%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP102^1 : 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 : n027.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 08:55:34 AM UTC 2026
% Result : Theorem 14.67s 3.38s
% Output : Refutation 14.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 82 ( 19 unt; 0 typ; 2 def)
% Number of atoms : 338 ( 121 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 542 ( 80 ~; 46 |; 4 &; 380 @)
% ( 2 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 95 ( 92 usr; 7 con; 0-3 aty)
% Number of variables : 98 ( 0 ^; 96 !; 2 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_7,type,
list_nat: $tType ).
thf(type_def_8,type,
list_a: $tType ).
thf(type_def_9,type,
a: $tType ).
thf(func_def_0,type,
list_nat: $tType ).
thf(func_def_1,type,
list_a: $tType ).
thf(func_def_2,type,
nat: $tType ).
thf(func_def_3,type,
a: $tType ).
thf(func_def_4,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_5,type,
list_asc_nat: list_nat > $o ).
thf(func_def_6,type,
list_desc_nat: list_nat > $o ).
thf(func_def_7,type,
list_strict_asc_nat: list_nat > $o ).
thf(func_def_8,type,
list_strict_desc_nat: list_nat > $o ).
thf(func_def_9,type,
listIn923761578nd_nat: list_nat > ( nat > nat ) > nat > nat ).
thf(func_def_10,type,
listIn1312259492pend_a: list_a > ( nat > a ) > nat > a ).
thf(func_def_11,type,
linorder_sorted_nat: list_nat > $o ).
thf(func_def_12,type,
list_ex_nat: ( nat > $o ) > list_nat > $o ).
thf(func_def_13,type,
list_ex_a: ( a > $o ) > list_a > $o ).
thf(func_def_14,type,
nth_nat: list_nat > nat > nat ).
thf(func_def_15,type,
nth_a: list_a > nat > a ).
thf(func_def_16,type,
rev_nat: list_nat > list_nat ).
thf(func_def_17,type,
rev_a: list_a > list_a ).
thf(func_def_18,type,
suc: nat > nat ).
thf(func_def_19,type,
size_size_list_nat: list_nat > nat ).
thf(func_def_20,type,
size_size_list_a: list_a > nat ).
thf(func_def_21,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_22,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_23,type,
f: nat > a ).
thf(func_def_24,type,
g: nat > a ).
thf(func_def_25,type,
xs: list_a ).
thf(func_def_26,type,
ys: list_a ).
thf(func_def_41,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_42,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_43,type,
sP2: nat > nat > nat > $o ).
thf(func_def_44,type,
sP3: nat > nat > nat > $o ).
thf(func_def_45,type,
sP4: nat > nat > nat > $o ).
thf(func_def_46,type,
sK5: ( nat > nat ) > nat ).
thf(func_def_47,type,
sK6: ( nat > nat ) > nat ).
thf(func_def_48,type,
sK7: ( nat > nat ) > nat ).
thf(func_def_49,type,
sK8: ( nat > nat ) > nat ).
thf(func_def_50,type,
sK9: list_a > list_a > nat ).
thf(func_def_51,type,
sK10: nat > nat ).
thf(func_def_52,type,
sK11: nat > nat ).
thf(func_def_53,type,
sK12: nat > nat ).
thf(func_def_54,type,
sK13: nat > nat ).
thf(func_def_55,type,
sK14: ( nat > nat ) > nat ).
thf(func_def_56,type,
sK15: ( nat > nat ) > nat ).
thf(func_def_57,type,
sK16: ( nat > nat ) > nat ).
thf(func_def_58,type,
sK17: ( nat > nat ) > nat ).
thf(func_def_59,type,
sK18: nat > nat ).
thf(func_def_60,type,
sK19: ( nat > $o ) > nat ).
thf(func_def_61,type,
sK20: ( nat > $o ) > nat ).
thf(func_def_62,type,
sK21: ( nat > $o ) > nat > nat ).
thf(func_def_63,type,
sK22: ( nat > nat > $o ) > nat ).
thf(func_def_64,type,
sK23: ( nat > nat > $o ) > nat ).
thf(func_def_65,type,
sK24: ( nat > nat > $o ) > nat ).
thf(func_def_66,type,
sK25: ( nat > nat > $o ) > nat ).
thf(func_def_67,type,
sK26: ( nat > nat ) > nat ).
thf(func_def_68,type,
sK27: ( nat > nat ) > nat ).
thf(func_def_69,type,
sK28: ( nat > nat ) > nat ).
thf(func_def_70,type,
sK29: ( nat > nat ) > nat ).
thf(func_def_71,type,
sK30: ( nat > $o ) > nat ).
thf(func_def_72,type,
sK31: nat > nat ).
thf(func_def_73,type,
sK32: ( nat > nat > $o ) > nat ).
thf(func_def_74,type,
sK33: ( nat > nat > $o ) > nat ).
thf(func_def_75,type,
sK34: ( nat > nat > $o ) > nat ).
thf(func_def_76,type,
sK35: ( nat > nat > $o ) > nat ).
thf(func_def_77,type,
sK36: ( nat > nat > $o ) > nat ).
thf(func_def_78,type,
sK37: nat > nat ).
thf(func_def_79,type,
sK38: nat > nat ).
thf(func_def_80,type,
sK39: ( nat > $o ) > nat ).
thf(func_def_81,type,
sK40: nat > nat ).
thf(func_def_82,type,
sK41: ( list_a > $o ) > list_a ).
thf(func_def_83,type,
sK42: ( nat > nat ) > nat ).
thf(func_def_84,type,
sK43: ( nat > nat ) > nat ).
thf(func_def_85,type,
sK44: ( nat > nat ) > nat ).
thf(func_def_86,type,
sK45: ( nat > nat ) > nat ).
thf(func_def_87,type,
sK46: nat > nat ).
thf(func_def_88,type,
sK47: nat > nat ).
thf(func_def_89,type,
sK48: nat > nat ).
thf(func_def_90,type,
sK49: nat > ( nat > $o ) > nat > nat ).
thf(func_def_91,type,
sK50: nat > nat > ( nat > $o ) > nat ).
thf(func_def_92,type,
sK51: ( nat > nat ) > nat ).
thf(func_def_93,type,
sK52: ( nat > nat ) > nat ).
thf(func_def_94,type,
sK53: ( nat > nat ) > nat ).
thf(func_def_95,type,
sK54: ( nat > nat ) > nat ).
thf(func_def_96,type,
sK55: nat > list_a ).
thf(func_def_97,type,
sK56: nat ).
thf(func_def_98,type,
sK57: ( nat > $o ) > nat > nat ).
thf(func_def_99,type,
sK58: ( nat > $o ) > nat > nat ).
thf(func_def_100,type,
sK59: ( nat > nat ) > nat ).
thf(func_def_101,type,
sK60: ( nat > nat ) > nat ).
thf(func_def_102,type,
sK61: ( nat > nat ) > nat ).
thf(func_def_103,type,
sK62: ( nat > nat ) > nat ).
thf(func_def_104,type,
sK63: ( nat > nat ) > nat ).
thf(func_def_105,type,
sK64: ( nat > nat ) > nat ).
thf(func_def_106,type,
sK65: nat > nat ).
thf(func_def_108,type,
ph67:
!>[X0: $tType] : X0 ).
thf(f1710,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1534,f1679,f1706]) ).
thf(f1706,plain,
~ spl66_3,
inference(avatar_contradiction_clause,[status(thm)],[f1705]) ).
thf(f1705,plain,
( $false
| ~ spl66_3 ),
inference(subsumption_resolution,[status(thm)],[f1680,f1183]) ).
thf(f1183,plain,
( ( ord_less_nat @ sK56 @ ( size_size_list_a @ xs ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f1032]) ).
thf(f1032,plain,
( ( ( ord_less_nat @ sK56 @ ( size_size_list_a @ xs ) )
= $true )
& ( ( nth_a @ ys @ sK56 )
!= ( nth_a @ xs @ sK56 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56])],[f930,f1031]) ).
thf(f1031,plain,
( ? [X0: nat] :
( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ xs ) )
= $true )
& ( ( nth_a @ xs @ X0 )
!= ( nth_a @ ys @ X0 ) ) )
=> ( ( ( ord_less_nat @ sK56 @ ( size_size_list_a @ xs ) )
= $true )
& ( ( nth_a @ ys @ sK56 )
!= ( nth_a @ xs @ sK56 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f930,plain,
? [X0: nat] :
( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ xs ) )
= $true )
& ( ( nth_a @ xs @ X0 )
!= ( nth_a @ ys @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f779]) ).
thf(f779,plain,
~ ! [X0: nat] :
( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ xs ) )
!= $true )
| ( ( nth_a @ xs @ X0 )
= ( nth_a @ ys @ X0 ) ) ),
inference(flattening,[status(thm)],[f284]) ).
thf(f284,plain,
~ ! [X0: nat] :
( ( ( nth_a @ xs @ X0 )
= ( nth_a @ ys @ X0 ) )
| ( ( ord_less_nat @ X0 @ ( size_size_list_a @ xs ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f283]) ).
thf(f283,plain,
~ ! [X0: nat] :
( ( ( nth_a @ xs @ X0 )
= ( nth_a @ ys @ X0 ) )
| ~ ( ord_less_nat @ X0 @ ( size_size_list_a @ xs ) ) ),
inference(rectify,[status(thm)],[f256]) ).
thf(f256,negated_conjecture,
~ ! [X5: nat] :
( ( ( nth_a @ xs @ X5 )
= ( nth_a @ ys @ X5 ) )
| ~ ( ord_less_nat @ X5 @ ( size_size_list_a @ xs ) ) ),
inference(negated_conjecture,[status(cth)],[f255]) ).
thf(f255,conjecture,
! [X5: nat] :
( ( ( nth_a @ xs @ X5 )
= ( nth_a @ ys @ X5 ) )
| ~ ( ord_less_nat @ X5 @ ( size_size_list_a @ xs ) ) ),
file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',conj_2) ).
thf(f1680,plain,
( ( ( ord_less_nat @ sK56 @ ( size_size_list_a @ xs ) )
!= $true )
| ~ spl66_3 ),
inference(backward_demodulation,[status(thm)],[f1242,f1516]) ).
thf(f1516,plain,
( ( ( size_size_list_a @ ys )
= sK56 )
| ~ spl66_3 ),
inference(avatar_component_clause,[status(thm)],[f1514]) ).
thf(f1514,definition,
( spl66_3
<=> ( ( size_size_list_a @ ys )
= sK56 ) ),
introduced(definition,[new_symbols(naming,[spl66_3])],[avatar_definition]) ).
thf(f1242,plain,
( ( ord_less_nat @ ( size_size_list_a @ ys ) @ ( size_size_list_a @ xs ) )
!= $true ),
inference(forward_literal_rewriting,[status(thm)],[f1063,f1056]) ).
thf(f1056,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_eq_nat @ X1 @ X0 )
!= $true )
| ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f825]) ).
thf(f825,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_eq_nat @ X1 @ X0 )
!= $true )
| ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f804]) ).
thf(f804,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_eq_nat @ X1 @ X0 )
= $true )
=> ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f274]) ).
thf(f274,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_eq_nat @ X1 @ X0 )
= $true )
=> ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f273]) ).
thf(f273,plain,
! [X0: nat,X1: nat] :
( ( ord_less_eq_nat @ X1 @ X0 )
=> ~ ( ord_less_nat @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f127]) ).
thf(f127,axiom,
! [X14: nat,X31: nat] :
( ( ord_less_eq_nat @ X31 @ X14 )
=> ~ ( ord_less_nat @ X14 @ X31 ) ),
file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',fact_126_leD) ).
thf(f1063,plain,
( ( ord_less_eq_nat @ ( size_size_list_a @ xs ) @ ( size_size_list_a @ ys ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f674]) ).
thf(f674,plain,
( ( ord_less_eq_nat @ ( size_size_list_a @ xs ) @ ( size_size_list_a @ ys ) )
= $true ),
inference(fool_elimination,[status(thm)],[f673]) ).
thf(f673,plain,
ord_less_eq_nat @ ( size_size_list_a @ xs ) @ ( size_size_list_a @ ys ),
inference(rectify,[status(thm)],[f254]) ).
thf(f254,axiom,
ord_less_eq_nat @ ( size_size_list_a @ xs ) @ ( size_size_list_a @ ys ),
file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',conj_1) ).
thf(f1679,plain,
spl66_4,
inference(avatar_contradiction_clause,[status(thm)],[f1678]) ).
thf(f1678,plain,
( $false
| spl66_4 ),
inference(subsumption_resolution,[status(thm)],[f1677,f1520]) ).
thf(f1520,plain,
( ( ( ord_less_eq_nat @ sK56 @ ( size_size_list_a @ ys ) )
!= $true )
| spl66_4 ),
inference(avatar_component_clause,[status(thm)],[f1518]) ).
thf(f1518,definition,
( spl66_4
<=> ( ( ord_less_eq_nat @ sK56 @ ( size_size_list_a @ ys ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl66_4])],[avatar_definition]) ).
thf(f1677,plain,
( ( ord_less_eq_nat @ sK56 @ ( size_size_list_a @ ys ) )
= $true ),
inference(forward_literal_rewriting,[status(thm)],[f1665,f1175]) ).
thf(f1175,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_eq_nat @ X1 @ X0 )
= $true )
| ( ( ord_less_nat @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f815]) ).
thf(f815,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X0 @ X1 )
= $true )
| ( ( ord_less_eq_nat @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f800]) ).
thf(f800,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X0 @ X1 )
!= $true )
=> ( ( ord_less_eq_nat @ X1 @ X0 )
= $true ) ),
inference(flattening,[status(thm)],[f595]) ).
thf(f595,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X0 @ X1 )
!= $true )
=> ( ( ord_less_eq_nat @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f594]) ).
thf(f594,plain,
! [X0: nat,X1: nat] :
( ~ ( ord_less_nat @ X0 @ X1 )
=> ( ord_less_eq_nat @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f126]) ).
thf(f126,axiom,
! [X14: nat,X31: nat] :
( ~ ( ord_less_nat @ X14 @ X31 )
=> ( ord_less_eq_nat @ X31 @ X14 ) ),
file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',fact_125_leI) ).
thf(f1665,plain,
( ( ord_less_nat @ ( size_size_list_a @ ys ) @ sK56 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1651]) ).
thf(f1651,plain,
( ( $true != $true )
| ( ( ord_less_nat @ ( size_size_list_a @ ys ) @ sK56 )
!= $true ) ),
inference(superposition,[status(thm)],[f1287,f1257]) ).
thf(f1257,plain,
( ( ord_less_eq_nat @ sK56 @ ( size_size_list_a @ xs ) )
= $true ),
inference(forward_literal_rewriting,[status(thm)],[f1256,f1175]) ).
thf(f1256,plain,
( ( ord_less_nat @ ( size_size_list_a @ xs ) @ sK56 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1244]) ).
thf(f1244,plain,
( ( ( ord_less_nat @ ( size_size_list_a @ xs ) @ sK56 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1106,f1183]) ).
thf(f1106,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X1 @ X0 )
!= $true )
| ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f806]) ).
thf(f806,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X0 @ X1 )
!= $true )
| ( ( ord_less_nat @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f796]) ).
thf(f796,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X1 @ X0 )
= $true )
=> ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f304]) ).
thf(f304,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X1 @ X0 )
= $true )
=> ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f303]) ).
thf(f303,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ X1 @ X0 )
=> ~ ( ord_less_nat @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f66]) ).
thf(f66,axiom,
! [X31: nat,X14: nat] :
( ( ord_less_nat @ X14 @ X31 )
=> ~ ( ord_less_nat @ X31 @ X14 ) ),
file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',fact_65_less__asym) ).
thf(f1287,plain,
! [X0: nat] :
( ( ( ord_less_eq_nat @ X0 @ ( size_size_list_a @ xs ) )
!= $true )
| ( ( ord_less_nat @ ( size_size_list_a @ ys ) @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1267]) ).
thf(f1267,plain,
! [X0: nat] :
( ( ( ord_less_nat @ ( size_size_list_a @ ys ) @ X0 )
!= $true )
| ( ( ord_less_eq_nat @ X0 @ ( size_size_list_a @ xs ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1242,f1070]) ).
thf(f1070,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( ord_less_nat @ X2 @ X0 )
= $true )
| ( ( ord_less_eq_nat @ X1 @ X0 )
!= $true )
| ( ( ord_less_nat @ X2 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f852]) ).
thf(f852,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( ord_less_nat @ X2 @ X1 )
!= $true )
| ( ( ord_less_eq_nat @ X1 @ X0 )
!= $true )
| ( ( ord_less_nat @ X2 @ X0 )
= $true ) ),
inference(flattening,[status(thm)],[f851]) ).
thf(f851,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( ord_less_nat @ X2 @ X0 )
= $true )
| ( ( ord_less_eq_nat @ X1 @ X0 )
!= $true )
| ( ( ord_less_nat @ X2 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f747]) ).
thf(f747,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( ord_less_nat @ X2 @ X1 )
= $true )
=> ( ( ( ord_less_eq_nat @ X1 @ X0 )
= $true )
=> ( ( ord_less_nat @ X2 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f746]) ).
thf(f746,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ord_less_nat @ X2 @ X1 )
=> ( ( ord_less_eq_nat @ X1 @ X0 )
=> ( ord_less_nat @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f112]) ).
thf(f112,axiom,
! [X32: nat,X31: nat,X14: nat] :
( ( ord_less_nat @ X14 @ X31 )
=> ( ( ord_less_eq_nat @ X31 @ X32 )
=> ( ord_less_nat @ X14 @ X32 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',fact_111_less__le__trans) ).
thf(f1534,plain,
( spl66_3
| ~ spl66_4 ),
inference(avatar_split_clause,[status(thm)],[f1533,f1518,f1514]) ).
thf(f1533,plain,
( ( ( size_size_list_a @ ys )
= sK56 )
| ( ( ord_less_eq_nat @ sK56 @ ( size_size_list_a @ ys ) )
!= $true ) ),
inference(forward_literal_rewriting,[status(thm)],[f1497,f1056]) ).
thf(f1497,plain,
( ( ( size_size_list_a @ ys )
= sK56 )
| ( ( ord_less_nat @ ( size_size_list_a @ ys ) @ sK56 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1481]) ).
thf(f1481,plain,
( ( ( ord_less_nat @ ( size_size_list_a @ ys ) @ sK56 )
= $true )
| ( ( size_size_list_a @ ys )
= sK56 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1477,f1066]) ).
thf(f1066,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X1 @ X0 )
= $true )
| ( ( ord_less_nat @ X0 @ X1 )
= $true )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f862]) ).
thf(f862,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( ( ord_less_nat @ X1 @ X0 )
= $true )
| ( ( ord_less_nat @ X0 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f861]) ).
thf(f861,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X0 @ X1 )
= $true )
| ( X0 = X1 )
| ( ( ord_less_nat @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f788]) ).
thf(f788,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X1 @ X0 )
!= $true )
=> ( ( X0 != X1 )
=> ( ( ord_less_nat @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f553]) ).
thf(f553,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X1 @ X0 )
!= $true )
=> ( ( X0 != X1 )
=> ( ( ord_less_nat @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f552]) ).
thf(f552,plain,
! [X0: nat,X1: nat] :
( ~ ( ord_less_nat @ X1 @ X0 )
=> ( ( X0 != X1 )
=> ( ord_less_nat @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f52]) ).
thf(f52,axiom,
! [X31: nat,X14: nat] :
( ~ ( ord_less_nat @ X14 @ X31 )
=> ( ( X14 != X31 )
=> ( ord_less_nat @ X31 @ X14 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',fact_51_linorder__cases) ).
thf(f1477,plain,
( ( ord_less_nat @ sK56 @ ( size_size_list_a @ ys ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f1472,f1183]) ).
thf(f1472,plain,
( ( ( ord_less_nat @ sK56 @ ( size_size_list_a @ xs ) )
!= $true )
| ( ( ord_less_nat @ sK56 @ ( size_size_list_a @ ys ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1471]) ).
thf(f1471,plain,
( ( ( ord_less_nat @ sK56 @ ( size_size_list_a @ xs ) )
!= $true )
| ( ( nth_a @ xs @ sK56 )
!= ( nth_a @ xs @ sK56 ) )
| ( ( ord_less_nat @ sK56 @ ( size_size_list_a @ ys ) )
!= $true ) ),
inference(superposition,[status(thm)],[f1182,f1385]) ).
thf(f1385,plain,
! [X0: nat] :
( ( ( nth_a @ xs @ X0 )
= ( nth_a @ ys @ X0 ) )
| ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
!= $true )
| ( ( ord_less_nat @ X0 @ ( size_size_list_a @ xs ) )
!= $true ) ),
inference(superposition,[status(thm)],[f1343,f1047]) ).
thf(f1047,plain,
! [X2: nat > a,X0: nat,X1: list_a] :
( ( ( listIn1312259492pend_a @ X1 @ X2 @ X0 )
= ( nth_a @ X1 @ X0 ) )
| ( ( ord_less_nat @ X0 @ ( size_size_list_a @ X1 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f847]) ).
thf(f847,plain,
! [X0: nat,X1: list_a,X2: nat > a] :
( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ X1 ) )
!= $true )
| ( ( listIn1312259492pend_a @ X1 @ X2 @ X0 )
= ( nth_a @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f672]) ).
thf(f672,plain,
! [X0: nat,X1: list_a,X2: nat > a] :
( ( ( ord_less_nat @ X0 @ ( size_size_list_a @ X1 ) )
= $true )
=> ( ( listIn1312259492pend_a @ X1 @ X2 @ X0 )
= ( nth_a @ X1 @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f671]) ).
thf(f671,plain,
! [X0: nat,X1: list_a,X2: nat > a] :
( ( ord_less_nat @ X0 @ ( size_size_list_a @ X1 ) )
=> ( ( listIn1312259492pend_a @ X1 @ X2 @ X0 )
= ( nth_a @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X4: nat,X0: list_a,X2: nat > a] :
( ( ord_less_nat @ X4 @ ( size_size_list_a @ X0 ) )
=> ( ( listIn1312259492pend_a @ X0 @ X2 @ X4 )
= ( nth_a @ X0 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',fact_3_i__append__nth1) ).
thf(f1343,plain,
! [X0: nat] :
( ( ( listIn1312259492pend_a @ xs @ f @ X0 )
= ( nth_a @ ys @ X0 ) )
| ( ( ord_less_nat @ X0 @ ( size_size_list_a @ ys ) )
!= $true ) ),
inference(superposition,[status(thm)],[f1138,f1047]) ).
thf(f1138,plain,
! [X0: nat] :
( ( listIn1312259492pend_a @ xs @ f @ X0 )
= ( listIn1312259492pend_a @ ys @ g @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f662]) ).
thf(f662,plain,
! [X0: nat] :
( ( listIn1312259492pend_a @ xs @ f @ X0 )
= ( listIn1312259492pend_a @ ys @ g @ X0 ) ),
inference(fool_elimination,[status(thm)],[f661]) ).
thf(f661,plain,
! [X0: nat] :
( ( listIn1312259492pend_a @ xs @ f @ X0 )
= ( listIn1312259492pend_a @ ys @ g @ X0 ) ),
inference(rectify,[status(thm)],[f253]) ).
thf(f253,axiom,
! [X49: nat] :
( ( listIn1312259492pend_a @ xs @ f @ X49 )
= ( listIn1312259492pend_a @ ys @ g @ X49 ) ),
file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',conj_0) ).
thf(f1182,plain,
( ( nth_a @ ys @ sK56 )
!= ( nth_a @ xs @ sK56 ) ),
inference(cnf_transformation,[status(thm)],[f1032]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP102^1 : 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
% 0.18/0.34 % Computer : n027.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 08:27:07 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : ITP102^1 : TPTP v9.2.1. Released v7.5.0.
% 0.28/0.47 % Domain : Interactive Theorem Proving
% 0.28/0.47 % Problem : Sledgehammer ListInf problem prob_77__5408624_1
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Des21]
% 0.28/0.47 % Names : ListInf/prob_77__5408624_1 [Des21]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0
% 0.28/0.47 % Syntax : Number of formulae : 282 ( 94 unt; 27 typ; 0 def)
% 0.28/0.47 % Number of atoms : 742 ( 227 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 12 ( 2 avg)
% 0.28/0.47 % Number of connectives : 2091 ( 94 ~; 24 |; 32 &;1556 @)
% 0.28/0.47 % ( 0 <=>; 385 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 18 ( 6 avg)
% 0.28/0.47 % Number of types : 5 ( 4 usr)
% 0.28/0.47 % Number of type conns : 112 ( 112 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 24 ( 23 usr; 2 con; 0-3 aty)
% 0.28/0.47 % Number of variables : 744 ( 62 ^; 640 !; 42 ?; 744 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:23.131
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % Could-be-implicit typings (4)
% 0.28/0.47 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.28/0.47 list_nat: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.28/0.47 list_a: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Nat__Onat,type,
% 0.28/0.47 nat: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_tf__a,type,
% 0.28/0.47 a: $tType ).
% 0.28/0.47
% 0.28/0.47 % Explicit typings (23)
% 0.28/0.47 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 0.28/0.47 minus_minus_nat: nat > nat > nat ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_List2_Olist__asc_001t__Nat__Onat,type,
% 0.28/0.47 list_asc_nat: list_nat > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_List2_Olist__desc_001t__Nat__Onat,type,
% 0.28/0.47 list_desc_nat: list_nat > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_List2_Olist__strict__asc_001t__Nat__Onat,type,
% 0.28/0.47 list_strict_asc_nat: list_nat > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_List2_Olist__strict__desc_001t__Nat__Onat,type,
% 0.28/0.47 list_strict_desc_nat: list_nat > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_ListInf__Mirabelle__akbajwqfbr_Oi__append_001t__Nat__Onat,type,
% 0.28/0.47 listIn923761578nd_nat: list_nat > ( nat > nat ) > nat > nat ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_ListInf__Mirabelle__akbajwqfbr_Oi__append_001tf__a,type,
% 0.28/0.47 listIn1312259492pend_a: list_a > ( nat > a ) > nat > a ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_List_Olinorder__class_Osorted_001t__Nat__Onat,type,
% 0.28/0.47 linorder_sorted_nat: list_nat > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_List_Olist__ex_001t__Nat__Onat,type,
% 0.28/0.47 list_ex_nat: ( nat > $o ) > list_nat > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_List_Olist__ex_001tf__a,type,
% 0.28/0.47 list_ex_a: ( a > $o ) > list_a > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 0.28/0.47 nth_nat: list_nat > nat > nat ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_List_Onth_001tf__a,type,
% 0.28/0.47 nth_a: list_a > nat > a ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_List_Orev_001t__Nat__Onat,type,
% 0.28/0.47 rev_nat: list_nat > list_nat ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_List_Orev_001tf__a,type,
% 0.28/0.47 rev_a: list_a > list_a ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Nat_OSuc,type,
% 0.28/0.47 suc: nat > nat ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 0.28/0.47 size_size_list_nat: list_nat > nat ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__a_J,type,
% 0.28/0.47 size_size_list_a: list_a > nat ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.28/0.47 ord_less_nat: nat > nat > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.28/0.47 ord_less_eq_nat: nat > nat > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_f,type,
% 0.28/0.47 f: nat > a ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_g,type,
% 0.28/0.47 g: nat > a ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_xs,type,
% 0.28/0.47 xs: list_a ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_ys,type,
% 0.28/0.47 ys: list_a ).
% 0.28/0.47
% 0.28/0.47 % Relevant facts (252)
% 0.28/0.47 thf(fact_0_i__append__eq__i__append__conv,axiom,
% 0.28/0.47 ! [Xs: list_nat,Ys: list_nat,F: nat > nat,G: nat > nat] :
% 0.28/0.47 ( ( ( size_size_list_nat @ Xs )
% 0.28/0.47 = ( size_size_list_nat @ Ys ) )
% 0.28/0.47 => ( ( ( listIn923761578nd_nat @ Xs @ F )
% 0.28/0.47 = ( listIn923761578nd_nat @ Ys @ G ) )
% 0.28/0.47 = ( ( Xs = Ys )
% 0.28/0.47 & ( F = G ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % i_append_eq_i_append_conv
% 0.28/0.47 thf(fact_1_i__append__eq__i__append__conv,axiom,
% 0.28/0.47 ! [Xs: list_a,Ys: list_a,F: nat > a,G: nat > a] :
% 0.28/0.47 ( ( ( size_size_list_a @ Xs )
% 0.28/0.47 = ( size_size_list_a @ Ys ) )
% 0.28/0.47 => ( ( ( listIn1312259492pend_a @ Xs @ F )
% 0.28/0.47 = ( listIn1312259492pend_a @ Ys @ G ) )
% 0.28/0.47 = ( ( Xs = Ys )
% 0.28/0.47 & ( F = G ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % i_append_eq_i_append_conv
% 0.28/0.47 thf(fact_2_i__append__nth1,axiom,
% 0.28/0.47 ! [N: nat,Xs: list_nat,F: nat > nat] :
% 0.28/0.47 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.28/0.47 => ( ( listIn923761578nd_nat @ Xs @ F @ N )
% 0.28/0.47 = ( nth_nat @ Xs @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % i_append_nth1
% 0.28/0.47 thf(fact_3_i__append__nth1,axiom,
% 0.28/0.47 ! [N: nat,Xs: list_a,F: nat > a] :
% 0.28/0.47 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.28/0.47 => ( ( listIn1312259492pend_a @ Xs @ F @ N )
% 0.28/0.47 = ( nth_a @ Xs @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % i_append_nth1
% 0.28/0.47 thf(fact_4_nth__equalityI,axiom,
% 0.28/0.47 ! [Xs: list_nat,Ys: list_nat] :
% 0.28/0.47 ( ( ( size_size_list_nat @ Xs )
% 0.28/0.47 = ( size_size_list_nat @ Ys ) )
% 0.28/0.47 => ( ! [I: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.28/0.47 => ( ( nth_nat @ Xs @ I )
% 0.28/0.47 = ( nth_nat @ Ys @ I ) ) )
% 0.28/0.47 => ( Xs = Ys ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % nth_equalityI
% 0.28/0.47 thf(fact_5_nth__equalityI,axiom,
% 0.28/0.47 ! [Xs: list_a,Ys: list_a] :
% 0.28/0.47 ( ( ( size_size_list_a @ Xs )
% 0.28/0.47 = ( size_size_list_a @ Ys ) )
% 0.28/0.47 => ( ! [I: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) )
% 0.28/0.47 => ( ( nth_a @ Xs @ I )
% 0.28/0.47 = ( nth_a @ Ys @ I ) ) )
% 0.28/0.47 => ( Xs = Ys ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % nth_equalityI
% 0.28/0.47 thf(fact_6_Skolem__list__nth,axiom,
% 0.28/0.47 ! [K: nat,P: nat > nat > $o] :
% 0.28/0.47 ( ( ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.28/0.47 => ? [X: nat] : ( P @ I2 @ X ) ) )
% 0.28/0.47 = ( ? [Xs2: list_nat] :
% 0.28/0.47 ( ( ( size_size_list_nat @ Xs2 )
% 0.28/0.47 = K )
% 0.28/0.47 & ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.28/0.47 => ( P @ I2 @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Skolem_list_nth
% 0.28/0.47 thf(fact_7_Skolem__list__nth,axiom,
% 0.28/0.47 ! [K: nat,P: nat > a > $o] :
% 0.28/0.47 ( ( ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.28/0.47 => ? [X: a] : ( P @ I2 @ X ) ) )
% 0.28/0.47 = ( ? [Xs2: list_a] :
% 0.28/0.47 ( ( ( size_size_list_a @ Xs2 )
% 0.28/0.47 = K )
% 0.28/0.47 & ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.28/0.47 => ( P @ I2 @ ( nth_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Skolem_list_nth
% 0.28/0.47 thf(fact_8_list__eq__iff__nth__eq,axiom,
% 0.28/0.47 ( ( ^ [Y: list_nat,Z: list_nat] : ( Y = Z ) )
% 0.28/0.47 = ( ^ [Xs2: list_nat,Ys2: list_nat] :
% 0.28/0.47 ( ( ( size_size_list_nat @ Xs2 )
% 0.28/0.47 = ( size_size_list_nat @ Ys2 ) )
% 0.28/0.47 & ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.28/0.47 => ( ( nth_nat @ Xs2 @ I2 )
% 0.28/0.47 = ( nth_nat @ Ys2 @ I2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_eq_iff_nth_eq
% 0.28/0.47 thf(fact_9_list__eq__iff__nth__eq,axiom,
% 0.28/0.47 ( ( ^ [Y: list_a,Z: list_a] : ( Y = Z ) )
% 0.28/0.47 = ( ^ [Xs2: list_a,Ys2: list_a] :
% 0.28/0.47 ( ( ( size_size_list_a @ Xs2 )
% 0.28/0.47 = ( size_size_list_a @ Ys2 ) )
% 0.28/0.47 & ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs2 ) )
% 0.28/0.47 => ( ( nth_a @ Xs2 @ I2 )
% 0.28/0.47 = ( nth_a @ Ys2 @ I2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_eq_iff_nth_eq
% 0.28/0.47 thf(fact_10_order__refl,axiom,
% 0.28/0.47 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 0.28/0.47
% 0.28/0.47 % order_refl
% 0.28/0.47 thf(fact_11_list__desc__trans__le,axiom,
% 0.28/0.47 ( list_desc_nat
% 0.28/0.47 = ( ^ [Xs2: list_nat] :
% 0.28/0.47 ! [J: nat] :
% 0.28/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.28/0.47 => ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ I2 @ J )
% 0.28/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_desc_trans_le
% 0.28/0.47 thf(fact_12_length__induct,axiom,
% 0.28/0.47 ! [P: list_nat > $o,Xs: list_nat] :
% 0.28/0.47 ( ! [Xs3: list_nat] :
% 0.28/0.47 ( ! [Ys3: list_nat] :
% 0.28/0.47 ( ( ord_less_nat @ ( size_size_list_nat @ Ys3 ) @ ( size_size_list_nat @ Xs3 ) )
% 0.28/0.47 => ( P @ Ys3 ) )
% 0.28/0.47 => ( P @ Xs3 ) )
% 0.28/0.47 => ( P @ Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % length_induct
% 0.28/0.47 thf(fact_13_length__induct,axiom,
% 0.28/0.47 ! [P: list_a > $o,Xs: list_a] :
% 0.28/0.47 ( ! [Xs3: list_a] :
% 0.28/0.47 ( ! [Ys3: list_a] :
% 0.28/0.47 ( ( ord_less_nat @ ( size_size_list_a @ Ys3 ) @ ( size_size_list_a @ Xs3 ) )
% 0.28/0.47 => ( P @ Ys3 ) )
% 0.28/0.47 => ( P @ Xs3 ) )
% 0.28/0.47 => ( P @ Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % length_induct
% 0.28/0.47 thf(fact_14_nat__less__le,axiom,
% 0.28/0.47 ( ord_less_nat
% 0.28/0.47 = ( ^ [M: nat,N2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ M @ N2 )
% 0.28/0.47 & ( M != N2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % nat_less_le
% 0.28/0.47 thf(fact_15_less__imp__le__nat,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_nat @ M2 @ N )
% 0.28/0.47 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_imp_le_nat
% 0.28/0.47 thf(fact_16_le__eq__less__or__eq,axiom,
% 0.28/0.47 ( ord_less_eq_nat
% 0.28/0.47 = ( ^ [M: nat,N2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ M @ N2 )
% 0.28/0.47 | ( M = N2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_eq_less_or_eq
% 0.28/0.47 thf(fact_17_less__or__eq__imp__le,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ( ord_less_nat @ M2 @ N )
% 0.28/0.47 | ( M2 = N ) )
% 0.28/0.47 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_or_eq_imp_le
% 0.28/0.47 thf(fact_18_le__neq__implies__less,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ M2 @ N )
% 0.28/0.47 => ( ( M2 != N )
% 0.28/0.47 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_neq_implies_less
% 0.28/0.47 thf(fact_19_less__mono__imp__le__mono,axiom,
% 0.28/0.47 ! [F: nat > nat,I3: nat,J2: nat] :
% 0.28/0.47 ( ! [I: nat,J3: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I @ J3 )
% 0.28/0.47 => ( ord_less_nat @ ( F @ I ) @ ( F @ J3 ) ) )
% 0.28/0.47 => ( ( ord_less_eq_nat @ I3 @ J2 )
% 0.28/0.47 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( F @ J2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_mono_imp_le_mono
% 0.28/0.47 thf(fact_20_dual__order_Oantisym,axiom,
% 0.28/0.47 ! [B: nat,A: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ B @ A )
% 0.28/0.47 => ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.47 => ( A = B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.antisym
% 0.28/0.47 thf(fact_21_dual__order_Oeq__iff,axiom,
% 0.28/0.47 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.28/0.47 = ( ^ [A2: nat,B2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.28/0.47 & ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.eq_iff
% 0.28/0.47 thf(fact_22_dual__order_Otrans,axiom,
% 0.28/0.47 ! [B: nat,A: nat,C: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ B @ A )
% 0.28/0.47 => ( ( ord_less_eq_nat @ C @ B )
% 0.28/0.47 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.trans
% 0.28/0.47 thf(fact_23_linorder__wlog,axiom,
% 0.28/0.47 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.28/0.47 ( ! [A3: nat,B3: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.28/0.47 => ( P @ A3 @ B3 ) )
% 0.28/0.47 => ( ! [A3: nat,B3: nat] :
% 0.28/0.47 ( ( P @ B3 @ A3 )
% 0.28/0.47 => ( P @ A3 @ B3 ) )
% 0.28/0.47 => ( P @ A @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linorder_wlog
% 0.28/0.47 thf(fact_24_dual__order_Orefl,axiom,
% 0.28/0.47 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.refl
% 0.28/0.47 thf(fact_25_order__trans,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.28/0.47 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.28/0.47 => ( ord_less_eq_nat @ X2 @ Z2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_trans
% 0.28/0.47 thf(fact_26_order__class_Oorder_Oantisym,axiom,
% 0.28/0.47 ! [A: nat,B: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.47 => ( ( ord_less_eq_nat @ B @ A )
% 0.28/0.47 => ( A = B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_class.order.antisym
% 0.28/0.47 thf(fact_27_ord__le__eq__trans,axiom,
% 0.28/0.47 ! [A: nat,B: nat,C: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.47 => ( ( B = C )
% 0.28/0.47 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_le_eq_trans
% 0.28/0.47 thf(fact_28_ord__eq__le__trans,axiom,
% 0.28/0.47 ! [A: nat,B: nat,C: nat] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.28/0.47 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_eq_le_trans
% 0.28/0.47 thf(fact_29_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.47 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.28/0.47 = ( ^ [A2: nat,B2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.28/0.47 & ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_class.order.eq_iff
% 0.28/0.47 thf(fact_30_antisym__conv,axiom,
% 0.28/0.47 ! [Y2: nat,X2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.28/0.47 => ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.28/0.47 = ( X2 = Y2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % antisym_conv
% 0.28/0.47 thf(fact_31_le__cases3,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.28/0.47 ( ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.28/0.47 => ~ ( ord_less_eq_nat @ Y2 @ Z2 ) )
% 0.28/0.47 => ( ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.28/0.47 => ~ ( ord_less_eq_nat @ X2 @ Z2 ) )
% 0.28/0.47 => ( ( ( ord_less_eq_nat @ X2 @ Z2 )
% 0.28/0.47 => ~ ( ord_less_eq_nat @ Z2 @ Y2 ) )
% 0.28/0.47 => ( ( ( ord_less_eq_nat @ Z2 @ Y2 )
% 0.28/0.47 => ~ ( ord_less_eq_nat @ Y2 @ X2 ) )
% 0.28/0.47 => ( ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.28/0.47 => ~ ( ord_less_eq_nat @ Z2 @ X2 ) )
% 0.28/0.47 => ~ ( ( ord_less_eq_nat @ Z2 @ X2 )
% 0.28/0.47 => ~ ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_cases3
% 0.28/0.47 thf(fact_32_order_Otrans,axiom,
% 0.28/0.47 ! [A: nat,B: nat,C: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.28/0.47 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order.trans
% 0.28/0.47 thf(fact_33_le__cases,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ~ ( ord_less_eq_nat @ X2 @ Y2 )
% 0.28/0.47 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_cases
% 0.28/0.47 thf(fact_34_eq__refl,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( X2 = Y2 )
% 0.28/0.47 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_refl
% 0.28/0.47 thf(fact_35_linear,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.28/0.47 | ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % linear
% 0.28/0.47 thf(fact_36_antisym,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.28/0.47 => ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.28/0.47 => ( X2 = Y2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % antisym
% 0.28/0.47 thf(fact_37_eq__iff,axiom,
% 0.28/0.47 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.28/0.47 = ( ^ [X3: nat,Y3: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.28/0.47 & ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_iff
% 0.28/0.47 thf(fact_38_ord__le__eq__subst,axiom,
% 0.28/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.47 => ( ( ( F @ B )
% 0.28/0.47 = C )
% 0.28/0.47 => ( ! [X4: nat,Y4: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.28/0.47 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_le_eq_subst
% 0.28/0.47 thf(fact_39_ord__eq__le__subst,axiom,
% 0.28/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.28/0.47 ( ( A
% 0.28/0.47 = ( F @ B ) )
% 0.28/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.28/0.47 => ( ! [X4: nat,Y4: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.28/0.47 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_eq_le_subst
% 0.28/0.47 thf(fact_40_order__subst2,axiom,
% 0.28/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.47 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.28/0.47 => ( ! [X4: nat,Y4: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.28/0.47 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst2
% 0.28/0.47 thf(fact_41_order__subst1,axiom,
% 0.28/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.28/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.28/0.47 => ( ! [X4: nat,Y4: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.28/0.47 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst1
% 0.28/0.47 thf(fact_42_dual__order_Ostrict__implies__not__eq,axiom,
% 0.28/0.47 ! [B: nat,A: nat] :
% 0.28/0.47 ( ( ord_less_nat @ B @ A )
% 0.28/0.47 => ( A != B ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.strict_implies_not_eq
% 0.28/0.47 thf(fact_43_order_Ostrict__implies__not__eq,axiom,
% 0.28/0.47 ! [A: nat,B: nat] :
% 0.28/0.47 ( ( ord_less_nat @ A @ B )
% 0.28/0.47 => ( A != B ) ) ).
