%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP126^1 : 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 : n009.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 08:55:45 AM UTC 2026
% Result : Theorem 188.71s 28.62s
% Output : Refutation 188.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 27
% Syntax : Number of formulae : 173 ( 33 unt; 0 typ; 6 def)
% Number of atoms : 804 ( 336 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 1474 ( 204 ~; 195 |; 32 &; 999 @)
% ( 18 <=>; 25 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 117 ( 114 usr; 18 con; 0-3 aty)
% Number of variables : 162 ( 0 ^; 147 !; 15 ?; 162 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
int: $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(type_def_8,type,
list_option_b: $tType ).
thf(type_def_9,type,
list_b: $tType ).
thf(type_def_10,type,
option_b: $tType ).
thf(type_def_11,type,
option_option_b: $tType ).
thf(type_def_12,type,
b: $tType ).
thf(type_def_13,type,
formula_a: $tType ).
thf(type_def_14,type,
set_nat: $tType ).
thf(func_def_0,type,
option_option_b: $tType ).
thf(func_def_1,type,
list_option_b: $tType ).
thf(func_def_2,type,
set_nat: $tType ).
thf(func_def_3,type,
option_b: $tType ).
thf(func_def_4,type,
formula_a: $tType ).
thf(func_def_5,type,
list_b: $tType ).
thf(func_def_6,type,
nat: $tType ).
thf(func_def_7,type,
int: $tType ).
thf(func_def_8,type,
b: $tType ).
thf(func_def_9,type,
plus_plus_int: int > int > int ).
thf(func_def_10,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_11,type,
zero_zero_int: int ).
thf(func_def_12,type,
zero_zero_nat: nat ).
thf(func_def_13,type,
if_nat: $o > nat > nat > nat ).
thf(func_def_14,type,
drop_option_b: nat > list_option_b > list_option_b ).
thf(func_def_15,type,
drop_b: nat > list_b > list_b ).
thf(func_def_16,type,
find_option_b: ( option_b > $o ) > list_option_b > option_option_b ).
thf(func_def_17,type,
find_b: ( b > $o ) > list_b > option_b ).
thf(func_def_18,type,
gen_length_option_b: nat > list_option_b > nat ).
thf(func_def_19,type,
gen_length_b: nat > list_b > nat ).
thf(func_def_20,type,
cons_option_b: option_b > list_option_b > list_option_b ).
thf(func_def_21,type,
cons_b: b > list_b > list_b ).
thf(func_def_22,type,
list_ex_option_b: ( option_b > $o ) > list_option_b > $o ).
thf(func_def_23,type,
list_ex_b: ( b > $o ) > list_b > $o ).
thf(func_def_24,type,
nth_option_b: list_option_b > nat > option_b ).
thf(func_def_25,type,
nth_b: list_b > nat > b ).
thf(func_def_26,type,
fvi_a: nat > formula_a > set_nat ).
thf(func_def_27,type,
suc: nat > nat ).
thf(func_def_28,type,
semiri2019852685at_int: nat > int ).
thf(func_def_29,type,
semiri1382578993at_nat: nat > nat ).
thf(func_def_30,type,
size_s1671393719tion_b: list_option_b > nat ).
thf(func_def_31,type,
size_size_list_b: list_b > nat ).
thf(func_def_32,type,
size_s684879735tion_b: option_option_b > nat ).
thf(func_def_33,type,
size_size_option_b: option_b > nat ).
thf(func_def_34,type,
nat_triangle: nat > nat ).
thf(func_def_35,type,
none_option_b: option_option_b ).
thf(func_def_36,type,
none_b: option_b ).
thf(func_def_37,type,
some_option_b: option_b > option_option_b ).
thf(func_def_38,type,
some_b: b > option_b ).
thf(func_def_39,type,
size_option_option_b: ( option_b > nat ) > option_option_b > nat ).
thf(func_def_40,type,
size_option_b: ( b > nat ) > option_b > nat ).
thf(func_def_41,type,
ord_less_int: int > int > $o ).
thf(func_def_42,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_43,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_44,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_45,type,
member_nat: nat > set_nat > $o ).
thf(func_def_46,type,
phi: formula_a ).
thf(func_def_47,type,
b2: nat ).
thf(func_def_48,type,
n: nat ).
thf(func_def_49,type,
v: list_option_b ).
thf(func_def_50,type,
x: b ).
thf(func_def_64,type,
sP0: ( option_b > option_b > $o ) > option_b > option_b > $o ).
thf(func_def_65,type,
sK1: ( nat > nat ) > nat ).
thf(func_def_66,type,
sK2: nat > nat ).
thf(func_def_67,type,
sK3: ( nat > nat > $o ) > nat ).
thf(func_def_68,type,
sK4: ( nat > nat > $o ) > nat ).
thf(func_def_69,type,
sK5: ( nat > nat > $o ) > nat ).
thf(func_def_70,type,
sK6: ( nat > nat > $o ) > nat ).
thf(func_def_71,type,
sK7: nat > nat > nat ).
thf(func_def_72,type,
sK8: list_option_b > nat > list_option_b ).
thf(func_def_73,type,
sK9: list_option_b > nat > option_b ).
thf(func_def_74,type,
sK10: nat > nat > nat ).
thf(func_def_75,type,
sK11: nat > ( nat > option_b > $o ) > option_b ).
thf(func_def_76,type,
sK12: list_option_b > nat > ( nat > option_b > $o ) > nat ).
thf(func_def_77,type,
sK13: nat > ( nat > option_b > $o ) > list_option_b ).
thf(func_def_78,type,
sK14: nat > ( nat > option_b > $o ) > nat ).
thf(func_def_79,type,
sK15: nat > formula_a > nat > nat ).
thf(func_def_80,type,
sK16: nat > nat > nat ).
thf(func_def_81,type,
sK17: ( nat > nat > $o ) > nat ).
thf(func_def_82,type,
sK18: ( nat > nat > $o ) > nat ).
thf(func_def_83,type,
sK19: ( nat > nat > $o ) > nat ).
thf(func_def_84,type,
sK20: ( nat > nat > $o ) > nat ).
thf(func_def_85,type,
sK21: nat > nat ).
thf(func_def_86,type,
sK22: ( nat > nat ) > nat ).
thf(func_def_87,type,
sK23: ( nat > $o ) > nat ).
thf(func_def_88,type,
sK24: ( nat > $o ) > nat > nat ).
thf(func_def_89,type,
sK25: ( nat > $o ) > nat > nat ).
thf(func_def_90,type,
sK26: option_b > b ).
thf(func_def_91,type,
sK27: option_b > b ).
thf(func_def_92,type,
sK28: nat ).
thf(func_def_93,type,
sK29: ( nat > nat > $o ) > nat ).
thf(func_def_94,type,
sK30: ( nat > nat > $o ) > nat ).
thf(func_def_95,type,
sK31: ( nat > nat > $o ) > nat ).
thf(func_def_96,type,
sK32: ( nat > nat > $o ) > nat ).
thf(func_def_97,type,
sK33: ( nat > nat > $o ) > nat ).
thf(func_def_98,type,
sK34: ( nat > $o ) > nat ).
thf(func_def_99,type,
sK35: list_option_b > list_option_b > nat ).
thf(func_def_100,type,
sK36: ( nat > $o ) > nat ).
thf(func_def_101,type,
sK37: ( nat > $o ) > nat > nat ).
thf(func_def_102,type,
sK38: ( nat > $o ) > nat > nat ).
thf(func_def_103,type,
sK39: nat > nat ).
thf(func_def_104,type,
sK40: nat > nat ).
thf(func_def_105,type,
sK41: ( nat > $o ) > nat > nat ).
thf(func_def_106,type,
sK42: ( nat > $o ) > nat > nat ).
thf(func_def_107,type,
sK43: ( option_b > option_b > $o ) > option_b > option_b > b ).
thf(func_def_108,type,
sK44: ( option_b > option_b > $o ) > option_b > option_b > b ).
thf(func_def_109,type,
sK45: option_b > b ).
thf(func_def_110,type,
sK46: ( nat > $o ) > nat ).
thf(func_def_111,type,
sK47: ( nat > $o ) > nat ).
thf(func_def_112,type,
sK48: nat > nat ).
thf(func_def_113,type,
sK49: ( nat > $o ) > nat ).
thf(func_def_114,type,
sK50: ( nat > $o ) > nat ).
thf(func_def_115,type,
sK51: nat > nat > nat ).
thf(func_def_116,type,
sK52: nat > ( nat > $o ) > nat ).
thf(func_def_117,type,
sK53: nat > ( nat > $o ) > nat ).
thf(func_def_118,type,
sK54: ( nat > $o ) > nat > nat ).
thf(func_def_119,type,
sK55: ( nat > $o ) > nat > nat ).
thf(func_def_120,type,
sK56: nat > nat > nat ).
thf(func_def_121,type,
sK57: nat > list_option_b ).
thf(func_def_122,type,
sK58: nat > nat > nat ).
thf(func_def_123,type,
sK59: ( list_option_b > $o ) > list_option_b ).
thf(func_def_124,type,
sK60: list_option_b > nat > option_b ).
thf(func_def_125,type,
sK61: list_option_b > nat > list_option_b ).
thf(func_def_126,type,
sK62: nat > nat > nat ).
thf(func_def_127,type,
sK63: ( option_b > $o ) > b ).
thf(func_def_128,type,
sK64: nat > nat > nat ).
thf(func_def_130,type,
ph66:
!>[X0: $tType] : X0 ).
thf(f77682,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1463,f1466,f8530,f8545,f8554,f59922,f59953,f60011,f77681]) ).
thf(f77681,plain,
( ~ spl65_2
| ~ spl65_553 ),
inference(avatar_contradiction_clause,[status(thm)],[f77680]) ).
thf(f77680,plain,
( $false
| ~ spl65_2
| ~ spl65_553 ),
inference(trivial_inequality_removal,[status(thm)],[f77677]) ).
thf(f77677,plain,
( ( $false = $true )
| ~ spl65_2
| ~ spl65_553 ),
inference(superposition,[status(thm)],[f1461,f59952]) ).
thf(f59952,plain,
( ( $false
= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ~ spl65_553 ),
inference(avatar_component_clause,[status(thm)],[f59950]) ).
thf(f59950,definition,
( spl65_553
<=> ( $false
= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) ) ),
introduced(definition,[new_symbols(naming,[spl65_553])],[avatar_definition]) ).
thf(f1461,plain,
( ( $true
= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ~ spl65_2 ),
inference(avatar_component_clause,[status(thm)],[f1460]) ).
thf(f1460,definition,
( spl65_2
<=> ( $true
= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) ) ),
introduced(definition,[new_symbols(naming,[spl65_2])],[avatar_definition]) ).
thf(f60011,plain,
( spl65_551
| ~ spl65_1
| ~ spl65_6 ),
inference(avatar_split_clause,[status(thm)],[f60006,f1656,f1456,f59940]) ).
thf(f59940,definition,
( spl65_551
<=> ( none_b
= ( nth_option_b @ v @ ( sK2 @ sK28 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl65_551])],[avatar_definition]) ).
thf(f1456,definition,
( spl65_1
<=> ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ sK28 ) ) ),
introduced(definition,[new_symbols(naming,[spl65_1])],[avatar_definition]) ).
thf(f1656,definition,
( spl65_6
<=> ( $true
= ( ord_less_nat @ zero_zero_nat @ sK28 ) ) ),
introduced(definition,[new_symbols(naming,[spl65_6])],[avatar_definition]) ).
thf(f60006,plain,
( ( none_b
= ( nth_option_b @ v @ ( sK2 @ sK28 ) ) )
| ~ spl65_1
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f8632,f1458]) ).
thf(f1458,plain,
( ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ sK28 ) )
| ~ spl65_1 ),
inference(avatar_component_clause,[status(thm)],[f1456]) ).
thf(f8632,plain,
( ! [X0: option_b,X1: list_option_b] :
( ( nth_option_b @ ( cons_option_b @ X0 @ X1 ) @ sK28 )
= ( nth_option_b @ X1 @ ( sK2 @ sK28 ) ) )
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f1300,f8559]) ).
thf(f8559,plain,
( ( sK28
= ( suc @ ( sK2 @ sK28 ) ) )
| ~ spl65_6 ),
inference(trivial_inequality_removal,[status(thm)],[f8556]) ).
thf(f8556,plain,
( ( $true != $true )
| ( sK28
= ( suc @ ( sK2 @ sK28 ) ) )
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f1104,f1658]) ).
thf(f1658,plain,
( ( $true
= ( ord_less_nat @ zero_zero_nat @ sK28 ) )
| ~ spl65_6 ),
inference(avatar_component_clause,[status(thm)],[f1656]) ).
thf(f1104,plain,
! [X0: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ X0 )
!= $true )
| ( ( suc @ ( sK2 @ X0 ) )
= X0 ) ),
inference(cnf_transformation,[status(thm)],[f927]) ).
thf(f927,plain,
! [X0: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ X0 )
!= $true )
| ( ( suc @ ( sK2 @ X0 ) )
= X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f837,f926]) ).
thf(f926,plain,
! [X0: nat] :
( ? [X1: nat] :
( ( suc @ X1 )
= X0 )
=> ( ( suc @ ( sK2 @ X0 ) )
= X0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f837,plain,
! [X0: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ X0 )
!= $true )
| ? [X1: nat] :
( ( suc @ X1 )
= X0 ) ),
inference(ennf_transformation,[status(thm)],[f552]) ).
thf(f552,plain,
! [X0: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ X0 )
= $true )
=> ? [X1: nat] :
( ( suc @ X1 )
= X0 ) ),
inference(fool_elimination,[status(thm)],[f551]) ).
thf(f551,plain,
! [X0: nat] :
( ( ord_less_nat @ zero_zero_nat @ X0 )
=> ? [X1: nat] :
( ( suc @ X1 )
= X0 ) ),
inference(rectify,[status(thm)],[f105]) ).
thf(f105,axiom,
! [X2: nat] :
( ( ord_less_nat @ zero_zero_nat @ X2 )
=> ? [X22: nat] :
( ( suc @ X22 )
= X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_104_gr0__implies__Suc) ).
thf(f1300,plain,
! [X2: nat,X0: option_b,X1: list_option_b] :
( ( nth_option_b @ ( cons_option_b @ X0 @ X1 ) @ ( suc @ X2 ) )
= ( nth_option_b @ X1 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: option_b,X1: list_option_b,X2: nat] :
( ( nth_option_b @ ( cons_option_b @ X0 @ X1 ) @ ( suc @ X2 ) )
= ( nth_option_b @ X1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_1_nth__Cons__Suc) ).
thf(f59953,plain,
( ~ spl65_551
| spl65_553
| ~ spl65_6 ),
inference(avatar_split_clause,[status(thm)],[f59948,f1656,f59950,f59940]) ).
thf(f59948,plain,
( ( none_b
!= ( nth_option_b @ v @ ( sK2 @ sK28 ) ) )
| ( $false
= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ~ spl65_6 ),
inference(subsumption_resolution,[status(thm)],[f59727,f23520]) ).
thf(f23520,plain,
( ( $true
= ( ord_less_nat @ ( sK2 @ sK28 ) @ ( size_s1671393719tion_b @ v ) ) )
| ~ spl65_6 ),
inference(forward_demodulation,[status(thm)],[f23510,f11705]) ).
thf(f11705,plain,
( ( ( sK2 @ sK28 )
= ( sK40 @ sK28 ) )
| ~ spl65_6 ),
inference(subsumption_resolution,[status(thm)],[f11704,f8609]) ).
thf(f8609,plain,
( ( ( sK2 @ sK28 )
!= sK28 )
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f1141,f8559]) ).
thf(f1141,plain,
! [X0: nat] :
( ( suc @ X0 )
!= X0 ),
inference(cnf_transformation,[status(thm)],[f751]) ).
thf(f751,plain,
! [X0: nat] :
( ( suc @ X0 )
!= X0 ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,axiom,
! [X2: nat] :
( ( suc @ X2 )
!= X2 ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_24_n__not__Suc__n) ).
thf(f11704,plain,
( ( ( sK2 @ sK28 )
= sK28 )
| ( ( sK2 @ sK28 )
= ( sK40 @ sK28 ) )
| ~ spl65_6 ),
inference(subsumption_resolution,[status(thm)],[f11703,f8929]) ).
thf(f8929,plain,
( ( ( ord_less_nat @ sK28 @ ( sK2 @ sK28 ) )
!= $true )
| ~ spl65_6 ),
inference(trivial_inequality_removal,[status(thm)],[f8855]) ).
thf(f8855,plain,
( ( $true != $true )
| ( ( ord_less_nat @ sK28 @ ( sK2 @ sK28 ) )
!= $true )
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f1298,f8615]) ).
thf(f8615,plain,
( ! [X0: nat] :
( ( $true
= ( ord_less_nat @ ( sK2 @ sK28 ) @ X0 ) )
| ( $true
!= ( ord_less_nat @ sK28 @ X0 ) ) )
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f1208,f8559]) ).
thf(f1208,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( ord_less_nat @ ( suc @ X1 ) @ X0 ) )
| ( $true
= ( ord_less_nat @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f900]) ).
thf(f900,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( ord_less_nat @ X1 @ X0 ) )
| ( $true
!= ( ord_less_nat @ ( suc @ X1 ) @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f642]) ).
thf(f642,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( ord_less_nat @ ( suc @ X1 ) @ X0 ) )
=> ( $true
= ( ord_less_nat @ X1 @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f641]) ).
thf(f641,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ ( suc @ X1 ) @ X0 )
=> ( ord_less_nat @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f80]) ).
thf(f80,axiom,
! [X2: nat,X4: nat] :
( ( ord_less_nat @ ( suc @ X4 ) @ X2 )
=> ( ord_less_nat @ X4 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_79_Suc__lessD) ).
thf(f1298,plain,
! [X0: nat] :
( $true
!= ( ord_less_nat @ X0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f769]) ).
thf(f769,plain,
! [X0: nat] :
( $true
!= ( ord_less_nat @ X0 @ X0 ) ),
inference(flattening,[status(thm)],[f723]) ).
thf(f723,plain,
! [X0: nat] :
( $true
!= ( ord_less_nat @ X0 @ X0 ) ),
inference(fool_elimination,[status(thm)],[f722]) ).
thf(f722,plain,
! [X0: nat] :
~ ( ord_less_nat @ X0 @ X0 ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,axiom,
! [X2: nat] :
~ ( ord_less_nat @ X2 @ X2 ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_29_less__irrefl__nat) ).
thf(f11703,plain,
( ( ( ord_less_nat @ sK28 @ ( sK2 @ sK28 ) )
= $true )
| ( ( sK2 @ sK28 )
= sK28 )
| ( ( sK2 @ sK28 )
= ( sK40 @ sK28 ) )
| ~ spl65_6 ),
inference(subsumption_resolution,[status(thm)],[f11697,f8741]) ).
thf(f8741,plain,
( ( $true
= ( ord_less_nat @ ( sK40 @ sK28 ) @ sK28 ) )
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f1433,f8561]) ).
thf(f8561,plain,
( ( ( suc @ ( sK40 @ sK28 ) )
= sK28 )
| ~ spl65_6 ),
inference(trivial_inequality_removal,[status(thm)],[f8557]) ).
thf(f8557,plain,
( ( ( suc @ ( sK40 @ sK28 ) )
= sK28 )
| ( $true != $true )
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f1228,f1658]) ).
thf(f1228,plain,
! [X0: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ X0 )
!= $true )
| ( ( suc @ ( sK40 @ X0 ) )
= X0 ) ),
inference(cnf_transformation,[status(thm)],[f1015]) ).
thf(f1015,plain,
! [X0: nat] :
( ( ( ( suc @ ( sK40 @ X0 ) )
= X0 )
| ( ( ord_less_nat @ zero_zero_nat @ X0 )
!= $true ) )
& ( ( ( ord_less_nat @ zero_zero_nat @ X0 )
= $true )
| ! [X2: nat] :
( ( suc @ X2 )
!= X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f1013,f1014]) ).
thf(f1014,plain,
! [X0: nat] :
( ? [X1: nat] :
( ( suc @ X1 )
= X0 )
=> ( ( suc @ ( sK40 @ X0 ) )
= X0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1013,plain,
! [X0: nat] :
( ( ? [X1: nat] :
( ( suc @ X1 )
= X0 )
| ( ( ord_less_nat @ zero_zero_nat @ X0 )
!= $true ) )
& ( ( ( ord_less_nat @ zero_zero_nat @ X0 )
= $true )
| ! [X2: nat] :
( ( suc @ X2 )
!= X0 ) ) ),
inference(rectify,[status(thm)],[f1012]) ).
thf(f1012,plain,
! [X0: nat] :
( ( ? [X1: nat] :
( ( suc @ X1 )
= X0 )
| ( ( ord_less_nat @ zero_zero_nat @ X0 )
!= $true ) )
& ( ( ( ord_less_nat @ zero_zero_nat @ X0 )
= $true )
| ! [X1: nat] :
( ( suc @ X1 )
!= X0 ) ) ),
inference(nnf_transformation,[status(thm)],[f727]) ).
thf(f727,plain,
! [X0: nat] :
( ? [X1: nat] :
( ( suc @ X1 )
= X0 )
<=> ( ( ord_less_nat @ zero_zero_nat @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f726]) ).
thf(f726,plain,
! [X0: nat] :
? [X1: nat] :
( ( ( suc @ X1 )
= X0 )
= ( ord_less_nat @ zero_zero_nat @ X0 ) ),
inference(rectify,[status(thm)],[f107]) ).
thf(f107,axiom,
! [X2: nat] :
? [X48: nat] :
( ( ( suc @ X48 )
= X2 )
= ( ord_less_nat @ zero_zero_nat @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_106_gr0__conv__Suc) ).
thf(f1433,plain,
! [X1: nat] :
( ( ord_less_nat @ X1 @ ( suc @ X1 ) )
= $true ),
inference(equality_resolution,[status(thm)],[f1288]) ).
thf(f1288,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( ord_less_nat @ X0 @ ( suc @ X1 ) ) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[status(thm)],[f1051]) ).
thf(f1051,plain,
! [X0: nat,X1: nat] :
( ( ( $true
= ( ord_less_nat @ X0 @ ( suc @ X1 ) ) )
| ( ( X0 != X1 )
& ( $true
!= ( ord_less_nat @ X0 @ X1 ) ) ) )
& ( ( X0 = X1 )
| ( $true
= ( ord_less_nat @ X0 @ X1 ) )
| ( $true
!= ( ord_less_nat @ X0 @ ( suc @ X1 ) ) ) ) ),
inference(flattening,[status(thm)],[f1050]) ).
thf(f1050,plain,
! [X0: nat,X1: nat] :
( ( ( $true
= ( ord_less_nat @ X0 @ ( suc @ X1 ) ) )
| ( ( X0 != X1 )
& ( $true
!= ( ord_less_nat @ X0 @ X1 ) ) ) )
& ( ( X0 = X1 )
| ( $true
= ( ord_less_nat @ X0 @ X1 ) )
| ( $true
!= ( ord_less_nat @ X0 @ ( suc @ X1 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f480]) ).
thf(f480,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( ord_less_nat @ X0 @ ( suc @ X1 ) ) )
<=> ( ( X0 = X1 )
| ( $true
= ( ord_less_nat @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f479]) ).
thf(f479,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ X0 @ X1 )
| ( ( X0 = X1 )
= ( ord_less_nat @ X0 @ ( suc @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f74]) ).
thf(f74,axiom,
! [X4: nat,X2: nat] :
( ( ord_less_nat @ X4 @ X2 )
| ( ( X2 = X4 )
= ( ord_less_nat @ X4 @ ( suc @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_73_less__Suc__eq) ).
thf(f11697,plain,
( ( $true
!= ( ord_less_nat @ ( sK40 @ sK28 ) @ sK28 ) )
| ( ( sK2 @ sK28 )
= ( sK40 @ sK28 ) )
| ( ( ord_less_nat @ sK28 @ ( sK2 @ sK28 ) )
= $true )
| ( ( sK2 @ sK28 )
= sK28 )
| ~ spl65_6 ),
inference(trivial_inequality_removal,[status(thm)],[f11682]) ).
thf(f11682,plain,
( ( ( ord_less_nat @ sK28 @ ( sK2 @ sK28 ) )
= $true )
| ( $true != $true )
| ( ( sK2 @ sK28 )
= sK28 )
| ( $true
!= ( ord_less_nat @ ( sK40 @ sK28 ) @ sK28 ) )
| ( ( sK2 @ sK28 )
= ( sK40 @ sK28 ) )
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f8698,f8625]) ).
thf(f8625,plain,
( ! [X0: nat] :
( ( ( ord_less_nat @ X0 @ ( sK2 @ sK28 ) )
= $true )
| ( $true
!= ( ord_less_nat @ X0 @ sK28 ) )
| ( ( sK2 @ sK28 )
= X0 ) )
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f1260,f8559]) ).
thf(f1260,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( ord_less_nat @ X1 @ ( suc @ X0 ) ) )
| ( X0 = X1 )
| ( $true
= ( ord_less_nat @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f1032]) ).
thf(f1032,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( ord_less_nat @ X1 @ X0 ) )
| ( ( ( $true
= ( ord_less_nat @ X1 @ ( suc @ X0 ) ) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( $true
!= ( ord_less_nat @ X1 @ ( suc @ X0 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f860]) ).
thf(f860,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( ord_less_nat @ X1 @ X0 ) )
| ( ( $true
= ( ord_less_nat @ X1 @ ( suc @ X0 ) ) )
<=> ( X0 = X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f754]) ).
thf(f754,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( ord_less_nat @ X1 @ X0 ) )
=> ( ( $true
= ( ord_less_nat @ X1 @ ( suc @ X0 ) ) )
<=> ( X0 = X1 ) ) ),
inference(flattening,[status(thm)],[f566]) ).
thf(f566,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( ord_less_nat @ X1 @ X0 ) )
=> ( ( $true
= ( ord_less_nat @ X1 @ ( suc @ X0 ) ) )
<=> ( X0 = X1 ) ) ),
inference(fool_elimination,[status(thm)],[f565]) ).
thf(f565,plain,
! [X0: nat,X1: nat] :
( ~ ( ord_less_nat @ X1 @ X0 )
=> ( ( X0 = X1 )
= ( ord_less_nat @ X1 @ ( suc @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f65]) ).
thf(f65,axiom,
! [X4: nat,X2: nat] :
( ~ ( ord_less_nat @ X2 @ X4 )
=> ( ( X2 = X4 )
= ( ord_less_nat @ X2 @ ( suc @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_64_not__less__less__Suc__eq) ).
thf(f8698,plain,
( ! [X0: nat] :
( ( ( ord_less_nat @ ( sK40 @ sK28 ) @ X0 )
!= $true )
| ( sK28 = X0 )
| ( $true
= ( ord_less_nat @ sK28 @ X0 ) ) )
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f1130,f8561]) ).
thf(f1130,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( ord_less_nat @ ( suc @ X0 ) @ X1 ) )
| ( $true
!= ( ord_less_nat @ X0 @ X1 ) )
| ( ( suc @ X0 )
= X1 ) ),
inference(cnf_transformation,[status(thm)],[f841]) ).
thf(f841,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( ord_less_nat @ ( suc @ X0 ) @ X1 ) )
| ( ( suc @ X0 )
= X1 )
| ( $true
!= ( ord_less_nat @ X0 @ X1 ) ) ),
inference(flattening,[status(thm)],[f840]) ).
thf(f840,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( ord_less_nat @ ( suc @ X0 ) @ X1 ) )
| ( ( suc @ X0 )
= X1 )
| ( $true
!= ( ord_less_nat @ X0 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f705]) ).
thf(f705,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( ord_less_nat @ X0 @ X1 ) )
=> ( ( ( suc @ X0 )
!= X1 )
=> ( $true
= ( ord_less_nat @ ( suc @ X0 ) @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f704]) ).
thf(f704,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ X0 @ X1 )
=> ( ( ( suc @ X0 )
!= X1 )
=> ( ord_less_nat @ ( suc @ X0 ) @ X1 ) ) ),
inference(rectify,[status(thm)],[f78]) ).
thf(f78,axiom,
! [X4: nat,X2: nat] :
( ( ord_less_nat @ X4 @ X2 )
=> ( ( ( suc @ X4 )
!= X2 )
=> ( ord_less_nat @ ( suc @ X4 ) @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_77_Suc__lessI) ).
thf(f23510,plain,
( ( $true
= ( ord_less_nat @ ( sK40 @ sK28 ) @ ( size_s1671393719tion_b @ v ) ) )
| ~ spl65_6 ),
inference(trivial_inequality_removal,[status(thm)],[f23439]) ).
thf(f23439,plain,
( ( $true
= ( ord_less_nat @ ( sK40 @ sK28 ) @ ( size_s1671393719tion_b @ v ) ) )
| ( $false = $true )
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f1464,f8753]) ).
thf(f8753,plain,
( ! [X0: nat] :
( ( ( ord_less_nat @ sK28 @ ( suc @ X0 ) )
= $false )
| ( ( ord_less_nat @ ( sK40 @ sK28 ) @ X0 )
= $true ) )
| ~ spl65_6 ),
inference(binary_proxy_clausification,[status(thm)],[f8735]) ).
thf(f8735,plain,
( ! [X0: nat] :
( ( ord_less_nat @ sK28 @ ( suc @ X0 ) )
= ( ord_less_nat @ ( sK40 @ sK28 ) @ X0 ) )
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f1372,f8561]) ).
thf(f1372,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ ( suc @ X0 ) @ ( suc @ X1 ) )
= ( ord_less_nat @ X0 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f753]) ).
thf(f753,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ ( suc @ X0 ) @ ( suc @ X1 ) )
= ( ord_less_nat @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
! [X4: nat,X2: nat] :
( ( ord_less_nat @ X4 @ X2 )
= ( ord_less_nat @ ( suc @ X4 ) @ ( suc @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_12_Suc__less__eq) ).
thf(f1464,plain,
( ( ord_less_nat @ sK28 @ ( suc @ ( size_s1671393719tion_b @ v ) ) )
= $true ),
inference(subsumption_resolution,[status(thm)],[f1384,f1359]) ).
thf(f1359,plain,
! [X0: option_b,X1: list_option_b] :
( ( size_s1671393719tion_b @ ( cons_option_b @ X0 @ X1 ) )
= ( suc @ ( size_s1671393719tion_b @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
thf(f122,axiom,
! [X0: option_b,X1: list_option_b] :
( ( size_s1671393719tion_b @ ( cons_option_b @ X0 @ X1 ) )
= ( suc @ ( size_s1671393719tion_b @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_121_length__Cons) ).
thf(f1384,plain,
( ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
!= ( suc @ ( size_s1671393719tion_b @ v ) ) )
| ( ( ord_less_nat @ sK28 @ ( suc @ ( size_s1671393719tion_b @ v ) ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f1184,f1163,f1163]) ).
thf(f1163,plain,
( ( size_s1671393719tion_b @ v )
= n ),
inference(cnf_transformation,[status(thm)],[f965]) ).
thf(f965,plain,
( ( ( size_s1671393719tion_b @ v )
= n )
& ! [X0: nat] :
( ( ( ord_less_nat @ X0 @ n )
!= $true )
| ( ( ( $true
!= ( member_nat @ X0 @ ( fvi_a @ ( suc @ b2 ) @ phi ) ) )
| ( none_b
!= ( nth_option_b @ v @ X0 ) ) )
& ( ( none_b
= ( nth_option_b @ v @ X0 ) )
| ( $true
= ( member_nat @ X0 @ ( fvi_a @ ( suc @ b2 ) @ phi ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f880]) ).
thf(f880,plain,
( ( ( size_s1671393719tion_b @ v )
= n )
& ! [X0: nat] :
( ( ( ord_less_nat @ X0 @ n )
!= $true )
| ( ( $true
!= ( member_nat @ X0 @ ( fvi_a @ ( suc @ b2 ) @ phi ) ) )
<=> ( none_b
= ( nth_option_b @ v @ X0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f741]) ).
thf(f741,plain,
( ( ( size_s1671393719tion_b @ v )
= n )
& ! [X0: nat] :
( ( ( ord_less_nat @ X0 @ n )
= $true )
=> ( ( $true
!= ( member_nat @ X0 @ ( fvi_a @ ( suc @ b2 ) @ phi ) ) )
<=> ( none_b
= ( nth_option_b @ v @ X0 ) ) ) ) ),
inference(flattening,[status(thm)],[f413]) ).
thf(f413,plain,
( ! [X0: nat] :
( ( ( ord_less_nat @ X0 @ n )
= $true )
=> ( ( none_b
= ( nth_option_b @ v @ X0 ) )
<=> ( $true
!= ( member_nat @ X0 @ ( fvi_a @ ( suc @ b2 ) @ phi ) ) ) ) )
& ( ( size_s1671393719tion_b @ v )
= n ) ),
inference(fool_elimination,[status(thm)],[f412]) ).
thf(f412,plain,
( ! [X0: nat] :
( ( ord_less_nat @ X0 @ n )
=> ( ( none_b
= ( nth_option_b @ v @ X0 ) )
= ( ~ ( member_nat @ X0 @ ( fvi_a @ ( suc @ b2 ) @ phi ) ) ) ) )
& ( ( size_s1671393719tion_b @ v )
= n ) ),
inference(rectify,[status(thm)],[f328]) ).
thf(f328,axiom,
( ! [X70: nat] :
( ( ord_less_nat @ X70 @ n )
=> ( ( none_b
= ( nth_option_b @ v @ X70 ) )
= ( ~ ( member_nat @ X70 @ ( fvi_a @ ( suc @ b2 ) @ phi ) ) ) ) )
& ( ( size_s1671393719tion_b @ v )
= n ) ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',conj_1) ).
thf(f1184,plain,
( ( $true
= ( ord_less_nat @ sK28 @ ( suc @ n ) ) )
| ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
!= ( suc @ n ) ) ),
inference(cnf_transformation,[status(thm)],[f986]) ).
thf(f986,plain,
( ( ( $true
= ( ord_less_nat @ sK28 @ ( suc @ n ) ) )
& ( ( $true
= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ( none_b
!= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ sK28 ) ) )
& ( ( $true
!= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ sK28 ) ) ) )
| ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
!= ( suc @ n ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f984,f985]) ).
thf(f985,plain,
( ? [X0: nat] :
( ( ( ord_less_nat @ X0 @ ( suc @ n ) )
= $true )
& ( ( $true
= ( member_nat @ X0 @ ( fvi_a @ b2 @ phi ) ) )
| ( none_b
!= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ X0 ) ) )
& ( ( $true
!= ( member_nat @ X0 @ ( fvi_a @ b2 @ phi ) ) )
| ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ X0 ) ) ) )
=> ( ( $true
= ( ord_less_nat @ sK28 @ ( suc @ n ) ) )
& ( ( $true
= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ( none_b
!= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ sK28 ) ) )
& ( ( $true
!= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ sK28 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f984,plain,
( ? [X0: nat] :
( ( ( ord_less_nat @ X0 @ ( suc @ n ) )
= $true )
& ( ( $true
= ( member_nat @ X0 @ ( fvi_a @ b2 @ phi ) ) )
| ( none_b
!= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ X0 ) ) )
& ( ( $true
!= ( member_nat @ X0 @ ( fvi_a @ b2 @ phi ) ) )
| ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ X0 ) ) ) )
| ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
!= ( suc @ n ) ) ),
inference(flattening,[status(thm)],[f983]) ).
thf(f983,plain,
( ? [X0: nat] :
( ( ( ord_less_nat @ X0 @ ( suc @ n ) )
= $true )
& ( ( $true
= ( member_nat @ X0 @ ( fvi_a @ b2 @ phi ) ) )
| ( none_b
!= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ X0 ) ) )
& ( ( $true
!= ( member_nat @ X0 @ ( fvi_a @ b2 @ phi ) ) )
| ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ X0 ) ) ) )
| ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
!= ( suc @ n ) ) ),
inference(nnf_transformation,[status(thm)],[f862]) ).
thf(f862,plain,
( ? [X0: nat] :
( ( ( ord_less_nat @ X0 @ ( suc @ n ) )
= $true )
& ( ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ X0 ) )
<~> ( $true
!= ( member_nat @ X0 @ ( fvi_a @ b2 @ phi ) ) ) ) )
| ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
!= ( suc @ n ) ) ),
inference(ennf_transformation,[status(thm)],[f740]) ).
thf(f740,plain,
~ ( ! [X0: nat] :
( ( ( ord_less_nat @ X0 @ ( suc @ n ) )
!= $true )
| ( ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ X0 ) )
<=> ( $true
!= ( member_nat @ X0 @ ( fvi_a @ b2 @ phi ) ) ) ) )
& ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
= ( suc @ n ) ) ),
inference(flattening,[status(thm)],[f333]) ).
thf(f333,plain,
~ ( ! [X0: nat] :
( ( ( ord_less_nat @ X0 @ ( suc @ n ) )
!= $true )
| ( ( $true
!= ( member_nat @ X0 @ ( fvi_a @ b2 @ phi ) ) )
<=> ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ X0 ) ) ) )
& ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
= ( suc @ n ) ) ),
inference(fool_elimination,[status(thm)],[f332]) ).
thf(f332,plain,
~ ( ! [X0: nat] :
( ~ ( ord_less_nat @ X0 @ ( suc @ n ) )
| ( ( ~ ( member_nat @ X0 @ ( fvi_a @ b2 @ phi ) ) )
= ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ X0 ) ) ) )
& ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
= ( suc @ n ) ) ),
inference(rectify,[status(thm)],[f330]) ).
thf(f330,negated_conjecture,
~ ( ! [X32: nat] :
( ~ ( ord_less_nat @ X32 @ ( suc @ n ) )
| ( ( ~ ( member_nat @ X32 @ ( fvi_a @ b2 @ phi ) ) )
= ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ X32 ) ) ) )
& ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
= ( suc @ n ) ) ),
inference(negated_conjecture,[status(cth)],[f329]) ).
thf(f329,conjecture,
( ! [X32: nat] :
( ~ ( ord_less_nat @ X32 @ ( suc @ n ) )
| ( ( ~ ( member_nat @ X32 @ ( fvi_a @ b2 @ phi ) ) )
= ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ X32 ) ) ) )
& ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
= ( suc @ n ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',conj_2) ).
thf(f59727,plain,
( ( none_b
!= ( nth_option_b @ v @ ( sK2 @ sK28 ) ) )
| ( $false
= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ( $true
!= ( ord_less_nat @ ( sK2 @ sK28 ) @ ( size_s1671393719tion_b @ v ) ) )
| ~ spl65_6 ),
inference(trivial_inequality_removal,[status(thm)],[f59717]) ).
thf(f59717,plain,
( ( $false
= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ( $true
!= ( ord_less_nat @ ( sK2 @ sK28 ) @ ( size_s1671393719tion_b @ v ) ) )
| ( none_b
!= ( nth_option_b @ v @ ( sK2 @ sK28 ) ) )
| ( $true != $true )
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f1382,f8661]) ).
thf(f8661,plain,
( ! [X0: nat,X1: formula_a] :
( ( $true
= ( member_nat @ ( sK2 @ sK28 ) @ ( fvi_a @ ( suc @ X0 ) @ X1 ) ) )
| ( $false
= ( member_nat @ sK28 @ ( fvi_a @ X0 @ X1 ) ) ) )
| ~ spl65_6 ),
inference(binary_proxy_clausification,[status(thm)],[f8631]) ).
thf(f8631,plain,
( ! [X0: nat,X1: formula_a] :
( ( member_nat @ ( sK2 @ sK28 ) @ ( fvi_a @ ( suc @ X0 ) @ X1 ) )
= ( member_nat @ sK28 @ ( fvi_a @ X0 @ X1 ) ) )
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f1289,f8559]) ).
thf(f1289,plain,
! [X2: formula_a,X0: nat,X1: nat] :
( ( member_nat @ ( suc @ X0 ) @ ( fvi_a @ X1 @ X2 ) )
= ( member_nat @ X0 @ ( fvi_a @ ( suc @ X1 ) @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f742]) ).
thf(f742,plain,
! [X0: nat,X1: nat,X2: formula_a] :
( ( member_nat @ ( suc @ X0 ) @ ( fvi_a @ X1 @ X2 ) )
= ( member_nat @ X0 @ ( fvi_a @ ( suc @ X1 ) @ X2 ) ) ),
inference(rectify,[status(thm)],[f124]) ).
thf(f124,axiom,
! [X0: nat,X53: nat,X54: formula_a] :
( ( member_nat @ X0 @ ( fvi_a @ ( suc @ X53 ) @ X54 ) )
= ( member_nat @ ( suc @ X0 ) @ ( fvi_a @ X53 @ X54 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_123_fvi__Suc) ).
thf(f1382,plain,
! [X0: nat] :
( ( $true
!= ( member_nat @ X0 @ ( fvi_a @ ( suc @ b2 ) @ phi ) ) )
| ( $true
!= ( ord_less_nat @ X0 @ ( size_s1671393719tion_b @ v ) ) )
| ( none_b
!= ( nth_option_b @ v @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f1162,f1163]) ).
thf(f1162,plain,
! [X0: nat] :
( ( ( ord_less_nat @ X0 @ n )
!= $true )
| ( $true
!= ( member_nat @ X0 @ ( fvi_a @ ( suc @ b2 ) @ phi ) ) )
| ( none_b
!= ( nth_option_b @ v @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f965]) ).
thf(f59922,plain,
( spl65_1
| spl65_2
| ~ spl65_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f59921]) ).
thf(f59921,plain,
( $false
| spl65_1
| spl65_2
| ~ spl65_6 ),
inference(subsumption_resolution,[status(thm)],[f59920,f23520]) ).
thf(f59920,plain,
( ( $true
!= ( ord_less_nat @ ( sK2 @ sK28 ) @ ( size_s1671393719tion_b @ v ) ) )
| spl65_1
| spl65_2
| ~ spl65_6 ),
inference(subsumption_resolution,[status(thm)],[f59919,f1462]) ).
thf(f1462,plain,
( ( $true
!= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| spl65_2 ),
inference(avatar_component_clause,[status(thm)],[f1460]) ).
thf(f59919,plain,
( ( $true
= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ( $true
!= ( ord_less_nat @ ( sK2 @ sK28 ) @ ( size_s1671393719tion_b @ v ) ) )
| spl65_1
| ~ spl65_6 ),
inference(subsumption_resolution,[status(thm)],[f59871,f11730]) ).
thf(f11730,plain,
( ( none_b
!= ( nth_option_b @ v @ ( sK2 @ sK28 ) ) )
| spl65_1
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f1457,f8632]) ).
thf(f1457,plain,
( ( none_b
!= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ sK28 ) )
| spl65_1 ),
inference(avatar_component_clause,[status(thm)],[f1456]) ).
thf(f59871,plain,
( ( none_b
= ( nth_option_b @ v @ ( sK2 @ sK28 ) ) )
| ( $true
!= ( ord_less_nat @ ( sK2 @ sK28 ) @ ( size_s1671393719tion_b @ v ) ) )
| ( $true
= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ~ spl65_6 ),
inference(trivial_inequality_removal,[status(thm)],[f59845]) ).
thf(f59845,plain,
( ( $true
= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ( $true
!= ( ord_less_nat @ ( sK2 @ sK28 ) @ ( size_s1671393719tion_b @ v ) ) )
| ( $false = $true )
| ( none_b
= ( nth_option_b @ v @ ( sK2 @ sK28 ) ) )
| ~ spl65_6 ),
inference(superposition,[status(thm)],[f8662,f1383]) ).
thf(f1383,plain,
! [X0: nat] :
( ( $true
= ( member_nat @ X0 @ ( fvi_a @ ( suc @ b2 ) @ phi ) ) )
| ( $true
!= ( ord_less_nat @ X0 @ ( size_s1671393719tion_b @ v ) ) )
| ( none_b
= ( nth_option_b @ v @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f1161,f1163]) ).
thf(f1161,plain,
! [X0: nat] :
( ( ( ord_less_nat @ X0 @ n )
!= $true )
| ( none_b
= ( nth_option_b @ v @ X0 ) )
| ( $true
= ( member_nat @ X0 @ ( fvi_a @ ( suc @ b2 ) @ phi ) ) ) ),
inference(cnf_transformation,[status(thm)],[f965]) ).
thf(f8662,plain,
( ! [X0: nat,X1: formula_a] :
( ( $false
= ( member_nat @ ( sK2 @ sK28 ) @ ( fvi_a @ ( suc @ X0 ) @ X1 ) ) )
| ( $true
= ( member_nat @ sK28 @ ( fvi_a @ X0 @ X1 ) ) ) )
| ~ spl65_6 ),
inference(binary_proxy_clausification,[status(thm)],[f8631]) ).
thf(f8554,plain,
( ~ spl65_1
| ~ spl65_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f8553]) ).
thf(f8553,plain,
( $false
| ~ spl65_1
| ~ spl65_11 ),
inference(subsumption_resolution,[status(thm)],[f8550,f1447]) ).
thf(f1447,plain,
! [X1: b] :
( none_b
!= ( some_b @ X1 ) ),
inference(equality_resolution,[status(thm)],[f1354]) ).
thf(f1354,plain,
! [X0: option_b,X1: b] :
( ( none_b != X0 )
| ( ( some_b @ X1 )
!= X0 ) ),
inference(cnf_transformation,[status(thm)],[f868]) ).
thf(f868,plain,
! [X0: option_b,X1: b] :
( ( none_b != X0 )
| ( ( some_b @ X1 )
!= X0 ) ),
inference(ennf_transformation,[status(thm)],[f766]) ).
thf(f766,plain,
! [X0: option_b,X1: b] :
( ( ( some_b @ X1 )
= X0 )
=> ( none_b != X0 ) ),
inference(rectify,[status(thm)],[f97]) ).
thf(f97,axiom,
! [X43: option_b,X12: b] :
( ( ( some_b @ X12 )
= X43 )
=> ( none_b != X43 ) ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_96_option_OdiscI) ).
thf(f8550,plain,
( ( none_b
= ( some_b @ x ) )
| ~ spl65_1
| ~ spl65_11 ),
inference(superposition,[status(thm)],[f1292,f8548]) ).
thf(f8548,plain,
( ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ zero_zero_nat ) )
| ~ spl65_1
| ~ spl65_11 ),
inference(forward_demodulation,[status(thm)],[f1458,f1791]) ).
thf(f1791,plain,
( ( zero_zero_nat = sK28 )
| ~ spl65_11 ),
inference(avatar_component_clause,[status(thm)],[f1789]) ).
thf(f1789,definition,
( spl65_11
<=> ( zero_zero_nat = sK28 ) ),
introduced(definition,[new_symbols(naming,[spl65_11])],[avatar_definition]) ).
thf(f1292,plain,
! [X0: option_b,X1: list_option_b] :
( ( nth_option_b @ ( cons_option_b @ X0 @ X1 ) @ zero_zero_nat )
= X0 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: option_b,X1: list_option_b] :
( ( nth_option_b @ ( cons_option_b @ X0 @ X1 ) @ zero_zero_nat )
= X0 ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_3_nth__Cons__0) ).
thf(f8545,plain,
( spl65_2
| ~ spl65_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f8544]) ).
thf(f8544,plain,
( $false
| spl65_2
| ~ spl65_11 ),
inference(subsumption_resolution,[status(thm)],[f8532,f1301]) ).
thf(f1301,plain,
( ( member_nat @ zero_zero_nat @ ( fvi_a @ b2 @ phi ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f365]) ).
thf(f365,plain,
( ( member_nat @ zero_zero_nat @ ( fvi_a @ b2 @ phi ) )
= $true ),
inference(fool_elimination,[status(thm)],[f364]) ).
thf(f364,plain,
member_nat @ zero_zero_nat @ ( fvi_a @ b2 @ phi ),
inference(rectify,[status(thm)],[f327]) ).
thf(f327,axiom,
member_nat @ zero_zero_nat @ ( fvi_a @ b2 @ phi ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',conj_0) ).
thf(f8532,plain,
( ( ( member_nat @ zero_zero_nat @ ( fvi_a @ b2 @ phi ) )
!= $true )
| spl65_2
| ~ spl65_11 ),
inference(superposition,[status(thm)],[f1462,f1791]) ).
thf(f8530,plain,
( spl65_11
| spl65_6 ),
inference(avatar_split_clause,[status(thm)],[f8501,f1656,f1789]) ).
thf(f8501,plain,
( ( zero_zero_nat = sK28 )
| spl65_6 ),
inference(trivial_inequality_removal,[status(thm)],[f8492]) ).
thf(f8492,plain,
( ( zero_zero_nat = sK28 )
| ( $true != $true )
| spl65_6 ),
inference(superposition,[status(thm)],[f1657,f1211]) ).
thf(f1211,plain,
! [X0: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ X0 )
= $true )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[status(thm)],[f1003]) ).
thf(f1003,plain,
! [X0: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ X0 )
!= $true )
| ( zero_zero_nat != X0 ) )
& ( ( zero_zero_nat = X0 )
| ( ( ord_less_nat @ zero_zero_nat @ X0 )
= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f781]) ).
thf(f781,plain,
! [X0: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ X0 )
!= $true )
<=> ( zero_zero_nat = X0 ) ),
inference(flattening,[status(thm)],[f478]) ).
thf(f478,plain,
! [X0: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ X0 )
!= $true )
<=> ( zero_zero_nat = X0 ) ),
inference(fool_elimination,[status(thm)],[f477]) ).
thf(f477,plain,
! [X0: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ X0 ) )
= ( zero_zero_nat = X0 ) ),
inference(rectify,[status(thm)],[f63]) ).
thf(f63,axiom,
! [X2: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ X2 ) )
= ( zero_zero_nat = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_62_not__gr0) ).
thf(f1657,plain,
( ( $true
!= ( ord_less_nat @ zero_zero_nat @ sK28 ) )
| spl65_6 ),
inference(avatar_component_clause,[status(thm)],[f1656]) ).
thf(f1466,plain,
( ~ spl65_1
| spl65_2 ),
inference(avatar_split_clause,[status(thm)],[f1465,f1460,f1456]) ).
thf(f1465,plain,
( ( $true
= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ( none_b
!= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ sK28 ) ) ),
inference(subsumption_resolution,[status(thm)],[f1385,f1359]) ).
thf(f1385,plain,
( ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
!= ( suc @ ( size_s1671393719tion_b @ v ) ) )
| ( $true
= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ( none_b
!= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ sK28 ) ) ),
inference(definition_unfolding,[status(thm)],[f1183,f1163]) ).
thf(f1183,plain,
( ( $true
= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ( none_b
!= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ sK28 ) )
| ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
!= ( suc @ n ) ) ),
inference(cnf_transformation,[status(thm)],[f986]) ).
thf(f1463,plain,
( spl65_1
| ~ spl65_2 ),
inference(avatar_split_clause,[status(thm)],[f1454,f1460,f1456]) ).
thf(f1454,plain,
( ( $true
!= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ sK28 ) ) ),
inference(subsumption_resolution,[status(thm)],[f1386,f1359]) ).
thf(f1386,plain,
( ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ sK28 ) )
| ( $true
!= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
!= ( suc @ ( size_s1671393719tion_b @ v ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1182,f1163]) ).
thf(f1182,plain,
( ( $true
!= ( member_nat @ sK28 @ ( fvi_a @ b2 @ phi ) ) )
| ( none_b
= ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ sK28 ) )
| ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
!= ( suc @ n ) ) ),
inference(cnf_transformation,[status(thm)],[f986]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP126^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n009.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 08:26:55 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.44 thf(spec,logic,$$dhol).
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % File : ITP126^1 : TPTP v9.2.1. Released v7.5.0.
% 0.18/0.44 % Domain : Interactive Theorem Proving
% 0.18/0.44 % Problem : Sledgehammer Monitor problem prob_770__6461298_1
% 0.18/0.44 % Version : Especial.
% 0.18/0.44 % English :
% 0.18/0.44
% 0.18/0.44 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.18/0.44 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.18/0.44 % Source : [Des21]
% 0.18/0.44 % Names : Monitor/prob_770__6461298_1 [Des21]
% 0.18/0.44
% 0.18/0.44 % Status : Theorem
% 0.18/0.44 % Rating : 0.89 v9.1.0, 0.88 v9.0.0, 0.90 v8.2.0, 1.00 v8.1.0, 0.91 v7.5.0
% 0.18/0.44 % Syntax : Number of formulae : 380 ( 210 unt; 51 typ; 0 def)
% 0.18/0.44 % Number of atoms : 729 ( 452 equ; 0 cnn)
% 0.18/0.44 % Maximal formula atoms : 4 ( 2 avg)
% 0.18/0.44 % Number of connectives : 2042 ( 105 ~; 15 |; 53 &;1643 @)
% 0.18/0.44 % ( 0 <=>; 226 =>; 0 <=; 0 <~>)
% 0.18/0.44 % Maximal formula depth : 16 ( 5 avg)
% 0.18/0.44 % Number of types : 10 ( 9 usr)
% 0.18/0.44 % Number of type conns : 123 ( 123 >; 0 *; 0 +; 0 <<)
% 0.18/0.44 % Number of symbols : 45 ( 42 usr; 11 con; 0-3 aty)
% 0.18/0.44 % Number of variables : 780 ( 40 ^; 698 !; 42 ?; 780 :)
% 0.18/0.44 % SPC : TH0_THM_EQU_NAR
% 0.18/0.44
% 0.18/0.44 % Comments : This file was generated by Sledgehammer 2021-02-23 15:33:17.167
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % Could-be-implicit typings (9)
% 0.18/0.44 thf(ty_n_t__Option__Ooption_It__Option__Ooption_Itf__b_J_J,type,
% 0.18/0.44 option_option_b: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__List__Olist_It__Option__Ooption_Itf__b_J_J,type,
% 0.18/0.44 list_option_b: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.18/0.44 set_nat: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__Option__Ooption_Itf__b_J,type,
% 0.18/0.44 option_b: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__MFOTL__Oformula_Itf__a_J,type,
% 0.18/0.44 formula_a: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__List__Olist_Itf__b_J,type,
% 0.18/0.44 list_b: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__Nat__Onat,type,
% 0.18/0.44 nat: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__Int__Oint,type,
% 0.18/0.44 int: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_tf__b,type,
% 0.18/0.44 b: $tType ).
% 0.18/0.44
% 0.18/0.44 % Explicit typings (42)
% 0.18/0.44 thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
% 0.18/0.44 plus_plus_int: int > int > int ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 0.18/0.44 plus_plus_nat: nat > nat > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 0.18/0.44 zero_zero_int: int ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.18/0.44 zero_zero_nat: nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_If_001t__Nat__Onat,type,
% 0.18/0.44 if_nat: $o > nat > nat > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Odrop_001t__Option__Ooption_Itf__b_J,type,
% 0.18/0.44 drop_option_b: nat > list_option_b > list_option_b ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Odrop_001tf__b,type,
% 0.18/0.44 drop_b: nat > list_b > list_b ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Ofind_001t__Option__Ooption_Itf__b_J,type,
% 0.18/0.44 find_option_b: ( option_b > $o ) > list_option_b > option_option_b ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Ofind_001tf__b,type,
% 0.18/0.44 find_b: ( b > $o ) > list_b > option_b ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Ogen__length_001t__Option__Ooption_Itf__b_J,type,
% 0.18/0.44 gen_length_option_b: nat > list_option_b > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Ogen__length_001tf__b,type,
% 0.18/0.44 gen_length_b: nat > list_b > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Olist_OCons_001t__Option__Ooption_Itf__b_J,type,
% 0.18/0.44 cons_option_b: option_b > list_option_b > list_option_b ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Olist_OCons_001tf__b,type,
% 0.18/0.44 cons_b: b > list_b > list_b ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Olist__ex_001t__Option__Ooption_Itf__b_J,type,
% 0.18/0.44 list_ex_option_b: ( option_b > $o ) > list_option_b > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Olist__ex_001tf__b,type,
% 0.18/0.44 list_ex_b: ( b > $o ) > list_b > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Onth_001t__Option__Ooption_Itf__b_J,type,
% 0.18/0.44 nth_option_b: list_option_b > nat > option_b ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Onth_001tf__b,type,
% 0.18/0.44 nth_b: list_b > nat > b ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_MFOTL_Ofvi_001tf__a,type,
% 0.18/0.44 fvi_a: nat > formula_a > set_nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Nat_OSuc,type,
% 0.18/0.44 suc: nat > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 0.18/0.44 semiri2019852685at_int: nat > int ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 0.18/0.44 semiri1382578993at_nat: nat > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Option__Ooption_Itf__b_J_J,type,
% 0.18/0.44 size_s1671393719tion_b: list_option_b > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__b_J,type,
% 0.18/0.44 size_size_list_b: list_b > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Option__Ooption_Itf__b_J_J,type,
% 0.18/0.44 size_s684879735tion_b: option_option_b > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_Itf__b_J,type,
% 0.18/0.44 size_size_option_b: option_b > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Nat__Bijection_Otriangle,type,
% 0.18/0.44 nat_triangle: nat > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Option_Ooption_ONone_001t__Option__Ooption_Itf__b_J,type,
% 0.18/0.44 none_option_b: option_option_b ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Option_Ooption_ONone_001tf__b,type,
% 0.18/0.44 none_b: option_b ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Option_Ooption_OSome_001t__Option__Ooption_Itf__b_J,type,
% 0.18/0.44 some_option_b: option_b > option_option_b ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Option_Ooption_OSome_001tf__b,type,
% 0.18/0.44 some_b: b > option_b ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Option_Ooption_Osize__option_001t__Option__Ooption_Itf__b_J,type,
% 0.18/0.44 size_option_option_b: ( option_b > nat ) > option_option_b > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Option_Ooption_Osize__option_001tf__b,type,
% 0.18/0.44 size_option_b: ( b > nat ) > option_b > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 0.18/0.44 ord_less_int: int > int > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.18/0.44 ord_less_nat: nat > nat > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.18/0.44 ord_less_eq_nat: nat > nat > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.18/0.44 collect_nat: ( nat > $o ) > set_nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_member_001t__Nat__Onat,type,
% 0.18/0.44 member_nat: nat > set_nat > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_v__092_060phi_062,type,
% 0.18/0.44 phi: formula_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_v_b,type,
% 0.18/0.44 b2: nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_v_n,type,
% 0.18/0.44 n: nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_v_v,type,
% 0.18/0.44 v: list_option_b ).
% 0.18/0.44
% 0.18/0.44 thf(sy_v_x,type,
% 0.18/0.44 x: b ).
% 0.18/0.44
% 0.18/0.44 % Relevant facts (323)
% 0.18/0.44 thf(fact_0_nth__Cons__Suc,axiom,
% 0.18/0.44 ! [X: b,Xs: list_b,N: nat] :
% 0.18/0.44 ( ( nth_b @ ( cons_b @ X @ Xs ) @ ( suc @ N ) )
% 0.18/0.44 = ( nth_b @ Xs @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % nth_Cons_Suc
% 0.18/0.44 thf(fact_1_nth__Cons__Suc,axiom,
% 0.18/0.44 ! [X: option_b,Xs: list_option_b,N: nat] :
% 0.18/0.44 ( ( nth_option_b @ ( cons_option_b @ X @ Xs ) @ ( suc @ N ) )
% 0.18/0.44 = ( nth_option_b @ Xs @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % nth_Cons_Suc
% 0.18/0.44 thf(fact_2_nth__Cons__0,axiom,
% 0.18/0.44 ! [X: b,Xs: list_b] :
% 0.18/0.44 ( ( nth_b @ ( cons_b @ X @ Xs ) @ zero_zero_nat )
% 0.18/0.44 = X ) ).
% 0.18/0.44
% 0.18/0.44 % nth_Cons_0
% 0.18/0.44 thf(fact_3_nth__Cons__0,axiom,
% 0.18/0.44 ! [X: option_b,Xs: list_option_b] :
% 0.18/0.44 ( ( nth_option_b @ ( cons_option_b @ X @ Xs ) @ zero_zero_nat )
% 0.18/0.44 = X ) ).
% 0.18/0.44
% 0.18/0.44 % nth_Cons_0
% 0.18/0.44 thf(fact_4_less__Suc0,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.18/0.44 = ( N = zero_zero_nat ) ) ).
% 0.18/0.44
% 0.18/0.44 % less_Suc0
% 0.18/0.44 thf(fact_5_zero__less__Suc,axiom,
% 0.18/0.44 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % zero_less_Suc
% 0.18/0.44 thf(fact_6_not__None__eq,axiom,
% 0.18/0.44 ! [X: option_option_b] :
% 0.18/0.44 ( ( X != none_option_b )
% 0.18/0.44 = ( ? [Y: option_b] :
% 0.18/0.44 ( X
% 0.18/0.44 = ( some_option_b @ Y ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % not_None_eq
% 0.18/0.44 thf(fact_7_not__None__eq,axiom,
% 0.18/0.44 ! [X: option_b] :
% 0.18/0.44 ( ( X != none_b )
% 0.18/0.44 = ( ? [Y: b] :
% 0.18/0.44 ( X
% 0.18/0.44 = ( some_b @ Y ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % not_None_eq
% 0.18/0.44 thf(fact_8_not__Some__eq,axiom,
% 0.18/0.44 ! [X: option_option_b] :
% 0.18/0.44 ( ( ! [Y: option_b] :
% 0.18/0.44 ( X
% 0.18/0.44 != ( some_option_b @ Y ) ) )
% 0.18/0.44 = ( X = none_option_b ) ) ).
% 0.18/0.44
% 0.18/0.44 % not_Some_eq
% 0.18/0.44 thf(fact_9_not__Some__eq,axiom,
% 0.18/0.44 ! [X: option_b] :
% 0.18/0.44 ( ( ! [Y: b] :
% 0.18/0.44 ( X
% 0.18/0.44 != ( some_b @ Y ) ) )
% 0.18/0.44 = ( X = none_b ) ) ).
% 0.18/0.44
% 0.18/0.44 % not_Some_eq
% 0.18/0.44 thf(fact_10_lessI,axiom,
% 0.18/0.44 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % lessI
% 0.18/0.44 thf(fact_11_Suc__mono,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M @ N )
% 0.18/0.44 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % Suc_mono
% 0.18/0.44 thf(fact_12_Suc__less__eq,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.18/0.44 = ( ord_less_nat @ M @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % Suc_less_eq
% 0.18/0.44 thf(fact_13_neq0__conv,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( N != zero_zero_nat )
% 0.18/0.44 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % neq0_conv
% 0.18/0.44 thf(fact_14_less__nat__zero__code,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.18/0.44
% 0.18/0.44 % less_nat_zero_code
% 0.18/0.44 thf(fact_15_bot__nat__0_Onot__eq__extremum,axiom,
% 0.18/0.44 ! [A: nat] :
% 0.18/0.44 ( ( A != zero_zero_nat )
% 0.18/0.44 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.18/0.44
% 0.18/0.44 % bot_nat_0.not_eq_extremum
% 0.18/0.44 thf(fact_16_list_Oinject,axiom,
% 0.18/0.44 ! [X21: b,X22: list_b,Y21: b,Y22: list_b] :
% 0.18/0.44 ( ( ( cons_b @ X21 @ X22 )
% 0.18/0.44 = ( cons_b @ Y21 @ Y22 ) )
% 0.18/0.44 = ( ( X21 = Y21 )
% 0.18/0.44 & ( X22 = Y22 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % list.inject
% 0.18/0.44 thf(fact_17_list_Oinject,axiom,
% 0.18/0.44 ! [X21: option_b,X22: list_option_b,Y21: option_b,Y22: list_option_b] :
% 0.18/0.44 ( ( ( cons_option_b @ X21 @ X22 )
% 0.18/0.44 = ( cons_option_b @ Y21 @ Y22 ) )
% 0.18/0.44 = ( ( X21 = Y21 )
% 0.18/0.44 & ( X22 = Y22 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % list.inject
% 0.18/0.44 thf(fact_18_old_Onat_Oinject,axiom,
% 0.18/0.44 ! [Nat: nat,Nat2: nat] :
% 0.18/0.44 ( ( ( suc @ Nat )
% 0.18/0.44 = ( suc @ Nat2 ) )
% 0.18/0.44 = ( Nat = Nat2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % old.nat.inject
% 0.18/0.44 thf(fact_19_nat_Oinject,axiom,
% 0.18/0.44 ! [X2: nat,Y2: nat] :
% 0.18/0.44 ( ( ( suc @ X2 )
% 0.18/0.44 = ( suc @ Y2 ) )
% 0.18/0.44 = ( X2 = Y2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % nat.inject
% 0.18/0.44 thf(fact_20_option_Oinject,axiom,
% 0.18/0.44 ! [X2: option_b,Y2: option_b] :
% 0.18/0.44 ( ( ( some_option_b @ X2 )
% 0.18/0.44 = ( some_option_b @ Y2 ) )
% 0.18/0.44 = ( X2 = Y2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % option.inject
% 0.18/0.44 thf(fact_21_option_Oinject,axiom,
% 0.18/0.44 ! [X2: b,Y2: b] :
% 0.18/0.44 ( ( ( some_b @ X2 )
% 0.18/0.44 = ( some_b @ Y2 ) )
% 0.18/0.44 = ( X2 = Y2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % option.inject
% 0.18/0.44 thf(fact_22_not__Cons__self2,axiom,
% 0.18/0.44 ! [X: b,Xs: list_b] :
% 0.18/0.44 ( ( cons_b @ X @ Xs )
% 0.18/0.44 != Xs ) ).
