%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP129^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 08:55:47 AM UTC 2026
% Result : Theorem 44.45s 7.99s
% Output : Refutation 44.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 109 ( 66 unt; 0 typ; 4 def)
% Number of atoms : 155 ( 117 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 703 ( 56 ~; 36 |; 0 &; 601 @)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 41 usr; 13 con; 0-3 aty)
% Number of variables : 95 ( 0 ^; 95 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
int: $tType ).
thf(type_def_6,type,
nat: $tType ).
thf(func_def_0,type,
nat: $tType ).
thf(func_def_1,type,
int: $tType ).
thf(func_def_2,type,
gbinomial_int: int > nat > int ).
thf(func_def_3,type,
gbinomial_nat: nat > nat > nat ).
thf(func_def_4,type,
one_one_int: int ).
thf(func_def_5,type,
one_one_nat: nat ).
thf(func_def_6,type,
plus_plus_int: int > int > int ).
thf(func_def_7,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_8,type,
times_times_int: int > int > int ).
thf(func_def_9,type,
times_times_nat: nat > nat > nat ).
thf(func_def_10,type,
zero_zero_int: int ).
thf(func_def_11,type,
zero_zero_nat: nat ).
thf(func_def_12,type,
nO_MATCH_int_int: int > int > $o ).
thf(func_def_13,type,
nO_MATCH_int_nat: int > nat > $o ).
thf(func_def_14,type,
nO_MATCH_nat_int: nat > int > $o ).
thf(func_def_15,type,
nO_MATCH_nat_nat: nat > nat > $o ).
thf(func_def_16,type,
if_nat: $o > nat > nat > nat ).
thf(func_def_17,type,
suc: nat > nat ).
thf(func_def_18,type,
semiri2019852685at_int: nat > int ).
thf(func_def_19,type,
semiri1382578993at_nat: nat > nat ).
thf(func_def_20,type,
nthRoo1352626670d_root: nat > nat > $o ).
thf(func_def_21,type,
power_power_int: int > nat > int ).
thf(func_def_22,type,
power_power_nat: nat > nat > nat ).
thf(func_def_23,type,
divide_divide_int: int > int > int ).
thf(func_def_24,type,
divide_divide_nat: nat > nat > nat ).
thf(func_def_25,type,
n: int ).
thf(func_def_26,type,
p: nat ).
thf(func_def_27,type,
pm: nat ).
thf(func_def_28,type,
x: int ).
thf(func_def_39,type,
sK0: ( nat > nat > $o ) > nat ).
thf(func_def_40,type,
sK1: ( nat > nat > $o ) > nat ).
thf(func_def_41,type,
sK2: ( nat > nat > $o ) > nat ).
thf(func_def_42,type,
sK3: ( nat > nat > $o ) > nat ).
thf(func_def_43,type,
sK4: nat > nat ).
thf(func_def_44,type,
sK5: ( nat > $o ) > nat ).
thf(func_def_45,type,
sK6: ( nat > $o ) > nat ).
thf(func_def_46,type,
sK7: nat > nat ).
thf(func_def_47,type,
sK8: ( nat > $o ) > nat ).
thf(func_def_49,type,
ph10:
!>[X0: $tType] : X0 ).
thf(f2676,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2451,f2656,f2663,f2665,f2675]) ).
thf(f2675,plain,
( ~ spl9_2
| spl9_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f2674]) ).
thf(f2674,plain,
( $false
| ~ spl9_2
| spl9_3 ),
inference(subsumption_resolution,[status(thm)],[f2672,f2326]) ).
thf(f2326,plain,
( ( x
!= ( semiri2019852685at_int @ zero_zero_nat ) )
| spl9_3 ),
inference(avatar_component_clause,[status(thm)],[f2325]) ).
thf(f2325,definition,
( spl9_3
<=> ( x
= ( semiri2019852685at_int @ zero_zero_nat ) ) ),
introduced(definition,[new_symbols(naming,[spl9_3])],[avatar_definition]) ).
thf(f2672,plain,
( ( x
= ( semiri2019852685at_int @ zero_zero_nat ) )
| ~ spl9_2 ),
inference(trivial_inequality_removal,[status(thm)],[f2669]) ).
thf(f2669,plain,
( ( x
= ( semiri2019852685at_int @ zero_zero_nat ) )
| ( ( semiri2019852685at_int @ zero_zero_nat )
!= ( semiri2019852685at_int @ zero_zero_nat ) )
| ~ spl9_2 ),
inference(superposition,[status(thm)],[f1468,f1568]) ).
thf(f1568,plain,
( ( ( semiri2019852685at_int @ zero_zero_nat )
= ( power_power_int @ x @ pm ) )
| ~ spl9_2 ),
inference(avatar_component_clause,[status(thm)],[f1566]) ).
thf(f1566,definition,
( spl9_2
<=> ( ( semiri2019852685at_int @ zero_zero_nat )
= ( power_power_int @ x @ pm ) ) ),
introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition]) ).
thf(f1468,plain,
! [X0: nat,X1: int] :
( ( ( semiri2019852685at_int @ zero_zero_nat )
!= ( power_power_int @ X1 @ X0 ) )
| ( ( semiri2019852685at_int @ zero_zero_nat )
= X1 ) ),
inference(definition_unfolding,[status(thm)],[f1331,f1110,f1110]) ).
thf(f1110,plain,
( zero_zero_int
= ( semiri2019852685at_int @ zero_zero_nat ) ),
inference(cnf_transformation,[status(thm)],[f342]) ).
thf(f342,plain,
( zero_zero_int
= ( semiri2019852685at_int @ zero_zero_nat ) ),
inference(fool_elimination,[status(thm)],[f187]) ).
thf(f187,axiom,
( zero_zero_int
= ( semiri2019852685at_int @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_186_of__nat__0) ).
thf(f1331,plain,
! [X0: nat,X1: int] :
( ( zero_zero_int
!= ( power_power_int @ X1 @ X0 ) )
| ( zero_zero_int = X1 ) ),
inference(cnf_transformation,[status(thm)],[f970]) ).
thf(f970,plain,
! [X0: nat,X1: int] :
( ( zero_zero_int
!= ( power_power_int @ X1 @ X0 ) )
| ( zero_zero_int = X1 ) ),
inference(ennf_transformation,[status(thm)],[f639]) ).
thf(f639,plain,
! [X0: nat,X1: int] :
( ( zero_zero_int != X1 )
=> ( zero_zero_int
!= ( power_power_int @ X1 @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f638]) ).
thf(f638,plain,
! [X0: nat,X1: int] :
( ( zero_zero_int != X1 )
=> ( zero_zero_int
!= ( power_power_int @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f268]) ).
thf(f268,axiom,
! [X1: nat,X5: int] :
( ( zero_zero_int != X5 )
=> ( ( power_power_int @ X5 @ X1 )
!= zero_zero_int ) ),
file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_267_power__not__zero) ).
thf(f2665,plain,
( spl9_6
| ~ spl9_1 ),
inference(avatar_split_clause,[status(thm)],[f2664,f1562,f2660]) ).
thf(f2660,definition,
( spl9_6
<=> ( x
= ( divide_divide_int @ ( times_times_int @ x @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_6])],[avatar_definition]) ).
thf(f1562,definition,
( spl9_1
<=> ( x
= ( divide_divide_int @ ( plus_plus_int @ x @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition]) ).
thf(f2664,plain,
( ( x
= ( divide_divide_int @ ( times_times_int @ x @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) )
| ~ spl9_1 ),
inference(forward_demodulation,[status(thm)],[f1563,f2314]) ).
thf(f2314,plain,
! [X0: nat] :
( ( plus_plus_int @ x @ ( times_times_int @ x @ ( semiri2019852685at_int @ X0 ) ) )
= ( times_times_int @ x @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f1426,f1104]) ).
thf(f1104,plain,
! [X0: nat,X1: nat] :
( ( semiri2019852685at_int @ ( plus_plus_nat @ X0 @ X1 ) )
= ( plus_plus_int @ ( semiri2019852685at_int @ X0 ) @ ( semiri2019852685at_int @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f838]) ).
thf(f838,plain,
! [X0: nat,X1: nat] :
( ( semiri2019852685at_int @ ( plus_plus_nat @ X0 @ X1 ) )
= ( plus_plus_int @ ( semiri2019852685at_int @ X0 ) @ ( semiri2019852685at_int @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f837]) ).
thf(f837,plain,
! [X0: nat,X1: nat] :
( ( semiri2019852685at_int @ ( plus_plus_nat @ X0 @ X1 ) )
= ( plus_plus_int @ ( semiri2019852685at_int @ X0 ) @ ( semiri2019852685at_int @ X1 ) ) ),
inference(rectify,[status(thm)],[f53]) ).
thf(f53,axiom,
! [X5: nat,X2: nat] :
( ( semiri2019852685at_int @ ( plus_plus_nat @ X5 @ X2 ) )
= ( plus_plus_int @ ( semiri2019852685at_int @ X5 ) @ ( semiri2019852685at_int @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_52_int__ops_I5_J) ).
thf(f1426,plain,
! [X0: int] :
( ( times_times_int @ x @ ( plus_plus_int @ ( semiri2019852685at_int @ one_one_nat ) @ X0 ) )
= ( plus_plus_int @ x @ ( times_times_int @ x @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f1225,f1065]) ).
thf(f1065,plain,
( one_one_int
= ( semiri2019852685at_int @ one_one_nat ) ),
inference(cnf_transformation,[status(thm)],[f513]) ).
thf(f513,plain,
( one_one_int
= ( semiri2019852685at_int @ one_one_nat ) ),
inference(fool_elimination,[status(thm)],[f123]) ).
thf(f123,axiom,
( one_one_int
= ( semiri2019852685at_int @ one_one_nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_122_of__nat__1) ).
thf(f1225,plain,
! [X0: int] :
( ( times_times_int @ x @ ( plus_plus_int @ one_one_int @ X0 ) )
= ( plus_plus_int @ x @ ( times_times_int @ x @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f337]) ).
thf(f337,plain,
! [X0: int] :
( ( times_times_int @ x @ ( plus_plus_int @ one_one_int @ X0 ) )
= ( plus_plus_int @ x @ ( times_times_int @ x @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f336]) ).
thf(f336,plain,
! [X0: int] :
( ( times_times_int @ x @ ( plus_plus_int @ one_one_int @ X0 ) )
= ( plus_plus_int @ x @ ( times_times_int @ x @ X0 ) ) ),
inference(rectify,[status(thm)],[f110]) ).
thf(f110,axiom,
! [X1: int] :
( ( plus_plus_int @ x @ ( times_times_int @ x @ X1 ) )
= ( times_times_int @ x @ ( plus_plus_int @ one_one_int @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_109__092_060open_062_092_060And_062n_O_Ax_A_L_Ax_A_K_An_A_061_Ax_A_K_A_I1_A_L_An_J_092_060close_062) ).
thf(f1563,plain,
( ( x
= ( divide_divide_int @ ( plus_plus_int @ x @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) )
| ~ spl9_1 ),
inference(avatar_component_clause,[status(thm)],[f1562]) ).
thf(f2663,plain,
( spl9_2
| ~ spl9_6 ),
inference(avatar_split_clause,[status(thm)],[f2658,f2660,f1566]) ).
thf(f2658,plain,
( ( ( semiri2019852685at_int @ zero_zero_nat )
= ( power_power_int @ x @ pm ) )
| ( x
!= ( divide_divide_int @ ( times_times_int @ x @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2657,f2314]) ).
thf(f2657,plain,
( ( ( semiri2019852685at_int @ zero_zero_nat )
= ( power_power_int @ x @ pm ) )
| ( x
!= ( divide_divide_int @ ( plus_plus_int @ x @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2652,f1736]) ).
thf(f1736,plain,
! [X0: int,X1: int] :
( ( plus_plus_int @ X1 @ X0 )
= ( plus_plus_int @ X0 @ X1 ) ),
inference(forward_demodulation,[status(thm)],[f1713,f1406]) ).
thf(f1406,plain,
! [X0: int] :
( ( plus_plus_int @ X0 @ ( semiri2019852685at_int @ zero_zero_nat ) )
= X0 ),
inference(definition_unfolding,[status(thm)],[f1195,f1110]) ).
thf(f1195,plain,
! [X0: int] :
( ( plus_plus_int @ X0 @ zero_zero_int )
= X0 ),
inference(cnf_transformation,[status(thm)],[f629]) ).
thf(f629,plain,
! [X0: int] :
( ( plus_plus_int @ X0 @ zero_zero_int )
= X0 ),
inference(fool_elimination,[status(thm)],[f628]) ).
thf(f628,plain,
! [X0: int] :
( ( plus_plus_int @ X0 @ zero_zero_int )
= X0 ),
inference(rectify,[status(thm)],[f258]) ).
thf(f258,axiom,
! [X5: int] :
( ( plus_plus_int @ X5 @ zero_zero_int )
= X5 ),
file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_257_verit__sum__simplify) ).
thf(f1713,plain,
! [X0: int,X1: int] :
( ( plus_plus_int @ X0 @ ( plus_plus_int @ X1 @ ( semiri2019852685at_int @ zero_zero_nat ) ) )
= ( plus_plus_int @ X1 @ X0 ) ),
inference(superposition,[status(thm)],[f1013,f1406]) ).
thf(f1013,plain,
! [X2: int,X0: int,X1: int] :
( ( plus_plus_int @ X2 @ ( plus_plus_int @ X0 @ X1 ) )
= ( plus_plus_int @ X0 @ ( plus_plus_int @ X2 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f693]) ).
thf(f693,plain,
! [X0: int,X1: int,X2: int] :
( ( plus_plus_int @ X2 @ ( plus_plus_int @ X0 @ X1 ) )
= ( plus_plus_int @ X0 @ ( plus_plus_int @ X2 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f692]) ).
thf(f692,plain,
! [X0: int,X1: int,X2: int] :
( ( plus_plus_int @ X2 @ ( plus_plus_int @ X0 @ X1 ) )
= ( plus_plus_int @ X0 @ ( plus_plus_int @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f89]) ).
thf(f89,axiom,
! [X2: int,X15: int,X5: int] :
( ( plus_plus_int @ X5 @ ( plus_plus_int @ X2 @ X15 ) )
= ( plus_plus_int @ X2 @ ( plus_plus_int @ X5 @ X15 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_88_add_Oleft__commute) ).
thf(f2652,plain,
( ( x
!= ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) @ x ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) )
| ( ( semiri2019852685at_int @ zero_zero_nat )
= ( power_power_int @ x @ pm ) ) ),
inference(superposition,[status(thm)],[f1737,f1385]) ).
thf(f1385,plain,
! [X0: int,X1: int] :
( ( ( divide_divide_int @ ( times_times_int @ X0 @ X1 ) @ X1 )
= X0 )
| ( ( semiri2019852685at_int @ zero_zero_nat )
= X1 ) ),
inference(definition_unfolding,[status(thm)],[f1134,f1110]) ).
thf(f1134,plain,
! [X0: int,X1: int] :
( ( ( divide_divide_int @ ( times_times_int @ X0 @ X1 ) @ X1 )
= X0 )
| ( zero_zero_int = X1 ) ),
inference(cnf_transformation,[status(thm)],[f989]) ).
thf(f989,plain,
! [X0: int,X1: int] :
( ( ( divide_divide_int @ ( times_times_int @ X0 @ X1 ) @ X1 )
= X0 )
| ( zero_zero_int = X1 ) ),
inference(ennf_transformation,[status(thm)],[f434]) ).
thf(f434,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != X1 )
=> ( ( divide_divide_int @ ( times_times_int @ X0 @ X1 ) @ X1 )
= X0 ) ),
inference(fool_elimination,[status(thm)],[f433]) ).
thf(f433,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != X1 )
=> ( ( divide_divide_int @ ( times_times_int @ X0 @ X1 ) @ X1 )
= X0 ) ),
inference(rectify,[status(thm)],[f224]) ).
thf(f224,axiom,
! [X5: int,X2: int] :
( ( zero_zero_int != X2 )
=> ( ( divide_divide_int @ ( times_times_int @ X5 @ X2 ) @ X2 )
= X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_223_nonzero__mult__div__cancel__right) ).
thf(f1737,plain,
( x
!= ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) @ ( divide_divide_int @ ( times_times_int @ x @ ( power_power_int @ x @ pm ) ) @ ( power_power_int @ x @ pm ) ) ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1515,f1736]) ).
thf(f1515,plain,
( x
!= ( divide_divide_int @ ( plus_plus_int @ ( divide_divide_int @ ( times_times_int @ x @ ( power_power_int @ x @ pm ) ) @ ( power_power_int @ x @ pm ) ) @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1514,f1286]) ).
thf(f1286,plain,
! [X0: nat,X1: int] :
( ( times_times_int @ X1 @ ( power_power_int @ X1 @ X0 ) )
= ( times_times_int @ ( power_power_int @ X1 @ X0 ) @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f631]) ).
thf(f631,plain,
! [X0: nat,X1: int] :
( ( times_times_int @ X1 @ ( power_power_int @ X1 @ X0 ) )
= ( times_times_int @ ( power_power_int @ X1 @ X0 ) @ X1 ) ),
inference(fool_elimination,[status(thm)],[f630]) ).
thf(f630,plain,
! [X0: nat,X1: int] :
( ( times_times_int @ X1 @ ( power_power_int @ X1 @ X0 ) )
= ( times_times_int @ ( power_power_int @ X1 @ X0 ) @ X1 ) ),
inference(rectify,[status(thm)],[f42]) ).
thf(f42,axiom,
! [X1: nat,X5: int] :
( ( times_times_int @ X5 @ ( power_power_int @ X5 @ X1 ) )
= ( times_times_int @ ( power_power_int @ X5 @ X1 ) @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_41_power__commutes) ).
thf(f1514,plain,
( x
!= ( divide_divide_int @ ( plus_plus_int @ ( divide_divide_int @ ( times_times_int @ ( power_power_int @ x @ pm ) @ x ) @ ( power_power_int @ x @ pm ) ) @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1448,f1366]) ).
thf(f1366,plain,
! [X0: int,X1: nat] :
( ( power_power_int @ X0 @ ( plus_plus_nat @ one_one_nat @ X1 ) )
= ( times_times_int @ ( power_power_int @ X0 @ X1 ) @ X0 ) ),
inference(definition_unfolding,[status(thm)],[f1093,f1100]) ).
thf(f1100,plain,
( suc
= ( plus_plus_nat @ one_one_nat ) ),
inference(cnf_transformation,[status(thm)],[f691]) ).
thf(f691,plain,
( suc
= ( plus_plus_nat @ one_one_nat ) ),
inference(fool_elimination,[status(thm)],[f296]) ).
thf(f296,axiom,
( suc
= ( plus_plus_nat @ one_one_nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_295_plus__1__eq__Suc) ).
thf(f1093,plain,
! [X0: int,X1: nat] :
( ( power_power_int @ X0 @ ( suc @ X1 ) )
= ( times_times_int @ ( power_power_int @ X0 @ X1 ) @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f859]) ).
thf(f859,plain,
! [X0: int,X1: nat] :
( ( power_power_int @ X0 @ ( suc @ X1 ) )
= ( times_times_int @ ( power_power_int @ X0 @ X1 ) @ X0 ) ),
inference(fool_elimination,[status(thm)],[f858]) ).
thf(f858,plain,
! [X0: int,X1: nat] :
( ( power_power_int @ X0 @ ( suc @ X1 ) )
= ( times_times_int @ ( power_power_int @ X0 @ X1 ) @ X0 ) ),
inference(rectify,[status(thm)],[f48]) ).
thf(f48,axiom,
! [X5: int,X1: nat] :
( ( power_power_int @ X5 @ ( suc @ X1 ) )
= ( times_times_int @ ( power_power_int @ X5 @ X1 ) @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_47_power__Suc2) ).
thf(f1448,plain,
( x
!= ( divide_divide_int @ ( plus_plus_int @ ( divide_divide_int @ ( power_power_int @ x @ ( plus_plus_nat @ one_one_nat @ pm ) ) @ ( power_power_int @ x @ pm ) ) @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1270,f1100,f1100]) ).
thf(f1270,plain,
( x
!= ( divide_divide_int @ ( plus_plus_int @ ( divide_divide_int @ ( power_power_int @ x @ ( suc @ pm ) ) @ ( power_power_int @ x @ pm ) ) @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) ) @ ( semiri2019852685at_int @ ( suc @ pm ) ) ) ),
inference(cnf_transformation,[status(thm)],[f902]) ).
thf(f902,plain,
( x
!= ( divide_divide_int @ ( plus_plus_int @ ( divide_divide_int @ ( power_power_int @ x @ ( suc @ pm ) ) @ ( power_power_int @ x @ pm ) ) @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) ) @ ( semiri2019852685at_int @ ( suc @ pm ) ) ) ),
inference(flattening,[status(thm)],[f743]) ).
thf(f743,plain,
( x
!= ( divide_divide_int @ ( plus_plus_int @ ( divide_divide_int @ ( power_power_int @ x @ ( suc @ pm ) ) @ ( power_power_int @ x @ pm ) ) @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) ) @ ( semiri2019852685at_int @ ( suc @ pm ) ) ) ),
inference(fool_elimination,[status(thm)],[f314]) ).
thf(f314,negated_conjecture,
( x
!= ( divide_divide_int @ ( plus_plus_int @ ( divide_divide_int @ ( power_power_int @ x @ ( suc @ pm ) ) @ ( power_power_int @ x @ pm ) ) @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) ) @ ( semiri2019852685at_int @ ( suc @ pm ) ) ) ),
inference(negated_conjecture,[status(cth)],[f313]) ).
thf(f313,conjecture,
( x
= ( divide_divide_int @ ( plus_plus_int @ ( divide_divide_int @ ( power_power_int @ x @ ( suc @ pm ) ) @ ( power_power_int @ x @ pm ) ) @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) ) @ ( semiri2019852685at_int @ ( suc @ pm ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',conj_0) ).
thf(f2656,plain,
spl9_1,
inference(avatar_contradiction_clause,[status(thm)],[f2655]) ).
thf(f2655,plain,
( $false
| spl9_1 ),
inference(subsumption_resolution,[status(thm)],[f2654,f1458]) ).
thf(f1458,plain,
! [X0: nat] :
( ( semiri2019852685at_int @ zero_zero_nat )
!= ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f1300,f1100,f1110]) ).
thf(f1300,plain,
! [X0: nat] :
( ( semiri2019852685at_int @ ( suc @ X0 ) )
!= zero_zero_int ),
inference(cnf_transformation,[status(thm)],[f808]) ).
thf(f808,plain,
! [X0: nat] :
( ( semiri2019852685at_int @ ( suc @ X0 ) )
!= zero_zero_int ),
inference(fool_elimination,[status(thm)],[f807]) ).
thf(f807,plain,
! [X0: nat] :
( ( semiri2019852685at_int @ ( suc @ X0 ) )
!= zero_zero_int ),
inference(rectify,[status(thm)],[f300]) ).
thf(f300,axiom,
! [X1: nat] :
( ( semiri2019852685at_int @ ( suc @ X1 ) )
!= zero_zero_int ),
file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_299_of__nat__neq__0) ).
thf(f2654,plain,
( ( ( semiri2019852685at_int @ zero_zero_nat )
= ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) )
| spl9_1 ),
inference(trivial_inequality_removal,[status(thm)],[f2653]) ).
thf(f2653,plain,
( ( ( semiri2019852685at_int @ zero_zero_nat )
= ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) )
| ( x != x )
| spl9_1 ),
inference(superposition,[status(thm)],[f2338,f1385]) ).
thf(f2338,plain,
( ( x
!= ( divide_divide_int @ ( times_times_int @ x @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) )
| spl9_1 ),
inference(backward_demodulation,[status(thm)],[f1564,f2314]) ).
thf(f1564,plain,
( ( x
!= ( divide_divide_int @ ( plus_plus_int @ x @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) )
| spl9_1 ),
inference(avatar_component_clause,[status(thm)],[f1562]) ).
thf(f2451,plain,
~ spl9_3,
inference(avatar_contradiction_clause,[status(thm)],[f2450]) ).
thf(f2450,plain,
( $false
| ~ spl9_3 ),
inference(subsumption_resolution,[status(thm)],[f2449,f2339]) ).
thf(f2339,plain,
( ! [X0: int] :
( x
= ( divide_divide_int @ x @ X0 ) )
| ~ spl9_3 ),
inference(backward_demodulation,[status(thm)],[f1338,f2327]) ).
thf(f2327,plain,
( ( x
= ( semiri2019852685at_int @ zero_zero_nat ) )
| ~ spl9_3 ),
inference(avatar_component_clause,[status(thm)],[f2325]) ).
thf(f1338,plain,
! [X0: int] :
( ( semiri2019852685at_int @ zero_zero_nat )
= ( divide_divide_int @ ( semiri2019852685at_int @ zero_zero_nat ) @ X0 ) ),
inference(definition_unfolding,[status(thm)],[f1010,f1110,f1110]) ).
thf(f1010,plain,
! [X0: int] :
( zero_zero_int
= ( divide_divide_int @ zero_zero_int @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f681]) ).
thf(f681,plain,
! [X0: int] :
( zero_zero_int
= ( divide_divide_int @ zero_zero_int @ X0 ) ),
inference(fool_elimination,[status(thm)],[f680]) ).
thf(f680,plain,
! [X0: int] :
( zero_zero_int
= ( divide_divide_int @ zero_zero_int @ X0 ) ),
inference(rectify,[status(thm)],[f181]) ).
thf(f181,axiom,
! [X5: int] :
( zero_zero_int
= ( divide_divide_int @ zero_zero_int @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_180_bits__div__0) ).
thf(f2449,plain,
( ( x
!= ( divide_divide_int @ x @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) )
| ~ spl9_3 ),
inference(forward_demodulation,[status(thm)],[f2448,f2358]) ).
thf(f2358,plain,
( ! [X0: int] :
( ( plus_plus_int @ X0 @ x )
= X0 )
| ~ spl9_3 ),
inference(backward_demodulation,[status(thm)],[f1406,f2327]) ).
thf(f2448,plain,
( ( x
!= ( divide_divide_int @ ( plus_plus_int @ x @ x ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) )
| ~ spl9_3 ),
inference(forward_demodulation,[status(thm)],[f2447,f2339]) ).
thf(f2447,plain,
( ( x
!= ( divide_divide_int @ ( plus_plus_int @ x @ ( divide_divide_int @ x @ ( power_power_int @ x @ pm ) ) ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) )
| ~ spl9_3 ),
inference(forward_demodulation,[status(thm)],[f2439,f2373]) ).
thf(f2373,plain,
( ! [X0: int] :
( x
= ( times_times_int @ x @ X0 ) )
| ~ spl9_3 ),
inference(backward_demodulation,[status(thm)],[f1464,f2327]) ).
thf(f1464,plain,
! [X0: int] :
( ( semiri2019852685at_int @ zero_zero_nat )
= ( times_times_int @ ( semiri2019852685at_int @ zero_zero_nat ) @ X0 ) ),
inference(definition_unfolding,[status(thm)],[f1315,f1110,f1110]) ).
thf(f1315,plain,
! [X0: int] :
( zero_zero_int
= ( times_times_int @ zero_zero_int @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f439]) ).
thf(f439,plain,
! [X0: int] :
( zero_zero_int
= ( times_times_int @ zero_zero_int @ X0 ) ),
inference(fool_elimination,[status(thm)],[f438]) ).
thf(f438,plain,
! [X0: int] :
( zero_zero_int
= ( times_times_int @ zero_zero_int @ X0 ) ),
inference(rectify,[status(thm)],[f289]) ).
thf(f289,axiom,
! [X28: int] :
( zero_zero_int
= ( times_times_int @ zero_zero_int @ X28 ) ),
file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_288_times__int__code_I2_J) ).
thf(f2439,plain,
( ( x
!= ( divide_divide_int @ ( plus_plus_int @ x @ ( divide_divide_int @ ( times_times_int @ x @ ( power_power_int @ x @ pm ) ) @ ( power_power_int @ x @ pm ) ) ) @ ( semiri2019852685at_int @ ( plus_plus_nat @ one_one_nat @ pm ) ) ) )
| ~ spl9_3 ),
inference(backward_demodulation,[status(thm)],[f1737,f2373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP129^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n015.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 08:27:31 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.43 ---- Original DTF file ---
% 0.17/0.43 thf(spec,logic,$$dhol).
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 % File : ITP129^1 : TPTP v9.2.1. Released v7.5.0.
% 0.17/0.43 % Domain : Interactive Theorem Proving
% 0.17/0.43 % Problem : Sledgehammer NthRoot_Impl problem prob_162__3274372_1
% 0.17/0.43 % Version : Especial.
% 0.17/0.43 % English :
% 0.17/0.43
% 0.17/0.43 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.17/0.43 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.17/0.43 % Source : [Des21]
% 0.17/0.43 % Names : NthRoot_Impl/prob_162__3274372_1 [Des21]
% 0.17/0.43
% 0.17/0.43 % Status : Theorem
% 0.17/0.43 % Rating : 0.56 v9.1.0, 0.50 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0
% 0.17/0.43 % Syntax : Number of formulae : 342 ( 235 unt; 29 typ; 0 def)
% 0.17/0.43 % Number of atoms : 593 ( 577 equ; 0 cnn)
% 0.17/0.43 % Maximal formula atoms : 4 ( 1 avg)
% 0.17/0.43 % Number of connectives : 1737 ( 77 ~; 23 |; 26 &;1515 @)
% 0.17/0.43 % ( 0 <=>; 96 =>; 0 <=; 0 <~>)
% 0.17/0.43 % Maximal formula depth : 13 ( 4 avg)
% 0.17/0.43 % Number of types : 3 ( 2 usr)
% 0.17/0.43 % Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% 0.17/0.43 % Number of symbols : 30 ( 27 usr; 10 con; 0-3 aty)
% 0.17/0.43 % Number of variables : 643 ( 15 ^; 627 !; 1 ?; 643 :)
% 0.17/0.43 % SPC : TH0_THM_EQU_NAR
% 0.17/0.43
% 0.17/0.43 % Comments : This file was generated by Sledgehammer 2021-02-23 15:40:53.242
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 % Could-be-implicit typings (2)
% 0.17/0.43 thf(ty_n_t__Nat__Onat,type,
% 0.17/0.43 nat: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_n_t__Int__Oint,type,
% 0.17/0.43 int: $tType ).
% 0.17/0.43
% 0.17/0.43 % Explicit typings (27)
% 0.17/0.43 thf(sy_c_Binomial_Ogbinomial_001t__Int__Oint,type,
% 0.17/0.43 gbinomial_int: int > nat > int ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Binomial_Ogbinomial_001t__Nat__Onat,type,
% 0.17/0.43 gbinomial_nat: nat > nat > nat ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
% 0.17/0.43 one_one_int: int ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.17/0.43 one_one_nat: nat ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
% 0.17/0.43 plus_plus_int: int > int > int ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 0.17/0.43 plus_plus_nat: nat > nat > nat ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Groups_Otimes__class_Otimes_001t__Int__Oint,type,
% 0.17/0.43 times_times_int: int > int > int ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 0.17/0.43 times_times_nat: nat > nat > nat ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 0.17/0.43 zero_zero_int: int ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.17/0.43 zero_zero_nat: nat ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_HOL_ONO__MATCH_001t__Int__Oint_001t__Int__Oint,type,
% 0.17/0.43 nO_MATCH_int_int: int > int > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_HOL_ONO__MATCH_001t__Int__Oint_001t__Nat__Onat,type,
% 0.17/0.43 nO_MATCH_int_nat: int > nat > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_HOL_ONO__MATCH_001t__Nat__Onat_001t__Int__Oint,type,
% 0.17/0.43 nO_MATCH_nat_int: nat > int > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_HOL_ONO__MATCH_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.17/0.43 nO_MATCH_nat_nat: nat > nat > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_If_001t__Nat__Onat,type,
% 0.17/0.43 if_nat: $o > nat > nat > nat ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Nat_OSuc,type,
% 0.17/0.43 suc: nat > nat ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 0.17/0.43 semiri2019852685at_int: nat > int ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 0.17/0.43 semiri1382578993at_nat: nat > nat ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_NthRoot__Impl__Mirabelle__bcfbdygymo_Ofixed__root,type,
% 0.17/0.43 nthRoo1352626670d_root: nat > nat > $o ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 0.17/0.43 power_power_int: int > nat > int ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
% 0.17/0.43 power_power_nat: nat > nat > nat ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 0.17/0.43 divide_divide_int: int > int > int ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 0.17/0.43 divide_divide_nat: nat > nat > nat ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_n,type,
% 0.17/0.43 n: int ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_p,type,
% 0.17/0.43 p: nat ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_pm,type,
% 0.17/0.43 pm: nat ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_x,type,
% 0.17/0.43 x: int ).
% 0.17/0.43
% 0.17/0.43 % Relevant facts (309)
% 0.17/0.43 thf(fact_0_xn,axiom,
% 0.17/0.43 ( ( power_power_int @ x @ p )
% 0.17/0.43 = n ) ).
% 0.17/0.43
% 0.17/0.43 % xn
% 0.17/0.43 thf(fact_1_of__nat__power,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( semiri1382578993at_nat @ ( power_power_nat @ M @ N ) )
% 0.17/0.43 = ( power_power_nat @ ( semiri1382578993at_nat @ M ) @ N ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_power
% 0.17/0.43 thf(fact_2_of__nat__power,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( semiri2019852685at_int @ ( power_power_nat @ M @ N ) )
% 0.17/0.43 = ( power_power_int @ ( semiri2019852685at_int @ M ) @ N ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_power
% 0.17/0.43 thf(fact_3_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.17/0.43 ! [B: nat,W: nat,X: nat] :
% 0.17/0.43 ( ( ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W )
% 0.17/0.43 = ( semiri1382578993at_nat @ X ) )
% 0.17/0.43 = ( ( power_power_nat @ B @ W )
% 0.17/0.43 = X ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_eq_of_nat_power_cancel_iff
% 0.17/0.43 thf(fact_4_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.17/0.43 ! [B: nat,W: nat,X: nat] :
% 0.17/0.43 ( ( ( power_power_int @ ( semiri2019852685at_int @ B ) @ W )
% 0.17/0.43 = ( semiri2019852685at_int @ X ) )
% 0.17/0.43 = ( ( power_power_nat @ B @ W )
% 0.17/0.43 = X ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_eq_of_nat_power_cancel_iff
% 0.17/0.43 thf(fact_5_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.17/0.43 ! [X: nat,B: nat,W: nat] :
% 0.17/0.43 ( ( ( semiri1382578993at_nat @ X )
% 0.17/0.43 = ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W ) )
% 0.17/0.43 = ( X
% 0.17/0.43 = ( power_power_nat @ B @ W ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_power_eq_of_nat_cancel_iff
% 0.17/0.43 thf(fact_6_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.17/0.43 ! [X: nat,B: nat,W: nat] :
% 0.17/0.43 ( ( ( semiri2019852685at_int @ X )
% 0.17/0.43 = ( power_power_int @ ( semiri2019852685at_int @ B ) @ W ) )
% 0.17/0.43 = ( X
% 0.17/0.43 = ( power_power_nat @ B @ W ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_power_eq_of_nat_cancel_iff
% 0.17/0.43 thf(fact_7_of__nat__add,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( semiri1382578993at_nat @ ( plus_plus_nat @ M @ N ) )
% 0.17/0.43 = ( plus_plus_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_add
% 0.17/0.43 thf(fact_8_of__nat__add,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( semiri2019852685at_int @ ( plus_plus_nat @ M @ N ) )
% 0.17/0.43 = ( plus_plus_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_add
% 0.17/0.43 thf(fact_9_of__nat__mult,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( semiri1382578993at_nat @ ( times_times_nat @ M @ N ) )
% 0.17/0.43 = ( times_times_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_mult
% 0.17/0.43 thf(fact_10_of__nat__mult,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( semiri2019852685at_int @ ( times_times_nat @ M @ N ) )
% 0.17/0.43 = ( times_times_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_mult
% 0.17/0.43 thf(fact_11_div__mult2__eq_H,axiom,
% 0.17/0.43 ! [A: int,M: nat,N: nat] :
% 0.17/0.43 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) )
% 0.17/0.43 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri2019852685at_int @ M ) ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % div_mult2_eq'
% 0.17/0.43 thf(fact_12_div__mult2__eq_H,axiom,
% 0.17/0.43 ! [A: nat,M: nat,N: nat] :
% 0.17/0.43 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) )
% 0.17/0.43 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1382578993at_nat @ M ) ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % div_mult2_eq'
% 0.17/0.43 thf(fact_13_power__Suc,axiom,
% 0.17/0.43 ! [A: int,N: nat] :
% 0.17/0.43 ( ( power_power_int @ A @ ( suc @ N ) )
% 0.17/0.43 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % power_Suc
% 0.17/0.43 thf(fact_14_power__Suc,axiom,
% 0.17/0.43 ! [A: nat,N: nat] :
% 0.17/0.43 ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.17/0.43 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % power_Suc
% 0.17/0.43 thf(fact_15_fixed__root__axioms,axiom,
% 0.17/0.43 nthRoo1352626670d_root @ p @ pm ).
% 0.17/0.43
% 0.17/0.43 % fixed_root_axioms
% 0.17/0.43 thf(fact_16_old_Onat_Oinject,axiom,
% 0.17/0.43 ! [Nat: nat,Nat2: nat] :
% 0.17/0.43 ( ( ( suc @ Nat )
% 0.17/0.43 = ( suc @ Nat2 ) )
% 0.17/0.43 = ( Nat = Nat2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % old.nat.inject
% 0.17/0.43 thf(fact_17_nat_Oinject,axiom,
% 0.17/0.43 ! [X2: nat,Y2: nat] :
% 0.17/0.43 ( ( ( suc @ X2 )
% 0.17/0.43 = ( suc @ Y2 ) )
% 0.17/0.43 = ( X2 = Y2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % nat.inject
% 0.17/0.43 thf(fact_18_of__nat__eq__iff,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( ( semiri2019852685at_int @ M )
% 0.17/0.43 = ( semiri2019852685at_int @ N ) )
% 0.17/0.43 = ( M = N ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_eq_iff
% 0.17/0.43 thf(fact_19_of__nat__eq__iff,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( ( semiri1382578993at_nat @ M )
% 0.17/0.43 = ( semiri1382578993at_nat @ N ) )
% 0.17/0.43 = ( M = N ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_eq_iff
% 0.17/0.43 thf(fact_20_p,axiom,
% 0.17/0.43 ( p
% 0.17/0.43 = ( suc @ pm ) ) ).
% 0.17/0.43
% 0.17/0.43 % p
% 0.17/0.43 thf(fact_21_add__Suc__right,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 0.17/0.43 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_Suc_right
% 0.17/0.43 thf(fact_22_mult__Suc__right,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( times_times_nat @ M @ ( suc @ N ) )
% 0.17/0.43 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_Suc_right
% 0.17/0.43 thf(fact_23_add__mult__distrib,axiom,
% 0.17/0.43 ! [M: nat,N: nat,K: nat] :
% 0.17/0.43 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 0.17/0.43 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_mult_distrib
% 0.17/0.43 thf(fact_24_add__mult__distrib2,axiom,
% 0.17/0.43 ! [K: nat,M: nat,N: nat] :
% 0.17/0.43 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 0.17/0.43 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_mult_distrib2
% 0.17/0.43 thf(fact_25_mult__Suc,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( times_times_nat @ ( suc @ M ) @ N )
% 0.17/0.43 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_Suc
% 0.17/0.43 thf(fact_26_div__mult2__eq,axiom,
% 0.17/0.43 ! [M: nat,N: nat,Q: nat] :
% 0.17/0.43 ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q ) )
% 0.17/0.43 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q ) ) ).
% 0.17/0.43
% 0.17/0.43 % div_mult2_eq
% 0.17/0.43 thf(fact_27_power__mult,axiom,
% 0.17/0.43 ! [A: int,M: nat,N: nat] :
% 0.17/0.43 ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 0.17/0.43 = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 0.17/0.43
% 0.17/0.43 % power_mult
% 0.17/0.43 thf(fact_28_power__mult,axiom,
% 0.17/0.43 ! [A: nat,M: nat,N: nat] :
% 0.17/0.43 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 0.17/0.43 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 0.17/0.43
% 0.17/0.43 % power_mult
% 0.17/0.43 thf(fact_29_add__Suc,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.17/0.43 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_Suc
% 0.17/0.43 thf(fact_30_nat__arith_Osuc1,axiom,
% 0.17/0.43 ! [A2: nat,K: nat,A: nat] :
% 0.17/0.43 ( ( A2
% 0.17/0.43 = ( plus_plus_nat @ K @ A ) )
% 0.17/0.43 => ( ( suc @ A2 )
% 0.17/0.43 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % nat_arith.suc1
% 0.17/0.43 thf(fact_31_add__Suc__shift,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.17/0.43 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_Suc_shift
% 0.17/0.43 thf(fact_32_Suc__mult__cancel1,axiom,
% 0.17/0.43 ! [K: nat,M: nat,N: nat] :
% 0.17/0.43 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 0.17/0.43 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.17/0.43 = ( M = N ) ) ).
% 0.17/0.43
% 0.17/0.43 % Suc_mult_cancel1
% 0.17/0.43 thf(fact_33_power__add,axiom,
% 0.17/0.43 ! [A: int,M: nat,N: nat] :
% 0.17/0.43 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 0.17/0.43 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % power_add
% 0.17/0.43 thf(fact_34_power__add,axiom,
% 0.17/0.43 ! [A: nat,M: nat,N: nat] :
% 0.17/0.43 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 0.17/0.43 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % power_add
% 0.17/0.43 thf(fact_35_n__not__Suc__n,axiom,
% 0.17/0.43 ! [N: nat] :
% 0.17/0.43 ( N
% 0.17/0.43 != ( suc @ N ) ) ).
% 0.17/0.43
% 0.17/0.43 % n_not_Suc_n
% 0.17/0.43 thf(fact_36_Suc__inject,axiom,
% 0.17/0.43 ! [X: nat,Y: nat] :
% 0.17/0.43 ( ( ( suc @ X )
% 0.17/0.43 = ( suc @ Y ) )
% 0.17/0.43 => ( X = Y ) ) ).