% 0.28/0.47
% 0.28/0.47 % order.strict_implies_not_eq
% 0.28/0.47 thf(fact_44_not__less__iff__gr__or__eq,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 0.28/0.47 = ( ( ord_less_nat @ Y2 @ X2 )
% 0.28/0.47 | ( X2 = Y2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_less_iff_gr_or_eq
% 0.28/0.47 thf(fact_45_dual__order_Ostrict__trans,axiom,
% 0.28/0.47 ! [B: nat,A: nat,C: nat] :
% 0.28/0.47 ( ( ord_less_nat @ B @ A )
% 0.28/0.47 => ( ( ord_less_nat @ C @ B )
% 0.28/0.47 => ( ord_less_nat @ C @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.strict_trans
% 0.28/0.47 thf(fact_46_linorder__less__wlog,axiom,
% 0.28/0.47 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.28/0.47 ( ! [A3: nat,B3: nat] :
% 0.28/0.47 ( ( ord_less_nat @ A3 @ B3 )
% 0.28/0.47 => ( P @ A3 @ B3 ) )
% 0.28/0.47 => ( ! [A3: nat] : ( P @ A3 @ A3 )
% 0.28/0.47 => ( ! [A3: nat,B3: nat] :
% 0.28/0.47 ( ( P @ B3 @ A3 )
% 0.28/0.47 => ( P @ A3 @ B3 ) )
% 0.28/0.47 => ( P @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linorder_less_wlog
% 0.28/0.47 thf(fact_47_exists__least__iff,axiom,
% 0.28/0.47 ( ( ^ [P2: nat > $o] :
% 0.28/0.47 ? [X: nat] : ( P2 @ X ) )
% 0.28/0.47 = ( ^ [P3: nat > $o] :
% 0.28/0.47 ? [N2: nat] :
% 0.28/0.47 ( ( P3 @ N2 )
% 0.28/0.47 & ! [M: nat] :
% 0.28/0.47 ( ( ord_less_nat @ M @ N2 )
% 0.28/0.47 => ~ ( P3 @ M ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % exists_least_iff
% 0.28/0.47 thf(fact_48_less__imp__not__less,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_imp_not_less
% 0.28/0.47 thf(fact_49_order_Ostrict__trans,axiom,
% 0.28/0.47 ! [A: nat,B: nat,C: nat] :
% 0.28/0.47 ( ( ord_less_nat @ A @ B )
% 0.28/0.47 => ( ( ord_less_nat @ B @ C )
% 0.28/0.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order.strict_trans
% 0.28/0.47 thf(fact_50_dual__order_Oirrefl,axiom,
% 0.28/0.47 ! [A: nat] :
% 0.28/0.47 ~ ( ord_less_nat @ A @ A ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.irrefl
% 0.28/0.47 thf(fact_51_linorder__cases,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 => ( ( X2 != Y2 )
% 0.28/0.47 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linorder_cases
% 0.28/0.47 thf(fact_52_less__imp__triv,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat,P: $o] :
% 0.28/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 => ( ( ord_less_nat @ Y2 @ X2 )
% 0.28/0.47 => P ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_imp_triv
% 0.28/0.47 thf(fact_53_less__imp__not__eq2,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 => ( Y2 != X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_imp_not_eq2
% 0.28/0.47 thf(fact_54_antisym__conv3,axiom,
% 0.28/0.47 ! [Y2: nat,X2: nat] :
% 0.28/0.47 ( ~ ( ord_less_nat @ Y2 @ X2 )
% 0.28/0.47 => ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 0.28/0.47 = ( X2 = Y2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % antisym_conv3
% 0.28/0.47 thf(fact_55_less__induct,axiom,
% 0.28/0.47 ! [P: nat > $o,A: nat] :
% 0.28/0.47 ( ! [X4: nat] :
% 0.28/0.47 ( ! [Y5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ Y5 @ X4 )
% 0.28/0.47 => ( P @ Y5 ) )
% 0.28/0.47 => ( P @ X4 ) )
% 0.28/0.47 => ( P @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_induct
% 0.28/0.47 thf(fact_56_less__not__sym,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_not_sym
% 0.28/0.47 thf(fact_57_less__imp__not__eq,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 => ( X2 != Y2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_imp_not_eq
% 0.28/0.47 thf(fact_58_dual__order_Oasym,axiom,
% 0.28/0.47 ! [B: nat,A: nat] :
% 0.28/0.47 ( ( ord_less_nat @ B @ A )
% 0.28/0.47 => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.asym
% 0.28/0.47 thf(fact_59_ord__less__eq__trans,axiom,
% 0.28/0.47 ! [A: nat,B: nat,C: nat] :
% 0.28/0.47 ( ( ord_less_nat @ A @ B )
% 0.28/0.47 => ( ( B = C )
% 0.28/0.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_less_eq_trans
% 0.28/0.47 thf(fact_60_ord__eq__less__trans,axiom,
% 0.28/0.47 ! [A: nat,B: nat,C: nat] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ( ord_less_nat @ B @ C )
% 0.28/0.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_eq_less_trans
% 0.28/0.47 thf(fact_61_less__irrefl,axiom,
% 0.28/0.47 ! [X2: nat] :
% 0.28/0.47 ~ ( ord_less_nat @ X2 @ X2 ) ).
% 0.28/0.47
% 0.28/0.47 % less_irrefl
% 0.28/0.47 thf(fact_62_less__linear,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 | ( X2 = Y2 )
% 0.28/0.47 | ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_linear
% 0.28/0.47 thf(fact_63_less__trans,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 => ( ( ord_less_nat @ Y2 @ Z2 )
% 0.28/0.47 => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_trans
% 0.28/0.47 thf(fact_64_less__asym_H,axiom,
% 0.28/0.47 ! [A: nat,B: nat] :
% 0.28/0.47 ( ( ord_less_nat @ A @ B )
% 0.28/0.47 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_asym'
% 0.28/0.47 thf(fact_65_less__asym,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_asym
% 0.28/0.47 thf(fact_66_less__imp__neq,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 => ( X2 != Y2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_imp_neq
% 0.28/0.47 thf(fact_67_order_Oasym,axiom,
% 0.28/0.47 ! [A: nat,B: nat] :
% 0.28/0.47 ( ( ord_less_nat @ A @ B )
% 0.28/0.47 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % order.asym
% 0.28/0.47 thf(fact_68_neq__iff,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( X2 != Y2 )
% 0.28/0.47 = ( ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 | ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % neq_iff
% 0.28/0.47 thf(fact_69_neqE,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( X2 != Y2 )
% 0.28/0.47 => ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % neqE
% 0.28/0.47 thf(fact_70_gt__ex,axiom,
% 0.28/0.47 ! [X2: nat] :
% 0.28/0.47 ? [X_1: nat] : ( ord_less_nat @ X2 @ X_1 ) ).
% 0.28/0.47
% 0.28/0.47 % gt_ex
% 0.28/0.47 thf(fact_71_order__less__subst2,axiom,
% 0.28/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.28/0.47 ( ( ord_less_nat @ A @ B )
% 0.28/0.47 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.28/0.47 => ( ! [X4: nat,Y4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X4 @ Y4 )
% 0.28/0.47 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_less_subst2
% 0.28/0.47 thf(fact_72_order__less__subst1,axiom,
% 0.28/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.28/0.47 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.28/0.47 => ( ( ord_less_nat @ B @ C )
% 0.28/0.47 => ( ! [X4: nat,Y4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X4 @ Y4 )
% 0.28/0.47 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_less_subst1
% 0.28/0.47 thf(fact_73_ord__less__eq__subst,axiom,
% 0.28/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.28/0.47 ( ( ord_less_nat @ A @ B )
% 0.28/0.47 => ( ( ( F @ B )
% 0.28/0.47 = C )
% 0.28/0.47 => ( ! [X4: nat,Y4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X4 @ Y4 )
% 0.28/0.47 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_less_eq_subst
% 0.28/0.47 thf(fact_74_ord__eq__less__subst,axiom,
% 0.28/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.28/0.47 ( ( A
% 0.28/0.47 = ( F @ B ) )
% 0.28/0.47 => ( ( ord_less_nat @ B @ C )
% 0.28/0.47 => ( ! [X4: nat,Y4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X4 @ Y4 )
% 0.28/0.47 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_eq_less_subst
% 0.28/0.47 thf(fact_75_linorder__neqE__nat,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( X2 != Y2 )
% 0.28/0.47 => ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linorder_neqE_nat
% 0.28/0.47 thf(fact_76_infinite__descent,axiom,
% 0.28/0.47 ! [P: nat > $o,N: nat] :
% 0.28/0.47 ( ! [N3: nat] :
% 0.28/0.47 ( ~ ( P @ N3 )
% 0.28/0.47 => ? [M3: nat] :
% 0.28/0.47 ( ( ord_less_nat @ M3 @ N3 )
% 0.28/0.47 & ~ ( P @ M3 ) ) )
% 0.28/0.47 => ( P @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % infinite_descent
% 0.28/0.47 thf(fact_77_nat__less__induct,axiom,
% 0.28/0.47 ! [P: nat > $o,N: nat] :
% 0.28/0.47 ( ! [N3: nat] :
% 0.28/0.47 ( ! [M3: nat] :
% 0.28/0.47 ( ( ord_less_nat @ M3 @ N3 )
% 0.28/0.47 => ( P @ M3 ) )
% 0.28/0.47 => ( P @ N3 ) )
% 0.28/0.47 => ( P @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % nat_less_induct
% 0.28/0.47 thf(fact_78_less__irrefl__nat,axiom,
% 0.28/0.47 ! [N: nat] :
% 0.28/0.47 ~ ( ord_less_nat @ N @ N ) ).
% 0.28/0.47
% 0.28/0.47 % less_irrefl_nat
% 0.28/0.47 thf(fact_79_less__not__refl3,axiom,
% 0.28/0.47 ! [S: nat,T: nat] :
% 0.28/0.47 ( ( ord_less_nat @ S @ T )
% 0.28/0.47 => ( S != T ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_not_refl3
% 0.28/0.47 thf(fact_80_less__not__refl2,axiom,
% 0.28/0.47 ! [N: nat,M2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ N @ M2 )
% 0.28/0.47 => ( M2 != N ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_not_refl2
% 0.28/0.47 thf(fact_81_less__not__refl,axiom,
% 0.28/0.47 ! [N: nat] :
% 0.28/0.47 ~ ( ord_less_nat @ N @ N ) ).
% 0.28/0.47
% 0.28/0.47 % less_not_refl
% 0.28/0.47 thf(fact_82_nat__neq__iff,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( M2 != N )
% 0.28/0.47 = ( ( ord_less_nat @ M2 @ N )
% 0.28/0.47 | ( ord_less_nat @ N @ M2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % nat_neq_iff
% 0.28/0.47 thf(fact_83_Nat_Oex__has__greatest__nat,axiom,
% 0.28/0.47 ! [P: nat > $o,K: nat,B: nat] :
% 0.28/0.47 ( ( P @ K )
% 0.28/0.47 => ( ! [Y4: nat] :
% 0.28/0.47 ( ( P @ Y4 )
% 0.28/0.47 => ( ord_less_eq_nat @ Y4 @ B ) )
% 0.28/0.47 => ? [X4: nat] :
% 0.28/0.47 ( ( P @ X4 )
% 0.28/0.47 & ! [Y5: nat] :
% 0.28/0.47 ( ( P @ Y5 )
% 0.28/0.47 => ( ord_less_eq_nat @ Y5 @ X4 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nat.ex_has_greatest_nat
% 0.28/0.47 thf(fact_84_nat__le__linear,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ M2 @ N )
% 0.28/0.47 | ( ord_less_eq_nat @ N @ M2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % nat_le_linear
% 0.28/0.47 thf(fact_85_le__antisym,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ M2 @ N )
% 0.28/0.47 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.28/0.47 => ( M2 = N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_antisym
% 0.28/0.47 thf(fact_86_eq__imp__le,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( M2 = N )
% 0.28/0.47 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_imp_le
% 0.28/0.47 thf(fact_87_le__trans,axiom,
% 0.28/0.47 ! [I3: nat,J2: nat,K: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ I3 @ J2 )
% 0.28/0.47 => ( ( ord_less_eq_nat @ J2 @ K )
% 0.28/0.47 => ( ord_less_eq_nat @ I3 @ K ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_trans
% 0.28/0.47 thf(fact_88_le__refl,axiom,
% 0.28/0.47 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.28/0.47
% 0.28/0.47 % le_refl
% 0.28/0.47 thf(fact_89_size__neq__size__imp__neq,axiom,
% 0.28/0.47 ! [X2: list_a,Y2: list_a] :
% 0.28/0.47 ( ( ( size_size_list_a @ X2 )
% 0.28/0.47 != ( size_size_list_a @ Y2 ) )
% 0.28/0.47 => ( X2 != Y2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % size_neq_size_imp_neq
% 0.28/0.47 thf(fact_90_size__neq__size__imp__neq,axiom,
% 0.28/0.47 ! [X2: list_nat,Y2: list_nat] :
% 0.28/0.47 ( ( ( size_size_list_nat @ X2 )
% 0.28/0.47 != ( size_size_list_nat @ Y2 ) )
% 0.28/0.47 => ( X2 != Y2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % size_neq_size_imp_neq
% 0.28/0.47 thf(fact_91_neq__if__length__neq,axiom,
% 0.28/0.47 ! [Xs: list_a,Ys: list_a] :
% 0.28/0.47 ( ( ( size_size_list_a @ Xs )
% 0.28/0.47 != ( size_size_list_a @ Ys ) )
% 0.28/0.47 => ( Xs != Ys ) ) ).
% 0.28/0.47
% 0.28/0.47 % neq_if_length_neq
% 0.28/0.47 thf(fact_92_neq__if__length__neq,axiom,
% 0.28/0.47 ! [Xs: list_nat,Ys: list_nat] :
% 0.28/0.47 ( ( ( size_size_list_nat @ Xs )
% 0.28/0.47 != ( size_size_list_nat @ Ys ) )
% 0.28/0.47 => ( Xs != Ys ) ) ).
% 0.28/0.47
% 0.28/0.47 % neq_if_length_neq
% 0.28/0.47 thf(fact_93_Ex__list__of__length,axiom,
% 0.28/0.47 ! [N: nat] :
% 0.28/0.47 ? [Xs3: list_a] :
% 0.28/0.47 ( ( size_size_list_a @ Xs3 )
% 0.28/0.47 = N ) ).
% 0.28/0.47
% 0.28/0.47 % Ex_list_of_length
% 0.28/0.47 thf(fact_94_Ex__list__of__length,axiom,
% 0.28/0.47 ! [N: nat] :
% 0.28/0.47 ? [Xs3: list_nat] :
% 0.28/0.47 ( ( size_size_list_nat @ Xs3 )
% 0.28/0.47 = N ) ).
% 0.28/0.47
% 0.28/0.47 % Ex_list_of_length
% 0.28/0.47 thf(fact_95_list__desc__trans,axiom,
% 0.28/0.47 ( list_desc_nat
% 0.28/0.47 = ( ^ [Xs2: list_nat] :
% 0.28/0.47 ! [J: nat] :
% 0.28/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.28/0.47 => ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.28/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_desc_trans
% 0.28/0.47 thf(fact_96_order_Onot__eq__order__implies__strict,axiom,
% 0.28/0.47 ! [A: nat,B: nat] :
% 0.28/0.47 ( ( A != B )
% 0.28/0.47 => ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.47 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order.not_eq_order_implies_strict
% 0.28/0.47 thf(fact_97_dual__order_Ostrict__implies__order,axiom,
% 0.28/0.47 ! [B: nat,A: nat] :
% 0.28/0.47 ( ( ord_less_nat @ B @ A )
% 0.28/0.47 => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.strict_implies_order
% 0.28/0.47 thf(fact_98_dual__order_Ostrict__iff__order,axiom,
% 0.28/0.47 ( ord_less_nat
% 0.28/0.47 = ( ^ [B2: nat,A2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.28/0.47 & ( A2 != B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.strict_iff_order
% 0.28/0.47 thf(fact_99_dual__order_Oorder__iff__strict,axiom,
% 0.28/0.47 ( ord_less_eq_nat
% 0.28/0.47 = ( ^ [B2: nat,A2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ B2 @ A2 )
% 0.28/0.47 | ( A2 = B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.order_iff_strict
% 0.28/0.47 thf(fact_100_order_Ostrict__implies__order,axiom,
% 0.28/0.47 ! [A: nat,B: nat] :
% 0.28/0.47 ( ( ord_less_nat @ A @ B )
% 0.28/0.47 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % order.strict_implies_order
% 0.28/0.47 thf(fact_101_dual__order_Ostrict__trans2,axiom,
% 0.28/0.47 ! [B: nat,A: nat,C: nat] :
% 0.28/0.47 ( ( ord_less_nat @ B @ A )
% 0.28/0.47 => ( ( ord_less_eq_nat @ C @ B )
% 0.28/0.47 => ( ord_less_nat @ C @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.strict_trans2
% 0.28/0.47 thf(fact_102_dual__order_Ostrict__trans1,axiom,
% 0.28/0.47 ! [B: nat,A: nat,C: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ B @ A )
% 0.28/0.47 => ( ( ord_less_nat @ C @ B )
% 0.28/0.47 => ( ord_less_nat @ C @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dual_order.strict_trans1
% 0.28/0.47 thf(fact_103_order_Ostrict__iff__order,axiom,
% 0.28/0.47 ( ord_less_nat
% 0.28/0.47 = ( ^ [A2: nat,B2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.28/0.47 & ( A2 != B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order.strict_iff_order
% 0.28/0.47 thf(fact_104_order_Oorder__iff__strict,axiom,
% 0.28/0.47 ( ord_less_eq_nat
% 0.28/0.47 = ( ^ [A2: nat,B2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.28/0.47 | ( A2 = B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order.order_iff_strict
% 0.28/0.47 thf(fact_105_order_Ostrict__trans2,axiom,
% 0.28/0.47 ! [A: nat,B: nat,C: nat] :
% 0.28/0.47 ( ( ord_less_nat @ A @ B )
% 0.28/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.28/0.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order.strict_trans2
% 0.28/0.47 thf(fact_106_order_Ostrict__trans1,axiom,
% 0.28/0.47 ! [A: nat,B: nat,C: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.47 => ( ( ord_less_nat @ B @ C )
% 0.28/0.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order.strict_trans1
% 0.28/0.47 thf(fact_107_not__le__imp__less,axiom,
% 0.28/0.47 ! [Y2: nat,X2: nat] :
% 0.28/0.47 ( ~ ( ord_less_eq_nat @ Y2 @ X2 )
% 0.28/0.47 => ( ord_less_nat @ X2 @ Y2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_le_imp_less
% 0.28/0.47 thf(fact_108_less__le__not__le,axiom,
% 0.28/0.47 ( ord_less_nat
% 0.28/0.47 = ( ^ [X3: nat,Y3: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.28/0.47 & ~ ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_le_not_le
% 0.28/0.47 thf(fact_109_le__imp__less__or__eq,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.28/0.47 => ( ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 | ( X2 = Y2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_imp_less_or_eq
% 0.28/0.47 thf(fact_110_le__less__linear,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.28/0.47 | ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_less_linear
% 0.28/0.47 thf(fact_111_less__le__trans,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.28/0.47 => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_le_trans
% 0.28/0.47 thf(fact_112_le__less__trans,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.28/0.47 => ( ( ord_less_nat @ Y2 @ Z2 )
% 0.28/0.47 => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_less_trans
% 0.28/0.47 thf(fact_113_less__imp__le,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_imp_le
% 0.28/0.47 thf(fact_114_antisym__conv2,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.28/0.47 => ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 0.28/0.47 = ( X2 = Y2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % antisym_conv2
% 0.28/0.47 thf(fact_115_antisym__conv1,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 => ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.28/0.47 = ( X2 = Y2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % antisym_conv1
% 0.28/0.47 thf(fact_116_le__neq__trans,axiom,
% 0.28/0.47 ! [A: nat,B: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.47 => ( ( A != B )
% 0.28/0.47 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_neq_trans
% 0.28/0.47 thf(fact_117_not__less,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 0.28/0.47 = ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_less
% 0.28/0.47 thf(fact_118_not__le,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ~ ( ord_less_eq_nat @ X2 @ Y2 ) )
% 0.28/0.47 = ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_le
% 0.28/0.47 thf(fact_119_order__less__le__subst2,axiom,
% 0.28/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.28/0.47 ( ( ord_less_nat @ A @ B )
% 0.28/0.47 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.28/0.47 => ( ! [X4: nat,Y4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X4 @ Y4 )
% 0.28/0.47 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_less_le_subst2
% 0.28/0.47 thf(fact_120_order__less__le__subst1,axiom,
% 0.28/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.28/0.47 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.28/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.28/0.47 => ( ! [X4: nat,Y4: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.28/0.47 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_less_le_subst1
% 0.28/0.47 thf(fact_121_order__le__less__subst2,axiom,
% 0.28/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.47 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.28/0.47 => ( ! [X4: nat,Y4: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.28/0.47 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_le_less_subst2
% 0.28/0.47 thf(fact_122_order__le__less__subst1,axiom,
% 0.28/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.28/0.47 => ( ( ord_less_nat @ B @ C )
% 0.28/0.47 => ( ! [X4: nat,Y4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X4 @ Y4 )
% 0.28/0.47 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_le_less_subst1
% 0.28/0.47 thf(fact_123_less__le,axiom,
% 0.28/0.47 ( ord_less_nat
% 0.28/0.47 = ( ^ [X3: nat,Y3: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.28/0.47 & ( X3 != Y3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_le
% 0.28/0.47 thf(fact_124_le__less,axiom,
% 0.28/0.47 ( ord_less_eq_nat
% 0.28/0.47 = ( ^ [X3: nat,Y3: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X3 @ Y3 )
% 0.28/0.47 | ( X3 = Y3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_less
% 0.28/0.47 thf(fact_125_leI,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.28/0.47 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % leI
% 0.28/0.47 thf(fact_126_leD,axiom,
% 0.28/0.47 ! [Y2: nat,X2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.28/0.47 => ~ ( ord_less_nat @ X2 @ Y2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % leD
% 0.28/0.47 thf(fact_127_list__strict__asc__trans__le,axiom,
% 0.28/0.47 ! [Xs: list_nat] :
% 0.28/0.47 ( ( list_strict_asc_nat @ Xs )
% 0.28/0.47 => ! [J4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ J4 @ ( size_size_list_nat @ Xs ) )
% 0.28/0.47 => ! [I4: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ I4 @ J4 )
% 0.28/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I4 ) @ ( nth_nat @ Xs @ J4 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_strict_asc_trans_le
% 0.28/0.47 thf(fact_128_list__asc__trans__le,axiom,
% 0.28/0.47 ( list_asc_nat
% 0.28/0.47 = ( ^ [Xs2: list_nat] :
% 0.28/0.47 ! [J: nat] :
% 0.28/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.28/0.47 => ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ I2 @ J )
% 0.28/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_asc_trans_le
% 0.28/0.47 thf(fact_129_list__strict__desc__trans,axiom,
% 0.28/0.47 ( list_strict_desc_nat
% 0.28/0.47 = ( ^ [Xs2: list_nat] :
% 0.28/0.47 ! [J: nat] :
% 0.28/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.28/0.47 => ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.28/0.47 => ( ord_less_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_strict_desc_trans
% 0.28/0.47 thf(fact_130_list__strict__asc__trans,axiom,
% 0.28/0.47 ( list_strict_asc_nat
% 0.28/0.47 = ( ^ [Xs2: list_nat] :
% 0.28/0.47 ! [J: nat] :
% 0.28/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.28/0.47 => ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.28/0.47 => ( ord_less_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_strict_asc_trans
% 0.28/0.47 thf(fact_131_list__asc__trans,axiom,
% 0.28/0.47 ( list_asc_nat
% 0.28/0.47 = ( ^ [Xs2: list_nat] :
% 0.28/0.47 ! [J: nat] :
% 0.28/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.28/0.47 => ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.28/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_asc_trans
% 0.28/0.47 thf(fact_132_nat__descend__induct,axiom,
% 0.28/0.47 ! [N: nat,P: nat > $o,M2: nat] :
% 0.28/0.47 ( ! [K2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ N @ K2 )
% 0.28/0.47 => ( P @ K2 ) )
% 0.28/0.47 => ( ! [K2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ K2 @ N )
% 0.28/0.47 => ( ! [I4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ K2 @ I4 )
% 0.28/0.47 => ( P @ I4 ) )
% 0.28/0.47 => ( P @ K2 ) ) )
% 0.28/0.47 => ( P @ M2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % nat_descend_induct
% 0.28/0.47 thf(fact_133_complete__interval,axiom,
% 0.28/0.47 ! [A: nat,B: nat,P: nat > $o] :
% 0.28/0.47 ( ( ord_less_nat @ A @ B )
% 0.28/0.47 => ( ( P @ A )
% 0.28/0.47 => ( ~ ( P @ B )
% 0.28/0.47 => ? [C2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ A @ C2 )
% 0.28/0.47 & ( ord_less_eq_nat @ C2 @ B )
% 0.28/0.47 & ! [X5: nat] :
% 0.28/0.47 ( ( ( ord_less_eq_nat @ A @ X5 )
% 0.28/0.47 & ( ord_less_nat @ X5 @ C2 ) )
% 0.28/0.47 => ( P @ X5 ) )
% 0.28/0.47 & ! [D: nat] :
% 0.28/0.47 ( ! [X4: nat] :
% 0.28/0.47 ( ( ( ord_less_eq_nat @ A @ X4 )
% 0.28/0.47 & ( ord_less_nat @ X4 @ D ) )
% 0.28/0.47 => ( P @ X4 ) )
% 0.28/0.47 => ( ord_less_eq_nat @ D @ C2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % complete_interval
% 0.28/0.47 thf(fact_134_le__greater__neq__conv,axiom,
% 0.28/0.47 ( ord_less_eq_nat
% 0.28/0.47 = ( ^ [N2: nat,A2: nat] :
% 0.28/0.47 ! [X3: nat] :
% 0.28/0.47 ( ( ord_less_nat @ A2 @ X3 )
% 0.28/0.47 => ( N2 != X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_greater_neq_conv
% 0.28/0.47 thf(fact_135_greater__le__neq__conv,axiom,
% 0.28/0.47 ( ord_less_nat
% 0.28/0.47 = ( ^ [A2: nat,N2: nat] :
% 0.28/0.47 ! [X3: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ X3 @ A2 )
% 0.28/0.47 => ( N2 != X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % greater_le_neq_conv
% 0.28/0.47 thf(fact_136_less__ge__neq__conv,axiom,
% 0.28/0.47 ( ord_less_nat
% 0.28/0.47 = ( ^ [N2: nat,A2: nat] :
% 0.28/0.47 ! [X3: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ A2 @ X3 )
% 0.28/0.47 => ( N2 != X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_ge_neq_conv
% 0.28/0.47 thf(fact_137_list__strict__asc__imp__list__asc,axiom,
% 0.28/0.47 ! [Xs: list_nat] :
% 0.28/0.47 ( ( list_strict_asc_nat @ Xs )
% 0.28/0.47 => ( list_asc_nat @ Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_strict_asc_imp_list_asc
% 0.28/0.47 thf(fact_138_list__strict__desc__imp__list__desc,axiom,
% 0.28/0.47 ! [Xs: list_nat] :
% 0.28/0.47 ( ( list_strict_desc_nat @ Xs )
% 0.28/0.47 => ( list_desc_nat @ Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_strict_desc_imp_list_desc
% 0.28/0.47 thf(fact_139_ge__less__neq__conv,axiom,
% 0.28/0.47 ( ord_less_eq_nat
% 0.28/0.47 = ( ^ [A2: nat,N2: nat] :
% 0.28/0.47 ! [X3: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X3 @ A2 )
% 0.28/0.47 => ( N2 != X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ge_less_neq_conv
% 0.28/0.47 thf(fact_140_minf_I8_J,axiom,
% 0.28/0.47 ! [T: nat] :
% 0.28/0.47 ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X5 @ Z3 )
% 0.28/0.47 => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 0.28/0.47
% 0.28/0.47 % minf(8)
% 0.28/0.47 thf(fact_141_minf_I6_J,axiom,
% 0.28/0.47 ! [T: nat] :
% 0.28/0.47 ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X5 @ Z3 )
% 0.28/0.47 => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 0.28/0.47
% 0.28/0.47 % minf(6)
% 0.28/0.47 thf(fact_142_pinf_I8_J,axiom,
% 0.28/0.47 ! [T: nat] :
% 0.28/0.47 ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ Z3 @ X5 )
% 0.28/0.47 => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pinf(8)
% 0.28/0.47 thf(fact_143_pinf_I1_J,axiom,
% 0.28/0.47 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.28/0.47 ( ? [Z4: nat] :
% 0.28/0.47 ! [X4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ Z4 @ X4 )
% 0.28/0.47 => ( ( P @ X4 )
% 0.28/0.47 = ( P4 @ X4 ) ) )
% 0.28/0.47 => ( ? [Z4: nat] :
% 0.28/0.47 ! [X4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ Z4 @ X4 )
% 0.28/0.47 => ( ( Q @ X4 )
% 0.28/0.47 = ( Q2 @ X4 ) ) )
% 0.28/0.47 => ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ Z3 @ X5 )
% 0.28/0.47 => ( ( ( P @ X5 )
% 0.28/0.47 & ( Q @ X5 ) )
% 0.28/0.47 = ( ( P4 @ X5 )
% 0.28/0.47 & ( Q2 @ X5 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pinf(1)
% 0.28/0.47 thf(fact_144_pinf_I2_J,axiom,
% 0.28/0.47 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.28/0.47 ( ? [Z4: nat] :
% 0.28/0.47 ! [X4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ Z4 @ X4 )
% 0.28/0.47 => ( ( P @ X4 )
% 0.28/0.47 = ( P4 @ X4 ) ) )
% 0.28/0.47 => ( ? [Z4: nat] :
% 0.28/0.47 ! [X4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ Z4 @ X4 )
% 0.28/0.47 => ( ( Q @ X4 )
% 0.28/0.47 = ( Q2 @ X4 ) ) )
% 0.28/0.47 => ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ Z3 @ X5 )
% 0.28/0.47 => ( ( ( P @ X5 )
% 0.28/0.47 | ( Q @ X5 ) )
% 0.28/0.47 = ( ( P4 @ X5 )
% 0.28/0.47 | ( Q2 @ X5 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pinf(2)
% 0.28/0.47 thf(fact_145_pinf_I3_J,axiom,
% 0.28/0.47 ! [T: nat] :
% 0.28/0.47 ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ Z3 @ X5 )
% 0.28/0.47 => ( X5 != T ) ) ).
% 0.28/0.47
% 0.28/0.47 % pinf(3)
% 0.28/0.47 thf(fact_146_pinf_I4_J,axiom,
% 0.28/0.47 ! [T: nat] :
% 0.28/0.47 ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ Z3 @ X5 )
% 0.28/0.47 => ( X5 != T ) ) ).
% 0.28/0.47
% 0.28/0.47 % pinf(4)
% 0.28/0.47 thf(fact_147_pinf_I5_J,axiom,
% 0.28/0.47 ! [T: nat] :
% 0.28/0.47 ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ Z3 @ X5 )
% 0.28/0.47 => ~ ( ord_less_nat @ X5 @ T ) ) ).
% 0.28/0.47
% 0.28/0.47 % pinf(5)
% 0.28/0.47 thf(fact_148_pinf_I7_J,axiom,
% 0.28/0.47 ! [T: nat] :
% 0.28/0.47 ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ Z3 @ X5 )
% 0.28/0.47 => ( ord_less_nat @ T @ X5 ) ) ).
