%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP061^1 : 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 : n011.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 08:55:14 AM UTC 2026
% Result : Theorem 44.22s 7.67s
% Output : Refutation 44.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 74 ( 51 unt; 0 typ; 4 def)
% Number of atoms : 208 ( 89 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 311 ( 26 ~; 17 |; 0 &; 255 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 120 ( 117 usr; 19 con; 0-4 aty)
% Number of variables : 63 ( 0 ^; 58 !; 5 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
config256849571t_unit: $tType ).
thf(type_def_6,type,
message_p_v: $tType ).
thf(type_def_8,type,
p: $tType ).
thf(type_def_9,type,
list_c1059388851t_unit: $tType ).
thf(type_def_10,type,
list_message_p_v: $tType ).
thf(type_def_11,type,
nat: $tType ).
thf(type_def_12,type,
set_message_p_v: $tType ).
thf(func_def_0,type,
list_c1059388851t_unit: $tType ).
thf(func_def_1,type,
config256849571t_unit: $tType ).
thf(func_def_2,type,
list_message_p_v: $tType ).
thf(func_def_3,type,
set_message_p_v: $tType ).
thf(func_def_4,type,
message_p_v: $tType ).
thf(func_def_5,type,
nat: $tType ).
thf(func_def_6,type,
p: $tType ).
thf(func_def_7,type,
enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
thf(func_def_8,type,
isReceiverOf_p_v: p > message_p_v > $o ).
thf(func_def_9,type,
firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
thf(func_def_10,type,
minimalEnabled_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > $o ).
thf(func_def_11,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_12,type,
one_one_nat: nat ).
thf(func_def_13,type,
prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
thf(func_def_14,type,
prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
thf(func_def_15,type,
nil_co1338500125t_unit: list_c1059388851t_unit ).
thf(func_def_16,type,
nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
thf(func_def_17,type,
nth_message_p_v: list_message_p_v > nat > message_p_v ).
thf(func_def_18,type,
suc: nat > nat ).
thf(func_def_19,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(func_def_20,type,
size_s1168481041ge_p_v: list_message_p_v > 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,
collect_message_p_v: ( message_p_v > $o ) > set_message_p_v ).
thf(func_def_24,type,
member_message_p_v: message_p_v > set_message_p_v > $o ).
thf(func_def_25,type,
occM: nat ).
thf(func_def_26,type,
occM2: nat ).
thf(func_def_27,type,
consumedMsg: message_p_v ).
thf(func_def_28,type,
fe: nat > list_c1059388851t_unit ).
thf(func_def_29,type,
firstOccSet: nat > set_message_p_v ).
thf(func_def_30,type,
ft: nat > list_message_p_v ).
thf(func_def_31,type,
index: nat ).
thf(func_def_32,type,
msg: message_p_v ).
thf(func_def_33,type,
msg2: message_p_v ).
thf(func_def_34,type,
msga: message_p_v ).
thf(func_def_35,type,
n0: nat ).
thf(func_def_36,type,
n: nat ).
thf(func_def_37,type,
p2: p ).
thf(func_def_52,type,
sP0: nat > nat > nat > $o ).
thf(func_def_53,type,
sP1: nat > nat > nat > $o ).
thf(func_def_54,type,
sP2: nat > nat > nat > $o ).
thf(func_def_55,type,
sK3: list_c1059388851t_unit > list_c1059388851t_unit > nat ).
thf(func_def_56,type,
sK4: ( nat > nat ) > nat ).
thf(func_def_57,type,
sK5: ( nat > nat ) > nat ).
thf(func_def_58,type,
sK6: nat > list_message_p_v ).
thf(func_def_59,type,
sK7: ( nat > $o ) > nat ).
thf(func_def_60,type,
sK8: nat > nat > ( nat > $o ) > nat ).
thf(func_def_61,type,
sK9: ( nat > nat ) > nat ).
thf(func_def_62,type,
sK10: ( message_p_v > $o ) > ( message_p_v > $o ) > message_p_v ).
thf(func_def_63,type,
sK11: ( nat > $o ) > nat ).
thf(func_def_64,type,
sK12: nat > nat ).
thf(func_def_65,type,
sK13: ( nat > nat ) > nat ).
thf(func_def_66,type,
sK14: ( nat > nat ) > nat ).
thf(func_def_67,type,
sK15: p ).
thf(func_def_68,type,
sK16: ( list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_69,type,
sK17: ( nat > $o ) > nat > nat ).
thf(func_def_70,type,
sK18: ( nat > $o ) > nat > nat ).
thf(func_def_71,type,
sK19: ( nat > $o ) > nat ).
thf(func_def_72,type,
sK20: ( list_message_p_v > $o ) > list_message_p_v ).
thf(func_def_73,type,
sK21: nat > nat > message_p_v > nat ).
thf(func_def_74,type,
sK22: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_75,type,
sK23: ( nat > nat ) > nat ).
thf(func_def_76,type,
sK24: ( nat > nat ) > nat ).
thf(func_def_77,type,
sK25: ( nat > nat ) > nat ).
thf(func_def_78,type,
sK26: ( nat > nat > $o ) > nat ).
thf(func_def_79,type,
sK27: ( nat > nat > $o ) > nat ).
thf(func_def_80,type,
sK28: ( nat > nat > $o ) > nat ).
thf(func_def_81,type,
sK29: ( nat > nat > $o ) > nat ).
thf(func_def_82,type,
sK30: ( nat > $o ) > nat ).
thf(func_def_83,type,
sK31: nat > nat > nat ).
thf(func_def_84,type,
sK32: ( nat > nat ) > nat ).
thf(func_def_85,type,
sK33: ( nat > nat ) > nat ).
thf(func_def_86,type,
sK34: ( nat > nat ) > nat ).
thf(func_def_87,type,
sK35: nat > nat ).
thf(func_def_88,type,
sK36: list_message_p_v > list_message_p_v > nat ).
thf(func_def_89,type,
sK37: ( nat > nat ) > nat ).
thf(func_def_90,type,
sK38: ( nat > nat ) > nat ).
thf(func_def_91,type,
sK39: ( nat > nat ) > nat ).
thf(func_def_92,type,
sK40: ( nat > nat ) > nat ).
thf(func_def_93,type,
sK41: ( nat > $o ) > nat > nat ).
thf(func_def_94,type,
sK42: ( nat > $o ) > nat > nat ).
thf(func_def_95,type,
sK43: ( nat > nat > $o ) > nat ).
thf(func_def_96,type,
sK44: ( nat > nat > $o ) > nat ).
thf(func_def_97,type,
sK45: ( nat > nat > $o ) > nat ).
thf(func_def_98,type,
sK46: ( nat > nat > $o ) > nat ).
thf(func_def_99,type,
sK47: ( nat > nat > $o ) > nat ).
thf(func_def_100,type,
sK48: ( nat > $o ) > nat ).
thf(func_def_101,type,
sK49: p ).
thf(func_def_102,type,
sK50: ( nat > nat ) > nat ).
thf(func_def_103,type,
sK51: ( nat > nat ) > nat ).
thf(func_def_104,type,
sK52: ( nat > nat ) > nat ).
thf(func_def_105,type,
sK53: ( nat > nat ) > nat ).
thf(func_def_106,type,
sK54: ( nat > nat ) > nat ).
thf(func_def_107,type,
sK55: ( nat > nat ) > nat ).
thf(func_def_108,type,
sK56: ( nat > $o ) > nat ).
thf(func_def_109,type,
sK57: nat > ( nat > $o ) > nat ).
thf(func_def_110,type,
sK58: ( nat > nat ) > nat ).
thf(func_def_111,type,
sK59: ( nat > nat ) > nat ).
thf(func_def_112,type,
sK60: ( nat > nat > $o ) > nat ).
thf(func_def_113,type,
sK61: ( nat > nat > $o ) > nat ).
thf(func_def_114,type,
sK62: ( nat > nat > $o ) > nat ).
thf(func_def_115,type,
sK63: ( nat > nat > $o ) > nat ).
thf(func_def_116,type,
sK64: ( nat > nat > $o ) > nat ).
thf(func_def_117,type,
sK65: nat > ( nat > $o ) > nat > nat ).
thf(func_def_118,type,
sK66: nat > list_c1059388851t_unit ).
thf(func_def_119,type,
sK67: ( nat > $o ) > nat ).
thf(func_def_120,type,
sK68: ( nat > $o ) > nat > nat ).
thf(func_def_121,type,
sK69: ( nat > nat ) > nat ).
thf(func_def_122,type,
sK70: ( nat > nat ) > nat ).
thf(func_def_123,type,
sK71: nat > nat > nat ).
thf(func_def_124,type,
sK72: ( nat > nat ) > nat ).
thf(func_def_125,type,
sK73: ( nat > nat ) > nat ).
thf(func_def_126,type,
sK74: ( nat > nat ) > nat ).
thf(func_def_127,type,
sK75: ( nat > nat > $o ) > nat ).
thf(func_def_128,type,
sK76: ( nat > nat > $o ) > nat ).
thf(func_def_129,type,
sK77: ( nat > nat > $o ) > nat ).
thf(func_def_130,type,
sK78: ( nat > nat > $o ) > nat ).
thf(func_def_131,type,
sK79: ( nat > nat ) > nat ).
thf(func_def_132,type,
sK80: ( nat > nat ) > nat ).
thf(func_def_133,type,
sF81: list_c1059388851t_unit ).
thf(func_def_134,type,
sF82: nat ).
thf(func_def_135,type,
sF83: nat > nat ).
thf(func_def_136,type,
sF84: nat ).
thf(func_def_138,type,
ph86:
!>[X0: $tType] : X0 ).
thf(f2139,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f2138]) ).
thf(f2138,plain,
$false = $true,
inference(forward_demodulation,[status(thm)],[f2137,f1775]) ).
thf(f1775,plain,
( $false
= ( ord_less_eq_nat @ sF82 @ occM2 ) ),
inference(boolean_simplification,[status(thm)],[f1770]) ).
thf(f1770,plain,
( ( ~ $true )
= ( ord_less_eq_nat @ sF82 @ occM2 ) ),
inference(superposition,[status(thm)],[f1468,f1454]) ).
thf(f1454,plain,
( $true
= ( ord_less_nat @ occM2 @ sF82 ) ),
inference(forward_demodulation,[status(thm)],[f1453,f1423]) ).
thf(f1423,definition,
( ( size_s1406904903t_unit @ sF81 )
= sF82 ),
introduced(definition,[],[function_definition]) ).
thf(f1453,plain,
( ( ord_less_nat @ occM2 @ ( size_s1406904903t_unit @ sF81 ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1319,f1422]) ).
thf(f1422,definition,
( ( fe @ index )
= sF81 ),
introduced(definition,[],[function_definition]) ).
thf(f1319,plain,
( ( ord_less_nat @ occM2 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f284]) ).
thf(f284,plain,
( ( ord_less_nat @ occM2 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f283]) ).
thf(f283,plain,
ord_less_nat @ occM2 @ ( size_s1406904903t_unit @ ( fe @ index ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
ord_less_nat @ occM2 @ ( size_s1406904903t_unit @ ( fe @ index ) ),
file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_0_AssumpOccMFirstOccurrence_I3_J) ).
thf(f1468,plain,
! [X0: nat,X1: nat] :
( ( ~ ( ord_less_nat @ X0 @ X1 ) )
= ( ord_less_eq_nat @ X1 @ X0 ) ),
inference(forward_demodulation,[status(thm)],[f1106,f1210]) ).
thf(f1210,plain,
! [X0: nat,X1: nat] :
( ( ord_less_eq_nat @ X0 @ X1 )
= ( ord_less_nat @ X0 @ ( suc @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f306]) ).
thf(f306,plain,
! [X0: nat,X1: nat] :
( ( ord_less_eq_nat @ X0 @ X1 )
= ( ord_less_nat @ X0 @ ( suc @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f305]) ).
thf(f305,plain,
! [X0: nat,X1: nat] :
( ( ord_less_eq_nat @ X0 @ X1 )
= ( ord_less_nat @ X0 @ ( suc @ X1 ) ) ),
inference(rectify,[status(thm)],[f64]) ).
thf(f64,axiom,
! [X13: nat,X3: nat] :
( ( ord_less_eq_nat @ X13 @ X3 )
= ( ord_less_nat @ X13 @ ( suc @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_63_less__Suc__eq__le) ).
thf(f1106,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ X1 @ ( suc @ X0 ) )
= ( ~ ( ord_less_nat @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f396]) ).
thf(f396,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ X1 @ ( suc @ X0 ) )
= ( ~ ( ord_less_nat @ X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f395]) ).
thf(f395,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ X1 @ ( suc @ X0 ) )
= ( ~ ( ord_less_nat @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f54]) ).
thf(f54,axiom,
! [X13: nat,X3: nat] :
( ( ord_less_nat @ X3 @ ( suc @ X13 ) )
= ( ~ ( ord_less_nat @ X13 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_53_not__less__eq) ).
thf(f2137,plain,
( $true
= ( ord_less_eq_nat @ sF82 @ occM2 ) ),
inference(backward_demodulation,[status(thm)],[f1956,f2135]) ).
thf(f2135,plain,
( ( suc @ sF84 )
= sF82 ),
inference(backward_demodulation,[status(thm)],[f2125,f2134]) ).
thf(f2134,plain,
( sF84
= ( sK12 @ sF82 ) ),
inference(forward_demodulation,[status(thm)],[f2133,f1425]) ).
thf(f1425,definition,
( ( sF83 @ one_one_nat )
= sF84 ),
introduced(definition,[],[function_definition]) ).
thf(f2133,plain,
( ( sF83 @ one_one_nat )
= ( sK12 @ sF82 ) ),
inference(forward_demodulation,[status(thm)],[f2127,f1479]) ).
thf(f1479,plain,
! [X1: nat] :
( ( minus_minus_nat @ sF82 @ X1 )
= ( sF83 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f1424]) ).
thf(f1424,definition,
( sF83
= ( minus_minus_nat @ sF82 ) ),
introduced(definition,[],[function_definition]) ).
thf(f2127,plain,
( ( minus_minus_nat @ sF82 @ one_one_nat )
= ( sK12 @ sF82 ) ),
inference(superposition,[status(thm)],[f1087,f2125]) ).
thf(f1087,plain,
! [X0: nat] :
( ( minus_minus_nat @ ( suc @ X0 ) @ one_one_nat )
= X0 ),
inference(cnf_transformation,[status(thm)],[f535]) ).
thf(f535,plain,
! [X0: nat] :
( ( minus_minus_nat @ ( suc @ X0 ) @ one_one_nat )
= X0 ),
inference(fool_elimination,[status(thm)],[f534]) ).
thf(f534,plain,
! [X0: nat] :
( ( minus_minus_nat @ ( suc @ X0 ) @ one_one_nat )
= X0 ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,axiom,
! [X3: nat] :
( ( minus_minus_nat @ ( suc @ X3 ) @ one_one_nat )
= X3 ),
file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_24_diff__Suc__1) ).
thf(f2125,plain,
( ( suc @ ( sK12 @ sF82 ) )
= sF82 ),
inference(trivial_inequality_removal,[status(thm)],[f2120]) ).
thf(f2120,plain,
( ( $true != $true )
| ( ( suc @ ( sK12 @ sF82 ) )
= sF82 ) ),
inference(superposition,[status(thm)],[f1142,f1955]) ).
thf(f1955,plain,
( ( ord_less_eq_nat @ ( suc @ occM2 ) @ sF82 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1953]) ).
thf(f1953,plain,
( ( ( ord_less_eq_nat @ ( suc @ occM2 ) @ sF82 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1111,f1454]) ).
thf(f1111,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X0 @ X1 )
!= $true )
| ( ( ord_less_eq_nat @ ( suc @ X0 ) @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f877]) ).
thf(f877,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_eq_nat @ ( suc @ X0 ) @ X1 )
= $true )
| ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f302]) ).
thf(f302,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X0 @ X1 )
= $true )
=> ( ( ord_less_eq_nat @ ( suc @ X0 ) @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f301]) ).
thf(f301,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ X0 @ X1 )
=> ( ord_less_eq_nat @ ( suc @ X0 ) @ X1 ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,axiom,
! [X13: nat,X3: nat] :
( ( ord_less_nat @ X13 @ X3 )
=> ( ord_less_eq_nat @ ( suc @ X13 ) @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_27_Suc__leI) ).
thf(f1142,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_eq_nat @ ( suc @ X0 ) @ X1 )
!= $true )
| ( ( suc @ ( sK12 @ X1 ) )
= X1 ) ),
inference(cnf_transformation,[status(thm)],[f984]) ).
thf(f984,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_eq_nat @ ( suc @ X0 ) @ X1 )
!= $true )
| ( ( suc @ ( sK12 @ X1 ) )
= X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f779,f983]) ).
thf(f983,plain,
! [X1: nat] :
( ? [X2: nat] :
( ( suc @ X2 )
= X1 )
=> ( ( suc @ ( sK12 @ X1 ) )
= X1 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f779,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_eq_nat @ ( suc @ X0 ) @ X1 )
!= $true )
| ? [X2: nat] :
( ( suc @ X2 )
= X1 ) ),
inference(ennf_transformation,[status(thm)],[f503]) ).
thf(f503,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_eq_nat @ ( suc @ X0 ) @ X1 )
= $true )
=> ? [X2: nat] :
( ( suc @ X2 )
= X1 ) ),
inference(fool_elimination,[status(thm)],[f502]) ).
thf(f502,plain,
! [X0: nat,X1: nat] :
( ( ord_less_eq_nat @ ( suc @ X0 ) @ X1 )
=> ? [X2: nat] :
( ( suc @ X2 )
= X1 ) ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,axiom,
! [X3: nat,X15: nat] :
( ( ord_less_eq_nat @ ( suc @ X3 ) @ X15 )
=> ? [X16: nat] :
( ( suc @ X16 )
= X15 ) ),
file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_31_Suc__le__D) ).
thf(f1956,plain,
( ( ord_less_eq_nat @ ( suc @ sF84 ) @ occM2 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1947]) ).
thf(f1947,plain,
( ( $true != $true )
| ( ( ord_less_eq_nat @ ( suc @ sF84 ) @ occM2 )
= $true ) ),
inference(superposition,[status(thm)],[f1111,f1818]) ).
thf(f1818,plain,
( ( ord_less_nat @ sF84 @ occM2 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f1817,f1426]) ).
thf(f1426,plain,
occM2 != sF84,
inference(definition_folding,[status(thm)],[f1295,f1425,f1424,f1423,f1422]) ).
thf(f1295,plain,
( occM2
!= ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ),
inference(cnf_transformation,[status(thm)],[f730]) ).
thf(f730,plain,
( occM2
!= ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ),
inference(flattening,[status(thm)],[f576]) ).
thf(f576,plain,
( occM2
!= ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ),
inference(fool_elimination,[status(thm)],[f237]) ).
thf(f237,negated_conjecture,
( occM2
!= ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ),
inference(negated_conjecture,[status(cth)],[f236]) ).
thf(f236,conjecture,
( occM2
= ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ),
file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',conj_0) ).
thf(f1817,plain,
( ( ( ord_less_nat @ sF84 @ occM2 )
= $true )
| ( occM2 = sF84 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1806]) ).
thf(f1806,plain,
( ( occM2 = sF84 )
| ( $true != $true )
| ( ( ord_less_nat @ sF84 @ occM2 )
= $true ) ),
inference(superposition,[status(thm)],[f1133,f1485]) ).
thf(f1485,plain,
( ( ord_less_eq_nat @ sF84 @ occM2 )
= $true ),
inference(forward_demodulation,[status(thm)],[f1482,f1425]) ).
thf(f1482,plain,
( ( ord_less_eq_nat @ ( sF83 @ one_one_nat ) @ occM2 )
= $true ),
inference(backward_demodulation,[status(thm)],[f1452,f1479]) ).
thf(f1452,plain,
( ( ord_less_eq_nat @ ( minus_minus_nat @ sF82 @ one_one_nat ) @ occM2 )
= $true ),
inference(backward_demodulation,[status(thm)],[f1444,f1423]) ).
thf(f1444,plain,
( ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ sF81 ) @ one_one_nat ) @ occM2 )
= $true ),
inference(backward_demodulation,[status(thm)],[f1392,f1422]) ).
thf(f1392,plain,
( ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ occM2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f607]) ).
thf(f607,plain,
( ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ occM2 )
= $true ),
inference(fool_elimination,[status(thm)],[f606]) ).
thf(f606,plain,
ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ occM2,
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ occM2,
file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_1__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_AOccM_092_060close_062) ).
thf(f1133,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_eq_nat @ X0 @ X1 )
!= $true )
| ( ( ord_less_nat @ X0 @ X1 )
= $true )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f798]) ).
thf(f798,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_eq_nat @ X0 @ X1 )
!= $true )
| ( X0 = X1 )
| ( ( ord_less_nat @ X0 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f797]) ).
thf(f797,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X0 @ X1 )
= $true )
| ( X0 = X1 )
| ( ( ord_less_eq_nat @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f342]) ).
thf(f342,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_eq_nat @ X0 @ X1 )
= $true )
=> ( ( X0 != X1 )
=> ( ( ord_less_nat @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f341]) ).
thf(f341,plain,
! [X0: nat,X1: nat] :
( ( ord_less_eq_nat @ X0 @ X1 )
=> ( ( X0 != X1 )
=> ( ord_less_nat @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f82]) ).
thf(f82,axiom,
! [X13: nat,X3: nat] :
( ( ord_less_eq_nat @ X13 @ X3 )
=> ( ( X3 != X13 )
=> ( ord_less_nat @ X13 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_81_le__neq__implies__less) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP061^1 : 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
% 0.16/0.34 % Computer : n011.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:24:47 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : ITP061^1 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.46 % Domain : Interactive Theorem Proving
% 0.31/0.46 % Problem : Sledgehammer FLPTheorem problem prob_979__3303242_1
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Des21]
% 0.31/0.46 % Names : FLPTheorem/prob_979__3303242_1 [Des21]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0
% 0.31/0.46 % Syntax : Number of formulae : 274 ( 94 unt; 38 typ; 0 def)
% 0.31/0.46 % Number of atoms : 616 ( 172 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 12 ( 2 avg)
% 0.31/0.46 % Number of connectives : 1864 ( 84 ~; 18 |; 27 &;1410 @)
% 0.31/0.46 % ( 0 <=>; 325 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 16 ( 7 avg)
% 0.31/0.46 % Number of types : 8 ( 7 usr)
% 0.31/0.46 % Number of type conns : 87 ( 87 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 32 ( 31 usr; 12 con; 0-4 aty)
% 0.31/0.46 % Number of variables : 600 ( 42 ^; 537 !; 21 ?; 600 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:31:50.858
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % Could-be-implicit typings (7)
% 0.31/0.46 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.31/0.46 list_c1059388851t_unit: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.31/0.46 config256849571t_unit: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.31/0.46 list_message_p_v: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.31/0.46 set_message_p_v: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.31/0.46 message_p_v: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Nat__Onat,type,
% 0.31/0.46 nat: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_tf__p,type,
% 0.31/0.46 p: $tType ).
% 0.31/0.46
% 0.31/0.46 % Explicit typings (31)
% 0.31/0.46 thf(sy_c_AsynchronousSystem_Oenabled_001tf__p_001tf__v_001tf__s,type,
% 0.31/0.46 enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_AsynchronousSystem_OisReceiverOf_001tf__p_001tf__v,type,
% 0.31/0.46 isReceiverOf_p_v: p > message_p_v > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Execution_Oexecution_OfirstOccurrence_001tf__p_001tf__v_001tf__s,type,
% 0.31/0.46 firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Execution_Oexecution_OminimalEnabled_001tf__p_001tf__v_001tf__s,type,
% 0.31/0.46 minimalEnabled_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 0.31/0.46 minus_minus_nat: nat > nat > nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.31/0.46 one_one_nat: nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.31/0.46 prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.31/0.46 prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.31/0.46 nil_co1338500125t_unit: list_c1059388851t_unit ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Onth_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.31/0.46 nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_List_Onth_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.31/0.46 nth_message_p_v: list_message_p_v > nat > message_p_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Nat_OSuc,type,
% 0.31/0.46 suc: nat > nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.31/0.46 size_s1406904903t_unit: list_c1059388851t_unit > nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.31/0.46 size_s1168481041ge_p_v: list_message_p_v > nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.31/0.46 ord_less_nat: nat > nat > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.31/0.46 ord_less_eq_nat: nat > nat > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.31/0.46 collect_message_p_v: ( message_p_v > $o ) > set_message_p_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.31/0.46 member_message_p_v: message_p_v > set_message_p_v > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_OccM_H____,type,
% 0.31/0.46 occM: nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_OccM____,type,
% 0.31/0.46 occM2: nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_consumedMsg____,type,
% 0.31/0.46 consumedMsg: message_p_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_fe____,type,
% 0.31/0.46 fe: nat > list_c1059388851t_unit ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_firstOccSet____,type,
% 0.31/0.46 firstOccSet: nat > set_message_p_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_ft____,type,
% 0.31/0.46 ft: nat > list_message_p_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_index____,type,
% 0.31/0.46 index: nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_msg_H____,type,
% 0.31/0.46 msg: message_p_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_msg____,type,
% 0.31/0.46 msg2: message_p_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_msga____,type,
% 0.31/0.46 msga: message_p_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_n0____,type,
% 0.31/0.46 n0: nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_n____,type,
% 0.31/0.46 n: nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_p____,type,
% 0.31/0.46 p2: p ).
% 0.31/0.46
% 0.31/0.46 % Relevant facts (235)
% 0.31/0.46 thf(fact_0_AssumpOccMFirstOccurrence_I3_J,axiom,
% 0.31/0.46 ord_less_nat @ occM2 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ).
% 0.31/0.46
% 0.31/0.46 % AssumpOccMFirstOccurrence(3)
% 0.31/0.46 thf(fact_1__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_AOccM_092_060close_062,axiom,
% 0.31/0.46 ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ occM2 ).
% 0.31/0.46
% 0.31/0.46 % \<open>length (fe index) - 1 \<le> OccM\<close>
% 0.31/0.46 thf(fact_2_OccM_H_I3_J,axiom,
% 0.31/0.46 ord_less_nat @ occM @ ( size_s1406904903t_unit @ ( fe @ index ) ) ).
% 0.31/0.46
% 0.31/0.46 % OccM'(3)
% 0.31/0.46 thf(fact_3__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062,axiom,
% 0.31/0.46 ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ).
% 0.31/0.46
% 0.31/0.46 % \<open>length (fe index) - 1 \<le> length (fe (Suc index)) - 1\<close>
% 0.31/0.46 thf(fact_4_NotEmpty_I2_J,axiom,
% 0.31/0.46 ( ( fe @ index )
% 0.31/0.46 != nil_co1338500125t_unit ) ).
% 0.31/0.46
% 0.31/0.46 % NotEmpty(2)
% 0.31/0.46 thf(fact_5_AssumptionFair_I2_J,axiom,
% 0.31/0.46 ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ) ).
% 0.31/0.46
% 0.31/0.46 % AssumptionFair(2)
% 0.31/0.46 thf(fact_6_one__natural_Orsp,axiom,
% 0.31/0.46 one_one_nat = one_one_nat ).
% 0.31/0.46
% 0.31/0.46 % one_natural.rsp
% 0.31/0.46 thf(fact_7_diff__commute,axiom,
% 0.31/0.46 ! [I: nat,J: nat,K: nat] :
% 0.31/0.46 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.31/0.46 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 0.31/0.46
% 0.31/0.46 % diff_commute
% 0.31/0.46 thf(fact_8_Ex__list__of__length,axiom,
% 0.31/0.46 ! [N: nat] :
% 0.31/0.46 ? [Xs: list_c1059388851t_unit] :
% 0.31/0.46 ( ( size_s1406904903t_unit @ Xs )
% 0.31/0.46 = N ) ).
% 0.31/0.46
% 0.31/0.46 % Ex_list_of_length
% 0.31/0.46 thf(fact_9_Ex__list__of__length,axiom,
% 0.31/0.46 ! [N: nat] :
% 0.31/0.46 ? [Xs: list_message_p_v] :
% 0.31/0.46 ( ( size_s1168481041ge_p_v @ Xs )
% 0.31/0.46 = N ) ).
% 0.31/0.46
% 0.31/0.46 % Ex_list_of_length
% 0.31/0.46 thf(fact_10_neq__if__length__neq,axiom,
% 0.31/0.46 ! [Xs2: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.31/0.46 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.31/0.46 != ( size_s1406904903t_unit @ Ys ) )
% 0.31/0.46 => ( Xs2 != Ys ) ) ).
% 0.31/0.46
% 0.31/0.46 % neq_if_length_neq
% 0.31/0.46 thf(fact_11_neq__if__length__neq,axiom,
% 0.31/0.46 ! [Xs2: list_message_p_v,Ys: list_message_p_v] :
% 0.31/0.46 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.31/0.46 != ( size_s1168481041ge_p_v @ Ys ) )
% 0.31/0.46 => ( Xs2 != Ys ) ) ).
% 0.31/0.46
% 0.31/0.46 % neq_if_length_neq
% 0.31/0.46 thf(fact_12_size__neq__size__imp__neq,axiom,
% 0.31/0.46 ! [X: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 0.31/0.46 ( ( ( size_s1406904903t_unit @ X )
% 0.31/0.46 != ( size_s1406904903t_unit @ Y ) )
% 0.31/0.46 => ( X != Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % size_neq_size_imp_neq
% 0.31/0.46 thf(fact_13_size__neq__size__imp__neq,axiom,
% 0.31/0.46 ! [X: list_message_p_v,Y: list_message_p_v] :
% 0.31/0.46 ( ( ( size_s1168481041ge_p_v @ X )
% 0.31/0.46 != ( size_s1168481041ge_p_v @ Y ) )
% 0.31/0.46 => ( X != Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % size_neq_size_imp_neq
% 0.31/0.46 thf(fact_14_nat_Oinject,axiom,
% 0.31/0.46 ! [X2: nat,Y2: nat] :
% 0.31/0.46 ( ( ( suc @ X2 )
% 0.31/0.46 = ( suc @ Y2 ) )
% 0.31/0.46 = ( X2 = Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % nat.inject
% 0.31/0.46 thf(fact_15_old_Onat_Oinject,axiom,
% 0.31/0.46 ! [Nat: nat,Nat2: nat] :
% 0.31/0.46 ( ( ( suc @ Nat )
% 0.31/0.46 = ( suc @ Nat2 ) )
% 0.31/0.46 = ( Nat = Nat2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.nat.inject
% 0.31/0.46 thf(fact_16_NotEmpty_I1_J,axiom,
% 0.31/0.46 ( ( fe @ ( suc @ index ) )
% 0.31/0.46 != nil_co1338500125t_unit ) ).
% 0.31/0.46
% 0.31/0.46 % NotEmpty(1)
% 0.31/0.46 thf(fact_17_lessI,axiom,
% 0.31/0.46 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.31/0.46
% 0.31/0.46 % lessI
% 0.31/0.46 thf(fact_18_Suc__mono,axiom,
% 0.31/0.46 ! [M: nat,N: nat] :
% 0.31/0.46 ( ( ord_less_nat @ M @ N )
% 0.31/0.46 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Suc_mono
% 0.31/0.46 thf(fact_19_Suc__less__eq,axiom,
% 0.31/0.46 ! [M: nat,N: nat] :
% 0.31/0.46 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.31/0.46 = ( ord_less_nat @ M @ N ) ) ).
% 0.31/0.46
% 0.31/0.46 % Suc_less_eq
% 0.31/0.46 thf(fact_20_Suc__le__mono,axiom,
% 0.31/0.46 ! [N: nat,M: nat] :
% 0.31/0.46 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.31/0.46 = ( ord_less_eq_nat @ N @ M ) ) ).
% 0.31/0.46
% 0.31/0.46 % Suc_le_mono
% 0.31/0.46 thf(fact_21_Suc__diff__diff,axiom,
% 0.31/0.46 ! [M: nat,N: nat,K: nat] :
% 0.31/0.46 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.31/0.46 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 0.31/0.46
% 0.31/0.46 % Suc_diff_diff
% 0.31/0.46 thf(fact_22_diff__Suc__Suc,axiom,
% 0.31/0.46 ! [M: nat,N: nat] :
% 0.31/0.46 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.31/0.46 = ( minus_minus_nat @ M @ N ) ) ).
% 0.31/0.46
% 0.31/0.46 % diff_Suc_Suc
% 0.31/0.46 thf(fact_23_diff__diff__cancel,axiom,
% 0.31/0.46 ! [I: nat,N: nat] :
% 0.31/0.46 ( ( ord_less_eq_nat @ I @ N )
% 0.31/0.46 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 0.31/0.46 = I ) ) ).
% 0.31/0.46
% 0.31/0.46 % diff_diff_cancel
% 0.31/0.46 thf(fact_24_diff__Suc__1,axiom,
% 0.31/0.46 ! [N: nat] :
% 0.31/0.46 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 0.31/0.46 = N ) ).
% 0.31/0.46
% 0.31/0.46 % diff_Suc_1
% 0.31/0.46 thf(fact_25_Nat_OlessE,axiom,
% 0.31/0.46 ! [I: nat,K: nat] :
% 0.31/0.46 ( ( ord_less_nat @ I @ K )
% 0.31/0.46 => ( ( K
% 0.31/0.46 != ( suc @ I ) )
% 0.31/0.46 => ~ ! [J2: nat] :
% 0.31/0.46 ( ( ord_less_nat @ I @ J2 )
% 0.31/0.46 => ( K
% 0.31/0.46 != ( suc @ J2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Nat.lessE
% 0.31/0.46 thf(fact_26_Suc__leD,axiom,
% 0.31/0.46 ! [M: nat,N: nat] :
% 0.31/0.46 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.31/0.46 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.31/0.46
% 0.31/0.46 % Suc_leD
% 0.31/0.46 thf(fact_27_Suc__leI,axiom,
% 0.31/0.46 ! [M: nat,N: nat] :
% 0.31/0.46 ( ( ord_less_nat @ M @ N )
% 0.31/0.46 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 0.31/0.46
% 0.31/0.46 % Suc_leI
% 0.31/0.46 thf(fact_28_le__SucE,axiom,
% 0.31/0.46 ! [M: nat,N: nat] :
% 0.31/0.46 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.31/0.46 => ( ~ ( ord_less_eq_nat @ M @ N )
% 0.31/0.46 => ( M
% 0.31/0.46 = ( suc @ N ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % le_SucE
% 0.31/0.46 thf(fact_29_le__SucI,axiom,
% 0.31/0.46 ! [M: nat,N: nat] :
% 0.31/0.46 ( ( ord_less_eq_nat @ M @ N )
% 0.31/0.46 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % le_SucI
% 0.31/0.46 thf(fact_30_le__refl,axiom,
% 0.31/0.46 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.31/0.46
% 0.31/0.46 % le_refl
% 0.31/0.46 thf(fact_31_Suc__le__D,axiom,
% 0.31/0.46 ! [N: nat,M2: nat] :
% 0.31/0.46 ( ( ord_less_eq_nat @ ( suc @ N ) @ M2 )
% 0.31/0.46 => ? [M3: nat] :
% 0.31/0.46 ( M2
% 0.31/0.46 = ( suc @ M3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Suc_le_D
% 0.31/0.46 thf(fact_32_le__trans,axiom,
% 0.31/0.46 ! [I: nat,J: nat,K: nat] :
% 0.31/0.46 ( ( ord_less_eq_nat @ I @ J )
% 0.31/0.46 => ( ( ord_less_eq_nat @ J @ K )
% 0.31/0.46 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % le_trans
% 0.31/0.46 thf(fact_33_Suc__le__eq,axiom,
% 0.31/0.46 ! [M: nat,N: nat] :
% 0.31/0.46 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.31/0.46 = ( ord_less_nat @ M @ N ) ) ).
% 0.31/0.46
% 0.31/0.46 % Suc_le_eq
% 0.31/0.46 thf(fact_34_Suc__lessD,axiom,
% 0.31/0.46 ! [M: nat,N: nat] :
% 0.31/0.46 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.31/0.46 => ( ord_less_nat @ M @ N ) ) ).
% 0.31/0.46
% 0.31/0.46 % Suc_lessD
% 0.31/0.46 thf(fact_35_Suc__lessE,axiom,
% 0.31/0.46 ! [I: nat,K: nat] :
% 0.31/0.46 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.31/0.46 => ~ ! [J2: nat] :
% 0.31/0.46 ( ( ord_less_nat @ I @ J2 )
% 0.31/0.46 => ( K
% 0.31/0.46 != ( suc @ J2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Suc_lessE
% 0.31/0.46 thf(fact_36_Suc__lessI,axiom,
% 0.31/0.46 ! [M: nat,N: nat] :
% 0.31/0.46 ( ( ord_less_nat @ M @ N )
% 0.31/0.46 => ( ( ( suc @ M )
% 0.31/0.46 != N )
% 0.31/0.46 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Suc_lessI
% 0.31/0.46 thf(fact_37_eq__imp__le,axiom,
% 0.31/0.46 ! [M: nat,N: nat] :
% 0.31/0.46 ( ( M = N )
% 0.31/0.46 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.31/0.46
% 0.31/0.46 % eq_imp_le
% 0.31/0.46 thf(fact_38_le__Suc__eq,axiom,
% 0.31/0.46 ! [M: nat,N: nat] :
% 0.31/0.46 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.31/0.46 = ( ( ord_less_eq_nat @ M @ N )
% 0.31/0.46 | ( M
% 0.31/0.46 = ( suc @ N ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % le_Suc_eq
% 0.31/0.46 thf(fact_39_less__SucE,axiom,
% 0.31/0.46 ! [M: nat,N: nat] :
% 0.31/0.46 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.31/0.46 => ( ~ ( ord_less_nat @ M @ N )
% 0.31/0.46 => ( M = N ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % less_SucE
% 0.31/0.46 thf(fact_40_less__SucI,axiom,
% 0.31/0.46 ! [M: nat,N: nat] :
% 0.31/0.46 ( ( ord_less_nat @ M @ N )
% 0.31/0.46 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % less_SucI
% 0.31/0.46 thf(fact_41_Suc__inject,axiom,
% 0.31/0.46 ! [X: nat,Y: nat] :
% 0.31/0.46 ( ( ( suc @ X )
% 0.31/0.46 = ( suc @ Y ) )
% 0.31/0.46 => ( X = Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % Suc_inject
% 0.31/0.46 thf(fact_42_dec__induct,axiom,
% 0.31/0.46 ! [I: nat,J: nat,P: nat > $o] :
% 0.31/0.46 ( ( ord_less_eq_nat @ I @ J )
% 0.31/0.46 => ( ( P @ I )
% 0.31/0.46 => ( ! [N2: nat] :
% 0.31/0.46 ( ( ord_less_eq_nat @ I @ N2 )
% 0.31/0.46 => ( ( ord_less_nat @ N2 @ J )
% 0.31/0.46 => ( ( P @ N2 )
% 0.31/0.46 => ( P @ ( suc @ N2 ) ) ) ) )
% 0.31/0.46 => ( P @ J ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % dec_induct
% 0.31/0.46 thf(fact_43_mem__Collect__eq,axiom,
% 0.31/0.46 ! [A: message_p_v,P: message_p_v > $o] :
% 0.31/0.46 ( ( member_message_p_v @ A @ ( collect_message_p_v @ P ) )
% 0.31/0.46 = ( P @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_Collect_eq
% 0.31/0.46 thf(fact_44_Collect__mem__eq,axiom,
% 0.31/0.46 ! [A2: set_message_p_v] :
% 0.31/0.46 ( ( collect_message_p_v
% 0.31/0.46 @ ^ [X3: message_p_v] : ( member_message_p_v @ X3 @ A2 ) )
% 0.31/0.46 = A2 ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mem_eq
% 0.31/0.46 thf(fact_45_Collect__cong,axiom,
% 0.31/0.46 ! [P: message_p_v > $o,Q: message_p_v > $o] :
% 0.31/0.46 ( ! [X4: message_p_v] :
% 0.31/0.46 ( ( P @ X4 )
% 0.31/0.46 = ( Q @ X4 ) )
% 0.31/0.46 => ( ( collect_message_p_v @ P )
% 0.31/0.46 = ( collect_message_p_v @ Q ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_cong
% 0.31/0.46 thf(fact_46_inc__induct,axiom,
% 0.31/0.46 ! [I: nat,J: nat,P: nat > $o] :
% 0.31/0.46 ( ( ord_less_eq_nat @ I @ J )
% 0.31/0.46 => ( ( P @ J )
% 0.31/0.46 => ( ! [N2: nat] :
% 0.31/0.46 ( ( ord_less_eq_nat @ I @ N2 )
% 0.31/0.46 => ( ( ord_less_nat @ N2 @ J )
% 0.31/0.46 => ( ( P @ ( suc @ N2 ) )
% 0.31/0.46 => ( P @ N2 ) ) ) )
% 0.31/0.46 => ( P @ I ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inc_induct
% 0.31/0.47 thf(fact_47_le__antisym,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.31/0.47 => ( ( ord_less_eq_nat @ N @ M )
% 0.31/0.47 => ( M = N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_antisym
% 0.31/0.47 thf(fact_48_Ex__less__Suc,axiom,
% 0.31/0.47 ! [N: nat,P: nat > $o] :
% 0.31/0.47 ( ( ? [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 0.31/0.47 & ( P @ I2 ) ) )
% 0.31/0.47 = ( ( P @ N )
% 0.31/0.47 | ? [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ N )
% 0.31/0.47 & ( P @ I2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Ex_less_Suc
% 0.31/0.47 thf(fact_49_less__Suc__eq,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.31/0.47 = ( ( ord_less_nat @ M @ N )
% 0.31/0.47 | ( M = N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_Suc_eq
% 0.31/0.47 thf(fact_50_n__not__Suc__n,axiom,
% 0.31/0.47 ! [N: nat] :
% 0.31/0.47 ( N
% 0.31/0.47 != ( suc @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % n_not_Suc_n
% 0.31/0.47 thf(fact_51_nat__less__le,axiom,
% 0.31/0.47 ( ord_less_nat
% 0.31/0.47 = ( ^ [M4: nat,N3: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.31/0.47 & ( M4 != N3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat_less_le
% 0.31/0.47 thf(fact_52_nat__neq__iff,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( M != N )
% 0.31/0.47 = ( ( ord_less_nat @ M @ N )
% 0.31/0.47 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat_neq_iff
% 0.31/0.47 thf(fact_53_not__less__eq,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ~ ( ord_less_nat @ M @ N ) )
% 0.31/0.47 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_less_eq
% 0.31/0.47 thf(fact_54_All__less__Suc,axiom,
% 0.31/0.47 ! [N: nat,P: nat > $o] :
% 0.31/0.47 ( ( ! [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 0.31/0.47 => ( P @ I2 ) ) )
% 0.31/0.47 = ( ( P @ N )
% 0.31/0.47 & ! [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ N )
% 0.31/0.47 => ( P @ I2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % All_less_Suc
% 0.31/0.47 thf(fact_55_Suc__le__lessD,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.31/0.47 => ( ord_less_nat @ M @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % Suc_le_lessD
% 0.31/0.47 thf(fact_56_Suc__less__eq2,axiom,
% 0.31/0.47 ! [N: nat,M: nat] :
% 0.31/0.47 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.31/0.47 = ( ? [M5: nat] :
% 0.31/0.47 ( ( M
% 0.31/0.47 = ( suc @ M5 ) )
% 0.31/0.47 & ( ord_less_nat @ N @ M5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Suc_less_eq2
% 0.31/0.47 thf(fact_57_less__antisym,axiom,
% 0.31/0.47 ! [N: nat,M: nat] :
% 0.31/0.47 ( ~ ( ord_less_nat @ N @ M )
% 0.31/0.47 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.31/0.47 => ( M = N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_antisym
% 0.31/0.47 thf(fact_58_Suc__less__SucD,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.31/0.47 => ( ord_less_nat @ M @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % Suc_less_SucD
% 0.31/0.47 thf(fact_59_less__not__refl,axiom,
% 0.31/0.47 ! [N: nat] :
% 0.31/0.47 ~ ( ord_less_nat @ N @ N ) ).