% 0.18/0.44
% 0.18/0.44 % not_Cons_self2
% 0.18/0.44 thf(fact_23_not__Cons__self2,axiom,
% 0.18/0.44 ! [X: option_b,Xs: list_option_b] :
% 0.18/0.44 ( ( cons_option_b @ X @ Xs )
% 0.18/0.44 != Xs ) ).
% 0.18/0.44
% 0.18/0.44 % not_Cons_self2
% 0.18/0.44 thf(fact_24_n__not__Suc__n,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( N
% 0.18/0.44 != ( suc @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % n_not_Suc_n
% 0.18/0.44 thf(fact_25_Suc__inject,axiom,
% 0.18/0.44 ! [X: nat,Y3: nat] :
% 0.18/0.44 ( ( ( suc @ X )
% 0.18/0.44 = ( suc @ Y3 ) )
% 0.18/0.44 => ( X = Y3 ) ) ).
% 0.18/0.44
% 0.18/0.44 % Suc_inject
% 0.18/0.44 thf(fact_26_linorder__neqE__nat,axiom,
% 0.18/0.44 ! [X: nat,Y3: nat] :
% 0.18/0.44 ( ( X != Y3 )
% 0.18/0.44 => ( ~ ( ord_less_nat @ X @ Y3 )
% 0.18/0.44 => ( ord_less_nat @ Y3 @ X ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % linorder_neqE_nat
% 0.18/0.44 thf(fact_27_infinite__descent,axiom,
% 0.18/0.44 ! [P: nat > $o,N: nat] :
% 0.18/0.44 ( ! [N2: nat] :
% 0.18/0.44 ( ~ ( P @ N2 )
% 0.18/0.44 => ? [M2: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M2 @ N2 )
% 0.18/0.44 & ~ ( P @ M2 ) ) )
% 0.18/0.44 => ( P @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % infinite_descent
% 0.18/0.44 thf(fact_28_nat__less__induct,axiom,
% 0.18/0.44 ! [P: nat > $o,N: nat] :
% 0.18/0.44 ( ! [N2: nat] :
% 0.18/0.44 ( ! [M2: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M2 @ N2 )
% 0.18/0.44 => ( P @ M2 ) )
% 0.18/0.44 => ( P @ N2 ) )
% 0.18/0.44 => ( P @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % nat_less_induct
% 0.18/0.44 thf(fact_29_less__irrefl__nat,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ~ ( ord_less_nat @ N @ N ) ).
% 0.18/0.44
% 0.18/0.44 % less_irrefl_nat
% 0.18/0.44 thf(fact_30_less__not__refl3,axiom,
% 0.18/0.44 ! [S: nat,T: nat] :
% 0.18/0.44 ( ( ord_less_nat @ S @ T )
% 0.18/0.44 => ( S != T ) ) ).
% 0.18/0.44
% 0.18/0.44 % less_not_refl3
% 0.18/0.44 thf(fact_31_less__not__refl2,axiom,
% 0.18/0.44 ! [N: nat,M: nat] :
% 0.18/0.44 ( ( ord_less_nat @ N @ M )
% 0.18/0.44 => ( M != N ) ) ).
% 0.18/0.44
% 0.18/0.44 % less_not_refl2
% 0.18/0.44 thf(fact_32_less__not__refl,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ~ ( ord_less_nat @ N @ N ) ).
% 0.18/0.44
% 0.18/0.44 % less_not_refl
% 0.18/0.44 thf(fact_33_nat__neq__iff,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( M != N )
% 0.18/0.44 = ( ( ord_less_nat @ M @ N )
% 0.18/0.44 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % nat_neq_iff
% 0.18/0.44 thf(fact_34_size__neq__size__imp__neq,axiom,
% 0.18/0.44 ! [X: option_b,Y3: option_b] :
% 0.18/0.44 ( ( ( size_size_option_b @ X )
% 0.18/0.44 != ( size_size_option_b @ Y3 ) )
% 0.18/0.44 => ( X != Y3 ) ) ).
% 0.18/0.44
% 0.18/0.44 % size_neq_size_imp_neq
% 0.18/0.44 thf(fact_35_size__neq__size__imp__neq,axiom,
% 0.18/0.44 ! [X: list_b,Y3: list_b] :
% 0.18/0.44 ( ( ( size_size_list_b @ X )
% 0.18/0.44 != ( size_size_list_b @ Y3 ) )
% 0.18/0.44 => ( X != Y3 ) ) ).
% 0.18/0.44
% 0.18/0.44 % size_neq_size_imp_neq
% 0.18/0.44 thf(fact_36_size__neq__size__imp__neq,axiom,
% 0.18/0.44 ! [X: list_option_b,Y3: list_option_b] :
% 0.18/0.44 ( ( ( size_s1671393719tion_b @ X )
% 0.18/0.44 != ( size_s1671393719tion_b @ Y3 ) )
% 0.18/0.44 => ( X != Y3 ) ) ).
% 0.18/0.44
% 0.18/0.44 % size_neq_size_imp_neq
% 0.18/0.44 thf(fact_37_neq__if__length__neq,axiom,
% 0.18/0.44 ! [Xs: list_b,Ys: list_b] :
% 0.18/0.44 ( ( ( size_size_list_b @ Xs )
% 0.18/0.44 != ( size_size_list_b @ Ys ) )
% 0.18/0.44 => ( Xs != Ys ) ) ).
% 0.18/0.44
% 0.18/0.44 % neq_if_length_neq
% 0.18/0.44 thf(fact_38_neq__if__length__neq,axiom,
% 0.18/0.44 ! [Xs: list_option_b,Ys: list_option_b] :
% 0.18/0.44 ( ( ( size_s1671393719tion_b @ Xs )
% 0.18/0.44 != ( size_s1671393719tion_b @ Ys ) )
% 0.18/0.44 => ( Xs != Ys ) ) ).
% 0.18/0.44
% 0.18/0.44 % neq_if_length_neq
% 0.18/0.44 thf(fact_39_Ex__list__of__length,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ? [Xs2: list_b] :
% 0.18/0.44 ( ( size_size_list_b @ Xs2 )
% 0.18/0.44 = N ) ).
% 0.18/0.44
% 0.18/0.44 % Ex_list_of_length
% 0.18/0.44 thf(fact_40_Ex__list__of__length,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ? [Xs2: list_option_b] :
% 0.18/0.44 ( ( size_s1671393719tion_b @ Xs2 )
% 0.18/0.44 = N ) ).
% 0.18/0.44
% 0.18/0.44 % Ex_list_of_length
% 0.18/0.44 thf(fact_41_not0__implies__Suc,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( N != zero_zero_nat )
% 0.18/0.44 => ? [M3: nat] :
% 0.18/0.44 ( N
% 0.18/0.44 = ( suc @ M3 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % not0_implies_Suc
% 0.18/0.44 thf(fact_42_old_Onat_Oinducts,axiom,
% 0.18/0.44 ! [P: nat > $o,Nat: nat] :
% 0.18/0.44 ( ( P @ zero_zero_nat )
% 0.18/0.44 => ( ! [Nat3: nat] :
% 0.18/0.44 ( ( P @ Nat3 )
% 0.18/0.44 => ( P @ ( suc @ Nat3 ) ) )
% 0.18/0.44 => ( P @ Nat ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % old.nat.inducts
% 0.18/0.44 thf(fact_43_old_Onat_Oexhaust,axiom,
% 0.18/0.44 ! [Y3: nat] :
% 0.18/0.44 ( ( Y3 != zero_zero_nat )
% 0.18/0.44 => ~ ! [Nat3: nat] :
% 0.18/0.44 ( Y3
% 0.18/0.44 != ( suc @ Nat3 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % old.nat.exhaust
% 0.18/0.44 thf(fact_44_Zero__not__Suc,axiom,
% 0.18/0.44 ! [M: nat] :
% 0.18/0.44 ( zero_zero_nat
% 0.18/0.44 != ( suc @ M ) ) ).
% 0.18/0.44
% 0.18/0.44 % Zero_not_Suc
% 0.18/0.44 thf(fact_45_Zero__neq__Suc,axiom,
% 0.18/0.44 ! [M: nat] :
% 0.18/0.44 ( zero_zero_nat
% 0.18/0.44 != ( suc @ M ) ) ).
% 0.18/0.44
% 0.18/0.44 % Zero_neq_Suc
% 0.18/0.44 thf(fact_46_Suc__neq__Zero,axiom,
% 0.18/0.44 ! [M: nat] :
% 0.18/0.44 ( ( suc @ M )
% 0.18/0.44 != zero_zero_nat ) ).
% 0.18/0.44
% 0.18/0.44 % Suc_neq_Zero
% 0.18/0.44 thf(fact_47_zero__induct,axiom,
% 0.18/0.44 ! [P: nat > $o,K: nat] :
% 0.18/0.44 ( ( P @ K )
% 0.18/0.44 => ( ! [N2: nat] :
% 0.18/0.44 ( ( P @ ( suc @ N2 ) )
% 0.18/0.44 => ( P @ N2 ) )
% 0.18/0.44 => ( P @ zero_zero_nat ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % zero_induct
% 0.18/0.44 thf(fact_48_diff__induct,axiom,
% 0.18/0.44 ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.18/0.44 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 0.18/0.44 => ( ! [Y4: nat] : ( P @ zero_zero_nat @ ( suc @ Y4 ) )
% 0.18/0.44 => ( ! [X3: nat,Y4: nat] :
% 0.18/0.44 ( ( P @ X3 @ Y4 )
% 0.18/0.44 => ( P @ ( suc @ X3 ) @ ( suc @ Y4 ) ) )
% 0.18/0.44 => ( P @ M @ N ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % diff_induct
% 0.18/0.44 thf(fact_49_nat__induct,axiom,
% 0.18/0.44 ! [P: nat > $o,N: nat] :
% 0.18/0.44 ( ( P @ zero_zero_nat )
% 0.18/0.44 => ( ! [N2: nat] :
% 0.18/0.44 ( ( P @ N2 )
% 0.18/0.44 => ( P @ ( suc @ N2 ) ) )
% 0.18/0.44 => ( P @ N ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % nat_induct
% 0.18/0.44 thf(fact_50_mem__Collect__eq,axiom,
% 0.18/0.44 ! [A: nat,P: nat > $o] :
% 0.18/0.44 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.18/0.44 = ( P @ A ) ) ).
% 0.18/0.44
% 0.18/0.44 % mem_Collect_eq
% 0.18/0.44 thf(fact_51_Collect__mem__eq,axiom,
% 0.18/0.44 ! [A2: set_nat] :
% 0.18/0.44 ( ( collect_nat
% 0.18/0.44 @ ^ [X4: nat] : ( member_nat @ X4 @ A2 ) )
% 0.18/0.44 = A2 ) ).
% 0.18/0.44
% 0.18/0.44 % Collect_mem_eq
% 0.18/0.44 thf(fact_52_Collect__cong,axiom,
% 0.18/0.44 ! [P: nat > $o,Q: nat > $o] :
% 0.18/0.44 ( ! [X3: nat] :
% 0.18/0.44 ( ( P @ X3 )
% 0.18/0.44 = ( Q @ X3 ) )
% 0.18/0.44 => ( ( collect_nat @ P )
% 0.18/0.44 = ( collect_nat @ Q ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % Collect_cong
% 0.18/0.44 thf(fact_53_nat_OdiscI,axiom,
% 0.18/0.44 ! [Nat: nat,X2: nat] :
% 0.18/0.44 ( ( Nat
% 0.18/0.44 = ( suc @ X2 ) )
% 0.18/0.44 => ( Nat != zero_zero_nat ) ) ).
% 0.18/0.44
% 0.18/0.44 % nat.discI
% 0.18/0.44 thf(fact_54_old_Onat_Odistinct_I1_J,axiom,
% 0.18/0.44 ! [Nat2: nat] :
% 0.18/0.44 ( zero_zero_nat
% 0.18/0.44 != ( suc @ Nat2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % old.nat.distinct(1)
% 0.18/0.44 thf(fact_55_old_Onat_Odistinct_I2_J,axiom,
% 0.18/0.44 ! [Nat2: nat] :
% 0.18/0.44 ( ( suc @ Nat2 )
% 0.18/0.44 != zero_zero_nat ) ).
% 0.18/0.44
% 0.18/0.44 % old.nat.distinct(2)
% 0.18/0.44 thf(fact_56_nat_Odistinct_I1_J,axiom,
% 0.18/0.44 ! [X2: nat] :
% 0.18/0.44 ( zero_zero_nat
% 0.18/0.44 != ( suc @ X2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % nat.distinct(1)
% 0.18/0.44 thf(fact_57_bot__nat__0_Oextremum__strict,axiom,
% 0.18/0.44 ! [A: nat] :
% 0.18/0.44 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.18/0.44
% 0.18/0.44 % bot_nat_0.extremum_strict
% 0.18/0.44 thf(fact_58_infinite__descent0,axiom,
% 0.18/0.44 ! [P: nat > $o,N: nat] :
% 0.18/0.44 ( ( P @ zero_zero_nat )
% 0.18/0.44 => ( ! [N2: nat] :
% 0.18/0.44 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.44 => ( ~ ( P @ N2 )
% 0.18/0.44 => ? [M2: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M2 @ N2 )
% 0.18/0.44 & ~ ( P @ M2 ) ) ) )
% 0.18/0.44 => ( P @ N ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % infinite_descent0
% 0.18/0.44 thf(fact_59_gr__implies__not0,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M @ N )
% 0.18/0.44 => ( N != zero_zero_nat ) ) ).
% 0.18/0.44
% 0.18/0.44 % gr_implies_not0
% 0.18/0.44 thf(fact_60_less__zeroE,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.18/0.44
% 0.18/0.44 % less_zeroE
% 0.18/0.44 thf(fact_61_not__less0,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.18/0.44
% 0.18/0.44 % not_less0
% 0.18/0.44 thf(fact_62_not__gr0,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.18/0.44 = ( N = zero_zero_nat ) ) ).
% 0.18/0.44
% 0.18/0.44 % not_gr0
% 0.18/0.44 thf(fact_63_gr0I,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( N != zero_zero_nat )
% 0.18/0.44 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % gr0I
% 0.18/0.44 thf(fact_64_not__less__less__Suc__eq,axiom,
% 0.18/0.44 ! [N: nat,M: nat] :
% 0.18/0.44 ( ~ ( ord_less_nat @ N @ M )
% 0.18/0.44 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.18/0.44 = ( N = M ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % not_less_less_Suc_eq
% 0.18/0.44 thf(fact_65_strict__inc__induct,axiom,
% 0.18/0.44 ! [I: nat,J: nat,P: nat > $o] :
% 0.18/0.44 ( ( ord_less_nat @ I @ J )
% 0.18/0.44 => ( ! [I2: nat] :
% 0.18/0.44 ( ( J
% 0.18/0.44 = ( suc @ I2 ) )
% 0.18/0.44 => ( P @ I2 ) )
% 0.18/0.44 => ( ! [I2: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I2 @ J )
% 0.18/0.44 => ( ( P @ ( suc @ I2 ) )
% 0.18/0.44 => ( P @ I2 ) ) )
% 0.18/0.44 => ( P @ I ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % strict_inc_induct
% 0.18/0.44 thf(fact_66_less__Suc__induct,axiom,
% 0.18/0.44 ! [I: nat,J: nat,P: nat > nat > $o] :
% 0.18/0.44 ( ( ord_less_nat @ I @ J )
% 0.18/0.44 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 0.18/0.44 => ( ! [I2: nat,J2: nat,K2: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I2 @ J2 )
% 0.18/0.44 => ( ( ord_less_nat @ J2 @ K2 )
% 0.18/0.44 => ( ( P @ I2 @ J2 )
% 0.18/0.44 => ( ( P @ J2 @ K2 )
% 0.18/0.44 => ( P @ I2 @ K2 ) ) ) ) )
% 0.18/0.44 => ( P @ I @ J ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % less_Suc_induct
% 0.18/0.44 thf(fact_67_less__trans__Suc,axiom,
% 0.18/0.44 ! [I: nat,J: nat,K: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I @ J )
% 0.18/0.44 => ( ( ord_less_nat @ J @ K )
% 0.18/0.44 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % less_trans_Suc
% 0.18/0.44 thf(fact_68_Suc__less__SucD,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.18/0.44 => ( ord_less_nat @ M @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % Suc_less_SucD
% 0.18/0.44 thf(fact_69_less__antisym,axiom,
% 0.18/0.44 ! [N: nat,M: nat] :
% 0.18/0.44 ( ~ ( ord_less_nat @ N @ M )
% 0.18/0.44 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.18/0.44 => ( M = N ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % less_antisym
% 0.18/0.44 thf(fact_70_Suc__less__eq2,axiom,
% 0.18/0.44 ! [N: nat,M: nat] :
% 0.18/0.44 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.18/0.44 = ( ? [M4: nat] :
% 0.18/0.44 ( ( M
% 0.18/0.44 = ( suc @ M4 ) )
% 0.18/0.44 & ( ord_less_nat @ N @ M4 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % Suc_less_eq2
% 0.18/0.44 thf(fact_71_All__less__Suc,axiom,
% 0.18/0.44 ! [N: nat,P: nat > $o] :
% 0.18/0.44 ( ( ! [I3: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.18/0.44 => ( P @ I3 ) ) )
% 0.18/0.44 = ( ( P @ N )
% 0.18/0.44 & ! [I3: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I3 @ N )
% 0.18/0.44 => ( P @ I3 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % All_less_Suc
% 0.18/0.44 thf(fact_72_not__less__eq,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( ~ ( ord_less_nat @ M @ N ) )
% 0.18/0.44 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % not_less_eq
% 0.18/0.44 thf(fact_73_less__Suc__eq,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.18/0.44 = ( ( ord_less_nat @ M @ N )
% 0.18/0.44 | ( M = N ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % less_Suc_eq
% 0.18/0.44 thf(fact_74_Ex__less__Suc,axiom,
% 0.18/0.44 ! [N: nat,P: nat > $o] :
% 0.18/0.44 ( ( ? [I3: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.18/0.44 & ( P @ I3 ) ) )
% 0.18/0.44 = ( ( P @ N )
% 0.18/0.44 | ? [I3: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I3 @ N )
% 0.18/0.44 & ( P @ I3 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % Ex_less_Suc
% 0.18/0.44 thf(fact_75_less__SucI,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M @ N )
% 0.18/0.44 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % less_SucI
% 0.18/0.44 thf(fact_76_less__SucE,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.18/0.44 => ( ~ ( ord_less_nat @ M @ N )
% 0.18/0.44 => ( M = N ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % less_SucE
% 0.18/0.44 thf(fact_77_Suc__lessI,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M @ N )
% 0.18/0.44 => ( ( ( suc @ M )
% 0.18/0.44 != N )
% 0.18/0.44 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % Suc_lessI
% 0.18/0.44 thf(fact_78_Suc__lessE,axiom,
% 0.18/0.44 ! [I: nat,K: nat] :
% 0.18/0.44 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.18/0.44 => ~ ! [J2: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I @ J2 )
% 0.18/0.44 => ( K
% 0.18/0.44 != ( suc @ J2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % Suc_lessE
% 0.18/0.44 thf(fact_79_Suc__lessD,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.18/0.44 => ( ord_less_nat @ M @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % Suc_lessD
% 0.18/0.44 thf(fact_80_Nat_OlessE,axiom,
% 0.18/0.44 ! [I: nat,K: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I @ K )
% 0.18/0.44 => ( ( K
% 0.18/0.44 != ( suc @ I ) )
% 0.18/0.44 => ~ ! [J2: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I @ J2 )
% 0.18/0.44 => ( K
% 0.18/0.44 != ( suc @ J2 ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % Nat.lessE
% 0.18/0.44 thf(fact_81_length__induct,axiom,
% 0.18/0.44 ! [P: list_b > $o,Xs: list_b] :
% 0.18/0.44 ( ! [Xs2: list_b] :
% 0.18/0.44 ( ! [Ys2: list_b] :
% 0.18/0.44 ( ( ord_less_nat @ ( size_size_list_b @ Ys2 ) @ ( size_size_list_b @ Xs2 ) )
% 0.18/0.44 => ( P @ Ys2 ) )
% 0.18/0.44 => ( P @ Xs2 ) )
% 0.18/0.44 => ( P @ Xs ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_induct
% 0.18/0.44 thf(fact_82_length__induct,axiom,
% 0.18/0.44 ! [P: list_option_b > $o,Xs: list_option_b] :
% 0.18/0.44 ( ! [Xs2: list_option_b] :
% 0.18/0.44 ( ! [Ys2: list_option_b] :
% 0.18/0.44 ( ( ord_less_nat @ ( size_s1671393719tion_b @ Ys2 ) @ ( size_s1671393719tion_b @ Xs2 ) )
% 0.18/0.44 => ( P @ Ys2 ) )
% 0.18/0.44 => ( P @ Xs2 ) )
% 0.18/0.44 => ( P @ Xs ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_induct
% 0.18/0.44 thf(fact_83_combine__options__cases,axiom,
% 0.18/0.44 ! [X: option_b,P: option_b > option_option_b > $o,Y3: option_option_b] :
% 0.18/0.44 ( ( ( X = none_b )
% 0.18/0.44 => ( P @ X @ Y3 ) )
% 0.18/0.44 => ( ( ( Y3 = none_option_b )
% 0.18/0.44 => ( P @ X @ Y3 ) )
% 0.18/0.44 => ( ! [A3: b,B: option_b] :
% 0.18/0.44 ( ( X
% 0.18/0.44 = ( some_b @ A3 ) )
% 0.18/0.44 => ( ( Y3
% 0.18/0.44 = ( some_option_b @ B ) )
% 0.18/0.44 => ( P @ X @ Y3 ) ) )
% 0.18/0.44 => ( P @ X @ Y3 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % combine_options_cases
% 0.18/0.44 thf(fact_84_combine__options__cases,axiom,
% 0.18/0.44 ! [X: option_option_b,P: option_option_b > option_b > $o,Y3: option_b] :
% 0.18/0.44 ( ( ( X = none_option_b )
% 0.18/0.44 => ( P @ X @ Y3 ) )
% 0.18/0.44 => ( ( ( Y3 = none_b )
% 0.18/0.44 => ( P @ X @ Y3 ) )
% 0.18/0.44 => ( ! [A3: option_b,B: b] :
% 0.18/0.44 ( ( X
% 0.18/0.44 = ( some_option_b @ A3 ) )
% 0.18/0.44 => ( ( Y3
% 0.18/0.44 = ( some_b @ B ) )
% 0.18/0.44 => ( P @ X @ Y3 ) ) )
% 0.18/0.44 => ( P @ X @ Y3 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % combine_options_cases
% 0.18/0.44 thf(fact_85_combine__options__cases,axiom,
% 0.18/0.44 ! [X: option_option_b,P: option_option_b > option_option_b > $o,Y3: option_option_b] :
% 0.18/0.44 ( ( ( X = none_option_b )
% 0.18/0.44 => ( P @ X @ Y3 ) )
% 0.18/0.44 => ( ( ( Y3 = none_option_b )
% 0.18/0.44 => ( P @ X @ Y3 ) )
% 0.18/0.44 => ( ! [A3: option_b,B: option_b] :
% 0.18/0.44 ( ( X
% 0.18/0.44 = ( some_option_b @ A3 ) )
% 0.18/0.44 => ( ( Y3
% 0.18/0.44 = ( some_option_b @ B ) )
% 0.18/0.44 => ( P @ X @ Y3 ) ) )
% 0.18/0.44 => ( P @ X @ Y3 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % combine_options_cases
% 0.18/0.44 thf(fact_86_combine__options__cases,axiom,
% 0.18/0.44 ! [X: option_b,P: option_b > option_b > $o,Y3: option_b] :
% 0.18/0.44 ( ( ( X = none_b )
% 0.18/0.44 => ( P @ X @ Y3 ) )
% 0.18/0.44 => ( ( ( Y3 = none_b )
% 0.18/0.44 => ( P @ X @ Y3 ) )
% 0.18/0.44 => ( ! [A3: b,B: b] :
% 0.18/0.44 ( ( X
% 0.18/0.44 = ( some_b @ A3 ) )
% 0.18/0.44 => ( ( Y3
% 0.18/0.44 = ( some_b @ B ) )
% 0.18/0.44 => ( P @ X @ Y3 ) ) )
% 0.18/0.44 => ( P @ X @ Y3 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % combine_options_cases
% 0.18/0.44 thf(fact_87_split__option__all,axiom,
% 0.18/0.44 ( ( ^ [P2: option_option_b > $o] :
% 0.18/0.44 ! [X5: option_option_b] : ( P2 @ X5 ) )
% 0.18/0.44 = ( ^ [P3: option_option_b > $o] :
% 0.18/0.44 ( ( P3 @ none_option_b )
% 0.18/0.44 & ! [X4: option_b] : ( P3 @ ( some_option_b @ X4 ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % split_option_all
% 0.18/0.44 thf(fact_88_split__option__all,axiom,
% 0.18/0.44 ( ( ^ [P2: option_b > $o] :
% 0.18/0.44 ! [X5: option_b] : ( P2 @ X5 ) )
% 0.18/0.44 = ( ^ [P3: option_b > $o] :
% 0.18/0.44 ( ( P3 @ none_b )
% 0.18/0.44 & ! [X4: b] : ( P3 @ ( some_b @ X4 ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % split_option_all
% 0.18/0.44 thf(fact_89_split__option__ex,axiom,
% 0.18/0.44 ( ( ^ [P2: option_option_b > $o] :
% 0.18/0.44 ? [X5: option_option_b] : ( P2 @ X5 ) )
% 0.18/0.44 = ( ^ [P3: option_option_b > $o] :
% 0.18/0.44 ( ( P3 @ none_option_b )
% 0.18/0.44 | ? [X4: option_b] : ( P3 @ ( some_option_b @ X4 ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % split_option_ex
% 0.18/0.44 thf(fact_90_split__option__ex,axiom,
% 0.18/0.44 ( ( ^ [P2: option_b > $o] :
% 0.18/0.44 ? [X5: option_b] : ( P2 @ X5 ) )
% 0.18/0.44 = ( ^ [P3: option_b > $o] :
% 0.18/0.44 ( ( P3 @ none_b )
% 0.18/0.44 | ? [X4: b] : ( P3 @ ( some_b @ X4 ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % split_option_ex
% 0.18/0.44 thf(fact_91_option_Oinducts,axiom,
% 0.18/0.44 ! [P: option_option_b > $o,Option: option_option_b] :
% 0.18/0.44 ( ( P @ none_option_b )
% 0.18/0.44 => ( ! [X3: option_b] : ( P @ ( some_option_b @ X3 ) )
% 0.18/0.44 => ( P @ Option ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % option.inducts
% 0.18/0.44 thf(fact_92_option_Oinducts,axiom,
% 0.18/0.44 ! [P: option_b > $o,Option: option_b] :
% 0.18/0.44 ( ( P @ none_b )
% 0.18/0.44 => ( ! [X3: b] : ( P @ ( some_b @ X3 ) )
% 0.18/0.44 => ( P @ Option ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % option.inducts
% 0.18/0.44 thf(fact_93_option_Oexhaust,axiom,
% 0.18/0.44 ! [Y3: option_option_b] :
% 0.18/0.44 ( ( Y3 != none_option_b )
% 0.18/0.44 => ~ ! [X23: option_b] :
% 0.18/0.44 ( Y3
% 0.18/0.44 != ( some_option_b @ X23 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % option.exhaust
% 0.18/0.44 thf(fact_94_option_Oexhaust,axiom,
% 0.18/0.44 ! [Y3: option_b] :
% 0.18/0.44 ( ( Y3 != none_b )
% 0.18/0.44 => ~ ! [X23: b] :
% 0.18/0.44 ( Y3
% 0.18/0.44 != ( some_b @ X23 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % option.exhaust
% 0.18/0.44 thf(fact_95_option_OdiscI,axiom,
% 0.18/0.44 ! [Option: option_option_b,X2: option_b] :
% 0.18/0.44 ( ( Option
% 0.18/0.44 = ( some_option_b @ X2 ) )
% 0.18/0.44 => ( Option != none_option_b ) ) ).
% 0.18/0.44
% 0.18/0.44 % option.discI
% 0.18/0.44 thf(fact_96_option_OdiscI,axiom,
% 0.18/0.44 ! [Option: option_b,X2: b] :
% 0.18/0.44 ( ( Option
% 0.18/0.44 = ( some_b @ X2 ) )
% 0.18/0.44 => ( Option != none_b ) ) ).
% 0.18/0.44
% 0.18/0.44 % option.discI
% 0.18/0.44 thf(fact_97_option_Odistinct_I1_J,axiom,
% 0.18/0.44 ! [X2: option_b] :
% 0.18/0.44 ( none_option_b
% 0.18/0.44 != ( some_option_b @ X2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % option.distinct(1)
% 0.18/0.44 thf(fact_98_option_Odistinct_I1_J,axiom,
% 0.18/0.44 ! [X2: b] :
% 0.18/0.44 ( none_b
% 0.18/0.44 != ( some_b @ X2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % option.distinct(1)
% 0.18/0.44 thf(fact_99_lift__Suc__mono__less__iff,axiom,
% 0.18/0.44 ! [F: nat > nat,N: nat,M: nat] :
% 0.18/0.44 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.18/0.44 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 0.18/0.44 = ( ord_less_nat @ N @ M ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % lift_Suc_mono_less_iff
% 0.18/0.44 thf(fact_100_lift__Suc__mono__less__iff,axiom,
% 0.18/0.44 ! [F: nat > int,N: nat,M: nat] :
% 0.18/0.44 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.18/0.44 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 0.18/0.44 = ( ord_less_nat @ N @ M ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % lift_Suc_mono_less_iff
% 0.18/0.44 thf(fact_101_lift__Suc__mono__less,axiom,
% 0.18/0.44 ! [F: nat > nat,N: nat,N3: nat] :
% 0.18/0.44 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.18/0.44 => ( ( ord_less_nat @ N @ N3 )
% 0.18/0.44 => ( ord_less_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % lift_Suc_mono_less
% 0.18/0.44 thf(fact_102_lift__Suc__mono__less,axiom,
% 0.18/0.44 ! [F: nat > int,N: nat,N3: nat] :
% 0.18/0.44 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.18/0.44 => ( ( ord_less_nat @ N @ N3 )
% 0.18/0.44 => ( ord_less_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % lift_Suc_mono_less
% 0.18/0.44 thf(fact_103_less__Suc__eq__0__disj,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.18/0.44 = ( ( M = zero_zero_nat )
% 0.18/0.44 | ? [J3: nat] :
% 0.18/0.44 ( ( M
% 0.18/0.44 = ( suc @ J3 ) )
% 0.18/0.44 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % less_Suc_eq_0_disj
% 0.18/0.44 thf(fact_104_gr0__implies__Suc,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.44 => ? [M3: nat] :
% 0.18/0.44 ( N
% 0.18/0.44 = ( suc @ M3 ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % gr0_implies_Suc
% 0.18/0.44 thf(fact_105_All__less__Suc2,axiom,
% 0.18/0.44 ! [N: nat,P: nat > $o] :
% 0.18/0.44 ( ( ! [I3: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.18/0.44 => ( P @ I3 ) ) )
% 0.18/0.44 = ( ( P @ zero_zero_nat )
% 0.18/0.44 & ! [I3: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I3 @ N )
% 0.18/0.44 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % All_less_Suc2
% 0.18/0.44 thf(fact_106_gr0__conv__Suc,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.44 = ( ? [M5: nat] :
% 0.18/0.44 ( N
% 0.18/0.44 = ( suc @ M5 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % gr0_conv_Suc
% 0.18/0.44 thf(fact_107_Ex__less__Suc2,axiom,
% 0.18/0.44 ! [N: nat,P: nat > $o] :
% 0.18/0.44 ( ( ? [I3: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.18/0.44 & ( P @ I3 ) ) )
% 0.18/0.44 = ( ( P @ zero_zero_nat )
% 0.18/0.44 | ? [I3: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I3 @ N )
% 0.18/0.44 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % Ex_less_Suc2
% 0.18/0.44 thf(fact_108_length__Suc__conv,axiom,
% 0.18/0.44 ! [Xs: list_b,N: nat] :
% 0.18/0.44 ( ( ( size_size_list_b @ Xs )
% 0.18/0.44 = ( suc @ N ) )
% 0.18/0.44 = ( ? [Y: b,Ys3: list_b] :
% 0.18/0.44 ( ( Xs
% 0.18/0.44 = ( cons_b @ Y @ Ys3 ) )
% 0.18/0.44 & ( ( size_size_list_b @ Ys3 )
% 0.18/0.44 = N ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_Suc_conv
% 0.18/0.44 thf(fact_109_length__Suc__conv,axiom,
% 0.18/0.44 ! [Xs: list_option_b,N: nat] :
% 0.18/0.44 ( ( ( size_s1671393719tion_b @ Xs )
% 0.18/0.44 = ( suc @ N ) )
% 0.18/0.44 = ( ? [Y: option_b,Ys3: list_option_b] :
% 0.18/0.44 ( ( Xs
% 0.18/0.44 = ( cons_option_b @ Y @ Ys3 ) )
% 0.18/0.44 & ( ( size_s1671393719tion_b @ Ys3 )
% 0.18/0.44 = N ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_Suc_conv
% 0.18/0.44 thf(fact_110_Suc__length__conv,axiom,
% 0.18/0.44 ! [N: nat,Xs: list_b] :
% 0.18/0.44 ( ( ( suc @ N )
% 0.18/0.44 = ( size_size_list_b @ Xs ) )
% 0.18/0.44 = ( ? [Y: b,Ys3: list_b] :
% 0.18/0.44 ( ( Xs
% 0.18/0.44 = ( cons_b @ Y @ Ys3 ) )
% 0.18/0.44 & ( ( size_size_list_b @ Ys3 )
% 0.18/0.44 = N ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % Suc_length_conv
% 0.18/0.44 thf(fact_111_Suc__length__conv,axiom,
% 0.18/0.44 ! [N: nat,Xs: list_option_b] :
% 0.18/0.44 ( ( ( suc @ N )
% 0.18/0.44 = ( size_s1671393719tion_b @ Xs ) )
% 0.18/0.44 = ( ? [Y: option_b,Ys3: list_option_b] :
% 0.18/0.44 ( ( Xs
% 0.18/0.44 = ( cons_option_b @ Y @ Ys3 ) )
% 0.18/0.44 & ( ( size_s1671393719tion_b @ Ys3 )
% 0.18/0.44 = N ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % Suc_length_conv
% 0.18/0.44 thf(fact_112_list__eq__iff__nth__eq,axiom,
% 0.18/0.44 ( ( ^ [Y5: list_b,Z: list_b] : ( Y5 = Z ) )
% 0.18/0.44 = ( ^ [Xs3: list_b,Ys3: list_b] :
% 0.18/0.44 ( ( ( size_size_list_b @ Xs3 )
% 0.18/0.44 = ( size_size_list_b @ Ys3 ) )
% 0.18/0.44 & ! [I3: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I3 @ ( size_size_list_b @ Xs3 ) )
% 0.18/0.44 => ( ( nth_b @ Xs3 @ I3 )
% 0.18/0.44 = ( nth_b @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % list_eq_iff_nth_eq
% 0.18/0.44 thf(fact_113_list__eq__iff__nth__eq,axiom,
% 0.18/0.44 ( ( ^ [Y5: list_option_b,Z: list_option_b] : ( Y5 = Z ) )
% 0.18/0.44 = ( ^ [Xs3: list_option_b,Ys3: list_option_b] :
% 0.18/0.44 ( ( ( size_s1671393719tion_b @ Xs3 )
% 0.18/0.44 = ( size_s1671393719tion_b @ Ys3 ) )
% 0.18/0.44 & ! [I3: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I3 @ ( size_s1671393719tion_b @ Xs3 ) )
% 0.18/0.44 => ( ( nth_option_b @ Xs3 @ I3 )
% 0.18/0.44 = ( nth_option_b @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % list_eq_iff_nth_eq
% 0.18/0.44 thf(fact_114_Skolem__list__nth,axiom,
% 0.18/0.44 ! [K: nat,P: nat > b > $o] :
% 0.18/0.44 ( ( ! [I3: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I3 @ K )
% 0.18/0.44 => ? [X5: b] : ( P @ I3 @ X5 ) ) )
% 0.18/0.44 = ( ? [Xs3: list_b] :
% 0.18/0.44 ( ( ( size_size_list_b @ Xs3 )
% 0.18/0.44 = K )
% 0.18/0.44 & ! [I3: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I3 @ K )
% 0.18/0.44 => ( P @ I3 @ ( nth_b @ Xs3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % Skolem_list_nth
% 0.18/0.44 thf(fact_115_Skolem__list__nth,axiom,
% 0.18/0.44 ! [K: nat,P: nat > option_b > $o] :
% 0.18/0.44 ( ( ! [I3: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I3 @ K )
% 0.18/0.44 => ? [X5: option_b] : ( P @ I3 @ X5 ) ) )
% 0.18/0.44 = ( ? [Xs3: list_option_b] :
% 0.18/0.44 ( ( ( size_s1671393719tion_b @ Xs3 )
% 0.18/0.44 = K )
% 0.18/0.44 & ! [I3: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I3 @ K )
% 0.18/0.44 => ( P @ I3 @ ( nth_option_b @ Xs3 @ I3 ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % Skolem_list_nth
% 0.18/0.44 thf(fact_116_nth__equalityI,axiom,
% 0.18/0.44 ! [Xs: list_b,Ys: list_b] :
% 0.18/0.44 ( ( ( size_size_list_b @ Xs )
% 0.18/0.44 = ( size_size_list_b @ Ys ) )
% 0.18/0.44 => ( ! [I2: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I2 @ ( size_size_list_b @ Xs ) )
% 0.18/0.44 => ( ( nth_b @ Xs @ I2 )
% 0.18/0.44 = ( nth_b @ Ys @ I2 ) ) )
% 0.18/0.44 => ( Xs = Ys ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % nth_equalityI
% 0.18/0.44 thf(fact_117_nth__equalityI,axiom,
% 0.18/0.44 ! [Xs: list_option_b,Ys: list_option_b] :
% 0.18/0.44 ( ( ( size_s1671393719tion_b @ Xs )
% 0.18/0.44 = ( size_s1671393719tion_b @ Ys ) )
% 0.18/0.44 => ( ! [I2: nat] :
% 0.18/0.44 ( ( ord_less_nat @ I2 @ ( size_s1671393719tion_b @ Xs ) )
% 0.18/0.44 => ( ( nth_option_b @ Xs @ I2 )
% 0.18/0.44 = ( nth_option_b @ Ys @ I2 ) ) )
% 0.18/0.44 => ( Xs = Ys ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % nth_equalityI
% 0.18/0.44 thf(fact_118_not__gr__zero,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.18/0.44 = ( N = zero_zero_nat ) ) ).
% 0.18/0.44
% 0.18/0.44 % not_gr_zero
% 0.18/0.44 thf(fact_119_fvi__Suc__bound,axiom,
% 0.18/0.44 ! [B2: nat,Phi: formula_a,N: nat] :
% 0.18/0.44 ( ! [X3: nat] :
% 0.18/0.44 ( ( member_nat @ X3 @ ( fvi_a @ ( suc @ B2 ) @ Phi ) )
% 0.18/0.44 => ( ord_less_nat @ X3 @ N ) )
% 0.18/0.44 => ! [X6: nat] :
% 0.18/0.44 ( ( member_nat @ X6 @ ( fvi_a @ B2 @ Phi ) )
% 0.18/0.44 => ( ord_less_nat @ X6 @ ( suc @ N ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % fvi_Suc_bound
% 0.18/0.44 thf(fact_120_length__Cons,axiom,
% 0.18/0.44 ! [X: b,Xs: list_b] :
% 0.18/0.44 ( ( size_size_list_b @ ( cons_b @ X @ Xs ) )
% 0.18/0.44 = ( suc @ ( size_size_list_b @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % length_Cons
% 0.18/0.45 thf(fact_121_length__Cons,axiom,
% 0.18/0.45 ! [X: option_b,Xs: list_option_b] :
% 0.18/0.45 ( ( size_s1671393719tion_b @ ( cons_option_b @ X @ Xs ) )
% 0.18/0.45 = ( suc @ ( size_s1671393719tion_b @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % length_Cons
% 0.18/0.45 thf(fact_122_option_Osize__gen_I1_J,axiom,
% 0.18/0.45 ! [X: b > nat] :
% 0.18/0.45 ( ( size_option_b @ X @ none_b )
% 0.18/0.45 = ( suc @ zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.size_gen(1)
% 0.18/0.45 thf(fact_123_fvi__Suc,axiom,
% 0.18/0.45 ! [X: nat,B2: nat,Phi: formula_a] :
% 0.18/0.45 ( ( member_nat @ X @ ( fvi_a @ ( suc @ B2 ) @ Phi ) )
% 0.18/0.45 = ( member_nat @ ( suc @ X ) @ ( fvi_a @ B2 @ Phi ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % fvi_Suc
% 0.18/0.45 thf(fact_124_option_Osize_I4_J,axiom,
% 0.18/0.45 ! [X2: option_b] :
% 0.18/0.45 ( ( size_s684879735tion_b @ ( some_option_b @ X2 ) )
% 0.18/0.45 = ( suc @ zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.size(4)
% 0.18/0.45 thf(fact_125_option_Osize_I4_J,axiom,
% 0.18/0.45 ! [X2: b] :
% 0.18/0.45 ( ( size_size_option_b @ ( some_b @ X2 ) )
% 0.18/0.45 = ( suc @ zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.size(4)
% 0.18/0.45 thf(fact_126_option_Osize_I3_J,axiom,
% 0.18/0.45 ( ( size_size_option_b @ none_b )
% 0.18/0.45 = ( suc @ zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.size(3)
% 0.18/0.45 thf(fact_127_find__Some__iff,axiom,
% 0.18/0.45 ! [P: b > $o,Xs: list_b,X: b] :
% 0.18/0.45 ( ( ( find_b @ P @ Xs )
% 0.18/0.45 = ( some_b @ X ) )
% 0.18/0.45 = ( ? [I3: nat] :
% 0.18/0.45 ( ( ord_less_nat @ I3 @ ( size_size_list_b @ Xs ) )
% 0.18/0.45 & ( P @ ( nth_b @ Xs @ I3 ) )
% 0.18/0.45 & ( X
% 0.18/0.45 = ( nth_b @ Xs @ I3 ) )
% 0.18/0.45 & ! [J3: nat] :
% 0.18/0.45 ( ( ord_less_nat @ J3 @ I3 )
% 0.18/0.45 => ~ ( P @ ( nth_b @ Xs @ J3 ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % find_Some_iff
% 0.18/0.45 thf(fact_128_find__Some__iff,axiom,
% 0.18/0.45 ! [P: option_b > $o,Xs: list_option_b,X: option_b] :
% 0.18/0.45 ( ( ( find_option_b @ P @ Xs )
% 0.18/0.45 = ( some_option_b @ X ) )
% 0.18/0.45 = ( ? [I3: nat] :
% 0.18/0.45 ( ( ord_less_nat @ I3 @ ( size_s1671393719tion_b @ Xs ) )
% 0.18/0.45 & ( P @ ( nth_option_b @ Xs @ I3 ) )
% 0.18/0.45 & ( X
% 0.18/0.45 = ( nth_option_b @ Xs @ I3 ) )
% 0.18/0.45 & ! [J3: nat] :
% 0.18/0.45 ( ( ord_less_nat @ J3 @ I3 )
% 0.18/0.45 => ~ ( P @ ( nth_option_b @ Xs @ J3 ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % find_Some_iff
% 0.18/0.45 thf(fact_129_exists__least__lemma,axiom,
% 0.18/0.45 ! [P: nat > $o] :
% 0.18/0.45 ( ~ ( P @ zero_zero_nat )
% 0.18/0.45 => ( ? [X_1: nat] : ( P @ X_1 )
% 0.18/0.45 => ? [N2: nat] :
% 0.18/0.45 ( ~ ( P @ N2 )
% 0.18/0.45 & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % exists_least_lemma
% 0.18/0.45 thf(fact_130_option_Osize__neq,axiom,
% 0.18/0.45 ! [X: option_b] :
% 0.18/0.45 ( ( size_size_option_b @ X )
% 0.18/0.45 != zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % option.size_neq
% 0.18/0.45 thf(fact_131_zero__reorient,axiom,
% 0.18/0.45 ! [X: nat] :
% 0.18/0.45 ( ( zero_zero_nat = X )
% 0.18/0.45 = ( X = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_reorient
% 0.18/0.45 thf(fact_132_zero__reorient,axiom,
% 0.18/0.45 ! [X: int] :
% 0.18/0.45 ( ( zero_zero_int = X )
% 0.18/0.45 = ( X = zero_zero_int ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_reorient
% 0.18/0.45 thf(fact_133_find_Osimps_I2_J,axiom,
% 0.18/0.45 ! [P: option_b > $o,X: option_b,Xs: list_option_b] :
% 0.18/0.45 ( ( ( P @ X )
% 0.18/0.45 => ( ( find_option_b @ P @ ( cons_option_b @ X @ Xs ) )
% 0.18/0.45 = ( some_option_b @ X ) ) )
% 0.18/0.45 & ( ~ ( P @ X )
% 0.18/0.45 => ( ( find_option_b @ P @ ( cons_option_b @ X @ Xs ) )
% 0.18/0.45 = ( find_option_b @ P @ Xs ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % find.simps(2)
% 0.18/0.45 thf(fact_134_find_Osimps_I2_J,axiom,
% 0.18/0.45 ! [P: b > $o,X: b,Xs: list_b] :
% 0.18/0.45 ( ( ( P @ X )
% 0.18/0.45 => ( ( find_b @ P @ ( cons_b @ X @ Xs ) )
% 0.18/0.45 = ( some_b @ X ) ) )
% 0.18/0.45 & ( ~ ( P @ X )
% 0.18/0.45 => ( ( find_b @ P @ ( cons_b @ X @ Xs ) )
% 0.18/0.45 = ( find_b @ P @ Xs ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % find.simps(2)
% 0.18/0.45 thf(fact_135_gr__zeroI,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( N != zero_zero_nat )
% 0.18/0.45 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % gr_zeroI
% 0.18/0.45 thf(fact_136_not__less__zero,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % not_less_zero
% 0.18/0.45 thf(fact_137_gr__implies__not__zero,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ M @ N )
% 0.18/0.45 => ( N != zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % gr_implies_not_zero
% 0.18/0.45 thf(fact_138_zero__less__iff__neq__zero,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 = ( N != zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_less_iff_neq_zero
% 0.18/0.45 thf(fact_139_list__decode_Ocases,axiom,
% 0.18/0.45 ! [X: nat] :
% 0.18/0.45 ( ( X != zero_zero_nat )
% 0.18/0.45 => ~ ! [N2: nat] :
% 0.18/0.45 ( X
% 0.18/0.45 != ( suc @ N2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_decode.cases
% 0.18/0.45 thf(fact_140_less__numeral__extra_I3_J,axiom,
% 0.18/0.45 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % less_numeral_extra(3)
% 0.18/0.45 thf(fact_141_less__numeral__extra_I3_J,axiom,
% 0.18/0.45 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.18/0.45
% 0.18/0.45 % less_numeral_extra(3)
% 0.18/0.45 thf(fact_142_length__code,axiom,
% 0.18/0.45 ( size_size_list_b
% 0.18/0.45 = ( gen_length_b @ zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % length_code
% 0.18/0.45 thf(fact_143_length__code,axiom,
% 0.18/0.45 ( size_s1671393719tion_b
% 0.18/0.45 = ( gen_length_option_b @ zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % length_code
% 0.18/0.45 thf(fact_144_gen__length__code_I2_J,axiom,
% 0.18/0.45 ! [N: nat,X: b,Xs: list_b] :
% 0.18/0.45 ( ( gen_length_b @ N @ ( cons_b @ X @ Xs ) )
% 0.18/0.45 = ( gen_length_b @ ( suc @ N ) @ Xs ) ) ).
% 0.18/0.45
% 0.18/0.45 % gen_length_code(2)
% 0.18/0.45 thf(fact_145_gen__length__code_I2_J,axiom,
% 0.18/0.45 ! [N: nat,X: option_b,Xs: list_option_b] :
% 0.18/0.45 ( ( gen_length_option_b @ N @ ( cons_option_b @ X @ Xs ) )
% 0.18/0.45 = ( gen_length_option_b @ ( suc @ N ) @ Xs ) ) ).
% 0.18/0.45
% 0.18/0.45 % gen_length_code(2)
% 0.18/0.45 thf(fact_146_option_Osize__gen_I2_J,axiom,
% 0.18/0.45 ! [X: option_b > nat,X2: option_b] :
% 0.18/0.45 ( ( size_option_option_b @ X @ ( some_option_b @ X2 ) )
% 0.18/0.45 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.size_gen(2)
% 0.18/0.45 thf(fact_147_option_Osize__gen_I2_J,axiom,
% 0.18/0.45 ! [X: b > nat,X2: b] :
% 0.18/0.45 ( ( size_option_b @ X @ ( some_b @ X2 ) )
% 0.18/0.45 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.size_gen(2)
% 0.18/0.45 thf(fact_148_Cons__nth__drop__Suc,axiom,
% 0.18/0.45 ! [I: nat,Xs: list_b] :
% 0.18/0.45 ( ( ord_less_nat @ I @ ( size_size_list_b @ Xs ) )
% 0.18/0.45 => ( ( cons_b @ ( nth_b @ Xs @ I ) @ ( drop_b @ ( suc @ I ) @ Xs ) )
% 0.18/0.45 = ( drop_b @ I @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Cons_nth_drop_Suc
% 0.18/0.45 thf(fact_149_Cons__nth__drop__Suc,axiom,
% 0.18/0.45 ! [I: nat,Xs: list_option_b] :
% 0.18/0.45 ( ( ord_less_nat @ I @ ( size_s1671393719tion_b @ Xs ) )
% 0.18/0.45 => ( ( cons_option_b @ ( nth_option_b @ Xs @ I ) @ ( drop_option_b @ ( suc @ I ) @ Xs ) )
% 0.18/0.45 = ( drop_option_b @ I @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Cons_nth_drop_Suc
% 0.18/0.45 thf(fact_150_list__ex__length,axiom,
% 0.18/0.45 ( list_ex_b
% 0.18/0.45 = ( ^ [P3: b > $o,Xs3: list_b] :
% 0.18/0.45 ? [N4: nat] :
% 0.18/0.45 ( ( ord_less_nat @ N4 @ ( size_size_list_b @ Xs3 ) )
% 0.18/0.45 & ( P3 @ ( nth_b @ Xs3 @ N4 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_ex_length
% 0.18/0.45 thf(fact_151_list__ex__length,axiom,
% 0.18/0.45 ( list_ex_option_b
% 0.18/0.45 = ( ^ [P3: option_b > $o,Xs3: list_option_b] :
% 0.18/0.45 ? [N4: nat] :
% 0.18/0.45 ( ( ord_less_nat @ N4 @ ( size_s1671393719tion_b @ Xs3 ) )
% 0.18/0.45 & ( P3 @ ( nth_option_b @ Xs3 @ N4 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_ex_length
% 0.18/0.45 thf(fact_152_of__nat__0__less__iff,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) )
% 0.18/0.45 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0_less_iff
% 0.18/0.45 thf(fact_153_of__nat__0__less__iff,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( ord_less_int @ zero_zero_int @ ( semiri2019852685at_int @ N ) )
% 0.18/0.45 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0_less_iff
% 0.18/0.45 thf(fact_154_add__left__cancel,axiom,
% 0.18/0.45 ! [A: nat,B2: nat,C: nat] :
% 0.18/0.45 ( ( ( plus_plus_nat @ A @ B2 )
% 0.18/0.45 = ( plus_plus_nat @ A @ C ) )
% 0.18/0.45 = ( B2 = C ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_left_cancel
% 0.18/0.45 thf(fact_155_add__left__cancel,axiom,
% 0.18/0.45 ! [A: int,B2: int,C: int] :
% 0.18/0.45 ( ( ( plus_plus_int @ A @ B2 )
% 0.18/0.45 = ( plus_plus_int @ A @ C ) )
% 0.18/0.45 = ( B2 = C ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_left_cancel
% 0.18/0.45 thf(fact_156_add__right__cancel,axiom,
% 0.18/0.45 ! [B2: nat,A: nat,C: nat] :
% 0.18/0.45 ( ( ( plus_plus_nat @ B2 @ A )
% 0.18/0.45 = ( plus_plus_nat @ C @ A ) )
% 0.18/0.45 = ( B2 = C ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_right_cancel
% 0.18/0.45 thf(fact_157_add__right__cancel,axiom,
% 0.18/0.45 ! [B2: int,A: int,C: int] :
% 0.18/0.45 ( ( ( plus_plus_int @ B2 @ A )
% 0.18/0.45 = ( plus_plus_int @ C @ A ) )
% 0.18/0.45 = ( B2 = C ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_right_cancel
% 0.18/0.45 thf(fact_158_of__nat__eq__iff,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ( semiri1382578993at_nat @ M )
% 0.18/0.45 = ( semiri1382578993at_nat @ N ) )
% 0.18/0.45 = ( M = N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_eq_iff
% 0.18/0.45 thf(fact_159_of__nat__eq__iff,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ( semiri2019852685at_int @ M )
% 0.18/0.45 = ( semiri2019852685at_int @ N ) )
% 0.18/0.45 = ( M = N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_eq_iff
% 0.18/0.45 thf(fact_160_zero__eq__add__iff__both__eq__0,axiom,
% 0.18/0.45 ! [X: nat,Y3: nat] :
% 0.18/0.45 ( ( zero_zero_nat
% 0.18/0.45 = ( plus_plus_nat @ X @ Y3 ) )
% 0.18/0.45 = ( ( X = zero_zero_nat )
% 0.18/0.45 & ( Y3 = zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_eq_add_iff_both_eq_0
% 0.18/0.45 thf(fact_161_add__eq__0__iff__both__eq__0,axiom,
% 0.18/0.45 ! [X: nat,Y3: nat] :
% 0.18/0.45 ( ( ( plus_plus_nat @ X @ Y3 )
% 0.18/0.45 = zero_zero_nat )
% 0.18/0.45 = ( ( X = zero_zero_nat )
% 0.18/0.45 & ( Y3 = zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_eq_0_iff_both_eq_0
% 0.18/0.45 thf(fact_162_add__cancel__right__right,axiom,
% 0.18/0.45 ! [A: nat,B2: nat] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( plus_plus_nat @ A @ B2 ) )
% 0.18/0.45 = ( B2 = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_cancel_right_right
% 0.18/0.45 thf(fact_163_add__cancel__right__right,axiom,
% 0.18/0.45 ! [A: int,B2: int] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( plus_plus_int @ A @ B2 ) )
% 0.18/0.45 = ( B2 = zero_zero_int ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_cancel_right_right
% 0.18/0.45 thf(fact_164_add__cancel__right__left,axiom,
% 0.18/0.45 ! [A: nat,B2: nat] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( plus_plus_nat @ B2 @ A ) )
% 0.18/0.45 = ( B2 = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_cancel_right_left
% 0.18/0.45 thf(fact_165_add__cancel__right__left,axiom,
% 0.18/0.45 ! [A: int,B2: int] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( plus_plus_int @ B2 @ A ) )
% 0.18/0.45 = ( B2 = zero_zero_int ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_cancel_right_left
% 0.18/0.45 thf(fact_166_add__cancel__left__right,axiom,
% 0.18/0.45 ! [A: nat,B2: nat] :
% 0.18/0.45 ( ( ( plus_plus_nat @ A @ B2 )
% 0.18/0.45 = A )
% 0.18/0.45 = ( B2 = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_cancel_left_right
% 0.18/0.45 thf(fact_167_add__cancel__left__right,axiom,
% 0.18/0.45 ! [A: int,B2: int] :
% 0.18/0.45 ( ( ( plus_plus_int @ A @ B2 )
% 0.18/0.45 = A )
% 0.18/0.45 = ( B2 = zero_zero_int ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_cancel_left_right
% 0.18/0.45 thf(fact_168_add__cancel__left__left,axiom,
% 0.18/0.45 ! [B2: nat,A: nat] :
% 0.18/0.45 ( ( ( plus_plus_nat @ B2 @ A )
% 0.18/0.45 = A )
% 0.18/0.45 = ( B2 = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_cancel_left_left
% 0.18/0.45 thf(fact_169_add__cancel__left__left,axiom,
% 0.18/0.45 ! [B2: int,A: int] :
% 0.18/0.45 ( ( ( plus_plus_int @ B2 @ A )
% 0.18/0.45 = A )
% 0.18/0.45 = ( B2 = zero_zero_int ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_cancel_left_left
% 0.18/0.45 thf(fact_170_double__zero__sym,axiom,
% 0.18/0.45 ! [A: int] :
% 0.18/0.45 ( ( zero_zero_int
% 0.18/0.45 = ( plus_plus_int @ A @ A ) )
% 0.18/0.45 = ( A = zero_zero_int ) ) ).
% 0.18/0.45
% 0.18/0.45 % double_zero_sym
% 0.18/0.45 thf(fact_171_double__zero,axiom,
% 0.18/0.45 ! [A: int] :
% 0.18/0.45 ( ( ( plus_plus_int @ A @ A )
% 0.18/0.45 = zero_zero_int )
% 0.18/0.45 = ( A = zero_zero_int ) ) ).
% 0.18/0.45
% 0.18/0.45 % double_zero
% 0.18/0.45 thf(fact_172_add_Oright__neutral,axiom,
% 0.18/0.45 ! [A: nat] :
% 0.18/0.45 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % add.right_neutral
% 0.18/0.45 thf(fact_173_add_Oright__neutral,axiom,
% 0.18/0.45 ! [A: int] :
% 0.18/0.45 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % add.right_neutral
% 0.18/0.45 thf(fact_174_add_Oleft__neutral,axiom,
% 0.18/0.45 ! [A: nat] :
% 0.18/0.45 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % add.left_neutral
% 0.18/0.45 thf(fact_175_add_Oleft__neutral,axiom,
% 0.18/0.45 ! [A: int] :
% 0.18/0.45 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % add.left_neutral
% 0.18/0.45 thf(fact_176_add__less__cancel__right,axiom,
% 0.18/0.45 ! [A: nat,C: nat,B2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 0.18/0.45 = ( ord_less_nat @ A @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_less_cancel_right
% 0.18/0.45 thf(fact_177_add__less__cancel__right,axiom,
% 0.18/0.45 ! [A: int,C: int,B2: int] :
% 0.18/0.45 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 0.18/0.45 = ( ord_less_int @ A @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_less_cancel_right
% 0.18/0.45 thf(fact_178_add__less__cancel__left,axiom,
% 0.18/0.45 ! [C: nat,A: nat,B2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 0.18/0.45 = ( ord_less_nat @ A @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_less_cancel_left
% 0.18/0.45 thf(fact_179_add__less__cancel__left,axiom,
% 0.18/0.45 ! [C: int,A: int,B2: int] :
% 0.18/0.45 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 0.18/0.45 = ( ord_less_int @ A @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_less_cancel_left
% 0.18/0.45 thf(fact_180_add__is__0,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ( plus_plus_nat @ M @ N )
% 0.18/0.45 = zero_zero_nat )
% 0.18/0.45 = ( ( M = zero_zero_nat )
% 0.18/0.45 & ( N = zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_is_0
% 0.18/0.45 thf(fact_181_Nat_Oadd__0__right,axiom,
% 0.18/0.45 ! [M: nat] :
% 0.18/0.45 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.18/0.45 = M ) ).
% 0.18/0.45
% 0.18/0.45 % Nat.add_0_right
% 0.18/0.45 thf(fact_182_add__Suc__right,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 0.18/0.45 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_Suc_right
% 0.18/0.45 thf(fact_183_nat__add__left__cancel__less,axiom,
% 0.18/0.45 ! [K: nat,M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.18/0.45 = ( ord_less_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % nat_add_left_cancel_less
% 0.18/0.45 thf(fact_184_drop0,axiom,
% 0.18/0.45 ( ( drop_option_b @ zero_zero_nat )
% 0.18/0.45 = ( ^ [X4: list_option_b] : X4 ) ) ).
% 0.18/0.45
% 0.18/0.45 % drop0
% 0.18/0.45 thf(fact_185_drop__drop,axiom,
% 0.18/0.45 ! [N: nat,M: nat,Xs: list_option_b] :
% 0.18/0.45 ( ( drop_option_b @ N @ ( drop_option_b @ M @ Xs ) )
% 0.18/0.45 = ( drop_option_b @ ( plus_plus_nat @ N @ M ) @ Xs ) ) ).
% 0.18/0.45
% 0.18/0.45 % drop_drop
% 0.18/0.45 thf(fact_186_list__ex__simps_I1_J,axiom,
% 0.18/0.45 ! [P: b > $o,X: b,Xs: list_b] :
% 0.18/0.45 ( ( list_ex_b @ P @ ( cons_b @ X @ Xs ) )
% 0.18/0.45 = ( ( P @ X )
% 0.18/0.45 | ( list_ex_b @ P @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_ex_simps(1)
% 0.18/0.45 thf(fact_187_list__ex__simps_I1_J,axiom,
% 0.18/0.45 ! [P: option_b > $o,X: option_b,Xs: list_option_b] :
% 0.18/0.45 ( ( list_ex_option_b @ P @ ( cons_option_b @ X @ Xs ) )
% 0.18/0.45 = ( ( P @ X )
% 0.18/0.45 | ( list_ex_option_b @ P @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_ex_simps(1)
% 0.18/0.45 thf(fact_188_add__less__same__cancel1,axiom,
% 0.18/0.45 ! [B2: nat,A: nat] :
% 0.18/0.45 ( ( ord_less_nat @ ( plus_plus_nat @ B2 @ A ) @ B2 )
% 0.18/0.45 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_less_same_cancel1
% 0.18/0.45 thf(fact_189_add__less__same__cancel1,axiom,
% 0.18/0.45 ! [B2: int,A: int] :
% 0.18/0.45 ( ( ord_less_int @ ( plus_plus_int @ B2 @ A ) @ B2 )
% 0.18/0.45 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_less_same_cancel1
% 0.18/0.45 thf(fact_190_add__less__same__cancel2,axiom,
% 0.18/0.45 ! [A: nat,B2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B2 ) @ B2 )
% 0.18/0.45 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_less_same_cancel2
% 0.18/0.45 thf(fact_191_add__less__same__cancel2,axiom,
% 0.18/0.45 ! [A: int,B2: int] :
% 0.18/0.45 ( ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ B2 )
% 0.18/0.45 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_less_same_cancel2
% 0.18/0.45 thf(fact_192_less__add__same__cancel1,axiom,
% 0.18/0.45 ! [A: nat,B2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B2 ) )
% 0.18/0.45 = ( ord_less_nat @ zero_zero_nat @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_add_same_cancel1
% 0.18/0.45 thf(fact_193_less__add__same__cancel1,axiom,
% 0.18/0.45 ! [A: int,B2: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B2 ) )
% 0.18/0.45 = ( ord_less_int @ zero_zero_int @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_add_same_cancel1
% 0.18/0.45 thf(fact_194_less__add__same__cancel2,axiom,
% 0.18/0.45 ! [A: nat,B2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B2 @ A ) )
% 0.18/0.45 = ( ord_less_nat @ zero_zero_nat @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_add_same_cancel2
% 0.18/0.45 thf(fact_195_less__add__same__cancel2,axiom,
% 0.18/0.45 ! [A: int,B2: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ ( plus_plus_int @ B2 @ A ) )
% 0.18/0.45 = ( ord_less_int @ zero_zero_int @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_add_same_cancel2
% 0.18/0.45 thf(fact_196_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.18/0.45 ! [A: int] :
% 0.18/0.45 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.18/0.45 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.18/0.45
% 0.18/0.45 % double_add_less_zero_iff_single_add_less_zero
% 0.18/0.45 thf(fact_197_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.18/0.45 ! [A: int] :
% 0.18/0.45 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.18/0.45 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_less_double_add_iff_zero_less_single_add
% 0.18/0.45 thf(fact_198_of__nat__0,axiom,
% 0.18/0.45 ( ( semiri1382578993at_nat @ zero_zero_nat )
% 0.18/0.45 = zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0
% 0.18/0.45 thf(fact_199_of__nat__0,axiom,
% 0.18/0.45 ( ( semiri2019852685at_int @ zero_zero_nat )
% 0.18/0.45 = zero_zero_int ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0
% 0.18/0.45 thf(fact_200_of__nat__0__eq__iff,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( zero_zero_nat
% 0.18/0.45 = ( semiri1382578993at_nat @ N ) )
% 0.18/0.45 = ( zero_zero_nat = N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0_eq_iff
% 0.18/0.45 thf(fact_201_of__nat__0__eq__iff,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( zero_zero_int
% 0.18/0.45 = ( semiri2019852685at_int @ N ) )
% 0.18/0.45 = ( zero_zero_nat = N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0_eq_iff
% 0.18/0.45 thf(fact_202_of__nat__eq__0__iff,axiom,
% 0.18/0.45 ! [M: nat] :
% 0.18/0.45 ( ( ( semiri1382578993at_nat @ M )
% 0.18/0.45 = zero_zero_nat )
% 0.18/0.45 = ( M = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_eq_0_iff
% 0.18/0.45 thf(fact_203_of__nat__eq__0__iff,axiom,
% 0.18/0.45 ! [M: nat] :
% 0.18/0.45 ( ( ( semiri2019852685at_int @ M )
% 0.18/0.45 = zero_zero_int )
% 0.18/0.45 = ( M = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_eq_0_iff
% 0.18/0.45 thf(fact_204_of__nat__less__iff,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
% 0.18/0.45 = ( ord_less_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_iff
% 0.18/0.45 thf(fact_205_of__nat__less__iff,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) )
% 0.18/0.45 = ( ord_less_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_iff
% 0.18/0.45 thf(fact_206_of__nat__add,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( semiri1382578993at_nat @ ( plus_plus_nat @ M @ N ) )
% 0.18/0.45 = ( plus_plus_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_add
% 0.18/0.45 thf(fact_207_of__nat__add,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( semiri2019852685at_int @ ( plus_plus_nat @ M @ N ) )
% 0.18/0.45 = ( plus_plus_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_add
% 0.18/0.45 thf(fact_208_add__gr__0,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 0.18/0.45 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.18/0.45 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_gr_0
% 0.18/0.45 thf(fact_209_drop__Suc__Cons,axiom,
% 0.18/0.45 ! [N: nat,X: b,Xs: list_b] :
% 0.18/0.45 ( ( drop_b @ ( suc @ N ) @ ( cons_b @ X @ Xs ) )
% 0.18/0.45 = ( drop_b @ N @ Xs ) ) ).
