820636t_unit @ ( fe @ index ) @ nMsg )
% 0.18/0.46 = ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ nMsg ) ) ).
% 0.18/0.46
% 0.18/0.46 % \<open>fe index ! nMsg = fe (Suc index) ! nMsg\<close>
% 0.18/0.46 thf(fact_103_ShorterTrace,axiom,
% 0.18/0.46 ord_less_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % ShorterTrace
% 0.18/0.46 thf(fact_104_NotEmpty_I1_J,axiom,
% 0.18/0.46 ( ( fe @ ( suc @ index ) )
% 0.18/0.46 != nil_co1338500125t_unit ) ).
% 0.18/0.46
% 0.18/0.46 % NotEmpty(1)
% 0.18/0.46 thf(fact_105_IPrefixList,axiom,
% 0.18/0.46 ! [I4: nat] : ( prefix47729710ge_p_v @ ( ft @ I4 ) @ ( ft @ ( suc @ I4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % IPrefixList
% 0.18/0.46 thf(fact_106_IPrefixListEx,axiom,
% 0.18/0.46 ! [I4: nat] : ( prefix1615116500t_unit @ ( fe @ I4 ) @ ( fe @ ( suc @ I4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % IPrefixListEx
% 0.18/0.46 thf(fact_107_NatPredicateTippingPoint,axiom,
% 0.18/0.46 ! [N22: nat,Pr: nat > $o] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ N22 )
% 0.18/0.46 => ( ( Pr @ zero_zero_nat )
% 0.18/0.46 => ( ~ ( Pr @ N22 )
% 0.18/0.46 => ? [N: nat] :
% 0.18/0.46 ( ( ord_less_nat @ N @ N22 )
% 0.18/0.46 & ( Pr @ N )
% 0.18/0.46 & ~ ( Pr @ ( suc @ N ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % NatPredicateTippingPoint
% 0.18/0.46 thf(fact_108_NotEmpty_I2_J,axiom,
% 0.18/0.46 ( ( fe @ index )
% 0.18/0.46 != nil_co1338500125t_unit ) ).
% 0.18/0.46
% 0.18/0.46 % NotEmpty(2)
% 0.18/0.46 thf(fact_109_AssumptionFair_I4_J,axiom,
% 0.18/0.46 isReceiverOf_p_v @ p2 @ msg ).
% 0.18/0.46
% 0.18/0.46 % AssumptionFair(4)
% 0.18/0.46 thf(fact_110_AssumpOcc6_I2_J,axiom,
% 0.18/0.46 ( msg
% 0.18/0.46 != ( nth_message_p_v @ ( ft @ index ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % AssumpOcc6(2)
% 0.18/0.46 thf(fact_111_Occ1,axiom,
% 0.18/0.46 ? [P2: p] : ( isReceiverOf_p_v @ P2 @ msg ) ).
% 0.18/0.46
% 0.18/0.46 % Occ1
% 0.18/0.46 thf(fact_112_AssumptionSubset2_I1_J,axiom,
% 0.18/0.46 ? [P2: p] : ( isReceiverOf_p_v @ P2 @ msgInSet ) ).
% 0.18/0.46
% 0.18/0.46 % AssumptionSubset2(1)
% 0.18/0.46 thf(fact_113_SameMsgOnLow,axiom,
% 0.18/0.46 ! [I4: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I4 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 0.18/0.46 => ( ( nth_message_p_v @ ( ft @ index ) @ I4 )
% 0.18/0.46 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % SameMsgOnLow
% 0.18/0.46 thf(fact_114_le__zero__eq,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 0.18/0.46 = ( N2 = zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_zero_eq
% 0.18/0.46 thf(fact_115_Suc__le__mono,axiom,
% 0.18/0.46 ! [N2: nat,M: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( suc @ M ) )
% 0.18/0.46 = ( ord_less_eq_nat @ N2 @ M ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_le_mono
% 0.18/0.46 thf(fact_116_le0,axiom,
% 0.18/0.46 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 0.18/0.46
% 0.18/0.46 % le0
% 0.18/0.46 thf(fact_117_bot__nat__0_Oextremum,axiom,
% 0.18/0.46 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.18/0.46
% 0.18/0.46 % bot_nat_0.extremum
% 0.18/0.46 thf(fact_118_diff__diff__cancel,axiom,
% 0.18/0.46 ! [I: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ I @ N2 )
% 0.18/0.46 => ( ( minus_minus_nat @ N2 @ ( minus_minus_nat @ N2 @ I ) )
% 0.18/0.46 = I ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_diff_cancel
% 0.18/0.46 thf(fact_119__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062,axiom,
% 0.18/0.46 ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ).
% 0.18/0.46
% 0.18/0.46 % \<open>length (fe index) - 1 \<le> length (fe (Suc index)) - 1\<close>
% 0.18/0.46 thf(fact_120__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ift_A_ISuc_Aindex_J_J_O_Alength_A_Ift_Aindex_J_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062,axiom,
% 0.18/0.46 ~ ? [I4: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I4 @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 0.18/0.46 & ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ I4 )
% 0.18/0.46 & ( msg
% 0.18/0.46 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % \<open>\<not> (\<exists>i<length (ft (Suc index)). length (ft index) \<le> i \<and> msg = ft (Suc index) ! i)\<close>
% 0.18/0.46 thf(fact_121_NotConsumedIntermediate,axiom,
% 0.18/0.46 ! [I4: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I4 @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 0.18/0.46 => ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ I4 )
% 0.18/0.46 => ( ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I4 )
% 0.18/0.46 != msg ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % NotConsumedIntermediate
% 0.18/0.46 thf(fact_122_OccSameMsg,axiom,
% 0.18/0.46 ! [N4: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ nMsg @ N4 )
% 0.18/0.46 => ( ( ord_less_nat @ N4 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 0.18/0.46 => ( ( nth_message_p_v @ ( ft @ index ) @ N4 )
% 0.18/0.46 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ N4 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % OccSameMsg
% 0.18/0.46 thf(fact_123_Occ5,axiom,
% 0.18/0.46 ! [N4: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ nMsg @ N4 )
% 0.18/0.46 => ( ( ord_less_nat @ N4 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 0.18/0.46 => ( msg
% 0.18/0.46 != ( nth_message_p_v @ ( ft @ index ) @ N4 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Occ5
% 0.18/0.46 thf(fact_124_diff__is__0__eq,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ( minus_minus_nat @ M @ N2 )
% 0.18/0.46 = zero_zero_nat )
% 0.18/0.46 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_is_0_eq
% 0.18/0.46 thf(fact_125_diff__is__0__eq_H,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.46 => ( ( minus_minus_nat @ M @ N2 )
% 0.18/0.46 = zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_is_0_eq'
% 0.18/0.46 thf(fact_126_less__one,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ N2 @ one_one_nat )
% 0.18/0.46 = ( N2 = zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_one
% 0.18/0.46 thf(fact_127_diff__Suc__1,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 0.18/0.46 = N2 ) ).
% 0.18/0.46
% 0.18/0.46 % diff_Suc_1
% 0.18/0.46 thf(fact_128_AssumptionSubset3_I5_J,axiom,
% 0.18/0.46 ! [N4: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ nMsg @ N4 )
% 0.18/0.46 => ( ( ord_less_nat @ N4 @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 0.18/0.46 => ( msg
% 0.18/0.46 != ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ N4 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % AssumptionSubset3(5)
% 0.18/0.46 thf(fact_129_AssumptionSubset2_I5_J,axiom,
% 0.18/0.46 ! [N4: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ n1 @ N4 )
% 0.18/0.46 => ( ( ord_less_nat @ N4 @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 0.18/0.46 => ( msgInSet
% 0.18/0.46 != ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ N4 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % AssumptionSubset2(5)
% 0.18/0.46 thf(fact_130__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_O_Alength_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062,axiom,
% 0.18/0.46 ~ ? [I4: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I4 @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) )
% 0.18/0.46 & ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ I4 )
% 0.18/0.46 & ( msg
% 0.18/0.46 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % \<open>\<not> (\<exists>i<length (fe (Suc index)) - 1. length (fe index) - 1 \<le> i \<and> msg = ft (Suc index) ! i)\<close>
% 0.18/0.46 thf(fact_131_Suc__diff__1,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.46 => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 0.18/0.46 = N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_diff_1
% 0.18/0.46 thf(fact_132_AssumptionFairContr,axiom,
% 0.18/0.46 ! [N4: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ n @ N4 )
% 0.18/0.46 => ! [N0: nat] :
% 0.18/0.46 ( ( ord_less_nat @ N0 @ ( size_s1168481041ge_p_v @ ( ft @ N4 ) ) )
% 0.18/0.46 => ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) @ N0 )
% 0.18/0.46 => ( msg
% 0.18/0.46 != ( nth_message_p_v @ ( ft @ N4 ) @ N0 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % AssumptionFairContr
% 0.18/0.46 thf(fact_133_AssumpOcc6_I3_J,axiom,
% 0.18/0.46 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) @ msg ).
% 0.18/0.46
% 0.18/0.46 % AssumpOcc6(3)
% 0.18/0.46 thf(fact_134_le__refl,axiom,
% 0.18/0.46 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ N2 ) ).
% 0.18/0.46
% 0.18/0.46 % le_refl
% 0.18/0.46 thf(fact_135_le__trans,axiom,
% 0.18/0.46 ! [I: nat,J: nat,K: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ I @ J )
% 0.18/0.46 => ( ( ord_less_eq_nat @ J @ K )
% 0.18/0.46 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_trans
% 0.18/0.46 thf(fact_136_eq__imp__le,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( M = N2 )
% 0.18/0.46 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % eq_imp_le
% 0.18/0.46 thf(fact_137_le__antisym,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.46 => ( ( ord_less_eq_nat @ N2 @ M )
% 0.18/0.46 => ( M = N2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_antisym
% 0.18/0.46 thf(fact_138_nat__le__linear,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.46 | ( ord_less_eq_nat @ N2 @ M ) ) ).
% 0.18/0.46
% 0.18/0.46 % nat_le_linear
% 0.18/0.46 thf(fact_139_one__reorient,axiom,
% 0.18/0.46 ! [X: nat] :
% 0.18/0.46 ( ( one_one_nat = X )
% 0.18/0.46 = ( X = one_one_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % one_reorient
% 0.18/0.46 thf(fact_140_Nat_Oex__has__greatest__nat,axiom,
% 0.18/0.46 ! [P: nat > $o,K: nat,B: nat] :
% 0.18/0.46 ( ( P @ K )
% 0.18/0.46 => ( ! [Y3: nat] :
% 0.18/0.46 ( ( P @ Y3 )
% 0.18/0.46 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.18/0.46 => ? [X3: nat] :
% 0.18/0.46 ( ( P @ X3 )
% 0.18/0.46 & ! [Y4: nat] :
% 0.18/0.46 ( ( P @ Y4 )
% 0.18/0.46 => ( ord_less_eq_nat @ Y4 @ X3 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Nat.ex_has_greatest_nat
% 0.18/0.46 thf(fact_141_PrefixListTransitive,axiom,
% 0.18/0.46 ! [L1: list_message_p_v,L2: list_message_p_v,L3: list_message_p_v] :
% 0.18/0.46 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.18/0.46 => ( ( prefix47729710ge_p_v @ L2 @ L3 )
% 0.18/0.46 => ( prefix47729710ge_p_v @ L1 @ L3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % PrefixListTransitive
% 0.18/0.46 thf(fact_142_PrefixListTransitive,axiom,
% 0.18/0.46 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit,L3: list_c1059388851t_unit] :
% 0.18/0.46 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.18/0.46 => ( ( prefix1615116500t_unit @ L2 @ L3 )
% 0.18/0.46 => ( prefix1615116500t_unit @ L1 @ L3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % PrefixListTransitive
% 0.18/0.46 thf(fact_143_MinPredicate,axiom,
% 0.18/0.46 ! [P: nat > $o] :
% 0.18/0.46 ( ? [X_1: nat] : ( P @ X_1 )
% 0.18/0.46 => ? [N02: nat] :
% 0.18/0.46 ( ( P @ N02 )
% 0.18/0.46 & ! [N4: nat] :
% 0.18/0.46 ( ( P @ N4 )
% 0.18/0.46 => ( ord_less_eq_nat @ N02 @ N4 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % MinPredicate
% 0.18/0.46 thf(fact_144_lift__Suc__antimono__le,axiom,
% 0.18/0.46 ! [F: nat > nat,N2: nat,N3: nat] :
% 0.18/0.46 ( ! [N: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 0.18/0.46 => ( ( ord_less_eq_nat @ N2 @ N3 )
% 0.18/0.46 => ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ N2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % lift_Suc_antimono_le
% 0.18/0.46 thf(fact_145_lift__Suc__mono__le,axiom,
% 0.18/0.46 ! [F: nat > nat,N2: nat,N3: nat] :
% 0.18/0.46 ( ! [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.18/0.46 => ( ( ord_less_eq_nat @ N2 @ N3 )
% 0.18/0.46 => ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ N3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % lift_Suc_mono_le
% 0.18/0.46 thf(fact_146_KeepProperty,axiom,
% 0.18/0.46 ! [Low: nat,P: nat > $o,Q: nat > $o] :
% 0.18/0.46 ( ! [I2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ Low @ I2 )
% 0.18/0.46 => ( ( P @ I2 )
% 0.18/0.46 => ( ( P @ ( suc @ I2 ) )
% 0.18/0.46 & ( Q @ I2 ) ) ) )
% 0.18/0.46 => ( ( P @ Low )
% 0.18/0.46 => ! [I4: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ Low @ I4 )
% 0.18/0.46 => ( Q @ I4 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % KeepProperty
% 0.18/0.46 thf(fact_147_PrefixSameOnLow,axiom,
% 0.18/0.46 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 0.18/0.46 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.18/0.46 => ! [Index: nat] :
% 0.18/0.46 ( ( ord_less_nat @ Index @ ( size_s1168481041ge_p_v @ L1 ) )
% 0.18/0.46 => ( ( nth_message_p_v @ L1 @ Index )
% 0.18/0.46 = ( nth_message_p_v @ L2 @ Index ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % PrefixSameOnLow
% 0.18/0.46 thf(fact_148_PrefixSameOnLow,axiom,
% 0.18/0.46 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 0.18/0.46 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.18/0.46 => ! [Index: nat] :
% 0.18/0.46 ( ( ord_less_nat @ Index @ ( size_s1406904903t_unit @ L1 ) )
% 0.18/0.46 => ( ( nth_co1649820636t_unit @ L1 @ Index )
% 0.18/0.46 = ( nth_co1649820636t_unit @ L2 @ Index ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % PrefixSameOnLow
% 0.18/0.46 thf(fact_149_zero__le,axiom,
% 0.18/0.46 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 0.18/0.46
% 0.18/0.46 % zero_le
% 0.18/0.46 thf(fact_150_Suc__leD,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 0.18/0.46 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_leD
% 0.18/0.46 thf(fact_151_le__SucE,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.18/0.46 => ( ~ ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.46 => ( M
% 0.18/0.46 = ( suc @ N2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_SucE
% 0.18/0.46 thf(fact_152_le__SucI,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.46 => ( ord_less_eq_nat @ M @ ( suc @ N2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_SucI
% 0.18/0.46 thf(fact_153_Suc__le__D,axiom,
% 0.18/0.46 ! [N2: nat,M6: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ M6 )
% 0.18/0.46 => ? [M3: nat] :
% 0.18/0.46 ( M6
% 0.18/0.46 = ( suc @ M3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_le_D
% 0.18/0.46 thf(fact_154_le__Suc__eq,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.18/0.46 = ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.46 | ( M
% 0.18/0.46 = ( suc @ N2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_Suc_eq
% 0.18/0.46 thf(fact_155_Suc__n__not__le__n,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ~ ( ord_less_eq_nat @ ( suc @ N2 ) @ N2 ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_n_not_le_n
% 0.18/0.46 thf(fact_156_not__less__eq__eq,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ~ ( ord_less_eq_nat @ M @ N2 ) )
% 0.18/0.46 = ( ord_less_eq_nat @ ( suc @ N2 ) @ M ) ) ).
% 0.18/0.46
% 0.18/0.46 % not_less_eq_eq
% 0.18/0.46 thf(fact_157_full__nat__induct,axiom,
% 0.18/0.46 ! [P: nat > $o,N2: nat] :
% 0.18/0.46 ( ! [N: nat] :
% 0.18/0.46 ( ! [M2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 0.18/0.46 => ( P @ M2 ) )
% 0.18/0.46 => ( P @ N ) )
% 0.18/0.46 => ( P @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % full_nat_induct
% 0.18/0.46 thf(fact_158_nat__induct__at__least,axiom,
% 0.18/0.46 ! [M: nat,N2: nat,P: nat > $o] :
% 0.18/0.46 ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.46 => ( ( P @ M )
% 0.18/0.46 => ( ! [N: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ M @ N )
% 0.18/0.46 => ( ( P @ N )
% 0.18/0.46 => ( P @ ( suc @ N ) ) ) )
% 0.18/0.46 => ( P @ N2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % nat_induct_at_least
% 0.18/0.46 thf(fact_159_transitive__stepwise__le,axiom,
% 0.18/0.46 ! [M: nat,N2: nat,R: nat > nat > $o] :
% 0.18/0.46 ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.46 => ( ! [X3: nat] : ( R @ X3 @ X3 )
% 0.18/0.46 => ( ! [X3: nat,Y3: nat,Z: nat] :
% 0.18/0.46 ( ( R @ X3 @ Y3 )
% 0.18/0.46 => ( ( R @ Y3 @ Z )
% 0.18/0.46 => ( R @ X3 @ Z ) ) )
% 0.18/0.46 => ( ! [N: nat] : ( R @ N @ ( suc @ N ) )
% 0.18/0.46 => ( R @ M @ N2 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % transitive_stepwise_le
% 0.18/0.46 thf(fact_160_less__eq__nat_Osimps_I1_J,axiom,
% 0.18/0.46 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 0.18/0.46
% 0.18/0.46 % less_eq_nat.simps(1)
% 0.18/0.46 thf(fact_161_le__0__eq,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 0.18/0.46 = ( N2 = zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_0_eq
% 0.18/0.46 thf(fact_162_bot__nat__0_Oextremum__unique,axiom,
% 0.18/0.46 ! [A: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.18/0.46 = ( A = zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % bot_nat_0.extremum_unique
% 0.18/0.46 thf(fact_163_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.18/0.46 ! [A: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.18/0.46 => ( A = zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % bot_nat_0.extremum_uniqueI
% 0.18/0.46 thf(fact_164_nat__less__le,axiom,
% 0.18/0.46 ( ord_less_nat
% 0.18/0.46 = ( ^ [M5: nat,N5: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ M5 @ N5 )
% 0.18/0.46 & ( M5 != N5 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % nat_less_le
% 0.18/0.46 thf(fact_165_less__imp__le__nat,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M @ N2 )
% 0.18/0.46 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_imp_le_nat
% 0.18/0.46 thf(fact_166_le__eq__less__or__eq,axiom,
% 0.18/0.46 ( ord_less_eq_nat
% 0.18/0.46 = ( ^ [M5: nat,N5: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M5 @ N5 )
% 0.18/0.46 | ( M5 = N5 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_eq_less_or_eq
% 0.18/0.46 thf(fact_167_less__or__eq__imp__le,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ( ord_less_nat @ M @ N2 )
% 0.18/0.46 | ( M = N2 ) )
% 0.18/0.46 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_or_eq_imp_le
% 0.18/0.46 thf(fact_168_le__neq__implies__less,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.46 => ( ( M != N2 )
% 0.18/0.46 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_neq_implies_less
% 0.18/0.46 thf(fact_169_less__mono__imp__le__mono,axiom,
% 0.18/0.46 ! [F: nat > nat,I: nat,J: nat] :
% 0.18/0.46 ( ! [I2: nat,J2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I2 @ J2 )
% 0.18/0.46 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 0.18/0.46 => ( ( ord_less_eq_nat @ I @ J )
% 0.18/0.46 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_mono_imp_le_mono
% 0.18/0.46 thf(fact_170_eq__diff__iff,axiom,
% 0.18/0.46 ! [K: nat,M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ K @ M )
% 0.18/0.46 => ( ( ord_less_eq_nat @ K @ N2 )
% 0.18/0.46 => ( ( ( minus_minus_nat @ M @ K )
% 0.18/0.46 = ( minus_minus_nat @ N2 @ K ) )
% 0.18/0.46 = ( M = N2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % eq_diff_iff
% 0.18/0.46 thf(fact_171_le__diff__iff,axiom,
% 0.18/0.46 ! [K: nat,M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ K @ M )
% 0.18/0.46 => ( ( ord_less_eq_nat @ K @ N2 )
% 0.18/0.46 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 0.18/0.46 = ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_diff_iff
% 0.18/0.46 thf(fact_172_Nat_Odiff__diff__eq,axiom,
% 0.18/0.46 ! [K: nat,M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ K @ M )
% 0.18/0.46 => ( ( ord_less_eq_nat @ K @ N2 )
% 0.18/0.46 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 0.18/0.46 = ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Nat.diff_diff_eq
% 0.18/0.46 thf(fact_173_diff__le__mono,axiom,
% 0.18/0.46 ! [M: nat,N2: nat,L: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.46 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N2 @ L ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_le_mono
% 0.18/0.46 thf(fact_174_diff__le__self,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ).
% 0.18/0.46
% 0.18/0.46 % diff_le_self
% 0.18/0.46 thf(fact_175_le__diff__iff_H,axiom,
% 0.18/0.46 ! [A: nat,C: nat,B: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ A @ C )
% 0.18/0.46 => ( ( ord_less_eq_nat @ B @ C )
% 0.18/0.46 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 0.18/0.46 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_diff_iff'
% 0.18/0.46 thf(fact_176_diff__le__mono2,axiom,
% 0.18/0.46 ! [M: nat,N2: nat,L: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.46 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_le_mono2
% 0.18/0.46 thf(fact_177_MinPredicate2,axiom,
% 0.18/0.46 ! [P: nat > $o] :
% 0.18/0.46 ( ? [X_1: nat] : ( P @ X_1 )
% 0.18/0.46 => ? [N02: nat] :
% 0.18/0.46 ( ( P @ N02 )
% 0.18/0.46 & ( ( N02 = zero_zero_nat )
% 0.18/0.46 | ~ ( P @ ( minus_minus_nat @ N02 @ one_one_nat ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % MinPredicate2
% 0.18/0.46 thf(fact_178_PrefixListMonotonicity,axiom,
% 0.18/0.46 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 0.18/0.46 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.18/0.46 => ( ord_less_nat @ ( size_s1168481041ge_p_v @ L1 ) @ ( size_s1168481041ge_p_v @ L2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % PrefixListMonotonicity
% 0.18/0.46 thf(fact_179_PrefixListMonotonicity,axiom,
% 0.18/0.46 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 0.18/0.46 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.18/0.46 => ( ord_less_nat @ ( size_s1406904903t_unit @ L1 ) @ ( size_s1406904903t_unit @ L2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % PrefixListMonotonicity
% 0.18/0.46 thf(fact_180_Suc__leI,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M @ N2 )
% 0.18/0.46 => ( ord_less_eq_nat @ ( suc @ M ) @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_leI
% 0.18/0.46 thf(fact_181_Suc__le__eq,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 0.18/0.46 = ( ord_less_nat @ M @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_le_eq
% 0.18/0.46 thf(fact_182_dec__induct,axiom,
% 0.18/0.46 ! [I: nat,J: nat,P: nat > $o] :
% 0.18/0.46 ( ( ord_less_eq_nat @ I @ J )
% 0.18/0.46 => ( ( P @ I )
% 0.18/0.46 => ( ! [N: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ I @ N )
% 0.18/0.46 => ( ( ord_less_nat @ N @ J )
% 0.18/0.46 => ( ( P @ N )
% 0.18/0.46 => ( P @ ( suc @ N ) ) ) ) )
% 0.18/0.46 => ( P @ J ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % dec_induct
% 0.18/0.46 thf(fact_183_inc__induct,axiom,
% 0.18/0.46 ! [I: nat,J: nat,P: nat > $o] :
% 0.18/0.46 ( ( ord_less_eq_nat @ I @ J )
% 0.18/0.46 => ( ( P @ J )
% 0.18/0.46 => ( ! [N: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ I @ N )
% 0.18/0.46 => ( ( ord_less_nat @ N @ J )
% 0.18/0.46 => ( ( P @ ( suc @ N ) )
% 0.18/0.46 => ( P @ N ) ) ) )
% 0.18/0.46 => ( P @ I ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % inc_induct
% 0.18/0.46 thf(fact_184_Suc__le__lessD,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 0.18/0.46 => ( ord_less_nat @ M @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_le_lessD
% 0.18/0.46 thf(fact_185_le__less__Suc__eq,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.46 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 0.18/0.46 = ( N2 = M ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_less_Suc_eq
% 0.18/0.46 thf(fact_186_less__Suc__eq__le,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.18/0.46 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_Suc_eq_le
% 0.18/0.46 thf(fact_187_less__eq__Suc__le,axiom,
% 0.18/0.46 ( ord_less_nat
% 0.18/0.46 = ( ^ [N5: nat] : ( ord_less_eq_nat @ ( suc @ N5 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_eq_Suc_le
% 0.18/0.46 thf(fact_188_le__imp__less__Suc,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ M @ N2 )
% 0.18/0.46 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % le_imp_less_Suc
% 0.18/0.46 thf(fact_189_ex__least__nat__le,axiom,
% 0.18/0.46 ! [P: nat > $o,N2: nat] :
% 0.18/0.46 ( ( P @ N2 )
% 0.18/0.46 => ( ~ ( P @ zero_zero_nat )
% 0.18/0.46 => ? [K2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ K2 @ N2 )
% 0.18/0.46 & ! [I4: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I4 @ K2 )
% 0.18/0.46 => ~ ( P @ I4 ) )
% 0.18/0.46 & ( P @ K2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % ex_least_nat_le
% 0.18/0.46 thf(fact_190_Suc__diff__le,axiom,
% 0.18/0.46 ! [N2: nat,M: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ N2 @ M )
% 0.18/0.46 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 0.18/0.46 = ( suc @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_diff_le
% 0.18/0.46 thf(fact_191_less__diff__iff,axiom,
% 0.18/0.46 ! [K: nat,M: nat,N2: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ K @ M )
% 0.18/0.46 => ( ( ord_less_eq_nat @ K @ N2 )
% 0.18/0.46 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 0.18/0.46 = ( ord_less_nat @ M @ N2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_diff_iff
% 0.18/0.46 thf(fact_192_diff__less__mono,axiom,
% 0.18/0.46 ! [A: nat,B: nat,C: nat] :
% 0.18/0.46 ( ( ord_less_nat @ A @ B )
% 0.18/0.46 => ( ( ord_less_eq_nat @ C @ A )
% 0.18/0.46 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_less_mono
% 0.18/0.46 thf(fact_193_One__nat__def,axiom,
% 0.18/0.46 ( one_one_nat
% 0.18/0.46 = ( suc @ zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 % One_nat_def
% 0.18/0.46 thf(fact_194_diff__Suc__eq__diff__pred,axiom,
% 0.18/0.46 ! [M: nat,N2: nat] :
% 0.18/0.46 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 0.18/0.46 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N2 ) ) ).
% 0.18/0.46
% 0.18/0.46 % diff_Suc_eq_diff_pred
% 0.18/0.46 thf(fact_195_ex__least__nat__less,axiom,
% 0.18/0.46 ! [P: nat > $o,N2: nat] :
% 0.18/0.46 ( ( P @ N2 )
% 0.18/0.46 => ( ~ ( P @ zero_zero_nat )
% 0.18/0.46 => ? [K2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ K2 @ N2 )
% 0.18/0.46 & ! [I4: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ I4 @ K2 )
% 0.18/0.46 => ~ ( P @ I4 ) )
% 0.18/0.46 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % ex_least_nat_less
% 0.18/0.46 thf(fact_196_nat__induct__non__zero,axiom,
% 0.18/0.46 ! [N2: nat,P: nat > $o] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.46 => ( ( P @ one_one_nat )
% 0.18/0.46 => ( ! [N: nat] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.46 => ( ( P @ N )
% 0.18/0.46 => ( P @ ( suc @ N ) ) ) )
% 0.18/0.46 => ( P @ N2 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % nat_induct_non_zero
% 0.18/0.46 thf(fact_197_Suc__pred_H,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.46 => ( N2
% 0.18/0.46 = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_pred'
% 0.18/0.46 thf(fact_198_Suc__diff__eq__diff__pred,axiom,
% 0.18/0.46 ! [N2: nat,M: nat] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.46 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 0.18/0.46 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Suc_diff_eq_diff_pred
% 0.18/0.46 thf(fact_199_AssumptionSubset2_I6_J,axiom,
% 0.18/0.46 ( ( n1 != zero_zero_nat )
% 0.18/0.46 => ( ~ ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) @ msgInSet )
% 0.18/0.46 | ( msgInSet
% 0.18/0.46 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % AssumptionSubset2(6)
% 0.18/0.46 thf(fact_200_AssumptionSubset3_I6_J,axiom,
% 0.18/0.46 ( ( nMsg != zero_zero_nat )
% 0.18/0.46 => ( ~ ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) @ msg )
% 0.18/0.46 | ( msg
% 0.18/0.46 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % AssumptionSubset3(6)
% 0.18/0.46 thf(fact_201_EnabledIntermediate,axiom,
% 0.18/0.46 ! [I4: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I4 @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) )
% 0.18/0.46 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ I4 )
% 0.18/0.46 => ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ I4 ) @ msg ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % EnabledIntermediate
% 0.18/0.46 thf(fact_202_length__greater__0__conv,axiom,
% 0.18/0.46 ! [Xs: list_c1059388851t_unit] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ Xs ) )
% 0.18/0.46 = ( Xs != nil_co1338500125t_unit ) ) ).