% 0.31/0.47
% 0.31/0.47 % less_not_refl
% 0.31/0.47 thf(fact_60_nat__le__linear,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.31/0.47 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat_le_linear
% 0.31/0.47 thf(fact_61_Suc__n__not__le__n,axiom,
% 0.31/0.47 ! [N: nat] :
% 0.31/0.47 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 0.31/0.47
% 0.31/0.47 % Suc_n_not_le_n
% 0.31/0.47 thf(fact_62_le__less__Suc__eq,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.31/0.47 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.31/0.47 = ( N = M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_less_Suc_eq
% 0.31/0.47 thf(fact_63_less__Suc__eq__le,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.31/0.47 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_Suc_eq_le
% 0.31/0.47 thf(fact_64_less__eq__Suc__le,axiom,
% 0.31/0.47 ( ord_less_nat
% 0.31/0.47 = ( ^ [N3: nat] : ( ord_less_eq_nat @ ( suc @ N3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_eq_Suc_le
% 0.31/0.47 thf(fact_65_less__not__refl2,axiom,
% 0.31/0.47 ! [N: nat,M: nat] :
% 0.31/0.47 ( ( ord_less_nat @ N @ M )
% 0.31/0.47 => ( M != N ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_not_refl2
% 0.31/0.47 thf(fact_66_less__not__refl3,axiom,
% 0.31/0.47 ! [S: nat,T: nat] :
% 0.31/0.47 ( ( ord_less_nat @ S @ T )
% 0.31/0.47 => ( S != T ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_not_refl3
% 0.31/0.47 thf(fact_67_less__trans__Suc,axiom,
% 0.31/0.47 ! [I: nat,J: nat,K: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I @ J )
% 0.31/0.47 => ( ( ord_less_nat @ J @ K )
% 0.31/0.47 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_trans_Suc
% 0.31/0.47 thf(fact_68_not__less__eq__eq,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 0.31/0.47 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_less_eq_eq
% 0.31/0.47 thf(fact_69_full__nat__induct,axiom,
% 0.31/0.47 ! [P: nat > $o,N: nat] :
% 0.31/0.47 ( ! [N2: nat] :
% 0.31/0.47 ( ! [M6: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ ( suc @ M6 ) @ N2 )
% 0.31/0.47 => ( P @ M6 ) )
% 0.31/0.47 => ( P @ N2 ) )
% 0.31/0.47 => ( P @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % full_nat_induct
% 0.31/0.47 thf(fact_70_le__imp__less__Suc,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.31/0.47 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_imp_less_Suc
% 0.31/0.47 thf(fact_71_less__Suc__induct,axiom,
% 0.31/0.47 ! [I: nat,J: nat,P: nat > nat > $o] :
% 0.31/0.47 ( ( ord_less_nat @ I @ J )
% 0.31/0.47 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 0.31/0.47 => ( ! [I3: nat,J2: nat,K2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I3 @ J2 )
% 0.31/0.47 => ( ( ord_less_nat @ J2 @ K2 )
% 0.31/0.47 => ( ( P @ I3 @ J2 )
% 0.31/0.47 => ( ( P @ J2 @ K2 )
% 0.31/0.47 => ( P @ I3 @ K2 ) ) ) ) )
% 0.31/0.47 => ( P @ I @ J ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_Suc_induct
% 0.31/0.47 thf(fact_72_less__imp__le__nat,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M @ N )
% 0.31/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_le_nat
% 0.31/0.47 thf(fact_73_less__irrefl__nat,axiom,
% 0.31/0.47 ! [N: nat] :
% 0.31/0.47 ~ ( ord_less_nat @ N @ N ) ).
% 0.31/0.47
% 0.31/0.47 % less_irrefl_nat
% 0.31/0.47 thf(fact_74_nat__less__induct,axiom,
% 0.31/0.47 ! [P: nat > $o,N: nat] :
% 0.31/0.47 ( ! [N2: nat] :
% 0.31/0.47 ( ! [M6: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M6 @ N2 )
% 0.31/0.47 => ( P @ M6 ) )
% 0.31/0.47 => ( P @ N2 ) )
% 0.31/0.47 => ( P @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat_less_induct
% 0.31/0.47 thf(fact_75_infinite__descent,axiom,
% 0.31/0.47 ! [P: nat > $o,N: nat] :
% 0.31/0.47 ( ! [N2: nat] :
% 0.31/0.47 ( ~ ( P @ N2 )
% 0.31/0.47 => ? [M6: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M6 @ N2 )
% 0.31/0.47 & ~ ( P @ M6 ) ) )
% 0.31/0.47 => ( P @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % infinite_descent
% 0.31/0.47 thf(fact_76_le__eq__less__or__eq,axiom,
% 0.31/0.47 ( ord_less_eq_nat
% 0.31/0.47 = ( ^ [M4: nat,N3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M4 @ N3 )
% 0.31/0.47 | ( M4 = N3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_eq_less_or_eq
% 0.31/0.47 thf(fact_77_less__or__eq__imp__le,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ( ord_less_nat @ M @ N )
% 0.31/0.47 | ( M = N ) )
% 0.31/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_or_eq_imp_le
% 0.31/0.47 thf(fact_78_linorder__neqE__nat,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( X != Y )
% 0.31/0.47 => ( ~ ( ord_less_nat @ X @ Y )
% 0.31/0.47 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linorder_neqE_nat
% 0.31/0.47 thf(fact_79_strict__inc__induct,axiom,
% 0.31/0.47 ! [I: nat,J: nat,P: nat > $o] :
% 0.31/0.47 ( ( ord_less_nat @ I @ J )
% 0.31/0.47 => ( ! [I3: nat] :
% 0.31/0.47 ( ( J
% 0.31/0.47 = ( suc @ I3 ) )
% 0.31/0.47 => ( P @ I3 ) )
% 0.31/0.47 => ( ! [I3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I3 @ J )
% 0.31/0.47 => ( ( P @ ( suc @ I3 ) )
% 0.31/0.47 => ( P @ I3 ) ) )
% 0.31/0.47 => ( P @ I ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % strict_inc_induct
% 0.31/0.47 thf(fact_80_Nat_Oex__has__greatest__nat,axiom,
% 0.31/0.47 ! [P: nat > $o,K: nat,B: nat] :
% 0.31/0.47 ( ( P @ K )
% 0.31/0.47 => ( ! [Y3: nat] :
% 0.31/0.47 ( ( P @ Y3 )
% 0.31/0.47 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.31/0.47 => ? [X4: nat] :
% 0.31/0.47 ( ( P @ X4 )
% 0.31/0.47 & ! [Y4: nat] :
% 0.31/0.47 ( ( P @ Y4 )
% 0.31/0.47 => ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Nat.ex_has_greatest_nat
% 0.31/0.47 thf(fact_81_le__neq__implies__less,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.31/0.47 => ( ( M != N )
% 0.31/0.47 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_neq_implies_less
% 0.31/0.47 thf(fact_82_nat__induct__at__least,axiom,
% 0.31/0.47 ! [M: nat,N: nat,P: nat > $o] :
% 0.31/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.31/0.47 => ( ( P @ M )
% 0.31/0.47 => ( ! [N2: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ M @ N2 )
% 0.31/0.47 => ( ( P @ N2 )
% 0.31/0.47 => ( P @ ( suc @ N2 ) ) ) )
% 0.31/0.47 => ( P @ N ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat_induct_at_least
% 0.31/0.47 thf(fact_83_not__less__less__Suc__eq,axiom,
% 0.31/0.47 ! [N: nat,M: nat] :
% 0.31/0.47 ( ~ ( ord_less_nat @ N @ M )
% 0.31/0.47 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.31/0.47 = ( N = M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_less_less_Suc_eq
% 0.31/0.47 thf(fact_84_less__mono__imp__le__mono,axiom,
% 0.31/0.47 ! [F: nat > nat,I: nat,J: nat] :
% 0.31/0.47 ( ! [I3: nat,J2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I3 @ J2 )
% 0.31/0.47 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 0.31/0.47 => ( ( ord_less_eq_nat @ I @ J )
% 0.31/0.47 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_mono_imp_le_mono
% 0.31/0.47 thf(fact_85_transitive__stepwise__le,axiom,
% 0.31/0.47 ! [M: nat,N: nat,R: nat > nat > $o] :
% 0.31/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.31/0.47 => ( ! [X4: nat] : ( R @ X4 @ X4 )
% 0.31/0.47 => ( ! [X4: nat,Y3: nat,Z: nat] :
% 0.31/0.47 ( ( R @ X4 @ Y3 )
% 0.31/0.47 => ( ( R @ Y3 @ Z )
% 0.31/0.47 => ( R @ X4 @ Z ) ) )
% 0.31/0.47 => ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
% 0.31/0.47 => ( R @ M @ N ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % transitive_stepwise_le
% 0.31/0.47 thf(fact_86_lift__Suc__mono__le,axiom,
% 0.31/0.47 ! [F: nat > nat,N: nat,N4: nat] :
% 0.31/0.47 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.31/0.47 => ( ( ord_less_eq_nat @ N @ N4 )
% 0.31/0.47 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % lift_Suc_mono_le
% 0.31/0.47 thf(fact_87_lift__Suc__mono__less,axiom,
% 0.31/0.47 ! [F: nat > nat,N: nat,N4: nat] :
% 0.31/0.47 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.31/0.47 => ( ( ord_less_nat @ N @ N4 )
% 0.31/0.47 => ( ord_less_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % lift_Suc_mono_less
% 0.31/0.47 thf(fact_88_lift__Suc__antimono__le,axiom,
% 0.31/0.47 ! [F: nat > nat,N: nat,N4: nat] :
% 0.31/0.47 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.31/0.47 => ( ( ord_less_eq_nat @ N @ N4 )
% 0.31/0.47 => ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % lift_Suc_antimono_le
% 0.31/0.47 thf(fact_89_lift__Suc__mono__less__iff,axiom,
% 0.31/0.47 ! [F: nat > nat,N: nat,M: nat] :
% 0.31/0.47 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.31/0.47 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 0.31/0.47 = ( ord_less_nat @ N @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % lift_Suc_mono_less_iff
% 0.31/0.47 thf(fact_90_diff__less__Suc,axiom,
% 0.31/0.47 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_less_Suc
% 0.31/0.47 thf(fact_91_Suc__diff__Suc,axiom,
% 0.31/0.47 ! [N: nat,M: nat] :
% 0.31/0.47 ( ( ord_less_nat @ N @ M )
% 0.31/0.47 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 0.31/0.47 = ( minus_minus_nat @ M @ N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Suc_diff_Suc
% 0.31/0.47 thf(fact_92_Suc__diff__le,axiom,
% 0.31/0.47 ! [N: nat,M: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ N @ M )
% 0.31/0.47 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.31/0.47 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Suc_diff_le
% 0.31/0.47 thf(fact_93_zero__induct__lemma,axiom,
% 0.31/0.47 ! [P: nat > $o,K: nat,I: nat] :
% 0.31/0.47 ( ( P @ K )
% 0.31/0.47 => ( ! [N2: nat] :
% 0.31/0.47 ( ( P @ ( suc @ N2 ) )
% 0.31/0.47 => ( P @ N2 ) )
% 0.31/0.47 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % zero_induct_lemma
% 0.31/0.47 thf(fact_94_diff__less__mono,axiom,
% 0.31/0.47 ! [A: nat,B: nat,C: nat] :
% 0.31/0.47 ( ( ord_less_nat @ A @ B )
% 0.31/0.47 => ( ( ord_less_eq_nat @ C @ A )
% 0.31/0.47 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_less_mono
% 0.31/0.47 thf(fact_95_less__diff__iff,axiom,
% 0.31/0.47 ! [K: nat,M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ K @ M )
% 0.31/0.47 => ( ( ord_less_eq_nat @ K @ N )
% 0.31/0.47 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.31/0.47 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_diff_iff
% 0.31/0.47 thf(fact_96_diff__Suc__eq__diff__pred,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.31/0.47 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_Suc_eq_diff_pred
% 0.31/0.47 thf(fact_97_length__induct,axiom,
% 0.31/0.47 ! [P: list_c1059388851t_unit > $o,Xs2: list_c1059388851t_unit] :
% 0.31/0.47 ( ! [Xs: list_c1059388851t_unit] :
% 0.31/0.47 ( ! [Ys2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( ord_less_nat @ ( size_s1406904903t_unit @ Ys2 ) @ ( size_s1406904903t_unit @ Xs ) )
% 0.31/0.47 => ( P @ Ys2 ) )
% 0.31/0.47 => ( P @ Xs ) )
% 0.31/0.47 => ( P @ Xs2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % length_induct
% 0.31/0.47 thf(fact_98_length__induct,axiom,
% 0.31/0.47 ! [P: list_message_p_v > $o,Xs2: list_message_p_v] :
% 0.31/0.47 ( ! [Xs: list_message_p_v] :
% 0.31/0.47 ( ! [Ys2: list_message_p_v] :
% 0.31/0.47 ( ( ord_less_nat @ ( size_s1168481041ge_p_v @ Ys2 ) @ ( size_s1168481041ge_p_v @ Xs ) )
% 0.31/0.47 => ( P @ Ys2 ) )
% 0.31/0.47 => ( P @ Xs ) )
% 0.31/0.47 => ( P @ Xs2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % length_induct
% 0.31/0.47 thf(fact_99_less__imp__diff__less,axiom,
% 0.31/0.47 ! [J: nat,K: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_nat @ J @ K )
% 0.31/0.47 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_diff_less
% 0.31/0.47 thf(fact_100_diff__less__mono2,axiom,
% 0.31/0.47 ! [M: nat,N: nat,L: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M @ N )
% 0.31/0.47 => ( ( ord_less_nat @ M @ L )
% 0.31/0.47 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_less_mono2
% 0.31/0.47 thf(fact_101_diff__le__mono2,axiom,
% 0.31/0.47 ! [M: nat,N: nat,L: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.31/0.47 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_le_mono2
% 0.31/0.47 thf(fact_102_le__diff__iff_H,axiom,
% 0.31/0.47 ! [A: nat,C: nat,B: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ A @ C )
% 0.31/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.31/0.47 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 0.31/0.47 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_diff_iff'
% 0.31/0.47 thf(fact_103_diff__le__self,axiom,
% 0.31/0.47 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.31/0.47
% 0.31/0.47 % diff_le_self
% 0.31/0.47 thf(fact_104_diff__le__mono,axiom,
% 0.31/0.47 ! [M: nat,N: nat,L: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.31/0.47 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_le_mono
% 0.31/0.47 thf(fact_105_Nat_Odiff__diff__eq,axiom,
% 0.31/0.47 ! [K: nat,M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ K @ M )
% 0.31/0.47 => ( ( ord_less_eq_nat @ K @ N )
% 0.31/0.47 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.31/0.47 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Nat.diff_diff_eq
% 0.31/0.47 thf(fact_106_le__diff__iff,axiom,
% 0.31/0.47 ! [K: nat,M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ K @ M )
% 0.31/0.47 => ( ( ord_less_eq_nat @ K @ N )
% 0.31/0.47 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.31/0.47 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_diff_iff
% 0.31/0.47 thf(fact_107_eq__diff__iff,axiom,
% 0.31/0.47 ! [K: nat,M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ K @ M )
% 0.31/0.47 => ( ( ord_less_eq_nat @ K @ N )
% 0.31/0.47 => ( ( ( minus_minus_nat @ M @ K )
% 0.31/0.47 = ( minus_minus_nat @ N @ K ) )
% 0.31/0.47 = ( M = N ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_diff_iff
% 0.31/0.47 thf(fact_108_one__reorient,axiom,
% 0.31/0.47 ! [X: nat] :
% 0.31/0.47 ( ( one_one_nat = X )
% 0.31/0.47 = ( X = one_one_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % one_reorient
% 0.31/0.47 thf(fact_109_diff__right__commute,axiom,
% 0.31/0.47 ! [A: nat,C: nat,B: nat] :
% 0.31/0.47 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 0.31/0.47 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_right_commute
% 0.31/0.47 thf(fact_110_Subset,axiom,
% 0.31/0.47 ! [MsgInSet: message_p_v] :
% 0.31/0.47 ( ( member_message_p_v @ MsgInSet @ ( firstOccSet @ ( suc @ index ) ) )
% 0.31/0.47 => ( member_message_p_v @ MsgInSet @ ( firstOccSet @ index ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Subset
% 0.31/0.47 thf(fact_111_SameCfgOnLow,axiom,
% 0.31/0.47 ! [I4: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I4 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
% 0.31/0.47 => ( ( nth_co1649820636t_unit @ ( fe @ index ) @ I4 )
% 0.31/0.47 = ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % SameCfgOnLow
% 0.31/0.47 thf(fact_112__092_060open_062_092_060not_062_AOccM_A_060_Alength_A_Ift_Aindex_J_092_060close_062,axiom,
% 0.31/0.47 ~ ( ord_less_nat @ occM2 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>\<not> OccM < length (ft index)\<close>
% 0.31/0.47 thf(fact_113_IPrefixListEx,axiom,
% 0.31/0.47 ! [I4: nat] : ( prefix1615116500t_unit @ ( fe @ I4 ) @ ( fe @ ( suc @ I4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % IPrefixListEx
% 0.31/0.47 thf(fact_114_order__refl,axiom,
% 0.31/0.47 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 0.31/0.47
% 0.31/0.47 % order_refl
% 0.31/0.47 thf(fact_115_nat__descend__induct,axiom,
% 0.31/0.47 ! [N: nat,P: nat > $o,M: nat] :
% 0.31/0.47 ( ! [K2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ N @ K2 )
% 0.31/0.47 => ( P @ K2 ) )
% 0.31/0.47 => ( ! [K2: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ K2 @ N )
% 0.31/0.47 => ( ! [I4: nat] :
% 0.31/0.47 ( ( ord_less_nat @ K2 @ I4 )
% 0.31/0.47 => ( P @ I4 ) )
% 0.31/0.47 => ( P @ K2 ) ) )
% 0.31/0.47 => ( P @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat_descend_induct
% 0.31/0.47 thf(fact_116_KeepProperty,axiom,
% 0.31/0.47 ! [Low: nat,P: nat > $o,Q: nat > $o] :
% 0.31/0.47 ( ! [I3: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ Low @ I3 )
% 0.31/0.47 => ( ( P @ I3 )
% 0.31/0.47 => ( ( P @ ( suc @ I3 ) )
% 0.31/0.47 & ( Q @ I3 ) ) ) )
% 0.31/0.47 => ( ( P @ Low )
% 0.31/0.47 => ! [I4: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ Low @ I4 )
% 0.31/0.47 => ( Q @ I4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % KeepProperty
% 0.31/0.47 thf(fact_117_less__numeral__extra_I4_J,axiom,
% 0.31/0.47 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.31/0.47
% 0.31/0.47 % less_numeral_extra(4)
% 0.31/0.47 thf(fact_118_le__numeral__extra_I4_J,axiom,
% 0.31/0.47 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.31/0.47
% 0.31/0.47 % le_numeral_extra(4)
% 0.31/0.47 thf(fact_119_LengthStep,axiom,
% 0.31/0.47 ord_less_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LengthStep
% 0.31/0.47 thf(fact_120_ConsumedMsg_I1_J,axiom,
% 0.31/0.47 minimalEnabled_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ consumedMsg ).
% 0.31/0.47
% 0.31/0.47 % ConsumedMsg(1)
% 0.31/0.47 thf(fact_121_PrefixListTransitive,axiom,
% 0.31/0.47 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit,L3: list_c1059388851t_unit] :
% 0.31/0.47 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.31/0.47 => ( ( prefix1615116500t_unit @ L2 @ L3 )
% 0.31/0.47 => ( prefix1615116500t_unit @ L1 @ L3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % PrefixListTransitive
% 0.31/0.47 thf(fact_122_PrefixListTransitive,axiom,
% 0.31/0.47 ! [L1: list_message_p_v,L2: list_message_p_v,L3: list_message_p_v] :
% 0.31/0.47 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.31/0.47 => ( ( prefix47729710ge_p_v @ L2 @ L3 )
% 0.31/0.47 => ( prefix47729710ge_p_v @ L1 @ L3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % PrefixListTransitive
% 0.31/0.47 thf(fact_123_PrefixSameOnLow,axiom,
% 0.31/0.47 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.31/0.47 => ! [Index: nat] :
% 0.31/0.47 ( ( ord_less_nat @ Index @ ( size_s1406904903t_unit @ L1 ) )
% 0.31/0.47 => ( ( nth_co1649820636t_unit @ L1 @ Index )
% 0.31/0.47 = ( nth_co1649820636t_unit @ L2 @ Index ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % PrefixSameOnLow
% 0.31/0.47 thf(fact_124_PrefixSameOnLow,axiom,
% 0.31/0.47 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 0.31/0.47 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.31/0.47 => ! [Index: nat] :
% 0.31/0.47 ( ( ord_less_nat @ Index @ ( size_s1168481041ge_p_v @ L1 ) )
% 0.31/0.47 => ( ( nth_message_p_v @ L1 @ Index )
% 0.31/0.47 = ( nth_message_p_v @ L2 @ Index ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % PrefixSameOnLow
% 0.31/0.47 thf(fact_125_PrefixListMonotonicity,axiom,
% 0.31/0.47 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.31/0.47 => ( ord_less_nat @ ( size_s1406904903t_unit @ L1 ) @ ( size_s1406904903t_unit @ L2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % PrefixListMonotonicity
% 0.31/0.47 thf(fact_126_PrefixListMonotonicity,axiom,
% 0.31/0.47 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 0.31/0.47 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.31/0.47 => ( ord_less_nat @ ( size_s1168481041ge_p_v @ L1 ) @ ( size_s1168481041ge_p_v @ L2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % PrefixListMonotonicity
% 0.31/0.47 thf(fact_127_nth__equalityI,axiom,
% 0.31/0.47 ! [Xs2: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.31/0.47 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.31/0.47 = ( size_s1406904903t_unit @ Ys ) )
% 0.31/0.47 => ( ! [I3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I3 @ ( size_s1406904903t_unit @ Xs2 ) )
% 0.31/0.47 => ( ( nth_co1649820636t_unit @ Xs2 @ I3 )
% 0.31/0.47 = ( nth_co1649820636t_unit @ Ys @ I3 ) ) )
% 0.31/0.47 => ( Xs2 = Ys ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nth_equalityI
% 0.31/0.47 thf(fact_128_nth__equalityI,axiom,
% 0.31/0.47 ! [Xs2: list_message_p_v,Ys: list_message_p_v] :
% 0.31/0.47 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.31/0.47 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.31/0.47 => ( ! [I3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I3 @ ( size_s1168481041ge_p_v @ Xs2 ) )
% 0.31/0.47 => ( ( nth_message_p_v @ Xs2 @ I3 )
% 0.31/0.47 = ( nth_message_p_v @ Ys @ I3 ) ) )
% 0.31/0.47 => ( Xs2 = Ys ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nth_equalityI
% 0.31/0.47 thf(fact_129_Skolem__list__nth,axiom,
% 0.31/0.47 ! [K: nat,P: nat > config256849571t_unit > $o] :
% 0.31/0.47 ( ( ! [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.31/0.47 => ? [X5: config256849571t_unit] : ( P @ I2 @ X5 ) ) )
% 0.31/0.47 = ( ? [Xs3: list_c1059388851t_unit] :
% 0.31/0.47 ( ( ( size_s1406904903t_unit @ Xs3 )
% 0.31/0.47 = K )
% 0.31/0.47 & ! [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.31/0.47 => ( P @ I2 @ ( nth_co1649820636t_unit @ Xs3 @ I2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Skolem_list_nth
% 0.31/0.47 thf(fact_130_Skolem__list__nth,axiom,
% 0.31/0.47 ! [K: nat,P: nat > message_p_v > $o] :
% 0.31/0.47 ( ( ! [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.31/0.47 => ? [X5: message_p_v] : ( P @ I2 @ X5 ) ) )
% 0.31/0.47 = ( ? [Xs3: list_message_p_v] :
% 0.31/0.47 ( ( ( size_s1168481041ge_p_v @ Xs3 )
% 0.31/0.47 = K )
% 0.31/0.47 & ! [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.31/0.47 => ( P @ I2 @ ( nth_message_p_v @ Xs3 @ I2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Skolem_list_nth
% 0.31/0.47 thf(fact_131_list__eq__iff__nth__eq,axiom,
% 0.31/0.47 ( ( ^ [Y5: list_c1059388851t_unit,Z2: list_c1059388851t_unit] : ( Y5 = Z2 ) )
% 0.31/0.47 = ( ^ [Xs3: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
% 0.31/0.47 ( ( ( size_s1406904903t_unit @ Xs3 )
% 0.31/0.47 = ( size_s1406904903t_unit @ Ys3 ) )
% 0.31/0.47 & ! [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ ( size_s1406904903t_unit @ Xs3 ) )
% 0.31/0.47 => ( ( nth_co1649820636t_unit @ Xs3 @ I2 )
% 0.31/0.47 = ( nth_co1649820636t_unit @ Ys3 @ I2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_eq_iff_nth_eq
% 0.31/0.47 thf(fact_132_list__eq__iff__nth__eq,axiom,
% 0.31/0.47 ( ( ^ [Y5: list_message_p_v,Z2: list_message_p_v] : ( Y5 = Z2 ) )
% 0.31/0.47 = ( ^ [Xs3: list_message_p_v,Ys3: list_message_p_v] :
% 0.31/0.47 ( ( ( size_s1168481041ge_p_v @ Xs3 )
% 0.31/0.47 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 0.31/0.47 & ! [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ ( size_s1168481041ge_p_v @ Xs3 ) )
% 0.31/0.47 => ( ( nth_message_p_v @ Xs3 @ I2 )
% 0.31/0.47 = ( nth_message_p_v @ Ys3 @ I2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_eq_iff_nth_eq
% 0.31/0.47 thf(fact_133_dual__order_Oantisym,axiom,
% 0.31/0.47 ! [B: nat,A: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ B @ A )
% 0.31/0.47 => ( ( ord_less_eq_nat @ A @ B )
% 0.31/0.47 => ( A = B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.antisym
% 0.31/0.47 thf(fact_134_dual__order_Oeq__iff,axiom,
% 0.31/0.47 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.31/0.47 = ( ^ [A3: nat,B2: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ B2 @ A3 )
% 0.31/0.47 & ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.eq_iff
% 0.31/0.47 thf(fact_135_dual__order_Otrans,axiom,
% 0.31/0.47 ! [B: nat,A: nat,C: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ B @ A )
% 0.31/0.47 => ( ( ord_less_eq_nat @ C @ B )
% 0.31/0.47 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.trans
% 0.31/0.47 thf(fact_136_linorder__wlog,axiom,
% 0.31/0.47 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.31/0.47 ( ! [A4: nat,B3: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ A4 @ B3 )
% 0.31/0.47 => ( P @ A4 @ B3 ) )
% 0.31/0.47 => ( ! [A4: nat,B3: nat] :
% 0.31/0.47 ( ( P @ B3 @ A4 )
% 0.31/0.47 => ( P @ A4 @ B3 ) )
% 0.31/0.47 => ( P @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linorder_wlog
% 0.31/0.47 thf(fact_137_dual__order_Orefl,axiom,
% 0.31/0.47 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.refl
% 0.31/0.47 thf(fact_138_order__trans,axiom,
% 0.31/0.47 ! [X: nat,Y: nat,Z3: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.31/0.47 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 0.31/0.47 => ( ord_less_eq_nat @ X @ Z3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_trans
% 0.31/0.47 thf(fact_139_order__class_Oorder_Oantisym,axiom,
% 0.31/0.47 ! [A: nat,B: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.31/0.47 => ( ( ord_less_eq_nat @ B @ A )
% 0.31/0.47 => ( A = B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_class.order.antisym
% 0.31/0.47 thf(fact_140_ord__le__eq__trans,axiom,
% 0.31/0.47 ! [A: nat,B: nat,C: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.31/0.47 => ( ( B = C )
% 0.31/0.47 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_le_eq_trans
% 0.31/0.47 thf(fact_141_ord__eq__le__trans,axiom,
% 0.31/0.47 ! [A: nat,B: nat,C: nat] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.31/0.47 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_le_trans
% 0.31/0.47 thf(fact_142_order__class_Oorder_Oeq__iff,axiom,
% 0.31/0.47 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.31/0.47 = ( ^ [A3: nat,B2: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ A3 @ B2 )
% 0.31/0.47 & ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_class.order.eq_iff
% 0.31/0.47 thf(fact_143_antisym__conv,axiom,
% 0.31/0.47 ! [Y: nat,X: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ Y @ X )
% 0.31/0.47 => ( ( ord_less_eq_nat @ X @ Y )
% 0.31/0.47 = ( X = Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym_conv
% 0.31/0.47 thf(fact_144_le__cases3,axiom,
% 0.31/0.47 ! [X: nat,Y: nat,Z3: nat] :
% 0.31/0.47 ( ( ( ord_less_eq_nat @ X @ Y )
% 0.31/0.47 => ~ ( ord_less_eq_nat @ Y @ Z3 ) )
% 0.31/0.47 => ( ( ( ord_less_eq_nat @ Y @ X )
% 0.31/0.47 => ~ ( ord_less_eq_nat @ X @ Z3 ) )
% 0.31/0.47 => ( ( ( ord_less_eq_nat @ X @ Z3 )
% 0.31/0.47 => ~ ( ord_less_eq_nat @ Z3 @ Y ) )
% 0.31/0.47 => ( ( ( ord_less_eq_nat @ Z3 @ Y )
% 0.31/0.47 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 0.31/0.47 => ( ( ( ord_less_eq_nat @ Y @ Z3 )
% 0.31/0.47 => ~ ( ord_less_eq_nat @ Z3 @ X ) )
% 0.31/0.47 => ~ ( ( ord_less_eq_nat @ Z3 @ X )
% 0.31/0.47 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_cases3
% 0.31/0.47 thf(fact_145_order_Otrans,axiom,
% 0.31/0.47 ! [A: nat,B: nat,C: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.31/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.31/0.47 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.trans
% 0.31/0.47 thf(fact_146_le__cases,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ~ ( ord_less_eq_nat @ X @ Y )
% 0.31/0.47 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_cases
% 0.31/0.47 thf(fact_147_eq__refl,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( X = Y )
% 0.31/0.47 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_refl
% 0.31/0.47 thf(fact_148_linear,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.31/0.47 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % linear
% 0.31/0.47 thf(fact_149_antisym,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.31/0.47 => ( ( ord_less_eq_nat @ Y @ X )
% 0.31/0.47 => ( X = Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym
% 0.31/0.47 thf(fact_150_eq__iff,axiom,
% 0.31/0.47 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.31/0.47 = ( ^ [X3: nat,Y6: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X3 @ Y6 )
% 0.31/0.47 & ( ord_less_eq_nat @ Y6 @ X3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_iff
% 0.31/0.47 thf(fact_151_ord__le__eq__subst,axiom,
% 0.31/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.31/0.47 => ( ( ( F @ B )
% 0.31/0.47 = C )
% 0.31/0.47 => ( ! [X4: nat,Y3: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.31/0.47 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.31/0.47 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_le_eq_subst
% 0.31/0.47 thf(fact_152_ord__eq__le__subst,axiom,
% 0.31/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( F @ B ) )
% 0.31/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.31/0.47 => ( ! [X4: nat,Y3: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.31/0.47 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.31/0.47 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_le_subst
% 0.31/0.47 thf(fact_153_order__subst2,axiom,
% 0.31/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.31/0.47 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.31/0.47 => ( ! [X4: nat,Y3: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.31/0.47 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.31/0.47 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_subst2
% 0.31/0.47 thf(fact_154_order__subst1,axiom,
% 0.31/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.31/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.31/0.47 => ( ! [X4: nat,Y3: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.31/0.47 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.31/0.47 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_subst1
% 0.31/0.47 thf(fact_155_dual__order_Ostrict__implies__not__eq,axiom,
% 0.31/0.47 ! [B: nat,A: nat] :
% 0.31/0.47 ( ( ord_less_nat @ B @ A )
% 0.31/0.47 => ( A != B ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_implies_not_eq
% 0.31/0.47 thf(fact_156_order_Ostrict__implies__not__eq,axiom,
% 0.31/0.47 ! [A: nat,B: nat] :
% 0.31/0.47 ( ( ord_less_nat @ A @ B )
% 0.31/0.47 => ( A != B ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.strict_implies_not_eq
% 0.31/0.47 thf(fact_157_not__less__iff__gr__or__eq,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.31/0.47 = ( ( ord_less_nat @ Y @ X )
% 0.31/0.47 | ( X = Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_less_iff_gr_or_eq
% 0.31/0.47 thf(fact_158_dual__order_Ostrict__trans,axiom,
% 0.31/0.47 ! [B: nat,A: nat,C: nat] :
% 0.31/0.47 ( ( ord_less_nat @ B @ A )
% 0.31/0.47 => ( ( ord_less_nat @ C @ B )
% 0.31/0.47 => ( ord_less_nat @ C @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_trans
% 0.31/0.47 thf(fact_159_linorder__less__wlog,axiom,
% 0.31/0.47 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.31/0.47 ( ! [A4: nat,B3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ A4 @ B3 )
% 0.31/0.47 => ( P @ A4 @ B3 ) )
% 0.31/0.47 => ( ! [A4: nat] : ( P @ A4 @ A4 )
% 0.31/0.47 => ( ! [A4: nat,B3: nat] :
% 0.31/0.47 ( ( P @ B3 @ A4 )
% 0.31/0.47 => ( P @ A4 @ B3 ) )
% 0.31/0.47 => ( P @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linorder_less_wlog
% 0.31/0.47 thf(fact_160_exists__least__iff,axiom,
% 0.31/0.47 ( ( ^ [P2: nat > $o] :
% 0.31/0.47 ? [X5: nat] : ( P2 @ X5 ) )
% 0.31/0.47 = ( ^ [P3: nat > $o] :
% 0.31/0.47 ? [N3: nat] :
% 0.31/0.47 ( ( P3 @ N3 )
% 0.31/0.47 & ! [M4: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M4 @ N3 )
% 0.31/0.47 => ~ ( P3 @ M4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % exists_least_iff
% 0.31/0.47 thf(fact_161_less__imp__not__less,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X @ Y )
% 0.31/0.47 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_not_less
% 0.31/0.47 thf(fact_162_order_Ostrict__trans,axiom,
% 0.31/0.47 ! [A: nat,B: nat,C: nat] :
% 0.31/0.47 ( ( ord_less_nat @ A @ B )
% 0.31/0.47 => ( ( ord_less_nat @ B @ C )
% 0.31/0.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.strict_trans
% 0.31/0.47 thf(fact_163_dual__order_Oirrefl,axiom,
% 0.31/0.47 ! [A: nat] :
% 0.31/0.47 ~ ( ord_less_nat @ A @ A ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.irrefl
% 0.31/0.47 thf(fact_164_linorder__cases,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ~ ( ord_less_nat @ X @ Y )
% 0.31/0.47 => ( ( X != Y )
% 0.31/0.47 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linorder_cases
% 0.31/0.47 thf(fact_165_less__imp__triv,axiom,
% 0.31/0.47 ! [X: nat,Y: nat,P: $o] :
% 0.31/0.47 ( ( ord_less_nat @ X @ Y )
% 0.31/0.47 => ( ( ord_less_nat @ Y @ X )
% 0.31/0.47 => P ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_triv
% 0.31/0.47 thf(fact_166_less__imp__not__eq2,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X @ Y )
% 0.31/0.47 => ( Y != X ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_not_eq2
% 0.31/0.47 thf(fact_167_antisym__conv3,axiom,
% 0.31/0.47 ! [Y: nat,X: nat] :
% 0.31/0.47 ( ~ ( ord_less_nat @ Y @ X )
% 0.31/0.47 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.31/0.47 = ( X = Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym_conv3
% 0.31/0.47 thf(fact_168_less__induct,axiom,
% 0.31/0.47 ! [P: nat > $o,A: nat] :
% 0.31/0.47 ( ! [X4: nat] :
% 0.31/0.47 ( ! [Y4: nat] :
% 0.31/0.47 ( ( ord_less_nat @ Y4 @ X4 )
% 0.31/0.47 => ( P @ Y4 ) )
% 0.31/0.47 => ( P @ X4 ) )
% 0.31/0.47 => ( P @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_induct
% 0.31/0.47 thf(fact_169_less__not__sym,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X @ Y )
% 0.31/0.47 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_not_sym
% 0.31/0.47 thf(fact_170_less__imp__not__eq,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X @ Y )
% 0.31/0.47 => ( X != Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_not_eq
% 0.31/0.47 thf(fact_171_dual__order_Oasym,axiom,
% 0.31/0.47 ! [B: nat,A: nat] :
% 0.31/0.47 ( ( ord_less_nat @ B @ A )
% 0.31/0.47 => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.asym
% 0.31/0.47 thf(fact_172_ord__less__eq__trans,axiom,
% 0.31/0.47 ! [A: nat,B: nat,C: nat] :
% 0.31/0.47 ( ( ord_less_nat @ A @ B )
% 0.31/0.47 => ( ( B = C )
% 0.31/0.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_less_eq_trans
% 0.31/0.47 thf(fact_173_ord__eq__less__trans,axiom,
% 0.31/0.47 ! [A: nat,B: nat,C: nat] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( ( ord_less_nat @ B @ C )
% 0.31/0.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_less_trans
% 0.31/0.47 thf(fact_174_less__irrefl,axiom,
% 0.31/0.47 ! [X: nat] :
% 0.31/0.47 ~ ( ord_less_nat @ X @ X ) ).