% 0.18/0.45
% 0.18/0.45 % drop_Suc_Cons
% 0.18/0.45 thf(fact_210_drop__Suc__Cons,axiom,
% 0.18/0.45 ! [N: nat,X: option_b,Xs: list_option_b] :
% 0.18/0.45 ( ( drop_option_b @ ( suc @ N ) @ ( cons_option_b @ X @ Xs ) )
% 0.18/0.45 = ( drop_option_b @ N @ Xs ) ) ).
% 0.18/0.45
% 0.18/0.45 % drop_Suc_Cons
% 0.18/0.45 thf(fact_211_is__num__normalize_I1_J,axiom,
% 0.18/0.45 ! [A: int,B2: int,C: int] :
% 0.18/0.45 ( ( plus_plus_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 0.18/0.45 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % is_num_normalize(1)
% 0.18/0.45 thf(fact_212_less__add__eq__less,axiom,
% 0.18/0.45 ! [K: nat,L: nat,M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ K @ L )
% 0.18/0.45 => ( ( ( plus_plus_nat @ M @ L )
% 0.18/0.45 = ( plus_plus_nat @ K @ N ) )
% 0.18/0.45 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_add_eq_less
% 0.18/0.45 thf(fact_213_trans__less__add2,axiom,
% 0.18/0.45 ! [I: nat,J: nat,M: nat] :
% 0.18/0.45 ( ( ord_less_nat @ I @ J )
% 0.18/0.45 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % trans_less_add2
% 0.18/0.45 thf(fact_214_trans__less__add1,axiom,
% 0.18/0.45 ! [I: nat,J: nat,M: nat] :
% 0.18/0.45 ( ( ord_less_nat @ I @ J )
% 0.18/0.45 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % trans_less_add1
% 0.18/0.45 thf(fact_215_add__less__mono1,axiom,
% 0.18/0.45 ! [I: nat,J: nat,K: nat] :
% 0.18/0.45 ( ( ord_less_nat @ I @ J )
% 0.18/0.45 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_less_mono1
% 0.18/0.45 thf(fact_216_not__add__less2,axiom,
% 0.18/0.45 ! [J: nat,I: nat] :
% 0.18/0.45 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 0.18/0.45
% 0.18/0.45 % not_add_less2
% 0.18/0.45 thf(fact_217_not__add__less1,axiom,
% 0.18/0.45 ! [I: nat,J: nat] :
% 0.18/0.45 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 0.18/0.45
% 0.18/0.45 % not_add_less1
% 0.18/0.45 thf(fact_218_add__less__mono,axiom,
% 0.18/0.45 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.18/0.45 ( ( ord_less_nat @ I @ J )
% 0.18/0.45 => ( ( ord_less_nat @ K @ L )
% 0.18/0.45 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_less_mono
% 0.18/0.45 thf(fact_219_add__lessD1,axiom,
% 0.18/0.45 ! [I: nat,J: nat,K: nat] :
% 0.18/0.45 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.18/0.45 => ( ord_less_nat @ I @ K ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_lessD1
% 0.18/0.45 thf(fact_220_add__Suc,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.18/0.45 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_Suc
% 0.18/0.45 thf(fact_221_nat__arith_Osuc1,axiom,
% 0.18/0.45 ! [A2: nat,K: nat,A: nat] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( plus_plus_nat @ K @ A ) )
% 0.18/0.45 => ( ( suc @ A2 )
% 0.18/0.45 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % nat_arith.suc1
% 0.18/0.45 thf(fact_222_add__Suc__shift,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.18/0.45 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_Suc_shift
% 0.18/0.45 thf(fact_223_add__eq__self__zero,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ( plus_plus_nat @ M @ N )
% 0.18/0.45 = M )
% 0.18/0.45 => ( N = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_eq_self_zero
% 0.18/0.45 thf(fact_224_plus__nat_Oadd__0,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.18/0.45 = N ) ).
% 0.18/0.45
% 0.18/0.45 % plus_nat.add_0
% 0.18/0.45 thf(fact_225_drop__0,axiom,
% 0.18/0.45 ! [Xs: list_option_b] :
% 0.18/0.45 ( ( drop_option_b @ zero_zero_nat @ Xs )
% 0.18/0.45 = Xs ) ).
% 0.18/0.45
% 0.18/0.45 % drop_0
% 0.18/0.45 thf(fact_226_add__less__imp__less__right,axiom,
% 0.18/0.45 ! [A: nat,C: nat,B2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 0.18/0.45 => ( ord_less_nat @ A @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_less_imp_less_right
% 0.18/0.45 thf(fact_227_add__less__imp__less__right,axiom,
% 0.18/0.45 ! [A: int,C: int,B2: int] :
% 0.18/0.45 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 0.18/0.45 => ( ord_less_int @ A @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_less_imp_less_right
% 0.18/0.45 thf(fact_228_add__less__imp__less__left,axiom,
% 0.18/0.45 ! [C: nat,A: nat,B2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 0.18/0.45 => ( ord_less_nat @ A @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_less_imp_less_left
% 0.18/0.45 thf(fact_229_add__less__imp__less__left,axiom,
% 0.18/0.45 ! [C: int,A: int,B2: int] :
% 0.18/0.45 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 0.18/0.45 => ( ord_less_int @ A @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_less_imp_less_left
% 0.18/0.45 thf(fact_230_add__strict__right__mono,axiom,
% 0.18/0.45 ! [A: nat,B2: nat,C: nat] :
% 0.18/0.45 ( ( ord_less_nat @ A @ B2 )
% 0.18/0.45 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_strict_right_mono
% 0.18/0.45 thf(fact_231_add__strict__right__mono,axiom,
% 0.18/0.45 ! [A: int,B2: int,C: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ B2 )
% 0.18/0.45 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_strict_right_mono
% 0.18/0.45 thf(fact_232_add__strict__left__mono,axiom,
% 0.18/0.45 ! [A: nat,B2: nat,C: nat] :
% 0.18/0.45 ( ( ord_less_nat @ A @ B2 )
% 0.18/0.45 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_strict_left_mono
% 0.18/0.45 thf(fact_233_add__strict__left__mono,axiom,
% 0.18/0.45 ! [A: int,B2: int,C: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ B2 )
% 0.18/0.45 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_strict_left_mono
% 0.18/0.45 thf(fact_234_add__strict__mono,axiom,
% 0.18/0.45 ! [A: nat,B2: nat,C: nat,D: nat] :
% 0.18/0.45 ( ( ord_less_nat @ A @ B2 )
% 0.18/0.45 => ( ( ord_less_nat @ C @ D )
% 0.18/0.45 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ D ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_strict_mono
% 0.18/0.45 thf(fact_235_add__strict__mono,axiom,
% 0.18/0.45 ! [A: int,B2: int,C: int,D: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ B2 )
% 0.18/0.45 => ( ( ord_less_int @ C @ D )
% 0.18/0.45 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ D ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_strict_mono
% 0.18/0.45 thf(fact_236_add__mono__thms__linordered__field_I1_J,axiom,
% 0.18/0.45 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.18/0.45 ( ( ( ord_less_nat @ I @ J )
% 0.18/0.45 & ( K = L ) )
% 0.18/0.45 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_mono_thms_linordered_field(1)
% 0.18/0.45 thf(fact_237_add__mono__thms__linordered__field_I1_J,axiom,
% 0.18/0.45 ! [I: int,J: int,K: int,L: int] :
% 0.18/0.45 ( ( ( ord_less_int @ I @ J )
% 0.18/0.45 & ( K = L ) )
% 0.18/0.45 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_mono_thms_linordered_field(1)
% 0.18/0.45 thf(fact_238_add__mono__thms__linordered__field_I2_J,axiom,
% 0.18/0.45 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.18/0.45 ( ( ( I = J )
% 0.18/0.45 & ( ord_less_nat @ K @ L ) )
% 0.18/0.45 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_mono_thms_linordered_field(2)
% 0.18/0.45 thf(fact_239_add__mono__thms__linordered__field_I2_J,axiom,
% 0.18/0.45 ! [I: int,J: int,K: int,L: int] :
% 0.18/0.45 ( ( ( I = J )
% 0.18/0.45 & ( ord_less_int @ K @ L ) )
% 0.18/0.45 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_mono_thms_linordered_field(2)
% 0.18/0.45 thf(fact_240_add__mono__thms__linordered__field_I5_J,axiom,
% 0.18/0.45 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.18/0.45 ( ( ( ord_less_nat @ I @ J )
% 0.18/0.45 & ( ord_less_nat @ K @ L ) )
% 0.18/0.45 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_mono_thms_linordered_field(5)
% 0.18/0.45 thf(fact_241_add__mono__thms__linordered__field_I5_J,axiom,
% 0.18/0.45 ! [I: int,J: int,K: int,L: int] :
% 0.18/0.45 ( ( ( ord_less_int @ I @ J )
% 0.18/0.45 & ( ord_less_int @ K @ L ) )
% 0.18/0.45 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_mono_thms_linordered_field(5)
% 0.18/0.45 thf(fact_242_add_Ogroup__left__neutral,axiom,
% 0.18/0.45 ! [A: int] :
% 0.18/0.45 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % add.group_left_neutral
% 0.18/0.45 thf(fact_243_add_Ocomm__neutral,axiom,
% 0.18/0.45 ! [A: nat] :
% 0.18/0.45 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % add.comm_neutral
% 0.18/0.45 thf(fact_244_add_Ocomm__neutral,axiom,
% 0.18/0.45 ! [A: int] :
% 0.18/0.45 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % add.comm_neutral
% 0.18/0.45 thf(fact_245_comm__monoid__add__class_Oadd__0,axiom,
% 0.18/0.45 ! [A: nat] :
% 0.18/0.45 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % comm_monoid_add_class.add_0
% 0.18/0.45 thf(fact_246_comm__monoid__add__class_Oadd__0,axiom,
% 0.18/0.45 ! [A: int] :
% 0.18/0.45 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % comm_monoid_add_class.add_0
% 0.18/0.45 thf(fact_247_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.18/0.45 ! [A: nat,B2: nat,C: nat] :
% 0.18/0.45 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 0.18/0.45 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ab_semigroup_add_class.add_ac(1)
% 0.18/0.45 thf(fact_248_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.18/0.45 ! [A: int,B2: int,C: int] :
% 0.18/0.45 ( ( plus_plus_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 0.18/0.45 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ab_semigroup_add_class.add_ac(1)
% 0.18/0.45 thf(fact_249_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.18/0.45 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.18/0.45 ( ( ( I = J )
% 0.18/0.45 & ( K = L ) )
% 0.18/0.45 => ( ( plus_plus_nat @ I @ K )
% 0.18/0.45 = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_mono_thms_linordered_semiring(4)
% 0.18/0.45 thf(fact_250_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.18/0.45 ! [I: int,J: int,K: int,L: int] :
% 0.18/0.45 ( ( ( I = J )
% 0.18/0.45 & ( K = L ) )
% 0.18/0.45 => ( ( plus_plus_int @ I @ K )
% 0.18/0.45 = ( plus_plus_int @ J @ L ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_mono_thms_linordered_semiring(4)
% 0.18/0.45 thf(fact_251_group__cancel_Oadd1,axiom,
% 0.18/0.45 ! [A2: nat,K: nat,A: nat,B2: nat] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( plus_plus_nat @ K @ A ) )
% 0.18/0.45 => ( ( plus_plus_nat @ A2 @ B2 )
% 0.18/0.45 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % group_cancel.add1
% 0.18/0.45 thf(fact_252_group__cancel_Oadd1,axiom,
% 0.18/0.45 ! [A2: int,K: int,A: int,B2: int] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( plus_plus_int @ K @ A ) )
% 0.18/0.45 => ( ( plus_plus_int @ A2 @ B2 )
% 0.18/0.45 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % group_cancel.add1
% 0.18/0.45 thf(fact_253_group__cancel_Oadd2,axiom,
% 0.18/0.45 ! [B3: nat,K: nat,B2: nat,A: nat] :
% 0.18/0.45 ( ( B3
% 0.18/0.45 = ( plus_plus_nat @ K @ B2 ) )
% 0.18/0.45 => ( ( plus_plus_nat @ A @ B3 )
% 0.18/0.45 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % group_cancel.add2
% 0.18/0.45 thf(fact_254_group__cancel_Oadd2,axiom,
% 0.18/0.45 ! [B3: int,K: int,B2: int,A: int] :
% 0.18/0.45 ( ( B3
% 0.18/0.45 = ( plus_plus_int @ K @ B2 ) )
% 0.18/0.45 => ( ( plus_plus_int @ A @ B3 )
% 0.18/0.45 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % group_cancel.add2
% 0.18/0.45 thf(fact_255_add_Oassoc,axiom,
% 0.18/0.45 ! [A: nat,B2: nat,C: nat] :
% 0.18/0.45 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 0.18/0.45 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add.assoc
% 0.18/0.45 thf(fact_256_add_Oassoc,axiom,
% 0.18/0.45 ! [A: int,B2: int,C: int] :
% 0.18/0.45 ( ( plus_plus_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 0.18/0.45 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add.assoc
% 0.18/0.45 thf(fact_257_add_Oleft__cancel,axiom,
% 0.18/0.45 ! [A: int,B2: int,C: int] :
% 0.18/0.45 ( ( ( plus_plus_int @ A @ B2 )
% 0.18/0.45 = ( plus_plus_int @ A @ C ) )
% 0.18/0.45 = ( B2 = C ) ) ).
% 0.18/0.45
% 0.18/0.45 % add.left_cancel
% 0.18/0.45 thf(fact_258_add_Oright__cancel,axiom,
% 0.18/0.45 ! [B2: int,A: int,C: int] :
% 0.18/0.45 ( ( ( plus_plus_int @ B2 @ A )
% 0.18/0.45 = ( plus_plus_int @ C @ A ) )
% 0.18/0.45 = ( B2 = C ) ) ).
% 0.18/0.45
% 0.18/0.45 % add.right_cancel
% 0.18/0.45 thf(fact_259_add_Ocommute,axiom,
% 0.18/0.45 ( plus_plus_nat
% 0.18/0.45 = ( ^ [A4: nat,B4: nat] : ( plus_plus_nat @ B4 @ A4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add.commute
% 0.18/0.45 thf(fact_260_add_Ocommute,axiom,
% 0.18/0.45 ( plus_plus_int
% 0.18/0.45 = ( ^ [A4: int,B4: int] : ( plus_plus_int @ B4 @ A4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add.commute
% 0.18/0.45 thf(fact_261_add_Oleft__commute,axiom,
% 0.18/0.45 ! [B2: nat,A: nat,C: nat] :
% 0.18/0.45 ( ( plus_plus_nat @ B2 @ ( plus_plus_nat @ A @ C ) )
% 0.18/0.45 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add.left_commute
% 0.18/0.45 thf(fact_262_add_Oleft__commute,axiom,
% 0.18/0.45 ! [B2: int,A: int,C: int] :
% 0.18/0.45 ( ( plus_plus_int @ B2 @ ( plus_plus_int @ A @ C ) )
% 0.18/0.45 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add.left_commute
% 0.18/0.45 thf(fact_263_add__left__imp__eq,axiom,
% 0.18/0.45 ! [A: nat,B2: nat,C: nat] :
% 0.18/0.45 ( ( ( plus_plus_nat @ A @ B2 )
% 0.18/0.45 = ( plus_plus_nat @ A @ C ) )
% 0.18/0.45 => ( B2 = C ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_left_imp_eq
% 0.18/0.45 thf(fact_264_add__left__imp__eq,axiom,
% 0.18/0.45 ! [A: int,B2: int,C: int] :
% 0.18/0.45 ( ( ( plus_plus_int @ A @ B2 )
% 0.18/0.45 = ( plus_plus_int @ A @ C ) )
% 0.18/0.45 => ( B2 = C ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_left_imp_eq
% 0.18/0.45 thf(fact_265_add__right__imp__eq,axiom,
% 0.18/0.45 ! [B2: nat,A: nat,C: nat] :
% 0.18/0.45 ( ( ( plus_plus_nat @ B2 @ A )
% 0.18/0.45 = ( plus_plus_nat @ C @ A ) )
% 0.18/0.45 => ( B2 = C ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_right_imp_eq
% 0.18/0.45 thf(fact_266_add__right__imp__eq,axiom,
% 0.18/0.45 ! [B2: int,A: int,C: int] :
% 0.18/0.45 ( ( ( plus_plus_int @ B2 @ A )
% 0.18/0.45 = ( plus_plus_int @ C @ A ) )
% 0.18/0.45 => ( B2 = C ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_right_imp_eq
% 0.18/0.45 thf(fact_267_of__nat__less__0__iff,axiom,
% 0.18/0.45 ! [M: nat] :
% 0.18/0.45 ~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_0_iff
% 0.18/0.45 thf(fact_268_of__nat__less__0__iff,axiom,
% 0.18/0.45 ! [M: nat] :
% 0.18/0.45 ~ ( ord_less_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_0_iff
% 0.18/0.45 thf(fact_269_of__nat__neq__0,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( semiri1382578993at_nat @ ( suc @ N ) )
% 0.18/0.45 != zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_neq_0
% 0.18/0.45 thf(fact_270_of__nat__neq__0,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( semiri2019852685at_int @ ( suc @ N ) )
% 0.18/0.45 != zero_zero_int ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_neq_0
% 0.18/0.45 thf(fact_271_less__imp__of__nat__less,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ M @ N )
% 0.18/0.45 => ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_of_nat_less
% 0.18/0.45 thf(fact_272_less__imp__of__nat__less,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ M @ N )
% 0.18/0.45 => ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_of_nat_less
% 0.18/0.45 thf(fact_273_of__nat__less__imp__less,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
% 0.18/0.45 => ( ord_less_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_imp_less
% 0.18/0.45 thf(fact_274_of__nat__less__imp__less,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) )
% 0.18/0.45 => ( ord_less_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_imp_less
% 0.18/0.45 thf(fact_275_add__neg__neg,axiom,
% 0.18/0.45 ! [A: nat,B2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.18/0.45 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 0.18/0.45 => ( ord_less_nat @ ( plus_plus_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_neg_neg
% 0.18/0.45 thf(fact_276_add__neg__neg,axiom,
% 0.18/0.45 ! [A: int,B2: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ zero_zero_int )
% 0.18/0.45 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 0.18/0.45 => ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_neg_neg
% 0.18/0.45 thf(fact_277_add__pos__pos,axiom,
% 0.18/0.45 ! [A: nat,B2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.18/0.45 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 0.18/0.45 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_pos_pos
% 0.18/0.45 thf(fact_278_add__pos__pos,axiom,
% 0.18/0.45 ! [A: int,B2: int] :
% 0.18/0.45 ( ( ord_less_int @ zero_zero_int @ A )
% 0.18/0.45 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.18/0.45 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_pos_pos
% 0.18/0.45 thf(fact_279_canonically__ordered__monoid__add__class_OlessE,axiom,
% 0.18/0.45 ! [A: nat,B2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ A @ B2 )
% 0.18/0.45 => ~ ! [C2: nat] :
% 0.18/0.45 ( ( B2
% 0.18/0.45 = ( plus_plus_nat @ A @ C2 ) )
% 0.18/0.45 => ( C2 = zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % canonically_ordered_monoid_add_class.lessE
% 0.18/0.45 thf(fact_280_pos__add__strict,axiom,
% 0.18/0.45 ! [A: nat,B2: nat,C: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.18/0.45 => ( ( ord_less_nat @ B2 @ C )
% 0.18/0.45 => ( ord_less_nat @ B2 @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pos_add_strict
% 0.18/0.45 thf(fact_281_pos__add__strict,axiom,
% 0.18/0.45 ! [A: int,B2: int,C: int] :
% 0.18/0.45 ( ( ord_less_int @ zero_zero_int @ A )
% 0.18/0.45 => ( ( ord_less_int @ B2 @ C )
% 0.18/0.45 => ( ord_less_int @ B2 @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pos_add_strict
% 0.18/0.45 thf(fact_282_nth__via__drop,axiom,
% 0.18/0.45 ! [N: nat,Xs: list_b,Y3: b,Ys: list_b] :
% 0.18/0.45 ( ( ( drop_b @ N @ Xs )
% 0.18/0.45 = ( cons_b @ Y3 @ Ys ) )
% 0.18/0.45 => ( ( nth_b @ Xs @ N )
% 0.18/0.45 = Y3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % nth_via_drop
% 0.18/0.45 thf(fact_283_nth__via__drop,axiom,
% 0.18/0.45 ! [N: nat,Xs: list_option_b,Y3: option_b,Ys: list_option_b] :
% 0.18/0.45 ( ( ( drop_option_b @ N @ Xs )
% 0.18/0.45 = ( cons_option_b @ Y3 @ Ys ) )
% 0.18/0.45 => ( ( nth_option_b @ Xs @ N )
% 0.18/0.45 = Y3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % nth_via_drop
% 0.18/0.45 thf(fact_284_add__is__1,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ( plus_plus_nat @ M @ N )
% 0.18/0.45 = ( suc @ zero_zero_nat ) )
% 0.18/0.45 = ( ( ( M
% 0.18/0.45 = ( suc @ zero_zero_nat ) )
% 0.18/0.45 & ( N = zero_zero_nat ) )
% 0.18/0.45 | ( ( M = zero_zero_nat )
% 0.18/0.45 & ( N
% 0.18/0.45 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_is_1
% 0.18/0.45 thf(fact_285_one__is__add,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ( suc @ zero_zero_nat )
% 0.18/0.45 = ( plus_plus_nat @ M @ N ) )
% 0.18/0.45 = ( ( ( M
% 0.18/0.45 = ( suc @ zero_zero_nat ) )
% 0.18/0.45 & ( N = zero_zero_nat ) )
% 0.18/0.45 | ( ( M = zero_zero_nat )
% 0.18/0.45 & ( N
% 0.18/0.45 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % one_is_add
% 0.18/0.45 thf(fact_286_less__imp__add__positive,axiom,
% 0.18/0.45 ! [I: nat,J: nat] :
% 0.18/0.45 ( ( ord_less_nat @ I @ J )
% 0.18/0.45 => ? [K2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.18/0.45 & ( ( plus_plus_nat @ I @ K2 )
% 0.18/0.45 = J ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_add_positive
% 0.18/0.45 thf(fact_287_less__natE,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ M @ N )
% 0.18/0.45 => ~ ! [Q2: nat] :
% 0.18/0.45 ( N
% 0.18/0.45 != ( suc @ ( plus_plus_nat @ M @ Q2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_natE
% 0.18/0.45 thf(fact_288_less__add__Suc1,axiom,
% 0.18/0.45 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_add_Suc1
% 0.18/0.45 thf(fact_289_less__add__Suc2,axiom,
% 0.18/0.45 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_add_Suc2
% 0.18/0.45 thf(fact_290_less__iff__Suc__add,axiom,
% 0.18/0.45 ( ord_less_nat
% 0.18/0.45 = ( ^ [M5: nat,N4: nat] :
% 0.18/0.45 ? [K3: nat] :
% 0.18/0.45 ( N4
% 0.18/0.45 = ( suc @ ( plus_plus_nat @ M5 @ K3 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_iff_Suc_add
% 0.18/0.45 thf(fact_291_less__imp__Suc__add,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ M @ N )
% 0.18/0.45 => ? [K2: nat] :
% 0.18/0.45 ( N
% 0.18/0.45 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_Suc_add
% 0.18/0.45 thf(fact_292_gen__length__def,axiom,
% 0.18/0.45 ( gen_length_b
% 0.18/0.45 = ( ^ [N4: nat,Xs3: list_b] : ( plus_plus_nat @ N4 @ ( size_size_list_b @ Xs3 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % gen_length_def
% 0.18/0.45 thf(fact_293_gen__length__def,axiom,
% 0.18/0.45 ( gen_length_option_b
% 0.18/0.45 = ( ^ [N4: nat,Xs3: list_option_b] : ( plus_plus_nat @ N4 @ ( size_s1671393719tion_b @ Xs3 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % gen_length_def
% 0.18/0.45 thf(fact_294_list_Osize_I4_J,axiom,
% 0.18/0.45 ! [X21: b,X22: list_b] :
% 0.18/0.45 ( ( size_size_list_b @ ( cons_b @ X21 @ X22 ) )
% 0.18/0.45 = ( plus_plus_nat @ ( size_size_list_b @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.size(4)
% 0.18/0.45 thf(fact_295_list_Osize_I4_J,axiom,
% 0.18/0.45 ! [X21: option_b,X22: list_option_b] :
% 0.18/0.45 ( ( size_s1671393719tion_b @ ( cons_option_b @ X21 @ X22 ) )
% 0.18/0.45 = ( plus_plus_nat @ ( size_s1671393719tion_b @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.size(4)
% 0.18/0.45 thf(fact_296_add__less__zeroD,axiom,
% 0.18/0.45 ! [X: int,Y3: int] :
% 0.18/0.45 ( ( ord_less_int @ ( plus_plus_int @ X @ Y3 ) @ zero_zero_int )
% 0.18/0.45 => ( ( ord_less_int @ X @ zero_zero_int )
% 0.18/0.45 | ( ord_less_int @ Y3 @ zero_zero_int ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_less_zeroD
% 0.18/0.45 thf(fact_297_Euclid__induct,axiom,
% 0.18/0.45 ! [P: nat > nat > $o,A: nat,B2: nat] :
% 0.18/0.45 ( ! [A3: nat,B: nat] :
% 0.18/0.45 ( ( P @ A3 @ B )
% 0.18/0.45 = ( P @ B @ A3 ) )
% 0.18/0.45 => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
% 0.18/0.45 => ( ! [A3: nat,B: nat] :
% 0.18/0.45 ( ( P @ A3 @ B )
% 0.18/0.45 => ( P @ A3 @ ( plus_plus_nat @ A3 @ B ) ) )
% 0.18/0.45 => ( P @ A @ B2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Euclid_induct
% 0.18/0.45 thf(fact_298_pos__int__cases,axiom,
% 0.18/0.45 ! [K: int] :
% 0.18/0.45 ( ( ord_less_int @ zero_zero_int @ K )
% 0.18/0.45 => ~ ! [N2: nat] :
% 0.18/0.45 ( ( K
% 0.18/0.45 = ( semiri2019852685at_int @ N2 ) )
% 0.18/0.45 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pos_int_cases
% 0.18/0.45 thf(fact_299_zero__less__imp__eq__int,axiom,
% 0.18/0.45 ! [K: int] :
% 0.18/0.45 ( ( ord_less_int @ zero_zero_int @ K )
% 0.18/0.45 => ? [N2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.45 & ( K
% 0.18/0.45 = ( semiri2019852685at_int @ N2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_less_imp_eq_int
% 0.18/0.45 thf(fact_300_zadd__int__left,axiom,
% 0.18/0.45 ! [M: nat,N: nat,Z2: int] :
% 0.18/0.45 ( ( plus_plus_int @ ( semiri2019852685at_int @ M ) @ ( plus_plus_int @ ( semiri2019852685at_int @ N ) @ Z2 ) )
% 0.18/0.45 = ( plus_plus_int @ ( semiri2019852685at_int @ ( plus_plus_nat @ M @ N ) ) @ Z2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % zadd_int_left
% 0.18/0.45 thf(fact_301_int__int__eq,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ( semiri2019852685at_int @ M )
% 0.18/0.45 = ( semiri2019852685at_int @ N ) )
% 0.18/0.45 = ( M = N ) ) ).
% 0.18/0.45
% 0.18/0.45 % int_int_eq
% 0.18/0.45 thf(fact_302_plus__int__code_I2_J,axiom,
% 0.18/0.45 ! [L: int] :
% 0.18/0.45 ( ( plus_plus_int @ zero_zero_int @ L )
% 0.18/0.45 = L ) ).
% 0.18/0.45
% 0.18/0.45 % plus_int_code(2)
% 0.18/0.45 thf(fact_303_plus__int__code_I1_J,axiom,
% 0.18/0.45 ! [K: int] :
% 0.18/0.45 ( ( plus_plus_int @ K @ zero_zero_int )
% 0.18/0.45 = K ) ).
% 0.18/0.45
% 0.18/0.45 % plus_int_code(1)
% 0.18/0.45 thf(fact_304_zless__iff__Suc__zadd,axiom,
% 0.18/0.45 ( ord_less_int
% 0.18/0.45 = ( ^ [W: int,Z3: int] :
% 0.18/0.45 ? [N4: nat] :
% 0.18/0.45 ( Z3
% 0.18/0.45 = ( plus_plus_int @ W @ ( semiri2019852685at_int @ ( suc @ N4 ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zless_iff_Suc_zadd
% 0.18/0.45 thf(fact_305_less__int__code_I1_J,axiom,
% 0.18/0.45 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.18/0.45
% 0.18/0.45 % less_int_code(1)
% 0.18/0.45 thf(fact_306_linorder__neqE__linordered__idom,axiom,
% 0.18/0.45 ! [X: int,Y3: int] :
% 0.18/0.45 ( ( X != Y3 )
% 0.18/0.45 => ( ~ ( ord_less_int @ X @ Y3 )
% 0.18/0.45 => ( ord_less_int @ Y3 @ X ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % linorder_neqE_linordered_idom
% 0.18/0.45 thf(fact_307_nat__int__comparison_I2_J,axiom,
% 0.18/0.45 ( ord_less_nat
% 0.18/0.45 = ( ^ [A4: nat,B4: nat] : ( ord_less_int @ ( semiri2019852685at_int @ A4 ) @ ( semiri2019852685at_int @ B4 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % nat_int_comparison(2)
% 0.18/0.45 thf(fact_308_int__ops_I1_J,axiom,
% 0.18/0.45 ( ( semiri2019852685at_int @ zero_zero_nat )
% 0.18/0.45 = zero_zero_int ) ).
% 0.18/0.45
% 0.18/0.45 % int_ops(1)
% 0.18/0.45 thf(fact_309_verit__comp__simplify1_I1_J,axiom,
% 0.18/0.45 ! [A: nat] :
% 0.18/0.45 ~ ( ord_less_nat @ A @ A ) ).
% 0.18/0.45
% 0.18/0.45 % verit_comp_simplify1(1)
% 0.18/0.45 thf(fact_310_verit__comp__simplify1_I1_J,axiom,
% 0.18/0.45 ! [A: int] :
% 0.18/0.45 ~ ( ord_less_int @ A @ A ) ).
% 0.18/0.45
% 0.18/0.45 % verit_comp_simplify1(1)
% 0.18/0.45 thf(fact_311_nat__int__comparison_I1_J,axiom,
% 0.18/0.45 ( ( ^ [Y5: nat,Z: nat] : ( Y5 = Z ) )
% 0.18/0.45 = ( ^ [A4: nat,B4: nat] :
% 0.18/0.45 ( ( semiri2019852685at_int @ A4 )
% 0.18/0.45 = ( semiri2019852685at_int @ B4 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % nat_int_comparison(1)
% 0.18/0.45 thf(fact_312_int__if,axiom,
% 0.18/0.45 ! [P: $o,A: nat,B2: nat] :
% 0.18/0.45 ( ( P
% 0.18/0.45 => ( ( semiri2019852685at_int @ ( if_nat @ P @ A @ B2 ) )
% 0.18/0.45 = ( semiri2019852685at_int @ A ) ) )
% 0.18/0.45 & ( ~ P
% 0.18/0.45 => ( ( semiri2019852685at_int @ ( if_nat @ P @ A @ B2 ) )
% 0.18/0.45 = ( semiri2019852685at_int @ B2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % int_if
% 0.18/0.45 thf(fact_313_verit__sum__simplify,axiom,
% 0.18/0.45 ! [A: nat] :
% 0.18/0.45 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % verit_sum_simplify
% 0.18/0.45 thf(fact_314_verit__sum__simplify,axiom,
% 0.18/0.45 ! [A: int] :
% 0.18/0.45 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % verit_sum_simplify
% 0.18/0.45 thf(fact_315_int__ops_I5_J,axiom,
% 0.18/0.45 ! [A: nat,B2: nat] :
% 0.18/0.45 ( ( semiri2019852685at_int @ ( plus_plus_nat @ A @ B2 ) )
% 0.18/0.45 = ( plus_plus_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % int_ops(5)
% 0.18/0.45 thf(fact_316_int__plus,axiom,
% 0.18/0.45 ! [N: nat,M: nat] :
% 0.18/0.45 ( ( semiri2019852685at_int @ ( plus_plus_nat @ N @ M ) )
% 0.18/0.45 = ( plus_plus_int @ ( semiri2019852685at_int @ N ) @ ( semiri2019852685at_int @ M ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % int_plus
% 0.18/0.45 thf(fact_317_triangle__Suc,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( nat_triangle @ ( suc @ N ) )
% 0.18/0.45 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % triangle_Suc
% 0.18/0.45 thf(fact_318_add__0__iff,axiom,
% 0.18/0.45 ! [B2: nat,A: nat] :
% 0.18/0.45 ( ( B2
% 0.18/0.45 = ( plus_plus_nat @ B2 @ A ) )
% 0.18/0.45 = ( A = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_0_iff
% 0.18/0.45 thf(fact_319_add__0__iff,axiom,
% 0.18/0.45 ! [B2: int,A: int] :
% 0.18/0.45 ( ( B2
% 0.18/0.45 = ( plus_plus_int @ B2 @ A ) )
% 0.18/0.45 = ( A = zero_zero_int ) ) ).
% 0.18/0.45
% 0.18/0.45 % add_0_iff
% 0.18/0.45 thf(fact_320_triangle__0,axiom,
% 0.18/0.45 ( ( nat_triangle @ zero_zero_nat )
% 0.18/0.45 = zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % triangle_0
% 0.18/0.45 thf(fact_321_nth__drop,axiom,
% 0.18/0.45 ! [N: nat,Xs: list_b,I: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ N @ ( size_size_list_b @ Xs ) )
% 0.18/0.45 => ( ( nth_b @ ( drop_b @ N @ Xs ) @ I )
% 0.18/0.45 = ( nth_b @ Xs @ ( plus_plus_nat @ N @ I ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % nth_drop
% 0.18/0.45 thf(fact_322_nth__drop,axiom,
% 0.18/0.45 ! [N: nat,Xs: list_option_b,I: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ N @ ( size_s1671393719tion_b @ Xs ) )
% 0.18/0.45 => ( ( nth_option_b @ ( drop_option_b @ N @ Xs ) @ I )
% 0.18/0.45 = ( nth_option_b @ Xs @ ( plus_plus_nat @ N @ I ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % nth_drop
% 0.18/0.45
% 0.18/0.45 % Helper facts (3)
% 0.18/0.45 thf(help_If_3_1_If_001t__Nat__Onat_T,axiom,
% 0.18/0.45 ! [P: $o] :
% 0.18/0.45 ( ( P = $true )
% 0.18/0.45 | ( P = $false ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.18/0.45 ! [X: nat,Y3: nat] :
% 0.18/0.45 ( ( if_nat @ $false @ X @ Y3 )
% 0.18/0.45 = Y3 ) ).
% 0.18/0.45
% 0.18/0.45 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.18/0.45 ! [X: nat,Y3: nat] :
% 0.18/0.45 ( ( if_nat @ $true @ X @ Y3 )
% 0.18/0.45 = X ) ).
% 0.18/0.45
% 0.18/0.45 % Conjectures (3)
% 0.18/0.45 thf(conj_0,hypothesis,
% 0.18/0.45 member_nat @ zero_zero_nat @ ( fvi_a @ b2 @ phi ) ).
% 0.18/0.45
% 0.18/0.45 thf(conj_1,hypothesis,
% 0.18/0.45 ( ( ( size_s1671393719tion_b @ v )
% 0.18/0.45 = n )
% 0.18/0.45 & ! [I4: nat] :
% 0.18/0.45 ( ( ord_less_nat @ I4 @ n )
% 0.18/0.45 => ( ( ( nth_option_b @ v @ I4 )
% 0.18/0.45 = none_b )
% 0.18/0.45 = ( ~ ( member_nat @ I4 @ ( fvi_a @ ( suc @ b2 ) @ phi ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(conj_2,conjecture,
% 0.18/0.45 ( ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
% 0.18/0.45 = ( suc @ n ) )
% 0.18/0.45 & ! [I2: nat] :
% 0.18/0.45 ( ~ ( ord_less_nat @ I2 @ ( suc @ n ) )
% 0.18/0.45 | ( ( ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ I2 )
% 0.18/0.45 = none_b )
% 0.18/0.45 = ( ~ ( member_nat @ I2 @ ( fvi_a @ b2 @ phi ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 3.50/1.99 ---- Embedded in THF ---
% 3.50/1.99 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.50/1.99 %%% Generated on Tue Feb 24 08:26:56 EST 2026
% 3.50/1.99 %%% using '$$dhol' embedding, version 1.3.0.
% 3.50/1.99 %%% Logic specification used:
% 3.50/1.99 %%% thf(spec, logic, $$dhol).
% 3.50/1.99
% 3.50/1.99 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2DTF31741.p
% See solution above
% 3.50/1.99 ------------------------
% 3.75/2.04 ---- Cleaned THF ---
% 3.75/2.04 thf(ty_n_t__Option__Ooption_It__Option__Ooption_Itf__b_J_J,type,
% 3.75/2.04 option_option_b: $tType ).
% 3.75/2.04
% 3.75/2.04 thf(ty_n_t__List__Olist_It__Option__Ooption_Itf__b_J_J,type,
% 3.75/2.04 list_option_b: $tType ).
% 3.75/2.04
% 3.75/2.04 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 3.75/2.04 set_nat: $tType ).
% 3.75/2.04
% 3.75/2.04 thf(ty_n_t__Option__Ooption_Itf__b_J,type,
% 3.75/2.04 option_b: $tType ).
% 3.75/2.04
% 3.75/2.04 thf(ty_n_t__MFOTL__Oformula_Itf__a_J,type,
% 3.75/2.04 formula_a: $tType ).
% 3.75/2.04
% 3.75/2.04 thf(ty_n_t__List__Olist_Itf__b_J,type,
% 3.75/2.04 list_b: $tType ).
% 3.75/2.04
% 3.75/2.04 thf(ty_n_t__Nat__Onat,type,
% 3.75/2.04 nat: $tType ).
% 3.75/2.04
% 3.75/2.04 thf(ty_n_t__Int__Oint,type,
% 3.75/2.04 int: $tType ).
% 3.75/2.04
% 3.75/2.04 thf(ty_n_tf__b,type,
% 3.75/2.04 b: $tType ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
% 3.75/2.04 plus_plus_int: int > int > int ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 3.75/2.04 plus_plus_nat: nat > nat > nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 3.75/2.04 zero_zero_int: int ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 3.75/2.04 zero_zero_nat: nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_If_001t__Nat__Onat,type,
% 3.75/2.04 if_nat: $o > nat > nat > nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_List_Odrop_001t__Option__Ooption_Itf__b_J,type,
% 3.75/2.04 drop_option_b: nat > list_option_b > list_option_b ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_List_Odrop_001tf__b,type,
% 3.75/2.04 drop_b: nat > list_b > list_b ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_List_Ofind_001t__Option__Ooption_Itf__b_J,type,
% 3.75/2.04 find_option_b: ( option_b > $o ) > list_option_b > option_option_b ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_List_Ofind_001tf__b,type,
% 3.75/2.04 find_b: ( b > $o ) > list_b > option_b ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_List_Ogen__length_001t__Option__Ooption_Itf__b_J,type,
% 3.75/2.04 gen_length_option_b: nat > list_option_b > nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_List_Ogen__length_001tf__b,type,
% 3.75/2.04 gen_length_b: nat > list_b > nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_List_Olist_OCons_001t__Option__Ooption_Itf__b_J,type,
% 3.75/2.04 cons_option_b: option_b > list_option_b > list_option_b ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_List_Olist_OCons_001tf__b,type,
% 3.75/2.04 cons_b: b > list_b > list_b ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_List_Olist__ex_001t__Option__Ooption_Itf__b_J,type,
% 3.75/2.04 list_ex_option_b: ( option_b > $o ) > list_option_b > $o ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_List_Olist__ex_001tf__b,type,
% 3.75/2.04 list_ex_b: ( b > $o ) > list_b > $o ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_List_Onth_001t__Option__Ooption_Itf__b_J,type,
% 3.75/2.04 nth_option_b: list_option_b > nat > option_b ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_List_Onth_001tf__b,type,
% 3.75/2.04 nth_b: list_b > nat > b ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_MFOTL_Ofvi_001tf__a,type,
% 3.75/2.04 fvi_a: nat > formula_a > set_nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Nat_OSuc,type,
% 3.75/2.04 suc: nat > nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 3.75/2.04 semiri2019852685at_int: nat > int ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 3.75/2.04 semiri1382578993at_nat: nat > nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Option__Ooption_Itf__b_J_J,type,
% 3.75/2.04 size_s1671393719tion_b: list_option_b > nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__b_J,type,
% 3.75/2.04 size_size_list_b: list_b > nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Option__Ooption_Itf__b_J_J,type,
% 3.75/2.04 size_s684879735tion_b: option_option_b > nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_Itf__b_J,type,
% 3.75/2.04 size_size_option_b: option_b > nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Nat__Bijection_Otriangle,type,
% 3.75/2.04 nat_triangle: nat > nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Option_Ooption_ONone_001t__Option__Ooption_Itf__b_J,type,
% 3.75/2.04 none_option_b: option_option_b ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Option_Ooption_ONone_001tf__b,type,
% 3.75/2.04 none_b: option_b ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Option_Ooption_OSome_001t__Option__Ooption_Itf__b_J,type,
% 3.75/2.04 some_option_b: option_b > option_option_b ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Option_Ooption_OSome_001tf__b,type,
% 3.75/2.04 some_b: b > option_b ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Option_Ooption_Osize__option_001t__Option__Ooption_Itf__b_J,type,
% 3.75/2.04 size_option_option_b: ( option_b > nat ) > option_option_b > nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Option_Ooption_Osize__option_001tf__b,type,
% 3.75/2.04 size_option_b: ( b > nat ) > option_b > nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 3.75/2.04 ord_less_int: int > int > $o ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 3.75/2.04 ord_less_nat: nat > nat > $o ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 3.75/2.04 ord_less_eq_nat: nat > nat > $o ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 3.75/2.04 collect_nat: ( nat > $o ) > set_nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_c_member_001t__Nat__Onat,type,
% 3.75/2.04 member_nat: nat > set_nat > $o ).
% 3.75/2.04
% 3.75/2.04 thf(sy_v__092_060phi_062,type,
% 3.75/2.04 phi: formula_a ).
% 3.75/2.04
% 3.75/2.04 thf(sy_v_b,type,
% 3.75/2.04 b2: nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_v_n,type,
% 3.75/2.04 n: nat ).
% 3.75/2.04
% 3.75/2.04 thf(sy_v_v,type,
% 3.75/2.04 v: list_option_b ).
% 3.75/2.04
% 3.75/2.04 thf(sy_v_x,type,
% 3.75/2.04 x: b ).
% 3.75/2.04
% 3.75/2.04 thf(fact_0_nth__Cons__Suc,axiom,
% 3.75/2.04 ! [X: b,Xs: list_b,N: nat] :
% 3.75/2.04 ( ( nth_b @ ( cons_b @ X @ Xs ) @ ( suc @ N ) )
% 3.75/2.04 = ( nth_b @ Xs @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_1_nth__Cons__Suc,axiom,
% 3.75/2.04 ! [X: option_b,Xs: list_option_b,N: nat] :
% 3.75/2.04 ( ( nth_option_b @ ( cons_option_b @ X @ Xs ) @ ( suc @ N ) )
% 3.75/2.04 = ( nth_option_b @ Xs @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_2_nth__Cons__0,axiom,
% 3.75/2.04 ! [X: b,Xs: list_b] :
% 3.75/2.04 ( ( nth_b @ ( cons_b @ X @ Xs ) @ zero_zero_nat )
% 3.75/2.04 = X ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_3_nth__Cons__0,axiom,
% 3.75/2.04 ! [X: option_b,Xs: list_option_b] :
% 3.75/2.04 ( ( nth_option_b @ ( cons_option_b @ X @ Xs ) @ zero_zero_nat )
% 3.75/2.04 = X ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_4_less__Suc0,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 3.75/2.04 = ( N = zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_5_zero__less__Suc,axiom,
% 3.75/2.04 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_6_not__None__eq,axiom,
% 3.75/2.04 ! [X: option_option_b] :
% 3.75/2.04 ( ( X != none_option_b )
% 3.75/2.04 = ( ? [Y: option_b] :
% 3.75/2.04 ( X
% 3.75/2.04 = ( some_option_b @ Y ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_7_not__None__eq,axiom,
% 3.75/2.04 ! [X: option_b] :
% 3.75/2.04 ( ( X != none_b )
% 3.75/2.04 = ( ? [Y: b] :
% 3.75/2.04 ( X
% 3.75/2.04 = ( some_b @ Y ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_8_not__Some__eq,axiom,
% 3.75/2.04 ! [X: option_option_b] :
% 3.75/2.04 ( ( ! [Y: option_b] :
% 3.75/2.04 ( X
% 3.75/2.04 != ( some_option_b @ Y ) ) )
% 3.75/2.04 = ( X = none_option_b ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_9_not__Some__eq,axiom,
% 3.75/2.04 ! [X: option_b] :
% 3.75/2.04 ( ( ! [Y: b] :
% 3.75/2.04 ( X
% 3.75/2.04 != ( some_b @ Y ) ) )
% 3.75/2.04 = ( X = none_b ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_10_lessI,axiom,
% 3.75/2.04 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_11_Suc__mono,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ M @ N )
% 3.75/2.04 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_12_Suc__less__eq,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 3.75/2.04 = ( ord_less_nat @ M @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_13_neq0__conv,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( N != zero_zero_nat )
% 3.75/2.04 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_14_less__nat__zero__code,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_15_bot__nat__0_Onot__eq__extremum,axiom,
% 3.75/2.04 ! [A: nat] :
% 3.75/2.04 ( ( A != zero_zero_nat )
% 3.75/2.04 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_16_list_Oinject,axiom,
% 3.75/2.04 ! [X21: b,X22: list_b,Y21: b,Y22: list_b] :
% 3.75/2.04 ( ( ( cons_b @ X21 @ X22 )
% 3.75/2.04 = ( cons_b @ Y21 @ Y22 ) )
% 3.75/2.04 = ( ( X21 = Y21 )
% 3.75/2.04 & ( X22 = Y22 ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_17_list_Oinject,axiom,
% 3.75/2.04 ! [X21: option_b,X22: list_option_b,Y21: option_b,Y22: list_option_b] :
% 3.75/2.04 ( ( ( cons_option_b @ X21 @ X22 )
% 3.75/2.04 = ( cons_option_b @ Y21 @ Y22 ) )
% 3.75/2.04 = ( ( X21 = Y21 )
% 3.75/2.04 & ( X22 = Y22 ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_18_old_Onat_Oinject,axiom,
% 3.75/2.04 ! [Nat: nat,Nat2: nat] :
% 3.75/2.04 ( ( ( suc @ Nat )
% 3.75/2.04 = ( suc @ Nat2 ) )
% 3.75/2.04 = ( Nat = Nat2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_19_nat_Oinject,axiom,
% 3.75/2.04 ! [X2: nat,Y2: nat] :
% 3.75/2.04 ( ( ( suc @ X2 )
% 3.75/2.04 = ( suc @ Y2 ) )
% 3.75/2.04 = ( X2 = Y2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_20_option_Oinject,axiom,
% 3.75/2.04 ! [X2: option_b,Y2: option_b] :
% 3.75/2.04 ( ( ( some_option_b @ X2 )
% 3.75/2.04 = ( some_option_b @ Y2 ) )
% 3.75/2.04 = ( X2 = Y2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_21_option_Oinject,axiom,
% 3.75/2.04 ! [X2: b,Y2: b] :
% 3.75/2.04 ( ( ( some_b @ X2 )
% 3.75/2.04 = ( some_b @ Y2 ) )
% 3.75/2.04 = ( X2 = Y2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_22_not__Cons__self2,axiom,
% 3.75/2.04 ! [X: b,Xs: list_b] :
% 3.75/2.04 ( ( cons_b @ X @ Xs )
% 3.75/2.04 != Xs ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_23_not__Cons__self2,axiom,
% 3.75/2.04 ! [X: option_b,Xs: list_option_b] :
% 3.75/2.04 ( ( cons_option_b @ X @ Xs )
% 3.75/2.04 != Xs ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_24_n__not__Suc__n,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( N
% 3.75/2.04 != ( suc @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_25_Suc__inject,axiom,
% 3.75/2.04 ! [X: nat,Y3: nat] :
% 3.75/2.04 ( ( ( suc @ X )
% 3.75/2.04 = ( suc @ Y3 ) )
% 3.75/2.04 => ( X = Y3 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_26_linorder__neqE__nat,axiom,
% 3.75/2.04 ! [X: nat,Y3: nat] :
% 3.75/2.04 ( ( X != Y3 )
% 3.75/2.04 => ( ~ ( ord_less_nat @ X @ Y3 )
% 3.75/2.04 => ( ord_less_nat @ Y3 @ X ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_27_infinite__descent,axiom,
% 3.75/2.04 ! [P: nat > $o,N: nat] :
% 3.75/2.04 ( ! [N2: nat] :
% 3.75/2.04 ( ~ ( P @ N2 )
% 3.75/2.04 => ? [M2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ M2 @ N2 )
% 3.75/2.04 & ~ ( P @ M2 ) ) )
% 3.75/2.04 => ( P @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_28_nat__less__induct,axiom,
% 3.75/2.04 ! [P: nat > $o,N: nat] :
% 3.75/2.04 ( ! [N2: nat] :
% 3.75/2.04 ( ! [M2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ M2 @ N2 )
% 3.75/2.04 => ( P @ M2 ) )
% 3.75/2.04 => ( P @ N2 ) )
% 3.75/2.04 => ( P @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_29_less__irrefl__nat,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ~ ( ord_less_nat @ N @ N ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_30_less__not__refl3,axiom,
% 3.75/2.04 ! [S: nat,T: nat] :
% 3.75/2.04 ( ( ord_less_nat @ S @ T )
% 3.75/2.04 => ( S != T ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_31_less__not__refl2,axiom,
% 3.75/2.04 ! [N: nat,M: nat] :
% 3.75/2.04 ( ( ord_less_nat @ N @ M )
% 3.75/2.04 => ( M != N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_32_less__not__refl,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ~ ( ord_less_nat @ N @ N ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_33_nat__neq__iff,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( M != N )
% 3.75/2.04 = ( ( ord_less_nat @ M @ N )
% 3.75/2.04 | ( ord_less_nat @ N @ M ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_34_size__neq__size__imp__neq,axiom,
% 3.75/2.04 ! [X: option_b,Y3: option_b] :
% 3.75/2.04 ( ( ( size_size_option_b @ X )
% 3.75/2.04 != ( size_size_option_b @ Y3 ) )
% 3.75/2.04 => ( X != Y3 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_35_size__neq__size__imp__neq,axiom,
% 3.75/2.04 ! [X: list_b,Y3: list_b] :
% 3.75/2.04 ( ( ( size_size_list_b @ X )
% 3.75/2.04 != ( size_size_list_b @ Y3 ) )
% 3.75/2.04 => ( X != Y3 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_36_size__neq__size__imp__neq,axiom,
% 3.75/2.04 ! [X: list_option_b,Y3: list_option_b] :
% 3.75/2.04 ( ( ( size_s1671393719tion_b @ X )
% 3.75/2.04 != ( size_s1671393719tion_b @ Y3 ) )
% 3.75/2.04 => ( X != Y3 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_37_neq__if__length__neq,axiom,
% 3.75/2.04 ! [Xs: list_b,Ys: list_b] :
% 3.75/2.04 ( ( ( size_size_list_b @ Xs )
% 3.75/2.04 != ( size_size_list_b @ Ys ) )
% 3.75/2.04 => ( Xs != Ys ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_38_neq__if__length__neq,axiom,
% 3.75/2.04 ! [Xs: list_option_b,Ys: list_option_b] :
% 3.75/2.04 ( ( ( size_s1671393719tion_b @ Xs )
% 3.75/2.04 != ( size_s1671393719tion_b @ Ys ) )
% 3.75/2.04 => ( Xs != Ys ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_39_Ex__list__of__length,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ? [Xs2: list_b] :
% 3.75/2.04 ( ( size_size_list_b @ Xs2 )
% 3.75/2.04 = N ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_40_Ex__list__of__length,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ? [Xs2: list_option_b] :
% 3.75/2.04 ( ( size_s1671393719tion_b @ Xs2 )
% 3.75/2.04 = N ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_41_not0__implies__Suc,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( N != zero_zero_nat )
% 3.75/2.04 => ? [M3: nat] :
% 3.75/2.04 ( N
% 3.75/2.04 = ( suc @ M3 ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_42_old_Onat_Oinducts,axiom,
% 3.75/2.04 ! [P: nat > $o,Nat: nat] :
% 3.75/2.04 ( ( P @ zero_zero_nat )
% 3.75/2.04 => ( ! [Nat3: nat] :
% 3.75/2.04 ( ( P @ Nat3 )
% 3.75/2.04 => ( P @ ( suc @ Nat3 ) ) )
% 3.75/2.04 => ( P @ Nat ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_43_old_Onat_Oexhaust,axiom,
% 3.75/2.04 ! [Y3: nat] :
% 3.75/2.04 ( ( Y3 != zero_zero_nat )
% 3.75/2.04 => ~ ! [Nat3: nat] :
% 3.75/2.04 ( Y3
% 3.75/2.04 != ( suc @ Nat3 ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_44_Zero__not__Suc,axiom,
% 3.75/2.04 ! [M: nat] :
% 3.75/2.04 ( zero_zero_nat
% 3.75/2.04 != ( suc @ M ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_45_Zero__neq__Suc,axiom,
% 3.75/2.04 ! [M: nat] :
% 3.75/2.04 ( zero_zero_nat
% 3.75/2.04 != ( suc @ M ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_46_Suc__neq__Zero,axiom,
% 3.75/2.04 ! [M: nat] :
% 3.75/2.04 ( ( suc @ M )
% 3.75/2.04 != zero_zero_nat ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_47_zero__induct,axiom,
% 3.75/2.04 ! [P: nat > $o,K: nat] :
% 3.75/2.04 ( ( P @ K )
% 3.75/2.04 => ( ! [N2: nat] :
% 3.75/2.04 ( ( P @ ( suc @ N2 ) )
% 3.75/2.04 => ( P @ N2 ) )
% 3.75/2.04 => ( P @ zero_zero_nat ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_48_diff__induct,axiom,
% 3.75/2.04 ! [P: nat > nat > $o,M: nat,N: nat] :
% 3.75/2.04 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 3.75/2.04 => ( ! [Y4: nat] : ( P @ zero_zero_nat @ ( suc @ Y4 ) )
% 3.75/2.04 => ( ! [X3: nat,Y4: nat] :
% 3.75/2.04 ( ( P @ X3 @ Y4 )
% 3.75/2.04 => ( P @ ( suc @ X3 ) @ ( suc @ Y4 ) ) )
% 3.75/2.04 => ( P @ M @ N ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_49_nat__induct,axiom,
% 3.75/2.04 ! [P: nat > $o,N: nat] :
% 3.75/2.04 ( ( P @ zero_zero_nat )
% 3.75/2.04 => ( ! [N2: nat] :
% 3.75/2.04 ( ( P @ N2 )
% 3.75/2.04 => ( P @ ( suc @ N2 ) ) )
% 3.75/2.04 => ( P @ N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_50_mem__Collect__eq,axiom,
% 3.75/2.04 ! [A: nat,P: nat > $o] :
% 3.75/2.04 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 3.75/2.04 = ( P @ A ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_51_Collect__mem__eq,axiom,
% 3.75/2.04 ! [A2: set_nat] :
% 3.75/2.04 ( ( collect_nat
% 3.75/2.04 @ ^ [X4: nat] : ( member_nat @ X4 @ A2 ) )
% 3.75/2.04 = A2 ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_52_Collect__cong,axiom,
% 3.75/2.04 ! [P: nat > $o,Q: nat > $o] :
% 3.75/2.04 ( ! [X3: nat] :
% 3.75/2.04 ( ( P @ X3 )
% 3.75/2.04 = ( Q @ X3 ) )
% 3.75/2.04 => ( ( collect_nat @ P )
% 3.75/2.04 = ( collect_nat @ Q ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_53_nat_OdiscI,axiom,
% 3.75/2.04 ! [Nat: nat,X2: nat] :
% 3.75/2.04 ( ( Nat
% 3.75/2.04 = ( suc @ X2 ) )
% 3.75/2.04 => ( Nat != zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_54_old_Onat_Odistinct_I1_J,axiom,
% 3.75/2.04 ! [Nat2: nat] :
% 3.75/2.04 ( zero_zero_nat
% 3.75/2.04 != ( suc @ Nat2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_55_old_Onat_Odistinct_I2_J,axiom,
% 3.75/2.04 ! [Nat2: nat] :
% 3.75/2.04 ( ( suc @ Nat2 )
% 3.75/2.04 != zero_zero_nat ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_56_nat_Odistinct_I1_J,axiom,
% 3.75/2.04 ! [X2: nat] :
% 3.75/2.04 ( zero_zero_nat
% 3.75/2.04 != ( suc @ X2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_57_bot__nat__0_Oextremum__strict,axiom,
% 3.75/2.04 ! [A: nat] :
% 3.75/2.04 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_58_infinite__descent0,axiom,
% 3.75/2.04 ! [P: nat > $o,N: nat] :
% 3.75/2.04 ( ( P @ zero_zero_nat )
% 3.75/2.04 => ( ! [N2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.75/2.04 => ( ~ ( P @ N2 )
% 3.75/2.04 => ? [M2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ M2 @ N2 )
% 3.75/2.04 & ~ ( P @ M2 ) ) ) )
% 3.75/2.04 => ( P @ N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_59_gr__implies__not0,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ M @ N )
% 3.75/2.04 => ( N != zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_60_less__zeroE,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_61_not__less0,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_62_not__gr0,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 3.75/2.04 = ( N = zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_63_gr0I,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( N != zero_zero_nat )
% 3.75/2.04 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_64_not__less__less__Suc__eq,axiom,
% 3.75/2.04 ! [N: nat,M: nat] :
% 3.75/2.04 ( ~ ( ord_less_nat @ N @ M )
% 3.75/2.04 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 3.75/2.04 = ( N = M ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_65_strict__inc__induct,axiom,
% 3.75/2.04 ! [I: nat,J: nat,P: nat > $o] :
% 3.75/2.04 ( ( ord_less_nat @ I @ J )
% 3.75/2.04 => ( ! [I2: nat] :
% 3.75/2.04 ( ( J
% 3.75/2.04 = ( suc @ I2 ) )
% 3.75/2.04 => ( P @ I2 ) )
% 3.75/2.04 => ( ! [I2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I2 @ J )
% 3.75/2.04 => ( ( P @ ( suc @ I2 ) )
% 3.75/2.04 => ( P @ I2 ) ) )
% 3.75/2.04 => ( P @ I ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_66_less__Suc__induct,axiom,
% 3.75/2.04 ! [I: nat,J: nat,P: nat > nat > $o] :
% 3.75/2.04 ( ( ord_less_nat @ I @ J )
% 3.75/2.04 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 3.75/2.04 => ( ! [I2: nat,J2: nat,K2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I2 @ J2 )
% 3.75/2.04 => ( ( ord_less_nat @ J2 @ K2 )
% 3.75/2.04 => ( ( P @ I2 @ J2 )
% 3.75/2.04 => ( ( P @ J2 @ K2 )
% 3.75/2.04 => ( P @ I2 @ K2 ) ) ) ) )
% 3.75/2.04 => ( P @ I @ J ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_67_less__trans__Suc,axiom,
% 3.75/2.04 ! [I: nat,J: nat,K: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I @ J )
% 3.75/2.04 => ( ( ord_less_nat @ J @ K )
% 3.75/2.04 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_68_Suc__less__SucD,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 3.75/2.04 => ( ord_less_nat @ M @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_69_less__antisym,axiom,
% 3.75/2.04 ! [N: nat,M: nat] :
% 3.75/2.04 ( ~ ( ord_less_nat @ N @ M )
% 3.75/2.04 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 3.75/2.04 => ( M = N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_70_Suc__less__eq2,axiom,
% 3.75/2.04 ! [N: nat,M: nat] :
% 3.75/2.04 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 3.75/2.04 = ( ? [M4: nat] :
% 3.75/2.04 ( ( M
% 3.75/2.04 = ( suc @ M4 ) )
% 3.75/2.04 & ( ord_less_nat @ N @ M4 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_71_All__less__Suc,axiom,
% 3.75/2.04 ! [N: nat,P: nat > $o] :
% 3.75/2.04 ( ( ! [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 3.75/2.04 => ( P @ I3 ) ) )
% 3.75/2.04 = ( ( P @ N )
% 3.75/2.04 & ! [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ N )
% 3.75/2.04 => ( P @ I3 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_72_not__less__eq,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ~ ( ord_less_nat @ M @ N ) )
% 3.75/2.04 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_73_less__Suc__eq,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 3.75/2.04 = ( ( ord_less_nat @ M @ N )
% 3.75/2.04 | ( M = N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_74_Ex__less__Suc,axiom,
% 3.75/2.04 ! [N: nat,P: nat > $o] :
% 3.75/2.04 ( ( ? [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 3.75/2.04 & ( P @ I3 ) ) )
% 3.75/2.04 = ( ( P @ N )
% 3.75/2.04 | ? [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ N )
% 3.75/2.04 & ( P @ I3 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_75_less__SucI,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ M @ N )
% 3.75/2.04 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_76_less__SucE,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 3.75/2.04 => ( ~ ( ord_less_nat @ M @ N )
% 3.75/2.04 => ( M = N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_77_Suc__lessI,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ M @ N )
% 3.75/2.04 => ( ( ( suc @ M )
% 3.75/2.04 != N )
% 3.75/2.04 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_78_Suc__lessE,axiom,
% 3.75/2.04 ! [I: nat,K: nat] :
% 3.75/2.04 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 3.75/2.04 => ~ ! [J2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I @ J2 )
% 3.75/2.04 => ( K
% 3.75/2.04 != ( suc @ J2 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_79_Suc__lessD,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 3.75/2.04 => ( ord_less_nat @ M @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_80_Nat_OlessE,axiom,
% 3.75/2.04 ! [I: nat,K: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I @ K )
% 3.75/2.04 => ( ( K
% 3.75/2.04 != ( suc @ I ) )
% 3.75/2.04 => ~ ! [J2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I @ J2 )
% 3.75/2.04 => ( K
% 3.75/2.04 != ( suc @ J2 ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_81_length__induct,axiom,
% 3.75/2.04 ! [P: list_b > $o,Xs: list_b] :
% 3.75/2.04 ( ! [Xs2: list_b] :
% 3.75/2.04 ( ! [Ys2: list_b] :
% 3.75/2.04 ( ( ord_less_nat @ ( size_size_list_b @ Ys2 ) @ ( size_size_list_b @ Xs2 ) )
% 3.75/2.04 => ( P @ Ys2 ) )
% 3.75/2.04 => ( P @ Xs2 ) )
% 3.75/2.04 => ( P @ Xs ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_82_length__induct,axiom,
% 3.75/2.04 ! [P: list_option_b > $o,Xs: list_option_b] :
% 3.75/2.04 ( ! [Xs2: list_option_b] :
% 3.75/2.04 ( ! [Ys2: list_option_b] :
% 3.75/2.04 ( ( ord_less_nat @ ( size_s1671393719tion_b @ Ys2 ) @ ( size_s1671393719tion_b @ Xs2 ) )
% 3.75/2.04 => ( P @ Ys2 ) )
% 3.75/2.04 => ( P @ Xs2 ) )
% 3.75/2.04 => ( P @ Xs ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_83_combine__options__cases,axiom,
% 3.75/2.04 ! [X: option_b,P: option_b > option_option_b > $o,Y3: option_option_b] :
% 3.75/2.04 ( ( ( X = none_b )
% 3.75/2.04 => ( P @ X @ Y3 ) )
% 3.75/2.04 => ( ( ( Y3 = none_option_b )
% 3.75/2.04 => ( P @ X @ Y3 ) )
% 3.75/2.04 => ( ! [A3: b,B: option_b] :
% 3.75/2.04 ( ( X
% 3.75/2.04 = ( some_b @ A3 ) )
% 3.75/2.04 => ( ( Y3
% 3.75/2.04 = ( some_option_b @ B ) )
% 3.75/2.04 => ( P @ X @ Y3 ) ) )
% 3.75/2.04 => ( P @ X @ Y3 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_84_combine__options__cases,axiom,
% 3.75/2.04 ! [X: option_option_b,P: option_option_b > option_b > $o,Y3: option_b] :
% 3.75/2.04 ( ( ( X = none_option_b )
% 3.75/2.04 => ( P @ X @ Y3 ) )
% 3.75/2.04 => ( ( ( Y3 = none_b )
% 3.75/2.04 => ( P @ X @ Y3 ) )
% 3.75/2.04 => ( ! [A3: option_b,B: b] :
% 3.75/2.04 ( ( X
% 3.75/2.04 = ( some_option_b @ A3 ) )
% 3.75/2.04 => ( ( Y3
% 3.75/2.04 = ( some_b @ B ) )
% 3.75/2.04 => ( P @ X @ Y3 ) ) )
% 3.75/2.04 => ( P @ X @ Y3 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_85_combine__options__cases,axiom,
% 3.75/2.04 ! [X: option_option_b,P: option_option_b > option_option_b > $o,Y3: option_option_b] :
% 3.75/2.04 ( ( ( X = none_option_b )
% 3.75/2.04 => ( P @ X @ Y3 ) )
% 3.75/2.04 => ( ( ( Y3 = none_option_b )
% 3.75/2.04 => ( P @ X @ Y3 ) )
% 3.75/2.04 => ( ! [A3: option_b,B: option_b] :
% 3.75/2.04 ( ( X
% 3.75/2.04 = ( some_option_b @ A3 ) )
% 3.75/2.04 => ( ( Y3
% 3.75/2.04 = ( some_option_b @ B ) )
% 3.75/2.04 => ( P @ X @ Y3 ) ) )