% 0.17/0.43
% 0.17/0.43 % Suc_inject
% 0.17/0.43 thf(fact_37_power__commuting__commutes,axiom,
% 0.17/0.43 ! [X: int,Y: int,N: nat] :
% 0.17/0.43 ( ( ( times_times_int @ X @ Y )
% 0.17/0.43 = ( times_times_int @ Y @ X ) )
% 0.17/0.43 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y )
% 0.17/0.43 = ( times_times_int @ Y @ ( power_power_int @ X @ N ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % power_commuting_commutes
% 0.17/0.43 thf(fact_38_power__commuting__commutes,axiom,
% 0.17/0.43 ! [X: nat,Y: nat,N: nat] :
% 0.17/0.43 ( ( ( times_times_nat @ X @ Y )
% 0.17/0.43 = ( times_times_nat @ Y @ X ) )
% 0.17/0.43 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y )
% 0.17/0.43 = ( times_times_nat @ Y @ ( power_power_nat @ X @ N ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % power_commuting_commutes
% 0.17/0.43 thf(fact_39_power__mult__distrib,axiom,
% 0.17/0.43 ! [A: int,B: int,N: nat] :
% 0.17/0.43 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 0.17/0.43 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % power_mult_distrib
% 0.17/0.43 thf(fact_40_power__mult__distrib,axiom,
% 0.17/0.43 ! [A: nat,B: nat,N: nat] :
% 0.17/0.43 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 0.17/0.43 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % power_mult_distrib
% 0.17/0.43 thf(fact_41_power__commutes,axiom,
% 0.17/0.43 ! [A: int,N: nat] :
% 0.17/0.43 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 0.17/0.43 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % power_commutes
% 0.17/0.43 thf(fact_42_power__commutes,axiom,
% 0.17/0.43 ! [A: nat,N: nat] :
% 0.17/0.43 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 0.17/0.43 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % power_commutes
% 0.17/0.43 thf(fact_43_mult__of__nat__commute,axiom,
% 0.17/0.43 ! [X: nat,Y: int] :
% 0.17/0.43 ( ( times_times_int @ ( semiri2019852685at_int @ X ) @ Y )
% 0.17/0.43 = ( times_times_int @ Y @ ( semiri2019852685at_int @ X ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_of_nat_commute
% 0.17/0.43 thf(fact_44_mult__of__nat__commute,axiom,
% 0.17/0.43 ! [X: nat,Y: nat] :
% 0.17/0.43 ( ( times_times_nat @ ( semiri1382578993at_nat @ X ) @ Y )
% 0.17/0.43 = ( times_times_nat @ Y @ ( semiri1382578993at_nat @ X ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_of_nat_commute
% 0.17/0.43 thf(fact_45_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( semiri2019852685at_int @ ( divide_divide_nat @ M @ N ) )
% 0.17/0.43 = ( divide_divide_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 0.17/0.43 thf(fact_46_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( semiri1382578993at_nat @ ( divide_divide_nat @ M @ N ) )
% 0.17/0.43 = ( divide_divide_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 0.17/0.43 thf(fact_47_power__Suc2,axiom,
% 0.17/0.43 ! [A: int,N: nat] :
% 0.17/0.43 ( ( power_power_int @ A @ ( suc @ N ) )
% 0.17/0.43 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 0.17/0.43
% 0.17/0.43 % power_Suc2
% 0.17/0.43 thf(fact_48_power__Suc2,axiom,
% 0.17/0.43 ! [A: nat,N: nat] :
% 0.17/0.43 ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.17/0.43 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 0.17/0.43
% 0.17/0.43 % power_Suc2
% 0.17/0.43 thf(fact_49_int__ops_I7_J,axiom,
% 0.17/0.43 ! [A: nat,B: nat] :
% 0.17/0.43 ( ( semiri2019852685at_int @ ( times_times_nat @ A @ B ) )
% 0.17/0.43 = ( times_times_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % int_ops(7)
% 0.17/0.43 thf(fact_50_zadd__int__left,axiom,
% 0.17/0.43 ! [M: nat,N: nat,Z: int] :
% 0.17/0.43 ( ( plus_plus_int @ ( semiri2019852685at_int @ M ) @ ( plus_plus_int @ ( semiri2019852685at_int @ N ) @ Z ) )
% 0.17/0.43 = ( plus_plus_int @ ( semiri2019852685at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 0.17/0.43
% 0.17/0.43 % zadd_int_left
% 0.17/0.43 thf(fact_51_int__plus,axiom,
% 0.17/0.43 ! [N: nat,M: nat] :
% 0.17/0.43 ( ( semiri2019852685at_int @ ( plus_plus_nat @ N @ M ) )
% 0.17/0.43 = ( plus_plus_int @ ( semiri2019852685at_int @ N ) @ ( semiri2019852685at_int @ M ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % int_plus
% 0.17/0.43 thf(fact_52_int__ops_I5_J,axiom,
% 0.17/0.43 ! [A: nat,B: nat] :
% 0.17/0.43 ( ( semiri2019852685at_int @ ( plus_plus_nat @ A @ B ) )
% 0.17/0.43 = ( plus_plus_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % int_ops(5)
% 0.17/0.43 thf(fact_53_add__right__cancel,axiom,
% 0.17/0.43 ! [B: int,A: int,C: int] :
% 0.17/0.43 ( ( ( plus_plus_int @ B @ A )
% 0.17/0.43 = ( plus_plus_int @ C @ A ) )
% 0.17/0.43 = ( B = C ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_right_cancel
% 0.17/0.43 thf(fact_54_add__right__cancel,axiom,
% 0.17/0.43 ! [B: nat,A: nat,C: nat] :
% 0.17/0.43 ( ( ( plus_plus_nat @ B @ A )
% 0.17/0.43 = ( plus_plus_nat @ C @ A ) )
% 0.17/0.43 = ( B = C ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_right_cancel
% 0.17/0.43 thf(fact_55_add__left__cancel,axiom,
% 0.17/0.43 ! [A: int,B: int,C: int] :
% 0.17/0.43 ( ( ( plus_plus_int @ A @ B )
% 0.17/0.43 = ( plus_plus_int @ A @ C ) )
% 0.17/0.43 = ( B = C ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_left_cancel
% 0.17/0.43 thf(fact_56_add__left__cancel,axiom,
% 0.17/0.43 ! [A: nat,B: nat,C: nat] :
% 0.17/0.43 ( ( ( plus_plus_nat @ A @ B )
% 0.17/0.43 = ( plus_plus_nat @ A @ C ) )
% 0.17/0.43 = ( B = C ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_left_cancel
% 0.17/0.43 thf(fact_57_zdiv__int,axiom,
% 0.17/0.43 ! [A: nat,B: nat] :
% 0.17/0.43 ( ( semiri2019852685at_int @ ( divide_divide_nat @ A @ B ) )
% 0.17/0.43 = ( divide_divide_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % zdiv_int
% 0.17/0.43 thf(fact_58_int__distrib_I1_J,axiom,
% 0.17/0.43 ! [Z1: int,Z2: int,W: int] :
% 0.17/0.43 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z2 ) @ W )
% 0.17/0.43 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z2 @ W ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % int_distrib(1)
% 0.17/0.43 thf(fact_59_int__distrib_I2_J,axiom,
% 0.17/0.43 ! [W: int,Z1: int,Z2: int] :
% 0.17/0.43 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z2 ) )
% 0.17/0.43 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % int_distrib(2)
% 0.17/0.43 thf(fact_60_left__add__mult__distrib,axiom,
% 0.17/0.43 ! [I: nat,U: nat,J: nat,K: nat] :
% 0.17/0.43 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 0.17/0.43 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 0.17/0.43
% 0.17/0.43 % left_add_mult_distrib
% 0.17/0.43 thf(fact_61_crossproduct__noteq,axiom,
% 0.17/0.43 ! [A: int,B: int,C: int,D: int] :
% 0.17/0.43 ( ( ( A != B )
% 0.17/0.43 & ( C != D ) )
% 0.17/0.43 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 0.17/0.43 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % crossproduct_noteq
% 0.17/0.43 thf(fact_62_crossproduct__noteq,axiom,
% 0.17/0.43 ! [A: nat,B: nat,C: nat,D: nat] :
% 0.17/0.43 ( ( ( A != B )
% 0.17/0.43 & ( C != D ) )
% 0.17/0.43 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 0.17/0.43 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % crossproduct_noteq
% 0.17/0.43 thf(fact_63_fixed__root_Op,axiom,
% 0.17/0.43 ! [P: nat,Pm: nat] :
% 0.17/0.43 ( ( nthRoo1352626670d_root @ P @ Pm )
% 0.17/0.43 => ( P
% 0.17/0.43 = ( suc @ Pm ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % fixed_root.p
% 0.17/0.43 thf(fact_64_fixed__root__def,axiom,
% 0.17/0.43 ( nthRoo1352626670d_root
% 0.17/0.43 = ( ^ [P2: nat,Pm2: nat] :
% 0.17/0.43 ( P2
% 0.17/0.43 = ( suc @ Pm2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % fixed_root_def
% 0.17/0.43 thf(fact_65_fixed__root_Ointro,axiom,
% 0.17/0.43 ! [P: nat,Pm: nat] :
% 0.17/0.43 ( ( P
% 0.17/0.43 = ( suc @ Pm ) )
% 0.17/0.43 => ( nthRoo1352626670d_root @ P @ Pm ) ) ).
% 0.17/0.43
% 0.17/0.43 % fixed_root.intro
% 0.17/0.43 thf(fact_66_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.17/0.43 ! [A: int,B: int,C: int] :
% 0.17/0.43 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.17/0.43 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ab_semigroup_mult_class.mult_ac(1)
% 0.17/0.43 thf(fact_67_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.17/0.43 ! [A: nat,B: nat,C: nat] :
% 0.17/0.43 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.17/0.43 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ab_semigroup_mult_class.mult_ac(1)
% 0.17/0.43 thf(fact_68_mult_Oassoc,axiom,
% 0.17/0.43 ! [A: int,B: int,C: int] :
% 0.17/0.43 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.17/0.43 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult.assoc
% 0.17/0.43 thf(fact_69_mult_Oassoc,axiom,
% 0.17/0.43 ! [A: nat,B: nat,C: nat] :
% 0.17/0.43 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.17/0.43 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult.assoc
% 0.17/0.43 thf(fact_70_mult_Ocommute,axiom,
% 0.17/0.43 ( times_times_int
% 0.17/0.43 = ( ^ [A3: int,B2: int] : ( times_times_int @ B2 @ A3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult.commute
% 0.17/0.43 thf(fact_71_mult_Ocommute,axiom,
% 0.17/0.43 ( times_times_nat
% 0.17/0.43 = ( ^ [A3: nat,B2: nat] : ( times_times_nat @ B2 @ A3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult.commute
% 0.17/0.43 thf(fact_72_mult_Oleft__commute,axiom,
% 0.17/0.43 ! [B: int,A: int,C: int] :
% 0.17/0.43 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 0.17/0.43 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult.left_commute
% 0.17/0.43 thf(fact_73_mult_Oleft__commute,axiom,
% 0.17/0.43 ! [B: nat,A: nat,C: nat] :
% 0.17/0.43 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 0.17/0.43 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult.left_commute
% 0.17/0.43 thf(fact_74_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.17/0.43 ! [A: int,B: int,C: int] :
% 0.17/0.43 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.17/0.43 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ab_semigroup_add_class.add_ac(1)
% 0.17/0.43 thf(fact_75_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.17/0.43 ! [A: nat,B: nat,C: nat] :
% 0.17/0.43 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.17/0.43 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ab_semigroup_add_class.add_ac(1)
% 0.17/0.43 thf(fact_76_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.17/0.43 ! [I: int,J: int,K: int,L: int] :
% 0.17/0.43 ( ( ( I = J )
% 0.17/0.43 & ( K = L ) )
% 0.17/0.43 => ( ( plus_plus_int @ I @ K )
% 0.17/0.43 = ( plus_plus_int @ J @ L ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_mono_thms_linordered_semiring(4)
% 0.17/0.43 thf(fact_77_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.17/0.43 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.17/0.43 ( ( ( I = J )
% 0.17/0.43 & ( K = L ) )
% 0.17/0.43 => ( ( plus_plus_nat @ I @ K )
% 0.17/0.43 = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_mono_thms_linordered_semiring(4)
% 0.17/0.43 thf(fact_78_group__cancel_Oadd1,axiom,
% 0.17/0.43 ! [A2: int,K: int,A: int,B: int] :
% 0.17/0.43 ( ( A2
% 0.17/0.43 = ( plus_plus_int @ K @ A ) )
% 0.17/0.43 => ( ( plus_plus_int @ A2 @ B )
% 0.17/0.43 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % group_cancel.add1
% 0.17/0.43 thf(fact_79_group__cancel_Oadd1,axiom,
% 0.17/0.43 ! [A2: nat,K: nat,A: nat,B: nat] :
% 0.17/0.43 ( ( A2
% 0.17/0.43 = ( plus_plus_nat @ K @ A ) )
% 0.17/0.43 => ( ( plus_plus_nat @ A2 @ B )
% 0.17/0.43 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % group_cancel.add1
% 0.17/0.43 thf(fact_80_group__cancel_Oadd2,axiom,
% 0.17/0.43 ! [B3: int,K: int,B: int,A: int] :
% 0.17/0.43 ( ( B3
% 0.17/0.43 = ( plus_plus_int @ K @ B ) )
% 0.17/0.43 => ( ( plus_plus_int @ A @ B3 )
% 0.17/0.43 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % group_cancel.add2
% 0.17/0.43 thf(fact_81_group__cancel_Oadd2,axiom,
% 0.17/0.43 ! [B3: nat,K: nat,B: nat,A: nat] :
% 0.17/0.43 ( ( B3
% 0.17/0.43 = ( plus_plus_nat @ K @ B ) )
% 0.17/0.43 => ( ( plus_plus_nat @ A @ B3 )
% 0.17/0.43 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % group_cancel.add2
% 0.17/0.43 thf(fact_82_add_Oassoc,axiom,
% 0.17/0.43 ! [A: int,B: int,C: int] :
% 0.17/0.43 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.17/0.43 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % add.assoc
% 0.17/0.43 thf(fact_83_add_Oassoc,axiom,
% 0.17/0.43 ! [A: nat,B: nat,C: nat] :
% 0.17/0.43 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.17/0.43 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % add.assoc
% 0.17/0.43 thf(fact_84_add_Oleft__cancel,axiom,
% 0.17/0.43 ! [A: int,B: int,C: int] :
% 0.17/0.43 ( ( ( plus_plus_int @ A @ B )
% 0.17/0.43 = ( plus_plus_int @ A @ C ) )
% 0.17/0.43 = ( B = C ) ) ).
% 0.17/0.43
% 0.17/0.43 % add.left_cancel
% 0.17/0.43 thf(fact_85_add_Oright__cancel,axiom,
% 0.17/0.43 ! [B: int,A: int,C: int] :
% 0.17/0.43 ( ( ( plus_plus_int @ B @ A )
% 0.17/0.43 = ( plus_plus_int @ C @ A ) )
% 0.17/0.43 = ( B = C ) ) ).
% 0.17/0.43
% 0.17/0.43 % add.right_cancel
% 0.17/0.43 thf(fact_86_add_Ocommute,axiom,
% 0.17/0.43 ( plus_plus_int
% 0.17/0.43 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % add.commute
% 0.17/0.43 thf(fact_87_add_Ocommute,axiom,
% 0.17/0.43 ( plus_plus_nat
% 0.17/0.43 = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % add.commute
% 0.17/0.43 thf(fact_88_add_Oleft__commute,axiom,
% 0.17/0.43 ! [B: int,A: int,C: int] :
% 0.17/0.43 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 0.17/0.43 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % add.left_commute
% 0.17/0.43 thf(fact_89_add_Oleft__commute,axiom,
% 0.17/0.43 ! [B: nat,A: nat,C: nat] :
% 0.17/0.43 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 0.17/0.43 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % add.left_commute
% 0.17/0.43 thf(fact_90_add__left__imp__eq,axiom,
% 0.17/0.43 ! [A: int,B: int,C: int] :
% 0.17/0.43 ( ( ( plus_plus_int @ A @ B )
% 0.17/0.43 = ( plus_plus_int @ A @ C ) )
% 0.17/0.43 => ( B = C ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_left_imp_eq
% 0.17/0.43 thf(fact_91_add__left__imp__eq,axiom,
% 0.17/0.43 ! [A: nat,B: nat,C: nat] :
% 0.17/0.43 ( ( ( plus_plus_nat @ A @ B )
% 0.17/0.43 = ( plus_plus_nat @ A @ C ) )
% 0.17/0.43 => ( B = C ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_left_imp_eq
% 0.17/0.43 thf(fact_92_add__right__imp__eq,axiom,
% 0.17/0.43 ! [B: int,A: int,C: int] :
% 0.17/0.43 ( ( ( plus_plus_int @ B @ A )
% 0.17/0.43 = ( plus_plus_int @ C @ A ) )
% 0.17/0.43 => ( B = C ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_right_imp_eq
% 0.17/0.43 thf(fact_93_add__right__imp__eq,axiom,
% 0.17/0.43 ! [B: nat,A: nat,C: nat] :
% 0.17/0.43 ( ( ( plus_plus_nat @ B @ A )
% 0.17/0.43 = ( plus_plus_nat @ C @ A ) )
% 0.17/0.43 => ( B = C ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_right_imp_eq
% 0.17/0.43 thf(fact_94_nat__int__comparison_I1_J,axiom,
% 0.17/0.43 ( ( ^ [Y3: nat,Z3: nat] : ( Y3 = Z3 ) )
% 0.17/0.43 = ( ^ [A3: nat,B2: nat] :
% 0.17/0.43 ( ( semiri2019852685at_int @ A3 )
% 0.17/0.43 = ( semiri2019852685at_int @ B2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % nat_int_comparison(1)
% 0.17/0.43 thf(fact_95_int__if,axiom,
% 0.17/0.43 ! [P3: $o,A: nat,B: nat] :
% 0.17/0.43 ( ( P3
% 0.17/0.43 => ( ( semiri2019852685at_int @ ( if_nat @ P3 @ A @ B ) )
% 0.17/0.43 = ( semiri2019852685at_int @ A ) ) )
% 0.17/0.43 & ( ~ P3
% 0.17/0.43 => ( ( semiri2019852685at_int @ ( if_nat @ P3 @ A @ B ) )
% 0.17/0.43 = ( semiri2019852685at_int @ B ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % int_if
% 0.17/0.43 thf(fact_96_int__int__eq,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( ( semiri2019852685at_int @ M )
% 0.17/0.43 = ( semiri2019852685at_int @ N ) )
% 0.17/0.43 = ( M = N ) ) ).
% 0.17/0.43
% 0.17/0.43 % int_int_eq
% 0.17/0.43 thf(fact_97_crossproduct__eq,axiom,
% 0.17/0.43 ! [W: int,Y: int,X: int,Z: int] :
% 0.17/0.43 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 0.17/0.43 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 0.17/0.43 = ( ( W = X )
% 0.17/0.43 | ( Y = Z ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % crossproduct_eq
% 0.17/0.43 thf(fact_98_crossproduct__eq,axiom,
% 0.17/0.43 ! [W: nat,Y: nat,X: nat,Z: nat] :
% 0.17/0.43 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 0.17/0.43 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 0.17/0.43 = ( ( W = X )
% 0.17/0.43 | ( Y = Z ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % crossproduct_eq
% 0.17/0.43 thf(fact_99_ring__class_Oring__distribs_I2_J,axiom,
% 0.17/0.43 ! [A: int,B: int,C: int] :
% 0.17/0.43 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.17/0.43 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ring_class.ring_distribs(2)
% 0.17/0.43 thf(fact_100_ring__class_Oring__distribs_I1_J,axiom,
% 0.17/0.43 ! [A: int,B: int,C: int] :
% 0.17/0.43 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.17/0.43 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ring_class.ring_distribs(1)
% 0.17/0.43 thf(fact_101_comm__semiring__class_Odistrib,axiom,
% 0.17/0.43 ! [A: int,B: int,C: int] :
% 0.17/0.43 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.17/0.43 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % comm_semiring_class.distrib
% 0.17/0.43 thf(fact_102_comm__semiring__class_Odistrib,axiom,
% 0.17/0.43 ! [A: nat,B: nat,C: nat] :
% 0.17/0.43 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.17/0.43 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % comm_semiring_class.distrib
% 0.17/0.43 thf(fact_103_distrib__left,axiom,
% 0.17/0.43 ! [A: int,B: int,C: int] :
% 0.17/0.43 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.17/0.43 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % distrib_left
% 0.17/0.43 thf(fact_104_distrib__left,axiom,
% 0.17/0.43 ! [A: nat,B: nat,C: nat] :
% 0.17/0.43 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.17/0.43 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % distrib_left
% 0.17/0.43 thf(fact_105_distrib__right,axiom,
% 0.17/0.43 ! [A: int,B: int,C: int] :
% 0.17/0.43 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.17/0.43 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % distrib_right
% 0.17/0.43 thf(fact_106_distrib__right,axiom,
% 0.17/0.43 ! [A: nat,B: nat,C: nat] :
% 0.17/0.43 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.17/0.43 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % distrib_right
% 0.17/0.43 thf(fact_107_combine__common__factor,axiom,
% 0.17/0.43 ! [A: int,E: int,B: int,C: int] :
% 0.17/0.43 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 0.17/0.43 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 0.17/0.43
% 0.17/0.43 % combine_common_factor
% 0.17/0.43 thf(fact_108_combine__common__factor,axiom,
% 0.17/0.43 ! [A: nat,E: nat,B: nat,C: nat] :
% 0.17/0.43 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 0.17/0.43 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 0.17/0.43
% 0.17/0.43 % combine_common_factor
% 0.17/0.43 thf(fact_109__092_060open_062_092_060And_062n_O_Ax_A_L_Ax_A_K_An_A_061_Ax_A_K_A_I1_A_L_An_J_092_060close_062,axiom,
% 0.17/0.43 ! [N: int] :
% 0.17/0.43 ( ( plus_plus_int @ x @ ( times_times_int @ x @ N ) )
% 0.17/0.43 = ( times_times_int @ x @ ( plus_plus_int @ one_one_int @ N ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % \<open>\<And>n. x + x * n = x * (1 + n)\<close>
% 0.17/0.43 thf(fact_110_mult_Oright__neutral,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( times_times_int @ A @ one_one_int )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % mult.right_neutral
% 0.17/0.43 thf(fact_111_mult_Oright__neutral,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( times_times_nat @ A @ one_one_nat )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % mult.right_neutral
% 0.17/0.43 thf(fact_112_mult_Oleft__neutral,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( times_times_int @ one_one_int @ A )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % mult.left_neutral
% 0.17/0.43 thf(fact_113_mult_Oleft__neutral,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( times_times_nat @ one_one_nat @ A )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % mult.left_neutral
% 0.17/0.43 thf(fact_114_div__by__1,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( divide_divide_int @ A @ one_one_int )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % div_by_1
% 0.17/0.43 thf(fact_115_div__by__1,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( divide_divide_nat @ A @ one_one_nat )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % div_by_1
% 0.17/0.43 thf(fact_116_power__one,axiom,
% 0.17/0.43 ! [N: nat] :
% 0.17/0.43 ( ( power_power_int @ one_one_int @ N )
% 0.17/0.43 = one_one_int ) ).
% 0.17/0.43
% 0.17/0.43 % power_one
% 0.17/0.43 thf(fact_117_power__one,axiom,
% 0.17/0.43 ! [N: nat] :
% 0.17/0.43 ( ( power_power_nat @ one_one_nat @ N )
% 0.17/0.43 = one_one_nat ) ).
% 0.17/0.43
% 0.17/0.43 % power_one
% 0.17/0.43 thf(fact_118_of__nat__eq__1__iff,axiom,
% 0.17/0.43 ! [N: nat] :
% 0.17/0.43 ( ( ( semiri2019852685at_int @ N )
% 0.17/0.43 = one_one_int )
% 0.17/0.43 = ( N = one_one_nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_eq_1_iff
% 0.17/0.43 thf(fact_119_of__nat__eq__1__iff,axiom,
% 0.17/0.43 ! [N: nat] :
% 0.17/0.43 ( ( ( semiri1382578993at_nat @ N )
% 0.17/0.43 = one_one_nat )
% 0.17/0.43 = ( N = one_one_nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_eq_1_iff
% 0.17/0.43 thf(fact_120_of__nat__1__eq__iff,axiom,
% 0.17/0.43 ! [N: nat] :
% 0.17/0.43 ( ( one_one_int
% 0.17/0.43 = ( semiri2019852685at_int @ N ) )
% 0.17/0.43 = ( N = one_one_nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_1_eq_iff
% 0.17/0.43 thf(fact_121_of__nat__1__eq__iff,axiom,
% 0.17/0.43 ! [N: nat] :
% 0.17/0.43 ( ( one_one_nat
% 0.17/0.43 = ( semiri1382578993at_nat @ N ) )
% 0.17/0.43 = ( N = one_one_nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_1_eq_iff
% 0.17/0.43 thf(fact_122_of__nat__1,axiom,
% 0.17/0.43 ( ( semiri2019852685at_int @ one_one_nat )
% 0.17/0.43 = one_one_int ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_1
% 0.17/0.43 thf(fact_123_of__nat__1,axiom,
% 0.17/0.43 ( ( semiri1382578993at_nat @ one_one_nat )
% 0.17/0.43 = one_one_nat ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_1
% 0.17/0.43 thf(fact_124_of__nat__Suc,axiom,
% 0.17/0.43 ! [M: nat] :
% 0.17/0.43 ( ( semiri2019852685at_int @ ( suc @ M ) )
% 0.17/0.43 = ( plus_plus_int @ one_one_int @ ( semiri2019852685at_int @ M ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_Suc
% 0.17/0.43 thf(fact_125_of__nat__Suc,axiom,
% 0.17/0.43 ! [M: nat] :
% 0.17/0.43 ( ( semiri1382578993at_nat @ ( suc @ M ) )
% 0.17/0.43 = ( plus_plus_nat @ one_one_nat @ ( semiri1382578993at_nat @ M ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_Suc
% 0.17/0.43 thf(fact_126_one__reorient,axiom,
% 0.17/0.43 ! [X: int] :
% 0.17/0.43 ( ( one_one_int = X )
% 0.17/0.43 = ( X = one_one_int ) ) ).
% 0.17/0.43
% 0.17/0.43 % one_reorient
% 0.17/0.43 thf(fact_127_one__reorient,axiom,
% 0.17/0.43 ! [X: nat] :
% 0.17/0.43 ( ( one_one_nat = X )
% 0.17/0.43 = ( X = one_one_nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % one_reorient
% 0.17/0.43 thf(fact_128_mult_Ocomm__neutral,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( times_times_int @ A @ one_one_int )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % mult.comm_neutral
% 0.17/0.43 thf(fact_129_mult_Ocomm__neutral,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( times_times_nat @ A @ one_one_nat )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % mult.comm_neutral
% 0.17/0.43 thf(fact_130_comm__monoid__mult__class_Omult__1,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( times_times_int @ one_one_int @ A )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % comm_monoid_mult_class.mult_1
% 0.17/0.43 thf(fact_131_comm__monoid__mult__class_Omult__1,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( times_times_nat @ one_one_nat @ A )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % comm_monoid_mult_class.mult_1
% 0.17/0.43 thf(fact_132_left__right__inverse__power,axiom,
% 0.17/0.43 ! [X: int,Y: int,N: nat] :
% 0.17/0.43 ( ( ( times_times_int @ X @ Y )
% 0.17/0.43 = one_one_int )
% 0.17/0.43 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 0.17/0.43 = one_one_int ) ) ).
% 0.17/0.43
% 0.17/0.43 % left_right_inverse_power
% 0.17/0.43 thf(fact_133_left__right__inverse__power,axiom,
% 0.17/0.43 ! [X: nat,Y: nat,N: nat] :
% 0.17/0.43 ( ( ( times_times_nat @ X @ Y )
% 0.17/0.43 = one_one_nat )
% 0.17/0.43 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) )
% 0.17/0.43 = one_one_nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % left_right_inverse_power
% 0.17/0.43 thf(fact_134_int__Suc,axiom,
% 0.17/0.43 ! [N: nat] :
% 0.17/0.43 ( ( semiri2019852685at_int @ ( suc @ N ) )
% 0.17/0.43 = ( plus_plus_int @ ( semiri2019852685at_int @ N ) @ one_one_int ) ) ).
% 0.17/0.43
% 0.17/0.43 % int_Suc
% 0.17/0.43 thf(fact_135_int__ops_I4_J,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( semiri2019852685at_int @ ( suc @ A ) )
% 0.17/0.43 = ( plus_plus_int @ ( semiri2019852685at_int @ A ) @ one_one_int ) ) ).
% 0.17/0.43
% 0.17/0.43 % int_ops(4)
% 0.17/0.43 thf(fact_136_bits__div__by__1,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( divide_divide_int @ A @ one_one_int )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % bits_div_by_1
% 0.17/0.43 thf(fact_137_bits__div__by__1,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( divide_divide_nat @ A @ one_one_nat )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % bits_div_by_1
% 0.17/0.43 thf(fact_138_distrib__right__NO__MATCH,axiom,
% 0.17/0.43 ! [X: int,Y: int,C: int,A: int,B: int] :
% 0.17/0.43 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ C )
% 0.17/0.43 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.17/0.43 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % distrib_right_NO_MATCH
% 0.17/0.43 thf(fact_139_distrib__right__NO__MATCH,axiom,
% 0.17/0.43 ! [X: int,Y: int,C: nat,A: nat,B: nat] :
% 0.17/0.43 ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ C )
% 0.17/0.43 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.17/0.43 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % distrib_right_NO_MATCH
% 0.17/0.43 thf(fact_140_distrib__right__NO__MATCH,axiom,
% 0.17/0.43 ! [X: nat,Y: nat,C: int,A: int,B: int] :
% 0.17/0.43 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ C )
% 0.17/0.43 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.17/0.43 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % distrib_right_NO_MATCH
% 0.17/0.43 thf(fact_141_distrib__right__NO__MATCH,axiom,
% 0.17/0.43 ! [X: nat,Y: nat,C: nat,A: nat,B: nat] :
% 0.17/0.43 ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ C )
% 0.17/0.43 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.17/0.43 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % distrib_right_NO_MATCH
% 0.17/0.43 thf(fact_142_distrib__left__NO__MATCH,axiom,
% 0.17/0.43 ! [X: int,Y: int,A: int,B: int,C: int] :
% 0.17/0.43 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ A )
% 0.17/0.43 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.17/0.43 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % distrib_left_NO_MATCH
% 0.17/0.43 thf(fact_143_distrib__left__NO__MATCH,axiom,
% 0.17/0.43 ! [X: int,Y: int,A: nat,B: nat,C: nat] :
% 0.17/0.43 ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ A )
% 0.17/0.43 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.17/0.43 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % distrib_left_NO_MATCH
% 0.17/0.43 thf(fact_144_distrib__left__NO__MATCH,axiom,
% 0.17/0.43 ! [X: nat,Y: nat,A: int,B: int,C: int] :
% 0.17/0.43 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ A )
% 0.17/0.43 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.17/0.43 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % distrib_left_NO_MATCH
% 0.17/0.43 thf(fact_145_distrib__left__NO__MATCH,axiom,
% 0.17/0.43 ! [X: nat,Y: nat,A: nat,B: nat,C: nat] :
% 0.17/0.43 ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ A )
% 0.17/0.43 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.17/0.43 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % distrib_left_NO_MATCH
% 0.17/0.43 thf(fact_146_Nat_Oadd__0__right,axiom,
% 0.17/0.43 ! [M: nat] :
% 0.17/0.43 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.17/0.43 = M ) ).
% 0.17/0.43
% 0.17/0.43 % Nat.add_0_right
% 0.17/0.43 thf(fact_147_add__is__0,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( ( plus_plus_nat @ M @ N )
% 0.17/0.43 = zero_zero_nat )
% 0.17/0.43 = ( ( M = zero_zero_nat )
% 0.17/0.43 & ( N = zero_zero_nat ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_is_0
% 0.17/0.43 thf(fact_148_mult__cancel2,axiom,
% 0.17/0.43 ! [M: nat,K: nat,N: nat] :
% 0.17/0.43 ( ( ( times_times_nat @ M @ K )
% 0.17/0.43 = ( times_times_nat @ N @ K ) )
% 0.17/0.43 = ( ( M = N )
% 0.17/0.43 | ( K = zero_zero_nat ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_cancel2
% 0.17/0.43 thf(fact_149_mult__cancel1,axiom,
% 0.17/0.43 ! [K: nat,M: nat,N: nat] :
% 0.17/0.43 ( ( ( times_times_nat @ K @ M )
% 0.17/0.43 = ( times_times_nat @ K @ N ) )
% 0.17/0.43 = ( ( M = N )
% 0.17/0.43 | ( K = zero_zero_nat ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_cancel1
% 0.17/0.43 thf(fact_150_mult__0__right,axiom,
% 0.17/0.43 ! [M: nat] :
% 0.17/0.43 ( ( times_times_nat @ M @ zero_zero_nat )
% 0.17/0.43 = zero_zero_nat ) ).
% 0.17/0.43
% 0.17/0.43 % mult_0_right
% 0.17/0.43 thf(fact_151_mult__is__0,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( ( times_times_nat @ M @ N )
% 0.17/0.43 = zero_zero_nat )
% 0.17/0.43 = ( ( M = zero_zero_nat )
% 0.17/0.43 | ( N = zero_zero_nat ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_is_0
% 0.17/0.43 thf(fact_152_mult__cancel__right,axiom,
% 0.17/0.43 ! [A: int,C: int,B: int] :
% 0.17/0.43 ( ( ( times_times_int @ A @ C )
% 0.17/0.43 = ( times_times_int @ B @ C ) )
% 0.17/0.43 = ( ( C = zero_zero_int )
% 0.17/0.43 | ( A = B ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_cancel_right
% 0.17/0.43 thf(fact_153_mult__cancel__right,axiom,
% 0.17/0.43 ! [A: nat,C: nat,B: nat] :
% 0.17/0.43 ( ( ( times_times_nat @ A @ C )
% 0.17/0.43 = ( times_times_nat @ B @ C ) )
% 0.17/0.43 = ( ( C = zero_zero_nat )
% 0.17/0.43 | ( A = B ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_cancel_right
% 0.17/0.43 thf(fact_154_mult__cancel__left,axiom,
% 0.17/0.43 ! [C: int,A: int,B: int] :
% 0.17/0.43 ( ( ( times_times_int @ C @ A )
% 0.17/0.43 = ( times_times_int @ C @ B ) )
% 0.17/0.43 = ( ( C = zero_zero_int )
% 0.17/0.43 | ( A = B ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_cancel_left
% 0.17/0.43 thf(fact_155_mult__cancel__left,axiom,
% 0.17/0.43 ! [C: nat,A: nat,B: nat] :
% 0.17/0.43 ( ( ( times_times_nat @ C @ A )
% 0.17/0.43 = ( times_times_nat @ C @ B ) )
% 0.17/0.43 = ( ( C = zero_zero_nat )
% 0.17/0.43 | ( A = B ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_cancel_left
% 0.17/0.43 thf(fact_156_mult__eq__0__iff,axiom,
% 0.17/0.43 ! [A: int,B: int] :
% 0.17/0.43 ( ( ( times_times_int @ A @ B )
% 0.17/0.43 = zero_zero_int )
% 0.17/0.43 = ( ( A = zero_zero_int )
% 0.17/0.43 | ( B = zero_zero_int ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_eq_0_iff
% 0.17/0.43 thf(fact_157_mult__eq__0__iff,axiom,
% 0.17/0.43 ! [A: nat,B: nat] :
% 0.17/0.43 ( ( ( times_times_nat @ A @ B )
% 0.17/0.43 = zero_zero_nat )
% 0.17/0.43 = ( ( A = zero_zero_nat )
% 0.17/0.43 | ( B = zero_zero_nat ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_eq_0_iff
% 0.17/0.43 thf(fact_158_mult__zero__right,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( times_times_int @ A @ zero_zero_int )
% 0.17/0.43 = zero_zero_int ) ).
% 0.17/0.43
% 0.17/0.43 % mult_zero_right
% 0.17/0.43 thf(fact_159_mult__zero__right,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( times_times_nat @ A @ zero_zero_nat )
% 0.17/0.43 = zero_zero_nat ) ).
% 0.17/0.43
% 0.17/0.43 % mult_zero_right
% 0.17/0.43 thf(fact_160_mult__zero__left,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( times_times_int @ zero_zero_int @ A )
% 0.17/0.43 = zero_zero_int ) ).
% 0.17/0.43
% 0.17/0.43 % mult_zero_left
% 0.17/0.43 thf(fact_161_mult__zero__left,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( times_times_nat @ zero_zero_nat @ A )
% 0.17/0.43 = zero_zero_nat ) ).
% 0.17/0.43
% 0.17/0.43 % mult_zero_left
% 0.17/0.43 thf(fact_162_add_Oleft__neutral,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % add.left_neutral
% 0.17/0.43 thf(fact_163_add_Oleft__neutral,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % add.left_neutral
% 0.17/0.43 thf(fact_164_add_Oright__neutral,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % add.right_neutral
% 0.17/0.43 thf(fact_165_add_Oright__neutral,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % add.right_neutral
% 0.17/0.43 thf(fact_166_double__zero,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( ( plus_plus_int @ A @ A )
% 0.17/0.43 = zero_zero_int )
% 0.17/0.43 = ( A = zero_zero_int ) ) ).
% 0.17/0.43
% 0.17/0.43 % double_zero
% 0.17/0.43 thf(fact_167_double__zero__sym,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( zero_zero_int
% 0.17/0.43 = ( plus_plus_int @ A @ A ) )
% 0.17/0.43 = ( A = zero_zero_int ) ) ).
% 0.17/0.43
% 0.17/0.43 % double_zero_sym
% 0.17/0.43 thf(fact_168_add__cancel__left__left,axiom,
% 0.17/0.43 ! [B: nat,A: nat] :
% 0.17/0.43 ( ( ( plus_plus_nat @ B @ A )
% 0.17/0.43 = A )
% 0.17/0.43 = ( B = zero_zero_nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_cancel_left_left
% 0.17/0.43 thf(fact_169_add__cancel__left__left,axiom,
% 0.17/0.43 ! [B: int,A: int] :
% 0.17/0.43 ( ( ( plus_plus_int @ B @ A )
% 0.17/0.43 = A )
% 0.17/0.43 = ( B = zero_zero_int ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_cancel_left_left
% 0.17/0.43 thf(fact_170_add__cancel__left__right,axiom,
% 0.17/0.43 ! [A: nat,B: nat] :
% 0.17/0.43 ( ( ( plus_plus_nat @ A @ B )
% 0.17/0.43 = A )
% 0.17/0.43 = ( B = zero_zero_nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_cancel_left_right
% 0.17/0.43 thf(fact_171_add__cancel__left__right,axiom,
% 0.17/0.43 ! [A: int,B: int] :
% 0.17/0.43 ( ( ( plus_plus_int @ A @ B )
% 0.17/0.43 = A )
% 0.17/0.43 = ( B = zero_zero_int ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_cancel_left_right
% 0.17/0.43 thf(fact_172_add__cancel__right__left,axiom,
% 0.17/0.43 ! [A: nat,B: nat] :
% 0.17/0.43 ( ( A
% 0.17/0.43 = ( plus_plus_nat @ B @ A ) )
% 0.17/0.43 = ( B = zero_zero_nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_cancel_right_left
% 0.17/0.43 thf(fact_173_add__cancel__right__left,axiom,
% 0.17/0.43 ! [A: int,B: int] :
% 0.17/0.43 ( ( A
% 0.17/0.43 = ( plus_plus_int @ B @ A ) )
% 0.17/0.43 = ( B = zero_zero_int ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_cancel_right_left
% 0.17/0.43 thf(fact_174_add__cancel__right__right,axiom,
% 0.17/0.43 ! [A: nat,B: nat] :
% 0.17/0.43 ( ( A
% 0.17/0.43 = ( plus_plus_nat @ A @ B ) )
% 0.17/0.43 = ( B = zero_zero_nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_cancel_right_right
% 0.17/0.43 thf(fact_175_add__cancel__right__right,axiom,
% 0.17/0.43 ! [A: int,B: int] :
% 0.17/0.43 ( ( A
% 0.17/0.43 = ( plus_plus_int @ A @ B ) )
% 0.17/0.43 = ( B = zero_zero_int ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_cancel_right_right
% 0.17/0.43 thf(fact_176_add__eq__0__iff__both__eq__0,axiom,
% 0.17/0.43 ! [X: nat,Y: nat] :
% 0.17/0.43 ( ( ( plus_plus_nat @ X @ Y )
% 0.17/0.43 = zero_zero_nat )
% 0.17/0.43 = ( ( X = zero_zero_nat )
% 0.17/0.43 & ( Y = zero_zero_nat ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % add_eq_0_iff_both_eq_0
% 0.17/0.43 thf(fact_177_zero__eq__add__iff__both__eq__0,axiom,
% 0.17/0.43 ! [X: nat,Y: nat] :
% 0.17/0.43 ( ( zero_zero_nat
% 0.17/0.43 = ( plus_plus_nat @ X @ Y ) )
% 0.17/0.43 = ( ( X = zero_zero_nat )
% 0.17/0.43 & ( Y = zero_zero_nat ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % zero_eq_add_iff_both_eq_0
% 0.17/0.43 thf(fact_178_bits__div__by__0,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( divide_divide_int @ A @ zero_zero_int )
% 0.17/0.43 = zero_zero_int ) ).
% 0.17/0.43
% 0.17/0.43 % bits_div_by_0
% 0.17/0.43 thf(fact_179_bits__div__by__0,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.17/0.43 = zero_zero_nat ) ).
% 0.17/0.43
% 0.17/0.43 % bits_div_by_0
% 0.17/0.43 thf(fact_180_bits__div__0,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( divide_divide_int @ zero_zero_int @ A )
% 0.17/0.43 = zero_zero_int ) ).
% 0.17/0.43
% 0.17/0.43 % bits_div_0
% 0.17/0.43 thf(fact_181_bits__div__0,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.17/0.43 = zero_zero_nat ) ).
% 0.17/0.43
% 0.17/0.43 % bits_div_0
% 0.17/0.43 thf(fact_182_div__by__0,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( divide_divide_int @ A @ zero_zero_int )
% 0.17/0.43 = zero_zero_int ) ).
% 0.17/0.43
% 0.17/0.43 % div_by_0
% 0.17/0.43 thf(fact_183_div__by__0,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.17/0.43 = zero_zero_nat ) ).
% 0.17/0.43
% 0.17/0.43 % div_by_0
% 0.17/0.43 thf(fact_184_div__0,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( divide_divide_int @ zero_zero_int @ A )
% 0.17/0.43 = zero_zero_int ) ).
% 0.17/0.43
% 0.17/0.43 % div_0
% 0.17/0.43 thf(fact_185_div__0,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.17/0.43 = zero_zero_nat ) ).
% 0.17/0.43
% 0.17/0.43 % div_0
% 0.17/0.43 thf(fact_186_of__nat__0,axiom,
% 0.17/0.43 ( ( semiri2019852685at_int @ zero_zero_nat )
% 0.17/0.43 = zero_zero_int ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_0
% 0.17/0.43 thf(fact_187_of__nat__0,axiom,
% 0.17/0.43 ( ( semiri1382578993at_nat @ zero_zero_nat )
% 0.17/0.43 = zero_zero_nat ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_0
% 0.17/0.43 thf(fact_188_of__nat__0__eq__iff,axiom,
% 0.17/0.43 ! [N: nat] :
% 0.17/0.43 ( ( zero_zero_int
% 0.17/0.43 = ( semiri2019852685at_int @ N ) )
% 0.17/0.43 = ( zero_zero_nat = N ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_0_eq_iff
% 0.17/0.43 thf(fact_189_of__nat__0__eq__iff,axiom,
% 0.17/0.43 ! [N: nat] :
% 0.17/0.43 ( ( zero_zero_nat
% 0.17/0.43 = ( semiri1382578993at_nat @ N ) )
% 0.17/0.43 = ( zero_zero_nat = N ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_0_eq_iff
% 0.17/0.43 thf(fact_190_of__nat__eq__0__iff,axiom,
% 0.17/0.43 ! [M: nat] :
% 0.17/0.43 ( ( ( semiri2019852685at_int @ M )
% 0.17/0.43 = zero_zero_int )
% 0.17/0.43 = ( M = zero_zero_nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_eq_0_iff
% 0.17/0.43 thf(fact_191_of__nat__eq__0__iff,axiom,
% 0.17/0.43 ! [M: nat] :
% 0.17/0.43 ( ( ( semiri1382578993at_nat @ M )
% 0.17/0.43 = zero_zero_nat )
% 0.17/0.43 = ( M = zero_zero_nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % of_nat_eq_0_iff
% 0.17/0.43 thf(fact_192_power__Suc0__right,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % power_Suc0_right
% 0.17/0.43 thf(fact_193_power__Suc0__right,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % power_Suc0_right
% 0.17/0.43 thf(fact_194_one__eq__mult__iff,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( ( suc @ zero_zero_nat )
% 0.17/0.43 = ( times_times_nat @ M @ N ) )
% 0.17/0.43 = ( ( M
% 0.17/0.43 = ( suc @ zero_zero_nat ) )
% 0.17/0.43 & ( N
% 0.17/0.43 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % one_eq_mult_iff
% 0.17/0.43 thf(fact_195_mult__eq__1__iff,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( ( times_times_nat @ M @ N )
% 0.17/0.43 = ( suc @ zero_zero_nat ) )
% 0.17/0.43 = ( ( M
% 0.17/0.43 = ( suc @ zero_zero_nat ) )
% 0.17/0.43 & ( N
% 0.17/0.43 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_eq_1_iff
% 0.17/0.43 thf(fact_196_power__one__right,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( power_power_int @ A @ one_one_nat )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % power_one_right
% 0.17/0.43 thf(fact_197_power__one__right,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( power_power_nat @ A @ one_one_nat )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % power_one_right
% 0.17/0.43 thf(fact_198_nat__mult__eq__1__iff,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( ( times_times_nat @ M @ N )
% 0.17/0.43 = one_one_nat )
% 0.17/0.43 = ( ( M = one_one_nat )
% 0.17/0.43 & ( N = one_one_nat ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % nat_mult_eq_1_iff
% 0.17/0.43 thf(fact_199_nat__1__eq__mult__iff,axiom,
% 0.17/0.43 ! [M: nat,N: nat] :
% 0.17/0.43 ( ( one_one_nat
% 0.17/0.43 = ( times_times_nat @ M @ N ) )
% 0.17/0.43 = ( ( M = one_one_nat )
% 0.17/0.43 & ( N = one_one_nat ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % nat_1_eq_mult_iff
% 0.17/0.43 thf(fact_200_div__by__Suc__0,axiom,
% 0.17/0.43 ! [M: nat] :
% 0.17/0.43 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.17/0.43 = M ) ).