% 0.31/0.47
% 0.31/0.47 % less_irrefl
% 0.31/0.47 thf(fact_175_less__linear,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X @ Y )
% 0.31/0.47 | ( X = Y )
% 0.31/0.47 | ( ord_less_nat @ Y @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_linear
% 0.31/0.47 thf(fact_176_less__trans,axiom,
% 0.31/0.47 ! [X: nat,Y: nat,Z3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X @ Y )
% 0.31/0.47 => ( ( ord_less_nat @ Y @ Z3 )
% 0.31/0.47 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_trans
% 0.31/0.47 thf(fact_177_less__asym_H,axiom,
% 0.31/0.47 ! [A: nat,B: nat] :
% 0.31/0.47 ( ( ord_less_nat @ A @ B )
% 0.31/0.47 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_asym'
% 0.31/0.47 thf(fact_178_less__asym,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X @ Y )
% 0.31/0.47 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_asym
% 0.31/0.47 thf(fact_179_less__imp__neq,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X @ Y )
% 0.31/0.47 => ( X != Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_neq
% 0.31/0.47 thf(fact_180_order_Oasym,axiom,
% 0.31/0.47 ! [A: nat,B: nat] :
% 0.31/0.47 ( ( ord_less_nat @ A @ B )
% 0.31/0.47 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.asym
% 0.31/0.47 thf(fact_181_neq__iff,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( X != Y )
% 0.31/0.47 = ( ( ord_less_nat @ X @ Y )
% 0.31/0.47 | ( ord_less_nat @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_iff
% 0.31/0.47 thf(fact_182_neqE,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( X != Y )
% 0.31/0.47 => ( ~ ( ord_less_nat @ X @ Y )
% 0.31/0.47 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neqE
% 0.31/0.47 thf(fact_183_gt__ex,axiom,
% 0.31/0.47 ! [X: nat] :
% 0.31/0.47 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 0.31/0.47
% 0.31/0.47 % gt_ex
% 0.31/0.47 thf(fact_184_order__less__subst2,axiom,
% 0.31/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.31/0.47 ( ( ord_less_nat @ A @ B )
% 0.31/0.47 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.31/0.47 => ( ! [X4: nat,Y3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X4 @ Y3 )
% 0.31/0.47 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.31/0.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_less_subst2
% 0.31/0.47 thf(fact_185_order__less__subst1,axiom,
% 0.31/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.31/0.47 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.31/0.47 => ( ( ord_less_nat @ B @ C )
% 0.31/0.47 => ( ! [X4: nat,Y3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X4 @ Y3 )
% 0.31/0.47 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.31/0.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_less_subst1
% 0.31/0.47 thf(fact_186_ord__less__eq__subst,axiom,
% 0.31/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.31/0.47 ( ( ord_less_nat @ A @ B )
% 0.31/0.47 => ( ( ( F @ B )
% 0.31/0.47 = C )
% 0.31/0.47 => ( ! [X4: nat,Y3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X4 @ Y3 )
% 0.31/0.47 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.31/0.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_less_eq_subst
% 0.31/0.47 thf(fact_187_ord__eq__less__subst,axiom,
% 0.31/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( F @ B ) )
% 0.31/0.47 => ( ( ord_less_nat @ B @ C )
% 0.31/0.47 => ( ! [X4: nat,Y3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X4 @ Y3 )
% 0.31/0.47 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.31/0.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_less_subst
% 0.31/0.47 thf(fact_188_MinPredicate,axiom,
% 0.31/0.47 ! [P: nat > $o] :
% 0.31/0.47 ( ? [X_12: nat] : ( P @ X_12 )
% 0.31/0.47 => ? [N0: nat] :
% 0.31/0.47 ( ( P @ N0 )
% 0.31/0.47 & ! [N5: nat] :
% 0.31/0.47 ( ( P @ N5 )
% 0.31/0.47 => ( ord_less_eq_nat @ N0 @ N5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % MinPredicate
% 0.31/0.47 thf(fact_189_order_Onot__eq__order__implies__strict,axiom,
% 0.31/0.47 ! [A: nat,B: nat] :
% 0.31/0.47 ( ( A != B )
% 0.31/0.47 => ( ( ord_less_eq_nat @ A @ B )
% 0.31/0.47 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.not_eq_order_implies_strict
% 0.31/0.47 thf(fact_190_dual__order_Ostrict__implies__order,axiom,
% 0.31/0.47 ! [B: nat,A: nat] :
% 0.31/0.47 ( ( ord_less_nat @ B @ A )
% 0.31/0.47 => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_implies_order
% 0.31/0.47 thf(fact_191_dual__order_Ostrict__iff__order,axiom,
% 0.31/0.47 ( ord_less_nat
% 0.31/0.47 = ( ^ [B2: nat,A3: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ B2 @ A3 )
% 0.31/0.47 & ( A3 != B2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_iff_order
% 0.31/0.47 thf(fact_192_dual__order_Oorder__iff__strict,axiom,
% 0.31/0.47 ( ord_less_eq_nat
% 0.31/0.47 = ( ^ [B2: nat,A3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ B2 @ A3 )
% 0.31/0.47 | ( A3 = B2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.order_iff_strict
% 0.31/0.47 thf(fact_193_order_Ostrict__implies__order,axiom,
% 0.31/0.47 ! [A: nat,B: nat] :
% 0.31/0.47 ( ( ord_less_nat @ A @ B )
% 0.31/0.47 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.strict_implies_order
% 0.31/0.47 thf(fact_194_dual__order_Ostrict__trans2,axiom,
% 0.31/0.47 ! [B: nat,A: nat,C: nat] :
% 0.31/0.47 ( ( ord_less_nat @ B @ A )
% 0.31/0.47 => ( ( ord_less_eq_nat @ C @ B )
% 0.31/0.47 => ( ord_less_nat @ C @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_trans2
% 0.31/0.47 thf(fact_195_dual__order_Ostrict__trans1,axiom,
% 0.31/0.47 ! [B: nat,A: nat,C: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ B @ A )
% 0.31/0.47 => ( ( ord_less_nat @ C @ B )
% 0.31/0.47 => ( ord_less_nat @ C @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_trans1
% 0.31/0.47 thf(fact_196_order_Ostrict__iff__order,axiom,
% 0.31/0.47 ( ord_less_nat
% 0.31/0.47 = ( ^ [A3: nat,B2: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ A3 @ B2 )
% 0.31/0.47 & ( A3 != B2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.strict_iff_order
% 0.31/0.47 thf(fact_197_order_Oorder__iff__strict,axiom,
% 0.31/0.47 ( ord_less_eq_nat
% 0.31/0.47 = ( ^ [A3: nat,B2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ A3 @ B2 )
% 0.31/0.47 | ( A3 = B2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.order_iff_strict
% 0.31/0.47 thf(fact_198_order_Ostrict__trans2,axiom,
% 0.31/0.47 ! [A: nat,B: nat,C: nat] :
% 0.31/0.47 ( ( ord_less_nat @ A @ B )
% 0.31/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.31/0.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.strict_trans2
% 0.31/0.47 thf(fact_199_order_Ostrict__trans1,axiom,
% 0.31/0.47 ! [A: nat,B: nat,C: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.31/0.47 => ( ( ord_less_nat @ B @ C )
% 0.31/0.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.strict_trans1
% 0.31/0.47 thf(fact_200_not__le__imp__less,axiom,
% 0.31/0.47 ! [Y: nat,X: nat] :
% 0.31/0.47 ( ~ ( ord_less_eq_nat @ Y @ X )
% 0.31/0.47 => ( ord_less_nat @ X @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_le_imp_less
% 0.31/0.47 thf(fact_201_less__le__not__le,axiom,
% 0.31/0.47 ( ord_less_nat
% 0.31/0.47 = ( ^ [X3: nat,Y6: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X3 @ Y6 )
% 0.31/0.47 & ~ ( ord_less_eq_nat @ Y6 @ X3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_le_not_le
% 0.31/0.47 thf(fact_202_le__imp__less__or__eq,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.31/0.47 => ( ( ord_less_nat @ X @ Y )
% 0.31/0.47 | ( X = Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_imp_less_or_eq
% 0.31/0.47 thf(fact_203_le__less__linear,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.31/0.47 | ( ord_less_nat @ Y @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_less_linear
% 0.31/0.47 thf(fact_204_less__le__trans,axiom,
% 0.31/0.47 ! [X: nat,Y: nat,Z3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X @ Y )
% 0.31/0.47 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 0.31/0.47 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_le_trans
% 0.31/0.47 thf(fact_205_le__less__trans,axiom,
% 0.31/0.47 ! [X: nat,Y: nat,Z3: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.31/0.47 => ( ( ord_less_nat @ Y @ Z3 )
% 0.31/0.47 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_less_trans
% 0.31/0.47 thf(fact_206_less__imp__le,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X @ Y )
% 0.31/0.47 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_le
% 0.31/0.47 thf(fact_207_antisym__conv2,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.31/0.47 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.31/0.47 = ( X = Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym_conv2
% 0.31/0.47 thf(fact_208_antisym__conv1,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ~ ( ord_less_nat @ X @ Y )
% 0.31/0.47 => ( ( ord_less_eq_nat @ X @ Y )
% 0.31/0.47 = ( X = Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym_conv1
% 0.31/0.47 thf(fact_209_le__neq__trans,axiom,
% 0.31/0.47 ! [A: nat,B: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.31/0.47 => ( ( A != B )
% 0.31/0.47 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_neq_trans
% 0.31/0.47 thf(fact_210_not__less,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.31/0.47 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_less
% 0.31/0.47 thf(fact_211_not__le,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 0.31/0.47 = ( ord_less_nat @ Y @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_le
% 0.31/0.47 thf(fact_212_order__less__le__subst2,axiom,
% 0.31/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.31/0.47 ( ( ord_less_nat @ A @ B )
% 0.31/0.47 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.31/0.47 => ( ! [X4: nat,Y3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X4 @ Y3 )
% 0.31/0.47 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.31/0.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_less_le_subst2
% 0.31/0.47 thf(fact_213_order__less__le__subst1,axiom,
% 0.31/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.31/0.47 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.31/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.31/0.47 => ( ! [X4: nat,Y3: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.31/0.47 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.31/0.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_less_le_subst1
% 0.31/0.47 thf(fact_214_order__le__less__subst2,axiom,
% 0.31/0.47 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.31/0.47 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.31/0.47 => ( ! [X4: nat,Y3: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.31/0.47 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.31/0.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_le_less_subst2
% 0.31/0.47 thf(fact_215_order__le__less__subst1,axiom,
% 0.31/0.47 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.31/0.47 => ( ( ord_less_nat @ B @ C )
% 0.31/0.47 => ( ! [X4: nat,Y3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X4 @ Y3 )
% 0.31/0.47 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.31/0.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_le_less_subst1
% 0.31/0.47 thf(fact_216_less__le,axiom,
% 0.31/0.47 ( ord_less_nat
% 0.31/0.47 = ( ^ [X3: nat,Y6: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ X3 @ Y6 )
% 0.31/0.47 & ( X3 != Y6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_le
% 0.31/0.47 thf(fact_217_le__less,axiom,
% 0.31/0.47 ( ord_less_eq_nat
% 0.31/0.47 = ( ^ [X3: nat,Y6: nat] :
% 0.31/0.47 ( ( ord_less_nat @ X3 @ Y6 )
% 0.31/0.47 | ( X3 = Y6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_less
% 0.31/0.47 thf(fact_218_leI,axiom,
% 0.31/0.47 ! [X: nat,Y: nat] :
% 0.31/0.47 ( ~ ( ord_less_nat @ X @ Y )
% 0.31/0.47 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % leI
% 0.31/0.47 thf(fact_219_leD,axiom,
% 0.31/0.47 ! [Y: nat,X: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ Y @ X )
% 0.31/0.47 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % leD
% 0.31/0.47 thf(fact_220_AssumpMinImplAllBigger,axiom,
% 0.31/0.47 minimalEnabled_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ msg ).
% 0.31/0.47
% 0.31/0.47 % AssumpMinImplAllBigger
% 0.31/0.47 thf(fact_221__092_060open_062execution_OfirstOccurrence_A_Ife_Aindex_J_A_Ift_Aindex_J_Amsg_AOccM_092_060close_062,axiom,
% 0.31/0.47 firstO1414030372_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ msga @ occM2 ).
% 0.31/0.47
% 0.31/0.47 % \<open>execution.firstOccurrence (fe index) (ft index) msg OccM\<close>
% 0.31/0.47 thf(fact_222_SameMsgOnLow,axiom,
% 0.31/0.47 ! [I4: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I4 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 0.31/0.47 => ( ( nth_message_p_v @ ( ft @ index ) @ I4 )
% 0.31/0.47 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % SameMsgOnLow
% 0.31/0.47 thf(fact_223_OccM_H_I5_J,axiom,
% 0.31/0.47 ! [N5: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ occM @ N5 )
% 0.31/0.47 => ( ( ord_less_nat @ N5 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 0.31/0.47 => ( msg
% 0.31/0.47 != ( nth_message_p_v @ ( ft @ index ) @ N5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % OccM'(5)
% 0.31/0.47 thf(fact_224_IPrefixList,axiom,
% 0.31/0.47 ! [I4: nat] : ( prefix47729710ge_p_v @ ( ft @ I4 ) @ ( ft @ ( suc @ I4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % IPrefixList
% 0.31/0.47 thf(fact_225_OccM_H_I1_J,axiom,
% 0.31/0.47 ? [P4: p] : ( isReceiverOf_p_v @ P4 @ msg ) ).
% 0.31/0.47
% 0.31/0.47 % OccM'(1)
% 0.31/0.47 thf(fact_226_FirstOccMsg_H,axiom,
% 0.31/0.47 firstO1414030372_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ msg @ occM ).
% 0.31/0.47
% 0.31/0.47 % FirstOccMsg'
% 0.31/0.47 thf(fact_227_AssumpOccMFirstOccurrence_I5_J,axiom,
% 0.31/0.47 ! [N5: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ occM2 @ N5 )
% 0.31/0.47 => ( ( ord_less_nat @ N5 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 0.31/0.47 => ( msga
% 0.31/0.47 != ( nth_message_p_v @ ( ft @ index ) @ N5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % AssumpOccMFirstOccurrence(5)
% 0.31/0.47 thf(fact_228_OccM_H_I4_J,axiom,
% 0.31/0.47 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ occM ) @ msg ).
% 0.31/0.47
% 0.31/0.47 % OccM'(4)
% 0.31/0.47 thf(fact_229_AssumptionFairContr,axiom,
% 0.31/0.47 ! [N5: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ n @ N5 )
% 0.31/0.47 => ! [N02: nat] :
% 0.31/0.47 ( ( ord_less_nat @ N02 @ ( size_s1168481041ge_p_v @ ( ft @ N5 ) ) )
% 0.31/0.47 => ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) @ N02 )
% 0.31/0.47 => ( msg2
% 0.31/0.47 != ( nth_message_p_v @ ( ft @ N5 ) @ N02 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % AssumptionFairContr
% 0.31/0.47 thf(fact_230_MessageStaysOrConsumed,axiom,
% 0.31/0.47 ! [N1: nat,N22: nat,N: nat,Msg: message_p_v] :
% 0.31/0.47 ( ( ( ord_less_eq_nat @ N1 @ N22 )
% 0.31/0.47 & ( ord_less_nat @ N22 @ ( size_s1406904903t_unit @ ( fe @ N ) ) )
% 0.31/0.47 & ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N ) @ N1 ) @ Msg ) )
% 0.31/0.47 => ( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N ) @ N22 ) @ Msg )
% 0.31/0.47 | ? [N03: nat] :
% 0.31/0.47 ( ( ord_less_eq_nat @ N1 @ N03 )
% 0.31/0.47 & ( ord_less_nat @ N03 @ ( size_s1168481041ge_p_v @ ( ft @ N ) ) )
% 0.31/0.47 & ( ( nth_message_p_v @ ( ft @ N ) @ N03 )
% 0.31/0.47 = Msg ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % MessageStaysOrConsumed
% 0.31/0.47 thf(fact_231__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_O_Alength_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Ai_A_092_060and_062_Amsg_____A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062,axiom,
% 0.31/0.47 ~ ? [I4: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I4 @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) )
% 0.31/0.47 & ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ I4 )
% 0.31/0.47 & ( msg2
% 0.31/0.47 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>\<not> (\<exists>i<length (fe (Suc index)) - 1. length (fe index) - 1 \<le> i \<and> msg__ = ft (Suc index) ! i)\<close>
% 0.31/0.47 thf(fact_232_AssumptionFair_I4_J,axiom,
% 0.31/0.47 isReceiverOf_p_v @ p2 @ msg2 ).
% 0.31/0.47
% 0.31/0.47 % AssumptionFair(4)
% 0.31/0.47 thf(fact_233_AssumpOccMFirstOccurrence_I1_J,axiom,
% 0.31/0.47 ? [P4: p] : ( isReceiverOf_p_v @ P4 @ msga ) ).
% 0.31/0.47
% 0.31/0.47 % AssumpOccMFirstOccurrence(1)
% 0.31/0.47 thf(fact_234_AssumptionFair_I3_J,axiom,
% 0.31/0.47 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ n0 ) @ msg2 ).
% 0.31/0.47
% 0.31/0.47 % AssumptionFair(3)
% 0.31/0.47
% 0.31/0.47 % Conjectures (1)
% 0.31/0.47 thf(conj_0,conjecture,
% 0.31/0.47 ( occM2
% 0.31/0.47 = ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 2.34/1.46 ---- Embedded in THF ---
% 2.34/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.34/1.46 %%% Generated on Tue Feb 24 08:24:48 EST 2026
% 2.34/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 2.34/1.46 %%% Logic specification used:
% 2.34/1.46 %%% thf(spec, logic, $$dhol).
% 2.34/1.46
% 2.34/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2DTF22021.p
% See solution above
% 2.34/1.46 ------------------------
% 2.34/1.49 ---- Cleaned THF ---
% 2.34/1.50 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 2.34/1.50 list_c1059388851t_unit: $tType ).
% 2.34/1.50
% 2.34/1.50 thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.34/1.50 config256849571t_unit: $tType ).
% 2.34/1.50
% 2.34/1.50 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 2.34/1.50 list_message_p_v: $tType ).
% 2.34/1.50
% 2.34/1.50 thf(ty_n_t__Set__Oset_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 2.34/1.50 set_message_p_v: $tType ).
% 2.34/1.50
% 2.34/1.50 thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.34/1.50 message_p_v: $tType ).
% 2.34/1.50
% 2.34/1.50 thf(ty_n_t__Nat__Onat,type,
% 2.34/1.50 nat: $tType ).
% 2.34/1.50
% 2.34/1.50 thf(ty_n_tf__p,type,
% 2.34/1.50 p: $tType ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_AsynchronousSystem_Oenabled_001tf__p_001tf__v_001tf__s,type,
% 2.34/1.50 enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_AsynchronousSystem_OisReceiverOf_001tf__p_001tf__v,type,
% 2.34/1.50 isReceiverOf_p_v: p > message_p_v > $o ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_Execution_Oexecution_OfirstOccurrence_001tf__p_001tf__v_001tf__s,type,
% 2.34/1.50 firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_Execution_Oexecution_OminimalEnabled_001tf__p_001tf__v_001tf__s,type,
% 2.34/1.50 minimalEnabled_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > $o ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 2.34/1.50 minus_minus_nat: nat > nat > nat ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 2.34/1.50 one_one_nat: nat ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.34/1.50 prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.34/1.50 prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.34/1.50 nil_co1338500125t_unit: list_c1059388851t_unit ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_List_Onth_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.34/1.50 nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_List_Onth_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.34/1.50 nth_message_p_v: list_message_p_v > nat > message_p_v ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_Nat_OSuc,type,
% 2.34/1.50 suc: nat > nat ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 2.34/1.50 size_s1406904903t_unit: list_c1059388851t_unit > nat ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 2.34/1.50 size_s1168481041ge_p_v: list_message_p_v > nat ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 2.34/1.50 ord_less_nat: nat > nat > $o ).
% 2.34/1.50
% 2.34/1.50 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 2.54/1.50 ord_less_eq_nat: nat > nat > $o ).
% 2.54/1.50
% 2.54/1.50 thf(sy_c_Set_OCollect_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.54/1.50 collect_message_p_v: ( message_p_v > $o ) > set_message_p_v ).
% 2.54/1.50
% 2.54/1.50 thf(sy_c_member_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.54/1.50 member_message_p_v: message_p_v > set_message_p_v > $o ).
% 2.54/1.50
% 2.54/1.50 thf(sy_v_OccM_H____,type,
% 2.54/1.50 occM: nat ).
% 2.54/1.50
% 2.54/1.50 thf(sy_v_OccM____,type,
% 2.54/1.50 occM2: nat ).
% 2.54/1.50
% 2.54/1.50 thf(sy_v_consumedMsg____,type,
% 2.54/1.50 consumedMsg: message_p_v ).
% 2.54/1.50
% 2.54/1.50 thf(sy_v_fe____,type,
% 2.54/1.50 fe: nat > list_c1059388851t_unit ).
% 2.54/1.50
% 2.54/1.50 thf(sy_v_firstOccSet____,type,
% 2.54/1.50 firstOccSet: nat > set_message_p_v ).
% 2.54/1.50
% 2.54/1.50 thf(sy_v_ft____,type,
% 2.54/1.50 ft: nat > list_message_p_v ).
% 2.54/1.50
% 2.54/1.50 thf(sy_v_index____,type,
% 2.54/1.50 index: nat ).
% 2.54/1.50
% 2.54/1.50 thf(sy_v_msg_H____,type,
% 2.54/1.50 msg: message_p_v ).
% 2.54/1.50
% 2.54/1.50 thf(sy_v_msg____,type,
% 2.54/1.50 msg2: message_p_v ).
% 2.54/1.50
% 2.54/1.50 thf(sy_v_msga____,type,
% 2.54/1.50 msga: message_p_v ).
% 2.54/1.50
% 2.54/1.50 thf(sy_v_n0____,type,
% 2.54/1.50 n0: nat ).
% 2.54/1.50
% 2.54/1.50 thf(sy_v_n____,type,
% 2.54/1.50 n: nat ).
% 2.54/1.50
% 2.54/1.50 thf(sy_v_p____,type,
% 2.54/1.50 p2: p ).
% 2.54/1.50
% 2.54/1.50 thf(fact_0_AssumpOccMFirstOccurrence_I3_J,axiom,
% 2.54/1.50 ord_less_nat @ occM2 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_1__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_AOccM_092_060close_062,axiom,
% 2.54/1.50 ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ occM2 ).
% 2.54/1.50
% 2.54/1.50 thf(fact_2_OccM_H_I3_J,axiom,
% 2.54/1.50 ord_less_nat @ occM @ ( size_s1406904903t_unit @ ( fe @ index ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_3__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062,axiom,
% 2.54/1.50 ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_4_NotEmpty_I2_J,axiom,
% 2.54/1.50 ( ( fe @ index )
% 2.54/1.50 != nil_co1338500125t_unit ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_5_AssumptionFair_I2_J,axiom,
% 2.54/1.50 ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_6_one__natural_Orsp,axiom,
% 2.54/1.50 one_one_nat = one_one_nat ).
% 2.54/1.50
% 2.54/1.50 thf(fact_7_diff__commute,axiom,
% 2.54/1.50 ! [I: nat,J: nat,K: nat] :
% 2.54/1.50 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 2.54/1.50 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_8_Ex__list__of__length,axiom,
% 2.54/1.50 ! [N: nat] :
% 2.54/1.50 ? [Xs: list_c1059388851t_unit] :
% 2.54/1.50 ( ( size_s1406904903t_unit @ Xs )
% 2.54/1.50 = N ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_9_Ex__list__of__length,axiom,
% 2.54/1.50 ! [N: nat] :
% 2.54/1.50 ? [Xs: list_message_p_v] :
% 2.54/1.50 ( ( size_s1168481041ge_p_v @ Xs )
% 2.54/1.50 = N ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_10_neq__if__length__neq,axiom,
% 2.54/1.50 ! [Xs2: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 2.54/1.50 ( ( ( size_s1406904903t_unit @ Xs2 )
% 2.54/1.50 != ( size_s1406904903t_unit @ Ys ) )
% 2.54/1.50 => ( Xs2 != Ys ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_11_neq__if__length__neq,axiom,
% 2.54/1.50 ! [Xs2: list_message_p_v,Ys: list_message_p_v] :
% 2.54/1.50 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 2.54/1.50 != ( size_s1168481041ge_p_v @ Ys ) )
% 2.54/1.50 => ( Xs2 != Ys ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_12_size__neq__size__imp__neq,axiom,
% 2.54/1.50 ! [X: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 2.54/1.50 ( ( ( size_s1406904903t_unit @ X )
% 2.54/1.50 != ( size_s1406904903t_unit @ Y ) )
% 2.54/1.50 => ( X != Y ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_13_size__neq__size__imp__neq,axiom,
% 2.54/1.50 ! [X: list_message_p_v,Y: list_message_p_v] :
% 2.54/1.50 ( ( ( size_s1168481041ge_p_v @ X )
% 2.54/1.50 != ( size_s1168481041ge_p_v @ Y ) )
% 2.54/1.50 => ( X != Y ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_14_nat_Oinject,axiom,
% 2.54/1.50 ! [X2: nat,Y2: nat] :
% 2.54/1.50 ( ( ( suc @ X2 )
% 2.54/1.50 = ( suc @ Y2 ) )
% 2.54/1.50 = ( X2 = Y2 ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_15_old_Onat_Oinject,axiom,
% 2.54/1.50 ! [Nat: nat,Nat2: nat] :
% 2.54/1.50 ( ( ( suc @ Nat )
% 2.54/1.50 = ( suc @ Nat2 ) )
% 2.54/1.50 = ( Nat = Nat2 ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_16_NotEmpty_I1_J,axiom,
% 2.54/1.50 ( ( fe @ ( suc @ index ) )
% 2.54/1.50 != nil_co1338500125t_unit ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_17_lessI,axiom,
% 2.54/1.50 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_18_Suc__mono,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_nat @ M @ N )
% 2.54/1.50 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_19_Suc__less__eq,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 2.54/1.50 = ( ord_less_nat @ M @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_20_Suc__le__mono,axiom,
% 2.54/1.50 ! [N: nat,M: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 2.54/1.50 = ( ord_less_eq_nat @ N @ M ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_21_Suc__diff__diff,axiom,
% 2.54/1.50 ! [M: nat,N: nat,K: nat] :
% 2.54/1.50 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 2.54/1.50 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_22_diff__Suc__Suc,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 2.54/1.50 = ( minus_minus_nat @ M @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_23_diff__diff__cancel,axiom,
% 2.54/1.50 ! [I: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ I @ N )
% 2.54/1.50 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 2.54/1.50 = I ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_24_diff__Suc__1,axiom,
% 2.54/1.50 ! [N: nat] :
% 2.54/1.50 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 2.54/1.50 = N ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_25_Nat_OlessE,axiom,
% 2.54/1.50 ! [I: nat,K: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I @ K )
% 2.54/1.50 => ( ( K
% 2.54/1.50 != ( suc @ I ) )
% 2.54/1.50 => ~ ! [J2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I @ J2 )
% 2.54/1.50 => ( K
% 2.54/1.50 != ( suc @ J2 ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_26_Suc__leD,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 2.54/1.50 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_27_Suc__leI,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_nat @ M @ N )
% 2.54/1.50 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_28_le__SucE,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 2.54/1.50 => ( ~ ( ord_less_eq_nat @ M @ N )
% 2.54/1.50 => ( M
% 2.54/1.50 = ( suc @ N ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_29_le__SucI,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.54/1.50 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_30_le__refl,axiom,
% 2.54/1.50 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_31_Suc__le__D,axiom,
% 2.54/1.50 ! [N: nat,M2: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ ( suc @ N ) @ M2 )
% 2.54/1.50 => ? [M3: nat] :
% 2.54/1.50 ( M2
% 2.54/1.50 = ( suc @ M3 ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_32_le__trans,axiom,
% 2.54/1.50 ! [I: nat,J: nat,K: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.54/1.50 => ( ( ord_less_eq_nat @ J @ K )
% 2.54/1.50 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_33_Suc__le__eq,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 2.54/1.50 = ( ord_less_nat @ M @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_34_Suc__lessD,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 2.54/1.50 => ( ord_less_nat @ M @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_35_Suc__lessE,axiom,
% 2.54/1.50 ! [I: nat,K: nat] :
% 2.54/1.50 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 2.54/1.50 => ~ ! [J2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I @ J2 )
% 2.54/1.50 => ( K
% 2.54/1.50 != ( suc @ J2 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_36_Suc__lessI,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_nat @ M @ N )
% 2.54/1.50 => ( ( ( suc @ M )
% 2.54/1.50 != N )
% 2.54/1.50 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_37_eq__imp__le,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( M = N )
% 2.54/1.50 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_38_le__Suc__eq,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 2.54/1.50 = ( ( ord_less_eq_nat @ M @ N )
% 2.54/1.50 | ( M
% 2.54/1.50 = ( suc @ N ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_39_less__SucE,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 2.54/1.50 => ( ~ ( ord_less_nat @ M @ N )
% 2.54/1.50 => ( M = N ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_40_less__SucI,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_nat @ M @ N )
% 2.54/1.50 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_41_Suc__inject,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ( suc @ X )
% 2.54/1.50 = ( suc @ Y ) )
% 2.54/1.50 => ( X = Y ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_42_dec__induct,axiom,
% 2.54/1.50 ! [I: nat,J: nat,P: nat > $o] :
% 2.54/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.54/1.50 => ( ( P @ I )
% 2.54/1.50 => ( ! [N2: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ I @ N2 )
% 2.54/1.50 => ( ( ord_less_nat @ N2 @ J )
% 2.54/1.50 => ( ( P @ N2 )
% 2.54/1.50 => ( P @ ( suc @ N2 ) ) ) ) )
% 2.54/1.50 => ( P @ J ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_43_mem__Collect__eq,axiom,
% 2.54/1.50 ! [A: message_p_v,P: message_p_v > $o] :
% 2.54/1.50 ( ( member_message_p_v @ A @ ( collect_message_p_v @ P ) )
% 2.54/1.50 = ( P @ A ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_44_Collect__mem__eq,axiom,
% 2.54/1.50 ! [A2: set_message_p_v] :
% 2.54/1.50 ( ( collect_message_p_v
% 2.54/1.50 @ ^ [X3: message_p_v] : ( member_message_p_v @ X3 @ A2 ) )
% 2.54/1.50 = A2 ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_45_Collect__cong,axiom,
% 2.54/1.50 ! [P: message_p_v > $o,Q: message_p_v > $o] :
% 2.54/1.50 ( ! [X4: message_p_v] :
% 2.54/1.50 ( ( P @ X4 )
% 2.54/1.50 = ( Q @ X4 ) )
% 2.54/1.50 => ( ( collect_message_p_v @ P )
% 2.54/1.50 = ( collect_message_p_v @ Q ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_46_inc__induct,axiom,
% 2.54/1.50 ! [I: nat,J: nat,P: nat > $o] :
% 2.54/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.54/1.50 => ( ( P @ J )
% 2.54/1.50 => ( ! [N2: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ I @ N2 )
% 2.54/1.50 => ( ( ord_less_nat @ N2 @ J )
% 2.54/1.50 => ( ( P @ ( suc @ N2 ) )
% 2.54/1.50 => ( P @ N2 ) ) ) )
% 2.54/1.50 => ( P @ I ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_47_le__antisym,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.54/1.50 => ( ( ord_less_eq_nat @ N @ M )
% 2.54/1.50 => ( M = N ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_48_Ex__less__Suc,axiom,
% 2.54/1.50 ! [N: nat,P: nat > $o] :
% 2.54/1.50 ( ( ? [I2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 2.54/1.50 & ( P @ I2 ) ) )
% 2.54/1.50 = ( ( P @ N )
% 2.54/1.50 | ? [I2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I2 @ N )
% 2.54/1.50 & ( P @ I2 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_49_less__Suc__eq,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 2.54/1.50 = ( ( ord_less_nat @ M @ N )
% 2.54/1.50 | ( M = N ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_50_n__not__Suc__n,axiom,
% 2.54/1.50 ! [N: nat] :
% 2.54/1.50 ( N
% 2.54/1.50 != ( suc @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_51_nat__less__le,axiom,
% 2.54/1.50 ( ord_less_nat
% 2.54/1.50 = ( ^ [M4: nat,N3: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ M4 @ N3 )
% 2.54/1.50 & ( M4 != N3 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_52_nat__neq__iff,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( M != N )
% 2.54/1.50 = ( ( ord_less_nat @ M @ N )
% 2.54/1.50 | ( ord_less_nat @ N @ M ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_53_not__less__eq,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ~ ( ord_less_nat @ M @ N ) )
% 2.54/1.50 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_54_All__less__Suc,axiom,
% 2.54/1.50 ! [N: nat,P: nat > $o] :
% 2.54/1.50 ( ( ! [I2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 2.54/1.50 => ( P @ I2 ) ) )
% 2.54/1.50 = ( ( P @ N )
% 2.54/1.50 & ! [I2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I2 @ N )
% 2.54/1.50 => ( P @ I2 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_55_Suc__le__lessD,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 2.54/1.50 => ( ord_less_nat @ M @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_56_Suc__less__eq2,axiom,
% 2.54/1.50 ! [N: nat,M: nat] :
% 2.54/1.50 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 2.54/1.50 = ( ? [M5: nat] :
% 2.54/1.50 ( ( M
% 2.54/1.50 = ( suc @ M5 ) )
% 2.54/1.50 & ( ord_less_nat @ N @ M5 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_57_less__antisym,axiom,
% 2.54/1.50 ! [N: nat,M: nat] :
% 2.54/1.50 ( ~ ( ord_less_nat @ N @ M )
% 2.54/1.50 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 2.54/1.50 => ( M = N ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_58_Suc__less__SucD,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 2.54/1.50 => ( ord_less_nat @ M @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_59_less__not__refl,axiom,
% 2.54/1.50 ! [N: nat] :
% 2.54/1.50 ~ ( ord_less_nat @ N @ N ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_60_nat__le__linear,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.54/1.50 | ( ord_less_eq_nat @ N @ M ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_61_Suc__n__not__le__n,axiom,
% 2.54/1.50 ! [N: nat] :
% 2.54/1.50 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_62_le__less__Suc__eq,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.54/1.50 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 2.54/1.50 = ( N = M ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_63_less__Suc__eq__le,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 2.54/1.50 = ( ord_less_eq_nat @ M @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_64_less__eq__Suc__le,axiom,
% 2.54/1.50 ( ord_less_nat
% 2.54/1.50 = ( ^ [N3: nat] : ( ord_less_eq_nat @ ( suc @ N3 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_65_less__not__refl2,axiom,
% 2.54/1.50 ! [N: nat,M: nat] :
% 2.54/1.50 ( ( ord_less_nat @ N @ M )
% 2.54/1.50 => ( M != N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_66_less__not__refl3,axiom,
% 2.54/1.50 ! [S: nat,T: nat] :
% 2.54/1.50 ( ( ord_less_nat @ S @ T )
% 2.54/1.50 => ( S != T ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_67_less__trans__Suc,axiom,
% 2.54/1.50 ! [I: nat,J: nat,K: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I @ J )
% 2.54/1.50 => ( ( ord_less_nat @ J @ K )
% 2.54/1.50 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_68_not__less__eq__eq,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 2.54/1.50 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_69_full__nat__induct,axiom,
% 2.54/1.50 ! [P: nat > $o,N: nat] :
% 2.54/1.50 ( ! [N2: nat] :
% 2.54/1.50 ( ! [M6: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ ( suc @ M6 ) @ N2 )
% 2.54/1.50 => ( P @ M6 ) )
% 2.54/1.50 => ( P @ N2 ) )
% 2.54/1.50 => ( P @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_70_le__imp__less__Suc,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.54/1.50 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_71_less__Suc__induct,axiom,
% 2.54/1.50 ! [I: nat,J: nat,P: nat > nat > $o] :
% 2.54/1.50 ( ( ord_less_nat @ I @ J )
% 2.54/1.50 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 2.54/1.50 => ( ! [I3: nat,J2: nat,K2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I3 @ J2 )
% 2.54/1.50 => ( ( ord_less_nat @ J2 @ K2 )
% 2.54/1.50 => ( ( P @ I3 @ J2 )
% 2.54/1.50 => ( ( P @ J2 @ K2 )
% 2.54/1.50 => ( P @ I3 @ K2 ) ) ) ) )
% 2.54/1.50 => ( P @ I @ J ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_72_less__imp__le__nat,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_nat @ M @ N )
% 2.54/1.50 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_73_less__irrefl__nat,axiom,
% 2.54/1.50 ! [N: nat] :
% 2.54/1.50 ~ ( ord_less_nat @ N @ N ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_74_nat__less__induct,axiom,
% 2.54/1.50 ! [P: nat > $o,N: nat] :
% 2.54/1.50 ( ! [N2: nat] :
% 2.54/1.50 ( ! [M6: nat] :
% 2.54/1.50 ( ( ord_less_nat @ M6 @ N2 )
% 2.54/1.50 => ( P @ M6 ) )
% 2.54/1.50 => ( P @ N2 ) )
% 2.54/1.50 => ( P @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_75_infinite__descent,axiom,
% 2.54/1.50 ! [P: nat > $o,N: nat] :
% 2.54/1.50 ( ! [N2: nat] :
% 2.54/1.50 ( ~ ( P @ N2 )
% 2.54/1.50 => ? [M6: nat] :
% 2.54/1.50 ( ( ord_less_nat @ M6 @ N2 )
% 2.54/1.50 & ~ ( P @ M6 ) ) )
% 2.54/1.50 => ( P @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_76_le__eq__less__or__eq,axiom,
% 2.54/1.50 ( ord_less_eq_nat
% 2.54/1.50 = ( ^ [M4: nat,N3: nat] :
% 2.54/1.50 ( ( ord_less_nat @ M4 @ N3 )
% 2.54/1.50 | ( M4 = N3 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_77_less__or__eq__imp__le,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ( ord_less_nat @ M @ N )
% 2.54/1.50 | ( M = N ) )
% 2.54/1.50 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_78_linorder__neqE__nat,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( X != Y )
% 2.54/1.50 => ( ~ ( ord_less_nat @ X @ Y )
% 2.54/1.50 => ( ord_less_nat @ Y @ X ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_79_strict__inc__induct,axiom,
% 2.54/1.50 ! [I: nat,J: nat,P: nat > $o] :
% 2.54/1.50 ( ( ord_less_nat @ I @ J )
% 2.54/1.50 => ( ! [I3: nat] :
% 2.54/1.50 ( ( J
% 2.54/1.50 = ( suc @ I3 ) )
% 2.54/1.50 => ( P @ I3 ) )
% 2.54/1.50 => ( ! [I3: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I3 @ J )
% 2.54/1.50 => ( ( P @ ( suc @ I3 ) )
% 2.54/1.50 => ( P @ I3 ) ) )
% 2.54/1.50 => ( P @ I ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_80_Nat_Oex__has__greatest__nat,axiom,
% 2.54/1.50 ! [P: nat > $o,K: nat,B: nat] :
% 2.54/1.50 ( ( P @ K )
% 2.54/1.50 => ( ! [Y3: nat] :
% 2.54/1.50 ( ( P @ Y3 )
% 2.54/1.50 => ( ord_less_eq_nat @ Y3 @ B ) )
% 2.54/1.50 => ? [X4: nat] :
% 2.54/1.50 ( ( P @ X4 )
% 2.54/1.50 & ! [Y4: nat] :
% 2.54/1.50 ( ( P @ Y4 )
% 2.54/1.50 => ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_81_le__neq__implies__less,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.54/1.50 => ( ( M != N )
% 2.54/1.50 => ( ord_less_nat @ M @ N ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_82_nat__induct__at__least,axiom,
% 2.54/1.50 ! [M: nat,N: nat,P: nat > $o] :
% 2.54/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.54/1.50 => ( ( P @ M )
% 2.54/1.50 => ( ! [N2: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ M @ N2 )
% 2.54/1.50 => ( ( P @ N2 )
% 2.54/1.50 => ( P @ ( suc @ N2 ) ) ) )
% 2.54/1.50 => ( P @ N ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_83_not__less__less__Suc__eq,axiom,
% 2.54/1.50 ! [N: nat,M: nat] :
% 2.54/1.50 ( ~ ( ord_less_nat @ N @ M )
% 2.54/1.50 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 2.54/1.50 = ( N = M ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_84_less__mono__imp__le__mono,axiom,
% 2.54/1.50 ! [F: nat > nat,I: nat,J: nat] :
% 2.54/1.50 ( ! [I3: nat,J2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I3 @ J2 )
% 2.54/1.50 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 2.54/1.50 => ( ( ord_less_eq_nat @ I @ J )
% 2.54/1.50 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_85_transitive__stepwise__le,axiom,
% 2.54/1.50 ! [M: nat,N: nat,R: nat > nat > $o] :
% 2.54/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.54/1.50 => ( ! [X4: nat] : ( R @ X4 @ X4 )
% 2.54/1.50 => ( ! [X4: nat,Y3: nat,Z: nat] :
% 2.54/1.50 ( ( R @ X4 @ Y3 )
% 2.54/1.50 => ( ( R @ Y3 @ Z )
% 2.54/1.50 => ( R @ X4 @ Z ) ) )
% 2.54/1.50 => ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
% 2.54/1.50 => ( R @ M @ N ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_86_lift__Suc__mono__le,axiom,
% 2.54/1.50 ! [F: nat > nat,N: nat,N4: nat] :
% 2.54/1.50 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 2.54/1.50 => ( ( ord_less_eq_nat @ N @ N4 )
% 2.54/1.50 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_87_lift__Suc__mono__less,axiom,
% 2.54/1.50 ! [F: nat > nat,N: nat,N4: nat] :
% 2.54/1.50 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 2.54/1.50 => ( ( ord_less_nat @ N @ N4 )
% 2.54/1.50 => ( ord_less_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_88_lift__Suc__antimono__le,axiom,
% 2.54/1.50 ! [F: nat > nat,N: nat,N4: nat] :
% 2.54/1.50 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 2.54/1.50 => ( ( ord_less_eq_nat @ N @ N4 )
% 2.54/1.50 => ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_89_lift__Suc__mono__less__iff,axiom,
% 2.54/1.50 ! [F: nat > nat,N: nat,M: nat] :
% 2.54/1.50 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 2.54/1.50 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 2.54/1.50 = ( ord_less_nat @ N @ M ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_90_diff__less__Suc,axiom,
% 2.54/1.50 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_91_Suc__diff__Suc,axiom,
% 2.54/1.50 ! [N: nat,M: nat] :
% 2.54/1.50 ( ( ord_less_nat @ N @ M )
% 2.54/1.50 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 2.54/1.50 = ( minus_minus_nat @ M @ N ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_92_Suc__diff__le,axiom,
% 2.54/1.50 ! [N: nat,M: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ N @ M )
% 2.54/1.50 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 2.54/1.50 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_93_zero__induct__lemma,axiom,
% 2.54/1.50 ! [P: nat > $o,K: nat,I: nat] :
% 2.54/1.50 ( ( P @ K )
% 2.54/1.50 => ( ! [N2: nat] :
% 2.54/1.50 ( ( P @ ( suc @ N2 ) )
% 2.54/1.50 => ( P @ N2 ) )
% 2.54/1.50 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_94_diff__less__mono,axiom,
% 2.54/1.50 ! [A: nat,B: nat,C: nat] :
% 2.54/1.50 ( ( ord_less_nat @ A @ B )
% 2.54/1.50 => ( ( ord_less_eq_nat @ C @ A )
% 2.54/1.50 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_95_less__diff__iff,axiom,
% 2.54/1.50 ! [K: nat,M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ K @ M )
% 2.54/1.50 => ( ( ord_less_eq_nat @ K @ N )
% 2.54/1.50 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 2.54/1.50 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_96_diff__Suc__eq__diff__pred,axiom,
% 2.54/1.50 ! [M: nat,N: nat] :
% 2.54/1.50 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 2.54/1.50 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_97_length__induct,axiom,
% 2.54/1.50 ! [P: list_c1059388851t_unit > $o,Xs2: list_c1059388851t_unit] :
% 2.54/1.50 ( ! [Xs: list_c1059388851t_unit] :
% 2.54/1.50 ( ! [Ys2: list_c1059388851t_unit] :
% 2.54/1.50 ( ( ord_less_nat @ ( size_s1406904903t_unit @ Ys2 ) @ ( size_s1406904903t_unit @ Xs ) )
% 2.54/1.50 => ( P @ Ys2 ) )
% 2.54/1.50 => ( P @ Xs ) )
% 2.54/1.50 => ( P @ Xs2 ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_98_length__induct,axiom,
% 2.54/1.50 ! [P: list_message_p_v > $o,Xs2: list_message_p_v] :
% 2.54/1.50 ( ! [Xs: list_message_p_v] :
% 2.54/1.50 ( ! [Ys2: list_message_p_v] :
% 2.54/1.50 ( ( ord_less_nat @ ( size_s1168481041ge_p_v @ Ys2 ) @ ( size_s1168481041ge_p_v @ Xs ) )
% 2.54/1.50 => ( P @ Ys2 ) )
% 2.54/1.50 => ( P @ Xs ) )
% 2.54/1.50 => ( P @ Xs2 ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_99_less__imp__diff__less,axiom,
% 2.54/1.50 ! [J: nat,K: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_nat @ J @ K )
% 2.54/1.50 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_100_diff__less__mono2,axiom,
% 2.54/1.50 ! [M: nat,N: nat,L: nat] :
% 2.54/1.50 ( ( ord_less_nat @ M @ N )
% 2.54/1.50 => ( ( ord_less_nat @ M @ L )
% 2.54/1.50 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_101_diff__le__mono2,axiom,
% 2.54/1.50 ! [M: nat,N: nat,L: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.54/1.50 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_102_le__diff__iff_H,axiom,
% 2.54/1.50 ! [A: nat,C: nat,B: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ A @ C )
% 2.54/1.50 => ( ( ord_less_eq_nat @ B @ C )
% 2.54/1.50 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 2.54/1.50 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_103_diff__le__self,axiom,
% 2.54/1.50 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_104_diff__le__mono,axiom,
% 2.54/1.50 ! [M: nat,N: nat,L: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.54/1.50 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_105_Nat_Odiff__diff__eq,axiom,
% 2.54/1.50 ! [K: nat,M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ K @ M )
% 2.54/1.50 => ( ( ord_less_eq_nat @ K @ N )
% 2.54/1.50 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 2.54/1.50 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_106_le__diff__iff,axiom,
% 2.54/1.50 ! [K: nat,M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ K @ M )
% 2.54/1.50 => ( ( ord_less_eq_nat @ K @ N )
% 2.54/1.50 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 2.54/1.50 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_107_eq__diff__iff,axiom,
% 2.54/1.50 ! [K: nat,M: nat,N: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ K @ M )
% 2.54/1.50 => ( ( ord_less_eq_nat @ K @ N )
% 2.54/1.50 => ( ( ( minus_minus_nat @ M @ K )
% 2.54/1.50 = ( minus_minus_nat @ N @ K ) )
% 2.54/1.50 = ( M = N ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_108_one__reorient,axiom,
% 2.54/1.50 ! [X: nat] :
% 2.54/1.50 ( ( one_one_nat = X )
% 2.54/1.50 = ( X = one_one_nat ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_109_diff__right__commute,axiom,
% 2.54/1.50 ! [A: nat,C: nat,B: nat] :
% 2.54/1.50 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 2.54/1.50 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_110_Subset,axiom,
% 2.54/1.50 ! [MsgInSet: message_p_v] :
% 2.54/1.50 ( ( member_message_p_v @ MsgInSet @ ( firstOccSet @ ( suc @ index ) ) )
% 2.54/1.50 => ( member_message_p_v @ MsgInSet @ ( firstOccSet @ index ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_111_SameCfgOnLow,axiom,
% 2.54/1.50 ! [I4: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I4 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
% 2.54/1.50 => ( ( nth_co1649820636t_unit @ ( fe @ index ) @ I4 )
% 2.54/1.50 = ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ I4 ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_112__092_060open_062_092_060not_062_AOccM_A_060_Alength_A_Ift_Aindex_J_092_060close_062,axiom,
% 2.54/1.50 ~ ( ord_less_nat @ occM2 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_113_IPrefixListEx,axiom,
% 2.54/1.50 ! [I4: nat] : ( prefix1615116500t_unit @ ( fe @ I4 ) @ ( fe @ ( suc @ I4 ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_114_order__refl,axiom,
% 2.54/1.50 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_115_nat__descend__induct,axiom,
% 2.54/1.50 ! [N: nat,P: nat > $o,M: nat] :
% 2.54/1.50 ( ! [K2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ N @ K2 )
% 2.54/1.50 => ( P @ K2 ) )
% 2.54/1.50 => ( ! [K2: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ K2 @ N )
% 2.54/1.50 => ( ! [I4: nat] :
% 2.54/1.50 ( ( ord_less_nat @ K2 @ I4 )
% 2.54/1.50 => ( P @ I4 ) )
% 2.54/1.50 => ( P @ K2 ) ) )
% 2.54/1.50 => ( P @ M ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_116_KeepProperty,axiom,
% 2.54/1.50 ! [Low: nat,P: nat > $o,Q: nat > $o] :
% 2.54/1.50 ( ! [I3: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ Low @ I3 )
% 2.54/1.50 => ( ( P @ I3 )
% 2.54/1.50 => ( ( P @ ( suc @ I3 ) )
% 2.54/1.50 & ( Q @ I3 ) ) ) )
% 2.54/1.50 => ( ( P @ Low )
% 2.54/1.50 => ! [I4: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ Low @ I4 )
% 2.54/1.50 => ( Q @ I4 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_117_less__numeral__extra_I4_J,axiom,
% 2.54/1.50 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_118_le__numeral__extra_I4_J,axiom,
% 2.54/1.50 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 2.54/1.50
% 2.54/1.50 thf(fact_119_LengthStep,axiom,
% 2.54/1.50 ord_less_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_120_ConsumedMsg_I1_J,axiom,
% 2.54/1.50 minimalEnabled_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ consumedMsg ).