% 3.75/2.04 => ( P @ X @ Y3 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_86_combine__options__cases,axiom,
% 3.75/2.04 ! [X: option_b,P: option_b > option_b > $o,Y3: option_b] :
% 3.75/2.04 ( ( ( X = none_b )
% 3.75/2.04 => ( P @ X @ Y3 ) )
% 3.75/2.04 => ( ( ( Y3 = none_b )
% 3.75/2.04 => ( P @ X @ Y3 ) )
% 3.75/2.04 => ( ! [A3: b,B: b] :
% 3.75/2.04 ( ( X
% 3.75/2.04 = ( some_b @ A3 ) )
% 3.75/2.04 => ( ( Y3
% 3.75/2.04 = ( some_b @ B ) )
% 3.75/2.04 => ( P @ X @ Y3 ) ) )
% 3.75/2.04 => ( P @ X @ Y3 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_87_split__option__all,axiom,
% 3.75/2.04 ( ( ^ [P2: option_option_b > $o] :
% 3.75/2.04 ! [X5: option_option_b] : ( P2 @ X5 ) )
% 3.75/2.04 = ( ^ [P3: option_option_b > $o] :
% 3.75/2.04 ( ( P3 @ none_option_b )
% 3.75/2.04 & ! [X4: option_b] : ( P3 @ ( some_option_b @ X4 ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_88_split__option__all,axiom,
% 3.75/2.04 ( ( ^ [P2: option_b > $o] :
% 3.75/2.04 ! [X5: option_b] : ( P2 @ X5 ) )
% 3.75/2.04 = ( ^ [P3: option_b > $o] :
% 3.75/2.04 ( ( P3 @ none_b )
% 3.75/2.04 & ! [X4: b] : ( P3 @ ( some_b @ X4 ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_89_split__option__ex,axiom,
% 3.75/2.04 ( ( ^ [P2: option_option_b > $o] :
% 3.75/2.04 ? [X5: option_option_b] : ( P2 @ X5 ) )
% 3.75/2.04 = ( ^ [P3: option_option_b > $o] :
% 3.75/2.04 ( ( P3 @ none_option_b )
% 3.75/2.04 | ? [X4: option_b] : ( P3 @ ( some_option_b @ X4 ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_90_split__option__ex,axiom,
% 3.75/2.04 ( ( ^ [P2: option_b > $o] :
% 3.75/2.04 ? [X5: option_b] : ( P2 @ X5 ) )
% 3.75/2.04 = ( ^ [P3: option_b > $o] :
% 3.75/2.04 ( ( P3 @ none_b )
% 3.75/2.04 | ? [X4: b] : ( P3 @ ( some_b @ X4 ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_91_option_Oinducts,axiom,
% 3.75/2.04 ! [P: option_option_b > $o,Option: option_option_b] :
% 3.75/2.04 ( ( P @ none_option_b )
% 3.75/2.04 => ( ! [X3: option_b] : ( P @ ( some_option_b @ X3 ) )
% 3.75/2.04 => ( P @ Option ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_92_option_Oinducts,axiom,
% 3.75/2.04 ! [P: option_b > $o,Option: option_b] :
% 3.75/2.04 ( ( P @ none_b )
% 3.75/2.04 => ( ! [X3: b] : ( P @ ( some_b @ X3 ) )
% 3.75/2.04 => ( P @ Option ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_93_option_Oexhaust,axiom,
% 3.75/2.04 ! [Y3: option_option_b] :
% 3.75/2.04 ( ( Y3 != none_option_b )
% 3.75/2.04 => ~ ! [X23: option_b] :
% 3.75/2.04 ( Y3
% 3.75/2.04 != ( some_option_b @ X23 ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_94_option_Oexhaust,axiom,
% 3.75/2.04 ! [Y3: option_b] :
% 3.75/2.04 ( ( Y3 != none_b )
% 3.75/2.04 => ~ ! [X23: b] :
% 3.75/2.04 ( Y3
% 3.75/2.04 != ( some_b @ X23 ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_95_option_OdiscI,axiom,
% 3.75/2.04 ! [Option: option_option_b,X2: option_b] :
% 3.75/2.04 ( ( Option
% 3.75/2.04 = ( some_option_b @ X2 ) )
% 3.75/2.04 => ( Option != none_option_b ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_96_option_OdiscI,axiom,
% 3.75/2.04 ! [Option: option_b,X2: b] :
% 3.75/2.04 ( ( Option
% 3.75/2.04 = ( some_b @ X2 ) )
% 3.75/2.04 => ( Option != none_b ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_97_option_Odistinct_I1_J,axiom,
% 3.75/2.04 ! [X2: option_b] :
% 3.75/2.04 ( none_option_b
% 3.75/2.04 != ( some_option_b @ X2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_98_option_Odistinct_I1_J,axiom,
% 3.75/2.04 ! [X2: b] :
% 3.75/2.04 ( none_b
% 3.75/2.04 != ( some_b @ X2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_99_lift__Suc__mono__less__iff,axiom,
% 3.75/2.04 ! [F: nat > nat,N: nat,M: nat] :
% 3.75/2.04 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 3.75/2.04 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 3.75/2.04 = ( ord_less_nat @ N @ M ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_100_lift__Suc__mono__less__iff,axiom,
% 3.75/2.04 ! [F: nat > int,N: nat,M: nat] :
% 3.75/2.04 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 3.75/2.04 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 3.75/2.04 = ( ord_less_nat @ N @ M ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_101_lift__Suc__mono__less,axiom,
% 3.75/2.04 ! [F: nat > nat,N: nat,N3: nat] :
% 3.75/2.04 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 3.75/2.04 => ( ( ord_less_nat @ N @ N3 )
% 3.75/2.04 => ( ord_less_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_102_lift__Suc__mono__less,axiom,
% 3.75/2.04 ! [F: nat > int,N: nat,N3: nat] :
% 3.75/2.04 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 3.75/2.04 => ( ( ord_less_nat @ N @ N3 )
% 3.75/2.04 => ( ord_less_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_103_less__Suc__eq__0__disj,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 3.75/2.04 = ( ( M = zero_zero_nat )
% 3.75/2.04 | ? [J3: nat] :
% 3.75/2.04 ( ( M
% 3.75/2.04 = ( suc @ J3 ) )
% 3.75/2.04 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_104_gr0__implies__Suc,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.75/2.04 => ? [M3: nat] :
% 3.75/2.04 ( N
% 3.75/2.04 = ( suc @ M3 ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_105_All__less__Suc2,axiom,
% 3.75/2.04 ! [N: nat,P: nat > $o] :
% 3.75/2.04 ( ( ! [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 3.75/2.04 => ( P @ I3 ) ) )
% 3.75/2.04 = ( ( P @ zero_zero_nat )
% 3.75/2.04 & ! [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ N )
% 3.75/2.04 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_106_gr0__conv__Suc,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.75/2.04 = ( ? [M5: nat] :
% 3.75/2.04 ( N
% 3.75/2.04 = ( suc @ M5 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_107_Ex__less__Suc2,axiom,
% 3.75/2.04 ! [N: nat,P: nat > $o] :
% 3.75/2.04 ( ( ? [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 3.75/2.04 & ( P @ I3 ) ) )
% 3.75/2.04 = ( ( P @ zero_zero_nat )
% 3.75/2.04 | ? [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ N )
% 3.75/2.04 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_108_length__Suc__conv,axiom,
% 3.75/2.04 ! [Xs: list_b,N: nat] :
% 3.75/2.04 ( ( ( size_size_list_b @ Xs )
% 3.75/2.04 = ( suc @ N ) )
% 3.75/2.04 = ( ? [Y: b,Ys3: list_b] :
% 3.75/2.04 ( ( Xs
% 3.75/2.04 = ( cons_b @ Y @ Ys3 ) )
% 3.75/2.04 & ( ( size_size_list_b @ Ys3 )
% 3.75/2.04 = N ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_109_length__Suc__conv,axiom,
% 3.75/2.04 ! [Xs: list_option_b,N: nat] :
% 3.75/2.04 ( ( ( size_s1671393719tion_b @ Xs )
% 3.75/2.04 = ( suc @ N ) )
% 3.75/2.04 = ( ? [Y: option_b,Ys3: list_option_b] :
% 3.75/2.04 ( ( Xs
% 3.75/2.04 = ( cons_option_b @ Y @ Ys3 ) )
% 3.75/2.04 & ( ( size_s1671393719tion_b @ Ys3 )
% 3.75/2.04 = N ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_110_Suc__length__conv,axiom,
% 3.75/2.04 ! [N: nat,Xs: list_b] :
% 3.75/2.04 ( ( ( suc @ N )
% 3.75/2.04 = ( size_size_list_b @ Xs ) )
% 3.75/2.04 = ( ? [Y: b,Ys3: list_b] :
% 3.75/2.04 ( ( Xs
% 3.75/2.04 = ( cons_b @ Y @ Ys3 ) )
% 3.75/2.04 & ( ( size_size_list_b @ Ys3 )
% 3.75/2.04 = N ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_111_Suc__length__conv,axiom,
% 3.75/2.04 ! [N: nat,Xs: list_option_b] :
% 3.75/2.04 ( ( ( suc @ N )
% 3.75/2.04 = ( size_s1671393719tion_b @ Xs ) )
% 3.75/2.04 = ( ? [Y: option_b,Ys3: list_option_b] :
% 3.75/2.04 ( ( Xs
% 3.75/2.04 = ( cons_option_b @ Y @ Ys3 ) )
% 3.75/2.04 & ( ( size_s1671393719tion_b @ Ys3 )
% 3.75/2.04 = N ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_112_list__eq__iff__nth__eq,axiom,
% 3.75/2.04 ( ( ^ [Y5: list_b,Z: list_b] : ( Y5 = Z ) )
% 3.75/2.04 = ( ^ [Xs3: list_b,Ys3: list_b] :
% 3.75/2.04 ( ( ( size_size_list_b @ Xs3 )
% 3.75/2.04 = ( size_size_list_b @ Ys3 ) )
% 3.75/2.04 & ! [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ ( size_size_list_b @ Xs3 ) )
% 3.75/2.04 => ( ( nth_b @ Xs3 @ I3 )
% 3.75/2.04 = ( nth_b @ Ys3 @ I3 ) ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_113_list__eq__iff__nth__eq,axiom,
% 3.75/2.04 ( ( ^ [Y5: list_option_b,Z: list_option_b] : ( Y5 = Z ) )
% 3.75/2.04 = ( ^ [Xs3: list_option_b,Ys3: list_option_b] :
% 3.75/2.04 ( ( ( size_s1671393719tion_b @ Xs3 )
% 3.75/2.04 = ( size_s1671393719tion_b @ Ys3 ) )
% 3.75/2.04 & ! [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ ( size_s1671393719tion_b @ Xs3 ) )
% 3.75/2.04 => ( ( nth_option_b @ Xs3 @ I3 )
% 3.75/2.04 = ( nth_option_b @ Ys3 @ I3 ) ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_114_Skolem__list__nth,axiom,
% 3.75/2.04 ! [K: nat,P: nat > b > $o] :
% 3.75/2.04 ( ( ! [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ K )
% 3.75/2.04 => ? [X5: b] : ( P @ I3 @ X5 ) ) )
% 3.75/2.04 = ( ? [Xs3: list_b] :
% 3.75/2.04 ( ( ( size_size_list_b @ Xs3 )
% 3.75/2.04 = K )
% 3.75/2.04 & ! [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ K )
% 3.75/2.04 => ( P @ I3 @ ( nth_b @ Xs3 @ I3 ) ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_115_Skolem__list__nth,axiom,
% 3.75/2.04 ! [K: nat,P: nat > option_b > $o] :
% 3.75/2.04 ( ( ! [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ K )
% 3.75/2.04 => ? [X5: option_b] : ( P @ I3 @ X5 ) ) )
% 3.75/2.04 = ( ? [Xs3: list_option_b] :
% 3.75/2.04 ( ( ( size_s1671393719tion_b @ Xs3 )
% 3.75/2.04 = K )
% 3.75/2.04 & ! [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ K )
% 3.75/2.04 => ( P @ I3 @ ( nth_option_b @ Xs3 @ I3 ) ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_116_nth__equalityI,axiom,
% 3.75/2.04 ! [Xs: list_b,Ys: list_b] :
% 3.75/2.04 ( ( ( size_size_list_b @ Xs )
% 3.75/2.04 = ( size_size_list_b @ Ys ) )
% 3.75/2.04 => ( ! [I2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I2 @ ( size_size_list_b @ Xs ) )
% 3.75/2.04 => ( ( nth_b @ Xs @ I2 )
% 3.75/2.04 = ( nth_b @ Ys @ I2 ) ) )
% 3.75/2.04 => ( Xs = Ys ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_117_nth__equalityI,axiom,
% 3.75/2.04 ! [Xs: list_option_b,Ys: list_option_b] :
% 3.75/2.04 ( ( ( size_s1671393719tion_b @ Xs )
% 3.75/2.04 = ( size_s1671393719tion_b @ Ys ) )
% 3.75/2.04 => ( ! [I2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I2 @ ( size_s1671393719tion_b @ Xs ) )
% 3.75/2.04 => ( ( nth_option_b @ Xs @ I2 )
% 3.75/2.04 = ( nth_option_b @ Ys @ I2 ) ) )
% 3.75/2.04 => ( Xs = Ys ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_118_not__gr__zero,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 3.75/2.04 = ( N = zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_119_fvi__Suc__bound,axiom,
% 3.75/2.04 ! [B2: nat,Phi: formula_a,N: nat] :
% 3.75/2.04 ( ! [X3: nat] :
% 3.75/2.04 ( ( member_nat @ X3 @ ( fvi_a @ ( suc @ B2 ) @ Phi ) )
% 3.75/2.04 => ( ord_less_nat @ X3 @ N ) )
% 3.75/2.04 => ! [X6: nat] :
% 3.75/2.04 ( ( member_nat @ X6 @ ( fvi_a @ B2 @ Phi ) )
% 3.75/2.04 => ( ord_less_nat @ X6 @ ( suc @ N ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_120_length__Cons,axiom,
% 3.75/2.04 ! [X: b,Xs: list_b] :
% 3.75/2.04 ( ( size_size_list_b @ ( cons_b @ X @ Xs ) )
% 3.75/2.04 = ( suc @ ( size_size_list_b @ Xs ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_121_length__Cons,axiom,
% 3.75/2.04 ! [X: option_b,Xs: list_option_b] :
% 3.75/2.04 ( ( size_s1671393719tion_b @ ( cons_option_b @ X @ Xs ) )
% 3.75/2.04 = ( suc @ ( size_s1671393719tion_b @ Xs ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_122_option_Osize__gen_I1_J,axiom,
% 3.75/2.04 ! [X: b > nat] :
% 3.75/2.04 ( ( size_option_b @ X @ none_b )
% 3.75/2.04 = ( suc @ zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_123_fvi__Suc,axiom,
% 3.75/2.04 ! [X: nat,B2: nat,Phi: formula_a] :
% 3.75/2.04 ( ( member_nat @ X @ ( fvi_a @ ( suc @ B2 ) @ Phi ) )
% 3.75/2.04 = ( member_nat @ ( suc @ X ) @ ( fvi_a @ B2 @ Phi ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_124_option_Osize_I4_J,axiom,
% 3.75/2.04 ! [X2: option_b] :
% 3.75/2.04 ( ( size_s684879735tion_b @ ( some_option_b @ X2 ) )
% 3.75/2.04 = ( suc @ zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_125_option_Osize_I4_J,axiom,
% 3.75/2.04 ! [X2: b] :
% 3.75/2.04 ( ( size_size_option_b @ ( some_b @ X2 ) )
% 3.75/2.04 = ( suc @ zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_126_option_Osize_I3_J,axiom,
% 3.75/2.04 ( ( size_size_option_b @ none_b )
% 3.75/2.04 = ( suc @ zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_127_find__Some__iff,axiom,
% 3.75/2.04 ! [P: b > $o,Xs: list_b,X: b] :
% 3.75/2.04 ( ( ( find_b @ P @ Xs )
% 3.75/2.04 = ( some_b @ X ) )
% 3.75/2.04 = ( ? [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ ( size_size_list_b @ Xs ) )
% 3.75/2.04 & ( P @ ( nth_b @ Xs @ I3 ) )
% 3.75/2.04 & ( X
% 3.75/2.04 = ( nth_b @ Xs @ I3 ) )
% 3.75/2.04 & ! [J3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ J3 @ I3 )
% 3.75/2.04 => ~ ( P @ ( nth_b @ Xs @ J3 ) ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_128_find__Some__iff,axiom,
% 3.75/2.04 ! [P: option_b > $o,Xs: list_option_b,X: option_b] :
% 3.75/2.04 ( ( ( find_option_b @ P @ Xs )
% 3.75/2.04 = ( some_option_b @ X ) )
% 3.75/2.04 = ( ? [I3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I3 @ ( size_s1671393719tion_b @ Xs ) )
% 3.75/2.04 & ( P @ ( nth_option_b @ Xs @ I3 ) )
% 3.75/2.04 & ( X
% 3.75/2.04 = ( nth_option_b @ Xs @ I3 ) )
% 3.75/2.04 & ! [J3: nat] :
% 3.75/2.04 ( ( ord_less_nat @ J3 @ I3 )
% 3.75/2.04 => ~ ( P @ ( nth_option_b @ Xs @ J3 ) ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_129_exists__least__lemma,axiom,
% 3.75/2.04 ! [P: nat > $o] :
% 3.75/2.04 ( ~ ( P @ zero_zero_nat )
% 3.75/2.04 => ( ? [X_1: nat] : ( P @ X_1 )
% 3.75/2.04 => ? [N2: nat] :
% 3.75/2.04 ( ~ ( P @ N2 )
% 3.75/2.04 & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_130_option_Osize__neq,axiom,
% 3.75/2.04 ! [X: option_b] :
% 3.75/2.04 ( ( size_size_option_b @ X )
% 3.75/2.04 != zero_zero_nat ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_131_zero__reorient,axiom,
% 3.75/2.04 ! [X: nat] :
% 3.75/2.04 ( ( zero_zero_nat = X )
% 3.75/2.04 = ( X = zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_132_zero__reorient,axiom,
% 3.75/2.04 ! [X: int] :
% 3.75/2.04 ( ( zero_zero_int = X )
% 3.75/2.04 = ( X = zero_zero_int ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_133_find_Osimps_I2_J,axiom,
% 3.75/2.04 ! [P: option_b > $o,X: option_b,Xs: list_option_b] :
% 3.75/2.04 ( ( ( P @ X )
% 3.75/2.04 => ( ( find_option_b @ P @ ( cons_option_b @ X @ Xs ) )
% 3.75/2.04 = ( some_option_b @ X ) ) )
% 3.75/2.04 & ( ~ ( P @ X )
% 3.75/2.04 => ( ( find_option_b @ P @ ( cons_option_b @ X @ Xs ) )
% 3.75/2.04 = ( find_option_b @ P @ Xs ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_134_find_Osimps_I2_J,axiom,
% 3.75/2.04 ! [P: b > $o,X: b,Xs: list_b] :
% 3.75/2.04 ( ( ( P @ X )
% 3.75/2.04 => ( ( find_b @ P @ ( cons_b @ X @ Xs ) )
% 3.75/2.04 = ( some_b @ X ) ) )
% 3.75/2.04 & ( ~ ( P @ X )
% 3.75/2.04 => ( ( find_b @ P @ ( cons_b @ X @ Xs ) )
% 3.75/2.04 = ( find_b @ P @ Xs ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_135_gr__zeroI,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( N != zero_zero_nat )
% 3.75/2.04 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_136_not__less__zero,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_137_gr__implies__not__zero,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ M @ N )
% 3.75/2.04 => ( N != zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_138_zero__less__iff__neq__zero,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.75/2.04 = ( N != zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_139_list__decode_Ocases,axiom,
% 3.75/2.04 ! [X: nat] :
% 3.75/2.04 ( ( X != zero_zero_nat )
% 3.75/2.04 => ~ ! [N2: nat] :
% 3.75/2.04 ( X
% 3.75/2.04 != ( suc @ N2 ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_140_less__numeral__extra_I3_J,axiom,
% 3.75/2.04 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_141_less__numeral__extra_I3_J,axiom,
% 3.75/2.04 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_142_length__code,axiom,
% 3.75/2.04 ( size_size_list_b
% 3.75/2.04 = ( gen_length_b @ zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_143_length__code,axiom,
% 3.75/2.04 ( size_s1671393719tion_b
% 3.75/2.04 = ( gen_length_option_b @ zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_144_gen__length__code_I2_J,axiom,
% 3.75/2.04 ! [N: nat,X: b,Xs: list_b] :
% 3.75/2.04 ( ( gen_length_b @ N @ ( cons_b @ X @ Xs ) )
% 3.75/2.04 = ( gen_length_b @ ( suc @ N ) @ Xs ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_145_gen__length__code_I2_J,axiom,
% 3.75/2.04 ! [N: nat,X: option_b,Xs: list_option_b] :
% 3.75/2.04 ( ( gen_length_option_b @ N @ ( cons_option_b @ X @ Xs ) )
% 3.75/2.04 = ( gen_length_option_b @ ( suc @ N ) @ Xs ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_146_option_Osize__gen_I2_J,axiom,
% 3.75/2.04 ! [X: option_b > nat,X2: option_b] :
% 3.75/2.04 ( ( size_option_option_b @ X @ ( some_option_b @ X2 ) )
% 3.75/2.04 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_147_option_Osize__gen_I2_J,axiom,
% 3.75/2.04 ! [X: b > nat,X2: b] :
% 3.75/2.04 ( ( size_option_b @ X @ ( some_b @ X2 ) )
% 3.75/2.04 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_148_Cons__nth__drop__Suc,axiom,
% 3.75/2.04 ! [I: nat,Xs: list_b] :
% 3.75/2.04 ( ( ord_less_nat @ I @ ( size_size_list_b @ Xs ) )
% 3.75/2.04 => ( ( cons_b @ ( nth_b @ Xs @ I ) @ ( drop_b @ ( suc @ I ) @ Xs ) )
% 3.75/2.04 = ( drop_b @ I @ Xs ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_149_Cons__nth__drop__Suc,axiom,
% 3.75/2.04 ! [I: nat,Xs: list_option_b] :
% 3.75/2.04 ( ( ord_less_nat @ I @ ( size_s1671393719tion_b @ Xs ) )
% 3.75/2.04 => ( ( cons_option_b @ ( nth_option_b @ Xs @ I ) @ ( drop_option_b @ ( suc @ I ) @ Xs ) )
% 3.75/2.04 = ( drop_option_b @ I @ Xs ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_150_list__ex__length,axiom,
% 3.75/2.04 ( list_ex_b
% 3.75/2.04 = ( ^ [P3: b > $o,Xs3: list_b] :
% 3.75/2.04 ? [N4: nat] :
% 3.75/2.04 ( ( ord_less_nat @ N4 @ ( size_size_list_b @ Xs3 ) )
% 3.75/2.04 & ( P3 @ ( nth_b @ Xs3 @ N4 ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_151_list__ex__length,axiom,
% 3.75/2.04 ( list_ex_option_b
% 3.75/2.04 = ( ^ [P3: option_b > $o,Xs3: list_option_b] :
% 3.75/2.04 ? [N4: nat] :
% 3.75/2.04 ( ( ord_less_nat @ N4 @ ( size_s1671393719tion_b @ Xs3 ) )
% 3.75/2.04 & ( P3 @ ( nth_option_b @ Xs3 @ N4 ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_152_of__nat__0__less__iff,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) )
% 3.75/2.04 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_153_of__nat__0__less__iff,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( ord_less_int @ zero_zero_int @ ( semiri2019852685at_int @ N ) )
% 3.75/2.04 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_154_add__left__cancel,axiom,
% 3.75/2.04 ! [A: nat,B2: nat,C: nat] :
% 3.75/2.04 ( ( ( plus_plus_nat @ A @ B2 )
% 3.75/2.04 = ( plus_plus_nat @ A @ C ) )
% 3.75/2.04 = ( B2 = C ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_155_add__left__cancel,axiom,
% 3.75/2.04 ! [A: int,B2: int,C: int] :
% 3.75/2.04 ( ( ( plus_plus_int @ A @ B2 )
% 3.75/2.04 = ( plus_plus_int @ A @ C ) )
% 3.75/2.04 = ( B2 = C ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_156_add__right__cancel,axiom,
% 3.75/2.04 ! [B2: nat,A: nat,C: nat] :
% 3.75/2.04 ( ( ( plus_plus_nat @ B2 @ A )
% 3.75/2.04 = ( plus_plus_nat @ C @ A ) )
% 3.75/2.04 = ( B2 = C ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_157_add__right__cancel,axiom,
% 3.75/2.04 ! [B2: int,A: int,C: int] :
% 3.75/2.04 ( ( ( plus_plus_int @ B2 @ A )
% 3.75/2.04 = ( plus_plus_int @ C @ A ) )
% 3.75/2.04 = ( B2 = C ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_158_of__nat__eq__iff,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ( semiri1382578993at_nat @ M )
% 3.75/2.04 = ( semiri1382578993at_nat @ N ) )
% 3.75/2.04 = ( M = N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_159_of__nat__eq__iff,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ( semiri2019852685at_int @ M )
% 3.75/2.04 = ( semiri2019852685at_int @ N ) )
% 3.75/2.04 = ( M = N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_160_zero__eq__add__iff__both__eq__0,axiom,
% 3.75/2.04 ! [X: nat,Y3: nat] :
% 3.75/2.04 ( ( zero_zero_nat
% 3.75/2.04 = ( plus_plus_nat @ X @ Y3 ) )
% 3.75/2.04 = ( ( X = zero_zero_nat )
% 3.75/2.04 & ( Y3 = zero_zero_nat ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_161_add__eq__0__iff__both__eq__0,axiom,
% 3.75/2.04 ! [X: nat,Y3: nat] :
% 3.75/2.04 ( ( ( plus_plus_nat @ X @ Y3 )
% 3.75/2.04 = zero_zero_nat )
% 3.75/2.04 = ( ( X = zero_zero_nat )
% 3.75/2.04 & ( Y3 = zero_zero_nat ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_162_add__cancel__right__right,axiom,
% 3.75/2.04 ! [A: nat,B2: nat] :
% 3.75/2.04 ( ( A
% 3.75/2.04 = ( plus_plus_nat @ A @ B2 ) )
% 3.75/2.04 = ( B2 = zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_163_add__cancel__right__right,axiom,
% 3.75/2.04 ! [A: int,B2: int] :
% 3.75/2.04 ( ( A
% 3.75/2.04 = ( plus_plus_int @ A @ B2 ) )
% 3.75/2.04 = ( B2 = zero_zero_int ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_164_add__cancel__right__left,axiom,
% 3.75/2.04 ! [A: nat,B2: nat] :
% 3.75/2.04 ( ( A
% 3.75/2.04 = ( plus_plus_nat @ B2 @ A ) )
% 3.75/2.04 = ( B2 = zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_165_add__cancel__right__left,axiom,
% 3.75/2.04 ! [A: int,B2: int] :
% 3.75/2.04 ( ( A
% 3.75/2.04 = ( plus_plus_int @ B2 @ A ) )
% 3.75/2.04 = ( B2 = zero_zero_int ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_166_add__cancel__left__right,axiom,
% 3.75/2.04 ! [A: nat,B2: nat] :
% 3.75/2.04 ( ( ( plus_plus_nat @ A @ B2 )
% 3.75/2.04 = A )
% 3.75/2.04 = ( B2 = zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_167_add__cancel__left__right,axiom,
% 3.75/2.04 ! [A: int,B2: int] :
% 3.75/2.04 ( ( ( plus_plus_int @ A @ B2 )
% 3.75/2.04 = A )
% 3.75/2.04 = ( B2 = zero_zero_int ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_168_add__cancel__left__left,axiom,
% 3.75/2.04 ! [B2: nat,A: nat] :
% 3.75/2.04 ( ( ( plus_plus_nat @ B2 @ A )
% 3.75/2.04 = A )
% 3.75/2.04 = ( B2 = zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_169_add__cancel__left__left,axiom,
% 3.75/2.04 ! [B2: int,A: int] :
% 3.75/2.04 ( ( ( plus_plus_int @ B2 @ A )
% 3.75/2.04 = A )
% 3.75/2.04 = ( B2 = zero_zero_int ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_170_double__zero__sym,axiom,
% 3.75/2.04 ! [A: int] :
% 3.75/2.04 ( ( zero_zero_int
% 3.75/2.04 = ( plus_plus_int @ A @ A ) )
% 3.75/2.04 = ( A = zero_zero_int ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_171_double__zero,axiom,
% 3.75/2.04 ! [A: int] :
% 3.75/2.04 ( ( ( plus_plus_int @ A @ A )
% 3.75/2.04 = zero_zero_int )
% 3.75/2.04 = ( A = zero_zero_int ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_172_add_Oright__neutral,axiom,
% 3.75/2.04 ! [A: nat] :
% 3.75/2.04 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 3.75/2.04 = A ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_173_add_Oright__neutral,axiom,
% 3.75/2.04 ! [A: int] :
% 3.75/2.04 ( ( plus_plus_int @ A @ zero_zero_int )
% 3.75/2.04 = A ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_174_add_Oleft__neutral,axiom,
% 3.75/2.04 ! [A: nat] :
% 3.75/2.04 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 3.75/2.04 = A ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_175_add_Oleft__neutral,axiom,
% 3.75/2.04 ! [A: int] :
% 3.75/2.04 ( ( plus_plus_int @ zero_zero_int @ A )
% 3.75/2.04 = A ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_176_add__less__cancel__right,axiom,
% 3.75/2.04 ! [A: nat,C: nat,B2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 3.75/2.04 = ( ord_less_nat @ A @ B2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_177_add__less__cancel__right,axiom,
% 3.75/2.04 ! [A: int,C: int,B2: int] :
% 3.75/2.04 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 3.75/2.04 = ( ord_less_int @ A @ B2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_178_add__less__cancel__left,axiom,
% 3.75/2.04 ! [C: nat,A: nat,B2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 3.75/2.04 = ( ord_less_nat @ A @ B2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_179_add__less__cancel__left,axiom,
% 3.75/2.04 ! [C: int,A: int,B2: int] :
% 3.75/2.04 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 3.75/2.04 = ( ord_less_int @ A @ B2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_180_add__is__0,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ( plus_plus_nat @ M @ N )
% 3.75/2.04 = zero_zero_nat )
% 3.75/2.04 = ( ( M = zero_zero_nat )
% 3.75/2.04 & ( N = zero_zero_nat ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_181_Nat_Oadd__0__right,axiom,
% 3.75/2.04 ! [M: nat] :
% 3.75/2.04 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 3.75/2.04 = M ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_182_add__Suc__right,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 3.75/2.04 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_183_nat__add__left__cancel__less,axiom,
% 3.75/2.04 ! [K: nat,M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 3.75/2.04 = ( ord_less_nat @ M @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_184_drop0,axiom,
% 3.75/2.04 ( ( drop_option_b @ zero_zero_nat )
% 3.75/2.04 = ( ^ [X4: list_option_b] : X4 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_185_drop__drop,axiom,
% 3.75/2.04 ! [N: nat,M: nat,Xs: list_option_b] :
% 3.75/2.04 ( ( drop_option_b @ N @ ( drop_option_b @ M @ Xs ) )
% 3.75/2.04 = ( drop_option_b @ ( plus_plus_nat @ N @ M ) @ Xs ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_186_list__ex__simps_I1_J,axiom,
% 3.75/2.04 ! [P: b > $o,X: b,Xs: list_b] :
% 3.75/2.04 ( ( list_ex_b @ P @ ( cons_b @ X @ Xs ) )
% 3.75/2.04 = ( ( P @ X )
% 3.75/2.04 | ( list_ex_b @ P @ Xs ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_187_list__ex__simps_I1_J,axiom,
% 3.75/2.04 ! [P: option_b > $o,X: option_b,Xs: list_option_b] :
% 3.75/2.04 ( ( list_ex_option_b @ P @ ( cons_option_b @ X @ Xs ) )
% 3.75/2.04 = ( ( P @ X )
% 3.75/2.04 | ( list_ex_option_b @ P @ Xs ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_188_add__less__same__cancel1,axiom,
% 3.75/2.04 ! [B2: nat,A: nat] :
% 3.75/2.04 ( ( ord_less_nat @ ( plus_plus_nat @ B2 @ A ) @ B2 )
% 3.75/2.04 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_189_add__less__same__cancel1,axiom,
% 3.75/2.04 ! [B2: int,A: int] :
% 3.75/2.04 ( ( ord_less_int @ ( plus_plus_int @ B2 @ A ) @ B2 )
% 3.75/2.04 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_190_add__less__same__cancel2,axiom,
% 3.75/2.04 ! [A: nat,B2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B2 ) @ B2 )
% 3.75/2.04 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_191_add__less__same__cancel2,axiom,
% 3.75/2.04 ! [A: int,B2: int] :
% 3.75/2.04 ( ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ B2 )
% 3.75/2.04 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_192_less__add__same__cancel1,axiom,
% 3.75/2.04 ! [A: nat,B2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B2 ) )
% 3.75/2.04 = ( ord_less_nat @ zero_zero_nat @ B2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_193_less__add__same__cancel1,axiom,
% 3.75/2.04 ! [A: int,B2: int] :
% 3.75/2.04 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B2 ) )
% 3.75/2.04 = ( ord_less_int @ zero_zero_int @ B2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_194_less__add__same__cancel2,axiom,
% 3.75/2.04 ! [A: nat,B2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B2 @ A ) )
% 3.75/2.04 = ( ord_less_nat @ zero_zero_nat @ B2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_195_less__add__same__cancel2,axiom,
% 3.75/2.04 ! [A: int,B2: int] :
% 3.75/2.04 ( ( ord_less_int @ A @ ( plus_plus_int @ B2 @ A ) )
% 3.75/2.04 = ( ord_less_int @ zero_zero_int @ B2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_196_double__add__less__zero__iff__single__add__less__zero,axiom,
% 3.75/2.04 ! [A: int] :
% 3.75/2.04 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 3.75/2.04 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_197_zero__less__double__add__iff__zero__less__single__add,axiom,
% 3.75/2.04 ! [A: int] :
% 3.75/2.04 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 3.75/2.04 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_198_of__nat__0,axiom,
% 3.75/2.04 ( ( semiri1382578993at_nat @ zero_zero_nat )
% 3.75/2.04 = zero_zero_nat ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_199_of__nat__0,axiom,
% 3.75/2.04 ( ( semiri2019852685at_int @ zero_zero_nat )
% 3.75/2.04 = zero_zero_int ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_200_of__nat__0__eq__iff,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( zero_zero_nat
% 3.75/2.04 = ( semiri1382578993at_nat @ N ) )
% 3.75/2.04 = ( zero_zero_nat = N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_201_of__nat__0__eq__iff,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( zero_zero_int
% 3.75/2.04 = ( semiri2019852685at_int @ N ) )
% 3.75/2.04 = ( zero_zero_nat = N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_202_of__nat__eq__0__iff,axiom,
% 3.75/2.04 ! [M: nat] :
% 3.75/2.04 ( ( ( semiri1382578993at_nat @ M )
% 3.75/2.04 = zero_zero_nat )
% 3.75/2.04 = ( M = zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_203_of__nat__eq__0__iff,axiom,
% 3.75/2.04 ! [M: nat] :
% 3.75/2.04 ( ( ( semiri2019852685at_int @ M )
% 3.75/2.04 = zero_zero_int )
% 3.75/2.04 = ( M = zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_204_of__nat__less__iff,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
% 3.75/2.04 = ( ord_less_nat @ M @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_205_of__nat__less__iff,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) )
% 3.75/2.04 = ( ord_less_nat @ M @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_206_of__nat__add,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( semiri1382578993at_nat @ ( plus_plus_nat @ M @ N ) )
% 3.75/2.04 = ( plus_plus_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_207_of__nat__add,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( semiri2019852685at_int @ ( plus_plus_nat @ M @ N ) )
% 3.75/2.04 = ( plus_plus_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_208_add__gr__0,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 3.75/2.04 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 3.75/2.04 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_209_drop__Suc__Cons,axiom,
% 3.75/2.04 ! [N: nat,X: b,Xs: list_b] :
% 3.75/2.04 ( ( drop_b @ ( suc @ N ) @ ( cons_b @ X @ Xs ) )
% 3.75/2.04 = ( drop_b @ N @ Xs ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_210_drop__Suc__Cons,axiom,
% 3.75/2.04 ! [N: nat,X: option_b,Xs: list_option_b] :
% 3.75/2.04 ( ( drop_option_b @ ( suc @ N ) @ ( cons_option_b @ X @ Xs ) )
% 3.75/2.04 = ( drop_option_b @ N @ Xs ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_211_is__num__normalize_I1_J,axiom,
% 3.75/2.04 ! [A: int,B2: int,C: int] :
% 3.75/2.04 ( ( plus_plus_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 3.75/2.04 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_212_less__add__eq__less,axiom,
% 3.75/2.04 ! [K: nat,L: nat,M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ K @ L )
% 3.75/2.04 => ( ( ( plus_plus_nat @ M @ L )
% 3.75/2.04 = ( plus_plus_nat @ K @ N ) )
% 3.75/2.04 => ( ord_less_nat @ M @ N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_213_trans__less__add2,axiom,
% 3.75/2.04 ! [I: nat,J: nat,M: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I @ J )
% 3.75/2.04 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_214_trans__less__add1,axiom,
% 3.75/2.04 ! [I: nat,J: nat,M: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I @ J )
% 3.75/2.04 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_215_add__less__mono1,axiom,
% 3.75/2.04 ! [I: nat,J: nat,K: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I @ J )
% 3.75/2.04 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_216_not__add__less2,axiom,
% 3.75/2.04 ! [J: nat,I: nat] :
% 3.75/2.04 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_217_not__add__less1,axiom,
% 3.75/2.04 ! [I: nat,J: nat] :
% 3.75/2.04 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_218_add__less__mono,axiom,
% 3.75/2.04 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I @ J )
% 3.75/2.04 => ( ( ord_less_nat @ K @ L )
% 3.75/2.04 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_219_add__lessD1,axiom,
% 3.75/2.04 ! [I: nat,J: nat,K: nat] :
% 3.75/2.04 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 3.75/2.04 => ( ord_less_nat @ I @ K ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_220_add__Suc,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 3.75/2.04 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_221_nat__arith_Osuc1,axiom,
% 3.75/2.04 ! [A2: nat,K: nat,A: nat] :
% 3.75/2.04 ( ( A2
% 3.75/2.04 = ( plus_plus_nat @ K @ A ) )
% 3.75/2.04 => ( ( suc @ A2 )
% 3.75/2.04 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_222_add__Suc__shift,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 3.75/2.04 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_223_add__eq__self__zero,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ( plus_plus_nat @ M @ N )
% 3.75/2.04 = M )
% 3.75/2.04 => ( N = zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_224_plus__nat_Oadd__0,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 3.75/2.04 = N ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_225_drop__0,axiom,
% 3.75/2.04 ! [Xs: list_option_b] :
% 3.75/2.04 ( ( drop_option_b @ zero_zero_nat @ Xs )
% 3.75/2.04 = Xs ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_226_add__less__imp__less__right,axiom,
% 3.75/2.04 ! [A: nat,C: nat,B2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 3.75/2.04 => ( ord_less_nat @ A @ B2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_227_add__less__imp__less__right,axiom,
% 3.75/2.04 ! [A: int,C: int,B2: int] :
% 3.75/2.04 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 3.75/2.04 => ( ord_less_int @ A @ B2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_228_add__less__imp__less__left,axiom,
% 3.75/2.04 ! [C: nat,A: nat,B2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 3.75/2.04 => ( ord_less_nat @ A @ B2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_229_add__less__imp__less__left,axiom,
% 3.75/2.04 ! [C: int,A: int,B2: int] :
% 3.75/2.04 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 3.75/2.04 => ( ord_less_int @ A @ B2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_230_add__strict__right__mono,axiom,
% 3.75/2.04 ! [A: nat,B2: nat,C: nat] :
% 3.75/2.04 ( ( ord_less_nat @ A @ B2 )
% 3.75/2.04 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_231_add__strict__right__mono,axiom,
% 3.75/2.04 ! [A: int,B2: int,C: int] :
% 3.75/2.04 ( ( ord_less_int @ A @ B2 )
% 3.75/2.04 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_232_add__strict__left__mono,axiom,
% 3.75/2.04 ! [A: nat,B2: nat,C: nat] :
% 3.75/2.04 ( ( ord_less_nat @ A @ B2 )
% 3.75/2.04 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_233_add__strict__left__mono,axiom,
% 3.75/2.04 ! [A: int,B2: int,C: int] :
% 3.75/2.04 ( ( ord_less_int @ A @ B2 )
% 3.75/2.04 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_234_add__strict__mono,axiom,
% 3.75/2.04 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.75/2.04 ( ( ord_less_nat @ A @ B2 )
% 3.75/2.04 => ( ( ord_less_nat @ C @ D )
% 3.75/2.04 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ D ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_235_add__strict__mono,axiom,
% 3.75/2.04 ! [A: int,B2: int,C: int,D: int] :
% 3.75/2.04 ( ( ord_less_int @ A @ B2 )
% 3.75/2.04 => ( ( ord_less_int @ C @ D )
% 3.75/2.04 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ D ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_236_add__mono__thms__linordered__field_I1_J,axiom,
% 3.75/2.04 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.75/2.04 ( ( ( ord_less_nat @ I @ J )
% 3.75/2.04 & ( K = L ) )
% 3.75/2.04 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_237_add__mono__thms__linordered__field_I1_J,axiom,
% 3.75/2.04 ! [I: int,J: int,K: int,L: int] :
% 3.75/2.04 ( ( ( ord_less_int @ I @ J )
% 3.75/2.04 & ( K = L ) )
% 3.75/2.04 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_238_add__mono__thms__linordered__field_I2_J,axiom,
% 3.75/2.04 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.75/2.04 ( ( ( I = J )
% 3.75/2.04 & ( ord_less_nat @ K @ L ) )
% 3.75/2.04 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_239_add__mono__thms__linordered__field_I2_J,axiom,
% 3.75/2.04 ! [I: int,J: int,K: int,L: int] :
% 3.75/2.04 ( ( ( I = J )
% 3.75/2.04 & ( ord_less_int @ K @ L ) )
% 3.75/2.04 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_240_add__mono__thms__linordered__field_I5_J,axiom,
% 3.75/2.04 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.75/2.04 ( ( ( ord_less_nat @ I @ J )
% 3.75/2.04 & ( ord_less_nat @ K @ L ) )
% 3.75/2.04 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_241_add__mono__thms__linordered__field_I5_J,axiom,
% 3.75/2.04 ! [I: int,J: int,K: int,L: int] :
% 3.75/2.04 ( ( ( ord_less_int @ I @ J )
% 3.75/2.04 & ( ord_less_int @ K @ L ) )
% 3.75/2.04 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_242_add_Ogroup__left__neutral,axiom,
% 3.75/2.04 ! [A: int] :
% 3.75/2.04 ( ( plus_plus_int @ zero_zero_int @ A )
% 3.75/2.04 = A ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_243_add_Ocomm__neutral,axiom,
% 3.75/2.04 ! [A: nat] :
% 3.75/2.04 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 3.75/2.04 = A ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_244_add_Ocomm__neutral,axiom,
% 3.75/2.04 ! [A: int] :
% 3.75/2.04 ( ( plus_plus_int @ A @ zero_zero_int )
% 3.75/2.04 = A ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_245_comm__monoid__add__class_Oadd__0,axiom,
% 3.75/2.04 ! [A: nat] :
% 3.75/2.04 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 3.75/2.04 = A ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_246_comm__monoid__add__class_Oadd__0,axiom,
% 3.75/2.04 ! [A: int] :
% 3.75/2.04 ( ( plus_plus_int @ zero_zero_int @ A )
% 3.75/2.04 = A ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_247_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 3.75/2.04 ! [A: nat,B2: nat,C: nat] :
% 3.75/2.04 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 3.75/2.04 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_248_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 3.75/2.04 ! [A: int,B2: int,C: int] :
% 3.75/2.04 ( ( plus_plus_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 3.75/2.04 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_249_add__mono__thms__linordered__semiring_I4_J,axiom,
% 3.75/2.04 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.75/2.04 ( ( ( I = J )
% 3.75/2.04 & ( K = L ) )
% 3.75/2.04 => ( ( plus_plus_nat @ I @ K )
% 3.75/2.04 = ( plus_plus_nat @ J @ L ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_250_add__mono__thms__linordered__semiring_I4_J,axiom,
% 3.75/2.04 ! [I: int,J: int,K: int,L: int] :
% 3.75/2.04 ( ( ( I = J )
% 3.75/2.04 & ( K = L ) )
% 3.75/2.04 => ( ( plus_plus_int @ I @ K )
% 3.75/2.04 = ( plus_plus_int @ J @ L ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_251_group__cancel_Oadd1,axiom,
% 3.75/2.04 ! [A2: nat,K: nat,A: nat,B2: nat] :
% 3.75/2.04 ( ( A2
% 3.75/2.04 = ( plus_plus_nat @ K @ A ) )
% 3.75/2.04 => ( ( plus_plus_nat @ A2 @ B2 )
% 3.75/2.04 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_252_group__cancel_Oadd1,axiom,
% 3.75/2.04 ! [A2: int,K: int,A: int,B2: int] :
% 3.75/2.04 ( ( A2
% 3.75/2.04 = ( plus_plus_int @ K @ A ) )
% 3.75/2.04 => ( ( plus_plus_int @ A2 @ B2 )
% 3.75/2.04 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_253_group__cancel_Oadd2,axiom,
% 3.75/2.04 ! [B3: nat,K: nat,B2: nat,A: nat] :
% 3.75/2.04 ( ( B3
% 3.75/2.04 = ( plus_plus_nat @ K @ B2 ) )
% 3.75/2.04 => ( ( plus_plus_nat @ A @ B3 )
% 3.75/2.04 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_254_group__cancel_Oadd2,axiom,
% 3.75/2.04 ! [B3: int,K: int,B2: int,A: int] :
% 3.75/2.04 ( ( B3
% 3.75/2.04 = ( plus_plus_int @ K @ B2 ) )
% 3.75/2.04 => ( ( plus_plus_int @ A @ B3 )
% 3.75/2.04 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_255_add_Oassoc,axiom,
% 3.75/2.04 ! [A: nat,B2: nat,C: nat] :
% 3.75/2.04 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 3.75/2.04 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_256_add_Oassoc,axiom,
% 3.75/2.04 ! [A: int,B2: int,C: int] :
% 3.75/2.04 ( ( plus_plus_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 3.75/2.04 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_257_add_Oleft__cancel,axiom,
% 3.75/2.04 ! [A: int,B2: int,C: int] :
% 3.75/2.04 ( ( ( plus_plus_int @ A @ B2 )
% 3.75/2.04 = ( plus_plus_int @ A @ C ) )
% 3.75/2.04 = ( B2 = C ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_258_add_Oright__cancel,axiom,
% 3.75/2.04 ! [B2: int,A: int,C: int] :
% 3.75/2.04 ( ( ( plus_plus_int @ B2 @ A )
% 3.75/2.04 = ( plus_plus_int @ C @ A ) )
% 3.75/2.04 = ( B2 = C ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_259_add_Ocommute,axiom,
% 3.75/2.04 ( plus_plus_nat
% 3.75/2.04 = ( ^ [A4: nat,B4: nat] : ( plus_plus_nat @ B4 @ A4 ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_260_add_Ocommute,axiom,
% 3.75/2.04 ( plus_plus_int
% 3.75/2.04 = ( ^ [A4: int,B4: int] : ( plus_plus_int @ B4 @ A4 ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_261_add_Oleft__commute,axiom,
% 3.75/2.04 ! [B2: nat,A: nat,C: nat] :
% 3.75/2.04 ( ( plus_plus_nat @ B2 @ ( plus_plus_nat @ A @ C ) )
% 3.75/2.04 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_262_add_Oleft__commute,axiom,
% 3.75/2.04 ! [B2: int,A: int,C: int] :
% 3.75/2.04 ( ( plus_plus_int @ B2 @ ( plus_plus_int @ A @ C ) )
% 3.75/2.04 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_263_add__left__imp__eq,axiom,
% 3.75/2.04 ! [A: nat,B2: nat,C: nat] :
% 3.75/2.04 ( ( ( plus_plus_nat @ A @ B2 )
% 3.75/2.04 = ( plus_plus_nat @ A @ C ) )
% 3.75/2.04 => ( B2 = C ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_264_add__left__imp__eq,axiom,
% 3.75/2.04 ! [A: int,B2: int,C: int] :
% 3.75/2.04 ( ( ( plus_plus_int @ A @ B2 )
% 3.75/2.04 = ( plus_plus_int @ A @ C ) )
% 3.75/2.04 => ( B2 = C ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_265_add__right__imp__eq,axiom,
% 3.75/2.04 ! [B2: nat,A: nat,C: nat] :
% 3.75/2.04 ( ( ( plus_plus_nat @ B2 @ A )
% 3.75/2.04 = ( plus_plus_nat @ C @ A ) )
% 3.75/2.04 => ( B2 = C ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_266_add__right__imp__eq,axiom,
% 3.75/2.04 ! [B2: int,A: int,C: int] :
% 3.75/2.04 ( ( ( plus_plus_int @ B2 @ A )
% 3.75/2.04 = ( plus_plus_int @ C @ A ) )
% 3.75/2.04 => ( B2 = C ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_267_of__nat__less__0__iff,axiom,
% 3.75/2.04 ! [M: nat] :
% 3.75/2.04 ~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_268_of__nat__less__0__iff,axiom,
% 3.75/2.04 ! [M: nat] :
% 3.75/2.04 ~ ( ord_less_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_269_of__nat__neq__0,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( semiri1382578993at_nat @ ( suc @ N ) )
% 3.75/2.04 != zero_zero_nat ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_270_of__nat__neq__0,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( semiri2019852685at_int @ ( suc @ N ) )
% 3.75/2.04 != zero_zero_int ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_271_less__imp__of__nat__less,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ M @ N )
% 3.75/2.04 => ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_272_less__imp__of__nat__less,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ M @ N )
% 3.75/2.04 => ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_273_of__nat__less__imp__less,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
% 3.75/2.04 => ( ord_less_nat @ M @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_274_of__nat__less__imp__less,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) )
% 3.75/2.04 => ( ord_less_nat @ M @ N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_275_add__neg__neg,axiom,
% 3.75/2.04 ! [A: nat,B2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ A @ zero_zero_nat )
% 3.75/2.04 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 3.75/2.04 => ( ord_less_nat @ ( plus_plus_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_276_add__neg__neg,axiom,
% 3.75/2.04 ! [A: int,B2: int] :
% 3.75/2.04 ( ( ord_less_int @ A @ zero_zero_int )
% 3.75/2.04 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 3.75/2.04 => ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_277_add__pos__pos,axiom,
% 3.75/2.04 ! [A: nat,B2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.75/2.04 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 3.75/2.04 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_278_add__pos__pos,axiom,
% 3.75/2.04 ! [A: int,B2: int] :
% 3.75/2.04 ( ( ord_less_int @ zero_zero_int @ A )
% 3.75/2.04 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.75/2.04 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_279_canonically__ordered__monoid__add__class_OlessE,axiom,
% 3.75/2.04 ! [A: nat,B2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ A @ B2 )
% 3.75/2.04 => ~ ! [C2: nat] :
% 3.75/2.04 ( ( B2
% 3.75/2.04 = ( plus_plus_nat @ A @ C2 ) )
% 3.75/2.04 => ( C2 = zero_zero_nat ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_280_pos__add__strict,axiom,
% 3.75/2.04 ! [A: nat,B2: nat,C: nat] :
% 3.75/2.04 ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.75/2.04 => ( ( ord_less_nat @ B2 @ C )
% 3.75/2.04 => ( ord_less_nat @ B2 @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_281_pos__add__strict,axiom,
% 3.75/2.04 ! [A: int,B2: int,C: int] :
% 3.75/2.04 ( ( ord_less_int @ zero_zero_int @ A )
% 3.75/2.04 => ( ( ord_less_int @ B2 @ C )
% 3.75/2.04 => ( ord_less_int @ B2 @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_282_nth__via__drop,axiom,
% 3.75/2.04 ! [N: nat,Xs: list_b,Y3: b,Ys: list_b] :
% 3.75/2.04 ( ( ( drop_b @ N @ Xs )
% 3.75/2.04 = ( cons_b @ Y3 @ Ys ) )
% 3.75/2.04 => ( ( nth_b @ Xs @ N )
% 3.75/2.04 = Y3 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_283_nth__via__drop,axiom,
% 3.75/2.04 ! [N: nat,Xs: list_option_b,Y3: option_b,Ys: list_option_b] :
% 3.75/2.04 ( ( ( drop_option_b @ N @ Xs )
% 3.75/2.04 = ( cons_option_b @ Y3 @ Ys ) )
% 3.75/2.04 => ( ( nth_option_b @ Xs @ N )
% 3.75/2.04 = Y3 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_284_add__is__1,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ( plus_plus_nat @ M @ N )
% 3.75/2.04 = ( suc @ zero_zero_nat ) )
% 3.75/2.04 = ( ( ( M
% 3.75/2.04 = ( suc @ zero_zero_nat ) )
% 3.75/2.04 & ( N = zero_zero_nat ) )
% 3.75/2.04 | ( ( M = zero_zero_nat )
% 3.75/2.04 & ( N
% 3.75/2.04 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_285_one__is__add,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ( suc @ zero_zero_nat )
% 3.75/2.04 = ( plus_plus_nat @ M @ N ) )
% 3.75/2.04 = ( ( ( M
% 3.75/2.04 = ( suc @ zero_zero_nat ) )
% 3.75/2.04 & ( N = zero_zero_nat ) )
% 3.75/2.04 | ( ( M = zero_zero_nat )
% 3.75/2.04 & ( N
% 3.75/2.04 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_286_less__imp__add__positive,axiom,
% 3.75/2.04 ! [I: nat,J: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I @ J )
% 3.75/2.04 => ? [K2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 3.75/2.04 & ( ( plus_plus_nat @ I @ K2 )
% 3.75/2.04 = J ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_287_less__natE,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ M @ N )
% 3.75/2.04 => ~ ! [Q2: nat] :
% 3.75/2.04 ( N
% 3.75/2.04 != ( suc @ ( plus_plus_nat @ M @ Q2 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_288_less__add__Suc1,axiom,
% 3.75/2.04 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_289_less__add__Suc2,axiom,
% 3.75/2.04 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_290_less__iff__Suc__add,axiom,
% 3.75/2.04 ( ord_less_nat
% 3.75/2.04 = ( ^ [M5: nat,N4: nat] :
% 3.75/2.04 ? [K3: nat] :
% 3.75/2.04 ( N4
% 3.75/2.04 = ( suc @ ( plus_plus_nat @ M5 @ K3 ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_291_less__imp__Suc__add,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ord_less_nat @ M @ N )
% 3.75/2.04 => ? [K2: nat] :
% 3.75/2.04 ( N
% 3.75/2.04 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_292_gen__length__def,axiom,
% 3.75/2.04 ( gen_length_b
% 3.75/2.04 = ( ^ [N4: nat,Xs3: list_b] : ( plus_plus_nat @ N4 @ ( size_size_list_b @ Xs3 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_293_gen__length__def,axiom,
% 3.75/2.04 ( gen_length_option_b
% 3.75/2.04 = ( ^ [N4: nat,Xs3: list_option_b] : ( plus_plus_nat @ N4 @ ( size_s1671393719tion_b @ Xs3 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_294_list_Osize_I4_J,axiom,
% 3.75/2.04 ! [X21: b,X22: list_b] :
% 3.75/2.04 ( ( size_size_list_b @ ( cons_b @ X21 @ X22 ) )
% 3.75/2.04 = ( plus_plus_nat @ ( size_size_list_b @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_295_list_Osize_I4_J,axiom,
% 3.75/2.04 ! [X21: option_b,X22: list_option_b] :
% 3.75/2.04 ( ( size_s1671393719tion_b @ ( cons_option_b @ X21 @ X22 ) )
% 3.75/2.04 = ( plus_plus_nat @ ( size_s1671393719tion_b @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_296_add__less__zeroD,axiom,
% 3.75/2.04 ! [X: int,Y3: int] :
% 3.75/2.04 ( ( ord_less_int @ ( plus_plus_int @ X @ Y3 ) @ zero_zero_int )
% 3.75/2.04 => ( ( ord_less_int @ X @ zero_zero_int )
% 3.75/2.04 | ( ord_less_int @ Y3 @ zero_zero_int ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_297_Euclid__induct,axiom,
% 3.75/2.04 ! [P: nat > nat > $o,A: nat,B2: nat] :
% 3.75/2.04 ( ! [A3: nat,B: nat] :
% 3.75/2.04 ( ( P @ A3 @ B )
% 3.75/2.04 = ( P @ B @ A3 ) )
% 3.75/2.04 => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
% 3.75/2.04 => ( ! [A3: nat,B: nat] :
% 3.75/2.04 ( ( P @ A3 @ B )
% 3.75/2.04 => ( P @ A3 @ ( plus_plus_nat @ A3 @ B ) ) )
% 3.75/2.04 => ( P @ A @ B2 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_298_pos__int__cases,axiom,
% 3.75/2.04 ! [K: int] :
% 3.75/2.04 ( ( ord_less_int @ zero_zero_int @ K )
% 3.75/2.04 => ~ ! [N2: nat] :
% 3.75/2.04 ( ( K
% 3.75/2.04 = ( semiri2019852685at_int @ N2 ) )
% 3.75/2.04 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_299_zero__less__imp__eq__int,axiom,
% 3.75/2.04 ! [K: int] :
% 3.75/2.04 ( ( ord_less_int @ zero_zero_int @ K )
% 3.75/2.04 => ? [N2: nat] :
% 3.75/2.04 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.75/2.04 & ( K
% 3.75/2.04 = ( semiri2019852685at_int @ N2 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_300_zadd__int__left,axiom,
% 3.75/2.04 ! [M: nat,N: nat,Z2: int] :
% 3.75/2.04 ( ( plus_plus_int @ ( semiri2019852685at_int @ M ) @ ( plus_plus_int @ ( semiri2019852685at_int @ N ) @ Z2 ) )
% 3.75/2.04 = ( plus_plus_int @ ( semiri2019852685at_int @ ( plus_plus_nat @ M @ N ) ) @ Z2 ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_301_int__int__eq,axiom,
% 3.75/2.04 ! [M: nat,N: nat] :
% 3.75/2.04 ( ( ( semiri2019852685at_int @ M )
% 3.75/2.04 = ( semiri2019852685at_int @ N ) )
% 3.75/2.04 = ( M = N ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_302_plus__int__code_I2_J,axiom,
% 3.75/2.04 ! [L: int] :
% 3.75/2.04 ( ( plus_plus_int @ zero_zero_int @ L )
% 3.75/2.04 = L ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_303_plus__int__code_I1_J,axiom,
% 3.75/2.04 ! [K: int] :
% 3.75/2.04 ( ( plus_plus_int @ K @ zero_zero_int )
% 3.75/2.04 = K ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_304_zless__iff__Suc__zadd,axiom,
% 3.75/2.04 ( ord_less_int
% 3.75/2.04 = ( ^ [W: int,Z3: int] :
% 3.75/2.04 ? [N4: nat] :
% 3.75/2.04 ( Z3
% 3.75/2.04 = ( plus_plus_int @ W @ ( semiri2019852685at_int @ ( suc @ N4 ) ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_305_less__int__code_I1_J,axiom,
% 3.75/2.04 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_306_linorder__neqE__linordered__idom,axiom,
% 3.75/2.04 ! [X: int,Y3: int] :
% 3.75/2.04 ( ( X != Y3 )
% 3.75/2.04 => ( ~ ( ord_less_int @ X @ Y3 )
% 3.75/2.04 => ( ord_less_int @ Y3 @ X ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_307_nat__int__comparison_I2_J,axiom,
% 3.75/2.04 ( ord_less_nat
% 3.75/2.04 = ( ^ [A4: nat,B4: nat] : ( ord_less_int @ ( semiri2019852685at_int @ A4 ) @ ( semiri2019852685at_int @ B4 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_308_int__ops_I1_J,axiom,
% 3.75/2.04 ( ( semiri2019852685at_int @ zero_zero_nat )
% 3.75/2.04 = zero_zero_int ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_309_verit__comp__simplify1_I1_J,axiom,
% 3.75/2.04 ! [A: nat] :
% 3.75/2.04 ~ ( ord_less_nat @ A @ A ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_310_verit__comp__simplify1_I1_J,axiom,
% 3.75/2.04 ! [A: int] :
% 3.75/2.04 ~ ( ord_less_int @ A @ A ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_311_nat__int__comparison_I1_J,axiom,
% 3.75/2.04 ( ( ^ [Y5: nat,Z: nat] : ( Y5 = Z ) )
% 3.75/2.04 = ( ^ [A4: nat,B4: nat] :
% 3.75/2.04 ( ( semiri2019852685at_int @ A4 )
% 3.75/2.04 = ( semiri2019852685at_int @ B4 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_312_int__if,axiom,
% 3.75/2.04 ! [P: $o,A: nat,B2: nat] :
% 3.75/2.04 ( ( P
% 3.75/2.04 => ( ( semiri2019852685at_int @ ( if_nat @ P @ A @ B2 ) )
% 3.75/2.04 = ( semiri2019852685at_int @ A ) ) )
% 3.75/2.04 & ( ~ P
% 3.75/2.04 => ( ( semiri2019852685at_int @ ( if_nat @ P @ A @ B2 ) )
% 3.75/2.04 = ( semiri2019852685at_int @ B2 ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_313_verit__sum__simplify,axiom,
% 3.75/2.04 ! [A: nat] :
% 3.75/2.04 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 3.75/2.04 = A ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_314_verit__sum__simplify,axiom,
% 3.75/2.04 ! [A: int] :
% 3.75/2.04 ( ( plus_plus_int @ A @ zero_zero_int )
% 3.75/2.04 = A ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_315_int__ops_I5_J,axiom,
% 3.75/2.04 ! [A: nat,B2: nat] :
% 3.75/2.04 ( ( semiri2019852685at_int @ ( plus_plus_nat @ A @ B2 ) )
% 3.75/2.04 = ( plus_plus_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B2 ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_316_int__plus,axiom,
% 3.75/2.04 ! [N: nat,M: nat] :
% 3.75/2.04 ( ( semiri2019852685at_int @ ( plus_plus_nat @ N @ M ) )
% 3.75/2.04 = ( plus_plus_int @ ( semiri2019852685at_int @ N ) @ ( semiri2019852685at_int @ M ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_317_triangle__Suc,axiom,
% 3.75/2.04 ! [N: nat] :
% 3.75/2.04 ( ( nat_triangle @ ( suc @ N ) )
% 3.75/2.04 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_318_add__0__iff,axiom,
% 3.75/2.04 ! [B2: nat,A: nat] :
% 3.75/2.04 ( ( B2
% 3.75/2.04 = ( plus_plus_nat @ B2 @ A ) )
% 3.75/2.04 = ( A = zero_zero_nat ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_319_add__0__iff,axiom,
% 3.75/2.04 ! [B2: int,A: int] :
% 3.75/2.04 ( ( B2
% 3.75/2.04 = ( plus_plus_int @ B2 @ A ) )
% 3.75/2.04 = ( A = zero_zero_int ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_320_triangle__0,axiom,
% 3.75/2.04 ( ( nat_triangle @ zero_zero_nat )
% 3.75/2.04 = zero_zero_nat ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_321_nth__drop,axiom,
% 3.75/2.04 ! [N: nat,Xs: list_b,I: nat] :
% 3.75/2.04 ( ( ord_less_eq_nat @ N @ ( size_size_list_b @ Xs ) )
% 3.75/2.04 => ( ( nth_b @ ( drop_b @ N @ Xs ) @ I )
% 3.75/2.04 = ( nth_b @ Xs @ ( plus_plus_nat @ N @ I ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(fact_322_nth__drop,axiom,
% 3.75/2.04 ! [N: nat,Xs: list_option_b,I: nat] :
% 3.75/2.04 ( ( ord_less_eq_nat @ N @ ( size_s1671393719tion_b @ Xs ) )
% 3.75/2.04 => ( ( nth_option_b @ ( drop_option_b @ N @ Xs ) @ I )
% 3.75/2.04 = ( nth_option_b @ Xs @ ( plus_plus_nat @ N @ I ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(help_If_3_1_If_001t__Nat__Onat_T,axiom,
% 3.75/2.04 ! [P: $o] :
% 3.75/2.04 ( ( P = $true )
% 3.75/2.04 | ( P = $false ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 3.75/2.04 ! [X: nat,Y3: nat] :
% 3.75/2.04 ( ( if_nat @ $false @ X @ Y3 )
% 3.75/2.04 = Y3 ) ).