% 0.17/0.43
% 0.17/0.43 % div_by_Suc_0
% 0.17/0.43 thf(fact_201_gbinomial__0_I1_J,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( gbinomial_int @ A @ zero_zero_nat )
% 0.17/0.43 = one_one_int ) ).
% 0.17/0.43
% 0.17/0.43 % gbinomial_0(1)
% 0.17/0.43 thf(fact_202_gbinomial__0_I1_J,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 0.17/0.43 = one_one_nat ) ).
% 0.17/0.43
% 0.17/0.43 % gbinomial_0(1)
% 0.17/0.43 thf(fact_203_nat__power__eq__Suc__0__iff,axiom,
% 0.17/0.43 ! [X: nat,M: nat] :
% 0.17/0.43 ( ( ( power_power_nat @ X @ M )
% 0.17/0.43 = ( suc @ zero_zero_nat ) )
% 0.17/0.43 = ( ( M = zero_zero_nat )
% 0.17/0.43 | ( X
% 0.17/0.43 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % nat_power_eq_Suc_0_iff
% 0.17/0.43 thf(fact_204_power__Suc__0,axiom,
% 0.17/0.43 ! [N: nat] :
% 0.17/0.43 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.17/0.43 = ( suc @ zero_zero_nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % power_Suc_0
% 0.17/0.43 thf(fact_205_nat__mult__div__cancel__disj,axiom,
% 0.17/0.43 ! [K: nat,M: nat,N: nat] :
% 0.17/0.43 ( ( ( K = zero_zero_nat )
% 0.17/0.43 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.17/0.43 = zero_zero_nat ) )
% 0.17/0.43 & ( ( K != zero_zero_nat )
% 0.17/0.43 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.17/0.43 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % nat_mult_div_cancel_disj
% 0.17/0.43 thf(fact_206_gbinomial__Suc0,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( gbinomial_nat @ A @ ( suc @ zero_zero_nat ) )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % gbinomial_Suc0
% 0.17/0.43 thf(fact_207_gbinomial__Suc0,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( gbinomial_int @ A @ ( suc @ zero_zero_nat ) )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % gbinomial_Suc0
% 0.17/0.43 thf(fact_208_gbinomial__1,axiom,
% 0.17/0.43 ! [A: nat] :
% 0.17/0.43 ( ( gbinomial_nat @ A @ one_one_nat )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % gbinomial_1
% 0.17/0.43 thf(fact_209_gbinomial__1,axiom,
% 0.17/0.43 ! [A: int] :
% 0.17/0.43 ( ( gbinomial_int @ A @ one_one_nat )
% 0.17/0.43 = A ) ).
% 0.17/0.43
% 0.17/0.43 % gbinomial_1
% 0.17/0.43 thf(fact_210_sum__squares__eq__zero__iff,axiom,
% 0.17/0.43 ! [X: int,Y: int] :
% 0.17/0.43 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 0.17/0.43 = zero_zero_int )
% 0.17/0.43 = ( ( X = zero_zero_int )
% 0.17/0.43 & ( Y = zero_zero_int ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % sum_squares_eq_zero_iff
% 0.17/0.43 thf(fact_211_mult__cancel__left1,axiom,
% 0.17/0.43 ! [C: int,B: int] :
% 0.17/0.43 ( ( C
% 0.17/0.43 = ( times_times_int @ C @ B ) )
% 0.17/0.43 = ( ( C = zero_zero_int )
% 0.17/0.43 | ( B = one_one_int ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_cancel_left1
% 0.17/0.43 thf(fact_212_mult__cancel__left2,axiom,
% 0.17/0.43 ! [C: int,A: int] :
% 0.17/0.43 ( ( ( times_times_int @ C @ A )
% 0.17/0.43 = C )
% 0.17/0.43 = ( ( C = zero_zero_int )
% 0.17/0.43 | ( A = one_one_int ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_cancel_left2
% 0.17/0.43 thf(fact_213_mult__cancel__right1,axiom,
% 0.17/0.43 ! [C: int,B: int] :
% 0.17/0.43 ( ( C
% 0.17/0.43 = ( times_times_int @ B @ C ) )
% 0.17/0.43 = ( ( C = zero_zero_int )
% 0.17/0.43 | ( B = one_one_int ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_cancel_right1
% 0.17/0.43 thf(fact_214_mult__cancel__right2,axiom,
% 0.17/0.43 ! [A: int,C: int] :
% 0.17/0.43 ( ( ( times_times_int @ A @ C )
% 0.17/0.43 = C )
% 0.17/0.43 = ( ( C = zero_zero_int )
% 0.17/0.43 | ( A = one_one_int ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mult_cancel_right2
% 0.17/0.43 thf(fact_215_div__mult__mult1,axiom,
% 0.17/0.43 ! [C: int,A: int,B: int] :
% 0.17/0.44 ( ( C != zero_zero_int )
% 0.17/0.44 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.17/0.44 = ( divide_divide_int @ A @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_mult_mult1
% 0.17/0.44 thf(fact_216_div__mult__mult1,axiom,
% 0.17/0.44 ! [C: nat,A: nat,B: nat] :
% 0.17/0.44 ( ( C != zero_zero_nat )
% 0.17/0.44 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.17/0.44 = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_mult_mult1
% 0.17/0.44 thf(fact_217_div__mult__mult2,axiom,
% 0.17/0.44 ! [C: int,A: int,B: int] :
% 0.17/0.44 ( ( C != zero_zero_int )
% 0.17/0.44 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.17/0.44 = ( divide_divide_int @ A @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_mult_mult2
% 0.17/0.44 thf(fact_218_div__mult__mult2,axiom,
% 0.17/0.44 ! [C: nat,A: nat,B: nat] :
% 0.17/0.44 ( ( C != zero_zero_nat )
% 0.17/0.44 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.17/0.44 = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_mult_mult2
% 0.17/0.44 thf(fact_219_div__mult__mult1__if,axiom,
% 0.17/0.44 ! [C: int,A: int,B: int] :
% 0.17/0.44 ( ( ( C = zero_zero_int )
% 0.17/0.44 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.17/0.44 = zero_zero_int ) )
% 0.17/0.44 & ( ( C != zero_zero_int )
% 0.17/0.44 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.17/0.44 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_mult_mult1_if
% 0.17/0.44 thf(fact_220_div__mult__mult1__if,axiom,
% 0.17/0.44 ! [C: nat,A: nat,B: nat] :
% 0.17/0.44 ( ( ( C = zero_zero_nat )
% 0.17/0.44 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.17/0.44 = zero_zero_nat ) )
% 0.17/0.44 & ( ( C != zero_zero_nat )
% 0.17/0.44 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.17/0.44 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_mult_mult1_if
% 0.17/0.44 thf(fact_221_nonzero__mult__div__cancel__left,axiom,
% 0.17/0.44 ! [A: int,B: int] :
% 0.17/0.44 ( ( A != zero_zero_int )
% 0.17/0.44 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 0.17/0.44 = B ) ) ).
% 0.17/0.44
% 0.17/0.44 % nonzero_mult_div_cancel_left
% 0.17/0.44 thf(fact_222_nonzero__mult__div__cancel__left,axiom,
% 0.17/0.44 ! [A: nat,B: nat] :
% 0.17/0.44 ( ( A != zero_zero_nat )
% 0.17/0.44 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 0.17/0.44 = B ) ) ).
% 0.17/0.44
% 0.17/0.44 % nonzero_mult_div_cancel_left
% 0.17/0.44 thf(fact_223_nonzero__mult__div__cancel__right,axiom,
% 0.17/0.44 ! [B: int,A: int] :
% 0.17/0.44 ( ( B != zero_zero_int )
% 0.17/0.44 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 0.17/0.44 = A ) ) ).
% 0.17/0.44
% 0.17/0.44 % nonzero_mult_div_cancel_right
% 0.17/0.44 thf(fact_224_nonzero__mult__div__cancel__right,axiom,
% 0.17/0.44 ! [B: nat,A: nat] :
% 0.17/0.44 ( ( B != zero_zero_nat )
% 0.17/0.44 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.17/0.44 = A ) ) ).
% 0.17/0.44
% 0.17/0.44 % nonzero_mult_div_cancel_right
% 0.17/0.44 thf(fact_225_div__self,axiom,
% 0.17/0.44 ! [A: int] :
% 0.17/0.44 ( ( A != zero_zero_int )
% 0.17/0.44 => ( ( divide_divide_int @ A @ A )
% 0.17/0.44 = one_one_int ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_self
% 0.17/0.44 thf(fact_226_div__self,axiom,
% 0.17/0.44 ! [A: nat] :
% 0.17/0.44 ( ( A != zero_zero_nat )
% 0.17/0.44 => ( ( divide_divide_nat @ A @ A )
% 0.17/0.44 = one_one_nat ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_self
% 0.17/0.44 thf(fact_227_power__0__Suc,axiom,
% 0.17/0.44 ! [N: nat] :
% 0.17/0.44 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 0.17/0.44 = zero_zero_int ) ).
% 0.17/0.44
% 0.17/0.44 % power_0_Suc
% 0.17/0.44 thf(fact_228_power__0__Suc,axiom,
% 0.17/0.44 ! [N: nat] :
% 0.17/0.44 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.17/0.44 = zero_zero_nat ) ).
% 0.17/0.44
% 0.17/0.44 % power_0_Suc
% 0.17/0.44 thf(fact_229_gbinomial__0_I2_J,axiom,
% 0.17/0.44 ! [K: nat] :
% 0.17/0.44 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 0.17/0.44 = zero_zero_nat ) ).
% 0.17/0.44
% 0.17/0.44 % gbinomial_0(2)
% 0.17/0.44 thf(fact_230_gbinomial__0_I2_J,axiom,
% 0.17/0.44 ! [K: nat] :
% 0.17/0.44 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 0.17/0.44 = zero_zero_int ) ).
% 0.17/0.44
% 0.17/0.44 % gbinomial_0(2)
% 0.17/0.44 thf(fact_231_div__mult__self1,axiom,
% 0.17/0.44 ! [B: int,A: int,C: int] :
% 0.17/0.44 ( ( B != zero_zero_int )
% 0.17/0.44 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.17/0.44 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_mult_self1
% 0.17/0.44 thf(fact_232_div__mult__self1,axiom,
% 0.17/0.44 ! [B: nat,A: nat,C: nat] :
% 0.17/0.44 ( ( B != zero_zero_nat )
% 0.17/0.44 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.17/0.44 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_mult_self1
% 0.17/0.44 thf(fact_233_div__mult__self2,axiom,
% 0.17/0.44 ! [B: int,A: int,C: int] :
% 0.17/0.44 ( ( B != zero_zero_int )
% 0.17/0.44 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.17/0.44 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_mult_self2
% 0.17/0.44 thf(fact_234_div__mult__self2,axiom,
% 0.17/0.44 ! [B: nat,A: nat,C: nat] :
% 0.17/0.44 ( ( B != zero_zero_nat )
% 0.17/0.44 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.17/0.44 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_mult_self2
% 0.17/0.44 thf(fact_235_div__mult__self3,axiom,
% 0.17/0.44 ! [B: int,C: int,A: int] :
% 0.17/0.44 ( ( B != zero_zero_int )
% 0.17/0.44 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.17/0.44 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_mult_self3
% 0.17/0.44 thf(fact_236_div__mult__self3,axiom,
% 0.17/0.44 ! [B: nat,C: nat,A: nat] :
% 0.17/0.44 ( ( B != zero_zero_nat )
% 0.17/0.44 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.17/0.44 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_mult_self3
% 0.17/0.44 thf(fact_237_div__mult__self4,axiom,
% 0.17/0.44 ! [B: int,C: int,A: int] :
% 0.17/0.44 ( ( B != zero_zero_int )
% 0.17/0.44 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.17/0.44 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_mult_self4
% 0.17/0.44 thf(fact_238_div__mult__self4,axiom,
% 0.17/0.44 ! [B: nat,C: nat,A: nat] :
% 0.17/0.44 ( ( B != zero_zero_nat )
% 0.17/0.44 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.17/0.44 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_mult_self4
% 0.17/0.44 thf(fact_239_One__nat__def,axiom,
% 0.17/0.44 ( one_one_nat
% 0.17/0.44 = ( suc @ zero_zero_nat ) ) ).
% 0.17/0.44
% 0.17/0.44 % One_nat_def
% 0.17/0.44 thf(fact_240_mult__eq__self__implies__10,axiom,
% 0.17/0.44 ! [M: nat,N: nat] :
% 0.17/0.44 ( ( M
% 0.17/0.44 = ( times_times_nat @ M @ N ) )
% 0.17/0.44 => ( ( N = one_one_nat )
% 0.17/0.44 | ( M = zero_zero_nat ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % mult_eq_self_implies_10
% 0.17/0.44 thf(fact_241_zero__reorient,axiom,
% 0.17/0.44 ! [X: nat] :
% 0.17/0.44 ( ( zero_zero_nat = X )
% 0.17/0.44 = ( X = zero_zero_nat ) ) ).
% 0.17/0.44
% 0.17/0.44 % zero_reorient
% 0.17/0.44 thf(fact_242_zero__reorient,axiom,
% 0.17/0.44 ! [X: int] :
% 0.17/0.44 ( ( zero_zero_int = X )
% 0.17/0.44 = ( X = zero_zero_int ) ) ).
% 0.17/0.44
% 0.17/0.44 % zero_reorient
% 0.17/0.44 thf(fact_243_int__ops_I1_J,axiom,
% 0.17/0.44 ( ( semiri2019852685at_int @ zero_zero_nat )
% 0.17/0.44 = zero_zero_int ) ).
% 0.17/0.44
% 0.17/0.44 % int_ops(1)
% 0.17/0.44 thf(fact_244_power__0__left,axiom,
% 0.17/0.44 ! [N: nat] :
% 0.17/0.44 ( ( ( N = zero_zero_nat )
% 0.17/0.44 => ( ( power_power_int @ zero_zero_int @ N )
% 0.17/0.44 = one_one_int ) )
% 0.17/0.44 & ( ( N != zero_zero_nat )
% 0.17/0.44 => ( ( power_power_int @ zero_zero_int @ N )
% 0.17/0.44 = zero_zero_int ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % power_0_left
% 0.17/0.44 thf(fact_245_power__0__left,axiom,
% 0.17/0.44 ! [N: nat] :
% 0.17/0.44 ( ( ( N = zero_zero_nat )
% 0.17/0.44 => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.17/0.44 = one_one_nat ) )
% 0.17/0.44 & ( ( N != zero_zero_nat )
% 0.17/0.44 => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.17/0.44 = zero_zero_nat ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % power_0_left
% 0.17/0.44 thf(fact_246_mult__right__cancel,axiom,
% 0.17/0.44 ! [C: int,A: int,B: int] :
% 0.17/0.44 ( ( C != zero_zero_int )
% 0.17/0.44 => ( ( ( times_times_int @ A @ C )
% 0.17/0.44 = ( times_times_int @ B @ C ) )
% 0.17/0.44 = ( A = B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % mult_right_cancel
% 0.17/0.44 thf(fact_247_mult__right__cancel,axiom,
% 0.17/0.44 ! [C: nat,A: nat,B: nat] :
% 0.17/0.44 ( ( C != zero_zero_nat )
% 0.17/0.44 => ( ( ( times_times_nat @ A @ C )
% 0.17/0.44 = ( times_times_nat @ B @ C ) )
% 0.17/0.44 = ( A = B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % mult_right_cancel
% 0.17/0.44 thf(fact_248_mult__left__cancel,axiom,
% 0.17/0.44 ! [C: int,A: int,B: int] :
% 0.17/0.44 ( ( C != zero_zero_int )
% 0.17/0.44 => ( ( ( times_times_int @ C @ A )
% 0.17/0.44 = ( times_times_int @ C @ B ) )
% 0.17/0.44 = ( A = B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % mult_left_cancel
% 0.17/0.44 thf(fact_249_mult__left__cancel,axiom,
% 0.17/0.44 ! [C: nat,A: nat,B: nat] :
% 0.17/0.44 ( ( C != zero_zero_nat )
% 0.17/0.44 => ( ( ( times_times_nat @ C @ A )
% 0.17/0.44 = ( times_times_nat @ C @ B ) )
% 0.17/0.44 = ( A = B ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % mult_left_cancel
% 0.17/0.44 thf(fact_250_no__zero__divisors,axiom,
% 0.17/0.44 ! [A: int,B: int] :
% 0.17/0.44 ( ( A != zero_zero_int )
% 0.17/0.44 => ( ( B != zero_zero_int )
% 0.17/0.44 => ( ( times_times_int @ A @ B )
% 0.17/0.44 != zero_zero_int ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % no_zero_divisors
% 0.17/0.44 thf(fact_251_no__zero__divisors,axiom,
% 0.17/0.44 ! [A: nat,B: nat] :
% 0.17/0.44 ( ( A != zero_zero_nat )
% 0.17/0.44 => ( ( B != zero_zero_nat )
% 0.17/0.44 => ( ( times_times_nat @ A @ B )
% 0.17/0.44 != zero_zero_nat ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % no_zero_divisors
% 0.17/0.44 thf(fact_252_divisors__zero,axiom,
% 0.17/0.44 ! [A: int,B: int] :
% 0.17/0.44 ( ( ( times_times_int @ A @ B )
% 0.17/0.44 = zero_zero_int )
% 0.17/0.44 => ( ( A = zero_zero_int )
% 0.17/0.44 | ( B = zero_zero_int ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % divisors_zero
% 0.17/0.44 thf(fact_253_divisors__zero,axiom,
% 0.17/0.44 ! [A: nat,B: nat] :
% 0.17/0.44 ( ( ( times_times_nat @ A @ B )
% 0.17/0.44 = zero_zero_nat )
% 0.17/0.44 => ( ( A = zero_zero_nat )
% 0.17/0.44 | ( B = zero_zero_nat ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % divisors_zero
% 0.17/0.44 thf(fact_254_mult__not__zero,axiom,
% 0.17/0.44 ! [A: int,B: int] :
% 0.17/0.44 ( ( ( times_times_int @ A @ B )
% 0.17/0.44 != zero_zero_int )
% 0.17/0.44 => ( ( A != zero_zero_int )
% 0.17/0.44 & ( B != zero_zero_int ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % mult_not_zero
% 0.17/0.44 thf(fact_255_mult__not__zero,axiom,
% 0.17/0.44 ! [A: nat,B: nat] :
% 0.17/0.44 ( ( ( times_times_nat @ A @ B )
% 0.17/0.44 != zero_zero_nat )
% 0.17/0.44 => ( ( A != zero_zero_nat )
% 0.17/0.44 & ( B != zero_zero_nat ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % mult_not_zero
% 0.17/0.44 thf(fact_256_verit__sum__simplify,axiom,
% 0.17/0.44 ! [A: nat] :
% 0.17/0.44 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % verit_sum_simplify
% 0.17/0.44 thf(fact_257_verit__sum__simplify,axiom,
% 0.17/0.44 ! [A: int] :
% 0.17/0.44 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % verit_sum_simplify
% 0.17/0.44 thf(fact_258_comm__monoid__add__class_Oadd__0,axiom,
% 0.17/0.44 ! [A: nat] :
% 0.17/0.44 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % comm_monoid_add_class.add_0
% 0.17/0.44 thf(fact_259_comm__monoid__add__class_Oadd__0,axiom,
% 0.17/0.44 ! [A: int] :
% 0.17/0.44 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % comm_monoid_add_class.add_0
% 0.17/0.44 thf(fact_260_add_Ocomm__neutral,axiom,
% 0.17/0.44 ! [A: nat] :
% 0.17/0.44 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add.comm_neutral
% 0.17/0.44 thf(fact_261_add_Ocomm__neutral,axiom,
% 0.17/0.44 ! [A: int] :
% 0.17/0.44 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add.comm_neutral
% 0.17/0.44 thf(fact_262_add_Ogroup__left__neutral,axiom,
% 0.17/0.44 ! [A: int] :
% 0.17/0.44 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.17/0.44 = A ) ).
% 0.17/0.44
% 0.17/0.44 % add.group_left_neutral
% 0.17/0.44 thf(fact_263_add__0__iff,axiom,
% 0.17/0.44 ! [B: nat,A: nat] :
% 0.17/0.44 ( ( B
% 0.17/0.44 = ( plus_plus_nat @ B @ A ) )
% 0.17/0.44 = ( A = zero_zero_nat ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_0_iff
% 0.17/0.44 thf(fact_264_add__0__iff,axiom,
% 0.17/0.44 ! [B: int,A: int] :
% 0.17/0.44 ( ( B
% 0.17/0.44 = ( plus_plus_int @ B @ A ) )
% 0.17/0.44 = ( A = zero_zero_int ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_0_iff
% 0.17/0.44 thf(fact_265_zero__neq__one,axiom,
% 0.17/0.44 zero_zero_nat != one_one_nat ).
% 0.17/0.44
% 0.17/0.44 % zero_neq_one
% 0.17/0.44 thf(fact_266_zero__neq__one,axiom,
% 0.17/0.44 zero_zero_int != one_one_int ).
% 0.17/0.44
% 0.17/0.44 % zero_neq_one
% 0.17/0.44 thf(fact_267_power__not__zero,axiom,
% 0.17/0.44 ! [A: int,N: nat] :
% 0.17/0.44 ( ( A != zero_zero_int )
% 0.17/0.44 => ( ( power_power_int @ A @ N )
% 0.17/0.44 != zero_zero_int ) ) ).
% 0.17/0.44
% 0.17/0.44 % power_not_zero
% 0.17/0.44 thf(fact_268_power__not__zero,axiom,
% 0.17/0.44 ! [A: nat,N: nat] :
% 0.17/0.44 ( ( A != zero_zero_nat )
% 0.17/0.44 => ( ( power_power_nat @ A @ N )
% 0.17/0.44 != zero_zero_nat ) ) ).
% 0.17/0.44
% 0.17/0.44 % power_not_zero
% 0.17/0.44 thf(fact_269_nat__mult__1__right,axiom,
% 0.17/0.44 ! [N: nat] :
% 0.17/0.44 ( ( times_times_nat @ N @ one_one_nat )
% 0.17/0.44 = N ) ).
% 0.17/0.44
% 0.17/0.44 % nat_mult_1_right
% 0.17/0.44 thf(fact_270_nat__mult__1,axiom,
% 0.17/0.44 ! [N: nat] :
% 0.17/0.44 ( ( times_times_nat @ one_one_nat @ N )
% 0.17/0.44 = N ) ).
% 0.17/0.44
% 0.17/0.44 % nat_mult_1
% 0.17/0.44 thf(fact_271_nat_Odistinct_I1_J,axiom,
% 0.17/0.44 ! [X2: nat] :
% 0.17/0.44 ( zero_zero_nat
% 0.17/0.44 != ( suc @ X2 ) ) ).
% 0.17/0.44
% 0.17/0.44 % nat.distinct(1)
% 0.17/0.44 thf(fact_272_old_Onat_Odistinct_I2_J,axiom,
% 0.17/0.44 ! [Nat2: nat] :
% 0.17/0.44 ( ( suc @ Nat2 )
% 0.17/0.44 != zero_zero_nat ) ).
% 0.17/0.44
% 0.17/0.44 % old.nat.distinct(2)
% 0.17/0.44 thf(fact_273_old_Onat_Odistinct_I1_J,axiom,
% 0.17/0.44 ! [Nat2: nat] :
% 0.17/0.44 ( zero_zero_nat
% 0.17/0.44 != ( suc @ Nat2 ) ) ).
% 0.17/0.44
% 0.17/0.44 % old.nat.distinct(1)
% 0.17/0.44 thf(fact_274_nat_OdiscI,axiom,
% 0.17/0.44 ! [Nat: nat,X2: nat] :
% 0.17/0.44 ( ( Nat
% 0.17/0.44 = ( suc @ X2 ) )
% 0.17/0.44 => ( Nat != zero_zero_nat ) ) ).
% 0.17/0.44
% 0.17/0.44 % nat.discI
% 0.17/0.44 thf(fact_275_nat__induct,axiom,
% 0.17/0.44 ! [P3: nat > $o,N: nat] :
% 0.17/0.44 ( ( P3 @ zero_zero_nat )
% 0.17/0.44 => ( ! [N2: nat] :
% 0.17/0.44 ( ( P3 @ N2 )
% 0.17/0.44 => ( P3 @ ( suc @ N2 ) ) )
% 0.17/0.44 => ( P3 @ N ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % nat_induct
% 0.17/0.44 thf(fact_276_diff__induct,axiom,
% 0.17/0.44 ! [P3: nat > nat > $o,M: nat,N: nat] :
% 0.17/0.44 ( ! [X3: nat] : ( P3 @ X3 @ zero_zero_nat )
% 0.17/0.44 => ( ! [Y4: nat] : ( P3 @ zero_zero_nat @ ( suc @ Y4 ) )
% 0.17/0.44 => ( ! [X3: nat,Y4: nat] :
% 0.17/0.44 ( ( P3 @ X3 @ Y4 )
% 0.17/0.44 => ( P3 @ ( suc @ X3 ) @ ( suc @ Y4 ) ) )
% 0.17/0.44 => ( P3 @ M @ N ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % diff_induct
% 0.17/0.44 thf(fact_277_zero__induct,axiom,
% 0.17/0.44 ! [P3: nat > $o,K: nat] :
% 0.17/0.44 ( ( P3 @ K )
% 0.17/0.44 => ( ! [N2: nat] :
% 0.17/0.44 ( ( P3 @ ( suc @ N2 ) )
% 0.17/0.44 => ( P3 @ N2 ) )
% 0.17/0.44 => ( P3 @ zero_zero_nat ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % zero_induct
% 0.17/0.44 thf(fact_278_Suc__neq__Zero,axiom,
% 0.17/0.44 ! [M: nat] :
% 0.17/0.44 ( ( suc @ M )
% 0.17/0.44 != zero_zero_nat ) ).
% 0.17/0.44
% 0.17/0.44 % Suc_neq_Zero
% 0.17/0.44 thf(fact_279_Zero__neq__Suc,axiom,
% 0.17/0.44 ! [M: nat] :
% 0.17/0.44 ( zero_zero_nat
% 0.17/0.44 != ( suc @ M ) ) ).
% 0.17/0.44
% 0.17/0.44 % Zero_neq_Suc
% 0.17/0.44 thf(fact_280_Zero__not__Suc,axiom,
% 0.17/0.44 ! [M: nat] :
% 0.17/0.44 ( zero_zero_nat
% 0.17/0.44 != ( suc @ M ) ) ).
% 0.17/0.44
% 0.17/0.44 % Zero_not_Suc
% 0.17/0.44 thf(fact_281_old_Onat_Oexhaust,axiom,
% 0.17/0.44 ! [Y: nat] :
% 0.17/0.44 ( ( Y != zero_zero_nat )
% 0.17/0.44 => ~ ! [Nat3: nat] :
% 0.17/0.44 ( Y
% 0.17/0.44 != ( suc @ Nat3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % old.nat.exhaust
% 0.17/0.44 thf(fact_282_old_Onat_Oinducts,axiom,
% 0.17/0.44 ! [P3: nat > $o,Nat: nat] :
% 0.17/0.44 ( ( P3 @ zero_zero_nat )
% 0.17/0.44 => ( ! [Nat3: nat] :
% 0.17/0.44 ( ( P3 @ Nat3 )
% 0.17/0.44 => ( P3 @ ( suc @ Nat3 ) ) )
% 0.17/0.44 => ( P3 @ Nat ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % old.nat.inducts
% 0.17/0.44 thf(fact_283_not0__implies__Suc,axiom,
% 0.17/0.44 ! [N: nat] :
% 0.17/0.44 ( ( N != zero_zero_nat )
% 0.17/0.44 => ? [M2: nat] :
% 0.17/0.44 ( N
% 0.17/0.44 = ( suc @ M2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % not0_implies_Suc
% 0.17/0.44 thf(fact_284_add__eq__self__zero,axiom,
% 0.17/0.44 ! [M: nat,N: nat] :
% 0.17/0.44 ( ( ( plus_plus_nat @ M @ N )
% 0.17/0.44 = M )
% 0.17/0.44 => ( N = zero_zero_nat ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_eq_self_zero
% 0.17/0.44 thf(fact_285_plus__nat_Oadd__0,axiom,
% 0.17/0.44 ! [N: nat] :
% 0.17/0.44 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.17/0.44 = N ) ).
% 0.17/0.44
% 0.17/0.44 % plus_nat.add_0
% 0.17/0.44 thf(fact_286_nat__mult__eq__cancel__disj,axiom,
% 0.17/0.44 ! [K: nat,M: nat,N: nat] :
% 0.17/0.44 ( ( ( times_times_nat @ K @ M )
% 0.17/0.44 = ( times_times_nat @ K @ N ) )
% 0.17/0.44 = ( ( K = zero_zero_nat )
% 0.17/0.44 | ( M = N ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % nat_mult_eq_cancel_disj
% 0.17/0.44 thf(fact_287_mult__0,axiom,
% 0.17/0.44 ! [N: nat] :
% 0.17/0.44 ( ( times_times_nat @ zero_zero_nat @ N )
% 0.17/0.44 = zero_zero_nat ) ).
% 0.17/0.44
% 0.17/0.44 % mult_0
% 0.17/0.44 thf(fact_288_times__int__code_I2_J,axiom,
% 0.17/0.44 ! [L: int] :
% 0.17/0.44 ( ( times_times_int @ zero_zero_int @ L )
% 0.17/0.44 = zero_zero_int ) ).
% 0.17/0.44
% 0.17/0.44 % times_int_code(2)
% 0.17/0.44 thf(fact_289_times__int__code_I1_J,axiom,
% 0.17/0.44 ! [K: int] :
% 0.17/0.44 ( ( times_times_int @ K @ zero_zero_int )
% 0.17/0.44 = zero_zero_int ) ).
% 0.17/0.44
% 0.17/0.44 % times_int_code(1)
% 0.17/0.44 thf(fact_290_plus__int__code_I2_J,axiom,
% 0.17/0.44 ! [L: int] :
% 0.17/0.44 ( ( plus_plus_int @ zero_zero_int @ L )
% 0.17/0.44 = L ) ).
% 0.17/0.44
% 0.17/0.44 % plus_int_code(2)
% 0.17/0.44 thf(fact_291_plus__int__code_I1_J,axiom,
% 0.17/0.44 ! [K: int] :
% 0.17/0.44 ( ( plus_plus_int @ K @ zero_zero_int )
% 0.17/0.44 = K ) ).
% 0.17/0.44
% 0.17/0.44 % plus_int_code(1)
% 0.17/0.44 thf(fact_292_add__scale__eq__noteq,axiom,
% 0.17/0.44 ! [R: int,A: int,B: int,C: int,D: int] :
% 0.17/0.44 ( ( R != zero_zero_int )
% 0.17/0.44 => ( ( ( A = B )
% 0.17/0.44 & ( C != D ) )
% 0.17/0.44 => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C ) )
% 0.17/0.44 != ( plus_plus_int @ B @ ( times_times_int @ R @ D ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_scale_eq_noteq
% 0.17/0.44 thf(fact_293_add__scale__eq__noteq,axiom,
% 0.17/0.44 ! [R: nat,A: nat,B: nat,C: nat,D: nat] :
% 0.17/0.44 ( ( R != zero_zero_nat )
% 0.17/0.44 => ( ( ( A = B )
% 0.17/0.44 & ( C != D ) )
% 0.17/0.44 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
% 0.17/0.44 != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_scale_eq_noteq
% 0.17/0.44 thf(fact_294_Suc__eq__plus1__left,axiom,
% 0.17/0.44 ( suc
% 0.17/0.44 = ( plus_plus_nat @ one_one_nat ) ) ).
% 0.17/0.44
% 0.17/0.44 % Suc_eq_plus1_left
% 0.17/0.44 thf(fact_295_plus__1__eq__Suc,axiom,
% 0.17/0.44 ( ( plus_plus_nat @ one_one_nat )
% 0.17/0.44 = suc ) ).
% 0.17/0.44
% 0.17/0.44 % plus_1_eq_Suc
% 0.17/0.44 thf(fact_296_Suc__eq__plus1,axiom,
% 0.17/0.44 ( suc
% 0.17/0.44 = ( ^ [N3: nat] : ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Suc_eq_plus1
% 0.17/0.44 thf(fact_297_power__0,axiom,
% 0.17/0.44 ! [A: int] :
% 0.17/0.44 ( ( power_power_int @ A @ zero_zero_nat )
% 0.17/0.44 = one_one_int ) ).
% 0.17/0.44
% 0.17/0.44 % power_0
% 0.17/0.44 thf(fact_298_power__0,axiom,
% 0.17/0.44 ! [A: nat] :
% 0.17/0.44 ( ( power_power_nat @ A @ zero_zero_nat )
% 0.17/0.44 = one_one_nat ) ).
% 0.17/0.44
% 0.17/0.44 % power_0
% 0.17/0.44 thf(fact_299_of__nat__neq__0,axiom,
% 0.17/0.44 ! [N: nat] :
% 0.17/0.44 ( ( semiri2019852685at_int @ ( suc @ N ) )
% 0.17/0.44 != zero_zero_int ) ).
% 0.17/0.44
% 0.17/0.44 % of_nat_neq_0
% 0.17/0.44 thf(fact_300_of__nat__neq__0,axiom,
% 0.17/0.44 ! [N: nat] :
% 0.17/0.44 ( ( semiri1382578993at_nat @ ( suc @ N ) )
% 0.17/0.44 != zero_zero_nat ) ).
% 0.17/0.44
% 0.17/0.44 % of_nat_neq_0
% 0.17/0.44 thf(fact_301_one__is__add,axiom,
% 0.17/0.44 ! [M: nat,N: nat] :
% 0.17/0.44 ( ( ( suc @ zero_zero_nat )
% 0.17/0.44 = ( plus_plus_nat @ M @ N ) )
% 0.17/0.44 = ( ( ( M
% 0.17/0.44 = ( suc @ zero_zero_nat ) )
% 0.17/0.44 & ( N = zero_zero_nat ) )
% 0.17/0.44 | ( ( M = zero_zero_nat )
% 0.17/0.44 & ( N
% 0.17/0.44 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % one_is_add
% 0.17/0.44 thf(fact_302_add__is__1,axiom,
% 0.17/0.44 ! [M: nat,N: nat] :
% 0.17/0.44 ( ( ( plus_plus_nat @ M @ N )
% 0.17/0.44 = ( suc @ zero_zero_nat ) )
% 0.17/0.44 = ( ( ( M
% 0.17/0.44 = ( suc @ zero_zero_nat ) )
% 0.17/0.44 & ( N = zero_zero_nat ) )
% 0.17/0.44 | ( ( M = zero_zero_nat )
% 0.17/0.44 & ( N
% 0.17/0.44 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % add_is_1
% 0.17/0.44 thf(fact_303_int__ops_I2_J,axiom,
% 0.17/0.44 ( ( semiri2019852685at_int @ one_one_nat )
% 0.17/0.44 = one_one_int ) ).
% 0.17/0.44
% 0.17/0.44 % int_ops(2)
% 0.17/0.44 thf(fact_304_odd__nonzero,axiom,
% 0.17/0.44 ! [Z: int] :
% 0.17/0.44 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 0.17/0.44 != zero_zero_int ) ).
% 0.17/0.44
% 0.17/0.44 % odd_nonzero
% 0.17/0.44 thf(fact_305_div__add__self1,axiom,
% 0.17/0.44 ! [B: int,A: int] :
% 0.17/0.44 ( ( B != zero_zero_int )
% 0.17/0.44 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.17/0.44 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_add_self1
% 0.17/0.44 thf(fact_306_div__add__self1,axiom,
% 0.17/0.44 ! [B: nat,A: nat] :
% 0.17/0.44 ( ( B != zero_zero_nat )
% 0.17/0.44 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.17/0.44 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_add_self1
% 0.17/0.44 thf(fact_307_div__add__self2,axiom,
% 0.17/0.44 ! [B: int,A: int] :
% 0.17/0.44 ( ( B != zero_zero_int )
% 0.17/0.44 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.17/0.44 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_add_self2
% 0.17/0.44 thf(fact_308_div__add__self2,axiom,
% 0.17/0.44 ! [B: nat,A: nat] :
% 0.17/0.44 ( ( B != zero_zero_nat )
% 0.17/0.44 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.17/0.44 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % div_add_self2
% 0.17/0.44
% 0.17/0.44 % Helper facts (3)
% 0.17/0.44 thf(help_If_3_1_If_001t__Nat__Onat_T,axiom,
% 0.17/0.44 ! [P3: $o] :
% 0.17/0.44 ( ( P3 = $true )
% 0.17/0.44 | ( P3 = $false ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.17/0.44 ! [X: nat,Y: nat] :
% 0.17/0.44 ( ( if_nat @ $false @ X @ Y )
% 0.17/0.44 = Y ) ).
% 0.17/0.44
% 0.17/0.44 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.17/0.44 ! [X: nat,Y: nat] :
% 0.17/0.44 ( ( if_nat @ $true @ X @ Y )
% 0.17/0.44 = X ) ).
% 0.17/0.44
% 0.17/0.44 % Conjectures (1)
% 0.17/0.44 thf(conj_0,conjecture,
% 0.17/0.44 ( ( divide_divide_int @ ( plus_plus_int @ ( divide_divide_int @ ( power_power_int @ x @ ( suc @ pm ) ) @ ( power_power_int @ x @ pm ) ) @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) ) @ ( semiri2019852685at_int @ ( suc @ pm ) ) )
% 0.17/0.44 = x ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 3.13/1.85 ---- Embedded in THF ---
% 3.13/1.85 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.13/1.85 %%% Generated on Tue Feb 24 08:27:33 EST 2026
% 3.13/1.85 %%% using '$$dhol' embedding, version 1.3.0.
% 3.13/1.85 %%% Logic specification used:
% 3.13/1.85 %%% thf(spec, logic, $$dhol).
% 3.13/1.85
% 3.13/1.85 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2DTF29722.p
% See solution above
% 3.13/1.85 ------------------------
% 3.13/1.89 ---- Cleaned THF ---
% 3.13/1.89 thf(ty_n_t__Nat__Onat,type,
% 3.13/1.89 nat: $tType ).
% 3.13/1.89
% 3.13/1.89 thf(ty_n_t__Int__Oint,type,
% 3.13/1.89 int: $tType ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Binomial_Ogbinomial_001t__Int__Oint,type,
% 3.13/1.89 gbinomial_int: int > nat > int ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Binomial_Ogbinomial_001t__Nat__Onat,type,
% 3.13/1.89 gbinomial_nat: nat > nat > nat ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
% 3.13/1.89 one_one_int: int ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 3.13/1.89 one_one_nat: nat ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
% 3.13/1.89 plus_plus_int: int > int > int ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 3.13/1.89 plus_plus_nat: nat > nat > nat ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Groups_Otimes__class_Otimes_001t__Int__Oint,type,
% 3.13/1.89 times_times_int: int > int > int ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 3.13/1.89 times_times_nat: nat > nat > nat ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 3.13/1.89 zero_zero_int: int ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 3.13/1.89 zero_zero_nat: nat ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_HOL_ONO__MATCH_001t__Int__Oint_001t__Int__Oint,type,
% 3.13/1.89 nO_MATCH_int_int: int > int > $o ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_HOL_ONO__MATCH_001t__Int__Oint_001t__Nat__Onat,type,
% 3.13/1.89 nO_MATCH_int_nat: int > nat > $o ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_HOL_ONO__MATCH_001t__Nat__Onat_001t__Int__Oint,type,
% 3.13/1.89 nO_MATCH_nat_int: nat > int > $o ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_HOL_ONO__MATCH_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.13/1.89 nO_MATCH_nat_nat: nat > nat > $o ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_If_001t__Nat__Onat,type,
% 3.13/1.89 if_nat: $o > nat > nat > nat ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Nat_OSuc,type,
% 3.13/1.89 suc: nat > nat ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 3.13/1.89 semiri2019852685at_int: nat > int ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 3.13/1.89 semiri1382578993at_nat: nat > nat ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_NthRoot__Impl__Mirabelle__bcfbdygymo_Ofixed__root,type,
% 3.13/1.89 nthRoo1352626670d_root: nat > nat > $o ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 3.13/1.89 power_power_int: int > nat > int ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
% 3.13/1.89 power_power_nat: nat > nat > nat ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 3.13/1.89 divide_divide_int: int > int > int ).
% 3.13/1.89
% 3.13/1.89 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 3.13/1.89 divide_divide_nat: nat > nat > nat ).
% 3.13/1.89
% 3.13/1.89 thf(sy_v_n,type,
% 3.13/1.89 n: int ).
% 3.13/1.89
% 3.13/1.89 thf(sy_v_p,type,
% 3.13/1.89 p: nat ).
% 3.13/1.89
% 3.13/1.89 thf(sy_v_pm,type,
% 3.13/1.89 pm: nat ).
% 3.13/1.89
% 3.13/1.89 thf(sy_v_x,type,
% 3.13/1.89 x: int ).
% 3.13/1.89
% 3.13/1.89 thf(fact_0_xn,axiom,
% 3.13/1.89 ( ( power_power_int @ x @ p )
% 3.13/1.89 = n ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_1_of__nat__power,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( semiri1382578993at_nat @ ( power_power_nat @ M @ N ) )
% 3.13/1.89 = ( power_power_nat @ ( semiri1382578993at_nat @ M ) @ N ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_2_of__nat__power,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( semiri2019852685at_int @ ( power_power_nat @ M @ N ) )
% 3.13/1.89 = ( power_power_int @ ( semiri2019852685at_int @ M ) @ N ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_3_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 3.13/1.89 ! [B: nat,W: nat,X: nat] :
% 3.13/1.89 ( ( ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W )
% 3.13/1.89 = ( semiri1382578993at_nat @ X ) )
% 3.13/1.89 = ( ( power_power_nat @ B @ W )
% 3.13/1.89 = X ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_4_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 3.13/1.89 ! [B: nat,W: nat,X: nat] :
% 3.13/1.89 ( ( ( power_power_int @ ( semiri2019852685at_int @ B ) @ W )
% 3.13/1.89 = ( semiri2019852685at_int @ X ) )
% 3.13/1.89 = ( ( power_power_nat @ B @ W )
% 3.13/1.89 = X ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_5_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 3.13/1.89 ! [X: nat,B: nat,W: nat] :
% 3.13/1.89 ( ( ( semiri1382578993at_nat @ X )
% 3.13/1.89 = ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W ) )
% 3.13/1.89 = ( X
% 3.13/1.89 = ( power_power_nat @ B @ W ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_6_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 3.13/1.89 ! [X: nat,B: nat,W: nat] :
% 3.13/1.89 ( ( ( semiri2019852685at_int @ X )
% 3.13/1.89 = ( power_power_int @ ( semiri2019852685at_int @ B ) @ W ) )
% 3.13/1.89 = ( X
% 3.13/1.89 = ( power_power_nat @ B @ W ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_7_of__nat__add,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( semiri1382578993at_nat @ ( plus_plus_nat @ M @ N ) )
% 3.13/1.89 = ( plus_plus_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_8_of__nat__add,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( semiri2019852685at_int @ ( plus_plus_nat @ M @ N ) )
% 3.13/1.89 = ( plus_plus_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_9_of__nat__mult,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( semiri1382578993at_nat @ ( times_times_nat @ M @ N ) )
% 3.13/1.89 = ( times_times_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_10_of__nat__mult,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( semiri2019852685at_int @ ( times_times_nat @ M @ N ) )
% 3.13/1.89 = ( times_times_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_11_div__mult2__eq_H,axiom,
% 3.13/1.89 ! [A: int,M: nat,N: nat] :
% 3.13/1.89 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) )
% 3.13/1.89 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri2019852685at_int @ M ) ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_12_div__mult2__eq_H,axiom,
% 3.13/1.89 ! [A: nat,M: nat,N: nat] :
% 3.13/1.89 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) )
% 3.13/1.89 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1382578993at_nat @ M ) ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_13_power__Suc,axiom,
% 3.13/1.89 ! [A: int,N: nat] :
% 3.13/1.89 ( ( power_power_int @ A @ ( suc @ N ) )
% 3.13/1.89 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_14_power__Suc,axiom,
% 3.13/1.89 ! [A: nat,N: nat] :
% 3.13/1.89 ( ( power_power_nat @ A @ ( suc @ N ) )
% 3.13/1.89 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_15_fixed__root__axioms,axiom,
% 3.13/1.89 nthRoo1352626670d_root @ p @ pm ).