% 2.54/1.50
% 2.54/1.50 thf(fact_121_PrefixListTransitive,axiom,
% 2.54/1.50 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit,L3: list_c1059388851t_unit] :
% 2.54/1.50 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 2.54/1.50 => ( ( prefix1615116500t_unit @ L2 @ L3 )
% 2.54/1.50 => ( prefix1615116500t_unit @ L1 @ L3 ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_122_PrefixListTransitive,axiom,
% 2.54/1.50 ! [L1: list_message_p_v,L2: list_message_p_v,L3: list_message_p_v] :
% 2.54/1.50 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 2.54/1.50 => ( ( prefix47729710ge_p_v @ L2 @ L3 )
% 2.54/1.50 => ( prefix47729710ge_p_v @ L1 @ L3 ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_123_PrefixSameOnLow,axiom,
% 2.54/1.50 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 2.54/1.50 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 2.54/1.50 => ! [Index: nat] :
% 2.54/1.50 ( ( ord_less_nat @ Index @ ( size_s1406904903t_unit @ L1 ) )
% 2.54/1.50 => ( ( nth_co1649820636t_unit @ L1 @ Index )
% 2.54/1.50 = ( nth_co1649820636t_unit @ L2 @ Index ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_124_PrefixSameOnLow,axiom,
% 2.54/1.50 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 2.54/1.50 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 2.54/1.50 => ! [Index: nat] :
% 2.54/1.50 ( ( ord_less_nat @ Index @ ( size_s1168481041ge_p_v @ L1 ) )
% 2.54/1.50 => ( ( nth_message_p_v @ L1 @ Index )
% 2.54/1.50 = ( nth_message_p_v @ L2 @ Index ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_125_PrefixListMonotonicity,axiom,
% 2.54/1.50 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 2.54/1.50 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 2.54/1.50 => ( ord_less_nat @ ( size_s1406904903t_unit @ L1 ) @ ( size_s1406904903t_unit @ L2 ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_126_PrefixListMonotonicity,axiom,
% 2.54/1.50 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 2.54/1.50 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 2.54/1.50 => ( ord_less_nat @ ( size_s1168481041ge_p_v @ L1 ) @ ( size_s1168481041ge_p_v @ L2 ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_127_nth__equalityI,axiom,
% 2.54/1.50 ! [Xs2: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 2.54/1.50 ( ( ( size_s1406904903t_unit @ Xs2 )
% 2.54/1.50 = ( size_s1406904903t_unit @ Ys ) )
% 2.54/1.50 => ( ! [I3: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I3 @ ( size_s1406904903t_unit @ Xs2 ) )
% 2.54/1.50 => ( ( nth_co1649820636t_unit @ Xs2 @ I3 )
% 2.54/1.50 = ( nth_co1649820636t_unit @ Ys @ I3 ) ) )
% 2.54/1.50 => ( Xs2 = Ys ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_128_nth__equalityI,axiom,
% 2.54/1.50 ! [Xs2: list_message_p_v,Ys: list_message_p_v] :
% 2.54/1.50 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 2.54/1.50 = ( size_s1168481041ge_p_v @ Ys ) )
% 2.54/1.50 => ( ! [I3: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I3 @ ( size_s1168481041ge_p_v @ Xs2 ) )
% 2.54/1.50 => ( ( nth_message_p_v @ Xs2 @ I3 )
% 2.54/1.50 = ( nth_message_p_v @ Ys @ I3 ) ) )
% 2.54/1.50 => ( Xs2 = Ys ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_129_Skolem__list__nth,axiom,
% 2.54/1.50 ! [K: nat,P: nat > config256849571t_unit > $o] :
% 2.54/1.50 ( ( ! [I2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I2 @ K )
% 2.54/1.50 => ? [X5: config256849571t_unit] : ( P @ I2 @ X5 ) ) )
% 2.54/1.50 = ( ? [Xs3: list_c1059388851t_unit] :
% 2.54/1.50 ( ( ( size_s1406904903t_unit @ Xs3 )
% 2.54/1.50 = K )
% 2.54/1.50 & ! [I2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I2 @ K )
% 2.54/1.50 => ( P @ I2 @ ( nth_co1649820636t_unit @ Xs3 @ I2 ) ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_130_Skolem__list__nth,axiom,
% 2.54/1.50 ! [K: nat,P: nat > message_p_v > $o] :
% 2.54/1.50 ( ( ! [I2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I2 @ K )
% 2.54/1.50 => ? [X5: message_p_v] : ( P @ I2 @ X5 ) ) )
% 2.54/1.50 = ( ? [Xs3: list_message_p_v] :
% 2.54/1.50 ( ( ( size_s1168481041ge_p_v @ Xs3 )
% 2.54/1.50 = K )
% 2.54/1.50 & ! [I2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I2 @ K )
% 2.54/1.50 => ( P @ I2 @ ( nth_message_p_v @ Xs3 @ I2 ) ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_131_list__eq__iff__nth__eq,axiom,
% 2.54/1.50 ( ( ^ [Y5: list_c1059388851t_unit,Z2: list_c1059388851t_unit] : ( Y5 = Z2 ) )
% 2.54/1.50 = ( ^ [Xs3: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
% 2.54/1.50 ( ( ( size_s1406904903t_unit @ Xs3 )
% 2.54/1.50 = ( size_s1406904903t_unit @ Ys3 ) )
% 2.54/1.50 & ! [I2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I2 @ ( size_s1406904903t_unit @ Xs3 ) )
% 2.54/1.50 => ( ( nth_co1649820636t_unit @ Xs3 @ I2 )
% 2.54/1.50 = ( nth_co1649820636t_unit @ Ys3 @ I2 ) ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_132_list__eq__iff__nth__eq,axiom,
% 2.54/1.50 ( ( ^ [Y5: list_message_p_v,Z2: list_message_p_v] : ( Y5 = Z2 ) )
% 2.54/1.50 = ( ^ [Xs3: list_message_p_v,Ys3: list_message_p_v] :
% 2.54/1.50 ( ( ( size_s1168481041ge_p_v @ Xs3 )
% 2.54/1.50 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 2.54/1.50 & ! [I2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I2 @ ( size_s1168481041ge_p_v @ Xs3 ) )
% 2.54/1.50 => ( ( nth_message_p_v @ Xs3 @ I2 )
% 2.54/1.50 = ( nth_message_p_v @ Ys3 @ I2 ) ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_133_dual__order_Oantisym,axiom,
% 2.54/1.50 ! [B: nat,A: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ B @ A )
% 2.54/1.50 => ( ( ord_less_eq_nat @ A @ B )
% 2.54/1.50 => ( A = B ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_134_dual__order_Oeq__iff,axiom,
% 2.54/1.50 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 2.54/1.50 = ( ^ [A3: nat,B2: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ B2 @ A3 )
% 2.54/1.50 & ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_135_dual__order_Otrans,axiom,
% 2.54/1.50 ! [B: nat,A: nat,C: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ B @ A )
% 2.54/1.50 => ( ( ord_less_eq_nat @ C @ B )
% 2.54/1.50 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_136_linorder__wlog,axiom,
% 2.54/1.50 ! [P: nat > nat > $o,A: nat,B: nat] :
% 2.54/1.50 ( ! [A4: nat,B3: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ A4 @ B3 )
% 2.54/1.50 => ( P @ A4 @ B3 ) )
% 2.54/1.50 => ( ! [A4: nat,B3: nat] :
% 2.54/1.50 ( ( P @ B3 @ A4 )
% 2.54/1.50 => ( P @ A4 @ B3 ) )
% 2.54/1.50 => ( P @ A @ B ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_137_dual__order_Orefl,axiom,
% 2.54/1.50 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_138_order__trans,axiom,
% 2.54/1.50 ! [X: nat,Y: nat,Z3: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X @ Y )
% 2.54/1.50 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 2.54/1.50 => ( ord_less_eq_nat @ X @ Z3 ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_139_order__class_Oorder_Oantisym,axiom,
% 2.54/1.50 ! [A: nat,B: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.54/1.50 => ( ( ord_less_eq_nat @ B @ A )
% 2.54/1.50 => ( A = B ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_140_ord__le__eq__trans,axiom,
% 2.54/1.50 ! [A: nat,B: nat,C: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.54/1.50 => ( ( B = C )
% 2.54/1.50 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_141_ord__eq__le__trans,axiom,
% 2.54/1.50 ! [A: nat,B: nat,C: nat] :
% 2.54/1.50 ( ( A = B )
% 2.54/1.50 => ( ( ord_less_eq_nat @ B @ C )
% 2.54/1.50 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_142_order__class_Oorder_Oeq__iff,axiom,
% 2.54/1.50 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 2.54/1.50 = ( ^ [A3: nat,B2: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ A3 @ B2 )
% 2.54/1.50 & ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_143_antisym__conv,axiom,
% 2.54/1.50 ! [Y: nat,X: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ Y @ X )
% 2.54/1.50 => ( ( ord_less_eq_nat @ X @ Y )
% 2.54/1.50 = ( X = Y ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_144_le__cases3,axiom,
% 2.54/1.50 ! [X: nat,Y: nat,Z3: nat] :
% 2.54/1.50 ( ( ( ord_less_eq_nat @ X @ Y )
% 2.54/1.50 => ~ ( ord_less_eq_nat @ Y @ Z3 ) )
% 2.54/1.50 => ( ( ( ord_less_eq_nat @ Y @ X )
% 2.54/1.50 => ~ ( ord_less_eq_nat @ X @ Z3 ) )
% 2.54/1.50 => ( ( ( ord_less_eq_nat @ X @ Z3 )
% 2.54/1.50 => ~ ( ord_less_eq_nat @ Z3 @ Y ) )
% 2.54/1.50 => ( ( ( ord_less_eq_nat @ Z3 @ Y )
% 2.54/1.50 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 2.54/1.50 => ( ( ( ord_less_eq_nat @ Y @ Z3 )
% 2.54/1.50 => ~ ( ord_less_eq_nat @ Z3 @ X ) )
% 2.54/1.50 => ~ ( ( ord_less_eq_nat @ Z3 @ X )
% 2.54/1.50 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_145_order_Otrans,axiom,
% 2.54/1.50 ! [A: nat,B: nat,C: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.54/1.50 => ( ( ord_less_eq_nat @ B @ C )
% 2.54/1.50 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_146_le__cases,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ~ ( ord_less_eq_nat @ X @ Y )
% 2.54/1.50 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_147_eq__refl,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( X = Y )
% 2.54/1.50 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_148_linear,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X @ Y )
% 2.54/1.50 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_149_antisym,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X @ Y )
% 2.54/1.50 => ( ( ord_less_eq_nat @ Y @ X )
% 2.54/1.50 => ( X = Y ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_150_eq__iff,axiom,
% 2.54/1.50 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 2.54/1.50 = ( ^ [X3: nat,Y6: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X3 @ Y6 )
% 2.54/1.50 & ( ord_less_eq_nat @ Y6 @ X3 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_151_ord__le__eq__subst,axiom,
% 2.54/1.50 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.54/1.50 => ( ( ( F @ B )
% 2.54/1.50 = C )
% 2.54/1.50 => ( ! [X4: nat,Y3: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 2.54/1.50 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.54/1.50 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_152_ord__eq__le__subst,axiom,
% 2.54/1.50 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.54/1.50 ( ( A
% 2.54/1.50 = ( F @ B ) )
% 2.54/1.50 => ( ( ord_less_eq_nat @ B @ C )
% 2.54/1.50 => ( ! [X4: nat,Y3: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 2.54/1.50 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.54/1.50 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_153_order__subst2,axiom,
% 2.54/1.50 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.54/1.50 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 2.54/1.50 => ( ! [X4: nat,Y3: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 2.54/1.50 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.54/1.50 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_154_order__subst1,axiom,
% 2.54/1.50 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 2.54/1.50 => ( ( ord_less_eq_nat @ B @ C )
% 2.54/1.50 => ( ! [X4: nat,Y3: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 2.54/1.50 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.54/1.50 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_155_dual__order_Ostrict__implies__not__eq,axiom,
% 2.54/1.50 ! [B: nat,A: nat] :
% 2.54/1.50 ( ( ord_less_nat @ B @ A )
% 2.54/1.50 => ( A != B ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_156_order_Ostrict__implies__not__eq,axiom,
% 2.54/1.50 ! [A: nat,B: nat] :
% 2.54/1.50 ( ( ord_less_nat @ A @ B )
% 2.54/1.50 => ( A != B ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_157_not__less__iff__gr__or__eq,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 2.54/1.50 = ( ( ord_less_nat @ Y @ X )
% 2.54/1.50 | ( X = Y ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_158_dual__order_Ostrict__trans,axiom,
% 2.54/1.50 ! [B: nat,A: nat,C: nat] :
% 2.54/1.50 ( ( ord_less_nat @ B @ A )
% 2.54/1.50 => ( ( ord_less_nat @ C @ B )
% 2.54/1.50 => ( ord_less_nat @ C @ A ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_159_linorder__less__wlog,axiom,
% 2.54/1.50 ! [P: nat > nat > $o,A: nat,B: nat] :
% 2.54/1.50 ( ! [A4: nat,B3: nat] :
% 2.54/1.50 ( ( ord_less_nat @ A4 @ B3 )
% 2.54/1.50 => ( P @ A4 @ B3 ) )
% 2.54/1.50 => ( ! [A4: nat] : ( P @ A4 @ A4 )
% 2.54/1.50 => ( ! [A4: nat,B3: nat] :
% 2.54/1.50 ( ( P @ B3 @ A4 )
% 2.54/1.50 => ( P @ A4 @ B3 ) )
% 2.54/1.50 => ( P @ A @ B ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_160_exists__least__iff,axiom,
% 2.54/1.50 ( ( ^ [P2: nat > $o] :
% 2.54/1.50 ? [X5: nat] : ( P2 @ X5 ) )
% 2.54/1.50 = ( ^ [P3: nat > $o] :
% 2.54/1.50 ? [N3: nat] :
% 2.54/1.50 ( ( P3 @ N3 )
% 2.54/1.50 & ! [M4: nat] :
% 2.54/1.50 ( ( ord_less_nat @ M4 @ N3 )
% 2.54/1.50 => ~ ( P3 @ M4 ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_161_less__imp__not__less,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X @ Y )
% 2.54/1.50 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_162_order_Ostrict__trans,axiom,
% 2.54/1.50 ! [A: nat,B: nat,C: nat] :
% 2.54/1.50 ( ( ord_less_nat @ A @ B )
% 2.54/1.50 => ( ( ord_less_nat @ B @ C )
% 2.54/1.50 => ( ord_less_nat @ A @ C ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_163_dual__order_Oirrefl,axiom,
% 2.54/1.50 ! [A: nat] :
% 2.54/1.50 ~ ( ord_less_nat @ A @ A ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_164_linorder__cases,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ~ ( ord_less_nat @ X @ Y )
% 2.54/1.50 => ( ( X != Y )
% 2.54/1.50 => ( ord_less_nat @ Y @ X ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_165_less__imp__triv,axiom,
% 2.54/1.50 ! [X: nat,Y: nat,P: $o] :
% 2.54/1.50 ( ( ord_less_nat @ X @ Y )
% 2.54/1.50 => ( ( ord_less_nat @ Y @ X )
% 2.54/1.50 => P ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_166_less__imp__not__eq2,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X @ Y )
% 2.54/1.50 => ( Y != X ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_167_antisym__conv3,axiom,
% 2.54/1.50 ! [Y: nat,X: nat] :
% 2.54/1.50 ( ~ ( ord_less_nat @ Y @ X )
% 2.54/1.50 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 2.54/1.50 = ( X = Y ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_168_less__induct,axiom,
% 2.54/1.50 ! [P: nat > $o,A: nat] :
% 2.54/1.50 ( ! [X4: nat] :
% 2.54/1.50 ( ! [Y4: nat] :
% 2.54/1.50 ( ( ord_less_nat @ Y4 @ X4 )
% 2.54/1.50 => ( P @ Y4 ) )
% 2.54/1.50 => ( P @ X4 ) )
% 2.54/1.50 => ( P @ A ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_169_less__not__sym,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X @ Y )
% 2.54/1.50 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_170_less__imp__not__eq,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X @ Y )
% 2.54/1.50 => ( X != Y ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_171_dual__order_Oasym,axiom,
% 2.54/1.50 ! [B: nat,A: nat] :
% 2.54/1.50 ( ( ord_less_nat @ B @ A )
% 2.54/1.50 => ~ ( ord_less_nat @ A @ B ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_172_ord__less__eq__trans,axiom,
% 2.54/1.50 ! [A: nat,B: nat,C: nat] :
% 2.54/1.50 ( ( ord_less_nat @ A @ B )
% 2.54/1.50 => ( ( B = C )
% 2.54/1.50 => ( ord_less_nat @ A @ C ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_173_ord__eq__less__trans,axiom,
% 2.54/1.50 ! [A: nat,B: nat,C: nat] :
% 2.54/1.50 ( ( A = B )
% 2.54/1.50 => ( ( ord_less_nat @ B @ C )
% 2.54/1.50 => ( ord_less_nat @ A @ C ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_174_less__irrefl,axiom,
% 2.54/1.50 ! [X: nat] :
% 2.54/1.50 ~ ( ord_less_nat @ X @ X ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_175_less__linear,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X @ Y )
% 2.54/1.50 | ( X = Y )
% 2.54/1.50 | ( ord_less_nat @ Y @ X ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_176_less__trans,axiom,
% 2.54/1.50 ! [X: nat,Y: nat,Z3: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X @ Y )
% 2.54/1.50 => ( ( ord_less_nat @ Y @ Z3 )
% 2.54/1.50 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_177_less__asym_H,axiom,
% 2.54/1.50 ! [A: nat,B: nat] :
% 2.54/1.50 ( ( ord_less_nat @ A @ B )
% 2.54/1.50 => ~ ( ord_less_nat @ B @ A ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_178_less__asym,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X @ Y )
% 2.54/1.50 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_179_less__imp__neq,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X @ Y )
% 2.54/1.50 => ( X != Y ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_180_order_Oasym,axiom,
% 2.54/1.50 ! [A: nat,B: nat] :
% 2.54/1.50 ( ( ord_less_nat @ A @ B )
% 2.54/1.50 => ~ ( ord_less_nat @ B @ A ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_181_neq__iff,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( X != Y )
% 2.54/1.50 = ( ( ord_less_nat @ X @ Y )
% 2.54/1.50 | ( ord_less_nat @ Y @ X ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_182_neqE,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( X != Y )
% 2.54/1.50 => ( ~ ( ord_less_nat @ X @ Y )
% 2.54/1.50 => ( ord_less_nat @ Y @ X ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_183_gt__ex,axiom,
% 2.54/1.50 ! [X: nat] :
% 2.54/1.50 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_184_order__less__subst2,axiom,
% 2.54/1.50 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.54/1.50 ( ( ord_less_nat @ A @ B )
% 2.54/1.50 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 2.54/1.50 => ( ! [X4: nat,Y3: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X4 @ Y3 )
% 2.54/1.50 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.54/1.50 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_185_order__less__subst1,axiom,
% 2.54/1.50 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.54/1.50 ( ( ord_less_nat @ A @ ( F @ B ) )
% 2.54/1.50 => ( ( ord_less_nat @ B @ C )
% 2.54/1.50 => ( ! [X4: nat,Y3: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X4 @ Y3 )
% 2.54/1.50 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.54/1.50 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_186_ord__less__eq__subst,axiom,
% 2.54/1.50 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.54/1.50 ( ( ord_less_nat @ A @ B )
% 2.54/1.50 => ( ( ( F @ B )
% 2.54/1.50 = C )
% 2.54/1.50 => ( ! [X4: nat,Y3: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X4 @ Y3 )
% 2.54/1.50 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.54/1.50 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_187_ord__eq__less__subst,axiom,
% 2.54/1.50 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.54/1.50 ( ( A
% 2.54/1.50 = ( F @ B ) )
% 2.54/1.50 => ( ( ord_less_nat @ B @ C )
% 2.54/1.50 => ( ! [X4: nat,Y3: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X4 @ Y3 )
% 2.54/1.50 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.54/1.50 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_188_MinPredicate,axiom,
% 2.54/1.50 ! [P: nat > $o] :
% 2.54/1.50 ( ? [X_12: nat] : ( P @ X_12 )
% 2.54/1.50 => ? [N0: nat] :
% 2.54/1.50 ( ( P @ N0 )
% 2.54/1.50 & ! [N5: nat] :
% 2.54/1.50 ( ( P @ N5 )
% 2.54/1.50 => ( ord_less_eq_nat @ N0 @ N5 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_189_order_Onot__eq__order__implies__strict,axiom,
% 2.54/1.50 ! [A: nat,B: nat] :
% 2.54/1.50 ( ( A != B )
% 2.54/1.50 => ( ( ord_less_eq_nat @ A @ B )
% 2.54/1.50 => ( ord_less_nat @ A @ B ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_190_dual__order_Ostrict__implies__order,axiom,
% 2.54/1.50 ! [B: nat,A: nat] :
% 2.54/1.50 ( ( ord_less_nat @ B @ A )
% 2.54/1.50 => ( ord_less_eq_nat @ B @ A ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_191_dual__order_Ostrict__iff__order,axiom,
% 2.54/1.50 ( ord_less_nat
% 2.54/1.50 = ( ^ [B2: nat,A3: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ B2 @ A3 )
% 2.54/1.50 & ( A3 != B2 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_192_dual__order_Oorder__iff__strict,axiom,
% 2.54/1.50 ( ord_less_eq_nat
% 2.54/1.50 = ( ^ [B2: nat,A3: nat] :
% 2.54/1.50 ( ( ord_less_nat @ B2 @ A3 )
% 2.54/1.50 | ( A3 = B2 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_193_order_Ostrict__implies__order,axiom,
% 2.54/1.50 ! [A: nat,B: nat] :
% 2.54/1.50 ( ( ord_less_nat @ A @ B )
% 2.54/1.50 => ( ord_less_eq_nat @ A @ B ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_194_dual__order_Ostrict__trans2,axiom,
% 2.54/1.50 ! [B: nat,A: nat,C: nat] :
% 2.54/1.50 ( ( ord_less_nat @ B @ A )
% 2.54/1.50 => ( ( ord_less_eq_nat @ C @ B )
% 2.54/1.50 => ( ord_less_nat @ C @ A ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_195_dual__order_Ostrict__trans1,axiom,
% 2.54/1.50 ! [B: nat,A: nat,C: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ B @ A )
% 2.54/1.50 => ( ( ord_less_nat @ C @ B )
% 2.54/1.50 => ( ord_less_nat @ C @ A ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_196_order_Ostrict__iff__order,axiom,
% 2.54/1.50 ( ord_less_nat
% 2.54/1.50 = ( ^ [A3: nat,B2: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ A3 @ B2 )
% 2.54/1.50 & ( A3 != B2 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_197_order_Oorder__iff__strict,axiom,
% 2.54/1.50 ( ord_less_eq_nat
% 2.54/1.50 = ( ^ [A3: nat,B2: nat] :
% 2.54/1.50 ( ( ord_less_nat @ A3 @ B2 )
% 2.54/1.50 | ( A3 = B2 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_198_order_Ostrict__trans2,axiom,
% 2.54/1.50 ! [A: nat,B: nat,C: nat] :
% 2.54/1.50 ( ( ord_less_nat @ A @ B )
% 2.54/1.50 => ( ( ord_less_eq_nat @ B @ C )
% 2.54/1.50 => ( ord_less_nat @ A @ C ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_199_order_Ostrict__trans1,axiom,
% 2.54/1.50 ! [A: nat,B: nat,C: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.54/1.50 => ( ( ord_less_nat @ B @ C )
% 2.54/1.50 => ( ord_less_nat @ A @ C ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_200_not__le__imp__less,axiom,
% 2.54/1.50 ! [Y: nat,X: nat] :
% 2.54/1.50 ( ~ ( ord_less_eq_nat @ Y @ X )
% 2.54/1.50 => ( ord_less_nat @ X @ Y ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_201_less__le__not__le,axiom,
% 2.54/1.50 ( ord_less_nat
% 2.54/1.50 = ( ^ [X3: nat,Y6: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X3 @ Y6 )
% 2.54/1.50 & ~ ( ord_less_eq_nat @ Y6 @ X3 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_202_le__imp__less__or__eq,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X @ Y )
% 2.54/1.50 => ( ( ord_less_nat @ X @ Y )
% 2.54/1.50 | ( X = Y ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_203_le__less__linear,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X @ Y )
% 2.54/1.50 | ( ord_less_nat @ Y @ X ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_204_less__le__trans,axiom,
% 2.54/1.50 ! [X: nat,Y: nat,Z3: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X @ Y )
% 2.54/1.50 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 2.54/1.50 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_205_le__less__trans,axiom,
% 2.54/1.50 ! [X: nat,Y: nat,Z3: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X @ Y )
% 2.54/1.50 => ( ( ord_less_nat @ Y @ Z3 )
% 2.54/1.50 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_206_less__imp__le,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X @ Y )
% 2.54/1.50 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_207_antisym__conv2,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X @ Y )
% 2.54/1.50 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 2.54/1.50 = ( X = Y ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_208_antisym__conv1,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ~ ( ord_less_nat @ X @ Y )
% 2.54/1.50 => ( ( ord_less_eq_nat @ X @ Y )
% 2.54/1.50 = ( X = Y ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_209_le__neq__trans,axiom,
% 2.54/1.50 ! [A: nat,B: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.54/1.50 => ( ( A != B )
% 2.54/1.50 => ( ord_less_nat @ A @ B ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_210_not__less,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 2.54/1.50 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_211_not__le,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 2.54/1.50 = ( ord_less_nat @ Y @ X ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_212_order__less__le__subst2,axiom,
% 2.54/1.50 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.54/1.50 ( ( ord_less_nat @ A @ B )
% 2.54/1.50 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 2.54/1.50 => ( ! [X4: nat,Y3: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X4 @ Y3 )
% 2.54/1.50 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.54/1.50 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_213_order__less__le__subst1,axiom,
% 2.54/1.50 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.54/1.50 ( ( ord_less_nat @ A @ ( F @ B ) )
% 2.54/1.50 => ( ( ord_less_eq_nat @ B @ C )
% 2.54/1.50 => ( ! [X4: nat,Y3: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 2.54/1.50 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.54/1.50 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_214_order__le__less__subst2,axiom,
% 2.54/1.50 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.54/1.50 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 2.54/1.50 => ( ! [X4: nat,Y3: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 2.54/1.50 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.54/1.50 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_215_order__le__less__subst1,axiom,
% 2.54/1.50 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 2.54/1.50 => ( ( ord_less_nat @ B @ C )
% 2.54/1.50 => ( ! [X4: nat,Y3: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X4 @ Y3 )
% 2.54/1.50 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 2.54/1.50 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_216_less__le,axiom,
% 2.54/1.50 ( ord_less_nat
% 2.54/1.50 = ( ^ [X3: nat,Y6: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ X3 @ Y6 )
% 2.54/1.50 & ( X3 != Y6 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_217_le__less,axiom,
% 2.54/1.50 ( ord_less_eq_nat
% 2.54/1.50 = ( ^ [X3: nat,Y6: nat] :
% 2.54/1.50 ( ( ord_less_nat @ X3 @ Y6 )
% 2.54/1.50 | ( X3 = Y6 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_218_leI,axiom,
% 2.54/1.50 ! [X: nat,Y: nat] :
% 2.54/1.50 ( ~ ( ord_less_nat @ X @ Y )
% 2.54/1.50 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_219_leD,axiom,
% 2.54/1.50 ! [Y: nat,X: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ Y @ X )
% 2.54/1.50 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_220_AssumpMinImplAllBigger,axiom,
% 2.54/1.50 minimalEnabled_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ msg ).
% 2.54/1.50
% 2.54/1.50 thf(fact_221__092_060open_062execution_OfirstOccurrence_A_Ife_Aindex_J_A_Ift_Aindex_J_Amsg_AOccM_092_060close_062,axiom,
% 2.54/1.50 firstO1414030372_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ msga @ occM2 ).
% 2.54/1.50
% 2.54/1.50 thf(fact_222_SameMsgOnLow,axiom,
% 2.54/1.50 ! [I4: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I4 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 2.54/1.50 => ( ( nth_message_p_v @ ( ft @ index ) @ I4 )
% 2.54/1.50 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_223_OccM_H_I5_J,axiom,
% 2.54/1.50 ! [N5: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ occM @ N5 )
% 2.54/1.50 => ( ( ord_less_nat @ N5 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 2.54/1.50 => ( msg
% 2.54/1.50 != ( nth_message_p_v @ ( ft @ index ) @ N5 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_224_IPrefixList,axiom,
% 2.54/1.50 ! [I4: nat] : ( prefix47729710ge_p_v @ ( ft @ I4 ) @ ( ft @ ( suc @ I4 ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_225_OccM_H_I1_J,axiom,
% 2.54/1.50 ? [P4: p] : ( isReceiverOf_p_v @ P4 @ msg ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_226_FirstOccMsg_H,axiom,
% 2.54/1.50 firstO1414030372_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ msg @ occM ).
% 2.54/1.50
% 2.54/1.50 thf(fact_227_AssumpOccMFirstOccurrence_I5_J,axiom,
% 2.54/1.50 ! [N5: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ occM2 @ N5 )
% 2.54/1.50 => ( ( ord_less_nat @ N5 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 2.54/1.50 => ( msga
% 2.54/1.50 != ( nth_message_p_v @ ( ft @ index ) @ N5 ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_228_OccM_H_I4_J,axiom,
% 2.54/1.50 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ occM ) @ msg ).
% 2.54/1.50
% 2.54/1.50 thf(fact_229_AssumptionFairContr,axiom,
% 2.54/1.50 ! [N5: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ n @ N5 )
% 2.54/1.50 => ! [N02: nat] :
% 2.54/1.50 ( ( ord_less_nat @ N02 @ ( size_s1168481041ge_p_v @ ( ft @ N5 ) ) )
% 2.54/1.50 => ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) @ N02 )
% 2.54/1.50 => ( msg2
% 2.54/1.50 != ( nth_message_p_v @ ( ft @ N5 ) @ N02 ) ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_230_MessageStaysOrConsumed,axiom,
% 2.54/1.50 ! [N1: nat,N22: nat,N: nat,Msg: message_p_v] :
% 2.54/1.50 ( ( ( ord_less_eq_nat @ N1 @ N22 )
% 2.54/1.50 & ( ord_less_nat @ N22 @ ( size_s1406904903t_unit @ ( fe @ N ) ) )
% 2.54/1.50 & ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N ) @ N1 ) @ Msg ) )
% 2.54/1.50 => ( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N ) @ N22 ) @ Msg )
% 2.54/1.50 | ? [N03: nat] :
% 2.54/1.50 ( ( ord_less_eq_nat @ N1 @ N03 )
% 2.54/1.50 & ( ord_less_nat @ N03 @ ( size_s1168481041ge_p_v @ ( ft @ N ) ) )
% 2.54/1.50 & ( ( nth_message_p_v @ ( ft @ N ) @ N03 )
% 2.54/1.50 = Msg ) ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_231__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_O_Alength_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Ai_A_092_060and_062_Amsg_____A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062,axiom,
% 2.54/1.50 ~ ? [I4: nat] :
% 2.54/1.50 ( ( ord_less_nat @ I4 @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) )
% 2.54/1.50 & ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ I4 )
% 2.54/1.50 & ( msg2
% 2.54/1.50 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_232_AssumptionFair_I4_J,axiom,
% 2.54/1.50 isReceiverOf_p_v @ p2 @ msg2 ).
% 2.54/1.50
% 2.54/1.50 thf(fact_233_AssumpOccMFirstOccurrence_I1_J,axiom,
% 2.54/1.50 ? [P4: p] : ( isReceiverOf_p_v @ P4 @ msga ) ).
% 2.54/1.50
% 2.54/1.50 thf(fact_234_AssumptionFair_I3_J,axiom,
% 2.54/1.50 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ n0 ) @ msg2 ).
% 2.54/1.50
% 2.54/1.50 thf(conj_0,conjecture,
% 2.54/1.50 ( occM2
% 2.54/1.50 = ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ) ).
% 2.54/1.50 ------------------------
% 2.54/1.52 % (22352)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_22021 for (2999ds/4Mi)
% 2.54/1.52 % (22353)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_22021 for (2999ds/27Mi)
% 2.54/1.52 % (22357)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22021 for (2999ds/18Mi)
% 2.54/1.52 % (22352)Instruction limit reached!
% 2.54/1.52 % (22352)------------------------------
% 2.54/1.52 % (22352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.52 % (22352)Termination reason: Unknown
% 2.54/1.52 % (22352)Termination phase: shuffling
% 2.54/1.52
% 2.54/1.52 % (22352)Memory used [KB]: 1279
% 2.54/1.52 % (22352)Time elapsed: 0.003 s
% 2.54/1.52 % (22352)Instructions burned: 4 (million)
% 2.54/1.52 % (22352)------------------------------
% 2.54/1.52 % (22352)------------------------------
% 2.54/1.53 % (22357)Instruction limit reached!