% 0.18/0.46
% 0.18/0.46 % length_greater_0_conv
% 0.18/0.46 thf(fact_203_length__greater__0__conv,axiom,
% 0.18/0.46 ! [Xs: list_message_p_v] :
% 0.18/0.46 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1168481041ge_p_v @ Xs ) )
% 0.18/0.46 = ( Xs != nil_message_p_v ) ) ).
% 0.18/0.46
% 0.18/0.46 % length_greater_0_conv
% 0.18/0.46 thf(fact_204_AssumptionFair_I2_J,axiom,
% 0.18/0.46 ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ) ).
% 0.18/0.46
% 0.18/0.46 % AssumptionFair(2)
% 0.18/0.46 thf(fact_205_Occ4,axiom,
% 0.18/0.46 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ nMsg ) @ msg ).
% 0.18/0.46
% 0.18/0.46 % Occ4
% 0.18/0.46 thf(fact_206_AssumptionFair_I3_J,axiom,
% 0.18/0.46 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ n0 ) @ msg ).
% 0.18/0.46
% 0.18/0.46 % AssumptionFair(3)
% 0.18/0.46 thf(fact_207_AssumptionSubset3_I4_J,axiom,
% 0.18/0.46 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ nMsg ) @ msg ).
% 0.18/0.46
% 0.18/0.46 % AssumptionSubset3(4)
% 0.18/0.46 thf(fact_208_AssumptionSubset2_I4_J,axiom,
% 0.18/0.46 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ n1 ) @ msgInSet ).
% 0.18/0.46
% 0.18/0.46 % AssumptionSubset2(4)
% 0.18/0.46 thf(fact_209_MessageStaysOrConsumed,axiom,
% 0.18/0.46 ! [N1: nat,N22: nat,N2: nat,Msg: message_p_v] :
% 0.18/0.46 ( ( ( ord_less_eq_nat @ N1 @ N22 )
% 0.18/0.46 & ( ord_less_nat @ N22 @ ( size_s1406904903t_unit @ ( fe @ N2 ) ) )
% 0.18/0.46 & ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N2 ) @ N1 ) @ Msg ) )
% 0.18/0.46 => ( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N2 ) @ N22 ) @ Msg )
% 0.18/0.46 | ? [N03: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ N1 @ N03 )
% 0.18/0.46 & ( ord_less_nat @ N03 @ ( size_s1168481041ge_p_v @ ( ft @ N2 ) ) )
% 0.18/0.46 & ( ( nth_message_p_v @ ( ft @ N2 ) @ N03 )
% 0.18/0.46 = Msg ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % MessageStaysOrConsumed
% 0.18/0.46 thf(fact_210__092_060open_062enabled_A_Ife_A_ISuc_Aindex_J_A_B_A_Ilength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_J_J_Amsg_092_060close_062,axiom,
% 0.18/0.46 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ) @ msg ).
% 0.18/0.46
% 0.18/0.46 % \<open>enabled (fe (Suc index) ! (length (fe (Suc index)) - 1)) msg\<close>
% 0.18/0.46 thf(fact_211_length__0__conv,axiom,
% 0.18/0.46 ! [Xs: list_c1059388851t_unit] :
% 0.18/0.46 ( ( ( size_s1406904903t_unit @ Xs )
% 0.18/0.46 = zero_zero_nat )
% 0.18/0.46 = ( Xs = nil_co1338500125t_unit ) ) ).
% 0.18/0.46
% 0.18/0.46 % length_0_conv
% 0.18/0.46 thf(fact_212_length__0__conv,axiom,
% 0.18/0.46 ! [Xs: list_message_p_v] :
% 0.18/0.46 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.18/0.46 = zero_zero_nat )
% 0.18/0.46 = ( Xs = nil_message_p_v ) ) ).
% 0.18/0.46
% 0.18/0.46 % length_0_conv
% 0.18/0.46 thf(fact_213_Occ2,axiom,
% 0.18/0.46 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ index ) ) @ msg ).
% 0.18/0.46
% 0.18/0.46 % Occ2
% 0.18/0.46 thf(fact_214_AssumptionCase1ImplThesis_H,axiom,
% 0.18/0.46 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg ).
% 0.18/0.46
% 0.18/0.46 % AssumptionCase1ImplThesis'
% 0.18/0.46 thf(fact_215_neq__if__length__neq,axiom,
% 0.18/0.46 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.18/0.46 ( ( ( size_s1406904903t_unit @ Xs )
% 0.18/0.46 != ( size_s1406904903t_unit @ Ys ) )
% 0.18/0.46 => ( Xs != Ys ) ) ).
% 0.18/0.46
% 0.18/0.46 % neq_if_length_neq
% 0.18/0.46 thf(fact_216_neq__if__length__neq,axiom,
% 0.18/0.46 ! [Xs: list_message_p_v,Ys: list_message_p_v] :
% 0.18/0.46 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.18/0.46 != ( size_s1168481041ge_p_v @ Ys ) )
% 0.18/0.46 => ( Xs != Ys ) ) ).
% 0.18/0.46
% 0.18/0.46 % neq_if_length_neq
% 0.18/0.46 thf(fact_217_Ex__list__of__length,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ? [Xs2: list_c1059388851t_unit] :
% 0.18/0.46 ( ( size_s1406904903t_unit @ Xs2 )
% 0.18/0.46 = N2 ) ).
% 0.18/0.46
% 0.18/0.46 % Ex_list_of_length
% 0.18/0.46 thf(fact_218_Ex__list__of__length,axiom,
% 0.18/0.46 ! [N2: nat] :
% 0.18/0.46 ? [Xs2: list_message_p_v] :
% 0.18/0.46 ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.18/0.46 = N2 ) ).
% 0.18/0.46
% 0.18/0.46 % Ex_list_of_length
% 0.18/0.46 thf(fact_219_length__induct,axiom,
% 0.18/0.46 ! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
% 0.18/0.46 ( ! [Xs2: list_c1059388851t_unit] :
% 0.18/0.46 ( ! [Ys2: list_c1059388851t_unit] :
% 0.18/0.46 ( ( ord_less_nat @ ( size_s1406904903t_unit @ Ys2 ) @ ( size_s1406904903t_unit @ Xs2 ) )
% 0.18/0.46 => ( P @ Ys2 ) )
% 0.18/0.46 => ( P @ Xs2 ) )
% 0.18/0.46 => ( P @ Xs ) ) ).
% 0.18/0.46
% 0.18/0.46 % length_induct
% 0.18/0.46 thf(fact_220_length__induct,axiom,
% 0.18/0.46 ! [P: list_message_p_v > $o,Xs: list_message_p_v] :
% 0.18/0.46 ( ! [Xs2: list_message_p_v] :
% 0.18/0.46 ( ! [Ys2: list_message_p_v] :
% 0.18/0.46 ( ( ord_less_nat @ ( size_s1168481041ge_p_v @ Ys2 ) @ ( size_s1168481041ge_p_v @ Xs2 ) )
% 0.18/0.46 => ( P @ Ys2 ) )
% 0.18/0.46 => ( P @ Xs2 ) )
% 0.18/0.46 => ( P @ Xs ) ) ).
% 0.18/0.46
% 0.18/0.46 % length_induct
% 0.18/0.46 thf(fact_221_list_Osize_I3_J,axiom,
% 0.18/0.46 ( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
% 0.18/0.46 = zero_zero_nat ) ).
% 0.18/0.46
% 0.18/0.46 % list.size(3)
% 0.18/0.46 thf(fact_222_list_Osize_I3_J,axiom,
% 0.18/0.46 ( ( size_s1168481041ge_p_v @ nil_message_p_v )
% 0.18/0.46 = zero_zero_nat ) ).
% 0.18/0.46
% 0.18/0.46 % list.size(3)
% 0.18/0.46 thf(fact_223_list__eq__iff__nth__eq,axiom,
% 0.18/0.46 ( ( ^ [Y5: list_c1059388851t_unit,Z2: list_c1059388851t_unit] : ( Y5 = Z2 ) )
% 0.18/0.46 = ( ^ [Xs3: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
% 0.18/0.46 ( ( ( size_s1406904903t_unit @ Xs3 )
% 0.18/0.46 = ( size_s1406904903t_unit @ Ys3 ) )
% 0.18/0.46 & ! [I3: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I3 @ ( size_s1406904903t_unit @ Xs3 ) )
% 0.18/0.46 => ( ( nth_co1649820636t_unit @ Xs3 @ I3 )
% 0.18/0.46 = ( nth_co1649820636t_unit @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % list_eq_iff_nth_eq
% 0.18/0.46 thf(fact_224_list__eq__iff__nth__eq,axiom,
% 0.18/0.46 ( ( ^ [Y5: list_message_p_v,Z2: list_message_p_v] : ( Y5 = Z2 ) )
% 0.18/0.46 = ( ^ [Xs3: list_message_p_v,Ys3: list_message_p_v] :
% 0.18/0.46 ( ( ( size_s1168481041ge_p_v @ Xs3 )
% 0.18/0.46 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 0.18/0.46 & ! [I3: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I3 @ ( size_s1168481041ge_p_v @ Xs3 ) )
% 0.18/0.46 => ( ( nth_message_p_v @ Xs3 @ I3 )
% 0.18/0.46 = ( nth_message_p_v @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % list_eq_iff_nth_eq
% 0.18/0.46 thf(fact_225_Skolem__list__nth,axiom,
% 0.18/0.46 ! [K: nat,P: nat > config256849571t_unit > $o] :
% 0.18/0.46 ( ( ! [I3: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I3 @ K )
% 0.18/0.46 => ? [X4: config256849571t_unit] : ( P @ I3 @ X4 ) ) )
% 0.18/0.46 = ( ? [Xs3: list_c1059388851t_unit] :
% 0.18/0.46 ( ( ( size_s1406904903t_unit @ Xs3 )
% 0.18/0.46 = K )
% 0.18/0.46 & ! [I3: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I3 @ K )
% 0.18/0.46 => ( P @ I3 @ ( nth_co1649820636t_unit @ Xs3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Skolem_list_nth
% 0.18/0.46 thf(fact_226_Skolem__list__nth,axiom,
% 0.18/0.46 ! [K: nat,P: nat > message_p_v > $o] :
% 0.18/0.46 ( ( ! [I3: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I3 @ K )
% 0.18/0.46 => ? [X4: message_p_v] : ( P @ I3 @ X4 ) ) )
% 0.18/0.46 = ( ? [Xs3: list_message_p_v] :
% 0.18/0.46 ( ( ( size_s1168481041ge_p_v @ Xs3 )
% 0.18/0.46 = K )
% 0.18/0.46 & ! [I3: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I3 @ K )
% 0.18/0.46 => ( P @ I3 @ ( nth_message_p_v @ Xs3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Skolem_list_nth
% 0.18/0.46 thf(fact_227_nth__equalityI,axiom,
% 0.18/0.46 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.18/0.46 ( ( ( size_s1406904903t_unit @ Xs )
% 0.18/0.46 = ( size_s1406904903t_unit @ Ys ) )
% 0.18/0.46 => ( ! [I2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I2 @ ( size_s1406904903t_unit @ Xs ) )
% 0.18/0.46 => ( ( nth_co1649820636t_unit @ Xs @ I2 )
% 0.18/0.46 = ( nth_co1649820636t_unit @ Ys @ I2 ) ) )
% 0.18/0.46 => ( Xs = Ys ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % nth_equalityI
% 0.18/0.46 thf(fact_228_nth__equalityI,axiom,
% 0.18/0.46 ! [Xs: list_message_p_v,Ys: list_message_p_v] :
% 0.18/0.46 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.18/0.46 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.18/0.46 => ( ! [I2: nat] :
% 0.18/0.46 ( ( ord_less_nat @ I2 @ ( size_s1168481041ge_p_v @ Xs ) )
% 0.18/0.46 => ( ( nth_message_p_v @ Xs @ I2 )
% 0.18/0.46 = ( nth_message_p_v @ Ys @ I2 ) ) )
% 0.18/0.46 => ( Xs = Ys ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % nth_equalityI
% 0.18/0.46 thf(fact_229_EnabledOrConsumed,axiom,
% 0.18/0.46 ( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) @ msg )
% 0.18/0.46 | ? [N03: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ n0 @ N03 )
% 0.18/0.46 & ( ord_less_nat @ N03 @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
% 0.18/0.46 & ( ( nth_message_p_v @ ( ft @ n ) @ N03 )
% 0.18/0.46 = msg ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % EnabledOrConsumed
% 0.18/0.46 thf(fact_230_Case2ImplThesis,axiom,
% 0.18/0.46 ( ? [N0: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ n0 @ N0 )
% 0.18/0.46 & ( ord_less_nat @ N0 @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
% 0.18/0.46 & ( ( nth_message_p_v @ ( ft @ n ) @ N0 )
% 0.18/0.46 = msg ) )
% 0.18/0.46 => ? [N6: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ n @ N6 )
% 0.18/0.46 & ? [N03: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ n0 @ N03 )
% 0.18/0.46 & ( ord_less_nat @ N03 @ ( size_s1168481041ge_p_v @ ( ft @ N6 ) ) )
% 0.18/0.46 & ( msg
% 0.18/0.46 = ( nth_message_p_v @ ( ft @ N6 ) @ N03 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Case2ImplThesis
% 0.18/0.46 thf(fact_231_EnabledInSuc,axiom,
% 0.18/0.46 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msg ).
% 0.18/0.46
% 0.18/0.46 % EnabledInSuc
% 0.18/0.46 thf(fact_232_AssumptionSubset2_I2_J,axiom,
% 0.18/0.46 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msgInSet ).
% 0.18/0.46
% 0.18/0.46 % AssumptionSubset2(2)
% 0.18/0.46 thf(fact_233_LastOfIndex,axiom,
% 0.18/0.46 ( ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) )
% 0.18/0.46 = ( last_c571238084t_unit @ ( fe @ index ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % LastOfIndex
% 0.18/0.46 thf(fact_234_EnabledOrConsumedAtLast,axiom,
% 0.18/0.46 ( ( enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg )
% 0.18/0.46 | ? [N03: nat] :
% 0.18/0.46 ( ( ord_less_eq_nat @ n0 @ N03 )
% 0.18/0.46 & ( ord_less_nat @ N03 @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
% 0.18/0.46 & ( ( nth_message_p_v @ ( ft @ n ) @ N03 )
% 0.18/0.46 = msg ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % EnabledOrConsumedAtLast
% 0.18/0.46 thf(fact_235_last__conv__nth,axiom,
% 0.18/0.46 ! [Xs: list_c1059388851t_unit] :
% 0.18/0.46 ( ( Xs != nil_co1338500125t_unit )
% 0.18/0.46 => ( ( last_c571238084t_unit @ Xs )
% 0.18/0.46 = ( nth_co1649820636t_unit @ Xs @ ( minus_minus_nat @ ( size_s1406904903t_unit @ Xs ) @ one_one_nat ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % last_conv_nth
% 0.18/0.46 thf(fact_236_last__conv__nth,axiom,
% 0.18/0.46 ! [Xs: list_message_p_v] :
% 0.18/0.46 ( ( Xs != nil_message_p_v )
% 0.18/0.46 => ( ( last_message_p_v @ Xs )
% 0.18/0.46 = ( nth_message_p_v @ Xs @ ( minus_minus_nat @ ( size_s1168481041ge_p_v @ Xs ) @ one_one_nat ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % last_conv_nth
% 0.18/0.46 thf(fact_237__092_060open_062_092_060And_062n0_Amsg_O_A_092_060forall_062n_O_Aexecution_OfirstOccurrence_A_Ife_An_J_A_Ift_An_J_Amsg_An0_A_092_060longrightarrow_062_Amsg_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062,axiom,
% 0.18/0.46 ! [Msg: message_p_v,N04: nat,N7: nat] :
% 0.18/0.46 ( ( firstO1414030372_p_v_s @ ( fe @ N7 ) @ ( ft @ N7 ) @ Msg @ N04 )
% 0.18/0.46 => ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ ( last_c571238084t_unit @ ( fe @ N7 ) ) @ Msg ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % \<open>\<And>n0 msg. \<forall>n. execution.firstOccurrence (fe n) (ft n) msg n0 \<longrightarrow> msg \<in># msgs (last (fe n))\<close>
% 0.18/0.46 thf(fact_238_le__numeral__extra_I3_J,axiom,
% 0.18/0.46 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.18/0.46
% 0.18/0.46 % le_numeral_extra(3)
% 0.18/0.46 thf(fact_239_less__numeral__extra_I3_J,axiom,
% 0.18/0.46 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.18/0.46
% 0.18/0.46 % less_numeral_extra(3)
% 0.18/0.46 thf(fact_240_le__numeral__extra_I4_J,axiom,
% 0.18/0.46 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.18/0.46
% 0.18/0.46 % le_numeral_extra(4)
% 0.18/0.46 thf(fact_241_less__numeral__extra_I4_J,axiom,
% 0.18/0.46 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.18/0.46
% 0.18/0.46 % less_numeral_extra(4)
% 0.18/0.46 thf(fact_242_less__numeral__extra_I1_J,axiom,
% 0.18/0.46 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.18/0.46
% 0.18/0.46 % less_numeral_extra(1)
% 0.18/0.46 thf(fact_243__092_060open_062_092_060forall_062n_O_A_092_060forall_062msg_H_092_060in_062firstOccSet_An_O_Amsg_H_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062,axiom,
% 0.18/0.46 ! [N7: nat,X5: message_p_v] :
% 0.18/0.46 ( ( member_message_p_v @ X5 @ ( firstOccSet @ N7 ) )
% 0.18/0.46 => ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ ( last_c571238084t_unit @ ( fe @ N7 ) ) @ X5 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % \<open>\<forall>n. \<forall>msg'\<in>firstOccSet n. msg' \<in># msgs (last (fe n))\<close>
% 0.18/0.46
% 0.18/0.46 % Conjectures (1)
% 0.18/0.46 thf(conj_0,conjecture,
% 0.18/0.46 ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ).
% 0.18/0.46
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 ------------------------
% 0.29/1.50 ---- Embedded in THF ---
% 0.29/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.29/1.51 %%% Generated on Tue Feb 24 08:24:58 EST 2026
% 0.29/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 0.29/1.51 %%% Logic specification used:
% 0.29/1.51 %%% thf(spec, logic, $$dhol).
% 0.29/1.51
% 0.29/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2DTF31470.p
% See solution above
% 0.29/1.51 ------------------------
% 0.29/1.52 ---- Cleaned THF ---
% 0.29/1.52 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.29/1.52 list_c1059388851t_unit: $tType ).
% 0.29/1.52
% 0.29/1.52 thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.29/1.52 config256849571t_unit: $tType ).
% 0.29/1.52
% 0.29/1.52 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.29/1.52 list_message_p_v: $tType ).
% 0.29/1.52
% 0.29/1.52 thf(ty_n_t__Set__Oset_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.29/1.52 set_message_p_v: $tType ).
% 0.29/1.52
% 0.29/1.52 thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.29/1.52 message_p_v: $tType ).
% 0.29/1.52
% 0.29/1.52 thf(ty_n_t__Nat__Onat,type,
% 0.29/1.52 nat: $tType ).
% 0.29/1.52
% 0.29/1.52 thf(ty_n_tf__p,type,
% 0.29/1.52 p: $tType ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_AsynchronousSystem_Oconfiguration_Omsgs_001tf__p_001tf__v_001tf__s_001t__Product____Type__Ounit,type,
% 0.29/1.52 msgs_p1029620568t_unit: config256849571t_unit > message_p_v > nat ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_AsynchronousSystem_Oenabled_001tf__p_001tf__v_001tf__s,type,
% 0.29/1.52 enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_AsynchronousSystem_OisReceiverOf_001tf__p_001tf__v,type,
% 0.29/1.52 isReceiverOf_p_v: p > message_p_v > $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Execution_Oexecution_OfirstOccurrence_001tf__p_001tf__v_001tf__s,type,
% 0.29/1.52 firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 0.29/1.52 minus_minus_nat: nat > nat > nat ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.29/1.52 one_one_nat: nat ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.29/1.52 zero_zero_nat: nat ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.29/1.52 prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.29/1.52 prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_List_Olast_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.29/1.52 last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_List_Olast_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.29/1.52 last_message_p_v: list_message_p_v > message_p_v ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.29/1.52 nil_co1338500125t_unit: list_c1059388851t_unit ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.29/1.52 nil_message_p_v: list_message_p_v ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_List_Onth_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.29/1.52 nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_List_Onth_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.29/1.52 nth_message_p_v: list_message_p_v > nat > message_p_v ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Nat_OSuc,type,
% 0.29/1.52 suc: nat > nat ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.29/1.52 size_s1406904903t_unit: list_c1059388851t_unit > nat ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.29/1.52 size_s1168481041ge_p_v: list_message_p_v > nat ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.29/1.52 ord_less_nat: nat > nat > $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.29/1.52 ord_less_eq_nat: nat > nat > $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_c_member_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.29/1.52 member_message_p_v: message_p_v > set_message_p_v > $o ).
% 0.29/1.52
% 0.29/1.52 thf(sy_v_fe____,type,
% 0.29/1.52 fe: nat > list_c1059388851t_unit ).
% 0.29/1.52
% 0.29/1.52 thf(sy_v_firstOccSet____,type,
% 0.29/1.52 firstOccSet: nat > set_message_p_v ).
% 0.29/1.52
% 0.29/1.52 thf(sy_v_ft____,type,
% 0.29/1.52 ft: nat > list_message_p_v ).
% 0.29/1.52
% 0.29/1.52 thf(sy_v_index____,type,
% 0.29/1.52 index: nat ).
% 0.29/1.52
% 0.29/1.52 thf(sy_v_msgInSet____,type,
% 0.29/1.52 msgInSet: message_p_v ).
% 0.29/1.52
% 0.29/1.52 thf(sy_v_msg____,type,
% 0.29/1.52 msg: message_p_v ).
% 0.29/1.52
% 0.29/1.52 thf(sy_v_n0____,type,
% 0.29/1.52 n0: nat ).
% 0.29/1.52
% 0.29/1.52 thf(sy_v_n1____,type,
% 0.29/1.52 n1: nat ).
% 0.29/1.52
% 0.29/1.52 thf(sy_v_nMsg____,type,
% 0.29/1.52 nMsg: nat ).
% 0.29/1.52
% 0.29/1.52 thf(sy_v_n____,type,
% 0.29/1.52 n: nat ).
% 0.29/1.52
% 0.29/1.52 thf(sy_v_p____,type,
% 0.29/1.52 p2: p ).
% 0.29/1.52
% 0.29/1.52 thf(fact_0_AssumpOcc6_I1_J,axiom,
% 0.29/1.52 ord_less_nat @ zero_zero_nat @ nMsg ).
% 0.29/1.52
% 0.29/1.52 thf(fact_1_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 0.29/1.52 ! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A4: config256849571t_unit,A5: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A6: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A7: nat] :
% 0.29/1.52 ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.29/1.52 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.29/1.52 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/1.52 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/1.52 => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.29/1.52 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.29/1.52 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.29/1.52 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/1.52 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/1.52 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.29/1.52 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_2_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 0.29/1.52 ! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A0: config256849571t_unit,A1: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A3: nat] :
% 0.29/1.52 ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.29/1.52 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.29/1.52 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/1.52 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/1.52 => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.29/1.52 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.29/1.52 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.29/1.52 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/1.52 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/1.52 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.29/1.52 => ( P @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_3_AssumptionSubset_I3_J,axiom,
% 0.29/1.52 firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg ).
% 0.29/1.52
% 0.29/1.52 thf(fact_4_SmallIndex,axiom,
% 0.29/1.52 ! [NMsg: nat] :
% 0.29/1.52 ( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ NMsg )
% 0.29/1.52 => ( ord_less_nat @ NMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_5_AssumptionSubset3_I3_J,axiom,
% 0.29/1.52 ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_6_AssumptionSubset2_I3_J,axiom,
% 0.29/1.52 ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_7_Suc__pred,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/1.52 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 0.29/1.52 = N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_8_zero__less__diff,axiom,
% 0.29/1.52 ! [N2: nat,M: nat] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) )
% 0.29/1.52 = ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_9_less__Suc0,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.29/1.52 = ( N2 = zero_zero_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_10_zero__less__Suc,axiom,
% 0.29/1.52 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_11_diff__0__eq__0,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 0.29/1.52 = zero_zero_nat ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_12_diff__self__eq__0,axiom,
% 0.29/1.52 ! [M: nat] :
% 0.29/1.52 ( ( minus_minus_nat @ M @ M )
% 0.29/1.52 = zero_zero_nat ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_13_diff__Suc__Suc,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.29/1.52 = ( minus_minus_nat @ M @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_14_Suc__diff__diff,axiom,
% 0.29/1.52 ! [M: nat,N2: nat,K: nat] :
% 0.29/1.52 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( suc @ K ) )
% 0.29/1.52 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N2 ) @ K ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_15_neq0__conv,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( N2 != zero_zero_nat )
% 0.29/1.52 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_16_less__nat__zero__code,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_17_old_Onat_Oinject,axiom,
% 0.29/1.52 ! [Nat: nat,Nat2: nat] :
% 0.29/1.52 ( ( ( suc @ Nat )
% 0.29/1.52 = ( suc @ Nat2 ) )
% 0.29/1.52 = ( Nat = Nat2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_18_nat_Oinject,axiom,
% 0.29/1.52 ! [X2: nat,Y2: nat] :
% 0.29/1.52 ( ( ( suc @ X2 )
% 0.29/1.52 = ( suc @ Y2 ) )
% 0.29/1.52 = ( X2 = Y2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_19_not__gr__zero,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 0.29/1.52 = ( N2 = zero_zero_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_20_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/1.52 ! [A: nat] :
% 0.29/1.52 ( ( minus_minus_nat @ A @ A )
% 0.29/1.52 = zero_zero_nat ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_21_diff__zero,axiom,
% 0.29/1.52 ! [A: nat] :
% 0.29/1.52 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.29/1.52 = A ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_22_zero__diff,axiom,
% 0.29/1.52 ! [A: nat] :
% 0.29/1.52 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.29/1.52 = zero_zero_nat ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_23_Suc__less__eq,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.29/1.52 = ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_24_Suc__mono,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M @ N2 )
% 0.29/1.52 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_25_lessI,axiom,
% 0.29/1.52 ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_26_bot__nat__0_Onot__eq__extremum,axiom,
% 0.29/1.52 ! [A: nat] :
% 0.29/1.52 ( ( A != zero_zero_nat )
% 0.29/1.52 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_27_AssumptionSubset_I2_J,axiom,
% 0.29/1.52 firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msgInSet @ n1 ).
% 0.29/1.52
% 0.29/1.52 thf(fact_28_AssumptionSubset_I1_J,axiom,
% 0.29/1.52 ord_less_eq_nat @ n1 @ nMsg ).