% 3.75/2.04
% 3.75/2.04 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 3.75/2.04 ! [X: nat,Y3: nat] :
% 3.75/2.04 ( ( if_nat @ $true @ X @ Y3 )
% 3.75/2.04 = X ) ).
% 3.75/2.04
% 3.75/2.04 thf(conj_0,hypothesis,
% 3.75/2.04 member_nat @ zero_zero_nat @ ( fvi_a @ b2 @ phi ) ).
% 3.75/2.04
% 3.75/2.04 thf(conj_1,hypothesis,
% 3.75/2.04 ( ( ( size_s1671393719tion_b @ v )
% 3.75/2.04 = n )
% 3.75/2.04 & ! [I4: nat] :
% 3.75/2.04 ( ( ord_less_nat @ I4 @ n )
% 3.75/2.04 => ( ( ( nth_option_b @ v @ I4 )
% 3.75/2.04 = none_b )
% 3.75/2.04 = ( ~ ( member_nat @ I4 @ ( fvi_a @ ( suc @ b2 ) @ phi ) ) ) ) ) ) ).
% 3.75/2.04
% 3.75/2.04 thf(conj_2,conjecture,
% 3.75/2.04 ( ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
% 3.75/2.04 = ( suc @ n ) )
% 3.75/2.04 & ! [I2: nat] :
% 3.75/2.04 ( ~ ( ord_less_nat @ I2 @ ( suc @ n ) )
% 3.75/2.04 | ( ( ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ I2 )
% 3.75/2.04 = none_b )
% 3.75/2.04 = ( ~ ( member_nat @ I2 @ ( fvi_a @ b2 @ phi ) ) ) ) ) ) ).
% 3.75/2.04 ------------------------
% 3.75/2.08 % (31843)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31741 for (2999ds/2Mi)
% 3.75/2.08 % (31840)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31741 for (2999ds/183Mi)
% 3.75/2.08 % (31845)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_31741 for (2999ds/275Mi)
% 3.75/2.08 % (31841)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_31741 for (2999ds/4Mi)
% 3.75/2.08 % (31844)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_31741 for (2999ds/2Mi)
% 3.75/2.08 % (31842)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_31741 for (2999ds/27Mi)
% 3.75/2.08 % (31846)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31741 for (2999ds/18Mi)
% 3.75/2.08 % (31843)Instruction limit reached!
% 3.75/2.08 % (31843)------------------------------
% 3.75/2.08 % (31843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.08 % (31843)Termination reason: Unknown
% 3.75/2.08 % (31843)Termination phase: shuffling
% 3.75/2.08
% 3.75/2.08 % (31843)Memory used [KB]: 1407
% 3.75/2.08 % (31843)Time elapsed: 0.004 s
% 3.75/2.08 % (31843)Instructions burned: 3 (million)
% 3.75/2.08 % (31843)------------------------------
% 3.75/2.08 % (31843)------------------------------
% 3.75/2.08 % (31844)Instruction limit reached!
% 3.75/2.08 % (31844)------------------------------
% 3.75/2.08 % (31844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.08 % (31844)Termination reason: Unknown
% 3.75/2.08 % (31844)Termination phase: shuffling
% 3.75/2.08
% 3.75/2.08 % (31844)Memory used [KB]: 1407
% 3.75/2.08 % (31844)Time elapsed: 0.004 s
% 3.75/2.08 % (31844)Instructions burned: 3 (million)
% 3.75/2.08 % (31844)------------------------------
% 3.75/2.08 % (31844)------------------------------
% 3.75/2.08 % (31841)Instruction limit reached!
% 3.75/2.08 % (31841)------------------------------
% 3.75/2.08 % (31841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.08 % (31841)Termination reason: Unknown
% 3.75/2.08 % (31841)Termination phase: shuffling
% 3.75/2.08
% 3.75/2.08 % (31841)Memory used [KB]: 1407
% 3.75/2.08 % (31841)Time elapsed: 0.005 s
% 3.75/2.08 % (31841)Instructions burned: 5 (million)
% 3.75/2.08 % (31841)------------------------------
% 3.75/2.08 % (31841)------------------------------
% 3.75/2.09 % (31846)Instruction limit reached!
% 3.75/2.09 % (31846)------------------------------
% 3.75/2.09 % (31846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.09 % (31846)Termination reason: Unknown
% 3.75/2.09 % (31846)Termination phase: Property scanning
% 3.75/2.09
% 3.75/2.09 % (31846)Memory used [KB]: 1663
% 3.75/2.09 % (31846)Time elapsed: 0.012 s
% 3.75/2.09 % (31846)Instructions burned: 18 (million)
% 3.75/2.09 % (31846)------------------------------
% 3.75/2.09 % (31846)------------------------------
% 3.75/2.09 % (31842)Instruction limit reached!
% 3.75/2.09 % (31842)------------------------------
% 3.75/2.09 % (31842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.09 % (31842)Termination reason: Unknown
% 3.75/2.09 % (31842)Termination phase: Property scanning
% 3.75/2.09
% 3.75/2.09 % (31842)Memory used [KB]: 1663
% 3.75/2.09 % (31842)Time elapsed: 0.017 s
% 3.75/2.09 % (31842)Instructions burned: 27 (million)
% 3.75/2.09 % (31842)------------------------------
% 3.75/2.09 % (31842)------------------------------
% 3.75/2.10 % (31849)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_31741 for (2999ds/15Mi)
% 3.75/2.10 % (31848)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_31741 for (2999ds/37Mi)
% 3.75/2.10 % (31847)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_31741 for (2999ds/3Mi)
% 3.75/2.10 % (31847)Instruction limit reached!
% 3.75/2.10 % (31847)------------------------------
% 3.75/2.10 % (31847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.10 % (31847)Termination reason: Unknown
% 3.75/2.10 % (31847)Termination phase: shuffling
% 3.75/2.10
% 3.75/2.10 % (31847)Memory used [KB]: 1407
% 3.75/2.10 % (31847)Time elapsed: 0.004 s
% 3.75/2.10 % (31847)Instructions burned: 3 (million)
% 3.75/2.10 % (31847)------------------------------
% 3.75/2.10 % (31847)------------------------------
% 3.75/2.11 % (31849)Instruction limit reached!
% 3.75/2.11 % (31849)------------------------------
% 3.75/2.11 % (31849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.11 % (31849)Termination reason: Unknown
% 3.75/2.11 % (31849)Termination phase: shuffling
% 3.75/2.11
% 3.75/2.11 % (31849)Memory used [KB]: 1663
% 3.75/2.11 % (31849)Time elapsed: 0.011 s
% 3.75/2.11 % (31849)Instructions burned: 15 (million)
% 3.75/2.11 % (31849)------------------------------
% 3.75/2.11 % (31849)------------------------------
% 3.75/2.11 % (31850)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_31741 for (2999ds/3Mi)
% 3.75/2.11 % (31850)Instruction limit reached!
% 3.75/2.11 % (31850)------------------------------
% 3.75/2.11 % (31850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.11 % (31850)Termination reason: Unknown
% 3.75/2.11 % (31850)Termination phase: shuffling
% 3.75/2.11
% 3.75/2.11 % (31850)Memory used [KB]: 1279
% 3.75/2.11 % (31850)Time elapsed: 0.004 s
% 3.75/2.11 % (31850)Instructions burned: 3 (million)
% 3.75/2.11 % (31850)------------------------------
% 3.75/2.11 % (31850)------------------------------
% 3.75/2.11 % (31851)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_31741 for (2999ds/1041Mi)
% 3.75/2.12 % (31848)Instruction limit reached!
% 3.75/2.12 % (31848)------------------------------
% 3.75/2.12 % (31848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.12 % (31848)Termination reason: Unknown
% 3.75/2.12 % (31848)Termination phase: shuffling
% 3.75/2.12
% 3.75/2.12 % (31848)Memory used [KB]: 2174
% 3.75/2.12 % (31848)Time elapsed: 0.022 s
% 3.75/2.12 % (31848)Instructions burned: 38 (million)
% 3.75/2.12 % (31848)------------------------------
% 3.75/2.12 % (31848)------------------------------
% 3.75/2.12 % (31852)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_31741 for (2999ds/7Mi)
% 3.75/2.13 % (31852)Instruction limit reached!
% 3.75/2.13 % (31852)------------------------------
% 3.75/2.13 % (31852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.75/2.13 % (31852)Termination reason: Unknown
% 3.75/2.13 % (31852)Termination phase: shuffling
% 3.75/2.13
% 3.75/2.13 % (31852)Memory used [KB]: 1535
% 3.75/2.13 % (31852)Time elapsed: 0.007 s
% 3.75/2.13 % (31852)Instructions burned: 8 (million)
% 3.75/2.13 % (31852)------------------------------
% 3.75/2.13 % (31852)------------------------------
% 3.79/2.13 % (31853)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_31741 for (2999ds/16Mi)
% 3.79/2.13 % (31854)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_31741 for (2999ds/3Mi)
% 3.79/2.13 % (31854)Instruction limit reached!
% 3.79/2.13 % (31854)------------------------------
% 3.79/2.13 % (31854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.13 % (31854)Termination reason: Unknown
% 3.79/2.13 % (31854)Termination phase: shuffling
% 3.79/2.13
% 3.79/2.13 % (31854)Memory used [KB]: 1407
% 3.79/2.13 % (31854)Time elapsed: 0.003 s
% 3.79/2.13 % (31854)Instructions burned: 3 (million)
% 3.79/2.13 % (31854)------------------------------
% 3.79/2.13 % (31854)------------------------------
% 3.79/2.14 % (31853)Instruction limit reached!
% 3.79/2.14 % (31853)------------------------------
% 3.79/2.14 % (31853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.14 % (31853)Termination reason: Unknown
% 3.79/2.14 % (31853)Termination phase: shuffling
% 3.79/2.14
% 3.79/2.14 % (31853)Memory used [KB]: 1663
% 3.79/2.14 % (31853)Time elapsed: 0.012 s
% 3.79/2.14 % (31853)Instructions burned: 17 (million)
% 3.79/2.14 % (31853)------------------------------
% 3.79/2.14 % (31853)------------------------------
% 3.79/2.14 % (31855)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_31741 for (2999ds/3Mi)
% 3.79/2.14 % (31855)Instruction limit reached!
% 3.79/2.14 % (31855)------------------------------
% 3.79/2.14 % (31855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.14 % (31855)Termination reason: Unknown
% 3.79/2.14 % (31855)Termination phase: shuffling
% 3.79/2.14
% 3.79/2.14 % (31855)Memory used [KB]: 1407
% 3.79/2.14 % (31855)Time elapsed: 0.004 s
% 3.79/2.14 % (31855)Instructions burned: 4 (million)
% 3.79/2.14 % (31855)------------------------------
% 3.79/2.14 % (31855)------------------------------
% 3.79/2.15 % (31856)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_31741 for (2999ds/7Mi)
% 3.79/2.15 % (31856)Instruction limit reached!
% 3.79/2.15 % (31856)------------------------------
% 3.79/2.15 % (31856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.15 % (31856)Termination reason: Unknown
% 3.79/2.15 % (31856)Termination phase: shuffling
% 3.79/2.15
% 3.79/2.15 % (31856)Memory used [KB]: 1407
% 3.79/2.15 % (31856)Time elapsed: 0.006 s
% 3.79/2.15 % (31856)Instructions burned: 7 (million)
% 3.79/2.15 % (31856)------------------------------
% 3.79/2.15 % (31856)------------------------------
% 3.79/2.15 % (31857)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_31741 for (2999ds/3Mi)
% 3.79/2.15 % (31857)Instruction limit reached!
% 3.79/2.15 % (31857)------------------------------
% 3.79/2.15 % (31857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.15 % (31857)Termination reason: Unknown
% 3.79/2.15 % (31857)Termination phase: shuffling
% 3.79/2.15
% 3.79/2.15 % (31857)Memory used [KB]: 1407
% 3.79/2.15 % (31857)Time elapsed: 0.004 s
% 3.79/2.15 % (31857)Instructions burned: 3 (million)
% 3.79/2.15 % (31857)------------------------------
% 3.79/2.15 % (31857)------------------------------
% 3.79/2.16 % (31858)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_31741 for (2998ds/4Mi)
% 3.79/2.16 % (31858)Instruction limit reached!
% 3.79/2.16 % (31858)------------------------------
% 3.79/2.16 % (31858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.16 % (31858)Termination reason: Unknown
% 3.79/2.16 % (31858)Termination phase: shuffling
% 3.79/2.16
% 3.79/2.16 % (31858)Memory used [KB]: 1407
% 3.79/2.16 % (31858)Time elapsed: 0.005 s
% 3.79/2.16 % (31858)Instructions burned: 5 (million)
% 3.79/2.16 % (31858)------------------------------
% 3.79/2.16 % (31858)------------------------------
% 3.79/2.16 % (31859)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_31741 for (2998ds/18Mi)
% 3.79/2.17 % (31860)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_31741 for (2998ds/710Mi)
% 3.79/2.17 % (31859)Instruction limit reached!
% 3.79/2.17 % (31859)------------------------------
% 3.79/2.17 % (31859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.17 % (31859)Termination reason: Unknown
% 3.79/2.17 % (31859)Termination phase: Property scanning
% 3.79/2.17
% 3.79/2.17 % (31859)Memory used [KB]: 1663
% 3.79/2.17 % (31859)Time elapsed: 0.012 s
% 3.79/2.17 % (31859)Instructions burned: 18 (million)
% 3.79/2.17 % (31859)------------------------------
% 3.79/2.17 % (31859)------------------------------
% 3.79/2.17 % (31861)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31741 for (2998ds/6Mi)
% 3.79/2.18 % (31840)Instruction limit reached!
% 3.79/2.18 % (31840)------------------------------
% 3.79/2.18 % (31840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.18 % (31840)Termination reason: Unknown
% 3.79/2.18 % (31840)Termination phase: Saturation
% 3.79/2.18
% 3.79/2.18 % (31840)Memory used [KB]: 7291
% 3.79/2.18 % (31840)Time elapsed: 0.099 s
% 3.79/2.18 % (31840)Instructions burned: 183 (million)
% 3.79/2.18 % (31840)------------------------------
% 3.79/2.18 % (31840)------------------------------
% 3.79/2.18 % (31861)Instruction limit reached!
% 3.79/2.18 % (31861)------------------------------
% 3.79/2.18 % (31861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.18 % (31861)Termination reason: Unknown
% 3.79/2.18 % (31861)Termination phase: shuffling
% 3.79/2.18
% 3.79/2.18 % (31861)Memory used [KB]: 1407
% 3.79/2.18 % (31861)Time elapsed: 0.006 s
% 3.79/2.18 % (31861)Instructions burned: 7 (million)
% 3.79/2.18 % (31861)------------------------------
% 3.79/2.18 % (31861)------------------------------
% 3.79/2.18 % (31862)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_31741 for (2998ds/902Mi)
% 3.79/2.19 % (31863)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_31741 for (2998ds/21Mi)
% 3.79/2.20 % (31864)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_31741 for (2998ds/5Mi)
% 3.79/2.20 % (31865)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_31741 for (2998ds/6Mi)
% 3.79/2.20 % (31864)Instruction limit reached!
% 3.79/2.20 % (31864)------------------------------
% 3.79/2.20 % (31864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.20 % (31864)Termination reason: Unknown
% 3.79/2.20 % (31864)Termination phase: shuffling
% 3.79/2.20
% 3.79/2.20 % (31864)Memory used [KB]: 1407
% 3.79/2.20 % (31864)Time elapsed: 0.005 s
% 3.79/2.20 % (31864)Instructions burned: 5 (million)
% 3.79/2.20 % (31864)------------------------------
% 3.79/2.20 % (31864)------------------------------
% 3.79/2.20 % (31865)Instruction limit reached!
% 3.79/2.20 % (31865)------------------------------
% 3.79/2.20 % (31865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.20 % (31865)Termination reason: Unknown
% 3.79/2.20 % (31865)Termination phase: shuffling
% 3.79/2.20
% 3.79/2.20 % (31865)Memory used [KB]: 1407
% 3.79/2.20 % (31865)Time elapsed: 0.006 s
% 3.79/2.20 % (31865)Instructions burned: 7 (million)
% 3.79/2.20 % (31865)------------------------------
% 3.79/2.20 % (31865)------------------------------
% 3.79/2.20 % (31863)Instruction limit reached!
% 3.79/2.20 % (31863)------------------------------
% 3.79/2.20 % (31863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.20 % (31863)Termination reason: Unknown
% 3.79/2.20 % (31863)Termination phase: shuffling
% 3.79/2.20
% 3.79/2.20 % (31863)Memory used [KB]: 1791
% 3.79/2.20 % (31863)Time elapsed: 0.014 s
% 3.79/2.20 % (31863)Instructions burned: 22 (million)
% 3.79/2.20 % (31863)------------------------------
% 3.79/2.20 % (31863)------------------------------
% 3.79/2.22 % (31866)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_31741 for (2998ds/377Mi)
% 3.79/2.22 % (31867)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_31741 for (2998ds/779Mi)
% 3.79/2.23 % (31868)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_31741 for (2998ds/19Mi)
% 3.79/2.24 % (31868)Instruction limit reached!
% 3.79/2.24 % (31868)------------------------------
% 3.79/2.24 % (31868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.24 % (31868)Termination reason: Unknown
% 3.79/2.24 % (31868)Termination phase: shuffling
% 3.79/2.24
% 3.79/2.24 % (31868)Memory used [KB]: 1663
% 3.79/2.24 % (31868)Time elapsed: 0.012 s
% 3.79/2.24 % (31868)Instructions burned: 19 (million)
% 3.79/2.24 % (31868)------------------------------
% 3.79/2.24 % (31868)------------------------------
% 3.79/2.24 % (31845)Instruction limit reached!
% 3.79/2.24 % (31845)------------------------------
% 3.79/2.24 % (31845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.24 % (31845)Termination reason: Unknown
% 3.79/2.24 % (31845)Termination phase: Saturation
% 3.79/2.24
% 3.79/2.24 % (31845)Memory used [KB]: 7036
% 3.79/2.24 % (31845)Time elapsed: 0.161 s
% 3.79/2.24 % (31845)Instructions burned: 275 (million)
% 3.79/2.24 % (31845)------------------------------
% 3.79/2.24 % (31845)------------------------------
% 3.79/2.26 % (31870)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_31741 for (2998ds/17Mi)
% 3.79/2.26 % (31869)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_31741 for (2998ds/879Mi)
% 3.79/2.26 % (31870)Instruction limit reached!
% 3.79/2.26 % (31870)------------------------------
% 3.79/2.26 % (31870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.26 % (31870)Termination reason: Unknown
% 3.79/2.26 % (31870)Termination phase: Property scanning
% 3.79/2.26
% 3.79/2.26 % (31870)Memory used [KB]: 1663
% 3.79/2.26 % (31870)Time elapsed: 0.008 s
% 3.79/2.26 % (31870)Instructions burned: 18 (million)
% 3.79/2.26 % (31870)------------------------------
% 3.79/2.26 % (31870)------------------------------
% 3.79/2.27 % (31871)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_31741 for (2997ds/3Mi)
% 3.79/2.28 % (31871)Instruction limit reached!
% 3.79/2.28 % (31871)------------------------------
% 3.79/2.28 % (31871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.28 % (31871)Termination reason: Unknown
% 3.79/2.28 % (31871)Termination phase: shuffling
% 3.79/2.28
% 3.79/2.28 % (31871)Memory used [KB]: 1407
% 3.79/2.28 % (31871)Time elapsed: 0.004 s
% 3.79/2.28 % (31871)Instructions burned: 4 (million)
% 3.79/2.28 % (31871)------------------------------
% 3.79/2.28 % (31871)------------------------------
% 3.79/2.30 % (31872)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_31741 for (2997ds/30Mi)
% 3.79/2.31 % (31872)Instruction limit reached!
% 3.79/2.31 % (31872)------------------------------
% 3.79/2.31 % (31872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.31 % (31872)Termination reason: Unknown
% 3.79/2.31 % (31872)Termination phase: Property scanning
% 3.79/2.31
% 3.79/2.31 % (31872)Memory used [KB]: 1791
% 3.79/2.31 % (31872)Time elapsed: 0.019 s
% 3.79/2.31 % (31872)Instructions burned: 30 (million)
% 3.79/2.31 % (31872)------------------------------
% 3.79/2.31 % (31872)------------------------------
% 3.79/2.34 % (31873)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_31741 for (2997ds/127Mi)
% 3.79/2.40 % (31873)Instruction limit reached!
% 3.79/2.40 % (31873)------------------------------
% 3.79/2.40 % (31873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.40 % (31873)Termination reason: Unknown
% 3.79/2.40 % (31873)Termination phase: Saturation
% 3.79/2.40
% 3.79/2.40 % (31873)Memory used [KB]: 7036
% 3.79/2.40 % (31873)Time elapsed: 0.071 s
% 3.79/2.40 % (31873)Instructions burned: 127 (million)
% 3.79/2.40 % (31873)------------------------------
% 3.79/2.40 % (31873)------------------------------
% 3.79/2.43 % (31874)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_31741 for (2996ds/100Mi)
% 3.79/2.44 % (31866)Instruction limit reached!
% 3.79/2.44 % (31866)------------------------------
% 3.79/2.44 % (31866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.44 % (31866)Termination reason: Unknown
% 3.79/2.44 % (31866)Termination phase: Saturation
% 3.79/2.44
% 3.79/2.44 % (31866)Memory used [KB]: 8571
% 3.79/2.44 % (31866)Time elapsed: 0.219 s
% 3.79/2.44 % (31866)Instructions burned: 377 (million)
% 3.79/2.44 % (31866)------------------------------
% 3.79/2.44 % (31866)------------------------------
% 3.79/2.46 % (31875)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_31741 for (2996ds/3Mi)
% 3.79/2.46 % (31875)Instruction limit reached!
% 3.79/2.46 % (31875)------------------------------
% 3.79/2.46 % (31875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.46 % (31875)Termination reason: Unknown
% 3.79/2.46 % (31875)Termination phase: shuffling
% 3.79/2.46
% 3.79/2.46 % (31875)Memory used [KB]: 1407
% 3.79/2.46 % (31875)Time elapsed: 0.004 s
% 3.79/2.46 % (31875)Instructions burned: 3 (million)
% 3.79/2.46 % (31875)------------------------------
% 3.79/2.46 % (31875)------------------------------
% 3.79/2.48 % (31874)Instruction limit reached!
% 3.79/2.48 % (31874)------------------------------
% 3.79/2.48 % (31874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.48 % (31874)Termination reason: Unknown
% 3.79/2.48 % (31874)Termination phase: Function definition elimination
% 3.79/2.48
% 3.79/2.48 % (31874)Memory used [KB]: 2302
% 3.79/2.48 % (31874)Time elapsed: 0.054 s
% 3.79/2.48 % (31874)Instructions burned: 100 (million)
% 3.79/2.48 % (31874)------------------------------
% 3.79/2.48 % (31874)------------------------------
% 3.79/2.48 % (31876)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_31741 for (2995ds/20Mi)
% 3.79/2.49 % (31876)Instruction limit reached!
% 3.79/2.49 % (31876)------------------------------
% 3.79/2.49 % (31876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.49 % (31876)Termination reason: Unknown
% 3.79/2.49 % (31876)Termination phase: Property scanning
% 3.79/2.49
% 3.79/2.49 % (31876)Memory used [KB]: 1663
% 3.79/2.49 % (31876)Time elapsed: 0.013 s
% 3.79/2.49 % (31876)Instructions burned: 20 (million)
% 3.79/2.49 % (31876)------------------------------
% 3.79/2.49 % (31876)------------------------------
% 3.79/2.50 % (31877)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_31741 for (2995ds/86Mi)
% 3.79/2.51 % (31878)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_31741 for (2995ds/107Mi)
% 3.79/2.55 % (31877)Instruction limit reached!
% 3.79/2.55 % (31877)------------------------------
% 3.79/2.55 % (31877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.55 % (31877)Termination reason: Unknown
% 3.79/2.55 % (31877)Termination phase: Saturation
% 3.79/2.55
% 3.79/2.55 % (31877)Memory used [KB]: 6524
% 3.79/2.55 % (31877)Time elapsed: 0.049 s
% 3.79/2.55 % (31877)Instructions burned: 86 (million)
% 3.79/2.55 % (31877)------------------------------
% 3.79/2.55 % (31877)------------------------------
% 3.79/2.57 % (31879)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_31741 for (2995ds/39Mi)
% 3.79/2.57 % (31878)Instruction limit reached!
% 3.79/2.57 % (31878)------------------------------
% 3.79/2.57 % (31878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.57 % (31878)Termination reason: Unknown
% 3.79/2.57 % (31878)Termination phase: Saturation
% 3.79/2.57
% 3.79/2.57 % (31878)Memory used [KB]: 6908
% 3.79/2.57 % (31878)Time elapsed: 0.061 s
% 3.79/2.57 % (31878)Instructions burned: 108 (million)
% 3.79/2.57 % (31878)------------------------------
% 3.79/2.57 % (31878)------------------------------
% 3.79/2.59 % (31879)Instruction limit reached!
% 3.79/2.59 % (31879)------------------------------
% 3.79/2.59 % (31879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.59 % (31879)Termination reason: Unknown
% 3.79/2.59 % (31879)Termination phase: shuffling
% 3.79/2.59
% 3.79/2.59 % (31879)Memory used [KB]: 2174
% 3.79/2.59 % (31879)Time elapsed: 0.022 s
% 3.79/2.59 % (31879)Instructions burned: 39 (million)
% 3.79/2.59 % (31879)------------------------------
% 3.79/2.59 % (31879)------------------------------
% 3.79/2.59 % (31880)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_31741 for (2994ds/448Mi)
% 3.79/2.59 % (31860)Instruction limit reached!
% 3.79/2.59 % (31860)------------------------------
% 3.79/2.59 % (31860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.59 % (31860)Termination reason: Unknown
% 3.79/2.59 % (31860)Termination phase: Saturation
% 3.79/2.59
% 3.79/2.59 % (31860)Memory used [KB]: 7931
% 3.79/2.59 % (31860)Time elapsed: 0.425 s
% 3.79/2.59 % (31860)Instructions burned: 710 (million)
% 3.79/2.59 % (31860)------------------------------
% 3.79/2.59 % (31860)------------------------------
% 3.79/2.61 % (31881)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_31741 for (2994ds/46Mi)
% 3.79/2.62 % (31882)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_31741 for (2994ds/98Mi)
% 3.79/2.63 % (31881)Instruction limit reached!
% 3.79/2.63 % (31881)------------------------------
% 3.79/2.63 % (31881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.63 % (31881)Termination reason: Unknown
% 3.79/2.63 % (31881)Termination phase: Preprocessing 3
% 3.79/2.63
% 3.79/2.63 % (31881)Memory used [KB]: 1918
% 3.79/2.63 % (31881)Time elapsed: 0.028 s
% 3.79/2.63 % (31881)Instructions burned: 46 (million)
% 3.79/2.63 % (31881)------------------------------
% 3.79/2.63 % (31881)------------------------------
% 3.79/2.66 % (31867)Instruction limit reached!
% 3.79/2.66 % (31867)------------------------------
% 3.79/2.66 % (31867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.66 % (31867)Termination reason: Unknown
% 3.79/2.66 % (31867)Termination phase: Saturation
% 3.79/2.66
% 3.79/2.66 % (31867)Memory used [KB]: 9210
% 3.79/2.66 % (31867)Time elapsed: 0.439 s
% 3.79/2.66 % (31867)Instructions burned: 779 (million)
% 3.79/2.66 % (31867)------------------------------
% 3.79/2.66 % (31867)------------------------------
% 3.79/2.66 % (31883)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_31741 for (2994ds/507Mi)
% 3.79/2.67 % (31882)Instruction limit reached!
% 3.79/2.67 % (31882)------------------------------
% 3.79/2.67 % (31882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.67 % (31882)Termination reason: Unknown
% 3.79/2.67 % (31882)Termination phase: Function definition elimination
% 3.79/2.67
% 3.79/2.67 % (31882)Memory used [KB]: 2302
% 3.79/2.67 % (31882)Time elapsed: 0.053 s
% 3.79/2.67 % (31882)Instructions burned: 98 (million)
% 3.79/2.67 % (31882)------------------------------
% 3.79/2.67 % (31882)------------------------------
% 3.79/2.68 % (31884)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_31741 for (2993ds/149Mi)
% 3.79/2.69 % (31885)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_31741 for (2993ds/39Mi)
% 3.79/2.69 % (31862)Instruction limit reached!
% 3.79/2.69 % (31862)------------------------------
% 3.79/2.69 % (31862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.69 % (31862)Termination reason: Unknown
% 3.79/2.69 % (31862)Termination phase: Saturation
% 3.79/2.69
% 3.79/2.69 % (31862)Memory used [KB]: 8699
% 3.79/2.69 % (31862)Time elapsed: 0.515 s
% 3.79/2.69 % (31862)Instructions burned: 902 (million)
% 3.79/2.69 % (31862)------------------------------
% 3.79/2.69 % (31862)------------------------------
% 3.79/2.71 % (31885)Instruction limit reached!
% 3.79/2.71 % (31885)------------------------------
% 3.79/2.71 % (31885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.71 % (31885)Termination reason: Unknown
% 3.79/2.71 % (31885)Termination phase: Preprocessing 3
% 3.79/2.71
% 3.79/2.71 % (31885)Memory used [KB]: 1918
% 3.79/2.71 % (31885)Time elapsed: 0.024 s
% 3.79/2.71 % (31885)Instructions burned: 39 (million)
% 3.79/2.71 % (31885)------------------------------
% 3.79/2.71 % (31885)------------------------------
% 3.79/2.72 % (31886)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_31741 for (2993ds/6Mi)
% 3.79/2.72 % (31886)Instruction limit reached!
% 3.79/2.72 % (31886)------------------------------
% 3.79/2.72 % (31886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.72 % (31886)Termination reason: Unknown
% 3.79/2.72 % (31886)Termination phase: shuffling
% 3.79/2.72
% 3.79/2.72 % (31886)Memory used [KB]: 1407
% 3.79/2.72 % (31886)Time elapsed: 0.006 s
% 3.79/2.72 % (31886)Instructions burned: 6 (million)
% 3.79/2.72 % (31886)------------------------------
% 3.79/2.72 % (31886)------------------------------
% 3.79/2.73 % (31851)Instruction limit reached!
% 3.79/2.73 % (31851)------------------------------
% 3.79/2.73 % (31851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.73 % (31851)Termination reason: Unknown
% 3.79/2.73 % (31851)Termination phase: Saturation
% 3.79/2.73
% 3.79/2.73 % (31851)Memory used [KB]: 9722
% 3.79/2.73 % (31851)Time elapsed: 0.618 s
% 3.79/2.73 % (31851)Instructions burned: 1042 (million)
% 3.79/2.73 % (31851)------------------------------
% 3.79/2.73 % (31851)------------------------------
% 3.79/2.73 % (31887)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_31741 for (2993ds/1087Mi)
% 3.79/2.74 % (31888)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_31741 for (2993ds/47Mi)
% 3.79/2.75 % (31889)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_31741 for (2993ds/44Mi)
% 3.79/2.76 % (31884)Instruction limit reached!
% 3.79/2.76 % (31884)------------------------------
% 3.79/2.76 % (31884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.76 % (31884)Termination reason: Unknown
% 3.79/2.76 % (31884)Termination phase: Saturation
% 3.79/2.76
% 3.79/2.76 % (31884)Memory used [KB]: 7164
% 3.79/2.76 % (31884)Time elapsed: 0.083 s
% 3.79/2.76 % (31884)Instructions burned: 150 (million)
% 3.79/2.76 % (31884)------------------------------
% 3.79/2.76 % (31884)------------------------------
% 3.79/2.77 % (31888)Instruction limit reached!
% 3.79/2.77 % (31888)------------------------------
% 3.79/2.77 % (31888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.77 % (31888)Termination reason: Unknown
% 3.79/2.77 % (31888)Termination phase: Property scanning
% 3.79/2.77
% 3.79/2.77 % (31888)Memory used [KB]: 2046
% 3.79/2.77 % (31888)Time elapsed: 0.028 s
% 3.79/2.77 % (31888)Instructions burned: 47 (million)
% 3.79/2.77 % (31888)------------------------------
% 3.79/2.77 % (31888)------------------------------
% 3.79/2.78 % (31889)Instruction limit reached!
% 3.79/2.78 % (31889)------------------------------
% 3.79/2.78 % (31889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.78 % (31889)Termination reason: Unknown
% 3.79/2.78 % (31889)Termination phase: Property scanning
% 3.79/2.78
% 3.79/2.78 % (31889)Memory used [KB]: 2174
% 3.79/2.78 % (31889)Time elapsed: 0.025 s
% 3.79/2.78 % (31889)Instructions burned: 44 (million)
% 3.79/2.78 % (31889)------------------------------
% 3.79/2.78 % (31889)------------------------------
% 3.79/2.78 % (31890)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_31741 for (2992ds/432Mi)
% 3.79/2.78 % (31869)Instruction limit reached!
% 3.79/2.78 % (31869)------------------------------
% 3.79/2.78 % (31869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.78 % (31869)Termination reason: Unknown
% 3.79/2.78 % (31869)Termination phase: Saturation
% 3.79/2.78
% 3.79/2.78 % (31869)Memory used [KB]: 7931
% 3.79/2.78 % (31869)Time elapsed: 0.527 s
% 3.79/2.78 % (31869)Instructions burned: 880 (million)
% 3.79/2.78 % (31869)------------------------------
% 3.79/2.78 % (31869)------------------------------
% 3.79/2.79 % (31891)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_31741 for (2992ds/62Mi)
% 3.79/2.80 % (31892)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_31741 for (2992ds/31Mi)
% 3.79/2.80 % (31893)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_31741 for (2992ds/96Mi)
% 3.79/2.81 % (31892)Instruction limit reached!
% 3.79/2.81 % (31892)------------------------------
% 3.79/2.81 % (31892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.81 % (31892)Termination reason: Unknown
% 3.79/2.81 % (31892)Termination phase: Preprocessing 1
% 3.79/2.81
% 3.79/2.81 % (31892)Memory used [KB]: 1791
% 3.79/2.81 % (31892)Time elapsed: 0.019 s
% 3.79/2.81 % (31892)Instructions burned: 31 (million)
% 3.79/2.81 % (31892)------------------------------
% 3.79/2.81 % (31892)------------------------------
% 3.79/2.82 % (31891)Instruction limit reached!
% 3.79/2.82 % (31891)------------------------------
% 3.79/2.82 % (31891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.82 % (31891)Termination reason: Unknown
% 3.79/2.82 % (31891)Termination phase: Property scanning
% 3.79/2.82
% 3.79/2.82 % (31891)Memory used [KB]: 2174
% 3.79/2.82 % (31891)Time elapsed: 0.034 s
% 3.79/2.82 % (31891)Instructions burned: 62 (million)
% 3.79/2.82 % (31891)------------------------------
% 3.79/2.82 % (31891)------------------------------
% 3.79/2.83 % (31894)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_31741 for (2992ds/453Mi)
% 3.79/2.84 % (31880)Instruction limit reached!
% 3.79/2.84 % (31880)------------------------------
% 3.79/2.84 % (31880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.84 % (31880)Termination reason: Unknown
% 3.79/2.84 % (31880)Termination phase: Saturation
% 3.79/2.84
% 3.79/2.84 % (31880)Memory used [KB]: 9083
% 3.79/2.84 % (31880)Time elapsed: 0.268 s
% 3.79/2.84 % (31880)Instructions burned: 449 (million)
% 3.79/2.84 % (31880)------------------------------
% 3.79/2.84 % (31880)------------------------------
% 3.79/2.84 % (31895)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_31741 for (2992ds/71Mi)
% 3.79/2.85 % (31893)Instruction limit reached!
% 3.79/2.85 % (31893)------------------------------
% 3.79/2.85 % (31893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.85 % (31893)Termination reason: Unknown
% 3.79/2.85 % (31893)Termination phase: Saturation
% 3.79/2.85
% 3.79/2.85 % (31893)Memory used [KB]: 6652
% 3.79/2.85 % (31893)Time elapsed: 0.054 s
% 3.79/2.85 % (31893)Instructions burned: 97 (million)
% 3.79/2.85 % (31893)------------------------------
% 3.79/2.85 % (31893)------------------------------
% 3.79/2.86 % (31896)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_31741 for (2992ds/83Mi)
% 3.79/2.88 % (31897)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_31741 for (2991ds/11Mi)
% 3.79/2.88 % (31895)Instruction limit reached!
% 3.79/2.88 % (31895)------------------------------
% 3.79/2.88 % (31895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.88 % (31895)Termination reason: Unknown
% 3.79/2.88 % (31895)Termination phase: Property scanning
% 3.79/2.88
% 3.79/2.88 % (31895)Memory used [KB]: 2174
% 3.79/2.88 % (31895)Time elapsed: 0.040 s
% 3.79/2.88 % (31895)Instructions burned: 71 (million)
% 3.79/2.88 % (31895)------------------------------
% 3.79/2.88 % (31895)------------------------------
% 3.79/2.88 % (31897)Instruction limit reached!
% 3.79/2.88 % (31897)------------------------------
% 3.79/2.88 % (31897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.88 % (31897)Termination reason: Unknown
% 3.79/2.88 % (31897)Termination phase: shuffling
% 3.79/2.88
% 3.79/2.88 % (31897)Memory used [KB]: 1663
% 3.79/2.88 % (31897)Time elapsed: 0.009 s
% 3.79/2.88 % (31897)Instructions burned: 12 (million)
% 3.79/2.88 % (31897)------------------------------
% 3.79/2.88 % (31897)------------------------------
% 3.79/2.90 % (31898)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_31741 for (2991ds/41Mi)
% 3.79/2.91 % (31899)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31741 for (2991ds/6Mi)
% 3.79/2.91 % (31896)Instruction limit reached!
% 3.79/2.91 % (31896)------------------------------
% 3.79/2.91 % (31896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.91 % (31896)Termination reason: Unknown
% 3.79/2.91 % (31896)Termination phase: Saturation
% 3.79/2.91
% 3.79/2.91 % (31896)Memory used [KB]: 6652
% 3.79/2.91 % (31896)Time elapsed: 0.050 s
% 3.79/2.91 % (31896)Instructions burned: 84 (million)
% 3.79/2.91 % (31896)------------------------------
% 3.79/2.91 % (31896)------------------------------
% 3.79/2.91 % (31899)Instruction limit reached!
% 3.79/2.91 % (31899)------------------------------
% 3.79/2.91 % (31899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.91 % (31899)Termination reason: Unknown
% 3.79/2.91 % (31899)Termination phase: shuffling
% 3.79/2.91
% 3.79/2.91 % (31899)Memory used [KB]: 1407
% 3.79/2.91 % (31899)Time elapsed: 0.006 s
% 3.79/2.91 % (31899)Instructions burned: 7 (million)
% 3.79/2.91 % (31899)------------------------------
% 3.79/2.91 % (31899)------------------------------
% 3.79/2.92 % (31898)Instruction limit reached!
% 3.79/2.92 % (31898)------------------------------
% 3.79/2.92 % (31898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.92 % (31898)Termination reason: Unknown
% 3.79/2.92 % (31898)Termination phase: Property scanning
% 3.79/2.92
% 3.79/2.92 % (31898)Memory used [KB]: 2174
% 3.79/2.92 % (31898)Time elapsed: 0.024 s
% 3.79/2.92 % (31898)Instructions burned: 42 (million)
% 3.79/2.92 % (31898)------------------------------
% 3.79/2.92 % (31898)------------------------------
% 3.79/2.93 % (31900)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_31741 for (2991ds/150Mi)
% 3.79/2.93 % (31901)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_31741 for (2991ds/343Mi)
% 3.79/2.94 % (31902)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_31741 for (2991ds/109Mi)
% 3.79/2.95 % (31883)Instruction limit reached!
% 3.79/2.95 % (31883)------------------------------
% 3.79/2.95 % (31883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/2.95 % (31883)Termination reason: Unknown
% 3.79/2.95 % (31883)Termination phase: Saturation
% 3.79/2.95
% 3.79/2.95 % (31883)Memory used [KB]: 8315
% 3.79/2.95 % (31883)Time elapsed: 0.297 s
% 3.79/2.95 % (31883)Instructions burned: 507 (million)
% 3.79/2.95 % (31883)------------------------------
% 3.79/2.95 % (31883)------------------------------
% 3.79/2.97 % (31903)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_31741 for (2990ds/253Mi)
% 3.79/3.00 % (31902)Instruction limit reached!
% 3.79/3.00 % (31902)------------------------------
% 3.79/3.00 % (31902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/3.00 % (31902)Termination reason: Unknown
% 3.79/3.00 % (31902)Termination phase: Saturation
% 3.79/3.00
% 3.79/3.00 % (31902)Memory used [KB]: 6652
% 3.79/3.00 % (31902)Time elapsed: 0.060 s
% 3.79/3.00 % (31902)Instructions burned: 109 (million)
% 3.79/3.00 % (31902)------------------------------
% 3.79/3.00 % (31902)------------------------------
% 3.79/3.01 % (31900)Instruction limit reached!
% 3.79/3.01 % (31900)------------------------------
% 3.79/3.01 % (31900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/3.01 % (31900)Termination reason: Unknown
% 3.79/3.01 % (31900)Termination phase: Saturation
% 3.79/3.01
% 3.79/3.01 % (31900)Memory used [KB]: 7164
% 3.79/3.01 % (31900)Time elapsed: 0.086 s
% 3.79/3.01 % (31900)Instructions burned: 151 (million)
% 3.79/3.01 % (31900)------------------------------
% 3.79/3.01 % (31900)------------------------------
% 3.79/3.02 % (31904)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_31741 for (2990ds/140Mi)
% 3.79/3.02 % (31890)Instruction limit reached!
% 3.79/3.02 % (31890)------------------------------
% 3.79/3.02 % (31890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.79/3.02 % (31890)Termination reason: Unknown
% 3.79/3.02 % (31890)Termination phase: Saturation
% 3.79/3.02
% 3.79/3.02 % (31890)Memory used [KB]: 3582
% 3.79/3.02 % (31890)Time elapsed: 0.245 s
% 3.79/3.02 % (31890)Instructions burned: 432 (million)
% 3.79/3.02 % (31890)------------------------------
% 3.79/3.02 % (31890)------------------------------
% 10.49/3.03 % (31905)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_31741 for (2990ds/614Mi)
% 10.49/3.04 % (31906)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_31741 for (2990ds/202Mi)
% 10.49/3.09 % (31894)Instruction limit reached!
% 10.49/3.09 % (31894)------------------------------
% 10.49/3.09 % (31894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.49/3.09 % (31894)Termination reason: Unknown
% 10.49/3.09 % (31894)Termination phase: Saturation
% 10.49/3.09
% 10.49/3.09 % (31894)Memory used [KB]: 7803
% 10.49/3.09 % (31894)Time elapsed: 0.257 s
% 10.49/3.09 % (31894)Instructions burned: 453 (million)
% 10.49/3.09 % (31894)------------------------------
% 10.49/3.09 % (31894)------------------------------
% 10.49/3.10 % (31904)Instruction limit reached!
% 10.49/3.10 % (31904)------------------------------
% 10.49/3.10 % (31904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.49/3.10 % (31904)Termination reason: Unknown
% 10.49/3.10 % (31904)Termination phase: Saturation
% 10.49/3.10
% 10.49/3.10 % (31904)Memory used [KB]: 7036
% 10.49/3.10 % (31904)Time elapsed: 0.084 s
% 10.49/3.10 % (31904)Instructions burned: 140 (million)
% 10.49/3.10 % (31904)------------------------------
% 10.49/3.10 % (31904)------------------------------
% 10.49/3.11 % (31907)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_31741 for (2989ds/339Mi)
% 10.49/3.12 % (31903)Instruction limit reached!
% 10.49/3.12 % (31903)------------------------------
% 10.49/3.12 % (31903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.49/3.12 % (31903)Termination reason: Unknown
% 10.49/3.12 % (31903)Termination phase: Saturation
% 10.49/3.12
% 10.49/3.12 % (31903)Memory used [KB]: 7419
% 10.49/3.12 % (31903)Time elapsed: 0.149 s
% 10.49/3.12 % (31903)Instructions burned: 254 (million)
% 10.49/3.12 % (31903)------------------------------
% 10.49/3.12 % (31903)------------------------------
% 10.49/3.12 % (31901)Instruction limit reached!
% 10.49/3.12 % (31901)------------------------------
% 10.49/3.12 % (31901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.49/3.12 % (31901)Termination reason: Unknown
% 10.49/3.12 % (31901)Termination phase: Saturation
% 10.49/3.12
% 10.49/3.12 % (31901)Memory used [KB]: 8059
% 10.49/3.12 % (31901)Time elapsed: 0.195 s
% 10.49/3.12 % (31901)Instructions burned: 343 (million)
% 10.49/3.12 % (31901)------------------------------
% 10.49/3.12 % (31901)------------------------------
% 10.49/3.12 % (31908)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_31741 for (2989ds/283Mi)
% 10.96/3.14 % (31909)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_31741 for (2989ds/134Mi)
% 10.96/3.14 % (31910)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_31741 for (2989ds/298Mi)
% 10.96/3.16 % (31906)Instruction limit reached!
% 10.96/3.16 % (31906)------------------------------
% 10.96/3.16 % (31906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.96/3.16 % (31906)Termination reason: Unknown
% 10.96/3.16 % (31906)Termination phase: Saturation
% 10.96/3.16
% 10.96/3.16 % (31906)Memory used [KB]: 7291
% 10.96/3.16 % (31906)Time elapsed: 0.120 s
% 10.96/3.16 % (31906)Instructions burned: 202 (million)
% 10.96/3.16 % (31906)------------------------------
% 10.96/3.16 % (31906)------------------------------
% 10.96/3.18 % (31912)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_31741 for (2988ds/192Mi)
% 11.17/3.21 % (31909)Instruction limit reached!
% 11.17/3.21 % (31909)------------------------------
% 11.17/3.21 % (31909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.17/3.21 % (31909)Termination reason: Unknown
% 11.17/3.21 % (31909)Termination phase: Saturation
% 11.17/3.21
% 11.17/3.21 % (31909)Memory used [KB]: 7036
% 11.17/3.21 % (31909)Time elapsed: 0.074 s
% 11.17/3.21 % (31909)Instructions burned: 135 (million)
% 11.17/3.21 % (31909)------------------------------
% 11.17/3.21 % (31909)------------------------------
% 11.17/3.24 % (31913)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_31741 for (2988ds/258Mi)
% 11.17/3.28 % (31908)Instruction limit reached!
% 11.17/3.28 % (31908)------------------------------
% 11.17/3.28 % (31908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.17/3.28 % (31908)Termination reason: Unknown
% 11.17/3.28 % (31908)Termination phase: Saturation
% 11.17/3.28
% 11.17/3.28 % (31908)Memory used [KB]: 7547
% 11.17/3.28 % (31908)Time elapsed: 0.160 s
% 11.17/3.28 % (31908)Instructions burned: 283 (million)
% 11.17/3.28 % (31908)------------------------------
% 11.17/3.28 % (31908)------------------------------
% 11.17/3.29 % (31912)Instruction limit reached!
% 11.17/3.29 % (31912)------------------------------
% 11.17/3.29 % (31912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.17/3.29 % (31912)Termination reason: Unknown
% 11.17/3.29 % (31912)Termination phase: Saturation
% 11.17/3.29
% 11.17/3.29 % (31912)Memory used [KB]: 7931
% 11.17/3.29 % (31912)Time elapsed: 0.107 s
% 11.17/3.29 % (31912)Instructions burned: 193 (million)
% 11.17/3.29 % (31912)------------------------------
% 11.17/3.29 % (31912)------------------------------
% 11.17/3.29 % (31907)Instruction limit reached!
% 11.17/3.29 % (31907)------------------------------
% 11.17/3.29 % (31907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.17/3.29 % (31907)Termination reason: Unknown
% 11.17/3.29 % (31907)Termination phase: Saturation
% 11.17/3.29
% 11.17/3.29 % (31907)Memory used [KB]: 7803
% 11.17/3.29 % (31907)Time elapsed: 0.182 s
% 11.17/3.29 % (31907)Instructions burned: 339 (million)
% 11.17/3.29 % (31907)------------------------------
% 11.17/3.29 % (31907)------------------------------
% 11.87/3.30 % (31910)Instruction limit reached!
% 11.87/3.30 % (31910)------------------------------
% 11.87/3.30 % (31910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.87/3.30 % (31910)Termination reason: Unknown
% 11.87/3.30 % (31910)Termination phase: Saturation
% 11.87/3.30
% 11.87/3.30 % (31910)Memory used [KB]: 7803
% 11.87/3.30 % (31910)Time elapsed: 0.160 s
% 11.87/3.30 % (31910)Instructions burned: 299 (million)
% 11.87/3.30 % (31910)------------------------------
% 11.87/3.30 % (31910)------------------------------
% 11.87/3.30 % (31914)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_31741 for (2987ds/90Mi)
% 11.87/3.31 % (31915)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_31741 for (2987ds/231Mi)
% 11.87/3.31 % (31916)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_31741 for (2987ds/458Mi)
% 11.87/3.32 % (31917)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_31741 for (2987ds/31Mi)
% 11.87/3.34 % (31917)Instruction limit reached!
% 11.87/3.34 % (31917)------------------------------
% 11.87/3.34 % (31917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.87/3.34 % (31917)Termination reason: Unknown
% 11.87/3.34 % (31917)Termination phase: Preprocessing 1
% 11.87/3.34
% 11.87/3.34 % (31917)Memory used [KB]: 1663
% 11.87/3.34 % (31917)Time elapsed: 0.019 s
% 11.87/3.34 % (31917)Instructions burned: 31 (million)
% 11.87/3.34 % (31917)------------------------------
% 11.87/3.34 % (31917)------------------------------
% 11.87/3.35 % (31914)Instruction limit reached!
% 11.87/3.35 % (31914)------------------------------
% 11.87/3.35 % (31914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.87/3.35 % (31914)Termination reason: Unknown
% 11.87/3.35 % (31914)Termination phase: Saturation
% 11.87/3.35
% 11.87/3.35 % (31914)Memory used [KB]: 6652
% 11.87/3.35 % (31914)Time elapsed: 0.051 s
% 11.87/3.35 % (31914)Instructions burned: 90 (million)
% 11.87/3.35 % (31914)------------------------------
% 11.87/3.35 % (31914)------------------------------
% 11.87/3.36 % (31918)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_31741 for (2987ds/297Mi)
% 11.87/3.37 % (31919)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_31741 for (2987ds/987Mi)
% 11.87/3.38 % (31887)Instruction limit reached!
% 11.87/3.38 % (31887)------------------------------
% 11.87/3.38 % (31887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.87/3.38 % (31887)Termination reason: Unknown
% 11.87/3.38 % (31887)Termination phase: Saturation
% 11.87/3.38
% 11.87/3.38 % (31887)Memory used [KB]: 8571
% 11.87/3.38 % (31887)Time elapsed: 0.648 s
% 11.87/3.38 % (31887)Instructions burned: 1088 (million)
% 11.87/3.38 % (31887)------------------------------
% 11.87/3.38 % (31887)------------------------------
% 11.87/3.38 % (31913)Instruction limit reached!
% 11.87/3.38 % (31913)------------------------------
% 11.87/3.38 % (31913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.87/3.38 % (31913)Termination reason: Unknown
% 11.87/3.38 % (31913)Termination phase: Saturation
% 11.87/3.38
% 11.87/3.38 % (31913)Memory used [KB]: 7419
% 11.87/3.38 % (31913)Time elapsed: 0.146 s
% 11.87/3.38 % (31913)Instructions burned: 258 (million)
% 11.87/3.38 % (31913)------------------------------
% 11.87/3.38 % (31913)------------------------------
% 11.87/3.38 % (31905)Instruction limit reached!
% 11.87/3.38 % (31905)------------------------------
% 11.87/3.38 % (31905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.87/3.38 % (31905)Termination reason: Unknown
% 11.87/3.38 % (31905)Termination phase: Saturation
% 11.87/3.38
% 11.87/3.38 % (31905)Memory used [KB]: 9083
% 11.87/3.38 % (31905)Time elapsed: 0.350 s
% 11.87/3.38 % (31905)Instructions burned: 614 (million)
% 11.87/3.38 % (31905)------------------------------
% 11.87/3.38 % (31905)------------------------------
% 12.79/3.40 % (31920)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_31741 for (2986ds/182Mi)
% 12.79/3.40 % (31921)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_31741 for (2986ds/182Mi)
% 12.79/3.40 % (31922)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_31741 for (2986ds/154Mi)
% 12.79/3.43 % (31915)Instruction limit reached!
% 12.79/3.43 % (31915)------------------------------
% 12.79/3.43 % (31915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.79/3.43 % (31915)Termination reason: Unknown
% 12.79/3.43 % (31915)Termination phase: Saturation
% 12.79/3.43
% 12.79/3.43 % (31915)Memory used [KB]: 7419
% 12.79/3.43 % (31915)Time elapsed: 0.125 s
% 12.79/3.43 % (31915)Instructions burned: 232 (million)
% 12.79/3.43 % (31915)------------------------------
% 12.79/3.43 % (31915)------------------------------
% 12.79/3.46 % (31923)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_31741 for (2986ds/79Mi)
% 12.79/3.48 % (31918)Instruction limit reached!
% 12.79/3.48 % (31918)------------------------------
% 12.79/3.48 % (31918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.79/3.48 % (31918)Termination reason: Unknown
% 12.79/3.48 % (31918)Termination phase: Saturation
% 12.79/3.48
% 12.79/3.48 % (31918)Memory used [KB]: 7547
% 12.79/3.48 % (31918)Time elapsed: 0.144 s
% 12.79/3.48 % (31918)Instructions burned: 299 (million)
% 12.79/3.48 % (31918)------------------------------
% 12.79/3.48 % (31918)------------------------------
% 12.79/3.48 % (31922)Instruction limit reached!
% 12.79/3.48 % (31922)------------------------------
% 12.79/3.48 % (31922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.79/3.48 % (31922)Termination reason: Unknown
% 12.79/3.48 % (31922)Termination phase: Saturation
% 12.79/3.48
% 12.79/3.48 % (31922)Memory used [KB]: 2558
% 12.79/3.48 % (31922)Time elapsed: 0.081 s
% 12.79/3.48 % (31922)Instructions burned: 155 (million)
% 12.79/3.48 % (31922)------------------------------
% 12.79/3.48 % (31922)------------------------------
% 12.79/3.49 % (31924)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_31741 for (2985ds/216Mi)
% 13.17/3.50 % (31920)Instruction limit reached!
% 13.17/3.50 % (31920)------------------------------
% 13.17/3.50 % (31920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.17/3.50 % (31920)Termination reason: Unknown
% 13.17/3.50 % (31920)Termination phase: Saturation
% 13.17/3.50
% 13.17/3.50 % (31920)Memory used [KB]: 7291
% 13.17/3.50 % (31920)Time elapsed: 0.100 s
% 13.17/3.50 % (31920)Instructions burned: 182 (million)
% 13.17/3.50 % (31920)------------------------------
% 13.17/3.50 % (31920)------------------------------
% 13.17/3.50 % (31923)Instruction limit reached!
% 13.17/3.50 % (31923)------------------------------
% 13.17/3.50 % (31923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.17/3.50 % (31923)Termination reason: Unknown
% 13.17/3.50 % (31923)Termination phase: Property scanning
% 13.17/3.50
% 13.17/3.50 % (31923)Memory used [KB]: 2046
% 13.17/3.50 % (31923)Time elapsed: 0.045 s
% 13.17/3.50 % (31923)Instructions burned: 79 (million)
% 13.17/3.50 % (31923)------------------------------
% 13.17/3.50 % (31923)------------------------------
% 13.17/3.51 % (31921)Instruction limit reached!
% 13.17/3.51 % (31921)------------------------------
% 13.17/3.51 % (31921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.17/3.51 % (31921)Termination reason: Unknown
% 13.17/3.51 % (31921)Termination phase: Saturation
% 13.17/3.51
% 13.17/3.51 % (31921)Memory used [KB]: 7164
% 13.17/3.51 % (31921)Time elapsed: 0.133 s
% 13.17/3.51 % (31921)Instructions burned: 183 (million)
% 13.17/3.51 % (31921)------------------------------
% 13.17/3.51 % (31921)------------------------------
% 13.17/3.52 % (31926)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_31741 for (2985ds/922Mi)
% 13.17/3.52 % (31927)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_31741 for (2985ds/182Mi)
% 13.17/3.52 % (31925)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_31741 for (2985ds/114Mi)
% 13.17/3.53 % (31928)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_31741 for (2985ds/164Mi)
% 13.17/3.57 % (31916)Instruction limit reached!
% 13.17/3.57 % (31916)------------------------------
% 13.17/3.57 % (31916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.17/3.57 % (31916)Termination reason: Unknown
% 13.17/3.57 % (31916)Termination phase: Saturation
% 13.17/3.57
% 13.17/3.57 % (31916)Memory used [KB]: 8699
% 13.17/3.57 % (31916)Time elapsed: 0.262 s
% 13.17/3.57 % (31916)Instructions burned: 459 (million)
% 13.17/3.57 % (31916)------------------------------
% 13.17/3.57 % (31916)------------------------------
% 13.17/3.58 % (31928)Instruction limit reached!
% 13.17/3.58 % (31928)------------------------------
% 13.17/3.58 % (31928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.17/3.58 % (31928)Termination reason: Unknown
% 13.17/3.58 % (31928)Termination phase: Saturation
% 13.17/3.58
% 13.17/3.58 % (31928)Memory used [KB]: 2686
% 13.17/3.58 % (31928)Time elapsed: 0.046 s
% 13.17/3.58 % (31928)Instructions burned: 167 (million)
% 13.17/3.58 % (31928)------------------------------
% 13.17/3.58 % (31928)------------------------------
% 13.17/3.58 % (31924)Instruction limit reached!
% 13.17/3.58 % (31924)------------------------------
% 13.17/3.58 % (31924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.17/3.58 % (31925)Instruction limit reached!
% 13.17/3.58 % (31925)------------------------------
% 13.17/3.58 % (31925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.17/3.58 % (31925)Termination reason: Unknown
% 13.17/3.58 % (31925)Termination phase: Saturation
% 13.17/3.58
% 13.17/3.58 % (31925)Memory used [KB]: 6908
% 13.17/3.58 % (31925)Time elapsed: 0.063 s
% 13.17/3.58 % (31925)Instructions burned: 115 (million)
% 13.17/3.58 % (31925)------------------------------
% 13.17/3.58 % (31925)------------------------------
% 13.17/3.58 % (31924)Termination reason: Unknown
% 13.17/3.58 % (31924)Termination phase: Saturation
% 13.17/3.58
% 13.17/3.58 % (31924)Memory used [KB]: 7164
% 13.17/3.58 % (31924)Time elapsed: 0.089 s
% 13.17/3.58 % (31924)Instructions burned: 216 (million)
% 13.17/3.58 % (31924)------------------------------
% 13.17/3.58 % (31924)------------------------------
% 13.17/3.59 % (31929)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_31741 for (2984ds/50Mi)
% 13.99/3.60 % (31930)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_31741 for (2984ds/368Mi)
% 13.99/3.60 % (31929)Instruction limit reached!
% 13.99/3.60 % (31929)------------------------------
% 13.99/3.60 % (31929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.99/3.60 % (31929)Termination reason: Unknown
% 13.99/3.60 % (31929)Termination phase: Property scanning
% 13.99/3.60
% 13.99/3.60 % (31929)Memory used [KB]: 2174
% 13.99/3.60 % (31929)Time elapsed: 0.016 s
% 13.99/3.60 % (31929)Instructions burned: 51 (million)
% 13.99/3.60 % (31929)------------------------------
% 13.99/3.60 % (31929)------------------------------
% 13.99/3.60 % (31931)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_31741 for (2984ds/1021Mi)
% 13.99/3.60 % (31932)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_31741 for (2984ds/267Mi)
% 13.99/3.61 % (31933)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_31741 for (2984ds/204Mi)
% 13.99/3.61 % (31927)Instruction limit reached!
% 13.99/3.61 % (31927)------------------------------
% 13.99/3.61 % (31927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.99/3.61 % (31927)Termination reason: Unknown
% 13.99/3.61 % (31927)Termination phase: Saturation
% 13.99/3.61
% 13.99/3.61 % (31927)Memory used [KB]: 7164
% 13.99/3.61 % (31927)Time elapsed: 0.096 s
% 13.99/3.61 % (31927)Instructions burned: 182 (million)
% 13.99/3.61 % (31927)------------------------------
% 13.99/3.61 % (31927)------------------------------
% 13.99/3.65 % (31934)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_31741 for (2984ds/26Mi)
% 13.99/3.66 % (31934)Instruction limit reached!
% 13.99/3.66 % (31934)------------------------------
% 13.99/3.66 % (31934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.99/3.66 % (31934)Termination reason: Unknown
% 13.99/3.66 % (31934)Termination phase: shuffling
% 13.99/3.66
% 13.99/3.66 % (31934)Memory used [KB]: 1791
% 13.99/3.66 % (31934)Time elapsed: 0.017 s
% 13.99/3.66 % (31934)Instructions burned: 27 (million)
% 13.99/3.66 % (31934)------------------------------
% 13.99/3.66 % (31934)------------------------------
% 13.99/3.67 % (31933)Instruction limit reached!