% 3.13/1.89
% 3.13/1.89 thf(fact_16_old_Onat_Oinject,axiom,
% 3.13/1.89 ! [Nat: nat,Nat2: nat] :
% 3.13/1.89 ( ( ( suc @ Nat )
% 3.13/1.89 = ( suc @ Nat2 ) )
% 3.13/1.89 = ( Nat = Nat2 ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_17_nat_Oinject,axiom,
% 3.13/1.89 ! [X2: nat,Y2: nat] :
% 3.13/1.89 ( ( ( suc @ X2 )
% 3.13/1.89 = ( suc @ Y2 ) )
% 3.13/1.89 = ( X2 = Y2 ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_18_of__nat__eq__iff,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( ( semiri2019852685at_int @ M )
% 3.13/1.89 = ( semiri2019852685at_int @ N ) )
% 3.13/1.89 = ( M = N ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_19_of__nat__eq__iff,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( ( semiri1382578993at_nat @ M )
% 3.13/1.89 = ( semiri1382578993at_nat @ N ) )
% 3.13/1.89 = ( M = N ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_20_p,axiom,
% 3.13/1.89 ( p
% 3.13/1.89 = ( suc @ pm ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_21_add__Suc__right,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 3.13/1.89 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_22_mult__Suc__right,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( times_times_nat @ M @ ( suc @ N ) )
% 3.13/1.89 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_23_add__mult__distrib,axiom,
% 3.13/1.89 ! [M: nat,N: nat,K: nat] :
% 3.13/1.89 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 3.13/1.89 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_24_add__mult__distrib2,axiom,
% 3.13/1.89 ! [K: nat,M: nat,N: nat] :
% 3.13/1.89 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 3.13/1.89 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_25_mult__Suc,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( times_times_nat @ ( suc @ M ) @ N )
% 3.13/1.89 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_26_div__mult2__eq,axiom,
% 3.13/1.89 ! [M: nat,N: nat,Q: nat] :
% 3.13/1.89 ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q ) )
% 3.13/1.89 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_27_power__mult,axiom,
% 3.13/1.89 ! [A: int,M: nat,N: nat] :
% 3.13/1.89 ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 3.13/1.89 = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_28_power__mult,axiom,
% 3.13/1.89 ! [A: nat,M: nat,N: nat] :
% 3.13/1.89 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 3.13/1.89 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_29_add__Suc,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 3.13/1.89 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_30_nat__arith_Osuc1,axiom,
% 3.13/1.89 ! [A2: nat,K: nat,A: nat] :
% 3.13/1.89 ( ( A2
% 3.13/1.89 = ( plus_plus_nat @ K @ A ) )
% 3.13/1.89 => ( ( suc @ A2 )
% 3.13/1.89 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_31_add__Suc__shift,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 3.13/1.89 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_32_Suc__mult__cancel1,axiom,
% 3.13/1.89 ! [K: nat,M: nat,N: nat] :
% 3.13/1.89 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 3.13/1.89 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 3.13/1.89 = ( M = N ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_33_power__add,axiom,
% 3.13/1.89 ! [A: int,M: nat,N: nat] :
% 3.13/1.89 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 3.13/1.89 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_34_power__add,axiom,
% 3.13/1.89 ! [A: nat,M: nat,N: nat] :
% 3.13/1.89 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 3.13/1.89 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_35_n__not__Suc__n,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( N
% 3.13/1.89 != ( suc @ N ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_36_Suc__inject,axiom,
% 3.13/1.89 ! [X: nat,Y: nat] :
% 3.13/1.89 ( ( ( suc @ X )
% 3.13/1.89 = ( suc @ Y ) )
% 3.13/1.89 => ( X = Y ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_37_power__commuting__commutes,axiom,
% 3.13/1.89 ! [X: int,Y: int,N: nat] :
% 3.13/1.89 ( ( ( times_times_int @ X @ Y )
% 3.13/1.89 = ( times_times_int @ Y @ X ) )
% 3.13/1.89 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y )
% 3.13/1.89 = ( times_times_int @ Y @ ( power_power_int @ X @ N ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_38_power__commuting__commutes,axiom,
% 3.13/1.89 ! [X: nat,Y: nat,N: nat] :
% 3.13/1.89 ( ( ( times_times_nat @ X @ Y )
% 3.13/1.89 = ( times_times_nat @ Y @ X ) )
% 3.13/1.89 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y )
% 3.13/1.89 = ( times_times_nat @ Y @ ( power_power_nat @ X @ N ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_39_power__mult__distrib,axiom,
% 3.13/1.89 ! [A: int,B: int,N: nat] :
% 3.13/1.89 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 3.13/1.89 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_40_power__mult__distrib,axiom,
% 3.13/1.89 ! [A: nat,B: nat,N: nat] :
% 3.13/1.89 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 3.13/1.89 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_41_power__commutes,axiom,
% 3.13/1.89 ! [A: int,N: nat] :
% 3.13/1.89 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 3.13/1.89 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_42_power__commutes,axiom,
% 3.13/1.89 ! [A: nat,N: nat] :
% 3.13/1.89 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 3.13/1.89 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_43_mult__of__nat__commute,axiom,
% 3.13/1.89 ! [X: nat,Y: int] :
% 3.13/1.89 ( ( times_times_int @ ( semiri2019852685at_int @ X ) @ Y )
% 3.13/1.89 = ( times_times_int @ Y @ ( semiri2019852685at_int @ X ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_44_mult__of__nat__commute,axiom,
% 3.13/1.89 ! [X: nat,Y: nat] :
% 3.13/1.89 ( ( times_times_nat @ ( semiri1382578993at_nat @ X ) @ Y )
% 3.13/1.89 = ( times_times_nat @ Y @ ( semiri1382578993at_nat @ X ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_45_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( semiri2019852685at_int @ ( divide_divide_nat @ M @ N ) )
% 3.13/1.89 = ( divide_divide_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_46_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( semiri1382578993at_nat @ ( divide_divide_nat @ M @ N ) )
% 3.13/1.89 = ( divide_divide_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_47_power__Suc2,axiom,
% 3.13/1.89 ! [A: int,N: nat] :
% 3.13/1.89 ( ( power_power_int @ A @ ( suc @ N ) )
% 3.13/1.89 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_48_power__Suc2,axiom,
% 3.13/1.89 ! [A: nat,N: nat] :
% 3.13/1.89 ( ( power_power_nat @ A @ ( suc @ N ) )
% 3.13/1.89 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_49_int__ops_I7_J,axiom,
% 3.13/1.89 ! [A: nat,B: nat] :
% 3.13/1.89 ( ( semiri2019852685at_int @ ( times_times_nat @ A @ B ) )
% 3.13/1.89 = ( times_times_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_50_zadd__int__left,axiom,
% 3.13/1.89 ! [M: nat,N: nat,Z: int] :
% 3.13/1.89 ( ( plus_plus_int @ ( semiri2019852685at_int @ M ) @ ( plus_plus_int @ ( semiri2019852685at_int @ N ) @ Z ) )
% 3.13/1.89 = ( plus_plus_int @ ( semiri2019852685at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_51_int__plus,axiom,
% 3.13/1.89 ! [N: nat,M: nat] :
% 3.13/1.89 ( ( semiri2019852685at_int @ ( plus_plus_nat @ N @ M ) )
% 3.13/1.89 = ( plus_plus_int @ ( semiri2019852685at_int @ N ) @ ( semiri2019852685at_int @ M ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_52_int__ops_I5_J,axiom,
% 3.13/1.89 ! [A: nat,B: nat] :
% 3.13/1.89 ( ( semiri2019852685at_int @ ( plus_plus_nat @ A @ B ) )
% 3.13/1.89 = ( plus_plus_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_53_add__right__cancel,axiom,
% 3.13/1.89 ! [B: int,A: int,C: int] :
% 3.13/1.89 ( ( ( plus_plus_int @ B @ A )
% 3.13/1.89 = ( plus_plus_int @ C @ A ) )
% 3.13/1.89 = ( B = C ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_54_add__right__cancel,axiom,
% 3.13/1.89 ! [B: nat,A: nat,C: nat] :
% 3.13/1.89 ( ( ( plus_plus_nat @ B @ A )
% 3.13/1.89 = ( plus_plus_nat @ C @ A ) )
% 3.13/1.89 = ( B = C ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_55_add__left__cancel,axiom,
% 3.13/1.89 ! [A: int,B: int,C: int] :
% 3.13/1.89 ( ( ( plus_plus_int @ A @ B )
% 3.13/1.89 = ( plus_plus_int @ A @ C ) )
% 3.13/1.89 = ( B = C ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_56_add__left__cancel,axiom,
% 3.13/1.89 ! [A: nat,B: nat,C: nat] :
% 3.13/1.89 ( ( ( plus_plus_nat @ A @ B )
% 3.13/1.89 = ( plus_plus_nat @ A @ C ) )
% 3.13/1.89 = ( B = C ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_57_zdiv__int,axiom,
% 3.13/1.89 ! [A: nat,B: nat] :
% 3.13/1.89 ( ( semiri2019852685at_int @ ( divide_divide_nat @ A @ B ) )
% 3.13/1.89 = ( divide_divide_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_58_int__distrib_I1_J,axiom,
% 3.13/1.89 ! [Z1: int,Z2: int,W: int] :
% 3.13/1.89 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z2 ) @ W )
% 3.13/1.89 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z2 @ W ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_59_int__distrib_I2_J,axiom,
% 3.13/1.89 ! [W: int,Z1: int,Z2: int] :
% 3.13/1.89 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z2 ) )
% 3.13/1.89 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z2 ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_60_left__add__mult__distrib,axiom,
% 3.13/1.89 ! [I: nat,U: nat,J: nat,K: nat] :
% 3.13/1.89 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 3.13/1.89 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_61_crossproduct__noteq,axiom,
% 3.13/1.89 ! [A: int,B: int,C: int,D: int] :
% 3.13/1.89 ( ( ( A != B )
% 3.13/1.89 & ( C != D ) )
% 3.13/1.89 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 3.13/1.89 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_62_crossproduct__noteq,axiom,
% 3.13/1.89 ! [A: nat,B: nat,C: nat,D: nat] :
% 3.13/1.89 ( ( ( A != B )
% 3.13/1.89 & ( C != D ) )
% 3.13/1.89 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 3.13/1.89 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_63_fixed__root_Op,axiom,
% 3.13/1.89 ! [P: nat,Pm: nat] :
% 3.13/1.89 ( ( nthRoo1352626670d_root @ P @ Pm )
% 3.13/1.89 => ( P
% 3.13/1.89 = ( suc @ Pm ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_64_fixed__root__def,axiom,
% 3.13/1.89 ( nthRoo1352626670d_root
% 3.13/1.89 = ( ^ [P2: nat,Pm2: nat] :
% 3.13/1.89 ( P2
% 3.13/1.89 = ( suc @ Pm2 ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_65_fixed__root_Ointro,axiom,
% 3.13/1.89 ! [P: nat,Pm: nat] :
% 3.13/1.89 ( ( P
% 3.13/1.89 = ( suc @ Pm ) )
% 3.13/1.89 => ( nthRoo1352626670d_root @ P @ Pm ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_66_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 3.13/1.89 ! [A: int,B: int,C: int] :
% 3.13/1.89 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 3.13/1.89 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_67_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 3.13/1.89 ! [A: nat,B: nat,C: nat] :
% 3.13/1.89 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 3.13/1.89 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_68_mult_Oassoc,axiom,
% 3.13/1.89 ! [A: int,B: int,C: int] :
% 3.13/1.89 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 3.13/1.89 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_69_mult_Oassoc,axiom,
% 3.13/1.89 ! [A: nat,B: nat,C: nat] :
% 3.13/1.89 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 3.13/1.89 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_70_mult_Ocommute,axiom,
% 3.13/1.89 ( times_times_int
% 3.13/1.89 = ( ^ [A3: int,B2: int] : ( times_times_int @ B2 @ A3 ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_71_mult_Ocommute,axiom,
% 3.13/1.89 ( times_times_nat
% 3.13/1.89 = ( ^ [A3: nat,B2: nat] : ( times_times_nat @ B2 @ A3 ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_72_mult_Oleft__commute,axiom,
% 3.13/1.89 ! [B: int,A: int,C: int] :
% 3.13/1.89 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 3.13/1.89 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_73_mult_Oleft__commute,axiom,
% 3.13/1.89 ! [B: nat,A: nat,C: nat] :
% 3.13/1.89 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 3.13/1.89 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_74_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 3.13/1.89 ! [A: int,B: int,C: int] :
% 3.13/1.89 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 3.13/1.89 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_75_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 3.13/1.89 ! [A: nat,B: nat,C: nat] :
% 3.13/1.89 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 3.13/1.89 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_76_add__mono__thms__linordered__semiring_I4_J,axiom,
% 3.13/1.89 ! [I: int,J: int,K: int,L: int] :
% 3.13/1.89 ( ( ( I = J )
% 3.13/1.89 & ( K = L ) )
% 3.13/1.89 => ( ( plus_plus_int @ I @ K )
% 3.13/1.89 = ( plus_plus_int @ J @ L ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_77_add__mono__thms__linordered__semiring_I4_J,axiom,
% 3.13/1.89 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.13/1.89 ( ( ( I = J )
% 3.13/1.89 & ( K = L ) )
% 3.13/1.89 => ( ( plus_plus_nat @ I @ K )
% 3.13/1.89 = ( plus_plus_nat @ J @ L ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_78_group__cancel_Oadd1,axiom,
% 3.13/1.89 ! [A2: int,K: int,A: int,B: int] :
% 3.13/1.89 ( ( A2
% 3.13/1.89 = ( plus_plus_int @ K @ A ) )
% 3.13/1.89 => ( ( plus_plus_int @ A2 @ B )
% 3.13/1.89 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_79_group__cancel_Oadd1,axiom,
% 3.13/1.89 ! [A2: nat,K: nat,A: nat,B: nat] :
% 3.13/1.89 ( ( A2
% 3.13/1.89 = ( plus_plus_nat @ K @ A ) )
% 3.13/1.89 => ( ( plus_plus_nat @ A2 @ B )
% 3.13/1.89 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_80_group__cancel_Oadd2,axiom,
% 3.13/1.89 ! [B3: int,K: int,B: int,A: int] :
% 3.13/1.89 ( ( B3
% 3.13/1.89 = ( plus_plus_int @ K @ B ) )
% 3.13/1.89 => ( ( plus_plus_int @ A @ B3 )
% 3.13/1.89 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_81_group__cancel_Oadd2,axiom,
% 3.13/1.89 ! [B3: nat,K: nat,B: nat,A: nat] :
% 3.13/1.89 ( ( B3
% 3.13/1.89 = ( plus_plus_nat @ K @ B ) )
% 3.13/1.89 => ( ( plus_plus_nat @ A @ B3 )
% 3.13/1.89 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_82_add_Oassoc,axiom,
% 3.13/1.89 ! [A: int,B: int,C: int] :
% 3.13/1.89 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 3.13/1.89 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_83_add_Oassoc,axiom,
% 3.13/1.89 ! [A: nat,B: nat,C: nat] :
% 3.13/1.89 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 3.13/1.89 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_84_add_Oleft__cancel,axiom,
% 3.13/1.89 ! [A: int,B: int,C: int] :
% 3.13/1.89 ( ( ( plus_plus_int @ A @ B )
% 3.13/1.89 = ( plus_plus_int @ A @ C ) )
% 3.13/1.89 = ( B = C ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_85_add_Oright__cancel,axiom,
% 3.13/1.89 ! [B: int,A: int,C: int] :
% 3.13/1.89 ( ( ( plus_plus_int @ B @ A )
% 3.13/1.89 = ( plus_plus_int @ C @ A ) )
% 3.13/1.89 = ( B = C ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_86_add_Ocommute,axiom,
% 3.13/1.89 ( plus_plus_int
% 3.13/1.89 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_87_add_Ocommute,axiom,
% 3.13/1.89 ( plus_plus_nat
% 3.13/1.89 = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_88_add_Oleft__commute,axiom,
% 3.13/1.89 ! [B: int,A: int,C: int] :
% 3.13/1.89 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 3.13/1.89 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_89_add_Oleft__commute,axiom,
% 3.13/1.89 ! [B: nat,A: nat,C: nat] :
% 3.13/1.89 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 3.13/1.89 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_90_add__left__imp__eq,axiom,
% 3.13/1.89 ! [A: int,B: int,C: int] :
% 3.13/1.89 ( ( ( plus_plus_int @ A @ B )
% 3.13/1.89 = ( plus_plus_int @ A @ C ) )
% 3.13/1.89 => ( B = C ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_91_add__left__imp__eq,axiom,
% 3.13/1.89 ! [A: nat,B: nat,C: nat] :
% 3.13/1.89 ( ( ( plus_plus_nat @ A @ B )
% 3.13/1.89 = ( plus_plus_nat @ A @ C ) )
% 3.13/1.89 => ( B = C ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_92_add__right__imp__eq,axiom,
% 3.13/1.89 ! [B: int,A: int,C: int] :
% 3.13/1.89 ( ( ( plus_plus_int @ B @ A )
% 3.13/1.89 = ( plus_plus_int @ C @ A ) )
% 3.13/1.89 => ( B = C ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_93_add__right__imp__eq,axiom,
% 3.13/1.89 ! [B: nat,A: nat,C: nat] :
% 3.13/1.89 ( ( ( plus_plus_nat @ B @ A )
% 3.13/1.89 = ( plus_plus_nat @ C @ A ) )
% 3.13/1.89 => ( B = C ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_94_nat__int__comparison_I1_J,axiom,
% 3.13/1.89 ( ( ^ [Y3: nat,Z3: nat] : ( Y3 = Z3 ) )
% 3.13/1.89 = ( ^ [A3: nat,B2: nat] :
% 3.13/1.89 ( ( semiri2019852685at_int @ A3 )
% 3.13/1.89 = ( semiri2019852685at_int @ B2 ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_95_int__if,axiom,
% 3.13/1.89 ! [P3: $o,A: nat,B: nat] :
% 3.13/1.89 ( ( P3
% 3.13/1.89 => ( ( semiri2019852685at_int @ ( if_nat @ P3 @ A @ B ) )
% 3.13/1.89 = ( semiri2019852685at_int @ A ) ) )
% 3.13/1.89 & ( ~ P3
% 3.13/1.89 => ( ( semiri2019852685at_int @ ( if_nat @ P3 @ A @ B ) )
% 3.13/1.89 = ( semiri2019852685at_int @ B ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_96_int__int__eq,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( ( semiri2019852685at_int @ M )
% 3.13/1.89 = ( semiri2019852685at_int @ N ) )
% 3.13/1.89 = ( M = N ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_97_crossproduct__eq,axiom,
% 3.13/1.89 ! [W: int,Y: int,X: int,Z: int] :
% 3.13/1.89 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 3.13/1.89 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 3.13/1.89 = ( ( W = X )
% 3.13/1.89 | ( Y = Z ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_98_crossproduct__eq,axiom,
% 3.13/1.89 ! [W: nat,Y: nat,X: nat,Z: nat] :
% 3.13/1.89 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 3.13/1.89 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 3.13/1.89 = ( ( W = X )
% 3.13/1.89 | ( Y = Z ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_99_ring__class_Oring__distribs_I2_J,axiom,
% 3.13/1.89 ! [A: int,B: int,C: int] :
% 3.13/1.89 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 3.13/1.89 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_100_ring__class_Oring__distribs_I1_J,axiom,
% 3.13/1.89 ! [A: int,B: int,C: int] :
% 3.13/1.89 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 3.13/1.89 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_101_comm__semiring__class_Odistrib,axiom,
% 3.13/1.89 ! [A: int,B: int,C: int] :
% 3.13/1.89 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 3.13/1.89 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_102_comm__semiring__class_Odistrib,axiom,
% 3.13/1.89 ! [A: nat,B: nat,C: nat] :
% 3.13/1.89 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 3.13/1.89 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_103_distrib__left,axiom,
% 3.13/1.89 ! [A: int,B: int,C: int] :
% 3.13/1.89 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 3.13/1.89 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_104_distrib__left,axiom,
% 3.13/1.89 ! [A: nat,B: nat,C: nat] :
% 3.13/1.89 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 3.13/1.89 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_105_distrib__right,axiom,
% 3.13/1.89 ! [A: int,B: int,C: int] :
% 3.13/1.89 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 3.13/1.89 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_106_distrib__right,axiom,
% 3.13/1.89 ! [A: nat,B: nat,C: nat] :
% 3.13/1.89 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 3.13/1.89 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_107_combine__common__factor,axiom,
% 3.13/1.89 ! [A: int,E: int,B: int,C: int] :
% 3.13/1.89 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 3.13/1.89 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_108_combine__common__factor,axiom,
% 3.13/1.89 ! [A: nat,E: nat,B: nat,C: nat] :
% 3.13/1.89 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 3.13/1.89 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_109__092_060open_062_092_060And_062n_O_Ax_A_L_Ax_A_K_An_A_061_Ax_A_K_A_I1_A_L_An_J_092_060close_062,axiom,
% 3.13/1.89 ! [N: int] :
% 3.13/1.89 ( ( plus_plus_int @ x @ ( times_times_int @ x @ N ) )
% 3.13/1.89 = ( times_times_int @ x @ ( plus_plus_int @ one_one_int @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_110_mult_Oright__neutral,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( times_times_int @ A @ one_one_int )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_111_mult_Oright__neutral,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( times_times_nat @ A @ one_one_nat )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_112_mult_Oleft__neutral,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( times_times_int @ one_one_int @ A )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_113_mult_Oleft__neutral,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( times_times_nat @ one_one_nat @ A )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_114_div__by__1,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( divide_divide_int @ A @ one_one_int )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_115_div__by__1,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( divide_divide_nat @ A @ one_one_nat )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_116_power__one,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( power_power_int @ one_one_int @ N )
% 3.13/1.89 = one_one_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_117_power__one,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( power_power_nat @ one_one_nat @ N )
% 3.13/1.89 = one_one_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_118_of__nat__eq__1__iff,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( ( semiri2019852685at_int @ N )
% 3.13/1.89 = one_one_int )
% 3.13/1.89 = ( N = one_one_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_119_of__nat__eq__1__iff,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( ( semiri1382578993at_nat @ N )
% 3.13/1.89 = one_one_nat )
% 3.13/1.89 = ( N = one_one_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_120_of__nat__1__eq__iff,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( one_one_int
% 3.13/1.89 = ( semiri2019852685at_int @ N ) )
% 3.13/1.89 = ( N = one_one_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_121_of__nat__1__eq__iff,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( one_one_nat
% 3.13/1.89 = ( semiri1382578993at_nat @ N ) )
% 3.13/1.89 = ( N = one_one_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_122_of__nat__1,axiom,
% 3.13/1.89 ( ( semiri2019852685at_int @ one_one_nat )
% 3.13/1.89 = one_one_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_123_of__nat__1,axiom,
% 3.13/1.89 ( ( semiri1382578993at_nat @ one_one_nat )
% 3.13/1.89 = one_one_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_124_of__nat__Suc,axiom,
% 3.13/1.89 ! [M: nat] :
% 3.13/1.89 ( ( semiri2019852685at_int @ ( suc @ M ) )
% 3.13/1.89 = ( plus_plus_int @ one_one_int @ ( semiri2019852685at_int @ M ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_125_of__nat__Suc,axiom,
% 3.13/1.89 ! [M: nat] :
% 3.13/1.89 ( ( semiri1382578993at_nat @ ( suc @ M ) )
% 3.13/1.89 = ( plus_plus_nat @ one_one_nat @ ( semiri1382578993at_nat @ M ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_126_one__reorient,axiom,
% 3.13/1.89 ! [X: int] :
% 3.13/1.89 ( ( one_one_int = X )
% 3.13/1.89 = ( X = one_one_int ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_127_one__reorient,axiom,
% 3.13/1.89 ! [X: nat] :
% 3.13/1.89 ( ( one_one_nat = X )
% 3.13/1.89 = ( X = one_one_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_128_mult_Ocomm__neutral,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( times_times_int @ A @ one_one_int )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_129_mult_Ocomm__neutral,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( times_times_nat @ A @ one_one_nat )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_130_comm__monoid__mult__class_Omult__1,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( times_times_int @ one_one_int @ A )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_131_comm__monoid__mult__class_Omult__1,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( times_times_nat @ one_one_nat @ A )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_132_left__right__inverse__power,axiom,
% 3.13/1.89 ! [X: int,Y: int,N: nat] :
% 3.13/1.89 ( ( ( times_times_int @ X @ Y )
% 3.13/1.89 = one_one_int )
% 3.13/1.89 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 3.13/1.89 = one_one_int ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_133_left__right__inverse__power,axiom,
% 3.13/1.89 ! [X: nat,Y: nat,N: nat] :
% 3.13/1.89 ( ( ( times_times_nat @ X @ Y )
% 3.13/1.89 = one_one_nat )
% 3.13/1.89 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) )
% 3.13/1.89 = one_one_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_134_int__Suc,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( semiri2019852685at_int @ ( suc @ N ) )
% 3.13/1.89 = ( plus_plus_int @ ( semiri2019852685at_int @ N ) @ one_one_int ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_135_int__ops_I4_J,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( semiri2019852685at_int @ ( suc @ A ) )
% 3.13/1.89 = ( plus_plus_int @ ( semiri2019852685at_int @ A ) @ one_one_int ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_136_bits__div__by__1,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( divide_divide_int @ A @ one_one_int )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_137_bits__div__by__1,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( divide_divide_nat @ A @ one_one_nat )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_138_distrib__right__NO__MATCH,axiom,
% 3.13/1.89 ! [X: int,Y: int,C: int,A: int,B: int] :
% 3.13/1.89 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ C )
% 3.13/1.89 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 3.13/1.89 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_139_distrib__right__NO__MATCH,axiom,
% 3.13/1.89 ! [X: int,Y: int,C: nat,A: nat,B: nat] :
% 3.13/1.89 ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ C )
% 3.13/1.89 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 3.13/1.89 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_140_distrib__right__NO__MATCH,axiom,
% 3.13/1.89 ! [X: nat,Y: nat,C: int,A: int,B: int] :
% 3.13/1.89 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ C )
% 3.13/1.89 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 3.13/1.89 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_141_distrib__right__NO__MATCH,axiom,
% 3.13/1.89 ! [X: nat,Y: nat,C: nat,A: nat,B: nat] :
% 3.13/1.89 ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ C )
% 3.13/1.89 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 3.13/1.89 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_142_distrib__left__NO__MATCH,axiom,
% 3.13/1.89 ! [X: int,Y: int,A: int,B: int,C: int] :
% 3.13/1.89 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ A )
% 3.13/1.89 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 3.13/1.89 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_143_distrib__left__NO__MATCH,axiom,
% 3.13/1.89 ! [X: int,Y: int,A: nat,B: nat,C: nat] :
% 3.13/1.89 ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ A )
% 3.13/1.89 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 3.13/1.89 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_144_distrib__left__NO__MATCH,axiom,
% 3.13/1.89 ! [X: nat,Y: nat,A: int,B: int,C: int] :
% 3.13/1.89 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ A )
% 3.13/1.89 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 3.13/1.89 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_145_distrib__left__NO__MATCH,axiom,
% 3.13/1.89 ! [X: nat,Y: nat,A: nat,B: nat,C: nat] :
% 3.13/1.89 ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ A )
% 3.13/1.89 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 3.13/1.89 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_146_Nat_Oadd__0__right,axiom,
% 3.13/1.89 ! [M: nat] :
% 3.13/1.89 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 3.13/1.89 = M ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_147_add__is__0,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( ( plus_plus_nat @ M @ N )
% 3.13/1.89 = zero_zero_nat )
% 3.13/1.89 = ( ( M = zero_zero_nat )
% 3.13/1.89 & ( N = zero_zero_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_148_mult__cancel2,axiom,
% 3.13/1.89 ! [M: nat,K: nat,N: nat] :
% 3.13/1.89 ( ( ( times_times_nat @ M @ K )
% 3.13/1.89 = ( times_times_nat @ N @ K ) )
% 3.13/1.89 = ( ( M = N )
% 3.13/1.89 | ( K = zero_zero_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_149_mult__cancel1,axiom,
% 3.13/1.89 ! [K: nat,M: nat,N: nat] :
% 3.13/1.89 ( ( ( times_times_nat @ K @ M )
% 3.13/1.89 = ( times_times_nat @ K @ N ) )
% 3.13/1.89 = ( ( M = N )
% 3.13/1.89 | ( K = zero_zero_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_150_mult__0__right,axiom,
% 3.13/1.89 ! [M: nat] :
% 3.13/1.89 ( ( times_times_nat @ M @ zero_zero_nat )
% 3.13/1.89 = zero_zero_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_151_mult__is__0,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( ( times_times_nat @ M @ N )
% 3.13/1.89 = zero_zero_nat )
% 3.13/1.89 = ( ( M = zero_zero_nat )
% 3.13/1.89 | ( N = zero_zero_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_152_mult__cancel__right,axiom,
% 3.13/1.89 ! [A: int,C: int,B: int] :
% 3.13/1.89 ( ( ( times_times_int @ A @ C )
% 3.13/1.89 = ( times_times_int @ B @ C ) )
% 3.13/1.89 = ( ( C = zero_zero_int )
% 3.13/1.89 | ( A = B ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_153_mult__cancel__right,axiom,
% 3.13/1.89 ! [A: nat,C: nat,B: nat] :
% 3.13/1.89 ( ( ( times_times_nat @ A @ C )
% 3.13/1.89 = ( times_times_nat @ B @ C ) )
% 3.13/1.89 = ( ( C = zero_zero_nat )
% 3.13/1.89 | ( A = B ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_154_mult__cancel__left,axiom,
% 3.13/1.89 ! [C: int,A: int,B: int] :
% 3.13/1.89 ( ( ( times_times_int @ C @ A )
% 3.13/1.89 = ( times_times_int @ C @ B ) )
% 3.13/1.89 = ( ( C = zero_zero_int )
% 3.13/1.89 | ( A = B ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_155_mult__cancel__left,axiom,
% 3.13/1.89 ! [C: nat,A: nat,B: nat] :
% 3.13/1.89 ( ( ( times_times_nat @ C @ A )
% 3.13/1.89 = ( times_times_nat @ C @ B ) )
% 3.13/1.89 = ( ( C = zero_zero_nat )
% 3.13/1.89 | ( A = B ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_156_mult__eq__0__iff,axiom,
% 3.13/1.89 ! [A: int,B: int] :
% 3.13/1.89 ( ( ( times_times_int @ A @ B )
% 3.13/1.89 = zero_zero_int )
% 3.13/1.89 = ( ( A = zero_zero_int )
% 3.13/1.89 | ( B = zero_zero_int ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_157_mult__eq__0__iff,axiom,
% 3.13/1.89 ! [A: nat,B: nat] :
% 3.13/1.89 ( ( ( times_times_nat @ A @ B )
% 3.13/1.89 = zero_zero_nat )
% 3.13/1.89 = ( ( A = zero_zero_nat )
% 3.13/1.89 | ( B = zero_zero_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_158_mult__zero__right,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( times_times_int @ A @ zero_zero_int )
% 3.13/1.89 = zero_zero_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_159_mult__zero__right,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( times_times_nat @ A @ zero_zero_nat )
% 3.13/1.89 = zero_zero_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_160_mult__zero__left,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( times_times_int @ zero_zero_int @ A )
% 3.13/1.89 = zero_zero_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_161_mult__zero__left,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( times_times_nat @ zero_zero_nat @ A )
% 3.13/1.89 = zero_zero_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_162_add_Oleft__neutral,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_163_add_Oleft__neutral,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( plus_plus_int @ zero_zero_int @ A )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_164_add_Oright__neutral,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_165_add_Oright__neutral,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( plus_plus_int @ A @ zero_zero_int )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_166_double__zero,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( ( plus_plus_int @ A @ A )
% 3.13/1.89 = zero_zero_int )
% 3.13/1.89 = ( A = zero_zero_int ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_167_double__zero__sym,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( zero_zero_int
% 3.13/1.89 = ( plus_plus_int @ A @ A ) )
% 3.13/1.89 = ( A = zero_zero_int ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_168_add__cancel__left__left,axiom,
% 3.13/1.89 ! [B: nat,A: nat] :
% 3.13/1.89 ( ( ( plus_plus_nat @ B @ A )
% 3.13/1.89 = A )
% 3.13/1.89 = ( B = zero_zero_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_169_add__cancel__left__left,axiom,
% 3.13/1.89 ! [B: int,A: int] :
% 3.13/1.89 ( ( ( plus_plus_int @ B @ A )
% 3.13/1.89 = A )
% 3.13/1.89 = ( B = zero_zero_int ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_170_add__cancel__left__right,axiom,
% 3.13/1.89 ! [A: nat,B: nat] :
% 3.13/1.89 ( ( ( plus_plus_nat @ A @ B )
% 3.13/1.89 = A )
% 3.13/1.89 = ( B = zero_zero_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_171_add__cancel__left__right,axiom,
% 3.13/1.89 ! [A: int,B: int] :
% 3.13/1.89 ( ( ( plus_plus_int @ A @ B )
% 3.13/1.89 = A )
% 3.13/1.89 = ( B = zero_zero_int ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_172_add__cancel__right__left,axiom,
% 3.13/1.89 ! [A: nat,B: nat] :
% 3.13/1.89 ( ( A
% 3.13/1.89 = ( plus_plus_nat @ B @ A ) )
% 3.13/1.89 = ( B = zero_zero_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_173_add__cancel__right__left,axiom,
% 3.13/1.89 ! [A: int,B: int] :
% 3.13/1.89 ( ( A
% 3.13/1.89 = ( plus_plus_int @ B @ A ) )
% 3.13/1.89 = ( B = zero_zero_int ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_174_add__cancel__right__right,axiom,
% 3.13/1.89 ! [A: nat,B: nat] :
% 3.13/1.89 ( ( A
% 3.13/1.89 = ( plus_plus_nat @ A @ B ) )
% 3.13/1.89 = ( B = zero_zero_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_175_add__cancel__right__right,axiom,
% 3.13/1.89 ! [A: int,B: int] :
% 3.13/1.89 ( ( A
% 3.13/1.89 = ( plus_plus_int @ A @ B ) )
% 3.13/1.89 = ( B = zero_zero_int ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_176_add__eq__0__iff__both__eq__0,axiom,
% 3.13/1.89 ! [X: nat,Y: nat] :
% 3.13/1.89 ( ( ( plus_plus_nat @ X @ Y )
% 3.13/1.89 = zero_zero_nat )
% 3.13/1.89 = ( ( X = zero_zero_nat )
% 3.13/1.89 & ( Y = zero_zero_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_177_zero__eq__add__iff__both__eq__0,axiom,
% 3.13/1.89 ! [X: nat,Y: nat] :
% 3.13/1.89 ( ( zero_zero_nat
% 3.13/1.89 = ( plus_plus_nat @ X @ Y ) )
% 3.13/1.89 = ( ( X = zero_zero_nat )
% 3.13/1.89 & ( Y = zero_zero_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_178_bits__div__by__0,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( divide_divide_int @ A @ zero_zero_int )
% 3.13/1.89 = zero_zero_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_179_bits__div__by__0,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 3.13/1.89 = zero_zero_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_180_bits__div__0,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( divide_divide_int @ zero_zero_int @ A )
% 3.13/1.89 = zero_zero_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_181_bits__div__0,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 3.13/1.89 = zero_zero_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_182_div__by__0,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( divide_divide_int @ A @ zero_zero_int )
% 3.13/1.89 = zero_zero_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_183_div__by__0,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 3.13/1.89 = zero_zero_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_184_div__0,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( divide_divide_int @ zero_zero_int @ A )
% 3.13/1.89 = zero_zero_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_185_div__0,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 3.13/1.89 = zero_zero_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_186_of__nat__0,axiom,
% 3.13/1.89 ( ( semiri2019852685at_int @ zero_zero_nat )
% 3.13/1.89 = zero_zero_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_187_of__nat__0,axiom,
% 3.13/1.89 ( ( semiri1382578993at_nat @ zero_zero_nat )
% 3.13/1.89 = zero_zero_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_188_of__nat__0__eq__iff,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( zero_zero_int
% 3.13/1.89 = ( semiri2019852685at_int @ N ) )
% 3.13/1.89 = ( zero_zero_nat = N ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_189_of__nat__0__eq__iff,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( zero_zero_nat
% 3.13/1.89 = ( semiri1382578993at_nat @ N ) )
% 3.13/1.89 = ( zero_zero_nat = N ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_190_of__nat__eq__0__iff,axiom,
% 3.13/1.89 ! [M: nat] :
% 3.13/1.89 ( ( ( semiri2019852685at_int @ M )
% 3.13/1.89 = zero_zero_int )
% 3.13/1.89 = ( M = zero_zero_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_191_of__nat__eq__0__iff,axiom,
% 3.13/1.89 ! [M: nat] :
% 3.13/1.89 ( ( ( semiri1382578993at_nat @ M )
% 3.13/1.89 = zero_zero_nat )
% 3.13/1.89 = ( M = zero_zero_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_192_power__Suc0__right,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_193_power__Suc0__right,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_194_one__eq__mult__iff,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( ( suc @ zero_zero_nat )
% 3.13/1.89 = ( times_times_nat @ M @ N ) )
% 3.13/1.89 = ( ( M
% 3.13/1.89 = ( suc @ zero_zero_nat ) )
% 3.13/1.89 & ( N
% 3.13/1.89 = ( suc @ zero_zero_nat ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_195_mult__eq__1__iff,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( ( times_times_nat @ M @ N )
% 3.13/1.89 = ( suc @ zero_zero_nat ) )
% 3.13/1.89 = ( ( M
% 3.13/1.89 = ( suc @ zero_zero_nat ) )
% 3.13/1.89 & ( N
% 3.13/1.89 = ( suc @ zero_zero_nat ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_196_power__one__right,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( power_power_int @ A @ one_one_nat )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_197_power__one__right,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( power_power_nat @ A @ one_one_nat )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_198_nat__mult__eq__1__iff,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( ( times_times_nat @ M @ N )
% 3.13/1.89 = one_one_nat )
% 3.13/1.89 = ( ( M = one_one_nat )
% 3.13/1.89 & ( N = one_one_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_199_nat__1__eq__mult__iff,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( one_one_nat
% 3.13/1.89 = ( times_times_nat @ M @ N ) )
% 3.13/1.89 = ( ( M = one_one_nat )
% 3.13/1.89 & ( N = one_one_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_200_div__by__Suc__0,axiom,
% 3.13/1.89 ! [M: nat] :
% 3.13/1.89 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 3.13/1.89 = M ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_201_gbinomial__0_I1_J,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( gbinomial_int @ A @ zero_zero_nat )
% 3.13/1.89 = one_one_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_202_gbinomial__0_I1_J,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 3.13/1.89 = one_one_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_203_nat__power__eq__Suc__0__iff,axiom,
% 3.13/1.89 ! [X: nat,M: nat] :
% 3.13/1.89 ( ( ( power_power_nat @ X @ M )
% 3.13/1.89 = ( suc @ zero_zero_nat ) )
% 3.13/1.89 = ( ( M = zero_zero_nat )
% 3.13/1.89 | ( X
% 3.13/1.89 = ( suc @ zero_zero_nat ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_204_power__Suc__0,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 3.13/1.89 = ( suc @ zero_zero_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_205_nat__mult__div__cancel__disj,axiom,
% 3.13/1.89 ! [K: nat,M: nat,N: nat] :
% 3.13/1.89 ( ( ( K = zero_zero_nat )
% 3.13/1.89 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 3.13/1.89 = zero_zero_nat ) )
% 3.13/1.89 & ( ( K != zero_zero_nat )
% 3.13/1.89 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 3.13/1.89 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_206_gbinomial__Suc0,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( gbinomial_nat @ A @ ( suc @ zero_zero_nat ) )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_207_gbinomial__Suc0,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( gbinomial_int @ A @ ( suc @ zero_zero_nat ) )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_208_gbinomial__1,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( gbinomial_nat @ A @ one_one_nat )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_209_gbinomial__1,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( gbinomial_int @ A @ one_one_nat )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_210_sum__squares__eq__zero__iff,axiom,
% 3.13/1.89 ! [X: int,Y: int] :
% 3.13/1.89 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 3.13/1.89 = zero_zero_int )
% 3.13/1.89 = ( ( X = zero_zero_int )
% 3.13/1.89 & ( Y = zero_zero_int ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_211_mult__cancel__left1,axiom,
% 3.13/1.89 ! [C: int,B: int] :
% 3.13/1.89 ( ( C
% 3.13/1.89 = ( times_times_int @ C @ B ) )
% 3.13/1.89 = ( ( C = zero_zero_int )
% 3.13/1.89 | ( B = one_one_int ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_212_mult__cancel__left2,axiom,
% 3.13/1.89 ! [C: int,A: int] :
% 3.13/1.89 ( ( ( times_times_int @ C @ A )
% 3.13/1.89 = C )
% 3.13/1.89 = ( ( C = zero_zero_int )
% 3.13/1.89 | ( A = one_one_int ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_213_mult__cancel__right1,axiom,
% 3.13/1.89 ! [C: int,B: int] :
% 3.13/1.89 ( ( C
% 3.13/1.89 = ( times_times_int @ B @ C ) )
% 3.13/1.89 = ( ( C = zero_zero_int )
% 3.13/1.89 | ( B = one_one_int ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_214_mult__cancel__right2,axiom,
% 3.13/1.89 ! [A: int,C: int] :
% 3.13/1.89 ( ( ( times_times_int @ A @ C )
% 3.13/1.89 = C )
% 3.13/1.89 = ( ( C = zero_zero_int )
% 3.13/1.89 | ( A = one_one_int ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_215_div__mult__mult1,axiom,
% 3.13/1.89 ! [C: int,A: int,B: int] :
% 3.13/1.89 ( ( C != zero_zero_int )
% 3.13/1.89 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 3.13/1.89 = ( divide_divide_int @ A @ B ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_216_div__mult__mult1,axiom,
% 3.13/1.89 ! [C: nat,A: nat,B: nat] :
% 3.13/1.89 ( ( C != zero_zero_nat )
% 3.13/1.89 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 3.13/1.89 = ( divide_divide_nat @ A @ B ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_217_div__mult__mult2,axiom,
% 3.13/1.89 ! [C: int,A: int,B: int] :
% 3.13/1.89 ( ( C != zero_zero_int )
% 3.13/1.89 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 3.13/1.89 = ( divide_divide_int @ A @ B ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_218_div__mult__mult2,axiom,
% 3.13/1.89 ! [C: nat,A: nat,B: nat] :
% 3.13/1.89 ( ( C != zero_zero_nat )
% 3.13/1.89 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 3.13/1.89 = ( divide_divide_nat @ A @ B ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_219_div__mult__mult1__if,axiom,
% 3.13/1.89 ! [C: int,A: int,B: int] :
% 3.13/1.89 ( ( ( C = zero_zero_int )
% 3.13/1.89 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 3.13/1.89 = zero_zero_int ) )
% 3.13/1.89 & ( ( C != zero_zero_int )
% 3.13/1.89 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 3.13/1.89 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_220_div__mult__mult1__if,axiom,
% 3.13/1.89 ! [C: nat,A: nat,B: nat] :
% 3.13/1.89 ( ( ( C = zero_zero_nat )
% 3.13/1.89 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 3.13/1.89 = zero_zero_nat ) )
% 3.13/1.89 & ( ( C != zero_zero_nat )
% 3.13/1.89 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 3.13/1.89 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_221_nonzero__mult__div__cancel__left,axiom,
% 3.13/1.89 ! [A: int,B: int] :
% 3.13/1.89 ( ( A != zero_zero_int )
% 3.13/1.89 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 3.13/1.89 = B ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_222_nonzero__mult__div__cancel__left,axiom,
% 3.13/1.89 ! [A: nat,B: nat] :
% 3.13/1.89 ( ( A != zero_zero_nat )
% 3.13/1.89 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 3.13/1.89 = B ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_223_nonzero__mult__div__cancel__right,axiom,
% 3.13/1.89 ! [B: int,A: int] :
% 3.13/1.89 ( ( B != zero_zero_int )
% 3.13/1.89 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 3.13/1.89 = A ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_224_nonzero__mult__div__cancel__right,axiom,
% 3.13/1.89 ! [B: nat,A: nat] :
% 3.13/1.89 ( ( B != zero_zero_nat )
% 3.13/1.89 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 3.13/1.89 = A ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_225_div__self,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( A != zero_zero_int )
% 3.13/1.89 => ( ( divide_divide_int @ A @ A )
% 3.13/1.89 = one_one_int ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_226_div__self,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( A != zero_zero_nat )
% 3.13/1.89 => ( ( divide_divide_nat @ A @ A )
% 3.13/1.89 = one_one_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_227_power__0__Suc,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 3.13/1.89 = zero_zero_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_228_power__0__Suc,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 3.13/1.89 = zero_zero_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_229_gbinomial__0_I2_J,axiom,
% 3.13/1.89 ! [K: nat] :
% 3.13/1.89 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 3.13/1.89 = zero_zero_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_230_gbinomial__0_I2_J,axiom,
% 3.13/1.89 ! [K: nat] :
% 3.13/1.89 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 3.13/1.89 = zero_zero_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_231_div__mult__self1,axiom,
% 3.13/1.89 ! [B: int,A: int,C: int] :
% 3.13/1.89 ( ( B != zero_zero_int )
% 3.13/1.89 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 3.13/1.89 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_232_div__mult__self1,axiom,
% 3.13/1.89 ! [B: nat,A: nat,C: nat] :
% 3.13/1.89 ( ( B != zero_zero_nat )
% 3.13/1.89 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 3.13/1.89 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_233_div__mult__self2,axiom,
% 3.13/1.89 ! [B: int,A: int,C: int] :
% 3.13/1.89 ( ( B != zero_zero_int )
% 3.13/1.89 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 3.13/1.89 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_234_div__mult__self2,axiom,
% 3.13/1.89 ! [B: nat,A: nat,C: nat] :
% 3.13/1.89 ( ( B != zero_zero_nat )
% 3.13/1.89 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 3.13/1.89 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_235_div__mult__self3,axiom,
% 3.13/1.89 ! [B: int,C: int,A: int] :
% 3.13/1.89 ( ( B != zero_zero_int )
% 3.13/1.89 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 3.13/1.89 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_236_div__mult__self3,axiom,
% 3.13/1.89 ! [B: nat,C: nat,A: nat] :
% 3.13/1.89 ( ( B != zero_zero_nat )
% 3.13/1.89 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 3.13/1.89 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_237_div__mult__self4,axiom,
% 3.13/1.89 ! [B: int,C: int,A: int] :
% 3.13/1.89 ( ( B != zero_zero_int )
% 3.13/1.89 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 3.13/1.89 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_238_div__mult__self4,axiom,
% 3.13/1.89 ! [B: nat,C: nat,A: nat] :
% 3.13/1.89 ( ( B != zero_zero_nat )
% 3.13/1.89 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 3.13/1.89 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_239_One__nat__def,axiom,
% 3.13/1.89 ( one_one_nat
% 3.13/1.89 = ( suc @ zero_zero_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_240_mult__eq__self__implies__10,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( M
% 3.13/1.89 = ( times_times_nat @ M @ N ) )
% 3.13/1.89 => ( ( N = one_one_nat )
% 3.13/1.89 | ( M = zero_zero_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_241_zero__reorient,axiom,
% 3.13/1.89 ! [X: nat] :
% 3.13/1.89 ( ( zero_zero_nat = X )
% 3.13/1.89 = ( X = zero_zero_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_242_zero__reorient,axiom,
% 3.13/1.89 ! [X: int] :
% 3.13/1.89 ( ( zero_zero_int = X )
% 3.13/1.89 = ( X = zero_zero_int ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_243_int__ops_I1_J,axiom,
% 3.13/1.89 ( ( semiri2019852685at_int @ zero_zero_nat )
% 3.13/1.89 = zero_zero_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_244_power__0__left,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( ( N = zero_zero_nat )
% 3.13/1.89 => ( ( power_power_int @ zero_zero_int @ N )
% 3.13/1.89 = one_one_int ) )
% 3.13/1.89 & ( ( N != zero_zero_nat )
% 3.13/1.89 => ( ( power_power_int @ zero_zero_int @ N )
% 3.13/1.89 = zero_zero_int ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_245_power__0__left,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( ( N = zero_zero_nat )
% 3.13/1.89 => ( ( power_power_nat @ zero_zero_nat @ N )
% 3.13/1.89 = one_one_nat ) )
% 3.13/1.89 & ( ( N != zero_zero_nat )
% 3.13/1.89 => ( ( power_power_nat @ zero_zero_nat @ N )
% 3.13/1.89 = zero_zero_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_246_mult__right__cancel,axiom,
% 3.13/1.89 ! [C: int,A: int,B: int] :
% 3.13/1.89 ( ( C != zero_zero_int )
% 3.13/1.89 => ( ( ( times_times_int @ A @ C )
% 3.13/1.89 = ( times_times_int @ B @ C ) )
% 3.13/1.89 = ( A = B ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_247_mult__right__cancel,axiom,
% 3.13/1.89 ! [C: nat,A: nat,B: nat] :
% 3.13/1.89 ( ( C != zero_zero_nat )
% 3.13/1.89 => ( ( ( times_times_nat @ A @ C )
% 3.13/1.89 = ( times_times_nat @ B @ C ) )
% 3.13/1.89 = ( A = B ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_248_mult__left__cancel,axiom,
% 3.13/1.89 ! [C: int,A: int,B: int] :
% 3.13/1.89 ( ( C != zero_zero_int )
% 3.13/1.89 => ( ( ( times_times_int @ C @ A )
% 3.13/1.89 = ( times_times_int @ C @ B ) )
% 3.13/1.89 = ( A = B ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_249_mult__left__cancel,axiom,
% 3.13/1.89 ! [C: nat,A: nat,B: nat] :
% 3.13/1.89 ( ( C != zero_zero_nat )
% 3.13/1.89 => ( ( ( times_times_nat @ C @ A )
% 3.13/1.89 = ( times_times_nat @ C @ B ) )
% 3.13/1.89 = ( A = B ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_250_no__zero__divisors,axiom,
% 3.13/1.89 ! [A: int,B: int] :
% 3.13/1.89 ( ( A != zero_zero_int )
% 3.13/1.89 => ( ( B != zero_zero_int )
% 3.13/1.89 => ( ( times_times_int @ A @ B )
% 3.13/1.89 != zero_zero_int ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_251_no__zero__divisors,axiom,
% 3.13/1.89 ! [A: nat,B: nat] :
% 3.13/1.89 ( ( A != zero_zero_nat )
% 3.13/1.89 => ( ( B != zero_zero_nat )
% 3.13/1.89 => ( ( times_times_nat @ A @ B )
% 3.13/1.89 != zero_zero_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_252_divisors__zero,axiom,
% 3.13/1.89 ! [A: int,B: int] :
% 3.13/1.89 ( ( ( times_times_int @ A @ B )
% 3.13/1.89 = zero_zero_int )
% 3.13/1.89 => ( ( A = zero_zero_int )
% 3.13/1.89 | ( B = zero_zero_int ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_253_divisors__zero,axiom,
% 3.13/1.89 ! [A: nat,B: nat] :
% 3.13/1.89 ( ( ( times_times_nat @ A @ B )
% 3.13/1.89 = zero_zero_nat )
% 3.13/1.89 => ( ( A = zero_zero_nat )
% 3.13/1.89 | ( B = zero_zero_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_254_mult__not__zero,axiom,
% 3.13/1.89 ! [A: int,B: int] :
% 3.13/1.89 ( ( ( times_times_int @ A @ B )
% 3.13/1.89 != zero_zero_int )
% 3.13/1.89 => ( ( A != zero_zero_int )
% 3.13/1.89 & ( B != zero_zero_int ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_255_mult__not__zero,axiom,
% 3.13/1.89 ! [A: nat,B: nat] :
% 3.13/1.89 ( ( ( times_times_nat @ A @ B )
% 3.13/1.89 != zero_zero_nat )
% 3.13/1.89 => ( ( A != zero_zero_nat )
% 3.13/1.89 & ( B != zero_zero_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_256_verit__sum__simplify,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_257_verit__sum__simplify,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( plus_plus_int @ A @ zero_zero_int )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_258_comm__monoid__add__class_Oadd__0,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_259_comm__monoid__add__class_Oadd__0,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( plus_plus_int @ zero_zero_int @ A )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_260_add_Ocomm__neutral,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_261_add_Ocomm__neutral,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( plus_plus_int @ A @ zero_zero_int )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_262_add_Ogroup__left__neutral,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( plus_plus_int @ zero_zero_int @ A )
% 3.13/1.89 = A ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_263_add__0__iff,axiom,
% 3.13/1.89 ! [B: nat,A: nat] :
% 3.13/1.89 ( ( B
% 3.13/1.89 = ( plus_plus_nat @ B @ A ) )
% 3.13/1.89 = ( A = zero_zero_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_264_add__0__iff,axiom,
% 3.13/1.89 ! [B: int,A: int] :
% 3.13/1.89 ( ( B
% 3.13/1.89 = ( plus_plus_int @ B @ A ) )
% 3.13/1.89 = ( A = zero_zero_int ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_265_zero__neq__one,axiom,
% 3.13/1.89 zero_zero_nat != one_one_nat ).