% 0.28/0.47
% 0.28/0.47 % pinf(7)
% 0.28/0.47 thf(fact_149_minf_I1_J,axiom,
% 0.28/0.47 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.28/0.47 ( ? [Z4: nat] :
% 0.28/0.47 ! [X4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X4 @ Z4 )
% 0.28/0.47 => ( ( P @ X4 )
% 0.28/0.47 = ( P4 @ X4 ) ) )
% 0.28/0.47 => ( ? [Z4: nat] :
% 0.28/0.47 ! [X4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X4 @ Z4 )
% 0.28/0.47 => ( ( Q @ X4 )
% 0.28/0.47 = ( Q2 @ X4 ) ) )
% 0.28/0.47 => ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X5 @ Z3 )
% 0.28/0.47 => ( ( ( P @ X5 )
% 0.28/0.47 & ( Q @ X5 ) )
% 0.28/0.47 = ( ( P4 @ X5 )
% 0.28/0.47 & ( Q2 @ X5 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % minf(1)
% 0.28/0.47 thf(fact_150_minf_I2_J,axiom,
% 0.28/0.47 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.28/0.47 ( ? [Z4: nat] :
% 0.28/0.47 ! [X4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X4 @ Z4 )
% 0.28/0.47 => ( ( P @ X4 )
% 0.28/0.47 = ( P4 @ X4 ) ) )
% 0.28/0.47 => ( ? [Z4: nat] :
% 0.28/0.47 ! [X4: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X4 @ Z4 )
% 0.28/0.47 => ( ( Q @ X4 )
% 0.28/0.47 = ( Q2 @ X4 ) ) )
% 0.28/0.47 => ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X5 @ Z3 )
% 0.28/0.47 => ( ( ( P @ X5 )
% 0.28/0.47 | ( Q @ X5 ) )
% 0.28/0.47 = ( ( P4 @ X5 )
% 0.28/0.47 | ( Q2 @ X5 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % minf(2)
% 0.28/0.47 thf(fact_151_minf_I3_J,axiom,
% 0.28/0.47 ! [T: nat] :
% 0.28/0.47 ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X5 @ Z3 )
% 0.28/0.47 => ( X5 != T ) ) ).
% 0.28/0.47
% 0.28/0.47 % minf(3)
% 0.28/0.47 thf(fact_152_minf_I4_J,axiom,
% 0.28/0.47 ! [T: nat] :
% 0.28/0.47 ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X5 @ Z3 )
% 0.28/0.47 => ( X5 != T ) ) ).
% 0.28/0.47
% 0.28/0.47 % minf(4)
% 0.28/0.47 thf(fact_153_minf_I5_J,axiom,
% 0.28/0.47 ! [T: nat] :
% 0.28/0.47 ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X5 @ Z3 )
% 0.28/0.47 => ( ord_less_nat @ X5 @ T ) ) ).
% 0.28/0.47
% 0.28/0.47 % minf(5)
% 0.28/0.47 thf(fact_154_minf_I7_J,axiom,
% 0.28/0.47 ! [T: nat] :
% 0.28/0.47 ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ X5 @ Z3 )
% 0.28/0.47 => ~ ( ord_less_nat @ T @ X5 ) ) ).
% 0.28/0.47
% 0.28/0.47 % minf(7)
% 0.28/0.47 thf(fact_155_pinf_I6_J,axiom,
% 0.28/0.47 ! [T: nat] :
% 0.28/0.47 ? [Z3: nat] :
% 0.28/0.47 ! [X5: nat] :
% 0.28/0.47 ( ( ord_less_nat @ Z3 @ X5 )
% 0.28/0.47 => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 0.28/0.47
% 0.28/0.47 % pinf(6)
% 0.28/0.47 thf(fact_156_verit__comp__simplify1_I3_J,axiom,
% 0.28/0.47 ! [B4: nat,A4: nat] :
% 0.28/0.47 ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
% 0.28/0.47 = ( ord_less_nat @ A4 @ B4 ) ) ).
% 0.28/0.47
% 0.28/0.47 % verit_comp_simplify1(3)
% 0.28/0.47 thf(fact_157_sorted__iff__nth__mono,axiom,
% 0.28/0.47 ( linorder_sorted_nat
% 0.28/0.47 = ( ^ [Xs2: list_nat] :
% 0.28/0.47 ! [I2: nat,J: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ I2 @ J )
% 0.28/0.47 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.28/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sorted_iff_nth_mono
% 0.28/0.47 thf(fact_158_sorted__nth__mono,axiom,
% 0.28/0.47 ! [Xs: list_nat,I3: nat,J2: nat] :
% 0.28/0.47 ( ( linorder_sorted_nat @ Xs )
% 0.28/0.47 => ( ( ord_less_eq_nat @ I3 @ J2 )
% 0.28/0.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 0.28/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I3 ) @ ( nth_nat @ Xs @ J2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sorted_nth_mono
% 0.28/0.47 thf(fact_159_list__ord__le__sorted__eq,axiom,
% 0.28/0.47 list_asc_nat = linorder_sorted_nat ).
% 0.28/0.47
% 0.28/0.47 % list_ord_le_sorted_eq
% 0.28/0.47 thf(fact_160_verit__la__disequality,axiom,
% 0.28/0.47 ! [A: nat,B: nat] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 | ~ ( ord_less_eq_nat @ A @ B )
% 0.28/0.47 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % verit_la_disequality
% 0.28/0.47 thf(fact_161_verit__comp__simplify1_I1_J,axiom,
% 0.28/0.47 ! [A: nat] :
% 0.28/0.47 ~ ( ord_less_nat @ A @ A ) ).
% 0.28/0.47
% 0.28/0.47 % verit_comp_simplify1(1)
% 0.28/0.47 thf(fact_162_sorted__iff__nth__mono__less,axiom,
% 0.28/0.47 ( linorder_sorted_nat
% 0.28/0.47 = ( ^ [Xs2: list_nat] :
% 0.28/0.47 ! [I2: nat,J: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.28/0.47 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.28/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sorted_iff_nth_mono_less
% 0.28/0.47 thf(fact_163_sorted__rev__nth__mono,axiom,
% 0.28/0.47 ! [Xs: list_nat,I3: nat,J2: nat] :
% 0.28/0.47 ( ( linorder_sorted_nat @ ( rev_nat @ Xs ) )
% 0.28/0.47 => ( ( ord_less_eq_nat @ I3 @ J2 )
% 0.28/0.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 0.28/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ J2 ) @ ( nth_nat @ Xs @ I3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sorted_rev_nth_mono
% 0.28/0.47 thf(fact_164_sorted__rev__iff__nth__mono,axiom,
% 0.28/0.47 ! [Xs: list_nat] :
% 0.28/0.47 ( ( linorder_sorted_nat @ ( rev_nat @ Xs ) )
% 0.28/0.47 = ( ! [I2: nat,J: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ I2 @ J )
% 0.28/0.47 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 0.28/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ J ) @ ( nth_nat @ Xs @ I2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sorted_rev_iff_nth_mono
% 0.28/0.47 thf(fact_165_sorted__iff__nth__Suc,axiom,
% 0.28/0.47 ( linorder_sorted_nat
% 0.28/0.47 = ( ^ [Xs2: list_nat] :
% 0.28/0.47 ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ ( suc @ I2 ) @ ( size_size_list_nat @ Xs2 ) )
% 0.28/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ ( suc @ I2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sorted_iff_nth_Suc
% 0.28/0.47 thf(fact_166_old_Onat_Oinject,axiom,
% 0.28/0.47 ! [Nat: nat,Nat2: nat] :
% 0.28/0.47 ( ( ( suc @ Nat )
% 0.28/0.47 = ( suc @ Nat2 ) )
% 0.28/0.47 = ( Nat = Nat2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % old.nat.inject
% 0.28/0.47 thf(fact_167_nat_Oinject,axiom,
% 0.28/0.47 ! [X22: nat,Y22: nat] :
% 0.28/0.47 ( ( ( suc @ X22 )
% 0.28/0.47 = ( suc @ Y22 ) )
% 0.28/0.47 = ( X22 = Y22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % nat.inject
% 0.28/0.47 thf(fact_168_rev__is__rev__conv,axiom,
% 0.28/0.47 ! [Xs: list_nat,Ys: list_nat] :
% 0.28/0.47 ( ( ( rev_nat @ Xs )
% 0.28/0.47 = ( rev_nat @ Ys ) )
% 0.28/0.47 = ( Xs = Ys ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_is_rev_conv
% 0.28/0.47 thf(fact_169_rev__is__rev__conv,axiom,
% 0.28/0.47 ! [Xs: list_a,Ys: list_a] :
% 0.28/0.47 ( ( ( rev_a @ Xs )
% 0.28/0.47 = ( rev_a @ Ys ) )
% 0.28/0.47 = ( Xs = Ys ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_is_rev_conv
% 0.28/0.47 thf(fact_170_rev__rev__ident,axiom,
% 0.28/0.47 ! [Xs: list_nat] :
% 0.28/0.47 ( ( rev_nat @ ( rev_nat @ Xs ) )
% 0.28/0.47 = Xs ) ).
% 0.28/0.47
% 0.28/0.47 % rev_rev_ident
% 0.28/0.47 thf(fact_171_rev__rev__ident,axiom,
% 0.28/0.47 ! [Xs: list_a] :
% 0.28/0.47 ( ( rev_a @ ( rev_a @ Xs ) )
% 0.28/0.47 = Xs ) ).
% 0.28/0.47
% 0.28/0.47 % rev_rev_ident
% 0.28/0.47 thf(fact_172_Suc__less__eq,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 0.28/0.47 = ( ord_less_nat @ M2 @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_less_eq
% 0.28/0.47 thf(fact_173_Suc__mono,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_nat @ M2 @ N )
% 0.28/0.47 => ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_mono
% 0.28/0.47 thf(fact_174_lessI,axiom,
% 0.28/0.47 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % lessI
% 0.28/0.47 thf(fact_175_Suc__le__mono,axiom,
% 0.28/0.47 ! [N: nat,M2: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M2 ) )
% 0.28/0.47 = ( ord_less_eq_nat @ N @ M2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_le_mono
% 0.28/0.47 thf(fact_176_length__rev,axiom,
% 0.28/0.47 ! [Xs: list_a] :
% 0.28/0.47 ( ( size_size_list_a @ ( rev_a @ Xs ) )
% 0.28/0.47 = ( size_size_list_a @ Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % length_rev
% 0.28/0.47 thf(fact_177_length__rev,axiom,
% 0.28/0.47 ! [Xs: list_nat] :
% 0.28/0.47 ( ( size_size_list_nat @ ( rev_nat @ Xs ) )
% 0.28/0.47 = ( size_size_list_nat @ Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % length_rev
% 0.28/0.47 thf(fact_178_Suc__leD,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 0.28/0.47 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_leD
% 0.28/0.47 thf(fact_179_le__SucE,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.28/0.47 => ( ~ ( ord_less_eq_nat @ M2 @ N )
% 0.28/0.47 => ( M2
% 0.28/0.47 = ( suc @ N ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_SucE
% 0.28/0.47 thf(fact_180_le__SucI,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ M2 @ N )
% 0.28/0.47 => ( ord_less_eq_nat @ M2 @ ( suc @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_SucI
% 0.28/0.47 thf(fact_181_Suc__le__D,axiom,
% 0.28/0.47 ! [N: nat,M4: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ ( suc @ N ) @ M4 )
% 0.28/0.47 => ? [M5: nat] :
% 0.28/0.47 ( M4
% 0.28/0.47 = ( suc @ M5 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_le_D
% 0.28/0.47 thf(fact_182_le__Suc__eq,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.28/0.47 = ( ( ord_less_eq_nat @ M2 @ N )
% 0.28/0.47 | ( M2
% 0.28/0.47 = ( suc @ N ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_Suc_eq
% 0.28/0.47 thf(fact_183_Suc__n__not__le__n,axiom,
% 0.28/0.47 ! [N: nat] :
% 0.28/0.47 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_n_not_le_n
% 0.28/0.47 thf(fact_184_not__less__eq__eq,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ~ ( ord_less_eq_nat @ M2 @ N ) )
% 0.28/0.47 = ( ord_less_eq_nat @ ( suc @ N ) @ M2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_less_eq_eq
% 0.28/0.47 thf(fact_185_full__nat__induct,axiom,
% 0.28/0.47 ! [P: nat > $o,N: nat] :
% 0.28/0.47 ( ! [N3: nat] :
% 0.28/0.47 ( ! [M3: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ ( suc @ M3 ) @ N3 )
% 0.28/0.47 => ( P @ M3 ) )
% 0.28/0.47 => ( P @ N3 ) )
% 0.28/0.47 => ( P @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % full_nat_induct
% 0.28/0.47 thf(fact_186_nat__induct__at__least,axiom,
% 0.28/0.47 ! [M2: nat,N: nat,P: nat > $o] :
% 0.28/0.47 ( ( ord_less_eq_nat @ M2 @ N )
% 0.28/0.47 => ( ( P @ M2 )
% 0.28/0.47 => ( ! [N3: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ M2 @ N3 )
% 0.28/0.47 => ( ( P @ N3 )
% 0.28/0.47 => ( P @ ( suc @ N3 ) ) ) )
% 0.28/0.47 => ( P @ N ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % nat_induct_at_least
% 0.28/0.47 thf(fact_187_transitive__stepwise__le,axiom,
% 0.28/0.47 ! [M2: nat,N: nat,R: nat > nat > $o] :
% 0.28/0.47 ( ( ord_less_eq_nat @ M2 @ N )
% 0.28/0.47 => ( ! [X4: nat] : ( R @ X4 @ X4 )
% 0.28/0.47 => ( ! [X4: nat,Y4: nat,Z3: nat] :
% 0.28/0.47 ( ( R @ X4 @ Y4 )
% 0.28/0.47 => ( ( R @ Y4 @ Z3 )
% 0.28/0.47 => ( R @ X4 @ Z3 ) ) )
% 0.28/0.47 => ( ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) )
% 0.28/0.47 => ( R @ M2 @ N ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % transitive_stepwise_le
% 0.28/0.47 thf(fact_188_n__not__Suc__n,axiom,
% 0.28/0.47 ! [N: nat] :
% 0.28/0.47 ( N
% 0.28/0.47 != ( suc @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % n_not_Suc_n
% 0.28/0.47 thf(fact_189_Suc__inject,axiom,
% 0.28/0.47 ! [X2: nat,Y2: nat] :
% 0.28/0.47 ( ( ( suc @ X2 )
% 0.28/0.47 = ( suc @ Y2 ) )
% 0.28/0.47 => ( X2 = Y2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_inject
% 0.28/0.47 thf(fact_190_rev__swap,axiom,
% 0.28/0.47 ! [Xs: list_nat,Ys: list_nat] :
% 0.28/0.47 ( ( ( rev_nat @ Xs )
% 0.28/0.47 = Ys )
% 0.28/0.47 = ( Xs
% 0.28/0.47 = ( rev_nat @ Ys ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_swap
% 0.28/0.47 thf(fact_191_rev__swap,axiom,
% 0.28/0.47 ! [Xs: list_a,Ys: list_a] :
% 0.28/0.47 ( ( ( rev_a @ Xs )
% 0.28/0.47 = Ys )
% 0.28/0.47 = ( Xs
% 0.28/0.47 = ( rev_a @ Ys ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_swap
% 0.28/0.47 thf(fact_192_not__less__less__Suc__eq,axiom,
% 0.28/0.47 ! [N: nat,M2: nat] :
% 0.28/0.47 ( ~ ( ord_less_nat @ N @ M2 )
% 0.28/0.47 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 0.28/0.47 = ( N = M2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_less_less_Suc_eq
% 0.28/0.47 thf(fact_193_strict__inc__induct,axiom,
% 0.28/0.47 ! [I3: nat,J2: nat,P: nat > $o] :
% 0.28/0.47 ( ( ord_less_nat @ I3 @ J2 )
% 0.28/0.47 => ( ! [I: nat] :
% 0.28/0.47 ( ( J2
% 0.28/0.47 = ( suc @ I ) )
% 0.28/0.47 => ( P @ I ) )
% 0.28/0.47 => ( ! [I: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I @ J2 )
% 0.28/0.47 => ( ( P @ ( suc @ I ) )
% 0.28/0.47 => ( P @ I ) ) )
% 0.28/0.47 => ( P @ I3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % strict_inc_induct
% 0.28/0.47 thf(fact_194_less__Suc__induct,axiom,
% 0.28/0.47 ! [I3: nat,J2: nat,P: nat > nat > $o] :
% 0.28/0.47 ( ( ord_less_nat @ I3 @ J2 )
% 0.28/0.47 => ( ! [I: nat] : ( P @ I @ ( suc @ I ) )
% 0.28/0.47 => ( ! [I: nat,J3: nat,K2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I @ J3 )
% 0.28/0.47 => ( ( ord_less_nat @ J3 @ K2 )
% 0.28/0.47 => ( ( P @ I @ J3 )
% 0.28/0.47 => ( ( P @ J3 @ K2 )
% 0.28/0.47 => ( P @ I @ K2 ) ) ) ) )
% 0.28/0.47 => ( P @ I3 @ J2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_Suc_induct
% 0.28/0.47 thf(fact_195_less__trans__Suc,axiom,
% 0.28/0.47 ! [I3: nat,J2: nat,K: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I3 @ J2 )
% 0.28/0.47 => ( ( ord_less_nat @ J2 @ K )
% 0.28/0.47 => ( ord_less_nat @ ( suc @ I3 ) @ K ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_trans_Suc
% 0.28/0.47 thf(fact_196_Suc__less__SucD,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 0.28/0.47 => ( ord_less_nat @ M2 @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_less_SucD
% 0.28/0.47 thf(fact_197_less__antisym,axiom,
% 0.28/0.47 ! [N: nat,M2: nat] :
% 0.28/0.47 ( ~ ( ord_less_nat @ N @ M2 )
% 0.28/0.47 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 0.28/0.47 => ( M2 = N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_antisym
% 0.28/0.47 thf(fact_198_Suc__less__eq2,axiom,
% 0.28/0.47 ! [N: nat,M2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.28/0.47 = ( ? [M6: nat] :
% 0.28/0.47 ( ( M2
% 0.28/0.47 = ( suc @ M6 ) )
% 0.28/0.47 & ( ord_less_nat @ N @ M6 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_less_eq2
% 0.28/0.47 thf(fact_199_All__less__Suc,axiom,
% 0.28/0.47 ! [N: nat,P: nat > $o] :
% 0.28/0.47 ( ( ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 0.28/0.47 => ( P @ I2 ) ) )
% 0.28/0.47 = ( ( P @ N )
% 0.28/0.47 & ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I2 @ N )
% 0.28/0.47 => ( P @ I2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % All_less_Suc
% 0.28/0.47 thf(fact_200_not__less__eq,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ~ ( ord_less_nat @ M2 @ N ) )
% 0.28/0.47 = ( ord_less_nat @ N @ ( suc @ M2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_less_eq
% 0.28/0.47 thf(fact_201_less__Suc__eq,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 0.28/0.47 = ( ( ord_less_nat @ M2 @ N )
% 0.28/0.47 | ( M2 = N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_Suc_eq
% 0.28/0.47 thf(fact_202_Ex__less__Suc,axiom,
% 0.28/0.47 ! [N: nat,P: nat > $o] :
% 0.28/0.47 ( ( ? [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 0.28/0.47 & ( P @ I2 ) ) )
% 0.28/0.47 = ( ( P @ N )
% 0.28/0.47 | ? [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I2 @ N )
% 0.28/0.47 & ( P @ I2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Ex_less_Suc
% 0.28/0.47 thf(fact_203_less__SucI,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_nat @ M2 @ N )
% 0.28/0.47 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_SucI
% 0.28/0.47 thf(fact_204_less__SucE,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 0.28/0.47 => ( ~ ( ord_less_nat @ M2 @ N )
% 0.28/0.47 => ( M2 = N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_SucE
% 0.28/0.47 thf(fact_205_Suc__lessI,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_nat @ M2 @ N )
% 0.28/0.47 => ( ( ( suc @ M2 )
% 0.28/0.47 != N )
% 0.28/0.47 => ( ord_less_nat @ ( suc @ M2 ) @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_lessI
% 0.28/0.47 thf(fact_206_Suc__lessE,axiom,
% 0.28/0.47 ! [I3: nat,K: nat] :
% 0.28/0.47 ( ( ord_less_nat @ ( suc @ I3 ) @ K )
% 0.28/0.47 => ~ ! [J3: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I3 @ J3 )
% 0.28/0.47 => ( K
% 0.28/0.47 != ( suc @ J3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_lessE
% 0.28/0.47 thf(fact_207_Suc__lessD,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_nat @ ( suc @ M2 ) @ N )
% 0.28/0.47 => ( ord_less_nat @ M2 @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_lessD
% 0.28/0.47 thf(fact_208_Nat_OlessE,axiom,
% 0.28/0.47 ! [I3: nat,K: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I3 @ K )
% 0.28/0.47 => ( ( K
% 0.28/0.47 != ( suc @ I3 ) )
% 0.28/0.47 => ~ ! [J3: nat] :
% 0.28/0.47 ( ( ord_less_nat @ I3 @ J3 )
% 0.28/0.47 => ( K
% 0.28/0.47 != ( suc @ J3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nat.lessE
% 0.28/0.47 thf(fact_209_lift__Suc__mono__less__iff,axiom,
% 0.28/0.47 ! [F: nat > nat,N: nat,M2: nat] :
% 0.28/0.47 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.28/0.47 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M2 ) )
% 0.28/0.47 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lift_Suc_mono_less_iff
% 0.28/0.47 thf(fact_210_lift__Suc__mono__less,axiom,
% 0.28/0.47 ! [F: nat > nat,N: nat,N4: nat] :
% 0.28/0.47 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.28/0.47 => ( ( ord_less_nat @ N @ N4 )
% 0.28/0.47 => ( ord_less_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lift_Suc_mono_less
% 0.28/0.47 thf(fact_211_lift__Suc__antimono__le,axiom,
% 0.28/0.47 ! [F: nat > nat,N: nat,N4: nat] :
% 0.28/0.47 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.28/0.47 => ( ( ord_less_eq_nat @ N @ N4 )
% 0.28/0.47 => ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lift_Suc_antimono_le
% 0.28/0.47 thf(fact_212_lift__Suc__mono__le,axiom,
% 0.28/0.47 ! [F: nat > nat,N: nat,N4: nat] :
% 0.28/0.47 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.28/0.47 => ( ( ord_less_eq_nat @ N @ N4 )
% 0.28/0.47 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % lift_Suc_mono_le
% 0.28/0.47 thf(fact_213_le__imp__less__Suc,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ M2 @ N )
% 0.28/0.47 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_imp_less_Suc
% 0.28/0.47 thf(fact_214_less__eq__Suc__le,axiom,
% 0.28/0.47 ( ord_less_nat
% 0.28/0.47 = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_eq_Suc_le
% 0.28/0.47 thf(fact_215_less__Suc__eq__le,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 0.28/0.47 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_Suc_eq_le
% 0.28/0.47 thf(fact_216_le__less__Suc__eq,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ M2 @ N )
% 0.28/0.47 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 0.28/0.47 = ( N = M2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_less_Suc_eq
% 0.28/0.47 thf(fact_217_Suc__le__lessD,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 0.28/0.47 => ( ord_less_nat @ M2 @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_le_lessD
% 0.28/0.47 thf(fact_218_inc__induct,axiom,
% 0.28/0.47 ! [I3: nat,J2: nat,P: nat > $o] :
% 0.28/0.47 ( ( ord_less_eq_nat @ I3 @ J2 )
% 0.28/0.47 => ( ( P @ J2 )
% 0.28/0.47 => ( ! [N3: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ I3 @ N3 )
% 0.28/0.47 => ( ( ord_less_nat @ N3 @ J2 )
% 0.28/0.47 => ( ( P @ ( suc @ N3 ) )
% 0.28/0.47 => ( P @ N3 ) ) ) )
% 0.28/0.47 => ( P @ I3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % inc_induct
% 0.28/0.47 thf(fact_219_dec__induct,axiom,
% 0.28/0.47 ! [I3: nat,J2: nat,P: nat > $o] :
% 0.28/0.47 ( ( ord_less_eq_nat @ I3 @ J2 )
% 0.28/0.47 => ( ( P @ I3 )
% 0.28/0.47 => ( ! [N3: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ I3 @ N3 )
% 0.28/0.47 => ( ( ord_less_nat @ N3 @ J2 )
% 0.28/0.47 => ( ( P @ N3 )
% 0.28/0.47 => ( P @ ( suc @ N3 ) ) ) ) )
% 0.28/0.47 => ( P @ J2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dec_induct
% 0.28/0.47 thf(fact_220_Suc__le__eq,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 0.28/0.47 = ( ord_less_nat @ M2 @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_le_eq
% 0.28/0.47 thf(fact_221_Suc__leI,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_nat @ M2 @ N )
% 0.28/0.47 => ( ord_less_eq_nat @ ( suc @ M2 ) @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_leI
% 0.28/0.47 thf(fact_222_sorted__rev__iff__nth__Suc,axiom,
% 0.28/0.47 ! [Xs: list_nat] :
% 0.28/0.47 ( ( linorder_sorted_nat @ ( rev_nat @ Xs ) )
% 0.28/0.47 = ( ! [I2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ ( suc @ I2 ) @ ( size_size_list_nat @ Xs ) )
% 0.28/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ ( suc @ I2 ) ) @ ( nth_nat @ Xs @ I2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sorted_rev_iff_nth_Suc
% 0.28/0.47 thf(fact_223_nat__induct_H,axiom,
% 0.28/0.47 ! [P: nat > $o,N0: nat,N: nat] :
% 0.28/0.47 ( ( P @ N0 )
% 0.28/0.47 => ( ! [N3: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ N0 @ N3 )
% 0.28/0.47 => ( ( P @ N3 )
% 0.28/0.47 => ( P @ ( suc @ N3 ) ) ) )
% 0.28/0.47 => ( ( ord_less_eq_nat @ N0 @ N )
% 0.28/0.47 => ( P @ N ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % nat_induct'
% 0.28/0.47 thf(fact_224_rev__nth,axiom,
% 0.28/0.47 ! [N: nat,Xs: list_a] :
% 0.28/0.47 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.28/0.47 => ( ( nth_a @ ( rev_a @ Xs ) @ N )
% 0.28/0.47 = ( nth_a @ Xs @ ( minus_minus_nat @ ( size_size_list_a @ Xs ) @ ( suc @ N ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_nth
% 0.28/0.47 thf(fact_225_rev__nth,axiom,
% 0.28/0.47 ! [N: nat,Xs: list_nat] :
% 0.28/0.47 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.28/0.47 => ( ( nth_nat @ ( rev_nat @ Xs ) @ N )
% 0.28/0.47 = ( nth_nat @ Xs @ ( minus_minus_nat @ ( size_size_list_nat @ Xs ) @ ( suc @ N ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_nth
% 0.28/0.47 thf(fact_226_list__ex__length,axiom,
% 0.28/0.47 ( list_ex_a
% 0.28/0.47 = ( ^ [P3: a > $o,Xs2: list_a] :
% 0.28/0.47 ? [N2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs2 ) )
% 0.28/0.47 & ( P3 @ ( nth_a @ Xs2 @ N2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_ex_length
% 0.28/0.47 thf(fact_227_list__ex__length,axiom,
% 0.28/0.47 ( list_ex_nat
% 0.28/0.47 = ( ^ [P3: nat > $o,Xs2: list_nat] :
% 0.28/0.47 ? [N2: nat] :
% 0.28/0.47 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs2 ) )
% 0.28/0.47 & ( P3 @ ( nth_nat @ Xs2 @ N2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % list_ex_length
% 0.28/0.47 thf(fact_228_Suc__diff__diff,axiom,
% 0.28/0.47 ! [M2: nat,N: nat,K: nat] :
% 0.28/0.47 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) @ ( suc @ K ) )
% 0.28/0.47 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ N ) @ K ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_diff_diff
% 0.28/0.47 thf(fact_229_diff__Suc__Suc,axiom,
% 0.28/0.47 ! [M2: nat,N: nat] :
% 0.28/0.47 ( ( minus_minus_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 0.28/0.47 = ( minus_minus_nat @ M2 @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % diff_Suc_Suc
% 0.28/0.47 thf(fact_230_diff__diff__cancel,axiom,
% 0.28/0.47 ! [I3: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq_nat @ I3 @ N )
% 0.28/0.47 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I3 ) )
% 0.28/0.47 = I3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % diff_diff_cancel
% 0.28/0.48 thf(fact_231_list__ex__rev,axiom,
% 0.28/0.48 ! [P: nat > $o,Xs: list_nat] :
% 0.28/0.48 ( ( list_ex_nat @ P @ ( rev_nat @ Xs ) )
% 0.28/0.48 = ( list_ex_nat @ P @ Xs ) ) ).
% 0.28/0.48
% 0.28/0.48 % list_ex_rev
% 0.28/0.48 thf(fact_232_list__ex__rev,axiom,
% 0.28/0.48 ! [P: a > $o,Xs: list_a] :
% 0.28/0.48 ( ( list_ex_a @ P @ ( rev_a @ Xs ) )
% 0.28/0.48 = ( list_ex_a @ P @ Xs ) ) ).
% 0.28/0.48
% 0.28/0.48 % list_ex_rev
% 0.28/0.48 thf(fact_233_i__append__nth2,axiom,
% 0.28/0.48 ! [Xs: list_nat,N: nat,F: nat > nat] :
% 0.28/0.48 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N )
% 0.28/0.48 => ( ( listIn923761578nd_nat @ Xs @ F @ N )
% 0.28/0.48 = ( F @ ( minus_minus_nat @ N @ ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % i_append_nth2
% 0.28/0.48 thf(fact_234_i__append__nth2,axiom,
% 0.28/0.48 ! [Xs: list_a,N: nat,F: nat > a] :
% 0.28/0.48 ( ( ord_less_eq_nat @ ( size_size_list_a @ Xs ) @ N )
% 0.28/0.48 => ( ( listIn1312259492pend_a @ Xs @ F @ N )
% 0.28/0.48 = ( F @ ( minus_minus_nat @ N @ ( size_size_list_a @ Xs ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % i_append_nth2
% 0.28/0.48 thf(fact_235_zero__induct__lemma,axiom,
% 0.28/0.48 ! [P: nat > $o,K: nat,I3: nat] :
% 0.28/0.48 ( ( P @ K )
% 0.28/0.48 => ( ! [N3: nat] :
% 0.28/0.48 ( ( P @ ( suc @ N3 ) )
% 0.28/0.48 => ( P @ N3 ) )
% 0.28/0.48 => ( P @ ( minus_minus_nat @ K @ I3 ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % zero_induct_lemma
% 0.28/0.48 thf(fact_236_less__diff__imp__less,axiom,
% 0.28/0.48 ! [I3: nat,J2: nat,M2: nat] :
% 0.28/0.48 ( ( ord_less_nat @ I3 @ ( minus_minus_nat @ J2 @ M2 ) )
% 0.28/0.48 => ( ord_less_nat @ I3 @ J2 ) ) ).
% 0.28/0.48
% 0.28/0.48 % less_diff_imp_less
% 0.28/0.48 thf(fact_237_nat__diff__left__cancel__eq1,axiom,
% 0.28/0.48 ! [K: nat,M2: nat,N: nat] :
% 0.28/0.48 ( ( ( minus_minus_nat @ K @ M2 )
% 0.28/0.48 = ( minus_minus_nat @ K @ N ) )
% 0.28/0.48 => ( ( ord_less_nat @ M2 @ K )
% 0.28/0.48 => ( M2 = N ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % nat_diff_left_cancel_eq1
% 0.28/0.48 thf(fact_238_nat__diff__left__cancel__eq2,axiom,
% 0.28/0.48 ! [K: nat,M2: nat,N: nat] :
% 0.28/0.48 ( ( ( minus_minus_nat @ K @ M2 )
% 0.28/0.48 = ( minus_minus_nat @ K @ N ) )
% 0.28/0.48 => ( ( ord_less_nat @ N @ K )
% 0.28/0.48 => ( M2 = N ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % nat_diff_left_cancel_eq2
% 0.28/0.48 thf(fact_239_nat__diff__left__cancel__less,axiom,
% 0.28/0.48 ! [K: nat,M2: nat,N: nat] :
% 0.28/0.48 ( ( ord_less_nat @ ( minus_minus_nat @ K @ M2 ) @ ( minus_minus_nat @ K @ N ) )
% 0.28/0.48 => ( ord_less_nat @ N @ M2 ) ) ).
% 0.28/0.48
% 0.28/0.48 % nat_diff_left_cancel_less
% 0.28/0.48 thf(fact_240_nat__diff__right__cancel__eq1,axiom,
% 0.28/0.48 ! [M2: nat,K: nat,N: nat] :
% 0.28/0.48 ( ( ( minus_minus_nat @ M2 @ K )
% 0.28/0.48 = ( minus_minus_nat @ N @ K ) )
% 0.28/0.48 => ( ( ord_less_nat @ K @ M2 )
% 0.28/0.48 => ( M2 = N ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % nat_diff_right_cancel_eq1
% 0.28/0.48 thf(fact_241_nat__diff__right__cancel__eq2,axiom,
% 0.28/0.48 ! [M2: nat,K: nat,N: nat] :
% 0.28/0.48 ( ( ( minus_minus_nat @ M2 @ K )
% 0.28/0.48 = ( minus_minus_nat @ N @ K ) )
% 0.28/0.48 => ( ( ord_less_nat @ K @ N )
% 0.28/0.48 => ( M2 = N ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % nat_diff_right_cancel_eq2
% 0.28/0.48 thf(fact_242_nat__diff__right__cancel__less,axiom,
% 0.28/0.48 ! [N: nat,K: nat,M2: nat] :
% 0.28/0.48 ( ( ord_less_nat @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M2 @ K ) )
% 0.28/0.48 => ( ord_less_nat @ N @ M2 ) ) ).
% 0.28/0.48
% 0.28/0.48 % nat_diff_right_cancel_less
% 0.28/0.48 thf(fact_243_diff__less__mono2,axiom,
% 0.28/0.48 ! [M2: nat,N: nat,L: nat] :
% 0.28/0.48 ( ( ord_less_nat @ M2 @ N )
% 0.28/0.48 => ( ( ord_less_nat @ M2 @ L )
% 0.28/0.48 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % diff_less_mono2
% 0.28/0.48 thf(fact_244_less__imp__diff__less,axiom,
% 0.28/0.48 ! [J2: nat,K: nat,N: nat] :
% 0.28/0.48 ( ( ord_less_nat @ J2 @ K )
% 0.28/0.48 => ( ord_less_nat @ ( minus_minus_nat @ J2 @ N ) @ K ) ) ).
% 0.28/0.48
% 0.28/0.48 % less_imp_diff_less
% 0.28/0.48 thf(fact_245_diff__commute,axiom,
% 0.28/0.48 ! [I3: nat,J2: nat,K: nat] :
% 0.28/0.48 ( ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J2 ) @ K )
% 0.28/0.48 = ( minus_minus_nat @ ( minus_minus_nat @ I3 @ K ) @ J2 ) ) ).
% 0.28/0.48
% 0.28/0.48 % diff_commute
% 0.28/0.48 thf(fact_246_diff__le__mono2,axiom,
% 0.28/0.48 ! [M2: nat,N: nat,L: nat] :
% 0.28/0.48 ( ( ord_less_eq_nat @ M2 @ N )
% 0.28/0.48 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % diff_le_mono2
% 0.28/0.48 thf(fact_247_le__diff__iff_H,axiom,
% 0.28/0.48 ! [A: nat,C: nat,B: nat] :
% 0.28/0.48 ( ( ord_less_eq_nat @ A @ C )
% 0.28/0.48 => ( ( ord_less_eq_nat @ B @ C )
% 0.28/0.48 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 0.28/0.48 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % le_diff_iff'
% 0.28/0.48 thf(fact_248_diff__le__self,axiom,
% 0.28/0.48 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ N ) @ M2 ) ).
% 0.28/0.48
% 0.28/0.48 % diff_le_self
% 0.28/0.48 thf(fact_249_diff__le__mono,axiom,
% 0.28/0.48 ! [M2: nat,N: nat,L: nat] :
% 0.28/0.48 ( ( ord_less_eq_nat @ M2 @ N )
% 0.28/0.48 => ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % diff_le_mono
% 0.28/0.48 thf(fact_250_Nat_Odiff__diff__eq,axiom,
% 0.28/0.48 ! [K: nat,M2: nat,N: nat] :
% 0.28/0.48 ( ( ord_less_eq_nat @ K @ M2 )
% 0.28/0.48 => ( ( ord_less_eq_nat @ K @ N )
% 0.28/0.48 => ( ( minus_minus_nat @ ( minus_minus_nat @ M2 @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.28/0.48 = ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % Nat.diff_diff_eq
% 0.28/0.48 thf(fact_251_le__diff__iff,axiom,
% 0.28/0.48 ! [K: nat,M2: nat,N: nat] :
% 0.28/0.48 ( ( ord_less_eq_nat @ K @ M2 )
% 0.28/0.48 => ( ( ord_less_eq_nat @ K @ N )
% 0.28/0.48 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.28/0.48 = ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % le_diff_iff
% 0.28/0.48
% 0.28/0.48 % Conjectures (3)
% 0.28/0.48 thf(conj_0,hypothesis,
% 0.28/0.48 ! [X5: nat] :
% 0.28/0.48 ( ( listIn1312259492pend_a @ xs @ f @ X5 )
% 0.28/0.48 = ( listIn1312259492pend_a @ ys @ g @ X5 ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(conj_1,hypothesis,
% 0.28/0.48 ord_less_eq_nat @ ( size_size_list_a @ xs ) @ ( size_size_list_a @ ys ) ).