% 13.99/3.67 % (31933)------------------------------
% 13.99/3.67 % (31933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.99/3.67 % (31933)Termination reason: Unknown
% 13.99/3.67 % (31933)Termination phase: Saturation
% 13.99/3.67
% 13.99/3.67 % (31933)Memory used [KB]: 7547
% 13.99/3.67 % (31933)Time elapsed: 0.062 s
% 13.99/3.67 % (31933)Instructions burned: 205 (million)
% 13.99/3.67 % (31933)------------------------------
% 13.99/3.67 % (31933)------------------------------
% 13.99/3.68 % (31935)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_31741 for (2983ds/53Mi)
% 13.99/3.69 % (31936)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_31741 for (2983ds/4436Mi)
% 14.24/3.72 % (31935)Instruction limit reached!
% 14.24/3.72 % (31935)------------------------------
% 14.24/3.72 % (31935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.24/3.72 % (31935)Termination reason: Unknown
% 14.24/3.72 % (31935)Termination phase: Property scanning
% 14.24/3.72
% 14.24/3.72 % (31935)Memory used [KB]: 2174
% 14.24/3.72 % (31935)Time elapsed: 0.029 s
% 14.24/3.72 % (31935)Instructions burned: 54 (million)
% 14.24/3.72 % (31935)------------------------------
% 14.24/3.72 % (31935)------------------------------
% 14.24/3.75 % (31937)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_31741 for (2983ds/1539Mi)
% 14.24/3.75 % (31932)Instruction limit reached!
% 14.24/3.75 % (31932)------------------------------
% 14.24/3.75 % (31932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.24/3.75 % (31932)Termination reason: Unknown
% 14.24/3.75 % (31932)Termination phase: Saturation
% 14.24/3.75
% 14.24/3.75 % (31932)Memory used [KB]: 7419
% 14.24/3.75 % (31932)Time elapsed: 0.146 s
% 14.24/3.75 % (31932)Instructions burned: 267 (million)
% 14.24/3.75 % (31932)------------------------------
% 14.24/3.75 % (31932)------------------------------
% 14.24/3.77 % (31938)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_31741 for (2982ds/408Mi)
% 14.24/3.80 % (31930)Instruction limit reached!
% 14.24/3.80 % (31930)------------------------------
% 14.24/3.80 % (31930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.24/3.80 % (31930)Termination reason: Unknown
% 14.24/3.80 % (31930)Termination phase: Saturation
% 14.24/3.80
% 14.24/3.80 % (31930)Memory used [KB]: 8315
% 14.24/3.80 % (31930)Time elapsed: 0.202 s
% 14.24/3.80 % (31930)Instructions burned: 368 (million)
% 14.24/3.80 % (31930)------------------------------
% 14.24/3.80 % (31930)------------------------------
% 14.45/3.82 % (31939)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_31741 for (2982ds/5205Mi)
% 14.66/3.93 % (31919)Instruction limit reached!
% 14.66/3.93 % (31919)------------------------------
% 14.66/3.93 % (31919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.66/3.93 % (31919)Termination reason: Unknown
% 14.66/3.93 % (31919)Termination phase: Saturation
% 14.66/3.93
% 14.66/3.93 % (31919)Memory used [KB]: 8955
% 14.66/3.93 % (31919)Time elapsed: 0.578 s
% 14.66/3.93 % (31919)Instructions burned: 988 (million)
% 14.66/3.93 % (31919)------------------------------
% 14.66/3.93 % (31919)------------------------------
% 14.66/3.95 % (31940)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_31741 for (2981ds/1913Mi)
% 14.66/4.00 % (31938)Instruction limit reached!
% 14.66/4.00 % (31938)------------------------------
% 14.66/4.00 % (31938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.66/4.00 % (31938)Termination reason: Unknown
% 14.66/4.00 % (31938)Termination phase: Saturation
% 14.66/4.00
% 14.66/4.00 % (31938)Memory used [KB]: 8059
% 14.66/4.00 % (31938)Time elapsed: 0.253 s
% 14.66/4.00 % (31938)Instructions burned: 408 (million)
% 14.66/4.00 % (31938)------------------------------
% 14.66/4.00 % (31938)------------------------------
% 17.16/4.03 % (31941)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_31741 for (2980ds/4350Mi)
% 17.16/4.05 % (31926)Instruction limit reached!
% 17.16/4.05 % (31926)------------------------------
% 17.16/4.05 % (31926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.16/4.05 % (31926)Termination reason: Unknown
% 17.16/4.05 % (31926)Termination phase: Saturation
% 17.16/4.05
% 17.16/4.05 % (31926)Memory used [KB]: 8187
% 17.16/4.05 % (31926)Time elapsed: 0.538 s
% 17.16/4.05 % (31926)Instructions burned: 922 (million)
% 17.16/4.05 % (31926)------------------------------
% 17.16/4.05 % (31926)------------------------------
% 17.16/4.08 % (31942)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_31741 for (2979ds/68Mi)
% 17.16/4.11 % (31942)Instruction limit reached!
% 17.16/4.11 % (31942)------------------------------
% 17.16/4.11 % (31942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.16/4.11 % (31942)Termination reason: Unknown
% 17.16/4.11 % (31942)Termination phase: Property scanning
% 17.16/4.11
% 17.16/4.11 % (31942)Memory used [KB]: 2046
% 17.16/4.11 % (31942)Time elapsed: 0.041 s
% 17.16/4.11 % (31942)Instructions burned: 69 (million)
% 17.16/4.11 % (31942)------------------------------
% 17.16/4.11 % (31942)------------------------------
% 17.77/4.14 % (31943)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_31741 for (2979ds/358Mi)
% 17.77/4.19 % (31931)Instruction limit reached!
% 17.77/4.19 % (31931)------------------------------
% 17.77/4.19 % (31931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.77/4.19 % (31931)Termination reason: Unknown
% 17.77/4.19 % (31931)Termination phase: Saturation
% 17.77/4.19
% 17.77/4.19 % (31931)Memory used [KB]: 9083
% 17.77/4.19 % (31931)Time elapsed: 0.588 s
% 17.77/4.19 % (31931)Instructions burned: 1022 (million)
% 17.77/4.19 % (31931)------------------------------
% 17.77/4.19 % (31931)------------------------------
% 18.16/4.21 % (31944)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_31741 for (2978ds/31Mi)
% 18.16/4.23 % (31944)Instruction limit reached!
% 18.16/4.23 % (31944)------------------------------
% 18.16/4.23 % (31944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.16/4.23 % (31944)Termination reason: Unknown
% 18.16/4.23 % (31944)Termination phase: Preprocessing 1
% 18.16/4.23
% 18.16/4.23 % (31944)Memory used [KB]: 1791
% 18.16/4.23 % (31944)Time elapsed: 0.019 s
% 18.16/4.23 % (31944)Instructions burned: 31 (million)
% 18.16/4.23 % (31944)------------------------------
% 18.16/4.23 % (31944)------------------------------
% 18.16/4.25 % (31945)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_31741 for (2978ds/279Mi)
% 18.59/4.34 % (31943)Instruction limit reached!
% 18.59/4.34 % (31943)------------------------------
% 18.59/4.34 % (31943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.59/4.34 % (31943)Termination reason: Unknown
% 18.59/4.34 % (31943)Termination phase: Saturation
% 18.59/4.34
% 18.59/4.34 % (31943)Memory used [KB]: 7931
% 18.59/4.34 % (31943)Time elapsed: 0.204 s
% 18.59/4.34 % (31943)Instructions burned: 358 (million)
% 18.59/4.34 % (31943)------------------------------
% 18.59/4.34 % (31943)------------------------------
% 18.59/4.34 % (31945)Refutation not found, incomplete strategy
% 18.59/4.34 % (31945)------------------------------
% 18.59/4.34 % (31945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.59/4.34 % (31945)Termination reason: Refutation not found, incomplete strategy
% 18.59/4.34
% 18.59/4.34
% 18.59/4.34 % (31945)Memory used [KB]: 7164
% 18.59/4.34 % (31945)Time elapsed: 0.095 s
% 18.59/4.34 % (31945)Instructions burned: 174 (million)
% 18.59/4.34 % (31945)------------------------------
% 18.59/4.34 % (31945)------------------------------
% 18.59/4.36 % (31946)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_31741 for (2977ds/258Mi)
% 18.59/4.37 % (31947)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_31741 for (2977ds/26Mi)
% 18.59/4.38 % (31947)Instruction limit reached!
% 18.59/4.38 % (31947)------------------------------
% 18.59/4.38 % (31947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.59/4.38 % (31947)Termination reason: Unknown
% 18.59/4.38 % (31947)Termination phase: shuffling
% 18.59/4.38
% 18.59/4.38 % (31947)Memory used [KB]: 1791
% 18.59/4.38 % (31947)Time elapsed: 0.016 s
% 18.59/4.38 % (31947)Instructions burned: 27 (million)
% 18.59/4.38 % (31947)------------------------------
% 18.59/4.38 % (31947)------------------------------
% 19.37/4.40 % (31948)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_31741 for (2976ds/995Mi)
% 19.78/4.51 % (31946)Instruction limit reached!
% 19.78/4.51 % (31946)------------------------------
% 19.78/4.51 % (31946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.78/4.51 % (31946)Termination reason: Unknown
% 19.78/4.51 % (31946)Termination phase: Saturation
% 19.78/4.51
% 19.78/4.51 % (31946)Memory used [KB]: 7547
% 19.78/4.51 % (31946)Time elapsed: 0.153 s
% 19.78/4.51 % (31946)Instructions burned: 258 (million)
% 19.78/4.51 % (31946)------------------------------
% 19.78/4.51 % (31946)------------------------------
% 19.78/4.53 % (31949)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_31741 for (2975ds/373Mi)
% 20.34/4.64 % (31937)Instruction limit reached!
% 20.34/4.64 % (31937)------------------------------
% 20.34/4.64 % (31937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.34/4.64 % (31937)Termination reason: Unknown
% 20.34/4.64 % (31937)Termination phase: Saturation
% 20.34/4.64
% 20.34/4.64 % (31937)Memory used [KB]: 9850
% 20.34/4.64 % (31937)Time elapsed: 0.899 s
% 20.34/4.64 % (31937)Instructions burned: 1540 (million)
% 20.34/4.64 % (31937)------------------------------
% 20.34/4.64 % (31937)------------------------------
% 20.34/4.67 % (31950)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_31741 for (2974ds/253Mi)
% 20.71/4.74 % (31949)Instruction limit reached!
% 20.71/4.74 % (31949)------------------------------
% 20.71/4.74 % (31949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.71/4.74 % (31949)Termination reason: Unknown
% 20.71/4.74 % (31949)Termination phase: Saturation
% 20.71/4.74
% 20.71/4.74 % (31949)Memory used [KB]: 8187
% 20.71/4.74 % (31949)Time elapsed: 0.212 s
% 20.71/4.74 % (31949)Instructions burned: 374 (million)
% 20.71/4.74 % (31949)------------------------------
% 20.71/4.74 % (31949)------------------------------
% 20.71/4.77 % (31951)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_31741 for (2973ds/832Mi)
% 21.25/4.81 % (31950)Instruction limit reached!
% 21.25/4.81 % (31950)------------------------------
% 21.25/4.81 % (31950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.25/4.81 % (31950)Termination reason: Unknown
% 21.25/4.81 % (31950)Termination phase: Saturation
% 21.25/4.81
% 21.25/4.81 % (31950)Memory used [KB]: 7675
% 21.25/4.81 % (31950)Time elapsed: 0.140 s
% 21.25/4.81 % (31950)Instructions burned: 254 (million)
% 21.25/4.81 % (31950)------------------------------
% 21.25/4.81 % (31950)------------------------------
% 21.25/4.83 % (31952)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_31741 for (2972ds/668Mi)
% 21.25/4.86 % (31940)Instruction limit reached!
% 21.25/4.86 % (31940)------------------------------
% 21.25/4.86 % (31940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.25/4.86 % (31940)Termination reason: Unknown
% 21.25/4.86 % (31940)Termination phase: Saturation
% 21.25/4.86
% 21.25/4.86 % (31940)Memory used [KB]: 3326
% 21.25/4.86 % (31940)Time elapsed: 0.933 s
% 21.25/4.86 % (31940)Instructions burned: 1913 (million)
% 21.25/4.86 % (31940)------------------------------
% 21.25/4.86 % (31940)------------------------------
% 21.25/4.88 % (31953)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_31741 for (2971ds/40Mi)
% 21.69/4.91 % (31953)Instruction limit reached!
% 21.69/4.91 % (31953)------------------------------
% 21.69/4.91 % (31953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.69/4.91 % (31953)Termination reason: Unknown
% 21.69/4.91 % (31953)Termination phase: shuffling
% 21.69/4.91
% 21.69/4.91 % (31953)Memory used [KB]: 2174
% 21.69/4.91 % (31953)Time elapsed: 0.024 s
% 21.69/4.91 % (31953)Instructions burned: 40 (million)
% 21.69/4.91 % (31953)------------------------------
% 21.69/4.91 % (31953)------------------------------
% 21.69/4.93 % (31954)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_31741 for (2971ds/294Mi)
% 21.69/4.97 % (31948)Instruction limit reached!
% 21.69/4.97 % (31948)------------------------------
% 21.69/4.97 % (31948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.69/4.97 % (31948)Termination reason: Unknown
% 21.69/4.97 % (31948)Termination phase: Saturation
% 21.69/4.97
% 21.69/4.97 % (31948)Memory used [KB]: 9978
% 21.69/4.97 % (31948)Time elapsed: 0.570 s
% 21.69/4.97 % (31948)Instructions burned: 995 (million)
% 21.69/4.97 % (31948)------------------------------
% 21.69/4.97 % (31948)------------------------------
% 21.69/4.99 % (31955)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_31741 for (2970ds/187Mi)
% 21.69/5.01 % (31954)Refutation not found, incomplete strategy
% 21.69/5.01 % (31954)------------------------------
% 21.69/5.01 % (31954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.69/5.01 % (31954)Termination reason: Refutation not found, incomplete strategy
% 21.69/5.01
% 21.69/5.01
% 21.69/5.01 % (31954)Memory used [KB]: 6908
% 21.69/5.01 % (31954)Time elapsed: 0.099 s
% 21.69/5.01 % (31954)Instructions burned: 140 (million)
% 21.69/5.01 % (31954)------------------------------
% 21.69/5.01 % (31954)------------------------------
% 24.22/5.04 % (31956)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_31741 for (2970ds/371Mi)
% 24.22/5.10 % (31955)Instruction limit reached!
% 24.22/5.10 % (31955)------------------------------
% 24.22/5.10 % (31955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.22/5.10 % (31955)Termination reason: Unknown
% 24.22/5.10 % (31955)Termination phase: Saturation
% 24.22/5.10
% 24.22/5.10 % (31955)Memory used [KB]: 7419
% 24.22/5.10 % (31955)Time elapsed: 0.105 s
% 24.22/5.10 % (31955)Instructions burned: 188 (million)
% 24.22/5.10 % (31955)------------------------------
% 24.22/5.10 % (31955)------------------------------
% 24.22/5.12 % (31957)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_31741 for (2969ds/1827Mi)
% 25.14/5.20 % (31952)Instruction limit reached!
% 25.14/5.20 % (31952)------------------------------
% 25.14/5.20 % (31952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.14/5.20 % (31952)Termination reason: Unknown
% 25.14/5.20 % (31952)Termination phase: Saturation
% 25.14/5.20
% 25.14/5.20 % (31952)Memory used [KB]: 14328
% 25.14/5.20 % (31952)Time elapsed: 0.374 s
% 25.14/5.20 % (31952)Instructions burned: 668 (million)
% 25.14/5.20 % (31952)------------------------------
% 25.14/5.20 % (31952)------------------------------
% 25.14/5.25 % (31958)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_31741 for (2968ds/70Mi)
% 25.14/5.25 % (31956)Instruction limit reached!
% 25.14/5.25 % (31956)------------------------------
% 25.14/5.25 % (31956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.14/5.25 % (31956)Termination reason: Unknown
% 25.14/5.25 % (31956)Termination phase: Saturation
% 25.14/5.25
% 25.14/5.25 % (31956)Memory used [KB]: 8443
% 25.14/5.25 % (31956)Time elapsed: 0.237 s
% 25.14/5.25 % (31956)Instructions burned: 371 (million)
% 25.14/5.25 % (31956)------------------------------
% 25.14/5.25 % (31956)------------------------------
% 25.14/5.25 % (31951)Instruction limit reached!
% 25.14/5.25 % (31951)------------------------------
% 25.14/5.25 % (31951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.14/5.25 % (31951)Termination reason: Unknown
% 25.14/5.25 % (31951)Termination phase: Saturation
% 25.14/5.25
% 25.14/5.25 % (31951)Memory used [KB]: 8443
% 25.14/5.25 % (31951)Time elapsed: 0.489 s
% 25.14/5.25 % (31951)Instructions burned: 833 (million)
% 25.14/5.25 % (31951)------------------------------
% 25.14/5.25 % (31951)------------------------------
% 25.14/5.27 % (31958)Instruction limit reached!
% 25.14/5.27 % (31958)------------------------------
% 25.14/5.27 % (31958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.14/5.27 % (31958)Termination reason: Unknown
% 25.14/5.27 % (31958)Termination phase: Property scanning
% 25.14/5.27
% 25.14/5.27 % (31958)Memory used [KB]: 2302
% 25.14/5.27 % (31958)Time elapsed: 0.023 s
% 25.14/5.27 % (31958)Instructions burned: 71 (million)
% 25.14/5.27 % (31958)------------------------------
% 25.14/5.27 % (31958)------------------------------
% 25.14/5.27 % (31959)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_31741 for (2968ds/316Mi)
% 25.14/5.27 % (31960)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_31741 for (2967ds/932Mi)
% 25.14/5.29 % (31961)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_31741 for (2967ds/4714Mi)
% 25.78/5.38 % (31959)Refutation not found, incomplete strategy
% 25.78/5.38 % (31959)------------------------------
% 25.78/5.38 % (31959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.78/5.38 % (31959)Termination reason: Refutation not found, incomplete strategy
% 25.78/5.38
% 25.78/5.38
% 25.78/5.38 % (31959)Memory used [KB]: 7419
% 25.78/5.38 % (31959)Time elapsed: 0.137 s
% 25.78/5.38 % (31959)Instructions burned: 210 (million)
% 25.78/5.38 % (31959)------------------------------
% 25.78/5.38 % (31959)------------------------------
% 26.22/5.41 % (31962)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_31741 for (2966ds/8250Mi)
% 26.22/5.42 % (31961)Refutation not found, incomplete strategy
% 26.22/5.42 % (31961)------------------------------
% 26.22/5.42 % (31961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.22/5.42 % (31961)Termination reason: Refutation not found, incomplete strategy
% 26.22/5.42
% 26.22/5.42
% 26.22/5.42 % (31961)Memory used [KB]: 7547
% 26.22/5.42 % (31961)Time elapsed: 0.126 s
% 26.22/5.42 % (31961)Instructions burned: 232 (million)
% 26.22/5.42 % (31961)------------------------------
% 26.22/5.42 % (31961)------------------------------
% 26.22/5.44 % (31963)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_31741 for (2966ds/770Mi)
% 27.56/5.81 % (31960)Instruction limit reached!
% 27.56/5.81 % (31960)------------------------------
% 27.56/5.81 % (31960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.56/5.81 % (31960)Termination reason: Unknown
% 27.56/5.81 % (31960)Termination phase: Saturation
% 27.56/5.81
% 27.56/5.81 % (31960)Memory used [KB]: 9978
% 27.56/5.81 % (31960)Time elapsed: 0.536 s
% 27.56/5.81 % (31960)Instructions burned: 933 (million)
% 27.56/5.81 % (31960)------------------------------
% 27.56/5.81 % (31960)------------------------------
% 27.56/5.83 % (31964)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_31741 for (2962ds/794Mi)
% 27.56/5.89 % (31963)Instruction limit reached!
% 27.56/5.89 % (31963)------------------------------
% 27.56/5.89 % (31963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.56/5.89 % (31963)Termination reason: Unknown
% 27.56/5.89 % (31963)Termination phase: Saturation
% 27.56/5.89
% 27.56/5.89 % (31963)Memory used [KB]: 7675
% 27.56/5.89 % (31963)Time elapsed: 0.453 s
% 27.56/5.89 % (31963)Instructions burned: 770 (million)
% 27.56/5.89 % (31963)------------------------------
% 27.56/5.89 % (31963)------------------------------
% 28.88/5.91 % (31965)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_31741 for (2961ds/464Mi)
% 31.85/6.18 % (31965)Instruction limit reached!
% 31.85/6.18 % (31965)------------------------------
% 31.85/6.18 % (31965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.85/6.18 % (31965)Termination reason: Unknown
% 31.85/6.18 % (31965)Termination phase: Saturation
% 31.85/6.18
% 31.85/6.18 % (31965)Memory used [KB]: 8187
% 31.85/6.18 % (31965)Time elapsed: 0.267 s
% 31.85/6.18 % (31965)Instructions burned: 465 (million)
% 31.85/6.18 % (31965)------------------------------
% 31.85/6.18 % (31965)------------------------------
% 31.85/6.20 % (31936)Instruction limit reached!
% 31.85/6.20 % (31936)------------------------------
% 31.85/6.20 % (31936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.85/6.20 % (31936)Termination reason: Unknown
% 31.85/6.20 % (31936)Termination phase: Saturation
% 31.85/6.20
% 31.85/6.20 % (31936)Memory used [KB]: 12792
% 31.85/6.20 % (31936)Time elapsed: 2.522 s
% 31.85/6.20 % (31936)Instructions burned: 4437 (million)
% 31.85/6.20 % (31936)------------------------------
% 31.85/6.20 % (31936)------------------------------
% 29.90/6.20 % (31966)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_31741 for (2958ds/1376Mi)
% 29.90/6.22 % (31957)Instruction limit reached!
% 29.90/6.22 % (31957)------------------------------
% 29.90/6.22 % (31957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.90/6.22 % (31957)Termination reason: Unknown
% 29.90/6.22 % (31957)Termination phase: Saturation
% 29.90/6.22
% 29.90/6.22 % (31957)Memory used [KB]: 9466
% 29.90/6.22 % (31957)Time elapsed: 1.123 s
% 29.90/6.22 % (31957)Instructions burned: 1828 (million)
% 29.90/6.22 % (31957)------------------------------
% 29.90/6.22 % (31957)------------------------------
% 29.90/6.22 % (31967)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_31741 for (2958ds/906Mi)
% 29.90/6.24 % (31968)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_31741 for (2958ds/434Mi)
% 29.90/6.29 % (31964)Instruction limit reached!
% 29.90/6.29 % (31964)------------------------------
% 29.90/6.29 % (31964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.90/6.29 % (31964)Termination reason: Unknown
% 29.90/6.29 % (31964)Termination phase: Saturation
% 29.90/6.29
% 29.90/6.29 % (31964)Memory used [KB]: 6012
% 29.90/6.29 % (31964)Time elapsed: 0.459 s
% 29.90/6.29 % (31964)Instructions burned: 794 (million)
% 29.90/6.29 % (31964)------------------------------
% 29.90/6.29 % (31964)------------------------------
% 32.76/6.31 % (31969)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_31741 for (2957ds/865Mi)
% 33.06/6.43 % (31941)Instruction limit reached!
% 33.06/6.43 % (31941)------------------------------
% 33.06/6.43 % (31941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.06/6.43 % (31941)Termination reason: Unknown
% 33.06/6.43 % (31941)Termination phase: Saturation
% 33.06/6.43
% 33.06/6.43 % (31941)Memory used [KB]: 13304
% 33.06/6.43 % (31941)Time elapsed: 2.411 s
% 33.06/6.43 % (31941)Instructions burned: 4351 (million)
% 33.06/6.43 % (31941)------------------------------
% 33.06/6.43 % (31941)------------------------------
% 33.06/6.46 % (31970)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_31741 for (2956ds/593Mi)
% 33.06/6.48 % (31968)Instruction limit reached!
% 33.06/6.48 % (31968)------------------------------
% 33.06/6.48 % (31968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.06/6.48 % (31968)Termination reason: Unknown
% 33.06/6.48 % (31968)Termination phase: Saturation
% 33.06/6.48
% 33.06/6.48 % (31968)Memory used [KB]: 7675
% 33.06/6.48 % (31968)Time elapsed: 0.243 s
% 33.06/6.48 % (31968)Instructions burned: 435 (million)
% 33.06/6.48 % (31968)------------------------------
% 33.06/6.48 % (31968)------------------------------
% 33.57/6.50 % (31971)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_31741 for (2955ds/443Mi)
% 33.97/6.75 % (31971)Instruction limit reached!
% 33.97/6.75 % (31971)------------------------------
% 33.97/6.75 % (31971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.97/6.75 % (31971)Termination reason: Unknown
% 33.97/6.75 % (31971)Termination phase: Saturation
% 33.97/6.75
% 33.97/6.75 % (31971)Memory used [KB]: 8315
% 33.97/6.76 % (31971)Time elapsed: 0.253 s
% 33.97/6.76 % (31971)Instructions burned: 443 (million)
% 33.97/6.76 % (31971)------------------------------
% 33.97/6.76 % (31971)------------------------------
% 33.97/6.78 % (31972)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_31741 for (2952ds/594Mi)
% 33.97/6.78 % (31970)Instruction limit reached!
% 33.97/6.78 % (31970)------------------------------
% 33.97/6.78 % (31970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.97/6.78 % (31970)Termination reason: Unknown
% 33.97/6.78 % (31970)Termination phase: Saturation
% 33.97/6.78
% 33.97/6.78 % (31970)Memory used [KB]: 9594
% 33.97/6.78 % (31970)Time elapsed: 0.328 s
% 33.97/6.78 % (31970)Instructions burned: 593 (million)
% 33.97/6.78 % (31970)------------------------------
% 33.97/6.78 % (31970)------------------------------
% 33.97/6.79 % (31967)Instruction limit reached!
% 33.97/6.79 % (31967)------------------------------
% 33.97/6.79 % (31967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.97/6.79 % (31967)Termination reason: Unknown
% 33.97/6.79 % (31967)Termination phase: Saturation
% 33.97/6.79
% 33.97/6.79 % (31967)Memory used [KB]: 12281
% 33.97/6.79 % (31967)Time elapsed: 0.572 s
% 33.97/6.79 % (31967)Instructions burned: 906 (million)
% 33.97/6.79 % (31967)------------------------------
% 33.97/6.79 % (31967)------------------------------
% 33.97/6.79 % (31969)Instruction limit reached!
% 33.97/6.79 % (31969)------------------------------
% 33.97/6.79 % (31969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.97/6.79 % (31969)Termination reason: Unknown
% 33.97/6.79 % (31969)Termination phase: Saturation
% 33.97/6.79
% 33.97/6.79 % (31969)Memory used [KB]: 9338
% 33.97/6.79 % (31969)Time elapsed: 0.484 s
% 33.97/6.79 % (31969)Instructions burned: 866 (million)
% 33.97/6.79 % (31969)------------------------------
% 33.97/6.79 % (31969)------------------------------
% 35.90/6.80 % (31939)Instruction limit reached!
% 35.90/6.80 % (31939)------------------------------
% 35.90/6.80 % (31939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.90/6.80 % (31939)Termination reason: Unknown
% 35.90/6.80 % (31939)Termination phase: Saturation
% 35.90/6.80
% 35.90/6.80 % (31939)Memory used [KB]: 13304
% 35.90/6.80 % (31939)Time elapsed: 2.983 s
% 35.90/6.80 % (31939)Instructions burned: 5205 (million)
% 35.90/6.80 % (31939)------------------------------
% 35.90/6.80 % (31939)------------------------------
% 35.90/6.80 % (31973)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_31741 for (2952ds/327Mi)
% 35.90/6.81 % (31974)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_31741 for (2952ds/5411Mi)
% 35.90/6.81 % (31975)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_31741 for (2952ds/1762Mi)
% 35.90/6.82 % (31976)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_31741 for (2952ds/96Mi)
% 35.90/6.87 % (31976)Instruction limit reached!
% 35.90/6.87 % (31976)------------------------------
% 35.90/6.87 % (31976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.90/6.87 % (31976)Termination reason: Unknown
% 35.90/6.87 % (31976)Termination phase: Function definition elimination
% 35.90/6.87
% 35.90/6.87 % (31976)Memory used [KB]: 2302
% 35.90/6.87 % (31976)Time elapsed: 0.051 s
% 35.90/6.87 % (31976)Instructions burned: 97 (million)
% 35.90/6.87 % (31976)------------------------------
% 35.90/6.87 % (31976)------------------------------
% 35.90/6.89 % (31977)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_31741 for (2951ds/503Mi)
% 36.08/6.99 % (31966)Instruction limit reached!
% 36.08/6.99 % (31966)------------------------------
% 36.08/6.99 % (31966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.08/6.99 % (31966)Termination reason: Unknown
% 36.08/6.99 % (31966)Termination phase: Saturation
% 36.08/6.99
% 36.08/6.99 % (31966)Memory used [KB]: 9850
% 36.08/6.99 % (31966)Time elapsed: 0.791 s
% 36.08/6.99 % (31966)Instructions burned: 1376 (million)
% 36.08/6.99 % (31966)------------------------------
% 36.08/6.99 % (31966)------------------------------
% 36.08/6.99 % (31973)Instruction limit reached!
% 36.08/6.99 % (31973)------------------------------
% 36.08/6.99 % (31973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.08/6.99 % (31973)Termination reason: Unknown
% 36.08/6.99 % (31973)Termination phase: Saturation
% 36.08/6.99
% 36.08/6.99 % (31973)Memory used [KB]: 7675
% 36.08/6.99 % (31973)Time elapsed: 0.192 s
% 36.08/6.99 % (31973)Instructions burned: 327 (million)
% 36.08/6.99 % (31973)------------------------------
% 36.08/6.99 % (31973)------------------------------
% 36.08/7.01 % (31978)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_31741 for (2950ds/90Mi)
% 36.08/7.02 % (31979)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_31741 for (2950ds/593Mi)
% 38.18/7.06 % (31978)Instruction limit reached!
% 38.18/7.06 % (31978)------------------------------
% 38.18/7.06 % (31978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.18/7.06 % (31978)Termination reason: Unknown
% 38.18/7.06 % (31978)Termination phase: Property scanning
% 38.18/7.06
% 38.18/7.06 % (31978)Memory used [KB]: 2046
% 38.18/7.06 % (31978)Time elapsed: 0.051 s
% 38.18/7.06 % (31978)Instructions burned: 91 (million)
% 38.18/7.06 % (31978)------------------------------
% 38.18/7.06 % (31978)------------------------------
% 38.18/7.08 % (31980)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_31741 for (2949ds/1512Mi)
% 38.18/7.12 % (31972)Instruction limit reached!
% 38.18/7.12 % (31972)------------------------------
% 38.18/7.12 % (31972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.18/7.12 % (31972)Termination reason: Unknown
% 38.18/7.12 % (31972)Termination phase: Saturation
% 38.18/7.12
% 38.18/7.12 % (31972)Memory used [KB]: 8187
% 38.18/7.12 % (31972)Time elapsed: 0.343 s
% 38.18/7.12 % (31972)Instructions burned: 595 (million)
% 38.18/7.12 % (31972)------------------------------
% 38.18/7.12 % (31972)------------------------------
% 38.81/7.14 % (31981)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_31741 for (2949ds/569Mi)
% 38.81/7.18 % (31977)Instruction limit reached!
% 38.81/7.18 % (31977)------------------------------
% 38.81/7.18 % (31977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.81/7.18 % (31977)Termination reason: Unknown
% 38.81/7.18 % (31977)Termination phase: Saturation
% 38.81/7.18
% 38.81/7.18 % (31977)Memory used [KB]: 7931
% 38.81/7.18 % (31977)Time elapsed: 0.286 s
% 38.81/7.18 % (31977)Instructions burned: 504 (million)
% 38.81/7.18 % (31977)------------------------------
% 38.81/7.18 % (31977)------------------------------
% 38.81/7.19 % (31982)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_31741 for (2948ds/501Mi)
% 39.12/7.28 % (31979)Instruction limit reached!
% 39.12/7.28 % (31979)------------------------------
% 39.12/7.28 % (31979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.12/7.28 % (31979)Termination reason: Unknown
% 39.12/7.28 % (31979)Termination phase: Saturation
% 39.12/7.28
% 39.12/7.28 % (31979)Memory used [KB]: 8827
% 39.12/7.28 % (31979)Time elapsed: 0.264 s
% 39.12/7.28 % (31979)Instructions burned: 595 (million)
% 39.12/7.28 % (31979)------------------------------
% 39.12/7.28 % (31979)------------------------------
% 39.12/7.29 % (31983)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_31741 for (2947ds/562Mi)
% 39.51/7.36 % (31982)Instruction limit reached!
% 39.51/7.36 % (31982)------------------------------
% 39.51/7.36 % (31982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.51/7.36 % (31982)Termination reason: Unknown
% 39.51/7.36 % (31982)Termination phase: Saturation
% 39.51/7.36
% 39.51/7.36 % (31982)Memory used [KB]: 8315
% 39.51/7.36 % (31982)Time elapsed: 0.170 s
% 39.51/7.36 % (31982)Instructions burned: 502 (million)
% 39.51/7.36 % (31982)------------------------------
% 39.51/7.36 % (31982)------------------------------
% 39.51/7.37 % (31984)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_31741 for (2946ds/406Mi)
% 40.00/7.45 % (31981)Instruction limit reached!
% 40.00/7.45 % (31981)------------------------------
% 40.00/7.45 % (31981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.00/7.45 % (31981)Termination reason: Unknown
% 40.00/7.45 % (31981)Termination phase: Saturation
% 40.00/7.45
% 40.00/7.45 % (31981)Memory used [KB]: 9083
% 40.00/7.45 % (31981)Time elapsed: 0.314 s
% 40.00/7.45 % (31981)Instructions burned: 571 (million)
% 40.00/7.45 % (31981)------------------------------
% 40.00/7.45 % (31981)------------------------------
% 40.00/7.46 % (31983)Instruction limit reached!
% 40.00/7.46 % (31983)------------------------------
% 40.00/7.46 % (31983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.00/7.46 % (31983)Termination reason: Unknown
% 40.00/7.46 % (31983)Termination phase: Saturation
% 40.00/7.46
% 40.00/7.46 % (31983)Memory used [KB]: 8827
% 40.00/7.46 % (31983)Time elapsed: 0.169 s
% 40.00/7.46 % (31983)Instructions burned: 563 (million)
% 40.00/7.46 % (31983)------------------------------
% 40.00/7.46 % (31983)------------------------------
% 40.00/7.46 % (31985)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_31741 for (2945ds/582Mi)
% 40.00/7.47 % (31986)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_31741 for (2945ds/456Mi)
% 40.81/7.50 % (31984)Instruction limit reached!
% 40.81/7.50 % (31984)------------------------------
% 40.81/7.50 % (31984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.81/7.50 % (31984)Termination reason: Unknown
% 40.81/7.50 % (31984)Termination phase: Saturation
% 40.81/7.50
% 40.81/7.50 % (31984)Memory used [KB]: 7803
% 40.81/7.50 % (31984)Time elapsed: 0.128 s
% 40.81/7.50 % (31984)Instructions burned: 406 (million)
% 40.81/7.50 % (31984)------------------------------
% 40.81/7.50 % (31984)------------------------------
% 40.81/7.51 % (31987)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_31741 for (2945ds/393Mi)
% 40.81/7.59 % (31975)Instruction limit reached!
% 40.81/7.59 % (31975)------------------------------
% 40.81/7.59 % (31975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.81/7.59 % (31975)Termination reason: Unknown
% 40.81/7.59 % (31975)Termination phase: Saturation
% 40.81/7.59
% 40.81/7.59 % (31975)Memory used [KB]: 8187
% 40.81/7.59 % (31975)Time elapsed: 0.784 s
% 40.81/7.59 % (31975)Instructions burned: 1762 (million)
% 40.81/7.59 % (31975)------------------------------
% 40.81/7.59 % (31975)------------------------------
% 41.26/7.61 % (31986)Instruction limit reached!
% 41.26/7.61 % (31986)------------------------------
% 41.26/7.61 % (31986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.26/7.61 % (31986)Termination reason: Unknown
% 41.26/7.61 % (31986)Termination phase: Saturation
% 41.26/7.61
% 41.26/7.61 % (31986)Memory used [KB]: 8187
% 41.26/7.61 % (31986)Time elapsed: 0.141 s
% 41.26/7.61 % (31986)Instructions burned: 456 (million)
% 41.26/7.61 % (31986)------------------------------
% 41.26/7.61 % (31986)------------------------------
% 41.26/7.61 % (31988)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_31741 for (2944ds/1335Mi)
% 41.26/7.62 % (31989)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_31741 for (2944ds/3373Mi)
% 41.26/7.62 % (31987)Instruction limit reached!
% 41.26/7.62 % (31987)------------------------------
% 41.26/7.62 % (31987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.26/7.62 % (31987)Termination reason: Unknown
% 41.26/7.62 % (31987)Termination phase: Saturation
% 41.26/7.62
% 41.26/7.62 % (31987)Memory used [KB]: 7803
% 41.26/7.62 % (31987)Time elapsed: 0.115 s
% 41.26/7.62 % (31987)Instructions burned: 394 (million)
% 41.26/7.62 % (31987)------------------------------
% 41.26/7.62 % (31987)------------------------------
% 41.26/7.63 % (31980)Instruction limit reached!
% 41.26/7.63 % (31980)------------------------------
% 41.26/7.63 % (31980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.26/7.63 % (31980)Termination reason: Unknown
% 41.26/7.63 % (31980)Termination phase: Saturation
% 41.26/7.63
% 41.26/7.63 % (31980)Memory used [KB]: 9083
% 41.26/7.63 % (31980)Time elapsed: 0.553 s
% 41.26/7.63 % (31980)Instructions burned: 1512 (million)
% 41.26/7.63 % (31980)------------------------------
% 41.26/7.63 % (31980)------------------------------
% 41.26/7.63 % (31990)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_31741 for (2944ds/474Mi)
% 41.26/7.64 % (31991)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_31741 for (2944ds/157Mi)
% 41.26/7.64 % (31985)Instruction limit reached!
% 41.26/7.64 % (31985)------------------------------
% 41.26/7.64 % (31985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.26/7.64 % (31985)Termination reason: Unknown
% 41.26/7.64 % (31985)Termination phase: Saturation
% 41.26/7.64
% 41.26/7.64 % (31985)Memory used [KB]: 7803
% 41.26/7.64 % (31985)Time elapsed: 0.181 s
% 41.26/7.64 % (31985)Instructions burned: 582 (million)
% 41.26/7.64 % (31985)------------------------------
% 41.26/7.64 % (31985)------------------------------
% 41.26/7.65 % (31992)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_31741 for (2944ds/590Mi)
% 41.26/7.68 % (31991)Instruction limit reached!
% 41.26/7.68 % (31991)------------------------------
% 41.26/7.68 % (31991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.26/7.68 % (31991)Termination reason: Unknown
% 41.26/7.68 % (31991)Termination phase: Saturation
% 41.26/7.68
% 41.26/7.68 % (31991)Memory used [KB]: 6908
% 41.26/7.68 % (31991)Time elapsed: 0.042 s
% 41.26/7.68 % (31991)Instructions burned: 160 (million)
% 41.26/7.68 % (31991)------------------------------
% 41.26/7.68 % (31991)------------------------------
% 41.26/7.69 % (31993)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_31741 for (2943ds/104Mi)
% 42.55/7.72 % (31993)Instruction limit reached!
% 42.55/7.72 % (31993)------------------------------
% 42.55/7.72 % (31993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.55/7.72 % (31993)Termination reason: Unknown
% 42.55/7.72 % (31993)Termination phase: Saturation
% 42.55/7.72
% 42.55/7.72 % (31993)Memory used [KB]: 2302
% 42.55/7.72 % (31993)Time elapsed: 0.032 s
% 42.55/7.72 % (31993)Instructions burned: 106 (million)
% 42.55/7.72 % (31993)------------------------------
% 42.55/7.72 % (31993)------------------------------
% 42.55/7.73 % (31994)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_31741 for (2943ds/414Mi)
% 42.55/7.77 % (31990)Instruction limit reached!
% 42.55/7.77 % (31990)------------------------------
% 42.55/7.77 % (31990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.55/7.77 % (31990)Termination reason: Unknown
% 42.55/7.77 % (31990)Termination phase: Saturation
% 42.55/7.77
% 42.55/7.77 % (31990)Memory used [KB]: 7803
% 42.55/7.77 % (31990)Time elapsed: 0.143 s
% 42.55/7.77 % (31990)Instructions burned: 476 (million)
% 42.55/7.77 % (31990)------------------------------
% 42.55/7.77 % (31990)------------------------------
% 42.55/7.78 % (31995)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_31741 for (2942ds/715Mi)
% 42.94/7.85 % (31994)Instruction limit reached!
% 42.94/7.85 % (31994)------------------------------
% 42.94/7.85 % (31994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.94/7.85 % (31994)Termination reason: Unknown
% 42.94/7.85 % (31994)Termination phase: Saturation
% 42.94/7.85
% 42.94/7.85 % (31994)Memory used [KB]: 7675
% 42.94/7.85 % (31994)Time elapsed: 0.142 s
% 42.94/7.85 % (31994)Instructions burned: 416 (million)
% 42.94/7.85 % (31994)------------------------------
% 42.94/7.85 % (31994)------------------------------
% 42.94/7.85 % (31992)Instruction limit reached!
% 42.94/7.85 % (31992)------------------------------
% 42.94/7.85 % (31992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.94/7.85 % (31992)Termination reason: Unknown
% 42.94/7.85 % (31992)Termination phase: Saturation
% 42.94/7.85
% 42.94/7.85 % (31992)Memory used [KB]: 9338
% 42.94/7.85 % (31992)Time elapsed: 0.198 s
% 42.94/7.85 % (31992)Instructions burned: 591 (million)
% 42.94/7.85 % (31992)------------------------------
% 42.94/7.85 % (31992)------------------------------
% 42.94/7.86 % (32021)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_31741 for (2941ds/961Mi)
% 42.94/7.86 % (32022)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_31741 for (2941ds/1213Mi)
% 43.46/8.01 % (31995)Instruction limit reached!
% 43.46/8.01 % (31995)------------------------------
% 43.46/8.01 % (31995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.46/8.01 % (31995)Termination reason: Unknown
% 43.46/8.01 % (31995)Termination phase: Saturation
% 43.46/8.01
% 43.46/8.01 % (31995)Memory used [KB]: 4221
% 43.46/8.01 % (31995)Time elapsed: 0.231 s
% 43.46/8.01 % (31995)Instructions burned: 716 (million)
% 43.46/8.01 % (31995)------------------------------
% 43.46/8.01 % (31995)------------------------------
% 45.04/8.02 % (32094)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_31741 for (2940ds/1979Mi)
% 45.04/8.03 % (31988)Instruction limit reached!
% 45.04/8.03 % (31988)------------------------------
% 45.04/8.03 % (31988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.04/8.03 % (31988)Termination reason: Unknown
% 45.04/8.03 % (31988)Termination phase: Saturation
% 45.04/8.03
% 45.04/8.03 % (31988)Memory used [KB]: 9722
% 45.04/8.03 % (31988)Time elapsed: 0.421 s
% 45.04/8.03 % (31988)Instructions burned: 1336 (million)
% 45.04/8.03 % (31988)------------------------------
% 45.04/8.03 % (31988)------------------------------
% 45.04/8.04 % (32104)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_31741 for (2940ds/481Mi)
% 45.57/8.17 % (32021)Instruction limit reached!
% 45.57/8.17 % (32021)------------------------------
% 45.57/8.17 % (32021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.57/8.17 % (32021)Termination reason: Unknown
% 45.57/8.17 % (32021)Termination phase: Saturation
% 45.57/8.17
% 45.57/8.17 % (32021)Memory used [KB]: 8315
% 45.57/8.17 % (32021)Time elapsed: 0.311 s
% 45.57/8.17 % (32021)Instructions burned: 963 (million)
% 45.57/8.17 % (32021)------------------------------
% 45.57/8.17 % (32021)------------------------------
% 45.57/8.18 % (32165)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_31741 for (2938ds/783Mi)
% 45.57/8.19 % (32104)Instruction limit reached!
% 45.57/8.19 % (32104)------------------------------
% 45.57/8.19 % (32104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.57/8.19 % (32104)Termination reason: Unknown
% 45.57/8.19 % (32104)Termination phase: Saturation
% 45.57/8.19
% 45.57/8.19 % (32104)Memory used [KB]: 7803
% 45.57/8.19 % (32104)Time elapsed: 0.149 s
% 45.57/8.19 % (32104)Instructions burned: 481 (million)
% 45.57/8.19 % (32104)------------------------------
% 45.57/8.19 % (32104)------------------------------
% 45.57/8.20 % (32171)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_31741 for (2938ds/432Mi)
% 46.53/8.30 % (32022)Instruction limit reached!
% 46.53/8.30 % (32022)------------------------------
% 46.53/8.30 % (32022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.53/8.30 % (32022)Termination reason: Unknown
% 46.53/8.30 % (32022)Termination phase: Saturation
% 46.53/8.30
% 46.53/8.30 % (32022)Memory used [KB]: 8571
% 46.53/8.30 % (32022)Time elapsed: 0.433 s
% 46.53/8.30 % (32022)Instructions burned: 1213 (million)
% 46.53/8.30 % (32022)------------------------------
% 46.53/8.30 % (32022)------------------------------
% 46.53/8.31 % (32214)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_31741 for (2937ds/1670Mi)
% 46.53/8.33 % (32171)Instruction limit reached!
% 46.53/8.33 % (32171)------------------------------
% 46.53/8.33 % (32171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.53/8.33 % (32171)Termination reason: Unknown
% 46.53/8.33 % (32171)Termination phase: Saturation
% 46.53/8.33
% 46.53/8.33 % (32171)Memory used [KB]: 7675
% 46.53/8.33 % (32171)Time elapsed: 0.137 s
% 46.53/8.33 % (32171)Instructions burned: 432 (million)
% 46.53/8.33 % (32171)------------------------------
% 46.53/8.33 % (32171)------------------------------
% 46.53/8.34 % (32230)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_31741 for (2937ds/90Mi)
% 46.53/8.37 % (32230)Instruction limit reached!
% 46.53/8.37 % (32230)------------------------------
% 46.53/8.37 % (32230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.53/8.37 % (32230)Termination reason: Unknown
% 46.53/8.37 % (32230)Termination phase: Property scanning
% 46.53/8.37
% 46.53/8.37 % (32230)Memory used [KB]: 2046
% 46.53/8.37 % (32230)Time elapsed: 0.026 s
% 46.53/8.37 % (32230)Instructions burned: 91 (million)
% 46.53/8.37 % (32230)------------------------------
% 46.53/8.37 % (32230)------------------------------
% 46.53/8.38 % (32234)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_31741 for (2936ds/346Mi)
% 47.02/8.42 % (32165)Instruction limit reached!
% 47.02/8.42 % (32165)------------------------------
% 47.02/8.42 % (32165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.02/8.42 % (32165)Termination reason: Unknown
% 47.02/8.42 % (32165)Termination phase: Saturation
% 47.02/8.42
% 47.02/8.42 % (32165)Memory used [KB]: 8315
% 47.02/8.42 % (32165)Time elapsed: 0.247 s
% 47.02/8.42 % (32165)Instructions burned: 784 (million)
% 47.02/8.42 % (32165)------------------------------
% 47.02/8.42 % (32165)------------------------------
% 47.02/8.43 % (32235)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_31741 for (2936ds/401Mi)
% 47.02/8.48 % (32234)Instruction limit reached!
% 47.02/8.48 % (32234)------------------------------
% 47.02/8.48 % (32234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.02/8.48 % (32234)Termination reason: Unknown
% 47.02/8.48 % (32234)Termination phase: Saturation
% 47.02/8.48
% 47.02/8.48 % (32234)Memory used [KB]: 7675
% 47.02/8.48 % (32234)Time elapsed: 0.101 s
% 47.02/8.48 % (32234)Instructions burned: 346 (million)
% 47.02/8.48 % (32234)------------------------------
% 47.02/8.48 % (32234)------------------------------
% 47.02/8.48 % (32236)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_31741 for (2935ds/6454Mi)
% 47.69/8.55 % (32235)Instruction limit reached!
% 47.69/8.55 % (32235)------------------------------
% 47.69/8.55 % (32235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.69/8.55 % (32235)Termination reason: Unknown
% 47.69/8.55 % (32235)Termination phase: Saturation
% 47.69/8.55
% 47.69/8.55 % (32235)Memory used [KB]: 9083
% 47.69/8.55 % (32235)Time elapsed: 0.112 s
% 47.69/8.55 % (32235)Instructions burned: 404 (million)
% 47.69/8.55 % (32235)------------------------------
% 47.69/8.55 % (32235)------------------------------
% 47.69/8.55 % (32237)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_31741 for (2934ds/283Mi)
% 48.10/8.63 % (32094)Instruction limit reached!
% 48.10/8.63 % (32094)------------------------------
% 48.10/8.63 % (32094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.10/8.63 % (32094)Termination reason: Unknown
% 48.10/8.63 % (32094)Termination phase: Saturation
% 48.10/8.63
% 48.10/8.63 % (32094)Memory used [KB]: 8571
% 48.10/8.63 % (32094)Time elapsed: 0.607 s
% 48.10/8.63 % (32094)Instructions burned: 1981 (million)
% 48.10/8.63 % (32094)------------------------------
% 48.10/8.63 % (32094)------------------------------
% 48.10/8.64 % (32238)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_31741 for (2934ds/865Mi)
% 48.10/8.64 % (32237)Instruction limit reached!
% 48.10/8.64 % (32237)------------------------------
% 48.10/8.64 % (32237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.10/8.64 % (32237)Termination reason: Unknown
% 48.10/8.64 % (32237)Termination phase: Saturation
% 48.10/8.64
% 48.10/8.64 % (32237)Memory used [KB]: 8059
% 48.10/8.64 % (32237)Time elapsed: 0.086 s
% 48.10/8.64 % (32237)Instructions burned: 284 (million)
% 48.10/8.64 % (32237)------------------------------
% 48.10/8.64 % (32237)------------------------------
% 48.10/8.65 % (32239)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_31741 for (2934ds/4528Mi)
% 48.10/8.65 % (31989)Instruction limit reached!
% 48.10/8.65 % (31989)------------------------------
% 48.10/8.65 % (31989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.10/8.65 % (31989)Termination reason: Unknown
% 48.10/8.65 % (31989)Termination phase: Saturation
% 48.10/8.65
% 48.10/8.65 % (31989)Memory used [KB]: 11129
% 48.10/8.65 % (31989)Time elapsed: 1.038 s
% 48.10/8.65 % (31989)Instructions burned: 3375 (million)
% 48.10/8.65 % (31989)------------------------------
% 48.10/8.65 % (31989)------------------------------
% 48.10/8.66 % (32240)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_31741 for (2933ds/1001Mi)
% 49.08/8.73 % (31974)Instruction limit reached!
% 49.08/8.73 % (31974)------------------------------
% 49.08/8.73 % (31974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.08/8.73 % (31974)Termination reason: Unknown
% 49.08/8.73 % (31974)Termination phase: Saturation
% 49.08/8.73
% 49.08/8.73 % (31974)Memory used [KB]: 11897
% 49.08/8.73 % (31974)Time elapsed: 1.918 s
% 49.08/8.73 % (31974)Instructions burned: 5413 (million)
% 49.08/8.73 % (31974)------------------------------
% 49.08/8.73 % (31974)------------------------------
% 49.08/8.74 % (32241)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_31741 for (2933ds/102Mi)
% 49.08/8.76 % (32241)Instruction limit reached!
% 49.08/8.76 % (32241)------------------------------
% 49.08/8.76 % (32241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.08/8.76 % (32241)Termination reason: Unknown
% 49.08/8.76 % (32241)Termination phase: Function definition elimination
% 49.08/8.76
% 49.08/8.76 % (32241)Memory used [KB]: 2430
% 49.08/8.76 % (32241)Time elapsed: 0.028 s
% 49.08/8.76 % (32241)Instructions burned: 104 (million)
% 49.08/8.76 % (32241)------------------------------
% 49.08/8.76 % (32241)------------------------------
% 49.08/8.77 % (32242)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_31741 for (2932ds/952Mi)
% 49.27/8.82 % (32214)Instruction limit reached!
% 49.27/8.82 % (32214)------------------------------
% 49.27/8.82 % (32214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.27/8.82 % (32214)Termination reason: Unknown
% 49.27/8.82 % (32214)Termination phase: Saturation
% 49.27/8.82
% 49.27/8.82 % (32214)Memory used [KB]: 10362
% 49.27/8.82 % (32214)Time elapsed: 0.506 s
% 49.27/8.82 % (32214)Instructions burned: 1671 (million)
% 49.27/8.82 % (32214)------------------------------
% 49.27/8.82 % (32214)------------------------------
% 49.27/8.83 % (32243)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_31741 for (2932ds/578Mi)
% 49.89/8.90 % (32238)Instruction limit reached!
% 49.89/8.90 % (32238)------------------------------
% 49.89/8.90 % (32238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.89/8.90 % (32238)Termination reason: Unknown
% 49.89/8.90 % (32238)Termination phase: Saturation
% 49.89/8.90
% 49.89/8.90 % (32238)Memory used [KB]: 8699
% 49.89/8.90 % (32238)Time elapsed: 0.267 s
% 49.89/8.90 % (32238)Instructions burned: 868 (million)
% 49.89/8.90 % (32238)------------------------------
% 49.89/8.90 % (32238)------------------------------
% 49.89/8.91 % (32244)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_31741 for (2931ds/643Mi)
% 49.89/8.93 % (31962)Instruction limit reached!
% 49.89/8.93 % (31962)------------------------------
% 49.89/8.93 % (31962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.89/8.93 % (31962)Termination reason: Unknown
% 49.89/8.93 % (31962)Termination phase: Saturation
% 49.89/8.93
% 49.89/8.93 % (31962)Memory used [KB]: 17782
% 49.89/8.93 % (31962)Time elapsed: 3.508 s
% 49.89/8.93 % (31962)Instructions burned: 8250 (million)
% 49.89/8.93 % (31962)------------------------------
% 49.89/8.93 % (31962)------------------------------
% 49.89/8.94 % (32245)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_31741 for (2931ds/865Mi)
% 49.89/8.98 % (32240)Instruction limit reached!
% 49.89/8.98 % (32240)------------------------------
% 49.89/8.98 % (32240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.89/8.98 % (32240)Termination reason: Unknown
% 49.89/8.98 % (32240)Termination phase: Saturation
% 49.89/8.98
% 49.89/8.98 % (32240)Memory used [KB]: 9083
% 49.89/8.98 % (32240)Time elapsed: 0.318 s
% 49.89/8.98 % (32240)Instructions burned: 1001 (million)
% 49.89/8.98 % (32240)------------------------------
% 49.89/8.98 % (32240)------------------------------
% 49.89/8.99 % (32246)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_31741 for (2930ds/1174Mi)
% 49.89/9.00 % (32243)Instruction limit reached!
% 49.89/9.00 % (32243)------------------------------
% 49.89/9.00 % (32243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.89/9.00 % (32243)Termination reason: Unknown
% 49.89/9.00 % (32243)Termination phase: Saturation
% 49.89/9.00
% 49.89/9.00 % (32243)Memory used [KB]: 7547
% 49.89/9.00 % (32243)Time elapsed: 0.176 s
% 49.89/9.00 % (32243)Instructions burned: 578 (million)
% 49.89/9.00 % (32243)------------------------------
% 49.89/9.00 % (32243)------------------------------
% 49.89/9.01 % (32247)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_31741 for (2930ds/644Mi)
% 52.15/9.07 % (32242)Instruction limit reached!
% 52.15/9.07 % (32242)------------------------------
% 52.15/9.07 % (32242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.15/9.07 % (32242)Termination reason: Unknown
% 52.15/9.07 % (32242)Termination phase: Saturation
% 52.15/9.07
% 52.15/9.07 % (32242)Memory used [KB]: 9083
% 52.15/9.07 % (32242)Time elapsed: 0.297 s
% 52.15/9.07 % (32242)Instructions burned: 953 (million)
% 52.15/9.07 % (32242)------------------------------
% 52.15/9.07 % (32242)------------------------------
% 52.15/9.08 % (32248)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_31741 for (2929ds/1201Mi)
% 52.15/9.10 % (32244)Instruction limit reached!
% 52.15/9.10 % (32244)------------------------------
% 52.15/9.10 % (32244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.15/9.10 % (32244)Termination reason: Unknown
% 52.15/9.10 % (32244)Termination phase: Saturation
% 52.15/9.10
% 52.15/9.10 % (32244)Memory used [KB]: 9338
% 52.15/9.10 % (32244)Time elapsed: 0.191 s
% 52.15/9.10 % (32244)Instructions burned: 644 (million)
% 52.15/9.10 % (32244)------------------------------
% 52.15/9.10 % (32244)------------------------------
% 52.15/9.11 % (32249)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_31741 for (2929ds/1046Mi)
% 52.97/9.20 % (32245)Instruction limit reached!
% 52.97/9.20 % (32245)------------------------------
% 52.97/9.20 % (32245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.97/9.20 % (32245)Termination reason: Unknown
% 52.97/9.20 % (32245)Termination phase: Saturation
% 52.97/9.20
% 52.97/9.20 % (32245)Memory used [KB]: 9338
% 52.97/9.20 % (32245)Time elapsed: 0.269 s
% 52.97/9.20 % (32245)Instructions burned: 866 (million)
% 52.97/9.20 % (32245)------------------------------
% 52.97/9.20 % (32245)------------------------------
% 52.97/9.21 % (32247)Instruction limit reached!
% 52.97/9.21 % (32247)------------------------------
% 52.97/9.21 % (32247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.97/9.21 % (32247)Termination reason: Unknown
% 52.97/9.21 % (32247)Termination phase: Saturation
% 52.97/9.21
% 52.97/9.21 % (32247)Memory used [KB]: 8571
% 52.97/9.21 % (32247)Time elapsed: 0.204 s
% 52.97/9.21 % (32247)Instructions burned: 644 (million)
% 52.97/9.21 % (32247)------------------------------
% 52.97/9.21 % (32247)------------------------------
% 52.97/9.21 % (32250)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_31741 for (2928ds/222Mi)
% 52.97/9.22 % (32251)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_31741 for (2928ds/68Mi)
% 52.97/9.24 % (32251)Instruction limit reached!
% 52.97/9.24 % (32251)------------------------------
% 52.97/9.24 % (32251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.97/9.24 % (32251)Termination reason: Unknown
% 52.97/9.24 % (32251)Termination phase: Property scanning
% 52.97/9.24
% 52.97/9.24 % (32251)Memory used [KB]: 2174
% 52.97/9.24 % (32251)Time elapsed: 0.022 s
% 52.97/9.24 % (32251)Instructions burned: 70 (million)
% 52.97/9.24 % (32251)------------------------------
% 52.97/9.24 % (32251)------------------------------
% 52.97/9.25 % (32252)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_31741 for (2928ds/454Mi)
% 52.97/9.28 % (32250)Instruction limit reached!
% 52.97/9.28 % (32250)------------------------------
% 52.97/9.28 % (32250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.97/9.28 % (32250)Termination reason: Unknown
% 52.97/9.28 % (32250)Termination phase: Saturation
% 52.97/9.28
% 52.97/9.28 % (32250)Memory used [KB]: 7419
% 52.97/9.28 % (32250)Time elapsed: 0.062 s
% 52.97/9.28 % (32250)Instructions burned: 224 (million)
% 52.97/9.28 % (32250)------------------------------
% 52.97/9.28 % (32250)------------------------------
% 52.97/9.28 % (32253)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_31741 for (2927ds/360Mi)
% 53.61/9.36 % (32246)Refutation not found, non-redundant clauses discarded% (32246)------------------------------
% 53.61/9.36 % (32246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.61/9.36 % (32246)Termination reason: Refutation not found, non-redundant clauses discarded
% 53.61/9.36
% 53.61/9.36 % (32246)Memory used [KB]: 9083
% 53.61/9.36 % (32246)Time elapsed: 0.366 s
% 53.61/9.36 % (32246)Instructions burned: 1172 (million)
% 53.61/9.36 % (32246)------------------------------
% 53.61/9.36 % (32246)------------------------------
% 53.61/9.37 % (32254)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_31741 for (2926ds/157Mi)
% 53.61/9.38 % (32252)Instruction limit reached!
% 53.61/9.38 % (32252)------------------------------
% 53.61/9.38 % (32252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.61/9.38 % (32252)Termination reason: Unknown
% 53.61/9.38 % (32252)Termination phase: Saturation
% 53.61/9.38
% 53.61/9.38 % (32252)Memory used [KB]: 13432
% 53.61/9.38 % (32252)Time elapsed: 0.132 s
% 53.61/9.38 % (32252)Instructions burned: 454 (million)
% 53.61/9.38 % (32252)------------------------------
% 53.61/9.38 % (32252)------------------------------
% 53.61/9.38 % (32253)Instruction limit reached!
% 53.61/9.38 % (32253)------------------------------
% 53.61/9.38 % (32253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.61/9.38 % (32253)Termination reason: Unknown
% 53.61/9.38 % (32253)Termination phase: Saturation
% 53.61/9.38
% 53.61/9.38 % (32253)Memory used [KB]: 8571
% 53.61/9.38 % (32253)Time elapsed: 0.101 s
% 53.61/9.38 % (32253)Instructions burned: 361 (million)
% 53.61/9.38 % (32253)------------------------------
% 53.61/9.38 % (32253)------------------------------
% 53.61/9.39 % (32256)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_31741 for (2926ds/2401Mi)
% 54.12/9.40 % (32255)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_31741 for (2926ds/5061Mi)
% 54.12/9.41 % (32254)Instruction limit reached!
% 54.12/9.41 % (32254)------------------------------
% 54.12/9.41 % (32254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.12/9.41 % (32254)Termination reason: Unknown
% 54.12/9.41 % (32254)Termination phase: Saturation
% 54.12/9.41
% 54.12/9.41 % (32254)Memory used [KB]: 6908
% 54.12/9.41 % (32254)Time elapsed: 0.043 s
% 54.12/9.41 % (32254)Instructions burned: 159 (million)
% 54.12/9.41 % (32254)------------------------------
% 54.12/9.41 % (32254)------------------------------
% 54.12/9.42 % (32257)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_31741 for (2926ds/5798Mi)
% 54.12/9.42 % (32248)Instruction limit reached!
% 54.12/9.42 % (32248)------------------------------
% 54.12/9.42 % (32248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.12/9.42 % (32248)Termination reason: Unknown
% 54.12/9.42 % (32248)Termination phase: Saturation
% 54.12/9.42
% 54.12/9.42 % (32248)Memory used [KB]: 11769
% 54.12/9.42 % (32248)Time elapsed: 0.346 s
% 54.12/9.42 % (32248)Instructions burned: 1204 (million)
% 54.12/9.42 % (32248)------------------------------
% 54.12/9.42 % (32248)------------------------------
% 54.12/9.43 % (32249)Instruction limit reached!
% 54.12/9.43 % (32249)------------------------------
% 54.12/9.43 % (32249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.12/9.43 % (32249)Termination reason: Unknown
% 54.12/9.43 % (32249)Termination phase: Saturation
% 54.12/9.43
% 54.12/9.43 % (32249)Memory used [KB]: 9466
% 54.12/9.43 % (32249)Time elapsed: 0.318 s
% 54.12/9.43 % (32249)Instructions burned: 1048 (million)
% 54.12/9.43 % (32249)------------------------------
% 54.12/9.43 % (32249)------------------------------
% 54.12/9.43 % (32258)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_31741 for (2926ds/346Mi)
% 54.12/9.44 % (32259)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_31741 for (2926ds/1321Mi)
% 55.05/9.53 % (32258)Instruction limit reached!
% 55.05/9.53 % (32258)------------------------------
% 55.05/9.53 % (32258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.05/9.53 % (32258)Termination reason: Unknown
% 55.05/9.53 % (32258)Termination phase: Saturation
% 55.05/9.53
% 55.05/9.53 % (32258)Memory used [KB]: 7675
% 55.05/9.53 % (32258)Time elapsed: 0.102 s
% 55.05/9.53 % (32258)Instructions burned: 346 (million)
% 55.05/9.53 % (32258)------------------------------
% 55.05/9.53 % (32258)------------------------------
% 55.05/9.54 % (32260)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_31741 for (2925ds/1312Mi)
% 55.77/9.84 % (32259)Instruction limit reached!
% 55.77/9.84 % (32259)------------------------------
% 55.77/9.84 % (32259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.77/9.84 % (32259)Termination reason: Unknown
% 55.77/9.84 % (32259)Termination phase: Saturation
% 55.77/9.84
% 55.77/9.84 % (32259)Memory used [KB]: 4477
% 55.77/9.84 % (32259)Time elapsed: 0.403 s
% 55.77/9.84 % (32259)Instructions burned: 1323 (million)
% 55.77/9.84 % (32259)------------------------------
% 55.77/9.84 % (32259)------------------------------
% 55.77/9.85 % (32261)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_31741 for (2921ds/672Mi)
% 55.77/9.90 % (32239)Instruction limit reached!