% 0.29/1.52
% 0.29/1.52 thf(fact_29_zero__reorient,axiom,
% 0.29/1.52 ! [X: nat] :
% 0.29/1.52 ( ( zero_zero_nat = X )
% 0.29/1.52 = ( X = zero_zero_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_30_diff__right__commute,axiom,
% 0.29/1.52 ! [A: nat,C: nat,B: nat] :
% 0.29/1.52 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 0.29/1.52 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_31_n__not__Suc__n,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( N2
% 0.29/1.52 != ( suc @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_32_Suc__inject,axiom,
% 0.29/1.52 ! [X: nat,Y: nat] :
% 0.29/1.52 ( ( ( suc @ X )
% 0.29/1.52 = ( suc @ Y ) )
% 0.29/1.52 => ( X = Y ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_33_linorder__neqE__nat,axiom,
% 0.29/1.52 ! [X: nat,Y: nat] :
% 0.29/1.52 ( ( X != Y )
% 0.29/1.52 => ( ~ ( ord_less_nat @ X @ Y )
% 0.29/1.52 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_34_infinite__descent,axiom,
% 0.29/1.52 ! [P: nat > $o,N2: nat] :
% 0.29/1.52 ( ! [N: nat] :
% 0.29/1.52 ( ~ ( P @ N )
% 0.29/1.52 => ? [M2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M2 @ N )
% 0.29/1.52 & ~ ( P @ M2 ) ) )
% 0.29/1.52 => ( P @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_35_nat__less__induct,axiom,
% 0.29/1.52 ! [P: nat > $o,N2: nat] :
% 0.29/1.52 ( ! [N: nat] :
% 0.29/1.52 ( ! [M2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M2 @ N )
% 0.29/1.52 => ( P @ M2 ) )
% 0.29/1.52 => ( P @ N ) )
% 0.29/1.52 => ( P @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_36_less__irrefl__nat,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_37_less__not__refl3,axiom,
% 0.29/1.52 ! [S: nat,T: nat] :
% 0.29/1.52 ( ( ord_less_nat @ S @ T )
% 0.29/1.52 => ( S != T ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_38_less__not__refl2,axiom,
% 0.29/1.52 ! [N2: nat,M: nat] :
% 0.29/1.52 ( ( ord_less_nat @ N2 @ M )
% 0.29/1.52 => ( M != N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_39_less__not__refl,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_40_nat__neq__iff,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( M != N2 )
% 0.29/1.52 = ( ( ord_less_nat @ M @ N2 )
% 0.29/1.52 | ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_41_size__neq__size__imp__neq,axiom,
% 0.29/1.52 ! [X: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 0.29/1.52 ( ( ( size_s1406904903t_unit @ X )
% 0.29/1.52 != ( size_s1406904903t_unit @ Y ) )
% 0.29/1.52 => ( X != Y ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_42_size__neq__size__imp__neq,axiom,
% 0.29/1.52 ! [X: list_message_p_v,Y: list_message_p_v] :
% 0.29/1.52 ( ( ( size_s1168481041ge_p_v @ X )
% 0.29/1.52 != ( size_s1168481041ge_p_v @ Y ) )
% 0.29/1.52 => ( X != Y ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_43_diff__commute,axiom,
% 0.29/1.52 ! [I: nat,J: nat,K: nat] :
% 0.29/1.52 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.29/1.52 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_44_zero__less__iff__neq__zero,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/1.52 = ( N2 != zero_zero_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_45_gr__implies__not__zero,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M @ N2 )
% 0.29/1.52 => ( N2 != zero_zero_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_46_not__less__zero,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_47_gr__zeroI,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( N2 != zero_zero_nat )
% 0.29/1.52 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_48_not0__implies__Suc,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( N2 != zero_zero_nat )
% 0.29/1.52 => ? [M3: nat] :
% 0.29/1.52 ( N2
% 0.29/1.52 = ( suc @ M3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_49_old_Onat_Oinducts,axiom,
% 0.29/1.52 ! [P: nat > $o,Nat: nat] :
% 0.29/1.52 ( ( P @ zero_zero_nat )
% 0.29/1.52 => ( ! [Nat3: nat] :
% 0.29/1.52 ( ( P @ Nat3 )
% 0.29/1.52 => ( P @ ( suc @ Nat3 ) ) )
% 0.29/1.52 => ( P @ Nat ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_50_old_Onat_Oexhaust,axiom,
% 0.29/1.52 ! [Y: nat] :
% 0.29/1.52 ( ( Y != zero_zero_nat )
% 0.29/1.52 => ~ ! [Nat3: nat] :
% 0.29/1.52 ( Y
% 0.29/1.52 != ( suc @ Nat3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_51_Zero__not__Suc,axiom,
% 0.29/1.52 ! [M: nat] :
% 0.29/1.52 ( zero_zero_nat
% 0.29/1.52 != ( suc @ M ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_52_Zero__neq__Suc,axiom,
% 0.29/1.52 ! [M: nat] :
% 0.29/1.52 ( zero_zero_nat
% 0.29/1.52 != ( suc @ M ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_53_Suc__neq__Zero,axiom,
% 0.29/1.52 ! [M: nat] :
% 0.29/1.52 ( ( suc @ M )
% 0.29/1.52 != zero_zero_nat ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_54_zero__induct,axiom,
% 0.29/1.52 ! [P: nat > $o,K: nat] :
% 0.29/1.52 ( ( P @ K )
% 0.29/1.52 => ( ! [N: nat] :
% 0.29/1.52 ( ( P @ ( suc @ N ) )
% 0.29/1.52 => ( P @ N ) )
% 0.29/1.52 => ( P @ zero_zero_nat ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_55_diff__induct,axiom,
% 0.29/1.52 ! [P: nat > nat > $o,M: nat,N2: nat] :
% 0.29/1.52 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 0.29/1.52 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 0.29/1.52 => ( ! [X3: nat,Y3: nat] :
% 0.29/1.52 ( ( P @ X3 @ Y3 )
% 0.29/1.52 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 0.29/1.52 => ( P @ M @ N2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_56_nat__induct,axiom,
% 0.29/1.52 ! [P: nat > $o,N2: nat] :
% 0.29/1.52 ( ( P @ zero_zero_nat )
% 0.29/1.52 => ( ! [N: nat] :
% 0.29/1.52 ( ( P @ N )
% 0.29/1.52 => ( P @ ( suc @ N ) ) )
% 0.29/1.52 => ( P @ N2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_57_nat_OdiscI,axiom,
% 0.29/1.52 ! [Nat: nat,X2: nat] :
% 0.29/1.52 ( ( Nat
% 0.29/1.52 = ( suc @ X2 ) )
% 0.29/1.52 => ( Nat != zero_zero_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_58_old_Onat_Odistinct_I1_J,axiom,
% 0.29/1.52 ! [Nat2: nat] :
% 0.29/1.52 ( zero_zero_nat
% 0.29/1.52 != ( suc @ Nat2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_59_old_Onat_Odistinct_I2_J,axiom,
% 0.29/1.52 ! [Nat2: nat] :
% 0.29/1.52 ( ( suc @ Nat2 )
% 0.29/1.52 != zero_zero_nat ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_60_nat_Odistinct_I1_J,axiom,
% 0.29/1.52 ! [X2: nat] :
% 0.29/1.52 ( zero_zero_nat
% 0.29/1.52 != ( suc @ X2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_61_not__less__less__Suc__eq,axiom,
% 0.29/1.52 ! [N2: nat,M: nat] :
% 0.29/1.52 ( ~ ( ord_less_nat @ N2 @ M )
% 0.29/1.52 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 0.29/1.52 = ( N2 = M ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_62_strict__inc__induct,axiom,
% 0.29/1.52 ! [I: nat,J: nat,P: nat > $o] :
% 0.29/1.52 ( ( ord_less_nat @ I @ J )
% 0.29/1.52 => ( ! [I2: nat] :
% 0.29/1.52 ( ( J
% 0.29/1.52 = ( suc @ I2 ) )
% 0.29/1.52 => ( P @ I2 ) )
% 0.29/1.52 => ( ! [I2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I2 @ J )
% 0.29/1.52 => ( ( P @ ( suc @ I2 ) )
% 0.29/1.52 => ( P @ I2 ) ) )
% 0.29/1.52 => ( P @ I ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_63_less__Suc__induct,axiom,
% 0.29/1.52 ! [I: nat,J: nat,P: nat > nat > $o] :
% 0.29/1.52 ( ( ord_less_nat @ I @ J )
% 0.29/1.52 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 0.29/1.52 => ( ! [I2: nat,J2: nat,K2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I2 @ J2 )
% 0.29/1.52 => ( ( ord_less_nat @ J2 @ K2 )
% 0.29/1.52 => ( ( P @ I2 @ J2 )
% 0.29/1.52 => ( ( P @ J2 @ K2 )
% 0.29/1.52 => ( P @ I2 @ K2 ) ) ) ) )
% 0.29/1.52 => ( P @ I @ J ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_64_less__trans__Suc,axiom,
% 0.29/1.52 ! [I: nat,J: nat,K: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I @ J )
% 0.29/1.52 => ( ( ord_less_nat @ J @ K )
% 0.29/1.52 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_65_Suc__less__SucD,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.29/1.52 => ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_66_less__antisym,axiom,
% 0.29/1.52 ! [N2: nat,M: nat] :
% 0.29/1.52 ( ~ ( ord_less_nat @ N2 @ M )
% 0.29/1.52 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 0.29/1.52 => ( M = N2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_67_Suc__less__eq2,axiom,
% 0.29/1.52 ! [N2: nat,M: nat] :
% 0.29/1.52 ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 0.29/1.52 = ( ? [M4: nat] :
% 0.29/1.52 ( ( M
% 0.29/1.52 = ( suc @ M4 ) )
% 0.29/1.52 & ( ord_less_nat @ N2 @ M4 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_68_All__less__Suc,axiom,
% 0.29/1.52 ! [N2: nat,P: nat > $o] :
% 0.29/1.52 ( ( ! [I3: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 0.29/1.52 => ( P @ I3 ) ) )
% 0.29/1.52 = ( ( P @ N2 )
% 0.29/1.52 & ! [I3: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I3 @ N2 )
% 0.29/1.52 => ( P @ I3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_69_not__less__eq,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ~ ( ord_less_nat @ M @ N2 ) )
% 0.29/1.52 = ( ord_less_nat @ N2 @ ( suc @ M ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_70_less__Suc__eq,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.29/1.52 = ( ( ord_less_nat @ M @ N2 )
% 0.29/1.52 | ( M = N2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_71_Ex__less__Suc,axiom,
% 0.29/1.52 ! [N2: nat,P: nat > $o] :
% 0.29/1.52 ( ( ? [I3: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 0.29/1.52 & ( P @ I3 ) ) )
% 0.29/1.52 = ( ( P @ N2 )
% 0.29/1.52 | ? [I3: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I3 @ N2 )
% 0.29/1.52 & ( P @ I3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_72_less__SucI,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M @ N2 )
% 0.29/1.52 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_73_less__SucE,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.29/1.52 => ( ~ ( ord_less_nat @ M @ N2 )
% 0.29/1.52 => ( M = N2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_74_Suc__lessI,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M @ N2 )
% 0.29/1.52 => ( ( ( suc @ M )
% 0.29/1.52 != N2 )
% 0.29/1.52 => ( ord_less_nat @ ( suc @ M ) @ N2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_75_Suc__lessE,axiom,
% 0.29/1.52 ! [I: nat,K: nat] :
% 0.29/1.52 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.29/1.52 => ~ ! [J2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I @ J2 )
% 0.29/1.52 => ( K
% 0.29/1.52 != ( suc @ J2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_76_Suc__lessD,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ ( suc @ M ) @ N2 )
% 0.29/1.52 => ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_77_Nat_OlessE,axiom,
% 0.29/1.52 ! [I: nat,K: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I @ K )
% 0.29/1.52 => ( ( K
% 0.29/1.52 != ( suc @ I ) )
% 0.29/1.52 => ~ ! [J2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I @ J2 )
% 0.29/1.52 => ( K
% 0.29/1.52 != ( suc @ J2 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_78_bot__nat__0_Oextremum__strict,axiom,
% 0.29/1.52 ! [A: nat] :
% 0.29/1.52 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_79_infinite__descent0,axiom,
% 0.29/1.52 ! [P: nat > $o,N2: nat] :
% 0.29/1.52 ( ( P @ zero_zero_nat )
% 0.29/1.52 => ( ! [N: nat] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/1.52 => ( ~ ( P @ N )
% 0.29/1.52 => ? [M2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M2 @ N )
% 0.29/1.52 & ~ ( P @ M2 ) ) ) )
% 0.29/1.52 => ( P @ N2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_80_gr__implies__not0,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M @ N2 )
% 0.29/1.52 => ( N2 != zero_zero_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_81_less__zeroE,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_82_not__less0,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_83_not__gr0,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 0.29/1.52 = ( N2 = zero_zero_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_84_gr0I,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( N2 != zero_zero_nat )
% 0.29/1.52 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_85_zero__induct__lemma,axiom,
% 0.29/1.52 ! [P: nat > $o,K: nat,I: nat] :
% 0.29/1.52 ( ( P @ K )
% 0.29/1.52 => ( ! [N: nat] :
% 0.29/1.52 ( ( P @ ( suc @ N ) )
% 0.29/1.52 => ( P @ N ) )
% 0.29/1.52 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_86_minus__nat_Odiff__0,axiom,
% 0.29/1.52 ! [M: nat] :
% 0.29/1.52 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.29/1.52 = M ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_87_diffs0__imp__equal,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ( minus_minus_nat @ M @ N2 )
% 0.29/1.52 = zero_zero_nat )
% 0.29/1.52 => ( ( ( minus_minus_nat @ N2 @ M )
% 0.29/1.52 = zero_zero_nat )
% 0.29/1.52 => ( M = N2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_88_less__imp__diff__less,axiom,
% 0.29/1.52 ! [J: nat,K: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ J @ K )
% 0.29/1.52 => ( ord_less_nat @ ( minus_minus_nat @ J @ N2 ) @ K ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_89_diff__less__mono2,axiom,
% 0.29/1.52 ! [M: nat,N2: nat,L: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M @ N2 )
% 0.29/1.52 => ( ( ord_less_nat @ M @ L )
% 0.29/1.52 => ( ord_less_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_90_lift__Suc__mono__less__iff,axiom,
% 0.29/1.52 ! [F: nat > nat,N2: nat,M: nat] :
% 0.29/1.52 ( ! [N: nat] : ( ord_less_nat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.29/1.52 => ( ( ord_less_nat @ ( F @ N2 ) @ ( F @ M ) )
% 0.29/1.52 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_91_lift__Suc__mono__less,axiom,
% 0.29/1.52 ! [F: nat > nat,N2: nat,N3: nat] :
% 0.29/1.52 ( ! [N: nat] : ( ord_less_nat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.29/1.52 => ( ( ord_less_nat @ N2 @ N3 )
% 0.29/1.52 => ( ord_less_nat @ ( F @ N2 ) @ ( F @ N3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_92_less__Suc__eq__0__disj,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.29/1.52 = ( ( M = zero_zero_nat )
% 0.29/1.52 | ? [J3: nat] :
% 0.29/1.52 ( ( M
% 0.29/1.52 = ( suc @ J3 ) )
% 0.29/1.52 & ( ord_less_nat @ J3 @ N2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_93_gr0__implies__Suc,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/1.52 => ? [M3: nat] :
% 0.29/1.52 ( N2
% 0.29/1.52 = ( suc @ M3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_94_All__less__Suc2,axiom,
% 0.29/1.52 ! [N2: nat,P: nat > $o] :
% 0.29/1.52 ( ( ! [I3: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 0.29/1.52 => ( P @ I3 ) ) )
% 0.29/1.52 = ( ( P @ zero_zero_nat )
% 0.29/1.52 & ! [I3: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I3 @ N2 )
% 0.29/1.52 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_95_gr0__conv__Suc,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/1.52 = ( ? [M5: nat] :
% 0.29/1.52 ( N2
% 0.29/1.52 = ( suc @ M5 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_96_Ex__less__Suc2,axiom,
% 0.29/1.52 ! [N2: nat,P: nat > $o] :
% 0.29/1.52 ( ( ? [I3: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 0.29/1.52 & ( P @ I3 ) ) )
% 0.29/1.52 = ( ( P @ zero_zero_nat )
% 0.29/1.52 | ? [I3: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I3 @ N2 )
% 0.29/1.52 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_97_diff__less__Suc,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ ( suc @ M ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_98_Suc__diff__Suc,axiom,
% 0.29/1.52 ! [N2: nat,M: nat] :
% 0.29/1.52 ( ( ord_less_nat @ N2 @ M )
% 0.29/1.52 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N2 ) ) )
% 0.29/1.52 = ( minus_minus_nat @ M @ N2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_99_diff__less,axiom,
% 0.29/1.52 ! [N2: nat,M: nat] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/1.52 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/1.52 => ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_100_diff__Suc__less,axiom,
% 0.29/1.52 ! [N2: nat,I: nat] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/1.52 => ( ord_less_nat @ ( minus_minus_nat @ N2 @ ( suc @ I ) ) @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_101_SameCfgOnLow,axiom,
% 0.29/1.52 ! [I4: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I4 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
% 0.29/1.52 => ( ( nth_co1649820636t_unit @ ( fe @ index ) @ I4 )
% 0.29/1.52 = ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_102__092_060open_062fe_Aindex_A_B_AnMsg_A_061_Afe_A_ISuc_Aindex_J_A_B_AnMsg_092_060close_062,axiom,
% 0.29/1.52 ( ( nth_co1649820636t_unit @ ( fe @ index ) @ nMsg )
% 0.29/1.52 = ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ nMsg ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_103_ShorterTrace,axiom,
% 0.29/1.52 ord_less_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_104_NotEmpty_I1_J,axiom,
% 0.29/1.52 ( ( fe @ ( suc @ index ) )
% 0.29/1.52 != nil_co1338500125t_unit ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_105_IPrefixList,axiom,
% 0.29/1.52 ! [I4: nat] : ( prefix47729710ge_p_v @ ( ft @ I4 ) @ ( ft @ ( suc @ I4 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_106_IPrefixListEx,axiom,
% 0.29/1.52 ! [I4: nat] : ( prefix1615116500t_unit @ ( fe @ I4 ) @ ( fe @ ( suc @ I4 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_107_NatPredicateTippingPoint,axiom,
% 0.29/1.52 ! [N22: nat,Pr: nat > $o] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ N22 )
% 0.29/1.52 => ( ( Pr @ zero_zero_nat )
% 0.29/1.52 => ( ~ ( Pr @ N22 )
% 0.29/1.52 => ? [N: nat] :
% 0.29/1.52 ( ( ord_less_nat @ N @ N22 )
% 0.29/1.52 & ( Pr @ N )
% 0.29/1.52 & ~ ( Pr @ ( suc @ N ) ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_108_NotEmpty_I2_J,axiom,
% 0.29/1.52 ( ( fe @ index )
% 0.29/1.52 != nil_co1338500125t_unit ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_109_AssumptionFair_I4_J,axiom,
% 0.29/1.52 isReceiverOf_p_v @ p2 @ msg ).
% 0.29/1.52
% 0.29/1.52 thf(fact_110_AssumpOcc6_I2_J,axiom,
% 0.29/1.52 ( msg
% 0.29/1.52 != ( nth_message_p_v @ ( ft @ index ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_111_Occ1,axiom,
% 0.29/1.52 ? [P2: p] : ( isReceiverOf_p_v @ P2 @ msg ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_112_AssumptionSubset2_I1_J,axiom,
% 0.29/1.52 ? [P2: p] : ( isReceiverOf_p_v @ P2 @ msgInSet ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_113_SameMsgOnLow,axiom,
% 0.29/1.52 ! [I4: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I4 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 0.29/1.52 => ( ( nth_message_p_v @ ( ft @ index ) @ I4 )
% 0.29/1.52 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_114_le__zero__eq,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 0.29/1.52 = ( N2 = zero_zero_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_115_Suc__le__mono,axiom,
% 0.29/1.52 ! [N2: nat,M: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( suc @ M ) )
% 0.29/1.52 = ( ord_less_eq_nat @ N2 @ M ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_116_le0,axiom,
% 0.29/1.52 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_117_bot__nat__0_Oextremum,axiom,
% 0.29/1.52 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_118_diff__diff__cancel,axiom,
% 0.29/1.52 ! [I: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ I @ N2 )
% 0.29/1.52 => ( ( minus_minus_nat @ N2 @ ( minus_minus_nat @ N2 @ I ) )
% 0.29/1.52 = I ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_119__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062,axiom,
% 0.29/1.52 ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_120__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ift_A_ISuc_Aindex_J_J_O_Alength_A_Ift_Aindex_J_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062,axiom,
% 0.29/1.52 ~ ? [I4: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I4 @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 0.29/1.52 & ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ I4 )
% 0.29/1.52 & ( msg
% 0.29/1.52 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_121_NotConsumedIntermediate,axiom,
% 0.29/1.52 ! [I4: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I4 @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 0.29/1.52 => ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ I4 )
% 0.29/1.52 => ( ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I4 )
% 0.29/1.52 != msg ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_122_OccSameMsg,axiom,
% 0.29/1.52 ! [N4: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ nMsg @ N4 )
% 0.29/1.52 => ( ( ord_less_nat @ N4 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 0.29/1.52 => ( ( nth_message_p_v @ ( ft @ index ) @ N4 )
% 0.29/1.52 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ N4 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_123_Occ5,axiom,
% 0.29/1.52 ! [N4: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ nMsg @ N4 )
% 0.29/1.52 => ( ( ord_less_nat @ N4 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 0.29/1.52 => ( msg
% 0.29/1.52 != ( nth_message_p_v @ ( ft @ index ) @ N4 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_124_diff__is__0__eq,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ( minus_minus_nat @ M @ N2 )
% 0.29/1.52 = zero_zero_nat )
% 0.29/1.52 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_125_diff__is__0__eq_H,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/1.52 => ( ( minus_minus_nat @ M @ N2 )
% 0.29/1.52 = zero_zero_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_126_less__one,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ N2 @ one_one_nat )
% 0.29/1.52 = ( N2 = zero_zero_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_127_diff__Suc__1,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 0.29/1.52 = N2 ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_128_AssumptionSubset3_I5_J,axiom,
% 0.29/1.52 ! [N4: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ nMsg @ N4 )
% 0.29/1.52 => ( ( ord_less_nat @ N4 @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 0.29/1.52 => ( msg
% 0.29/1.52 != ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ N4 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_129_AssumptionSubset2_I5_J,axiom,
% 0.29/1.52 ! [N4: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ n1 @ N4 )
% 0.29/1.52 => ( ( ord_less_nat @ N4 @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 0.29/1.52 => ( msgInSet
% 0.29/1.52 != ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ N4 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_130__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_O_Alength_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062,axiom,
% 0.29/1.52 ~ ? [I4: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I4 @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) )
% 0.29/1.52 & ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ I4 )
% 0.29/1.52 & ( msg
% 0.29/1.52 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_131_Suc__diff__1,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/1.52 => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 0.29/1.52 = N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_132_AssumptionFairContr,axiom,
% 0.29/1.52 ! [N4: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ n @ N4 )
% 0.29/1.52 => ! [N0: nat] :
% 0.29/1.52 ( ( ord_less_nat @ N0 @ ( size_s1168481041ge_p_v @ ( ft @ N4 ) ) )
% 0.29/1.52 => ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) @ N0 )
% 0.29/1.52 => ( msg
% 0.29/1.52 != ( nth_message_p_v @ ( ft @ N4 ) @ N0 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_133_AssumpOcc6_I3_J,axiom,
% 0.29/1.52 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) @ msg ).