% 2.54/1.53 % (22357)------------------------------
% 2.54/1.53 % (22357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.53 % (22357)Termination reason: Unknown
% 2.54/1.53 % (22357)Termination phase: Property scanning
% 2.54/1.53
% 2.54/1.53 % (22357)Memory used [KB]: 1535
% 2.54/1.53 % (22357)Time elapsed: 0.007 s
% 2.54/1.53 % (22357)Instructions burned: 18 (million)
% 2.54/1.53 % (22357)------------------------------
% 2.54/1.53 % (22357)------------------------------
% 2.54/1.53 % (22351)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22021 for (2999ds/183Mi)
% 2.54/1.53 % (22354)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22021 for (2999ds/2Mi)
% 2.54/1.53 % (22355)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_22021 for (2999ds/2Mi)
% 2.54/1.53 % (22356)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_22021 for (2999ds/275Mi)
% 2.54/1.53 % (22353)Instruction limit reached!
% 2.54/1.53 % (22353)------------------------------
% 2.54/1.53 % (22353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.53 % (22353)Termination reason: Unknown
% 2.54/1.53 % (22353)Termination phase: Preprocessing 1
% 2.54/1.53
% 2.54/1.53 % (22353)Memory used [KB]: 1535
% 2.54/1.53 % (22353)Time elapsed: 0.010 s
% 2.54/1.53 % (22353)Instructions burned: 27 (million)
% 2.54/1.53 % (22353)------------------------------
% 2.54/1.53 % (22353)------------------------------
% 2.54/1.53 % (22354)Instruction limit reached!
% 2.54/1.53 % (22354)------------------------------
% 2.54/1.53 % (22354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.53 % (22354)Termination reason: Unknown
% 2.54/1.53 % (22354)Termination phase: shuffling
% 2.54/1.53
% 2.54/1.53 % (22354)Memory used [KB]: 1279
% 2.54/1.53 % (22354)Time elapsed: 0.004 s
% 2.54/1.53 % (22354)Instructions burned: 3 (million)
% 2.54/1.53 % (22354)------------------------------
% 2.54/1.53 % (22354)------------------------------
% 2.54/1.53 % (22355)Instruction limit reached!
% 2.54/1.53 % (22355)------------------------------
% 2.54/1.53 % (22355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.53 % (22355)Termination reason: Unknown
% 2.54/1.53 % (22355)Termination phase: shuffling
% 2.54/1.53
% 2.54/1.53 % (22355)Memory used [KB]: 1279
% 2.54/1.53 % (22355)Time elapsed: 0.004 s
% 2.54/1.53 % (22355)Instructions burned: 3 (million)
% 2.54/1.53 % (22355)------------------------------
% 2.54/1.53 % (22355)------------------------------
% 2.54/1.53 % (22358)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22021 for (2999ds/3Mi)
% 2.54/1.53 % (22358)Instruction limit reached!
% 2.54/1.53 % (22358)------------------------------
% 2.54/1.53 % (22358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.53 % (22358)Termination reason: Unknown
% 2.54/1.53 % (22358)Termination phase: shuffling
% 2.54/1.53
% 2.54/1.53 % (22358)Memory used [KB]: 1279
% 2.54/1.53 % (22358)Time elapsed: 0.002 s
% 2.54/1.53 % (22358)Instructions burned: 3 (million)
% 2.54/1.53 % (22358)------------------------------
% 2.54/1.53 % (22358)------------------------------
% 2.54/1.54 % (22359)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_22021 for (2999ds/37Mi)
% 2.54/1.54 % (22360)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_22021 for (2999ds/15Mi)
% 2.54/1.54 % (22363)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22021 for (2999ds/7Mi)
% 2.54/1.54 % (22360)Instruction limit reached!
% 2.54/1.54 % (22360)------------------------------
% 2.54/1.54 % (22360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.54 % (22360)Termination reason: Unknown
% 2.54/1.54 % (22360)Termination phase: shuffling
% 2.54/1.54
% 2.54/1.54 % (22360)Memory used [KB]: 1535
% 2.54/1.54 % (22360)Time elapsed: 0.006 s
% 2.54/1.54 % (22360)Instructions burned: 15 (million)
% 2.54/1.54 % (22360)------------------------------
% 2.54/1.54 % (22360)------------------------------
% 2.54/1.55 % (22363)Instruction limit reached!
% 2.54/1.55 % (22363)------------------------------
% 2.54/1.55 % (22363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.55 % (22363)Termination reason: Unknown
% 2.54/1.55 % (22363)Termination phase: shuffling
% 2.54/1.55
% 2.54/1.55 % (22363)Memory used [KB]: 1407
% 2.54/1.55 % (22363)Time elapsed: 0.004 s
% 2.54/1.55 % (22363)Instructions burned: 9 (million)
% 2.54/1.55 % (22363)------------------------------
% 2.54/1.55 % (22363)------------------------------
% 2.54/1.55 % (22359)Instruction limit reached!
% 2.54/1.55 % (22359)------------------------------
% 2.54/1.55 % (22359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.55 % (22359)Termination reason: Unknown
% 2.54/1.55 % (22359)Termination phase: Property scanning
% 2.54/1.55
% 2.54/1.55 % (22359)Memory used [KB]: 1791
% 2.54/1.55 % (22359)Time elapsed: 0.011 s
% 2.54/1.55 % (22359)Instructions burned: 37 (million)
% 2.54/1.55 % (22359)------------------------------
% 2.54/1.55 % (22359)------------------------------
% 2.54/1.55 % (22361)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_22021 for (2999ds/3Mi)
% 2.54/1.55 % (22362)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_22021 for (2999ds/1041Mi)
% 2.54/1.55 % (22361)Instruction limit reached!
% 2.54/1.55 % (22361)------------------------------
% 2.54/1.55 % (22361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.55 % (22361)Termination reason: Unknown
% 2.54/1.55 % (22361)Termination phase: shuffling
% 2.54/1.55
% 2.54/1.55 % (22361)Memory used [KB]: 1279
% 2.54/1.55 % (22361)Time elapsed: 0.004 s
% 2.54/1.55 % (22361)Instructions burned: 3 (million)
% 2.54/1.55 % (22361)------------------------------
% 2.54/1.55 % (22361)------------------------------
% 2.54/1.55 % (22364)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22021 for (2999ds/16Mi)
% 2.54/1.56 % (22365)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_22021 for (2999ds/3Mi)
% 2.54/1.56 % (22365)Instruction limit reached!
% 2.54/1.56 % (22365)------------------------------
% 2.54/1.56 % (22365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.56 % (22365)Termination reason: Unknown
% 2.54/1.56 % (22365)Termination phase: shuffling
% 2.54/1.56
% 2.54/1.56 % (22365)Memory used [KB]: 1279
% 2.54/1.56 % (22365)Time elapsed: 0.002 s
% 2.54/1.56 % (22365)Instructions burned: 3 (million)
% 2.54/1.56 % (22365)------------------------------
% 2.54/1.56 % (22365)------------------------------
% 2.54/1.56 % (22366)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_22021 for (2999ds/3Mi)
% 2.54/1.56 % (22366)Instruction limit reached!
% 2.54/1.56 % (22366)------------------------------
% 2.54/1.56 % (22366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.56 % (22366)Termination reason: Unknown
% 2.54/1.56 % (22366)Termination phase: shuffling
% 2.54/1.56
% 2.54/1.56 % (22366)Memory used [KB]: 1279
% 2.54/1.56 % (22366)Time elapsed: 0.002 s
% 2.54/1.56 % (22366)Instructions burned: 3 (million)
% 2.54/1.56 % (22366)------------------------------
% 2.54/1.56 % (22366)------------------------------
% 2.54/1.56 % (22364)Instruction limit reached!
% 2.54/1.56 % (22364)------------------------------
% 2.54/1.56 % (22364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.56 % (22364)Termination reason: Unknown
% 2.54/1.56 % (22364)Termination phase: shuffling
% 2.54/1.56
% 2.54/1.56 % (22364)Memory used [KB]: 1535
% 2.54/1.56 % (22364)Time elapsed: 0.006 s
% 2.54/1.56 % (22364)Instructions burned: 16 (million)
% 2.54/1.56 % (22364)------------------------------
% 2.54/1.56 % (22364)------------------------------
% 2.54/1.57 % (22368)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22021 for (2999ds/3Mi)
% 2.54/1.57 % (22368)Instruction limit reached!
% 2.54/1.57 % (22368)------------------------------
% 2.54/1.57 % (22368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (22368)Termination reason: Unknown
% 2.54/1.57 % (22368)Termination phase: shuffling
% 2.54/1.57
% 2.54/1.57 % (22368)Memory used [KB]: 1279
% 2.54/1.57 % (22368)Time elapsed: 0.002 s
% 2.54/1.57 % (22368)Instructions burned: 3 (million)
% 2.54/1.57 % (22368)------------------------------
% 2.54/1.57 % (22368)------------------------------
% 2.54/1.57 % (22369)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22021 for (2999ds/4Mi)
% 2.54/1.57 % (22370)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22021 for (2999ds/18Mi)
% 2.54/1.57 % (22367)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22021 for (2999ds/7Mi)
% 2.54/1.57 % (22369)Instruction limit reached!
% 2.54/1.57 % (22369)------------------------------
% 2.54/1.57 % (22369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (22369)Termination reason: Unknown
% 2.54/1.57 % (22369)Termination phase: shuffling
% 2.54/1.57
% 2.54/1.57 % (22369)Memory used [KB]: 1407
% 2.54/1.57 % (22369)Time elapsed: 0.003 s
% 2.54/1.57 % (22369)Instructions burned: 6 (million)
% 2.54/1.57 % (22369)------------------------------
% 2.54/1.57 % (22369)------------------------------
% 2.54/1.57 % (22367)Instruction limit reached!
% 2.54/1.57 % (22367)------------------------------
% 2.54/1.57 % (22367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (22367)Termination reason: Unknown
% 2.54/1.57 % (22367)Termination phase: shuffling
% 2.54/1.57
% 2.54/1.57 % (22367)Memory used [KB]: 1407
% 2.54/1.57 % (22367)Time elapsed: 0.006 s
% 2.54/1.57 % (22367)Instructions burned: 7 (million)
% 2.54/1.57 % (22367)------------------------------
% 2.54/1.57 % (22367)------------------------------
% 2.54/1.57 % (22356)Refutation not found, incomplete strategy
% 2.54/1.57 % (22356)------------------------------
% 2.54/1.57 % (22356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (22356)Termination reason: Refutation not found, incomplete strategy
% 2.54/1.57
% 2.54/1.57
% 2.54/1.57 % (22356)Memory used [KB]: 6652
% 2.54/1.57 % (22356)Time elapsed: 0.044 s
% 2.54/1.57 % (22356)Instructions burned: 76 (million)
% 2.54/1.57 % (22356)------------------------------
% 2.54/1.57 % (22356)------------------------------
% 2.54/1.57 % (22370)Instruction limit reached!
% 2.54/1.57 % (22370)------------------------------
% 2.54/1.57 % (22370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (22370)Termination reason: Unknown
% 2.54/1.57 % (22370)Termination phase: Property scanning
% 2.54/1.57
% 2.54/1.57 % (22370)Memory used [KB]: 1535
% 2.54/1.57 % (22370)Time elapsed: 0.007 s
% 2.54/1.57 % (22370)Instructions burned: 19 (million)
% 2.54/1.57 % (22370)------------------------------
% 2.54/1.57 % (22370)------------------------------
% 2.54/1.58 % (22371)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22021 for (2999ds/710Mi)
% 2.54/1.58 % (22372)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22021 for (2999ds/6Mi)
% 2.54/1.58 % (22372)Instruction limit reached!
% 2.54/1.58 % (22372)------------------------------
% 2.54/1.58 % (22372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.58 % (22372)Termination reason: Unknown
% 2.54/1.58 % (22372)Termination phase: shuffling
% 2.54/1.58
% 2.54/1.58 % (22372)Memory used [KB]: 1279
% 2.54/1.58 % (22372)Time elapsed: 0.003 s
% 2.54/1.58 % (22372)Instructions burned: 6 (million)
% 2.54/1.58 % (22372)------------------------------
% 2.54/1.58 % (22372)------------------------------
% 2.54/1.58 % (22375)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22021 for (2999ds/5Mi)
% 2.54/1.59 % (22375)Instruction limit reached!
% 2.54/1.59 % (22375)------------------------------
% 2.54/1.59 % (22375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.59 % (22375)Termination reason: Unknown
% 2.54/1.59 % (22375)Termination phase: shuffling
% 2.54/1.59
% 2.54/1.59 % (22375)Memory used [KB]: 1279
% 2.54/1.59 % (22375)Time elapsed: 0.003 s
% 2.54/1.59 % (22375)Instructions burned: 7 (million)
% 2.54/1.59 % (22375)------------------------------
% 2.54/1.59 % (22375)------------------------------
% 2.54/1.59 % (22373)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_22021 for (2999ds/902Mi)
% 2.54/1.59 % (22376)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_22021 for (2999ds/6Mi)
% 2.54/1.59 % (22374)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_22021 for (2999ds/21Mi)
% 2.54/1.59 % (22376)Instruction limit reached!
% 2.54/1.59 % (22376)------------------------------
% 2.54/1.59 % (22376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.59 % (22376)Termination reason: Unknown
% 2.54/1.59 % (22376)Termination phase: shuffling
% 2.54/1.59
% 2.54/1.59 % (22376)Memory used [KB]: 1407
% 2.54/1.59 % (22376)Time elapsed: 0.003 s
% 2.54/1.59 % (22376)Instructions burned: 7 (million)
% 2.54/1.59 % (22376)------------------------------
% 2.54/1.59 % (22376)------------------------------
% 2.54/1.60 % (22377)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22021 for (2999ds/377Mi)
% 2.54/1.60 % (22378)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_22021 for (2999ds/779Mi)
% 2.54/1.60 % (22374)Instruction limit reached!
% 2.54/1.60 % (22374)------------------------------
% 2.54/1.60 % (22374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.60 % (22374)Termination reason: Unknown
% 2.54/1.60 % (22374)Termination phase: Property scanning
% 2.54/1.60
% 2.54/1.60 % (22374)Memory used [KB]: 1535
% 2.54/1.60 % (22374)Time elapsed: 0.014 s
% 2.54/1.60 % (22374)Instructions burned: 21 (million)
% 2.54/1.60 % (22374)------------------------------
% 2.54/1.60 % (22374)------------------------------
% 2.54/1.60 % (22351)Instruction limit reached!
% 2.54/1.60 % (22351)------------------------------
% 2.54/1.60 % (22351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.60 % (22351)Termination reason: Unknown
% 2.54/1.60 % (22351)Termination phase: Saturation
% 2.54/1.60
% 2.54/1.60 % (22351)Memory used [KB]: 7036
% 2.54/1.60 % (22351)Time elapsed: 0.076 s
% 2.54/1.60 % (22351)Instructions burned: 184 (million)
% 2.54/1.60 % (22351)------------------------------
% 2.54/1.60 % (22351)------------------------------
% 2.54/1.61 % (22380)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22021 for (2999ds/879Mi)
% 2.54/1.62 % (22373)Refutation not found, incomplete strategy
% 2.54/1.62 % (22373)------------------------------
% 2.54/1.62 % (22373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.62 % (22373)Termination reason: Refutation not found, incomplete strategy
% 2.54/1.62
% 2.54/1.62
% 2.54/1.62 % (22373)Memory used [KB]: 6652
% 2.54/1.62 % (22373)Time elapsed: 0.031 s
% 2.54/1.62 % (22373)Instructions burned: 82 (million)
% 2.54/1.62 % (22373)------------------------------
% 2.54/1.62 % (22373)------------------------------
% 2.54/1.62 % (22379)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_22021 for (2999ds/19Mi)
% 2.54/1.63 % (22381)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22021 for (2998ds/17Mi)
% 2.54/1.63 % (22379)Instruction limit reached!
% 2.54/1.63 % (22379)------------------------------
% 2.54/1.63 % (22379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.63 % (22379)Termination reason: Unknown
% 2.54/1.63 % (22379)Termination phase: shuffling
% 2.54/1.63
% 2.54/1.63 % (22379)Memory used [KB]: 1663
% 2.54/1.63 % (22379)Time elapsed: 0.012 s
% 2.54/1.63 % (22379)Instructions burned: 19 (million)
% 2.54/1.63 % (22379)------------------------------
% 2.54/1.63 % (22379)------------------------------
% 2.54/1.64 % (22381)Instruction limit reached!
% 2.54/1.64 % (22381)------------------------------
% 2.54/1.64 % (22381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.64 % (22381)Termination reason: Unknown
% 2.54/1.64 % (22381)Termination phase: Property scanning
% 2.54/1.64
% 2.54/1.64 % (22381)Memory used [KB]: 1535
% 2.54/1.64 % (22381)Time elapsed: 0.008 s
% 2.54/1.64 % (22381)Instructions burned: 18 (million)
% 2.54/1.64 % (22381)------------------------------
% 2.54/1.64 % (22381)------------------------------
% 2.54/1.65 % (22383)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22021 for (2998ds/30Mi)
% 2.54/1.65 % (22382)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22021 for (2998ds/3Mi)
% 2.54/1.65 % (22382)Instruction limit reached!
% 2.54/1.65 % (22382)------------------------------
% 2.54/1.65 % (22382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.65 % (22382)Termination reason: Unknown
% 2.54/1.65 % (22382)Termination phase: shuffling
% 2.54/1.65
% 2.54/1.65 % (22382)Memory used [KB]: 1279
% 2.54/1.65 % (22382)Time elapsed: 0.004 s
% 2.54/1.65 % (22382)Instructions burned: 3 (million)
% 2.54/1.65 % (22382)------------------------------
% 2.54/1.65 % (22382)------------------------------
% 2.54/1.66 % (22383)Instruction limit reached!
% 2.54/1.66 % (22383)------------------------------
% 2.54/1.66 % (22383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.66 % (22383)Termination reason: Unknown
% 2.54/1.66 % (22383)Termination phase: Preprocessing 3
% 2.54/1.66
% 2.54/1.66 % (22383)Memory used [KB]: 1663
% 2.54/1.66 % (22383)Time elapsed: 0.012 s
% 2.54/1.66 % (22383)Instructions burned: 32 (million)
% 2.54/1.66 % (22383)------------------------------
% 2.54/1.66 % (22383)------------------------------
% 2.54/1.67 % (22385)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22021 for (2998ds/100Mi)
% 2.54/1.67 % (22384)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22021 for (2998ds/127Mi)
% 2.54/1.69 % (22385)Instruction limit reached!
% 2.54/1.69 % (22385)------------------------------
% 2.54/1.69 % (22385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.69 % (22385)Termination reason: Unknown
% 2.54/1.69 % (22385)Termination phase: Property scanning
% 2.54/1.69
% 2.54/1.69 % (22385)Memory used [KB]: 2046
% 2.54/1.69 % (22385)Time elapsed: 0.029 s
% 2.54/1.69 % (22385)Instructions burned: 101 (million)
% 2.54/1.69 % (22385)------------------------------
% 2.54/1.69 % (22385)------------------------------
% 2.54/1.70 % (22386)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_22021 for (2998ds/3Mi)
% 2.54/1.71 % (22386)Instruction limit reached!
% 2.54/1.71 % (22386)------------------------------
% 2.54/1.71 % (22386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.71 % (22386)Termination reason: Unknown
% 2.54/1.71 % (22386)Termination phase: shuffling
% 2.54/1.71
% 2.54/1.71 % (22386)Memory used [KB]: 1279
% 2.54/1.71 % (22386)Time elapsed: 0.003 s
% 2.54/1.71 % (22386)Instructions burned: 4 (million)
% 2.54/1.71 % (22386)------------------------------
% 2.54/1.71 % (22386)------------------------------
% 2.54/1.71 % (22377)Instruction limit reached!
% 2.54/1.71 % (22377)------------------------------
% 2.54/1.71 % (22377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.71 % (22377)Termination reason: Unknown
% 2.54/1.71 % (22377)Termination phase: Saturation
% 2.54/1.71
% 2.54/1.71 % (22377)Memory used [KB]: 7547
% 2.54/1.71 % (22377)Time elapsed: 0.116 s
% 2.54/1.71 % (22377)Instructions burned: 377 (million)
% 2.54/1.71 % (22377)------------------------------
% 2.54/1.71 % (22377)------------------------------
% 2.54/1.72 % (22387)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_22021 for (2998ds/20Mi)
% 2.54/1.72 % (22384)Instruction limit reached!
% 2.54/1.72 % (22384)------------------------------
% 2.54/1.72 % (22384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.72 % (22384)Termination reason: Unknown
% 2.54/1.72 % (22384)Termination phase: Saturation
% 2.54/1.72
% 2.54/1.72 % (22384)Memory used [KB]: 6908
% 2.54/1.72 % (22384)Time elapsed: 0.054 s
% 2.54/1.72 % (22384)Instructions burned: 129 (million)
% 2.54/1.72 % (22384)------------------------------
% 2.54/1.72 % (22384)------------------------------
% 2.54/1.72 % (22388)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_22021 for (2998ds/86Mi)
% 2.54/1.72 % (22387)Instruction limit reached!
% 2.54/1.72 % (22387)------------------------------
% 2.54/1.72 % (22387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.72 % (22387)Termination reason: Unknown
% 2.54/1.72 % (22387)Termination phase: Property scanning
% 2.54/1.72
% 2.54/1.72 % (22387)Memory used [KB]: 1535
% 2.54/1.72 % (22387)Time elapsed: 0.009 s
% 2.54/1.72 % (22387)Instructions burned: 22 (million)
% 2.54/1.72 % (22387)------------------------------
% 2.54/1.72 % (22387)------------------------------
% 2.54/1.73 % (22389)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_22021 for (2997ds/107Mi)
% 2.54/1.73 % (22390)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_22021 for (2997ds/39Mi)
% 2.54/1.74 % (22388)Instruction limit reached!
% 2.54/1.74 % (22388)------------------------------
% 2.54/1.74 % (22388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.74 % (22388)Termination reason: Unknown
% 2.54/1.74 % (22388)Termination phase: Saturation
% 2.54/1.74
% 2.54/1.74 % (22388)Memory used [KB]: 6524
% 2.54/1.74 % (22388)Time elapsed: 0.025 s
% 2.54/1.74 % (22388)Instructions burned: 88 (million)
% 2.54/1.74 % (22388)------------------------------
% 2.54/1.74 % (22388)------------------------------
% 2.54/1.74 % (22390)Instruction limit reached!
% 2.54/1.74 % (22390)------------------------------
% 2.54/1.74 % (22390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.74 % (22390)Termination reason: Unknown
% 2.54/1.74 % (22390)Termination phase: Property scanning
% 2.54/1.74
% 2.54/1.74 % (22390)Memory used [KB]: 1791
% 2.54/1.74 % (22390)Time elapsed: 0.013 s
% 2.54/1.74 % (22390)Instructions burned: 40 (million)
% 2.54/1.74 % (22390)------------------------------
% 2.54/1.74 % (22390)------------------------------
% 2.54/1.75 % (22391)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_22021 for (2997ds/448Mi)
% 2.54/1.75 % (22392)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_22021 for (2997ds/46Mi)
% 2.54/1.76 % (22389)Instruction limit reached!
% 2.54/1.76 % (22389)------------------------------
% 2.54/1.76 % (22389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.76 % (22389)Termination reason: Unknown
% 2.54/1.76 % (22389)Termination phase: Saturation
% 2.54/1.76
% 2.54/1.76 % (22389)Memory used [KB]: 6652
% 2.54/1.76 % (22389)Time elapsed: 0.034 s
% 2.54/1.76 % (22389)Instructions burned: 107 (million)
% 2.54/1.76 % (22389)------------------------------
% 2.54/1.76 % (22389)------------------------------
% 2.54/1.77 % (22392)Instruction limit reached!
% 2.54/1.77 % (22392)------------------------------
% 2.54/1.77 % (22392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.77 % (22392)Termination reason: Unknown
% 2.54/1.77 % (22392)Termination phase: Property scanning
% 2.54/1.77
% 2.54/1.77 % (22392)Memory used [KB]: 1791
% 2.54/1.77 % (22392)Time elapsed: 0.017 s
% 2.54/1.77 % (22392)Instructions burned: 48 (million)
% 2.54/1.77 % (22392)------------------------------
% 2.54/1.77 % (22392)------------------------------
% 2.54/1.77 % (22393)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_22021 for (2997ds/98Mi)
% 2.54/1.78 % (22394)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_22021 for (2997ds/507Mi)
% 2.54/1.79 % (22371)Instruction limit reached!
% 2.54/1.79 % (22371)------------------------------
% 2.54/1.79 % (22371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.79 % (22371)Termination reason: Unknown
% 2.54/1.79 % (22371)Termination phase: Saturation
% 2.54/1.79
% 2.54/1.79 % (22371)Memory used [KB]: 7931
% 2.54/1.79 % (22371)Time elapsed: 0.219 s
% 2.54/1.79 % (22371)Instructions burned: 711 (million)
% 2.54/1.79 % (22371)------------------------------
% 2.54/1.79 % (22371)------------------------------
% 2.54/1.80 % (22393)Instruction limit reached!
% 2.54/1.80 % (22393)------------------------------
% 2.54/1.80 % (22393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.80 % (22393)Termination reason: Unknown
% 2.54/1.80 % (22393)Termination phase: Property scanning
% 2.54/1.80
% 2.54/1.80 % (22393)Memory used [KB]: 2046
% 2.54/1.80 % (22393)Time elapsed: 0.029 s
% 2.54/1.80 % (22393)Instructions burned: 101 (million)
% 2.54/1.80 % (22393)------------------------------
% 2.54/1.80 % (22393)------------------------------
% 2.54/1.80 % (22395)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_22021 for (2997ds/149Mi)
% 2.54/1.81 % (22396)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_22021 for (2997ds/39Mi)
% 2.54/1.82 % (22394)Refutation not found, incomplete strategy
% 2.54/1.82 % (22394)------------------------------
% 2.54/1.82 % (22394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.82 % (22394)Termination reason: Refutation not found, incomplete strategy
% 2.54/1.82
% 2.54/1.82
% 2.54/1.82 % (22394)Memory used [KB]: 7036
% 2.54/1.82 % (22394)Time elapsed: 0.037 s
% 2.54/1.82 % (22394)Instructions burned: 114 (million)
% 2.54/1.82 % (22394)------------------------------
% 2.54/1.82 % (22394)------------------------------
% 2.54/1.82 % (22396)Instruction limit reached!
% 2.54/1.82 % (22396)------------------------------
% 2.54/1.82 % (22396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.82 % (22396)Termination reason: Unknown
% 2.54/1.82 % (22396)Termination phase: Property scanning
% 2.54/1.82
% 2.54/1.82 % (22396)Memory used [KB]: 1791
% 2.54/1.82 % (22396)Time elapsed: 0.015 s
% 2.54/1.82 % (22396)Instructions burned: 42 (million)
% 2.54/1.82 % (22396)------------------------------
% 2.54/1.82 % (22396)------------------------------
% 2.54/1.83 % (22397)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_22021 for (2996ds/6Mi)
% 2.54/1.83 % (22397)Instruction limit reached!
% 2.54/1.83 % (22397)------------------------------
% 2.54/1.83 % (22397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.83 % (22397)Termination reason: Unknown
% 2.54/1.83 % (22397)Termination phase: shuffling
% 2.54/1.83
% 2.54/1.83 % (22397)Memory used [KB]: 1407
% 2.54/1.83 % (22397)Time elapsed: 0.004 s
% 2.54/1.83 % (22397)Instructions burned: 8 (million)
% 2.54/1.83 % (22397)------------------------------
% 2.54/1.83 % (22397)------------------------------
% 2.54/1.83 % (22398)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_22021 for (2996ds/1087Mi)
% 2.54/1.84 % (22378)Instruction limit reached!
% 2.54/1.84 % (22378)------------------------------
% 2.54/1.84 % (22378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.84 % (22378)Termination reason: Unknown
% 2.54/1.84 % (22378)Termination phase: Saturation
% 2.54/1.84
% 2.54/1.84 % (22378)Memory used [KB]: 8187
% 2.54/1.84 % (22378)Time elapsed: 0.236 s
% 2.54/1.84 % (22378)Instructions burned: 781 (million)
% 2.54/1.84 % (22378)------------------------------
% 2.54/1.84 % (22378)------------------------------
% 2.54/1.84 % (22399)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_22021 for (2996ds/47Mi)
% 2.54/1.85 % (22400)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_22021 for (2996ds/44Mi)
% 2.54/1.85 % (22395)Instruction limit reached!
% 2.54/1.85 % (22395)------------------------------
% 2.54/1.85 % (22395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.85 % (22395)Termination reason: Unknown
% 2.54/1.85 % (22395)Termination phase: Saturation
% 2.54/1.85
% 2.54/1.85 % (22395)Memory used [KB]: 6780
% 2.54/1.85 % (22395)Time elapsed: 0.044 s
% 2.54/1.85 % (22395)Instructions burned: 151 (million)
% 2.54/1.85 % (22395)------------------------------
% 2.54/1.85 % (22395)------------------------------
% 2.54/1.85 % (22399)Instruction limit reached!
% 2.54/1.85 % (22399)------------------------------
% 2.54/1.85 % (22399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.85 % (22399)Termination reason: Unknown
% 2.54/1.85 % (22399)Termination phase: Function definition elimination
% 2.54/1.85
% 2.54/1.85 % (22399)Memory used [KB]: 1918
% 2.54/1.85 % (22399)Time elapsed: 0.017 s
% 2.54/1.85 % (22399)Instructions burned: 49 (million)
% 2.54/1.85 % (22399)------------------------------
% 2.54/1.85 % (22399)------------------------------
% 2.54/1.86 % (22401)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_22021 for (2996ds/432Mi)
% 2.54/1.86 % (22400)Instruction limit reached!
% 2.54/1.86 % (22400)------------------------------
% 2.54/1.86 % (22400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.86 % (22400)Termination reason: Unknown
% 2.54/1.86 % (22400)Termination phase: Property scanning
% 2.54/1.86
% 2.54/1.86 % (22400)Memory used [KB]: 1791
% 2.54/1.86 % (22400)Time elapsed: 0.013 s
% 2.54/1.86 % (22400)Instructions burned: 46 (million)
% 2.54/1.86 % (22400)------------------------------
% 2.54/1.86 % (22400)------------------------------
% 2.54/1.86 % (22402)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_22021 for (2996ds/62Mi)
% 2.54/1.87 % (22403)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_22021 for (2996ds/31Mi)
% 2.54/1.88 % (22403)Instruction limit reached!
% 2.54/1.88 % (22403)------------------------------
% 2.54/1.88 % (22403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.88 % (22403)Termination reason: Unknown
% 2.54/1.88 % (22403)Termination phase: Preprocessing 3
% 2.54/1.88
% 2.54/1.88 % (22403)Memory used [KB]: 1663
% 2.54/1.88 % (22403)Time elapsed: 0.011 s
% 2.54/1.88 % (22403)Instructions burned: 31 (million)
% 2.54/1.88 % (22403)------------------------------
% 2.54/1.88 % (22403)------------------------------
% 2.54/1.88 % (22402)Instruction limit reached!
% 2.54/1.88 % (22402)------------------------------
% 2.54/1.88 % (22402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.88 % (22402)Termination reason: Unknown
% 2.54/1.88 % (22402)Termination phase: Property scanning
% 2.54/1.88
% 2.54/1.88 % (22402)Memory used [KB]: 1918
% 2.54/1.88 % (22402)Time elapsed: 0.019 s
% 2.54/1.88 % (22402)Instructions burned: 62 (million)
% 2.54/1.88 % (22402)------------------------------
% 2.54/1.88 % (22402)------------------------------
% 2.54/1.89 % (22391)Instruction limit reached!
% 2.54/1.89 % (22391)------------------------------
% 2.54/1.89 % (22391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.89 % (22391)Termination reason: Unknown
% 2.54/1.89 % (22391)Termination phase: Saturation
% 2.54/1.89
% 2.54/1.89 % (22391)Memory used [KB]: 7675
% 2.54/1.89 % (22391)Time elapsed: 0.157 s
% 2.54/1.89 % (22391)Instructions burned: 448 (million)
% 2.54/1.89 % (22391)------------------------------
% 2.54/1.89 % (22391)------------------------------
% 2.54/1.89 % (22404)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_22021 for (2996ds/96Mi)
% 2.54/1.89 % (22405)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_22021 for (2996ds/453Mi)
% 2.54/1.90 % (22406)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_22021 for (2996ds/71Mi)
% 2.54/1.91 % (22380)Instruction limit reached!
% 2.54/1.91 % (22380)------------------------------
% 2.54/1.91 % (22380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.91 % (22380)Termination reason: Unknown
% 2.54/1.91 % (22380)Termination phase: Saturation
% 2.54/1.91
% 2.54/1.91 % (22380)Memory used [KB]: 8187
% 2.54/1.91 % (22380)Time elapsed: 0.301 s
% 2.54/1.91 % (22380)Instructions burned: 880 (million)
% 2.54/1.91 % (22380)------------------------------
% 2.54/1.91 % (22380)------------------------------
% 2.54/1.91 % (22404)Instruction limit reached!
% 2.54/1.91 % (22404)------------------------------
% 2.54/1.91 % (22404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.91 % (22404)Termination reason: Unknown
% 2.54/1.91 % (22404)Termination phase: Saturation
% 2.54/1.91
% 2.54/1.91 % (22404)Memory used [KB]: 6524
% 2.54/1.91 % (22404)Time elapsed: 0.028 s
% 2.54/1.91 % (22404)Instructions burned: 98 (million)
% 2.54/1.91 % (22404)------------------------------
% 2.54/1.91 % (22404)------------------------------
% 2.54/1.92 % (22406)Instruction limit reached!
% 2.54/1.92 % (22406)------------------------------
% 2.54/1.92 % (22406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.92 % (22406)Termination reason: Unknown
% 2.54/1.92 % (22406)Termination phase: Property scanning
% 2.54/1.92
% 2.54/1.92 % (22406)Memory used [KB]: 1918
% 2.54/1.92 % (22406)Time elapsed: 0.021 s
% 2.54/1.92 % (22406)Instructions burned: 73 (million)
% 2.54/1.92 % (22406)------------------------------
% 2.54/1.92 % (22406)------------------------------
% 2.54/1.92 % (22407)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_22021 for (2995ds/83Mi)
% 2.54/1.92 % (22408)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_22021 for (2995ds/11Mi)
% 2.54/1.93 % (22409)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_22021 for (2995ds/41Mi)
% 2.54/1.93 % (22408)Instruction limit reached!
% 2.54/1.93 % (22408)------------------------------
% 2.54/1.93 % (22408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.93 % (22408)Termination reason: Unknown
% 2.54/1.93 % (22408)Termination phase: shuffling
% 2.54/1.93
% 2.54/1.93 % (22408)Memory used [KB]: 1535
% 2.54/1.93 % (22408)Time elapsed: 0.005 s
% 2.54/1.93 % (22408)Instructions burned: 13 (million)
% 2.54/1.93 % (22408)------------------------------
% 2.54/1.93 % (22408)------------------------------
% 2.54/1.93 % (22362)Instruction limit reached!
% 2.54/1.93 % (22362)------------------------------
% 2.54/1.93 % (22362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.93 % (22362)Termination reason: Unknown
% 2.54/1.93 % (22362)Termination phase: Saturation
% 2.54/1.93
% 2.54/1.93 % (22362)Memory used [KB]: 9466
% 2.54/1.93 % (22362)Time elapsed: 0.381 s
% 2.54/1.93 % (22362)Instructions burned: 1043 (million)
% 2.54/1.93 % (22362)------------------------------
% 2.54/1.93 % (22362)------------------------------
% 2.54/1.94 % (22410)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22021 for (2995ds/6Mi)
% 2.54/1.94 % (22409)Instruction limit reached!
% 2.54/1.94 % (22409)------------------------------
% 2.54/1.94 % (22409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.94 % (22409)Termination reason: Unknown
% 2.54/1.94 % (22409)Termination phase: Property scanning
% 2.54/1.94
% 2.54/1.94 % (22409)Memory used [KB]: 1791
% 2.54/1.94 % (22409)Time elapsed: 0.013 s
% 2.54/1.94 % (22409)Instructions burned: 43 (million)
% 2.54/1.94 % (22409)------------------------------
% 2.54/1.94 % (22409)------------------------------
% 2.54/1.94 % (22411)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_22021 for (2995ds/150Mi)
% 2.54/1.94 % (22410)Instruction limit reached!
% 2.54/1.94 % (22410)------------------------------
% 2.54/1.94 % (22410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.94 % (22410)Termination reason: Unknown
% 2.54/1.94 % (22410)Termination phase: shuffling
% 2.54/1.94
% 2.54/1.94 % (22410)Memory used [KB]: 1407
% 2.54/1.94 % (22410)Time elapsed: 0.004 s
% 2.54/1.94 % (22410)Instructions burned: 8 (million)
% 2.54/1.94 % (22410)------------------------------
% 2.54/1.94 % (22410)------------------------------
% 2.54/1.95 % (22412)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_22021 for (2995ds/343Mi)
% 2.54/1.95 % (22407)Instruction limit reached!
% 2.54/1.95 % (22407)------------------------------
% 2.54/1.95 % (22407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.95 % (22407)Termination reason: Unknown
% 2.54/1.95 % (22407)Termination phase: Saturation
% 2.54/1.95
% 2.54/1.95 % (22407)Memory used [KB]: 6524
% 2.54/1.95 % (22407)Time elapsed: 0.027 s
% 2.54/1.95 % (22407)Instructions burned: 85 (million)
% 2.54/1.95 % (22407)------------------------------
% 2.54/1.95 % (22407)------------------------------
% 2.54/1.95 % (22413)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_22021 for (2995ds/109Mi)
% 2.54/1.96 % (22414)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_22021 for (2995ds/253Mi)
% 2.54/1.98 % (22413)Instruction limit reached!
% 2.54/1.98 % (22413)------------------------------
% 2.54/1.98 % (22413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.98 % (22413)Termination reason: Unknown
% 2.54/1.98 % (22413)Termination phase: Saturation
% 2.54/1.98
% 2.54/1.98 % (22413)Memory used [KB]: 6652
% 2.54/1.98 % (22413)Time elapsed: 0.034 s
% 2.54/1.98 % (22413)Instructions burned: 110 (million)
% 2.54/1.98 % (22413)------------------------------
% 2.54/1.98 % (22413)------------------------------
% 2.54/1.99 % (22411)Instruction limit reached!
% 2.54/1.99 % (22411)------------------------------
% 2.54/1.99 % (22411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.99 % (22411)Termination reason: Unknown
% 2.54/1.99 % (22411)Termination phase: Saturation
% 2.54/1.99
% 2.54/1.99 % (22411)Memory used [KB]: 7036
% 2.54/1.99 % (22411)Time elapsed: 0.049 s
% 2.54/1.99 % (22411)Instructions burned: 152 (million)
% 2.54/1.99 % (22411)------------------------------
% 2.54/1.99 % (22411)------------------------------
% 2.54/1.99 % (22414)Refutation not found, incomplete strategy
% 2.54/1.99 % (22414)------------------------------
% 2.54/1.99 % (22414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.99 % (22414)Termination reason: Refutation not found, incomplete strategy
% 2.54/1.99
% 2.54/1.99
% 2.54/1.99 % (22414)Memory used [KB]: 6780
% 2.54/1.99 % (22414)Time elapsed: 0.031 s
% 2.54/1.99 % (22414)Instructions burned: 95 (million)
% 2.54/1.99 % (22414)------------------------------
% 2.54/1.99 % (22414)------------------------------
% 2.54/1.99 % (22401)Instruction limit reached!
% 2.54/1.99 % (22401)------------------------------
% 2.54/1.99 % (22401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.99 % (22401)Termination reason: Unknown
% 2.54/1.99 % (22401)Termination phase: Saturation
% 2.54/1.99
% 2.54/1.99 % (22401)Memory used [KB]: 3454
% 2.54/1.99 % (22401)Time elapsed: 0.133 s
% 2.54/1.99 % (22401)Instructions burned: 435 (million)
% 2.54/1.99 % (22401)------------------------------
% 2.54/1.99 % (22401)------------------------------
% 2.54/1.99 % (22415)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_22021 for (2995ds/140Mi)
% 2.54/2.00 % (22416)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_22021 for (2995ds/614Mi)
% 2.54/2.00 % (22418)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_22021 for (2995ds/339Mi)
% 2.54/2.01 % (22417)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_22021 for (2995ds/202Mi)
% 6.00/2.03 % (22405)Instruction limit reached!
% 6.00/2.03 % (22405)------------------------------
% 6.00/2.03 % (22405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.00/2.03 % (22405)Termination reason: Unknown
% 6.00/2.03 % (22405)Termination phase: Saturation
% 6.00/2.03
% 6.00/2.03 % (22405)Memory used [KB]: 7419
% 6.00/2.03 % (22405)Time elapsed: 0.138 s
% 6.00/2.03 % (22405)Instructions burned: 453 (million)
% 6.00/2.03 % (22405)------------------------------
% 6.00/2.03 % (22405)------------------------------
% 6.00/2.04 % (22417)Refutation not found, incomplete strategy
% 6.00/2.04 % (22417)------------------------------
% 6.00/2.04 % (22417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.00/2.04 % (22417)Termination reason: Refutation not found, incomplete strategy
% 6.00/2.04
% 6.00/2.04
% 6.00/2.04 % (22417)Memory used [KB]: 6268
% 6.00/2.04 % (22417)Time elapsed: 0.029 s
% 6.00/2.04 % (22417)Instructions burned: 48 (million)
% 6.00/2.04 % (22417)------------------------------
% 6.00/2.04 % (22417)------------------------------
% 6.00/2.04 % (22419)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_22021 for (2994ds/283Mi)
% 6.00/2.04 % (22415)Instruction limit reached!