% 0.28/0.48
% 0.28/0.48 thf(conj_2,conjecture,
% 0.28/0.48 ! [I: nat] :
% 0.28/0.48 ( ~ ( ord_less_nat @ I @ ( size_size_list_a @ xs ) )
% 0.28/0.48 | ( ( nth_a @ xs @ I )
% 0.28/0.48 = ( nth_a @ ys @ I ) ) ) ).
% 0.28/0.48
% 0.28/0.48 %------------------------------------------------------------------------------
% 0.28/0.48 ------------------------
% 2.23/1.47 ---- Embedded in THF ---
% 2.23/1.47 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.23/1.47 %%% Generated on Tue Feb 24 08:27:08 EST 2026
% 2.23/1.47 %%% using '$$dhol' embedding, version 1.3.0.
% 2.23/1.47 %%% Logic specification used:
% 2.23/1.47 %%% thf(spec, logic, $$dhol).
% 2.23/1.47
% 2.23/1.47 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2DTF23273.p
% See solution above
% 2.23/1.47 ------------------------
% 2.47/1.51 ---- Cleaned THF ---
% 2.47/1.51 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 2.47/1.51 list_nat: $tType ).
% 2.47/1.51
% 2.47/1.51 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 2.47/1.51 list_a: $tType ).
% 2.47/1.51
% 2.47/1.51 thf(ty_n_t__Nat__Onat,type,
% 2.47/1.51 nat: $tType ).
% 2.47/1.51
% 2.47/1.51 thf(ty_n_tf__a,type,
% 2.47/1.51 a: $tType ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 2.47/1.51 minus_minus_nat: nat > nat > nat ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_List2_Olist__asc_001t__Nat__Onat,type,
% 2.47/1.51 list_asc_nat: list_nat > $o ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_List2_Olist__desc_001t__Nat__Onat,type,
% 2.47/1.51 list_desc_nat: list_nat > $o ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_List2_Olist__strict__asc_001t__Nat__Onat,type,
% 2.47/1.51 list_strict_asc_nat: list_nat > $o ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_List2_Olist__strict__desc_001t__Nat__Onat,type,
% 2.47/1.51 list_strict_desc_nat: list_nat > $o ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_ListInf__Mirabelle__akbajwqfbr_Oi__append_001t__Nat__Onat,type,
% 2.47/1.51 listIn923761578nd_nat: list_nat > ( nat > nat ) > nat > nat ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_ListInf__Mirabelle__akbajwqfbr_Oi__append_001tf__a,type,
% 2.47/1.51 listIn1312259492pend_a: list_a > ( nat > a ) > nat > a ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_List_Olinorder__class_Osorted_001t__Nat__Onat,type,
% 2.47/1.51 linorder_sorted_nat: list_nat > $o ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_List_Olist__ex_001t__Nat__Onat,type,
% 2.47/1.51 list_ex_nat: ( nat > $o ) > list_nat > $o ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_List_Olist__ex_001tf__a,type,
% 2.47/1.51 list_ex_a: ( a > $o ) > list_a > $o ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 2.47/1.51 nth_nat: list_nat > nat > nat ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_List_Onth_001tf__a,type,
% 2.47/1.51 nth_a: list_a > nat > a ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_List_Orev_001t__Nat__Onat,type,
% 2.47/1.51 rev_nat: list_nat > list_nat ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_List_Orev_001tf__a,type,
% 2.47/1.51 rev_a: list_a > list_a ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_Nat_OSuc,type,
% 2.47/1.51 suc: nat > nat ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 2.47/1.51 size_size_list_nat: list_nat > nat ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__a_J,type,
% 2.47/1.51 size_size_list_a: list_a > nat ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 2.47/1.51 ord_less_nat: nat > nat > $o ).
% 2.47/1.51
% 2.47/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 2.47/1.51 ord_less_eq_nat: nat > nat > $o ).
% 2.47/1.51
% 2.47/1.51 thf(sy_v_f,type,
% 2.47/1.51 f: nat > a ).
% 2.47/1.51
% 2.47/1.51 thf(sy_v_g,type,
% 2.47/1.51 g: nat > a ).
% 2.47/1.51
% 2.47/1.51 thf(sy_v_xs,type,
% 2.47/1.51 xs: list_a ).
% 2.47/1.51
% 2.47/1.51 thf(sy_v_ys,type,
% 2.47/1.51 ys: list_a ).
% 2.47/1.51
% 2.47/1.51 thf(fact_0_i__append__eq__i__append__conv,axiom,
% 2.47/1.51 ! [Xs: list_nat,Ys: list_nat,F: nat > nat,G: nat > nat] :
% 2.47/1.51 ( ( ( size_size_list_nat @ Xs )
% 2.47/1.51 = ( size_size_list_nat @ Ys ) )
% 2.47/1.51 => ( ( ( listIn923761578nd_nat @ Xs @ F )
% 2.47/1.51 = ( listIn923761578nd_nat @ Ys @ G ) )
% 2.47/1.51 = ( ( Xs = Ys )
% 2.47/1.51 & ( F = G ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_1_i__append__eq__i__append__conv,axiom,
% 2.47/1.51 ! [Xs: list_a,Ys: list_a,F: nat > a,G: nat > a] :
% 2.47/1.51 ( ( ( size_size_list_a @ Xs )
% 2.47/1.51 = ( size_size_list_a @ Ys ) )
% 2.47/1.51 => ( ( ( listIn1312259492pend_a @ Xs @ F )
% 2.47/1.51 = ( listIn1312259492pend_a @ Ys @ G ) )
% 2.47/1.51 = ( ( Xs = Ys )
% 2.47/1.51 & ( F = G ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_2_i__append__nth1,axiom,
% 2.47/1.51 ! [N: nat,Xs: list_nat,F: nat > nat] :
% 2.47/1.51 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.47/1.51 => ( ( listIn923761578nd_nat @ Xs @ F @ N )
% 2.47/1.51 = ( nth_nat @ Xs @ N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_3_i__append__nth1,axiom,
% 2.47/1.51 ! [N: nat,Xs: list_a,F: nat > a] :
% 2.47/1.51 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 2.47/1.51 => ( ( listIn1312259492pend_a @ Xs @ F @ N )
% 2.47/1.51 = ( nth_a @ Xs @ N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_4_nth__equalityI,axiom,
% 2.47/1.51 ! [Xs: list_nat,Ys: list_nat] :
% 2.47/1.51 ( ( ( size_size_list_nat @ Xs )
% 2.47/1.51 = ( size_size_list_nat @ Ys ) )
% 2.47/1.51 => ( ! [I: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.47/1.51 => ( ( nth_nat @ Xs @ I )
% 2.47/1.51 = ( nth_nat @ Ys @ I ) ) )
% 2.47/1.51 => ( Xs = Ys ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_5_nth__equalityI,axiom,
% 2.47/1.51 ! [Xs: list_a,Ys: list_a] :
% 2.47/1.51 ( ( ( size_size_list_a @ Xs )
% 2.47/1.51 = ( size_size_list_a @ Ys ) )
% 2.47/1.51 => ( ! [I: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) )
% 2.47/1.51 => ( ( nth_a @ Xs @ I )
% 2.47/1.51 = ( nth_a @ Ys @ I ) ) )
% 2.47/1.51 => ( Xs = Ys ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_6_Skolem__list__nth,axiom,
% 2.47/1.51 ! [K: nat,P: nat > nat > $o] :
% 2.47/1.51 ( ( ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I2 @ K )
% 2.47/1.51 => ? [X: nat] : ( P @ I2 @ X ) ) )
% 2.47/1.51 = ( ? [Xs2: list_nat] :
% 2.47/1.51 ( ( ( size_size_list_nat @ Xs2 )
% 2.47/1.51 = K )
% 2.47/1.51 & ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I2 @ K )
% 2.47/1.51 => ( P @ I2 @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_7_Skolem__list__nth,axiom,
% 2.47/1.51 ! [K: nat,P: nat > a > $o] :
% 2.47/1.51 ( ( ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I2 @ K )
% 2.47/1.51 => ? [X: a] : ( P @ I2 @ X ) ) )
% 2.47/1.51 = ( ? [Xs2: list_a] :
% 2.47/1.51 ( ( ( size_size_list_a @ Xs2 )
% 2.47/1.51 = K )
% 2.47/1.51 & ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I2 @ K )
% 2.47/1.51 => ( P @ I2 @ ( nth_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_8_list__eq__iff__nth__eq,axiom,
% 2.47/1.51 ( ( ^ [Y: list_nat,Z: list_nat] : ( Y = Z ) )
% 2.47/1.51 = ( ^ [Xs2: list_nat,Ys2: list_nat] :
% 2.47/1.51 ( ( ( size_size_list_nat @ Xs2 )
% 2.47/1.51 = ( size_size_list_nat @ Ys2 ) )
% 2.47/1.51 & ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 2.47/1.51 => ( ( nth_nat @ Xs2 @ I2 )
% 2.47/1.51 = ( nth_nat @ Ys2 @ I2 ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_9_list__eq__iff__nth__eq,axiom,
% 2.47/1.51 ( ( ^ [Y: list_a,Z: list_a] : ( Y = Z ) )
% 2.47/1.51 = ( ^ [Xs2: list_a,Ys2: list_a] :
% 2.47/1.51 ( ( ( size_size_list_a @ Xs2 )
% 2.47/1.51 = ( size_size_list_a @ Ys2 ) )
% 2.47/1.51 & ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs2 ) )
% 2.47/1.51 => ( ( nth_a @ Xs2 @ I2 )
% 2.47/1.51 = ( nth_a @ Ys2 @ I2 ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_10_order__refl,axiom,
% 2.47/1.51 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_11_list__desc__trans__le,axiom,
% 2.47/1.51 ( list_desc_nat
% 2.47/1.51 = ( ^ [Xs2: list_nat] :
% 2.47/1.51 ! [J: nat] :
% 2.47/1.51 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 2.47/1.51 => ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ I2 @ J )
% 2.47/1.51 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_12_length__induct,axiom,
% 2.47/1.51 ! [P: list_nat > $o,Xs: list_nat] :
% 2.47/1.51 ( ! [Xs3: list_nat] :
% 2.47/1.51 ( ! [Ys3: list_nat] :
% 2.47/1.51 ( ( ord_less_nat @ ( size_size_list_nat @ Ys3 ) @ ( size_size_list_nat @ Xs3 ) )
% 2.47/1.51 => ( P @ Ys3 ) )
% 2.47/1.51 => ( P @ Xs3 ) )
% 2.47/1.51 => ( P @ Xs ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_13_length__induct,axiom,
% 2.47/1.51 ! [P: list_a > $o,Xs: list_a] :
% 2.47/1.51 ( ! [Xs3: list_a] :
% 2.47/1.51 ( ! [Ys3: list_a] :
% 2.47/1.51 ( ( ord_less_nat @ ( size_size_list_a @ Ys3 ) @ ( size_size_list_a @ Xs3 ) )
% 2.47/1.51 => ( P @ Ys3 ) )
% 2.47/1.51 => ( P @ Xs3 ) )
% 2.47/1.51 => ( P @ Xs ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_14_nat__less__le,axiom,
% 2.47/1.51 ( ord_less_nat
% 2.47/1.51 = ( ^ [M: nat,N2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ M @ N2 )
% 2.47/1.51 & ( M != N2 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_15_less__imp__le__nat,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_nat @ M2 @ N )
% 2.47/1.51 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_16_le__eq__less__or__eq,axiom,
% 2.47/1.51 ( ord_less_eq_nat
% 2.47/1.51 = ( ^ [M: nat,N2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ M @ N2 )
% 2.47/1.51 | ( M = N2 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_17_less__or__eq__imp__le,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ( ord_less_nat @ M2 @ N )
% 2.47/1.51 | ( M2 = N ) )
% 2.47/1.51 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_18_le__neq__implies__less,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ M2 @ N )
% 2.47/1.51 => ( ( M2 != N )
% 2.47/1.51 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_19_less__mono__imp__le__mono,axiom,
% 2.47/1.51 ! [F: nat > nat,I3: nat,J2: nat] :
% 2.47/1.51 ( ! [I: nat,J3: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I @ J3 )
% 2.47/1.51 => ( ord_less_nat @ ( F @ I ) @ ( F @ J3 ) ) )
% 2.47/1.51 => ( ( ord_less_eq_nat @ I3 @ J2 )
% 2.47/1.51 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( F @ J2 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_20_dual__order_Oantisym,axiom,
% 2.47/1.51 ! [B: nat,A: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ B @ A )
% 2.47/1.51 => ( ( ord_less_eq_nat @ A @ B )
% 2.47/1.51 => ( A = B ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_21_dual__order_Oeq__iff,axiom,
% 2.47/1.51 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 2.47/1.51 = ( ^ [A2: nat,B2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.47/1.51 & ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_22_dual__order_Otrans,axiom,
% 2.47/1.51 ! [B: nat,A: nat,C: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ B @ A )
% 2.47/1.51 => ( ( ord_less_eq_nat @ C @ B )
% 2.47/1.51 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_23_linorder__wlog,axiom,
% 2.47/1.51 ! [P: nat > nat > $o,A: nat,B: nat] :
% 2.47/1.51 ( ! [A3: nat,B3: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A3 @ B3 )
% 2.47/1.51 => ( P @ A3 @ B3 ) )
% 2.47/1.51 => ( ! [A3: nat,B3: nat] :
% 2.47/1.51 ( ( P @ B3 @ A3 )
% 2.47/1.51 => ( P @ A3 @ B3 ) )
% 2.47/1.51 => ( P @ A @ B ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_24_dual__order_Orefl,axiom,
% 2.47/1.51 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_25_order__trans,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.47/1.51 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 2.47/1.51 => ( ord_less_eq_nat @ X2 @ Z2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_26_order__class_Oorder_Oantisym,axiom,
% 2.47/1.51 ! [A: nat,B: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A @ B )
% 2.47/1.51 => ( ( ord_less_eq_nat @ B @ A )
% 2.47/1.51 => ( A = B ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_27_ord__le__eq__trans,axiom,
% 2.47/1.51 ! [A: nat,B: nat,C: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A @ B )
% 2.47/1.51 => ( ( B = C )
% 2.47/1.51 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_28_ord__eq__le__trans,axiom,
% 2.47/1.51 ! [A: nat,B: nat,C: nat] :
% 2.47/1.51 ( ( A = B )
% 2.47/1.51 => ( ( ord_less_eq_nat @ B @ C )
% 2.47/1.51 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_29_order__class_Oorder_Oeq__iff,axiom,
% 2.47/1.51 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 2.47/1.51 = ( ^ [A2: nat,B2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.47/1.51 & ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_30_antisym__conv,axiom,
% 2.47/1.51 ! [Y2: nat,X2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 2.47/1.51 => ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.47/1.51 = ( X2 = Y2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_31_le__cases3,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.47/1.51 ( ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.47/1.51 => ~ ( ord_less_eq_nat @ Y2 @ Z2 ) )
% 2.47/1.51 => ( ( ( ord_less_eq_nat @ Y2 @ X2 )
% 2.47/1.51 => ~ ( ord_less_eq_nat @ X2 @ Z2 ) )
% 2.47/1.51 => ( ( ( ord_less_eq_nat @ X2 @ Z2 )
% 2.47/1.51 => ~ ( ord_less_eq_nat @ Z2 @ Y2 ) )
% 2.47/1.51 => ( ( ( ord_less_eq_nat @ Z2 @ Y2 )
% 2.47/1.51 => ~ ( ord_less_eq_nat @ Y2 @ X2 ) )
% 2.47/1.51 => ( ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 2.47/1.51 => ~ ( ord_less_eq_nat @ Z2 @ X2 ) )
% 2.47/1.51 => ~ ( ( ord_less_eq_nat @ Z2 @ X2 )
% 2.47/1.51 => ~ ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_32_order_Otrans,axiom,
% 2.47/1.51 ! [A: nat,B: nat,C: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A @ B )
% 2.47/1.51 => ( ( ord_less_eq_nat @ B @ C )
% 2.47/1.51 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_33_le__cases,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ~ ( ord_less_eq_nat @ X2 @ Y2 )
% 2.47/1.51 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_34_eq__refl,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( X2 = Y2 )
% 2.47/1.51 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_35_linear,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.47/1.51 | ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_36_antisym,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.47/1.51 => ( ( ord_less_eq_nat @ Y2 @ X2 )
% 2.47/1.51 => ( X2 = Y2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_37_eq__iff,axiom,
% 2.47/1.51 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 2.47/1.51 = ( ^ [X3: nat,Y3: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.47/1.51 & ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_38_ord__le__eq__subst,axiom,
% 2.47/1.51 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A @ B )
% 2.47/1.51 => ( ( ( F @ B )
% 2.47/1.51 = C )
% 2.47/1.51 => ( ! [X4: nat,Y4: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 2.47/1.51 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.47/1.51 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_39_ord__eq__le__subst,axiom,
% 2.47/1.51 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.47/1.51 ( ( A
% 2.47/1.51 = ( F @ B ) )
% 2.47/1.51 => ( ( ord_less_eq_nat @ B @ C )
% 2.47/1.51 => ( ! [X4: nat,Y4: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 2.47/1.51 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.47/1.51 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_40_order__subst2,axiom,
% 2.47/1.51 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A @ B )
% 2.47/1.51 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 2.47/1.51 => ( ! [X4: nat,Y4: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 2.47/1.51 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.47/1.51 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_41_order__subst1,axiom,
% 2.47/1.51 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 2.47/1.51 => ( ( ord_less_eq_nat @ B @ C )
% 2.47/1.51 => ( ! [X4: nat,Y4: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 2.47/1.51 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.47/1.51 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_42_dual__order_Ostrict__implies__not__eq,axiom,
% 2.47/1.51 ! [B: nat,A: nat] :
% 2.47/1.51 ( ( ord_less_nat @ B @ A )
% 2.47/1.51 => ( A != B ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_43_order_Ostrict__implies__not__eq,axiom,
% 2.47/1.51 ! [A: nat,B: nat] :
% 2.47/1.51 ( ( ord_less_nat @ A @ B )
% 2.47/1.51 => ( A != B ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_44_not__less__iff__gr__or__eq,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 2.47/1.51 = ( ( ord_less_nat @ Y2 @ X2 )
% 2.47/1.51 | ( X2 = Y2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_45_dual__order_Ostrict__trans,axiom,
% 2.47/1.51 ! [B: nat,A: nat,C: nat] :
% 2.47/1.51 ( ( ord_less_nat @ B @ A )
% 2.47/1.51 => ( ( ord_less_nat @ C @ B )
% 2.47/1.51 => ( ord_less_nat @ C @ A ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_46_linorder__less__wlog,axiom,
% 2.47/1.51 ! [P: nat > nat > $o,A: nat,B: nat] :
% 2.47/1.51 ( ! [A3: nat,B3: nat] :
% 2.47/1.51 ( ( ord_less_nat @ A3 @ B3 )
% 2.47/1.51 => ( P @ A3 @ B3 ) )
% 2.47/1.51 => ( ! [A3: nat] : ( P @ A3 @ A3 )
% 2.47/1.51 => ( ! [A3: nat,B3: nat] :
% 2.47/1.51 ( ( P @ B3 @ A3 )
% 2.47/1.51 => ( P @ A3 @ B3 ) )
% 2.47/1.51 => ( P @ A @ B ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_47_exists__least__iff,axiom,
% 2.47/1.51 ( ( ^ [P2: nat > $o] :
% 2.47/1.51 ? [X: nat] : ( P2 @ X ) )
% 2.47/1.51 = ( ^ [P3: nat > $o] :
% 2.47/1.51 ? [N2: nat] :
% 2.47/1.51 ( ( P3 @ N2 )
% 2.47/1.51 & ! [M: nat] :
% 2.47/1.51 ( ( ord_less_nat @ M @ N2 )
% 2.47/1.51 => ~ ( P3 @ M ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_48_less__imp__not__less,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_49_order_Ostrict__trans,axiom,
% 2.47/1.51 ! [A: nat,B: nat,C: nat] :
% 2.47/1.51 ( ( ord_less_nat @ A @ B )
% 2.47/1.51 => ( ( ord_less_nat @ B @ C )
% 2.47/1.51 => ( ord_less_nat @ A @ C ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_50_dual__order_Oirrefl,axiom,
% 2.47/1.51 ! [A: nat] :
% 2.47/1.51 ~ ( ord_less_nat @ A @ A ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_51_linorder__cases,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ~ ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 => ( ( X2 != Y2 )
% 2.47/1.51 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_52_less__imp__triv,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat,P: $o] :
% 2.47/1.51 ( ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 => ( ( ord_less_nat @ Y2 @ X2 )
% 2.47/1.51 => P ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_53_less__imp__not__eq2,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 => ( Y2 != X2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_54_antisym__conv3,axiom,
% 2.47/1.51 ! [Y2: nat,X2: nat] :
% 2.47/1.51 ( ~ ( ord_less_nat @ Y2 @ X2 )
% 2.47/1.51 => ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 2.47/1.51 = ( X2 = Y2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_55_less__induct,axiom,
% 2.47/1.51 ! [P: nat > $o,A: nat] :
% 2.47/1.51 ( ! [X4: nat] :
% 2.47/1.51 ( ! [Y5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ Y5 @ X4 )
% 2.47/1.51 => ( P @ Y5 ) )
% 2.47/1.51 => ( P @ X4 ) )
% 2.47/1.51 => ( P @ A ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_56_less__not__sym,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_57_less__imp__not__eq,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 => ( X2 != Y2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_58_dual__order_Oasym,axiom,
% 2.47/1.51 ! [B: nat,A: nat] :
% 2.47/1.51 ( ( ord_less_nat @ B @ A )
% 2.47/1.51 => ~ ( ord_less_nat @ A @ B ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_59_ord__less__eq__trans,axiom,
% 2.47/1.51 ! [A: nat,B: nat,C: nat] :
% 2.47/1.51 ( ( ord_less_nat @ A @ B )
% 2.47/1.51 => ( ( B = C )
% 2.47/1.51 => ( ord_less_nat @ A @ C ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_60_ord__eq__less__trans,axiom,
% 2.47/1.51 ! [A: nat,B: nat,C: nat] :
% 2.47/1.51 ( ( A = B )
% 2.47/1.51 => ( ( ord_less_nat @ B @ C )
% 2.47/1.51 => ( ord_less_nat @ A @ C ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_61_less__irrefl,axiom,
% 2.47/1.51 ! [X2: nat] :
% 2.47/1.51 ~ ( ord_less_nat @ X2 @ X2 ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_62_less__linear,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 | ( X2 = Y2 )
% 2.47/1.51 | ( ord_less_nat @ Y2 @ X2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_63_less__trans,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 => ( ( ord_less_nat @ Y2 @ Z2 )
% 2.47/1.51 => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_64_less__asym_H,axiom,
% 2.47/1.51 ! [A: nat,B: nat] :
% 2.47/1.51 ( ( ord_less_nat @ A @ B )
% 2.47/1.51 => ~ ( ord_less_nat @ B @ A ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_65_less__asym,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_66_less__imp__neq,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 => ( X2 != Y2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_67_order_Oasym,axiom,
% 2.47/1.51 ! [A: nat,B: nat] :
% 2.47/1.51 ( ( ord_less_nat @ A @ B )
% 2.47/1.51 => ~ ( ord_less_nat @ B @ A ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_68_neq__iff,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( X2 != Y2 )
% 2.47/1.51 = ( ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 | ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_69_neqE,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( X2 != Y2 )
% 2.47/1.51 => ( ~ ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_70_gt__ex,axiom,
% 2.47/1.51 ! [X2: nat] :
% 2.47/1.51 ? [X_1: nat] : ( ord_less_nat @ X2 @ X_1 ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_71_order__less__subst2,axiom,
% 2.47/1.51 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.47/1.51 ( ( ord_less_nat @ A @ B )
% 2.47/1.51 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 2.47/1.51 => ( ! [X4: nat,Y4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X4 @ Y4 )
% 2.47/1.51 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.47/1.51 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_72_order__less__subst1,axiom,
% 2.47/1.51 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.47/1.51 ( ( ord_less_nat @ A @ ( F @ B ) )
% 2.47/1.51 => ( ( ord_less_nat @ B @ C )
% 2.47/1.51 => ( ! [X4: nat,Y4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X4 @ Y4 )
% 2.47/1.51 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.47/1.51 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_73_ord__less__eq__subst,axiom,
% 2.47/1.51 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.47/1.51 ( ( ord_less_nat @ A @ B )
% 2.47/1.51 => ( ( ( F @ B )
% 2.47/1.51 = C )
% 2.47/1.51 => ( ! [X4: nat,Y4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X4 @ Y4 )
% 2.47/1.51 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.47/1.51 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_74_ord__eq__less__subst,axiom,
% 2.47/1.51 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.47/1.51 ( ( A
% 2.47/1.51 = ( F @ B ) )
% 2.47/1.51 => ( ( ord_less_nat @ B @ C )
% 2.47/1.51 => ( ! [X4: nat,Y4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X4 @ Y4 )
% 2.47/1.51 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.47/1.51 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_75_linorder__neqE__nat,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( X2 != Y2 )
% 2.47/1.51 => ( ~ ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_76_infinite__descent,axiom,
% 2.47/1.51 ! [P: nat > $o,N: nat] :
% 2.47/1.51 ( ! [N3: nat] :
% 2.47/1.51 ( ~ ( P @ N3 )
% 2.47/1.51 => ? [M3: nat] :
% 2.47/1.51 ( ( ord_less_nat @ M3 @ N3 )
% 2.47/1.51 & ~ ( P @ M3 ) ) )
% 2.47/1.51 => ( P @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_77_nat__less__induct,axiom,
% 2.47/1.51 ! [P: nat > $o,N: nat] :
% 2.47/1.51 ( ! [N3: nat] :
% 2.47/1.51 ( ! [M3: nat] :
% 2.47/1.51 ( ( ord_less_nat @ M3 @ N3 )
% 2.47/1.51 => ( P @ M3 ) )
% 2.47/1.51 => ( P @ N3 ) )
% 2.47/1.51 => ( P @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_78_less__irrefl__nat,axiom,
% 2.47/1.51 ! [N: nat] :
% 2.47/1.51 ~ ( ord_less_nat @ N @ N ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_79_less__not__refl3,axiom,
% 2.47/1.51 ! [S: nat,T: nat] :
% 2.47/1.51 ( ( ord_less_nat @ S @ T )
% 2.47/1.51 => ( S != T ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_80_less__not__refl2,axiom,
% 2.47/1.51 ! [N: nat,M2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ N @ M2 )
% 2.47/1.51 => ( M2 != N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_81_less__not__refl,axiom,
% 2.47/1.51 ! [N: nat] :
% 2.47/1.51 ~ ( ord_less_nat @ N @ N ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_82_nat__neq__iff,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( M2 != N )
% 2.47/1.51 = ( ( ord_less_nat @ M2 @ N )
% 2.47/1.51 | ( ord_less_nat @ N @ M2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_83_Nat_Oex__has__greatest__nat,axiom,
% 2.47/1.51 ! [P: nat > $o,K: nat,B: nat] :
% 2.47/1.51 ( ( P @ K )
% 2.47/1.51 => ( ! [Y4: nat] :
% 2.47/1.51 ( ( P @ Y4 )
% 2.47/1.51 => ( ord_less_eq_nat @ Y4 @ B ) )
% 2.47/1.51 => ? [X4: nat] :
% 2.47/1.51 ( ( P @ X4 )
% 2.47/1.51 & ! [Y5: nat] :
% 2.47/1.51 ( ( P @ Y5 )
% 2.47/1.51 => ( ord_less_eq_nat @ Y5 @ X4 ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_84_nat__le__linear,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ M2 @ N )
% 2.47/1.51 | ( ord_less_eq_nat @ N @ M2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_85_le__antisym,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ M2 @ N )
% 2.47/1.51 => ( ( ord_less_eq_nat @ N @ M2 )
% 2.47/1.51 => ( M2 = N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_86_eq__imp__le,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( M2 = N )
% 2.47/1.51 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_87_le__trans,axiom,
% 2.47/1.51 ! [I3: nat,J2: nat,K: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ I3 @ J2 )
% 2.47/1.51 => ( ( ord_less_eq_nat @ J2 @ K )
% 2.47/1.51 => ( ord_less_eq_nat @ I3 @ K ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_88_le__refl,axiom,
% 2.47/1.51 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_89_size__neq__size__imp__neq,axiom,
% 2.47/1.51 ! [X2: list_a,Y2: list_a] :
% 2.47/1.51 ( ( ( size_size_list_a @ X2 )
% 2.47/1.51 != ( size_size_list_a @ Y2 ) )
% 2.47/1.51 => ( X2 != Y2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_90_size__neq__size__imp__neq,axiom,
% 2.47/1.51 ! [X2: list_nat,Y2: list_nat] :
% 2.47/1.51 ( ( ( size_size_list_nat @ X2 )
% 2.47/1.51 != ( size_size_list_nat @ Y2 ) )
% 2.47/1.51 => ( X2 != Y2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_91_neq__if__length__neq,axiom,
% 2.47/1.51 ! [Xs: list_a,Ys: list_a] :
% 2.47/1.51 ( ( ( size_size_list_a @ Xs )
% 2.47/1.51 != ( size_size_list_a @ Ys ) )
% 2.47/1.51 => ( Xs != Ys ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_92_neq__if__length__neq,axiom,
% 2.47/1.51 ! [Xs: list_nat,Ys: list_nat] :
% 2.47/1.51 ( ( ( size_size_list_nat @ Xs )
% 2.47/1.51 != ( size_size_list_nat @ Ys ) )
% 2.47/1.51 => ( Xs != Ys ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_93_Ex__list__of__length,axiom,
% 2.47/1.51 ! [N: nat] :
% 2.47/1.51 ? [Xs3: list_a] :
% 2.47/1.51 ( ( size_size_list_a @ Xs3 )
% 2.47/1.51 = N ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_94_Ex__list__of__length,axiom,
% 2.47/1.51 ! [N: nat] :
% 2.47/1.51 ? [Xs3: list_nat] :
% 2.47/1.51 ( ( size_size_list_nat @ Xs3 )
% 2.47/1.51 = N ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_95_list__desc__trans,axiom,
% 2.47/1.51 ( list_desc_nat
% 2.47/1.51 = ( ^ [Xs2: list_nat] :
% 2.47/1.51 ! [J: nat] :
% 2.47/1.51 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 2.47/1.51 => ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I2 @ J )
% 2.47/1.51 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_96_order_Onot__eq__order__implies__strict,axiom,
% 2.47/1.51 ! [A: nat,B: nat] :
% 2.47/1.51 ( ( A != B )
% 2.47/1.51 => ( ( ord_less_eq_nat @ A @ B )
% 2.47/1.51 => ( ord_less_nat @ A @ B ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_97_dual__order_Ostrict__implies__order,axiom,
% 2.47/1.51 ! [B: nat,A: nat] :
% 2.47/1.51 ( ( ord_less_nat @ B @ A )
% 2.47/1.51 => ( ord_less_eq_nat @ B @ A ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_98_dual__order_Ostrict__iff__order,axiom,
% 2.47/1.51 ( ord_less_nat
% 2.47/1.51 = ( ^ [B2: nat,A2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.47/1.51 & ( A2 != B2 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_99_dual__order_Oorder__iff__strict,axiom,
% 2.47/1.51 ( ord_less_eq_nat
% 2.47/1.51 = ( ^ [B2: nat,A2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ B2 @ A2 )
% 2.47/1.51 | ( A2 = B2 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_100_order_Ostrict__implies__order,axiom,
% 2.47/1.51 ! [A: nat,B: nat] :
% 2.47/1.51 ( ( ord_less_nat @ A @ B )
% 2.47/1.51 => ( ord_less_eq_nat @ A @ B ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_101_dual__order_Ostrict__trans2,axiom,
% 2.47/1.51 ! [B: nat,A: nat,C: nat] :
% 2.47/1.51 ( ( ord_less_nat @ B @ A )
% 2.47/1.51 => ( ( ord_less_eq_nat @ C @ B )
% 2.47/1.51 => ( ord_less_nat @ C @ A ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_102_dual__order_Ostrict__trans1,axiom,
% 2.47/1.51 ! [B: nat,A: nat,C: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ B @ A )
% 2.47/1.51 => ( ( ord_less_nat @ C @ B )
% 2.47/1.51 => ( ord_less_nat @ C @ A ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_103_order_Ostrict__iff__order,axiom,
% 2.47/1.51 ( ord_less_nat
% 2.47/1.51 = ( ^ [A2: nat,B2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.47/1.51 & ( A2 != B2 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_104_order_Oorder__iff__strict,axiom,
% 2.47/1.51 ( ord_less_eq_nat
% 2.47/1.51 = ( ^ [A2: nat,B2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ A2 @ B2 )
% 2.47/1.51 | ( A2 = B2 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_105_order_Ostrict__trans2,axiom,
% 2.47/1.51 ! [A: nat,B: nat,C: nat] :
% 2.47/1.51 ( ( ord_less_nat @ A @ B )
% 2.47/1.51 => ( ( ord_less_eq_nat @ B @ C )
% 2.47/1.51 => ( ord_less_nat @ A @ C ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_106_order_Ostrict__trans1,axiom,
% 2.47/1.51 ! [A: nat,B: nat,C: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A @ B )
% 2.47/1.51 => ( ( ord_less_nat @ B @ C )
% 2.47/1.51 => ( ord_less_nat @ A @ C ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_107_not__le__imp__less,axiom,
% 2.47/1.51 ! [Y2: nat,X2: nat] :
% 2.47/1.51 ( ~ ( ord_less_eq_nat @ Y2 @ X2 )
% 2.47/1.51 => ( ord_less_nat @ X2 @ Y2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_108_less__le__not__le,axiom,
% 2.47/1.51 ( ord_less_nat
% 2.47/1.51 = ( ^ [X3: nat,Y3: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.47/1.51 & ~ ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_109_le__imp__less__or__eq,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.47/1.51 => ( ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 | ( X2 = Y2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_110_le__less__linear,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.47/1.51 | ( ord_less_nat @ Y2 @ X2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_111_less__le__trans,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 2.47/1.51 => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_112_le__less__trans,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.47/1.51 => ( ( ord_less_nat @ Y2 @ Z2 )
% 2.47/1.51 => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_113_less__imp__le,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_114_antisym__conv2,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.47/1.51 => ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 2.47/1.51 = ( X2 = Y2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_115_antisym__conv1,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ~ ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 => ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.47/1.51 = ( X2 = Y2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_116_le__neq__trans,axiom,
% 2.47/1.51 ! [A: nat,B: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A @ B )
% 2.47/1.51 => ( ( A != B )
% 2.47/1.51 => ( ord_less_nat @ A @ B ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_117_not__less,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 2.47/1.51 = ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_118_not__le,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ~ ( ord_less_eq_nat @ X2 @ Y2 ) )
% 2.47/1.51 = ( ord_less_nat @ Y2 @ X2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_119_order__less__le__subst2,axiom,
% 2.47/1.51 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.47/1.51 ( ( ord_less_nat @ A @ B )
% 2.47/1.51 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 2.47/1.51 => ( ! [X4: nat,Y4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X4 @ Y4 )
% 2.47/1.51 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.47/1.51 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_120_order__less__le__subst1,axiom,
% 2.47/1.51 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.47/1.51 ( ( ord_less_nat @ A @ ( F @ B ) )
% 2.47/1.51 => ( ( ord_less_eq_nat @ B @ C )
% 2.47/1.51 => ( ! [X4: nat,Y4: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 2.47/1.51 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.47/1.51 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_121_order__le__less__subst2,axiom,
% 2.47/1.51 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A @ B )
% 2.47/1.51 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 2.47/1.51 => ( ! [X4: nat,Y4: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 2.47/1.51 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.47/1.51 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_122_order__le__less__subst1,axiom,
% 2.47/1.51 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 2.47/1.51 => ( ( ord_less_nat @ B @ C )
% 2.47/1.51 => ( ! [X4: nat,Y4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X4 @ Y4 )
% 2.47/1.51 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.47/1.51 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_123_less__le,axiom,
% 2.47/1.51 ( ord_less_nat
% 2.47/1.51 = ( ^ [X3: nat,Y3: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.47/1.51 & ( X3 != Y3 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_124_le__less,axiom,