% 3.13/1.89
% 3.13/1.89 thf(fact_266_zero__neq__one,axiom,
% 3.13/1.89 zero_zero_int != one_one_int ).
% 3.13/1.89
% 3.13/1.89 thf(fact_267_power__not__zero,axiom,
% 3.13/1.89 ! [A: int,N: nat] :
% 3.13/1.89 ( ( A != zero_zero_int )
% 3.13/1.89 => ( ( power_power_int @ A @ N )
% 3.13/1.89 != zero_zero_int ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_268_power__not__zero,axiom,
% 3.13/1.89 ! [A: nat,N: nat] :
% 3.13/1.89 ( ( A != zero_zero_nat )
% 3.13/1.89 => ( ( power_power_nat @ A @ N )
% 3.13/1.89 != zero_zero_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_269_nat__mult__1__right,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( times_times_nat @ N @ one_one_nat )
% 3.13/1.89 = N ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_270_nat__mult__1,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( times_times_nat @ one_one_nat @ N )
% 3.13/1.89 = N ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_271_nat_Odistinct_I1_J,axiom,
% 3.13/1.89 ! [X2: nat] :
% 3.13/1.89 ( zero_zero_nat
% 3.13/1.89 != ( suc @ X2 ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_272_old_Onat_Odistinct_I2_J,axiom,
% 3.13/1.89 ! [Nat2: nat] :
% 3.13/1.89 ( ( suc @ Nat2 )
% 3.13/1.89 != zero_zero_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_273_old_Onat_Odistinct_I1_J,axiom,
% 3.13/1.89 ! [Nat2: nat] :
% 3.13/1.89 ( zero_zero_nat
% 3.13/1.89 != ( suc @ Nat2 ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_274_nat_OdiscI,axiom,
% 3.13/1.89 ! [Nat: nat,X2: nat] :
% 3.13/1.89 ( ( Nat
% 3.13/1.89 = ( suc @ X2 ) )
% 3.13/1.89 => ( Nat != zero_zero_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_275_nat__induct,axiom,
% 3.13/1.89 ! [P3: nat > $o,N: nat] :
% 3.13/1.89 ( ( P3 @ zero_zero_nat )
% 3.13/1.89 => ( ! [N2: nat] :
% 3.13/1.89 ( ( P3 @ N2 )
% 3.13/1.89 => ( P3 @ ( suc @ N2 ) ) )
% 3.13/1.89 => ( P3 @ N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_276_diff__induct,axiom,
% 3.13/1.89 ! [P3: nat > nat > $o,M: nat,N: nat] :
% 3.13/1.89 ( ! [X3: nat] : ( P3 @ X3 @ zero_zero_nat )
% 3.13/1.89 => ( ! [Y4: nat] : ( P3 @ zero_zero_nat @ ( suc @ Y4 ) )
% 3.13/1.89 => ( ! [X3: nat,Y4: nat] :
% 3.13/1.89 ( ( P3 @ X3 @ Y4 )
% 3.13/1.89 => ( P3 @ ( suc @ X3 ) @ ( suc @ Y4 ) ) )
% 3.13/1.89 => ( P3 @ M @ N ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_277_zero__induct,axiom,
% 3.13/1.89 ! [P3: nat > $o,K: nat] :
% 3.13/1.89 ( ( P3 @ K )
% 3.13/1.89 => ( ! [N2: nat] :
% 3.13/1.89 ( ( P3 @ ( suc @ N2 ) )
% 3.13/1.89 => ( P3 @ N2 ) )
% 3.13/1.89 => ( P3 @ zero_zero_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_278_Suc__neq__Zero,axiom,
% 3.13/1.89 ! [M: nat] :
% 3.13/1.89 ( ( suc @ M )
% 3.13/1.89 != zero_zero_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_279_Zero__neq__Suc,axiom,
% 3.13/1.89 ! [M: nat] :
% 3.13/1.89 ( zero_zero_nat
% 3.13/1.89 != ( suc @ M ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_280_Zero__not__Suc,axiom,
% 3.13/1.89 ! [M: nat] :
% 3.13/1.89 ( zero_zero_nat
% 3.13/1.89 != ( suc @ M ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_281_old_Onat_Oexhaust,axiom,
% 3.13/1.89 ! [Y: nat] :
% 3.13/1.89 ( ( Y != zero_zero_nat )
% 3.13/1.89 => ~ ! [Nat3: nat] :
% 3.13/1.89 ( Y
% 3.13/1.89 != ( suc @ Nat3 ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_282_old_Onat_Oinducts,axiom,
% 3.13/1.89 ! [P3: nat > $o,Nat: nat] :
% 3.13/1.89 ( ( P3 @ zero_zero_nat )
% 3.13/1.89 => ( ! [Nat3: nat] :
% 3.13/1.89 ( ( P3 @ Nat3 )
% 3.13/1.89 => ( P3 @ ( suc @ Nat3 ) ) )
% 3.13/1.89 => ( P3 @ Nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_283_not0__implies__Suc,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( N != zero_zero_nat )
% 3.13/1.89 => ? [M2: nat] :
% 3.13/1.89 ( N
% 3.13/1.89 = ( suc @ M2 ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_284_add__eq__self__zero,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( ( plus_plus_nat @ M @ N )
% 3.13/1.89 = M )
% 3.13/1.89 => ( N = zero_zero_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_285_plus__nat_Oadd__0,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 3.13/1.89 = N ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_286_nat__mult__eq__cancel__disj,axiom,
% 3.13/1.89 ! [K: nat,M: nat,N: nat] :
% 3.13/1.89 ( ( ( times_times_nat @ K @ M )
% 3.13/1.89 = ( times_times_nat @ K @ N ) )
% 3.13/1.89 = ( ( K = zero_zero_nat )
% 3.13/1.89 | ( M = N ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_287_mult__0,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( times_times_nat @ zero_zero_nat @ N )
% 3.13/1.89 = zero_zero_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_288_times__int__code_I2_J,axiom,
% 3.13/1.89 ! [L: int] :
% 3.13/1.89 ( ( times_times_int @ zero_zero_int @ L )
% 3.13/1.89 = zero_zero_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_289_times__int__code_I1_J,axiom,
% 3.13/1.89 ! [K: int] :
% 3.13/1.89 ( ( times_times_int @ K @ zero_zero_int )
% 3.13/1.89 = zero_zero_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_290_plus__int__code_I2_J,axiom,
% 3.13/1.89 ! [L: int] :
% 3.13/1.89 ( ( plus_plus_int @ zero_zero_int @ L )
% 3.13/1.89 = L ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_291_plus__int__code_I1_J,axiom,
% 3.13/1.89 ! [K: int] :
% 3.13/1.89 ( ( plus_plus_int @ K @ zero_zero_int )
% 3.13/1.89 = K ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_292_add__scale__eq__noteq,axiom,
% 3.13/1.89 ! [R: int,A: int,B: int,C: int,D: int] :
% 3.13/1.89 ( ( R != zero_zero_int )
% 3.13/1.89 => ( ( ( A = B )
% 3.13/1.89 & ( C != D ) )
% 3.13/1.89 => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C ) )
% 3.13/1.89 != ( plus_plus_int @ B @ ( times_times_int @ R @ D ) ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_293_add__scale__eq__noteq,axiom,
% 3.13/1.89 ! [R: nat,A: nat,B: nat,C: nat,D: nat] :
% 3.13/1.89 ( ( R != zero_zero_nat )
% 3.13/1.89 => ( ( ( A = B )
% 3.13/1.89 & ( C != D ) )
% 3.13/1.89 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
% 3.13/1.89 != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_294_Suc__eq__plus1__left,axiom,
% 3.13/1.89 ( suc
% 3.13/1.89 = ( plus_plus_nat @ one_one_nat ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_295_plus__1__eq__Suc,axiom,
% 3.13/1.89 ( ( plus_plus_nat @ one_one_nat )
% 3.13/1.89 = suc ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_296_Suc__eq__plus1,axiom,
% 3.13/1.89 ( suc
% 3.13/1.89 = ( ^ [N3: nat] : ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_297_power__0,axiom,
% 3.13/1.89 ! [A: int] :
% 3.13/1.89 ( ( power_power_int @ A @ zero_zero_nat )
% 3.13/1.89 = one_one_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_298_power__0,axiom,
% 3.13/1.89 ! [A: nat] :
% 3.13/1.89 ( ( power_power_nat @ A @ zero_zero_nat )
% 3.13/1.89 = one_one_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_299_of__nat__neq__0,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( semiri2019852685at_int @ ( suc @ N ) )
% 3.13/1.89 != zero_zero_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_300_of__nat__neq__0,axiom,
% 3.13/1.89 ! [N: nat] :
% 3.13/1.89 ( ( semiri1382578993at_nat @ ( suc @ N ) )
% 3.13/1.89 != zero_zero_nat ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_301_one__is__add,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( ( suc @ zero_zero_nat )
% 3.13/1.89 = ( plus_plus_nat @ M @ N ) )
% 3.13/1.89 = ( ( ( M
% 3.13/1.89 = ( suc @ zero_zero_nat ) )
% 3.13/1.89 & ( N = zero_zero_nat ) )
% 3.13/1.89 | ( ( M = zero_zero_nat )
% 3.13/1.89 & ( N
% 3.13/1.89 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_302_add__is__1,axiom,
% 3.13/1.89 ! [M: nat,N: nat] :
% 3.13/1.89 ( ( ( plus_plus_nat @ M @ N )
% 3.13/1.89 = ( suc @ zero_zero_nat ) )
% 3.13/1.89 = ( ( ( M
% 3.13/1.89 = ( suc @ zero_zero_nat ) )
% 3.13/1.89 & ( N = zero_zero_nat ) )
% 3.13/1.89 | ( ( M = zero_zero_nat )
% 3.13/1.89 & ( N
% 3.13/1.89 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_303_int__ops_I2_J,axiom,
% 3.13/1.89 ( ( semiri2019852685at_int @ one_one_nat )
% 3.13/1.89 = one_one_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_304_odd__nonzero,axiom,
% 3.13/1.89 ! [Z: int] :
% 3.13/1.89 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 3.13/1.89 != zero_zero_int ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_305_div__add__self1,axiom,
% 3.13/1.89 ! [B: int,A: int] :
% 3.13/1.89 ( ( B != zero_zero_int )
% 3.13/1.89 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 3.13/1.89 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_306_div__add__self1,axiom,
% 3.13/1.89 ! [B: nat,A: nat] :
% 3.13/1.89 ( ( B != zero_zero_nat )
% 3.13/1.89 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 3.13/1.89 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_307_div__add__self2,axiom,
% 3.13/1.89 ! [B: int,A: int] :
% 3.13/1.89 ( ( B != zero_zero_int )
% 3.13/1.89 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 3.13/1.89 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(fact_308_div__add__self2,axiom,
% 3.13/1.89 ! [B: nat,A: nat] :
% 3.13/1.89 ( ( B != zero_zero_nat )
% 3.13/1.89 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 3.13/1.89 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(help_If_3_1_If_001t__Nat__Onat_T,axiom,
% 3.13/1.89 ! [P3: $o] :
% 3.13/1.89 ( ( P3 = $true )
% 3.13/1.89 | ( P3 = $false ) ) ).
% 3.13/1.89
% 3.13/1.89 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 3.13/1.89 ! [X: nat,Y: nat] :
% 3.13/1.89 ( ( if_nat @ $false @ X @ Y )
% 3.13/1.89 = Y ) ).
% 3.13/1.89
% 3.13/1.89 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 3.13/1.89 ! [X: nat,Y: nat] :
% 3.13/1.89 ( ( if_nat @ $true @ X @ Y )
% 3.13/1.89 = X ) ).
% 3.13/1.89
% 3.13/1.89 thf(conj_0,conjecture,
% 3.13/1.89 ( ( divide_divide_int @ ( plus_plus_int @ ( divide_divide_int @ ( power_power_int @ x @ ( suc @ pm ) ) @ ( power_power_int @ x @ pm ) ) @ ( times_times_int @ x @ ( semiri2019852685at_int @ pm ) ) ) @ ( semiri2019852685at_int @ ( suc @ pm ) ) )
% 3.13/1.89 = x ) ).
% 3.13/1.89 ------------------------
% 3.28/1.93 % (29822)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_29722 for (2999ds/27Mi)
% 3.28/1.93 % (29823)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29722 for (2999ds/2Mi)
% 3.28/1.93 % (29820)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29722 for (2999ds/183Mi)
% 3.28/1.93 % (29826)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29722 for (2999ds/18Mi)
% 3.28/1.93 % (29825)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_29722 for (2999ds/275Mi)
% 3.28/1.93 % (29824)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_29722 for (2999ds/2Mi)
% 3.28/1.93 % (29821)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_29722 for (2999ds/4Mi)
% 3.28/1.93 % (29823)Instruction limit reached!
% 3.28/1.93 % (29823)------------------------------
% 3.28/1.93 % (29823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.93 % (29823)Termination reason: Unknown
% 3.28/1.93 % (29824)Instruction limit reached!
% 3.28/1.93 % (29824)------------------------------
% 3.28/1.93 % (29824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.93 % (29823)Termination phase: shuffling
% 3.28/1.93
% 3.28/1.93 % (29823)Memory used [KB]: 1279
% 3.28/1.93 % (29823)Time elapsed: 0.004 s
% 3.28/1.93 % (29823)Instructions burned: 3 (million)
% 3.28/1.93 % (29823)------------------------------
% 3.28/1.93 % (29823)------------------------------
% 3.28/1.93 % (29824)Termination reason: Unknown
% 3.28/1.93 % (29824)Termination phase: shuffling
% 3.28/1.93
% 3.28/1.93 % (29824)Memory used [KB]: 1279
% 3.28/1.93 % (29824)Time elapsed: 0.004 s
% 3.28/1.93 % (29824)Instructions burned: 3 (million)
% 3.28/1.93 % (29824)------------------------------
% 3.28/1.93 % (29824)------------------------------
% 3.28/1.93 % (29821)Instruction limit reached!
% 3.28/1.93 % (29821)------------------------------
% 3.28/1.93 % (29821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.93 % (29821)Termination reason: Unknown
% 3.28/1.93 % (29821)Termination phase: shuffling
% 3.28/1.93
% 3.28/1.93 % (29821)Memory used [KB]: 1407
% 3.28/1.93 % (29821)Time elapsed: 0.005 s
% 3.28/1.93 % (29821)Instructions burned: 5 (million)
% 3.28/1.93 % (29821)------------------------------
% 3.28/1.93 % (29821)------------------------------
% 3.28/1.94 % (29826)Instruction limit reached!
% 3.28/1.94 % (29826)------------------------------
% 3.28/1.94 % (29826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.94 % (29826)Termination reason: Unknown
% 3.28/1.94 % (29826)Termination phase: Preprocessing 1
% 3.28/1.94
% 3.28/1.94 % (29826)Memory used [KB]: 1535
% 3.28/1.94 % (29826)Time elapsed: 0.012 s
% 3.28/1.94 % (29826)Instructions burned: 19 (million)
% 3.28/1.94 % (29826)------------------------------
% 3.28/1.94 % (29826)------------------------------
% 3.28/1.94 % (29822)Instruction limit reached!
% 3.28/1.94 % (29822)------------------------------
% 3.28/1.94 % (29822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.94 % (29822)Termination reason: Unknown
% 3.28/1.94 % (29822)Termination phase: Clausification
% 3.28/1.94
% 3.28/1.94 % (29822)Memory used [KB]: 1535
% 3.28/1.94 % (29822)Time elapsed: 0.016 s
% 3.28/1.94 % (29822)Instructions burned: 27 (million)
% 3.28/1.94 % (29822)------------------------------
% 3.28/1.94 % (29822)------------------------------
% 3.28/1.95 % (29827)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29722 for (2999ds/3Mi)
% 3.28/1.95 % (29829)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_29722 for (2999ds/15Mi)
% 3.28/1.95 % (29828)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_29722 for (2999ds/37Mi)
% 3.28/1.95 % (29827)Instruction limit reached!
% 3.28/1.95 % (29827)------------------------------
% 3.28/1.95 % (29827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.95 % (29827)Termination reason: Unknown
% 3.28/1.95 % (29827)Termination phase: shuffling
% 3.28/1.95
% 3.28/1.95 % (29827)Memory used [KB]: 1279
% 3.28/1.95 % (29827)Time elapsed: 0.004 s
% 3.28/1.95 % (29827)Instructions burned: 4 (million)
% 3.28/1.95 % (29827)------------------------------
% 3.28/1.95 % (29827)------------------------------
% 3.28/1.95 % (29829)Instruction limit reached!
% 3.28/1.95 % (29829)------------------------------
% 3.28/1.95 % (29829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.95 % (29829)Termination reason: Unknown
% 3.28/1.95 % (29829)Termination phase: Property scanning
% 3.28/1.95
% 3.28/1.95 % (29829)Memory used [KB]: 1407
% 3.28/1.95 % (29829)Time elapsed: 0.010 s
% 3.28/1.95 % (29829)Instructions burned: 16 (million)
% 3.28/1.95 % (29829)------------------------------
% 3.28/1.95 % (29829)------------------------------
% 3.28/1.95 % (29830)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_29722 for (2999ds/3Mi)
% 3.28/1.96 % (29830)Instruction limit reached!
% 3.28/1.96 % (29830)------------------------------
% 3.28/1.96 % (29830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.96 % (29830)Termination reason: Unknown
% 3.28/1.96 % (29830)Termination phase: shuffling
% 3.28/1.96
% 3.28/1.96 % (29830)Memory used [KB]: 1279
% 3.28/1.96 % (29830)Time elapsed: 0.005 s
% 3.28/1.96 % (29830)Instructions burned: 4 (million)
% 3.28/1.96 % (29830)------------------------------
% 3.28/1.96 % (29830)------------------------------
% 3.28/1.96 % (29831)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_29722 for (2999ds/1041Mi)
% 3.28/1.96 % (29828)Instruction limit reached!
% 3.28/1.96 % (29828)------------------------------
% 3.28/1.96 % (29828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.96 % (29828)Termination reason: Unknown
% 3.28/1.96 % (29828)Termination phase: shuffling
% 3.28/1.96
% 3.28/1.96 % (29828)Memory used [KB]: 2046
% 3.28/1.96 % (29828)Time elapsed: 0.020 s
% 3.28/1.96 % (29828)Instructions burned: 37 (million)
% 3.28/1.96 % (29828)------------------------------
% 3.28/1.96 % (29828)------------------------------
% 3.28/1.97 % (29832)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29722 for (2999ds/7Mi)
% 3.28/1.97 % (29832)Instruction limit reached!
% 3.28/1.97 % (29832)------------------------------
% 3.28/1.97 % (29832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.97 % (29832)Termination reason: Unknown
% 3.28/1.97 % (29832)Termination phase: shuffling
% 3.28/1.97
% 3.28/1.97 % (29832)Memory used [KB]: 1407
% 3.28/1.97 % (29832)Time elapsed: 0.006 s
% 3.28/1.97 % (29832)Instructions burned: 7 (million)
% 3.28/1.97 % (29832)------------------------------
% 3.28/1.97 % (29832)------------------------------
% 3.28/1.97 % (29825)Refutation not found, incomplete strategy
% 3.28/1.97 % (29825)------------------------------
% 3.28/1.97 % (29825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.97 % (29825)Termination reason: Refutation not found, incomplete strategy
% 3.28/1.97
% 3.28/1.97
% 3.28/1.97 % (29825)Memory used [KB]: 6780
% 3.28/1.97 % (29825)Time elapsed: 0.049 s
% 3.28/1.97 % (29825)Instructions burned: 85 (million)
% 3.28/1.97 % (29825)------------------------------
% 3.28/1.97 % (29825)------------------------------
% 3.28/1.97 % (29833)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29722 for (2999ds/16Mi)
% 3.28/1.98 % (29834)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_29722 for (2999ds/3Mi)
% 3.28/1.98 % (29834)Instruction limit reached!
% 3.28/1.98 % (29834)------------------------------
% 3.28/1.98 % (29834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.98 % (29834)Termination reason: Unknown
% 3.28/1.98 % (29834)Termination phase: shuffling
% 3.28/1.98
% 3.28/1.98 % (29834)Memory used [KB]: 1279
% 3.28/1.98 % (29834)Time elapsed: 0.004 s
% 3.28/1.98 % (29834)Instructions burned: 3 (million)
% 3.28/1.98 % (29834)------------------------------
% 3.28/1.98 % (29834)------------------------------
% 3.28/1.98 % (29833)Instruction limit reached!
% 3.28/1.98 % (29833)------------------------------
% 3.28/1.98 % (29833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.98 % (29833)Termination reason: Unknown
% 3.28/1.98 % (29833)Termination phase: Property scanning
% 3.28/1.98
% 3.28/1.98 % (29833)Memory used [KB]: 1407
% 3.28/1.98 % (29833)Time elapsed: 0.010 s
% 3.28/1.98 % (29833)Instructions burned: 16 (million)
% 3.28/1.98 % (29833)------------------------------
% 3.28/1.98 % (29833)------------------------------
% 3.28/1.98 % (29835)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_29722 for (2999ds/3Mi)
% 3.28/1.98 % (29835)Instruction limit reached!
% 3.28/1.98 % (29835)------------------------------
% 3.28/1.98 % (29835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.98 % (29835)Termination reason: Unknown
% 3.28/1.98 % (29835)Termination phase: shuffling
% 3.28/1.98
% 3.28/1.98 % (29835)Memory used [KB]: 1279
% 3.28/1.98 % (29835)Time elapsed: 0.004 s
% 3.28/1.98 % (29835)Instructions burned: 3 (million)
% 3.28/1.98 % (29835)------------------------------
% 3.28/1.98 % (29835)------------------------------
% 3.28/1.99 % (29836)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29722 for (2999ds/7Mi)
% 3.28/1.99 % (29837)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_29722 for (2999ds/3Mi)
% 3.28/1.99 % (29837)Instruction limit reached!
% 3.28/1.99 % (29837)------------------------------
% 3.28/1.99 % (29837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.99 % (29837)Termination reason: Unknown
% 3.28/1.99 % (29837)Termination phase: shuffling
% 3.28/1.99
% 3.28/1.99 % (29837)Memory used [KB]: 1279
% 3.28/1.99 % (29837)Time elapsed: 0.004 s
% 3.28/1.99 % (29837)Instructions burned: 3 (million)
% 3.28/1.99 % (29837)------------------------------
% 3.28/1.99 % (29837)------------------------------
% 3.28/1.99 % (29836)Instruction limit reached!
% 3.28/1.99 % (29836)------------------------------
% 3.28/1.99 % (29836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.99 % (29836)Termination reason: Unknown
% 3.28/1.99 % (29836)Termination phase: shuffling
% 3.28/1.99
% 3.28/1.99 % (29836)Memory used [KB]: 1407
% 3.28/1.99 % (29836)Time elapsed: 0.007 s
% 3.28/1.99 % (29836)Instructions burned: 8 (million)
% 3.28/1.99 % (29836)------------------------------
% 3.28/1.99 % (29836)------------------------------
% 3.28/2.00 % (29838)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29722 for (2999ds/4Mi)
% 3.28/2.00 % (29838)Instruction limit reached!
% 3.28/2.00 % (29838)------------------------------
% 3.28/2.00 % (29838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/2.00 % (29838)Termination reason: Unknown
% 3.28/2.00 % (29838)Termination phase: shuffling
% 3.28/2.00
% 3.28/2.00 % (29838)Memory used [KB]: 1407
% 3.28/2.00 % (29838)Time elapsed: 0.005 s
% 3.28/2.00 % (29838)Instructions burned: 5 (million)
% 3.28/2.00 % (29838)------------------------------
% 3.28/2.00 % (29838)------------------------------
% 3.28/2.00 % (29839)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29722 for (2999ds/18Mi)
% 3.28/2.00 % (29840)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_29722 for (2999ds/710Mi)
% 3.28/2.01 % (29839)Instruction limit reached!
% 3.28/2.01 % (29839)------------------------------
% 3.28/2.01 % (29839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/2.01 % (29839)Termination reason: Unknown
% 3.28/2.01 % (29839)Termination phase: Property scanning
% 3.28/2.01
% 3.28/2.01 % (29839)Memory used [KB]: 1407
% 3.28/2.01 % (29839)Time elapsed: 0.011 s
% 3.28/2.01 % (29839)Instructions burned: 18 (million)
% 3.28/2.01 % (29839)------------------------------
% 3.28/2.01 % (29839)------------------------------
% 3.28/2.01 % (29842)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_29722 for (2999ds/902Mi)
% 3.28/2.01 % (29841)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29722 for (2999ds/6Mi)
% 3.28/2.01 % (29841)Instruction limit reached!
% 3.28/2.01 % (29841)------------------------------
% 3.28/2.01 % (29841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/2.01 % (29841)Termination reason: Unknown
% 3.28/2.01 % (29841)Termination phase: shuffling
% 3.28/2.01
% 3.28/2.01 % (29841)Memory used [KB]: 1407
% 3.28/2.01 % (29841)Time elapsed: 0.005 s
% 3.28/2.01 % (29841)Instructions burned: 6 (million)
% 3.28/2.01 % (29841)------------------------------
% 3.28/2.01 % (29841)------------------------------
% 3.28/2.02 % (29843)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_29722 for (2999ds/21Mi)
% 3.28/2.02 % (29820)Instruction limit reached!
% 3.28/2.02 % (29820)------------------------------
% 3.28/2.02 % (29820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/2.02 % (29820)Termination reason: Unknown
% 4.02/2.02 % (29820)Termination phase: Saturation
% 4.02/2.02
% 4.02/2.02 % (29820)Memory used [KB]: 6780
% 4.02/2.02 % (29820)Time elapsed: 0.101 s
% 4.02/2.02 % (29820)Instructions burned: 183 (million)
% 4.02/2.02 % (29820)------------------------------
% 4.02/2.02 % (29820)------------------------------
% 4.02/2.03 % (29844)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_29722 for (2998ds/5Mi)
% 4.02/2.03 % (29843)Instruction limit reached!
% 4.02/2.03 % (29843)------------------------------
% 4.02/2.03 % (29843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/2.03 % (29843)Termination reason: Unknown
% 4.02/2.03 % (29843)Termination phase: Property scanning
% 4.02/2.03
% 4.02/2.03 % (29843)Memory used [KB]: 1535
% 4.02/2.03 % (29843)Time elapsed: 0.013 s
% 4.02/2.03 % (29843)Instructions burned: 21 (million)
% 4.02/2.03 % (29843)------------------------------
% 4.02/2.03 % (29843)------------------------------
% 4.02/2.03 % (29844)Instruction limit reached!
% 4.02/2.03 % (29844)------------------------------
% 4.02/2.03 % (29844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/2.03 % (29844)Termination reason: Unknown
% 4.02/2.03 % (29844)Termination phase: shuffling
% 4.02/2.03
% 4.02/2.03 % (29844)Memory used [KB]: 1407
% 4.02/2.03 % (29844)Time elapsed: 0.005 s
% 4.02/2.03 % (29844)Instructions burned: 6 (million)
% 4.02/2.03 % (29844)------------------------------
% 4.02/2.03 % (29844)------------------------------
% 4.02/2.03 % (29845)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_29722 for (2998ds/6Mi)
% 4.02/2.04 % (29845)Instruction limit reached!
% 4.02/2.04 % (29845)------------------------------
% 4.02/2.04 % (29845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/2.04 % (29845)Termination reason: Unknown
% 4.02/2.04 % (29845)Termination phase: shuffling
% 4.02/2.04
% 4.02/2.04 % (29845)Memory used [KB]: 1407
% 4.02/2.04 % (29845)Time elapsed: 0.005 s
% 4.02/2.04 % (29845)Instructions burned: 6 (million)
% 4.02/2.04 % (29845)------------------------------
% 4.02/2.04 % (29845)------------------------------
% 4.02/2.04 % (29846)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_29722 for (2998ds/377Mi)
% 4.02/2.05 % (29847)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_29722 for (2998ds/779Mi)
% 4.02/2.05 % (29842)Refutation not found, incomplete strategy
% 4.02/2.05 % (29842)------------------------------
% 4.02/2.05 % (29842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/2.05 % (29842)Termination reason: Refutation not found, incomplete strategy
% 4.02/2.05
% 4.02/2.05
% 4.02/2.05 % (29842)Memory used [KB]: 6396
% 4.02/2.05 % (29842)Time elapsed: 0.037 s
% 4.02/2.05 % (29842)Instructions burned: 68 (million)
% 4.02/2.05 % (29842)------------------------------
% 4.02/2.05 % (29842)------------------------------
% 4.02/2.05 % (29848)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_29722 for (2998ds/19Mi)
% 4.02/2.06 % (29849)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_29722 for (2998ds/879Mi)
% 4.02/2.06 % (29848)Instruction limit reached!
% 4.02/2.06 % (29848)------------------------------
% 4.02/2.06 % (29848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/2.06 % (29848)Termination reason: Unknown
% 4.02/2.06 % (29848)Termination phase: shuffling
% 4.02/2.06
% 4.02/2.06 % (29848)Memory used [KB]: 1663
% 4.02/2.06 % (29848)Time elapsed: 0.012 s
% 4.02/2.06 % (29848)Instructions burned: 21 (million)
% 4.02/2.06 % (29848)------------------------------
% 4.02/2.06 % (29848)------------------------------
% 4.02/2.07 % (29850)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_29722 for (2998ds/17Mi)
% 4.02/2.08 % (29850)Instruction limit reached!
% 4.02/2.08 % (29850)------------------------------
% 4.02/2.08 % (29850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/2.08 % (29850)Termination reason: Unknown
% 4.02/2.08 % (29850)Termination phase: Property scanning
% 4.02/2.08
% 4.02/2.08 % (29850)Memory used [KB]: 1407
% 4.02/2.08 % (29850)Time elapsed: 0.011 s
% 4.02/2.08 % (29850)Instructions burned: 19 (million)
% 4.02/2.08 % (29850)------------------------------
% 4.02/2.08 % (29850)------------------------------
% 4.02/2.08 % (29851)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_29722 for (2998ds/3Mi)
% 4.02/2.08 % (29851)Instruction limit reached!
% 4.02/2.08 % (29851)------------------------------
% 4.02/2.08 % (29851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/2.08 % (29851)Termination reason: Unknown
% 4.02/2.08 % (29851)Termination phase: shuffling
% 4.02/2.08
% 4.02/2.08 % (29851)Memory used [KB]: 1279
% 4.02/2.08 % (29851)Time elapsed: 0.003 s
% 4.02/2.08 % (29851)Instructions burned: 3 (million)
% 4.02/2.08 % (29851)------------------------------
% 4.02/2.08 % (29851)------------------------------
% 4.02/2.10 % (29852)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_29722 for (2998ds/30Mi)
% 4.02/2.10 % (29853)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_29722 for (2998ds/127Mi)
% 4.02/2.11 % (29852)Instruction limit reached!
% 4.02/2.11 % (29852)------------------------------
% 4.02/2.11 % (29852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.02/2.11 % (29852)Termination reason: Unknown
% 4.02/2.11 % (29852)Termination phase: Property scanning
% 4.02/2.11
% 4.02/2.11 % (29852)Memory used [KB]: 1535
% 4.02/2.11 % (29852)Time elapsed: 0.017 s
% 4.02/2.11 % (29852)Instructions burned: 30 (million)
% 4.02/2.11 % (29852)------------------------------
% 4.02/2.11 % (29852)------------------------------
% 4.45/2.13 % (29854)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_29722 for (2997ds/100Mi)
% 4.45/2.17 % (29853)Instruction limit reached!
% 4.45/2.17 % (29853)------------------------------
% 4.45/2.17 % (29853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.45/2.17 % (29853)Termination reason: Unknown
% 4.45/2.17 % (29853)Termination phase: Saturation
% 4.45/2.17
% 4.45/2.17 % (29853)Memory used [KB]: 6524
% 4.45/2.17 % (29853)Time elapsed: 0.098 s
% 4.45/2.17 % (29853)Instructions burned: 128 (million)
% 4.45/2.17 % (29853)------------------------------
% 4.45/2.17 % (29853)------------------------------
% 4.45/2.18 % (29854)Instruction limit reached!
% 4.45/2.18 % (29854)------------------------------
% 4.45/2.18 % (29854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.45/2.18 % (29854)Termination reason: Unknown
% 4.45/2.18 % (29854)Termination phase: Property scanning
% 4.45/2.18
% 4.45/2.18 % (29854)Memory used [KB]: 2174
% 4.45/2.18 % (29854)Time elapsed: 0.051 s
% 4.45/2.18 % (29854)Instructions burned: 101 (million)
% 4.45/2.18 % (29854)------------------------------
% 4.45/2.18 % (29854)------------------------------
% 4.45/2.19 % (29855)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_29722 for (2997ds/3Mi)
% 4.45/2.19 % (29855)Instruction limit reached!
% 4.45/2.19 % (29855)------------------------------
% 4.45/2.19 % (29855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.45/2.19 % (29855)Termination reason: Unknown
% 4.45/2.19 % (29855)Termination phase: shuffling
% 4.45/2.19
% 4.45/2.19 % (29855)Memory used [KB]: 1279
% 4.45/2.19 % (29855)Time elapsed: 0.004 s
% 4.45/2.19 % (29855)Instructions burned: 4 (million)
% 4.45/2.19 % (29855)------------------------------
% 4.45/2.19 % (29855)------------------------------
% 4.76/2.20 % (29856)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_29722 for (2997ds/20Mi)
% 4.76/2.21 % (29856)Instruction limit reached!
% 4.76/2.21 % (29856)------------------------------
% 4.76/2.21 % (29856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.76/2.21 % (29856)Termination reason: Unknown
% 4.76/2.21 % (29856)Termination phase: SInE selection
% 4.76/2.21
% 4.76/2.21 % (29856)Memory used [KB]: 1407
% 4.76/2.21 % (29856)Time elapsed: 0.013 s
% 4.76/2.21 % (29856)Instructions burned: 21 (million)
% 4.76/2.21 % (29856)------------------------------
% 4.76/2.21 % (29856)------------------------------
% 4.76/2.22 % (29857)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_29722 for (2996ds/86Mi)
% 4.76/2.23 % (29858)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_29722 for (2996ds/107Mi)
% 4.76/2.25 % (29846)Instruction limit reached!
% 4.76/2.25 % (29846)------------------------------
% 4.76/2.25 % (29846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.76/2.25 % (29846)Termination reason: Unknown
% 4.76/2.25 % (29846)Termination phase: Saturation
% 4.76/2.25
% 4.76/2.25 % (29846)Memory used [KB]: 6908
% 4.76/2.25 % (29846)Time elapsed: 0.213 s
% 4.76/2.25 % (29846)Instructions burned: 378 (million)
% 4.76/2.25 % (29846)------------------------------
% 4.76/2.25 % (29846)------------------------------
% 4.76/2.26 % (29857)Instruction limit reached!
% 4.76/2.26 % (29857)------------------------------
% 4.76/2.26 % (29857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.76/2.26 % (29857)Termination reason: Unknown
% 4.76/2.26 % (29857)Termination phase: Saturation
% 4.76/2.26
% 4.76/2.26 % (29857)Memory used [KB]: 6524
% 4.76/2.26 % (29857)Time elapsed: 0.048 s
% 4.76/2.26 % (29857)Instructions burned: 87 (million)
% 4.76/2.26 % (29857)------------------------------
% 4.76/2.26 % (29857)------------------------------
% 4.76/2.28 % (29859)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_29722 for (2996ds/39Mi)
% 4.76/2.28 % (29860)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_29722 for (2996ds/448Mi)
% 4.76/2.29 % (29858)Instruction limit reached!