% 6.00/2.04 % (22415)------------------------------
% 6.00/2.04 % (22415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.00/2.04 % (22415)Termination reason: Unknown
% 6.00/2.04 % (22415)Termination phase: Saturation
% 6.00/2.04
% 6.00/2.04 % (22415)Memory used [KB]: 6524
% 6.00/2.04 % (22415)Time elapsed: 0.047 s
% 6.00/2.04 % (22415)Instructions burned: 141 (million)
% 6.00/2.04 % (22415)------------------------------
% 6.00/2.04 % (22415)------------------------------
% 6.00/2.05 % (22421)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_22021 for (2994ds/298Mi)
% 6.00/2.05 % (22420)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_22021 for (2994ds/134Mi)
% 6.00/2.06 % (22412)Instruction limit reached!
% 6.00/2.06 % (22412)------------------------------
% 6.00/2.06 % (22412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.00/2.06 % (22412)Termination reason: Unknown
% 6.00/2.06 % (22412)Termination phase: Saturation
% 6.00/2.06
% 6.00/2.06 % (22412)Memory used [KB]: 7291
% 6.00/2.06 % (22412)Time elapsed: 0.112 s
% 6.00/2.06 % (22412)Instructions burned: 344 (million)
% 6.00/2.06 % (22412)------------------------------
% 6.00/2.06 % (22412)------------------------------
% 6.00/2.07 % (22422)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_22021 for (2994ds/192Mi)
% 6.00/2.10 % (22418)Instruction limit reached!
% 6.00/2.10 % (22418)------------------------------
% 6.00/2.10 % (22418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.00/2.10 % (22418)Termination reason: Unknown
% 6.00/2.10 % (22418)Termination phase: Saturation
% 6.00/2.10
% 6.00/2.10 % (22418)Memory used [KB]: 7164
% 6.00/2.10 % (22418)Time elapsed: 0.105 s
% 6.00/2.10 % (22418)Instructions burned: 341 (million)
% 6.00/2.10 % (22418)------------------------------
% 6.00/2.10 % (22418)------------------------------
% 6.00/2.11 % (22423)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_22021 for (2993ds/258Mi)
% 6.43/2.12 % (22420)Instruction limit reached!
% 6.43/2.12 % (22420)------------------------------
% 6.43/2.12 % (22420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.43/2.12 % (22420)Termination reason: Unknown
% 6.43/2.12 % (22420)Termination phase: Saturation
% 6.43/2.12
% 6.43/2.12 % (22420)Memory used [KB]: 6780
% 6.43/2.12 % (22420)Time elapsed: 0.069 s
% 6.43/2.12 % (22420)Instructions burned: 134 (million)
% 6.43/2.12 % (22420)------------------------------
% 6.43/2.12 % (22420)------------------------------
% 6.43/2.12 % (22419)Instruction limit reached!
% 6.43/2.12 % (22419)------------------------------
% 6.43/2.12 % (22419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.43/2.12 % (22419)Termination reason: Unknown
% 6.43/2.12 % (22419)Termination phase: Saturation
% 6.43/2.12
% 6.43/2.12 % (22419)Memory used [KB]: 7291
% 6.43/2.12 % (22419)Time elapsed: 0.106 s
% 6.43/2.12 % (22419)Instructions burned: 283 (million)
% 6.43/2.12 % (22419)------------------------------
% 6.43/2.12 % (22419)------------------------------
% 6.43/2.13 % (22422)Instruction limit reached!
% 6.43/2.13 % (22422)------------------------------
% 6.43/2.13 % (22422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.43/2.13 % (22422)Termination reason: Unknown
% 6.43/2.13 % (22422)Termination phase: Saturation
% 6.43/2.13
% 6.43/2.13 % (22422)Memory used [KB]: 7547
% 6.43/2.13 % (22422)Time elapsed: 0.060 s
% 6.43/2.13 % (22422)Instructions burned: 192 (million)
% 6.43/2.13 % (22422)------------------------------
% 6.43/2.13 % (22422)------------------------------
% 6.43/2.13 % (22421)Instruction limit reached!
% 6.43/2.13 % (22421)------------------------------
% 6.43/2.13 % (22421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.43/2.13 % (22421)Termination reason: Unknown
% 6.43/2.13 % (22421)Termination phase: Saturation
% 6.43/2.13
% 6.43/2.13 % (22421)Memory used [KB]: 7675
% 6.43/2.13 % (22421)Time elapsed: 0.084 s
% 6.43/2.13 % (22421)Instructions burned: 299 (million)
% 6.43/2.13 % (22421)------------------------------
% 6.43/2.13 % (22421)------------------------------
% 6.43/2.13 % (22424)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_22021 for (2993ds/90Mi)
% 6.43/2.13 % (22425)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_22021 for (2993ds/231Mi)
% 6.43/2.14 % (22426)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_22021 for (2993ds/458Mi)
% 6.43/2.14 % (22427)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_22021 for (2993ds/31Mi)
% 6.43/2.15 % (22427)Instruction limit reached!
% 6.43/2.15 % (22427)------------------------------
% 6.43/2.15 % (22427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.43/2.15 % (22427)Termination reason: Unknown
% 6.43/2.15 % (22427)Termination phase: Preprocessing 3
% 6.43/2.15
% 6.43/2.15 % (22427)Memory used [KB]: 1791
% 6.43/2.15 % (22427)Time elapsed: 0.011 s
% 6.43/2.15 % (22427)Instructions burned: 33 (million)
% 6.43/2.15 % (22427)------------------------------
% 6.43/2.15 % (22427)------------------------------
% 6.43/2.15 % (22423)Refutation not found, incomplete strategy
% 6.43/2.15 % (22423)------------------------------
% 6.43/2.15 % (22423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.43/2.15 % (22423)Termination reason: Refutation not found, incomplete strategy
% 6.43/2.15
% 6.43/2.15
% 6.43/2.15 % (22423)Memory used [KB]: 7164
% 6.43/2.15 % (22423)Time elapsed: 0.043 s
% 6.43/2.15 % (22423)Instructions burned: 146 (million)
% 6.43/2.15 % (22423)------------------------------
% 6.43/2.15 % (22423)------------------------------
% 6.43/2.16 % (22424)Instruction limit reached!
% 6.43/2.16 % (22424)------------------------------
% 6.43/2.16 % (22424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.43/2.16 % (22424)Termination reason: Unknown
% 6.43/2.16 % (22424)Termination phase: Saturation
% 6.43/2.16
% 6.43/2.16 % (22424)Memory used [KB]: 6524
% 6.43/2.16 % (22424)Time elapsed: 0.026 s
% 6.43/2.16 % (22424)Instructions burned: 90 (million)
% 6.43/2.16 % (22424)------------------------------
% 6.43/2.16 % (22424)------------------------------
% 6.43/2.16 % (22428)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_22021 for (2993ds/297Mi)
% 6.43/2.16 % (22429)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_22021 for (2993ds/987Mi)
% 6.43/2.17 % (22430)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_22021 for (2993ds/182Mi)
% 6.43/2.18 % (22416)Instruction limit reached!
% 6.43/2.18 % (22416)------------------------------
% 6.43/2.18 % (22416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.43/2.18 % (22416)Termination reason: Unknown
% 6.43/2.18 % (22416)Termination phase: Saturation
% 6.43/2.18
% 6.43/2.18 % (22416)Memory used [KB]: 8443
% 6.43/2.18 % (22416)Time elapsed: 0.186 s
% 6.43/2.18 % (22416)Instructions burned: 617 (million)
% 6.43/2.18 % (22416)------------------------------
% 6.43/2.18 % (22416)------------------------------
% 6.43/2.19 % (22431)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_22021 for (2993ds/182Mi)
% 6.43/2.19 % (22398)Instruction limit reached!
% 6.43/2.19 % (22398)------------------------------
% 6.43/2.19 % (22398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.43/2.19 % (22398)Termination reason: Unknown
% 6.43/2.19 % (22398)Termination phase: Saturation
% 6.43/2.19
% 6.43/2.19 % (22398)Memory used [KB]: 8315
% 6.43/2.19 % (22398)Time elapsed: 0.362 s
% 6.43/2.19 % (22398)Instructions burned: 1089 (million)
% 6.43/2.19 % (22398)------------------------------
% 6.43/2.19 % (22398)------------------------------
% 7.04/2.20 % (22432)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_22021 for (2993ds/154Mi)
% 7.04/2.21 % (22425)Instruction limit reached!
% 7.04/2.21 % (22425)------------------------------
% 7.04/2.21 % (22425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.04/2.21 % (22425)Termination reason: Unknown
% 7.04/2.21 % (22425)Termination phase: Saturation
% 7.04/2.21
% 7.04/2.21 % (22425)Memory used [KB]: 7291
% 7.04/2.21 % (22425)Time elapsed: 0.074 s
% 7.04/2.21 % (22425)Instructions burned: 232 (million)
% 7.04/2.21 % (22425)------------------------------
% 7.04/2.21 % (22425)------------------------------
% 7.04/2.22 % (22433)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_22021 for (2992ds/79Mi)
% 7.04/2.22 % (22430)Instruction limit reached!
% 7.04/2.22 % (22430)------------------------------
% 7.04/2.22 % (22430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.04/2.22 % (22430)Termination reason: Unknown
% 7.04/2.22 % (22430)Termination phase: Saturation
% 7.04/2.22
% 7.04/2.22 % (22430)Memory used [KB]: 7036
% 7.04/2.22 % (22430)Time elapsed: 0.054 s
% 7.04/2.22 % (22430)Instructions burned: 182 (million)
% 7.04/2.22 % (22430)------------------------------
% 7.04/2.22 % (22430)------------------------------
% 7.04/2.23 % (22434)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_22021 for (2992ds/216Mi)
% 7.04/2.24 % (22433)Instruction limit reached!
% 7.04/2.24 % (22433)------------------------------
% 7.04/2.24 % (22433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.04/2.24 % (22433)Termination reason: Unknown
% 7.04/2.24 % (22433)Termination phase: Saturation
% 7.04/2.24
% 7.04/2.24 % (22433)Memory used [KB]: 6524
% 7.04/2.24 % (22433)Time elapsed: 0.025 s
% 7.04/2.24 % (22433)Instructions burned: 79 (million)
% 7.04/2.24 % (22433)------------------------------
% 7.04/2.24 % (22433)------------------------------
% 7.04/2.24 % (22432)Refutation not found, incomplete strategy
% 7.04/2.24 % (22432)------------------------------
% 7.04/2.24 % (22432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.04/2.24 % (22432)Termination reason: Refutation not found, incomplete strategy
% 7.04/2.24
% 7.04/2.24
% 7.04/2.24 % (22432)Memory used [KB]: 7036
% 7.04/2.24 % (22432)Time elapsed: 0.039 s
% 7.04/2.24 % (22432)Instructions burned: 140 (million)
% 7.04/2.24 % (22432)------------------------------
% 7.04/2.24 % (22432)------------------------------
% 7.04/2.25 % (22428)Instruction limit reached!
% 7.04/2.25 % (22428)------------------------------
% 7.04/2.25 % (22428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.04/2.25 % (22428)Termination reason: Unknown
% 7.04/2.25 % (22428)Termination phase: Saturation
% 7.04/2.25
% 7.04/2.25 % (22428)Memory used [KB]: 7164
% 7.04/2.25 % (22428)Time elapsed: 0.087 s
% 7.04/2.25 % (22428)Instructions burned: 299 (million)
% 7.04/2.25 % (22428)------------------------------
% 7.04/2.25 % (22428)------------------------------
% 7.04/2.25 % (22431)Instruction limit reached!
% 7.04/2.25 % (22431)------------------------------
% 7.04/2.25 % (22431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.04/2.25 % (22431)Termination reason: Unknown
% 7.04/2.25 % (22431)Termination phase: Saturation
% 7.04/2.25
% 7.04/2.25 % (22431)Memory used [KB]: 6908
% 7.04/2.25 % (22431)Time elapsed: 0.059 s
% 7.04/2.25 % (22431)Instructions burned: 182 (million)
% 7.04/2.25 % (22431)------------------------------
% 7.04/2.25 % (22431)------------------------------
% 7.04/2.25 % (22435)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_22021 for (2992ds/114Mi)
% 7.04/2.25 % (22436)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_22021 for (2992ds/922Mi)
% 7.04/2.25 % (22437)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_22021 for (2992ds/182Mi)
% 7.04/2.26 % (22438)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_22021 for (2992ds/164Mi)
% 7.04/2.28 % (22426)Instruction limit reached!
% 7.04/2.28 % (22426)------------------------------
% 7.04/2.28 % (22426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.04/2.28 % (22426)Termination reason: Unknown
% 7.04/2.28 % (22426)Termination phase: Saturation
% 7.04/2.28
% 7.04/2.28 % (22426)Memory used [KB]: 7675
% 7.04/2.28 % (22426)Time elapsed: 0.143 s
% 7.04/2.28 % (22426)Instructions burned: 459 (million)
% 7.04/2.28 % (22426)------------------------------
% 7.04/2.28 % (22426)------------------------------
% 7.04/2.29 % (22435)Instruction limit reached!
% 7.04/2.29 % (22435)------------------------------
% 7.04/2.29 % (22435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.04/2.29 % (22435)Termination reason: Unknown
% 7.04/2.29 % (22435)Termination phase: Saturation
% 7.04/2.29
% 7.04/2.29 % (22435)Memory used [KB]: 6780
% 7.04/2.29 % (22435)Time elapsed: 0.038 s
% 7.04/2.29 % (22435)Instructions burned: 116 (million)
% 7.04/2.29 % (22435)------------------------------
% 7.04/2.29 % (22435)------------------------------
% 7.04/2.29 % (22434)Instruction limit reached!
% 7.04/2.29 % (22434)------------------------------
% 7.04/2.29 % (22434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.04/2.29 % (22434)Termination reason: Unknown
% 7.04/2.29 % (22434)Termination phase: Saturation
% 7.04/2.29
% 7.04/2.29 % (22434)Memory used [KB]: 7164
% 7.04/2.29 % (22434)Time elapsed: 0.059 s
% 7.04/2.29 % (22434)Instructions burned: 216 (million)
% 7.04/2.29 % (22434)------------------------------
% 7.04/2.29 % (22434)------------------------------
% 7.04/2.29 % (22439)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_22021 for (2992ds/50Mi)
% 7.04/2.30 % (22440)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_22021 for (2992ds/368Mi)
% 7.04/2.30 % (22441)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_22021 for (2992ds/1021Mi)
% 7.71/2.30 % (22438)Instruction limit reached!
% 7.71/2.30 % (22438)------------------------------
% 7.71/2.30 % (22438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.71/2.30 % (22438)Termination reason: Unknown
% 7.71/2.30 % (22438)Termination phase: Saturation
% 7.71/2.30
% 7.71/2.30 % (22438)Memory used [KB]: 2302
% 7.71/2.30 % (22438)Time elapsed: 0.044 s
% 7.71/2.30 % (22438)Instructions burned: 164 (million)
% 7.71/2.30 % (22438)------------------------------
% 7.71/2.30 % (22438)------------------------------
% 7.71/2.30 % (22439)Instruction limit reached!
% 7.71/2.30 % (22439)------------------------------
% 7.71/2.30 % (22439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.71/2.30 % (22439)Termination reason: Unknown
% 7.71/2.30 % (22439)Termination phase: Property scanning
% 7.71/2.30
% 7.71/2.30 % (22439)Memory used [KB]: 1791
% 7.71/2.30 % (22439)Time elapsed: 0.014 s
% 7.71/2.30 % (22439)Instructions burned: 50 (million)
% 7.71/2.30 % (22439)------------------------------
% 7.71/2.30 % (22439)------------------------------
% 7.71/2.30 % (22437)Instruction limit reached!
% 7.71/2.30 % (22437)------------------------------
% 7.71/2.30 % (22437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.71/2.30 % (22437)Termination reason: Unknown
% 7.71/2.30 % (22437)Termination phase: Saturation
% 7.71/2.30
% 7.71/2.30 % (22437)Memory used [KB]: 7164
% 7.71/2.30 % (22437)Time elapsed: 0.049 s
% 7.71/2.30 % (22437)Instructions burned: 182 (million)
% 7.71/2.30 % (22437)------------------------------
% 7.71/2.30 % (22437)------------------------------
% 7.71/2.31 % (22443)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_22021 for (2992ds/204Mi)
% 7.71/2.31 % (22444)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_22021 for (2992ds/26Mi)
% 7.71/2.32 % (22442)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_22021 for (2992ds/267Mi)
% 7.71/2.32 % (22444)Instruction limit reached!
% 7.71/2.32 % (22444)------------------------------
% 7.71/2.32 % (22444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.71/2.32 % (22444)Termination reason: Unknown
% 7.71/2.32 % (22444)Termination phase: shuffling
% 7.71/2.32
% 7.71/2.32 % (22444)Memory used [KB]: 1791
% 7.71/2.32 % (22444)Time elapsed: 0.009 s
% 7.71/2.32 % (22444)Instructions burned: 27 (million)
% 7.71/2.32 % (22444)------------------------------
% 7.71/2.32 % (22444)------------------------------
% 7.71/2.33 % (22445)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_22021 for (2991ds/53Mi)
% 7.71/2.34 % (22445)Instruction limit reached!
% 7.71/2.34 % (22445)------------------------------
% 7.71/2.34 % (22445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.71/2.34 % (22445)Termination reason: Unknown
% 7.71/2.34 % (22445)Termination phase: Property scanning
% 7.71/2.34
% 7.71/2.34 % (22445)Memory used [KB]: 1918
% 7.71/2.34 % (22445)Time elapsed: 0.015 s
% 7.71/2.34 % (22445)Instructions burned: 54 (million)
% 7.71/2.34 % (22445)------------------------------
% 7.71/2.34 % (22445)------------------------------
% 7.71/2.35 % (22446)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_22021 for (2991ds/4436Mi)
% 7.71/2.37 % (22443)Instruction limit reached!
% 7.71/2.37 % (22443)------------------------------
% 7.71/2.37 % (22443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.71/2.37 % (22443)Termination reason: Unknown
% 7.71/2.37 % (22443)Termination phase: Saturation
% 7.71/2.37
% 7.71/2.37 % (22443)Memory used [KB]: 7164
% 7.71/2.37 % (22443)Time elapsed: 0.062 s
% 7.71/2.37 % (22443)Instructions burned: 204 (million)
% 7.71/2.37 % (22443)------------------------------
% 7.71/2.37 % (22443)------------------------------
% 7.71/2.38 % (22447)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_22021 for (2991ds/1539Mi)
% 7.95/2.42 % (22440)Instruction limit reached!
% 7.95/2.42 % (22440)------------------------------
% 7.95/2.42 % (22440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.95/2.42 % (22440)Termination reason: Unknown
% 7.95/2.42 % (22440)Termination phase: Saturation
% 7.95/2.42
% 7.95/2.42 % (22440)Memory used [KB]: 7547
% 7.95/2.42 % (22440)Time elapsed: 0.124 s
% 7.95/2.42 % (22440)Instructions burned: 368 (million)
% 7.95/2.42 % (22440)------------------------------
% 7.95/2.42 % (22440)------------------------------
% 7.95/2.43 % (22448)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_22021 for (2990ds/408Mi)
% 7.95/2.43 % (22442)Instruction limit reached!
% 7.95/2.43 % (22442)------------------------------
% 7.95/2.43 % (22442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.95/2.43 % (22442)Termination reason: Unknown
% 7.95/2.43 % (22442)Termination phase: Saturation
% 7.95/2.43
% 7.95/2.43 % (22442)Memory used [KB]: 7419
% 7.95/2.43 % (22442)Time elapsed: 0.113 s
% 7.95/2.43 % (22442)Instructions burned: 268 (million)
% 7.95/2.43 % (22442)------------------------------
% 7.95/2.43 % (22442)------------------------------
% 7.95/2.44 % (22449)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_22021 for (2990ds/5205Mi)
% 7.95/2.46 % (22448)Refutation not found, incomplete strategy
% 7.95/2.46 % (22448)------------------------------
% 7.95/2.46 % (22448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.95/2.46 % (22448)Termination reason: Refutation not found, incomplete strategy
% 7.95/2.46
% 7.95/2.46
% 7.95/2.46 % (22448)Memory used [KB]: 6908
% 7.95/2.46 % (22448)Time elapsed: 0.030 s
% 7.95/2.46 % (22448)Instructions burned: 90 (million)
% 7.95/2.46 % (22448)------------------------------
% 7.95/2.46 % (22448)------------------------------
% 7.95/2.46 % (22429)Instruction limit reached!
% 7.95/2.46 % (22429)------------------------------
% 7.95/2.46 % (22429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.95/2.46 % (22429)Termination reason: Unknown
% 7.95/2.46 % (22429)Termination phase: Saturation
% 7.95/2.46
% 7.95/2.46 % (22429)Memory used [KB]: 8571
% 7.95/2.46 % (22429)Time elapsed: 0.298 s
% 7.95/2.46 % (22429)Instructions burned: 988 (million)
% 7.95/2.46 % (22429)------------------------------
% 7.95/2.46 % (22429)------------------------------
% 7.95/2.47 % (22450)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_22021 for (2990ds/1913Mi)
% 7.95/2.47 % (22451)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_22021 for (2990ds/4350Mi)
% 7.95/2.48 % (22451)Refutation not found, incomplete strategy
% 7.95/2.48 % (22451)------------------------------
% 7.95/2.48 % (22451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.95/2.48 % (22451)Termination reason: Refutation not found, incomplete strategy
% 7.95/2.48
% 7.95/2.48
% 7.95/2.48 % (22451)Memory used [KB]: 6140
% 7.95/2.48 % (22451)Time elapsed: 0.014 s
% 7.95/2.48 % (22451)Instructions burned: 40 (million)
% 7.95/2.48 % (22451)------------------------------
% 7.95/2.48 % (22451)------------------------------
% 7.95/2.49 % (22452)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_22021 for (2990ds/68Mi)
% 8.58/2.51 % (22452)Instruction limit reached!
% 8.58/2.51 % (22452)------------------------------
% 8.58/2.51 % (22452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.51 % (22452)Termination reason: Unknown
% 8.58/2.51 % (22452)Termination phase: Property scanning
% 8.58/2.51
% 8.58/2.51 % (22452)Memory used [KB]: 1918
% 8.58/2.51 % (22452)Time elapsed: 0.022 s
% 8.58/2.51 % (22452)Instructions burned: 71 (million)
% 8.58/2.51 % (22452)------------------------------
% 8.58/2.51 % (22452)------------------------------
% 8.58/2.52 % (22453)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_22021 for (2990ds/358Mi)
% 8.58/2.54 % (22436)Instruction limit reached!
% 8.58/2.54 % (22436)------------------------------
% 8.58/2.54 % (22436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.54 % (22436)Termination reason: Unknown
% 8.58/2.54 % (22436)Termination phase: Saturation
% 8.58/2.54
% 8.58/2.54 % (22436)Memory used [KB]: 8443
% 8.58/2.54 % (22436)Time elapsed: 0.289 s
% 8.58/2.54 % (22436)Instructions burned: 924 (million)
% 8.58/2.54 % (22436)------------------------------
% 8.58/2.54 % (22436)------------------------------
% 8.58/2.55 % (22454)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_22021 for (2989ds/31Mi)
% 8.58/2.56 % (22454)Instruction limit reached!
% 8.58/2.56 % (22454)------------------------------
% 8.58/2.56 % (22454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.56 % (22454)Termination reason: Unknown
% 8.58/2.56 % (22454)Termination phase: Preprocessing 3
% 8.58/2.56
% 8.58/2.56 % (22454)Memory used [KB]: 1791
% 8.58/2.56 % (22454)Time elapsed: 0.011 s
% 8.58/2.56 % (22454)Instructions burned: 33 (million)
% 8.58/2.56 % (22454)------------------------------
% 8.58/2.56 % (22454)------------------------------
% 8.58/2.57 % (22455)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_22021 for (2989ds/279Mi)
% 8.93/2.61 % (22455)Refutation not found, incomplete strategy
% 8.93/2.61 % (22455)------------------------------
% 8.93/2.61 % (22455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.93/2.61 % (22455)Termination reason: Refutation not found, incomplete strategy
% 8.93/2.61
% 8.93/2.61
% 8.93/2.61 % (22455)Memory used [KB]: 6908
% 8.93/2.61 % (22455)Time elapsed: 0.038 s
% 8.93/2.61 % (22455)Instructions burned: 138 (million)
% 8.93/2.61 % (22455)------------------------------
% 8.93/2.61 % (22455)------------------------------
% 8.93/2.62 % (22456)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_22021 for (2989ds/258Mi)
% 8.93/2.62 % (22441)Instruction limit reached!
% 8.93/2.62 % (22441)------------------------------
% 8.93/2.62 % (22441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.93/2.62 % (22441)Termination reason: Unknown
% 8.93/2.62 % (22441)Termination phase: Saturation
% 8.93/2.62
% 8.93/2.62 % (22441)Memory used [KB]: 8443
% 8.93/2.62 % (22441)Time elapsed: 0.321 s
% 8.93/2.62 % (22441)Instructions burned: 1021 (million)
% 8.93/2.62 % (22441)------------------------------
% 8.93/2.62 % (22441)------------------------------
% 8.93/2.63 % (22457)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_22021 for (2989ds/26Mi)
% 8.93/2.63 % (22457)Instruction limit reached!
% 8.93/2.63 % (22457)------------------------------
% 8.93/2.63 % (22457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.93/2.63 % (22457)Termination reason: Unknown
% 8.93/2.63 % (22457)Termination phase: shuffling
% 8.93/2.63
% 8.93/2.63 % (22457)Memory used [KB]: 1791
% 8.93/2.63 % (22457)Time elapsed: 0.009 s
% 8.93/2.63 % (22457)Instructions burned: 27 (million)
% 8.93/2.63 % (22457)------------------------------
% 8.93/2.63 % (22457)------------------------------
% 8.93/2.63 % (22453)Instruction limit reached!
% 8.93/2.63 % (22453)------------------------------
% 8.93/2.63 % (22453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.93/2.63 % (22453)Termination reason: Unknown
% 8.93/2.63 % (22453)Termination phase: Saturation
% 8.93/2.63
% 8.93/2.63 % (22453)Memory used [KB]: 7291
% 8.93/2.63 % (22453)Time elapsed: 0.111 s
% 8.93/2.63 % (22453)Instructions burned: 358 (million)
% 8.93/2.63 % (22453)------------------------------
% 8.93/2.63 % (22453)------------------------------
% 8.93/2.64 % (22458)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_22021 for (2988ds/995Mi)
% 8.93/2.64 % (22459)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_22021 for (2988ds/373Mi)
% 9.44/2.70 % (22456)Instruction limit reached!
% 9.44/2.70 % (22456)------------------------------
% 9.44/2.70 % (22456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.70 % (22456)Termination reason: Unknown
% 9.44/2.70 % (22456)Termination phase: Saturation
% 9.44/2.70
% 9.44/2.70 % (22456)Memory used [KB]: 7164
% 9.44/2.70 % (22456)Time elapsed: 0.084 s
% 9.44/2.70 % (22456)Instructions burned: 260 (million)
% 9.44/2.70 % (22456)------------------------------
% 9.44/2.70 % (22456)------------------------------
% 9.44/2.71 % (22460)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_22021 for (2988ds/253Mi)
% 9.44/2.76 % (22459)Instruction limit reached!
% 9.44/2.76 % (22459)------------------------------
% 9.44/2.76 % (22459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.76 % (22459)Termination reason: Unknown
% 9.44/2.76 % (22459)Termination phase: Saturation
% 9.44/2.76
% 9.44/2.76 % (22459)Memory used [KB]: 7547
% 9.44/2.76 % (22459)Time elapsed: 0.118 s
% 9.44/2.76 % (22459)Instructions burned: 375 (million)
% 9.44/2.76 % (22459)------------------------------
% 9.44/2.76 % (22459)------------------------------
% 9.44/2.77 % (22461)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_22021 for (2987ds/832Mi)
% 9.44/2.78 % (22460)Instruction limit reached!
% 9.44/2.78 % (22460)------------------------------
% 9.44/2.78 % (22460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.78 % (22460)Termination reason: Unknown
% 9.44/2.78 % (22460)Termination phase: Saturation
% 9.44/2.78
% 9.44/2.78 % (22460)Memory used [KB]: 7547
% 9.44/2.78 % (22460)Time elapsed: 0.094 s
% 9.44/2.78 % (22460)Instructions burned: 255 (million)
% 9.44/2.78 % (22460)------------------------------
% 9.44/2.78 % (22460)------------------------------
% 9.44/2.79 % (22462)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_22021 for (2987ds/668Mi)
% 9.44/2.80 % (22461)Refutation not found, incomplete strategy
% 9.44/2.80 % (22461)------------------------------
% 9.44/2.80 % (22461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.44/2.80 % (22461)Termination reason: Refutation not found, incomplete strategy
% 9.44/2.80
% 9.44/2.80
% 9.44/2.80 % (22461)Memory used [KB]: 6780
% 9.44/2.80 % (22461)Time elapsed: 0.026 s
% 9.44/2.80 % (22461)Instructions burned: 88 (million)
% 9.44/2.80 % (22461)------------------------------
% 9.44/2.80 % (22461)------------------------------
% 9.75/2.81 % (22463)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_22021 for (2987ds/40Mi)
% 9.75/2.82 % (22463)Instruction limit reached!
% 9.75/2.82 % (22463)------------------------------
% 9.75/2.82 % (22463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.82 % (22463)Termination reason: Unknown
% 9.75/2.82 % (22463)Termination phase: Property scanning
% 9.75/2.82
% 9.75/2.82 % (22463)Memory used [KB]: 1791
% 9.75/2.82 % (22463)Time elapsed: 0.012 s
% 9.75/2.82 % (22463)Instructions burned: 42 (million)
% 9.75/2.82 % (22463)------------------------------
% 9.75/2.82 % (22463)------------------------------
% 9.75/2.83 % (22464)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_22021 for (2987ds/294Mi)
% 9.75/2.85 % (22464)Refutation not found, incomplete strategy
% 9.75/2.85 % (22464)------------------------------
% 9.75/2.85 % (22464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.85 % (22464)Termination reason: Refutation not found, incomplete strategy
% 9.75/2.85
% 9.75/2.85
% 9.75/2.85 % (22464)Memory used [KB]: 6396
% 9.75/2.85 % (22464)Time elapsed: 0.020 s
% 9.75/2.85 % (22464)Instructions burned: 74 (million)
% 9.75/2.85 % (22464)------------------------------
% 9.75/2.85 % (22464)------------------------------
% 9.75/2.86 % (22465)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_22021 for (2986ds/187Mi)
% 9.75/2.87 % (22447)Instruction limit reached!
% 9.75/2.87 % (22447)------------------------------
% 9.75/2.87 % (22447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.87 % (22447)Termination reason: Unknown
% 9.75/2.87 % (22447)Termination phase: Saturation
% 9.75/2.87
% 9.75/2.87 % (22447)Memory used [KB]: 9210
% 9.75/2.87 % (22447)Time elapsed: 0.489 s
% 9.75/2.87 % (22447)Instructions burned: 1540 (million)
% 9.75/2.87 % (22447)------------------------------
% 9.75/2.87 % (22447)------------------------------
% 9.75/2.88 % (22466)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_22021 for (2986ds/371Mi)
% 10.33/2.91 % (22465)Instruction limit reached!
% 10.33/2.91 % (22465)------------------------------
% 10.33/2.91 % (22465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/2.91 % (22465)Termination reason: Unknown
% 10.33/2.91 % (22465)Termination phase: Saturation
% 10.33/2.91
% 10.33/2.91 % (22465)Memory used [KB]: 7164
% 10.33/2.91 % (22465)Time elapsed: 0.081 s
% 10.33/2.91 % (22465)Instructions burned: 188 (million)
% 10.33/2.91 % (22465)------------------------------
% 10.33/2.91 % (22465)------------------------------
% 10.33/2.92 % (22467)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_22021 for (2985ds/1827Mi)
% 10.33/2.95 % (22458)Instruction limit reached!
% 10.33/2.95 % (22458)------------------------------
% 10.33/2.95 % (22458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/2.95 % (22458)Termination reason: Unknown
% 10.33/2.95 % (22458)Termination phase: Saturation
% 10.33/2.95
% 10.33/2.95 % (22458)Memory used [KB]: 9083
% 10.33/2.95 % (22458)Time elapsed: 0.304 s
% 10.33/2.95 % (22458)Instructions burned: 996 (million)
% 10.33/2.95 % (22458)------------------------------
% 10.33/2.95 % (22458)------------------------------
% 10.33/2.96 % (22468)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_22021 for (2985ds/70Mi)
% 10.33/2.97 % (22468)Instruction limit reached!
% 10.33/2.97 % (22468)------------------------------
% 10.33/2.97 % (22468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/2.97 % (22468)Termination reason: Unknown
% 10.33/2.97 % (22468)Termination phase: Property scanning
% 10.33/2.97
% 10.33/2.97 % (22468)Memory used [KB]: 1918
% 10.33/2.97 % (22468)Time elapsed: 0.019 s
% 10.33/2.97 % (22468)Instructions burned: 70 (million)
% 10.33/2.97 % (22468)------------------------------
% 10.33/2.97 % (22468)------------------------------
% 10.33/2.98 % (22469)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_22021 for (2985ds/316Mi)
% 10.33/2.99 % (22462)Instruction limit reached!
% 10.33/2.99 % (22462)------------------------------
% 10.33/2.99 % (22462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/2.99 % (22462)Termination reason: Unknown
% 10.33/2.99 % (22462)Termination phase: Saturation
% 10.33/2.99
% 10.33/2.99 % (22462)Memory used [KB]: 13816
% 10.33/2.99 % (22462)Time elapsed: 0.201 s
% 10.33/2.99 % (22462)Instructions burned: 671 (million)
% 10.33/2.99 % (22462)------------------------------
% 10.33/2.99 % (22462)------------------------------
% 10.33/3.00 % (22466)Refutation not found, non-redundant clauses discarded% (22466)------------------------------
% 10.33/3.00 % (22466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/3.00 % (22466)Termination reason: Refutation not found, non-redundant clauses discarded
% 10.33/3.00
% 10.33/3.00 % (22466)Memory used [KB]: 7036
% 10.33/3.00 % (22466)Time elapsed: 0.117 s
% 10.33/3.00 % (22466)Instructions burned: 368 (million)
% 10.33/3.00 % (22466)------------------------------
% 10.33/3.00 % (22466)------------------------------
% 10.33/3.00 % (22470)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_22021 for (2985ds/932Mi)
% 10.33/3.01 % (22471)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_22021 for (2985ds/4714Mi)
% 12.99/3.02 % (22469)Refutation not found, incomplete strategy
% 12.99/3.02 % (22469)------------------------------
% 12.99/3.02 % (22469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.99/3.02 % (22469)Termination reason: Refutation not found, incomplete strategy
% 12.99/3.02
% 12.99/3.02
% 12.99/3.02 % (22469)Memory used [KB]: 6908
% 12.99/3.02 % (22469)Time elapsed: 0.041 s
% 12.99/3.02 % (22469)Instructions burned: 154 (million)
% 12.99/3.02 % (22469)------------------------------
% 12.99/3.02 % (22469)------------------------------
% 12.99/3.03 % (22472)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_22021 for (2984ds/8250Mi)
% 12.99/3.05 % (22471)Refutation not found, incomplete strategy
% 12.99/3.05 % (22471)------------------------------
% 12.99/3.05 % (22471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.99/3.05 % (22471)Termination reason: Refutation not found, incomplete strategy
% 12.99/3.05
% 12.99/3.05
% 12.99/3.05 % (22471)Memory used [KB]: 7036
% 12.99/3.05 % (22471)Time elapsed: 0.043 s
% 12.99/3.05 % (22471)Instructions burned: 157 (million)
% 12.99/3.05 % (22471)------------------------------
% 12.99/3.05 % (22471)------------------------------
% 12.99/3.06 % (22450)Instruction limit reached!
% 12.99/3.06 % (22450)------------------------------
% 12.99/3.06 % (22450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.99/3.06 % (22450)Termination reason: Unknown
% 12.99/3.06 % (22450)Termination phase: Saturation
% 12.99/3.06
% 12.99/3.06 % (22450)Memory used [KB]: 3582
% 12.99/3.06 % (22450)Time elapsed: 0.590 s
% 12.99/3.06 % (22450)Instructions burned: 1915 (million)
% 12.99/3.06 % (22450)------------------------------
% 12.99/3.06 % (22450)------------------------------
% 12.99/3.06 % (22473)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_22021 for (2984ds/770Mi)
% 12.99/3.06 % (22474)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_22021 for (2984ds/794Mi)
% 12.99/3.07 % (22473)Refutation not found, incomplete strategy
% 12.99/3.07 % (22473)------------------------------
% 12.99/3.07 % (22473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.99/3.07 % (22473)Termination reason: Refutation not found, incomplete strategy
% 12.99/3.07
% 12.99/3.07
% 12.99/3.07 % (22473)Memory used [KB]: 6140
% 12.99/3.07 % (22473)Time elapsed: 0.012 s
% 12.99/3.07 % (22473)Instructions burned: 36 (million)
% 12.99/3.07 % (22473)------------------------------
% 12.99/3.07 % (22473)------------------------------
% 12.99/3.08 % (22475)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_22021 for (2984ds/464Mi)
% 13.88/3.22 % (22475)Instruction limit reached!
% 13.88/3.22 % (22475)------------------------------
% 13.88/3.22 % (22475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.88/3.22 % (22475)Termination reason: Unknown
% 13.88/3.22 % (22475)Termination phase: Saturation
% 13.88/3.22
% 13.88/3.22 % (22475)Memory used [KB]: 6908
% 13.88/3.22 % (22475)Time elapsed: 0.141 s
% 13.88/3.22 % (22475)Instructions burned: 465 (million)
% 13.88/3.22 % (22475)------------------------------
% 13.88/3.22 % (22475)------------------------------
% 13.88/3.23 % (22476)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_22021 for (2982ds/1376Mi)
% 13.88/3.28 % (22470)Instruction limit reached!
% 13.88/3.28 % (22470)------------------------------
% 13.88/3.28 % (22470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.88/3.28 % (22470)Termination reason: Unknown
% 13.88/3.28 % (22470)Termination phase: Saturation
% 13.88/3.28
% 13.88/3.28 % (22470)Memory used [KB]: 9338
% 13.88/3.28 % (22470)Time elapsed: 0.286 s
% 13.88/3.28 % (22470)Instructions burned: 934 (million)
% 13.88/3.28 % (22470)------------------------------
% 13.88/3.28 % (22470)------------------------------
% 13.88/3.29 % (22477)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_22021 for (2982ds/906Mi)
% 14.43/3.31 % (22474)Instruction limit reached!
% 14.43/3.31 % (22474)------------------------------
% 14.43/3.31 % (22474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.43/3.31 % (22474)Termination reason: Unknown
% 14.43/3.31 % (22474)Termination phase: Saturation
% 14.43/3.31
% 14.43/3.31 % (22474)Memory used [KB]: 5884
% 14.43/3.31 % (22474)Time elapsed: 0.242 s
% 14.43/3.31 % (22474)Instructions burned: 796 (million)
% 14.43/3.31 % (22474)------------------------------
% 14.43/3.31 % (22474)------------------------------
% 14.43/3.32 % (22478)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_22021 for (2982ds/434Mi)
% 14.43/3.34 % (22478)Refutation not found, incomplete strategy
% 14.43/3.34 % (22478)------------------------------
% 14.43/3.34 % (22478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.43/3.34 % (22478)Termination reason: Refutation not found, incomplete strategy
% 14.43/3.34
% 14.43/3.34
% 14.43/3.34 % (22478)Memory used [KB]: 6652
% 14.43/3.34 % (22478)Time elapsed: 0.045 s
% 14.43/3.34 % (22478)Instructions burned: 77 (million)
% 14.43/3.34 % (22478)------------------------------
% 14.43/3.34 % (22478)------------------------------
% 14.43/3.35 % (22479)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_22021 for (2981ds/865Mi)
% 15.31/3.50 % (22467)Instruction limit reached!
% 15.31/3.50 % (22467)------------------------------
% 15.31/3.50 % (22467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.31/3.50 % (22467)Termination reason: Unknown
% 15.31/3.50 % (22467)Termination phase: Saturation
% 15.31/3.50
% 15.31/3.50 % (22467)Memory used [KB]: 9338
% 15.31/3.50 % (22467)Time elapsed: 0.581 s
% 15.31/3.50 % (22467)Instructions burned: 1829 (million)
% 15.31/3.50 % (22467)------------------------------
% 15.31/3.50 % (22467)------------------------------
% 15.31/3.51 % (22480)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_22021 for (2979ds/593Mi)
% 15.31/3.60 % (22477)Instruction limit reached!
% 15.31/3.60 % (22477)------------------------------
% 15.31/3.60 % (22477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.31/3.60 % (22477)Termination reason: Unknown
% 15.31/3.60 % (22477)Termination phase: Saturation
% 15.31/3.60
% 15.31/3.60 % (22477)Memory used [KB]: 12665
% 15.31/3.60 % (22477)Time elapsed: 0.325 s
% 15.31/3.60 % (22477)Instructions burned: 906 (million)
% 15.31/3.60 % (22477)------------------------------
% 15.31/3.60 % (22477)------------------------------
% 15.52/3.60 % (22479)Instruction limit reached!