% 55.77/9.90 % (32239)------------------------------
% 55.77/9.90 % (32239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.77/9.90 % (32239)Termination reason: Unknown
% 55.77/9.90 % (32239)Termination phase: Saturation
% 55.77/9.90
% 55.77/9.90 % (32239)Memory used [KB]: 6652
% 55.77/9.90 % (32239)Time elapsed: 1.247 s
% 55.77/9.90 % (32239)Instructions burned: 4530 (million)
% 55.77/9.90 % (32239)------------------------------
% 55.77/9.90 % (32239)------------------------------
% 55.13/9.91 % (32262)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_31741 for (2921ds/1897Mi)
% 55.13/9.93 % (32260)Instruction limit reached!
% 55.13/9.93 % (32260)------------------------------
% 55.13/9.93 % (32260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.13/9.93 % (32260)Termination reason: Unknown
% 55.13/9.93 % (32260)Termination phase: Saturation
% 55.13/9.93
% 55.13/9.93 % (32260)Memory used [KB]: 8699
% 55.13/9.93 % (32260)Time elapsed: 0.391 s
% 55.13/9.93 % (32260)Instructions burned: 1315 (million)
% 55.13/9.93 % (32260)------------------------------
% 55.13/9.93 % (32260)------------------------------
% 55.13/9.94 % (32263)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_31741 for (2921ds/1202Mi)
% 59.07/10.07 % (32261)Instruction limit reached!
% 59.07/10.07 % (32261)------------------------------
% 59.07/10.07 % (32261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.07/10.07 % (32261)Termination reason: Unknown
% 59.07/10.07 % (32261)Termination phase: Saturation
% 59.07/10.07
% 59.07/10.07 % (32261)Memory used [KB]: 8699
% 59.07/10.07 % (32261)Time elapsed: 0.217 s
% 59.07/10.07 % (32261)Instructions burned: 673 (million)
% 59.07/10.07 % (32261)------------------------------
% 59.07/10.07 % (32261)------------------------------
% 59.07/10.08 % (32264)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_31741 for (2919ds/1493Mi)
% 59.75/10.13 % (32264)Refutation not found, incomplete strategy
% 59.75/10.13 % (32264)------------------------------
% 59.75/10.13 % (32264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.75/10.13 % (32264)Termination reason: Refutation not found, incomplete strategy
% 59.75/10.13
% 59.75/10.13
% 59.75/10.13 % (32264)Memory used [KB]: 7164
% 59.75/10.13 % (32264)Time elapsed: 0.049 s
% 59.75/10.13 % (32264)Instructions burned: 175 (million)
% 59.75/10.13 % (32264)------------------------------
% 59.75/10.13 % (32264)------------------------------
% 59.75/10.13 % (32256)Instruction limit reached!
% 59.75/10.13 % (32256)------------------------------
% 59.75/10.13 % (32256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.75/10.13 % (32256)Termination reason: Unknown
% 59.75/10.13 % (32256)Termination phase: Saturation
% 59.75/10.13
% 59.75/10.13 % (32256)Memory used [KB]: 8315
% 59.75/10.13 % (32256)Time elapsed: 0.758 s
% 59.75/10.13 % (32256)Instructions burned: 2403 (million)
% 59.75/10.13 % (32256)------------------------------
% 59.75/10.13 % (32256)------------------------------
% 59.75/10.14 % (32265)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_31741 for (2919ds/7679Mi)
% 59.75/10.14 % (32266)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_31741 for (2919ds/340Mi)
% 60.23/10.24 % (32266)Instruction limit reached!
% 60.23/10.24 % (32266)------------------------------
% 60.23/10.24 % (32266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.23/10.24 % (32266)Termination reason: Unknown
% 60.23/10.24 % (32266)Termination phase: Saturation
% 60.23/10.24
% 60.23/10.24 % (32266)Memory used [KB]: 8955
% 60.23/10.24 % (32266)Time elapsed: 0.102 s
% 60.23/10.24 % (32266)Instructions burned: 341 (million)
% 60.23/10.24 % (32266)------------------------------
% 60.23/10.24 % (32266)------------------------------
% 60.23/10.25 % (32267)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_31741 for (2917ds/3672Mi)
% 60.84/10.31 % (32263)Instruction limit reached!
% 60.84/10.31 % (32263)------------------------------
% 60.84/10.31 % (32263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.84/10.31 % (32263)Termination reason: Unknown
% 60.84/10.31 % (32263)Termination phase: Saturation
% 60.84/10.31
% 60.84/10.31 % (32263)Memory used [KB]: 5245
% 60.84/10.31 % (32263)Time elapsed: 0.371 s
% 60.84/10.31 % (32263)Instructions burned: 1203 (million)
% 60.84/10.31 % (32263)------------------------------
% 60.84/10.31 % (32263)------------------------------
% 60.84/10.32 % (32268)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_31741 for (2917ds/1535Mi)
% 61.66/10.51 % (32262)Instruction limit reached!
% 61.66/10.51 % (32262)------------------------------
% 61.66/10.51 % (32262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.66/10.51 % (32262)Termination reason: Unknown
% 61.66/10.51 % (32262)Termination phase: Saturation
% 61.66/10.51
% 61.66/10.51 % (32262)Memory used [KB]: 9722
% 61.66/10.51 % (32262)Time elapsed: 0.601 s
% 61.66/10.51 % (32262)Instructions burned: 1897 (million)
% 61.66/10.51 % (32262)------------------------------
% 61.66/10.51 % (32262)------------------------------
% 61.66/10.52 % (32269)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_31741 for (2915ds/4637Mi)
% 61.66/10.55 % (32236)Instruction limit reached!
% 61.66/10.55 % (32236)------------------------------
% 61.66/10.55 % (32236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.66/10.55 % (32236)Termination reason: Unknown
% 61.66/10.55 % (32236)Termination phase: Saturation
% 61.66/10.55
% 61.66/10.55 % (32236)Memory used [KB]: 11257
% 61.66/10.55 % (32236)Time elapsed: 2.066 s
% 61.66/10.55 % (32236)Instructions burned: 6456 (million)
% 61.66/10.55 % (32236)------------------------------
% 61.66/10.55 % (32236)------------------------------
% 61.66/10.56 % (32270)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_31741 for (2914ds/3174Mi)
% 62.14/10.78 % (32268)Instruction limit reached!
% 62.14/10.78 % (32268)------------------------------
% 62.14/10.78 % (32268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.14/10.78 % (32268)Termination reason: Unknown
% 62.14/10.78 % (32268)Termination phase: Saturation
% 62.14/10.78
% 62.14/10.78 % (32268)Memory used [KB]: 12281
% 62.14/10.78 % (32268)Time elapsed: 0.457 s
% 62.14/10.78 % (32268)Instructions burned: 1536 (million)
% 62.14/10.78 % (32268)------------------------------
% 62.14/10.78 % (32268)------------------------------
% 62.14/10.79 % (32271)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_31741 for (2912ds/307Mi)
% 62.81/10.88 % (32271)Instruction limit reached!
% 62.81/10.88 % (32271)------------------------------
% 62.81/10.88 % (32271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.81/10.88 % (32271)Termination reason: Unknown
% 62.81/10.88 % (32271)Termination phase: Saturation
% 62.81/10.88
% 62.81/10.88 % (32271)Memory used [KB]: 7547
% 62.81/10.88 % (32271)Time elapsed: 0.091 s
% 62.81/10.88 % (32271)Instructions burned: 310 (million)
% 62.81/10.88 % (32271)------------------------------
% 62.81/10.88 % (32271)------------------------------
% 62.81/10.89 % (32272)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_31741 for (2911ds/3619Mi)
% 66.07/11.06 % (32255)Instruction limit reached!
% 66.07/11.06 % (32255)------------------------------
% 66.07/11.06 % (32255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.07/11.06 % (32255)Termination reason: Unknown
% 66.07/11.06 % (32255)Termination phase: Saturation
% 66.07/11.06
% 66.07/11.06 % (32255)Memory used [KB]: 12409
% 66.07/11.06 % (32255)Time elapsed: 1.675 s
% 66.07/11.06 % (32255)Instructions burned: 5061 (million)
% 66.07/11.06 % (32255)------------------------------
% 66.07/11.06 % (32255)------------------------------
% 66.07/11.08 % (32273)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_31741 for (2909ds/2325Mi)
% 67.25/11.24 % (32257)Instruction limit reached!
% 67.25/11.24 % (32257)------------------------------
% 67.25/11.24 % (32257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.25/11.24 % (32257)Termination reason: Unknown
% 67.25/11.24 % (32257)Termination phase: Saturation
% 67.25/11.24
% 67.25/11.24 % (32257)Memory used [KB]: 9850
% 67.25/11.24 % (32257)Time elapsed: 1.848 s
% 67.25/11.24 % (32257)Instructions burned: 5798 (million)
% 67.25/11.24 % (32257)------------------------------
% 67.25/11.24 % (32257)------------------------------
% 67.25/11.25 % (32274)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_31741 for (2908ds/2341Mi)
% 68.29/11.41 % (32267)Instruction limit reached!
% 68.29/11.41 % (32267)------------------------------
% 68.29/11.41 % (32267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.29/11.41 % (32267)Termination reason: Unknown
% 68.29/11.41 % (32267)Termination phase: Saturation
% 68.29/11.41
% 68.29/11.41 % (32267)Memory used [KB]: 11897
% 68.29/11.41 % (32267)Time elapsed: 1.157 s
% 68.29/11.41 % (32267)Instructions burned: 3672 (million)
% 68.29/11.41 % (32267)------------------------------
% 68.29/11.41 % (32267)------------------------------
% 68.29/11.42 % (32275)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_31741 for (2906ds/7257Mi)
% 68.72/11.56 % (32270)Instruction limit reached!
% 68.72/11.56 % (32270)------------------------------
% 68.72/11.56 % (32270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.72/11.56 % (32270)Termination reason: Unknown
% 68.72/11.56 % (32270)Termination phase: Saturation
% 68.72/11.56
% 68.72/11.56 % (32270)Memory used [KB]: 11129
% 68.72/11.56 % (32270)Time elapsed: 1.0000 s
% 68.72/11.56 % (32270)Instructions burned: 3174 (million)
% 68.72/11.56 % (32270)------------------------------
% 68.72/11.56 % (32270)------------------------------
% 68.72/11.57 % (32276)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_31741 for (2904ds/3710Mi)
% 69.70/11.88 % (32273)Refutation not found, non-redundant clauses discarded% (32273)------------------------------
% 69.70/11.88 % (32273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.70/11.88 % (32273)Termination reason: Refutation not found, non-redundant clauses discarded
% 69.70/11.88
% 69.70/11.88 % (32273)Memory used [KB]: 10106
% 69.70/11.88 % (32273)Time elapsed: 0.801 s
% 69.70/11.88 % (32273)Instructions burned: 2323 (million)
% 69.70/11.88 % (32273)------------------------------
% 69.70/11.88 % (32273)------------------------------
% 69.70/11.89 % (32277)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_31741 for (2901ds/326Mi)
% 70.81/11.98 % (32272)Instruction limit reached!
% 70.81/11.98 % (32272)------------------------------
% 70.81/11.98 % (32272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.81/11.98 % (32272)Termination reason: Unknown
% 70.81/11.98 % (32272)Termination phase: Saturation
% 70.81/11.98
% 70.81/11.98 % (32272)Memory used [KB]: 11769
% 70.81/11.98 % (32272)Time elapsed: 1.096 s
% 70.81/11.98 % (32272)Instructions burned: 3621 (million)
% 70.81/11.98 % (32272)------------------------------
% 70.81/11.98 % (32272)------------------------------
% 70.81/11.99 % (32274)Instruction limit reached!
% 70.81/11.99 % (32274)------------------------------
% 70.81/11.99 % (32274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.81/11.99 % (32274)Termination reason: Unknown
% 70.81/11.99 % (32274)Termination phase: Saturation
% 70.81/11.99
% 70.81/11.99 % (32274)Memory used [KB]: 9466
% 70.81/11.99 % (32274)Time elapsed: 0.740 s
% 70.81/11.99 % (32274)Instructions burned: 2341 (million)
% 70.81/11.99 % (32274)------------------------------
% 70.81/11.99 % (32274)------------------------------
% 70.81/11.99 % (32278)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_31741 for (2900ds/1100Mi)
% 70.81/11.99 % (32277)Instruction limit reached!
% 70.81/11.99 % (32277)------------------------------
% 70.81/11.99 % (32277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.81/11.99 % (32277)Termination reason: Unknown
% 70.81/11.99 % (32277)Termination phase: Saturation
% 70.81/11.99
% 70.81/11.99 % (32277)Memory used [KB]: 7291
% 70.81/11.99 % (32277)Time elapsed: 0.131 s
% 70.81/11.99 % (32277)Instructions burned: 328 (million)
% 70.81/11.99 % (32277)------------------------------
% 70.81/11.99 % (32277)------------------------------
% 70.81/12.00 % (32279)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_31741 for (2900ds/406Mi)
% 70.81/12.00 % (32280)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_31741 for (2900ds/1871Mi)
% 70.81/12.01 % (32269)Instruction limit reached!
% 70.81/12.01 % (32269)------------------------------
% 70.81/12.01 % (32269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.81/12.01 % (32269)Termination reason: Unknown
% 70.81/12.01 % (32269)Termination phase: Saturation
% 70.81/12.01
% 70.81/12.01 % (32269)Memory used [KB]: 11769
% 70.81/12.01 % (32269)Time elapsed: 1.492 s
% 70.81/12.01 % (32269)Instructions burned: 4639 (million)
% 70.81/12.01 % (32269)------------------------------
% 70.81/12.01 % (32269)------------------------------
% 70.81/12.02 % (32281)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_31741 for (2900ds/1194Mi)
% 73.79/12.13 % (32279)Instruction limit reached!
% 73.79/12.13 % (32279)------------------------------
% 73.79/12.13 % (32279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.79/12.13 % (32279)Termination reason: Unknown
% 73.79/12.13 % (32279)Termination phase: Saturation
% 73.79/12.13
% 73.79/12.13 % (32279)Memory used [KB]: 7675
% 73.79/12.13 % (32279)Time elapsed: 0.152 s
% 73.79/12.13 % (32279)Instructions burned: 406 (million)
% 73.79/12.13 % (32279)------------------------------
% 73.79/12.13 % (32279)------------------------------
% 73.79/12.14 % (32282)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_31741 for (2899ds/474Mi)
% 74.15/12.28 % (32282)Instruction limit reached!
% 74.15/12.28 % (32282)------------------------------
% 74.15/12.28 % (32282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.15/12.28 % (32282)Termination reason: Unknown
% 74.15/12.28 % (32282)Termination phase: Saturation
% 74.15/12.28
% 74.15/12.28 % (32282)Memory used [KB]: 7931
% 74.15/12.28 % (32282)Time elapsed: 0.141 s
% 74.15/12.28 % (32282)Instructions burned: 476 (million)
% 74.15/12.28 % (32282)------------------------------
% 74.15/12.28 % (32282)------------------------------
% 74.15/12.29 % (32283)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_31741 for (2897ds/3115Mi)
% 74.80/12.34 % (32278)Instruction limit reached!
% 74.80/12.34 % (32278)------------------------------
% 74.80/12.34 % (32278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.80/12.34 % (32278)Termination reason: Unknown
% 74.80/12.34 % (32278)Termination phase: Saturation
% 74.80/12.34
% 74.80/12.34 % (32278)Memory used [KB]: 10746
% 74.80/12.34 % (32278)Time elapsed: 0.374 s
% 74.80/12.34 % (32278)Instructions burned: 1101 (million)
% 74.80/12.34 % (32278)------------------------------
% 74.80/12.34 % (32278)------------------------------
% 74.80/12.35 % (32284)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_31741 for (2897ds/831Mi)
% 74.80/12.39 % (32281)Instruction limit reached!
% 74.80/12.39 % (32281)------------------------------
% 74.80/12.39 % (32281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.80/12.39 % (32281)Termination reason: Unknown
% 74.80/12.39 % (32281)Termination phase: Saturation
% 74.80/12.39
% 74.80/12.39 % (32281)Memory used [KB]: 9210
% 74.80/12.39 % (32281)Time elapsed: 0.376 s
% 74.80/12.39 % (32281)Instructions burned: 1194 (million)
% 74.80/12.39 % (32281)------------------------------
% 74.80/12.39 % (32281)------------------------------
% 75.66/12.40 % (32285)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_31741 for (2896ds/1188Mi)
% 75.66/12.43 % (32265)Instruction limit reached!
% 75.66/12.43 % (32265)------------------------------
% 75.66/12.43 % (32265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.66/12.43 % (32265)Termination reason: Unknown
% 75.66/12.43 % (32265)Termination phase: Saturation
% 75.66/12.43
% 75.66/12.43 % (32265)Memory used [KB]: 16247
% 75.66/12.43 % (32265)Time elapsed: 2.299 s
% 75.66/12.43 % (32265)Instructions burned: 7679 (million)
% 75.66/12.43 % (32265)------------------------------
% 75.66/12.43 % (32265)------------------------------
% 75.66/12.45 % (32286)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_31741 for (2896ds/2868Mi)
% 76.00/12.51 % (32286)Refutation not found, incomplete strategy
% 76.00/12.51 % (32286)------------------------------
% 76.00/12.51 % (32286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.00/12.51 % (32286)Termination reason: Refutation not found, incomplete strategy
% 76.00/12.51
% 76.00/12.51
% 76.00/12.51 % (32286)Memory used [KB]: 7675
% 76.00/12.51 % (32286)Time elapsed: 0.067 s
% 76.00/12.51 % (32286)Instructions burned: 236 (million)
% 76.00/12.51 % (32286)------------------------------
% 76.00/12.51 % (32286)------------------------------
% 76.00/12.52 % (32287)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_31741 for (2895ds/1516Mi)
% 76.37/12.61 % (32284)Instruction limit reached!
% 76.37/12.61 % (32284)------------------------------
% 76.37/12.61 % (32284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.37/12.61 % (32284)Termination reason: Unknown
% 76.37/12.61 % (32284)Termination phase: Saturation
% 76.37/12.61
% 76.37/12.61 % (32284)Memory used [KB]: 8955
% 76.37/12.61 % (32284)Time elapsed: 0.253 s
% 76.37/12.61 % (32284)Instructions burned: 832 (million)
% 76.37/12.61 % (32284)------------------------------
% 76.37/12.61 % (32284)------------------------------
% 76.37/12.61 % (32280)Instruction limit reached!
% 76.37/12.61 % (32280)------------------------------
% 76.37/12.61 % (32280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.37/12.61 % (32280)Termination reason: Unknown
% 76.37/12.61 % (32280)Termination phase: Saturation
% 76.37/12.61
% 76.37/12.61 % (32280)Memory used [KB]: 10362
% 76.37/12.61 % (32280)Time elapsed: 0.605 s
% 76.37/12.61 % (32280)Instructions burned: 1874 (million)
% 76.37/12.61 % (32280)------------------------------
% 76.37/12.61 % (32280)------------------------------
% 76.37/12.62 % (32288)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_31741 for (2894ds/2321Mi)
% 76.37/12.62 % (32289)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_31741 for (2894ds/2812Mi)
% 76.37/12.68 % (32276)Instruction limit reached!
% 76.37/12.68 % (32276)------------------------------
% 76.37/12.68 % (32276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.37/12.68 % (32276)Termination reason: Unknown
% 76.37/12.68 % (32276)Termination phase: Saturation
% 76.37/12.68
% 76.37/12.68 % (32276)Memory used [KB]: 17398
% 76.37/12.68 % (32276)Time elapsed: 1.130 s
% 76.37/12.68 % (32276)Instructions burned: 3712 (million)
% 76.37/12.68 % (32276)------------------------------
% 76.37/12.68 % (32276)------------------------------
% 76.37/12.68 % (32288)Refutation not found, incomplete strategy
% 76.37/12.68 % (32288)------------------------------
% 76.37/12.68 % (32288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.37/12.68 % (32288)Termination reason: Refutation not found, incomplete strategy
% 76.37/12.68
% 76.37/12.68
% 76.37/12.68 % (32288)Memory used [KB]: 7675
% 76.37/12.68 % (32288)Time elapsed: 0.062 s
% 76.37/12.68 % (32288)Instructions burned: 228 (million)
% 76.37/12.68 % (32288)------------------------------
% 76.37/12.68 % (32288)------------------------------
% 76.37/12.69 % (32290)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_31741 for (2893ds/4604Mi)
% 76.37/12.69 % (32291)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_31741 for (2893ds/2678Mi)
% 76.92/12.77 % (32285)Instruction limit reached!
% 76.92/12.77 % (32285)------------------------------
% 76.92/12.77 % (32285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.92/12.77 % (32285)Termination reason: Unknown
% 76.92/12.77 % (32285)Termination phase: Saturation
% 76.92/12.77
% 76.92/12.77 % (32285)Memory used [KB]: 9338
% 76.92/12.77 % (32285)Time elapsed: 0.365 s
% 76.92/12.77 % (32285)Instructions burned: 1189 (million)
% 76.92/12.77 % (32285)------------------------------
% 76.92/12.77 % (32285)------------------------------
% 76.92/12.78 % (32292)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_31741 for (2892ds/643Mi)
% 77.51/12.96 % (32292)Instruction limit reached!
% 77.51/12.96 % (32292)------------------------------
% 77.51/12.96 % (32292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.51/12.96 % (32292)Termination reason: Unknown
% 77.51/12.96 % (32292)Termination phase: Saturation
% 77.51/12.96
% 77.51/12.96 % (32292)Memory used [KB]: 9338
% 77.51/12.96 % (32292)Time elapsed: 0.189 s
% 77.51/12.96 % (32292)Instructions burned: 645 (million)
% 77.51/12.96 % (32292)------------------------------
% 77.51/12.96 % (32292)------------------------------
% 77.51/12.97 % (32293)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_31741 for (2890ds/458Mi)
% 77.51/12.99 % (32287)Instruction limit reached!
% 77.51/12.99 % (32287)------------------------------
% 77.51/12.99 % (32287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.51/12.99 % (32287)Termination reason: Unknown
% 77.51/12.99 % (32287)Termination phase: Saturation
% 77.51/12.99
% 77.51/12.99 % (32287)Memory used [KB]: 9850
% 77.51/12.99 % (32287)Time elapsed: 0.466 s
% 77.51/12.99 % (32287)Instructions burned: 1517 (million)
% 77.51/12.99 % (32287)------------------------------
% 77.51/12.99 % (32287)------------------------------
% 77.51/13.00 % (32294)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_31741 for (2890ds/2546Mi)
% 80.20/13.10 % (32293)Instruction limit reached!
% 80.20/13.10 % (32293)------------------------------
% 80.20/13.10 % (32293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.20/13.10 % (32293)Termination reason: Unknown
% 80.20/13.10 % (32293)Termination phase: Saturation
% 80.20/13.10
% 80.20/13.10 % (32293)Memory used [KB]: 8571
% 80.20/13.10 % (32293)Time elapsed: 0.131 s
% 80.20/13.10 % (32293)Instructions burned: 459 (million)
% 80.20/13.10 % (32293)------------------------------
% 80.20/13.10 % (32293)------------------------------
% 80.20/13.11 % (32295)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_31741 for (2889ds/1432Mi)
% 81.31/13.26 % (32283)Instruction limit reached!
% 81.31/13.26 % (32283)------------------------------
% 81.31/13.26 % (32283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.31/13.26 % (32283)Termination reason: Unknown
% 81.31/13.26 % (32283)Termination phase: Saturation
% 81.31/13.26
% 81.31/13.26 % (32283)Memory used [KB]: 12409
% 81.31/13.26 % (32283)Time elapsed: 0.968 s
% 81.31/13.26 % (32283)Instructions burned: 3115 (million)
% 81.31/13.26 % (32283)------------------------------
% 81.31/13.26 % (32283)------------------------------
% 81.31/13.27 % (32296)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_31741 for (2887ds/386Mi)
% 81.90/13.37 % (32296)Instruction limit reached!
% 81.90/13.37 % (32296)------------------------------
% 81.90/13.37 % (32296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.90/13.37 % (32296)Termination reason: Unknown
% 81.90/13.37 % (32296)Termination phase: Saturation
% 81.90/13.37
% 81.90/13.37 % (32296)Memory used [KB]: 8827
% 81.90/13.37 % (32296)Time elapsed: 0.107 s
% 81.90/13.37 % (32296)Instructions burned: 389 (million)
% 81.90/13.37 % (32296)------------------------------
% 81.90/13.37 % (32296)------------------------------
% 81.90/13.38 % (32297)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_31741 for (2886ds/360Mi)
% 82.51/13.45 % (32295)Instruction limit reached!
% 82.51/13.45 % (32295)------------------------------
% 82.51/13.45 % (32295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.51/13.45 % (32295)Termination reason: Unknown
% 82.51/13.45 % (32295)Termination phase: Saturation
% 82.51/13.45
% 82.51/13.45 % (32295)Memory used [KB]: 15223
% 82.51/13.45 % (32295)Time elapsed: 0.339 s
% 82.51/13.45 % (32295)Instructions burned: 1436 (million)
% 82.51/13.45 % (32295)------------------------------
% 82.51/13.45 % (32295)------------------------------
% 82.51/13.46 % (32298)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_31741 for (2885ds/5446Mi)
% 82.51/13.48 % (32291)Instruction limit reached!
% 82.51/13.48 % (32291)------------------------------
% 82.51/13.48 % (32291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.51/13.48 % (32291)Termination reason: Unknown
% 82.51/13.48 % (32291)Termination phase: Saturation
% 82.51/13.48
% 82.51/13.48 % (32291)Memory used [KB]: 10362
% 82.51/13.48 % (32291)Time elapsed: 0.794 s
% 82.51/13.48 % (32291)Instructions burned: 2678 (million)
% 82.51/13.48 % (32291)------------------------------
% 82.51/13.48 % (32291)------------------------------
% 82.51/13.48 % (32297)Instruction limit reached!
% 82.51/13.48 % (32297)------------------------------
% 82.51/13.48 % (32297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.51/13.48 % (32297)Termination reason: Unknown
% 82.51/13.48 % (32297)Termination phase: Saturation
% 82.51/13.48
% 82.51/13.48 % (32297)Memory used [KB]: 8827
% 82.51/13.48 % (32297)Time elapsed: 0.101 s
% 82.51/13.48 % (32297)Instructions burned: 363 (million)
% 82.51/13.48 % (32297)------------------------------
% 82.51/13.48 % (32297)------------------------------
% 82.51/13.49 % (32299)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_31741 for (2885ds/2573Mi)
% 82.51/13.49 % (32300)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=2655:si=on:rtra=on_0 on DTF2THF_31741 for (2885ds/2655Mi)
% 83.47/13.51 % (32289)Instruction limit reached!
% 83.47/13.51 % (32289)------------------------------
% 83.47/13.51 % (32289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.47/13.51 % (32289)Termination reason: Unknown
% 83.47/13.51 % (32289)Termination phase: Saturation
% 83.47/13.51
% 83.47/13.51 % (32289)Memory used [KB]: 10490
% 83.47/13.51 % (32289)Time elapsed: 0.889 s
% 83.47/13.51 % (32289)Instructions burned: 2812 (million)
% 83.47/13.51 % (32289)------------------------------
% 83.47/13.51 % (32289)------------------------------
% 83.47/13.52 % (32301)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_31741 for (2885ds/2781Mi)
% 84.09/13.70 % (32275)Instruction limit reached!
% 84.09/13.70 % (32275)------------------------------
% 84.09/13.70 % (32275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.09/13.70 % (32275)Termination reason: Unknown
% 84.09/13.70 % (32275)Termination phase: Saturation
% 84.09/13.70
% 84.09/13.70 % (32275)Memory used [KB]: 14967
% 84.09/13.70 % (32275)Time elapsed: 2.304 s
% 84.09/13.70 % (32275)Instructions burned: 7259 (million)
% 84.09/13.70 % (32275)------------------------------
% 84.09/13.70 % (32275)------------------------------
% 84.09/13.71 % (32302)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_31741 for (2883ds/307Mi)
% 84.09/13.79 % (32294)Instruction limit reached!
% 84.09/13.79 % (32294)------------------------------
% 84.09/13.79 % (32294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.09/13.79 % (32294)Termination reason: Unknown
% 84.09/13.79 % (32294)Termination phase: Saturation
% 84.09/13.79
% 84.09/13.79 % (32294)Memory used [KB]: 9466
% 84.09/13.79 % (32294)Time elapsed: 0.796 s
% 84.09/13.79 % (32294)Instructions burned: 2546 (million)
% 84.09/13.79 % (32294)------------------------------
% 84.09/13.79 % (32294)------------------------------
% 84.09/13.80 % (32302)Instruction limit reached!
% 84.09/13.80 % (32302)------------------------------
% 84.09/13.80 % (32302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.09/13.80 % (32302)Termination reason: Unknown
% 84.09/13.80 % (32302)Termination phase: Saturation
% 84.09/13.80
% 84.09/13.80 % (32302)Memory used [KB]: 7547
% 84.31/13.80 % (32302)Time elapsed: 0.089 s
% 84.31/13.80 % (32302)Instructions burned: 307 (million)
% 84.31/13.80 % (32302)------------------------------
% 84.31/13.80 % (32302)------------------------------
% 84.31/13.80 % (32303)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_31741 for (2882ds/1548Mi)
% 84.31/13.81 % (32304)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_31741 for (2882ds/5214Mi)
% 87.24/14.10 % (32290)Instruction limit reached!
% 87.24/14.10 % (32290)------------------------------
% 87.24/14.10 % (32290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.24/14.10 % (32290)Termination reason: Unknown
% 87.24/14.10 % (32290)Termination phase: Saturation
% 87.24/14.10
% 87.24/14.10 % (32290)Memory used [KB]: 13944
% 87.24/14.10 % (32290)Time elapsed: 1.407 s
% 87.24/14.10 % (32290)Instructions burned: 4604 (million)
% 87.24/14.10 % (32290)------------------------------
% 87.24/14.10 % (32290)------------------------------
% 87.24/14.11 % (32305)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_31741 for (2879ds/3201Mi)
% 88.35/14.27 % (32299)Instruction limit reached!
% 88.35/14.27 % (32299)------------------------------
% 88.35/14.27 % (32299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 88.35/14.27 % (32299)Termination reason: Unknown
% 88.35/14.27 % (32299)Termination phase: Saturation
% 88.35/14.27
% 88.35/14.27 % (32299)Memory used [KB]: 10234
% 88.35/14.27 % (32299)Time elapsed: 0.784 s
% 88.35/14.27 % (32299)Instructions burned: 2576 (million)
% 88.35/14.27 % (32299)------------------------------
% 88.35/14.27 % (32299)------------------------------
% 88.35/14.28 % (32303)Instruction limit reached!
% 88.35/14.28 % (32303)------------------------------
% 88.35/14.28 % (32303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 88.35/14.28 % (32303)Termination reason: Unknown
% 88.35/14.28 % (32303)Termination phase: Saturation
% 88.35/14.28
% 88.35/14.28 % (32303)Memory used [KB]: 10234
% 88.35/14.28 % (32303)Time elapsed: 0.483 s
% 88.35/14.28 % (32303)Instructions burned: 1551 (million)
% 88.35/14.28 % (32303)------------------------------
% 88.35/14.28 % (32303)------------------------------
% 88.35/14.28 % (32320)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_31741 for (2877ds/454Mi)
% 88.35/14.29 % (32300)Instruction limit reached!
% 88.35/14.29 % (32300)------------------------------
% 88.35/14.29 % (32300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 88.35/14.29 % (32300)Termination reason: Unknown
% 88.35/14.29 % (32300)Termination phase: Saturation
% 88.35/14.29
% 88.35/14.29 % (32300)Memory used [KB]: 12025
% 88.35/14.29 % (32300)Time elapsed: 0.797 s
% 88.35/14.29 % (32300)Instructions burned: 2658 (million)
% 88.35/14.29 % (32300)------------------------------
% 88.35/14.29 % (32300)------------------------------
% 88.35/14.29 % (32321)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_31741 for (2877ds/3049Mi)
% 88.94/14.30 % (32324)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_31741 for (2877ds/7311Mi)
% 88.94/14.37 % (32301)Instruction limit reached!
% 88.94/14.37 % (32301)------------------------------
% 88.94/14.37 % (32301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 88.94/14.37 % (32301)Termination reason: Unknown
% 88.94/14.37 % (32301)Termination phase: Saturation
% 88.94/14.37
% 88.94/14.37 % (32301)Memory used [KB]: 5884
% 88.94/14.37 % (32301)Time elapsed: 0.852 s
% 88.94/14.37 % (32301)Instructions burned: 2783 (million)
% 88.94/14.37 % (32301)------------------------------
% 88.94/14.37 % (32301)------------------------------
% 88.94/14.38 % (32345)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_31741 for (2876ds/6804Mi)
% 89.21/14.41 % (32320)Instruction limit reached!
% 89.21/14.41 % (32320)------------------------------
% 89.21/14.41 % (32320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.21/14.41 % (32320)Termination reason: Unknown
% 89.21/14.41 % (32320)Termination phase: Saturation
% 89.21/14.41
% 89.21/14.41 % (32320)Memory used [KB]: 13432
% 89.21/14.41 % (32320)Time elapsed: 0.132 s
% 89.21/14.41 % (32320)Instructions burned: 455 (million)
% 89.21/14.41 % (32320)------------------------------
% 89.21/14.41 % (32320)------------------------------
% 89.21/14.42 % (32371)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_31741 for (2876ds/1683Mi)
% 90.36/14.96 % (32371)Instruction limit reached!
% 90.36/14.96 % (32371)------------------------------
% 90.36/14.96 % (32371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.36/14.96 % (32371)Termination reason: Unknown
% 90.36/14.96 % (32371)Termination phase: Saturation
% 90.36/14.96
% 90.36/14.96 % (32371)Memory used [KB]: 9466
% 90.36/14.96 % (32371)Time elapsed: 0.535 s
% 90.36/14.96 % (32371)Instructions burned: 1685 (million)
% 90.36/14.96 % (32371)------------------------------
% 90.36/14.96 % (32371)------------------------------
% 90.36/14.97 % (32576)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_31741 for (2870ds/4688Mi)
% 94.32/15.11 % (32305)Instruction limit reached!
% 94.32/15.11 % (32305)------------------------------
% 94.32/15.11 % (32305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 94.32/15.11 % (32305)Termination reason: Unknown
% 94.32/15.11 % (32305)Termination phase: Saturation
% 94.32/15.11
% 94.32/15.11 % (32305)Memory used [KB]: 11513
% 94.32/15.11 % (32305)Time elapsed: 1.030 s
% 94.32/15.11 % (32305)Instructions burned: 3203 (million)
% 94.32/15.11 % (32305)------------------------------
% 94.32/15.11 % (32305)------------------------------
% 95.02/15.14 % (32672)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_31741 for (2869ds/2207Mi)
% 95.36/15.20 % (32298)Instruction limit reached!
% 95.36/15.20 % (32298)------------------------------
% 95.36/15.20 % (32298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.36/15.20 % (32298)Termination reason: Unknown
% 95.36/15.20 % (32298)Termination phase: Saturation
% 95.36/15.20
% 95.36/15.20 % (32298)Memory used [KB]: 16119
% 95.36/15.20 % (32298)Time elapsed: 1.742 s
% 95.36/15.20 % (32298)Instructions burned: 5448 (million)
% 95.36/15.20 % (32298)------------------------------
% 95.36/15.20 % (32298)------------------------------
% 95.36/15.21 % (32702)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=8216:si=on:rtra=on_0 on DTF2THF_31741 for (2868ds/8216Mi)
% 95.36/15.22 % (32321)Instruction limit reached!
% 95.36/15.22 % (32321)------------------------------
% 95.36/15.22 % (32321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.36/15.22 % (32321)Termination reason: Unknown
% 95.36/15.22 % (32321)Termination phase: Saturation
% 95.36/15.22
% 95.36/15.22 % (32321)Memory used [KB]: 9466
% 95.36/15.22 % (32321)Time elapsed: 0.933 s
% 95.36/15.22 % (32321)Instructions burned: 3050 (million)
% 95.36/15.22 % (32321)------------------------------
% 95.36/15.22 % (32321)------------------------------
% 95.36/15.24 % (32703)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_31741 for (2868ds/430Mi)
% 95.82/15.36 % (32703)Instruction limit reached!
% 95.82/15.36 % (32703)------------------------------
% 95.82/15.36 % (32703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.82/15.36 % (32703)Termination reason: Unknown
% 95.82/15.36 % (32703)Termination phase: Saturation
% 95.82/15.36
% 95.82/15.36 % (32703)Memory used [KB]: 8571
% 95.82/15.36 % (32703)Time elapsed: 0.127 s
% 95.82/15.36 % (32703)Instructions burned: 432 (million)
% 95.82/15.36 % (32703)------------------------------
% 95.82/15.36 % (32703)------------------------------
% 95.82/15.37 % (32747)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_31741 for (2866ds/2012Mi)
% 96.36/15.44 % (32304)Instruction limit reached!
% 96.36/15.44 % (32304)------------------------------
% 96.36/15.44 % (32304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 96.36/15.44 % (32304)Termination reason: Unknown
% 96.36/15.44 % (32304)Termination phase: Saturation
% 96.36/15.44
% 96.36/15.44 % (32304)Memory used [KB]: 12153
% 96.36/15.44 % (32304)Time elapsed: 1.632 s
% 96.36/15.44 % (32304)Instructions burned: 5217 (million)
% 96.36/15.44 % (32304)------------------------------
% 96.36/15.44 % (32304)------------------------------
% 96.36/15.45 % (321)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=631:si=on:rtra=on_0 on DTF2THF_31741 for (2866ds/631Mi)
% 97.01/15.64 % (321)Instruction limit reached!
% 97.01/15.64 % (321)------------------------------
% 97.01/15.64 % (321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.01/15.64 % (321)Termination reason: Unknown
% 97.01/15.64 % (321)Termination phase: Saturation
% 97.01/15.64
% 97.01/15.64 % (321)Memory used [KB]: 8571
% 97.01/15.64 % (321)Time elapsed: 0.190 s
% 97.01/15.64 % (321)Instructions burned: 632 (million)
% 97.01/15.64 % (321)------------------------------
% 97.01/15.64 % (321)------------------------------
% 97.01/15.65 % (330)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_31741 for (2864ds/8785Mi)
% 97.82/15.86 % (32672)Instruction limit reached!
% 97.82/15.86 % (32672)------------------------------
% 97.82/15.86 % (32672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.82/15.86 % (32672)Termination reason: Unknown
% 97.82/15.86 % (32672)Termination phase: Saturation
% 97.82/15.86
% 97.82/15.86 % (32672)Memory used [KB]: 9466
% 97.82/15.86 % (32672)Time elapsed: 0.719 s
% 97.82/15.86 % (32672)Instructions burned: 2209 (million)
% 97.82/15.86 % (32672)------------------------------
% 97.82/15.86 % (32672)------------------------------
% 97.82/15.87 % (331)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_31741 for (2861ds/739Mi)
% 98.85/16.00 % (32747)Instruction limit reached!
% 98.85/16.00 % (32747)------------------------------
% 98.85/16.00 % (32747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.85/16.00 % (32747)Termination reason: Unknown
% 98.85/16.00 % (32747)Termination phase: Saturation
% 98.85/16.00
% 98.85/16.00 % (32747)Memory used [KB]: 20468
% 98.85/16.00 % (32747)Time elapsed: 0.629 s
% 98.85/16.00 % (32747)Instructions burned: 2013 (million)
% 98.85/16.00 % (32747)------------------------------
% 98.85/16.00 % (32747)------------------------------
% 98.85/16.01 % (333)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_31741 for (2860ds/5473Mi)
% 101.81/16.15 % (331)Instruction limit reached!
% 101.81/16.15 % (331)------------------------------
% 101.81/16.15 % (331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 101.81/16.15 % (331)Termination reason: Unknown
% 101.81/16.15 % (331)Termination phase: Saturation
% 101.81/16.15
% 101.81/16.15 % (331)Memory used [KB]: 8315
% 101.81/16.15 % (331)Time elapsed: 0.277 s
% 101.81/16.15 % (331)Instructions burned: 739 (million)
% 101.81/16.15 % (331)------------------------------
% 101.81/16.15 % (331)------------------------------
% 101.81/16.16 % (334)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_31741 for (2858ds/43570Mi)
% 103.70/16.58 % (32576)Instruction limit reached!
% 103.70/16.58 % (32576)------------------------------
% 103.70/16.58 % (32576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 103.70/16.58 % (32576)Termination reason: Unknown
% 103.70/16.58 % (32576)Termination phase: Saturation
% 103.70/16.58
% 103.70/16.58 % (32576)Memory used [KB]: 9083
% 103.70/16.58 % (32576)Time elapsed: 1.616 s
% 103.70/16.58 % (32576)Instructions burned: 4689 (million)
% 103.70/16.58 % (32576)------------------------------
% 103.70/16.58 % (32576)------------------------------
% 103.70/16.59 % (363)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_31741 for (2854ds/8382Mi)
% 104.20/16.64 % (32345)Instruction limit reached!
% 104.20/16.64 % (32345)------------------------------
% 104.20/16.64 % (32345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.20/16.64 % (32345)Termination reason: Unknown
% 104.20/16.64 % (32345)Termination phase: Saturation
% 104.20/16.64
% 104.20/16.64 % (32345)Memory used [KB]: 11513
% 104.20/16.64 % (32345)Time elapsed: 2.255 s
% 104.20/16.64 % (32345)Instructions burned: 6804 (million)
% 104.20/16.64 % (32345)------------------------------
% 104.20/16.64 % (32345)------------------------------
% 104.20/16.65 % (392)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_31741 for (2854ds/407Mi)
% 104.20/16.67 % (32324)Refutation not found, non-redundant clauses discarded% (32324)------------------------------
% 104.20/16.67 % (32324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.20/16.67 % (32324)Termination reason: Refutation not found, non-redundant clauses discarded
% 104.20/16.67
% 104.20/16.67 % (32324)Memory used [KB]: 13176
% 104.20/16.67 % (32324)Time elapsed: 2.370 s
% 104.20/16.67 % (32324)Instructions burned: 6930 (million)
% 104.20/16.67 % (32324)------------------------------
% 104.20/16.67 % (32324)------------------------------
% 104.20/16.68 % (404)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_31741 for (2853ds/2971Mi)
% 104.54/16.74 % (404)Refutation not found, incomplete strategy
% 104.54/16.74 % (404)------------------------------
% 104.54/16.74 % (404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.54/16.74 % (404)Termination reason: Refutation not found, incomplete strategy
% 104.54/16.74
% 104.54/16.74
% 104.54/16.74 % (404)Memory used [KB]: 7675
% 104.54/16.74 % (404)Time elapsed: 0.063 s
% 104.54/16.74 % (404)Instructions burned: 234 (million)
% 104.54/16.74 % (404)------------------------------
% 104.54/16.74 % (404)------------------------------
% 104.54/16.75 % (432)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_31741 for (2853ds/9822Mi)
% 104.54/16.78 % (392)Instruction limit reached!
% 104.54/16.78 % (392)------------------------------
% 104.54/16.78 % (392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.54/16.78 % (392)Termination reason: Unknown
% 104.54/16.78 % (392)Termination phase: Saturation
% 104.54/16.78
% 104.54/16.78 % (392)Memory used [KB]: 8443
% 104.54/16.78 % (392)Time elapsed: 0.124 s
% 104.54/16.78 % (392)Instructions burned: 409 (million)
% 104.54/16.78 % (392)------------------------------
% 104.54/16.78 % (392)------------------------------
% 104.54/16.79 % (460)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_31741 for (2852ds/8425Mi)
% 112.93/17.74 % (333)Instruction limit reached!
% 112.93/17.74 % (333)------------------------------
% 112.93/17.74 % (333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 112.93/17.74 % (333)Termination reason: Unknown
% 112.93/17.74 % (333)Termination phase: Saturation
% 112.93/17.74
% 112.93/17.74 % (333)Memory used [KB]: 10874
% 112.93/17.74 % (333)Time elapsed: 1.735 s
% 112.93/17.74 % (333)Instructions burned: 5474 (million)
% 112.93/17.74 % (333)------------------------------
% 112.93/17.74 % (333)------------------------------
% 112.93/17.75 % (630)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_31741 for (2843ds/3107Mi)
% 114.19/17.96 % (32702)Instruction limit reached!
% 114.19/17.96 % (32702)------------------------------
% 114.19/17.96 % (32702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.19/17.96 % (32702)Termination reason: Unknown
% 114.19/17.96 % (32702)Termination phase: Saturation
% 114.19/17.96
% 114.19/17.96 % (32702)Memory used [KB]: 12665
% 114.19/17.96 % (32702)Time elapsed: 2.751 s
% 114.19/17.96 % (32702)Instructions burned: 8219 (million)
% 114.19/17.96 % (32702)------------------------------
% 114.19/17.96 % (32702)------------------------------
% 114.19/17.97 % (631)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_31741 for (2840ds/7967Mi)
% 115.13/18.04 % (631)Refutation not found, incomplete strategy
% 115.13/18.04 % (631)------------------------------
% 115.13/18.04 % (631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 115.13/18.04 % (631)Termination reason: Refutation not found, incomplete strategy
% 115.13/18.04
% 115.13/18.04
% 115.13/18.04 % (631)Memory used [KB]: 7675
% 115.13/18.04 % (631)Time elapsed: 0.064 s
% 115.13/18.04 % (631)Instructions burned: 230 (million)
% 115.13/18.04 % (631)------------------------------
% 115.13/18.04 % (631)------------------------------
% 115.13/18.05 % (632)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_31741 for (2840ds/3629Mi)
% 118.72/18.62 % (330)Instruction limit reached!
% 118.72/18.62 % (330)------------------------------
% 118.72/18.62 % (330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 118.72/18.62 % (330)Termination reason: Unknown
% 118.72/18.62 % (330)Termination phase: Saturation
% 118.72/18.62
% 118.72/18.62 % (330)Memory used [KB]: 15095
% 118.72/18.62 % (330)Time elapsed: 2.982 s
% 118.72/18.62 % (330)Instructions burned: 8787 (million)
% 118.72/18.62 % (330)------------------------------
% 118.72/18.62 % (330)------------------------------
% 118.72/18.63 % (633)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_31741 for (2834ds/939Mi)
% 119.25/18.71 % (630)Instruction limit reached!
% 119.25/18.71 % (630)------------------------------
% 119.25/18.71 % (630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.25/18.71 % (630)Termination reason: Unknown
% 119.25/18.71 % (630)Termination phase: Saturation
% 119.25/18.71
% 119.25/18.71 % (630)Memory used [KB]: 9978
% 119.25/18.71 % (630)Time elapsed: 0.956 s
% 119.25/18.71 % (630)Instructions burned: 3108 (million)
% 119.25/18.71 % (630)------------------------------
% 119.25/18.71 % (630)------------------------------
% 119.25/18.72 % (636)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_31741 for (2833ds/1188Mi)
% 119.66/18.89 % (633)Instruction limit reached!
% 119.66/18.89 % (633)------------------------------
% 119.66/18.89 % (633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.66/18.89 % (633)Termination reason: Unknown
% 119.66/18.89 % (633)Termination phase: Saturation
% 119.66/18.89
% 119.66/18.89 % (633)Memory used [KB]: 8955
% 119.66/18.89 % (633)Time elapsed: 0.265 s
% 119.66/18.89 % (633)Instructions burned: 943 (million)
% 119.66/18.89 % (633)------------------------------
% 119.66/18.89 % (633)------------------------------
% 120.35/18.90 % (637)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_31741 for (2831ds/3205Mi)
% 122.20/19.08 % (636)Instruction limit reached!
% 122.20/19.08 % (636)------------------------------
% 122.20/19.08 % (636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 122.20/19.08 % (636)Termination reason: Unknown
% 122.20/19.08 % (636)Termination phase: Saturation
% 122.20/19.08
% 122.20/19.08 % (636)Memory used [KB]: 8699
% 122.20/19.08 % (636)Time elapsed: 0.364 s
% 122.20/19.08 % (636)Instructions burned: 1189 (million)
% 122.20/19.08 % (636)------------------------------
% 122.20/19.08 % (636)------------------------------
% 122.20/19.09 % (638)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_31741 for (2829ds/865Mi)
% 122.96/19.18 % (632)Instruction limit reached!
% 122.96/19.18 % (632)------------------------------
% 122.96/19.18 % (632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 122.96/19.18 % (632)Termination reason: Unknown
% 122.96/19.18 % (632)Termination phase: Saturation
% 122.96/19.18
% 122.96/19.18 % (632)Memory used [KB]: 10874
% 122.96/19.18 % (632)Time elapsed: 1.132 s
% 122.96/19.18 % (632)Instructions burned: 3630 (million)
% 122.96/19.18 % (632)------------------------------
% 122.96/19.18 % (632)------------------------------
% 122.96/19.19 % (639)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_31741 for (2828ds/7469Mi)
% 123.37/19.28 % (363)Instruction limit reached!
% 123.37/19.28 % (363)------------------------------
% 123.37/19.28 % (363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 123.37/19.28 % (363)Termination reason: Unknown
% 123.37/19.28 % (363)Termination phase: Saturation
% 123.37/19.28
% 123.37/19.28 % (363)Memory used [KB]: 15095
% 123.37/19.28 % (363)Time elapsed: 2.689 s
% 123.37/19.28 % (363)Instructions burned: 8384 (million)
% 123.37/19.28 % (363)------------------------------
% 123.37/19.28 % (363)------------------------------
% 123.37/19.29 % (641)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_31741 for (2827ds/4165Mi)
% 123.86/19.36 % (638)Instruction limit reached!
% 123.86/19.36 % (638)------------------------------
% 123.86/19.36 % (638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 123.86/19.36 % (638)Termination reason: Unknown
% 123.86/19.36 % (638)Termination phase: Saturation
% 123.86/19.36
% 123.86/19.36 % (638)Memory used [KB]: 9466
% 123.86/19.36 % (638)Time elapsed: 0.294 s
% 123.86/19.36 % (638)Instructions burned: 866 (million)
% 123.86/19.36 % (638)------------------------------
% 123.86/19.36 % (638)------------------------------
% 123.86/19.37 % (642)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_31741 for (2826ds/13468Mi)
% 124.54/19.45 % (460)Instruction limit reached!
% 124.54/19.45 % (460)------------------------------
% 124.54/19.45 % (460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 124.54/19.45 % (460)Termination reason: Unknown
% 124.54/19.45 % (460)Termination phase: Saturation
% 124.54/19.45
% 124.54/19.45 % (460)Memory used [KB]: 10234
% 124.54/19.45 % (460)Time elapsed: 2.664 s
% 124.54/19.45 % (460)Instructions burned: 8427 (million)
% 124.54/19.45 % (460)------------------------------
% 124.54/19.45 % (460)------------------------------
% 124.54/19.46 % (643)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_31741 for (2826ds/2635Mi)
% 125.51/19.70 % (432)Instruction limit reached!
% 125.51/19.70 % (432)------------------------------
% 125.51/19.70 % (432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 125.51/19.70 % (432)Termination reason: Unknown
% 125.51/19.70 % (432)Termination phase: Saturation
% 125.51/19.70
% 125.51/19.70 % (432)Memory used [KB]: 18549
% 125.51/19.70 % (432)Time elapsed: 2.952 s
% 125.51/19.70 % (432)Instructions burned: 9822 (million)
% 125.51/19.70 % (432)------------------------------
% 125.51/19.70 % (432)------------------------------
% 125.51/19.71 % (644)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=631:si=on:rtra=on_0 on DTF2THF_31741 for (2823ds/631Mi)
% 125.93/19.91 % (644)Instruction limit reached!
% 125.93/19.91 % (644)------------------------------
% 125.93/19.91 % (644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 125.93/19.91 % (644)Termination reason: Unknown
% 125.93/19.91 % (644)Termination phase: Saturation
% 125.93/19.91
% 125.93/19.91 % (644)Memory used [KB]: 9338
% 125.93/19.91 % (644)Time elapsed: 0.194 s
% 125.93/19.91 % (644)Instructions burned: 633 (million)
% 125.93/19.91 % (644)------------------------------
% 125.93/19.91 % (644)------------------------------
% 125.93/19.92 % (646)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_31741 for (2821ds/15557Mi)
% 125.93/19.92 % (637)Instruction limit reached!
% 125.93/19.92 % (637)------------------------------
% 125.93/19.92 % (637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 125.93/19.92 % (637)Termination reason: Unknown
% 125.93/19.92 % (637)Termination phase: Saturation
% 125.93/19.92
% 125.93/19.92 % (637)Memory used [KB]: 13432
% 125.93/19.92 % (637)Time elapsed: 1.020 s
% 125.93/19.92 % (637)Instructions burned: 3206 (million)
% 125.93/19.92 % (637)------------------------------
% 125.93/19.92 % (637)------------------------------
% 125.93/19.93 % (647)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_31741 for (2821ds/2142Mi)
% 130.51/20.27 % (643)Instruction limit reached!
% 130.51/20.27 % (643)------------------------------
% 130.51/20.27 % (643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 130.51/20.27 % (643)Termination reason: Unknown
% 130.51/20.27 % (643)Termination phase: Saturation
% 130.51/20.27
% 130.51/20.27 % (643)Memory used [KB]: 11129
% 130.51/20.27 % (643)Time elapsed: 0.833 s
% 130.51/20.27 % (643)Instructions burned: 2636 (million)
% 130.51/20.27 % (643)------------------------------
% 130.51/20.27 % (643)------------------------------
% 130.51/20.28 % (663)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on DTF2THF_31741 for (2817ds/5624Mi)
% 132.39/20.59 % (641)Instruction limit reached!
% 132.39/20.59 % (641)------------------------------
% 132.39/20.59 % (641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 132.39/20.59 % (641)Termination reason: Unknown
% 132.39/20.59 % (641)Termination phase: Saturation
% 132.39/20.59
% 132.39/20.59 % (641)Memory used [KB]: 10618
% 132.39/20.59 % (641)Time elapsed: 1.327 s
% 132.39/20.59 % (641)Instructions burned: 4167 (million)
% 132.39/20.59 % (641)------------------------------
% 132.39/20.59 % (641)------------------------------
% 132.99/20.60 % (664)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on DTF2THF_31741 for (2814ds/1665Mi)
% 132.99/20.61 % (647)Instruction limit reached!
% 132.99/20.61 % (647)------------------------------
% 132.99/20.61 % (647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 132.99/20.61 % (647)Termination reason: Unknown
% 132.99/20.61 % (647)Termination phase: Saturation
% 132.99/20.61
% 132.99/20.61 % (647)Memory used [KB]: 9594
% 132.99/20.61 % (647)Time elapsed: 0.680 s
% 132.99/20.61 % (647)Instructions burned: 2144 (million)
% 132.99/20.61 % (647)------------------------------
% 132.99/20.61 % (647)------------------------------
% 132.99/20.62 % (665)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on DTF2THF_31741 for (2814ds/64912Mi)
% 136.23/21.10 % (664)Instruction limit reached!
% 136.23/21.10 % (664)------------------------------
% 136.23/21.10 % (664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 136.23/21.10 % (664)Termination reason: Unknown
% 136.23/21.10 % (664)Termination phase: Saturation
% 136.23/21.10
% 136.23/21.10 % (664)Memory used [KB]: 10234
% 136.23/21.10 % (664)Time elapsed: 0.502 s
% 136.23/21.10 % (664)Instructions burned: 1668 (million)
% 136.23/21.10 % (664)------------------------------
% 136.23/21.10 % (664)------------------------------
% 136.23/21.11 % (666)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on DTF2THF_31741 for (2809ds/7801Mi)
% 138.65/21.42 % (639)Instruction limit reached!
% 138.65/21.42 % (639)------------------------------
% 138.65/21.42 % (639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 138.65/21.42 % (639)Termination reason: Unknown
% 138.65/21.42 % (639)Termination phase: Saturation
% 138.65/21.42
% 138.65/21.42 % (639)Memory used [KB]: 9978
% 138.65/21.42 % (639)Time elapsed: 2.260 s
% 138.65/21.42 % (639)Instructions burned: 7472 (million)
% 138.65/21.42 % (639)------------------------------
% 138.65/21.42 % (639)------------------------------
% 138.65/21.43 % (667)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on DTF2THF_31741 for (2806ds/15194Mi)
% 143.26/22.03 % (663)Instruction limit reached!
% 143.26/22.03 % (663)------------------------------
% 143.26/22.03 % (663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 143.26/22.03 % (663)Termination reason: Unknown
% 143.26/22.03 % (663)Termination phase: Saturation
% 143.26/22.03
% 143.26/22.03 % (663)Memory used [KB]: 11897
% 143.26/22.03 % (663)Time elapsed: 1.751 s
% 143.26/22.03 % (663)Instructions burned: 5624 (million)
% 143.26/22.03 % (663)------------------------------
% 143.26/22.03 % (663)------------------------------
% 143.26/22.04 % (668)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=6753:si=on:rtra=on_0 on DTF2THF_31741 for (2800ds/6753Mi)
% 153.68/23.51 % (666)Instruction limit reached!
% 153.68/23.51 % (666)------------------------------
% 153.68/23.51 % (666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 153.68/23.51 % (666)Termination reason: Unknown
% 153.68/23.51 % (666)Termination phase: Saturation
% 153.68/23.51
% 153.68/23.51 % (666)Memory used [KB]: 9338
% 153.68/23.51 % (666)Time elapsed: 2.396 s
% 153.68/23.51 % (666)Instructions burned: 7801 (million)
% 153.68/23.51 % (666)------------------------------
% 153.68/23.51 % (666)------------------------------
% 153.68/23.52 % (669)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on DTF2THF_31741 for (2785ds/1003Mi)
% 154.30/23.70 % (642)Instruction limit reached!
% 154.30/23.70 % (642)------------------------------
% 154.30/23.70 % (642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 154.30/23.70 % (642)Termination reason: Unknown
% 154.30/23.70 % (642)Termination phase: Saturation
% 154.30/23.70
% 154.30/23.70 % (642)Memory used [KB]: 18293
% 154.30/23.70 % (642)Time elapsed: 4.351 s
% 154.30/23.70 % (642)Instructions burned: 13469 (million)
% 154.30/23.70 % (642)------------------------------
% 154.30/23.70 % (642)------------------------------
% 154.91/23.71 % (670)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on DTF2THF_31741 for (2783ds/13018Mi)
% 155.43/23.82 % (669)Instruction limit reached!
% 155.43/23.82 % (669)------------------------------
% 155.43/23.82 % (669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.43/23.82 % (669)Termination reason: Unknown
% 155.43/23.82 % (669)Termination phase: Saturation
% 155.43/23.82
% 155.43/23.82 % (669)Memory used [KB]: 9083
% 155.43/23.82 % (669)Time elapsed: 0.306 s
% 155.43/23.82 % (669)Instructions burned: 1003 (million)
% 155.43/23.82 % (669)------------------------------
% 155.43/23.82 % (669)------------------------------
% 155.43/23.83 % (671)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on DTF2THF_31741 for (2782ds/1267Mi)
% 158.09/24.16 % (668)Instruction limit reached!
% 158.09/24.16 % (668)------------------------------
% 158.09/24.16 % (668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 158.09/24.16 % (668)Termination reason: Unknown
% 158.09/24.16 % (668)Termination phase: Saturation
% 158.09/24.16
% 158.09/24.16 % (668)Memory used [KB]: 12920
% 158.09/24.16 % (668)Time elapsed: 2.124 s
% 158.09/24.16 % (668)Instructions burned: 6753 (million)
% 158.09/24.16 % (668)------------------------------
% 158.09/24.16 % (668)------------------------------
% 158.09/24.17 % (672)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=2570:si=on:rtra=on_0 on DTF2THF_31741 for (2778ds/2570Mi)
% 158.57/24.22 % (671)Instruction limit reached!
% 158.57/24.22 % (671)------------------------------
% 158.57/24.22 % (671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 158.57/24.22 % (671)Termination reason: Unknown
% 158.57/24.22 % (671)Termination phase: Saturation
% 158.57/24.22
% 158.57/24.22 % (671)Memory used [KB]: 9466
% 158.57/24.22 % (671)Time elapsed: 0.392 s
% 158.57/24.22 % (671)Instructions burned: 1268 (million)
% 158.57/24.22 % (671)------------------------------
% 158.57/24.22 % (671)------------------------------
% 158.57/24.23 % (673)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_31741 for (2778ds/13163Mi)
% 160.10/24.57 % (646)Instruction limit reached!
% 160.10/24.57 % (646)------------------------------
% 160.10/24.57 % (646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 160.10/24.57 % (646)Termination reason: Unknown
% 160.10/24.57 % (646)Termination phase: Saturation
% 160.10/24.57
% 160.10/24.57 % (646)Memory used [KB]: 18038
% 160.10/24.57 % (646)Time elapsed: 4.653 s
% 160.10/24.57 % (646)Instructions burned: 15557 (million)
% 160.10/24.57 % (646)------------------------------
% 160.10/24.57 % (646)------------------------------
% 160.10/24.58 % (674)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_31741 for (2774ds/5087Mi)
% 161.77/24.96 % (672)Instruction limit reached!
% 161.77/24.96 % (672)------------------------------
% 161.77/24.96 % (672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 161.77/24.96 % (672)Termination reason: Unknown
% 161.77/24.96 % (672)Termination phase: Saturation
% 161.77/24.96
% 161.77/24.96 % (672)Memory used [KB]: 8315
% 161.77/24.96 % (672)Time elapsed: 0.810 s
% 161.77/24.96 % (672)Instructions burned: 2570 (million)
% 161.77/24.96 % (672)------------------------------
% 161.77/24.96 % (672)------------------------------
% 161.77/24.97 % (675)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on DTF2THF_31741 for (2770ds/10380Mi)
% 172.62/26.20 % (667)Instruction limit reached!
% 172.62/26.20 % (667)------------------------------
% 172.62/26.20 % (667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 172.62/26.20 % (667)Termination reason: Unknown
% 172.62/26.20 % (667)Termination phase: Saturation
% 172.62/26.20
% 172.62/26.20 % (667)Memory used [KB]: 20852
% 172.62/26.20 % (667)Time elapsed: 4.766 s
% 172.62/26.20 % (667)Instructions burned: 15194 (million)
% 172.62/26.20 % (667)------------------------------
% 172.62/26.20 % (667)------------------------------
% 172.62/26.20 % (674)Instruction limit reached!
% 172.62/26.20 % (674)------------------------------
% 172.62/26.20 % (674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 172.62/26.20 % (674)Termination reason: Unknown
% 172.62/26.20 % (674)Termination phase: Saturation
% 172.62/26.20
% 172.62/26.20 % (674)Memory used [KB]: 10746
% 172.62/26.20 % (674)Time elapsed: 1.643 s
% 172.62/26.20 % (674)Instructions burned: 5087 (million)
% 172.62/26.20 % (674)------------------------------
% 172.62/26.20 % (674)------------------------------
% 172.62/26.21 % (676)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4218:si=on:rtra=on_0 on DTF2THF_31741 for (2758ds/4218Mi)
% 172.62/26.21 % (677)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on DTF2THF_31741 for (2758ds/3971Mi)
% 179.64/27.25 % (677)Instruction limit reached!
% 179.64/27.25 % (677)------------------------------
% 179.64/27.25 % (677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 179.64/27.25 % (677)Termination reason: Unknown
% 179.64/27.25 % (677)Termination phase: Saturation
% 179.64/27.25
% 179.64/27.25 % (677)Memory used [KB]: 11129
% 179.64/27.25 % (677)Time elapsed: 1.041 s
% 179.64/27.25 % (677)Instructions burned: 3973 (million)
% 179.64/27.25 % (677)------------------------------
% 179.64/27.25 % (677)------------------------------
% 179.64/27.26 % (678)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=14014:si=on:rtra=on_0 on DTF2THF_31741 for (2747ds/14014Mi)
% 180.91/27.45 % (676)Instruction limit reached!
% 180.91/27.45 % (676)------------------------------
% 180.91/27.45 % (676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 180.91/27.45 % (676)Termination reason: Unknown
% 180.91/27.45 % (676)Termination phase: Saturation
% 180.91/27.45
% 180.91/27.45 % (676)Memory used [KB]: 11897
% 180.91/27.45 % (676)Time elapsed: 1.247 s
% 180.91/27.45 % (676)Instructions burned: 4221 (million)
% 180.91/27.45 % (676)------------------------------
% 180.91/27.45 % (676)------------------------------
% 180.91/27.47 % (679)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_31741 for (2745ds/8517Mi)
% 181.47/27.57 % (670)Instruction limit reached!