% 2.47/1.51 ( ord_less_eq_nat
% 2.47/1.51 = ( ^ [X3: nat,Y3: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X3 @ Y3 )
% 2.47/1.51 | ( X3 = Y3 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_125_leI,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ~ ( ord_less_nat @ X2 @ Y2 )
% 2.47/1.51 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_126_leD,axiom,
% 2.47/1.51 ! [Y2: nat,X2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 2.47/1.51 => ~ ( ord_less_nat @ X2 @ Y2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_127_list__strict__asc__trans__le,axiom,
% 2.47/1.51 ! [Xs: list_nat] :
% 2.47/1.51 ( ( list_strict_asc_nat @ Xs )
% 2.47/1.51 => ! [J4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ J4 @ ( size_size_list_nat @ Xs ) )
% 2.47/1.51 => ! [I4: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ I4 @ J4 )
% 2.47/1.51 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I4 ) @ ( nth_nat @ Xs @ J4 ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_128_list__asc__trans__le,axiom,
% 2.47/1.51 ( list_asc_nat
% 2.47/1.51 = ( ^ [Xs2: list_nat] :
% 2.47/1.51 ! [J: nat] :
% 2.47/1.51 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 2.47/1.51 => ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ I2 @ J )
% 2.47/1.51 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_129_list__strict__desc__trans,axiom,
% 2.47/1.51 ( list_strict_desc_nat
% 2.47/1.51 = ( ^ [Xs2: list_nat] :
% 2.47/1.51 ! [J: nat] :
% 2.47/1.51 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 2.47/1.51 => ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I2 @ J )
% 2.47/1.51 => ( ord_less_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_130_list__strict__asc__trans,axiom,
% 2.47/1.51 ( list_strict_asc_nat
% 2.47/1.51 = ( ^ [Xs2: list_nat] :
% 2.47/1.51 ! [J: nat] :
% 2.47/1.51 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 2.47/1.51 => ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I2 @ J )
% 2.47/1.51 => ( ord_less_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_131_list__asc__trans,axiom,
% 2.47/1.51 ( list_asc_nat
% 2.47/1.51 = ( ^ [Xs2: list_nat] :
% 2.47/1.51 ! [J: nat] :
% 2.47/1.51 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 2.47/1.51 => ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I2 @ J )
% 2.47/1.51 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_132_nat__descend__induct,axiom,
% 2.47/1.51 ! [N: nat,P: nat > $o,M2: nat] :
% 2.47/1.51 ( ! [K2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ N @ K2 )
% 2.47/1.51 => ( P @ K2 ) )
% 2.47/1.51 => ( ! [K2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ K2 @ N )
% 2.47/1.51 => ( ! [I4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ K2 @ I4 )
% 2.47/1.51 => ( P @ I4 ) )
% 2.47/1.51 => ( P @ K2 ) ) )
% 2.47/1.51 => ( P @ M2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_133_complete__interval,axiom,
% 2.47/1.51 ! [A: nat,B: nat,P: nat > $o] :
% 2.47/1.51 ( ( ord_less_nat @ A @ B )
% 2.47/1.51 => ( ( P @ A )
% 2.47/1.51 => ( ~ ( P @ B )
% 2.47/1.51 => ? [C2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A @ C2 )
% 2.47/1.51 & ( ord_less_eq_nat @ C2 @ B )
% 2.47/1.51 & ! [X5: nat] :
% 2.47/1.51 ( ( ( ord_less_eq_nat @ A @ X5 )
% 2.47/1.51 & ( ord_less_nat @ X5 @ C2 ) )
% 2.47/1.51 => ( P @ X5 ) )
% 2.47/1.51 & ! [D: nat] :
% 2.47/1.51 ( ! [X4: nat] :
% 2.47/1.51 ( ( ( ord_less_eq_nat @ A @ X4 )
% 2.47/1.51 & ( ord_less_nat @ X4 @ D ) )
% 2.47/1.51 => ( P @ X4 ) )
% 2.47/1.51 => ( ord_less_eq_nat @ D @ C2 ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_134_le__greater__neq__conv,axiom,
% 2.47/1.51 ( ord_less_eq_nat
% 2.47/1.51 = ( ^ [N2: nat,A2: nat] :
% 2.47/1.51 ! [X3: nat] :
% 2.47/1.51 ( ( ord_less_nat @ A2 @ X3 )
% 2.47/1.51 => ( N2 != X3 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_135_greater__le__neq__conv,axiom,
% 2.47/1.51 ( ord_less_nat
% 2.47/1.51 = ( ^ [A2: nat,N2: nat] :
% 2.47/1.51 ! [X3: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ X3 @ A2 )
% 2.47/1.51 => ( N2 != X3 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_136_less__ge__neq__conv,axiom,
% 2.47/1.51 ( ord_less_nat
% 2.47/1.51 = ( ^ [N2: nat,A2: nat] :
% 2.47/1.51 ! [X3: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A2 @ X3 )
% 2.47/1.51 => ( N2 != X3 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_137_list__strict__asc__imp__list__asc,axiom,
% 2.47/1.51 ! [Xs: list_nat] :
% 2.47/1.51 ( ( list_strict_asc_nat @ Xs )
% 2.47/1.51 => ( list_asc_nat @ Xs ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_138_list__strict__desc__imp__list__desc,axiom,
% 2.47/1.51 ! [Xs: list_nat] :
% 2.47/1.51 ( ( list_strict_desc_nat @ Xs )
% 2.47/1.51 => ( list_desc_nat @ Xs ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_139_ge__less__neq__conv,axiom,
% 2.47/1.51 ( ord_less_eq_nat
% 2.47/1.51 = ( ^ [A2: nat,N2: nat] :
% 2.47/1.51 ! [X3: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X3 @ A2 )
% 2.47/1.51 => ( N2 != X3 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_140_minf_I8_J,axiom,
% 2.47/1.51 ! [T: nat] :
% 2.47/1.51 ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X5 @ Z3 )
% 2.47/1.51 => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_141_minf_I6_J,axiom,
% 2.47/1.51 ! [T: nat] :
% 2.47/1.51 ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X5 @ Z3 )
% 2.47/1.51 => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_142_pinf_I8_J,axiom,
% 2.47/1.51 ! [T: nat] :
% 2.47/1.51 ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ Z3 @ X5 )
% 2.47/1.51 => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_143_pinf_I1_J,axiom,
% 2.47/1.51 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 2.47/1.51 ( ? [Z4: nat] :
% 2.47/1.51 ! [X4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ Z4 @ X4 )
% 2.47/1.51 => ( ( P @ X4 )
% 2.47/1.51 = ( P4 @ X4 ) ) )
% 2.47/1.51 => ( ? [Z4: nat] :
% 2.47/1.51 ! [X4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ Z4 @ X4 )
% 2.47/1.51 => ( ( Q @ X4 )
% 2.47/1.51 = ( Q2 @ X4 ) ) )
% 2.47/1.51 => ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ Z3 @ X5 )
% 2.47/1.51 => ( ( ( P @ X5 )
% 2.47/1.51 & ( Q @ X5 ) )
% 2.47/1.51 = ( ( P4 @ X5 )
% 2.47/1.51 & ( Q2 @ X5 ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_144_pinf_I2_J,axiom,
% 2.47/1.51 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 2.47/1.51 ( ? [Z4: nat] :
% 2.47/1.51 ! [X4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ Z4 @ X4 )
% 2.47/1.51 => ( ( P @ X4 )
% 2.47/1.51 = ( P4 @ X4 ) ) )
% 2.47/1.51 => ( ? [Z4: nat] :
% 2.47/1.51 ! [X4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ Z4 @ X4 )
% 2.47/1.51 => ( ( Q @ X4 )
% 2.47/1.51 = ( Q2 @ X4 ) ) )
% 2.47/1.51 => ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ Z3 @ X5 )
% 2.47/1.51 => ( ( ( P @ X5 )
% 2.47/1.51 | ( Q @ X5 ) )
% 2.47/1.51 = ( ( P4 @ X5 )
% 2.47/1.51 | ( Q2 @ X5 ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_145_pinf_I3_J,axiom,
% 2.47/1.51 ! [T: nat] :
% 2.47/1.51 ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ Z3 @ X5 )
% 2.47/1.51 => ( X5 != T ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_146_pinf_I4_J,axiom,
% 2.47/1.51 ! [T: nat] :
% 2.47/1.51 ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ Z3 @ X5 )
% 2.47/1.51 => ( X5 != T ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_147_pinf_I5_J,axiom,
% 2.47/1.51 ! [T: nat] :
% 2.47/1.51 ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ Z3 @ X5 )
% 2.47/1.51 => ~ ( ord_less_nat @ X5 @ T ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_148_pinf_I7_J,axiom,
% 2.47/1.51 ! [T: nat] :
% 2.47/1.51 ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ Z3 @ X5 )
% 2.47/1.51 => ( ord_less_nat @ T @ X5 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_149_minf_I1_J,axiom,
% 2.47/1.51 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 2.47/1.51 ( ? [Z4: nat] :
% 2.47/1.51 ! [X4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X4 @ Z4 )
% 2.47/1.51 => ( ( P @ X4 )
% 2.47/1.51 = ( P4 @ X4 ) ) )
% 2.47/1.51 => ( ? [Z4: nat] :
% 2.47/1.51 ! [X4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X4 @ Z4 )
% 2.47/1.51 => ( ( Q @ X4 )
% 2.47/1.51 = ( Q2 @ X4 ) ) )
% 2.47/1.51 => ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X5 @ Z3 )
% 2.47/1.51 => ( ( ( P @ X5 )
% 2.47/1.51 & ( Q @ X5 ) )
% 2.47/1.51 = ( ( P4 @ X5 )
% 2.47/1.51 & ( Q2 @ X5 ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_150_minf_I2_J,axiom,
% 2.47/1.51 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 2.47/1.51 ( ? [Z4: nat] :
% 2.47/1.51 ! [X4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X4 @ Z4 )
% 2.47/1.51 => ( ( P @ X4 )
% 2.47/1.51 = ( P4 @ X4 ) ) )
% 2.47/1.51 => ( ? [Z4: nat] :
% 2.47/1.51 ! [X4: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X4 @ Z4 )
% 2.47/1.51 => ( ( Q @ X4 )
% 2.47/1.51 = ( Q2 @ X4 ) ) )
% 2.47/1.51 => ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X5 @ Z3 )
% 2.47/1.51 => ( ( ( P @ X5 )
% 2.47/1.51 | ( Q @ X5 ) )
% 2.47/1.51 = ( ( P4 @ X5 )
% 2.47/1.51 | ( Q2 @ X5 ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_151_minf_I3_J,axiom,
% 2.47/1.51 ! [T: nat] :
% 2.47/1.51 ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X5 @ Z3 )
% 2.47/1.51 => ( X5 != T ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_152_minf_I4_J,axiom,
% 2.47/1.51 ! [T: nat] :
% 2.47/1.51 ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X5 @ Z3 )
% 2.47/1.51 => ( X5 != T ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_153_minf_I5_J,axiom,
% 2.47/1.51 ! [T: nat] :
% 2.47/1.51 ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X5 @ Z3 )
% 2.47/1.51 => ( ord_less_nat @ X5 @ T ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_154_minf_I7_J,axiom,
% 2.47/1.51 ! [T: nat] :
% 2.47/1.51 ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ X5 @ Z3 )
% 2.47/1.51 => ~ ( ord_less_nat @ T @ X5 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_155_pinf_I6_J,axiom,
% 2.47/1.51 ! [T: nat] :
% 2.47/1.51 ? [Z3: nat] :
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( ord_less_nat @ Z3 @ X5 )
% 2.47/1.51 => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_156_verit__comp__simplify1_I3_J,axiom,
% 2.47/1.51 ! [B4: nat,A4: nat] :
% 2.47/1.51 ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
% 2.47/1.51 = ( ord_less_nat @ A4 @ B4 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_157_sorted__iff__nth__mono,axiom,
% 2.47/1.51 ( linorder_sorted_nat
% 2.47/1.51 = ( ^ [Xs2: list_nat] :
% 2.47/1.51 ! [I2: nat,J: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ I2 @ J )
% 2.47/1.51 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 2.47/1.51 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_158_sorted__nth__mono,axiom,
% 2.47/1.51 ! [Xs: list_nat,I3: nat,J2: nat] :
% 2.47/1.51 ( ( linorder_sorted_nat @ Xs )
% 2.47/1.51 => ( ( ord_less_eq_nat @ I3 @ J2 )
% 2.47/1.51 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 2.47/1.51 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I3 ) @ ( nth_nat @ Xs @ J2 ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_159_list__ord__le__sorted__eq,axiom,
% 2.47/1.51 list_asc_nat = linorder_sorted_nat ).
% 2.47/1.51
% 2.47/1.51 thf(fact_160_verit__la__disequality,axiom,
% 2.47/1.51 ! [A: nat,B: nat] :
% 2.47/1.51 ( ( A = B )
% 2.47/1.51 | ~ ( ord_less_eq_nat @ A @ B )
% 2.47/1.51 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_161_verit__comp__simplify1_I1_J,axiom,
% 2.47/1.51 ! [A: nat] :
% 2.47/1.51 ~ ( ord_less_nat @ A @ A ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_162_sorted__iff__nth__mono__less,axiom,
% 2.47/1.51 ( linorder_sorted_nat
% 2.47/1.51 = ( ^ [Xs2: list_nat] :
% 2.47/1.51 ! [I2: nat,J: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I2 @ J )
% 2.47/1.51 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 2.47/1.51 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_163_sorted__rev__nth__mono,axiom,
% 2.47/1.51 ! [Xs: list_nat,I3: nat,J2: nat] :
% 2.47/1.51 ( ( linorder_sorted_nat @ ( rev_nat @ Xs ) )
% 2.47/1.51 => ( ( ord_less_eq_nat @ I3 @ J2 )
% 2.47/1.51 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 2.47/1.51 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ J2 ) @ ( nth_nat @ Xs @ I3 ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_164_sorted__rev__iff__nth__mono,axiom,
% 2.47/1.51 ! [Xs: list_nat] :
% 2.47/1.51 ( ( linorder_sorted_nat @ ( rev_nat @ Xs ) )
% 2.47/1.51 = ( ! [I2: nat,J: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ I2 @ J )
% 2.47/1.51 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 2.47/1.51 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ J ) @ ( nth_nat @ Xs @ I2 ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_165_sorted__iff__nth__Suc,axiom,
% 2.47/1.51 ( linorder_sorted_nat
% 2.47/1.51 = ( ^ [Xs2: list_nat] :
% 2.47/1.51 ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ ( suc @ I2 ) @ ( size_size_list_nat @ Xs2 ) )
% 2.47/1.51 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ ( suc @ I2 ) ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_166_old_Onat_Oinject,axiom,
% 2.47/1.51 ! [Nat: nat,Nat2: nat] :
% 2.47/1.51 ( ( ( suc @ Nat )
% 2.47/1.51 = ( suc @ Nat2 ) )
% 2.47/1.51 = ( Nat = Nat2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_167_nat_Oinject,axiom,
% 2.47/1.51 ! [X22: nat,Y22: nat] :
% 2.47/1.51 ( ( ( suc @ X22 )
% 2.47/1.51 = ( suc @ Y22 ) )
% 2.47/1.51 = ( X22 = Y22 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_168_rev__is__rev__conv,axiom,
% 2.47/1.51 ! [Xs: list_nat,Ys: list_nat] :
% 2.47/1.51 ( ( ( rev_nat @ Xs )
% 2.47/1.51 = ( rev_nat @ Ys ) )
% 2.47/1.51 = ( Xs = Ys ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_169_rev__is__rev__conv,axiom,
% 2.47/1.51 ! [Xs: list_a,Ys: list_a] :
% 2.47/1.51 ( ( ( rev_a @ Xs )
% 2.47/1.51 = ( rev_a @ Ys ) )
% 2.47/1.51 = ( Xs = Ys ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_170_rev__rev__ident,axiom,
% 2.47/1.51 ! [Xs: list_nat] :
% 2.47/1.51 ( ( rev_nat @ ( rev_nat @ Xs ) )
% 2.47/1.51 = Xs ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_171_rev__rev__ident,axiom,
% 2.47/1.51 ! [Xs: list_a] :
% 2.47/1.51 ( ( rev_a @ ( rev_a @ Xs ) )
% 2.47/1.51 = Xs ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_172_Suc__less__eq,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 2.47/1.51 = ( ord_less_nat @ M2 @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_173_Suc__mono,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_nat @ M2 @ N )
% 2.47/1.51 => ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_174_lessI,axiom,
% 2.47/1.51 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_175_Suc__le__mono,axiom,
% 2.47/1.51 ! [N: nat,M2: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M2 ) )
% 2.47/1.51 = ( ord_less_eq_nat @ N @ M2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_176_length__rev,axiom,
% 2.47/1.51 ! [Xs: list_a] :
% 2.47/1.51 ( ( size_size_list_a @ ( rev_a @ Xs ) )
% 2.47/1.51 = ( size_size_list_a @ Xs ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_177_length__rev,axiom,
% 2.47/1.51 ! [Xs: list_nat] :
% 2.47/1.51 ( ( size_size_list_nat @ ( rev_nat @ Xs ) )
% 2.47/1.51 = ( size_size_list_nat @ Xs ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_178_Suc__leD,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 2.47/1.51 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_179_le__SucE,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 2.47/1.51 => ( ~ ( ord_less_eq_nat @ M2 @ N )
% 2.47/1.51 => ( M2
% 2.47/1.51 = ( suc @ N ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_180_le__SucI,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ M2 @ N )
% 2.47/1.51 => ( ord_less_eq_nat @ M2 @ ( suc @ N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_181_Suc__le__D,axiom,
% 2.47/1.51 ! [N: nat,M4: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ ( suc @ N ) @ M4 )
% 2.47/1.51 => ? [M5: nat] :
% 2.47/1.51 ( M4
% 2.47/1.51 = ( suc @ M5 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_182_le__Suc__eq,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 2.47/1.51 = ( ( ord_less_eq_nat @ M2 @ N )
% 2.47/1.51 | ( M2
% 2.47/1.51 = ( suc @ N ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_183_Suc__n__not__le__n,axiom,
% 2.47/1.51 ! [N: nat] :
% 2.47/1.51 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_184_not__less__eq__eq,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ~ ( ord_less_eq_nat @ M2 @ N ) )
% 2.47/1.51 = ( ord_less_eq_nat @ ( suc @ N ) @ M2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_185_full__nat__induct,axiom,
% 2.47/1.51 ! [P: nat > $o,N: nat] :
% 2.47/1.51 ( ! [N3: nat] :
% 2.47/1.51 ( ! [M3: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ ( suc @ M3 ) @ N3 )
% 2.47/1.51 => ( P @ M3 ) )
% 2.47/1.51 => ( P @ N3 ) )
% 2.47/1.51 => ( P @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_186_nat__induct__at__least,axiom,
% 2.47/1.51 ! [M2: nat,N: nat,P: nat > $o] :
% 2.47/1.51 ( ( ord_less_eq_nat @ M2 @ N )
% 2.47/1.51 => ( ( P @ M2 )
% 2.47/1.51 => ( ! [N3: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ M2 @ N3 )
% 2.47/1.51 => ( ( P @ N3 )
% 2.47/1.51 => ( P @ ( suc @ N3 ) ) ) )
% 2.47/1.51 => ( P @ N ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_187_transitive__stepwise__le,axiom,
% 2.47/1.51 ! [M2: nat,N: nat,R: nat > nat > $o] :
% 2.47/1.51 ( ( ord_less_eq_nat @ M2 @ N )
% 2.47/1.51 => ( ! [X4: nat] : ( R @ X4 @ X4 )
% 2.47/1.51 => ( ! [X4: nat,Y4: nat,Z3: nat] :
% 2.47/1.51 ( ( R @ X4 @ Y4 )
% 2.47/1.51 => ( ( R @ Y4 @ Z3 )
% 2.47/1.51 => ( R @ X4 @ Z3 ) ) )
% 2.47/1.51 => ( ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) )
% 2.47/1.51 => ( R @ M2 @ N ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_188_n__not__Suc__n,axiom,
% 2.47/1.51 ! [N: nat] :
% 2.47/1.51 ( N
% 2.47/1.51 != ( suc @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_189_Suc__inject,axiom,
% 2.47/1.51 ! [X2: nat,Y2: nat] :
% 2.47/1.51 ( ( ( suc @ X2 )
% 2.47/1.51 = ( suc @ Y2 ) )
% 2.47/1.51 => ( X2 = Y2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_190_rev__swap,axiom,
% 2.47/1.51 ! [Xs: list_nat,Ys: list_nat] :
% 2.47/1.51 ( ( ( rev_nat @ Xs )
% 2.47/1.51 = Ys )
% 2.47/1.51 = ( Xs
% 2.47/1.51 = ( rev_nat @ Ys ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_191_rev__swap,axiom,
% 2.47/1.51 ! [Xs: list_a,Ys: list_a] :
% 2.47/1.51 ( ( ( rev_a @ Xs )
% 2.47/1.51 = Ys )
% 2.47/1.51 = ( Xs
% 2.47/1.51 = ( rev_a @ Ys ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_192_not__less__less__Suc__eq,axiom,
% 2.47/1.51 ! [N: nat,M2: nat] :
% 2.47/1.51 ( ~ ( ord_less_nat @ N @ M2 )
% 2.47/1.51 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 2.47/1.51 = ( N = M2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_193_strict__inc__induct,axiom,
% 2.47/1.51 ! [I3: nat,J2: nat,P: nat > $o] :
% 2.47/1.51 ( ( ord_less_nat @ I3 @ J2 )
% 2.47/1.51 => ( ! [I: nat] :
% 2.47/1.51 ( ( J2
% 2.47/1.51 = ( suc @ I ) )
% 2.47/1.51 => ( P @ I ) )
% 2.47/1.51 => ( ! [I: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I @ J2 )
% 2.47/1.51 => ( ( P @ ( suc @ I ) )
% 2.47/1.51 => ( P @ I ) ) )
% 2.47/1.51 => ( P @ I3 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_194_less__Suc__induct,axiom,
% 2.47/1.51 ! [I3: nat,J2: nat,P: nat > nat > $o] :
% 2.47/1.51 ( ( ord_less_nat @ I3 @ J2 )
% 2.47/1.51 => ( ! [I: nat] : ( P @ I @ ( suc @ I ) )
% 2.47/1.51 => ( ! [I: nat,J3: nat,K2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I @ J3 )
% 2.47/1.51 => ( ( ord_less_nat @ J3 @ K2 )
% 2.47/1.51 => ( ( P @ I @ J3 )
% 2.47/1.51 => ( ( P @ J3 @ K2 )
% 2.47/1.51 => ( P @ I @ K2 ) ) ) ) )
% 2.47/1.51 => ( P @ I3 @ J2 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_195_less__trans__Suc,axiom,
% 2.47/1.51 ! [I3: nat,J2: nat,K: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I3 @ J2 )
% 2.47/1.51 => ( ( ord_less_nat @ J2 @ K )
% 2.47/1.51 => ( ord_less_nat @ ( suc @ I3 ) @ K ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_196_Suc__less__SucD,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 2.47/1.51 => ( ord_less_nat @ M2 @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_197_less__antisym,axiom,
% 2.47/1.51 ! [N: nat,M2: nat] :
% 2.47/1.51 ( ~ ( ord_less_nat @ N @ M2 )
% 2.47/1.51 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 2.47/1.51 => ( M2 = N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_198_Suc__less__eq2,axiom,
% 2.47/1.51 ! [N: nat,M2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 2.47/1.51 = ( ? [M6: nat] :
% 2.47/1.51 ( ( M2
% 2.47/1.51 = ( suc @ M6 ) )
% 2.47/1.51 & ( ord_less_nat @ N @ M6 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_199_All__less__Suc,axiom,
% 2.47/1.51 ! [N: nat,P: nat > $o] :
% 2.47/1.51 ( ( ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 2.47/1.51 => ( P @ I2 ) ) )
% 2.47/1.51 = ( ( P @ N )
% 2.47/1.51 & ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I2 @ N )
% 2.47/1.51 => ( P @ I2 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_200_not__less__eq,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ~ ( ord_less_nat @ M2 @ N ) )
% 2.47/1.51 = ( ord_less_nat @ N @ ( suc @ M2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_201_less__Suc__eq,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 2.47/1.51 = ( ( ord_less_nat @ M2 @ N )
% 2.47/1.51 | ( M2 = N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_202_Ex__less__Suc,axiom,
% 2.47/1.51 ! [N: nat,P: nat > $o] :
% 2.47/1.51 ( ( ? [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 2.47/1.51 & ( P @ I2 ) ) )
% 2.47/1.51 = ( ( P @ N )
% 2.47/1.51 | ? [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I2 @ N )
% 2.47/1.51 & ( P @ I2 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_203_less__SucI,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_nat @ M2 @ N )
% 2.47/1.51 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_204_less__SucE,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 2.47/1.51 => ( ~ ( ord_less_nat @ M2 @ N )
% 2.47/1.51 => ( M2 = N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_205_Suc__lessI,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_nat @ M2 @ N )
% 2.47/1.51 => ( ( ( suc @ M2 )
% 2.47/1.51 != N )
% 2.47/1.51 => ( ord_less_nat @ ( suc @ M2 ) @ N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_206_Suc__lessE,axiom,
% 2.47/1.51 ! [I3: nat,K: nat] :
% 2.47/1.51 ( ( ord_less_nat @ ( suc @ I3 ) @ K )
% 2.47/1.51 => ~ ! [J3: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I3 @ J3 )
% 2.47/1.51 => ( K
% 2.47/1.51 != ( suc @ J3 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_207_Suc__lessD,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_nat @ ( suc @ M2 ) @ N )
% 2.47/1.51 => ( ord_less_nat @ M2 @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_208_Nat_OlessE,axiom,
% 2.47/1.51 ! [I3: nat,K: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I3 @ K )
% 2.47/1.51 => ( ( K
% 2.47/1.51 != ( suc @ I3 ) )
% 2.47/1.51 => ~ ! [J3: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I3 @ J3 )
% 2.47/1.51 => ( K
% 2.47/1.51 != ( suc @ J3 ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_209_lift__Suc__mono__less__iff,axiom,
% 2.47/1.51 ! [F: nat > nat,N: nat,M2: nat] :
% 2.47/1.51 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 2.47/1.51 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M2 ) )
% 2.47/1.51 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_210_lift__Suc__mono__less,axiom,
% 2.47/1.51 ! [F: nat > nat,N: nat,N4: nat] :
% 2.47/1.51 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 2.47/1.51 => ( ( ord_less_nat @ N @ N4 )
% 2.47/1.51 => ( ord_less_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_211_lift__Suc__antimono__le,axiom,
% 2.47/1.51 ! [F: nat > nat,N: nat,N4: nat] :
% 2.47/1.51 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 2.47/1.51 => ( ( ord_less_eq_nat @ N @ N4 )
% 2.47/1.51 => ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_212_lift__Suc__mono__le,axiom,
% 2.47/1.51 ! [F: nat > nat,N: nat,N4: nat] :
% 2.47/1.51 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 2.47/1.51 => ( ( ord_less_eq_nat @ N @ N4 )
% 2.47/1.51 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_213_le__imp__less__Suc,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ M2 @ N )
% 2.47/1.51 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_214_less__eq__Suc__le,axiom,
% 2.47/1.51 ( ord_less_nat
% 2.47/1.51 = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_215_less__Suc__eq__le,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 2.47/1.51 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_216_le__less__Suc__eq,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ M2 @ N )
% 2.47/1.51 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 2.47/1.51 = ( N = M2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_217_Suc__le__lessD,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 2.47/1.51 => ( ord_less_nat @ M2 @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_218_inc__induct,axiom,
% 2.47/1.51 ! [I3: nat,J2: nat,P: nat > $o] :
% 2.47/1.51 ( ( ord_less_eq_nat @ I3 @ J2 )
% 2.47/1.51 => ( ( P @ J2 )
% 2.47/1.51 => ( ! [N3: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ I3 @ N3 )
% 2.47/1.51 => ( ( ord_less_nat @ N3 @ J2 )
% 2.47/1.51 => ( ( P @ ( suc @ N3 ) )
% 2.47/1.51 => ( P @ N3 ) ) ) )
% 2.47/1.51 => ( P @ I3 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_219_dec__induct,axiom,
% 2.47/1.51 ! [I3: nat,J2: nat,P: nat > $o] :
% 2.47/1.51 ( ( ord_less_eq_nat @ I3 @ J2 )
% 2.47/1.51 => ( ( P @ I3 )
% 2.47/1.51 => ( ! [N3: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ I3 @ N3 )
% 2.47/1.51 => ( ( ord_less_nat @ N3 @ J2 )
% 2.47/1.51 => ( ( P @ N3 )
% 2.47/1.51 => ( P @ ( suc @ N3 ) ) ) ) )
% 2.47/1.51 => ( P @ J2 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_220_Suc__le__eq,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 2.47/1.51 = ( ord_less_nat @ M2 @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_221_Suc__leI,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_nat @ M2 @ N )
% 2.47/1.51 => ( ord_less_eq_nat @ ( suc @ M2 ) @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_222_sorted__rev__iff__nth__Suc,axiom,
% 2.47/1.51 ! [Xs: list_nat] :
% 2.47/1.51 ( ( linorder_sorted_nat @ ( rev_nat @ Xs ) )
% 2.47/1.51 = ( ! [I2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ ( suc @ I2 ) @ ( size_size_list_nat @ Xs ) )
% 2.47/1.51 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ ( suc @ I2 ) ) @ ( nth_nat @ Xs @ I2 ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_223_nat__induct_H,axiom,
% 2.47/1.51 ! [P: nat > $o,N0: nat,N: nat] :
% 2.47/1.51 ( ( P @ N0 )
% 2.47/1.51 => ( ! [N3: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ N0 @ N3 )
% 2.47/1.51 => ( ( P @ N3 )
% 2.47/1.51 => ( P @ ( suc @ N3 ) ) ) )
% 2.47/1.51 => ( ( ord_less_eq_nat @ N0 @ N )
% 2.47/1.51 => ( P @ N ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_224_rev__nth,axiom,
% 2.47/1.51 ! [N: nat,Xs: list_a] :
% 2.47/1.51 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 2.47/1.51 => ( ( nth_a @ ( rev_a @ Xs ) @ N )
% 2.47/1.51 = ( nth_a @ Xs @ ( minus_minus_nat @ ( size_size_list_a @ Xs ) @ ( suc @ N ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_225_rev__nth,axiom,
% 2.47/1.51 ! [N: nat,Xs: list_nat] :
% 2.47/1.51 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.47/1.51 => ( ( nth_nat @ ( rev_nat @ Xs ) @ N )
% 2.47/1.51 = ( nth_nat @ Xs @ ( minus_minus_nat @ ( size_size_list_nat @ Xs ) @ ( suc @ N ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_226_list__ex__length,axiom,
% 2.47/1.51 ( list_ex_a
% 2.47/1.51 = ( ^ [P3: a > $o,Xs2: list_a] :
% 2.47/1.51 ? [N2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs2 ) )
% 2.47/1.51 & ( P3 @ ( nth_a @ Xs2 @ N2 ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_227_list__ex__length,axiom,
% 2.47/1.51 ( list_ex_nat
% 2.47/1.51 = ( ^ [P3: nat > $o,Xs2: list_nat] :
% 2.47/1.51 ? [N2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs2 ) )
% 2.47/1.51 & ( P3 @ ( nth_nat @ Xs2 @ N2 ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_228_Suc__diff__diff,axiom,
% 2.47/1.51 ! [M2: nat,N: nat,K: nat] :
% 2.47/1.51 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) @ ( suc @ K ) )
% 2.47/1.51 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ N ) @ K ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_229_diff__Suc__Suc,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] :
% 2.47/1.51 ( ( minus_minus_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 2.47/1.51 = ( minus_minus_nat @ M2 @ N ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_230_diff__diff__cancel,axiom,
% 2.47/1.51 ! [I3: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ I3 @ N )
% 2.47/1.51 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I3 ) )
% 2.47/1.51 = I3 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_231_list__ex__rev,axiom,
% 2.47/1.51 ! [P: nat > $o,Xs: list_nat] :
% 2.47/1.51 ( ( list_ex_nat @ P @ ( rev_nat @ Xs ) )
% 2.47/1.51 = ( list_ex_nat @ P @ Xs ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_232_list__ex__rev,axiom,
% 2.47/1.51 ! [P: a > $o,Xs: list_a] :
% 2.47/1.51 ( ( list_ex_a @ P @ ( rev_a @ Xs ) )
% 2.47/1.51 = ( list_ex_a @ P @ Xs ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_233_i__append__nth2,axiom,
% 2.47/1.51 ! [Xs: list_nat,N: nat,F: nat > nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N )
% 2.47/1.51 => ( ( listIn923761578nd_nat @ Xs @ F @ N )
% 2.47/1.51 = ( F @ ( minus_minus_nat @ N @ ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_234_i__append__nth2,axiom,
% 2.47/1.51 ! [Xs: list_a,N: nat,F: nat > a] :
% 2.47/1.51 ( ( ord_less_eq_nat @ ( size_size_list_a @ Xs ) @ N )
% 2.47/1.51 => ( ( listIn1312259492pend_a @ Xs @ F @ N )
% 2.47/1.51 = ( F @ ( minus_minus_nat @ N @ ( size_size_list_a @ Xs ) ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_235_zero__induct__lemma,axiom,
% 2.47/1.51 ! [P: nat > $o,K: nat,I3: nat] :
% 2.47/1.51 ( ( P @ K )
% 2.47/1.51 => ( ! [N3: nat] :
% 2.47/1.51 ( ( P @ ( suc @ N3 ) )
% 2.47/1.51 => ( P @ N3 ) )
% 2.47/1.51 => ( P @ ( minus_minus_nat @ K @ I3 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_236_less__diff__imp__less,axiom,
% 2.47/1.51 ! [I3: nat,J2: nat,M2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ I3 @ ( minus_minus_nat @ J2 @ M2 ) )
% 2.47/1.51 => ( ord_less_nat @ I3 @ J2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_237_nat__diff__left__cancel__eq1,axiom,
% 2.47/1.51 ! [K: nat,M2: nat,N: nat] :
% 2.47/1.51 ( ( ( minus_minus_nat @ K @ M2 )
% 2.47/1.51 = ( minus_minus_nat @ K @ N ) )
% 2.47/1.51 => ( ( ord_less_nat @ M2 @ K )
% 2.47/1.51 => ( M2 = N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_238_nat__diff__left__cancel__eq2,axiom,
% 2.47/1.51 ! [K: nat,M2: nat,N: nat] :
% 2.47/1.51 ( ( ( minus_minus_nat @ K @ M2 )
% 2.47/1.51 = ( minus_minus_nat @ K @ N ) )
% 2.47/1.51 => ( ( ord_less_nat @ N @ K )
% 2.47/1.51 => ( M2 = N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_239_nat__diff__left__cancel__less,axiom,
% 2.47/1.51 ! [K: nat,M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_nat @ ( minus_minus_nat @ K @ M2 ) @ ( minus_minus_nat @ K @ N ) )
% 2.47/1.51 => ( ord_less_nat @ N @ M2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_240_nat__diff__right__cancel__eq1,axiom,
% 2.47/1.51 ! [M2: nat,K: nat,N: nat] :
% 2.47/1.51 ( ( ( minus_minus_nat @ M2 @ K )
% 2.47/1.51 = ( minus_minus_nat @ N @ K ) )
% 2.47/1.51 => ( ( ord_less_nat @ K @ M2 )
% 2.47/1.51 => ( M2 = N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_241_nat__diff__right__cancel__eq2,axiom,
% 2.47/1.51 ! [M2: nat,K: nat,N: nat] :
% 2.47/1.51 ( ( ( minus_minus_nat @ M2 @ K )
% 2.47/1.51 = ( minus_minus_nat @ N @ K ) )
% 2.47/1.51 => ( ( ord_less_nat @ K @ N )
% 2.47/1.51 => ( M2 = N ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_242_nat__diff__right__cancel__less,axiom,
% 2.47/1.51 ! [N: nat,K: nat,M2: nat] :
% 2.47/1.51 ( ( ord_less_nat @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M2 @ K ) )
% 2.47/1.51 => ( ord_less_nat @ N @ M2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_243_diff__less__mono2,axiom,
% 2.47/1.51 ! [M2: nat,N: nat,L: nat] :
% 2.47/1.51 ( ( ord_less_nat @ M2 @ N )
% 2.47/1.51 => ( ( ord_less_nat @ M2 @ L )
% 2.47/1.51 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_244_less__imp__diff__less,axiom,
% 2.47/1.51 ! [J2: nat,K: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_nat @ J2 @ K )
% 2.47/1.51 => ( ord_less_nat @ ( minus_minus_nat @ J2 @ N ) @ K ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_245_diff__commute,axiom,
% 2.47/1.51 ! [I3: nat,J2: nat,K: nat] :
% 2.47/1.51 ( ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J2 ) @ K )
% 2.47/1.51 = ( minus_minus_nat @ ( minus_minus_nat @ I3 @ K ) @ J2 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_246_diff__le__mono2,axiom,
% 2.47/1.51 ! [M2: nat,N: nat,L: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ M2 @ N )
% 2.47/1.51 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_247_le__diff__iff_H,axiom,
% 2.47/1.51 ! [A: nat,C: nat,B: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ A @ C )
% 2.47/1.51 => ( ( ord_less_eq_nat @ B @ C )
% 2.47/1.51 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 2.47/1.51 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_248_diff__le__self,axiom,
% 2.47/1.51 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ N ) @ M2 ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_249_diff__le__mono,axiom,
% 2.47/1.51 ! [M2: nat,N: nat,L: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ M2 @ N )
% 2.47/1.51 => ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_250_Nat_Odiff__diff__eq,axiom,
% 2.47/1.51 ! [K: nat,M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ K @ M2 )
% 2.47/1.51 => ( ( ord_less_eq_nat @ K @ N )
% 2.47/1.51 => ( ( minus_minus_nat @ ( minus_minus_nat @ M2 @ K ) @ ( minus_minus_nat @ N @ K ) )
% 2.47/1.51 = ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(fact_251_le__diff__iff,axiom,
% 2.47/1.51 ! [K: nat,M2: nat,N: nat] :
% 2.47/1.51 ( ( ord_less_eq_nat @ K @ M2 )
% 2.47/1.51 => ( ( ord_less_eq_nat @ K @ N )
% 2.47/1.51 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ K ) @ ( minus_minus_nat @ N @ K ) )
% 2.47/1.51 = ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(conj_0,hypothesis,
% 2.47/1.51 ! [X5: nat] :
% 2.47/1.51 ( ( listIn1312259492pend_a @ xs @ f @ X5 )
% 2.47/1.51 = ( listIn1312259492pend_a @ ys @ g @ X5 ) ) ).