% 15.52/3.60 % (22479)------------------------------
% 15.52/3.60 % (22479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.52/3.60 % (22479)Termination reason: Unknown
% 15.52/3.60 % (22479)Termination phase: Saturation
% 15.52/3.60
% 15.52/3.60 % (22479)Memory used [KB]: 8187
% 15.52/3.60 % (22479)Time elapsed: 0.255 s
% 15.52/3.60 % (22479)Instructions burned: 866 (million)
% 15.52/3.60 % (22479)------------------------------
% 15.52/3.60 % (22479)------------------------------
% 15.52/3.61 % (22481)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_22021 for (2979ds/443Mi)
% 15.52/3.61 % (22482)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_22021 for (2978ds/594Mi)
% 15.52/3.65 % (22476)Instruction limit reached!
% 15.52/3.65 % (22476)------------------------------
% 15.52/3.65 % (22476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.52/3.65 % (22476)Termination reason: Unknown
% 15.52/3.65 % (22476)Termination phase: Saturation
% 15.52/3.65
% 15.52/3.65 % (22476)Memory used [KB]: 12281
% 15.52/3.65 % (22476)Time elapsed: 0.443 s
% 15.52/3.65 % (22476)Instructions burned: 1378 (million)
% 15.52/3.65 % (22476)------------------------------
% 15.52/3.65 % (22476)------------------------------
% 15.52/3.66 % (22483)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_22021 for (2978ds/327Mi)
% 15.52/3.69 % (22480)Instruction limit reached!
% 15.52/3.69 % (22480)------------------------------
% 15.52/3.69 % (22480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.52/3.69 % (22480)Termination reason: Unknown
% 15.52/3.69 % (22480)Termination phase: Saturation
% 15.52/3.69
% 15.52/3.69 % (22480)Memory used [KB]: 8315
% 15.52/3.69 % (22480)Time elapsed: 0.181 s
% 15.52/3.69 % (22480)Instructions burned: 593 (million)
% 15.52/3.69 % (22480)------------------------------
% 15.52/3.69 % (22480)------------------------------
% 16.92/3.70 % (22484)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_22021 for (2978ds/5411Mi)
% 16.92/3.72 % (22484)Refutation not found, incomplete strategy
% 16.92/3.72 % (22484)------------------------------
% 16.92/3.72 % (22484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.92/3.72 % (22484)Termination reason: Refutation not found, incomplete strategy
% 16.92/3.72
% 16.92/3.72
% 16.92/3.72 % (22484)Memory used [KB]: 6652
% 16.92/3.72 % (22484)Time elapsed: 0.023 s
% 16.92/3.72 % (22484)Instructions burned: 75 (million)
% 16.92/3.72 % (22484)------------------------------
% 16.92/3.72 % (22484)------------------------------
% 16.92/3.73 % (22485)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_22021 for (2977ds/1762Mi)
% 16.92/3.74 % (22481)Instruction limit reached!
% 16.92/3.74 % (22481)------------------------------
% 16.92/3.74 % (22481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.92/3.74 % (22481)Termination reason: Unknown
% 16.92/3.74 % (22481)Termination phase: Saturation
% 16.92/3.74
% 16.92/3.74 % (22481)Memory used [KB]: 7803
% 16.92/3.74 % (22481)Time elapsed: 0.138 s
% 16.92/3.74 % (22481)Instructions burned: 445 (million)
% 16.92/3.74 % (22481)------------------------------
% 16.92/3.74 % (22481)------------------------------
% 16.92/3.75 % (22486)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_22021 for (2977ds/96Mi)
% 16.92/3.75 % (22446)Instruction limit reached!
% 16.92/3.75 % (22446)------------------------------
% 16.92/3.75 % (22446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.92/3.75 % (22446)Termination reason: Unknown
% 16.92/3.75 % (22446)Termination phase: Saturation
% 16.92/3.75
% 16.92/3.75 % (22446)Memory used [KB]: 11897
% 16.92/3.75 % (22446)Time elapsed: 1.403 s
% 16.92/3.75 % (22446)Instructions burned: 4438 (million)
% 16.92/3.75 % (22446)------------------------------
% 16.92/3.75 % (22446)------------------------------
% 16.92/3.76 % (22483)Instruction limit reached!
% 16.92/3.76 % (22483)------------------------------
% 16.92/3.76 % (22483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.92/3.76 % (22483)Termination reason: Unknown
% 16.92/3.76 % (22483)Termination phase: Saturation
% 16.92/3.76
% 16.92/3.76 % (22483)Memory used [KB]: 7675
% 16.92/3.76 % (22483)Time elapsed: 0.102 s
% 16.92/3.76 % (22483)Instructions burned: 330 (million)
% 16.92/3.76 % (22483)------------------------------
% 16.92/3.76 % (22483)------------------------------
% 16.92/3.76 % (22487)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_22021 for (2977ds/503Mi)
% 16.92/3.77 % (22488)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_22021 for (2977ds/90Mi)
% 16.92/3.78 % (22486)Instruction limit reached!
% 16.92/3.78 % (22486)------------------------------
% 16.92/3.78 % (22486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.92/3.78 % (22486)Termination reason: Unknown
% 16.92/3.78 % (22486)Termination phase: Property scanning
% 16.92/3.78
% 16.92/3.78 % (22486)Memory used [KB]: 2046
% 16.92/3.78 % (22486)Time elapsed: 0.025 s
% 16.92/3.78 % (22486)Instructions burned: 96 (million)
% 16.92/3.78 % (22486)------------------------------
% 16.92/3.78 % (22486)------------------------------
% 16.92/3.79 % (22489)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_22021 for (2977ds/593Mi)
% 16.92/3.79 % (22487)Refutation not found, incomplete strategy
% 16.92/3.79 % (22487)------------------------------
% 16.92/3.79 % (22487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.92/3.79 % (22487)Termination reason: Refutation not found, incomplete strategy
% 16.92/3.79
% 16.92/3.79
% 16.92/3.79 % (22487)Memory used [KB]: 6780
% 16.92/3.79 % (22487)Time elapsed: 0.027 s
% 16.92/3.79 % (22487)Instructions burned: 87 (million)
% 16.92/3.79 % (22487)------------------------------
% 16.92/3.79 % (22487)------------------------------
% 16.92/3.79 % (22488)Instruction limit reached!
% 16.92/3.79 % (22488)------------------------------
% 16.92/3.79 % (22488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.92/3.79 % (22488)Termination reason: Unknown
% 16.92/3.79 % (22488)Termination phase: Saturation
% 16.92/3.79
% 16.92/3.79 % (22488)Memory used [KB]: 6524
% 16.92/3.79 % (22488)Time elapsed: 0.026 s
% 16.92/3.79 % (22488)Instructions burned: 90 (million)
% 16.92/3.79 % (22488)------------------------------
% 16.92/3.79 % (22488)------------------------------
% 17.48/3.80 % (22482)Instruction limit reached!
% 17.48/3.80 % (22482)------------------------------
% 17.48/3.80 % (22482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.48/3.80 % (22482)Termination reason: Unknown
% 17.48/3.80 % (22482)Termination phase: Saturation
% 17.48/3.80
% 17.48/3.80 % (22482)Memory used [KB]: 7291
% 17.48/3.80 % (22482)Time elapsed: 0.187 s
% 17.48/3.80 % (22482)Instructions burned: 596 (million)
% 17.48/3.80 % (22482)------------------------------
% 17.48/3.80 % (22482)------------------------------
% 17.48/3.80 % (22490)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_22021 for (2977ds/1512Mi)
% 17.48/3.80 % (22491)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_22021 for (2977ds/569Mi)
% 17.48/3.81 % (22492)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_22021 for (2977ds/501Mi)
% 17.48/3.83 % (22490)Refutation not found, incomplete strategy
% 17.48/3.83 % (22490)------------------------------
% 17.48/3.83 % (22490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.48/3.83 % (22490)Termination reason: Refutation not found, incomplete strategy
% 17.48/3.83
% 17.48/3.83
% 17.48/3.83 % (22490)Memory used [KB]: 6780
% 17.48/3.83 % (22490)Time elapsed: 0.029 s
% 17.48/3.83 % (22490)Instructions burned: 92 (million)
% 17.48/3.83 % (22490)------------------------------
% 17.48/3.83 % (22490)------------------------------
% 17.48/3.84 % (22493)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_22021 for (2976ds/562Mi)
% 17.48/3.85 % (22492)Refutation not found, incomplete strategy
% 17.48/3.85 % (22492)------------------------------
% 17.48/3.85 % (22492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.48/3.85 % (22492)Termination reason: Refutation not found, incomplete strategy
% 17.48/3.85
% 17.48/3.85
% 17.48/3.85 % (22492)Memory used [KB]: 7291
% 17.48/3.85 % (22492)Time elapsed: 0.041 s
% 17.48/3.85 % (22492)Instructions burned: 135 (million)
% 17.48/3.85 % (22492)------------------------------
% 17.48/3.85 % (22492)------------------------------
% 17.48/3.86 % (22494)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_22021 for (2976ds/406Mi)
% 17.86/3.97 % (22491)Instruction limit reached!
% 17.86/3.97 % (22491)------------------------------
% 17.86/3.97 % (22491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.86/3.97 % (22491)Termination reason: Unknown
% 17.86/3.97 % (22491)Termination phase: Saturation
% 17.86/3.97
% 17.86/3.97 % (22491)Memory used [KB]: 7803
% 17.86/3.97 % (22491)Time elapsed: 0.167 s
% 17.86/3.97 % (22491)Instructions burned: 571 (million)
% 17.86/3.97 % (22491)------------------------------
% 17.86/3.97 % (22491)------------------------------
% 17.86/3.97 % (22489)Instruction limit reached!
% 17.86/3.97 % (22489)------------------------------
% 17.86/3.97 % (22489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.86/3.97 % (22489)Termination reason: Unknown
% 17.86/3.97 % (22489)Termination phase: Saturation
% 17.86/3.97
% 17.86/3.97 % (22489)Memory used [KB]: 7547
% 17.86/3.97 % (22489)Time elapsed: 0.188 s
% 17.86/3.97 % (22489)Instructions burned: 593 (million)
% 17.86/3.97 % (22489)------------------------------
% 17.86/3.97 % (22489)------------------------------
% 17.86/3.98 % (22494)Refutation not found, non-redundant clauses discarded% (22494)------------------------------
% 17.86/3.98 % (22494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.86/3.98 % (22494)Termination reason: Refutation not found, non-redundant clauses discarded
% 17.86/3.98
% 17.86/3.98 % (22494)Memory used [KB]: 7291
% 17.86/3.98 % (22494)Time elapsed: 0.119 s
% 17.86/3.98 % (22494)Instructions burned: 382 (million)
% 17.86/3.98 % (22494)------------------------------
% 17.86/3.98 % (22494)------------------------------
% 17.86/3.98 % (22495)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_22021 for (2975ds/582Mi)
% 17.86/3.98 % (22496)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_22021 for (2975ds/456Mi)
% 17.86/3.99 % (22497)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_22021 for (2975ds/393Mi)
% 17.86/4.00 % (22493)Instruction limit reached!
% 17.86/4.00 % (22493)------------------------------
% 17.86/4.00 % (22493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.86/4.00 % (22493)Termination reason: Unknown
% 17.86/4.00 % (22493)Termination phase: Saturation
% 17.86/4.00
% 17.86/4.00 % (22493)Memory used [KB]: 7675
% 17.86/4.00 % (22493)Time elapsed: 0.163 s
% 17.86/4.00 % (22493)Instructions burned: 562 (million)
% 17.86/4.00 % (22493)------------------------------
% 17.86/4.00 % (22493)------------------------------
% 17.86/4.01 % (22498)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_22021 for (2975ds/1335Mi)
% 20.09/4.02 % (22496)Refutation not found, incomplete strategy
% 20.09/4.02 % (22496)------------------------------
% 20.09/4.02 % (22496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.09/4.02 % (22496)Termination reason: Refutation not found, incomplete strategy
% 20.09/4.02
% 20.09/4.02
% 20.09/4.02 % (22496)Memory used [KB]: 7291
% 20.09/4.02 % (22496)Time elapsed: 0.042 s
% 20.09/4.02 % (22496)Instructions burned: 143 (million)
% 20.09/4.02 % (22496)------------------------------
% 20.09/4.02 % (22496)------------------------------
% 20.09/4.03 % (22499)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_22021 for (2974ds/3373Mi)
% 20.09/4.10 % (22449)Instruction limit reached!
% 20.09/4.10 % (22449)------------------------------
% 20.09/4.10 % (22449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.09/4.10 % (22449)Termination reason: Unknown
% 20.09/4.10 % (22449)Termination phase: Saturation
% 20.09/4.10
% 20.09/4.10 % (22449)Memory used [KB]: 17398
% 20.09/4.10 % (22449)Time elapsed: 1.658 s
% 20.09/4.10 % (22449)Instructions burned: 5206 (million)
% 20.09/4.10 % (22449)------------------------------
% 20.09/4.10 % (22449)------------------------------
% 20.09/4.10 % (22497)Instruction limit reached!
% 20.09/4.10 % (22497)------------------------------
% 20.09/4.10 % (22497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.09/4.10 % (22497)Termination reason: Unknown
% 20.09/4.10 % (22497)Termination phase: Saturation
% 20.09/4.10
% 20.09/4.10 % (22497)Memory used [KB]: 7419
% 20.09/4.10 % (22497)Time elapsed: 0.112 s
% 20.09/4.10 % (22497)Instructions burned: 393 (million)
% 20.09/4.10 % (22497)------------------------------
% 20.09/4.10 % (22497)------------------------------
% 20.09/4.11 % (22500)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_22021 for (2974ds/474Mi)
% 20.09/4.11 % (22501)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_22021 for (2974ds/157Mi)
% 20.57/4.15 % (22501)Instruction limit reached!
% 20.57/4.15 % (22501)------------------------------
% 20.57/4.15 % (22501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.57/4.15 % (22501)Termination reason: Unknown
% 20.57/4.15 % (22501)Termination phase: Saturation
% 20.57/4.15
% 20.57/4.15 % (22501)Memory used [KB]: 6780
% 20.57/4.15 % (22501)Time elapsed: 0.044 s
% 20.57/4.15 % (22501)Instructions burned: 160 (million)
% 20.57/4.15 % (22501)------------------------------
% 20.57/4.15 % (22501)------------------------------
% 20.57/4.16 % (22502)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_22021 for (2973ds/590Mi)
% 20.57/4.16 % (22495)Instruction limit reached!
% 20.57/4.16 % (22495)------------------------------
% 20.57/4.16 % (22495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.57/4.16 % (22495)Termination reason: Unknown
% 20.57/4.16 % (22495)Termination phase: Saturation
% 20.57/4.16
% 20.57/4.16 % (22495)Memory used [KB]: 7547
% 20.57/4.16 % (22495)Time elapsed: 0.180 s
% 20.57/4.16 % (22495)Instructions burned: 582 (million)
% 20.57/4.16 % (22495)------------------------------
% 20.57/4.16 % (22495)------------------------------
% 20.57/4.17 % (22503)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_22021 for (2973ds/104Mi)
% 20.80/4.20 % (22503)Instruction limit reached!
% 20.80/4.20 % (22503)------------------------------
% 20.80/4.20 % (22503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.80/4.20 % (22503)Termination reason: Unknown
% 20.80/4.20 % (22503)Termination phase: Saturation
% 20.80/4.20
% 20.80/4.20 % (22503)Memory used [KB]: 2430
% 20.80/4.20 % (22503)Time elapsed: 0.031 s
% 20.80/4.20 % (22503)Instructions burned: 107 (million)
% 20.80/4.20 % (22503)------------------------------
% 20.80/4.20 % (22503)------------------------------
% 20.80/4.21 % (22504)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_22021 for (2973ds/414Mi)
% 20.80/4.25 % (22485)Instruction limit reached!
% 20.80/4.25 % (22485)------------------------------
% 20.80/4.25 % (22485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.80/4.25 % (22485)Termination reason: Unknown
% 20.80/4.25 % (22485)Termination phase: Saturation
% 20.80/4.25
% 20.80/4.25 % (22485)Memory used [KB]: 8443
% 20.80/4.25 % (22485)Time elapsed: 0.517 s
% 20.80/4.25 % (22485)Instructions burned: 1762 (million)
% 20.80/4.25 % (22485)------------------------------
% 20.80/4.25 % (22485)------------------------------
% 20.80/4.25 % (22500)Instruction limit reached!
% 20.80/4.25 % (22500)------------------------------
% 20.80/4.25 % (22500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.80/4.25 % (22500)Termination reason: Unknown
% 20.80/4.25 % (22500)Termination phase: Saturation
% 20.80/4.25
% 20.80/4.25 % (22500)Memory used [KB]: 7675
% 20.80/4.25 % (22500)Time elapsed: 0.146 s
% 20.80/4.25 % (22500)Instructions burned: 474 (million)
% 20.80/4.25 % (22500)------------------------------
% 20.80/4.25 % (22500)------------------------------
% 20.80/4.26 % (22505)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_22021 for (2972ds/715Mi)
% 20.80/4.26 % (22506)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_22021 for (2972ds/961Mi)
% 21.15/4.32 % (22504)Instruction limit reached!
% 21.15/4.32 % (22504)------------------------------
% 21.15/4.32 % (22504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.15/4.32 % (22504)Termination reason: Unknown
% 21.15/4.32 % (22504)Termination phase: Saturation
% 21.15/4.32
% 21.15/4.32 % (22504)Memory used [KB]: 7419
% 21.15/4.32 % (22504)Time elapsed: 0.118 s
% 21.15/4.32 % (22504)Instructions burned: 416 (million)
% 21.15/4.32 % (22504)------------------------------
% 21.15/4.32 % (22504)------------------------------
% 21.15/4.33 % (22507)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_22021 for (2971ds/1213Mi)
% 21.15/4.34 % (22502)Instruction limit reached!
% 21.15/4.34 % (22502)------------------------------
% 21.15/4.34 % (22502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.15/4.34 % (22502)Termination reason: Unknown
% 21.15/4.34 % (22502)Termination phase: Saturation
% 21.15/4.34
% 21.15/4.34 % (22502)Memory used [KB]: 6524
% 21.15/4.34 % (22502)Time elapsed: 0.178 s
% 21.15/4.34 % (22502)Instructions burned: 590 (million)
% 21.15/4.34 % (22502)------------------------------
% 21.15/4.34 % (22502)------------------------------
% 21.15/4.35 % (22508)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_22021 for (2971ds/1979Mi)
% 21.57/4.40 % (22498)Instruction limit reached!
% 21.57/4.40 % (22498)------------------------------
% 21.57/4.40 % (22498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.57/4.40 % (22498)Termination reason: Unknown
% 21.57/4.40 % (22498)Termination phase: Saturation
% 21.57/4.40
% 21.57/4.40 % (22498)Memory used [KB]: 8315
% 21.57/4.40 % (22498)Time elapsed: 0.395 s
% 21.57/4.40 % (22498)Instructions burned: 1335 (million)
% 21.57/4.40 % (22498)------------------------------
% 21.57/4.40 % (22498)------------------------------
% 21.57/4.41 % (22509)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_22021 for (2971ds/481Mi)
% 21.57/4.48 % (22505)Instruction limit reached!
% 21.57/4.48 % (22505)------------------------------
% 21.57/4.48 % (22505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.57/4.48 % (22505)Termination reason: Unknown
% 21.57/4.48 % (22505)Termination phase: Saturation
% 21.57/4.48
% 21.57/4.48 % (22505)Memory used [KB]: 4733
% 21.57/4.48 % (22505)Time elapsed: 0.219 s
% 21.57/4.48 % (22505)Instructions burned: 717 (million)
% 21.57/4.48 % (22505)------------------------------
% 21.57/4.48 % (22505)------------------------------
% 21.57/4.49 % (22510)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_22021 for (2970ds/783Mi)
% 22.31/4.56 % (22509)Instruction limit reached!
% 22.31/4.56 % (22509)------------------------------
% 22.31/4.56 % (22509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.31/4.56 % (22509)Termination reason: Unknown
% 22.31/4.56 % (22509)Termination phase: Saturation
% 22.31/4.56
% 22.31/4.56 % (22509)Memory used [KB]: 7675
% 22.31/4.56 % (22509)Time elapsed: 0.168 s
% 22.31/4.56 % (22509)Instructions burned: 483 (million)
% 22.31/4.56 % (22509)------------------------------
% 22.31/4.56 % (22509)------------------------------
% 22.31/4.56 % (22506)Instruction limit reached!
% 22.31/4.56 % (22506)------------------------------
% 22.31/4.56 % (22506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.31/4.56 % (22506)Termination reason: Unknown
% 22.31/4.56 % (22506)Termination phase: Saturation
% 22.31/4.56
% 22.31/4.56 % (22506)Memory used [KB]: 7931
% 22.31/4.56 % (22506)Time elapsed: 0.301 s
% 22.31/4.56 % (22506)Instructions burned: 962 (million)
% 22.31/4.56 % (22506)------------------------------
% 22.31/4.56 % (22506)------------------------------
% 22.31/4.57 % (22511)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_22021 for (2969ds/432Mi)
% 22.31/4.57 % (22512)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_22021 for (2969ds/1670Mi)
% 22.97/4.71 % (22507)Instruction limit reached!
% 22.97/4.71 % (22507)------------------------------
% 22.97/4.71 % (22507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.97/4.71 % (22507)Termination reason: Unknown
% 22.97/4.71 % (22507)Termination phase: Saturation
% 22.97/4.71
% 22.97/4.71 % (22507)Memory used [KB]: 8443
% 22.97/4.71 % (22507)Time elapsed: 0.395 s
% 22.97/4.71 % (22507)Instructions burned: 1216 (million)
% 22.97/4.71 % (22507)------------------------------
% 22.97/4.71 % (22507)------------------------------
% 22.97/4.71 % (22511)Instruction limit reached!
% 22.97/4.71 % (22511)------------------------------
% 22.97/4.71 % (22511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.97/4.71 % (22511)Termination reason: Unknown
% 22.97/4.71 % (22511)Termination phase: Saturation
% 22.97/4.71
% 22.97/4.71 % (22511)Memory used [KB]: 7675
% 22.97/4.71 % (22511)Time elapsed: 0.164 s
% 22.97/4.71 % (22511)Instructions burned: 434 (million)
% 22.97/4.71 % (22511)------------------------------
% 22.97/4.71 % (22511)------------------------------
% 22.97/4.72 % (22513)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_22021 for (2967ds/90Mi)
% 22.97/4.72 % (22514)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_22021 for (2967ds/346Mi)
% 22.97/4.73 % (22510)Instruction limit reached!
% 22.97/4.73 % (22510)------------------------------
% 22.97/4.73 % (22510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.97/4.73 % (22510)Termination reason: Unknown
% 22.97/4.73 % (22510)Termination phase: Saturation
% 22.97/4.73
% 22.97/4.73 % (22510)Memory used [KB]: 8187
% 22.97/4.73 % (22510)Time elapsed: 0.268 s
% 22.97/4.73 % (22510)Instructions burned: 784 (million)
% 22.97/4.73 % (22510)------------------------------
% 22.97/4.73 % (22510)------------------------------
% 22.97/4.74 % (22515)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_22021 for (2967ds/401Mi)
% 22.97/4.74 % (22513)Instruction limit reached!
% 22.97/4.74 % (22513)------------------------------
% 22.97/4.74 % (22513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.97/4.74 % (22513)Termination reason: Unknown
% 22.97/4.74 % (22513)Termination phase: Saturation
% 22.97/4.74
% 22.97/4.74 % (22513)Memory used [KB]: 6524
% 22.97/4.74 % (22513)Time elapsed: 0.026 s
% 22.97/4.74 % (22513)Instructions burned: 91 (million)
% 22.97/4.74 % (22513)------------------------------
% 22.97/4.74 % (22513)------------------------------
% 22.97/4.75 % (22516)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_22021 for (2967ds/6454Mi)
% 23.90/4.82 % (22514)Instruction limit reached!
% 23.90/4.82 % (22514)------------------------------
% 23.90/4.82 % (22514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.90/4.82 % (22514)Termination reason: Unknown
% 23.90/4.82 % (22514)Termination phase: Saturation
% 23.90/4.82
% 23.90/4.82 % (22514)Memory used [KB]: 7419
% 23.90/4.82 % (22514)Time elapsed: 0.103 s
% 23.90/4.82 % (22514)Instructions burned: 346 (million)
% 23.90/4.82 % (22514)------------------------------
% 23.90/4.82 % (22514)------------------------------
% 23.90/4.83 % (22517)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_22021 for (2966ds/283Mi)
% 23.90/4.86 % (22515)Instruction limit reached!
% 23.90/4.86 % (22515)------------------------------
% 23.90/4.86 % (22515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.90/4.86 % (22515)Termination reason: Unknown
% 23.90/4.86 % (22515)Termination phase: Saturation
% 23.90/4.86
% 23.90/4.86 % (22515)Memory used [KB]: 7931
% 23.90/4.86 % (22515)Time elapsed: 0.119 s
% 23.90/4.86 % (22515)Instructions burned: 401 (million)
% 23.90/4.86 % (22515)------------------------------
% 23.90/4.86 % (22515)------------------------------
% 23.90/4.87 % (22518)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_22021 for (2966ds/865Mi)
% 24.24/4.91 % (22518)Refutation not found, incomplete strategy
% 24.24/4.91 % (22518)------------------------------
% 24.24/4.91 % (22518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.24/4.91 % (22518)Termination reason: Refutation not found, incomplete strategy
% 24.24/4.91
% 24.24/4.91
% 24.24/4.91 % (22518)Memory used [KB]: 7419
% 24.24/4.91 % (22518)Time elapsed: 0.042 s
% 24.24/4.91 % (22518)Instructions burned: 142 (million)
% 24.24/4.91 % (22518)------------------------------
% 24.24/4.91 % (22518)------------------------------
% 24.24/4.92 % (22517)Instruction limit reached!
% 24.24/4.92 % (22517)------------------------------
% 24.24/4.92 % (22517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.24/4.92 % (22517)Termination reason: Unknown
% 24.24/4.92 % (22517)Termination phase: Saturation
% 24.24/4.92
% 24.24/4.92 % (22517)Memory used [KB]: 7291
% 24.24/4.92 % (22517)Time elapsed: 0.090 s
% 24.24/4.92 % (22517)Instructions burned: 285 (million)
% 24.24/4.92 % (22517)------------------------------
% 24.24/4.92 % (22517)------------------------------
% 24.24/4.92 % (22519)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_22021 for (2965ds/4528Mi)
% 24.24/4.93 % (22520)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_22021 for (2965ds/1001Mi)
% 24.24/4.93 % (22519)Refutation not found, incomplete strategy
% 24.24/4.93 % (22519)------------------------------
% 24.24/4.93 % (22519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.24/4.93 % (22519)Termination reason: Refutation not found, incomplete strategy
% 24.24/4.93
% 24.24/4.93
% 24.24/4.93 % (22519)Memory used [KB]: 1663
% 24.24/4.93 % (22519)Time elapsed: 0.013 s
% 24.24/4.93 % (22519)Instructions burned: 37 (million)
% 24.24/4.93 % (22519)------------------------------
% 24.24/4.93 % (22519)------------------------------
% 24.24/4.94 % (22521)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_22021 for (2965ds/102Mi)
% 24.24/4.97 % (22508)Instruction limit reached!
% 24.24/4.97 % (22508)------------------------------
% 24.24/4.97 % (22508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.24/4.97 % (22508)Termination reason: Unknown
% 24.24/4.97 % (22508)Termination phase: Saturation
% 24.24/4.97
% 24.24/4.97 % (22508)Memory used [KB]: 7803
% 24.24/4.97 % (22508)Time elapsed: 0.644 s
% 24.24/4.97 % (22508)Instructions burned: 1980 (million)
% 24.24/4.97 % (22508)------------------------------
% 24.24/4.97 % (22508)------------------------------
% 24.24/4.97 % (22521)Instruction limit reached!
% 24.24/4.97 % (22521)------------------------------
% 24.24/4.97 % (22521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.24/4.97 % (22521)Termination reason: Unknown
% 24.24/4.97 % (22521)Termination phase: Property scanning
% 24.24/4.97
% 24.24/4.97 % (22521)Memory used [KB]: 2046
% 24.24/4.97 % (22521)Time elapsed: 0.027 s
% 24.24/4.97 % (22521)Instructions burned: 103 (million)
% 24.24/4.97 % (22521)------------------------------
% 24.24/4.97 % (22521)------------------------------
% 24.24/4.98 % (22522)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_22021 for (2965ds/952Mi)
% 24.24/4.98 % (22523)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_22021 for (2965ds/578Mi)
% 27.11/5.03 % (22499)Instruction limit reached!
% 27.11/5.03 % (22499)------------------------------
% 27.11/5.03 % (22499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.11/5.03 % (22499)Termination reason: Unknown
% 27.11/5.03 % (22499)Termination phase: Saturation
% 27.11/5.03
% 27.11/5.03 % (22499)Memory used [KB]: 11897
% 27.11/5.03 % (22499)Time elapsed: 1.002 s
% 27.11/5.03 % (22499)Instructions burned: 3373 (million)
% 27.11/5.03 % (22499)------------------------------
% 27.11/5.03 % (22499)------------------------------
% 27.11/5.04 % (22524)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_22021 for (2964ds/643Mi)
% 27.11/5.08 % (22512)Instruction limit reached!
% 27.11/5.08 % (22512)------------------------------
% 27.11/5.08 % (22512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.11/5.08 % (22512)Termination reason: Unknown
% 27.11/5.08 % (22512)Termination phase: Saturation
% 27.11/5.08
% 27.11/5.08 % (22512)Memory used [KB]: 9722
% 27.11/5.08 % (22512)Time elapsed: 0.537 s
% 27.11/5.08 % (22512)Instructions burned: 1670 (million)
% 27.11/5.08 % (22512)------------------------------
% 27.11/5.08 % (22512)------------------------------
% 27.11/5.09 % (22525)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_22021 for (2964ds/865Mi)
% 27.71/5.15 % (22523)Instruction limit reached!
% 27.71/5.15 % (22523)------------------------------
% 27.71/5.15 % (22523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.71/5.15 % (22523)Termination reason: Unknown
% 27.71/5.15 % (22523)Termination phase: Saturation
% 27.71/5.15
% 27.71/5.15 % (22523)Memory used [KB]: 7419
% 27.71/5.15 % (22523)Time elapsed: 0.175 s
% 27.71/5.15 % (22523)Instructions burned: 579 (million)
% 27.71/5.15 % (22523)------------------------------
% 27.71/5.15 % (22523)------------------------------
% 27.71/5.16 % (22526)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_22021 for (2963ds/1174Mi)
% 28.05/5.23 % (22520)Instruction limit reached!
% 28.05/5.23 % (22520)------------------------------
% 28.05/5.23 % (22520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.05/5.23 % (22520)Termination reason: Unknown
% 28.05/5.23 % (22520)Termination phase: Saturation
% 28.05/5.23
% 28.05/5.23 % (22520)Memory used [KB]: 9210
% 28.05/5.23 % (22520)Time elapsed: 0.307 s
% 28.05/5.23 % (22520)Instructions burned: 1003 (million)
% 28.05/5.23 % (22520)------------------------------
% 28.05/5.23 % (22520)------------------------------
% 28.05/5.24 % (22524)Instruction limit reached!
% 28.05/5.24 % (22524)------------------------------
% 28.05/5.24 % (22524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.05/5.24 % (22524)Termination reason: Unknown
% 28.05/5.24 % (22524)Termination phase: Saturation
% 28.05/5.24
% 28.05/5.24 % (22524)Memory used [KB]: 8955
% 28.05/5.24 % (22524)Time elapsed: 0.197 s
% 28.05/5.24 % (22524)Instructions burned: 645 (million)
% 28.05/5.24 % (22524)------------------------------
% 28.05/5.24 % (22524)------------------------------
% 28.05/5.24 % (22527)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_22021 for (2962ds/644Mi)
% 28.05/5.25 % (22528)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_22021 for (2962ds/1201Mi)
% 28.05/5.27 % (22522)Instruction limit reached!
% 28.05/5.27 % (22522)------------------------------
% 28.05/5.27 % (22522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.05/5.27 % (22522)Termination reason: Unknown
% 28.05/5.27 % (22522)Termination phase: Saturation
% 28.05/5.27
% 28.05/5.27 % (22522)Memory used [KB]: 8955
% 28.05/5.27 % (22522)Time elapsed: 0.300 s
% 28.05/5.27 % (22522)Instructions burned: 953 (million)
% 28.05/5.27 % (22522)------------------------------
% 28.05/5.27 % (22522)------------------------------
% 28.05/5.28 % (22529)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_22021 for (2962ds/1046Mi)
% 28.05/5.29 % (22527)Refutation not found, incomplete strategy
% 28.05/5.29 % (22527)------------------------------
% 28.05/5.29 % (22527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.05/5.29 % (22527)Termination reason: Refutation not found, incomplete strategy
% 28.05/5.29
% 28.05/5.29
% 28.05/5.29 % (22527)Memory used [KB]: 7547
% 28.05/5.29 % (22527)Time elapsed: 0.043 s
% 28.05/5.29 % (22527)Instructions burned: 143 (million)
% 28.05/5.29 % (22527)------------------------------
% 28.05/5.29 % (22527)------------------------------
% 28.05/5.30 % (22530)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_22021 for (2962ds/222Mi)
% 28.64/5.36 % (22530)Instruction limit reached!
% 28.64/5.36 % (22530)------------------------------
% 28.64/5.36 % (22530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.64/5.36 % (22530)Termination reason: Unknown
% 28.64/5.36 % (22530)Termination phase: Saturation
% 28.64/5.36
% 28.64/5.36 % (22530)Memory used [KB]: 7291
% 28.64/5.36 % (22530)Time elapsed: 0.063 s
% 28.64/5.36 % (22530)Instructions burned: 224 (million)
% 28.64/5.36 % (22530)------------------------------
% 28.64/5.36 % (22530)------------------------------
% 28.64/5.36 % (22525)Instruction limit reached!
% 28.64/5.36 % (22525)------------------------------
% 28.64/5.36 % (22525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.64/5.36 % (22525)Termination reason: Unknown
% 28.64/5.36 % (22525)Termination phase: Saturation
% 28.64/5.36
% 28.64/5.36 % (22525)Memory used [KB]: 9210
% 28.64/5.36 % (22525)Time elapsed: 0.269 s
% 28.64/5.36 % (22525)Instructions burned: 866 (million)
% 28.64/5.36 % (22525)------------------------------
% 28.64/5.36 % (22525)------------------------------
% 28.64/5.37 % (22531)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_22021 for (2961ds/68Mi)
% 28.64/5.37 % (22532)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_22021 for (2961ds/454Mi)
% 28.64/5.39 % (22531)Instruction limit reached!
% 28.64/5.39 % (22531)------------------------------
% 28.64/5.39 % (22531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.64/5.39 % (22531)Termination reason: Unknown
% 28.64/5.39 % (22531)Termination phase: Property scanning
% 28.64/5.39
% 28.64/5.39 % (22531)Memory used [KB]: 1918
% 28.64/5.39 % (22531)Time elapsed: 0.021 s
% 28.64/5.39 % (22531)Instructions burned: 71 (million)
% 28.64/5.39 % (22531)------------------------------
% 28.64/5.39 % (22531)------------------------------
% 29.22/5.40 % (22533)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_22021 for (2961ds/360Mi)
% 29.42/5.50 % (22533)Instruction limit reached!
% 29.42/5.50 % (22533)------------------------------
% 29.42/5.50 % (22533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.42/5.50 % (22533)Termination reason: Unknown
% 29.42/5.50 % (22533)Termination phase: Saturation
% 29.42/5.50
% 29.42/5.50 % (22533)Memory used [KB]: 7931
% 29.42/5.50 % (22533)Time elapsed: 0.102 s
% 29.42/5.50 % (22533)Instructions burned: 362 (million)
% 29.42/5.50 % (22533)------------------------------
% 29.42/5.50 % (22533)------------------------------
% 29.42/5.50 % (22532)Instruction limit reached!
% 29.42/5.50 % (22532)------------------------------
% 29.42/5.50 % (22532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.42/5.50 % (22532)Termination reason: Unknown
% 29.42/5.50 % (22532)Termination phase: Saturation
% 29.42/5.50
% 29.42/5.50 % (22532)Memory used [KB]: 12537
% 29.42/5.50 % (22532)Time elapsed: 0.134 s
% 29.42/5.50 % (22532)Instructions burned: 454 (million)
% 29.42/5.50 % (22532)------------------------------
% 29.42/5.50 % (22532)------------------------------
% 29.42/5.51 % (22534)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_22021 for (2960ds/157Mi)
% 29.42/5.51 % (22526)Instruction limit reached!
% 29.42/5.51 % (22526)------------------------------
% 29.42/5.51 % (22526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.42/5.51 % (22526)Termination reason: Unknown
% 29.42/5.51 % (22526)Termination phase: Saturation
% 29.42/5.51
% 29.42/5.51 % (22526)Memory used [KB]: 9210
% 29.42/5.51 % (22526)Time elapsed: 0.354 s
% 29.42/5.51 % (22526)Instructions burned: 1175 (million)
% 29.42/5.51 % (22526)------------------------------
% 29.42/5.51 % (22526)------------------------------
% 29.42/5.51 % (22535)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_22021 for (2960ds/5061Mi)
% 29.42/5.52 % (22536)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_22021 for (2959ds/2401Mi)
% 29.42/5.55 % (22534)Instruction limit reached!
% 29.42/5.55 % (22534)------------------------------
% 29.42/5.55 % (22534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.42/5.55 % (22534)Termination reason: Unknown
% 29.42/5.55 % (22534)Termination phase: Saturation
% 29.42/5.55
% 29.42/5.55 % (22534)Memory used [KB]: 6780
% 29.42/5.55 % (22534)Time elapsed: 0.042 s
% 29.42/5.55 % (22534)Instructions burned: 158 (million)
% 29.42/5.55 % (22534)------------------------------
% 29.42/5.55 % (22534)------------------------------
% 29.42/5.56 % (22537)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_22021 for (2959ds/5798Mi)
% 29.42/5.59 % (22529)Instruction limit reached!
% 29.42/5.59 % (22529)------------------------------
% 29.42/5.59 % (22529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.42/5.59 % (22529)Termination reason: Unknown
% 29.42/5.59 % (22529)Termination phase: Saturation
% 29.42/5.59
% 29.42/5.59 % (22529)Memory used [KB]: 8187
% 29.42/5.59 % (22529)Time elapsed: 0.310 s
% 29.42/5.59 % (22529)Instructions burned: 1047 (million)
% 29.42/5.59 % (22529)------------------------------
% 29.42/5.59 % (22529)------------------------------
% 30.62/5.60 % (22538)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_22021 for (2959ds/346Mi)
% 30.62/5.61 % (22528)Instruction limit reached!
% 30.62/5.61 % (22528)------------------------------
% 30.62/5.61 % (22528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.62/5.61 % (22528)Termination reason: Unknown
% 30.62/5.61 % (22528)Termination phase: Saturation
% 30.62/5.61
% 30.62/5.61 % (22528)Memory used [KB]: 9722
% 30.62/5.61 % (22528)Time elapsed: 0.362 s
% 30.62/5.61 % (22528)Instructions burned: 1202 (million)
% 30.62/5.61 % (22528)------------------------------
% 30.62/5.61 % (22528)------------------------------
% 30.62/5.62 % (22539)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_22021 for (2959ds/1321Mi)
% 30.62/5.64 % (22472)Instruction limit reached!
% 30.62/5.64 % (22472)------------------------------
% 30.62/5.64 % (22472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.62/5.64 % (22472)Termination reason: Unknown
% 30.62/5.64 % (22472)Termination phase: Saturation
% 30.62/5.64
% 30.62/5.64 % (22472)Memory used [KB]: 17142
% 30.62/5.64 % (22472)Time elapsed: 2.613 s
% 30.62/5.64 % (22472)Instructions burned: 8252 (million)
% 30.62/5.64 % (22472)------------------------------
% 30.62/5.64 % (22472)------------------------------
% 30.62/5.65 % (22539)Refutation not found, incomplete strategy
% 30.62/5.65 % (22539)------------------------------
% 30.62/5.65 % (22539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.62/5.65 % (22539)Termination reason: Refutation not found, incomplete strategy
% 30.62/5.65
% 30.62/5.65
% 30.62/5.65 % (22539)Memory used [KB]: 2302
% 30.62/5.65 % (22539)Time elapsed: 0.027 s
% 30.62/5.65 % (22539)Instructions burned: 88 (million)
% 30.62/5.65 % (22539)------------------------------
% 30.62/5.65 % (22539)------------------------------
% 30.62/5.66 % (22540)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_22021 for (2958ds/1312Mi)
% 30.62/5.66 % (22541)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_22021 for (2958ds/672Mi)
% 31.18/5.71 % (22538)Instruction limit reached!