% 0.29/1.52
% 0.29/1.52 thf(fact_134_le__refl,axiom,
% 0.29/1.52 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ N2 ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_135_le__trans,axiom,
% 0.29/1.52 ! [I: nat,J: nat,K: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ I @ J )
% 0.29/1.52 => ( ( ord_less_eq_nat @ J @ K )
% 0.29/1.52 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_136_eq__imp__le,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( M = N2 )
% 0.29/1.52 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_137_le__antisym,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/1.52 => ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/1.52 => ( M = N2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_138_nat__le__linear,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/1.52 | ( ord_less_eq_nat @ N2 @ M ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_139_one__reorient,axiom,
% 0.29/1.52 ! [X: nat] :
% 0.29/1.52 ( ( one_one_nat = X )
% 0.29/1.52 = ( X = one_one_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_140_Nat_Oex__has__greatest__nat,axiom,
% 0.29/1.52 ! [P: nat > $o,K: nat,B: nat] :
% 0.29/1.52 ( ( P @ K )
% 0.29/1.52 => ( ! [Y3: nat] :
% 0.29/1.52 ( ( P @ Y3 )
% 0.29/1.52 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.29/1.52 => ? [X3: nat] :
% 0.29/1.52 ( ( P @ X3 )
% 0.29/1.52 & ! [Y4: nat] :
% 0.29/1.52 ( ( P @ Y4 )
% 0.29/1.52 => ( ord_less_eq_nat @ Y4 @ X3 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_141_PrefixListTransitive,axiom,
% 0.29/1.52 ! [L1: list_message_p_v,L2: list_message_p_v,L3: list_message_p_v] :
% 0.29/1.52 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.29/1.52 => ( ( prefix47729710ge_p_v @ L2 @ L3 )
% 0.29/1.52 => ( prefix47729710ge_p_v @ L1 @ L3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_142_PrefixListTransitive,axiom,
% 0.29/1.52 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit,L3: list_c1059388851t_unit] :
% 0.29/1.52 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.29/1.52 => ( ( prefix1615116500t_unit @ L2 @ L3 )
% 0.29/1.52 => ( prefix1615116500t_unit @ L1 @ L3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_143_MinPredicate,axiom,
% 0.29/1.52 ! [P: nat > $o] :
% 0.29/1.52 ( ? [X_1: nat] : ( P @ X_1 )
% 0.29/1.52 => ? [N02: nat] :
% 0.29/1.52 ( ( P @ N02 )
% 0.29/1.52 & ! [N4: nat] :
% 0.29/1.52 ( ( P @ N4 )
% 0.29/1.52 => ( ord_less_eq_nat @ N02 @ N4 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_144_lift__Suc__antimono__le,axiom,
% 0.29/1.52 ! [F: nat > nat,N2: nat,N3: nat] :
% 0.29/1.52 ( ! [N: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 0.29/1.52 => ( ( ord_less_eq_nat @ N2 @ N3 )
% 0.29/1.52 => ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ N2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_145_lift__Suc__mono__le,axiom,
% 0.29/1.52 ! [F: nat > nat,N2: nat,N3: nat] :
% 0.29/1.52 ( ! [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.29/1.52 => ( ( ord_less_eq_nat @ N2 @ N3 )
% 0.29/1.52 => ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ N3 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_146_KeepProperty,axiom,
% 0.29/1.52 ! [Low: nat,P: nat > $o,Q: nat > $o] :
% 0.29/1.52 ( ! [I2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ Low @ I2 )
% 0.29/1.52 => ( ( P @ I2 )
% 0.29/1.52 => ( ( P @ ( suc @ I2 ) )
% 0.29/1.52 & ( Q @ I2 ) ) ) )
% 0.29/1.52 => ( ( P @ Low )
% 0.29/1.52 => ! [I4: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ Low @ I4 )
% 0.29/1.52 => ( Q @ I4 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_147_PrefixSameOnLow,axiom,
% 0.29/1.52 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 0.29/1.52 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.29/1.52 => ! [Index: nat] :
% 0.29/1.52 ( ( ord_less_nat @ Index @ ( size_s1168481041ge_p_v @ L1 ) )
% 0.29/1.52 => ( ( nth_message_p_v @ L1 @ Index )
% 0.29/1.52 = ( nth_message_p_v @ L2 @ Index ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_148_PrefixSameOnLow,axiom,
% 0.29/1.52 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 0.29/1.52 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.29/1.52 => ! [Index: nat] :
% 0.29/1.52 ( ( ord_less_nat @ Index @ ( size_s1406904903t_unit @ L1 ) )
% 0.29/1.52 => ( ( nth_co1649820636t_unit @ L1 @ Index )
% 0.29/1.52 = ( nth_co1649820636t_unit @ L2 @ Index ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_149_zero__le,axiom,
% 0.29/1.52 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_150_Suc__leD,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 0.29/1.52 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_151_le__SucE,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.29/1.52 => ( ~ ( ord_less_eq_nat @ M @ N2 )
% 0.29/1.52 => ( M
% 0.29/1.52 = ( suc @ N2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_152_le__SucI,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/1.52 => ( ord_less_eq_nat @ M @ ( suc @ N2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_153_Suc__le__D,axiom,
% 0.29/1.52 ! [N2: nat,M6: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ M6 )
% 0.29/1.52 => ? [M3: nat] :
% 0.29/1.52 ( M6
% 0.29/1.52 = ( suc @ M3 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_154_le__Suc__eq,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 0.29/1.52 = ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/1.52 | ( M
% 0.29/1.52 = ( suc @ N2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_155_Suc__n__not__le__n,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ~ ( ord_less_eq_nat @ ( suc @ N2 ) @ N2 ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_156_not__less__eq__eq,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ~ ( ord_less_eq_nat @ M @ N2 ) )
% 0.29/1.52 = ( ord_less_eq_nat @ ( suc @ N2 ) @ M ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_157_full__nat__induct,axiom,
% 0.29/1.52 ! [P: nat > $o,N2: nat] :
% 0.29/1.52 ( ! [N: nat] :
% 0.29/1.52 ( ! [M2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 0.29/1.52 => ( P @ M2 ) )
% 0.29/1.52 => ( P @ N ) )
% 0.29/1.52 => ( P @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_158_nat__induct__at__least,axiom,
% 0.29/1.52 ! [M: nat,N2: nat,P: nat > $o] :
% 0.29/1.52 ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/1.52 => ( ( P @ M )
% 0.29/1.52 => ( ! [N: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ M @ N )
% 0.29/1.52 => ( ( P @ N )
% 0.29/1.52 => ( P @ ( suc @ N ) ) ) )
% 0.29/1.52 => ( P @ N2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_159_transitive__stepwise__le,axiom,
% 0.29/1.52 ! [M: nat,N2: nat,R: nat > nat > $o] :
% 0.29/1.52 ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/1.52 => ( ! [X3: nat] : ( R @ X3 @ X3 )
% 0.29/1.52 => ( ! [X3: nat,Y3: nat,Z: nat] :
% 0.29/1.52 ( ( R @ X3 @ Y3 )
% 0.29/1.52 => ( ( R @ Y3 @ Z )
% 0.29/1.52 => ( R @ X3 @ Z ) ) )
% 0.29/1.52 => ( ! [N: nat] : ( R @ N @ ( suc @ N ) )
% 0.29/1.52 => ( R @ M @ N2 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_160_less__eq__nat_Osimps_I1_J,axiom,
% 0.29/1.52 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_161_le__0__eq,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 0.29/1.52 = ( N2 = zero_zero_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_162_bot__nat__0_Oextremum__unique,axiom,
% 0.29/1.52 ! [A: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/1.52 = ( A = zero_zero_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_163_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.29/1.52 ! [A: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/1.52 => ( A = zero_zero_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_164_nat__less__le,axiom,
% 0.29/1.52 ( ord_less_nat
% 0.29/1.52 = ( ^ [M5: nat,N5: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ M5 @ N5 )
% 0.29/1.52 & ( M5 != N5 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_165_less__imp__le__nat,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M @ N2 )
% 0.29/1.52 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_166_le__eq__less__or__eq,axiom,
% 0.29/1.52 ( ord_less_eq_nat
% 0.29/1.52 = ( ^ [M5: nat,N5: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M5 @ N5 )
% 0.29/1.52 | ( M5 = N5 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_167_less__or__eq__imp__le,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ( ord_less_nat @ M @ N2 )
% 0.29/1.52 | ( M = N2 ) )
% 0.29/1.52 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_168_le__neq__implies__less,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/1.52 => ( ( M != N2 )
% 0.29/1.52 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_169_less__mono__imp__le__mono,axiom,
% 0.29/1.52 ! [F: nat > nat,I: nat,J: nat] :
% 0.29/1.52 ( ! [I2: nat,J2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I2 @ J2 )
% 0.29/1.52 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 0.29/1.52 => ( ( ord_less_eq_nat @ I @ J )
% 0.29/1.52 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_170_eq__diff__iff,axiom,
% 0.29/1.52 ! [K: nat,M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ K @ M )
% 0.29/1.52 => ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/1.52 => ( ( ( minus_minus_nat @ M @ K )
% 0.29/1.52 = ( minus_minus_nat @ N2 @ K ) )
% 0.29/1.52 = ( M = N2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_171_le__diff__iff,axiom,
% 0.29/1.52 ! [K: nat,M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ K @ M )
% 0.29/1.52 => ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/1.52 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 0.29/1.52 = ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_172_Nat_Odiff__diff__eq,axiom,
% 0.29/1.52 ! [K: nat,M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ K @ M )
% 0.29/1.52 => ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/1.52 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 0.29/1.52 = ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_173_diff__le__mono,axiom,
% 0.29/1.52 ! [M: nat,N2: nat,L: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/1.52 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N2 @ L ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_174_diff__le__self,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_175_le__diff__iff_H,axiom,
% 0.29/1.52 ! [A: nat,C: nat,B: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ A @ C )
% 0.29/1.52 => ( ( ord_less_eq_nat @ B @ C )
% 0.29/1.52 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 0.29/1.52 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_176_diff__le__mono2,axiom,
% 0.29/1.52 ! [M: nat,N2: nat,L: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/1.52 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_177_MinPredicate2,axiom,
% 0.29/1.52 ! [P: nat > $o] :
% 0.29/1.52 ( ? [X_1: nat] : ( P @ X_1 )
% 0.29/1.52 => ? [N02: nat] :
% 0.29/1.52 ( ( P @ N02 )
% 0.29/1.52 & ( ( N02 = zero_zero_nat )
% 0.29/1.52 | ~ ( P @ ( minus_minus_nat @ N02 @ one_one_nat ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_178_PrefixListMonotonicity,axiom,
% 0.29/1.52 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 0.29/1.52 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.29/1.52 => ( ord_less_nat @ ( size_s1168481041ge_p_v @ L1 ) @ ( size_s1168481041ge_p_v @ L2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_179_PrefixListMonotonicity,axiom,
% 0.29/1.52 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 0.29/1.52 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.29/1.52 => ( ord_less_nat @ ( size_s1406904903t_unit @ L1 ) @ ( size_s1406904903t_unit @ L2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_180_Suc__leI,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M @ N2 )
% 0.29/1.52 => ( ord_less_eq_nat @ ( suc @ M ) @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_181_Suc__le__eq,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 0.29/1.52 = ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_182_dec__induct,axiom,
% 0.29/1.52 ! [I: nat,J: nat,P: nat > $o] :
% 0.29/1.52 ( ( ord_less_eq_nat @ I @ J )
% 0.29/1.52 => ( ( P @ I )
% 0.29/1.52 => ( ! [N: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ I @ N )
% 0.29/1.52 => ( ( ord_less_nat @ N @ J )
% 0.29/1.52 => ( ( P @ N )
% 0.29/1.52 => ( P @ ( suc @ N ) ) ) ) )
% 0.29/1.52 => ( P @ J ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_183_inc__induct,axiom,
% 0.29/1.52 ! [I: nat,J: nat,P: nat > $o] :
% 0.29/1.52 ( ( ord_less_eq_nat @ I @ J )
% 0.29/1.52 => ( ( P @ J )
% 0.29/1.52 => ( ! [N: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ I @ N )
% 0.29/1.52 => ( ( ord_less_nat @ N @ J )
% 0.29/1.52 => ( ( P @ ( suc @ N ) )
% 0.29/1.52 => ( P @ N ) ) ) )
% 0.29/1.52 => ( P @ I ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_184_Suc__le__lessD,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 0.29/1.52 => ( ord_less_nat @ M @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_185_le__less__Suc__eq,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/1.52 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 0.29/1.52 = ( N2 = M ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_186_less__Suc__eq__le,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 0.29/1.52 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_187_less__eq__Suc__le,axiom,
% 0.29/1.52 ( ord_less_nat
% 0.29/1.52 = ( ^ [N5: nat] : ( ord_less_eq_nat @ ( suc @ N5 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_188_le__imp__less__Suc,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/1.52 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_189_ex__least__nat__le,axiom,
% 0.29/1.52 ! [P: nat > $o,N2: nat] :
% 0.29/1.52 ( ( P @ N2 )
% 0.29/1.52 => ( ~ ( P @ zero_zero_nat )
% 0.29/1.52 => ? [K2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ K2 @ N2 )
% 0.29/1.52 & ! [I4: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I4 @ K2 )
% 0.29/1.52 => ~ ( P @ I4 ) )
% 0.29/1.52 & ( P @ K2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_190_Suc__diff__le,axiom,
% 0.29/1.52 ! [N2: nat,M: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ N2 @ M )
% 0.29/1.52 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 0.29/1.52 = ( suc @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_191_less__diff__iff,axiom,
% 0.29/1.52 ! [K: nat,M: nat,N2: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ K @ M )
% 0.29/1.52 => ( ( ord_less_eq_nat @ K @ N2 )
% 0.29/1.52 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 0.29/1.52 = ( ord_less_nat @ M @ N2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_192_diff__less__mono,axiom,
% 0.29/1.52 ! [A: nat,B: nat,C: nat] :
% 0.29/1.52 ( ( ord_less_nat @ A @ B )
% 0.29/1.52 => ( ( ord_less_eq_nat @ C @ A )
% 0.29/1.52 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_193_One__nat__def,axiom,
% 0.29/1.52 ( one_one_nat
% 0.29/1.52 = ( suc @ zero_zero_nat ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_194_diff__Suc__eq__diff__pred,axiom,
% 0.29/1.52 ! [M: nat,N2: nat] :
% 0.29/1.52 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 0.29/1.52 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N2 ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_195_ex__least__nat__less,axiom,
% 0.29/1.52 ! [P: nat > $o,N2: nat] :
% 0.29/1.52 ( ( P @ N2 )
% 0.29/1.52 => ( ~ ( P @ zero_zero_nat )
% 0.29/1.52 => ? [K2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ K2 @ N2 )
% 0.29/1.52 & ! [I4: nat] :
% 0.29/1.52 ( ( ord_less_eq_nat @ I4 @ K2 )
% 0.29/1.52 => ~ ( P @ I4 ) )
% 0.29/1.52 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_196_nat__induct__non__zero,axiom,
% 0.29/1.52 ! [N2: nat,P: nat > $o] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/1.52 => ( ( P @ one_one_nat )
% 0.29/1.52 => ( ! [N: nat] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/1.52 => ( ( P @ N )
% 0.29/1.52 => ( P @ ( suc @ N ) ) ) )
% 0.29/1.52 => ( P @ N2 ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_197_Suc__pred_H,axiom,
% 0.29/1.52 ! [N2: nat] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/1.52 => ( N2
% 0.29/1.52 = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_198_Suc__diff__eq__diff__pred,axiom,
% 0.29/1.52 ! [N2: nat,M: nat] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/1.52 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 0.29/1.52 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_199_AssumptionSubset2_I6_J,axiom,
% 0.29/1.52 ( ( n1 != zero_zero_nat )
% 0.29/1.52 => ( ~ ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) @ msgInSet )
% 0.29/1.52 | ( msgInSet
% 0.29/1.52 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_200_AssumptionSubset3_I6_J,axiom,
% 0.29/1.52 ( ( nMsg != zero_zero_nat )
% 0.29/1.52 => ( ~ ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) @ msg )
% 0.29/1.52 | ( msg
% 0.29/1.52 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_201_EnabledIntermediate,axiom,
% 0.29/1.52 ! [I4: nat] :
% 0.29/1.52 ( ( ord_less_nat @ I4 @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) )
% 0.29/1.52 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ I4 )
% 0.29/1.52 => ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ I4 ) @ msg ) ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_202_length__greater__0__conv,axiom,
% 0.29/1.52 ! [Xs: list_c1059388851t_unit] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ Xs ) )
% 0.29/1.52 = ( Xs != nil_co1338500125t_unit ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_203_length__greater__0__conv,axiom,
% 0.29/1.52 ! [Xs: list_message_p_v] :
% 0.29/1.52 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1168481041ge_p_v @ Xs ) )
% 0.29/1.52 = ( Xs != nil_message_p_v ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_204_AssumptionFair_I2_J,axiom,
% 0.29/1.52 ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ) ).
% 0.29/1.52
% 0.29/1.52 thf(fact_205_Occ4,axiom,
% 0.29/1.52 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ nMsg ) @ msg ).
% 0.29/1.52
% 0.29/1.52 thf(fact_206_AssumptionFair_I3_J,axiom,
% 0.29/1.52 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ n0 ) @ msg ).
% 0.29/1.52
% 0.29/1.52 thf(fact_207_AssumptionSubset3_I4_J,axiom,
% 0.29/1.52 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ nMsg ) @ msg ).
% 0.29/1.52
% 0.29/1.52 thf(fact_208_AssumptionSubset2_I4_J,axiom,
% 0.29/1.52 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ n1 ) @ msgInSet ).
% 0.29/1.52
% 0.29/1.52 thf(fact_209_MessageStaysOrConsumed,axiom,
% 0.29/1.52 ! [N1: nat,N22: nat,N2: nat,Msg: message_p_v] :
% 0.29/1.52 ( ( ( ord_less_eq_nat @ N1 @ N22 )
% 0.29/1.52 & ( ord_less_nat @ N22 @ ( size_s1406904903t_unit @ ( fe @ N2 ) ) )
% 0.29/1.52 & ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N2 ) @ N1 ) @ Msg ) )
% 0.29/1.52 => ( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N2 ) @ N22 ) @ Msg )
% 0.29/1.53 | ? [N03: nat] :
% 0.29/1.53 ( ( ord_less_eq_nat @ N1 @ N03 )
% 0.29/1.53 & ( ord_less_nat @ N03 @ ( size_s1168481041ge_p_v @ ( ft @ N2 ) ) )
% 0.29/1.53 & ( ( nth_message_p_v @ ( ft @ N2 ) @ N03 )
% 0.29/1.53 = Msg ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_210__092_060open_062enabled_A_Ife_A_ISuc_Aindex_J_A_B_A_Ilength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_J_J_Amsg_092_060close_062,axiom,
% 0.29/1.53 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ) @ msg ).
% 0.29/1.53
% 0.29/1.53 thf(fact_211_length__0__conv,axiom,
% 0.29/1.53 ! [Xs: list_c1059388851t_unit] :
% 0.29/1.53 ( ( ( size_s1406904903t_unit @ Xs )
% 0.29/1.53 = zero_zero_nat )
% 0.29/1.53 = ( Xs = nil_co1338500125t_unit ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_212_length__0__conv,axiom,
% 0.29/1.53 ! [Xs: list_message_p_v] :
% 0.29/1.53 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.29/1.53 = zero_zero_nat )
% 0.29/1.53 = ( Xs = nil_message_p_v ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_213_Occ2,axiom,
% 0.29/1.53 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ index ) ) @ msg ).
% 0.29/1.53
% 0.29/1.53 thf(fact_214_AssumptionCase1ImplThesis_H,axiom,
% 0.29/1.53 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg ).
% 0.29/1.53
% 0.29/1.53 thf(fact_215_neq__if__length__neq,axiom,
% 0.29/1.53 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.29/1.53 ( ( ( size_s1406904903t_unit @ Xs )
% 0.29/1.53 != ( size_s1406904903t_unit @ Ys ) )
% 0.29/1.53 => ( Xs != Ys ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_216_neq__if__length__neq,axiom,
% 0.29/1.53 ! [Xs: list_message_p_v,Ys: list_message_p_v] :
% 0.29/1.53 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.29/1.53 != ( size_s1168481041ge_p_v @ Ys ) )
% 0.29/1.53 => ( Xs != Ys ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_217_Ex__list__of__length,axiom,
% 0.29/1.53 ! [N2: nat] :
% 0.29/1.53 ? [Xs2: list_c1059388851t_unit] :
% 0.29/1.53 ( ( size_s1406904903t_unit @ Xs2 )
% 0.29/1.53 = N2 ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_218_Ex__list__of__length,axiom,
% 0.29/1.53 ! [N2: nat] :
% 0.29/1.53 ? [Xs2: list_message_p_v] :
% 0.29/1.53 ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.29/1.53 = N2 ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_219_length__induct,axiom,
% 0.29/1.53 ! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
% 0.29/1.53 ( ! [Xs2: list_c1059388851t_unit] :
% 0.29/1.53 ( ! [Ys2: list_c1059388851t_unit] :
% 0.29/1.53 ( ( ord_less_nat @ ( size_s1406904903t_unit @ Ys2 ) @ ( size_s1406904903t_unit @ Xs2 ) )
% 0.29/1.53 => ( P @ Ys2 ) )
% 0.29/1.53 => ( P @ Xs2 ) )
% 0.29/1.53 => ( P @ Xs ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_220_length__induct,axiom,
% 0.29/1.53 ! [P: list_message_p_v > $o,Xs: list_message_p_v] :
% 0.29/1.53 ( ! [Xs2: list_message_p_v] :
% 0.29/1.53 ( ! [Ys2: list_message_p_v] :
% 0.29/1.53 ( ( ord_less_nat @ ( size_s1168481041ge_p_v @ Ys2 ) @ ( size_s1168481041ge_p_v @ Xs2 ) )
% 0.29/1.53 => ( P @ Ys2 ) )
% 0.29/1.53 => ( P @ Xs2 ) )
% 0.29/1.53 => ( P @ Xs ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_221_list_Osize_I3_J,axiom,
% 0.29/1.53 ( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
% 0.29/1.53 = zero_zero_nat ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_222_list_Osize_I3_J,axiom,
% 0.29/1.53 ( ( size_s1168481041ge_p_v @ nil_message_p_v )
% 0.29/1.53 = zero_zero_nat ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_223_list__eq__iff__nth__eq,axiom,
% 0.29/1.53 ( ( ^ [Y5: list_c1059388851t_unit,Z2: list_c1059388851t_unit] : ( Y5 = Z2 ) )
% 0.29/1.53 = ( ^ [Xs3: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
% 0.29/1.53 ( ( ( size_s1406904903t_unit @ Xs3 )
% 0.29/1.53 = ( size_s1406904903t_unit @ Ys3 ) )
% 0.29/1.53 & ! [I3: nat] :
% 0.29/1.53 ( ( ord_less_nat @ I3 @ ( size_s1406904903t_unit @ Xs3 ) )
% 0.29/1.53 => ( ( nth_co1649820636t_unit @ Xs3 @ I3 )
% 0.29/1.53 = ( nth_co1649820636t_unit @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_224_list__eq__iff__nth__eq,axiom,
% 0.29/1.53 ( ( ^ [Y5: list_message_p_v,Z2: list_message_p_v] : ( Y5 = Z2 ) )
% 0.29/1.53 = ( ^ [Xs3: list_message_p_v,Ys3: list_message_p_v] :
% 0.29/1.53 ( ( ( size_s1168481041ge_p_v @ Xs3 )
% 0.29/1.53 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 0.29/1.53 & ! [I3: nat] :
% 0.29/1.53 ( ( ord_less_nat @ I3 @ ( size_s1168481041ge_p_v @ Xs3 ) )
% 0.29/1.53 => ( ( nth_message_p_v @ Xs3 @ I3 )
% 0.29/1.53 = ( nth_message_p_v @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_225_Skolem__list__nth,axiom,
% 0.29/1.53 ! [K: nat,P: nat > config256849571t_unit > $o] :
% 0.29/1.53 ( ( ! [I3: nat] :
% 0.29/1.53 ( ( ord_less_nat @ I3 @ K )
% 0.29/1.53 => ? [X4: config256849571t_unit] : ( P @ I3 @ X4 ) ) )
% 0.29/1.53 = ( ? [Xs3: list_c1059388851t_unit] :
% 0.29/1.53 ( ( ( size_s1406904903t_unit @ Xs3 )
% 0.29/1.53 = K )
% 0.29/1.53 & ! [I3: nat] :
% 0.29/1.53 ( ( ord_less_nat @ I3 @ K )
% 0.29/1.53 => ( P @ I3 @ ( nth_co1649820636t_unit @ Xs3 @ I3 ) ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_226_Skolem__list__nth,axiom,
% 0.29/1.53 ! [K: nat,P: nat > message_p_v > $o] :
% 0.29/1.53 ( ( ! [I3: nat] :
% 0.29/1.53 ( ( ord_less_nat @ I3 @ K )
% 0.29/1.53 => ? [X4: message_p_v] : ( P @ I3 @ X4 ) ) )
% 0.29/1.53 = ( ? [Xs3: list_message_p_v] :
% 0.29/1.53 ( ( ( size_s1168481041ge_p_v @ Xs3 )
% 0.29/1.53 = K )
% 0.29/1.53 & ! [I3: nat] :
% 0.29/1.53 ( ( ord_less_nat @ I3 @ K )
% 0.29/1.53 => ( P @ I3 @ ( nth_message_p_v @ Xs3 @ I3 ) ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_227_nth__equalityI,axiom,
% 0.29/1.53 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.29/1.53 ( ( ( size_s1406904903t_unit @ Xs )
% 0.29/1.53 = ( size_s1406904903t_unit @ Ys ) )
% 0.29/1.53 => ( ! [I2: nat] :
% 0.29/1.53 ( ( ord_less_nat @ I2 @ ( size_s1406904903t_unit @ Xs ) )
% 0.29/1.53 => ( ( nth_co1649820636t_unit @ Xs @ I2 )
% 0.29/1.53 = ( nth_co1649820636t_unit @ Ys @ I2 ) ) )
% 0.29/1.53 => ( Xs = Ys ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_228_nth__equalityI,axiom,
% 0.29/1.53 ! [Xs: list_message_p_v,Ys: list_message_p_v] :
% 0.29/1.53 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.29/1.53 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.29/1.53 => ( ! [I2: nat] :
% 0.29/1.53 ( ( ord_less_nat @ I2 @ ( size_s1168481041ge_p_v @ Xs ) )
% 0.29/1.53 => ( ( nth_message_p_v @ Xs @ I2 )
% 0.29/1.53 = ( nth_message_p_v @ Ys @ I2 ) ) )
% 0.29/1.53 => ( Xs = Ys ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_229_EnabledOrConsumed,axiom,
% 0.29/1.53 ( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) @ msg )
% 0.29/1.53 | ? [N03: nat] :
% 0.29/1.53 ( ( ord_less_eq_nat @ n0 @ N03 )
% 0.29/1.53 & ( ord_less_nat @ N03 @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
% 0.29/1.53 & ( ( nth_message_p_v @ ( ft @ n ) @ N03 )
% 0.29/1.53 = msg ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_230_Case2ImplThesis,axiom,
% 0.29/1.53 ( ? [N0: nat] :
% 0.29/1.53 ( ( ord_less_eq_nat @ n0 @ N0 )
% 0.29/1.53 & ( ord_less_nat @ N0 @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
% 0.29/1.53 & ( ( nth_message_p_v @ ( ft @ n ) @ N0 )
% 0.29/1.53 = msg ) )
% 0.29/1.53 => ? [N6: nat] :
% 0.29/1.53 ( ( ord_less_eq_nat @ n @ N6 )
% 0.29/1.53 & ? [N03: nat] :
% 0.29/1.53 ( ( ord_less_eq_nat @ n0 @ N03 )
% 0.29/1.53 & ( ord_less_nat @ N03 @ ( size_s1168481041ge_p_v @ ( ft @ N6 ) ) )
% 0.29/1.53 & ( msg
% 0.29/1.53 = ( nth_message_p_v @ ( ft @ N6 ) @ N03 ) ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_231_EnabledInSuc,axiom,
% 0.29/1.53 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msg ).
% 0.29/1.53
% 0.29/1.53 thf(fact_232_AssumptionSubset2_I2_J,axiom,
% 0.29/1.53 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msgInSet ).
% 0.29/1.53
% 0.29/1.53 thf(fact_233_LastOfIndex,axiom,
% 0.29/1.53 ( ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) )
% 0.29/1.53 = ( last_c571238084t_unit @ ( fe @ index ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_234_EnabledOrConsumedAtLast,axiom,
% 0.29/1.53 ( ( enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg )
% 0.29/1.53 | ? [N03: nat] :
% 0.29/1.53 ( ( ord_less_eq_nat @ n0 @ N03 )
% 0.29/1.53 & ( ord_less_nat @ N03 @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
% 0.29/1.53 & ( ( nth_message_p_v @ ( ft @ n ) @ N03 )
% 0.29/1.53 = msg ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_235_last__conv__nth,axiom,
% 0.29/1.53 ! [Xs: list_c1059388851t_unit] :
% 0.29/1.53 ( ( Xs != nil_co1338500125t_unit )
% 0.29/1.53 => ( ( last_c571238084t_unit @ Xs )
% 0.29/1.53 = ( nth_co1649820636t_unit @ Xs @ ( minus_minus_nat @ ( size_s1406904903t_unit @ Xs ) @ one_one_nat ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_236_last__conv__nth,axiom,
% 0.29/1.53 ! [Xs: list_message_p_v] :
% 0.29/1.53 ( ( Xs != nil_message_p_v )
% 0.29/1.53 => ( ( last_message_p_v @ Xs )
% 0.29/1.53 = ( nth_message_p_v @ Xs @ ( minus_minus_nat @ ( size_s1168481041ge_p_v @ Xs ) @ one_one_nat ) ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_237__092_060open_062_092_060And_062n0_Amsg_O_A_092_060forall_062n_O_Aexecution_OfirstOccurrence_A_Ife_An_J_A_Ift_An_J_Amsg_An0_A_092_060longrightarrow_062_Amsg_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062,axiom,
% 0.29/1.53 ! [Msg: message_p_v,N04: nat,N7: nat] :
% 0.29/1.53 ( ( firstO1414030372_p_v_s @ ( fe @ N7 ) @ ( ft @ N7 ) @ Msg @ N04 )
% 0.29/1.53 => ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ ( last_c571238084t_unit @ ( fe @ N7 ) ) @ Msg ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_238_le__numeral__extra_I3_J,axiom,
% 0.29/1.53 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.29/1.53
% 0.29/1.53 thf(fact_239_less__numeral__extra_I3_J,axiom,
% 0.29/1.53 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_240_le__numeral__extra_I4_J,axiom,
% 0.29/1.53 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.29/1.53
% 0.29/1.53 thf(fact_241_less__numeral__extra_I4_J,axiom,
% 0.29/1.53 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.29/1.53
% 0.29/1.53 thf(fact_242_less__numeral__extra_I1_J,axiom,
% 0.29/1.53 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/1.53
% 0.29/1.53 thf(fact_243__092_060open_062_092_060forall_062n_O_A_092_060forall_062msg_H_092_060in_062firstOccSet_An_O_Amsg_H_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062,axiom,
% 0.29/1.53 ! [N7: nat,X5: message_p_v] :
% 0.29/1.53 ( ( member_message_p_v @ X5 @ ( firstOccSet @ N7 ) )
% 0.29/1.53 => ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ ( last_c571238084t_unit @ ( fe @ N7 ) ) @ X5 ) ) ) ).
% 0.29/1.53
% 0.29/1.53 thf(conj_0,conjecture,
% 0.29/1.53 ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ).
% 0.29/1.53 ------------------------
% 0.29/1.54 % (31575)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/183Mi)
% 0.29/1.54 % (31577)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_31470 for (2999ds/27Mi)
% 0.29/1.54 % (31580)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_31470 for (2999ds/275Mi)
% 0.29/1.54 % (31576)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_31470 for (2999ds/4Mi)
% 0.29/1.54 % (31581)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/18Mi)
% 0.29/1.54 % (31576)Instruction limit reached!
% 0.29/1.54 % (31576)------------------------------
% 0.29/1.54 % (31576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.54 % (31576)Termination reason: Unknown
% 0.29/1.54 % (31576)Termination phase: shuffling
% 0.29/1.54
% 0.29/1.54 % (31576)Memory used [KB]: 1279
% 0.29/1.54 % (31576)Time elapsed: 0.003 s
% 0.29/1.54 % (31576)Instructions burned: 6 (million)
% 0.29/1.54 % (31576)------------------------------
% 0.29/1.54 % (31576)------------------------------
% 0.29/1.55 % (31581)Instruction limit reached!
% 0.29/1.55 % (31581)------------------------------
% 0.29/1.55 % (31581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.55 % (31581)Termination reason: Unknown
% 0.29/1.55 % (31581)Termination phase: Property scanning
% 0.29/1.55
% 0.29/1.55 % (31581)Memory used [KB]: 1535
% 0.29/1.55 % (31581)Time elapsed: 0.007 s
% 0.29/1.55 % (31581)Instructions burned: 19 (million)
% 0.29/1.55 % (31581)------------------------------
% 0.29/1.55 % (31581)------------------------------
% 0.29/1.55 % (31578)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/2Mi)
% 0.29/1.55 % (31579)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_31470 for (2999ds/2Mi)
% 0.29/1.55 % (31577)Instruction limit reached!
% 0.29/1.55 % (31577)------------------------------
% 0.29/1.55 % (31577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.55 % (31577)Termination reason: Unknown
% 0.29/1.55 % (31577)Termination phase: Preprocessing 2
% 0.29/1.55
% 0.29/1.55 % (31577)Memory used [KB]: 1535
% 0.29/1.55 % (31577)Time elapsed: 0.010 s
% 0.29/1.55 % (31577)Instructions burned: 29 (million)
% 0.29/1.55 % (31577)------------------------------
% 0.29/1.55 % (31577)------------------------------
% 0.29/1.55 % (31578)Instruction limit reached!
% 0.29/1.55 % (31578)------------------------------
% 0.29/1.55 % (31578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.55 % (31578)Termination reason: Unknown
% 0.29/1.55 % (31579)Instruction limit reached!
% 0.29/1.55 % (31579)------------------------------
% 0.29/1.55 % (31579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.55 % (31578)Termination phase: shuffling
% 0.29/1.55
% 0.29/1.55 % (31578)Memory used [KB]: 1279
% 0.29/1.55 % (31578)Time elapsed: 0.003 s
% 0.29/1.55 % (31578)Instructions burned: 2 (million)
% 0.29/1.55 % (31578)------------------------------
% 0.29/1.55 % (31578)------------------------------
% 0.29/1.55 % (31579)Termination reason: Unknown
% 0.29/1.55 % (31579)Termination phase: shuffling
% 0.29/1.55
% 0.29/1.55 % (31579)Memory used [KB]: 1279
% 0.29/1.55 % (31579)Time elapsed: 0.003 s
% 0.29/1.55 % (31579)Instructions burned: 2 (million)
% 0.29/1.55 % (31579)------------------------------
% 0.29/1.55 % (31579)------------------------------
% 0.29/1.55 % (31582)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/3Mi)
% 0.29/1.55 % (31582)Instruction limit reached!