% 2.47/1.51
% 2.47/1.51 thf(conj_1,hypothesis,
% 2.47/1.51 ord_less_eq_nat @ ( size_size_list_a @ xs ) @ ( size_size_list_a @ ys ) ).
% 2.47/1.51
% 2.47/1.51 thf(conj_2,conjecture,
% 2.47/1.51 ! [I: nat] :
% 2.47/1.51 ( ~ ( ord_less_nat @ I @ ( size_size_list_a @ xs ) )
% 2.47/1.51 | ( ( nth_a @ xs @ I )
% 2.47/1.51 = ( nth_a @ ys @ I ) ) ) ).
% 2.47/1.51 ------------------------
% 2.47/1.53 % (23564)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_23273 for (2999ds/4Mi)
% 2.47/1.54 % (23569)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23273 for (2999ds/18Mi)
% 2.47/1.54 % (23563)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23273 for (2999ds/183Mi)
% 2.47/1.54 % (23564)Instruction limit reached!
% 2.47/1.54 % (23564)------------------------------
% 2.47/1.54 % (23564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.54 % (23564)Termination reason: Unknown
% 2.47/1.54 % (23564)Termination phase: shuffling
% 2.47/1.54
% 2.47/1.54 % (23564)Memory used [KB]: 1407
% 2.47/1.54 % (23564)Time elapsed: 0.003 s
% 2.47/1.54 % (23564)Instructions burned: 5 (million)
% 2.47/1.54 % (23564)------------------------------
% 2.47/1.54 % (23564)------------------------------
% 2.47/1.54 % (23569)Instruction limit reached!
% 2.47/1.54 % (23569)------------------------------
% 2.47/1.54 % (23569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.54 % (23569)Termination reason: Unknown
% 2.47/1.54 % (23569)Termination phase: shuffling
% 2.47/1.54
% 2.47/1.54 % (23569)Memory used [KB]: 1663
% 2.47/1.54 % (23569)Time elapsed: 0.007 s
% 2.47/1.54 % (23569)Instructions burned: 18 (million)
% 2.47/1.54 % (23569)------------------------------
% 2.47/1.54 % (23569)------------------------------
% 2.47/1.54 % (23565)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_23273 for (2999ds/27Mi)
% 2.47/1.54 % (23566)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23273 for (2999ds/2Mi)
% 2.47/1.54 % (23567)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_23273 for (2999ds/2Mi)
% 2.47/1.54 % (23568)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_23273 for (2999ds/275Mi)
% 2.47/1.54 % (23566)Instruction limit reached!
% 2.47/1.54 % (23566)------------------------------
% 2.47/1.54 % (23566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.54 % (23566)Termination reason: Unknown
% 2.47/1.54 % (23566)Termination phase: shuffling
% 2.47/1.54
% 2.47/1.54 % (23566)Memory used [KB]: 1279
% 2.47/1.54 % (23566)Time elapsed: 0.004 s
% 2.47/1.54 % (23566)Instructions burned: 3 (million)
% 2.47/1.54 % (23566)------------------------------
% 2.47/1.54 % (23566)------------------------------
% 2.47/1.54 % (23567)Instruction limit reached!
% 2.47/1.54 % (23567)------------------------------
% 2.47/1.54 % (23567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.54 % (23567)Termination reason: Unknown
% 2.47/1.54 % (23567)Termination phase: shuffling
% 2.47/1.54
% 2.47/1.54 % (23567)Memory used [KB]: 1279
% 2.47/1.54 % (23567)Time elapsed: 0.004 s
% 2.47/1.54 % (23567)Instructions burned: 3 (million)
% 2.47/1.54 % (23567)------------------------------
% 2.47/1.54 % (23567)------------------------------
% 2.47/1.55 % (23570)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23273 for (2999ds/3Mi)
% 2.47/1.55 % (23570)Instruction limit reached!
% 2.47/1.55 % (23570)------------------------------
% 2.47/1.55 % (23570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.55 % (23570)Termination reason: Unknown
% 2.47/1.55 % (23570)Termination phase: shuffling
% 2.47/1.55
% 2.47/1.55 % (23570)Memory used [KB]: 1279
% 2.47/1.55 % (23570)Time elapsed: 0.002 s
% 2.47/1.55 % (23570)Instructions burned: 3 (million)
% 2.47/1.55 % (23570)------------------------------
% 2.47/1.55 % (23570)------------------------------
% 2.47/1.55 % (23571)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_23273 for (2999ds/37Mi)
% 2.47/1.56 % (23574)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_23273 for (2999ds/1041Mi)
% 2.47/1.56 % (23565)Instruction limit reached!
% 2.47/1.56 % (23565)------------------------------
% 2.47/1.56 % (23565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.56 % (23565)Termination reason: Unknown
% 2.47/1.56 % (23565)Termination phase: Property scanning
% 2.47/1.56
% 2.47/1.56 % (23565)Memory used [KB]: 1663
% 2.47/1.56 % (23565)Time elapsed: 0.018 s
% 2.47/1.56 % (23565)Instructions burned: 28 (million)
% 2.47/1.56 % (23565)------------------------------
% 2.47/1.56 % (23565)------------------------------
% 2.47/1.56 % (23571)Instruction limit reached!
% 2.47/1.56 % (23571)------------------------------
% 2.47/1.56 % (23571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.56 % (23571)Termination reason: Unknown
% 2.47/1.56 % (23571)Termination phase: Property scanning
% 2.47/1.56
% 2.47/1.56 % (23571)Memory used [KB]: 2046
% 2.47/1.56 % (23571)Time elapsed: 0.011 s
% 2.47/1.56 % (23571)Instructions burned: 37 (million)
% 2.47/1.56 % (23571)------------------------------
% 2.47/1.56 % (23571)------------------------------
% 2.47/1.56 % (23572)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_23273 for (2999ds/15Mi)
% 2.47/1.56 % (23573)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_23273 for (2999ds/3Mi)
% 2.47/1.56 % (23573)Instruction limit reached!
% 2.47/1.56 % (23573)------------------------------
% 2.47/1.56 % (23573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.56 % (23573)Termination reason: Unknown
% 2.47/1.56 % (23573)Termination phase: shuffling
% 2.47/1.56
% 2.47/1.56 % (23573)Memory used [KB]: 1279
% 2.47/1.56 % (23573)Time elapsed: 0.004 s
% 2.47/1.56 % (23573)Instructions burned: 4 (million)
% 2.47/1.56 % (23573)------------------------------
% 2.47/1.56 % (23573)------------------------------
% 2.47/1.57 % (23576)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23273 for (2999ds/16Mi)
% 2.47/1.57 % (23572)Instruction limit reached!
% 2.47/1.57 % (23572)------------------------------
% 2.47/1.57 % (23572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.57 % (23572)Termination reason: Unknown
% 2.47/1.57 % (23572)Termination phase: shuffling
% 2.47/1.57
% 2.47/1.57 % (23572)Memory used [KB]: 1535
% 2.47/1.57 % (23572)Time elapsed: 0.011 s
% 2.47/1.57 % (23572)Instructions burned: 15 (million)
% 2.47/1.57 % (23572)------------------------------
% 2.47/1.57 % (23572)------------------------------
% 2.47/1.57 % (23576)Instruction limit reached!
% 2.47/1.57 % (23576)------------------------------
% 2.47/1.57 % (23576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.57 % (23576)Termination reason: Unknown
% 2.47/1.57 % (23576)Termination phase: shuffling
% 2.47/1.57
% 2.47/1.57 % (23576)Memory used [KB]: 1535
% 2.47/1.57 % (23576)Time elapsed: 0.006 s
% 2.47/1.57 % (23576)Instructions burned: 16 (million)
% 2.47/1.57 % (23576)------------------------------
% 2.47/1.57 % (23576)------------------------------
% 2.47/1.58 % (23575)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23273 for (2999ds/7Mi)
% 2.47/1.58 % (23575)Instruction limit reached!
% 2.47/1.58 % (23575)------------------------------
% 2.47/1.58 % (23575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.58 % (23575)Termination reason: Unknown
% 2.47/1.58 % (23575)Termination phase: shuffling
% 2.47/1.58
% 2.47/1.58 % (23575)Memory used [KB]: 1407
% 2.47/1.58 % (23575)Time elapsed: 0.006 s
% 2.47/1.58 % (23575)Instructions burned: 7 (million)
% 2.47/1.58 % (23575)------------------------------
% 2.47/1.58 % (23575)------------------------------
% 2.47/1.58 % (23577)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_23273 for (2999ds/3Mi)
% 2.47/1.58 % (23577)Instruction limit reached!
% 2.47/1.58 % (23577)------------------------------
% 2.47/1.58 % (23577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.58 % (23577)Termination reason: Unknown
% 2.47/1.58 % (23577)Termination phase: shuffling
% 2.47/1.58
% 2.47/1.58 % (23577)Memory used [KB]: 1279
% 2.47/1.58 % (23577)Time elapsed: 0.004 s
% 2.47/1.58 % (23577)Instructions burned: 4 (million)
% 2.47/1.58 % (23577)------------------------------
% 2.47/1.58 % (23577)------------------------------
% 2.47/1.58 % (23579)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23273 for (2999ds/7Mi)
% 2.47/1.59 % (23579)Instruction limit reached!
% 2.47/1.59 % (23579)------------------------------
% 2.47/1.59 % (23579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.59 % (23579)Termination reason: Unknown
% 2.47/1.59 % (23579)Termination phase: shuffling
% 2.47/1.59
% 2.47/1.59 % (23579)Memory used [KB]: 1407
% 2.47/1.59 % (23579)Time elapsed: 0.004 s
% 2.47/1.59 % (23579)Instructions burned: 9 (million)
% 2.47/1.59 % (23579)------------------------------
% 2.47/1.59 % (23579)------------------------------
% 2.47/1.59 % (23578)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_23273 for (2999ds/3Mi)
% 2.47/1.59 % (23563)Instruction limit reached!
% 2.47/1.59 % (23563)------------------------------
% 2.47/1.59 % (23563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.59 % (23563)Termination reason: Unknown
% 2.47/1.59 % (23563)Termination phase: Saturation
% 2.47/1.59
% 2.47/1.59 % (23563)Memory used [KB]: 7036
% 2.47/1.59 % (23563)Time elapsed: 0.055 s
% 2.47/1.59 % (23563)Instructions burned: 185 (million)
% 2.47/1.59 % (23563)------------------------------
% 2.47/1.59 % (23563)------------------------------
% 2.47/1.59 % (23578)Instruction limit reached!
% 2.47/1.59 % (23578)------------------------------
% 2.47/1.59 % (23578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.59 % (23578)Termination reason: Unknown
% 2.47/1.59 % (23578)Termination phase: shuffling
% 2.47/1.59
% 2.47/1.59 % (23578)Memory used [KB]: 1279
% 2.47/1.59 % (23578)Time elapsed: 0.004 s
% 2.47/1.59 % (23578)Instructions burned: 4 (million)
% 2.47/1.59 % (23578)------------------------------
% 2.47/1.59 % (23578)------------------------------
% 2.51/1.60 % (23582)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_23273 for (2999ds/18Mi)
% 2.51/1.60 % (23580)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23273 for (2999ds/3Mi)
% 2.51/1.60 % (23583)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_23273 for (2999ds/710Mi)
% 2.51/1.60 % (23580)Instruction limit reached!
% 2.51/1.60 % (23580)------------------------------
% 2.51/1.60 % (23580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.60 % (23580)Termination reason: Unknown
% 2.51/1.60 % (23580)Termination phase: shuffling
% 2.51/1.60
% 2.51/1.60 % (23580)Memory used [KB]: 1279
% 2.51/1.60 % (23580)Time elapsed: 0.004 s
% 2.51/1.60 % (23580)Instructions burned: 4 (million)
% 2.51/1.60 % (23580)------------------------------
% 2.51/1.60 % (23580)------------------------------
% 2.51/1.60 % (23581)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_23273 for (2999ds/4Mi)
% 2.51/1.60 % (23582)Instruction limit reached!
% 2.51/1.60 % (23582)------------------------------
% 2.51/1.60 % (23582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.60 % (23582)Termination reason: Unknown
% 2.51/1.60 % (23582)Termination phase: Property scanning
% 2.51/1.60
% 2.51/1.60 % (23582)Memory used [KB]: 1663
% 2.51/1.60 % (23582)Time elapsed: 0.007 s
% 2.51/1.60 % (23582)Instructions burned: 19 (million)
% 2.51/1.60 % (23582)------------------------------
% 2.51/1.60 % (23582)------------------------------
% 2.51/1.60 % (23581)Instruction limit reached!
% 2.51/1.60 % (23581)------------------------------
% 2.51/1.60 % (23581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.60 % (23581)Termination reason: Unknown
% 2.51/1.60 % (23581)Termination phase: shuffling
% 2.51/1.60
% 2.51/1.60 % (23581)Memory used [KB]: 1279
% 2.51/1.60 % (23581)Time elapsed: 0.004 s
% 2.51/1.60 % (23581)Instructions burned: 4 (million)
% 2.51/1.60 % (23581)------------------------------
% 2.51/1.60 % (23581)------------------------------
% 2.51/1.61 % (23584)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23273 for (2999ds/6Mi)
% 2.51/1.61 % (23586)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_23273 for (2999ds/21Mi)
% 2.51/1.61 % (23584)Instruction limit reached!
% 2.51/1.61 % (23584)------------------------------
% 2.51/1.61 % (23584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.61 % (23584)Termination reason: Unknown
% 2.51/1.61 % (23584)Termination phase: shuffling
% 2.51/1.61
% 2.51/1.61 % (23584)Memory used [KB]: 1407
% 2.51/1.61 % (23584)Time elapsed: 0.006 s
% 2.51/1.61 % (23584)Instructions burned: 7 (million)
% 2.51/1.61 % (23584)------------------------------
% 2.51/1.61 % (23584)------------------------------
% 2.51/1.61 % (23585)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_23273 for (2999ds/902Mi)
% 2.51/1.62 % (23586)Instruction limit reached!
% 2.51/1.62 % (23586)------------------------------
% 2.51/1.62 % (23586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.62 % (23586)Termination reason: Unknown
% 2.51/1.62 % (23586)Termination phase: Property scanning
% 2.51/1.62
% 2.51/1.62 % (23586)Memory used [KB]: 1663
% 2.51/1.62 % (23586)Time elapsed: 0.008 s
% 2.51/1.62 % (23586)Instructions burned: 24 (million)
% 2.51/1.62 % (23586)------------------------------
% 2.51/1.62 % (23586)------------------------------
% 2.51/1.62 % (23587)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_23273 for (2999ds/5Mi)
% 2.51/1.62 % (23587)Instruction limit reached!
% 2.51/1.62 % (23587)------------------------------
% 2.51/1.62 % (23587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.62 % (23587)Termination reason: Unknown
% 2.51/1.62 % (23587)Termination phase: shuffling
% 2.51/1.62
% 2.51/1.62 % (23587)Memory used [KB]: 1407
% 2.51/1.62 % (23587)Time elapsed: 0.005 s
% 2.51/1.62 % (23587)Instructions burned: 6 (million)
% 2.51/1.62 % (23587)------------------------------
% 2.51/1.62 % (23587)------------------------------
% 2.51/1.63 % (23589)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_23273 for (2999ds/377Mi)
% 2.51/1.63 % (23588)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_23273 for (2999ds/6Mi)
% 2.51/1.63 % (23588)Instruction limit reached!
% 2.51/1.63 % (23588)------------------------------
% 2.51/1.63 % (23588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.63 % (23588)Termination reason: Unknown
% 2.51/1.63 % (23588)Termination phase: shuffling
% 2.51/1.63
% 2.51/1.63 % (23588)Memory used [KB]: 1407
% 2.51/1.63 % (23588)Time elapsed: 0.005 s
% 2.51/1.63 % (23588)Instructions burned: 6 (million)
% 2.51/1.63 % (23588)------------------------------
% 2.51/1.63 % (23588)------------------------------
% 2.51/1.64 % (23590)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_23273 for (2999ds/779Mi)
% 2.51/1.65 % (23591)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_23273 for (2998ds/19Mi)
% 2.51/1.65 % (23591)Instruction limit reached!
% 2.51/1.65 % (23591)------------------------------
% 2.51/1.65 % (23591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.65 % (23591)Termination reason: Unknown
% 2.51/1.65 % (23591)Termination phase: shuffling
% 2.51/1.65
% 2.51/1.65 % (23591)Memory used [KB]: 1663
% 2.51/1.65 % (23591)Time elapsed: 0.008 s
% 2.51/1.65 % (23591)Instructions burned: 20 (million)
% 2.51/1.65 % (23591)------------------------------
% 2.51/1.65 % (23591)------------------------------
% 2.51/1.66 % (23568)Instruction limit reached!
% 2.51/1.66 % (23568)------------------------------
% 2.51/1.66 % (23568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.66 % (23568)Termination reason: Unknown
% 2.51/1.66 % (23568)Termination phase: Saturation
% 2.51/1.66
% 2.51/1.66 % (23568)Memory used [KB]: 7036
% 2.51/1.66 % (23568)Time elapsed: 0.119 s
% 2.51/1.66 % (23568)Instructions burned: 277 (million)
% 2.51/1.66 % (23568)------------------------------
% 2.51/1.66 % (23568)------------------------------
% 2.51/1.66 % (23592)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_23273 for (2998ds/879Mi)
% 2.51/1.67 % (23593)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_23273 for (2998ds/17Mi)
% 2.51/1.68 % (23593)Instruction limit reached!
% 2.51/1.68 % (23593)------------------------------
% 2.51/1.68 % (23593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.68 % (23593)Termination reason: Unknown
% 2.51/1.68 % (23593)Termination phase: shuffling
% 2.51/1.68
% 2.51/1.68 % (23593)Memory used [KB]: 1663
% 2.51/1.68 % (23593)Time elapsed: 0.008 s
% 2.51/1.68 % (23593)Instructions burned: 19 (million)
% 2.51/1.68 % (23593)------------------------------
% 2.51/1.68 % (23593)------------------------------
% 2.51/1.69 % (23594)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23273 for (2998ds/3Mi)
% 2.51/1.69 % (23594)Instruction limit reached!
% 2.51/1.69 % (23594)------------------------------
% 2.51/1.69 % (23594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.69 % (23594)Termination reason: Unknown
% 2.51/1.69 % (23594)Termination phase: shuffling
% 2.51/1.69
% 2.51/1.69 % (23594)Memory used [KB]: 1279
% 2.51/1.69 % (23594)Time elapsed: 0.003 s
% 2.51/1.69 % (23594)Instructions burned: 4 (million)
% 2.51/1.69 % (23594)------------------------------
% 2.51/1.69 % (23594)------------------------------
% 2.51/1.70 % (23595)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_23273 for (2998ds/30Mi)
% 2.51/1.71 % (23595)Instruction limit reached!
% 2.51/1.71 % (23595)------------------------------
% 2.51/1.71 % (23595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.71 % (23595)Termination reason: Unknown
% 2.51/1.71 % (23595)Termination phase: Preprocessing 1
% 2.51/1.71
% 2.51/1.71 % (23595)Memory used [KB]: 1663
% 2.51/1.71 % (23595)Time elapsed: 0.012 s
% 2.51/1.71 % (23595)Instructions burned: 33 (million)
% 2.51/1.71 % (23595)------------------------------
% 2.51/1.71 % (23595)------------------------------
% 2.51/1.72 % (23596)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_23273 for (2997ds/127Mi)
% 2.51/1.73 % (23589)Instruction limit reached!
% 2.51/1.73 % (23589)------------------------------
% 2.51/1.73 % (23589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.73 % (23589)Termination reason: Unknown
% 2.51/1.73 % (23589)Termination phase: Saturation
% 2.51/1.73
% 2.51/1.73 % (23589)Memory used [KB]: 7931
% 2.51/1.73 % (23589)Time elapsed: 0.104 s
% 2.51/1.73 % (23589)Instructions burned: 379 (million)
% 2.51/1.73 % (23589)------------------------------
% 2.51/1.73 % (23589)------------------------------
% 2.51/1.74 % (23597)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_23273 for (2997ds/100Mi)
% 2.51/1.76 % (23596)Instruction limit reached!
% 2.51/1.76 % (23596)------------------------------
% 2.51/1.76 % (23596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.76 % (23596)Termination reason: Unknown
% 2.51/1.76 % (23596)Termination phase: Saturation
% 2.51/1.76
% 2.51/1.76 % (23596)Memory used [KB]: 6780
% 2.51/1.76 % (23596)Time elapsed: 0.039 s
% 2.51/1.76 % (23596)Instructions burned: 129 (million)
% 2.51/1.76 % (23596)------------------------------
% 2.51/1.76 % (23596)------------------------------
% 2.51/1.77 % (23597)Instruction limit reached!
% 2.51/1.77 % (23597)------------------------------
% 2.51/1.77 % (23597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.77 % (23597)Termination reason: Unknown
% 2.51/1.77 % (23597)Termination phase: Property scanning
% 2.51/1.77
% 2.51/1.77 % (23597)Memory used [KB]: 2174
% 2.51/1.77 % (23597)Time elapsed: 0.026 s
% 2.51/1.77 % (23597)Instructions burned: 100 (million)
% 2.51/1.77 % (23597)------------------------------
% 2.51/1.77 % (23597)------------------------------
% 2.51/1.77 % (23598)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_23273 for (2997ds/3Mi)
% 2.51/1.77 % (23598)Instruction limit reached!
% 2.51/1.77 % (23598)------------------------------
% 2.51/1.77 % (23598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.77 % (23598)Termination reason: Unknown
% 2.51/1.77 % (23598)Termination phase: shuffling
% 2.51/1.77
% 2.51/1.77 % (23598)Memory used [KB]: 1279
% 2.51/1.77 % (23598)Time elapsed: 0.003 s
% 2.51/1.77 % (23598)Instructions burned: 4 (million)
% 2.51/1.77 % (23598)------------------------------
% 2.51/1.77 % (23598)------------------------------
% 2.51/1.77 % (23599)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_23273 for (2997ds/20Mi)
% 2.51/1.78 % (23600)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_23273 for (2997ds/86Mi)
% 2.51/1.78 % (23599)Instruction limit reached!
% 2.51/1.78 % (23599)------------------------------
% 2.51/1.78 % (23599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.78 % (23599)Termination reason: Unknown
% 2.51/1.78 % (23599)Termination phase: Property scanning
% 2.51/1.78
% 2.51/1.78 % (23599)Memory used [KB]: 1663
% 2.51/1.78 % (23599)Time elapsed: 0.008 s
% 2.51/1.78 % (23599)Instructions burned: 23 (million)
% 2.51/1.78 % (23599)------------------------------
% 2.51/1.78 % (23599)------------------------------
% 2.51/1.79 % (23601)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_23273 for (2997ds/107Mi)
% 2.51/1.80 % (23600)Instruction limit reached!
% 2.51/1.80 % (23600)------------------------------
% 2.51/1.80 % (23600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.80 % (23600)Termination reason: Unknown
% 2.51/1.80 % (23600)Termination phase: Property scanning
% 2.51/1.80
% 2.51/1.80 % (23600)Memory used [KB]: 2174
% 2.51/1.80 % (23600)Time elapsed: 0.027 s
% 2.51/1.80 % (23600)Instructions burned: 88 (million)
% 2.51/1.80 % (23600)------------------------------
% 2.51/1.80 % (23600)------------------------------
% 2.51/1.81 % (23602)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_23273 for (2997ds/39Mi)
% 2.51/1.82 % (23601)Instruction limit reached!
% 2.51/1.82 % (23601)------------------------------
% 2.51/1.82 % (23601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.82 % (23601)Termination reason: Unknown
% 2.51/1.82 % (23601)Termination phase: Saturation
% 2.51/1.82
% 2.51/1.82 % (23601)Memory used [KB]: 6652
% 2.51/1.82 % (23601)Time elapsed: 0.030 s
% 2.51/1.82 % (23601)Instructions burned: 109 (million)
% 2.51/1.82 % (23601)------------------------------
% 2.51/1.82 % (23601)------------------------------
% 2.51/1.82 % (23602)Instruction limit reached!
% 2.51/1.82 % (23602)------------------------------
% 2.51/1.82 % (23602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.82 % (23602)Termination reason: Unknown
% 2.51/1.82 % (23602)Termination phase: Property scanning
% 2.51/1.82
% 2.51/1.82 % (23602)Memory used [KB]: 2046
% 2.51/1.82 % (23602)Time elapsed: 0.013 s
% 2.51/1.82 % (23602)Instructions burned: 40 (million)
% 2.51/1.82 % (23602)------------------------------
% 2.51/1.82 % (23602)------------------------------
% 2.51/1.83 % (23603)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_23273 for (2996ds/448Mi)
% 2.51/1.83 % (23604)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_23273 for (2996ds/46Mi)
% 2.51/1.83 % (23583)Instruction limit reached!
% 2.51/1.83 % (23583)------------------------------
% 2.51/1.83 % (23583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.83 % (23583)Termination reason: Unknown
% 2.51/1.83 % (23583)Termination phase: Saturation
% 2.51/1.83
% 2.51/1.83 % (23583)Memory used [KB]: 8315
% 2.51/1.83 % (23583)Time elapsed: 0.236 s
% 2.51/1.83 % (23583)Instructions burned: 711 (million)
% 2.51/1.83 % (23583)------------------------------
% 2.51/1.83 % (23583)------------------------------
% 2.51/1.84 % (23605)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_23273 for (2996ds/98Mi)
% 2.51/1.85 % (23604)Instruction limit reached!
% 2.51/1.85 % (23604)------------------------------
% 2.51/1.85 % (23604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.85 % (23604)Termination reason: Unknown
% 2.51/1.85 % (23604)Termination phase: Preprocessing 3
% 2.51/1.85
% 2.51/1.85 % (23604)Memory used [KB]: 2046
% 2.51/1.85 % (23604)Time elapsed: 0.017 s
% 2.51/1.85 % (23604)Instructions burned: 49 (million)
% 2.51/1.85 % (23604)------------------------------
% 2.51/1.85 % (23604)------------------------------
% 2.51/1.86 % (23606)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_23273 for (2996ds/507Mi)
% 2.51/1.86 % (23574)Instruction limit reached!
% 2.51/1.86 % (23574)------------------------------
% 2.51/1.86 % (23574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.86 % (23574)Termination reason: Unknown
% 2.51/1.86 % (23574)Termination phase: Saturation
% 2.51/1.86
% 2.51/1.86 % (23574)Memory used [KB]: 8571
% 2.51/1.86 % (23574)Time elapsed: 0.306 s
% 2.51/1.86 % (23574)Instructions burned: 1044 (million)
% 2.51/1.86 % (23574)------------------------------
% 2.51/1.86 % (23574)------------------------------
% 2.51/1.87 % (23607)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_23273 for (2996ds/149Mi)
% 2.51/1.87 % (23605)Instruction limit reached!
% 2.51/1.87 % (23605)------------------------------
% 2.51/1.87 % (23605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.87 % (23605)Termination reason: Unknown
% 2.51/1.87 % (23605)Termination phase: Property scanning
% 2.51/1.87
% 2.51/1.87 % (23605)Memory used [KB]: 2174
% 2.51/1.87 % (23605)Time elapsed: 0.029 s
% 2.51/1.87 % (23605)Instructions burned: 100 (million)
% 2.51/1.87 % (23605)------------------------------
% 2.51/1.87 % (23605)------------------------------
% 2.51/1.88 % (23608)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_23273 for (2996ds/39Mi)
% 2.51/1.89 % (23590)Instruction limit reached!
% 2.51/1.89 % (23590)------------------------------
% 2.51/1.89 % (23590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.89 % (23590)Termination reason: Unknown
% 2.51/1.89 % (23590)Termination phase: Saturation
% 2.51/1.89
% 2.51/1.89 % (23590)Memory used [KB]: 8187
% 2.51/1.89 % (23590)Time elapsed: 0.247 s
% 2.51/1.89 % (23590)Instructions burned: 780 (million)
% 2.51/1.89 % (23590)------------------------------
% 2.51/1.89 % (23590)------------------------------
% 2.51/1.89 % (23585)Instruction limit reached!
% 2.51/1.89 % (23585)------------------------------
% 2.51/1.89 % (23585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.89 % (23585)Termination reason: Unknown
% 2.51/1.89 % (23585)Termination phase: Saturation
% 2.51/1.89
% 2.51/1.89 % (23585)Memory used [KB]: 8315
% 2.51/1.89 % (23585)Time elapsed: 0.275 s
% 2.51/1.89 % (23585)Instructions burned: 902 (million)
% 2.51/1.89 % (23585)------------------------------
% 2.51/1.89 % (23585)------------------------------
% 2.51/1.89 % (23608)Instruction limit reached!
% 2.51/1.89 % (23608)------------------------------
% 2.51/1.89 % (23608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.89 % (23608)Termination reason: Unknown
% 2.51/1.89 % (23608)Termination phase: Preprocessing 3
% 2.51/1.89
% 2.51/1.89 % (23608)Memory used [KB]: 2046
% 2.51/1.89 % (23608)Time elapsed: 0.014 s
% 2.51/1.89 % (23608)Instructions burned: 42 (million)
% 2.51/1.89 % (23608)------------------------------
% 2.51/1.89 % (23608)------------------------------
% 2.51/1.90 % (23609)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_23273 for (2996ds/6Mi)
% 2.51/1.90 % (23610)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_23273 for (2996ds/1087Mi)
% 2.51/1.90 % (23609)Instruction limit reached!
% 2.51/1.90 % (23609)------------------------------
% 2.51/1.90 % (23609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.90 % (23609)Termination reason: Unknown
% 2.51/1.90 % (23609)Termination phase: shuffling
% 2.51/1.90
% 2.51/1.90 % (23609)Memory used [KB]: 1407
% 2.51/1.90 % (23609)Time elapsed: 0.004 s
% 2.51/1.90 % (23609)Instructions burned: 7 (million)
% 2.51/1.90 % (23609)------------------------------
% 2.51/1.90 % (23609)------------------------------
% 2.51/1.90 % (23611)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_23273 for (2996ds/47Mi)
% 2.51/1.91 % (23612)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_23273 for (2996ds/44Mi)
% 2.51/1.91 % (23607)Instruction limit reached!
% 2.51/1.91 % (23607)------------------------------
% 2.51/1.91 % (23607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.91 % (23607)Termination reason: Unknown
% 2.51/1.91 % (23607)Termination phase: Saturation
% 2.51/1.91
% 2.51/1.91 % (23607)Memory used [KB]: 6780
% 2.51/1.91 % (23607)Time elapsed: 0.041 s
% 2.51/1.91 % (23607)Instructions burned: 149 (million)
% 2.51/1.91 % (23607)------------------------------
% 2.51/1.91 % (23607)------------------------------
% 2.51/1.92 % (23611)Instruction limit reached!
% 2.51/1.92 % (23611)------------------------------
% 2.51/1.92 % (23611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.92 % (23611)Termination reason: Unknown
% 2.51/1.92 % (23611)Termination phase: Property scanning
% 2.51/1.92
% 2.51/1.92 % (23611)Memory used [KB]: 2046
% 2.51/1.92 % (23611)Time elapsed: 0.015 s
% 2.51/1.92 % (23611)Instructions burned: 49 (million)
% 2.51/1.92 % (23611)------------------------------
% 2.51/1.92 % (23611)------------------------------
% 2.51/1.92 % (23613)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_23273 for (2996ds/432Mi)
% 2.51/1.92 % (23612)Instruction limit reached!
% 2.51/1.92 % (23612)------------------------------
% 2.51/1.92 % (23612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.92 % (23612)Termination reason: Unknown
% 2.51/1.92 % (23612)Termination phase: Property scanning
% 2.51/1.92
% 2.51/1.92 % (23612)Memory used [KB]: 2046
% 2.51/1.92 % (23612)Time elapsed: 0.015 s
% 2.51/1.92 % (23612)Instructions burned: 47 (million)
% 2.51/1.92 % (23612)------------------------------
% 2.51/1.92 % (23612)------------------------------
% 2.51/1.93 % (23614)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_23273 for (2996ds/62Mi)
% 2.51/1.93 % (23615)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_23273 for (2995ds/31Mi)
% 2.51/1.94 % (23615)Instruction limit reached!
% 2.51/1.94 % (23615)------------------------------
% 2.51/1.94 % (23615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.94 % (23615)Termination reason: Unknown
% 2.51/1.94 % (23615)Termination phase: Preprocessing 2
% 2.51/1.94
% 2.51/1.94 % (23615)Memory used [KB]: 1663
% 2.51/1.94 % (23615)Time elapsed: 0.012 s
% 2.51/1.94 % (23615)Instructions burned: 33 (million)
% 2.51/1.94 % (23615)------------------------------
% 2.51/1.94 % (23615)------------------------------
% 2.51/1.94 % (23614)Instruction limit reached!
% 2.51/1.94 % (23614)------------------------------
% 2.51/1.94 % (23614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.94 % (23614)Termination reason: Unknown
% 2.51/1.94 % (23614)Termination phase: Property scanning
% 2.51/1.94
% 2.51/1.94 % (23614)Memory used [KB]: 2046
% 2.51/1.94 % (23614)Time elapsed: 0.017 s
% 2.51/1.94 % (23614)Instructions burned: 63 (million)
% 2.51/1.94 % (23614)------------------------------
% 2.51/1.94 % (23614)------------------------------
% 2.51/1.95 % (23616)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_23273 for (2995ds/96Mi)
% 2.51/1.95 % (23617)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_23273 for (2995ds/453Mi)
% 2.51/1.95 % (23603)Instruction limit reached!
% 2.51/1.95 % (23603)------------------------------
% 2.51/1.95 % (23603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.95 % (23603)Termination reason: Unknown
% 2.51/1.95 % (23603)Termination phase: Saturation
% 2.51/1.95
% 2.51/1.95 % (23603)Memory used [KB]: 7931
% 2.51/1.95 % (23603)Time elapsed: 0.125 s
% 2.51/1.95 % (23603)Instructions burned: 448 (million)
% 2.51/1.95 % (23603)------------------------------
% 2.51/1.95 % (23603)------------------------------
% 2.51/1.96 % (23592)Instruction limit reached!
% 2.51/1.96 % (23592)------------------------------
% 2.51/1.96 % (23592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.96 % (23592)Termination reason: Unknown
% 2.51/1.96 % (23592)Termination phase: Saturation
% 2.51/1.96
% 2.51/1.96 % (23592)Memory used [KB]: 7164
% 2.51/1.96 % (23592)Time elapsed: 0.294 s
% 2.51/1.96 % (23592)Instructions burned: 880 (million)
% 2.51/1.96 % (23592)------------------------------
% 2.51/1.96 % (23592)------------------------------
% 2.51/1.96 % (23618)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_23273 for (2995ds/71Mi)
% 2.51/1.97 % (23619)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_23273 for (2995ds/83Mi)
% 2.51/1.98 % (23616)Instruction limit reached!
% 2.51/1.98 % (23616)------------------------------
% 2.51/1.98 % (23616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.98 % (23616)Termination reason: Unknown
% 2.51/1.98 % (23616)Termination phase: Saturation
% 2.51/1.98
% 2.51/1.98 % (23616)Memory used [KB]: 6652
% 2.51/1.98 % (23616)Time elapsed: 0.028 s
% 2.51/1.98 % (23616)Instructions burned: 99 (million)
% 2.51/1.98 % (23616)------------------------------
% 2.51/1.98 % (23616)------------------------------
% 2.51/1.98 % (23618)Instruction limit reached!
% 2.51/1.98 % (23618)------------------------------
% 2.51/1.98 % (23618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.98 % (23618)Termination reason: Unknown
% 2.51/1.98 % (23618)Termination phase: Property scanning
% 2.51/1.98
% 2.51/1.98 % (23618)Memory used [KB]: 2174
% 2.51/1.98 % (23618)Time elapsed: 0.022 s
% 2.51/1.98 % (23618)Instructions burned: 75 (million)
% 2.51/1.98 % (23618)------------------------------
% 2.51/1.98 % (23618)------------------------------
% 2.51/1.99 % (23620)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_23273 for (2995ds/11Mi)
% 2.51/1.99 % (23620)Instruction limit reached!