% 4.76/2.29 % (29858)------------------------------
% 4.76/2.29 % (29858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.76/2.29 % (29858)Termination reason: Unknown
% 4.76/2.29 % (29858)Termination phase: Saturation
% 4.76/2.29
% 4.76/2.29 % (29858)Memory used [KB]: 6524
% 4.76/2.29 % (29858)Time elapsed: 0.059 s
% 4.76/2.29 % (29858)Instructions burned: 108 (million)
% 4.76/2.29 % (29858)------------------------------
% 4.76/2.29 % (29858)------------------------------
% 4.76/2.29 % (29859)Instruction limit reached!
% 4.76/2.29 % (29859)------------------------------
% 4.76/2.29 % (29859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.76/2.29 % (29859)Termination reason: Unknown
% 4.76/2.29 % (29859)Termination phase: Property scanning
% 4.76/2.29
% 4.76/2.29 % (29859)Memory used [KB]: 2046
% 4.76/2.29 % (29859)Time elapsed: 0.022 s
% 4.76/2.29 % (29859)Instructions burned: 39 (million)
% 4.76/2.29 % (29859)------------------------------
% 4.76/2.29 % (29859)------------------------------
% 5.40/2.31 % (29861)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_29722 for (2995ds/46Mi)
% 5.40/2.32 % (29862)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_29722 for (2995ds/98Mi)
% 5.40/2.33 % (29861)Instruction limit reached!
% 5.40/2.33 % (29861)------------------------------
% 5.40/2.33 % (29861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.40/2.33 % (29861)Termination reason: Unknown
% 5.40/2.33 % (29861)Termination phase: Property scanning
% 5.40/2.33
% 5.40/2.33 % (29861)Memory used [KB]: 1663
% 5.40/2.33 % (29861)Time elapsed: 0.026 s
% 5.40/2.33 % (29861)Instructions burned: 47 (million)
% 5.40/2.33 % (29861)------------------------------
% 5.40/2.33 % (29861)------------------------------
% 5.40/2.36 % (29863)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_29722 for (2995ds/507Mi)
% 5.40/2.36 % (29862)Instruction limit reached!
% 5.40/2.36 % (29862)------------------------------
% 5.40/2.36 % (29862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.40/2.36 % (29862)Termination reason: Unknown
% 5.40/2.36 % (29862)Termination phase: Property scanning
% 5.40/2.36
% 5.40/2.36 % (29862)Memory used [KB]: 2174
% 5.40/2.36 % (29862)Time elapsed: 0.050 s
% 5.40/2.36 % (29862)Instructions burned: 99 (million)
% 5.40/2.36 % (29862)------------------------------
% 5.40/2.36 % (29862)------------------------------
% 5.40/2.39 % (29864)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_29722 for (2995ds/149Mi)
% 5.40/2.39 % (29840)Instruction limit reached!
% 5.40/2.39 % (29840)------------------------------
% 5.40/2.39 % (29840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.40/2.39 % (29840)Termination reason: Unknown
% 5.40/2.39 % (29840)Termination phase: Saturation
% 5.40/2.39
% 5.40/2.39 % (29840)Memory used [KB]: 7036
% 5.40/2.39 % (29840)Time elapsed: 0.390 s
% 5.40/2.39 % (29840)Instructions burned: 710 (million)
% 5.40/2.39 % (29840)------------------------------
% 5.40/2.39 % (29840)------------------------------
% 5.74/2.41 % (29863)Refutation not found, incomplete strategy
% 5.74/2.41 % (29863)------------------------------
% 5.74/2.41 % (29863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.41 % (29863)Termination reason: Refutation not found, incomplete strategy
% 5.74/2.41
% 5.74/2.41
% 5.74/2.41 % (29863)Memory used [KB]: 6780
% 5.74/2.41 % (29863)Time elapsed: 0.052 s
% 5.74/2.41 % (29863)Instructions burned: 92 (million)
% 5.74/2.41 % (29863)------------------------------
% 5.74/2.41 % (29863)------------------------------
% 5.74/2.41 % (29865)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_29722 for (2995ds/39Mi)
% 5.74/2.43 % (29866)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_29722 for (2994ds/6Mi)
% 5.74/2.43 % (29866)Instruction limit reached!
% 5.74/2.43 % (29866)------------------------------
% 5.74/2.43 % (29866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.43 % (29866)Termination reason: Unknown
% 5.74/2.43 % (29866)Termination phase: shuffling
% 5.74/2.43
% 5.74/2.43 % (29866)Memory used [KB]: 1407
% 5.74/2.43 % (29866)Time elapsed: 0.005 s
% 5.74/2.43 % (29866)Instructions burned: 6 (million)
% 5.74/2.43 % (29866)------------------------------
% 5.74/2.43 % (29866)------------------------------
% 5.74/2.43 % (29865)Instruction limit reached!
% 5.74/2.43 % (29865)------------------------------
% 5.74/2.43 % (29865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.43 % (29865)Termination reason: Unknown
% 5.74/2.43 % (29865)Termination phase: Function definition elimination
% 5.74/2.43
% 5.74/2.43 % (29865)Memory used [KB]: 1663
% 5.74/2.43 % (29865)Time elapsed: 0.022 s
% 5.74/2.43 % (29865)Instructions burned: 40 (million)
% 5.74/2.43 % (29865)------------------------------
% 5.74/2.43 % (29865)------------------------------
% 5.74/2.45 % (29868)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_29722 for (2994ds/47Mi)
% 5.74/2.45 % (29867)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_29722 for (2994ds/1087Mi)
% 5.74/2.47 % (29864)Instruction limit reached!
% 5.74/2.47 % (29864)------------------------------
% 5.74/2.47 % (29864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.47 % (29864)Termination reason: Unknown
% 5.74/2.47 % (29864)Termination phase: Saturation
% 5.74/2.47
% 5.74/2.47 % (29864)Memory used [KB]: 6524
% 5.74/2.47 % (29864)Time elapsed: 0.085 s
% 5.74/2.47 % (29864)Instructions burned: 149 (million)
% 5.74/2.47 % (29864)------------------------------
% 5.74/2.47 % (29864)------------------------------
% 5.74/2.47 % (29847)Instruction limit reached!
% 5.74/2.47 % (29847)------------------------------
% 5.74/2.47 % (29847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.47 % (29847)Termination reason: Unknown
% 5.74/2.47 % (29847)Termination phase: Saturation
% 5.74/2.47
% 5.74/2.47 % (29847)Memory used [KB]: 8059
% 5.74/2.47 % (29847)Time elapsed: 0.447 s
% 5.74/2.47 % (29847)Instructions burned: 779 (million)
% 5.74/2.47 % (29847)------------------------------
% 5.74/2.47 % (29847)------------------------------
% 5.74/2.47 % (29868)Instruction limit reached!
% 5.74/2.47 % (29868)------------------------------
% 5.74/2.47 % (29868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.47 % (29868)Termination reason: Unknown
% 5.74/2.47 % (29868)Termination phase: Property scanning
% 5.74/2.47
% 5.74/2.47 % (29868)Memory used [KB]: 1663
% 5.74/2.47 % (29868)Time elapsed: 0.025 s
% 5.74/2.47 % (29868)Instructions burned: 47 (million)
% 5.74/2.47 % (29868)------------------------------
% 5.74/2.47 % (29868)------------------------------
% 5.74/2.49 % (29869)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_29722 for (2994ds/44Mi)
% 5.74/2.49 % (29870)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_29722 for (2994ds/432Mi)
% 5.74/2.49 % (29871)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_29722 for (2994ds/62Mi)
% 6.58/2.51 % (29869)Instruction limit reached!
% 6.58/2.51 % (29869)------------------------------
% 6.58/2.51 % (29869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.58/2.51 % (29869)Termination reason: Unknown
% 6.58/2.51 % (29869)Termination phase: Property scanning
% 6.58/2.51
% 6.58/2.51 % (29869)Memory used [KB]: 2046
% 6.58/2.51 % (29869)Time elapsed: 0.024 s
% 6.58/2.51 % (29869)Instructions burned: 44 (million)
% 6.58/2.51 % (29869)------------------------------
% 6.58/2.51 % (29869)------------------------------
% 6.58/2.52 % (29871)Instruction limit reached!
% 6.58/2.52 % (29871)------------------------------
% 6.58/2.52 % (29871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.58/2.52 % (29871)Termination reason: Unknown
% 6.58/2.52 % (29871)Termination phase: Property scanning
% 6.58/2.52
% 6.58/2.52 % (29871)Memory used [KB]: 2046
% 6.58/2.52 % (29871)Time elapsed: 0.033 s
% 6.58/2.52 % (29871)Instructions burned: 63 (million)
% 6.58/2.52 % (29871)------------------------------
% 6.58/2.52 % (29871)------------------------------
% 6.58/2.53 % (29860)Instruction limit reached!
% 6.58/2.53 % (29860)------------------------------
% 6.58/2.53 % (29860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.58/2.53 % (29860)Termination reason: Unknown
% 6.58/2.53 % (29860)Termination phase: Saturation
% 6.58/2.53
% 6.58/2.53 % (29860)Memory used [KB]: 7931
% 6.58/2.53 % (29860)Time elapsed: 0.247 s
% 6.58/2.53 % (29860)Instructions burned: 448 (million)
% 6.58/2.53 % (29860)------------------------------
% 6.58/2.53 % (29860)------------------------------
% 6.58/2.53 % (29872)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_29722 for (2993ds/31Mi)
% 6.58/2.54 % (29831)Instruction limit reached!
% 6.58/2.54 % (29831)------------------------------
% 6.58/2.54 % (29831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.58/2.54 % (29831)Termination reason: Unknown
% 6.58/2.54 % (29831)Termination phase: Saturation
% 6.58/2.54
% 6.58/2.54 % (29831)Memory used [KB]: 8571
% 6.58/2.54 % (29831)Time elapsed: 0.581 s
% 6.58/2.54 % (29831)Instructions burned: 1042 (million)
% 6.58/2.54 % (29831)------------------------------
% 6.58/2.54 % (29831)------------------------------
% 6.58/2.54 % (29849)Instruction limit reached!
% 6.58/2.54 % (29849)------------------------------
% 6.58/2.54 % (29849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.58/2.54 % (29849)Termination reason: Unknown
% 6.58/2.54 % (29849)Termination phase: Saturation
% 6.58/2.54
% 6.58/2.54 % (29849)Memory used [KB]: 7164
% 6.58/2.54 % (29849)Time elapsed: 0.512 s
% 6.58/2.54 % (29849)Instructions burned: 880 (million)
% 6.58/2.54 % (29849)------------------------------
% 6.58/2.54 % (29849)------------------------------
% 6.58/2.54 % (29873)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_29722 for (2993ds/96Mi)
% 6.58/2.55 % (29872)Instruction limit reached!
% 6.58/2.55 % (29872)------------------------------
% 6.58/2.55 % (29872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.58/2.55 % (29872)Termination reason: Unknown
% 6.58/2.55 % (29872)Termination phase: Property scanning
% 6.58/2.55
% 6.58/2.55 % (29872)Memory used [KB]: 1535
% 6.58/2.55 % (29872)Time elapsed: 0.018 s
% 6.58/2.55 % (29872)Instructions burned: 31 (million)
% 6.58/2.55 % (29872)------------------------------
% 6.58/2.55 % (29872)------------------------------
% 6.58/2.55 % (29874)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_29722 for (2993ds/453Mi)
% 6.58/2.56 % (29875)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_29722 for (2993ds/71Mi)
% 6.58/2.56 % (29876)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_29722 for (2993ds/83Mi)
% 6.58/2.56 % (29877)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_29722 for (2993ds/11Mi)
% 6.58/2.57 % (29877)Instruction limit reached!
% 6.58/2.57 % (29877)------------------------------
% 6.58/2.57 % (29877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.58/2.57 % (29877)Termination reason: Unknown
% 6.58/2.57 % (29877)Termination phase: shuffling
% 6.58/2.57
% 6.58/2.57 % (29877)Memory used [KB]: 1535
% 6.58/2.57 % (29877)Time elapsed: 0.007 s
% 6.58/2.57 % (29877)Instructions burned: 12 (million)
% 6.58/2.57 % (29877)------------------------------
% 6.58/2.57 % (29877)------------------------------
% 6.58/2.59 % (29878)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_29722 for (2993ds/41Mi)
% 6.58/2.59 % (29875)Instruction limit reached!
% 6.58/2.59 % (29875)------------------------------
% 6.58/2.59 % (29875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.58/2.59 % (29875)Termination reason: Unknown
% 6.58/2.59 % (29875)Termination phase: Saturation
% 6.58/2.59
% 6.58/2.59 % (29875)Memory used [KB]: 6396
% 6.58/2.59 % (29875)Time elapsed: 0.039 s
% 6.58/2.59 % (29875)Instructions burned: 72 (million)
% 6.58/2.59 % (29875)------------------------------
% 6.58/2.59 % (29875)------------------------------
% 6.58/2.59 % (29873)Instruction limit reached!
% 6.58/2.59 % (29873)------------------------------
% 6.58/2.59 % (29873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.58/2.59 % (29873)Termination reason: Unknown
% 6.58/2.59 % (29873)Termination phase: Saturation
% 6.58/2.59
% 6.58/2.60 % (29873)Memory used [KB]: 6396
% 6.58/2.60 % (29873)Time elapsed: 0.054 s
% 6.58/2.60 % (29873)Instructions burned: 97 (million)
% 6.58/2.60 % (29873)------------------------------
% 6.58/2.60 % (29873)------------------------------
% 7.66/2.61 % (29876)Instruction limit reached!
% 7.66/2.61 % (29876)------------------------------
% 7.66/2.61 % (29876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.66/2.61 % (29876)Termination reason: Unknown
% 7.66/2.61 % (29876)Termination phase: Saturation
% 7.66/2.61
% 7.66/2.61 % (29876)Memory used [KB]: 6396
% 7.66/2.61 % (29876)Time elapsed: 0.046 s
% 7.66/2.61 % (29876)Instructions burned: 83 (million)
% 7.66/2.61 % (29876)------------------------------
% 7.66/2.61 % (29876)------------------------------
% 7.66/2.61 % (29878)Instruction limit reached!
% 7.66/2.61 % (29878)------------------------------
% 7.66/2.61 % (29878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.66/2.61 % (29878)Termination reason: Unknown
% 7.66/2.61 % (29878)Termination phase: Property scanning
% 7.66/2.61
% 7.66/2.61 % (29878)Memory used [KB]: 2046
% 7.66/2.61 % (29878)Time elapsed: 0.023 s
% 7.66/2.61 % (29878)Instructions burned: 42 (million)
% 7.66/2.61 % (29878)------------------------------
% 7.66/2.61 % (29878)------------------------------
% 7.66/2.61 % (29879)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29722 for (2993ds/6Mi)
% 7.66/2.61 % (29880)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_29722 for (2993ds/150Mi)
% 7.66/2.62 % (29879)Instruction limit reached!
% 7.66/2.62 % (29879)------------------------------
% 7.66/2.62 % (29879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.66/2.62 % (29879)Termination reason: Unknown
% 7.66/2.62 % (29879)Termination phase: shuffling
% 7.66/2.62
% 7.66/2.62 % (29879)Memory used [KB]: 1407
% 7.66/2.62 % (29879)Time elapsed: 0.006 s
% 7.66/2.62 % (29879)Instructions burned: 7 (million)
% 7.66/2.62 % (29879)------------------------------
% 7.66/2.62 % (29879)------------------------------
% 7.66/2.63 % (29881)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_29722 for (2992ds/343Mi)
% 7.66/2.63 % (29882)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_29722 for (2992ds/109Mi)
% 7.66/2.64 % (29883)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_29722 for (2992ds/253Mi)
% 7.66/2.69 % (29882)Instruction limit reached!
% 7.66/2.69 % (29882)------------------------------
% 7.66/2.69 % (29882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.66/2.69 % (29882)Termination reason: Unknown
% 7.66/2.69 % (29882)Termination phase: Saturation
% 7.66/2.69
% 7.66/2.69 % (29882)Memory used [KB]: 6524
% 7.66/2.69 % (29882)Time elapsed: 0.060 s
% 7.66/2.69 % (29882)Instructions burned: 109 (million)
% 7.66/2.69 % (29882)------------------------------
% 7.66/2.69 % (29882)------------------------------
% 7.87/2.70 % (29880)Instruction limit reached!
% 7.87/2.70 % (29880)------------------------------
% 7.87/2.70 % (29880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.70 % (29880)Termination reason: Unknown
% 7.87/2.70 % (29880)Termination phase: Saturation
% 7.87/2.70
% 7.87/2.70 % (29880)Memory used [KB]: 6780
% 7.87/2.70 % (29880)Time elapsed: 0.085 s
% 7.87/2.70 % (29880)Instructions burned: 150 (million)
% 7.87/2.70 % (29880)------------------------------
% 7.87/2.70 % (29880)------------------------------
% 7.87/2.71 % (29884)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_29722 for (2992ds/140Mi)
% 7.87/2.72 % (29885)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_29722 for (2992ds/614Mi)
% 7.87/2.72 % (29870)Instruction limit reached!
% 7.87/2.72 % (29870)------------------------------
% 7.87/2.72 % (29870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.72 % (29870)Termination reason: Unknown
% 7.87/2.72 % (29870)Termination phase: Saturation
% 7.87/2.72
% 7.87/2.72 % (29870)Memory used [KB]: 3070
% 7.87/2.72 % (29870)Time elapsed: 0.236 s
% 7.87/2.72 % (29870)Instructions burned: 432 (million)
% 7.87/2.72 % (29870)------------------------------
% 7.87/2.72 % (29870)------------------------------
% 7.87/2.75 % (29886)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_29722 for (2991ds/202Mi)
% 7.87/2.77 % (29883)Instruction limit reached!
% 7.87/2.77 % (29883)------------------------------
% 7.87/2.77 % (29883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.77 % (29883)Termination reason: Unknown
% 7.87/2.77 % (29883)Termination phase: Saturation
% 7.87/2.77
% 7.87/2.77 % (29883)Memory used [KB]: 7164
% 7.87/2.77 % (29883)Time elapsed: 0.139 s
% 7.87/2.77 % (29883)Instructions burned: 253 (million)
% 7.87/2.77 % (29883)------------------------------
% 7.87/2.77 % (29883)------------------------------
% 7.87/2.77 % (29886)Refutation not found, incomplete strategy
% 7.87/2.77 % (29886)------------------------------
% 7.87/2.77 % (29886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.77 % (29886)Termination reason: Refutation not found, incomplete strategy
% 7.87/2.77
% 7.87/2.77
% 7.87/2.77 % (29886)Memory used [KB]: 6268
% 7.87/2.77 % (29886)Time elapsed: 0.031 s
% 7.87/2.77 % (29886)Instructions burned: 52 (million)
% 7.87/2.77 % (29886)------------------------------
% 7.87/2.77 % (29886)------------------------------
% 7.87/2.79 % (29884)Instruction limit reached!
% 7.87/2.79 % (29884)------------------------------
% 7.87/2.79 % (29884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.79 % (29884)Termination reason: Unknown
% 7.87/2.79 % (29884)Termination phase: Saturation
% 7.87/2.79
% 7.87/2.79 % (29884)Memory used [KB]: 6652
% 7.87/2.79 % (29884)Time elapsed: 0.079 s
% 7.87/2.79 % (29884)Instructions burned: 140 (million)
% 7.87/2.79 % (29884)------------------------------
% 7.87/2.79 % (29884)------------------------------
% 7.87/2.79 % (29874)Instruction limit reached!
% 7.87/2.79 % (29874)------------------------------
% 7.87/2.79 % (29874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.79 % (29874)Termination reason: Unknown
% 7.87/2.79 % (29874)Termination phase: Saturation
% 7.87/2.79
% 7.87/2.79 % (29874)Memory used [KB]: 7164
% 7.87/2.79 % (29874)Time elapsed: 0.247 s
% 7.87/2.79 % (29874)Instructions burned: 453 (million)
% 7.87/2.79 % (29874)------------------------------
% 7.87/2.79 % (29874)------------------------------
% 7.87/2.79 % (29888)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_29722 for (2991ds/283Mi)
% 7.87/2.79 % (29887)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_29722 for (2991ds/339Mi)
% 8.80/2.81 % (29889)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_29722 for (2991ds/134Mi)
% 8.80/2.81 % (29890)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_29722 for (2990ds/298Mi)
% 8.80/2.82 % (29881)Instruction limit reached!
% 8.80/2.82 % (29881)------------------------------
% 8.80/2.82 % (29881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.82 % (29881)Termination reason: Unknown
% 8.80/2.82 % (29881)Termination phase: Saturation
% 8.80/2.82
% 8.80/2.82 % (29881)Memory used [KB]: 7164
% 8.80/2.82 % (29881)Time elapsed: 0.193 s
% 8.80/2.82 % (29881)Instructions burned: 344 (million)
% 8.80/2.82 % (29881)------------------------------
% 8.80/2.82 % (29881)------------------------------
% 8.80/2.84 % (29891)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_29722 for (2990ds/192Mi)
% 8.80/2.88 % (29889)Instruction limit reached!
% 8.80/2.88 % (29889)------------------------------
% 8.80/2.88 % (29889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.88 % (29889)Termination reason: Unknown
% 8.80/2.88 % (29889)Termination phase: Saturation
% 8.80/2.88
% 8.80/2.88 % (29889)Memory used [KB]: 6524
% 8.80/2.88 % (29889)Time elapsed: 0.097 s
% 8.80/2.88 % (29889)Instructions burned: 135 (million)
% 8.80/2.88 % (29889)------------------------------
% 8.80/2.88 % (29889)------------------------------
% 9.09/2.90 % (29892)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_29722 for (2990ds/258Mi)
% 9.09/2.94 % (29891)Instruction limit reached!
% 9.09/2.94 % (29891)------------------------------
% 9.09/2.94 % (29891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.94 % (29891)Termination reason: Unknown
% 9.09/2.94 % (29891)Termination phase: Saturation
% 9.09/2.94
% 9.09/2.94 % (29891)Memory used [KB]: 7164
% 9.09/2.94 % (29891)Time elapsed: 0.106 s
% 9.09/2.94 % (29891)Instructions burned: 192 (million)
% 9.09/2.94 % (29891)------------------------------
% 9.09/2.94 % (29891)------------------------------
% 9.09/2.94 % (29888)Instruction limit reached!
% 9.09/2.94 % (29888)------------------------------
% 9.09/2.94 % (29888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.94 % (29888)Termination reason: Unknown
% 9.09/2.94 % (29888)Termination phase: Saturation
% 9.09/2.94
% 9.09/2.94 % (29888)Memory used [KB]: 7036
% 9.09/2.94 % (29888)Time elapsed: 0.175 s
% 9.09/2.94 % (29888)Instructions burned: 283 (million)
% 9.09/2.94 % (29888)------------------------------
% 9.09/2.94 % (29888)------------------------------
% 9.09/2.96 % (29893)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_29722 for (2989ds/90Mi)
% 9.09/2.97 % (29894)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_29722 for (2989ds/231Mi)
% 9.09/2.97 % (29890)Instruction limit reached!
% 9.09/2.97 % (29890)------------------------------
% 9.09/2.97 % (29890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.97 % (29890)Termination reason: Unknown
% 9.09/2.97 % (29890)Termination phase: Saturation
% 9.09/2.97
% 9.09/2.97 % (29890)Memory used [KB]: 7675
% 9.09/2.97 % (29890)Time elapsed: 0.157 s
% 9.09/2.97 % (29890)Instructions burned: 298 (million)
% 9.09/2.97 % (29890)------------------------------
% 9.09/2.97 % (29890)------------------------------
% 9.09/2.97 % (29887)Instruction limit reached!
% 9.09/2.97 % (29887)------------------------------
% 9.09/2.97 % (29887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.97 % (29887)Termination reason: Unknown
% 9.09/2.97 % (29887)Termination phase: Saturation
% 9.09/2.97
% 9.09/2.97 % (29887)Memory used [KB]: 7291
% 9.09/2.97 % (29887)Time elapsed: 0.199 s
% 9.09/2.97 % (29887)Instructions burned: 340 (million)
% 9.09/2.97 % (29887)------------------------------
% 9.09/2.97 % (29887)------------------------------
% 9.09/2.99 % (29895)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_29722 for (2989ds/458Mi)
% 9.09/2.99 % (29896)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_29722 for (2989ds/31Mi)
% 9.09/3.01 % (29896)Instruction limit reached!
% 9.09/3.01 % (29896)------------------------------
% 9.09/3.01 % (29896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/3.01 % (29896)Termination reason: Unknown
% 9.09/3.01 % (29896)Termination phase: Property scanning
% 9.09/3.01
% 9.09/3.01 % (29896)Memory used [KB]: 1535
% 9.09/3.01 % (29896)Time elapsed: 0.018 s
% 9.09/3.01 % (29896)Instructions burned: 32 (million)
% 9.09/3.01 % (29896)------------------------------
% 9.09/3.01 % (29896)------------------------------
% 9.09/3.01 % (29893)Instruction limit reached!
% 9.09/3.01 % (29893)------------------------------
% 9.09/3.01 % (29893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/3.01 % (29893)Termination reason: Unknown
% 9.09/3.01 % (29893)Termination phase: Saturation
% 9.09/3.01
% 9.09/3.01 % (29893)Memory used [KB]: 6524
% 9.09/3.01 % (29893)Time elapsed: 0.050 s
% 9.09/3.01 % (29893)Instructions burned: 91 (million)
% 9.09/3.01 % (29893)------------------------------
% 9.09/3.01 % (29893)------------------------------
% 11.02/3.03 % (29897)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_29722 for (2988ds/297Mi)
% 11.02/3.03 % (29898)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_29722 for (2988ds/987Mi)
% 11.02/3.05 % (29892)Instruction limit reached!
% 11.02/3.05 % (29892)------------------------------
% 11.02/3.05 % (29892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.02/3.05 % (29892)Termination reason: Unknown
% 11.02/3.05 % (29892)Termination phase: Saturation
% 11.02/3.05
% 11.02/3.05 % (29892)Memory used [KB]: 6780
% 11.02/3.05 % (29892)Time elapsed: 0.143 s
% 11.02/3.05 % (29892)Instructions burned: 259 (million)
% 11.02/3.05 % (29892)------------------------------
% 11.02/3.05 % (29892)------------------------------
% 11.02/3.05 % (29867)Instruction limit reached!
% 11.02/3.05 % (29867)------------------------------
% 11.02/3.05 % (29867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.02/3.05 % (29867)Termination reason: Unknown
% 11.02/3.05 % (29867)Termination phase: Saturation
% 11.02/3.05
% 11.02/3.05 % (29867)Memory used [KB]: 7803
% 11.02/3.05 % (29867)Time elapsed: 0.606 s
% 11.02/3.05 % (29867)Instructions burned: 1088 (million)
% 11.02/3.05 % (29867)------------------------------
% 11.02/3.05 % (29867)------------------------------
% 11.02/3.06 % (29885)Instruction limit reached!
% 11.02/3.06 % (29885)------------------------------
% 11.02/3.06 % (29885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.02/3.06 % (29885)Termination reason: Unknown
% 11.02/3.06 % (29885)Termination phase: Saturation
% 11.02/3.06
% 11.02/3.06 % (29885)Memory used [KB]: 7803
% 11.02/3.06 % (29885)Time elapsed: 0.345 s
% 11.02/3.06 % (29885)Instructions burned: 615 (million)
% 11.02/3.06 % (29885)------------------------------
% 11.02/3.06 % (29885)------------------------------
% 11.02/3.07 % (29899)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_29722 for (2988ds/182Mi)
% 11.02/3.08 % (29900)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_29722 for (2988ds/182Mi)
% 11.02/3.08 % (29901)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_29722 for (2988ds/154Mi)
% 11.02/3.09 % (29894)Instruction limit reached!
% 11.02/3.09 % (29894)------------------------------
% 11.02/3.09 % (29894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.02/3.09 % (29894)Termination reason: Unknown
% 11.02/3.09 % (29894)Termination phase: Saturation
% 11.02/3.09
% 11.02/3.09 % (29894)Memory used [KB]: 7164
% 11.02/3.09 % (29894)Time elapsed: 0.125 s
% 11.02/3.09 % (29894)Instructions burned: 232 (million)
% 11.02/3.09 % (29894)------------------------------
% 11.02/3.09 % (29894)------------------------------
% 11.02/3.11 % (29902)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_29722 for (2988ds/79Mi)
% 11.32/3.15 % (29902)Instruction limit reached!
% 11.32/3.15 % (29902)------------------------------
% 11.32/3.15 % (29902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.32/3.15 % (29902)Termination reason: Unknown
% 11.32/3.15 % (29902)Termination phase: Saturation
% 11.32/3.15
% 11.32/3.15 % (29902)Memory used [KB]: 6396
% 11.32/3.15 % (29902)Time elapsed: 0.044 s
% 11.32/3.15 % (29902)Instructions burned: 79 (million)
% 11.32/3.15 % (29902)------------------------------
% 11.32/3.15 % (29902)------------------------------
% 11.32/3.16 % (29901)Refutation not found, incomplete strategy
% 11.32/3.16 % (29901)------------------------------
% 11.32/3.16 % (29901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.32/3.16 % (29901)Termination reason: Refutation not found, incomplete strategy
% 11.32/3.16
% 11.32/3.16
% 11.32/3.16 % (29901)Memory used [KB]: 6908
% 11.32/3.16 % (29901)Time elapsed: 0.079 s
% 11.32/3.16 % (29901)Instructions burned: 153 (million)
% 11.32/3.16 % (29901)------------------------------
% 11.32/3.16 % (29901)------------------------------
% 11.32/3.17 % (29899)Instruction limit reached!
% 11.32/3.17 % (29899)------------------------------
% 11.32/3.17 % (29899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.32/3.17 % (29899)Termination reason: Unknown
% 11.32/3.17 % (29899)Termination phase: Saturation
% 11.32/3.17
% 11.32/3.17 % (29899)Memory used [KB]: 6652
% 11.32/3.17 % (29899)Time elapsed: 0.102 s
% 11.32/3.17 % (29899)Instructions burned: 182 (million)
% 11.32/3.17 % (29899)------------------------------
% 11.32/3.17 % (29899)------------------------------
% 11.32/3.17 % (29903)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_29722 for (2987ds/216Mi)
% 11.32/3.18 % (29900)Instruction limit reached!
% 11.32/3.18 % (29900)------------------------------
% 11.32/3.18 % (29900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.32/3.18 % (29900)Termination reason: Unknown
% 11.32/3.18 % (29900)Termination phase: Saturation
% 11.32/3.18
% 11.32/3.18 % (29900)Memory used [KB]: 6652
% 11.32/3.18 % (29900)Time elapsed: 0.104 s
% 11.32/3.18 % (29900)Instructions burned: 183 (million)
% 11.32/3.18 % (29900)------------------------------
% 11.32/3.18 % (29900)------------------------------
% 11.32/3.18 % (29904)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_29722 for (2987ds/114Mi)
% 11.32/3.18 % (29897)Instruction limit reached!
% 11.32/3.18 % (29897)------------------------------
% 11.32/3.18 % (29897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.32/3.18 % (29897)Termination reason: Unknown
% 11.32/3.18 % (29897)Termination phase: Saturation
% 11.32/3.18
% 11.32/3.18 % (29897)Memory used [KB]: 7036
% 11.32/3.18 % (29897)Time elapsed: 0.159 s
% 11.32/3.18 % (29897)Instructions burned: 298 (million)
% 11.32/3.18 % (29897)------------------------------
% 11.32/3.18 % (29897)------------------------------
% 11.32/3.19 % (29905)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_29722 for (2987ds/922Mi)
% 11.32/3.20 % (29906)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_29722 for (2987ds/182Mi)
% 11.97/3.20 % (29907)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_29722 for (2987ds/164Mi)
% 11.97/3.24 % (29904)Instruction limit reached!
% 11.97/3.24 % (29904)------------------------------
% 11.97/3.24 % (29904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.24 % (29904)Termination reason: Unknown
% 11.97/3.24 % (29904)Termination phase: Saturation
% 11.97/3.24
% 11.97/3.24 % (29904)Memory used [KB]: 6652
% 11.97/3.24 % (29904)Time elapsed: 0.063 s
% 11.97/3.24 % (29904)Instructions burned: 115 (million)
% 11.97/3.24 % (29904)------------------------------
% 11.97/3.24 % (29904)------------------------------
% 11.97/3.24 % (29895)Instruction limit reached!
% 11.97/3.24 % (29895)------------------------------
% 11.97/3.24 % (29895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.24 % (29895)Termination reason: Unknown
% 11.97/3.24 % (29895)Termination phase: Saturation
% 11.97/3.24
% 11.97/3.24 % (29895)Memory used [KB]: 7291
% 11.97/3.24 % (29895)Time elapsed: 0.257 s
% 11.97/3.24 % (29895)Instructions burned: 458 (million)
% 11.97/3.24 % (29895)------------------------------
% 11.97/3.24 % (29895)------------------------------
% 11.97/3.26 % (29908)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_29722 for (2986ds/50Mi)
% 11.97/3.26 % (29909)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_29722 for (2986ds/368Mi)
% 11.97/3.28 % (29903)Instruction limit reached!
% 11.97/3.28 % (29903)------------------------------
% 11.97/3.28 % (29903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.28 % (29903)Termination reason: Unknown
% 11.97/3.28 % (29903)Termination phase: Saturation
% 11.97/3.28
% 11.97/3.28 % (29903)Memory used [KB]: 7291
% 11.97/3.28 % (29903)Time elapsed: 0.113 s
% 11.97/3.28 % (29903)Instructions burned: 216 (million)
% 11.97/3.28 % (29903)------------------------------
% 11.97/3.28 % (29903)------------------------------
% 11.97/3.28 % (29908)Instruction limit reached!
% 11.97/3.28 % (29908)------------------------------
% 11.97/3.28 % (29908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.28 % (29908)Termination reason: Unknown
% 11.97/3.28 % (29908)Termination phase: Property scanning
% 11.97/3.28
% 11.97/3.28 % (29908)Memory used [KB]: 2046
% 11.97/3.28 % (29908)Time elapsed: 0.027 s
% 11.97/3.28 % (29908)Instructions burned: 51 (million)
% 11.97/3.28 % (29908)------------------------------
% 11.97/3.28 % (29908)------------------------------
% 11.97/3.28 % (29907)Instruction limit reached!
% 11.97/3.28 % (29907)------------------------------
% 11.97/3.28 % (29907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.28 % (29907)Termination reason: Unknown
% 11.97/3.28 % (29907)Termination phase: Saturation
% 11.97/3.28
% 11.97/3.28 % (29907)Memory used [KB]: 2302
% 11.97/3.28 % (29907)Time elapsed: 0.084 s
% 11.97/3.28 % (29907)Instructions burned: 165 (million)
% 11.97/3.28 % (29907)------------------------------
% 11.97/3.28 % (29907)------------------------------
% 11.97/3.29 % (29906)Instruction limit reached!
% 11.97/3.29 % (29906)------------------------------
% 11.97/3.29 % (29906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.29 % (29906)Termination reason: Unknown
% 11.97/3.29 % (29906)Termination phase: Saturation
% 11.97/3.29
% 11.97/3.29 % (29906)Memory used [KB]: 6908
% 11.97/3.29 % (29906)Time elapsed: 0.095 s
% 11.97/3.29 % (29906)Instructions burned: 183 (million)
% 11.97/3.29 % (29906)------------------------------
% 11.97/3.29 % (29906)------------------------------
% 12.49/3.30 % (29910)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_29722 for (2986ds/1021Mi)
% 12.49/3.30 % (29912)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_29722 for (2986ds/204Mi)
% 12.49/3.30 % (29911)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_29722 for (2986ds/267Mi)
% 12.49/3.31 % (29913)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_29722 for (2986ds/26Mi)
% 12.49/3.32 % (29913)Instruction limit reached!
% 12.49/3.32 % (29913)------------------------------
% 12.49/3.32 % (29913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.49/3.32 % (29913)Termination reason: Unknown
% 12.49/3.32 % (29913)Termination phase: shuffling
% 12.49/3.32
% 12.49/3.32 % (29913)Memory used [KB]: 1791
% 12.49/3.32 % (29913)Time elapsed: 0.015 s
% 12.49/3.32 % (29913)Instructions burned: 26 (million)
% 12.49/3.32 % (29913)------------------------------
% 12.49/3.32 % (29913)------------------------------
% 12.49/3.34 % (29914)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_29722 for (2985ds/53Mi)
% 12.49/3.37 % (29914)Instruction limit reached!
% 12.49/3.37 % (29914)------------------------------
% 12.49/3.37 % (29914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.49/3.37 % (29914)Termination reason: Unknown
% 12.49/3.37 % (29914)Termination phase: Property scanning
% 12.49/3.37
% 12.49/3.37 % (29914)Memory used [KB]: 2046
% 12.49/3.37 % (29914)Time elapsed: 0.028 s
% 12.49/3.37 % (29914)Instructions burned: 53 (million)
% 12.49/3.37 % (29914)------------------------------
% 12.49/3.37 % (29914)------------------------------
% 12.49/3.39 % (29915)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_29722 for (2985ds/4436Mi)
% 12.56/3.41 % (29912)Instruction limit reached!
% 12.56/3.41 % (29912)------------------------------
% 12.56/3.41 % (29912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.56/3.41 % (29912)Termination reason: Unknown
% 12.56/3.41 % (29912)Termination phase: Saturation
% 12.56/3.41
% 12.56/3.41 % (29912)Memory used [KB]: 6652
% 12.56/3.41 % (29912)Time elapsed: 0.112 s
% 12.56/3.41 % (29912)Instructions burned: 205 (million)
% 12.56/3.41 % (29912)------------------------------
% 12.56/3.41 % (29912)------------------------------
% 12.56/3.43 % (29916)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_29722 for (2984ds/1539Mi)
% 12.56/3.44 % (29911)Instruction limit reached!
% 12.56/3.44 % (29911)------------------------------
% 12.56/3.44 % (29911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.56/3.44 % (29911)Termination reason: Unknown
% 12.56/3.44 % (29911)Termination phase: Saturation
% 12.56/3.44
% 12.56/3.44 % (29911)Memory used [KB]: 7036
% 12.56/3.44 % (29911)Time elapsed: 0.144 s
% 12.56/3.44 % (29911)Instructions burned: 267 (million)
% 12.56/3.44 % (29911)------------------------------
% 12.56/3.44 % (29911)------------------------------
% 12.56/3.46 % (29909)Instruction limit reached!
% 12.56/3.46 % (29909)------------------------------
% 12.56/3.46 % (29909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.56/3.46 % (29909)Termination reason: Unknown
% 12.56/3.46 % (29909)Termination phase: Saturation
% 12.56/3.46
% 12.56/3.46 % (29909)Memory used [KB]: 6780
% 12.56/3.46 % (29909)Time elapsed: 0.199 s
% 12.56/3.46 % (29909)Instructions burned: 368 (million)
% 12.56/3.46 % (29909)------------------------------
% 12.56/3.46 % (29909)------------------------------
% 12.56/3.47 % (29917)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_29722 for (2984ds/408Mi)
% 12.56/3.48 % (29918)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_29722 for (2984ds/5205Mi)
% 13.07/3.51 % (29917)Refutation not found, incomplete strategy
% 13.07/3.51 % (29917)------------------------------
% 13.07/3.51 % (29917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.07/3.51 % (29917)Termination reason: Refutation not found, incomplete strategy
% 13.07/3.51
% 13.07/3.51
% 13.07/3.51 % (29917)Memory used [KB]: 6652
% 13.07/3.51 % (29917)Time elapsed: 0.043 s
% 13.07/3.51 % (29917)Instructions burned: 75 (million)
% 13.07/3.51 % (29917)------------------------------
% 13.07/3.51 % (29917)------------------------------
% 13.07/3.53 % (29919)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_29722 for (2983ds/1913Mi)
% 13.07/3.56 % (29898)Instruction limit reached!
% 13.07/3.56 % (29898)------------------------------
% 13.07/3.56 % (29898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.07/3.56 % (29898)Termination reason: Unknown
% 13.07/3.56 % (29898)Termination phase: Saturation
% 13.07/3.56
% 13.07/3.56 % (29898)Memory used [KB]: 8315
% 13.07/3.56 % (29898)Time elapsed: 0.529 s
% 13.07/3.56 % (29898)Instructions burned: 988 (million)
% 13.07/3.56 % (29898)------------------------------
% 13.07/3.56 % (29898)------------------------------
% 13.07/3.58 % (29920)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_29722 for (2983ds/4350Mi)
% 13.68/3.61 % (29920)Refutation not found, incomplete strategy
% 13.68/3.61 % (29920)------------------------------
% 13.68/3.61 % (29920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.68/3.61 % (29920)Termination reason: Refutation not found, incomplete strategy
% 13.68/3.61
% 13.68/3.61
% 13.68/3.61 % (29920)Memory used [KB]: 6140
% 13.68/3.61 % (29920)Time elapsed: 0.028 s
% 13.68/3.61 % (29920)Instructions burned: 47 (million)
% 13.68/3.61 % (29920)------------------------------
% 13.68/3.61 % (29920)------------------------------
% 13.68/3.63 % (29921)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_29722 for (2982ds/68Mi)
% 13.68/3.66 % (29921)Instruction limit reached!
% 13.68/3.66 % (29921)------------------------------
% 13.68/3.66 % (29921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.68/3.66 % (29921)Termination reason: Unknown
% 13.68/3.66 % (29921)Termination phase: Saturation
% 13.68/3.66
% 13.68/3.66 % (29921)Memory used [KB]: 6268
% 13.68/3.66 % (29921)Time elapsed: 0.037 s
% 13.68/3.66 % (29921)Instructions burned: 68 (million)
% 13.68/3.66 % (29921)------------------------------
% 13.68/3.66 % (29921)------------------------------
% 13.68/3.68 % (29922)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_29722 for (2982ds/358Mi)
% 13.68/3.69 % (29905)Instruction limit reached!
% 13.68/3.69 % (29905)------------------------------
% 13.68/3.69 % (29905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.68/3.69 % (29905)Termination reason: Unknown
% 13.68/3.69 % (29905)Termination phase: Saturation
% 13.68/3.69
% 13.68/3.69 % (29905)Memory used [KB]: 7675
% 13.68/3.69 % (29905)Time elapsed: 0.504 s
% 13.68/3.69 % (29905)Instructions burned: 922 (million)
% 13.68/3.69 % (29905)------------------------------
% 13.68/3.69 % (29905)------------------------------
% 14.30/3.71 % (29923)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_29722 for (2982ds/31Mi)
% 14.30/3.73 % (29923)Instruction limit reached!
% 14.30/3.73 % (29923)------------------------------
% 14.30/3.73 % (29923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.30/3.73 % (29923)Termination reason: Unknown
% 14.30/3.73 % (29923)Termination phase: Property scanning
% 14.30/3.73
% 14.30/3.73 % (29923)Memory used [KB]: 1535
% 14.30/3.73 % (29923)Time elapsed: 0.019 s
% 14.30/3.73 % (29923)Instructions burned: 32 (million)
% 14.30/3.73 % (29923)------------------------------
% 14.30/3.73 % (29923)------------------------------
% 14.30/3.75 % (29924)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_29722 for (2981ds/279Mi)
% 14.34/3.82 % (29924)Refutation not found, incomplete strategy
% 14.34/3.82 % (29924)------------------------------
% 14.34/3.82 % (29924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.34/3.82 % (29924)Termination reason: Refutation not found, incomplete strategy
% 14.34/3.82
% 14.34/3.82
% 14.34/3.82 % (29924)Memory used [KB]: 6908
% 14.34/3.82 % (29924)Time elapsed: 0.077 s
% 14.34/3.82 % (29924)Instructions burned: 145 (million)
% 14.34/3.82 % (29924)------------------------------
% 14.34/3.82 % (29924)------------------------------
% 14.34/3.84 % (29925)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_29722 for (2980ds/258Mi)
% 14.34/3.86 % (29910)Instruction limit reached!