% 0.29/1.55 % (31582)------------------------------
% 0.29/1.55 % (31582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.55 % (31582)Termination reason: Unknown
% 0.29/1.55 % (31582)Termination phase: shuffling
% 0.29/1.55
% 0.29/1.55 % (31582)Memory used [KB]: 1279
% 0.29/1.55 % (31582)Time elapsed: 0.002 s
% 0.29/1.55 % (31582)Instructions burned: 4 (million)
% 0.29/1.55 % (31582)------------------------------
% 0.29/1.55 % (31582)------------------------------
% 0.29/1.56 % (31583)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_31470 for (2999ds/37Mi)
% 0.29/1.56 % (31584)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_31470 for (2999ds/15Mi)
% 0.29/1.56 % (31587)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/7Mi)
% 0.29/1.56 % (31584)Instruction limit reached!
% 0.29/1.56 % (31584)------------------------------
% 0.29/1.56 % (31584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.56 % (31584)Termination reason: Unknown
% 0.29/1.56 % (31584)Termination phase: shuffling
% 0.29/1.56
% 0.29/1.56 % (31584)Memory used [KB]: 1535
% 0.29/1.56 % (31584)Time elapsed: 0.006 s
% 0.29/1.56 % (31584)Instructions burned: 16 (million)
% 0.29/1.56 % (31584)------------------------------
% 0.29/1.56 % (31584)------------------------------
% 0.29/1.57 % (31587)Instruction limit reached!
% 0.29/1.57 % (31587)------------------------------
% 0.29/1.57 % (31587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.57 % (31587)Termination reason: Unknown
% 0.29/1.57 % (31587)Termination phase: shuffling
% 0.29/1.57
% 0.29/1.57 % (31587)Memory used [KB]: 1407
% 0.29/1.57 % (31587)Time elapsed: 0.004 s
% 0.29/1.57 % (31587)Instructions burned: 10 (million)
% 0.29/1.57 % (31587)------------------------------
% 0.29/1.57 % (31587)------------------------------
% 0.29/1.57 % (31585)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_31470 for (2999ds/3Mi)
% 0.29/1.57 % (31583)Instruction limit reached!
% 0.29/1.57 % (31583)------------------------------
% 0.29/1.57 % (31583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.57 % (31583)Termination reason: Unknown
% 0.29/1.57 % (31583)Termination phase: Property scanning
% 0.29/1.57
% 0.29/1.57 % (31583)Memory used [KB]: 1791
% 0.29/1.57 % (31583)Time elapsed: 0.011 s
% 0.29/1.57 % (31583)Instructions burned: 39 (million)
% 0.29/1.57 % (31583)------------------------------
% 0.29/1.57 % (31583)------------------------------
% 0.29/1.57 % (31586)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_31470 for (2999ds/1041Mi)
% 0.29/1.57 % (31585)Instruction limit reached!
% 0.29/1.57 % (31585)------------------------------
% 0.29/1.57 % (31585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.57 % (31585)Termination reason: Unknown
% 0.29/1.57 % (31585)Termination phase: shuffling
% 0.29/1.57
% 0.29/1.57 % (31585)Memory used [KB]: 1279
% 0.29/1.57 % (31585)Time elapsed: 0.003 s
% 0.29/1.57 % (31585)Instructions burned: 3 (million)
% 0.29/1.57 % (31585)------------------------------
% 0.29/1.57 % (31585)------------------------------
% 0.29/1.57 % (31588)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/16Mi)
% 0.29/1.58 % (31589)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_31470 for (2999ds/3Mi)
% 0.29/1.58 % (31590)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_31470 for (2999ds/3Mi)
% 0.29/1.58 % (31589)Instruction limit reached!
% 0.29/1.58 % (31589)------------------------------
% 0.29/1.58 % (31589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.58 % (31589)Termination reason: Unknown
% 0.29/1.58 % (31589)Termination phase: shuffling
% 0.29/1.58
% 0.29/1.58 % (31589)Memory used [KB]: 1279
% 0.29/1.58 % (31589)Time elapsed: 0.002 s
% 0.29/1.58 % (31589)Instructions burned: 3 (million)
% 0.29/1.58 % (31589)------------------------------
% 0.29/1.58 % (31589)------------------------------
% 0.29/1.58 % (31590)Instruction limit reached!
% 0.29/1.58 % (31590)------------------------------
% 0.29/1.58 % (31590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.58 % (31590)Termination reason: Unknown
% 0.29/1.58 % (31590)Termination phase: shuffling
% 0.29/1.58
% 0.29/1.58 % (31590)Memory used [KB]: 1279
% 0.29/1.58 % (31590)Time elapsed: 0.002 s
% 0.29/1.58 % (31590)Instructions burned: 3 (million)
% 0.29/1.58 % (31590)------------------------------
% 0.29/1.58 % (31590)------------------------------
% 0.29/1.58 % (31591)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/7Mi)
% 0.29/1.58 % (31588)Instruction limit reached!
% 0.29/1.58 % (31588)------------------------------
% 0.29/1.58 % (31588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.58 % (31588)Termination reason: Unknown
% 0.29/1.58 % (31588)Termination phase: shuffling
% 0.29/1.58
% 0.29/1.58 % (31588)Memory used [KB]: 1535
% 0.29/1.58 % (31588)Time elapsed: 0.006 s
% 0.29/1.58 % (31588)Instructions burned: 16 (million)
% 0.29/1.58 % (31588)------------------------------
% 0.29/1.58 % (31588)------------------------------
% 0.29/1.58 % (31591)Instruction limit reached!
% 0.29/1.58 % (31591)------------------------------
% 0.29/1.58 % (31591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.58 % (31591)Termination reason: Unknown
% 0.29/1.58 % (31591)Termination phase: shuffling
% 0.29/1.58
% 0.29/1.58 % (31591)Memory used [KB]: 1407
% 0.29/1.58 % (31591)Time elapsed: 0.004 s
% 0.29/1.58 % (31591)Instructions burned: 9 (million)
% 0.29/1.58 % (31591)------------------------------
% 0.29/1.58 % (31591)------------------------------
% 0.29/1.59 % (31592)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/3Mi)
% 0.29/1.59 % (31593)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/4Mi)
% 0.29/1.59 % (31592)Instruction limit reached!
% 0.29/1.59 % (31592)------------------------------
% 0.29/1.59 % (31592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.59 % (31592)Termination reason: Unknown
% 0.29/1.59 % (31592)Termination phase: shuffling
% 0.29/1.59
% 0.29/1.59 % (31592)Memory used [KB]: 1279
% 0.29/1.59 % (31592)Time elapsed: 0.002 s
% 0.29/1.59 % (31592)Instructions burned: 4 (million)
% 0.29/1.59 % (31592)------------------------------
% 0.29/1.59 % (31592)------------------------------
% 0.29/1.59 % (31593)Instruction limit reached!
% 0.29/1.59 % (31593)------------------------------
% 0.29/1.59 % (31593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.59 % (31593)Termination reason: Unknown
% 0.29/1.59 % (31593)Termination phase: shuffling
% 0.29/1.59
% 0.29/1.59 % (31593)Memory used [KB]: 1279
% 0.29/1.59 % (31593)Time elapsed: 0.002 s
% 0.29/1.59 % (31593)Instructions burned: 4 (million)
% 0.29/1.59 % (31593)------------------------------
% 0.29/1.59 % (31593)------------------------------
% 0.29/1.59 % (31594)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/18Mi)
% 0.29/1.59 % (31595)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/710Mi)
% 0.29/1.59 % (31575)Instruction limit reached!
% 0.29/1.59 % (31575)------------------------------
% 0.29/1.59 % (31575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.59 % (31575)Termination reason: Unknown
% 0.29/1.59 % (31575)Termination phase: Saturation
% 0.29/1.59
% 0.29/1.59 % (31575)Memory used [KB]: 7036
% 0.29/1.59 % (31575)Time elapsed: 0.054 s
% 0.29/1.59 % (31575)Instructions burned: 185 (million)
% 0.29/1.59 % (31575)------------------------------
% 0.29/1.59 % (31575)------------------------------
% 0.29/1.59 % (31594)Instruction limit reached!
% 0.29/1.59 % (31594)------------------------------
% 0.29/1.59 % (31594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.59 % (31594)Termination reason: Unknown
% 0.29/1.59 % (31594)Termination phase: Property scanning
% 0.29/1.59
% 0.29/1.59 % (31594)Memory used [KB]: 1535
% 0.29/1.59 % (31594)Time elapsed: 0.007 s
% 0.29/1.59 % (31594)Instructions burned: 20 (million)
% 0.29/1.59 % (31594)------------------------------
% 0.29/1.59 % (31594)------------------------------
% 2.36/1.60 % (31596)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/6Mi)
% 2.36/1.60 % (31597)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_31470 for (2999ds/902Mi)
% 2.36/1.60 % (31596)Instruction limit reached!
% 2.36/1.60 % (31596)------------------------------
% 2.36/1.60 % (31596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.60 % (31596)Termination reason: Unknown
% 2.36/1.60 % (31596)Termination phase: shuffling
% 2.36/1.60
% 2.36/1.60 % (31596)Memory used [KB]: 1407
% 2.36/1.60 % (31596)Time elapsed: 0.003 s
% 2.36/1.60 % (31596)Instructions burned: 7 (million)
% 2.36/1.60 % (31596)------------------------------
% 2.36/1.60 % (31596)------------------------------
% 2.36/1.60 % (31598)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_31470 for (2999ds/21Mi)
% 2.36/1.60 % (31599)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/5Mi)
% 2.36/1.61 % (31599)Instruction limit reached!
% 2.36/1.61 % (31599)------------------------------
% 2.36/1.61 % (31599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.61 % (31599)Termination reason: Unknown
% 2.36/1.61 % (31599)Termination phase: shuffling
% 2.36/1.61
% 2.36/1.61 % (31599)Memory used [KB]: 1407
% 2.36/1.61 % (31599)Time elapsed: 0.003 s
% 2.36/1.61 % (31599)Instructions burned: 8 (million)
% 2.36/1.61 % (31599)------------------------------
% 2.36/1.61 % (31599)------------------------------
% 2.36/1.61 % (31600)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_31470 for (2999ds/6Mi)
% 2.36/1.61 % (31600)Instruction limit reached!
% 2.36/1.61 % (31600)------------------------------
% 2.36/1.61 % (31600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.61 % (31600)Termination reason: Unknown
% 2.36/1.61 % (31600)Termination phase: shuffling
% 2.36/1.61
% 2.36/1.61 % (31600)Memory used [KB]: 1407
% 2.36/1.61 % (31600)Time elapsed: 0.003 s
% 2.36/1.61 % (31600)Instructions burned: 8 (million)
% 2.36/1.61 % (31600)------------------------------
% 2.36/1.61 % (31600)------------------------------
% 2.36/1.61 % (31598)Instruction limit reached!
% 2.36/1.61 % (31598)------------------------------
% 2.36/1.61 % (31598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.61 % (31598)Termination reason: Unknown
% 2.36/1.61 % (31598)Termination phase: Property scanning
% 2.36/1.61
% 2.36/1.61 % (31598)Memory used [KB]: 1535
% 2.36/1.61 % (31598)Time elapsed: 0.008 s
% 2.36/1.61 % (31598)Instructions burned: 24 (million)
% 2.36/1.61 % (31598)------------------------------
% 2.36/1.61 % (31598)------------------------------
% 2.36/1.61 % (31601)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/377Mi)
% 2.36/1.62 % (31602)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_31470 for (2999ds/779Mi)
% 2.36/1.62 % (31603)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_31470 for (2999ds/19Mi)
% 2.36/1.63 % (31603)Instruction limit reached!
% 2.36/1.63 % (31603)------------------------------
% 2.36/1.63 % (31603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.63 % (31603)Termination reason: Unknown
% 2.36/1.63 % (31603)Termination phase: shuffling
% 2.36/1.63
% 2.36/1.63 % (31603)Memory used [KB]: 1663
% 2.36/1.63 % (31603)Time elapsed: 0.007 s
% 2.36/1.63 % (31603)Instructions burned: 22 (million)
% 2.36/1.63 % (31603)------------------------------
% 2.36/1.63 % (31603)------------------------------
% 2.36/1.63 % (31580)Instruction limit reached!
% 2.36/1.63 % (31580)------------------------------
% 2.36/1.63 % (31580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.63 % (31580)Termination reason: Unknown
% 2.36/1.63 % (31580)Termination phase: Saturation
% 2.36/1.63
% 2.36/1.63 % (31580)Memory used [KB]: 7291
% 2.36/1.63 % (31580)Time elapsed: 0.086 s
% 2.36/1.63 % (31580)Instructions burned: 277 (million)
% 2.36/1.63 % (31580)------------------------------
% 2.36/1.63 % (31580)------------------------------
% 2.36/1.64 % (31604)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/879Mi)
% 2.36/1.64 % (31605)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/17Mi)
% 2.36/1.64 % (31605)Instruction limit reached!
% 2.36/1.64 % (31605)------------------------------
% 2.36/1.64 % (31605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.64 % (31605)Termination reason: Unknown
% 2.36/1.64 % (31605)Termination phase: Property scanning
% 2.36/1.64
% 2.36/1.64 % (31605)Memory used [KB]: 1535
% 2.36/1.64 % (31605)Time elapsed: 0.007 s
% 2.36/1.64 % (31605)Instructions burned: 19 (million)
% 2.36/1.64 % (31605)------------------------------
% 2.36/1.64 % (31605)------------------------------
% 2.36/1.65 % (31606)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_31470 for (2999ds/3Mi)
% 2.36/1.65 % (31606)Instruction limit reached!
% 2.36/1.65 % (31606)------------------------------
% 2.36/1.65 % (31606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.65 % (31606)Termination reason: Unknown
% 2.36/1.65 % (31606)Termination phase: shuffling
% 2.36/1.65
% 2.36/1.65 % (31606)Memory used [KB]: 1279
% 2.36/1.65 % (31606)Time elapsed: 0.002 s
% 2.36/1.65 % (31606)Instructions burned: 3 (million)
% 2.36/1.65 % (31606)------------------------------
% 2.36/1.65 % (31606)------------------------------
% 2.36/1.66 % (31607)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_31470 for (2998ds/30Mi)
% 2.36/1.67 % (31607)Instruction limit reached!
% 2.36/1.67 % (31607)------------------------------
% 2.36/1.67 % (31607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.67 % (31607)Termination reason: Unknown
% 2.36/1.67 % (31607)Termination phase: Preprocessing 2
% 2.36/1.67
% 2.36/1.67 % (31607)Memory used [KB]: 1535
% 2.36/1.67 % (31607)Time elapsed: 0.010 s
% 2.36/1.67 % (31607)Instructions burned: 30 (million)
% 2.36/1.67 % (31607)------------------------------
% 2.36/1.67 % (31607)------------------------------
% 2.36/1.68 % (31608)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_31470 for (2998ds/127Mi)
% 2.36/1.72 % (31608)Instruction limit reached!
% 2.36/1.72 % (31608)------------------------------
% 2.36/1.72 % (31608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.72 % (31608)Termination reason: Unknown
% 2.36/1.72 % (31608)Termination phase: Saturation
% 2.36/1.72
% 2.36/1.72 % (31608)Memory used [KB]: 6780
% 2.36/1.72 % (31608)Time elapsed: 0.041 s
% 2.36/1.72 % (31608)Instructions burned: 128 (million)
% 2.36/1.72 % (31608)------------------------------
% 2.36/1.72 % (31608)------------------------------
% 2.36/1.73 % (31609)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_31470 for (2998ds/100Mi)
% 2.36/1.74 % (31601)Instruction limit reached!
% 2.36/1.74 % (31601)------------------------------
% 2.36/1.74 % (31601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.74 % (31601)Termination reason: Unknown
% 2.36/1.74 % (31601)Termination phase: Saturation
% 2.36/1.74
% 2.36/1.74 % (31601)Memory used [KB]: 7675
% 2.36/1.74 % (31601)Time elapsed: 0.121 s
% 2.36/1.74 % (31601)Instructions burned: 378 (million)
% 2.36/1.74 % (31601)------------------------------
% 2.36/1.74 % (31601)------------------------------
% 2.36/1.74 % (31610)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_31470 for (2998ds/3Mi)
% 2.36/1.75 % (31610)Instruction limit reached!
% 2.36/1.75 % (31610)------------------------------
% 2.36/1.75 % (31610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.75 % (31610)Termination reason: Unknown
% 2.36/1.75 % (31610)Termination phase: shuffling
% 2.36/1.75
% 2.36/1.75 % (31610)Memory used [KB]: 1279
% 2.36/1.75 % (31610)Time elapsed: 0.002 s
% 2.36/1.75 % (31610)Instructions burned: 3 (million)
% 2.36/1.75 % (31610)------------------------------
% 2.36/1.75 % (31610)------------------------------
% 2.36/1.76 % (31611)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_31470 for (2997ds/20Mi)
% 2.36/1.76 % (31609)Instruction limit reached!
% 2.36/1.76 % (31609)------------------------------
% 2.36/1.76 % (31609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.76 % (31609)Termination reason: Unknown
% 2.36/1.76 % (31609)Termination phase: Property scanning
% 2.36/1.76
% 2.36/1.76 % (31609)Memory used [KB]: 2046
% 2.36/1.76 % (31609)Time elapsed: 0.027 s
% 2.36/1.76 % (31609)Instructions burned: 102 (million)
% 2.36/1.76 % (31609)------------------------------
% 2.36/1.76 % (31609)------------------------------
% 2.36/1.76 % (31611)Instruction limit reached!
% 2.36/1.76 % (31611)------------------------------
% 2.36/1.76 % (31611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.76 % (31611)Termination reason: Unknown
% 2.36/1.76 % (31611)Termination phase: Property scanning
% 2.36/1.76
% 2.36/1.76 % (31611)Memory used [KB]: 1535
% 2.36/1.76 % (31611)Time elapsed: 0.008 s
% 2.36/1.76 % (31611)Instructions burned: 21 (million)
% 2.36/1.76 % (31611)------------------------------
% 2.36/1.76 % (31611)------------------------------
% 2.36/1.77 % (31612)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_31470 for (2997ds/86Mi)
% 2.36/1.77 % (31613)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_31470 for (2997ds/107Mi)
% 2.36/1.79 % (31612)Instruction limit reached!
% 2.36/1.79 % (31612)------------------------------
% 2.36/1.79 % (31612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.79 % (31612)Termination reason: Unknown
% 2.36/1.79 % (31612)Termination phase: Saturation
% 2.36/1.79
% 2.36/1.79 % (31612)Memory used [KB]: 6524
% 2.36/1.79 % (31612)Time elapsed: 0.026 s
% 2.36/1.79 % (31612)Instructions burned: 88 (million)
% 2.36/1.79 % (31612)------------------------------
% 2.36/1.79 % (31612)------------------------------
% 2.36/1.80 % (31624)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_31470 for (2997ds/39Mi)
% 2.36/1.80 % (31613)Instruction limit reached!
% 2.36/1.80 % (31613)------------------------------
% 2.36/1.80 % (31613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.80 % (31613)Termination reason: Unknown
% 2.36/1.80 % (31613)Termination phase: Saturation
% 2.36/1.80
% 2.36/1.80 % (31613)Memory used [KB]: 6652
% 2.36/1.80 % (31613)Time elapsed: 0.032 s
% 2.36/1.80 % (31613)Instructions burned: 110 (million)
% 2.36/1.80 % (31613)------------------------------
% 2.36/1.80 % (31613)------------------------------
% 2.36/1.81 % (31624)Instruction limit reached!
% 2.36/1.81 % (31624)------------------------------
% 2.36/1.81 % (31624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.81 % (31624)Termination reason: Unknown
% 2.36/1.81 % (31624)Termination phase: Property scanning
% 2.36/1.81
% 2.36/1.81 % (31624)Memory used [KB]: 1791
% 2.36/1.81 % (31624)Time elapsed: 0.011 s
% 2.36/1.81 % (31624)Instructions burned: 39 (million)
% 2.36/1.81 % (31624)------------------------------
% 2.36/1.81 % (31624)------------------------------
% 2.36/1.81 % (31630)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_31470 for (2997ds/448Mi)
% 2.36/1.82 % (31595)Instruction limit reached!
% 2.36/1.82 % (31595)------------------------------
% 2.36/1.82 % (31595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.82 % (31595)Termination reason: Unknown
% 2.36/1.82 % (31595)Termination phase: Saturation
% 2.36/1.82
% 2.36/1.82 % (31595)Memory used [KB]: 7675
% 2.36/1.82 % (31595)Time elapsed: 0.227 s
% 2.36/1.82 % (31595)Instructions burned: 711 (million)
% 2.36/1.82 % (31595)------------------------------
% 2.36/1.82 % (31595)------------------------------
% 2.36/1.82 % (31634)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_31470 for (2997ds/46Mi)
% 2.36/1.83 % (31638)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_31470 for (2997ds/98Mi)
% 2.36/1.83 % (31634)Instruction limit reached!
% 2.36/1.83 % (31634)------------------------------
% 2.36/1.83 % (31634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.83 % (31634)Termination reason: Unknown
% 2.36/1.83 % (31634)Termination phase: Property scanning
% 2.36/1.83
% 2.36/1.83 % (31634)Memory used [KB]: 1918
% 2.36/1.83 % (31634)Time elapsed: 0.015 s
% 2.36/1.83 % (31634)Instructions burned: 48 (million)
% 2.36/1.83 % (31634)------------------------------
% 2.36/1.83 % (31634)------------------------------
% 2.36/1.84 % (31645)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_31470 for (2997ds/507Mi)
% 2.36/1.85 % (31638)Instruction limit reached!
% 2.36/1.85 % (31638)------------------------------
% 2.36/1.85 % (31638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.85 % (31638)Termination reason: Unknown
% 2.36/1.85 % (31638)Termination phase: Property scanning
% 2.36/1.85
% 2.36/1.85 % (31638)Memory used [KB]: 2046
% 2.36/1.85 % (31638)Time elapsed: 0.027 s
% 2.36/1.85 % (31638)Instructions burned: 99 (million)
% 2.36/1.85 % (31638)------------------------------
% 2.36/1.85 % (31638)------------------------------
% 2.36/1.86 % (31602)Instruction limit reached!
% 2.36/1.86 % (31602)------------------------------
% 2.36/1.86 % (31602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.86 % (31602)Termination reason: Unknown
% 2.36/1.86 % (31602)Termination phase: Saturation
% 2.36/1.86
% 2.36/1.86 % (31602)Memory used [KB]: 7803
% 2.36/1.86 % (31602)Time elapsed: 0.243 s
% 2.36/1.86 % (31602)Instructions burned: 780 (million)
% 2.36/1.86 % (31602)------------------------------
% 2.36/1.86 % (31602)------------------------------
% 2.36/1.86 % (31656)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_31470 for (2996ds/149Mi)
% 2.36/1.87 % (31661)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_31470 for (2996ds/39Mi)
% 2.36/1.88 % (31597)Instruction limit reached!
% 2.36/1.88 % (31597)------------------------------
% 2.36/1.88 % (31597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.88 % (31597)Termination reason: Unknown
% 2.36/1.88 % (31597)Termination phase: Saturation
% 2.36/1.88
% 2.36/1.88 % (31597)Memory used [KB]: 9338
% 2.36/1.88 % (31597)Time elapsed: 0.279 s
% 2.36/1.88 % (31597)Instructions burned: 905 (million)
% 2.36/1.88 % (31597)------------------------------
% 2.36/1.88 % (31597)------------------------------
% 2.36/1.88 % (31661)Instruction limit reached!
% 2.36/1.88 % (31661)------------------------------
% 2.36/1.88 % (31661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.88 % (31661)Termination reason: Unknown
% 2.36/1.88 % (31661)Termination phase: Property scanning
% 2.36/1.88
% 2.36/1.88 % (31661)Memory used [KB]: 1918
% 2.36/1.88 % (31661)Time elapsed: 0.013 s
% 2.36/1.88 % (31661)Instructions burned: 40 (million)
% 2.36/1.88 % (31661)------------------------------
% 2.36/1.88 % (31661)------------------------------
% 2.36/1.88 % (31666)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_31470 for (2996ds/6Mi)
% 2.36/1.89 % (31666)Instruction limit reached!
% 2.36/1.89 % (31666)------------------------------
% 2.36/1.89 % (31666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.89 % (31666)Termination reason: Unknown
% 2.36/1.89 % (31666)Termination phase: shuffling
% 2.36/1.89
% 2.36/1.89 % (31666)Memory used [KB]: 1407
% 2.36/1.89 % (31666)Time elapsed: 0.003 s
% 2.36/1.89 % (31666)Instructions burned: 7 (million)
% 2.36/1.89 % (31666)------------------------------
% 2.36/1.89 % (31666)------------------------------
% 2.36/1.89 % (31670)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_31470 for (2996ds/1087Mi)
% 2.36/1.90 % (31673)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_31470 for (2996ds/47Mi)
% 2.36/1.91 % (31656)Instruction limit reached!
% 2.36/1.91 % (31656)------------------------------
% 2.36/1.91 % (31656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.91 % (31656)Termination reason: Unknown
% 2.36/1.91 % (31656)Termination phase: Saturation
% 2.36/1.91
% 2.36/1.91 % (31656)Memory used [KB]: 6780
% 2.36/1.91 % (31656)Time elapsed: 0.066 s
% 2.36/1.91 % (31656)Instructions burned: 149 (million)
% 2.36/1.91 % (31656)------------------------------
% 2.36/1.91 % (31656)------------------------------
% 2.36/1.91 % (31673)Instruction limit reached!
% 2.36/1.91 % (31673)------------------------------
% 2.36/1.91 % (31673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.91 % (31673)Termination reason: Unknown
% 2.36/1.91 % (31673)Termination phase: Property scanning
% 2.36/1.91
% 2.36/1.91 % (31673)Memory used [KB]: 1918
% 2.36/1.91 % (31673)Time elapsed: 0.016 s
% 2.36/1.91 % (31673)Instructions burned: 50 (million)
% 2.36/1.91 % (31673)------------------------------
% 2.36/1.91 % (31673)------------------------------
% 2.36/1.92 % (31681)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_31470 for (2996ds/44Mi)
% 2.36/1.92 % (31683)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_31470 for (2996ds/432Mi)
% 2.36/1.92 % (31586)Instruction limit reached!
% 2.36/1.92 % (31586)------------------------------
% 2.36/1.92 % (31586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.92 % (31586)Termination reason: Unknown
% 2.36/1.92 % (31586)Termination phase: Saturation
% 2.36/1.92
% 2.36/1.92 % (31586)Memory used [KB]: 8827
% 2.36/1.92 % (31586)Time elapsed: 0.356 s
% 2.36/1.92 % (31586)Instructions burned: 1042 (million)
% 2.36/1.92 % (31586)------------------------------
% 2.36/1.92 % (31586)------------------------------
% 2.36/1.92 % (31604)Instruction limit reached!
% 2.36/1.92 % (31604)------------------------------
% 2.36/1.92 % (31604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.92 % (31604)Termination reason: Unknown
% 2.36/1.92 % (31604)Termination phase: Saturation
% 2.36/1.92
% 2.36/1.92 % (31604)Memory used [KB]: 7547
% 2.36/1.92 % (31604)Time elapsed: 0.290 s
% 2.36/1.92 % (31604)Instructions burned: 881 (million)
% 2.36/1.92 % (31604)------------------------------
% 2.36/1.92 % (31604)------------------------------
% 2.36/1.93 % (31681)Instruction limit reached!
% 2.36/1.93 % (31681)------------------------------
% 2.36/1.93 % (31681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.93 % (31681)Termination reason: Unknown
% 2.36/1.93 % (31681)Termination phase: Property scanning
% 2.36/1.93
% 2.36/1.93 % (31681)Memory used [KB]: 1791
% 2.36/1.93 % (31681)Time elapsed: 0.013 s
% 2.36/1.93 % (31681)Instructions burned: 45 (million)
% 2.36/1.93 % (31681)------------------------------
% 2.36/1.93 % (31681)------------------------------
% 2.36/1.93 % (31687)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_31470 for (2996ds/62Mi)
% 2.36/1.93 % (31689)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_31470 for (2996ds/31Mi)
% 2.36/1.94 % (31693)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_31470 for (2996ds/96Mi)
% 2.36/1.94 % (31689)Instruction limit reached!
% 2.36/1.94 % (31689)------------------------------
% 2.36/1.94 % (31689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.94 % (31689)Termination reason: Unknown
% 2.36/1.94 % (31689)Termination phase: Preprocessing 3
% 2.36/1.94
% 2.36/1.94 % (31689)Memory used [KB]: 1663
% 2.36/1.94 % (31689)Time elapsed: 0.011 s
% 2.36/1.94 % (31689)Instructions burned: 33 (million)
% 2.36/1.94 % (31689)------------------------------
% 2.36/1.94 % (31689)------------------------------
% 2.36/1.95 % (31630)Instruction limit reached!
% 2.36/1.95 % (31630)------------------------------
% 2.36/1.95 % (31630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.95 % (31630)Termination reason: Unknown
% 2.36/1.95 % (31630)Termination phase: Saturation
% 2.36/1.95
% 2.36/1.95 % (31630)Memory used [KB]: 7803
% 2.36/1.95 % (31630)Time elapsed: 0.159 s
% 2.36/1.95 % (31630)Instructions burned: 451 (million)
% 2.36/1.95 % (31630)------------------------------
% 2.36/1.95 % (31630)------------------------------
% 2.36/1.95 % (31687)Instruction limit reached!