% 2.51/1.99 % (23620)------------------------------
% 2.51/1.99 % (23620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.99 % (23620)Termination reason: Unknown
% 2.51/1.99 % (23620)Termination phase: shuffling
% 2.51/1.99
% 2.51/1.99 % (23620)Memory used [KB]: 1407
% 2.51/1.99 % (23620)Time elapsed: 0.004 s
% 2.51/1.99 % (23620)Instructions burned: 12 (million)
% 2.51/1.99 % (23620)------------------------------
% 2.51/1.99 % (23620)------------------------------
% 2.51/1.99 % (23619)Instruction limit reached!
% 2.51/1.99 % (23619)------------------------------
% 2.51/1.99 % (23619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.99 % (23619)Termination reason: Unknown
% 2.51/1.99 % (23619)Termination phase: Property scanning
% 2.51/1.99
% 2.51/1.99 % (23619)Memory used [KB]: 2046
% 2.51/1.99 % (23619)Time elapsed: 0.027 s
% 2.51/1.99 % (23619)Instructions burned: 86 (million)
% 2.51/1.99 % (23619)------------------------------
% 2.51/1.99 % (23619)------------------------------
% 2.51/1.99 % (23621)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_23273 for (2995ds/41Mi)
% 2.51/2.00 % (23622)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23273 for (2995ds/6Mi)
% 2.51/2.00 % (23622)Instruction limit reached!
% 2.51/2.00 % (23622)------------------------------
% 2.51/2.00 % (23622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/2.00 % (23622)Termination reason: Unknown
% 2.51/2.00 % (23622)Termination phase: shuffling
% 2.51/2.00
% 2.51/2.00 % (23622)Memory used [KB]: 1407
% 2.51/2.00 % (23622)Time elapsed: 0.003 s
% 2.51/2.00 % (23622)Instructions burned: 7 (million)
% 2.51/2.00 % (23622)------------------------------
% 2.51/2.00 % (23622)------------------------------
% 2.51/2.00 % (23623)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_23273 for (2995ds/150Mi)
% 2.51/2.00 % (23621)Instruction limit reached!
% 2.51/2.00 % (23621)------------------------------
% 2.51/2.00 % (23621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/2.00 % (23621)Termination reason: Unknown
% 2.51/2.00 % (23621)Termination phase: Property scanning
% 2.51/2.00
% 2.51/2.00 % (23621)Memory used [KB]: 2046
% 2.51/2.00 % (23621)Time elapsed: 0.012 s
% 2.51/2.00 % (23621)Instructions burned: 42 (million)
% 2.51/2.00 % (23621)------------------------------
% 2.51/2.00 % (23621)------------------------------
% 2.51/2.01 % (23624)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_23273 for (2995ds/343Mi)
% 2.51/2.01 % (23625)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_23273 for (2995ds/109Mi)
% 2.51/2.02 % (23606)Instruction limit reached!
% 2.51/2.02 % (23606)------------------------------
% 2.51/2.02 % (23606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/2.02 % (23606)Termination reason: Unknown
% 2.51/2.02 % (23606)Termination phase: Saturation
% 2.51/2.02
% 2.51/2.02 % (23606)Memory used [KB]: 8187
% 2.51/2.02 % (23606)Time elapsed: 0.158 s
% 2.51/2.02 % (23606)Instructions burned: 510 (million)
% 2.51/2.02 % (23606)------------------------------
% 2.51/2.02 % (23606)------------------------------
% 5.93/2.03 % (23626)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_23273 for (2995ds/253Mi)
% 5.93/2.04 % (23625)Instruction limit reached!
% 5.93/2.04 % (23625)------------------------------
% 5.93/2.04 % (23625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.04 % (23625)Termination reason: Unknown
% 5.93/2.04 % (23625)Termination phase: Saturation
% 5.93/2.04
% 5.93/2.04 % (23625)Memory used [KB]: 6652
% 5.93/2.04 % (23625)Time elapsed: 0.031 s
% 5.93/2.04 % (23625)Instructions burned: 111 (million)
% 5.93/2.04 % (23625)------------------------------
% 5.93/2.04 % (23625)------------------------------
% 5.93/2.04 % (23623)Instruction limit reached!
% 5.93/2.04 % (23623)------------------------------
% 5.93/2.04 % (23623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.04 % (23623)Termination reason: Unknown
% 5.93/2.04 % (23623)Termination phase: Saturation
% 5.93/2.04
% 5.93/2.04 % (23623)Memory used [KB]: 7036
% 5.93/2.04 % (23623)Time elapsed: 0.043 s
% 5.93/2.04 % (23623)Instructions burned: 152 (million)
% 5.93/2.04 % (23623)------------------------------
% 5.93/2.04 % (23623)------------------------------
% 5.93/2.05 % (23613)Instruction limit reached!
% 5.93/2.05 % (23613)------------------------------
% 5.93/2.05 % (23613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.05 % (23613)Termination reason: Unknown
% 5.93/2.05 % (23613)Termination phase: Saturation
% 5.93/2.05
% 5.93/2.05 % (23613)Memory used [KB]: 3454
% 5.93/2.05 % (23613)Time elapsed: 0.126 s
% 5.93/2.05 % (23613)Instructions burned: 432 (million)
% 5.93/2.05 % (23613)------------------------------
% 5.93/2.05 % (23613)------------------------------
% 5.93/2.05 % (23627)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_23273 for (2994ds/140Mi)
% 5.93/2.05 % (23628)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_23273 for (2994ds/614Mi)
% 5.93/2.06 % (23629)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_23273 for (2994ds/202Mi)
% 5.93/2.09 % (23617)Instruction limit reached!
% 5.93/2.09 % (23617)------------------------------
% 5.93/2.09 % (23617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.09 % (23617)Termination reason: Unknown
% 5.93/2.09 % (23617)Termination phase: Saturation
% 5.93/2.09
% 5.93/2.09 % (23617)Memory used [KB]: 7419
% 5.93/2.09 % (23617)Time elapsed: 0.137 s
% 5.93/2.09 % (23617)Instructions burned: 455 (million)
% 5.93/2.09 % (23617)------------------------------
% 5.93/2.09 % (23617)------------------------------
% 5.93/2.10 % (23627)Instruction limit reached!
% 5.93/2.10 % (23627)------------------------------
% 5.93/2.10 % (23627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.10 % (23627)Termination reason: Unknown
% 5.93/2.10 % (23627)Termination phase: Saturation
% 5.93/2.10
% 5.93/2.10 % (23627)Memory used [KB]: 6652
% 5.93/2.10 % (23627)Time elapsed: 0.070 s
% 5.93/2.10 % (23627)Instructions burned: 142 (million)
% 5.93/2.10 % (23627)------------------------------
% 5.93/2.10 % (23627)------------------------------
% 5.93/2.10 % (23630)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_23273 for (2994ds/339Mi)
% 5.93/2.10 % (23626)Instruction limit reached!
% 5.93/2.10 % (23626)------------------------------
% 5.93/2.10 % (23626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.10 % (23626)Termination reason: Unknown
% 5.93/2.10 % (23626)Termination phase: Saturation
% 5.93/2.10
% 5.93/2.10 % (23626)Memory used [KB]: 7803
% 5.93/2.10 % (23626)Time elapsed: 0.076 s
% 5.93/2.10 % (23626)Instructions burned: 255 (million)
% 5.93/2.10 % (23626)------------------------------
% 5.93/2.10 % (23626)------------------------------
% 5.93/2.11 % (23631)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_23273 for (2994ds/283Mi)
% 5.93/2.11 % (23624)Instruction limit reached!
% 5.93/2.11 % (23624)------------------------------
% 5.93/2.11 % (23624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.11 % (23624)Termination reason: Unknown
% 5.93/2.11 % (23624)Termination phase: Saturation
% 5.93/2.11
% 5.93/2.11 % (23624)Memory used [KB]: 7419
% 5.93/2.11 % (23624)Time elapsed: 0.098 s
% 5.93/2.11 % (23624)Instructions burned: 345 (million)
% 5.93/2.11 % (23624)------------------------------
% 5.93/2.11 % (23624)------------------------------
% 5.93/2.11 % (23632)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_23273 for (2994ds/134Mi)
% 5.93/2.12 % (23629)Instruction limit reached!
% 5.93/2.12 % (23629)------------------------------
% 5.93/2.12 % (23629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.12 % (23629)Termination reason: Unknown
% 5.93/2.12 % (23629)Termination phase: Saturation
% 5.93/2.12
% 5.93/2.12 % (23629)Memory used [KB]: 7036
% 5.93/2.12 % (23629)Time elapsed: 0.089 s
% 5.93/2.12 % (23629)Instructions burned: 205 (million)
% 5.93/2.12 % (23629)------------------------------
% 5.93/2.12 % (23629)------------------------------
% 5.93/2.12 % (23633)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_23273 for (2994ds/298Mi)
% 6.52/2.13 % (23634)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_23273 for (2993ds/192Mi)
% 6.52/2.15 % (23632)Instruction limit reached!
% 6.52/2.15 % (23632)------------------------------
% 6.52/2.15 % (23632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.15 % (23632)Termination reason: Unknown
% 6.52/2.15 % (23632)Termination phase: Saturation
% 6.52/2.15
% 6.52/2.15 % (23632)Memory used [KB]: 6780
% 6.52/2.15 % (23632)Time elapsed: 0.038 s
% 6.52/2.15 % (23632)Instructions burned: 136 (million)
% 6.52/2.15 % (23632)------------------------------
% 6.52/2.15 % (23632)------------------------------
% 6.52/2.16 % (23635)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_23273 for (2993ds/258Mi)
% 6.52/2.18 % (23634)Instruction limit reached!
% 6.52/2.18 % (23634)------------------------------
% 6.52/2.18 % (23634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.18 % (23634)Termination reason: Unknown
% 6.52/2.18 % (23634)Termination phase: Saturation
% 6.52/2.18
% 6.52/2.18 % (23634)Memory used [KB]: 3198
% 6.52/2.18 % (23634)Time elapsed: 0.056 s
% 6.52/2.18 % (23634)Instructions burned: 192 (million)
% 6.52/2.18 % (23634)------------------------------
% 6.52/2.18 % (23634)------------------------------
% 6.52/2.19 % (23631)Instruction limit reached!
% 6.52/2.19 % (23631)------------------------------
% 6.52/2.19 % (23631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.19 % (23631)Termination reason: Unknown
% 6.52/2.19 % (23631)Termination phase: Saturation
% 6.52/2.19
% 6.52/2.19 % (23631)Memory used [KB]: 7291
% 6.52/2.19 % (23631)Time elapsed: 0.080 s
% 6.52/2.19 % (23631)Instructions burned: 283 (million)
% 6.52/2.19 % (23631)------------------------------
% 6.52/2.19 % (23631)------------------------------
% 6.52/2.19 % (23636)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_23273 for (2993ds/90Mi)
% 6.52/2.19 % (23630)Instruction limit reached!
% 6.52/2.19 % (23630)------------------------------
% 6.52/2.19 % (23630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.19 % (23630)Termination reason: Unknown
% 6.52/2.19 % (23630)Termination phase: Saturation
% 6.52/2.19
% 6.52/2.19 % (23630)Memory used [KB]: 7164
% 6.52/2.19 % (23630)Time elapsed: 0.097 s
% 6.52/2.19 % (23630)Instructions burned: 341 (million)
% 6.52/2.19 % (23630)------------------------------
% 6.52/2.19 % (23630)------------------------------
% 6.52/2.20 % (23637)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_23273 for (2993ds/231Mi)
% 6.90/2.20 % (23633)Instruction limit reached!
% 6.90/2.20 % (23633)------------------------------
% 6.90/2.20 % (23633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.20 % (23633)Termination reason: Unknown
% 6.90/2.20 % (23633)Termination phase: Saturation
% 6.90/2.20
% 6.90/2.20 % (23633)Memory used [KB]: 7419
% 6.90/2.20 % (23633)Time elapsed: 0.080 s
% 6.90/2.20 % (23633)Instructions burned: 299 (million)
% 6.90/2.20 % (23633)------------------------------
% 6.90/2.20 % (23633)------------------------------
% 6.90/2.20 % (23638)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_23273 for (2993ds/458Mi)
% 6.90/2.21 % (23639)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_23273 for (2993ds/31Mi)
% 6.90/2.21 % (23636)Instruction limit reached!
% 6.90/2.21 % (23636)------------------------------
% 6.90/2.21 % (23636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.21 % (23636)Termination reason: Unknown
% 6.90/2.21 % (23636)Termination phase: Property scanning
% 6.90/2.21
% 6.90/2.21 % (23636)Memory used [KB]: 2174
% 6.90/2.21 % (23636)Time elapsed: 0.026 s
% 6.90/2.21 % (23636)Instructions burned: 93 (million)
% 6.90/2.21 % (23636)------------------------------
% 6.90/2.21 % (23636)------------------------------
% 6.90/2.22 % (23639)Instruction limit reached!
% 6.90/2.22 % (23639)------------------------------
% 6.90/2.22 % (23639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.22 % (23639)Termination reason: Unknown
% 6.90/2.22 % (23639)Termination phase: Preprocessing 1
% 6.90/2.22
% 6.90/2.22 % (23639)Memory used [KB]: 1663
% 6.90/2.22 % (23639)Time elapsed: 0.010 s
% 6.90/2.22 % (23639)Instructions burned: 31 (million)
% 6.90/2.22 % (23639)------------------------------
% 6.90/2.22 % (23639)------------------------------
% 6.90/2.22 % (23640)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_23273 for (2993ds/297Mi)
% 6.90/2.23 % (23641)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_23273 for (2992ds/987Mi)
% 6.90/2.23 % (23628)Instruction limit reached!
% 6.90/2.23 % (23628)------------------------------
% 6.90/2.23 % (23628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.23 % (23628)Termination reason: Unknown
% 6.90/2.23 % (23628)Termination phase: Saturation
% 6.90/2.23
% 6.90/2.23 % (23628)Memory used [KB]: 9083
% 6.90/2.23 % (23628)Time elapsed: 0.199 s
% 6.90/2.23 % (23628)Instructions burned: 614 (million)
% 6.90/2.23 % (23628)------------------------------
% 6.90/2.23 % (23628)------------------------------
% 6.90/2.23 % (23635)Instruction limit reached!
% 6.90/2.23 % (23635)------------------------------
% 6.90/2.23 % (23635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.23 % (23635)Termination reason: Unknown
% 6.90/2.23 % (23635)Termination phase: Saturation
% 6.90/2.23
% 6.90/2.23 % (23635)Memory used [KB]: 7419
% 6.90/2.23 % (23635)Time elapsed: 0.074 s
% 6.90/2.23 % (23635)Instructions burned: 261 (million)
% 6.90/2.23 % (23635)------------------------------
% 6.90/2.23 % (23635)------------------------------
% 6.90/2.24 % (23642)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_23273 for (2992ds/182Mi)
% 6.90/2.24 % (23643)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_23273 for (2992ds/182Mi)
% 6.90/2.25 % (23610)Instruction limit reached!
% 6.90/2.25 % (23610)------------------------------
% 6.90/2.25 % (23610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.25 % (23610)Termination reason: Unknown
% 6.90/2.25 % (23610)Termination phase: Saturation
% 6.90/2.25
% 6.90/2.25 % (23610)Memory used [KB]: 8955
% 6.90/2.25 % (23610)Time elapsed: 0.351 s
% 6.90/2.25 % (23610)Instructions burned: 1088 (million)
% 6.90/2.25 % (23610)------------------------------
% 6.90/2.25 % (23610)------------------------------
% 6.90/2.26 % (23644)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_23273 for (2992ds/154Mi)
% 6.90/2.26 % (23637)Instruction limit reached!
% 6.90/2.26 % (23637)------------------------------
% 6.90/2.26 % (23637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.26 % (23637)Termination reason: Unknown
% 6.90/2.26 % (23637)Termination phase: Saturation
% 6.90/2.26
% 6.90/2.26 % (23637)Memory used [KB]: 7291
% 6.90/2.26 % (23637)Time elapsed: 0.066 s
% 6.90/2.26 % (23637)Instructions burned: 233 (million)
% 6.90/2.26 % (23637)------------------------------
% 6.90/2.26 % (23637)------------------------------
% 6.90/2.27 % (23645)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_23273 for (2992ds/79Mi)
% 6.90/2.29 % (23642)Instruction limit reached!
% 6.90/2.29 % (23642)------------------------------
% 6.90/2.29 % (23642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.29 % (23642)Termination reason: Unknown
% 6.90/2.29 % (23642)Termination phase: Saturation
% 6.90/2.29
% 6.90/2.29 % (23642)Memory used [KB]: 7036
% 6.90/2.29 % (23642)Time elapsed: 0.051 s
% 6.90/2.29 % (23642)Instructions burned: 184 (million)
% 6.90/2.29 % (23642)------------------------------
% 6.90/2.29 % (23642)------------------------------
% 6.90/2.29 % (23645)Instruction limit reached!
% 6.90/2.29 % (23645)------------------------------
% 6.90/2.29 % (23645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.29 % (23645)Termination reason: Unknown
% 6.90/2.29 % (23645)Termination phase: Property scanning
% 6.90/2.29
% 6.90/2.29 % (23645)Memory used [KB]: 2046
% 6.90/2.29 % (23645)Time elapsed: 0.024 s
% 6.90/2.29 % (23645)Instructions burned: 81 (million)
% 6.90/2.29 % (23645)------------------------------
% 6.90/2.29 % (23645)------------------------------
% 6.90/2.29 % (23643)Instruction limit reached!
% 6.90/2.29 % (23643)------------------------------
% 6.90/2.29 % (23643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.29 % (23643)Termination reason: Unknown
% 6.90/2.29 % (23643)Termination phase: Saturation
% 6.90/2.29
% 6.90/2.29 % (23643)Memory used [KB]: 6908
% 6.90/2.29 % (23643)Time elapsed: 0.057 s
% 6.90/2.29 % (23643)Instructions burned: 184 (million)
% 6.90/2.29 % (23643)------------------------------
% 6.90/2.29 % (23643)------------------------------
% 6.90/2.30 % (23646)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_23273 for (2992ds/216Mi)
% 7.59/2.30 % (23644)Instruction limit reached!
% 7.59/2.30 % (23644)------------------------------
% 7.59/2.30 % (23644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.30 % (23644)Termination reason: Unknown
% 7.59/2.30 % (23644)Termination phase: Saturation
% 7.59/2.30
% 7.59/2.30 % (23644)Memory used [KB]: 2302
% 7.59/2.30 % (23644)Time elapsed: 0.041 s
% 7.59/2.30 % (23644)Instructions burned: 154 (million)
% 7.59/2.30 % (23644)------------------------------
% 7.59/2.30 % (23644)------------------------------
% 7.59/2.30 % (23647)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_23273 for (2992ds/114Mi)
% 7.59/2.30 % (23648)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_23273 for (2992ds/922Mi)
% 7.59/2.31 % (23649)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_23273 for (2992ds/182Mi)
% 7.59/2.31 % (23640)Instruction limit reached!
% 7.59/2.31 % (23640)------------------------------
% 7.59/2.31 % (23640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.31 % (23640)Termination reason: Unknown
% 7.59/2.31 % (23640)Termination phase: Saturation
% 7.59/2.31
% 7.59/2.31 % (23640)Memory used [KB]: 7164
% 7.59/2.31 % (23640)Time elapsed: 0.085 s
% 7.59/2.31 % (23640)Instructions burned: 299 (million)
% 7.59/2.31 % (23640)------------------------------
% 7.59/2.31 % (23640)------------------------------
% 7.59/2.32 % (23650)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_23273 for (2992ds/164Mi)
% 7.59/2.33 % (23638)Instruction limit reached!
% 7.59/2.33 % (23638)------------------------------
% 7.59/2.33 % (23638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.33 % (23638)Termination reason: Unknown
% 7.59/2.33 % (23638)Termination phase: Saturation
% 7.59/2.33
% 7.59/2.33 % (23638)Memory used [KB]: 7675
% 7.59/2.33 % (23638)Time elapsed: 0.129 s
% 7.59/2.33 % (23638)Instructions burned: 461 (million)
% 7.59/2.33 % (23638)------------------------------
% 7.59/2.33 % (23638)------------------------------
% 7.59/2.33 % (23647)Instruction limit reached!
% 7.59/2.33 % (23647)------------------------------
% 7.59/2.33 % (23647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.33 % (23647)Termination reason: Unknown
% 7.59/2.33 % (23647)Termination phase: Saturation
% 7.59/2.33
% 7.59/2.33 % (23647)Memory used [KB]: 6652
% 7.59/2.33 % (23647)Time elapsed: 0.032 s
% 7.59/2.33 % (23647)Instructions burned: 115 (million)
% 7.59/2.33 % (23647)------------------------------
% 7.59/2.33 % (23647)------------------------------
% 7.59/2.34 % (23651)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_23273 for (2991ds/50Mi)
% 7.59/2.34 % (23652)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_23273 for (2991ds/368Mi)
% 7.59/2.35 % (23646)Instruction limit reached!
% 7.59/2.35 % (23646)------------------------------
% 7.59/2.35 % (23646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.35 % (23646)Termination reason: Unknown
% 7.59/2.35 % (23646)Termination phase: Saturation
% 7.59/2.35
% 7.59/2.35 % (23646)Memory used [KB]: 7164
% 7.59/2.35 % (23646)Time elapsed: 0.057 s
% 7.59/2.35 % (23646)Instructions burned: 217 (million)
% 7.59/2.35 % (23646)------------------------------
% 7.59/2.35 % (23646)------------------------------
% 7.59/2.35 % (23649)Instruction limit reached!
% 7.59/2.35 % (23649)------------------------------
% 7.59/2.35 % (23649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.35 % (23649)Termination reason: Unknown
% 7.59/2.35 % (23649)Termination phase: Saturation
% 7.59/2.35
% 7.59/2.35 % (23649)Memory used [KB]: 7036
% 7.59/2.35 % (23649)Time elapsed: 0.047 s
% 7.59/2.35 % (23649)Instructions burned: 182 (million)
% 7.59/2.35 % (23649)------------------------------
% 7.59/2.35 % (23649)------------------------------
% 7.59/2.35 % (23651)Instruction limit reached!
% 7.59/2.35 % (23651)------------------------------
% 7.59/2.35 % (23651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.35 % (23651)Termination reason: Unknown
% 7.59/2.35 % (23651)Termination phase: Property scanning
% 7.59/2.35
% 7.59/2.35 % (23651)Memory used [KB]: 2046
% 7.59/2.35 % (23651)Time elapsed: 0.014 s
% 7.59/2.35 % (23651)Instructions burned: 50 (million)
% 7.59/2.35 % (23651)------------------------------
% 7.59/2.35 % (23651)------------------------------
% 7.59/2.36 % (23650)Instruction limit reached!
% 7.59/2.36 % (23650)------------------------------
% 7.59/2.36 % (23650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.36 % (23650)Termination reason: Unknown
% 7.59/2.36 % (23650)Termination phase: Saturation
% 7.59/2.36
% 7.59/2.36 % (23650)Memory used [KB]: 2302
% 7.59/2.36 % (23650)Time elapsed: 0.043 s
% 7.59/2.36 % (23650)Instructions burned: 165 (million)
% 7.59/2.36 % (23650)------------------------------
% 7.59/2.36 % (23650)------------------------------
% 7.59/2.36 % (23653)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_23273 for (2991ds/1021Mi)
% 7.59/2.36 % (23654)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_23273 for (2991ds/267Mi)
% 7.59/2.36 % (23655)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_23273 for (2991ds/204Mi)
% 7.59/2.37 % (23656)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_23273 for (2991ds/26Mi)
% 7.59/2.38 % (23656)Instruction limit reached!
% 7.59/2.38 % (23656)------------------------------
% 7.59/2.38 % (23656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.38 % (23656)Termination reason: Unknown
% 7.59/2.38 % (23656)Termination phase: shuffling
% 7.59/2.38
% 7.59/2.38 % (23656)Memory used [KB]: 1791
% 7.59/2.38 % (23656)Time elapsed: 0.008 s
% 7.59/2.38 % (23656)Instructions burned: 26 (million)
% 7.59/2.38 % (23656)------------------------------
% 7.59/2.38 % (23656)------------------------------
% 7.59/2.39 % (23657)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_23273 for (2991ds/53Mi)
% 8.12/2.40 % (23657)Instruction limit reached!
% 8.12/2.40 % (23657)------------------------------
% 8.12/2.40 % (23657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.40 % (23657)Termination reason: Unknown
% 8.12/2.40 % (23657)Termination phase: Property scanning
% 8.12/2.40
% 8.12/2.40 % (23657)Memory used [KB]: 2046
% 8.12/2.40 % (23657)Time elapsed: 0.015 s
% 8.12/2.40 % (23657)Instructions burned: 53 (million)
% 8.12/2.40 % (23657)------------------------------
% 8.12/2.40 % (23657)------------------------------
% 8.12/2.41 % (23658)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_23273 for (2991ds/4436Mi)
% 8.12/2.42 % (23655)Instruction limit reached!
% 8.12/2.42 % (23655)------------------------------
% 8.12/2.42 % (23655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.42 % (23655)Termination reason: Unknown
% 8.12/2.42 % (23655)Termination phase: Saturation
% 8.12/2.42
% 8.12/2.42 % (23655)Memory used [KB]: 7036
% 8.12/2.42 % (23655)Time elapsed: 0.057 s
% 8.12/2.42 % (23655)Instructions burned: 204 (million)
% 8.12/2.42 % (23655)------------------------------
% 8.12/2.42 % (23655)------------------------------
% 8.12/2.43 % (23659)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_23273 for (2991ds/1539Mi)
% 8.12/2.43 % (23654)Instruction limit reached!
% 8.12/2.43 % (23654)------------------------------
% 8.12/2.43 % (23654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.43 % (23654)Termination reason: Unknown
% 8.12/2.43 % (23654)Termination phase: Saturation
% 8.12/2.43
% 8.12/2.43 % (23654)Memory used [KB]: 7291
% 8.12/2.43 % (23654)Time elapsed: 0.074 s
% 8.12/2.43 % (23654)Instructions burned: 267 (million)
% 8.12/2.43 % (23654)------------------------------
% 8.12/2.43 % (23654)------------------------------
% 8.12/2.44 % (23652)Instruction limit reached!
% 8.12/2.44 % (23652)------------------------------
% 8.12/2.44 % (23652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.44 % (23652)Termination reason: Unknown
% 8.12/2.44 % (23652)Termination phase: Saturation
% 8.12/2.44
% 8.12/2.44 % (23652)Memory used [KB]: 7547
% 8.12/2.44 % (23652)Time elapsed: 0.102 s
% 8.12/2.44 % (23652)Instructions burned: 368 (million)
% 8.12/2.44 % (23652)------------------------------
% 8.12/2.44 % (23652)------------------------------
% 8.12/2.44 % (23660)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_23273 for (2990ds/408Mi)
% 8.12/2.45 % (23661)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_23273 for (2990ds/5205Mi)
% 8.42/2.52 % (23641)Instruction limit reached!
% 8.42/2.52 % (23641)------------------------------
% 8.42/2.52 % (23641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.52 % (23641)Termination reason: Unknown
% 8.42/2.52 % (23641)Termination phase: Saturation
% 8.42/2.52
% 8.42/2.52 % (23641)Memory used [KB]: 8571
% 8.42/2.52 % (23641)Time elapsed: 0.294 s
% 8.42/2.52 % (23641)Instructions burned: 988 (million)
% 8.42/2.52 % (23641)------------------------------
% 8.42/2.52 % (23641)------------------------------
% 8.42/2.53 % (23662)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_23273 for (2990ds/1913Mi)
% 8.42/2.56 % (23660)Instruction limit reached!
% 8.42/2.56 % (23660)------------------------------
% 8.42/2.56 % (23660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.56 % (23660)Termination reason: Unknown
% 8.42/2.56 % (23660)Termination phase: Saturation
% 8.42/2.56
% 8.42/2.56 % (23660)Memory used [KB]: 7931
% 8.42/2.56 % (23660)Time elapsed: 0.138 s
% 8.42/2.56 % (23660)Instructions burned: 410 (million)
% 8.42/2.56 % (23660)------------------------------
% 8.42/2.56 % (23660)------------------------------
% 8.42/2.57 % (23663)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_23273 for (2989ds/4350Mi)
% 8.42/2.59 % (23648)Instruction limit reached!
% 8.42/2.59 % (23648)------------------------------
% 8.42/2.59 % (23648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.42/2.59 % (23648)Termination reason: Unknown
% 8.42/2.59 % (23648)Termination phase: Saturation
% 8.42/2.59
% 8.42/2.59 % (23648)Memory used [KB]: 8443
% 8.42/2.59 % (23648)Time elapsed: 0.282 s
% 8.42/2.59 % (23648)Instructions burned: 922 (million)
% 8.42/2.59 % (23648)------------------------------
% 8.42/2.59 % (23648)------------------------------
% 8.42/2.59 % (23664)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_23273 for (2989ds/68Mi)
% 9.13/2.61 % (23664)Instruction limit reached!
% 9.13/2.61 % (23664)------------------------------
% 9.13/2.61 % (23664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.13/2.61 % (23664)Termination reason: Unknown
% 9.13/2.61 % (23664)Termination phase: Function definition elimination
% 9.13/2.61
% 9.13/2.61 % (23664)Memory used [KB]: 2046
% 9.13/2.61 % (23664)Time elapsed: 0.020 s
% 9.13/2.61 % (23664)Instructions burned: 69 (million)
% 9.13/2.61 % (23664)------------------------------
% 9.13/2.61 % (23664)------------------------------
% 9.13/2.62 % (23665)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_23273 for (2989ds/358Mi)
% 9.13/2.68 % (23653)Instruction limit reached!
% 9.13/2.68 % (23653)------------------------------
% 9.13/2.68 % (23653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.13/2.68 % (23653)Termination reason: Unknown
% 9.13/2.68 % (23653)Termination phase: Saturation
% 9.13/2.68
% 9.13/2.68 % (23653)Memory used [KB]: 8443
% 9.13/2.68 % (23653)Time elapsed: 0.320 s
% 9.13/2.68 % (23653)Instructions burned: 1023 (million)
% 9.13/2.68 % (23653)------------------------------
% 9.13/2.68 % (23653)------------------------------
% 9.13/2.69 % (23666)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_23273 for (2988ds/31Mi)
% 9.49/2.70 % (23666)Instruction limit reached!
% 9.49/2.70 % (23666)------------------------------
% 9.49/2.70 % (23666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.49/2.70 % (23666)Termination reason: Unknown
% 9.49/2.70 % (23666)Termination phase: Preprocessing 1
% 9.49/2.70
% 9.49/2.70 % (23666)Memory used [KB]: 1663
% 9.49/2.70 % (23666)Time elapsed: 0.010 s
% 9.49/2.70 % (23666)Instructions burned: 31 (million)
% 9.49/2.70 % (23666)------------------------------
% 9.49/2.70 % (23666)------------------------------
% 9.49/2.71 % (23667)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_23273 for (2988ds/279Mi)
% 9.49/2.73 % (23665)Instruction limit reached!
% 9.49/2.73 % (23665)------------------------------
% 9.49/2.73 % (23665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.49/2.73 % (23665)Termination reason: Unknown
% 9.49/2.73 % (23665)Termination phase: Saturation
% 9.49/2.73
% 9.49/2.73 % (23665)Memory used [KB]: 7419
% 9.49/2.73 % (23665)Time elapsed: 0.126 s
% 9.49/2.73 % (23665)Instructions burned: 358 (million)
% 9.49/2.73 % (23665)------------------------------
% 9.49/2.73 % (23665)------------------------------
% 9.49/2.73 % (23668)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_23273 for (2987ds/258Mi)
% 9.49/2.75 % (23667)Refutation not found, incomplete strategy
% 9.49/2.75 % (23667)------------------------------
% 9.49/2.75 % (23667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.49/2.75 % (23667)Termination reason: Refutation not found, incomplete strategy
% 9.49/2.75
% 9.49/2.75
% 9.49/2.75 % (23667)Memory used [KB]: 6908
% 9.49/2.75 % (23667)Time elapsed: 0.040 s
% 9.49/2.75 % (23667)Instructions burned: 153 (million)
% 9.49/2.75 % (23667)------------------------------
% 9.49/2.75 % (23667)------------------------------
% 9.49/2.76 % (23669)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_23273 for (2987ds/26Mi)
% 9.49/2.76 % (23669)Instruction limit reached!
% 9.49/2.76 % (23669)------------------------------
% 9.49/2.76 % (23669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.49/2.76 % (23669)Termination reason: Unknown
% 9.49/2.76 % (23669)Termination phase: shuffling
% 9.49/2.76
% 9.49/2.76 % (23669)Memory used [KB]: 1791
% 9.49/2.76 % (23669)Time elapsed: 0.008 s
% 9.49/2.76 % (23669)Instructions burned: 26 (million)
% 9.49/2.76 % (23669)------------------------------
% 9.49/2.76 % (23669)------------------------------
% 9.49/2.77 % (23670)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_23273 for (2987ds/995Mi)
% 9.68/2.81 % (23668)Instruction limit reached!
% 9.68/2.81 % (23668)------------------------------
% 9.68/2.81 % (23668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.68/2.81 % (23668)Termination reason: Unknown
% 9.68/2.81 % (23668)Termination phase: Saturation
% 9.68/2.81
% 9.68/2.81 % (23668)Memory used [KB]: 7036
% 9.68/2.81 % (23668)Time elapsed: 0.078 s
% 9.68/2.81 % (23668)Instructions burned: 258 (million)
% 9.68/2.81 % (23668)------------------------------
% 9.68/2.81 % (23668)------------------------------
% 9.68/2.82 % (23671)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_23273 for (2986ds/373Mi)
% 9.77/2.91 % (23659)Instruction limit reached!
% 9.77/2.91 % (23659)------------------------------
% 9.77/2.91 % (23659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.77/2.91 % (23659)Termination reason: Unknown
% 9.77/2.91 % (23659)Termination phase: Saturation
% 9.77/2.91
% 9.77/2.91 % (23659)Memory used [KB]: 8955
% 9.77/2.91 % (23659)Time elapsed: 0.502 s
% 9.77/2.91 % (23659)Instructions burned: 1539 (million)
% 9.77/2.91 % (23659)------------------------------
% 9.77/2.91 % (23659)------------------------------
% 9.77/2.92 % (23672)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_23273 for (2986ds/253Mi)
% 9.77/2.93 % (23671)Instruction limit reached!
% 9.77/2.93 % (23671)------------------------------
% 9.77/2.93 % (23671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.77/2.93 % (23671)Termination reason: Unknown
% 9.77/2.93 % (23671)Termination phase: Saturation
% 9.77/2.93
% 9.77/2.93 % (23671)Memory used [KB]: 7675
% 9.77/2.93 % (23671)Time elapsed: 0.112 s
% 9.77/2.93 % (23671)Instructions burned: 374 (million)
% 9.77/2.93 % (23671)------------------------------
% 9.77/2.93 % (23671)------------------------------
% 9.77/2.94 % (23673)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_23273 for (2985ds/832Mi)
% 9.77/2.98 % (23672)Instruction limit reached!
% 9.77/2.98 % (23672)------------------------------
% 9.77/2.98 % (23672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.77/2.98 % (23672)Termination reason: Unknown
% 9.77/2.98 % (23672)Termination phase: Saturation
% 9.77/2.98
% 9.77/2.98 % (23672)Memory used [KB]: 7419
% 9.77/2.98 % (23672)Time elapsed: 0.067 s
% 9.77/2.98 % (23672)Instructions burned: 255 (million)
% 9.77/2.98 % (23672)------------------------------
% 9.77/2.98 % (23672)------------------------------
% 9.77/2.99 % (23674)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_23273 for (2985ds/668Mi)
% 12.96/3.07 % (23670)Instruction limit reached!
% 12.96/3.07 % (23670)------------------------------
% 12.96/3.07 % (23670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.07 % (23670)Termination reason: Unknown
% 12.96/3.07 % (23670)Termination phase: Saturation
% 12.96/3.07
% 12.96/3.07 % (23670)Memory used [KB]: 9083
% 12.96/3.07 % (23670)Time elapsed: 0.296 s
% 12.96/3.07 % (23670)Instructions burned: 995 (million)
% 12.96/3.07 % (23670)------------------------------
% 12.96/3.07 % (23670)------------------------------
% 12.96/3.08 % (23675)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_23273 for (2984ds/40Mi)
% 12.96/3.09 % (23675)Instruction limit reached!
% 12.96/3.09 % (23675)------------------------------
% 12.96/3.09 % (23675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.09 % (23675)Termination reason: Unknown
% 12.96/3.09 % (23675)Termination phase: Property scanning
% 12.96/3.09
% 12.96/3.09 % (23675)Memory used [KB]: 2046
% 12.96/3.09 % (23675)Time elapsed: 0.013 s
% 12.96/3.09 % (23675)Instructions burned: 43 (million)
% 12.96/3.09 % (23675)------------------------------
% 12.96/3.09 % (23675)------------------------------
% 12.96/3.10 % (23676)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_23273 for (2984ds/294Mi)
% 12.96/3.12 % (23662)Instruction limit reached!