% 14.34/3.86 % (29910)------------------------------
% 14.34/3.86 % (29910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.34/3.86 % (29910)Termination reason: Unknown
% 14.34/3.86 % (29910)Termination phase: Saturation
% 14.34/3.86
% 14.34/3.86 % (29910)Memory used [KB]: 7803
% 14.34/3.86 % (29910)Time elapsed: 0.564 s
% 14.34/3.86 % (29910)Instructions burned: 1021 (million)
% 14.34/3.86 % (29910)------------------------------
% 14.34/3.86 % (29910)------------------------------
% 14.34/3.88 % (29922)Instruction limit reached!
% 14.34/3.88 % (29922)------------------------------
% 14.34/3.88 % (29922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.34/3.88 % (29922)Termination reason: Unknown
% 14.34/3.88 % (29922)Termination phase: Saturation
% 14.34/3.88
% 14.34/3.88 % (29922)Memory used [KB]: 6908
% 14.34/3.88 % (29922)Time elapsed: 0.219 s
% 14.34/3.88 % (29922)Instructions burned: 359 (million)
% 14.34/3.88 % (29922)------------------------------
% 14.34/3.88 % (29922)------------------------------
% 14.34/3.88 % (29926)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_29722 for (2980ds/26Mi)
% 15.23/3.90 % (29926)Instruction limit reached!
% 15.23/3.90 % (29926)------------------------------
% 15.23/3.90 % (29926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.23/3.90 % (29926)Termination reason: Unknown
% 15.23/3.90 % (29926)Termination phase: shuffling
% 15.23/3.90
% 15.23/3.90 % (29926)Memory used [KB]: 1791
% 15.23/3.90 % (29926)Time elapsed: 0.015 s
% 15.23/3.90 % (29926)Instructions burned: 26 (million)
% 15.23/3.90 % (29926)------------------------------
% 15.23/3.90 % (29926)------------------------------
% 15.23/3.90 % (29927)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_29722 for (2980ds/995Mi)
% 15.23/3.92 % (29928)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_29722 for (2979ds/373Mi)
% 15.23/3.99 % (29925)Instruction limit reached!
% 15.23/3.99 % (29925)------------------------------
% 15.23/3.99 % (29925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.23/3.99 % (29925)Termination reason: Unknown
% 15.23/3.99 % (29925)Termination phase: Saturation
% 15.23/3.99
% 15.23/3.99 % (29925)Memory used [KB]: 6908
% 15.23/3.99 % (29925)Time elapsed: 0.148 s
% 15.23/3.99 % (29925)Instructions burned: 258 (million)
% 15.23/3.99 % (29925)------------------------------
% 15.23/3.99 % (29925)------------------------------
% 15.23/4.01 % (29929)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_29722 for (2978ds/253Mi)
% 18.03/4.12 % (29928)Instruction limit reached!
% 18.03/4.12 % (29928)------------------------------
% 18.03/4.12 % (29928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.03/4.12 % (29928)Termination reason: Unknown
% 18.03/4.12 % (29928)Termination phase: Saturation
% 18.03/4.12
% 18.03/4.12 % (29928)Memory used [KB]: 6780
% 18.03/4.12 % (29928)Time elapsed: 0.203 s
% 18.03/4.12 % (29928)Instructions burned: 373 (million)
% 18.03/4.12 % (29928)------------------------------
% 18.03/4.12 % (29928)------------------------------
% 18.74/4.14 % (29930)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_29722 for (2977ds/832Mi)
% 18.74/4.14 % (29929)Instruction limit reached!
% 18.74/4.14 % (29929)------------------------------
% 18.74/4.14 % (29929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.74/4.14 % (29929)Termination reason: Unknown
% 18.74/4.14 % (29929)Termination phase: Saturation
% 18.74/4.14
% 18.74/4.14 % (29929)Memory used [KB]: 7291
% 18.74/4.14 % (29929)Time elapsed: 0.135 s
% 18.74/4.14 % (29929)Instructions burned: 253 (million)
% 18.74/4.14 % (29929)------------------------------
% 18.74/4.14 % (29929)------------------------------
% 18.74/4.16 % (29931)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_29722 for (2977ds/668Mi)
% 18.74/4.18 % (29930)Refutation not found, incomplete strategy
% 18.74/4.18 % (29930)------------------------------
% 18.74/4.18 % (29930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.74/4.18 % (29930)Termination reason: Refutation not found, incomplete strategy
% 18.74/4.18
% 18.74/4.18
% 18.74/4.18 % (29930)Memory used [KB]: 6652
% 18.74/4.18 % (29930)Time elapsed: 0.042 s
% 18.74/4.18 % (29930)Instructions burned: 74 (million)
% 18.74/4.18 % (29930)------------------------------
% 18.74/4.18 % (29930)------------------------------
% 19.18/4.20 % (29932)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_29722 for (2977ds/40Mi)
% 19.18/4.22 % (29932)Instruction limit reached!
% 19.18/4.22 % (29932)------------------------------
% 19.18/4.22 % (29932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.18/4.22 % (29932)Termination reason: Unknown
% 19.18/4.22 % (29932)Termination phase: Property scanning
% 19.18/4.22
% 19.18/4.22 % (29932)Memory used [KB]: 2046
% 19.18/4.22 % (29932)Time elapsed: 0.022 s
% 19.18/4.22 % (29932)Instructions burned: 40 (million)
% 19.18/4.22 % (29932)------------------------------
% 19.18/4.22 % (29932)------------------------------
% 19.18/4.24 % (29933)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_29722 for (2976ds/294Mi)
% 19.18/4.25 % (29916)Instruction limit reached!
% 19.18/4.25 % (29916)------------------------------
% 19.18/4.25 % (29916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.18/4.25 % (29916)Termination reason: Unknown
% 19.18/4.25 % (29916)Termination phase: Saturation
% 19.18/4.25
% 19.18/4.25 % (29916)Memory used [KB]: 8443
% 19.18/4.25 % (29916)Time elapsed: 0.824 s
% 19.18/4.25 % (29916)Instructions burned: 1539 (million)
% 19.18/4.25 % (29916)------------------------------
% 19.18/4.25 % (29916)------------------------------
% 19.18/4.28 % (29934)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_29722 for (2976ds/187Mi)
% 19.18/4.30 % (29933)Refutation not found, incomplete strategy
% 19.18/4.30 % (29933)------------------------------
% 19.18/4.30 % (29933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.18/4.30 % (29933)Termination reason: Refutation not found, incomplete strategy
% 19.18/4.30
% 19.18/4.30
% 19.18/4.30 % (29933)Memory used [KB]: 6780
% 19.18/4.30 % (29933)Time elapsed: 0.053 s
% 19.18/4.30 % (29933)Instructions burned: 102 (million)
% 19.18/4.30 % (29933)------------------------------
% 19.18/4.30 % (29933)------------------------------
% 19.69/4.32 % (29935)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_29722 for (2975ds/371Mi)
% 19.69/4.37 % (29934)Instruction limit reached!
% 19.69/4.37 % (29934)------------------------------
% 19.69/4.37 % (29934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.69/4.37 % (29934)Termination reason: Unknown
% 19.69/4.37 % (29934)Termination phase: Saturation
% 19.69/4.37
% 19.69/4.37 % (29934)Memory used [KB]: 6524
% 19.69/4.37 % (29934)Time elapsed: 0.098 s
% 19.69/4.37 % (29934)Instructions burned: 189 (million)
% 19.69/4.37 % (29934)------------------------------
% 19.69/4.37 % (29934)------------------------------
% 19.69/4.39 % (29936)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_29722 for (2975ds/1827Mi)
% 20.28/4.45 % (29927)Instruction limit reached!
% 20.28/4.45 % (29927)------------------------------
% 20.28/4.45 % (29927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.28/4.45 % (29927)Termination reason: Unknown
% 20.28/4.45 % (29927)Termination phase: Saturation
% 20.28/4.45
% 20.28/4.45 % (29927)Memory used [KB]: 9210
% 20.28/4.45 % (29927)Time elapsed: 0.553 s
% 20.28/4.45 % (29927)Instructions burned: 995 (million)
% 20.28/4.45 % (29927)------------------------------
% 20.28/4.45 % (29927)------------------------------
% 20.28/4.47 % (29937)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_29722 for (2974ds/70Mi)
% 20.65/4.51 % (29937)Instruction limit reached!
% 20.65/4.51 % (29937)------------------------------
% 20.65/4.51 % (29937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.65/4.51 % (29937)Termination reason: Unknown
% 20.65/4.51 % (29937)Termination phase: Property scanning
% 20.65/4.51
% 20.65/4.51 % (29937)Memory used [KB]: 2046
% 20.65/4.51 % (29937)Time elapsed: 0.038 s
% 20.65/4.51 % (29937)Instructions burned: 71 (million)
% 20.65/4.51 % (29937)------------------------------
% 20.65/4.51 % (29937)------------------------------
% 20.65/4.52 % (29919)Instruction limit reached!
% 20.65/4.52 % (29919)------------------------------
% 20.65/4.52 % (29919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.65/4.52 % (29919)Termination reason: Unknown
% 20.65/4.52 % (29919)Termination phase: Saturation
% 20.65/4.52
% 20.65/4.52 % (29919)Memory used [KB]: 3326
% 20.65/4.52 % (29919)Time elapsed: 0.999 s
% 20.65/4.52 % (29919)Instructions burned: 1913 (million)
% 20.65/4.52 % (29919)------------------------------
% 20.65/4.52 % (29919)------------------------------
% 20.65/4.53 % (29938)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_29722 for (2973ds/316Mi)
% 20.65/4.53 % (29931)Instruction limit reached!
% 20.65/4.53 % (29931)------------------------------
% 20.65/4.53 % (29931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.65/4.53 % (29931)Termination reason: Unknown
% 20.65/4.53 % (29931)Termination phase: Saturation
% 20.65/4.53
% 20.65/4.53 % (29931)Memory used [KB]: 14200
% 20.65/4.53 % (29931)Time elapsed: 0.369 s
% 20.65/4.53 % (29931)Instructions burned: 668 (million)
% 20.65/4.53 % (29931)------------------------------
% 20.65/4.53 % (29931)------------------------------
% 20.65/4.53 % (29935)Instruction limit reached!
% 20.65/4.53 % (29935)------------------------------
% 20.65/4.53 % (29935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.65/4.53 % (29935)Termination reason: Unknown
% 20.65/4.53 % (29935)Termination phase: Saturation
% 20.65/4.53
% 20.65/4.53 % (29935)Memory used [KB]: 6908
% 20.65/4.53 % (29935)Time elapsed: 0.216 s
% 20.65/4.53 % (29935)Instructions burned: 371 (million)
% 20.65/4.53 % (29935)------------------------------
% 20.65/4.53 % (29935)------------------------------
% 20.65/4.54 % (29939)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_29722 for (2973ds/932Mi)
% 20.65/4.55 % (29941)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_29722 for (2973ds/8250Mi)
% 20.65/4.55 % (29940)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_29722 for (2973ds/4714Mi)
% 21.57/4.60 % (29938)Refutation not found, incomplete strategy
% 21.57/4.60 % (29938)------------------------------
% 21.57/4.60 % (29938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.57/4.60 % (29938)Termination reason: Refutation not found, incomplete strategy
% 21.57/4.60
% 21.57/4.60
% 21.57/4.60 % (29938)Memory used [KB]: 6908
% 21.57/4.60 % (29938)Time elapsed: 0.075 s
% 21.57/4.60 % (29938)Instructions burned: 144 (million)
% 21.57/4.60 % (29938)------------------------------
% 21.57/4.60 % (29938)------------------------------
% 21.57/4.62 % (29942)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_29722 for (2972ds/770Mi)
% 21.57/4.63 % (29940)Refutation not found, incomplete strategy
% 21.57/4.63 % (29940)------------------------------
% 21.57/4.63 % (29940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.57/4.63 % (29940)Termination reason: Refutation not found, incomplete strategy
% 21.57/4.63
% 21.57/4.63
% 21.57/4.63 % (29940)Memory used [KB]: 7036
% 21.57/4.63 % (29940)Time elapsed: 0.079 s
% 21.57/4.63 % (29940)Instructions burned: 151 (million)
% 21.57/4.63 % (29940)------------------------------
% 21.57/4.63 % (29940)------------------------------
% 21.57/4.65 % (29943)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_29722 for (2972ds/794Mi)
% 21.57/4.66 % (29942)Refutation not found, incomplete strategy
% 21.57/4.66 % (29942)------------------------------
% 21.57/4.66 % (29942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.57/4.66 % (29942)Termination reason: Refutation not found, incomplete strategy
% 21.57/4.66
% 21.57/4.66
% 21.57/4.66 % (29942)Memory used [KB]: 6396
% 21.57/4.66 % (29942)Time elapsed: 0.033 s
% 21.57/4.66 % (29942)Instructions burned: 58 (million)
% 21.57/4.66 % (29942)------------------------------
% 21.57/4.66 % (29942)------------------------------
% 21.57/4.68 % (29944)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_29722 for (2972ds/464Mi)
% 22.40/4.93 % (29944)Instruction limit reached!
% 22.40/4.93 % (29944)------------------------------
% 22.40/4.93 % (29944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.40/4.93 % (29944)Termination reason: Unknown
% 22.40/4.93 % (29944)Termination phase: Saturation
% 22.40/4.93
% 22.40/4.93 % (29944)Memory used [KB]: 6908
% 22.40/4.93 % (29944)Time elapsed: 0.257 s
% 22.40/4.93 % (29944)Instructions burned: 464 (million)
% 22.40/4.93 % (29944)------------------------------
% 22.40/4.93 % (29944)------------------------------
% 22.40/4.95 % (29945)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_29722 for (2969ds/1376Mi)
% 25.00/5.07 % (29939)Instruction limit reached!
% 25.00/5.07 % (29939)------------------------------
% 25.00/5.07 % (29939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.00/5.07 % (29939)Termination reason: Unknown
% 25.00/5.07 % (29939)Termination phase: Saturation
% 25.00/5.07
% 25.00/5.07 % (29939)Memory used [KB]: 8699
% 25.00/5.07 % (29939)Time elapsed: 0.528 s
% 25.00/5.07 % (29939)Instructions burned: 933 (million)
% 25.00/5.07 % (29939)------------------------------
% 25.00/5.07 % (29939)------------------------------
% 25.00/5.09 % (29943)Instruction limit reached!
% 25.00/5.09 % (29943)------------------------------
% 25.00/5.09 % (29943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.00/5.09 % (29943)Termination reason: Unknown
% 25.00/5.09 % (29943)Termination phase: Saturation
% 25.00/5.09
% 25.00/5.09 % (29943)Memory used [KB]: 3965
% 25.00/5.09 % (29943)Time elapsed: 0.444 s
% 25.00/5.09 % (29943)Instructions burned: 794 (million)
% 25.00/5.09 % (29943)------------------------------
% 25.00/5.09 % (29943)------------------------------
% 25.00/5.09 % (29946)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_29722 for (2968ds/906Mi)
% 25.00/5.11 % (29947)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_29722 for (2968ds/434Mi)
% 25.67/5.15 % (29947)Refutation not found, incomplete strategy
% 25.67/5.15 % (29947)------------------------------
% 25.67/5.15 % (29947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.67/5.15 % (29947)Termination reason: Refutation not found, incomplete strategy
% 25.67/5.15
% 25.67/5.15
% 25.67/5.15 % (29947)Memory used [KB]: 6524
% 25.67/5.15 % (29947)Time elapsed: 0.039 s
% 25.67/5.15 % (29947)Instructions burned: 70 (million)
% 25.67/5.15 % (29947)------------------------------
% 25.67/5.15 % (29947)------------------------------
% 25.67/5.17 % (29948)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_29722 for (2967ds/865Mi)
% 26.57/5.39 % (29936)Instruction limit reached!
% 26.57/5.39 % (29936)------------------------------
% 26.57/5.39 % (29936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.57/5.39 % (29936)Termination reason: Unknown
% 26.57/5.39 % (29936)Termination phase: Saturation
% 26.57/5.39
% 26.57/5.39 % (29936)Memory used [KB]: 9083
% 26.57/5.39 % (29936)Time elapsed: 0.999 s
% 26.57/5.39 % (29936)Instructions burned: 1828 (million)
% 26.57/5.39 % (29936)------------------------------
% 26.57/5.39 % (29936)------------------------------
% 27.08/5.41 % (29949)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_29722 for (2965ds/593Mi)
% 27.87/5.60 % (29946)Instruction limit reached!
% 27.87/5.60 % (29946)------------------------------
% 27.87/5.60 % (29946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.87/5.60 % (29946)Termination reason: Unknown
% 27.87/5.60 % (29946)Termination phase: Saturation
% 27.87/5.60
% 27.87/5.60 % (29946)Memory used [KB]: 8315
% 27.87/5.60 % (29946)Time elapsed: 0.511 s
% 27.87/5.60 % (29946)Instructions burned: 907 (million)
% 27.87/5.60 % (29946)------------------------------
% 27.87/5.60 % (29946)------------------------------
% 27.87/5.62 % (29950)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_29722 for (2962ds/443Mi)
% 27.87/5.64 % (29948)Instruction limit reached!
% 27.87/5.64 % (29948)------------------------------
% 27.87/5.64 % (29948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.87/5.64 % (29948)Termination reason: Unknown
% 27.87/5.64 % (29948)Termination phase: Saturation
% 27.87/5.64
% 27.87/5.64 % (29948)Memory used [KB]: 8571
% 27.87/5.64 % (29948)Time elapsed: 0.475 s
% 27.87/5.64 % (29948)Instructions burned: 865 (million)
% 27.87/5.64 % (29948)------------------------------
% 27.87/5.64 % (29948)------------------------------
% 27.87/5.67 % (29951)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_29722 for (2962ds/594Mi)
% 29.30/5.73 % (29945)Instruction limit reached!
% 29.30/5.73 % (29945)------------------------------
% 29.30/5.73 % (29945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.30/5.73 % (29945)Termination reason: Unknown
% 29.30/5.73 % (29945)Termination phase: Saturation
% 29.30/5.73
% 29.30/5.73 % (29945)Memory used [KB]: 10490
% 29.30/5.73 % (29945)Time elapsed: 0.777 s
% 29.30/5.73 % (29945)Instructions burned: 1377 (million)
% 29.30/5.73 % (29945)------------------------------
% 29.30/5.73 % (29945)------------------------------
% 29.30/5.73 % (29949)Instruction limit reached!
% 29.30/5.73 % (29949)------------------------------
% 29.30/5.73 % (29949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.30/5.73 % (29949)Termination reason: Unknown
% 29.30/5.73 % (29949)Termination phase: Saturation
% 29.30/5.73
% 29.30/5.73 % (29949)Memory used [KB]: 8315
% 29.30/5.73 % (29949)Time elapsed: 0.325 s
% 29.30/5.73 % (29949)Instructions burned: 593 (million)
% 29.30/5.73 % (29949)------------------------------
% 29.30/5.73 % (29949)------------------------------
% 29.30/5.75 % (29952)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_29722 for (2961ds/327Mi)
% 29.30/5.76 % (29953)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_29722 for (2961ds/5411Mi)
% 29.98/5.80 % (29953)Refutation not found, incomplete strategy
% 29.98/5.80 % (29953)------------------------------
% 29.98/5.80 % (29953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.98/5.80 % (29953)Termination reason: Refutation not found, incomplete strategy
% 29.98/5.80
% 29.98/5.80
% 29.98/5.80 % (29953)Memory used [KB]: 6780
% 29.98/5.80 % (29953)Time elapsed: 0.050 s
% 29.98/5.80 % (29953)Instructions burned: 87 (million)
% 29.98/5.80 % (29953)------------------------------
% 29.98/5.80 % (29953)------------------------------
% 29.98/5.82 % (29954)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_29722 for (2960ds/1762Mi)
% 29.98/5.86 % (29950)Instruction limit reached!
% 29.98/5.86 % (29950)------------------------------
% 29.98/5.86 % (29950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.98/5.86 % (29950)Termination reason: Unknown
% 29.98/5.86 % (29950)Termination phase: Saturation
% 29.98/5.86
% 29.98/5.86 % (29950)Memory used [KB]: 6908
% 29.98/5.86 % (29950)Time elapsed: 0.236 s
% 29.98/5.86 % (29950)Instructions burned: 444 (million)
% 29.98/5.86 % (29950)------------------------------
% 29.98/5.86 % (29950)------------------------------
% 29.98/5.88 % (29955)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_29722 for (2960ds/96Mi)
% 29.98/5.88 % (29915)Instruction limit reached!
% 29.98/5.88 % (29915)------------------------------
% 29.98/5.88 % (29915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.98/5.88 % (29915)Termination reason: Unknown
% 29.98/5.88 % (29915)Termination phase: Saturation
% 29.98/5.88
% 29.98/5.88 % (29915)Memory used [KB]: 11513
% 29.98/5.88 % (29915)Time elapsed: 2.492 s
% 29.98/5.88 % (29915)Instructions burned: 4436 (million)
% 29.98/5.88 % (29915)------------------------------
% 29.98/5.88 % (29915)------------------------------
% 30.59/5.90 % (29956)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_29722 for (2960ds/503Mi)
% 30.59/5.92 % (29955)Instruction limit reached!
% 30.59/5.92 % (29955)------------------------------
% 30.59/5.92 % (29955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.59/5.92 % (29955)Termination reason: Unknown
% 30.59/5.92 % (29955)Termination phase: Property scanning
% 30.59/5.92
% 30.59/5.92 % (29955)Memory used [KB]: 2174
% 30.59/5.92 % (29955)Time elapsed: 0.049 s
% 30.59/5.92 % (29955)Instructions burned: 97 (million)
% 30.59/5.92 % (29955)------------------------------
% 30.59/5.92 % (29955)------------------------------
% 30.59/5.93 % (29952)Instruction limit reached!
% 30.59/5.93 % (29952)------------------------------
% 30.59/5.93 % (29952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.59/5.93 % (29952)Termination reason: Unknown
% 30.59/5.93 % (29952)Termination phase: Saturation
% 30.59/5.93
% 30.59/5.93 % (29952)Memory used [KB]: 7164
% 30.59/5.93 % (29952)Time elapsed: 0.184 s
% 30.59/5.93 % (29952)Instructions burned: 328 (million)
% 30.59/5.93 % (29952)------------------------------
% 30.59/5.93 % (29952)------------------------------
% 30.59/5.94 % (29957)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_29722 for (2959ds/90Mi)
% 30.59/5.95 % (29956)Refutation not found, incomplete strategy
% 30.59/5.95 % (29956)------------------------------
% 30.59/5.95 % (29956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.59/5.95 % (29956)Termination reason: Refutation not found, incomplete strategy
% 30.59/5.95
% 30.59/5.95
% 30.59/5.95 % (29956)Memory used [KB]: 6780
% 30.59/5.95 % (29956)Time elapsed: 0.047 s
% 30.59/5.95 % (29956)Instructions burned: 82 (million)
% 30.59/5.95 % (29956)------------------------------
% 30.59/5.95 % (29956)------------------------------
% 30.59/5.95 % (29958)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_29722 for (2959ds/593Mi)
% 30.59/5.97 % (29959)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_29722 for (2959ds/1512Mi)
% 30.59/5.99 % (29951)Instruction limit reached!
% 30.59/5.99 % (29951)------------------------------
% 30.59/5.99 % (29951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.59/5.99 % (29951)Termination reason: Unknown
% 30.59/5.99 % (29951)Termination phase: Saturation
% 30.59/5.99
% 30.59/5.99 % (29951)Memory used [KB]: 7164
% 30.59/5.99 % (29951)Time elapsed: 0.323 s
% 30.59/5.99 % (29951)Instructions burned: 594 (million)
% 30.59/5.99 % (29951)------------------------------
% 30.59/5.99 % (29951)------------------------------
% 30.59/5.99 % (29957)Instruction limit reached!
% 30.59/5.99 % (29957)------------------------------
% 30.59/5.99 % (29957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.59/5.99 % (29957)Termination reason: Unknown
% 30.59/5.99 % (29957)Termination phase: Saturation
% 30.59/5.99
% 30.59/5.99 % (29957)Memory used [KB]: 6524
% 30.59/5.99 % (29957)Time elapsed: 0.049 s
% 30.59/5.99 % (29957)Instructions burned: 90 (million)
% 30.59/5.99 % (29957)------------------------------
% 30.59/5.99 % (29957)------------------------------
% 30.59/6.01 % (29960)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_29722 for (2959ds/569Mi)
% 30.59/6.01 % (29961)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_29722 for (2959ds/501Mi)
% 30.59/6.02 % (29959)Refutation not found, incomplete strategy
% 30.59/6.02 % (29959)------------------------------
% 30.59/6.02 % (29959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.59/6.02 % (29959)Termination reason: Refutation not found, incomplete strategy
% 30.59/6.02
% 30.59/6.02
% 30.59/6.02 % (29959)Memory used [KB]: 6780
% 30.59/6.02 % (29959)Time elapsed: 0.052 s
% 30.59/6.02 % (29959)Instructions burned: 91 (million)
% 30.59/6.02 % (29959)------------------------------
% 30.59/6.02 % (29959)------------------------------
% 32.04/6.04 % (29962)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_29722 for (2958ds/562Mi)
% 32.04/6.06 % (29961)Refutation not found, incomplete strategy
% 32.04/6.06 % (29961)------------------------------
% 32.04/6.06 % (29961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.04/6.06 % (29961)Termination reason: Refutation not found, incomplete strategy
% 32.04/6.06
% 32.04/6.06
% 32.04/6.06 % (29961)Memory used [KB]: 6780
% 32.04/6.06 % (29961)Time elapsed: 0.051 s
% 32.04/6.06 % (29961)Instructions burned: 93 (million)
% 32.04/6.06 % (29961)------------------------------
% 32.04/6.06 % (29961)------------------------------
% 32.04/6.08 % (29963)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_29722 for (2958ds/406Mi)
% 32.93/6.27 % (29958)Instruction limit reached!
% 32.93/6.27 % (29958)------------------------------
% 32.93/6.27 % (29958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.93/6.27 % (29958)Termination reason: Unknown
% 32.93/6.27 % (29958)Termination phase: Saturation
% 32.93/6.27
% 32.93/6.27 % (29958)Memory used [KB]: 7036
% 32.93/6.27 % (29958)Time elapsed: 0.322 s
% 32.93/6.27 % (29958)Instructions burned: 593 (million)
% 32.93/6.27 % (29958)------------------------------
% 32.93/6.27 % (29958)------------------------------
% 32.93/6.29 % (29964)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_29722 for (2956ds/582Mi)
% 33.41/6.31 % (29963)Instruction limit reached!
% 33.41/6.31 % (29963)------------------------------
% 33.41/6.31 % (29963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.41/6.31 % (29963)Termination reason: Unknown
% 33.41/6.31 % (29963)Termination phase: Saturation
% 33.41/6.31
% 33.41/6.31 % (29963)Memory used [KB]: 7291
% 33.41/6.31 % (29963)Time elapsed: 0.230 s
% 33.41/6.31 % (29963)Instructions burned: 406 (million)
% 33.41/6.31 % (29963)------------------------------
% 33.41/6.31 % (29963)------------------------------
% 33.41/6.31 % (29960)Instruction limit reached!
% 33.41/6.31 % (29960)------------------------------
% 33.41/6.31 % (29960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.41/6.31 % (29960)Termination reason: Unknown
% 33.41/6.31 % (29960)Termination phase: Saturation
% 33.41/6.31
% 33.41/6.31 % (29960)Memory used [KB]: 8955
% 33.41/6.31 % (29960)Time elapsed: 0.331 s
% 33.41/6.31 % (29960)Instructions burned: 569 (million)
% 33.41/6.31 % (29960)------------------------------
% 33.41/6.31 % (29960)------------------------------
% 33.41/6.33 % (29965)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_29722 for (2955ds/456Mi)
% 33.41/6.33 % (29966)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_29722 for (2955ds/393Mi)
% 33.41/6.34 % (29962)Instruction limit reached!
% 33.41/6.34 % (29962)------------------------------
% 33.41/6.34 % (29962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.41/6.34 % (29962)Termination reason: Unknown
% 33.41/6.34 % (29962)Termination phase: Saturation
% 33.41/6.34
% 33.41/6.34 % (29962)Memory used [KB]: 7931
% 33.41/6.34 % (29962)Time elapsed: 0.304 s
% 33.41/6.34 % (29962)Instructions burned: 562 (million)
% 33.41/6.34 % (29962)------------------------------
% 33.41/6.34 % (29962)------------------------------
% 33.41/6.36 % (29967)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_29722 for (2955ds/1335Mi)
% 34.31/6.44 % (29918)Instruction limit reached!
% 34.31/6.44 % (29918)------------------------------
% 34.31/6.44 % (29918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.31/6.44 % (29918)Termination reason: Unknown
% 34.31/6.44 % (29918)Termination phase: Saturation
% 34.31/6.44
% 34.31/6.44 % (29918)Memory used [KB]: 14583
% 34.31/6.44 % (29918)Time elapsed: 2.959 s
% 34.31/6.44 % (29918)Instructions burned: 5206 (million)
% 34.31/6.44 % (29918)------------------------------
% 34.31/6.44 % (29918)------------------------------
% 34.31/6.46 % (29968)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_29722 for (2954ds/3373Mi)
% 34.57/6.54 % (29966)Instruction limit reached!
% 34.57/6.54 % (29966)------------------------------
% 34.57/6.54 % (29966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.57/6.54 % (29966)Termination reason: Unknown
% 34.57/6.54 % (29966)Termination phase: Saturation
% 34.57/6.54
% 34.57/6.54 % (29966)Memory used [KB]: 7547
% 34.57/6.54 % (29966)Time elapsed: 0.209 s
% 34.57/6.54 % (29966)Instructions burned: 394 (million)
% 34.57/6.54 % (29966)------------------------------
% 34.57/6.54 % (29966)------------------------------
% 34.57/6.56 % (29969)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_29722 for (2953ds/474Mi)
% 34.57/6.58 % (29965)Instruction limit reached!
% 34.57/6.58 % (29965)------------------------------
% 34.57/6.58 % (29965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.57/6.58 % (29965)Termination reason: Unknown
% 34.57/6.58 % (29965)Termination phase: Saturation
% 34.57/6.58
% 34.57/6.58 % (29965)Memory used [KB]: 7291
% 34.57/6.58 % (29965)Time elapsed: 0.252 s
% 34.57/6.58 % (29965)Instructions burned: 457 (million)
% 34.57/6.58 % (29965)------------------------------
% 34.57/6.58 % (29965)------------------------------
% 35.26/6.60 % (29970)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_29722 for (2953ds/157Mi)
% 35.26/6.61 % (29964)Instruction limit reached!
% 35.26/6.61 % (29964)------------------------------
% 35.26/6.61 % (29964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.26/6.61 % (29964)Termination reason: Unknown
% 35.26/6.61 % (29964)Termination phase: Saturation
% 35.26/6.61
% 35.26/6.61 % (29964)Memory used [KB]: 6908
% 35.26/6.61 % (29964)Time elapsed: 0.324 s
% 35.26/6.61 % (29964)Instructions burned: 582 (million)
% 35.26/6.61 % (29964)------------------------------
% 35.26/6.61 % (29964)------------------------------
% 35.26/6.64 % (29971)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_29722 for (2952ds/590Mi)
% 35.26/6.68 % (29970)Instruction limit reached!
% 35.26/6.68 % (29970)------------------------------
% 35.26/6.68 % (29970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.26/6.68 % (29970)Termination reason: Unknown
% 35.26/6.68 % (29970)Termination phase: Saturation
% 35.26/6.68
% 35.26/6.68 % (29970)Memory used [KB]: 6780
% 35.26/6.68 % (29970)Time elapsed: 0.081 s
% 35.26/6.68 % (29970)Instructions burned: 157 (million)
% 35.26/6.68 % (29970)------------------------------
% 35.26/6.68 % (29970)------------------------------
% 35.90/6.70 % (29972)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_29722 for (2952ds/104Mi)
% 35.90/6.76 % (29972)Instruction limit reached!
% 35.90/6.76 % (29972)------------------------------
% 35.90/6.76 % (29972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.90/6.76 % (29972)Termination reason: Unknown
% 35.90/6.76 % (29972)Termination phase: Saturation
% 35.90/6.76
% 35.90/6.76 % (29972)Memory used [KB]: 7036
% 35.90/6.76 % (29972)Time elapsed: 0.058 s
% 35.90/6.76 % (29972)Instructions burned: 105 (million)
% 35.90/6.76 % (29972)------------------------------
% 35.90/6.76 % (29972)------------------------------
% 35.90/6.77 % (29954)Instruction limit reached!
% 35.90/6.77 % (29954)------------------------------
% 35.90/6.77 % (29954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.90/6.77 % (29954)Termination reason: Unknown
% 35.90/6.77 % (29954)Termination phase: Saturation
% 35.90/6.77
% 35.90/6.77 % (29954)Memory used [KB]: 7803
% 35.90/6.77 % (29954)Time elapsed: 0.952 s
% 35.90/6.77 % (29954)Instructions burned: 1763 (million)
% 35.90/6.77 % (29954)------------------------------
% 35.90/6.77 % (29954)------------------------------
% 35.90/6.78 % (29973)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_29722 for (2951ds/414Mi)
% 35.90/6.80 % (29974)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_29722 for (2951ds/715Mi)
% 36.18/6.81 % (29969)Instruction limit reached!
% 36.18/6.81 % (29969)------------------------------
% 36.18/6.81 % (29969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.18/6.81 % (29969)Termination reason: Unknown
% 36.18/6.81 % (29969)Termination phase: Saturation
% 36.18/6.81
% 36.18/6.81 % (29969)Memory used [KB]: 7164
% 36.18/6.81 % (29969)Time elapsed: 0.252 s
% 36.18/6.81 % (29969)Instructions burned: 474 (million)
% 36.18/6.81 % (29969)------------------------------
% 36.18/6.81 % (29969)------------------------------
% 36.18/6.83 % (29975)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_29722 for (2950ds/961Mi)
% 36.56/6.92 % (29971)Instruction limit reached!
% 36.56/6.92 % (29971)------------------------------
% 36.56/6.92 % (29971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.56/6.92 % (29971)Termination reason: Unknown
% 36.56/6.92 % (29971)Termination phase: Saturation
% 36.56/6.92
% 36.56/6.92 % (29971)Memory used [KB]: 7419
% 36.56/6.92 % (29971)Time elapsed: 0.289 s
% 36.56/6.92 % (29971)Instructions burned: 591 (million)
% 36.56/6.92 % (29971)------------------------------
% 36.56/6.92 % (29971)------------------------------
% 36.56/6.94 % (29976)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_29722 for (2949ds/1213Mi)
% 36.56/7.00 % (29973)Instruction limit reached!
% 36.56/7.00 % (29973)------------------------------
% 36.56/7.00 % (29973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.56/7.00 % (29973)Termination reason: Unknown
% 36.56/7.00 % (29973)Termination phase: Saturation
% 36.56/7.00
% 36.56/7.00 % (29973)Memory used [KB]: 7036
% 36.56/7.00 % (29973)Time elapsed: 0.219 s
% 36.56/7.00 % (29973)Instructions burned: 415 (million)
% 36.56/7.00 % (29973)------------------------------
% 36.56/7.00 % (29973)------------------------------
% 36.56/7.00 % (29967)Instruction limit reached!
% 36.56/7.00 % (29967)------------------------------
% 36.56/7.00 % (29967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.56/7.00 % (29967)Termination reason: Unknown
% 36.56/7.00 % (29967)Termination phase: Saturation
% 36.56/7.00
% 36.56/7.00 % (29967)Memory used [KB]: 8187
% 36.56/7.00 % (29967)Time elapsed: 0.641 s
% 36.56/7.00 % (29967)Instructions burned: 1337 (million)
% 36.56/7.00 % (29967)------------------------------
% 36.56/7.00 % (29967)------------------------------
% 36.56/7.01 % (29977)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_29722 for (2948ds/1979Mi)
% 36.56/7.02 % (29978)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_29722 for (2948ds/481Mi)
% 38.99/7.09 % (29974)Instruction limit reached!
% 38.99/7.09 % (29974)------------------------------
% 38.99/7.09 % (29974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.99/7.09 % (29974)Termination reason: Unknown
% 38.99/7.09 % (29974)Termination phase: Saturation
% 38.99/7.09
% 38.99/7.09 % (29974)Memory used [KB]: 3198
% 38.99/7.09 % (29974)Time elapsed: 0.293 s
% 38.99/7.09 % (29974)Instructions burned: 716 (million)
% 38.99/7.09 % (29974)------------------------------
% 38.99/7.09 % (29974)------------------------------
% 38.99/7.10 % (29979)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_29722 for (2948ds/783Mi)
% 39.46/7.17 % (29978)Instruction limit reached!
% 39.46/7.17 % (29978)------------------------------
% 39.46/7.17 % (29978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.46/7.17 % (29978)Termination reason: Unknown
% 39.46/7.17 % (29978)Termination phase: Saturation
% 39.46/7.17
% 39.46/7.17 % (29978)Memory used [KB]: 7419
% 39.46/7.17 % (29978)Time elapsed: 0.152 s
% 39.46/7.17 % (29978)Instructions burned: 482 (million)
% 39.46/7.17 % (29978)------------------------------
% 39.46/7.17 % (29978)------------------------------
% 39.46/7.17 % (29975)Instruction limit reached!
% 39.46/7.17 % (29975)------------------------------
% 39.46/7.17 % (29975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.46/7.17 % (29975)Termination reason: Unknown
% 39.46/7.17 % (29975)Termination phase: Saturation
% 39.46/7.17
% 39.46/7.17 % (29975)Memory used [KB]: 7164
% 39.46/7.17 % (29975)Time elapsed: 0.340 s
% 39.46/7.17 % (29975)Instructions burned: 961 (million)
% 39.46/7.17 % (29975)------------------------------
% 39.46/7.17 % (29975)------------------------------
% 39.46/7.18 % (29980)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_29722 for (2947ds/432Mi)
% 39.46/7.18 % (29981)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_29722 for (2947ds/1670Mi)
% 39.90/7.27 % (29980)Instruction limit reached!
% 39.90/7.27 % (29980)------------------------------
% 39.90/7.27 % (29980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.90/7.27 % (29980)Termination reason: Unknown
% 39.90/7.27 % (29980)Termination phase: Saturation
% 39.90/7.27
% 39.90/7.27 % (29980)Memory used [KB]: 6396
% 39.90/7.27 % (29980)Time elapsed: 0.097 s
% 39.90/7.27 % (29980)Instructions burned: 436 (million)
% 39.90/7.27 % (29980)------------------------------
% 39.90/7.27 % (29980)------------------------------
% 39.90/7.28 % (29991)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_29722 for (2946ds/90Mi)
% 40.29/7.31 % (29991)Instruction limit reached!
% 40.29/7.31 % (29991)------------------------------
% 40.29/7.31 % (29991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.29/7.31 % (29991)Termination reason: Unknown
% 40.29/7.31 % (29991)Termination phase: Saturation
% 40.29/7.31
% 40.29/7.31 % (29991)Memory used [KB]: 6524
% 40.29/7.31 % (29991)Time elapsed: 0.028 s
% 40.29/7.31 % (29991)Instructions burned: 91 (million)
% 40.29/7.31 % (29991)------------------------------
% 40.29/7.31 % (29991)------------------------------
% 40.29/7.32 % (30006)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_29722 for (2945ds/346Mi)
% 40.29/7.34 % (29979)Instruction limit reached!
% 40.29/7.34 % (29979)------------------------------
% 40.29/7.34 % (29979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.29/7.34 % (29979)Termination reason: Unknown
% 40.29/7.34 % (29979)Termination phase: Saturation
% 40.29/7.34
% 40.29/7.34 % (29979)Memory used [KB]: 7931
% 40.29/7.34 % (29979)Time elapsed: 0.245 s
% 40.29/7.34 % (29979)Instructions burned: 783 (million)
% 40.29/7.34 % (29979)------------------------------
% 40.29/7.34 % (29979)------------------------------
% 40.29/7.35 % (30020)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_29722 for (2945ds/401Mi)
% 40.29/7.35 % (29976)Instruction limit reached!
% 40.29/7.35 % (29976)------------------------------
% 40.29/7.35 % (29976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.29/7.35 % (29976)Termination reason: Unknown
% 40.29/7.35 % (29976)Termination phase: Saturation
% 40.29/7.35
% 40.29/7.35 % (29976)Memory used [KB]: 7931
% 40.29/7.35 % (29976)Time elapsed: 0.415 s
% 40.29/7.35 % (29976)Instructions burned: 1214 (million)
% 40.29/7.35 % (29976)------------------------------
% 40.29/7.35 % (29976)------------------------------
% 40.29/7.36 % (30025)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_29722 for (2945ds/6454Mi)
% 40.86/7.42 % (30006)Instruction limit reached!
% 40.86/7.42 % (30006)------------------------------
% 40.86/7.42 % (30006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.86/7.42 % (30006)Termination reason: Unknown
% 40.86/7.42 % (30006)Termination phase: Saturation
% 40.86/7.42
% 40.86/7.42 % (30006)Memory used [KB]: 7164
% 40.86/7.42 % (30006)Time elapsed: 0.105 s
% 40.86/7.42 % (30006)Instructions burned: 348 (million)
% 40.86/7.42 % (30006)------------------------------
% 40.86/7.42 % (30006)------------------------------
% 40.86/7.43 % (30052)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_29722 for (2944ds/283Mi)
% 40.86/7.47 % (30020)Instruction limit reached!
% 40.86/7.47 % (30020)------------------------------
% 40.86/7.47 % (30020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.86/7.47 % (30020)Termination reason: Unknown
% 40.86/7.47 % (30020)Termination phase: Saturation
% 40.86/7.47
% 40.86/7.47 % (30020)Memory used [KB]: 7931
% 40.86/7.47 % (30020)Time elapsed: 0.119 s
% 40.86/7.47 % (30020)Instructions burned: 403 (million)
% 40.86/7.47 % (30020)------------------------------
% 40.86/7.47 % (30020)------------------------------
% 40.86/7.48 % (30073)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_29722 for (2944ds/865Mi)
% 41.30/7.51 % (30073)Refutation not found, incomplete strategy
% 41.30/7.51 % (30073)------------------------------
% 41.30/7.51 % (30073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.30/7.51 % (30073)Termination reason: Refutation not found, incomplete strategy
% 41.30/7.51
% 41.30/7.51
% 41.30/7.51 % (30073)Memory used [KB]: 7036
% 41.30/7.51 % (30073)Time elapsed: 0.033 s
% 41.30/7.51 % (30073)Instructions burned: 111 (million)
% 41.30/7.51 % (30073)------------------------------
% 41.30/7.51 % (30073)------------------------------
% 41.30/7.52 % (30093)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_29722 for (2943ds/4528Mi)
% 41.30/7.53 % (30052)Instruction limit reached!
% 41.30/7.53 % (30052)------------------------------
% 41.30/7.53 % (30052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.30/7.53 % (30052)Termination reason: Unknown
% 41.30/7.53 % (30052)Termination phase: Saturation
% 41.30/7.53
% 41.30/7.53 % (30052)Memory used [KB]: 6908
% 41.30/7.53 % (30052)Time elapsed: 0.093 s
% 41.30/7.53 % (30052)Instructions burned: 286 (million)
% 41.30/7.53 % (30052)------------------------------
% 41.30/7.53 % (30052)------------------------------
% 41.30/7.53 % (30099)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_29722 for (2943ds/1001Mi)
% 41.30/7.54 % (30093)Refutation not found, incomplete strategy
% 41.30/7.54 % (30093)------------------------------
% 41.30/7.54 % (30093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.30/7.54 % (30093)Termination reason: Refutation not found, incomplete strategy
% 41.30/7.54
% 41.30/7.54
% 41.30/7.54 % (30093)Memory used [KB]: 1918
% 41.30/7.54 % (30093)Time elapsed: 0.018 s
% 41.30/7.54 % (30093)Instructions burned: 58 (million)
% 41.30/7.54 % (30093)------------------------------
% 41.30/7.54 % (30093)------------------------------
% 41.30/7.55 % (30105)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_29722 for (2943ds/102Mi)
% 41.30/7.57 % (30105)Instruction limit reached!
% 41.30/7.57 % (30105)------------------------------
% 41.30/7.57 % (30105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.30/7.57 % (30105)Termination reason: Unknown
% 41.30/7.57 % (30105)Termination phase: Property scanning
% 41.30/7.57
% 41.30/7.57 % (30105)Memory used [KB]: 2174
% 41.30/7.57 % (30105)Time elapsed: 0.027 s
% 41.30/7.57 % (30105)Instructions burned: 105 (million)
% 41.30/7.57 % (30105)------------------------------
% 41.30/7.57 % (30105)------------------------------
% 41.30/7.58 % (30123)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_29722 for (2943ds/952Mi)
% 41.72/7.66 % (29977)Instruction limit reached!