% 2.36/1.95 % (31687)------------------------------
% 2.36/1.95 % (31687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.95 % (31687)Termination reason: Unknown
% 2.36/1.95 % (31687)Termination phase: Property scanning
% 2.36/1.95
% 2.36/1.95 % (31687)Memory used [KB]: 1918
% 2.36/1.95 % (31687)Time elapsed: 0.017 s
% 2.36/1.95 % (31687)Instructions burned: 62 (million)
% 2.36/1.95 % (31687)------------------------------
% 2.36/1.95 % (31687)------------------------------
% 2.36/1.95 % (31696)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_31470 for (2995ds/453Mi)
% 2.36/1.96 % (31697)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_31470 for (2995ds/71Mi)
% 2.36/1.96 % (31698)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_31470 for (2995ds/83Mi)
% 2.36/1.96 % (31693)Instruction limit reached!
% 2.36/1.96 % (31693)------------------------------
% 2.36/1.96 % (31693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.96 % (31693)Termination reason: Unknown
% 2.36/1.96 % (31693)Termination phase: Saturation
% 2.36/1.96
% 2.36/1.96 % (31693)Memory used [KB]: 6524
% 2.36/1.96 % (31693)Time elapsed: 0.028 s
% 2.36/1.96 % (31693)Instructions burned: 98 (million)
% 2.36/1.96 % (31693)------------------------------
% 2.36/1.96 % (31693)------------------------------
% 2.36/1.97 % (31711)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_31470 for (2995ds/11Mi)
% 2.36/1.98 % (31711)Instruction limit reached!
% 2.36/1.98 % (31711)------------------------------
% 2.36/1.98 % (31711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.98 % (31711)Termination reason: Unknown
% 2.36/1.98 % (31711)Termination phase: shuffling
% 2.36/1.98
% 2.36/1.98 % (31711)Memory used [KB]: 1535
% 2.36/1.98 % (31711)Time elapsed: 0.005 s
% 2.36/1.98 % (31711)Instructions burned: 13 (million)
% 2.36/1.98 % (31711)------------------------------
% 2.36/1.98 % (31711)------------------------------
% 2.36/1.98 % (31697)Instruction limit reached!
% 2.36/1.98 % (31697)------------------------------
% 2.36/1.98 % (31697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.98 % (31697)Termination reason: Unknown
% 2.36/1.98 % (31697)Termination phase: Property scanning
% 2.36/1.98
% 2.36/1.98 % (31697)Memory used [KB]: 1918
% 2.36/1.98 % (31697)Time elapsed: 0.022 s
% 2.36/1.98 % (31697)Instructions burned: 75 (million)
% 2.36/1.98 % (31697)------------------------------
% 2.36/1.98 % (31697)------------------------------
% 2.36/1.98 % (31698)Instruction limit reached!
% 2.36/1.98 % (31698)------------------------------
% 2.36/1.98 % (31698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.98 % (31698)Termination reason: Unknown
% 2.36/1.98 % (31698)Termination phase: Saturation
% 2.36/1.98
% 2.36/1.98 % (31698)Memory used [KB]: 6524
% 2.36/1.98 % (31698)Time elapsed: 0.026 s
% 2.36/1.98 % (31698)Instructions burned: 84 (million)
% 2.36/1.98 % (31698)------------------------------
% 2.36/1.98 % (31698)------------------------------
% 2.36/1.99 % (31720)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_31470 for (2995ds/41Mi)
% 2.36/1.99 % (31721)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31470 for (2995ds/6Mi)
% 2.36/1.99 % (31721)Instruction limit reached!
% 2.36/1.99 % (31721)------------------------------
% 2.36/1.99 % (31721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/1.99 % (31721)Termination reason: Unknown
% 2.36/1.99 % (31721)Termination phase: shuffling
% 2.36/1.99
% 2.36/1.99 % (31721)Memory used [KB]: 1407
% 2.36/1.99 % (31721)Time elapsed: 0.003 s
% 2.36/1.99 % (31721)Instructions burned: 7 (million)
% 2.36/1.99 % (31721)------------------------------
% 2.36/1.99 % (31721)------------------------------
% 2.36/1.99 % (31722)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_31470 for (2995ds/150Mi)
% 2.36/2.00 % (31720)Instruction limit reached!
% 2.36/2.00 % (31720)------------------------------
% 2.36/2.00 % (31720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/2.00 % (31720)Termination reason: Unknown
% 2.36/2.00 % (31720)Termination phase: Property scanning
% 2.36/2.00
% 2.36/2.00 % (31720)Memory used [KB]: 1791
% 2.36/2.00 % (31720)Time elapsed: 0.012 s
% 2.36/2.00 % (31720)Instructions burned: 43 (million)
% 2.36/2.00 % (31720)------------------------------
% 2.36/2.00 % (31720)------------------------------
% 2.36/2.00 % (31723)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_31470 for (2995ds/343Mi)
% 2.36/2.00 % (31645)Instruction limit reached!
% 2.36/2.00 % (31645)------------------------------
% 2.36/2.00 % (31645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.36/2.00 % (31645)Termination reason: Unknown
% 2.36/2.00 % (31645)Termination phase: Saturation
% 2.36/2.00
% 2.36/2.00 % (31645)Memory used [KB]: 8059
% 2.36/2.00 % (31645)Time elapsed: 0.185 s
% 2.36/2.00 % (31645)Instructions burned: 508 (million)
% 2.36/2.00 % (31645)------------------------------
% 2.36/2.00 % (31645)------------------------------
% 2.36/2.01 % (31729)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_31470 for (2995ds/109Mi)
% 5.64/2.01 % (31736)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_31470 for (2995ds/253Mi)
% 5.64/2.04 % (31722)Instruction limit reached!
% 5.64/2.04 % (31722)------------------------------
% 5.64/2.04 % (31722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.04 % (31722)Termination reason: Unknown
% 5.64/2.04 % (31722)Termination phase: Saturation
% 5.64/2.04
% 5.64/2.04 % (31722)Memory used [KB]: 7036
% 5.64/2.04 % (31722)Time elapsed: 0.045 s
% 5.64/2.04 % (31722)Instructions burned: 150 (million)
% 5.64/2.04 % (31722)------------------------------
% 5.64/2.04 % (31722)------------------------------
% 5.64/2.04 % (31729)Instruction limit reached!
% 5.64/2.04 % (31729)------------------------------
% 5.64/2.04 % (31729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.04 % (31729)Termination reason: Unknown
% 5.64/2.04 % (31729)Termination phase: Saturation
% 5.64/2.04
% 5.64/2.04 % (31729)Memory used [KB]: 6652
% 5.64/2.04 % (31729)Time elapsed: 0.032 s
% 5.64/2.04 % (31729)Instructions burned: 111 (million)
% 5.64/2.04 % (31729)------------------------------
% 5.64/2.04 % (31729)------------------------------
% 5.64/2.05 % (31750)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_31470 for (2994ds/140Mi)
% 5.64/2.05 % (31751)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_31470 for (2994ds/614Mi)
% 5.64/2.05 % (31683)Instruction limit reached!
% 5.64/2.05 % (31683)------------------------------
% 5.64/2.05 % (31683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.05 % (31683)Termination reason: Unknown
% 5.64/2.05 % (31683)Termination phase: Saturation
% 5.64/2.05
% 5.64/2.05 % (31683)Memory used [KB]: 3454
% 5.64/2.05 % (31683)Time elapsed: 0.133 s
% 5.64/2.05 % (31683)Instructions burned: 435 (million)
% 5.64/2.05 % (31683)------------------------------
% 5.64/2.05 % (31683)------------------------------
% 5.64/2.06 % (31763)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_31470 for (2994ds/202Mi)
% 5.64/2.09 % (31696)Instruction limit reached!
% 5.64/2.09 % (31696)------------------------------
% 5.64/2.09 % (31696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.09 % (31696)Termination reason: Unknown
% 5.64/2.09 % (31696)Termination phase: Saturation
% 5.64/2.09
% 5.64/2.09 % (31696)Memory used [KB]: 7291
% 5.64/2.09 % (31696)Time elapsed: 0.136 s
% 5.64/2.09 % (31696)Instructions burned: 453 (million)
% 5.64/2.09 % (31696)------------------------------
% 5.64/2.09 % (31696)------------------------------
% 5.64/2.09 % (31736)Instruction limit reached!
% 5.64/2.09 % (31736)------------------------------
% 5.64/2.09 % (31736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.09 % (31736)Termination reason: Unknown
% 5.64/2.09 % (31736)Termination phase: Saturation
% 5.64/2.09
% 5.64/2.09 % (31736)Memory used [KB]: 7547
% 5.64/2.09 % (31736)Time elapsed: 0.080 s
% 5.64/2.09 % (31736)Instructions burned: 254 (million)
% 5.64/2.09 % (31736)------------------------------
% 5.64/2.09 % (31736)------------------------------
% 5.64/2.09 % (31750)Instruction limit reached!
% 5.64/2.09 % (31750)------------------------------
% 5.64/2.09 % (31750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.64/2.09 % (31750)Termination reason: Unknown
% 5.64/2.09 % (31750)Termination phase: Saturation
% 5.64/2.09
% 5.64/2.09 % (31750)Memory used [KB]: 6524
% 5.64/2.09 % (31750)Time elapsed: 0.048 s
% 5.64/2.09 % (31750)Instructions burned: 141 (million)
% 5.64/2.09 % (31750)------------------------------
% 5.64/2.09 % (31750)------------------------------
% 5.64/2.10 % (31779)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_31470 for (2994ds/339Mi)
% 5.64/2.10 % (31782)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_31470 for (2994ds/283Mi)
% 5.64/2.10 % (31783)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_31470 for (2994ds/134Mi)
% 6.19/2.12 % (31763)Instruction limit reached!
% 6.19/2.12 % (31763)------------------------------
% 6.19/2.12 % (31763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.12 % (31763)Termination reason: Unknown
% 6.19/2.12 % (31763)Termination phase: Saturation
% 6.19/2.12
% 6.19/2.12 % (31763)Memory used [KB]: 7291
% 6.19/2.12 % (31763)Time elapsed: 0.063 s
% 6.19/2.12 % (31763)Instructions burned: 203 (million)
% 6.19/2.12 % (31763)------------------------------
% 6.19/2.12 % (31763)------------------------------
% 6.19/2.13 % (31793)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_31470 for (2994ds/298Mi)
% 6.19/2.14 % (31783)Instruction limit reached!
% 6.19/2.14 % (31783)------------------------------
% 6.19/2.14 % (31783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.14 % (31783)Termination reason: Unknown
% 6.19/2.14 % (31783)Termination phase: Saturation
% 6.19/2.14
% 6.19/2.14 % (31783)Memory used [KB]: 6780
% 6.19/2.14 % (31783)Time elapsed: 0.040 s
% 6.19/2.14 % (31783)Instructions burned: 134 (million)
% 6.19/2.14 % (31783)------------------------------
% 6.19/2.14 % (31783)------------------------------
% 6.19/2.15 % (31799)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_31470 for (2993ds/192Mi)
% 6.19/2.15 % (31723)Instruction limit reached!
% 6.19/2.15 % (31723)------------------------------
% 6.19/2.15 % (31723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.15 % (31723)Termination reason: Unknown
% 6.19/2.15 % (31723)Termination phase: Saturation
% 6.19/2.15
% 6.19/2.15 % (31723)Memory used [KB]: 7164
% 6.19/2.15 % (31723)Time elapsed: 0.151 s
% 6.19/2.15 % (31723)Instructions burned: 344 (million)
% 6.19/2.15 % (31723)------------------------------
% 6.19/2.15 % (31723)------------------------------
% 6.19/2.16 % (31804)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_31470 for (2993ds/258Mi)
% 6.19/2.19 % (31782)Instruction limit reached!
% 6.19/2.19 % (31782)------------------------------
% 6.19/2.19 % (31782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.19 % (31782)Termination reason: Unknown
% 6.19/2.19 % (31782)Termination phase: Saturation
% 6.19/2.19
% 6.19/2.19 % (31782)Memory used [KB]: 7291
% 6.19/2.19 % (31782)Time elapsed: 0.086 s
% 6.19/2.19 % (31782)Instructions burned: 284 (million)
% 6.19/2.19 % (31782)------------------------------
% 6.19/2.19 % (31782)------------------------------
% 6.19/2.20 % (31818)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_31470 for (2993ds/90Mi)
% 6.54/2.20 % (31779)Instruction limit reached!
% 6.54/2.20 % (31779)------------------------------
% 6.54/2.20 % (31779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.20 % (31779)Termination reason: Unknown
% 6.54/2.20 % (31779)Termination phase: Saturation
% 6.54/2.20
% 6.54/2.20 % (31779)Memory used [KB]: 7291
% 6.54/2.20 % (31779)Time elapsed: 0.100 s
% 6.54/2.20 % (31779)Instructions burned: 339 (million)
% 6.54/2.20 % (31779)------------------------------
% 6.54/2.20 % (31779)------------------------------
% 6.54/2.21 % (31822)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_31470 for (2993ds/231Mi)
% 6.54/2.21 % (31799)Instruction limit reached!
% 6.54/2.21 % (31799)------------------------------
% 6.54/2.21 % (31799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.21 % (31799)Termination reason: Unknown
% 6.54/2.21 % (31799)Termination phase: Saturation
% 6.54/2.21
% 6.54/2.21 % (31799)Memory used [KB]: 7547
% 6.54/2.21 % (31799)Time elapsed: 0.058 s
% 6.54/2.21 % (31799)Instructions burned: 195 (million)
% 6.54/2.21 % (31799)------------------------------
% 6.54/2.21 % (31799)------------------------------
% 6.54/2.22 % (31793)Instruction limit reached!
% 6.54/2.22 % (31793)------------------------------
% 6.54/2.22 % (31793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.22 % (31793)Termination reason: Unknown
% 6.54/2.22 % (31793)Termination phase: Saturation
% 6.54/2.22
% 6.54/2.22 % (31793)Memory used [KB]: 7803
% 6.54/2.22 % (31793)Time elapsed: 0.083 s
% 6.54/2.22 % (31793)Instructions burned: 299 (million)
% 6.54/2.22 % (31793)------------------------------
% 6.54/2.22 % (31793)------------------------------
% 6.54/2.22 % (31824)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_31470 for (2993ds/458Mi)
% 6.54/2.22 % (31818)Instruction limit reached!
% 6.54/2.22 % (31818)------------------------------
% 6.54/2.22 % (31818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.22 % (31818)Termination reason: Unknown
% 6.54/2.22 % (31818)Termination phase: Saturation
% 6.54/2.22
% 6.54/2.22 % (31818)Memory used [KB]: 6524
% 6.54/2.22 % (31818)Time elapsed: 0.027 s
% 6.54/2.22 % (31818)Instructions burned: 91 (million)
% 6.54/2.22 % (31818)------------------------------
% 6.54/2.22 % (31818)------------------------------
% 6.54/2.23 % (31826)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_31470 for (2993ds/31Mi)
% 6.54/2.23 % (31828)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_31470 for (2993ds/297Mi)
% 6.54/2.23 % (31751)Instruction limit reached!
% 6.54/2.23 % (31751)------------------------------
% 6.54/2.23 % (31751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.23 % (31751)Termination reason: Unknown
% 6.54/2.23 % (31751)Termination phase: Saturation
% 6.54/2.23
% 6.54/2.23 % (31751)Memory used [KB]: 8443
% 6.54/2.23 % (31751)Time elapsed: 0.188 s
% 6.54/2.23 % (31751)Instructions burned: 616 (million)
% 6.54/2.23 % (31751)------------------------------
% 6.54/2.23 % (31751)------------------------------
% 6.54/2.24 % (31826)Instruction limit reached!
% 6.54/2.24 % (31826)------------------------------
% 6.54/2.24 % (31826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.24 % (31826)Termination reason: Unknown
% 6.54/2.24 % (31826)Termination phase: Preprocessing 3
% 6.54/2.24
% 6.54/2.24 % (31826)Memory used [KB]: 1663
% 6.54/2.24 % (31826)Time elapsed: 0.011 s
% 6.54/2.24 % (31826)Instructions burned: 31 (million)
% 6.54/2.24 % (31826)------------------------------
% 6.54/2.24 % (31826)------------------------------
% 6.54/2.24 % (31804)Instruction limit reached!
% 6.54/2.24 % (31804)------------------------------
% 6.54/2.24 % (31804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.24 % (31804)Termination reason: Unknown
% 6.54/2.24 % (31804)Termination phase: Saturation
% 6.54/2.24
% 6.54/2.24 % (31804)Memory used [KB]: 7291
% 6.54/2.24 % (31804)Time elapsed: 0.078 s
% 6.54/2.24 % (31804)Instructions burned: 258 (million)
% 6.54/2.24 % (31804)------------------------------
% 6.54/2.24 % (31804)------------------------------
% 6.54/2.24 % (31670)Instruction limit reached!
% 6.54/2.24 % (31670)------------------------------
% 6.54/2.24 % (31670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.24 % (31670)Termination reason: Unknown
% 6.54/2.24 % (31670)Termination phase: Saturation
% 6.54/2.24
% 6.54/2.24 % (31670)Memory used [KB]: 8187
% 6.54/2.24 % (31670)Time elapsed: 0.353 s
% 6.54/2.24 % (31670)Instructions burned: 1088 (million)
% 6.54/2.24 % (31670)------------------------------
% 6.54/2.24 % (31670)------------------------------
% 6.54/2.24 % (31835)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_31470 for (2993ds/987Mi)
% 6.54/2.24 % (31836)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_31470 for (2993ds/182Mi)
% 6.54/2.25 % (31837)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_31470 for (2993ds/182Mi)
% 6.54/2.25 % (31838)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_31470 for (2993ds/154Mi)
% 6.54/2.27 % (31822)Instruction limit reached!
% 6.54/2.27 % (31822)------------------------------
% 6.54/2.27 % (31822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.27 % (31822)Termination reason: Unknown
% 6.54/2.27 % (31822)Termination phase: Saturation
% 6.54/2.27
% 6.54/2.27 % (31822)Memory used [KB]: 7164
% 6.54/2.27 % (31822)Time elapsed: 0.068 s
% 6.54/2.27 % (31822)Instructions burned: 233 (million)
% 6.54/2.27 % (31822)------------------------------
% 6.54/2.27 % (31822)------------------------------
% 6.54/2.28 % (31845)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_31470 for (2992ds/79Mi)
% 6.54/2.29 % (31838)Refutation not found, incomplete strategy
% 6.54/2.29 % (31838)------------------------------
% 6.54/2.29 % (31838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.29 % (31838)Termination reason: Refutation not found, incomplete strategy
% 6.54/2.29
% 6.54/2.29
% 6.54/2.29 % (31838)Memory used [KB]: 7036
% 6.54/2.29 % (31838)Time elapsed: 0.040 s
% 6.54/2.29 % (31838)Instructions burned: 144 (million)
% 6.54/2.29 % (31838)------------------------------
% 6.54/2.29 % (31838)------------------------------
% 7.33/2.30 % (31836)Instruction limit reached!
% 7.33/2.30 % (31836)------------------------------
% 7.33/2.30 % (31836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.30 % (31836)Termination reason: Unknown
% 7.33/2.30 % (31836)Termination phase: Saturation
% 7.33/2.30
% 7.33/2.30 % (31836)Memory used [KB]: 6908
% 7.33/2.30 % (31836)Time elapsed: 0.055 s
% 7.33/2.30 % (31836)Instructions burned: 183 (million)
% 7.33/2.30 % (31836)------------------------------
% 7.33/2.30 % (31836)------------------------------
% 7.33/2.30 % (31850)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_31470 for (2992ds/216Mi)
% 7.33/2.31 % (31837)Instruction limit reached!
% 7.33/2.31 % (31837)------------------------------
% 7.33/2.31 % (31837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.31 % (31837)Termination reason: Unknown
% 7.33/2.31 % (31837)Termination phase: Saturation
% 7.33/2.31
% 7.33/2.31 % (31837)Memory used [KB]: 6908
% 7.33/2.31 % (31837)Time elapsed: 0.080 s
% 7.33/2.31 % (31837)Instructions burned: 184 (million)
% 7.33/2.31 % (31837)------------------------------
% 7.33/2.31 % (31837)------------------------------
% 7.33/2.31 % (31845)Instruction limit reached!
% 7.33/2.31 % (31845)------------------------------
% 7.33/2.31 % (31845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.31 % (31845)Termination reason: Unknown
% 7.33/2.31 % (31845)Termination phase: Saturation
% 7.33/2.31
% 7.33/2.31 % (31845)Memory used [KB]: 6524
% 7.33/2.31 % (31845)Time elapsed: 0.024 s
% 7.33/2.31 % (31845)Instructions burned: 81 (million)
% 7.33/2.31 % (31845)------------------------------
% 7.33/2.31 % (31845)------------------------------
% 7.33/2.31 % (31854)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_31470 for (2992ds/114Mi)
% 7.33/2.32 % (31859)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_31470 for (2992ds/922Mi)
% 7.33/2.32 % (31860)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_31470 for (2992ds/182Mi)
% 7.33/2.32 % (31828)Instruction limit reached!
% 7.33/2.32 % (31828)------------------------------
% 7.33/2.32 % (31828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.32 % (31828)Termination reason: Unknown
% 7.33/2.32 % (31828)Termination phase: Saturation
% 7.33/2.32
% 7.33/2.32 % (31828)Memory used [KB]: 7036
% 7.33/2.32 % (31828)Time elapsed: 0.087 s
% 7.33/2.32 % (31828)Instructions burned: 298 (million)
% 7.33/2.32 % (31828)------------------------------
% 7.33/2.32 % (31828)------------------------------
% 7.33/2.33 % (31868)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_31470 for (2992ds/164Mi)
% 7.33/2.34 % (31854)Instruction limit reached!
% 7.33/2.34 % (31854)------------------------------
% 7.33/2.34 % (31854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.34 % (31854)Termination reason: Unknown
% 7.33/2.34 % (31854)Termination phase: Saturation
% 7.33/2.34
% 7.33/2.34 % (31854)Memory used [KB]: 6652
% 7.33/2.34 % (31854)Time elapsed: 0.033 s
% 7.33/2.34 % (31854)Instructions burned: 114 (million)
% 7.33/2.34 % (31854)------------------------------
% 7.33/2.34 % (31854)------------------------------
% 7.33/2.35 % (31882)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_31470 for (2991ds/50Mi)
% 7.33/2.36 % (31824)Instruction limit reached!
% 7.33/2.36 % (31824)------------------------------
% 7.33/2.36 % (31824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.36 % (31824)Termination reason: Unknown
% 7.33/2.36 % (31824)Termination phase: Saturation
% 7.33/2.36
% 7.33/2.36 % (31824)Memory used [KB]: 7675
% 7.33/2.36 % (31824)Time elapsed: 0.146 s
% 7.33/2.36 % (31824)Instructions burned: 459 (million)
% 7.33/2.36 % (31824)------------------------------
% 7.33/2.36 % (31824)------------------------------
% 7.33/2.36 % (31850)Instruction limit reached!
% 7.33/2.36 % (31850)------------------------------
% 7.33/2.36 % (31850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.36 % (31850)Termination reason: Unknown
% 7.33/2.36 % (31850)Termination phase: Saturation
% 7.33/2.36
% 7.33/2.36 % (31850)Memory used [KB]: 7291
% 7.33/2.36 % (31850)Time elapsed: 0.061 s
% 7.33/2.36 % (31850)Instructions burned: 217 (million)
% 7.33/2.36 % (31850)------------------------------
% 7.33/2.36 % (31850)------------------------------
% 7.33/2.36 % (31882)Instruction limit reached!
% 7.33/2.36 % (31882)------------------------------
% 7.33/2.36 % (31882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.36 % (31882)Termination reason: Unknown
% 7.33/2.36 % (31882)Termination phase: Clausification
% 7.33/2.36
% 7.33/2.36 % (31882)Memory used [KB]: 1791
% 7.33/2.36 % (31882)Time elapsed: 0.014 s
% 7.33/2.36 % (31882)Instructions burned: 50 (million)
% 7.33/2.36 % (31882)------------------------------
% 7.33/2.36 % (31882)------------------------------
% 7.33/2.37 % (31860)Instruction limit reached!
% 7.33/2.37 % (31860)------------------------------
% 7.33/2.37 % (31860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.37 % (31860)Termination reason: Unknown
% 7.33/2.37 % (31860)Termination phase: Saturation
% 7.33/2.37
% 7.33/2.37 % (31860)Memory used [KB]: 6780
% 7.33/2.37 % (31860)Time elapsed: 0.051 s
% 7.33/2.37 % (31860)Instructions burned: 184 (million)
% 7.33/2.37 % (31860)------------------------------
% 7.33/2.37 % (31860)------------------------------
% 7.33/2.37 % (31890)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_31470 for (2991ds/368Mi)
% 7.33/2.37 % (31868)Instruction limit reached!
% 7.33/2.37 % (31868)------------------------------
% 7.33/2.37 % (31868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.37 % (31868)Termination reason: Unknown
% 7.33/2.37 % (31868)Termination phase: Saturation
% 7.33/2.37
% 7.33/2.37 % (31868)Memory used [KB]: 2302
% 7.33/2.37 % (31868)Time elapsed: 0.046 s
% 7.33/2.37 % (31868)Instructions burned: 164 (million)
% 7.33/2.37 % (31868)------------------------------
% 7.33/2.37 % (31868)------------------------------
% 7.33/2.37 % (31891)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_31470 for (2991ds/1021Mi)
% 7.33/2.37 % (31892)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_31470 for (2991ds/267Mi)
% 7.33/2.38 % (31894)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_31470 for (2991ds/204Mi)
% 7.33/2.38 % (31898)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_31470 for (2991ds/26Mi)
% 7.33/2.39 % (31898)Instruction limit reached!
% 7.33/2.39 % (31898)------------------------------
% 7.33/2.39 % (31898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.39 % (31898)Termination reason: Unknown
% 7.33/2.39 % (31898)Termination phase: shuffling
% 7.33/2.39
% 7.33/2.39 % (31898)Memory used [KB]: 1791
% 7.33/2.39 % (31898)Time elapsed: 0.009 s
% 7.33/2.39 % (31898)Instructions burned: 29 (million)
% 7.33/2.39 % (31898)------------------------------
% 7.33/2.39 % (31898)------------------------------
% 8.01/2.40 % (31899)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_31470 for (2991ds/53Mi)
% 8.01/2.41 % (31899)Instruction limit reached!
% 8.01/2.41 % (31899)------------------------------
% 8.01/2.41 % (31899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.41 % (31899)Termination reason: Unknown
% 8.01/2.41 % (31899)Termination phase: Property scanning
% 8.01/2.41
% 8.01/2.41 % (31899)Memory used [KB]: 2046
% 8.01/2.41 % (31899)Time elapsed: 0.015 s
% 8.01/2.41 % (31899)Instructions burned: 54 (million)
% 8.01/2.41 % (31899)------------------------------
% 8.01/2.41 % (31899)------------------------------
% 8.01/2.42 % (31900)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_31470 for (2991ds/4436Mi)
% 8.01/2.44 % (31894)Instruction limit reached!
% 8.01/2.44 % (31894)------------------------------
% 8.01/2.44 % (31894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.44 % (31894)Termination reason: Unknown
% 8.01/2.44 % (31894)Termination phase: Saturation
% 8.01/2.44
% 8.01/2.44 % (31894)Memory used [KB]: 7036
% 8.01/2.44 % (31894)Time elapsed: 0.063 s
% 8.01/2.44 % (31894)Instructions burned: 205 (million)
% 8.01/2.44 % (31894)------------------------------
% 8.01/2.44 % (31894)------------------------------
% 8.01/2.45 % (31901)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_31470 for (2990ds/1539Mi)
% 8.01/2.45 % (31892)Instruction limit reached!
% 8.01/2.45 % (31892)------------------------------
% 8.01/2.45 % (31892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.45 % (31892)Termination reason: Unknown
% 8.01/2.45 % (31892)Termination phase: Saturation
% 8.01/2.45
% 8.01/2.45 % (31892)Memory used [KB]: 7036
% 8.01/2.45 % (31892)Time elapsed: 0.081 s
% 8.01/2.45 % (31892)Instructions burned: 269 (million)
% 8.01/2.45 % (31892)------------------------------
% 8.01/2.45 % (31892)------------------------------
% 8.01/2.46 % (31902)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_31470 for (2990ds/408Mi)
% 8.01/2.48 % (31890)Instruction limit reached!