% 181.47/27.57 % (670)------------------------------
% 181.47/27.57 % (670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 181.47/27.57 % (670)Termination reason: Unknown
% 181.47/27.57 % (670)Termination phase: Saturation
% 181.47/27.57
% 181.47/27.57 % (670)Memory used [KB]: 23539
% 181.47/27.57 % (670)Time elapsed: 3.864 s
% 181.47/27.57 % (670)Instructions burned: 13018 (million)
% 181.47/27.57 % (670)------------------------------
% 181.47/27.57 % (670)------------------------------
% 181.47/27.58 % (680)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_31741 for (2744ds/10148Mi)
% 185.37/28.12 % (675)Refutation not found, non-redundant clauses discarded% (675)------------------------------
% 185.37/28.12 % (675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 185.37/28.12 % (675)Termination reason: Refutation not found, non-redundant clauses discarded
% 185.37/28.12
% 185.37/28.12 % (675)Memory used [KB]: 11769
% 185.37/28.12 % (675)Time elapsed: 3.179 s
% 185.37/28.12 % (675)Instructions burned: 10362 (million)
% 185.37/28.12 % (675)------------------------------
% 185.37/28.12 % (675)------------------------------
% 186.16/28.13 % (681)lrs+10_1:2_ntd=on:nwc=10.0:plsq=on:plsqc=1:plsqr=2,1:ss=axioms:i=9078:si=on:rtra=on_0 on DTF2THF_31741 for (2739ds/9078Mi)
% 187.20/28.30 % (673)Instruction limit reached!
% 187.20/28.30 % (673)------------------------------
% 187.20/28.30 % (673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 187.20/28.30 % (673)Termination reason: Unknown
% 187.20/28.30 % (673)Termination phase: Saturation
% 187.20/28.30
% 187.20/28.30 % (673)Memory used [KB]: 10874
% 187.20/28.30 % (673)Time elapsed: 4.092 s
% 187.20/28.30 % (673)Instructions burned: 13164 (million)
% 187.20/28.30 % (673)------------------------------
% 187.20/28.30 % (673)------------------------------
% 187.20/28.31 % (682)lrs+2_1:1_bet=on:bsr=on:cnfonf=lazy_pi_sigma_gen:er=filter:kws=inv_frequency:ntd=on:sd=3:ss=axioms:i=16164:si=on:rtra=on_0 on DTF2THF_31741 for (2737ds/16164Mi)
% 188.71/28.61 % (334)First to succeed.
% 188.71/28.62 % (334)Refutation found. Thanks to Tanya!
% 188.71/28.62 % SZS status Theorem for DTF2THF_31741
% 188.71/28.62 % SZS output start Proof for DTF2THF_31741
% 188.71/28.62 thf(type_def_5, type, int: $tType).
% 188.71/28.62 thf(type_def_7, type, nat: $tType).
% 188.71/28.62 thf(type_def_8, type, list_option_b: $tType).
% 188.71/28.62 thf(type_def_9, type, list_b: $tType).
% 188.71/28.62 thf(type_def_10, type, option_b: $tType).
% 188.71/28.62 thf(type_def_11, type, option_option_b: $tType).
% 188.71/28.62 thf(type_def_12, type, b: $tType).
% 188.71/28.62 thf(type_def_13, type, formula_a: $tType).
% 188.71/28.62 thf(type_def_14, type, set_nat: $tType).
% 188.71/28.62 thf(func_def_0, type, option_option_b: $tType).
% 188.71/28.62 thf(func_def_1, type, list_option_b: $tType).
% 188.71/28.62 thf(func_def_2, type, set_nat: $tType).
% 188.71/28.62 thf(func_def_3, type, option_b: $tType).
% 188.71/28.62 thf(func_def_4, type, formula_a: $tType).
% 188.71/28.62 thf(func_def_5, type, list_b: $tType).
% 188.71/28.62 thf(func_def_6, type, nat: $tType).
% 188.71/28.62 thf(func_def_7, type, int: $tType).
% 188.71/28.62 thf(func_def_8, type, b: $tType).
% 188.71/28.62 thf(func_def_9, type, plus_plus_int: int > int > int).
% 188.71/28.62 thf(func_def_10, type, plus_plus_nat: nat > nat > nat).
% 188.71/28.62 thf(func_def_11, type, zero_zero_int: int).
% 188.71/28.62 thf(func_def_12, type, zero_zero_nat: nat).
% 188.71/28.62 thf(func_def_13, type, if_nat: $o > nat > nat > nat).
% 188.71/28.62 thf(func_def_14, type, drop_option_b: nat > list_option_b > list_option_b).
% 188.71/28.62 thf(func_def_15, type, drop_b: nat > list_b > list_b).
% 188.71/28.62 thf(func_def_16, type, find_option_b: (option_b > $o) > list_option_b > option_option_b).
% 188.71/28.62 thf(func_def_17, type, find_b: (b > $o) > list_b > option_b).
% 188.71/28.62 thf(func_def_18, type, gen_length_option_b: nat > list_option_b > nat).
% 188.71/28.62 thf(func_def_19, type, gen_length_b: nat > list_b > nat).
% 188.71/28.62 thf(func_def_20, type, cons_option_b: option_b > list_option_b > list_option_b).
% 188.71/28.62 thf(func_def_21, type, cons_b: b > list_b > list_b).
% 188.71/28.62 thf(func_def_22, type, list_ex_option_b: (option_b > $o) > list_option_b > $o).
% 188.71/28.62 thf(func_def_23, type, list_ex_b: (b > $o) > list_b > $o).
% 188.71/28.62 thf(func_def_24, type, nth_option_b: list_option_b > nat > option_b).
% 188.71/28.62 thf(func_def_25, type, nth_b: list_b > nat > b).
% 188.71/28.62 thf(func_def_26, type, fvi_a: nat > formula_a > set_nat).
% 188.71/28.62 thf(func_def_27, type, suc: nat > nat).
% 188.71/28.62 thf(func_def_28, type, semiri2019852685at_int: nat > int).
% 188.71/28.62 thf(func_def_29, type, semiri1382578993at_nat: nat > nat).
% 188.71/28.62 thf(func_def_30, type, size_s1671393719tion_b: list_option_b > nat).
% 188.71/28.62 thf(func_def_31, type, size_size_list_b: list_b > nat).
% 188.71/28.62 thf(func_def_32, type, size_s684879735tion_b: option_option_b > nat).
% 188.71/28.62 thf(func_def_33, type, size_size_option_b: option_b > nat).
% 188.71/28.62 thf(func_def_34, type, nat_triangle: nat > nat).
% 188.71/28.62 thf(func_def_35, type, none_option_b: option_option_b).
% 188.71/28.62 thf(func_def_36, type, none_b: option_b).
% 188.71/28.62 thf(func_def_37, type, some_option_b: option_b > option_option_b).
% 188.71/28.62 thf(func_def_38, type, some_b: b > option_b).
% 188.71/28.62 thf(func_def_39, type, size_option_option_b: (option_b > nat) > option_option_b > nat).
% 188.71/28.62 thf(func_def_40, type, size_option_b: (b > nat) > option_b > nat).
% 188.71/28.62 thf(func_def_41, type, ord_less_int: int > int > $o).
% 188.71/28.62 thf(func_def_42, type, ord_less_nat: nat > nat > $o).
% 188.71/28.62 thf(func_def_43, type, ord_less_eq_nat: nat > nat > $o).
% 188.71/28.62 thf(func_def_44, type, collect_nat: (nat > $o) > set_nat).
% 188.71/28.62 thf(func_def_45, type, member_nat: nat > set_nat > $o).
% 188.71/28.62 thf(func_def_46, type, phi: formula_a).
% 188.71/28.62 thf(func_def_47, type, b2: nat).
% 188.71/28.62 thf(func_def_48, type, n: nat).
% 188.71/28.62 thf(func_def_49, type, v: list_option_b).
% 188.71/28.62 thf(func_def_50, type, x: b).
% 188.71/28.62 thf(func_def_64, type, sP0: (option_b > option_b > $o) > option_b > option_b > $o).
% 188.71/28.62 thf(func_def_65, type, sK1: (nat > nat) > nat).
% 188.71/28.62 thf(func_def_66, type, sK2: nat > nat).
% 188.71/28.62 thf(func_def_67, type, sK3: (nat > nat > $o) > nat).
% 188.71/28.62 thf(func_def_68, type, sK4: (nat > nat > $o) > nat).
% 188.71/28.62 thf(func_def_69, type, sK5: (nat > nat > $o) > nat).
% 188.71/28.62 thf(func_def_70, type, sK6: (nat > nat > $o) > nat).
% 188.71/28.62 thf(func_def_71, type, sK7: nat > nat > nat).
% 188.71/28.62 thf(func_def_72, type, sK8: list_option_b > nat > list_option_b).
% 188.71/28.62 thf(func_def_73, type, sK9: list_option_b > nat > option_b).
% 188.71/28.62 thf(func_def_74, type, sK10: nat > nat > nat).
% 188.71/28.62 thf(func_def_75, type, sK11: nat > (nat > option_b > $o) > option_b).
% 188.71/28.62 thf(func_def_76, type, sK12: list_option_b > nat > (nat > option_b > $o) > nat).
% 188.71/28.62 thf(func_def_77, type, sK13: nat > (nat > option_b > $o) > list_option_b).
% 188.71/28.62 thf(func_def_78, type, sK14: nat > (nat > option_b > $o) > nat).
% 188.71/28.62 thf(func_def_79, type, sK15: nat > formula_a > nat > nat).
% 188.71/28.62 thf(func_def_80, type, sK16: nat > nat > nat).
% 188.71/28.62 thf(func_def_81, type, sK17: (nat > nat > $o) > nat).
% 188.71/28.62 thf(func_def_82, type, sK18: (nat > nat > $o) > nat).
% 188.71/28.62 thf(func_def_83, type, sK19: (nat > nat > $o) > nat).
% 188.71/28.62 thf(func_def_84, type, sK20: (nat > nat > $o) > nat).
% 188.71/28.62 thf(func_def_85, type, sK21: nat > nat).
% 188.71/28.62 thf(func_def_86, type, sK22: (nat > nat) > nat).
% 188.71/28.62 thf(func_def_87, type, sK23: (nat > $o) > nat).
% 188.71/28.62 thf(func_def_88, type, sK24: (nat > $o) > nat > nat).
% 188.71/28.62 thf(func_def_89, type, sK25: (nat > $o) > nat > nat).
% 188.71/28.62 thf(func_def_90, type, sK26: option_b > b).
% 188.71/28.62 thf(func_def_91, type, sK27: option_b > b).
% 188.71/28.62 thf(func_def_92, type, sK28: nat).
% 188.71/28.62 thf(func_def_93, type, sK29: (nat > nat > $o) > nat).
% 188.71/28.62 thf(func_def_94, type, sK30: (nat > nat > $o) > nat).
% 188.71/28.62 thf(func_def_95, type, sK31: (nat > nat > $o) > nat).
% 188.71/28.62 thf(func_def_96, type, sK32: (nat > nat > $o) > nat).
% 188.71/28.62 thf(func_def_97, type, sK33: (nat > nat > $o) > nat).
% 188.71/28.62 thf(func_def_98, type, sK34: (nat > $o) > nat).
% 188.71/28.62 thf(func_def_99, type, sK35: list_option_b > list_option_b > nat).
% 188.71/28.62 thf(func_def_100, type, sK36: (nat > $o) > nat).
% 188.71/28.62 thf(func_def_101, type, sK37: (nat > $o) > nat > nat).
% 188.71/28.62 thf(func_def_102, type, sK38: (nat > $o) > nat > nat).
% 188.71/28.62 thf(func_def_103, type, sK39: nat > nat).
% 188.71/28.62 thf(func_def_104, type, sK40: nat > nat).
% 188.71/28.62 thf(func_def_105, type, sK41: (nat > $o) > nat > nat).
% 188.71/28.62 thf(func_def_106, type, sK42: (nat > $o) > nat > nat).
% 188.71/28.62 thf(func_def_107, type, sK43: (option_b > option_b > $o) > option_b > option_b > b).
% 188.71/28.62 thf(func_def_108, type, sK44: (option_b > option_b > $o) > option_b > option_b > b).
% 188.71/28.62 thf(func_def_109, type, sK45: option_b > b).
% 188.71/28.62 thf(func_def_110, type, sK46: (nat > $o) > nat).
% 188.71/28.62 thf(func_def_111, type, sK47: (nat > $o) > nat).
% 188.71/28.62 thf(func_def_112, type, sK48: nat > nat).
% 188.71/28.62 thf(func_def_113, type, sK49: (nat > $o) > nat).
% 188.71/28.62 thf(func_def_114, type, sK50: (nat > $o) > nat).
% 188.71/28.62 thf(func_def_115, type, sK51: nat > nat > nat).
% 188.71/28.62 thf(func_def_116, type, sK52: nat > (nat > $o) > nat).
% 188.71/28.62 thf(func_def_117, type, sK53: nat > (nat > $o) > nat).
% 188.71/28.62 thf(func_def_118, type, sK54: (nat > $o) > nat > nat).
% 188.71/28.62 thf(func_def_119, type, sK55: (nat > $o) > nat > nat).
% 188.71/28.62 thf(func_def_120, type, sK56: nat > nat > nat).
% 188.71/28.62 thf(func_def_121, type, sK57: nat > list_option_b).
% 188.71/28.62 thf(func_def_122, type, sK58: nat > nat > nat).
% 188.71/28.62 thf(func_def_123, type, sK59: (list_option_b > $o) > list_option_b).
% 188.71/28.62 thf(func_def_124, type, sK60: list_option_b > nat > option_b).
% 188.71/28.62 thf(func_def_125, type, sK61: list_option_b > nat > list_option_b).
% 188.71/28.62 thf(func_def_126, type, sK62: nat > nat > nat).
% 188.71/28.62 thf(func_def_127, type, sK63: (option_b > $o) > b).
% 188.71/28.62 thf(func_def_128, type, sK64: nat > nat > nat).
% 188.71/28.62 thf(func_def_130, type, ph66: !>[X0: $tType]:(X0)).
% 188.71/28.62 thf(f77682,plain,(
% 188.71/28.62 $false),
% 188.71/28.62 inference(avatar_sat_refutation,[status(thm)],[f1463,f1466,f8530,f8545,f8554,f59922,f59953,f60011,f77681])).
% 188.71/28.62 thf(f77681,plain,(
% 188.71/28.62 ~spl65_2 | ~spl65_553),
% 188.71/28.62 inference(avatar_contradiction_clause,[status(thm)],[f77680])).
% 188.71/28.62 thf(f77680,plain,(
% 188.71/28.62 $false | (~spl65_2 | ~spl65_553)),
% 188.71/28.62 inference(trivial_inequality_removal,[status(thm)],[f77677])).
% 188.71/28.62 thf(f77677,plain,(
% 188.71/28.62 ($false = $true) | (~spl65_2 | ~spl65_553)),
% 188.71/28.62 inference(superposition,[status(thm)],[f1461,f59952])).
% 188.71/28.62 thf(f59952,plain,(
% 188.71/28.62 ($false = (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | ~spl65_553),
% 188.71/28.62 inference(avatar_component_clause,[status(thm)],[f59950])).
% 188.71/28.62 thf(f59950,definition,(
% 188.71/28.62 spl65_553 <=> ($false = (member_nat @ sK28 @ (fvi_a @ b2 @ phi)))),
% 188.71/28.62 introduced(definition,[new_symbols(naming,[spl65_553])],[avatar_definition])).
% 188.71/28.62 thf(f1461,plain,(
% 188.71/28.62 ($true = (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | ~spl65_2),
% 188.71/28.62 inference(avatar_component_clause,[status(thm)],[f1460])).
% 188.71/28.62 thf(f1460,definition,(
% 188.71/28.62 spl65_2 <=> ($true = (member_nat @ sK28 @ (fvi_a @ b2 @ phi)))),
% 188.71/28.62 introduced(definition,[new_symbols(naming,[spl65_2])],[avatar_definition])).
% 188.71/28.62 thf(f60011,plain,(
% 188.71/28.62 spl65_551 | ~spl65_1 | ~spl65_6),
% 188.71/28.62 inference(avatar_split_clause,[status(thm)],[f60006,f1656,f1456,f59940])).
% 188.71/28.62 thf(f59940,definition,(
% 188.71/28.62 spl65_551 <=> (none_b = (nth_option_b @ v @ (sK2 @ sK28)))),
% 188.71/28.62 introduced(definition,[new_symbols(naming,[spl65_551])],[avatar_definition])).
% 188.71/28.62 thf(f1456,definition,(
% 188.71/28.62 spl65_1 <=> (none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ sK28))),
% 188.71/28.62 introduced(definition,[new_symbols(naming,[spl65_1])],[avatar_definition])).
% 188.71/28.62 thf(f1656,definition,(
% 188.71/28.62 spl65_6 <=> ($true = (ord_less_nat @ zero_zero_nat @ sK28))),
% 188.71/28.62 introduced(definition,[new_symbols(naming,[spl65_6])],[avatar_definition])).
% 188.71/28.62 thf(f60006,plain,(
% 188.71/28.62 (none_b = (nth_option_b @ v @ (sK2 @ sK28))) | (~spl65_1 | ~spl65_6)),
% 188.71/28.62 inference(superposition,[status(thm)],[f8632,f1458])).
% 188.71/28.62 thf(f1458,plain,(
% 188.71/28.62 (none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ sK28)) | ~spl65_1),
% 188.71/28.62 inference(avatar_component_clause,[status(thm)],[f1456])).
% 188.71/28.62 thf(f8632,plain,(
% 188.71/28.62 ( ! [X0 : option_b,X1 : list_option_b] : (((nth_option_b @ (cons_option_b @ X0 @ X1) @ sK28) = (nth_option_b @ X1 @ (sK2 @ sK28)))) ) | ~spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f1300,f8559])).
% 188.71/28.62 thf(f8559,plain,(
% 188.71/28.62 (sK28 = (suc @ (sK2 @ sK28))) | ~spl65_6),
% 188.71/28.62 inference(trivial_inequality_removal,[status(thm)],[f8556])).
% 188.71/28.62 thf(f8556,plain,(
% 188.71/28.62 ($true != $true) | (sK28 = (suc @ (sK2 @ sK28))) | ~spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f1104,f1658])).
% 188.71/28.62 thf(f1658,plain,(
% 188.71/28.62 ($true = (ord_less_nat @ zero_zero_nat @ sK28)) | ~spl65_6),
% 188.71/28.62 inference(avatar_component_clause,[status(thm)],[f1656])).
% 188.71/28.62 thf(f1104,plain,(
% 188.71/28.62 ( ! [X0 : nat] : (((ord_less_nat @ zero_zero_nat @ X0) != $true) | ((suc @ (sK2 @ X0)) = X0)) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f927])).
% 188.71/28.62 thf(f927,plain,(
% 188.71/28.62 ! [X0 : nat] : (((ord_less_nat @ zero_zero_nat @ X0) != $true) | ((suc @ (sK2 @ X0)) = X0))),
% 188.71/28.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f837,f926])).
% 188.71/28.62 thf(f926,plain,(
% 188.71/28.62 ! [X0 : nat] : (? [X1 : nat] : ((suc @ X1) = X0) => ((suc @ (sK2 @ X0)) = X0))),
% 188.71/28.62 introduced(definition,[],[choice_axiom])).
% 188.71/28.62 thf(f837,plain,(
% 188.71/28.62 ! [X0 : nat] : (((ord_less_nat @ zero_zero_nat @ X0) != $true) | ? [X1 : nat] : ((suc @ X1) = X0))),
% 188.71/28.62 inference(ennf_transformation,[status(thm)],[f552])).
% 188.71/28.62 thf(f552,plain,(
% 188.71/28.62 ! [X0 : nat] : (((ord_less_nat @ zero_zero_nat @ X0) = $true) => ? [X1 : nat] : ((suc @ X1) = X0))),
% 188.71/28.62 inference(fool_elimination,[status(thm)],[f551])).
% 188.71/28.62 thf(f551,plain,(
% 188.71/28.62 ! [X0 : nat] : ((ord_less_nat @ zero_zero_nat @ X0) => ? [X1 : nat] : ((suc @ X1) = X0))),
% 188.71/28.62 inference(rectify,[status(thm)],[f105])).
% 188.71/28.62 thf(f105,axiom,(
% 188.71/28.62 ! [X2 : nat] : ((ord_less_nat @ zero_zero_nat @ X2) => ? [X22 : nat] : ((suc @ X22) = X2))),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_104_gr0__implies__Suc)).
% 188.71/28.62 thf(f1300,plain,(
% 188.71/28.62 ( ! [X2 : nat,X0 : option_b,X1 : list_option_b] : (((nth_option_b @ (cons_option_b @ X0 @ X1) @ (suc @ X2)) = (nth_option_b @ X1 @ X2))) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f2])).
% 188.71/28.62 thf(f2,axiom,(
% 188.71/28.62 ! [X0 : option_b,X1 : list_option_b,X2 : nat] : ((nth_option_b @ (cons_option_b @ X0 @ X1) @ (suc @ X2)) = (nth_option_b @ X1 @ X2))),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_1_nth__Cons__Suc)).
% 188.71/28.62 thf(f59953,plain,(
% 188.71/28.62 ~spl65_551 | spl65_553 | ~spl65_6),
% 188.71/28.62 inference(avatar_split_clause,[status(thm)],[f59948,f1656,f59950,f59940])).
% 188.71/28.62 thf(f59948,plain,(
% 188.71/28.62 (none_b != (nth_option_b @ v @ (sK2 @ sK28))) | ($false = (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | ~spl65_6),
% 188.71/28.62 inference(subsumption_resolution,[status(thm)],[f59727,f23520])).
% 188.71/28.62 thf(f23520,plain,(
% 188.71/28.62 ($true = (ord_less_nat @ (sK2 @ sK28) @ (size_s1671393719tion_b @ v))) | ~spl65_6),
% 188.71/28.62 inference(forward_demodulation,[status(thm)],[f23510,f11705])).
% 188.71/28.62 thf(f11705,plain,(
% 188.71/28.62 ((sK2 @ sK28) = (sK40 @ sK28)) | ~spl65_6),
% 188.71/28.62 inference(subsumption_resolution,[status(thm)],[f11704,f8609])).
% 188.71/28.62 thf(f8609,plain,(
% 188.71/28.62 ((sK2 @ sK28) != sK28) | ~spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f1141,f8559])).
% 188.71/28.62 thf(f1141,plain,(
% 188.71/28.62 ( ! [X0 : nat] : (((suc @ X0) != X0)) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f751])).
% 188.71/28.62 thf(f751,plain,(
% 188.71/28.62 ! [X0 : nat] : ((suc @ X0) != X0)),
% 188.71/28.62 inference(rectify,[status(thm)],[f25])).
% 188.71/28.62 thf(f25,axiom,(
% 188.71/28.62 ! [X2 : nat] : ((suc @ X2) != X2)),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_24_n__not__Suc__n)).
% 188.71/28.62 thf(f11704,plain,(
% 188.71/28.62 ((sK2 @ sK28) = sK28) | ((sK2 @ sK28) = (sK40 @ sK28)) | ~spl65_6),
% 188.71/28.62 inference(subsumption_resolution,[status(thm)],[f11703,f8929])).
% 188.71/28.62 thf(f8929,plain,(
% 188.71/28.62 ((ord_less_nat @ sK28 @ (sK2 @ sK28)) != $true) | ~spl65_6),
% 188.71/28.62 inference(trivial_inequality_removal,[status(thm)],[f8855])).
% 188.71/28.62 thf(f8855,plain,(
% 188.71/28.62 ($true != $true) | ((ord_less_nat @ sK28 @ (sK2 @ sK28)) != $true) | ~spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f1298,f8615])).
% 188.71/28.62 thf(f8615,plain,(
% 188.71/28.62 ( ! [X0 : nat] : (($true = (ord_less_nat @ (sK2 @ sK28) @ X0)) | ($true != (ord_less_nat @ sK28 @ X0))) ) | ~spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f1208,f8559])).
% 188.71/28.62 thf(f1208,plain,(
% 188.71/28.62 ( ! [X0 : nat,X1 : nat] : (($true != (ord_less_nat @ (suc @ X1) @ X0)) | ($true = (ord_less_nat @ X1 @ X0))) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f900])).
% 188.71/28.62 thf(f900,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : (($true = (ord_less_nat @ X1 @ X0)) | ($true != (ord_less_nat @ (suc @ X1) @ X0)))),
% 188.71/28.62 inference(ennf_transformation,[status(thm)],[f642])).
% 188.71/28.62 thf(f642,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : (($true = (ord_less_nat @ (suc @ X1) @ X0)) => ($true = (ord_less_nat @ X1 @ X0)))),
% 188.71/28.62 inference(fool_elimination,[status(thm)],[f641])).
% 188.71/28.62 thf(f641,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ (suc @ X1) @ X0) => (ord_less_nat @ X1 @ X0))),
% 188.71/28.62 inference(rectify,[status(thm)],[f80])).
% 188.71/28.62 thf(f80,axiom,(
% 188.71/28.62 ! [X2 : nat,X4 : nat] : ((ord_less_nat @ (suc @ X4) @ X2) => (ord_less_nat @ X4 @ X2))),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_79_Suc__lessD)).
% 188.71/28.62 thf(f1298,plain,(
% 188.71/28.62 ( ! [X0 : nat] : (($true != (ord_less_nat @ X0 @ X0))) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f769])).
% 188.71/28.62 thf(f769,plain,(
% 188.71/28.62 ! [X0 : nat] : ($true != (ord_less_nat @ X0 @ X0))),
% 188.71/28.62 inference(flattening,[status(thm)],[f723])).
% 188.71/28.62 thf(f723,plain,(
% 188.71/28.62 ! [X0 : nat] : ~($true = (ord_less_nat @ X0 @ X0))),
% 188.71/28.62 inference(fool_elimination,[status(thm)],[f722])).
% 188.71/28.62 thf(f722,plain,(
% 188.71/28.62 ! [X0 : nat] : ~(ord_less_nat @ X0 @ X0)),
% 188.71/28.62 inference(rectify,[status(thm)],[f30])).
% 188.71/28.62 thf(f30,axiom,(
% 188.71/28.62 ! [X2 : nat] : ~(ord_less_nat @ X2 @ X2)),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_29_less__irrefl__nat)).
% 188.71/28.62 thf(f11703,plain,(
% 188.71/28.62 ((ord_less_nat @ sK28 @ (sK2 @ sK28)) = $true) | ((sK2 @ sK28) = sK28) | ((sK2 @ sK28) = (sK40 @ sK28)) | ~spl65_6),
% 188.71/28.62 inference(subsumption_resolution,[status(thm)],[f11697,f8741])).
% 188.71/28.62 thf(f8741,plain,(
% 188.71/28.62 ($true = (ord_less_nat @ (sK40 @ sK28) @ sK28)) | ~spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f1433,f8561])).
% 188.71/28.62 thf(f8561,plain,(
% 188.71/28.62 ((suc @ (sK40 @ sK28)) = sK28) | ~spl65_6),
% 188.71/28.62 inference(trivial_inequality_removal,[status(thm)],[f8557])).
% 188.71/28.62 thf(f8557,plain,(
% 188.71/28.62 ((suc @ (sK40 @ sK28)) = sK28) | ($true != $true) | ~spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f1228,f1658])).
% 188.71/28.62 thf(f1228,plain,(
% 188.71/28.62 ( ! [X0 : nat] : (((ord_less_nat @ zero_zero_nat @ X0) != $true) | ((suc @ (sK40 @ X0)) = X0)) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f1015])).
% 188.71/28.62 thf(f1015,plain,(
% 188.71/28.62 ! [X0 : nat] : ((((suc @ (sK40 @ X0)) = X0) | ((ord_less_nat @ zero_zero_nat @ X0) != $true)) & (((ord_less_nat @ zero_zero_nat @ X0) = $true) | ! [X2 : nat] : ((suc @ X2) != X0)))),
% 188.71/28.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f1013,f1014])).
% 188.71/28.62 thf(f1014,plain,(
% 188.71/28.62 ! [X0 : nat] : (? [X1 : nat] : ((suc @ X1) = X0) => ((suc @ (sK40 @ X0)) = X0))),
% 188.71/28.62 introduced(definition,[],[choice_axiom])).
% 188.71/28.62 thf(f1013,plain,(
% 188.71/28.62 ! [X0 : nat] : ((? [X1 : nat] : ((suc @ X1) = X0) | ((ord_less_nat @ zero_zero_nat @ X0) != $true)) & (((ord_less_nat @ zero_zero_nat @ X0) = $true) | ! [X2 : nat] : ((suc @ X2) != X0)))),
% 188.71/28.62 inference(rectify,[status(thm)],[f1012])).
% 188.71/28.62 thf(f1012,plain,(
% 188.71/28.62 ! [X0 : nat] : ((? [X1 : nat] : ((suc @ X1) = X0) | ((ord_less_nat @ zero_zero_nat @ X0) != $true)) & (((ord_less_nat @ zero_zero_nat @ X0) = $true) | ! [X1 : nat] : ((suc @ X1) != X0)))),
% 188.71/28.62 inference(nnf_transformation,[status(thm)],[f727])).
% 188.71/28.62 thf(f727,plain,(
% 188.71/28.62 ! [X0 : nat] : (? [X1 : nat] : ((suc @ X1) = X0) <=> ((ord_less_nat @ zero_zero_nat @ X0) = $true))),
% 188.71/28.62 inference(fool_elimination,[status(thm)],[f726])).
% 188.71/28.62 thf(f726,plain,(
% 188.71/28.62 ! [X0 : nat] : (? [X1 : nat] : ((suc @ X1) = X0) = (ord_less_nat @ zero_zero_nat @ X0))),
% 188.71/28.62 inference(rectify,[status(thm)],[f107])).
% 188.71/28.62 thf(f107,axiom,(
% 188.71/28.62 ! [X2 : nat] : (? [X48 : nat] : ((suc @ X48) = X2) = (ord_less_nat @ zero_zero_nat @ X2))),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_106_gr0__conv__Suc)).
% 188.71/28.62 thf(f1433,plain,(
% 188.71/28.62 ( ! [X1 : nat] : (((ord_less_nat @ X1 @ (suc @ X1)) = $true)) )),
% 188.71/28.62 inference(equality_resolution,[status(thm)],[f1288])).
% 188.71/28.62 thf(f1288,plain,(
% 188.71/28.62 ( ! [X0 : nat,X1 : nat] : (($true = (ord_less_nat @ X0 @ (suc @ X1))) | (X0 != X1)) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f1051])).
% 188.71/28.62 thf(f1051,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : ((($true = (ord_less_nat @ X0 @ (suc @ X1))) | ((X0 != X1) & ($true != (ord_less_nat @ X0 @ X1)))) & ((X0 = X1) | ($true = (ord_less_nat @ X0 @ X1)) | ($true != (ord_less_nat @ X0 @ (suc @ X1)))))),
% 188.71/28.62 inference(flattening,[status(thm)],[f1050])).
% 188.71/28.62 thf(f1050,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : ((($true = (ord_less_nat @ X0 @ (suc @ X1))) | ((X0 != X1) & ($true != (ord_less_nat @ X0 @ X1)))) & (((X0 = X1) | ($true = (ord_less_nat @ X0 @ X1))) | ($true != (ord_less_nat @ X0 @ (suc @ X1)))))),
% 188.71/28.62 inference(nnf_transformation,[status(thm)],[f480])).
% 188.71/28.62 thf(f480,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : (($true = (ord_less_nat @ X0 @ (suc @ X1))) <=> ((X0 = X1) | ($true = (ord_less_nat @ X0 @ X1))))),
% 188.71/28.62 inference(fool_elimination,[status(thm)],[f479])).
% 188.71/28.62 thf(f479,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X0 @ X1) | (X0 = X1) = (ord_less_nat @ X0 @ (suc @ X1)))),
% 188.71/28.62 inference(rectify,[status(thm)],[f74])).
% 188.71/28.62 thf(f74,axiom,(
% 188.71/28.62 ! [X4 : nat,X2 : nat] : ((ord_less_nat @ X4 @ X2) | (X2 = X4) = (ord_less_nat @ X4 @ (suc @ X2)))),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_73_less__Suc__eq)).
% 188.71/28.62 thf(f11697,plain,(
% 188.71/28.62 ($true != (ord_less_nat @ (sK40 @ sK28) @ sK28)) | ((sK2 @ sK28) = (sK40 @ sK28)) | ((ord_less_nat @ sK28 @ (sK2 @ sK28)) = $true) | ((sK2 @ sK28) = sK28) | ~spl65_6),
% 188.71/28.62 inference(trivial_inequality_removal,[status(thm)],[f11682])).
% 188.71/28.62 thf(f11682,plain,(
% 188.71/28.62 ((ord_less_nat @ sK28 @ (sK2 @ sK28)) = $true) | ($true != $true) | ((sK2 @ sK28) = sK28) | ($true != (ord_less_nat @ (sK40 @ sK28) @ sK28)) | ((sK2 @ sK28) = (sK40 @ sK28)) | ~spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f8698,f8625])).
% 188.71/28.62 thf(f8625,plain,(
% 188.71/28.62 ( ! [X0 : nat] : (((ord_less_nat @ X0 @ (sK2 @ sK28)) = $true) | ($true != (ord_less_nat @ X0 @ sK28)) | ((sK2 @ sK28) = X0)) ) | ~spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f1260,f8559])).
% 188.71/28.62 thf(f1260,plain,(
% 188.71/28.62 ( ! [X0 : nat,X1 : nat] : (($true != (ord_less_nat @ X1 @ (suc @ X0))) | (X0 = X1) | ($true = (ord_less_nat @ X1 @ X0))) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f1032])).
% 188.71/28.62 thf(f1032,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : (($true = (ord_less_nat @ X1 @ X0)) | ((($true = (ord_less_nat @ X1 @ (suc @ X0))) | (X0 != X1)) & ((X0 = X1) | ($true != (ord_less_nat @ X1 @ (suc @ X0))))))),
% 188.71/28.62 inference(nnf_transformation,[status(thm)],[f860])).
% 188.71/28.62 thf(f860,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : (($true = (ord_less_nat @ X1 @ X0)) | (($true = (ord_less_nat @ X1 @ (suc @ X0))) <=> (X0 = X1)))),
% 188.71/28.62 inference(ennf_transformation,[status(thm)],[f754])).
% 188.71/28.62 thf(f754,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : (($true != (ord_less_nat @ X1 @ X0)) => (($true = (ord_less_nat @ X1 @ (suc @ X0))) <=> (X0 = X1)))),
% 188.71/28.62 inference(flattening,[status(thm)],[f566])).
% 188.71/28.62 thf(f566,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : (~($true = (ord_less_nat @ X1 @ X0)) => (($true = (ord_less_nat @ X1 @ (suc @ X0))) <=> (X0 = X1)))),
% 188.71/28.62 inference(fool_elimination,[status(thm)],[f565])).
% 188.71/28.62 thf(f565,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : (~(ord_less_nat @ X1 @ X0) => ((X0 = X1) = (ord_less_nat @ X1 @ (suc @ X0))))),
% 188.71/28.62 inference(rectify,[status(thm)],[f65])).
% 188.71/28.62 thf(f65,axiom,(
% 188.71/28.62 ! [X4 : nat,X2 : nat] : (~(ord_less_nat @ X2 @ X4) => ((X2 = X4) = (ord_less_nat @ X2 @ (suc @ X4))))),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_64_not__less__less__Suc__eq)).
% 188.71/28.62 thf(f8698,plain,(
% 188.71/28.62 ( ! [X0 : nat] : (((ord_less_nat @ (sK40 @ sK28) @ X0) != $true) | (sK28 = X0) | ($true = (ord_less_nat @ sK28 @ X0))) ) | ~spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f1130,f8561])).
% 188.71/28.62 thf(f1130,plain,(
% 188.71/28.62 ( ! [X0 : nat,X1 : nat] : (($true = (ord_less_nat @ (suc @ X0) @ X1)) | ($true != (ord_less_nat @ X0 @ X1)) | ((suc @ X0) = X1)) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f841])).
% 188.71/28.62 thf(f841,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : (($true = (ord_less_nat @ (suc @ X0) @ X1)) | ((suc @ X0) = X1) | ($true != (ord_less_nat @ X0 @ X1)))),
% 188.71/28.62 inference(flattening,[status(thm)],[f840])).
% 188.71/28.62 thf(f840,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : ((($true = (ord_less_nat @ (suc @ X0) @ X1)) | ((suc @ X0) = X1)) | ($true != (ord_less_nat @ X0 @ X1)))),
% 188.71/28.62 inference(ennf_transformation,[status(thm)],[f705])).
% 188.71/28.62 thf(f705,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : (($true = (ord_less_nat @ X0 @ X1)) => (((suc @ X0) != X1) => ($true = (ord_less_nat @ (suc @ X0) @ X1))))),
% 188.71/28.62 inference(fool_elimination,[status(thm)],[f704])).
% 188.71/28.62 thf(f704,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X0 @ X1) => (((suc @ X0) != X1) => (ord_less_nat @ (suc @ X0) @ X1)))),
% 188.71/28.62 inference(rectify,[status(thm)],[f78])).
% 188.71/28.62 thf(f78,axiom,(
% 188.71/28.62 ! [X4 : nat,X2 : nat] : ((ord_less_nat @ X4 @ X2) => (((suc @ X4) != X2) => (ord_less_nat @ (suc @ X4) @ X2)))),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_77_Suc__lessI)).
% 188.71/28.62 thf(f23510,plain,(
% 188.71/28.62 ($true = (ord_less_nat @ (sK40 @ sK28) @ (size_s1671393719tion_b @ v))) | ~spl65_6),
% 188.71/28.62 inference(trivial_inequality_removal,[status(thm)],[f23439])).
% 188.71/28.62 thf(f23439,plain,(
% 188.71/28.62 ($true = (ord_less_nat @ (sK40 @ sK28) @ (size_s1671393719tion_b @ v))) | ($false = $true) | ~spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f1464,f8753])).
% 188.71/28.62 thf(f8753,plain,(
% 188.71/28.62 ( ! [X0 : nat] : (((ord_less_nat @ sK28 @ (suc @ X0)) = $false) | ((ord_less_nat @ (sK40 @ sK28) @ X0) = $true)) ) | ~spl65_6),
% 188.71/28.62 inference(binary_proxy_clausification,[status(thm)],[f8735])).
% 188.71/28.62 thf(f8735,plain,(
% 188.71/28.62 ( ! [X0 : nat] : (((ord_less_nat @ sK28 @ (suc @ X0)) = (ord_less_nat @ (sK40 @ sK28) @ X0))) ) | ~spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f1372,f8561])).
% 188.71/28.62 thf(f1372,plain,(
% 188.71/28.62 ( ! [X0 : nat,X1 : nat] : (((ord_less_nat @ (suc @ X0) @ (suc @ X1)) = (ord_less_nat @ X0 @ X1))) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f753])).
% 188.71/28.62 thf(f753,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ (suc @ X0) @ (suc @ X1)) = (ord_less_nat @ X0 @ X1))),
% 188.71/28.62 inference(rectify,[status(thm)],[f13])).
% 188.71/28.62 thf(f13,axiom,(
% 188.71/28.62 ! [X4 : nat,X2 : nat] : ((ord_less_nat @ X4 @ X2) = (ord_less_nat @ (suc @ X4) @ (suc @ X2)))),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_12_Suc__less__eq)).
% 188.71/28.62 thf(f1464,plain,(
% 188.71/28.62 ((ord_less_nat @ sK28 @ (suc @ (size_s1671393719tion_b @ v))) = $true)),
% 188.71/28.62 inference(subsumption_resolution,[status(thm)],[f1384,f1359])).
% 188.71/28.62 thf(f1359,plain,(
% 188.71/28.62 ( ! [X0 : option_b,X1 : list_option_b] : (((size_s1671393719tion_b @ (cons_option_b @ X0 @ X1)) = (suc @ (size_s1671393719tion_b @ X1)))) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f122])).
% 188.71/28.62 thf(f122,axiom,(
% 188.71/28.62 ! [X0 : option_b,X1 : list_option_b] : ((size_s1671393719tion_b @ (cons_option_b @ X0 @ X1)) = (suc @ (size_s1671393719tion_b @ X1)))),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_121_length__Cons)).
% 188.71/28.62 thf(f1384,plain,(
% 188.71/28.62 ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) != (suc @ (size_s1671393719tion_b @ v))) | ((ord_less_nat @ sK28 @ (suc @ (size_s1671393719tion_b @ v))) = $true)),
% 188.71/28.62 inference(definition_unfolding,[status(thm)],[f1184,f1163,f1163])).
% 188.71/28.62 thf(f1163,plain,(
% 188.71/28.62 ((size_s1671393719tion_b @ v) = n)),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f965])).
% 188.71/28.62 thf(f965,plain,(
% 188.71/28.62 ((size_s1671393719tion_b @ v) = n) & ! [X0 : nat] : (((ord_less_nat @ X0 @ n) != $true) | ((($true != (member_nat @ X0 @ (fvi_a @ (suc @ b2) @ phi))) | (none_b != (nth_option_b @ v @ X0))) & ((none_b = (nth_option_b @ v @ X0)) | ($true = (member_nat @ X0 @ (fvi_a @ (suc @ b2) @ phi))))))),
% 188.71/28.62 inference(nnf_transformation,[status(thm)],[f880])).
% 188.71/28.62 thf(f880,plain,(
% 188.71/28.62 ((size_s1671393719tion_b @ v) = n) & ! [X0 : nat] : (((ord_less_nat @ X0 @ n) != $true) | (($true != (member_nat @ X0 @ (fvi_a @ (suc @ b2) @ phi))) <=> (none_b = (nth_option_b @ v @ X0))))),
% 188.71/28.62 inference(ennf_transformation,[status(thm)],[f741])).
% 188.71/28.62 thf(f741,plain,(
% 188.71/28.62 ((size_s1671393719tion_b @ v) = n) & ! [X0 : nat] : (((ord_less_nat @ X0 @ n) = $true) => (($true != (member_nat @ X0 @ (fvi_a @ (suc @ b2) @ phi))) <=> (none_b = (nth_option_b @ v @ X0))))),
% 188.71/28.62 inference(flattening,[status(thm)],[f413])).
% 188.71/28.62 thf(f413,plain,(
% 188.71/28.62 ! [X0 : nat] : (((ord_less_nat @ X0 @ n) = $true) => ((none_b = (nth_option_b @ v @ X0)) <=> ~($true = (member_nat @ X0 @ (fvi_a @ (suc @ b2) @ phi))))) & ((size_s1671393719tion_b @ v) = n)),
% 188.71/28.62 inference(fool_elimination,[status(thm)],[f412])).
% 188.71/28.62 thf(f412,plain,(
% 188.71/28.62 ! [X0 : nat] : ((ord_less_nat @ X0 @ n) => ((none_b = (nth_option_b @ v @ X0)) = ~(member_nat @ X0 @ (fvi_a @ (suc @ b2) @ phi)))) & ((size_s1671393719tion_b @ v) = n)),
% 188.71/28.62 inference(rectify,[status(thm)],[f328])).
% 188.71/28.62 thf(f328,axiom,(
% 188.71/28.62 ! [X70 : nat] : ((ord_less_nat @ X70 @ n) => ((none_b = (nth_option_b @ v @ X70)) = ~(member_nat @ X70 @ (fvi_a @ (suc @ b2) @ phi)))) & ((size_s1671393719tion_b @ v) = n)),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',conj_1)).
% 188.71/28.62 thf(f1184,plain,(
% 188.71/28.62 ($true = (ord_less_nat @ sK28 @ (suc @ n))) | ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) != (suc @ n))),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f986])).
% 188.71/28.62 thf(f986,plain,(
% 188.71/28.62 (($true = (ord_less_nat @ sK28 @ (suc @ n))) & (($true = (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | (none_b != (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ sK28))) & (($true != (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | (none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ sK28)))) | ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) != (suc @ n))),
% 188.71/28.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f984,f985])).
% 188.71/28.62 thf(f985,plain,(
% 188.71/28.62 ? [X0 : nat] : (((ord_less_nat @ X0 @ (suc @ n)) = $true) & (($true = (member_nat @ X0 @ (fvi_a @ b2 @ phi))) | (none_b != (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ X0))) & (($true != (member_nat @ X0 @ (fvi_a @ b2 @ phi))) | (none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ X0)))) => (($true = (ord_less_nat @ sK28 @ (suc @ n))) & (($true = (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | (none_b != (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ sK28))) & (($true != (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | (none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ sK28))))),
% 188.71/28.62 introduced(definition,[],[choice_axiom])).
% 188.71/28.62 thf(f984,plain,(
% 188.71/28.62 ? [X0 : nat] : (((ord_less_nat @ X0 @ (suc @ n)) = $true) & (($true = (member_nat @ X0 @ (fvi_a @ b2 @ phi))) | (none_b != (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ X0))) & (($true != (member_nat @ X0 @ (fvi_a @ b2 @ phi))) | (none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ X0)))) | ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) != (suc @ n))),
% 188.71/28.62 inference(flattening,[status(thm)],[f983])).
% 188.71/28.62 thf(f983,plain,(
% 188.71/28.62 ? [X0 : nat] : (((ord_less_nat @ X0 @ (suc @ n)) = $true) & ((($true = (member_nat @ X0 @ (fvi_a @ b2 @ phi))) | (none_b != (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ X0))) & (($true != (member_nat @ X0 @ (fvi_a @ b2 @ phi))) | (none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ X0))))) | ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) != (suc @ n))),
% 188.71/28.62 inference(nnf_transformation,[status(thm)],[f862])).
% 188.71/28.62 thf(f862,plain,(
% 188.71/28.62 ? [X0 : nat] : (((ord_less_nat @ X0 @ (suc @ n)) = $true) & ((none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ X0)) <~> ($true != (member_nat @ X0 @ (fvi_a @ b2 @ phi))))) | ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) != (suc @ n))),
% 188.71/28.62 inference(ennf_transformation,[status(thm)],[f740])).
% 188.71/28.62 thf(f740,plain,(
% 188.71/28.62 ~(! [X0 : nat] : (((ord_less_nat @ X0 @ (suc @ n)) != $true) | ((none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ X0)) <=> ($true != (member_nat @ X0 @ (fvi_a @ b2 @ phi))))) & ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) = (suc @ n)))),
% 188.71/28.62 inference(flattening,[status(thm)],[f333])).
% 188.71/28.62 thf(f333,plain,(
% 188.71/28.62 ~(! [X0 : nat] : (~((ord_less_nat @ X0 @ (suc @ n)) = $true) | (~($true = (member_nat @ X0 @ (fvi_a @ b2 @ phi))) <=> (none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ X0)))) & ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) = (suc @ n)))),
% 188.71/28.62 inference(fool_elimination,[status(thm)],[f332])).
% 188.71/28.62 thf(f332,plain,(
% 188.71/28.62 ~(! [X0 : nat] : (~(ord_less_nat @ X0 @ (suc @ n)) | (~(member_nat @ X0 @ (fvi_a @ b2 @ phi)) = (none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ X0)))) & ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) = (suc @ n)))),
% 188.71/28.62 inference(rectify,[status(thm)],[f330])).
% 188.71/28.62 thf(f330,negated_conjecture,(
% 188.71/28.62 ~(! [X32 : nat] : (~(ord_less_nat @ X32 @ (suc @ n)) | (~(member_nat @ X32 @ (fvi_a @ b2 @ phi)) = (none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ X32)))) & ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) = (suc @ n)))),
% 188.71/28.62 inference(negated_conjecture,[status(cth)],[f329])).
% 188.71/28.62 thf(f329,conjecture,(
% 188.71/28.62 ! [X32 : nat] : (~(ord_less_nat @ X32 @ (suc @ n)) | (~(member_nat @ X32 @ (fvi_a @ b2 @ phi)) = (none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ X32)))) & ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) = (suc @ n))),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',conj_2)).
% 188.71/28.62 thf(f59727,plain,(
% 188.71/28.62 (none_b != (nth_option_b @ v @ (sK2 @ sK28))) | ($false = (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | ($true != (ord_less_nat @ (sK2 @ sK28) @ (size_s1671393719tion_b @ v))) | ~spl65_6),
% 188.71/28.62 inference(trivial_inequality_removal,[status(thm)],[f59717])).
% 188.71/28.62 thf(f59717,plain,(
% 188.71/28.62 ($false = (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | ($true != (ord_less_nat @ (sK2 @ sK28) @ (size_s1671393719tion_b @ v))) | (none_b != (nth_option_b @ v @ (sK2 @ sK28))) | ($true != $true) | ~spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f1382,f8661])).
% 188.71/28.62 thf(f8661,plain,(
% 188.71/28.62 ( ! [X0 : nat,X1 : formula_a] : (($true = (member_nat @ (sK2 @ sK28) @ (fvi_a @ (suc @ X0) @ X1))) | ($false = (member_nat @ sK28 @ (fvi_a @ X0 @ X1)))) ) | ~spl65_6),
% 188.71/28.62 inference(binary_proxy_clausification,[status(thm)],[f8631])).
% 188.71/28.62 thf(f8631,plain,(
% 188.71/28.62 ( ! [X0 : nat,X1 : formula_a] : (((member_nat @ (sK2 @ sK28) @ (fvi_a @ (suc @ X0) @ X1)) = (member_nat @ sK28 @ (fvi_a @ X0 @ X1)))) ) | ~spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f1289,f8559])).
% 188.71/28.62 thf(f1289,plain,(
% 188.71/28.62 ( ! [X2 : formula_a,X0 : nat,X1 : nat] : (((member_nat @ (suc @ X0) @ (fvi_a @ X1 @ X2)) = (member_nat @ X0 @ (fvi_a @ (suc @ X1) @ X2)))) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f742])).
% 188.71/28.62 thf(f742,plain,(
% 188.71/28.62 ! [X0 : nat,X1 : nat,X2 : formula_a] : ((member_nat @ (suc @ X0) @ (fvi_a @ X1 @ X2)) = (member_nat @ X0 @ (fvi_a @ (suc @ X1) @ X2)))),
% 188.71/28.62 inference(rectify,[status(thm)],[f124])).
% 188.71/28.62 thf(f124,axiom,(
% 188.71/28.62 ! [X0 : nat,X53 : nat,X54 : formula_a] : ((member_nat @ X0 @ (fvi_a @ (suc @ X53) @ X54)) = (member_nat @ (suc @ X0) @ (fvi_a @ X53 @ X54)))),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_123_fvi__Suc)).
% 188.71/28.62 thf(f1382,plain,(
% 188.71/28.62 ( ! [X0 : nat] : (($true != (member_nat @ X0 @ (fvi_a @ (suc @ b2) @ phi))) | ($true != (ord_less_nat @ X0 @ (size_s1671393719tion_b @ v))) | (none_b != (nth_option_b @ v @ X0))) )),
% 188.71/28.62 inference(definition_unfolding,[status(thm)],[f1162,f1163])).
% 188.71/28.62 thf(f1162,plain,(
% 188.71/28.62 ( ! [X0 : nat] : (((ord_less_nat @ X0 @ n) != $true) | ($true != (member_nat @ X0 @ (fvi_a @ (suc @ b2) @ phi))) | (none_b != (nth_option_b @ v @ X0))) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f965])).
% 188.71/28.62 thf(f59922,plain,(
% 188.71/28.62 spl65_1 | spl65_2 | ~spl65_6),
% 188.71/28.62 inference(avatar_contradiction_clause,[status(thm)],[f59921])).
% 188.71/28.62 thf(f59921,plain,(
% 188.71/28.62 $false | (spl65_1 | spl65_2 | ~spl65_6)),
% 188.71/28.62 inference(subsumption_resolution,[status(thm)],[f59920,f23520])).
% 188.71/28.62 thf(f59920,plain,(
% 188.71/28.62 ($true != (ord_less_nat @ (sK2 @ sK28) @ (size_s1671393719tion_b @ v))) | (spl65_1 | spl65_2 | ~spl65_6)),
% 188.71/28.62 inference(subsumption_resolution,[status(thm)],[f59919,f1462])).
% 188.71/28.62 thf(f1462,plain,(
% 188.71/28.62 ($true != (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | spl65_2),
% 188.71/28.62 inference(avatar_component_clause,[status(thm)],[f1460])).
% 188.71/28.62 thf(f59919,plain,(
% 188.71/28.62 ($true = (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | ($true != (ord_less_nat @ (sK2 @ sK28) @ (size_s1671393719tion_b @ v))) | (spl65_1 | ~spl65_6)),
% 188.71/28.62 inference(subsumption_resolution,[status(thm)],[f59871,f11730])).
% 188.71/28.62 thf(f11730,plain,(
% 188.71/28.62 (none_b != (nth_option_b @ v @ (sK2 @ sK28))) | (spl65_1 | ~spl65_6)),
% 188.71/28.62 inference(superposition,[status(thm)],[f1457,f8632])).
% 188.71/28.62 thf(f1457,plain,(
% 188.71/28.62 (none_b != (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ sK28)) | spl65_1),
% 188.71/28.62 inference(avatar_component_clause,[status(thm)],[f1456])).
% 188.71/28.62 thf(f59871,plain,(
% 188.71/28.62 (none_b = (nth_option_b @ v @ (sK2 @ sK28))) | ($true != (ord_less_nat @ (sK2 @ sK28) @ (size_s1671393719tion_b @ v))) | ($true = (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | ~spl65_6),
% 188.71/28.62 inference(trivial_inequality_removal,[status(thm)],[f59845])).
% 188.71/28.62 thf(f59845,plain,(
% 188.71/28.62 ($true = (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | ($true != (ord_less_nat @ (sK2 @ sK28) @ (size_s1671393719tion_b @ v))) | ($false = $true) | (none_b = (nth_option_b @ v @ (sK2 @ sK28))) | ~spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f8662,f1383])).
% 188.71/28.62 thf(f1383,plain,(
% 188.71/28.62 ( ! [X0 : nat] : (($true = (member_nat @ X0 @ (fvi_a @ (suc @ b2) @ phi))) | ($true != (ord_less_nat @ X0 @ (size_s1671393719tion_b @ v))) | (none_b = (nth_option_b @ v @ X0))) )),
% 188.71/28.62 inference(definition_unfolding,[status(thm)],[f1161,f1163])).
% 188.71/28.62 thf(f1161,plain,(
% 188.71/28.62 ( ! [X0 : nat] : (((ord_less_nat @ X0 @ n) != $true) | (none_b = (nth_option_b @ v @ X0)) | ($true = (member_nat @ X0 @ (fvi_a @ (suc @ b2) @ phi)))) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f965])).
% 188.71/28.62 thf(f8662,plain,(
% 188.71/28.62 ( ! [X0 : nat,X1 : formula_a] : (($false = (member_nat @ (sK2 @ sK28) @ (fvi_a @ (suc @ X0) @ X1))) | ($true = (member_nat @ sK28 @ (fvi_a @ X0 @ X1)))) ) | ~spl65_6),
% 188.71/28.62 inference(binary_proxy_clausification,[status(thm)],[f8631])).
% 188.71/28.62 thf(f8554,plain,(
% 188.71/28.62 ~spl65_1 | ~spl65_11),
% 188.71/28.62 inference(avatar_contradiction_clause,[status(thm)],[f8553])).
% 188.71/28.62 thf(f8553,plain,(
% 188.71/28.62 $false | (~spl65_1 | ~spl65_11)),
% 188.71/28.62 inference(subsumption_resolution,[status(thm)],[f8550,f1447])).
% 188.71/28.62 thf(f1447,plain,(
% 188.71/28.62 ( ! [X1 : b] : ((none_b != (some_b @ X1))) )),
% 188.71/28.62 inference(equality_resolution,[status(thm)],[f1354])).
% 188.71/28.62 thf(f1354,plain,(
% 188.71/28.62 ( ! [X0 : option_b,X1 : b] : ((none_b != X0) | ((some_b @ X1) != X0)) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f868])).
% 188.71/28.62 thf(f868,plain,(
% 188.71/28.62 ! [X0 : option_b,X1 : b] : ((none_b != X0) | ((some_b @ X1) != X0))),
% 188.71/28.62 inference(ennf_transformation,[status(thm)],[f766])).
% 188.71/28.62 thf(f766,plain,(
% 188.71/28.62 ! [X0 : option_b,X1 : b] : (((some_b @ X1) = X0) => (none_b != X0))),
% 188.71/28.62 inference(rectify,[status(thm)],[f97])).
% 188.71/28.62 thf(f97,axiom,(
% 188.71/28.62 ! [X43 : option_b,X12 : b] : (((some_b @ X12) = X43) => (none_b != X43))),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_96_option_OdiscI)).
% 188.71/28.62 thf(f8550,plain,(
% 188.71/28.62 (none_b = (some_b @ x)) | (~spl65_1 | ~spl65_11)),
% 188.71/28.62 inference(superposition,[status(thm)],[f1292,f8548])).
% 188.71/28.62 thf(f8548,plain,(
% 188.71/28.62 (none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ zero_zero_nat)) | (~spl65_1 | ~spl65_11)),
% 188.71/28.62 inference(forward_demodulation,[status(thm)],[f1458,f1791])).
% 188.71/28.62 thf(f1791,plain,(
% 188.71/28.62 (zero_zero_nat = sK28) | ~spl65_11),
% 188.71/28.62 inference(avatar_component_clause,[status(thm)],[f1789])).
% 188.71/28.62 thf(f1789,definition,(
% 188.71/28.62 spl65_11 <=> (zero_zero_nat = sK28)),
% 188.71/28.62 introduced(definition,[new_symbols(naming,[spl65_11])],[avatar_definition])).
% 188.71/28.62 thf(f1292,plain,(
% 188.71/28.62 ( ! [X0 : option_b,X1 : list_option_b] : (((nth_option_b @ (cons_option_b @ X0 @ X1) @ zero_zero_nat) = X0)) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f4])).
% 188.71/28.62 thf(f4,axiom,(
% 188.71/28.62 ! [X0 : option_b,X1 : list_option_b] : ((nth_option_b @ (cons_option_b @ X0 @ X1) @ zero_zero_nat) = X0)),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_3_nth__Cons__0)).
% 188.71/28.62 thf(f8545,plain,(
% 188.71/28.62 spl65_2 | ~spl65_11),
% 188.71/28.62 inference(avatar_contradiction_clause,[status(thm)],[f8544])).
% 188.71/28.62 thf(f8544,plain,(
% 188.71/28.62 $false | (spl65_2 | ~spl65_11)),
% 188.71/28.62 inference(subsumption_resolution,[status(thm)],[f8532,f1301])).
% 188.71/28.62 thf(f1301,plain,(
% 188.71/28.62 ((member_nat @ zero_zero_nat @ (fvi_a @ b2 @ phi)) = $true)),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f365])).
% 188.71/28.62 thf(f365,plain,(
% 188.71/28.62 ((member_nat @ zero_zero_nat @ (fvi_a @ b2 @ phi)) = $true)),
% 188.71/28.62 inference(fool_elimination,[status(thm)],[f364])).
% 188.71/28.62 thf(f364,plain,(
% 188.71/28.62 (member_nat @ zero_zero_nat @ (fvi_a @ b2 @ phi))),
% 188.71/28.62 inference(rectify,[status(thm)],[f327])).
% 188.71/28.62 thf(f327,axiom,(
% 188.71/28.62 (member_nat @ zero_zero_nat @ (fvi_a @ b2 @ phi))),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',conj_0)).
% 188.71/28.62 thf(f8532,plain,(
% 188.71/28.62 ((member_nat @ zero_zero_nat @ (fvi_a @ b2 @ phi)) != $true) | (spl65_2 | ~spl65_11)),
% 188.71/28.62 inference(superposition,[status(thm)],[f1462,f1791])).
% 188.71/28.62 thf(f8530,plain,(
% 188.71/28.62 spl65_11 | spl65_6),
% 188.71/28.62 inference(avatar_split_clause,[status(thm)],[f8501,f1656,f1789])).
% 188.71/28.62 thf(f8501,plain,(
% 188.71/28.62 (zero_zero_nat = sK28) | spl65_6),
% 188.71/28.62 inference(trivial_inequality_removal,[status(thm)],[f8492])).
% 188.71/28.62 thf(f8492,plain,(
% 188.71/28.62 (zero_zero_nat = sK28) | ($true != $true) | spl65_6),
% 188.71/28.62 inference(superposition,[status(thm)],[f1657,f1211])).
% 188.71/28.62 thf(f1211,plain,(
% 188.71/28.62 ( ! [X0 : nat] : (((ord_less_nat @ zero_zero_nat @ X0) = $true) | (zero_zero_nat = X0)) )),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f1003])).
% 188.71/28.62 thf(f1003,plain,(
% 188.71/28.62 ! [X0 : nat] : ((((ord_less_nat @ zero_zero_nat @ X0) != $true) | (zero_zero_nat != X0)) & ((zero_zero_nat = X0) | ((ord_less_nat @ zero_zero_nat @ X0) = $true)))),
% 188.71/28.62 inference(nnf_transformation,[status(thm)],[f781])).
% 188.71/28.62 thf(f781,plain,(
% 188.71/28.62 ! [X0 : nat] : (((ord_less_nat @ zero_zero_nat @ X0) != $true) <=> (zero_zero_nat = X0))),
% 188.71/28.62 inference(flattening,[status(thm)],[f478])).
% 188.71/28.62 thf(f478,plain,(
% 188.71/28.62 ! [X0 : nat] : (~((ord_less_nat @ zero_zero_nat @ X0) = $true) <=> (zero_zero_nat = X0))),
% 188.71/28.62 inference(fool_elimination,[status(thm)],[f477])).
% 188.71/28.62 thf(f477,plain,(
% 188.71/28.62 ! [X0 : nat] : (~(ord_less_nat @ zero_zero_nat @ X0) = (zero_zero_nat = X0))),
% 188.71/28.62 inference(rectify,[status(thm)],[f63])).
% 188.71/28.62 thf(f63,axiom,(
% 188.71/28.62 ! [X2 : nat] : (~(ord_less_nat @ zero_zero_nat @ X2) = (zero_zero_nat = X2))),
% 188.71/28.62 file('/export/starexec/sandbox/tmp/tmp.B82FTHBpU8/DTF2THF_31741.p',fact_62_not__gr0)).
% 188.71/28.62 thf(f1657,plain,(
% 188.71/28.62 ($true != (ord_less_nat @ zero_zero_nat @ sK28)) | spl65_6),
% 188.71/28.62 inference(avatar_component_clause,[status(thm)],[f1656])).
% 188.71/28.62 thf(f1466,plain,(
% 188.71/28.62 ~spl65_1 | spl65_2),
% 188.71/28.62 inference(avatar_split_clause,[status(thm)],[f1465,f1460,f1456])).
% 188.71/28.62 thf(f1465,plain,(
% 188.71/28.62 ($true = (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | (none_b != (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ sK28))),
% 188.71/28.62 inference(subsumption_resolution,[status(thm)],[f1385,f1359])).
% 188.71/28.62 thf(f1385,plain,(
% 188.71/28.62 ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) != (suc @ (size_s1671393719tion_b @ v))) | ($true = (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | (none_b != (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ sK28))),
% 188.71/28.62 inference(definition_unfolding,[status(thm)],[f1183,f1163])).
% 188.71/28.62 thf(f1183,plain,(
% 188.71/28.62 ($true = (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | (none_b != (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ sK28)) | ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) != (suc @ n))),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f986])).
% 188.71/28.62 thf(f1463,plain,(
% 188.71/28.62 spl65_1 | ~spl65_2),
% 188.71/28.62 inference(avatar_split_clause,[status(thm)],[f1454,f1460,f1456])).
% 188.71/28.62 thf(f1454,plain,(
% 188.71/28.62 ($true != (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | (none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ sK28))),
% 188.71/28.62 inference(subsumption_resolution,[status(thm)],[f1386,f1359])).
% 188.71/28.62 thf(f1386,plain,(
% 188.71/28.62 (none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ sK28)) | ($true != (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) != (suc @ (size_s1671393719tion_b @ v)))),
% 188.71/28.62 inference(definition_unfolding,[status(thm)],[f1182,f1163])).
% 188.71/28.62 thf(f1182,plain,(
% 188.71/28.62 ($true != (member_nat @ sK28 @ (fvi_a @ b2 @ phi))) | (none_b = (nth_option_b @ (cons_option_b @ (some_b @ x) @ v) @ sK28)) | ((size_s1671393719tion_b @ (cons_option_b @ (some_b @ x) @ v)) != (suc @ n))),
% 188.71/28.62 inference(cnf_transformation,[status(thm)],[f986])).
% 188.71/28.62 % SZS output end Proof for DTF2THF_31741
% 188.71/28.62 % (334)------------------------------
% 188.71/28.62 % (334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 188.71/28.62 % (334)Termination reason: Refutation
% 188.71/28.62
% 188.71/28.62 % (334)Memory used [KB]: 30703
% 188.71/28.62 % (334)Time elapsed: 12.453 s
% 188.71/28.62 % (334)Instructions burned: 38641 (million)
% 188.71/28.62 % (334)------------------------------
% 188.71/28.62 % (334)------------------------------
% 188.71/28.62 % (31839)Success in time 26.583 s
%------------------------------------------------------------------------------