% 31.18/5.71 % (22538)------------------------------
% 31.18/5.71 % (22538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.18/5.71 % (22538)Termination reason: Unknown
% 31.18/5.71 % (22538)Termination phase: Saturation
% 31.18/5.71
% 31.18/5.71 % (22538)Memory used [KB]: 7419
% 31.18/5.71 % (22538)Time elapsed: 0.104 s
% 31.18/5.71 % (22538)Instructions burned: 346 (million)
% 31.18/5.71 % (22538)------------------------------
% 31.18/5.71 % (22538)------------------------------
% 31.18/5.72 % (22542)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_22021 for (2958ds/1897Mi)
% 31.18/5.74 % (22542)Refutation not found, incomplete strategy
% 31.18/5.74 % (22542)------------------------------
% 31.18/5.74 % (22542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.18/5.74 % (22542)Termination reason: Refutation not found, incomplete strategy
% 31.18/5.74
% 31.18/5.74
% 31.18/5.74 % (22542)Memory used [KB]: 6908
% 31.18/5.74 % (22542)Time elapsed: 0.029 s
% 31.18/5.74 % (22542)Instructions burned: 96 (million)
% 31.18/5.74 % (22542)------------------------------
% 31.18/5.74 % (22542)------------------------------
% 31.18/5.75 % (22543)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_22021 for (2957ds/1202Mi)
% 31.43/5.87 % (22541)Instruction limit reached!
% 31.43/5.87 % (22541)------------------------------
% 31.43/5.87 % (22541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.43/5.87 % (22541)Termination reason: Unknown
% 31.43/5.87 % (22541)Termination phase: Saturation
% 31.43/5.87
% 31.43/5.87 % (22541)Memory used [KB]: 8443
% 31.43/5.87 % (22541)Time elapsed: 0.215 s
% 31.43/5.87 % (22541)Instructions burned: 672 (million)
% 31.43/5.87 % (22541)------------------------------
% 31.43/5.87 % (22541)------------------------------
% 31.43/5.88 % (22544)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_22021 for (2956ds/1493Mi)
% 31.75/5.92 % (22544)Refutation not found, incomplete strategy
% 31.75/5.92 % (22544)------------------------------
% 31.75/5.92 % (22544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.75/5.92 % (22544)Termination reason: Refutation not found, incomplete strategy
% 31.75/5.92
% 31.75/5.92
% 31.75/5.92 % (22544)Memory used [KB]: 6780
% 31.75/5.92 % (22544)Time elapsed: 0.039 s
% 31.75/5.92 % (22544)Instructions burned: 137 (million)
% 31.75/5.92 % (22544)------------------------------
% 31.75/5.92 % (22544)------------------------------
% 31.75/5.93 % (22545)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_22021 for (2955ds/7679Mi)
% 34.13/6.05 % (22540)Instruction limit reached!
% 34.13/6.05 % (22540)------------------------------
% 34.13/6.05 % (22540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.13/6.05 % (22540)Termination reason: Unknown
% 34.13/6.05 % (22540)Termination phase: Saturation
% 34.13/6.05
% 34.13/6.05 % (22540)Memory used [KB]: 8443
% 34.13/6.05 % (22540)Time elapsed: 0.396 s
% 34.13/6.05 % (22540)Instructions burned: 1312 (million)
% 34.13/6.05 % (22540)------------------------------
% 34.13/6.05 % (22540)------------------------------
% 34.13/6.06 % (22546)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_22021 for (2954ds/340Mi)
% 34.78/6.13 % (22543)Instruction limit reached!
% 34.78/6.13 % (22543)------------------------------
% 34.78/6.13 % (22543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.78/6.13 % (22543)Termination reason: Unknown
% 34.78/6.13 % (22543)Termination phase: Saturation
% 34.78/6.13
% 34.78/6.13 % (22543)Memory used [KB]: 3709
% 34.78/6.13 % (22543)Time elapsed: 0.373 s
% 34.78/6.13 % (22543)Instructions burned: 1202 (million)
% 34.78/6.13 % (22543)------------------------------
% 34.78/6.13 % (22543)------------------------------
% 34.78/6.14 % (22547)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_22021 for (2953ds/3672Mi)
% 34.78/6.16 % (22546)Instruction limit reached!
% 34.78/6.16 % (22546)------------------------------
% 34.78/6.16 % (22546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.78/6.16 % (22546)Termination reason: Unknown
% 34.78/6.16 % (22546)Termination phase: Saturation
% 34.78/6.16
% 34.78/6.16 % (22546)Memory used [KB]: 7164
% 34.78/6.16 % (22546)Time elapsed: 0.104 s
% 34.78/6.16 % (22546)Instructions burned: 340 (million)
% 34.78/6.16 % (22546)------------------------------
% 34.78/6.16 % (22546)------------------------------
% 34.78/6.17 % (22548)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_22021 for (2953ds/1535Mi)
% 35.26/6.27 % (22536)Instruction limit reached!
% 35.26/6.27 % (22536)------------------------------
% 35.26/6.27 % (22536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.26/6.27 % (22536)Termination reason: Unknown
% 35.26/6.27 % (22536)Termination phase: Saturation
% 35.26/6.27
% 35.26/6.27 % (22536)Memory used [KB]: 6524
% 35.26/6.27 % (22536)Time elapsed: 0.749 s
% 35.26/6.27 % (22536)Instructions burned: 2401 (million)
% 35.26/6.27 % (22536)------------------------------
% 35.26/6.27 % (22536)------------------------------
% 35.26/6.28 % (22549)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_22021 for (2952ds/4637Mi)
% 36.96/6.62 % (22548)Instruction limit reached!
% 36.96/6.62 % (22548)------------------------------
% 36.96/6.62 % (22548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.96/6.62 % (22548)Termination reason: Unknown
% 36.96/6.62 % (22548)Termination phase: Saturation
% 36.96/6.62
% 36.96/6.62 % (22548)Memory used [KB]: 9850
% 36.96/6.62 % (22548)Time elapsed: 0.444 s
% 36.96/6.62 % (22548)Instructions burned: 1538 (million)
% 36.96/6.62 % (22548)------------------------------
% 36.96/6.62 % (22548)------------------------------
% 36.96/6.63 % (22550)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_22021 for (2948ds/3174Mi)
% 36.96/6.67 % (22516)Instruction limit reached!
% 36.96/6.67 % (22516)------------------------------
% 36.96/6.67 % (22516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.96/6.67 % (22516)Termination reason: Unknown
% 36.96/6.67 % (22516)Termination phase: Saturation
% 36.96/6.67
% 36.96/6.67 % (22516)Memory used [KB]: 14456
% 36.96/6.67 % (22516)Time elapsed: 1.920 s
% 36.96/6.67 % (22516)Instructions burned: 6454 (million)
% 36.96/6.67 % (22516)------------------------------
% 36.96/6.67 % (22516)------------------------------
% 36.96/6.68 % (22551)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_22021 for (2948ds/307Mi)
% 37.80/6.77 % (22551)Instruction limit reached!
% 37.80/6.77 % (22551)------------------------------
% 37.80/6.77 % (22551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.80/6.77 % (22551)Termination reason: Unknown
% 37.80/6.77 % (22551)Termination phase: Saturation
% 37.80/6.77
% 37.80/6.77 % (22551)Memory used [KB]: 7164
% 37.80/6.77 % (22551)Time elapsed: 0.089 s
% 37.80/6.77 % (22551)Instructions burned: 308 (million)
% 37.80/6.77 % (22551)------------------------------
% 37.80/6.77 % (22551)------------------------------
% 37.80/6.78 % (22552)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_22021 for (2947ds/3619Mi)
% 38.21/6.80 % (22552)Refutation not found, incomplete strategy
% 38.21/6.80 % (22552)------------------------------
% 38.21/6.80 % (22552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.21/6.80 % (22552)Termination reason: Refutation not found, incomplete strategy
% 38.21/6.80
% 38.21/6.80
% 38.21/6.80 % (22552)Memory used [KB]: 6652
% 38.21/6.80 % (22552)Time elapsed: 0.026 s
% 38.21/6.80 % (22552)Instructions burned: 83 (million)
% 38.21/6.80 % (22552)------------------------------
% 38.21/6.80 % (22552)------------------------------
% 38.21/6.81 % (22553)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_22021 for (2947ds/2325Mi)
% 41.15/7.06 % (22535)Instruction limit reached!
% 41.15/7.06 % (22535)------------------------------
% 41.15/7.06 % (22535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.15/7.06 % (22535)Termination reason: Unknown
% 41.15/7.06 % (22535)Termination phase: Saturation
% 41.15/7.06
% 41.15/7.06 % (22535)Memory used [KB]: 10362
% 41.15/7.06 % (22535)Time elapsed: 1.551 s
% 41.15/7.06 % (22535)Instructions burned: 5062 (million)
% 41.15/7.06 % (22535)------------------------------
% 41.15/7.06 % (22535)------------------------------
% 41.15/7.07 % (22554)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_22021 for (2944ds/2341Mi)
% 42.25/7.27 % (22547)Instruction limit reached!
% 42.25/7.27 % (22547)------------------------------
% 42.25/7.27 % (22547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.25/7.27 % (22547)Termination reason: Unknown
% 42.25/7.27 % (22547)Termination phase: Saturation
% 42.25/7.27
% 42.25/7.27 % (22547)Memory used [KB]: 11641
% 42.25/7.27 % (22547)Time elapsed: 1.137 s
% 42.25/7.27 % (22547)Instructions burned: 3674 (million)
% 42.25/7.27 % (22547)------------------------------
% 42.25/7.27 % (22547)------------------------------
% 42.25/7.28 % (22555)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_22021 for (2942ds/7257Mi)
% 42.84/7.31 % (22555)Refutation not found, incomplete strategy
% 42.84/7.31 % (22555)------------------------------
% 42.84/7.31 % (22555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.84/7.31 % (22555)Termination reason: Refutation not found, incomplete strategy
% 42.84/7.31
% 42.84/7.31
% 42.84/7.31 % (22555)Memory used [KB]: 6780
% 42.84/7.31 % (22555)Time elapsed: 0.027 s
% 42.84/7.31 % (22555)Instructions burned: 85 (million)
% 42.84/7.31 % (22555)------------------------------
% 42.84/7.31 % (22555)------------------------------
% 42.84/7.32 % (22556)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_22021 for (2942ds/3710Mi)
% 42.84/7.35 % (22537)Instruction limit reached!
% 42.84/7.35 % (22537)------------------------------
% 42.84/7.35 % (22537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.84/7.35 % (22537)Termination reason: Unknown
% 42.84/7.35 % (22537)Termination phase: Saturation
% 42.84/7.35
% 42.84/7.35 % (22537)Memory used [KB]: 10490
% 42.84/7.35 % (22537)Time elapsed: 1.791 s
% 42.84/7.35 % (22537)Instructions burned: 5799 (million)
% 42.84/7.35 % (22537)------------------------------
% 42.84/7.35 % (22537)------------------------------
% 42.84/7.36 % (22557)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_22021 for (2941ds/326Mi)
% 43.34/7.46 % (22557)Instruction limit reached!
% 43.34/7.46 % (22557)------------------------------
% 43.34/7.46 % (22557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.34/7.46 % (22557)Termination reason: Unknown
% 43.34/7.46 % (22557)Termination phase: Saturation
% 43.34/7.46
% 43.34/7.46 % (22557)Memory used [KB]: 7291
% 43.34/7.46 % (22557)Time elapsed: 0.124 s
% 43.34/7.46 % (22557)Instructions burned: 328 (million)
% 43.34/7.46 % (22557)------------------------------
% 43.34/7.46 % (22557)------------------------------
% 43.34/7.47 % (22558)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_22021 for (2940ds/1100Mi)
% 43.85/7.54 % (22553)Instruction limit reached!
% 43.85/7.54 % (22553)------------------------------
% 43.85/7.54 % (22553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.85/7.54 % (22553)Termination reason: Unknown
% 43.85/7.54 % (22553)Termination phase: Saturation
% 43.85/7.54
% 43.85/7.54 % (22553)Memory used [KB]: 9594
% 43.85/7.54 % (22553)Time elapsed: 0.732 s
% 43.85/7.54 % (22553)Instructions burned: 2325 (million)
% 43.85/7.54 % (22553)------------------------------
% 43.85/7.54 % (22553)------------------------------
% 43.85/7.55 % (22559)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_22021 for (2939ds/406Mi)
% 44.22/7.61 % (22550)Instruction limit reached!
% 44.22/7.61 % (22550)------------------------------
% 44.22/7.61 % (22550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.22/7.61 % (22550)Termination reason: Unknown
% 44.22/7.61 % (22550)Termination phase: Saturation
% 44.22/7.61
% 44.22/7.61 % (22550)Memory used [KB]: 9210
% 44.22/7.61 % (22550)Time elapsed: 0.987 s
% 44.22/7.61 % (22550)Instructions burned: 3174 (million)
% 44.22/7.61 % (22550)------------------------------
% 44.22/7.61 % (22550)------------------------------
% 44.22/7.62 % (22560)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_22021 for (2939ds/1871Mi)
% 44.22/7.66 % (22559)First to succeed.
% 44.22/7.67 % (22559)Refutation found. Thanks to Tanya!
% 44.22/7.67 % SZS status Theorem for DTF2THF_22021
% 44.22/7.67 % SZS output start Proof for DTF2THF_22021
% 44.22/7.67 thf(type_def_5, type, config256849571t_unit: $tType).
% 44.22/7.67 thf(type_def_6, type, message_p_v: $tType).
% 44.22/7.67 thf(type_def_8, type, p: $tType).
% 44.22/7.67 thf(type_def_9, type, list_c1059388851t_unit: $tType).
% 44.22/7.67 thf(type_def_10, type, list_message_p_v: $tType).
% 44.22/7.67 thf(type_def_11, type, nat: $tType).
% 44.22/7.67 thf(type_def_12, type, set_message_p_v: $tType).
% 44.22/7.67 thf(func_def_0, type, list_c1059388851t_unit: $tType).
% 44.22/7.67 thf(func_def_1, type, config256849571t_unit: $tType).
% 44.22/7.67 thf(func_def_2, type, list_message_p_v: $tType).
% 44.22/7.67 thf(func_def_3, type, set_message_p_v: $tType).
% 44.22/7.67 thf(func_def_4, type, message_p_v: $tType).
% 44.22/7.67 thf(func_def_5, type, nat: $tType).
% 44.22/7.67 thf(func_def_6, type, p: $tType).
% 44.22/7.67 thf(func_def_7, type, enabled_p_v_s: config256849571t_unit > message_p_v > $o).
% 44.22/7.67 thf(func_def_8, type, isReceiverOf_p_v: p > message_p_v > $o).
% 44.22/7.67 thf(func_def_9, type, firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o).
% 44.22/7.67 thf(func_def_10, type, minimalEnabled_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > $o).
% 44.22/7.67 thf(func_def_11, type, minus_minus_nat: nat > nat > nat).
% 44.22/7.67 thf(func_def_12, type, one_one_nat: nat).
% 44.22/7.67 thf(func_def_13, type, prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o).
% 44.22/7.67 thf(func_def_14, type, prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o).
% 44.22/7.67 thf(func_def_15, type, nil_co1338500125t_unit: list_c1059388851t_unit).
% 44.22/7.67 thf(func_def_16, type, nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit).
% 44.22/7.67 thf(func_def_17, type, nth_message_p_v: list_message_p_v > nat > message_p_v).
% 44.22/7.67 thf(func_def_18, type, suc: nat > nat).
% 44.22/7.67 thf(func_def_19, type, size_s1406904903t_unit: list_c1059388851t_unit > nat).
% 44.22/7.67 thf(func_def_20, type, size_s1168481041ge_p_v: list_message_p_v > nat).
% 44.22/7.67 thf(func_def_21, type, ord_less_nat: nat > nat > $o).
% 44.22/7.67 thf(func_def_22, type, ord_less_eq_nat: nat > nat > $o).
% 44.22/7.67 thf(func_def_23, type, collect_message_p_v: (message_p_v > $o) > set_message_p_v).
% 44.22/7.67 thf(func_def_24, type, member_message_p_v: message_p_v > set_message_p_v > $o).
% 44.22/7.67 thf(func_def_25, type, occM: nat).
% 44.22/7.67 thf(func_def_26, type, occM2: nat).
% 44.22/7.67 thf(func_def_27, type, consumedMsg: message_p_v).
% 44.22/7.67 thf(func_def_28, type, fe: nat > list_c1059388851t_unit).
% 44.22/7.67 thf(func_def_29, type, firstOccSet: nat > set_message_p_v).
% 44.22/7.67 thf(func_def_30, type, ft: nat > list_message_p_v).
% 44.22/7.67 thf(func_def_31, type, index: nat).
% 44.22/7.67 thf(func_def_32, type, msg: message_p_v).
% 44.22/7.67 thf(func_def_33, type, msg2: message_p_v).
% 44.22/7.67 thf(func_def_34, type, msga: message_p_v).
% 44.22/7.67 thf(func_def_35, type, n0: nat).
% 44.22/7.67 thf(func_def_36, type, n: nat).
% 44.22/7.67 thf(func_def_37, type, p2: p).
% 44.22/7.67 thf(func_def_52, type, sP0: nat > nat > nat > $o).
% 44.22/7.67 thf(func_def_53, type, sP1: nat > nat > nat > $o).
% 44.22/7.67 thf(func_def_54, type, sP2: nat > nat > nat > $o).
% 44.22/7.67 thf(func_def_55, type, sK3: list_c1059388851t_unit > list_c1059388851t_unit > nat).
% 44.22/7.67 thf(func_def_56, type, sK4: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_57, type, sK5: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_58, type, sK6: nat > list_message_p_v).
% 44.22/7.67 thf(func_def_59, type, sK7: (nat > $o) > nat).
% 44.22/7.67 thf(func_def_60, type, sK8: nat > nat > (nat > $o) > nat).
% 44.22/7.67 thf(func_def_61, type, sK9: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_62, type, sK10: (message_p_v > $o) > (message_p_v > $o) > message_p_v).
% 44.22/7.67 thf(func_def_63, type, sK11: (nat > $o) > nat).
% 44.22/7.67 thf(func_def_64, type, sK12: nat > nat).
% 44.22/7.67 thf(func_def_65, type, sK13: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_66, type, sK14: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_67, type, sK15: p).
% 44.22/7.67 thf(func_def_68, type, sK16: (list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 44.22/7.67 thf(func_def_69, type, sK17: (nat > $o) > nat > nat).
% 44.22/7.67 thf(func_def_70, type, sK18: (nat > $o) > nat > nat).
% 44.22/7.67 thf(func_def_71, type, sK19: (nat > $o) > nat).
% 44.22/7.67 thf(func_def_72, type, sK20: (list_message_p_v > $o) > list_message_p_v).
% 44.22/7.67 thf(func_def_73, type, sK21: nat > nat > message_p_v > nat).
% 44.22/7.67 thf(func_def_74, type, sK22: nat > (nat > $o) > (nat > $o) > nat).
% 44.22/7.67 thf(func_def_75, type, sK23: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_76, type, sK24: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_77, type, sK25: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_78, type, sK26: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_79, type, sK27: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_80, type, sK28: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_81, type, sK29: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_82, type, sK30: (nat > $o) > nat).
% 44.22/7.67 thf(func_def_83, type, sK31: nat > nat > nat).
% 44.22/7.67 thf(func_def_84, type, sK32: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_85, type, sK33: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_86, type, sK34: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_87, type, sK35: nat > nat).
% 44.22/7.67 thf(func_def_88, type, sK36: list_message_p_v > list_message_p_v > nat).
% 44.22/7.67 thf(func_def_89, type, sK37: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_90, type, sK38: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_91, type, sK39: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_92, type, sK40: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_93, type, sK41: (nat > $o) > nat > nat).
% 44.22/7.67 thf(func_def_94, type, sK42: (nat > $o) > nat > nat).
% 44.22/7.67 thf(func_def_95, type, sK43: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_96, type, sK44: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_97, type, sK45: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_98, type, sK46: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_99, type, sK47: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_100, type, sK48: (nat > $o) > nat).
% 44.22/7.67 thf(func_def_101, type, sK49: p).
% 44.22/7.67 thf(func_def_102, type, sK50: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_103, type, sK51: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_104, type, sK52: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_105, type, sK53: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_106, type, sK54: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_107, type, sK55: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_108, type, sK56: (nat > $o) > nat).
% 44.22/7.67 thf(func_def_109, type, sK57: nat > (nat > $o) > nat).
% 44.22/7.67 thf(func_def_110, type, sK58: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_111, type, sK59: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_112, type, sK60: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_113, type, sK61: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_114, type, sK62: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_115, type, sK63: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_116, type, sK64: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_117, type, sK65: nat > (nat > $o) > nat > nat).
% 44.22/7.67 thf(func_def_118, type, sK66: nat > list_c1059388851t_unit).
% 44.22/7.67 thf(func_def_119, type, sK67: (nat > $o) > nat).
% 44.22/7.67 thf(func_def_120, type, sK68: (nat > $o) > nat > nat).
% 44.22/7.67 thf(func_def_121, type, sK69: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_122, type, sK70: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_123, type, sK71: nat > nat > nat).
% 44.22/7.67 thf(func_def_124, type, sK72: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_125, type, sK73: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_126, type, sK74: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_127, type, sK75: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_128, type, sK76: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_129, type, sK77: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_130, type, sK78: (nat > nat > $o) > nat).
% 44.22/7.67 thf(func_def_131, type, sK79: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_132, type, sK80: (nat > nat) > nat).
% 44.22/7.67 thf(func_def_133, type, sF81: list_c1059388851t_unit).
% 44.22/7.67 thf(func_def_134, type, sF82: nat).
% 44.22/7.67 thf(func_def_135, type, sF83: nat > nat).
% 44.22/7.67 thf(func_def_136, type, sF84: nat).
% 44.22/7.67 thf(func_def_138, type, ph86: !>[X0: $tType]:(X0)).
% 44.22/7.67 thf(f2139,plain,(
% 44.22/7.67 $false),
% 44.22/7.67 inference(trivial_inequality_removal,[status(thm)],[f2138])).
% 44.22/7.67 thf(f2138,plain,(
% 44.22/7.67 ($false = $true)),
% 44.22/7.67 inference(forward_demodulation,[status(thm)],[f2137,f1775])).
% 44.22/7.67 thf(f1775,plain,(
% 44.22/7.67 ($false = (ord_less_eq_nat @ sF82 @ occM2))),
% 44.22/7.67 inference(boolean_simplification,[status(thm)],[f1770])).
% 44.22/7.67 thf(f1770,plain,(
% 44.22/7.67 ((~ $true) = (ord_less_eq_nat @ sF82 @ occM2))),
% 44.22/7.67 inference(superposition,[status(thm)],[f1468,f1454])).
% 44.22/7.67 thf(f1454,plain,(
% 44.22/7.67 ($true = (ord_less_nat @ occM2 @ sF82))),
% 44.22/7.67 inference(forward_demodulation,[status(thm)],[f1453,f1423])).
% 44.22/7.67 thf(f1423,definition,(
% 44.22/7.67 ((size_s1406904903t_unit @ sF81) = sF82)),
% 44.22/7.67 introduced(definition,[],[function_definition])).
% 44.22/7.67 thf(f1453,plain,(
% 44.22/7.67 ((ord_less_nat @ occM2 @ (size_s1406904903t_unit @ sF81)) = $true)),
% 44.22/7.67 inference(forward_demodulation,[status(thm)],[f1319,f1422])).
% 44.22/7.67 thf(f1422,definition,(
% 44.22/7.67 ((fe @ index) = sF81)),
% 44.22/7.67 introduced(definition,[],[function_definition])).
% 44.22/7.67 thf(f1319,plain,(
% 44.22/7.67 ((ord_less_nat @ occM2 @ (size_s1406904903t_unit @ (fe @ index))) = $true)),
% 44.22/7.67 inference(cnf_transformation,[status(thm)],[f284])).
% 44.22/7.67 thf(f284,plain,(
% 44.22/7.67 ((ord_less_nat @ occM2 @ (size_s1406904903t_unit @ (fe @ index))) = $true)),
% 44.22/7.67 inference(fool_elimination,[status(thm)],[f283])).
% 44.22/7.67 thf(f283,plain,(
% 44.22/7.67 (ord_less_nat @ occM2 @ (size_s1406904903t_unit @ (fe @ index)))),
% 44.22/7.67 inference(rectify,[status(thm)],[f1])).
% 44.22/7.67 thf(f1,axiom,(
% 44.22/7.67 (ord_less_nat @ occM2 @ (size_s1406904903t_unit @ (fe @ index)))),
% 44.22/7.67 file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_0_AssumpOccMFirstOccurrence_I3_J)).
% 44.22/7.67 thf(f1468,plain,(
% 44.22/7.67 ( ! [X0 : nat,X1 : nat] : (((~ (ord_less_nat @ X0 @ X1)) = (ord_less_eq_nat @ X1 @ X0))) )),
% 44.22/7.67 inference(forward_demodulation,[status(thm)],[f1106,f1210])).
% 44.22/7.67 thf(f1210,plain,(
% 44.22/7.67 ( ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ X0 @ X1) = (ord_less_nat @ X0 @ (suc @ X1)))) )),
% 44.22/7.67 inference(cnf_transformation,[status(thm)],[f306])).
% 44.22/7.67 thf(f306,plain,(
% 44.22/7.67 ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ X0 @ X1) = (ord_less_nat @ X0 @ (suc @ X1)))),
% 44.22/7.67 inference(fool_elimination,[status(thm)],[f305])).
% 44.22/7.67 thf(f305,plain,(
% 44.22/7.67 ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ X0 @ X1) = (ord_less_nat @ X0 @ (suc @ X1)))),
% 44.22/7.67 inference(rectify,[status(thm)],[f64])).
% 44.22/7.67 thf(f64,axiom,(
% 44.22/7.67 ! [X13 : nat,X3 : nat] : ((ord_less_eq_nat @ X13 @ X3) = (ord_less_nat @ X13 @ (suc @ X3)))),
% 44.22/7.67 file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_63_less__Suc__eq__le)).
% 44.22/7.67 thf(f1106,plain,(
% 44.22/7.67 ( ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X1 @ (suc @ X0)) = (~ (ord_less_nat @ X0 @ X1)))) )),
% 44.22/7.67 inference(cnf_transformation,[status(thm)],[f396])).
% 44.22/7.67 thf(f396,plain,(
% 44.22/7.67 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X1 @ (suc @ X0)) = (~ (ord_less_nat @ X0 @ X1)))),
% 44.22/7.67 inference(fool_elimination,[status(thm)],[f395])).
% 44.22/7.67 thf(f395,plain,(
% 44.22/7.67 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X1 @ (suc @ X0)) = ~(ord_less_nat @ X0 @ X1))),
% 44.22/7.67 inference(rectify,[status(thm)],[f54])).
% 44.22/7.67 thf(f54,axiom,(
% 44.22/7.67 ! [X13 : nat,X3 : nat] : ((ord_less_nat @ X3 @ (suc @ X13)) = ~(ord_less_nat @ X13 @ X3))),
% 44.22/7.67 file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_53_not__less__eq)).
% 44.22/7.67 thf(f2137,plain,(
% 44.22/7.67 ($true = (ord_less_eq_nat @ sF82 @ occM2))),
% 44.22/7.67 inference(backward_demodulation,[status(thm)],[f1956,f2135])).
% 44.22/7.67 thf(f2135,plain,(
% 44.22/7.67 ((suc @ sF84) = sF82)),
% 44.22/7.67 inference(backward_demodulation,[status(thm)],[f2125,f2134])).
% 44.22/7.67 thf(f2134,plain,(
% 44.22/7.67 (sF84 = (sK12 @ sF82))),
% 44.22/7.67 inference(forward_demodulation,[status(thm)],[f2133,f1425])).
% 44.22/7.67 thf(f1425,definition,(
% 44.22/7.67 ((sF83 @ one_one_nat) = sF84)),
% 44.22/7.67 introduced(definition,[],[function_definition])).
% 44.22/7.67 thf(f2133,plain,(
% 44.22/7.67 ((sF83 @ one_one_nat) = (sK12 @ sF82))),
% 44.22/7.67 inference(forward_demodulation,[status(thm)],[f2127,f1479])).
% 44.22/7.67 thf(f1479,plain,(
% 44.22/7.67 ( ! [X1 : nat] : (((minus_minus_nat @ sF82 @ X1) = (sF83 @ X1))) )),
% 44.22/7.67 inference(argument_congruence,[status(thm)],[f1424])).
% 44.22/7.67 thf(f1424,definition,(
% 44.22/7.67 (sF83 = (minus_minus_nat @ sF82))),
% 44.22/7.67 introduced(definition,[],[function_definition])).
% 44.22/7.67 thf(f2127,plain,(
% 44.22/7.67 ((minus_minus_nat @ sF82 @ one_one_nat) = (sK12 @ sF82))),
% 44.22/7.67 inference(superposition,[status(thm)],[f1087,f2125])).
% 44.22/7.67 thf(f1087,plain,(
% 44.22/7.67 ( ! [X0 : nat] : (((minus_minus_nat @ (suc @ X0) @ one_one_nat) = X0)) )),
% 44.22/7.67 inference(cnf_transformation,[status(thm)],[f535])).
% 44.22/7.67 thf(f535,plain,(
% 44.22/7.67 ! [X0 : nat] : ((minus_minus_nat @ (suc @ X0) @ one_one_nat) = X0)),
% 44.22/7.67 inference(fool_elimination,[status(thm)],[f534])).
% 44.22/7.67 thf(f534,plain,(
% 44.22/7.67 ! [X0 : nat] : ((minus_minus_nat @ (suc @ X0) @ one_one_nat) = X0)),
% 44.22/7.67 inference(rectify,[status(thm)],[f25])).
% 44.22/7.67 thf(f25,axiom,(
% 44.22/7.67 ! [X3 : nat] : ((minus_minus_nat @ (suc @ X3) @ one_one_nat) = X3)),
% 44.22/7.67 file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_24_diff__Suc__1)).
% 44.22/7.67 thf(f2125,plain,(
% 44.22/7.67 ((suc @ (sK12 @ sF82)) = sF82)),
% 44.22/7.67 inference(trivial_inequality_removal,[status(thm)],[f2120])).
% 44.22/7.67 thf(f2120,plain,(
% 44.22/7.67 ($true != $true) | ((suc @ (sK12 @ sF82)) = sF82)),
% 44.22/7.67 inference(superposition,[status(thm)],[f1142,f1955])).
% 44.22/7.67 thf(f1955,plain,(
% 44.22/7.67 ((ord_less_eq_nat @ (suc @ occM2) @ sF82) = $true)),
% 44.22/7.67 inference(trivial_inequality_removal,[status(thm)],[f1953])).
% 44.22/7.67 thf(f1953,plain,(
% 44.22/7.67 ((ord_less_eq_nat @ (suc @ occM2) @ sF82) = $true) | ($true != $true)),
% 44.22/7.67 inference(superposition,[status(thm)],[f1111,f1454])).
% 44.22/7.67 thf(f1111,plain,(
% 44.22/7.67 ( ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X0 @ X1) != $true) | ((ord_less_eq_nat @ (suc @ X0) @ X1) = $true)) )),
% 44.22/7.67 inference(cnf_transformation,[status(thm)],[f877])).
% 44.22/7.67 thf(f877,plain,(
% 44.22/7.67 ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ (suc @ X0) @ X1) = $true) | ((ord_less_nat @ X0 @ X1) != $true))),
% 44.22/7.67 inference(ennf_transformation,[status(thm)],[f302])).
% 44.22/7.67 thf(f302,plain,(
% 44.22/7.67 ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X0 @ X1) = $true) => ((ord_less_eq_nat @ (suc @ X0) @ X1) = $true))),
% 44.22/7.67 inference(fool_elimination,[status(thm)],[f301])).
% 44.22/7.67 thf(f301,plain,(
% 44.22/7.67 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X0 @ X1) => (ord_less_eq_nat @ (suc @ X0) @ X1))),
% 44.22/7.67 inference(rectify,[status(thm)],[f28])).
% 44.22/7.67 thf(f28,axiom,(
% 44.22/7.67 ! [X13 : nat,X3 : nat] : ((ord_less_nat @ X13 @ X3) => (ord_less_eq_nat @ (suc @ X13) @ X3))),
% 44.22/7.67 file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_27_Suc__leI)).
% 44.22/7.67 thf(f1142,plain,(
% 44.22/7.67 ( ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ (suc @ X0) @ X1) != $true) | ((suc @ (sK12 @ X1)) = X1)) )),
% 44.22/7.67 inference(cnf_transformation,[status(thm)],[f984])).
% 44.22/7.67 thf(f984,plain,(
% 44.22/7.67 ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ (suc @ X0) @ X1) != $true) | ((suc @ (sK12 @ X1)) = X1))),
% 44.22/7.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f779,f983])).
% 44.22/7.67 thf(f983,plain,(
% 44.22/7.67 ! [X1 : nat] : (? [X2 : nat] : ((suc @ X2) = X1) => ((suc @ (sK12 @ X1)) = X1))),
% 44.22/7.67 introduced(definition,[],[choice_axiom])).
% 44.22/7.67 thf(f779,plain,(
% 44.22/7.67 ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ (suc @ X0) @ X1) != $true) | ? [X2 : nat] : ((suc @ X2) = X1))),
% 44.22/7.67 inference(ennf_transformation,[status(thm)],[f503])).
% 44.22/7.67 thf(f503,plain,(
% 44.22/7.67 ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ (suc @ X0) @ X1) = $true) => ? [X2 : nat] : ((suc @ X2) = X1))),
% 44.22/7.67 inference(fool_elimination,[status(thm)],[f502])).
% 44.22/7.67 thf(f502,plain,(
% 44.22/7.67 ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ (suc @ X0) @ X1) => ? [X2 : nat] : ((suc @ X2) = X1))),
% 44.22/7.67 inference(rectify,[status(thm)],[f32])).
% 44.22/7.67 thf(f32,axiom,(
% 44.22/7.67 ! [X3 : nat,X15 : nat] : ((ord_less_eq_nat @ (suc @ X3) @ X15) => ? [X16 : nat] : ((suc @ X16) = X15))),
% 44.22/7.67 file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_31_Suc__le__D)).
% 44.22/7.67 thf(f1956,plain,(
% 44.22/7.67 ((ord_less_eq_nat @ (suc @ sF84) @ occM2) = $true)),
% 44.22/7.67 inference(trivial_inequality_removal,[status(thm)],[f1947])).
% 44.22/7.67 thf(f1947,plain,(
% 44.22/7.67 ($true != $true) | ((ord_less_eq_nat @ (suc @ sF84) @ occM2) = $true)),
% 44.22/7.67 inference(superposition,[status(thm)],[f1111,f1818])).
% 44.22/7.67 thf(f1818,plain,(
% 44.22/7.67 ((ord_less_nat @ sF84 @ occM2) = $true)),
% 44.22/7.67 inference(subsumption_resolution,[status(thm)],[f1817,f1426])).
% 44.22/7.67 thf(f1426,plain,(
% 44.22/7.67 (occM2 != sF84)),
% 44.22/7.67 inference(definition_folding,[status(thm)],[f1295,f1425,f1424,f1423,f1422])).
% 44.22/7.67 thf(f1295,plain,(
% 44.22/7.67 (occM2 != (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ one_one_nat))),
% 44.22/7.67 inference(cnf_transformation,[status(thm)],[f730])).
% 44.22/7.67 thf(f730,plain,(
% 44.22/7.67 (occM2 != (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ one_one_nat))),
% 44.22/7.67 inference(flattening,[status(thm)],[f576])).
% 44.22/7.67 thf(f576,plain,(
% 44.22/7.67 ~(occM2 = (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ one_one_nat))),
% 44.22/7.67 inference(fool_elimination,[status(thm)],[f237])).
% 44.22/7.67 thf(f237,negated_conjecture,(
% 44.22/7.67 ~(occM2 = (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ one_one_nat))),
% 44.22/7.67 inference(negated_conjecture,[status(cth)],[f236])).
% 44.22/7.67 thf(f236,conjecture,(
% 44.22/7.67 (occM2 = (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ one_one_nat))),
% 44.22/7.67 file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',conj_0)).
% 44.22/7.67 thf(f1817,plain,(
% 44.22/7.67 ((ord_less_nat @ sF84 @ occM2) = $true) | (occM2 = sF84)),
% 44.22/7.67 inference(trivial_inequality_removal,[status(thm)],[f1806])).
% 44.22/7.67 thf(f1806,plain,(
% 44.22/7.67 (occM2 = sF84) | ($true != $true) | ((ord_less_nat @ sF84 @ occM2) = $true)),
% 44.22/7.67 inference(superposition,[status(thm)],[f1133,f1485])).
% 44.22/7.67 thf(f1485,plain,(
% 44.22/7.67 ((ord_less_eq_nat @ sF84 @ occM2) = $true)),
% 44.22/7.67 inference(forward_demodulation,[status(thm)],[f1482,f1425])).
% 44.22/7.67 thf(f1482,plain,(
% 44.22/7.67 ((ord_less_eq_nat @ (sF83 @ one_one_nat) @ occM2) = $true)),
% 44.22/7.67 inference(backward_demodulation,[status(thm)],[f1452,f1479])).
% 44.22/7.67 thf(f1452,plain,(
% 44.22/7.67 ((ord_less_eq_nat @ (minus_minus_nat @ sF82 @ one_one_nat) @ occM2) = $true)),
% 44.22/7.67 inference(backward_demodulation,[status(thm)],[f1444,f1423])).
% 44.22/7.67 thf(f1444,plain,(
% 44.22/7.67 ((ord_less_eq_nat @ (minus_minus_nat @ (size_s1406904903t_unit @ sF81) @ one_one_nat) @ occM2) = $true)),
% 44.22/7.67 inference(backward_demodulation,[status(thm)],[f1392,f1422])).
% 44.22/7.67 thf(f1392,plain,(
% 44.22/7.67 ((ord_less_eq_nat @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ one_one_nat) @ occM2) = $true)),
% 44.22/7.67 inference(cnf_transformation,[status(thm)],[f607])).
% 44.22/7.67 thf(f607,plain,(
% 44.22/7.67 ((ord_less_eq_nat @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ one_one_nat) @ occM2) = $true)),
% 44.22/7.67 inference(fool_elimination,[status(thm)],[f606])).
% 44.22/7.67 thf(f606,plain,(
% 44.22/7.67 (ord_less_eq_nat @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ one_one_nat) @ occM2)),
% 44.22/7.67 inference(rectify,[status(thm)],[f2])).
% 44.22/7.67 thf(f2,axiom,(
% 44.22/7.67 (ord_less_eq_nat @ (minus_minus_nat @ (size_s1406904903t_unit @ (fe @ index)) @ one_one_nat) @ occM2)),
% 44.22/7.67 file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_1__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_AOccM_092_060close_062)).
% 44.22/7.67 thf(f1133,plain,(
% 44.22/7.67 ( ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ X0 @ X1) != $true) | ((ord_less_nat @ X0 @ X1) = $true) | (X0 = X1)) )),
% 44.22/7.67 inference(cnf_transformation,[status(thm)],[f798])).
% 44.22/7.67 thf(f798,plain,(
% 44.22/7.67 ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ X0 @ X1) != $true) | (X0 = X1) | ((ord_less_nat @ X0 @ X1) = $true))),
% 44.22/7.67 inference(flattening,[status(thm)],[f797])).
% 44.22/7.67 thf(f797,plain,(
% 44.22/7.67 ! [X0 : nat,X1 : nat] : ((((ord_less_nat @ X0 @ X1) = $true) | (X0 = X1)) | ((ord_less_eq_nat @ X0 @ X1) != $true))),
% 44.22/7.67 inference(ennf_transformation,[status(thm)],[f342])).
% 44.22/7.67 thf(f342,plain,(
% 44.22/7.67 ! [X0 : nat,X1 : nat] : (((ord_less_eq_nat @ X0 @ X1) = $true) => ((X0 != X1) => ((ord_less_nat @ X0 @ X1) = $true)))),
% 44.22/7.67 inference(fool_elimination,[status(thm)],[f341])).
% 44.22/7.67 thf(f341,plain,(
% 44.22/7.67 ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ X0 @ X1) => ((X0 != X1) => (ord_less_nat @ X0 @ X1)))),
% 44.22/7.67 inference(rectify,[status(thm)],[f82])).
% 44.22/7.67 thf(f82,axiom,(
% 44.22/7.67 ! [X13 : nat,X3 : nat] : ((ord_less_eq_nat @ X13 @ X3) => ((X3 != X13) => (ord_less_nat @ X13 @ X3)))),
% 44.22/7.67 file('/export/starexec/sandbox/tmp/tmp.6bdD5H4cZZ/DTF2THF_22021.p',fact_81_le__neq__implies__less)).
% 44.22/7.67 % SZS output end Proof for DTF2THF_22021
% 44.22/7.67 % (22559)------------------------------
% 44.22/7.67 % (22559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.22/7.67 % (22559)Termination reason: Refutation
% 44.22/7.67
% 44.22/7.67 % (22559)Memory used [KB]: 7291
% 44.22/7.67 % (22559)Time elapsed: 0.134 s
% 44.22/7.67 % (22559)Instructions burned: 338 (million)
% 44.22/7.67 % (22559)------------------------------
% 44.22/7.67 % (22559)------------------------------
% 44.22/7.67 % (22350)Success in time 6.146 s
%------------------------------------------------------------------------------