% 8.01/2.48 % (31890)------------------------------
% 8.01/2.48 % (31890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.48 % (31890)Termination reason: Unknown
% 8.01/2.48 % (31890)Termination phase: Saturation
% 8.01/2.48
% 8.01/2.48 % (31890)Memory used [KB]: 7931
% 8.01/2.48 % (31890)Time elapsed: 0.106 s
% 8.01/2.48 % (31890)Instructions burned: 368 (million)
% 8.01/2.48 % (31890)------------------------------
% 8.01/2.48 % (31890)------------------------------
% 8.01/2.49 % (31903)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_31470 for (2990ds/5205Mi)
% 8.31/2.54 % (31835)Instruction limit reached!
% 8.31/2.54 % (31835)------------------------------
% 8.31/2.54 % (31835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.31/2.54 % (31835)Termination reason: Unknown
% 8.31/2.54 % (31835)Termination phase: Saturation
% 8.31/2.54
% 8.31/2.54 % (31835)Memory used [KB]: 8699
% 8.31/2.54 % (31835)Time elapsed: 0.302 s
% 8.31/2.54 % (31835)Instructions burned: 988 (million)
% 8.31/2.54 % (31835)------------------------------
% 8.31/2.54 % (31835)------------------------------
% 8.31/2.55 % (31904)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_31470 for (2989ds/1913Mi)
% 8.31/2.58 % (31902)Instruction limit reached!
% 8.31/2.58 % (31902)------------------------------
% 8.31/2.58 % (31902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.31/2.58 % (31902)Termination reason: Unknown
% 8.31/2.58 % (31902)Termination phase: Saturation
% 8.31/2.58
% 8.31/2.58 % (31902)Memory used [KB]: 7803
% 8.31/2.58 % (31902)Time elapsed: 0.123 s
% 8.31/2.58 % (31902)Instructions burned: 410 (million)
% 8.31/2.58 % (31902)------------------------------
% 8.31/2.58 % (31902)------------------------------
% 8.31/2.59 % (31905)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_31470 for (2989ds/4350Mi)
% 8.76/2.61 % (31859)Instruction limit reached!
% 8.76/2.61 % (31859)------------------------------
% 8.76/2.61 % (31859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.76/2.61 % (31859)Termination reason: Unknown
% 8.76/2.61 % (31859)Termination phase: Saturation
% 8.76/2.61
% 8.76/2.61 % (31859)Memory used [KB]: 8187
% 8.76/2.61 % (31859)Time elapsed: 0.294 s
% 8.76/2.61 % (31859)Instructions burned: 922 (million)
% 8.76/2.61 % (31859)------------------------------
% 8.76/2.61 % (31859)------------------------------
% 8.76/2.62 % (31906)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_31470 for (2989ds/68Mi)
% 8.76/2.64 % (31906)Instruction limit reached!
% 8.76/2.64 % (31906)------------------------------
% 8.76/2.64 % (31906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.76/2.64 % (31906)Termination reason: Unknown
% 8.76/2.64 % (31906)Termination phase: Property scanning
% 8.76/2.64
% 8.76/2.64 % (31906)Memory used [KB]: 1918
% 8.76/2.64 % (31906)Time elapsed: 0.022 s
% 8.76/2.64 % (31906)Instructions burned: 71 (million)
% 8.76/2.64 % (31906)------------------------------
% 8.76/2.64 % (31906)------------------------------
% 8.76/2.65 % (31907)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_31470 for (2988ds/358Mi)
% 8.76/2.69 % (31891)Instruction limit reached!
% 8.76/2.69 % (31891)------------------------------
% 8.76/2.69 % (31891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.76/2.69 % (31891)Termination reason: Unknown
% 8.76/2.69 % (31891)Termination phase: Saturation
% 8.76/2.69
% 8.76/2.69 % (31891)Memory used [KB]: 8443
% 8.76/2.69 % (31891)Time elapsed: 0.322 s
% 8.76/2.69 % (31891)Instructions burned: 1021 (million)
% 8.76/2.69 % (31891)------------------------------
% 8.76/2.69 % (31891)------------------------------
% 9.42/2.70 % (31908)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_31470 for (2988ds/31Mi)
% 9.42/2.71 % (31908)Instruction limit reached!
% 9.42/2.71 % (31908)------------------------------
% 9.42/2.71 % (31908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.42/2.71 % (31908)Termination reason: Unknown
% 9.42/2.71 % (31908)Termination phase: Preprocessing 3
% 9.42/2.71
% 9.42/2.71 % (31908)Memory used [KB]: 1663
% 9.42/2.71 % (31908)Time elapsed: 0.011 s
% 9.42/2.71 % (31908)Instructions burned: 33 (million)
% 9.42/2.71 % (31908)------------------------------
% 9.42/2.71 % (31908)------------------------------
% 9.42/2.72 % (31909)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_31470 for (2988ds/279Mi)
% 9.42/2.76 % (31909)Refutation not found, incomplete strategy
% 9.42/2.76 % (31909)------------------------------
% 9.42/2.76 % (31909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.42/2.76 % (31909)Termination reason: Refutation not found, incomplete strategy
% 9.42/2.76
% 9.42/2.76
% 9.42/2.76 % (31909)Memory used [KB]: 6908
% 9.42/2.76 % (31909)Time elapsed: 0.035 s
% 9.42/2.76 % (31909)Instructions burned: 130 (million)
% 9.42/2.76 % (31909)------------------------------
% 9.42/2.76 % (31909)------------------------------
% 9.42/2.76 % (31907)Instruction limit reached!
% 9.42/2.76 % (31907)------------------------------
% 9.42/2.76 % (31907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.42/2.76 % (31907)Termination reason: Unknown
% 9.42/2.76 % (31907)Termination phase: Saturation
% 9.42/2.76
% 9.42/2.76 % (31907)Memory used [KB]: 7291
% 9.42/2.76 % (31907)Time elapsed: 0.112 s
% 9.42/2.76 % (31907)Instructions burned: 359 (million)
% 9.42/2.76 % (31907)------------------------------
% 9.42/2.76 % (31907)------------------------------
% 9.42/2.77 % (31910)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_31470 for (2987ds/258Mi)
% 9.42/2.77 % (31911)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_31470 for (2987ds/26Mi)
% 9.42/2.78 % (31911)Instruction limit reached!
% 9.42/2.78 % (31911)------------------------------
% 9.42/2.78 % (31911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.42/2.78 % (31911)Termination reason: Unknown
% 9.42/2.78 % (31911)Termination phase: shuffling
% 9.42/2.78
% 9.42/2.78 % (31911)Memory used [KB]: 1663
% 9.42/2.78 % (31911)Time elapsed: 0.008 s
% 9.42/2.78 % (31911)Instructions burned: 26 (million)
% 9.42/2.78 % (31911)------------------------------
% 9.42/2.78 % (31911)------------------------------
% 9.42/2.79 % (31912)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_31470 for (2987ds/995Mi)
% 9.63/2.85 % (31910)Instruction limit reached!
% 9.63/2.85 % (31910)------------------------------
% 9.63/2.85 % (31910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.63/2.85 % (31910)Termination reason: Unknown
% 9.63/2.85 % (31910)Termination phase: Saturation
% 9.63/2.85
% 9.63/2.85 % (31910)Memory used [KB]: 7291
% 9.63/2.85 % (31910)Time elapsed: 0.081 s
% 9.63/2.85 % (31910)Instructions burned: 258 (million)
% 9.63/2.85 % (31910)------------------------------
% 9.63/2.85 % (31910)------------------------------
% 9.63/2.86 % (31913)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_31470 for (2986ds/373Mi)
% 9.71/2.93 % (31901)Instruction limit reached!
% 9.71/2.93 % (31901)------------------------------
% 9.71/2.93 % (31901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.71/2.93 % (31901)Termination reason: Unknown
% 9.71/2.93 % (31901)Termination phase: Saturation
% 9.71/2.93
% 9.71/2.93 % (31901)Memory used [KB]: 9083
% 9.71/2.93 % (31901)Time elapsed: 0.485 s
% 9.71/2.93 % (31901)Instructions burned: 1542 (million)
% 9.71/2.93 % (31901)------------------------------
% 9.71/2.93 % (31901)------------------------------
% 9.71/2.94 % (31914)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_31470 for (2986ds/253Mi)
% 9.71/2.97 % (31913)Instruction limit reached!
% 9.71/2.97 % (31913)------------------------------
% 9.71/2.97 % (31913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.71/2.97 % (31913)Termination reason: Unknown
% 9.71/2.97 % (31913)Termination phase: Saturation
% 9.71/2.97
% 9.71/2.97 % (31913)Memory used [KB]: 7419
% 9.71/2.97 % (31913)Time elapsed: 0.115 s
% 9.71/2.97 % (31913)Instructions burned: 374 (million)
% 9.71/2.97 % (31913)------------------------------
% 9.71/2.97 % (31913)------------------------------
% 9.71/2.98 % (31915)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_31470 for (2985ds/832Mi)
% 9.71/3.01 % (31914)Instruction limit reached!
% 9.71/3.01 % (31914)------------------------------
% 9.71/3.01 % (31914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.71/3.01 % (31914)Termination reason: Unknown
% 9.71/3.01 % (31914)Termination phase: Saturation
% 9.71/3.01
% 9.71/3.01 % (31914)Memory used [KB]: 7547
% 9.71/3.01 % (31914)Time elapsed: 0.073 s
% 9.71/3.01 % (31914)Instructions burned: 254 (million)
% 9.71/3.01 % (31914)------------------------------
% 9.71/3.01 % (31914)------------------------------
% 9.71/3.02 % (31916)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_31470 for (2985ds/668Mi)
% 12.74/3.09 % (31912)Instruction limit reached!
% 12.74/3.09 % (31912)------------------------------
% 12.74/3.09 % (31912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.74/3.09 % (31912)Termination reason: Unknown
% 12.74/3.09 % (31912)Termination phase: Saturation
% 12.74/3.09
% 12.74/3.09 % (31912)Memory used [KB]: 9083
% 12.74/3.09 % (31912)Time elapsed: 0.301 s
% 12.74/3.09 % (31912)Instructions burned: 997 (million)
% 12.74/3.09 % (31912)------------------------------
% 12.74/3.09 % (31912)------------------------------
% 12.74/3.10 % (31917)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_31470 for (2984ds/40Mi)
% 12.74/3.11 % (31917)Instruction limit reached!
% 12.74/3.11 % (31917)------------------------------
% 12.74/3.11 % (31917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.74/3.11 % (31917)Termination reason: Unknown
% 12.74/3.11 % (31917)Termination phase: Property scanning
% 12.74/3.11
% 12.74/3.11 % (31917)Memory used [KB]: 1918
% 12.74/3.11 % (31917)Time elapsed: 0.013 s
% 12.74/3.11 % (31917)Instructions burned: 42 (million)
% 12.74/3.11 % (31917)------------------------------
% 12.74/3.11 % (31917)------------------------------
% 12.74/3.12 % (31918)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_31470 for (2984ds/294Mi)
% 12.74/3.12 % (31903)First to succeed.
% 13.34/3.13 % (31903)Refutation found. Thanks to Tanya!
% 13.34/3.13 % SZS status Theorem for DTF2THF_31470
% 13.34/3.13 % SZS output start Proof for DTF2THF_31470
% 13.34/3.13 thf(type_def_5, type, config256849571t_unit: $tType).
% 13.34/3.13 thf(type_def_6, type, message_p_v: $tType).
% 13.34/3.13 thf(type_def_7, type, nat: $tType).
% 13.34/3.13 thf(type_def_9, type, p: $tType).
% 13.34/3.13 thf(type_def_10, type, list_c1059388851t_unit: $tType).
% 13.34/3.13 thf(type_def_11, type, list_message_p_v: $tType).
% 13.34/3.13 thf(type_def_12, type, set_message_p_v: $tType).
% 13.34/3.13 thf(func_def_0, type, list_c1059388851t_unit: $tType).
% 13.34/3.13 thf(func_def_1, type, config256849571t_unit: $tType).
% 13.34/3.13 thf(func_def_2, type, list_message_p_v: $tType).
% 13.34/3.13 thf(func_def_3, type, set_message_p_v: $tType).
% 13.34/3.13 thf(func_def_4, type, message_p_v: $tType).
% 13.34/3.13 thf(func_def_5, type, nat: $tType).
% 13.34/3.13 thf(func_def_6, type, p: $tType).
% 13.34/3.13 thf(func_def_7, type, msgs_p1029620568t_unit: config256849571t_unit > message_p_v > nat).
% 13.34/3.13 thf(func_def_8, type, enabled_p_v_s: config256849571t_unit > message_p_v > $o).
% 13.34/3.13 thf(func_def_9, type, isReceiverOf_p_v: p > message_p_v > $o).
% 13.34/3.13 thf(func_def_10, type, firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o).
% 13.34/3.13 thf(func_def_11, type, minus_minus_nat: nat > nat > nat).
% 13.34/3.13 thf(func_def_12, type, one_one_nat: nat).
% 13.34/3.13 thf(func_def_13, type, zero_zero_nat: nat).
% 13.34/3.13 thf(func_def_14, type, prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o).
% 13.34/3.13 thf(func_def_15, type, prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o).
% 13.34/3.13 thf(func_def_16, type, last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit).
% 13.34/3.13 thf(func_def_17, type, last_message_p_v: list_message_p_v > message_p_v).
% 13.34/3.13 thf(func_def_18, type, nil_co1338500125t_unit: list_c1059388851t_unit).
% 13.34/3.13 thf(func_def_19, type, nil_message_p_v: list_message_p_v).
% 13.34/3.13 thf(func_def_20, type, nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit).
% 13.34/3.13 thf(func_def_21, type, nth_message_p_v: list_message_p_v > nat > message_p_v).
% 13.34/3.13 thf(func_def_22, type, suc: nat > nat).
% 13.34/3.13 thf(func_def_23, type, size_s1406904903t_unit: list_c1059388851t_unit > nat).
% 13.34/3.13 thf(func_def_24, type, size_s1168481041ge_p_v: list_message_p_v > nat).
% 13.34/3.13 thf(func_def_25, type, ord_less_nat: nat > nat > $o).
% 13.34/3.13 thf(func_def_26, type, ord_less_eq_nat: nat > nat > $o).
% 13.34/3.13 thf(func_def_27, type, member_message_p_v: message_p_v > set_message_p_v > $o).
% 13.34/3.13 thf(func_def_28, type, fe: nat > list_c1059388851t_unit).
% 13.34/3.13 thf(func_def_29, type, firstOccSet: nat > set_message_p_v).
% 13.34/3.13 thf(func_def_30, type, ft: nat > list_message_p_v).
% 13.34/3.13 thf(func_def_31, type, index: nat).
% 13.34/3.13 thf(func_def_32, type, msgInSet: message_p_v).
% 13.34/3.13 thf(func_def_33, type, msg: message_p_v).
% 13.34/3.13 thf(func_def_34, type, n0: nat).
% 13.34/3.13 thf(func_def_35, type, n1: nat).
% 13.34/3.13 thf(func_def_36, type, nMsg: nat).
% 13.34/3.13 thf(func_def_37, type, n: nat).
% 13.34/3.13 thf(func_def_38, type, p2: p).
% 13.34/3.13 thf(func_def_61, type, ph1: !>[X0: $tType]:(X0)).
% 13.34/3.13 thf(func_def_62, type, sK2: p).
% 13.34/3.13 thf(func_def_63, type, sK3: p).
% 13.34/3.13 thf(func_def_64, type, sK4: nat > list_message_p_v).
% 13.34/3.13 thf(func_def_65, type, sK5: nat > list_c1059388851t_unit).
% 13.34/3.13 thf(func_def_66, type, sK6: nat).
% 13.34/3.13 thf(f13703,plain,(
% 13.34/3.13 $false),
% 13.34/3.13 inference(trivial_inequality_removal,[status(thm)],[f13702])).
% 13.34/3.13 thf(f13702,plain,(
% 13.34/3.13 ($true = $false)),
% 13.34/3.13 inference(boolean_simplification,[status(thm)],[f13701])).
% 13.34/3.13 thf(f13701,plain,(
% 13.34/3.13 ((~ $false) = $false)),
% 13.34/3.13 inference(forward_demodulation,[status(thm)],[f13700,f5274])).
% 13.34/3.13 thf(f5274,plain,(
% 13.34/3.13 ((ord_less_nat @ nMsg @ sK6) = $false)),
% 13.34/3.13 inference(superposition,[status(thm)],[f1730,f5246])).
% 13.34/3.13 thf(f5246,plain,(
% 13.34/3.13 (nMsg = (suc @ sK6))),
% 13.34/3.13 inference(equality_proxy_clausification,[status(thm)],[f5214])).
% 13.34/3.13 thf(f5214,plain,(
% 13.34/3.13 ($true = ((suc @ sK6) = nMsg))),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f5211])).
% 13.34/3.13 thf(f5211,plain,(
% 13.34/3.13 (((^[Y0 : nat]: ((suc @ Y0) = nMsg)) @ sK6) = $true)),
% 13.34/3.13 inference(sigma_clausification,[status(thm)],[f2486])).
% 13.34/3.13 thf(f2486,plain,(
% 13.34/3.13 ($true = (?? @ nat @ (^[Y0 : nat]: ((suc @ Y0) = nMsg))))),
% 13.34/3.13 inference(boolean_simplification,[status(thm)],[f2461])).
% 13.34/3.13 thf(f2461,plain,(
% 13.34/3.13 ($true = ($true => (?? @ nat @ (^[Y0 : nat]: ((suc @ Y0) = nMsg)))))),
% 13.34/3.13 inference(superposition,[status(thm)],[f2456,f1234])).
% 13.34/3.13 thf(f1234,plain,(
% 13.34/3.13 ((ord_less_nat @ (size_s1406904903t_unit @ nil_co1338500125t_unit) @ nMsg) = $true)),
% 13.34/3.13 inference(forward_demodulation,[status(thm)],[f1087,f1107])).
% 13.34/3.13 thf(f1107,plain,(
% 13.34/3.13 ((size_s1406904903t_unit @ nil_co1338500125t_unit) = (size_s1168481041ge_p_v @ nil_message_p_v))),
% 13.34/3.13 inference(definition_unfolding,[status(thm)],[f939,f909])).
% 13.34/3.13 thf(f909,plain,(
% 13.34/3.13 (zero_zero_nat = (size_s1168481041ge_p_v @ nil_message_p_v))),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f556])).
% 13.34/3.13 thf(f556,plain,(
% 13.34/3.13 (zero_zero_nat = (size_s1168481041ge_p_v @ nil_message_p_v))),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f223])).
% 13.34/3.13 thf(f223,axiom,(
% 13.34/3.13 (zero_zero_nat = (size_s1168481041ge_p_v @ nil_message_p_v))),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_222_list_Osize_I3_J)).
% 13.34/3.13 thf(f939,plain,(
% 13.34/3.13 (zero_zero_nat = (size_s1406904903t_unit @ nil_co1338500125t_unit))),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f555])).
% 13.34/3.13 thf(f555,plain,(
% 13.34/3.13 (zero_zero_nat = (size_s1406904903t_unit @ nil_co1338500125t_unit))),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f222])).
% 13.34/3.13 thf(f222,axiom,(
% 13.34/3.13 (zero_zero_nat = (size_s1406904903t_unit @ nil_co1338500125t_unit))),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_221_list_Osize_I3_J)).
% 13.34/3.13 thf(f1087,plain,(
% 13.34/3.13 ($true = (ord_less_nat @ (size_s1168481041ge_p_v @ nil_message_p_v) @ nMsg))),
% 13.34/3.13 inference(definition_unfolding,[status(thm)],[f908,f909])).
% 13.34/3.13 thf(f908,plain,(
% 13.34/3.13 ((ord_less_nat @ zero_zero_nat @ nMsg) = $true)),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f494])).
% 13.34/3.13 thf(f494,plain,(
% 13.34/3.13 ((ord_less_nat @ zero_zero_nat @ nMsg) = $true)),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f493])).
% 13.34/3.13 thf(f493,plain,(
% 13.34/3.13 (ord_less_nat @ zero_zero_nat @ nMsg)),
% 13.34/3.13 inference(rectify,[status(thm)],[f1])).
% 13.34/3.13 thf(f1,axiom,(
% 13.34/3.13 (ord_less_nat @ zero_zero_nat @ nMsg)),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_0_AssumpOcc6_I1_J)).
% 13.34/3.13 thf(f2456,plain,(
% 13.34/3.13 ( ! [X1 : nat] : ((((ord_less_nat @ (size_s1406904903t_unit @ nil_co1338500125t_unit) @ X1) => (?? @ nat @ (^[Y0 : nat]: ((suc @ Y0) = X1)))) = $true)) )),
% 13.34/3.13 inference(forward_demodulation,[status(thm)],[f2455,f1107])).
% 13.34/3.13 thf(f2455,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = ((ord_less_nat @ (size_s1168481041ge_p_v @ nil_message_p_v) @ X1) => (?? @ nat @ (^[Y0 : nat]: ((suc @ Y0) = X1)))))) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f2454])).
% 13.34/3.13 thf(f2454,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: ((ord_less_nat @ (size_s1168481041ge_p_v @ nil_message_p_v) @ Y0) => (?? @ nat @ (^[Y1 : nat]: ((suc @ Y1) = Y0))))) @ X1))) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f1028])).
% 13.34/3.13 thf(f1028,plain,(
% 13.34/3.13 ((!! @ nat @ (^[Y0 : nat]: ((ord_less_nat @ (size_s1168481041ge_p_v @ nil_message_p_v) @ Y0) => (?? @ nat @ (^[Y1 : nat]: ((suc @ Y1) = Y0)))))) = $true)),
% 13.34/3.13 inference(definition_unfolding,[status(thm)],[f810,f909])).
% 13.34/3.13 thf(f810,plain,(
% 13.34/3.13 ((!! @ nat @ (^[Y0 : nat]: ((ord_less_nat @ zero_zero_nat @ Y0) => (?? @ nat @ (^[Y1 : nat]: ((suc @ Y1) = Y0)))))) = $true)),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f402])).
% 13.34/3.13 thf(f402,plain,(
% 13.34/3.13 ((!! @ nat @ (^[Y0 : nat]: ((ord_less_nat @ zero_zero_nat @ Y0) => (?? @ nat @ (^[Y1 : nat]: ((suc @ Y1) = Y0)))))) = $true)),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f401])).
% 13.34/3.13 thf(f401,plain,(
% 13.34/3.13 ! [X0 : nat] : ((ord_less_nat @ zero_zero_nat @ X0) => ? [X1 : nat] : ((suc @ X1) = X0))),
% 13.34/3.13 inference(rectify,[status(thm)],[f94])).
% 13.34/3.13 thf(f94,axiom,(
% 13.34/3.13 ! [X15 : nat] : ((ord_less_nat @ zero_zero_nat @ X15) => ? [X32 : nat] : ((suc @ X32) = X15))),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_93_gr0__implies__Suc)).
% 13.34/3.13 thf(f1730,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (((ord_less_nat @ (suc @ X1) @ X1) = $false)) )),
% 13.34/3.13 inference(not_proxy_clausification,[status(thm)],[f1729])).
% 13.34/3.13 thf(f1729,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = (~ (ord_less_nat @ (suc @ X1) @ X1)))) )),
% 13.34/3.13 inference(boolean_simplification,[status(thm)],[f1728])).
% 13.34/3.13 thf(f1728,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (((~ ((ord_less_nat @ (suc @ X1) @ X1) | $false)) = $true)) )),
% 13.34/3.13 inference(forward_demodulation,[status(thm)],[f1727,f1276])).
% 13.34/3.13 thf(f1276,plain,(
% 13.34/3.13 ( ! [X1 : nat] : ((((suc @ X1) = X1) = $false)) )),
% 13.34/3.13 inference(not_proxy_clausification,[status(thm)],[f1275])).
% 13.34/3.13 thf(f1275,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (((~ ((suc @ X1) = X1)) = $true)) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f1274])).
% 13.34/3.13 thf(f1274,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (~ ((suc @ Y0) = Y0))) @ X1))) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f749])).
% 13.34/3.13 thf(f749,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (~ ((suc @ Y0) = Y0)))))),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f264])).
% 13.34/3.13 thf(f264,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (~ ((suc @ Y0) = Y0)))))),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f263])).
% 13.34/3.13 thf(f263,plain,(
% 13.34/3.13 ! [X0 : nat] : ((suc @ X0) != X0)),
% 13.34/3.13 inference(rectify,[status(thm)],[f32])).
% 13.34/3.13 thf(f32,axiom,(
% 13.34/3.13 ! [X15 : nat] : ((suc @ X15) != X15)),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_31_n__not__Suc__n)).
% 13.34/3.13 thf(f1727,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = (~ ((ord_less_nat @ (suc @ X1) @ X1) | ((suc @ X1) = X1))))) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f1726])).
% 13.34/3.13 thf(f1726,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (~ ((ord_less_nat @ (suc @ Y0) @ Y0) | ((suc @ Y0) = Y0)))) @ X1))) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f1158])).
% 13.34/3.13 thf(f1158,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (~ ((ord_less_nat @ (suc @ Y0) @ Y0) | ((suc @ Y0) = Y0))))))),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f1088])).
% 13.34/3.13 thf(f1088,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (~ ((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ (suc @ Y0) @ Y0)))))),
% 13.34/3.13 inference(definition_unfolding,[status(thm)],[f910,f967])).
% 13.34/3.13 thf(f967,plain,(
% 13.34/3.13 (ord_less_eq_nat = (^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_nat @ Y0 @ Y1) | (Y0 = Y1))))))),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f324])).
% 13.34/3.13 thf(f324,plain,(
% 13.34/3.13 (ord_less_eq_nat = (^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_nat @ Y0 @ Y1) | (Y0 = Y1))))))),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f323])).
% 13.34/3.13 thf(f323,plain,(
% 13.34/3.13 ((^[X0 : nat, X1 : nat] : ((X0 = X1) | (ord_less_nat @ X0 @ X1))) = ord_less_eq_nat)),
% 13.34/3.13 inference(rectify,[status(thm)],[f167])).
% 13.34/3.13 thf(f167,axiom,(
% 13.34/3.13 ((^[X45 : nat, X63 : nat] : ((X45 = X63) | (ord_less_nat @ X45 @ X63))) = ord_less_eq_nat)),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_166_le__eq__less__or__eq)).
% 13.34/3.13 thf(f910,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (~ (ord_less_eq_nat @ (suc @ Y0) @ Y0)))))),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f256])).
% 13.34/3.13 thf(f256,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (~ (ord_less_eq_nat @ (suc @ Y0) @ Y0)))))),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f255])).
% 13.34/3.13 thf(f255,plain,(
% 13.34/3.13 ! [X0 : nat] : ~(ord_less_eq_nat @ (suc @ X0) @ X0)),
% 13.34/3.13 inference(rectify,[status(thm)],[f156])).
% 13.34/3.13 thf(f156,axiom,(
% 13.34/3.13 ! [X15 : nat] : ~(ord_less_eq_nat @ (suc @ X15) @ X15)),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_155_Suc__n__not__le__n)).
% 13.34/3.13 thf(f13700,plain,(
% 13.34/3.13 ((~ (ord_less_nat @ nMsg @ sK6)) = $false)),
% 13.34/3.13 inference(forward_demodulation,[status(thm)],[f13699,f5293])).
% 13.34/3.13 thf(f5293,plain,(
% 13.34/3.13 ($false = (sK6 = nMsg))),
% 13.34/3.13 inference(superposition,[status(thm)],[f3712,f5246])).
% 13.34/3.13 thf(f3712,plain,(
% 13.34/3.13 ( ! [X0 : nat] : (((X0 = (suc @ X0)) = $false)) )),
% 13.34/3.13 inference(superposition,[status(thm)],[f1276,f3612])).
% 13.34/3.13 thf(f3612,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : ((((suc @ X1) = (suc @ X2)) = (X2 = X1))) )),
% 13.34/3.13 inference(equality_proxy_clausification,[status(thm)],[f3603])).
% 13.34/3.13 thf(f3603,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : (($true = (((suc @ X1) = (suc @ X2)) = (X2 = X1)))) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f3602])).
% 13.34/3.13 thf(f3602,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : (($true = ((^[Y0 : nat]: (((suc @ X1) = (suc @ Y0)) = (Y0 = X1))) @ X2))) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f3596])).
% 13.34/3.13 thf(f3596,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: (((suc @ X1) = (suc @ Y0)) = (Y0 = X1)))))) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f3595])).
% 13.34/3.13 thf(f3595,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (((suc @ Y0) = (suc @ Y1)) = (Y1 = Y0))))) @ X1))) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f957])).
% 13.34/3.13 thf(f957,plain,(
% 13.34/3.13 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (((suc @ Y0) = (suc @ Y1)) = (Y1 = Y0)))))) = $true)),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f392])).
% 13.34/3.13 thf(f392,plain,(
% 13.34/3.13 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (((suc @ Y0) = (suc @ Y1)) = (Y1 = Y0)))))) = $true)),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f391])).
% 13.34/3.13 thf(f391,plain,(
% 13.34/3.13 ! [X0 : nat,X1 : nat] : (((suc @ X1) = (suc @ X0)) = (X0 = X1))),
% 13.34/3.13 inference(rectify,[status(thm)],[f19])).