% 12.96/3.12 % (23662)------------------------------
% 12.96/3.12 % (23662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.12 % (23662)Termination reason: Unknown
% 12.96/3.12 % (23662)Termination phase: Saturation
% 12.96/3.12
% 12.96/3.12 % (23662)Memory used [KB]: 4477
% 12.96/3.12 % (23662)Time elapsed: 0.618 s
% 12.96/3.12 % (23662)Instructions burned: 1915 (million)
% 12.96/3.12 % (23662)------------------------------
% 12.96/3.12 % (23662)------------------------------
% 13.64/3.13 % (23677)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_23273 for (2984ds/187Mi)
% 13.64/3.18 % (23676)Instruction limit reached!
% 13.64/3.18 % (23676)------------------------------
% 13.64/3.18 % (23676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.64/3.18 % (23676)Termination reason: Unknown
% 13.64/3.18 % (23676)Termination phase: Saturation
% 13.64/3.18
% 13.64/3.18 % (23676)Memory used [KB]: 7036
% 13.64/3.18 % (23676)Time elapsed: 0.105 s
% 13.64/3.18 % (23676)Instructions burned: 296 (million)
% 13.64/3.18 % (23676)------------------------------
% 13.64/3.18 % (23676)------------------------------
% 13.64/3.18 % (23677)Instruction limit reached!
% 13.64/3.18 % (23677)------------------------------
% 13.64/3.18 % (23677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.64/3.18 % (23677)Termination reason: Unknown
% 13.64/3.18 % (23677)Termination phase: Saturation
% 13.64/3.18
% 13.64/3.18 % (23677)Memory used [KB]: 7036
% 13.64/3.18 % (23677)Time elapsed: 0.054 s
% 13.64/3.18 % (23677)Instructions burned: 187 (million)
% 13.64/3.18 % (23677)------------------------------
% 13.64/3.18 % (23677)------------------------------
% 13.64/3.19 % (23673)Instruction limit reached!
% 13.64/3.19 % (23673)------------------------------
% 13.64/3.19 % (23673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.64/3.19 % (23673)Termination reason: Unknown
% 13.64/3.19 % (23673)Termination phase: Saturation
% 13.64/3.19
% 13.64/3.19 % (23673)Memory used [KB]: 7547
% 13.64/3.19 % (23673)Time elapsed: 0.246 s
% 13.64/3.19 % (23673)Instructions burned: 835 (million)
% 13.64/3.19 % (23673)------------------------------
% 13.64/3.19 % (23673)------------------------------
% 13.64/3.19 % (23674)Instruction limit reached!
% 13.64/3.19 % (23674)------------------------------
% 13.64/3.19 % (23674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.64/3.19 % (23674)Termination reason: Unknown
% 13.64/3.19 % (23674)Termination phase: Saturation
% 13.64/3.19
% 13.64/3.19 % (23674)Memory used [KB]: 13688
% 13.64/3.19 % (23674)Time elapsed: 0.197 s
% 13.64/3.19 % (23674)Instructions burned: 668 (million)
% 13.64/3.19 % (23674)------------------------------
% 13.64/3.19 % (23674)------------------------------
% 13.64/3.19 % (23678)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_23273 for (2983ds/371Mi)
% 13.64/3.19 % (23679)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_23273 for (2983ds/1827Mi)
% 13.64/3.20 % (23680)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_23273 for (2983ds/70Mi)
% 14.18/3.20 % (23681)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_23273 for (2983ds/316Mi)
% 14.18/3.22 % (23680)Instruction limit reached!
% 14.18/3.22 % (23680)------------------------------
% 14.18/3.22 % (23680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.18/3.22 % (23680)Termination reason: Unknown
% 14.18/3.22 % (23680)Termination phase: Property scanning
% 14.18/3.22
% 14.18/3.22 % (23680)Memory used [KB]: 2046
% 14.18/3.22 % (23680)Time elapsed: 0.020 s
% 14.18/3.22 % (23680)Instructions burned: 73 (million)
% 14.18/3.22 % (23680)------------------------------
% 14.18/3.22 % (23680)------------------------------
% 14.18/3.22 % (23682)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_23273 for (2982ds/932Mi)
% 14.18/3.25 % (23681)Refutation not found, incomplete strategy
% 14.18/3.25 % (23681)------------------------------
% 14.18/3.25 % (23681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.18/3.25 % (23681)Termination reason: Refutation not found, incomplete strategy
% 14.18/3.25
% 14.18/3.25
% 14.18/3.25 % (23681)Memory used [KB]: 7036
% 14.18/3.25 % (23681)Time elapsed: 0.047 s
% 14.18/3.25 % (23681)Instructions burned: 177 (million)
% 14.18/3.25 % (23681)------------------------------
% 14.18/3.25 % (23681)------------------------------
% 14.18/3.26 % (23683)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_23273 for (2982ds/4714Mi)
% 14.18/3.29 % (23678)Instruction limit reached!
% 14.18/3.29 % (23678)------------------------------
% 14.18/3.29 % (23678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.18/3.29 % (23678)Termination reason: Unknown
% 14.18/3.29 % (23678)Termination phase: Saturation
% 14.18/3.29
% 14.18/3.29 % (23678)Memory used [KB]: 7675
% 14.18/3.29 % (23678)Time elapsed: 0.102 s
% 14.18/3.29 % (23678)Instructions burned: 371 (million)
% 14.18/3.29 % (23678)------------------------------
% 14.18/3.29 % (23678)------------------------------
% 14.67/3.30 % (23684)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_23273 for (2982ds/8250Mi)
% 14.67/3.31 % (23683)Refutation not found, incomplete strategy
% 14.67/3.31 % (23683)------------------------------
% 14.67/3.31 % (23683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.67/3.31 % (23683)Termination reason: Refutation not found, incomplete strategy
% 14.67/3.31
% 14.67/3.31
% 14.67/3.31 % (23683)Memory used [KB]: 7291
% 14.67/3.31 % (23683)Time elapsed: 0.056 s
% 14.67/3.31 % (23683)Instructions burned: 210 (million)
% 14.67/3.31 % (23683)------------------------------
% 14.67/3.31 % (23683)------------------------------
% 14.67/3.32 % (23685)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_23273 for (2981ds/770Mi)
% 14.67/3.38 % (23685)First to succeed.
% 14.67/3.38 % (23685)Refutation found. Thanks to Tanya!
% 14.67/3.38 % SZS status Theorem for DTF2THF_23273
% 14.67/3.38 % SZS output start Proof for DTF2THF_23273
% 14.67/3.38 thf(type_def_5, type, nat: $tType).
% 14.67/3.38 thf(type_def_7, type, list_nat: $tType).
% 14.67/3.38 thf(type_def_8, type, list_a: $tType).
% 14.67/3.38 thf(type_def_9, type, a: $tType).
% 14.67/3.38 thf(func_def_0, type, list_nat: $tType).
% 14.67/3.38 thf(func_def_1, type, list_a: $tType).
% 14.67/3.38 thf(func_def_2, type, nat: $tType).
% 14.67/3.38 thf(func_def_3, type, a: $tType).
% 14.67/3.38 thf(func_def_4, type, minus_minus_nat: nat > nat > nat).
% 14.67/3.38 thf(func_def_5, type, list_asc_nat: list_nat > $o).
% 14.67/3.38 thf(func_def_6, type, list_desc_nat: list_nat > $o).
% 14.67/3.38 thf(func_def_7, type, list_strict_asc_nat: list_nat > $o).
% 14.67/3.38 thf(func_def_8, type, list_strict_desc_nat: list_nat > $o).
% 14.67/3.38 thf(func_def_9, type, listIn923761578nd_nat: list_nat > (nat > nat) > nat > nat).
% 14.67/3.38 thf(func_def_10, type, listIn1312259492pend_a: list_a > (nat > a) > nat > a).
% 14.67/3.38 thf(func_def_11, type, linorder_sorted_nat: list_nat > $o).
% 14.67/3.38 thf(func_def_12, type, list_ex_nat: (nat > $o) > list_nat > $o).
% 14.67/3.38 thf(func_def_13, type, list_ex_a: (a > $o) > list_a > $o).
% 14.67/3.38 thf(func_def_14, type, nth_nat: list_nat > nat > nat).
% 14.67/3.38 thf(func_def_15, type, nth_a: list_a > nat > a).
% 14.67/3.38 thf(func_def_16, type, rev_nat: list_nat > list_nat).
% 14.67/3.38 thf(func_def_17, type, rev_a: list_a > list_a).
% 14.67/3.38 thf(func_def_18, type, suc: nat > nat).
% 14.67/3.38 thf(func_def_19, type, size_size_list_nat: list_nat > nat).
% 14.67/3.38 thf(func_def_20, type, size_size_list_a: list_a > nat).
% 14.67/3.38 thf(func_def_21, type, ord_less_nat: nat > nat > $o).
% 14.67/3.38 thf(func_def_22, type, ord_less_eq_nat: nat > nat > $o).
% 14.67/3.38 thf(func_def_23, type, f: nat > a).
% 14.67/3.38 thf(func_def_24, type, g: nat > a).
% 14.67/3.38 thf(func_def_25, type, xs: list_a).
% 14.67/3.38 thf(func_def_26, type, ys: list_a).
% 14.67/3.38 thf(func_def_41, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 14.67/3.38 thf(func_def_42, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 14.67/3.38 thf(func_def_43, type, sP2: nat > nat > nat > $o).
% 14.67/3.38 thf(func_def_44, type, sP3: nat > nat > nat > $o).
% 14.67/3.38 thf(func_def_45, type, sP4: nat > nat > nat > $o).
% 14.67/3.38 thf(func_def_46, type, sK5: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_47, type, sK6: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_48, type, sK7: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_49, type, sK8: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_50, type, sK9: list_a > list_a > nat).
% 14.67/3.38 thf(func_def_51, type, sK10: nat > nat).
% 14.67/3.38 thf(func_def_52, type, sK11: nat > nat).
% 14.67/3.38 thf(func_def_53, type, sK12: nat > nat).
% 14.67/3.38 thf(func_def_54, type, sK13: nat > nat).
% 14.67/3.38 thf(func_def_55, type, sK14: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_56, type, sK15: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_57, type, sK16: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_58, type, sK17: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_59, type, sK18: nat > nat).
% 14.67/3.38 thf(func_def_60, type, sK19: (nat > $o) > nat).
% 14.67/3.38 thf(func_def_61, type, sK20: (nat > $o) > nat).
% 14.67/3.38 thf(func_def_62, type, sK21: (nat > $o) > nat > nat).
% 14.67/3.38 thf(func_def_63, type, sK22: (nat > nat > $o) > nat).
% 14.67/3.38 thf(func_def_64, type, sK23: (nat > nat > $o) > nat).
% 14.67/3.38 thf(func_def_65, type, sK24: (nat > nat > $o) > nat).
% 14.67/3.38 thf(func_def_66, type, sK25: (nat > nat > $o) > nat).
% 14.67/3.38 thf(func_def_67, type, sK26: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_68, type, sK27: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_69, type, sK28: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_70, type, sK29: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_71, type, sK30: (nat > $o) > nat).
% 14.67/3.38 thf(func_def_72, type, sK31: nat > nat).
% 14.67/3.38 thf(func_def_73, type, sK32: (nat > nat > $o) > nat).
% 14.67/3.38 thf(func_def_74, type, sK33: (nat > nat > $o) > nat).
% 14.67/3.38 thf(func_def_75, type, sK34: (nat > nat > $o) > nat).
% 14.67/3.38 thf(func_def_76, type, sK35: (nat > nat > $o) > nat).
% 14.67/3.38 thf(func_def_77, type, sK36: (nat > nat > $o) > nat).
% 14.67/3.38 thf(func_def_78, type, sK37: nat > nat).
% 14.67/3.38 thf(func_def_79, type, sK38: nat > nat).
% 14.67/3.38 thf(func_def_80, type, sK39: (nat > $o) > nat).
% 14.67/3.38 thf(func_def_81, type, sK40: nat > nat).
% 14.67/3.38 thf(func_def_82, type, sK41: (list_a > $o) > list_a).
% 14.67/3.38 thf(func_def_83, type, sK42: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_84, type, sK43: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_85, type, sK44: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_86, type, sK45: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_87, type, sK46: nat > nat).
% 14.67/3.38 thf(func_def_88, type, sK47: nat > nat).
% 14.67/3.38 thf(func_def_89, type, sK48: nat > nat).
% 14.67/3.38 thf(func_def_90, type, sK49: nat > (nat > $o) > nat > nat).
% 14.67/3.38 thf(func_def_91, type, sK50: nat > nat > (nat > $o) > nat).
% 14.67/3.38 thf(func_def_92, type, sK51: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_93, type, sK52: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_94, type, sK53: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_95, type, sK54: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_96, type, sK55: nat > list_a).
% 14.67/3.38 thf(func_def_97, type, sK56: nat).
% 14.67/3.38 thf(func_def_98, type, sK57: (nat > $o) > nat > nat).
% 14.67/3.38 thf(func_def_99, type, sK58: (nat > $o) > nat > nat).
% 14.67/3.38 thf(func_def_100, type, sK59: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_101, type, sK60: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_102, type, sK61: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_103, type, sK62: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_104, type, sK63: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_105, type, sK64: (nat > nat) > nat).
% 14.67/3.38 thf(func_def_106, type, sK65: nat > nat).
% 14.67/3.38 thf(func_def_108, type, ph67: !>[X0: $tType]:(X0)).
% 14.67/3.38 thf(f1710,plain,(
% 14.67/3.38 $false),
% 14.67/3.38 inference(avatar_sat_refutation,[status(thm)],[f1534,f1679,f1706])).
% 14.67/3.38 thf(f1706,plain,(
% 14.67/3.38 ~spl66_3),
% 14.67/3.38 inference(avatar_contradiction_clause,[status(thm)],[f1705])).
% 14.67/3.38 thf(f1705,plain,(
% 14.67/3.38 $false | ~spl66_3),
% 14.67/3.38 inference(subsumption_resolution,[status(thm)],[f1680,f1183])).
% 14.67/3.38 thf(f1183,plain,(
% 14.67/3.38 ((ord_less_nat @ sK56 @ (size_size_list_a @ xs)) = $true)),
% 14.67/3.38 inference(cnf_transformation,[status(thm)],[f1032])).
% 14.67/3.38 thf(f1032,plain,(
% 14.67/3.38 ((ord_less_nat @ sK56 @ (size_size_list_a @ xs)) = $true) & ((nth_a @ ys @ sK56) != (nth_a @ xs @ sK56))),
% 14.67/3.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK56])],[f930,f1031])).
% 14.67/3.38 thf(f1031,plain,(
% 14.67/3.38 ? [X0 : nat] : (((ord_less_nat @ X0 @ (size_size_list_a @ xs)) = $true) & ((nth_a @ xs @ X0) != (nth_a @ ys @ X0))) => (((ord_less_nat @ sK56 @ (size_size_list_a @ xs)) = $true) & ((nth_a @ ys @ sK56) != (nth_a @ xs @ sK56)))),
% 14.67/3.38 introduced(definition,[],[choice_axiom])).
% 14.67/3.38 thf(f930,plain,(
% 14.67/3.38 ? [X0 : nat] : (((ord_less_nat @ X0 @ (size_size_list_a @ xs)) = $true) & ((nth_a @ xs @ X0) != (nth_a @ ys @ X0)))),
% 14.67/3.38 inference(ennf_transformation,[status(thm)],[f779])).
% 14.67/3.38 thf(f779,plain,(
% 14.67/3.38 ~! [X0 : nat] : (((ord_less_nat @ X0 @ (size_size_list_a @ xs)) != $true) | ((nth_a @ xs @ X0) = (nth_a @ ys @ X0)))),
% 14.67/3.38 inference(flattening,[status(thm)],[f284])).
% 14.67/3.38 thf(f284,plain,(
% 14.67/3.38 ~! [X0 : nat] : (((nth_a @ xs @ X0) = (nth_a @ ys @ X0)) | ~((ord_less_nat @ X0 @ (size_size_list_a @ xs)) = $true))),
% 14.67/3.38 inference(fool_elimination,[status(thm)],[f283])).
% 14.67/3.38 thf(f283,plain,(
% 14.67/3.38 ~! [X0 : nat] : (((nth_a @ xs @ X0) = (nth_a @ ys @ X0)) | ~(ord_less_nat @ X0 @ (size_size_list_a @ xs)))),
% 14.67/3.38 inference(rectify,[status(thm)],[f256])).
% 14.67/3.38 thf(f256,negated_conjecture,(
% 14.67/3.38 ~! [X5 : nat] : (((nth_a @ xs @ X5) = (nth_a @ ys @ X5)) | ~(ord_less_nat @ X5 @ (size_size_list_a @ xs)))),
% 14.67/3.38 inference(negated_conjecture,[status(cth)],[f255])).
% 14.67/3.38 thf(f255,conjecture,(
% 14.67/3.38 ! [X5 : nat] : (((nth_a @ xs @ X5) = (nth_a @ ys @ X5)) | ~(ord_less_nat @ X5 @ (size_size_list_a @ xs)))),
% 14.67/3.38 file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',conj_2)).
% 14.67/3.38 thf(f1680,plain,(
% 14.67/3.38 ((ord_less_nat @ sK56 @ (size_size_list_a @ xs)) != $true) | ~spl66_3),
% 14.67/3.38 inference(backward_demodulation,[status(thm)],[f1242,f1516])).
% 14.67/3.38 thf(f1516,plain,(
% 14.67/3.38 ((size_size_list_a @ ys) = sK56) | ~spl66_3),
% 14.67/3.38 inference(avatar_component_clause,[status(thm)],[f1514])).
% 14.67/3.38 thf(f1514,definition,(
% 14.67/3.38 spl66_3 <=> ((size_size_list_a @ ys) = sK56)),
% 14.67/3.38 introduced(definition,[new_symbols(naming,[spl66_3])],[avatar_definition])).
% 14.67/3.38 thf(f1242,plain,(
% 14.67/3.38 ((ord_less_nat @ (size_size_list_a @ ys) @ (size_size_list_a @ xs)) != $true)),
% 14.67/3.38 inference(forward_literal_rewriting,[status(thm)],[f1063,f1056])).
% 14.67/3.38 thf(f1056,plain,(
% 14.67/3.38 ( ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ X1 @ X0) != $true) | ((ord_less_nat @ X0 @ X1) != $true)) )),
% 14.67/3.38 inference(cnf_transformation,[status(thm)],[f825])).
% 14.67/3.38 thf(f825,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ X1 @ X0) != $true) | ((ord_less_nat @ X0 @ X1) != $true))),
% 14.67/3.38 inference(ennf_transformation,[status(thm)],[f804])).
% 14.67/3.38 thf(f804,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ X1 @ X0) = $true) => ((ord_less_nat @ X0 @ X1) != $true))),
% 14.67/3.38 inference(flattening,[status(thm)],[f274])).
% 14.67/3.38 thf(f274,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ X1 @ X0) = $true) => ~((ord_less_nat @ X0 @ X1) = $true))),
% 14.67/3.38 inference(fool_elimination,[status(thm)],[f273])).
% 14.67/3.38 thf(f273,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ X1 @ X0) => ~(ord_less_nat @ X0 @ X1))),
% 14.67/3.38 inference(rectify,[status(thm)],[f127])).
% 14.67/3.38 thf(f127,axiom,(
% 14.67/3.38 ! [X14 : nat,X31 : nat] : ((ord_less_eq_nat @ X31 @ X14) => ~(ord_less_nat @ X14 @ X31))),
% 14.67/3.38 file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',fact_126_leD)).
% 14.67/3.38 thf(f1063,plain,(
% 14.67/3.38 ((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys)) = $true)),
% 14.67/3.38 inference(cnf_transformation,[status(thm)],[f674])).
% 14.67/3.38 thf(f674,plain,(
% 14.67/3.38 ((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys)) = $true)),
% 14.67/3.38 inference(fool_elimination,[status(thm)],[f673])).
% 14.67/3.38 thf(f673,plain,(
% 14.67/3.38 (ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys))),
% 14.67/3.38 inference(rectify,[status(thm)],[f254])).
% 14.67/3.38 thf(f254,axiom,(
% 14.67/3.38 (ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys))),
% 14.67/3.38 file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',conj_1)).
% 14.67/3.38 thf(f1679,plain,(
% 14.67/3.38 spl66_4),
% 14.67/3.38 inference(avatar_contradiction_clause,[status(thm)],[f1678])).
% 14.67/3.38 thf(f1678,plain,(
% 14.67/3.38 $false | spl66_4),
% 14.67/3.38 inference(subsumption_resolution,[status(thm)],[f1677,f1520])).
% 14.67/3.38 thf(f1520,plain,(
% 14.67/3.38 ((ord_less_eq_nat @ sK56 @ (size_size_list_a @ ys)) != $true) | spl66_4),
% 14.67/3.38 inference(avatar_component_clause,[status(thm)],[f1518])).
% 14.67/3.38 thf(f1518,definition,(
% 14.67/3.38 spl66_4 <=> ((ord_less_eq_nat @ sK56 @ (size_size_list_a @ ys)) = $true)),
% 14.67/3.38 introduced(definition,[new_symbols(naming,[spl66_4])],[avatar_definition])).
% 14.67/3.38 thf(f1677,plain,(
% 14.67/3.38 ((ord_less_eq_nat @ sK56 @ (size_size_list_a @ ys)) = $true)),
% 14.67/3.38 inference(forward_literal_rewriting,[status(thm)],[f1665,f1175])).
% 14.67/3.38 thf(f1175,plain,(
% 14.67/3.38 ( ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ X1 @ X0) = $true) | ((ord_less_nat @ X0 @ X1) = $true)) )),
% 14.67/3.38 inference(cnf_transformation,[status(thm)],[f815])).
% 14.67/3.38 thf(f815,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X0 @ X1) = $true) | ((ord_less_eq_nat @ X1 @ X0) = $true))),
% 14.67/3.38 inference(ennf_transformation,[status(thm)],[f800])).
% 14.67/3.38 thf(f800,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X0 @ X1) != $true) => ((ord_less_eq_nat @ X1 @ X0) = $true))),
% 14.67/3.38 inference(flattening,[status(thm)],[f595])).
% 14.67/3.38 thf(f595,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : (~((ord_less_nat @ X0 @ X1) = $true) => ((ord_less_eq_nat @ X1 @ X0) = $true))),
% 14.67/3.38 inference(fool_elimination,[status(thm)],[f594])).
% 14.67/3.38 thf(f594,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : (~(ord_less_nat @ X0 @ X1) => (ord_less_eq_nat @ X1 @ X0))),
% 14.67/3.38 inference(rectify,[status(thm)],[f126])).
% 14.67/3.38 thf(f126,axiom,(
% 14.67/3.38 ! [X14 : nat,X31 : nat] : (~(ord_less_nat @ X14 @ X31) => (ord_less_eq_nat @ X31 @ X14))),
% 14.67/3.38 file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',fact_125_leI)).
% 14.67/3.38 thf(f1665,plain,(
% 14.67/3.38 ((ord_less_nat @ (size_size_list_a @ ys) @ sK56) != $true)),
% 14.67/3.38 inference(trivial_inequality_removal,[status(thm)],[f1651])).
% 14.67/3.38 thf(f1651,plain,(
% 14.67/3.38 ($true != $true) | ((ord_less_nat @ (size_size_list_a @ ys) @ sK56) != $true)),
% 14.67/3.38 inference(superposition,[status(thm)],[f1287,f1257])).
% 14.67/3.38 thf(f1257,plain,(
% 14.67/3.38 ((ord_less_eq_nat @ sK56 @ (size_size_list_a @ xs)) = $true)),
% 14.67/3.38 inference(forward_literal_rewriting,[status(thm)],[f1256,f1175])).
% 14.67/3.38 thf(f1256,plain,(
% 14.67/3.38 ((ord_less_nat @ (size_size_list_a @ xs) @ sK56) != $true)),
% 14.67/3.38 inference(trivial_inequality_removal,[status(thm)],[f1244])).
% 14.67/3.38 thf(f1244,plain,(
% 14.67/3.38 ((ord_less_nat @ (size_size_list_a @ xs) @ sK56) != $true) | ($true != $true)),
% 14.67/3.38 inference(superposition,[status(thm)],[f1106,f1183])).
% 14.67/3.38 thf(f1106,plain,(
% 14.67/3.38 ( ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X1 @ X0) != $true) | ((ord_less_nat @ X0 @ X1) != $true)) )),
% 14.67/3.38 inference(cnf_transformation,[status(thm)],[f806])).
% 14.67/3.38 thf(f806,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X0 @ X1) != $true) | ((ord_less_nat @ X1 @ X0) != $true))),
% 14.67/3.38 inference(ennf_transformation,[status(thm)],[f796])).
% 14.67/3.38 thf(f796,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X1 @ X0) = $true) => ((ord_less_nat @ X0 @ X1) != $true))),
% 14.67/3.38 inference(flattening,[status(thm)],[f304])).
% 14.67/3.38 thf(f304,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X1 @ X0) = $true) => ~((ord_less_nat @ X0 @ X1) = $true))),
% 14.67/3.38 inference(fool_elimination,[status(thm)],[f303])).
% 14.67/3.38 thf(f303,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X1 @ X0) => ~(ord_less_nat @ X0 @ X1))),
% 14.67/3.38 inference(rectify,[status(thm)],[f66])).
% 14.67/3.38 thf(f66,axiom,(
% 14.67/3.38 ! [X31 : nat,X14 : nat] : ((ord_less_nat @ X14 @ X31) => ~(ord_less_nat @ X31 @ X14))),
% 14.67/3.38 file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',fact_65_less__asym)).
% 14.67/3.38 thf(f1287,plain,(
% 14.67/3.38 ( ! [X0 : nat] : (((ord_less_eq_nat @ X0 @ (size_size_list_a @ xs)) != $true) | ((ord_less_nat @ (size_size_list_a @ ys) @ X0) != $true)) )),
% 14.67/3.38 inference(trivial_inequality_removal,[status(thm)],[f1267])).
% 14.67/3.38 thf(f1267,plain,(
% 14.67/3.38 ( ! [X0 : nat] : (((ord_less_nat @ (size_size_list_a @ ys) @ X0) != $true) | ((ord_less_eq_nat @ X0 @ (size_size_list_a @ xs)) != $true) | ($true != $true)) )),
% 14.67/3.38 inference(superposition,[status(thm)],[f1242,f1070])).
% 14.67/3.38 thf(f1070,plain,(
% 14.67/3.38 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((ord_less_nat @ X2 @ X0) = $true) | ((ord_less_eq_nat @ X1 @ X0) != $true) | ((ord_less_nat @ X2 @ X1) != $true)) )),
% 14.67/3.38 inference(cnf_transformation,[status(thm)],[f852])).
% 14.67/3.38 thf(f852,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat,X2 : nat] : (((ord_less_nat @ X2 @ X1) != $true) | ((ord_less_eq_nat @ X1 @ X0) != $true) | ((ord_less_nat @ X2 @ X0) = $true))),
% 14.67/3.38 inference(flattening,[status(thm)],[f851])).
% 14.67/3.38 thf(f851,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat,X2 : nat] : ((((ord_less_nat @ X2 @ X0) = $true) | ((ord_less_eq_nat @ X1 @ X0) != $true)) | ((ord_less_nat @ X2 @ X1) != $true))),
% 14.67/3.38 inference(ennf_transformation,[status(thm)],[f747])).
% 14.67/3.38 thf(f747,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat,X2 : nat] : (((ord_less_nat @ X2 @ X1) = $true) => (((ord_less_eq_nat @ X1 @ X0) = $true) => ((ord_less_nat @ X2 @ X0) = $true)))),
% 14.67/3.38 inference(fool_elimination,[status(thm)],[f746])).
% 14.67/3.38 thf(f746,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat,X2 : nat] : ((ord_less_nat @ X2 @ X1) => ((ord_less_eq_nat @ X1 @ X0) => (ord_less_nat @ X2 @ X0)))),
% 14.67/3.38 inference(rectify,[status(thm)],[f112])).
% 14.67/3.38 thf(f112,axiom,(
% 14.67/3.38 ! [X32 : nat,X31 : nat,X14 : nat] : ((ord_less_nat @ X14 @ X31) => ((ord_less_eq_nat @ X31 @ X32) => (ord_less_nat @ X14 @ X32)))),
% 14.67/3.38 file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',fact_111_less__le__trans)).
% 14.67/3.38 thf(f1534,plain,(
% 14.67/3.38 spl66_3 | ~spl66_4),
% 14.67/3.38 inference(avatar_split_clause,[status(thm)],[f1533,f1518,f1514])).
% 14.67/3.38 thf(f1533,plain,(
% 14.67/3.38 ((size_size_list_a @ ys) = sK56) | ((ord_less_eq_nat @ sK56 @ (size_size_list_a @ ys)) != $true)),
% 14.67/3.38 inference(forward_literal_rewriting,[status(thm)],[f1497,f1056])).
% 14.67/3.38 thf(f1497,plain,(
% 14.67/3.38 ((size_size_list_a @ ys) = sK56) | ((ord_less_nat @ (size_size_list_a @ ys) @ sK56) = $true)),
% 14.67/3.38 inference(trivial_inequality_removal,[status(thm)],[f1481])).
% 14.67/3.38 thf(f1481,plain,(
% 14.67/3.38 ((ord_less_nat @ (size_size_list_a @ ys) @ sK56) = $true) | ((size_size_list_a @ ys) = sK56) | ($true != $true)),
% 14.67/3.38 inference(superposition,[status(thm)],[f1477,f1066])).
% 14.67/3.38 thf(f1066,plain,(
% 14.67/3.38 ( ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X1 @ X0) = $true) | ((ord_less_nat @ X0 @ X1) = $true) | (X0 = X1)) )),
% 14.67/3.38 inference(cnf_transformation,[status(thm)],[f862])).
% 14.67/3.38 thf(f862,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : ((X0 = X1) | ((ord_less_nat @ X1 @ X0) = $true) | ((ord_less_nat @ X0 @ X1) = $true))),
% 14.67/3.38 inference(flattening,[status(thm)],[f861])).
% 14.67/3.38 thf(f861,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : ((((ord_less_nat @ X0 @ X1) = $true) | (X0 = X1)) | ((ord_less_nat @ X1 @ X0) = $true))),
% 14.67/3.38 inference(ennf_transformation,[status(thm)],[f788])).
% 14.67/3.38 thf(f788,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X1 @ X0) != $true) => ((X0 != X1) => ((ord_less_nat @ X0 @ X1) = $true)))),
% 14.67/3.38 inference(flattening,[status(thm)],[f553])).
% 14.67/3.38 thf(f553,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : (~((ord_less_nat @ X1 @ X0) = $true) => ((X0 != X1) => ((ord_less_nat @ X0 @ X1) = $true)))),
% 14.67/3.38 inference(fool_elimination,[status(thm)],[f552])).
% 14.67/3.38 thf(f552,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : nat] : (~(ord_less_nat @ X1 @ X0) => ((X0 != X1) => (ord_less_nat @ X0 @ X1)))),
% 14.67/3.38 inference(rectify,[status(thm)],[f52])).
% 14.67/3.38 thf(f52,axiom,(
% 14.67/3.38 ! [X31 : nat,X14 : nat] : (~(ord_less_nat @ X14 @ X31) => ((X14 != X31) => (ord_less_nat @ X31 @ X14)))),
% 14.67/3.38 file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',fact_51_linorder__cases)).
% 14.67/3.38 thf(f1477,plain,(
% 14.67/3.38 ((ord_less_nat @ sK56 @ (size_size_list_a @ ys)) != $true)),
% 14.67/3.38 inference(subsumption_resolution,[status(thm)],[f1472,f1183])).
% 14.67/3.38 thf(f1472,plain,(
% 14.67/3.38 ((ord_less_nat @ sK56 @ (size_size_list_a @ xs)) != $true) | ((ord_less_nat @ sK56 @ (size_size_list_a @ ys)) != $true)),
% 14.67/3.38 inference(trivial_inequality_removal,[status(thm)],[f1471])).
% 14.67/3.38 thf(f1471,plain,(
% 14.67/3.38 ((ord_less_nat @ sK56 @ (size_size_list_a @ xs)) != $true) | ((nth_a @ xs @ sK56) != (nth_a @ xs @ sK56)) | ((ord_less_nat @ sK56 @ (size_size_list_a @ ys)) != $true)),
% 14.67/3.38 inference(superposition,[status(thm)],[f1182,f1385])).
% 14.67/3.38 thf(f1385,plain,(
% 14.67/3.38 ( ! [X0 : nat] : (((nth_a @ xs @ X0) = (nth_a @ ys @ X0)) | ((ord_less_nat @ X0 @ (size_size_list_a @ ys)) != $true) | ((ord_less_nat @ X0 @ (size_size_list_a @ xs)) != $true)) )),
% 14.67/3.38 inference(superposition,[status(thm)],[f1343,f1047])).
% 14.67/3.38 thf(f1047,plain,(
% 14.67/3.38 ( ! [X2 : nat > a,X0 : nat,X1 : list_a] : (((listIn1312259492pend_a @ X1 @ X2 @ X0) = (nth_a @ X1 @ X0)) | ((ord_less_nat @ X0 @ (size_size_list_a @ X1)) != $true)) )),
% 14.67/3.38 inference(cnf_transformation,[status(thm)],[f847])).
% 14.67/3.38 thf(f847,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : list_a,X2 : nat > a] : (((ord_less_nat @ X0 @ (size_size_list_a @ X1)) != $true) | ((listIn1312259492pend_a @ X1 @ X2 @ X0) = (nth_a @ X1 @ X0)))),
% 14.67/3.38 inference(ennf_transformation,[status(thm)],[f672])).
% 14.67/3.38 thf(f672,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : list_a,X2 : nat > a] : (((ord_less_nat @ X0 @ (size_size_list_a @ X1)) = $true) => ((listIn1312259492pend_a @ X1 @ X2 @ X0) = (nth_a @ X1 @ X0)))),
% 14.67/3.38 inference(fool_elimination,[status(thm)],[f671])).
% 14.67/3.38 thf(f671,plain,(
% 14.67/3.38 ! [X0 : nat,X1 : list_a,X2 : nat > a] : ((ord_less_nat @ X0 @ (size_size_list_a @ X1)) => ((listIn1312259492pend_a @ X1 @ X2 @ X0) = (nth_a @ X1 @ X0)))),
% 14.67/3.38 inference(rectify,[status(thm)],[f4])).
% 14.67/3.38 thf(f4,axiom,(
% 14.67/3.38 ! [X4 : nat,X0 : list_a,X2 : nat > a] : ((ord_less_nat @ X4 @ (size_size_list_a @ X0)) => ((listIn1312259492pend_a @ X0 @ X2 @ X4) = (nth_a @ X0 @ X4)))),
% 14.67/3.38 file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',fact_3_i__append__nth1)).
% 14.67/3.38 thf(f1343,plain,(
% 14.67/3.38 ( ! [X0 : nat] : (((listIn1312259492pend_a @ xs @ f @ X0) = (nth_a @ ys @ X0)) | ((ord_less_nat @ X0 @ (size_size_list_a @ ys)) != $true)) )),
% 14.67/3.38 inference(superposition,[status(thm)],[f1138,f1047])).
% 14.67/3.38 thf(f1138,plain,(
% 14.67/3.38 ( ! [X0 : nat] : (((listIn1312259492pend_a @ xs @ f @ X0) = (listIn1312259492pend_a @ ys @ g @ X0))) )),
% 14.67/3.38 inference(cnf_transformation,[status(thm)],[f662])).
% 14.67/3.38 thf(f662,plain,(
% 14.67/3.38 ! [X0 : nat] : ((listIn1312259492pend_a @ xs @ f @ X0) = (listIn1312259492pend_a @ ys @ g @ X0))),
% 14.67/3.38 inference(fool_elimination,[status(thm)],[f661])).
% 14.67/3.38 thf(f661,plain,(
% 14.67/3.38 ! [X0 : nat] : ((listIn1312259492pend_a @ xs @ f @ X0) = (listIn1312259492pend_a @ ys @ g @ X0))),
% 14.67/3.38 inference(rectify,[status(thm)],[f253])).
% 14.67/3.38 thf(f253,axiom,(
% 14.67/3.38 ! [X49 : nat] : ((listIn1312259492pend_a @ xs @ f @ X49) = (listIn1312259492pend_a @ ys @ g @ X49))),
% 14.67/3.38 file('/export/starexec/sandbox/tmp/tmp.E2xVH6SSKq/DTF2THF_23273.p',conj_0)).
% 14.67/3.38 thf(f1182,plain,(
% 14.67/3.38 ((nth_a @ ys @ sK56) != (nth_a @ xs @ sK56))),
% 14.67/3.38 inference(cnf_transformation,[status(thm)],[f1032])).
% 14.67/3.38 % SZS output end Proof for DTF2THF_23273
% 14.67/3.38 % (23685)------------------------------
% 14.67/3.38 % (23685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.67/3.38 % (23685)Termination reason: Refutation
% 14.67/3.38
% 14.67/3.38 % (23685)Memory used [KB]: 6908
% 14.67/3.38 % (23685)Time elapsed: 0.063 s
% 14.67/3.38 % (23685)Instructions burned: 205 (million)
% 14.67/3.38 % (23685)------------------------------
% 14.67/3.38 % (23685)------------------------------
% 14.67/3.38 % (23562)Success in time 1.875 s
%------------------------------------------------------------------------------