% 13.34/3.13 thf(f19,axiom,(
% 13.34/3.13 ! [X20 : nat,X21 : nat] : (((suc @ X20) = (suc @ X21)) = (X20 = X21))),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_18_nat_Oinject)).
% 13.34/3.13 thf(f13699,plain,(
% 13.34/3.13 ((~ (ord_less_nat @ nMsg @ sK6)) = (sK6 = nMsg))),
% 13.34/3.13 inference(forward_demodulation,[status(thm)],[f13660,f1340])).
% 13.34/3.13 thf(f1340,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (((minus_minus_nat @ (suc @ X1) @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit))) = X1)) )),
% 13.34/3.13 inference(equality_proxy_clausification,[status(thm)],[f1339])).
% 13.34/3.13 thf(f1339,plain,(
% 13.34/3.13 ( ! [X1 : nat] : ((((minus_minus_nat @ (suc @ X1) @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit))) = X1) = $true)) )),
% 13.34/3.13 inference(forward_demodulation,[status(thm)],[f1338,f1107])).
% 13.34/3.13 thf(f1338,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = ((minus_minus_nat @ (suc @ X1) @ (suc @ (size_s1168481041ge_p_v @ nil_message_p_v))) = X1))) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f1337])).
% 13.34/3.13 thf(f1337,plain,(
% 13.34/3.13 ( ! [X1 : nat] : ((((^[Y0 : nat]: ((minus_minus_nat @ (suc @ Y0) @ (suc @ (size_s1168481041ge_p_v @ nil_message_p_v))) = Y0)) @ X1) = $true)) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f1057])).
% 13.34/3.13 thf(f1057,plain,(
% 13.34/3.13 ((!! @ nat @ (^[Y0 : nat]: ((minus_minus_nat @ (suc @ Y0) @ (suc @ (size_s1168481041ge_p_v @ nil_message_p_v))) = Y0))) = $true)),
% 13.34/3.13 inference(definition_unfolding,[status(thm)],[f852,f975])).
% 13.34/3.13 thf(f975,plain,(
% 13.34/3.13 (one_one_nat = (suc @ (size_s1168481041ge_p_v @ nil_message_p_v)))),
% 13.34/3.13 inference(definition_unfolding,[status(thm)],[f771,f909])).
% 13.34/3.13 thf(f771,plain,(
% 13.34/3.13 ((suc @ zero_zero_nat) = one_one_nat)),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f290])).
% 13.34/3.13 thf(f290,plain,(
% 13.34/3.13 ((suc @ zero_zero_nat) = one_one_nat)),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f194])).
% 13.34/3.13 thf(f194,axiom,(
% 13.34/3.13 ((suc @ zero_zero_nat) = one_one_nat)),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_193_One__nat__def)).
% 13.34/3.13 thf(f852,plain,(
% 13.34/3.13 ((!! @ nat @ (^[Y0 : nat]: ((minus_minus_nat @ (suc @ Y0) @ one_one_nat) = Y0))) = $true)),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f338])).
% 13.34/3.13 thf(f338,plain,(
% 13.34/3.13 ((!! @ nat @ (^[Y0 : nat]: ((minus_minus_nat @ (suc @ Y0) @ one_one_nat) = Y0))) = $true)),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f337])).
% 13.34/3.13 thf(f337,plain,(
% 13.34/3.13 ! [X0 : nat] : ((minus_minus_nat @ (suc @ X0) @ one_one_nat) = X0)),
% 13.34/3.13 inference(rectify,[status(thm)],[f128])).
% 13.34/3.13 thf(f128,axiom,(
% 13.34/3.13 ! [X15 : nat] : ((minus_minus_nat @ (suc @ X15) @ one_one_nat) = X15)),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_127_diff__Suc__1)).
% 13.34/3.13 thf(f13660,plain,(
% 13.34/3.13 ((sK6 = (minus_minus_nat @ (suc @ nMsg) @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit)))) = (~ (ord_less_nat @ (minus_minus_nat @ (suc @ nMsg) @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit))) @ sK6)))),
% 13.34/3.13 inference(backward_demodulation,[status(thm)],[f10770,f13626])).
% 13.34/3.13 thf(f13626,plain,(
% 13.34/3.13 ((size_s1406904903t_unit @ (fe @ index)) = (suc @ nMsg))),
% 13.34/3.13 inference(equality_proxy_clausification,[status(thm)],[f11283])).
% 13.34/3.13 thf(f11283,plain,(
% 13.34/3.13 ($true = ((suc @ nMsg) = (size_s1406904903t_unit @ (fe @ index))))),
% 13.34/3.13 inference(backward_demodulation,[status(thm)],[f10904,f11280])).
% 13.34/3.13 thf(f11280,plain,(
% 13.34/3.13 ($true = (ord_less_nat @ nMsg @ (size_s1406904903t_unit @ (fe @ index))))),
% 13.34/3.13 inference(boolean_simplification,[status(thm)],[f11274])).
% 13.34/3.13 thf(f11274,plain,(
% 13.34/3.13 ($true = ($true => (ord_less_nat @ nMsg @ (size_s1406904903t_unit @ (fe @ index)))))),
% 13.34/3.13 inference(superposition,[status(thm)],[f11225,f945])).
% 13.34/3.13 thf(f945,plain,(
% 13.34/3.13 ((firstO1414030372_p_v_s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ nMsg) = $true)),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f653])).
% 13.34/3.13 thf(f653,plain,(
% 13.34/3.13 ((firstO1414030372_p_v_s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ nMsg) = $true)),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f652])).
% 13.34/3.13 thf(f652,plain,(
% 13.34/3.13 (firstO1414030372_p_v_s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ nMsg)),
% 13.34/3.13 inference(rectify,[status(thm)],[f4])).
% 13.34/3.13 thf(f4,axiom,(
% 13.34/3.13 (firstO1414030372_p_v_s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ nMsg)),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_3_AssumptionSubset_I3_J)).
% 13.34/3.13 thf(f11225,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = ((firstO1414030372_p_v_s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ X1) => (ord_less_nat @ X1 @ (size_s1406904903t_unit @ (fe @ index)))))) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f11224])).
% 13.34/3.13 thf(f11224,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: ((firstO1414030372_p_v_s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ Y0) => (ord_less_nat @ Y0 @ (size_s1406904903t_unit @ (fe @ index))))) @ X1))) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f740])).
% 13.34/3.13 thf(f740,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: ((firstO1414030372_p_v_s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ Y0) => (ord_less_nat @ Y0 @ (size_s1406904903t_unit @ (fe @ index)))))))),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f698])).
% 13.34/3.13 thf(f698,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: ((firstO1414030372_p_v_s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ Y0) => (ord_less_nat @ Y0 @ (size_s1406904903t_unit @ (fe @ index)))))))),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f697])).
% 13.34/3.13 thf(f697,plain,(
% 13.34/3.13 ! [X0 : nat] : ((firstO1414030372_p_v_s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ X0) => (ord_less_nat @ X0 @ (size_s1406904903t_unit @ (fe @ index))))),
% 13.34/3.13 inference(rectify,[status(thm)],[f5])).
% 13.34/3.13 thf(f5,axiom,(
% 13.34/3.13 ! [X14 : nat] : ((firstO1414030372_p_v_s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ X14) => (ord_less_nat @ X14 @ (size_s1406904903t_unit @ (fe @ index))))),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_4_SmallIndex)).
% 13.34/3.13 thf(f10904,plain,(
% 13.34/3.13 ((ord_less_nat @ nMsg @ (size_s1406904903t_unit @ (fe @ index))) = ((suc @ nMsg) = (size_s1406904903t_unit @ (fe @ index))))),
% 13.34/3.13 inference(boolean_simplification,[status(thm)],[f10903])).
% 13.34/3.13 thf(f10903,plain,(
% 13.34/3.13 (((suc @ nMsg) = (size_s1406904903t_unit @ (fe @ index))) = (~ (~ (ord_less_nat @ nMsg @ (size_s1406904903t_unit @ (fe @ index))))))),
% 13.34/3.13 inference(forward_demodulation,[status(thm)],[f10759,f2797])).
% 13.34/3.13 thf(f2797,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : (((ord_less_nat @ X1 @ (suc @ X2)) = (~ (ord_less_nat @ X2 @ X1)))) )),
% 13.34/3.13 inference(equality_proxy_clausification,[status(thm)],[f2792])).
% 13.34/3.13 thf(f2792,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : ((((ord_less_nat @ X1 @ (suc @ X2)) = (~ (ord_less_nat @ X2 @ X1))) = $true)) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f2791])).
% 13.34/3.13 thf(f2791,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : ((((^[Y0 : nat]: ((ord_less_nat @ X1 @ (suc @ Y0)) = (~ (ord_less_nat @ Y0 @ X1)))) @ X2) = $true)) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f2783])).
% 13.34/3.13 thf(f2783,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (((!! @ nat @ (^[Y0 : nat]: ((ord_less_nat @ X1 @ (suc @ Y0)) = (~ (ord_less_nat @ Y0 @ X1))))) = $true)) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f2782])).
% 13.34/3.13 thf(f2782,plain,(
% 13.34/3.13 ( ! [X1 : nat] : ((((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_nat @ Y0 @ (suc @ Y1)) = (~ (ord_less_nat @ Y1 @ Y0)))))) @ X1) = $true)) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f961])).
% 13.34/3.13 thf(f961,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_nat @ Y0 @ (suc @ Y1)) = (~ (ord_less_nat @ Y1 @ Y0))))))))),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f700])).
% 13.34/3.13 thf(f700,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_nat @ Y0 @ (suc @ Y1)) = (~ (ord_less_nat @ Y1 @ Y0))))))))),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f699])).
% 13.34/3.13 thf(f699,plain,(
% 13.34/3.13 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X1 @ (suc @ X0)) = ~(ord_less_nat @ X0 @ X1))),
% 13.34/3.13 inference(rectify,[status(thm)],[f70])).
% 13.34/3.13 thf(f70,axiom,(
% 13.34/3.13 ! [X16 : nat,X15 : nat] : ((ord_less_nat @ X15 @ (suc @ X16)) = ~(ord_less_nat @ X16 @ X15))),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_69_not__less__eq)).
% 13.34/3.13 thf(f10759,plain,(
% 13.34/3.13 ((~ (ord_less_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ nMsg))) = ((suc @ nMsg) = (size_s1406904903t_unit @ (fe @ index))))),
% 13.34/3.13 inference(boolean_simplification,[status(thm)],[f10666])).
% 13.34/3.13 thf(f10666,plain,(
% 13.34/3.13 (($false | ((suc @ nMsg) = (size_s1406904903t_unit @ (fe @ index)))) = (~ (ord_less_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ nMsg))))),
% 13.34/3.13 inference(superposition,[status(thm)],[f9402,f4896])).
% 13.34/3.13 thf(f4896,plain,(
% 13.34/3.13 ((ord_less_nat @ (suc @ nMsg) @ (size_s1406904903t_unit @ (fe @ index))) = $false)),
% 13.34/3.13 inference(not_proxy_clausification,[status(thm)],[f4886])).
% 13.34/3.13 thf(f4886,plain,(
% 13.34/3.13 ($true = (~ (ord_less_nat @ (suc @ nMsg) @ (size_s1406904903t_unit @ (fe @ index)))))),
% 13.34/3.13 inference(backward_demodulation,[status(thm)],[f4625,f4885])).
% 13.34/3.13 thf(f4885,plain,(
% 13.34/3.13 ( ! [X0 : nat,X1 : nat] : (((ord_less_nat @ (suc @ X1) @ X0) = (ord_less_nat @ X1 @ (minus_minus_nat @ X0 @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit)))))) )),
% 13.34/3.13 inference(forward_demodulation,[status(thm)],[f4876,f3838])).
% 13.34/3.13 thf(f3838,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : (((ord_less_nat @ (size_s1406904903t_unit @ nil_co1338500125t_unit) @ (minus_minus_nat @ X2 @ X1)) = (ord_less_nat @ X1 @ X2))) )),
% 13.34/3.13 inference(equality_proxy_clausification,[status(thm)],[f3837])).
% 13.34/3.13 thf(f3837,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : ((((ord_less_nat @ X1 @ X2) = (ord_less_nat @ (size_s1406904903t_unit @ nil_co1338500125t_unit) @ (minus_minus_nat @ X2 @ X1))) = $true)) )),
% 13.34/3.13 inference(forward_demodulation,[status(thm)],[f3836,f1107])).
% 13.34/3.13 thf(f3836,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : ((((ord_less_nat @ X1 @ X2) = (ord_less_nat @ (size_s1168481041ge_p_v @ nil_message_p_v) @ (minus_minus_nat @ X2 @ X1))) = $true)) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f3835])).
% 13.34/3.13 thf(f3835,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : ((((^[Y0 : nat]: ((ord_less_nat @ X1 @ Y0) = (ord_less_nat @ (size_s1168481041ge_p_v @ nil_message_p_v) @ (minus_minus_nat @ Y0 @ X1)))) @ X2) = $true)) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f3824])).
% 13.34/3.13 thf(f3824,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((ord_less_nat @ X1 @ Y0) = (ord_less_nat @ (size_s1168481041ge_p_v @ nil_message_p_v) @ (minus_minus_nat @ Y0 @ X1))))))) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f3823])).
% 13.34/3.13 thf(f3823,plain,(
% 13.34/3.13 ( ! [X1 : nat] : ((((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_nat @ Y0 @ Y1) = (ord_less_nat @ (size_s1168481041ge_p_v @ nil_message_p_v) @ (minus_minus_nat @ Y1 @ Y0)))))) @ X1) = $true)) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f1035])).
% 13.34/3.13 thf(f1035,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_nat @ Y0 @ Y1) = (ord_less_nat @ (size_s1168481041ge_p_v @ nil_message_p_v) @ (minus_minus_nat @ Y1 @ Y0))))))))),
% 13.34/3.13 inference(definition_unfolding,[status(thm)],[f822,f909])).
% 13.34/3.13 thf(f822,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_nat @ Y0 @ Y1) = (ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ Y1 @ Y0))))))))),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f452])).
% 13.34/3.13 thf(f452,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_nat @ Y0 @ Y1) = (ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ Y1 @ Y0))))))))),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f451])).
% 13.34/3.13 thf(f451,plain,(
% 13.34/3.13 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X1 @ X0) = (ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ X0 @ X1)))),
% 13.34/3.13 inference(rectify,[status(thm)],[f9])).
% 13.34/3.13 thf(f9,axiom,(
% 13.34/3.13 ! [X15 : nat,X16 : nat] : ((ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ X15 @ X16)) = (ord_less_nat @ X16 @ X15))),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_8_zero__less__diff)).
% 13.34/3.13 thf(f4876,plain,(
% 13.34/3.13 ( ! [X0 : nat,X1 : nat] : (((ord_less_nat @ (size_s1406904903t_unit @ nil_co1338500125t_unit) @ (minus_minus_nat @ X0 @ (suc @ X1))) = (ord_less_nat @ X1 @ (minus_minus_nat @ X0 @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit)))))) )),
% 13.34/3.13 inference(superposition,[status(thm)],[f3838,f4818])).
% 13.34/3.13 thf(f4818,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : (((minus_minus_nat @ (minus_minus_nat @ X2 @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit))) @ X1) = (minus_minus_nat @ X2 @ (suc @ X1)))) )),
% 13.34/3.13 inference(equality_proxy_clausification,[status(thm)],[f4806])).
% 13.34/3.13 thf(f4806,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : (($true = ((minus_minus_nat @ (minus_minus_nat @ X2 @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit))) @ X1) = (minus_minus_nat @ X2 @ (suc @ X1))))) )),
% 13.34/3.13 inference(forward_demodulation,[status(thm)],[f4805,f1107])).
% 13.34/3.13 thf(f4805,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : ((((minus_minus_nat @ (minus_minus_nat @ X2 @ (suc @ (size_s1168481041ge_p_v @ nil_message_p_v))) @ X1) = (minus_minus_nat @ X2 @ (suc @ X1))) = $true)) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f4804])).
% 13.34/3.13 thf(f4804,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : ((((^[Y0 : nat]: ((minus_minus_nat @ (minus_minus_nat @ Y0 @ (suc @ (size_s1168481041ge_p_v @ nil_message_p_v))) @ X1) = (minus_minus_nat @ Y0 @ (suc @ X1)))) @ X2) = $true)) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f4788])).
% 13.34/3.13 thf(f4788,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((minus_minus_nat @ (minus_minus_nat @ Y0 @ (suc @ (size_s1168481041ge_p_v @ nil_message_p_v))) @ X1) = (minus_minus_nat @ Y0 @ (suc @ X1))))))) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f4787])).
% 13.34/3.13 thf(f4787,plain,(
% 13.34/3.13 ( ! [X1 : nat] : ((((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((minus_minus_nat @ (minus_minus_nat @ Y1 @ (suc @ (size_s1168481041ge_p_v @ nil_message_p_v))) @ Y0) = (minus_minus_nat @ Y1 @ (suc @ Y0)))))) @ X1) = $true)) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f1102])).
% 13.34/3.13 thf(f1102,plain,(
% 13.34/3.13 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((minus_minus_nat @ (minus_minus_nat @ Y1 @ (suc @ (size_s1168481041ge_p_v @ nil_message_p_v))) @ Y0) = (minus_minus_nat @ Y1 @ (suc @ Y0))))))) = $true)),
% 13.34/3.13 inference(definition_unfolding,[status(thm)],[f927,f975])).
% 13.34/3.13 thf(f927,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((minus_minus_nat @ (minus_minus_nat @ Y1 @ one_one_nat) @ Y0) = (minus_minus_nat @ Y1 @ (suc @ Y0))))))))),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f356])).
% 13.34/3.13 thf(f356,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((minus_minus_nat @ (minus_minus_nat @ Y1 @ one_one_nat) @ Y0) = (minus_minus_nat @ Y1 @ (suc @ Y0))))))))),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f355])).
% 13.34/3.13 thf(f355,plain,(
% 13.34/3.13 ! [X0 : nat,X1 : nat] : ((minus_minus_nat @ (minus_minus_nat @ X0 @ one_one_nat) @ X1) = (minus_minus_nat @ X0 @ (suc @ X1)))),
% 13.34/3.13 inference(rectify,[status(thm)],[f195])).
% 13.34/3.13 thf(f195,axiom,(
% 13.34/3.13 ! [X16 : nat,X15 : nat] : ((minus_minus_nat @ X16 @ (suc @ X15)) = (minus_minus_nat @ (minus_minus_nat @ X16 @ one_one_nat) @ X15))),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_194_diff__Suc__eq__diff__pred)).
% 13.34/3.13 thf(f4625,plain,(
% 13.34/3.13 ($true = (~ (ord_less_nat @ nMsg @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit))))))),
% 13.34/3.13 inference(boolean_simplification,[status(thm)],[f4568])).
% 13.34/3.13 thf(f4568,plain,(
% 13.34/3.13 ($true = ((ord_less_nat @ nMsg @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit)))) => $false))),
% 13.34/3.13 inference(superposition,[status(thm)],[f4547,f1740])).
% 13.34/3.13 thf(f1740,plain,(
% 13.34/3.13 ((ord_less_nat @ (minus_minus_nat @ nMsg @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit))) @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit)))) = $false)),
% 13.34/3.13 inference(not_proxy_clausification,[status(thm)],[f1224])).
% 13.34/3.13 thf(f1224,plain,(
% 13.34/3.13 ((~ (ord_less_nat @ (minus_minus_nat @ nMsg @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit))) @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit))))) = $true)),
% 13.34/3.13 inference(forward_demodulation,[status(thm)],[f1094,f1107])).
% 13.34/3.13 thf(f1094,plain,(
% 13.34/3.13 ($true = (~ (ord_less_nat @ (minus_minus_nat @ nMsg @ (suc @ (size_s1168481041ge_p_v @ nil_message_p_v))) @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ (size_s1168481041ge_p_v @ nil_message_p_v))))))),
% 13.34/3.13 inference(definition_unfolding,[status(thm)],[f918,f909,f909])).
% 13.34/3.13 thf(f918,plain,(
% 13.34/3.13 ($true = (~ (ord_less_nat @ (minus_minus_nat @ nMsg @ (suc @ zero_zero_nat)) @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ zero_zero_nat)))))),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f318])).
% 13.34/3.13 thf(f318,plain,(
% 13.34/3.13 ($true = (~ (ord_less_nat @ (minus_minus_nat @ nMsg @ (suc @ zero_zero_nat)) @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ zero_zero_nat)))))),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f317])).
% 13.34/3.13 thf(f317,plain,(
% 13.34/3.13 ~(ord_less_nat @ (minus_minus_nat @ nMsg @ (suc @ zero_zero_nat)) @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ zero_zero_nat)))),
% 13.34/3.13 inference(rectify,[status(thm)],[f246])).
% 13.34/3.13 thf(f246,negated_conjecture,(
% 13.34/3.13 ~(ord_less_nat @ (minus_minus_nat @ nMsg @ (suc @ zero_zero_nat)) @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ zero_zero_nat)))),
% 13.34/3.13 inference(negated_conjecture,[status(cth)],[f245])).
% 13.34/3.13 thf(f245,conjecture,(
% 13.34/3.13 (ord_less_nat @ (minus_minus_nat @ nMsg @ (suc @ zero_zero_nat)) @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ zero_zero_nat)))),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',conj_0)).
% 13.34/3.13 thf(f4547,plain,(
% 13.34/3.13 ( ! [X2 : nat,X3 : nat,X1 : nat] : (($true = ((ord_less_nat @ X2 @ X1) => (ord_less_nat @ (minus_minus_nat @ X2 @ X3) @ X1)))) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f4546])).
% 13.34/3.13 thf(f4546,plain,(
% 13.34/3.13 ( ! [X2 : nat,X3 : nat,X1 : nat] : (($true = ((^[Y0 : nat]: ((ord_less_nat @ X2 @ X1) => (ord_less_nat @ (minus_minus_nat @ X2 @ Y0) @ X1))) @ X3))) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f4540])).
% 13.34/3.13 thf(f4540,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((ord_less_nat @ X2 @ X1) => (ord_less_nat @ (minus_minus_nat @ X2 @ Y0) @ X1)))))) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f4539])).
% 13.34/3.13 thf(f4539,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_nat @ Y0 @ X1) => (ord_less_nat @ (minus_minus_nat @ Y0 @ Y1) @ X1))))) @ X2))) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f4443])).
% 13.34/3.13 thf(f4443,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_nat @ Y0 @ X1) => (ord_less_nat @ (minus_minus_nat @ Y0 @ Y1) @ X1)))))))) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f4442])).
% 13.34/3.13 thf(f4442,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (!! @ nat @ (^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y0) => (ord_less_nat @ (minus_minus_nat @ Y1 @ Y2) @ Y0))))))) @ X1))) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f849])).
% 13.34/3.13 thf(f849,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (!! @ nat @ (^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y0) => (ord_less_nat @ (minus_minus_nat @ Y1 @ Y2) @ Y0)))))))))),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f627])).
% 13.34/3.13 thf(f627,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (!! @ nat @ (^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y0) => (ord_less_nat @ (minus_minus_nat @ Y1 @ Y2) @ Y0)))))))))),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f626])).
% 13.34/3.13 thf(f626,plain,(
% 13.34/3.13 ! [X0 : nat,X1 : nat,X2 : nat] : ((ord_less_nat @ X1 @ X2) => (ord_less_nat @ (minus_minus_nat @ X1 @ X0) @ X2))),
% 13.34/3.13 inference(rectify,[status(thm)],[f89])).
% 13.34/3.13 thf(f89,axiom,(
% 13.34/3.13 ! [X15 : nat,X31 : nat,X17 : nat] : ((ord_less_nat @ X31 @ X17) => (ord_less_nat @ (minus_minus_nat @ X31 @ X15) @ X17))),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_88_less__imp__diff__less)).
% 13.34/3.13 thf(f9402,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : (((~ (ord_less_nat @ X1 @ X2)) = ((ord_less_nat @ X2 @ X1) | (X2 = X1)))) )),
% 13.34/3.13 inference(equality_proxy_clausification,[status(thm)],[f9364])).
% 13.34/3.13 thf(f9364,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : (((((ord_less_nat @ X2 @ X1) | (X2 = X1)) = (~ (ord_less_nat @ X1 @ X2))) = $true)) )),
% 13.34/3.13 inference(forward_demodulation,[status(thm)],[f9363,f2797])).
% 13.34/3.13 thf(f9363,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : (($true = (((ord_less_nat @ X2 @ X1) | (X2 = X1)) = (ord_less_nat @ X2 @ (suc @ X1))))) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f9362])).
% 13.34/3.13 thf(f9362,plain,(
% 13.34/3.13 ( ! [X2 : nat,X1 : nat] : ((((^[Y0 : nat]: (((ord_less_nat @ Y0 @ X1) | (Y0 = X1)) = (ord_less_nat @ Y0 @ (suc @ X1)))) @ X2) = $true)) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f9360])).
% 13.34/3.13 thf(f9360,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (((!! @ nat @ (^[Y0 : nat]: (((ord_less_nat @ Y0 @ X1) | (Y0 = X1)) = (ord_less_nat @ Y0 @ (suc @ X1))))) = $true)) )),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f9359])).
% 13.34/3.13 thf(f9359,plain,(
% 13.34/3.13 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (((ord_less_nat @ Y1 @ Y0) | (Y1 = Y0)) = (ord_less_nat @ Y1 @ (suc @ Y0)))))) @ X1))) )),
% 13.34/3.13 inference(pi_clausification,[status(thm)],[f1206])).
% 13.34/3.13 thf(f1206,plain,(
% 13.34/3.13 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (((ord_less_nat @ Y1 @ Y0) | (Y1 = Y0)) = (ord_less_nat @ Y1 @ (suc @ Y0))))))) = $true)),
% 13.34/3.13 inference(beta_eta_normalization,[status(thm)],[f1024])).
% 13.34/3.13 thf(f1024,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (((^[Y2 : nat]: ((^[Y3 : nat]: ((ord_less_nat @ Y2 @ Y3) | (Y2 = Y3))))) @ Y1 @ Y0) = (ord_less_nat @ Y1 @ (suc @ Y0))))))))),
% 13.34/3.13 inference(definition_unfolding,[status(thm)],[f803,f967])).
% 13.34/3.13 thf(f803,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_eq_nat @ Y1 @ Y0) = (ord_less_nat @ Y1 @ (suc @ Y0))))))))),
% 13.34/3.13 inference(cnf_transformation,[status(thm)],[f554])).
% 13.34/3.13 thf(f554,plain,(
% 13.34/3.13 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_eq_nat @ Y1 @ Y0) = (ord_less_nat @ Y1 @ (suc @ Y0))))))))),
% 13.34/3.13 inference(fool_elimination,[status(thm)],[f553])).
% 13.34/3.13 thf(f553,plain,(
% 13.34/3.13 ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ X0 @ X1) = (ord_less_nat @ X0 @ (suc @ X1)))),
% 13.34/3.13 inference(rectify,[status(thm)],[f187])).
% 13.34/3.13 thf(f187,axiom,(
% 13.34/3.13 ! [X16 : nat,X15 : nat] : ((ord_less_nat @ X16 @ (suc @ X15)) = (ord_less_eq_nat @ X16 @ X15))),
% 13.34/3.13 file('/export/starexec/sandbox/tmp/tmp.zjn8GSLv8s/DTF2THF_31470.p',fact_186_less__Suc__eq__le)).
% 13.34/3.13 thf(f10770,plain,(
% 13.34/3.13 ((~ (ord_less_nat @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit))) @ sK6)) = (sK6 = (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit)))))),
% 13.34/3.13 inference(boolean_simplification,[status(thm)],[f10699])).
% 13.34/3.13 thf(f10699,plain,(
% 13.34/3.13 (($false | (sK6 = (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit))))) = (~ (ord_less_nat @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit))) @ sK6)))),
% 13.34/3.13 inference(superposition,[status(thm)],[f9402,f5301])).
% 13.34/3.13 thf(f5301,plain,(
% 13.34/3.13 ((ord_less_nat @ sK6 @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit)))) = $false)),
% 13.34/3.13 inference(backward_demodulation,[status(thm)],[f1740,f5271])).
% 13.34/3.13 thf(f5271,plain,(
% 13.34/3.13 ((minus_minus_nat @ nMsg @ (suc @ (size_s1406904903t_unit @ nil_co1338500125t_unit))) = sK6)),
% 13.34/3.13 inference(superposition,[status(thm)],[f1340,f5246])).
% 13.34/3.13 % SZS output end Proof for DTF2THF_31470
% 13.34/3.13 % (31903)------------------------------
% 13.34/3.13 % (31903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.34/3.13 % (31903)Termination reason: Refutation
% 13.34/3.13
% 13.34/3.13 % (31903)Memory used [KB]: 11129
% 13.34/3.13 % (31903)Time elapsed: 0.639 s
% 13.34/3.13 % (31903)Instructions burned: 2028 (million)
% 13.34/3.13 % (31903)------------------------------
% 13.34/3.13 % (31903)------------------------------
% 13.34/3.13 % (31574)Success in time 1.599 s
%------------------------------------------------------------------------------