% 41.72/7.66 % (29977)------------------------------
% 41.72/7.66 % (29977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.72/7.66 % (29977)Termination reason: Unknown
% 41.72/7.66 % (29977)Termination phase: Saturation
% 41.72/7.66
% 41.72/7.66 % (29977)Memory used [KB]: 7164
% 41.72/7.66 % (29977)Time elapsed: 0.646 s
% 41.72/7.66 % (29977)Instructions burned: 1980 (million)
% 41.72/7.66 % (29977)------------------------------
% 41.72/7.66 % (29977)------------------------------
% 41.72/7.67 % (30154)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_29722 for (2942ds/578Mi)
% 41.72/7.68 % (29981)Instruction limit reached!
% 41.72/7.68 % (29981)------------------------------
% 41.72/7.68 % (29981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.72/7.68 % (29981)Termination reason: Unknown
% 41.72/7.68 % (29981)Termination phase: Saturation
% 41.72/7.68
% 41.72/7.68 % (29981)Memory used [KB]: 9594
% 41.72/7.68 % (29981)Time elapsed: 0.507 s
% 41.72/7.68 % (29981)Instructions burned: 1672 (million)
% 41.72/7.68 % (29981)------------------------------
% 41.72/7.68 % (29981)------------------------------
% 41.72/7.69 % (30163)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_29722 for (2942ds/643Mi)
% 43.08/7.75 % (29968)Instruction limit reached!
% 43.08/7.75 % (29968)------------------------------
% 43.08/7.75 % (29968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.08/7.75 % (29968)Termination reason: Unknown
% 43.08/7.75 % (29968)Termination phase: Saturation
% 43.08/7.75
% 43.08/7.75 % (29968)Memory used [KB]: 10874
% 43.08/7.75 % (29968)Time elapsed: 1.293 s
% 43.08/7.75 % (29968)Instructions burned: 3374 (million)
% 43.08/7.75 % (29968)------------------------------
% 43.08/7.75 % (29968)------------------------------
% 43.08/7.76 % (30178)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_29722 for (2941ds/865Mi)
% 43.26/7.84 % (30154)Instruction limit reached!
% 43.26/7.84 % (30154)------------------------------
% 43.26/7.84 % (30154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.26/7.84 % (30154)Termination reason: Unknown
% 43.26/7.84 % (30154)Termination phase: Saturation
% 43.26/7.84
% 43.26/7.84 % (30154)Memory used [KB]: 7291
% 43.26/7.84 % (30154)Time elapsed: 0.178 s
% 43.26/7.84 % (30154)Instructions burned: 579 (million)
% 43.26/7.84 % (30154)------------------------------
% 43.26/7.84 % (30154)------------------------------
% 43.26/7.85 % (30099)Instruction limit reached!
% 43.26/7.85 % (30099)------------------------------
% 43.26/7.85 % (30099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.26/7.85 % (30099)Termination reason: Unknown
% 43.26/7.85 % (30099)Termination phase: Saturation
% 43.26/7.85
% 43.26/7.85 % (30099)Memory used [KB]: 8187
% 43.26/7.85 % (30099)Time elapsed: 0.316 s
% 43.26/7.85 % (30099)Instructions burned: 1003 (million)
% 43.26/7.85 % (30099)------------------------------
% 43.26/7.85 % (30099)------------------------------
% 43.26/7.85 % (30222)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_29722 for (2940ds/1174Mi)
% 43.26/7.86 % (30225)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_29722 for (2940ds/644Mi)
% 43.26/7.89 % (30123)Instruction limit reached!
% 43.26/7.89 % (30123)------------------------------
% 43.26/7.89 % (30123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.26/7.89 % (30123)Termination reason: Unknown
% 43.26/7.89 % (30123)Termination phase: Saturation
% 43.26/7.89
% 43.26/7.89 % (30123)Memory used [KB]: 8059
% 43.26/7.89 % (30123)Time elapsed: 0.306 s
% 43.26/7.89 % (30123)Instructions burned: 953 (million)
% 43.26/7.89 % (30123)------------------------------
% 43.26/7.89 % (30123)------------------------------
% 43.26/7.89 % (30163)Instruction limit reached!
% 43.26/7.89 % (30163)------------------------------
% 43.26/7.89 % (30163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.26/7.89 % (30163)Termination reason: Unknown
% 43.26/7.89 % (30163)Termination phase: Saturation
% 43.26/7.89
% 43.26/7.89 % (30163)Memory used [KB]: 8059
% 43.26/7.89 % (30163)Time elapsed: 0.199 s
% 43.26/7.89 % (30163)Instructions burned: 643 (million)
% 43.26/7.89 % (30163)------------------------------
% 43.26/7.89 % (30163)------------------------------
% 43.26/7.89 % (30225)Refutation not found, incomplete strategy
% 43.26/7.89 % (30225)------------------------------
% 43.26/7.89 % (30225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.26/7.89 % (30225)Termination reason: Refutation not found, incomplete strategy
% 43.26/7.89
% 43.26/7.89
% 43.26/7.89 % (30225)Memory used [KB]: 7036
% 43.26/7.89 % (30225)Time elapsed: 0.034 s
% 43.26/7.89 % (30225)Instructions burned: 107 (million)
% 43.26/7.89 % (30225)------------------------------
% 43.26/7.89 % (30225)------------------------------
% 44.45/7.90 % (30226)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_29722 for (2940ds/1201Mi)
% 44.45/7.90 % (30227)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_29722 for (2939ds/1046Mi)
% 44.45/7.90 % (30228)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_29722 for (2939ds/222Mi)
% 44.45/7.96 % (30228)Instruction limit reached!
% 44.45/7.96 % (30228)------------------------------
% 44.45/7.96 % (30228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.45/7.96 % (30228)Termination reason: Unknown
% 44.45/7.96 % (30228)Termination phase: Saturation
% 44.45/7.96
% 44.45/7.96 % (30228)Memory used [KB]: 7291
% 44.45/7.96 % (30228)Time elapsed: 0.063 s
% 44.45/7.96 % (30228)Instructions burned: 223 (million)
% 44.45/7.96 % (30228)------------------------------
% 44.45/7.96 % (30228)------------------------------
% 44.45/7.97 % (30229)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_29722 for (2939ds/68Mi)
% 44.45/7.99 % (30178)First to succeed.
% 44.45/7.99 % (30229)Instruction limit reached!
% 44.45/7.99 % (30229)------------------------------
% 44.45/7.99 % (30229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.45/7.99 % (30229)Termination reason: Unknown
% 44.45/7.99 % (30229)Termination phase: Saturation
% 44.45/7.99
% 44.45/7.99 % (30229)Memory used [KB]: 6268
% 44.45/7.99 % (30229)Time elapsed: 0.020 s
% 44.45/7.99 % (30229)Instructions burned: 70 (million)
% 44.45/7.99 % (30229)------------------------------
% 44.45/7.99 % (30229)------------------------------
% 44.45/7.99 % (30178)Refutation found. Thanks to Tanya!
% 44.45/7.99 % SZS status Theorem for DTF2THF_29722
% 44.45/7.99 % SZS output start Proof for DTF2THF_29722
% 44.45/7.99 thf(type_def_5, type, int: $tType).
% 44.45/7.99 thf(type_def_6, type, nat: $tType).
% 44.45/7.99 thf(func_def_0, type, nat: $tType).
% 44.45/7.99 thf(func_def_1, type, int: $tType).
% 44.45/7.99 thf(func_def_2, type, gbinomial_int: int > nat > int).
% 44.45/7.99 thf(func_def_3, type, gbinomial_nat: nat > nat > nat).
% 44.45/7.99 thf(func_def_4, type, one_one_int: int).
% 44.45/7.99 thf(func_def_5, type, one_one_nat: nat).
% 44.45/7.99 thf(func_def_6, type, plus_plus_int: int > int > int).
% 44.45/7.99 thf(func_def_7, type, plus_plus_nat: nat > nat > nat).
% 44.45/7.99 thf(func_def_8, type, times_times_int: int > int > int).
% 44.45/7.99 thf(func_def_9, type, times_times_nat: nat > nat > nat).
% 44.45/7.99 thf(func_def_10, type, zero_zero_int: int).
% 44.45/7.99 thf(func_def_11, type, zero_zero_nat: nat).
% 44.45/7.99 thf(func_def_12, type, nO_MATCH_int_int: int > int > $o).
% 44.45/7.99 thf(func_def_13, type, nO_MATCH_int_nat: int > nat > $o).
% 44.45/7.99 thf(func_def_14, type, nO_MATCH_nat_int: nat > int > $o).
% 44.45/7.99 thf(func_def_15, type, nO_MATCH_nat_nat: nat > nat > $o).
% 44.45/7.99 thf(func_def_16, type, if_nat: $o > nat > nat > nat).
% 44.45/7.99 thf(func_def_17, type, suc: nat > nat).
% 44.45/7.99 thf(func_def_18, type, semiri2019852685at_int: nat > int).
% 44.45/7.99 thf(func_def_19, type, semiri1382578993at_nat: nat > nat).
% 44.45/7.99 thf(func_def_20, type, nthRoo1352626670d_root: nat > nat > $o).
% 44.45/7.99 thf(func_def_21, type, power_power_int: int > nat > int).
% 44.45/7.99 thf(func_def_22, type, power_power_nat: nat > nat > nat).
% 44.45/7.99 thf(func_def_23, type, divide_divide_int: int > int > int).
% 44.45/7.99 thf(func_def_24, type, divide_divide_nat: nat > nat > nat).
% 44.45/7.99 thf(func_def_25, type, n: int).
% 44.45/7.99 thf(func_def_26, type, p: nat).
% 44.45/7.99 thf(func_def_27, type, pm: nat).
% 44.45/7.99 thf(func_def_28, type, x: int).
% 44.45/7.99 thf(func_def_39, type, sK0: (nat > nat > $o) > nat).
% 44.45/7.99 thf(func_def_40, type, sK1: (nat > nat > $o) > nat).
% 44.45/7.99 thf(func_def_41, type, sK2: (nat > nat > $o) > nat).
% 44.45/7.99 thf(func_def_42, type, sK3: (nat > nat > $o) > nat).
% 44.45/7.99 thf(func_def_43, type, sK4: nat > nat).
% 44.45/7.99 thf(func_def_44, type, sK5: (nat > $o) > nat).
% 44.45/7.99 thf(func_def_45, type, sK6: (nat > $o) > nat).
% 44.45/7.99 thf(func_def_46, type, sK7: nat > nat).
% 44.45/7.99 thf(func_def_47, type, sK8: (nat > $o) > nat).
% 44.45/7.99 thf(func_def_49, type, ph10: !>[X0: $tType]:(X0)).
% 44.45/7.99 thf(f2676,plain,(
% 44.45/7.99 $false),
% 44.45/7.99 inference(avatar_sat_refutation,[status(thm)],[f2451,f2656,f2663,f2665,f2675])).
% 44.45/7.99 thf(f2675,plain,(
% 44.45/7.99 ~spl9_2 | spl9_3),
% 44.45/7.99 inference(avatar_contradiction_clause,[status(thm)],[f2674])).
% 44.45/7.99 thf(f2674,plain,(
% 44.45/7.99 $false | (~spl9_2 | spl9_3)),
% 44.45/7.99 inference(subsumption_resolution,[status(thm)],[f2672,f2326])).
% 44.45/7.99 thf(f2326,plain,(
% 44.45/7.99 (x != (semiri2019852685at_int @ zero_zero_nat)) | spl9_3),
% 44.45/7.99 inference(avatar_component_clause,[status(thm)],[f2325])).
% 44.45/7.99 thf(f2325,definition,(
% 44.45/7.99 spl9_3 <=> (x = (semiri2019852685at_int @ zero_zero_nat))),
% 44.45/7.99 introduced(definition,[new_symbols(naming,[spl9_3])],[avatar_definition])).
% 44.45/7.99 thf(f2672,plain,(
% 44.45/7.99 (x = (semiri2019852685at_int @ zero_zero_nat)) | ~spl9_2),
% 44.45/7.99 inference(trivial_inequality_removal,[status(thm)],[f2669])).
% 44.45/7.99 thf(f2669,plain,(
% 44.45/7.99 (x = (semiri2019852685at_int @ zero_zero_nat)) | ((semiri2019852685at_int @ zero_zero_nat) != (semiri2019852685at_int @ zero_zero_nat)) | ~spl9_2),
% 44.45/7.99 inference(superposition,[status(thm)],[f1468,f1568])).
% 44.45/7.99 thf(f1568,plain,(
% 44.45/7.99 ((semiri2019852685at_int @ zero_zero_nat) = (power_power_int @ x @ pm)) | ~spl9_2),
% 44.45/7.99 inference(avatar_component_clause,[status(thm)],[f1566])).
% 44.45/7.99 thf(f1566,definition,(
% 44.45/7.99 spl9_2 <=> ((semiri2019852685at_int @ zero_zero_nat) = (power_power_int @ x @ pm))),
% 44.45/7.99 introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition])).
% 44.45/7.99 thf(f1468,plain,(
% 44.45/7.99 ( ! [X0 : nat,X1 : int] : (((semiri2019852685at_int @ zero_zero_nat) != (power_power_int @ X1 @ X0)) | ((semiri2019852685at_int @ zero_zero_nat) = X1)) )),
% 44.45/7.99 inference(definition_unfolding,[status(thm)],[f1331,f1110,f1110])).
% 44.45/7.99 thf(f1110,plain,(
% 44.45/7.99 (zero_zero_int = (semiri2019852685at_int @ zero_zero_nat))),
% 44.45/7.99 inference(cnf_transformation,[status(thm)],[f342])).
% 44.45/7.99 thf(f342,plain,(
% 44.45/7.99 (zero_zero_int = (semiri2019852685at_int @ zero_zero_nat))),
% 44.45/7.99 inference(fool_elimination,[status(thm)],[f187])).
% 44.45/7.99 thf(f187,axiom,(
% 44.45/7.99 (zero_zero_int = (semiri2019852685at_int @ zero_zero_nat))),
% 44.45/7.99 file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_186_of__nat__0)).
% 44.45/7.99 thf(f1331,plain,(
% 44.45/7.99 ( ! [X0 : nat,X1 : int] : ((zero_zero_int != (power_power_int @ X1 @ X0)) | (zero_zero_int = X1)) )),
% 44.45/7.99 inference(cnf_transformation,[status(thm)],[f970])).
% 44.45/7.99 thf(f970,plain,(
% 44.45/7.99 ! [X0 : nat,X1 : int] : ((zero_zero_int != (power_power_int @ X1 @ X0)) | (zero_zero_int = X1))),
% 44.45/7.99 inference(ennf_transformation,[status(thm)],[f639])).
% 44.45/7.99 thf(f639,plain,(
% 44.45/7.99 ! [X0 : nat,X1 : int] : ((zero_zero_int != X1) => (zero_zero_int != (power_power_int @ X1 @ X0)))),
% 44.45/7.99 inference(fool_elimination,[status(thm)],[f638])).
% 44.45/7.99 thf(f638,plain,(
% 44.45/7.99 ! [X0 : nat,X1 : int] : ((zero_zero_int != X1) => (zero_zero_int != (power_power_int @ X1 @ X0)))),
% 44.45/7.99 inference(rectify,[status(thm)],[f268])).
% 44.45/7.99 thf(f268,axiom,(
% 44.45/7.99 ! [X1 : nat,X5 : int] : ((zero_zero_int != X5) => ((power_power_int @ X5 @ X1) != zero_zero_int))),
% 44.45/7.99 file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_267_power__not__zero)).
% 44.45/7.99 thf(f2665,plain,(
% 44.45/7.99 spl9_6 | ~spl9_1),
% 44.45/7.99 inference(avatar_split_clause,[status(thm)],[f2664,f1562,f2660])).
% 44.45/8.00 thf(f2660,definition,(
% 44.45/8.00 spl9_6 <=> (x = (divide_divide_int @ (times_times_int @ x @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm))) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm))))),
% 44.45/8.00 introduced(definition,[new_symbols(naming,[spl9_6])],[avatar_definition])).
% 44.45/8.00 thf(f1562,definition,(
% 44.45/8.00 spl9_1 <=> (x = (divide_divide_int @ (plus_plus_int @ x @ (times_times_int @ x @ (semiri2019852685at_int @ pm))) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm))))),
% 44.45/8.00 introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition])).
% 44.45/8.00 thf(f2664,plain,(
% 44.45/8.00 (x = (divide_divide_int @ (times_times_int @ x @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm))) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm)))) | ~spl9_1),
% 44.45/8.00 inference(forward_demodulation,[status(thm)],[f1563,f2314])).
% 44.45/8.00 thf(f2314,plain,(
% 44.45/8.00 ( ! [X0 : nat] : (((plus_plus_int @ x @ (times_times_int @ x @ (semiri2019852685at_int @ X0))) = (times_times_int @ x @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ X0))))) )),
% 44.45/8.00 inference(superposition,[status(thm)],[f1426,f1104])).
% 44.45/8.00 thf(f1104,plain,(
% 44.45/8.00 ( ! [X0 : nat,X1 : nat] : (((semiri2019852685at_int @ (plus_plus_nat @ X0 @ X1)) = (plus_plus_int @ (semiri2019852685at_int @ X0) @ (semiri2019852685at_int @ X1)))) )),
% 44.45/8.00 inference(cnf_transformation,[status(thm)],[f838])).
% 44.45/8.00 thf(f838,plain,(
% 44.45/8.00 ! [X0 : nat,X1 : nat] : ((semiri2019852685at_int @ (plus_plus_nat @ X0 @ X1)) = (plus_plus_int @ (semiri2019852685at_int @ X0) @ (semiri2019852685at_int @ X1)))),
% 44.45/8.00 inference(fool_elimination,[status(thm)],[f837])).
% 44.45/8.00 thf(f837,plain,(
% 44.45/8.00 ! [X0 : nat,X1 : nat] : ((semiri2019852685at_int @ (plus_plus_nat @ X0 @ X1)) = (plus_plus_int @ (semiri2019852685at_int @ X0) @ (semiri2019852685at_int @ X1)))),
% 44.45/8.00 inference(rectify,[status(thm)],[f53])).
% 44.45/8.00 thf(f53,axiom,(
% 44.45/8.00 ! [X5 : nat,X2 : nat] : ((semiri2019852685at_int @ (plus_plus_nat @ X5 @ X2)) = (plus_plus_int @ (semiri2019852685at_int @ X5) @ (semiri2019852685at_int @ X2)))),
% 44.45/8.00 file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_52_int__ops_I5_J)).
% 44.45/8.00 thf(f1426,plain,(
% 44.45/8.00 ( ! [X0 : int] : (((times_times_int @ x @ (plus_plus_int @ (semiri2019852685at_int @ one_one_nat) @ X0)) = (plus_plus_int @ x @ (times_times_int @ x @ X0)))) )),
% 44.45/8.00 inference(definition_unfolding,[status(thm)],[f1225,f1065])).
% 44.45/8.00 thf(f1065,plain,(
% 44.45/8.00 (one_one_int = (semiri2019852685at_int @ one_one_nat))),
% 44.45/8.00 inference(cnf_transformation,[status(thm)],[f513])).
% 44.45/8.00 thf(f513,plain,(
% 44.45/8.00 (one_one_int = (semiri2019852685at_int @ one_one_nat))),
% 44.45/8.00 inference(fool_elimination,[status(thm)],[f123])).
% 44.45/8.00 thf(f123,axiom,(
% 44.45/8.00 (one_one_int = (semiri2019852685at_int @ one_one_nat))),
% 44.45/8.00 file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_122_of__nat__1)).
% 44.45/8.00 thf(f1225,plain,(
% 44.45/8.00 ( ! [X0 : int] : (((times_times_int @ x @ (plus_plus_int @ one_one_int @ X0)) = (plus_plus_int @ x @ (times_times_int @ x @ X0)))) )),
% 44.45/8.00 inference(cnf_transformation,[status(thm)],[f337])).
% 44.45/8.00 thf(f337,plain,(
% 44.45/8.00 ! [X0 : int] : ((times_times_int @ x @ (plus_plus_int @ one_one_int @ X0)) = (plus_plus_int @ x @ (times_times_int @ x @ X0)))),
% 44.45/8.00 inference(fool_elimination,[status(thm)],[f336])).
% 44.45/8.00 thf(f336,plain,(
% 44.45/8.00 ! [X0 : int] : ((times_times_int @ x @ (plus_plus_int @ one_one_int @ X0)) = (plus_plus_int @ x @ (times_times_int @ x @ X0)))),
% 44.45/8.00 inference(rectify,[status(thm)],[f110])).
% 44.45/8.00 thf(f110,axiom,(
% 44.45/8.00 ! [X1 : int] : ((plus_plus_int @ x @ (times_times_int @ x @ X1)) = (times_times_int @ x @ (plus_plus_int @ one_one_int @ X1)))),
% 44.45/8.00 file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_109__092_060open_062_092_060And_062n_O_Ax_A_L_Ax_A_K_An_A_061_Ax_A_K_A_I1_A_L_An_J_092_060close_062)).
% 44.45/8.00 thf(f1563,plain,(
% 44.45/8.00 (x = (divide_divide_int @ (plus_plus_int @ x @ (times_times_int @ x @ (semiri2019852685at_int @ pm))) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm)))) | ~spl9_1),
% 44.45/8.00 inference(avatar_component_clause,[status(thm)],[f1562])).
% 44.45/8.00 thf(f2663,plain,(
% 44.45/8.00 spl9_2 | ~spl9_6),
% 44.45/8.00 inference(avatar_split_clause,[status(thm)],[f2658,f2660,f1566])).
% 44.45/8.00 thf(f2658,plain,(
% 44.45/8.00 ((semiri2019852685at_int @ zero_zero_nat) = (power_power_int @ x @ pm)) | (x != (divide_divide_int @ (times_times_int @ x @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm))) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm))))),
% 44.45/8.00 inference(forward_demodulation,[status(thm)],[f2657,f2314])).
% 44.45/8.00 thf(f2657,plain,(
% 44.45/8.00 ((semiri2019852685at_int @ zero_zero_nat) = (power_power_int @ x @ pm)) | (x != (divide_divide_int @ (plus_plus_int @ x @ (times_times_int @ x @ (semiri2019852685at_int @ pm))) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm))))),
% 44.45/8.00 inference(forward_demodulation,[status(thm)],[f2652,f1736])).
% 44.45/8.00 thf(f1736,plain,(
% 44.45/8.00 ( ! [X0 : int,X1 : int] : (((plus_plus_int @ X1 @ X0) = (plus_plus_int @ X0 @ X1))) )),
% 44.45/8.00 inference(forward_demodulation,[status(thm)],[f1713,f1406])).
% 44.45/8.00 thf(f1406,plain,(
% 44.45/8.00 ( ! [X0 : int] : (((plus_plus_int @ X0 @ (semiri2019852685at_int @ zero_zero_nat)) = X0)) )),
% 44.45/8.00 inference(definition_unfolding,[status(thm)],[f1195,f1110])).
% 44.45/8.00 thf(f1195,plain,(
% 44.45/8.00 ( ! [X0 : int] : (((plus_plus_int @ X0 @ zero_zero_int) = X0)) )),
% 44.45/8.00 inference(cnf_transformation,[status(thm)],[f629])).
% 44.45/8.00 thf(f629,plain,(
% 44.45/8.00 ! [X0 : int] : ((plus_plus_int @ X0 @ zero_zero_int) = X0)),
% 44.45/8.00 inference(fool_elimination,[status(thm)],[f628])).
% 44.45/8.00 thf(f628,plain,(
% 44.45/8.00 ! [X0 : int] : ((plus_plus_int @ X0 @ zero_zero_int) = X0)),
% 44.45/8.00 inference(rectify,[status(thm)],[f258])).
% 44.45/8.00 thf(f258,axiom,(
% 44.45/8.00 ! [X5 : int] : ((plus_plus_int @ X5 @ zero_zero_int) = X5)),
% 44.45/8.00 file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_257_verit__sum__simplify)).
% 44.45/8.00 thf(f1713,plain,(
% 44.45/8.00 ( ! [X0 : int,X1 : int] : (((plus_plus_int @ X0 @ (plus_plus_int @ X1 @ (semiri2019852685at_int @ zero_zero_nat))) = (plus_plus_int @ X1 @ X0))) )),
% 44.45/8.00 inference(superposition,[status(thm)],[f1013,f1406])).
% 44.45/8.00 thf(f1013,plain,(
% 44.45/8.00 ( ! [X2 : int,X0 : int,X1 : int] : (((plus_plus_int @ X2 @ (plus_plus_int @ X0 @ X1)) = (plus_plus_int @ X0 @ (plus_plus_int @ X2 @ X1)))) )),
% 44.45/8.00 inference(cnf_transformation,[status(thm)],[f693])).
% 44.45/8.00 thf(f693,plain,(
% 44.45/8.00 ! [X0 : int,X1 : int,X2 : int] : ((plus_plus_int @ X2 @ (plus_plus_int @ X0 @ X1)) = (plus_plus_int @ X0 @ (plus_plus_int @ X2 @ X1)))),
% 44.45/8.00 inference(fool_elimination,[status(thm)],[f692])).
% 44.45/8.00 thf(f692,plain,(
% 44.45/8.00 ! [X0 : int,X1 : int,X2 : int] : ((plus_plus_int @ X2 @ (plus_plus_int @ X0 @ X1)) = (plus_plus_int @ X0 @ (plus_plus_int @ X2 @ X1)))),
% 44.45/8.00 inference(rectify,[status(thm)],[f89])).
% 44.45/8.00 thf(f89,axiom,(
% 44.45/8.00 ! [X2 : int,X15 : int,X5 : int] : ((plus_plus_int @ X5 @ (plus_plus_int @ X2 @ X15)) = (plus_plus_int @ X2 @ (plus_plus_int @ X5 @ X15)))),
% 44.45/8.00 file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_88_add_Oleft__commute)).
% 44.45/8.00 thf(f2652,plain,(
% 44.45/8.00 (x != (divide_divide_int @ (plus_plus_int @ (times_times_int @ x @ (semiri2019852685at_int @ pm)) @ x) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm)))) | ((semiri2019852685at_int @ zero_zero_nat) = (power_power_int @ x @ pm))),
% 44.45/8.00 inference(superposition,[status(thm)],[f1737,f1385])).
% 44.45/8.00 thf(f1385,plain,(
% 44.45/8.00 ( ! [X0 : int,X1 : int] : (((divide_divide_int @ (times_times_int @ X0 @ X1) @ X1) = X0) | ((semiri2019852685at_int @ zero_zero_nat) = X1)) )),
% 44.45/8.00 inference(definition_unfolding,[status(thm)],[f1134,f1110])).
% 44.45/8.00 thf(f1134,plain,(
% 44.45/8.00 ( ! [X0 : int,X1 : int] : (((divide_divide_int @ (times_times_int @ X0 @ X1) @ X1) = X0) | (zero_zero_int = X1)) )),
% 44.45/8.00 inference(cnf_transformation,[status(thm)],[f989])).
% 44.45/8.00 thf(f989,plain,(
% 44.45/8.00 ! [X0 : int,X1 : int] : (((divide_divide_int @ (times_times_int @ X0 @ X1) @ X1) = X0) | (zero_zero_int = X1))),
% 44.45/8.00 inference(ennf_transformation,[status(thm)],[f434])).
% 44.45/8.00 thf(f434,plain,(
% 44.45/8.00 ! [X0 : int,X1 : int] : ((zero_zero_int != X1) => ((divide_divide_int @ (times_times_int @ X0 @ X1) @ X1) = X0))),
% 44.45/8.00 inference(fool_elimination,[status(thm)],[f433])).
% 44.45/8.00 thf(f433,plain,(
% 44.45/8.00 ! [X0 : int,X1 : int] : ((zero_zero_int != X1) => ((divide_divide_int @ (times_times_int @ X0 @ X1) @ X1) = X0))),
% 44.45/8.00 inference(rectify,[status(thm)],[f224])).
% 44.45/8.00 thf(f224,axiom,(
% 44.45/8.00 ! [X5 : int,X2 : int] : ((zero_zero_int != X2) => ((divide_divide_int @ (times_times_int @ X5 @ X2) @ X2) = X5))),
% 44.45/8.00 file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_223_nonzero__mult__div__cancel__right)).
% 44.45/8.00 thf(f1737,plain,(
% 44.45/8.00 (x != (divide_divide_int @ (plus_plus_int @ (times_times_int @ x @ (semiri2019852685at_int @ pm)) @ (divide_divide_int @ (times_times_int @ x @ (power_power_int @ x @ pm)) @ (power_power_int @ x @ pm))) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm))))),
% 44.45/8.00 inference(backward_demodulation,[status(thm)],[f1515,f1736])).
% 44.45/8.00 thf(f1515,plain,(
% 44.45/8.00 (x != (divide_divide_int @ (plus_plus_int @ (divide_divide_int @ (times_times_int @ x @ (power_power_int @ x @ pm)) @ (power_power_int @ x @ pm)) @ (times_times_int @ x @ (semiri2019852685at_int @ pm))) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm))))),
% 44.45/8.00 inference(forward_demodulation,[status(thm)],[f1514,f1286])).
% 44.45/8.00 thf(f1286,plain,(
% 44.45/8.00 ( ! [X0 : nat,X1 : int] : (((times_times_int @ X1 @ (power_power_int @ X1 @ X0)) = (times_times_int @ (power_power_int @ X1 @ X0) @ X1))) )),
% 44.45/8.00 inference(cnf_transformation,[status(thm)],[f631])).
% 44.45/8.00 thf(f631,plain,(
% 44.45/8.00 ! [X0 : nat,X1 : int] : ((times_times_int @ X1 @ (power_power_int @ X1 @ X0)) = (times_times_int @ (power_power_int @ X1 @ X0) @ X1))),
% 44.45/8.00 inference(fool_elimination,[status(thm)],[f630])).
% 44.45/8.00 thf(f630,plain,(
% 44.45/8.00 ! [X0 : nat,X1 : int] : ((times_times_int @ X1 @ (power_power_int @ X1 @ X0)) = (times_times_int @ (power_power_int @ X1 @ X0) @ X1))),
% 44.45/8.00 inference(rectify,[status(thm)],[f42])).
% 44.45/8.00 thf(f42,axiom,(
% 44.45/8.00 ! [X1 : nat,X5 : int] : ((times_times_int @ X5 @ (power_power_int @ X5 @ X1)) = (times_times_int @ (power_power_int @ X5 @ X1) @ X5))),
% 44.45/8.00 file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_41_power__commutes)).
% 44.45/8.00 thf(f1514,plain,(
% 44.45/8.00 (x != (divide_divide_int @ (plus_plus_int @ (divide_divide_int @ (times_times_int @ (power_power_int @ x @ pm) @ x) @ (power_power_int @ x @ pm)) @ (times_times_int @ x @ (semiri2019852685at_int @ pm))) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm))))),
% 44.45/8.00 inference(forward_demodulation,[status(thm)],[f1448,f1366])).
% 44.45/8.00 thf(f1366,plain,(
% 44.45/8.00 ( ! [X0 : int,X1 : nat] : (((power_power_int @ X0 @ (plus_plus_nat @ one_one_nat @ X1)) = (times_times_int @ (power_power_int @ X0 @ X1) @ X0))) )),
% 44.45/8.00 inference(definition_unfolding,[status(thm)],[f1093,f1100])).
% 44.45/8.00 thf(f1100,plain,(
% 44.45/8.00 (suc = (plus_plus_nat @ one_one_nat))),
% 44.45/8.00 inference(cnf_transformation,[status(thm)],[f691])).
% 44.45/8.00 thf(f691,plain,(
% 44.45/8.00 (suc = (plus_plus_nat @ one_one_nat))),
% 44.45/8.00 inference(fool_elimination,[status(thm)],[f296])).
% 44.45/8.00 thf(f296,axiom,(
% 44.45/8.00 (suc = (plus_plus_nat @ one_one_nat))),
% 44.45/8.00 file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_295_plus__1__eq__Suc)).
% 44.45/8.00 thf(f1093,plain,(
% 44.45/8.00 ( ! [X0 : int,X1 : nat] : (((power_power_int @ X0 @ (suc @ X1)) = (times_times_int @ (power_power_int @ X0 @ X1) @ X0))) )),
% 44.45/8.00 inference(cnf_transformation,[status(thm)],[f859])).
% 44.45/8.00 thf(f859,plain,(
% 44.45/8.00 ! [X0 : int,X1 : nat] : ((power_power_int @ X0 @ (suc @ X1)) = (times_times_int @ (power_power_int @ X0 @ X1) @ X0))),
% 44.45/8.00 inference(fool_elimination,[status(thm)],[f858])).
% 44.45/8.00 thf(f858,plain,(
% 44.45/8.00 ! [X0 : int,X1 : nat] : ((power_power_int @ X0 @ (suc @ X1)) = (times_times_int @ (power_power_int @ X0 @ X1) @ X0))),
% 44.45/8.00 inference(rectify,[status(thm)],[f48])).
% 44.45/8.00 thf(f48,axiom,(
% 44.45/8.00 ! [X5 : int,X1 : nat] : ((power_power_int @ X5 @ (suc @ X1)) = (times_times_int @ (power_power_int @ X5 @ X1) @ X5))),
% 44.45/8.00 file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_47_power__Suc2)).
% 44.45/8.00 thf(f1448,plain,(
% 44.45/8.00 (x != (divide_divide_int @ (plus_plus_int @ (divide_divide_int @ (power_power_int @ x @ (plus_plus_nat @ one_one_nat @ pm)) @ (power_power_int @ x @ pm)) @ (times_times_int @ x @ (semiri2019852685at_int @ pm))) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm))))),
% 44.45/8.00 inference(definition_unfolding,[status(thm)],[f1270,f1100,f1100])).
% 44.45/8.00 thf(f1270,plain,(
% 44.45/8.00 (x != (divide_divide_int @ (plus_plus_int @ (divide_divide_int @ (power_power_int @ x @ (suc @ pm)) @ (power_power_int @ x @ pm)) @ (times_times_int @ x @ (semiri2019852685at_int @ pm))) @ (semiri2019852685at_int @ (suc @ pm))))),
% 44.45/8.00 inference(cnf_transformation,[status(thm)],[f902])).
% 44.45/8.00 thf(f902,plain,(
% 44.45/8.00 (x != (divide_divide_int @ (plus_plus_int @ (divide_divide_int @ (power_power_int @ x @ (suc @ pm)) @ (power_power_int @ x @ pm)) @ (times_times_int @ x @ (semiri2019852685at_int @ pm))) @ (semiri2019852685at_int @ (suc @ pm))))),
% 44.45/8.00 inference(flattening,[status(thm)],[f743])).
% 44.45/8.00 thf(f743,plain,(
% 44.45/8.00 ~(x = (divide_divide_int @ (plus_plus_int @ (divide_divide_int @ (power_power_int @ x @ (suc @ pm)) @ (power_power_int @ x @ pm)) @ (times_times_int @ x @ (semiri2019852685at_int @ pm))) @ (semiri2019852685at_int @ (suc @ pm))))),
% 44.45/8.00 inference(fool_elimination,[status(thm)],[f314])).
% 44.45/8.00 thf(f314,negated_conjecture,(
% 44.45/8.00 ~(x = (divide_divide_int @ (plus_plus_int @ (divide_divide_int @ (power_power_int @ x @ (suc @ pm)) @ (power_power_int @ x @ pm)) @ (times_times_int @ x @ (semiri2019852685at_int @ pm))) @ (semiri2019852685at_int @ (suc @ pm))))),
% 44.45/8.00 inference(negated_conjecture,[status(cth)],[f313])).
% 44.45/8.00 thf(f313,conjecture,(
% 44.45/8.00 (x = (divide_divide_int @ (plus_plus_int @ (divide_divide_int @ (power_power_int @ x @ (suc @ pm)) @ (power_power_int @ x @ pm)) @ (times_times_int @ x @ (semiri2019852685at_int @ pm))) @ (semiri2019852685at_int @ (suc @ pm))))),
% 44.45/8.00 file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',conj_0)).
% 44.45/8.00 thf(f2656,plain,(
% 44.45/8.00 spl9_1),
% 44.45/8.00 inference(avatar_contradiction_clause,[status(thm)],[f2655])).
% 44.45/8.00 thf(f2655,plain,(
% 44.45/8.00 $false | spl9_1),
% 44.45/8.00 inference(subsumption_resolution,[status(thm)],[f2654,f1458])).
% 44.45/8.00 thf(f1458,plain,(
% 44.45/8.00 ( ! [X0 : nat] : (((semiri2019852685at_int @ zero_zero_nat) != (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ X0)))) )),
% 44.45/8.00 inference(definition_unfolding,[status(thm)],[f1300,f1100,f1110])).
% 44.45/8.00 thf(f1300,plain,(
% 44.45/8.00 ( ! [X0 : nat] : (((semiri2019852685at_int @ (suc @ X0)) != zero_zero_int)) )),
% 44.45/8.00 inference(cnf_transformation,[status(thm)],[f808])).
% 44.45/8.00 thf(f808,plain,(
% 44.45/8.00 ! [X0 : nat] : ((semiri2019852685at_int @ (suc @ X0)) != zero_zero_int)),
% 44.45/8.00 inference(fool_elimination,[status(thm)],[f807])).
% 44.45/8.00 thf(f807,plain,(
% 44.45/8.00 ! [X0 : nat] : ((semiri2019852685at_int @ (suc @ X0)) != zero_zero_int)),
% 44.45/8.00 inference(rectify,[status(thm)],[f300])).
% 44.45/8.00 thf(f300,axiom,(
% 44.45/8.00 ! [X1 : nat] : ((semiri2019852685at_int @ (suc @ X1)) != zero_zero_int)),
% 44.45/8.00 file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_299_of__nat__neq__0)).
% 44.45/8.00 thf(f2654,plain,(
% 44.45/8.00 ((semiri2019852685at_int @ zero_zero_nat) = (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm))) | spl9_1),
% 44.45/8.00 inference(trivial_inequality_removal,[status(thm)],[f2653])).
% 44.45/8.00 thf(f2653,plain,(
% 44.45/8.00 ((semiri2019852685at_int @ zero_zero_nat) = (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm))) | (x != x) | spl9_1),
% 44.45/8.00 inference(superposition,[status(thm)],[f2338,f1385])).
% 44.45/8.00 thf(f2338,plain,(
% 44.45/8.00 (x != (divide_divide_int @ (times_times_int @ x @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm))) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm)))) | spl9_1),
% 44.45/8.00 inference(backward_demodulation,[status(thm)],[f1564,f2314])).
% 44.45/8.00 thf(f1564,plain,(
% 44.45/8.00 (x != (divide_divide_int @ (plus_plus_int @ x @ (times_times_int @ x @ (semiri2019852685at_int @ pm))) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm)))) | spl9_1),
% 44.45/8.00 inference(avatar_component_clause,[status(thm)],[f1562])).
% 44.45/8.00 thf(f2451,plain,(
% 44.45/8.00 ~spl9_3),
% 44.45/8.00 inference(avatar_contradiction_clause,[status(thm)],[f2450])).
% 44.45/8.00 thf(f2450,plain,(
% 44.45/8.00 $false | ~spl9_3),
% 44.45/8.00 inference(subsumption_resolution,[status(thm)],[f2449,f2339])).
% 44.45/8.00 thf(f2339,plain,(
% 44.45/8.00 ( ! [X0 : int] : ((x = (divide_divide_int @ x @ X0))) ) | ~spl9_3),
% 44.45/8.00 inference(backward_demodulation,[status(thm)],[f1338,f2327])).
% 44.45/8.00 thf(f2327,plain,(
% 44.45/8.00 (x = (semiri2019852685at_int @ zero_zero_nat)) | ~spl9_3),
% 44.45/8.00 inference(avatar_component_clause,[status(thm)],[f2325])).
% 44.45/8.00 thf(f1338,plain,(
% 44.45/8.00 ( ! [X0 : int] : (((semiri2019852685at_int @ zero_zero_nat) = (divide_divide_int @ (semiri2019852685at_int @ zero_zero_nat) @ X0))) )),
% 44.45/8.00 inference(definition_unfolding,[status(thm)],[f1010,f1110,f1110])).
% 44.45/8.00 thf(f1010,plain,(
% 44.45/8.00 ( ! [X0 : int] : ((zero_zero_int = (divide_divide_int @ zero_zero_int @ X0))) )),
% 44.45/8.00 inference(cnf_transformation,[status(thm)],[f681])).
% 44.45/8.00 thf(f681,plain,(
% 44.45/8.00 ! [X0 : int] : (zero_zero_int = (divide_divide_int @ zero_zero_int @ X0))),
% 44.45/8.00 inference(fool_elimination,[status(thm)],[f680])).
% 44.45/8.00 thf(f680,plain,(
% 44.45/8.00 ! [X0 : int] : (zero_zero_int = (divide_divide_int @ zero_zero_int @ X0))),
% 44.45/8.00 inference(rectify,[status(thm)],[f181])).
% 44.45/8.00 thf(f181,axiom,(
% 44.45/8.00 ! [X5 : int] : (zero_zero_int = (divide_divide_int @ zero_zero_int @ X5))),
% 44.45/8.00 file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_180_bits__div__0)).
% 44.45/8.00 thf(f2449,plain,(
% 44.45/8.00 (x != (divide_divide_int @ x @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm)))) | ~spl9_3),
% 44.45/8.00 inference(forward_demodulation,[status(thm)],[f2448,f2358])).
% 44.45/8.00 thf(f2358,plain,(
% 44.45/8.00 ( ! [X0 : int] : (((plus_plus_int @ X0 @ x) = X0)) ) | ~spl9_3),
% 44.45/8.00 inference(backward_demodulation,[status(thm)],[f1406,f2327])).
% 44.45/8.00 thf(f2448,plain,(
% 44.45/8.00 (x != (divide_divide_int @ (plus_plus_int @ x @ x) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm)))) | ~spl9_3),
% 44.45/8.00 inference(forward_demodulation,[status(thm)],[f2447,f2339])).
% 44.45/8.00 thf(f2447,plain,(
% 44.45/8.00 (x != (divide_divide_int @ (plus_plus_int @ x @ (divide_divide_int @ x @ (power_power_int @ x @ pm))) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm)))) | ~spl9_3),
% 44.45/8.00 inference(forward_demodulation,[status(thm)],[f2439,f2373])).
% 44.45/8.00 thf(f2373,plain,(
% 44.45/8.00 ( ! [X0 : int] : ((x = (times_times_int @ x @ X0))) ) | ~spl9_3),
% 44.45/8.00 inference(backward_demodulation,[status(thm)],[f1464,f2327])).
% 44.45/8.00 thf(f1464,plain,(
% 44.45/8.00 ( ! [X0 : int] : (((semiri2019852685at_int @ zero_zero_nat) = (times_times_int @ (semiri2019852685at_int @ zero_zero_nat) @ X0))) )),
% 44.45/8.00 inference(definition_unfolding,[status(thm)],[f1315,f1110,f1110])).
% 44.45/8.00 thf(f1315,plain,(
% 44.45/8.00 ( ! [X0 : int] : ((zero_zero_int = (times_times_int @ zero_zero_int @ X0))) )),
% 44.45/8.00 inference(cnf_transformation,[status(thm)],[f439])).
% 44.45/8.00 thf(f439,plain,(
% 44.45/8.00 ! [X0 : int] : (zero_zero_int = (times_times_int @ zero_zero_int @ X0))),
% 44.45/8.00 inference(fool_elimination,[status(thm)],[f438])).
% 44.45/8.00 thf(f438,plain,(
% 44.45/8.00 ! [X0 : int] : (zero_zero_int = (times_times_int @ zero_zero_int @ X0))),
% 44.45/8.00 inference(rectify,[status(thm)],[f289])).
% 44.45/8.00 thf(f289,axiom,(
% 44.45/8.00 ! [X28 : int] : (zero_zero_int = (times_times_int @ zero_zero_int @ X28))),
% 44.45/8.00 file('/export/starexec/sandbox2/tmp/tmp.EqWVLgxOph/DTF2THF_29722.p',fact_288_times__int__code_I2_J)).
% 44.45/8.00 thf(f2439,plain,(
% 44.45/8.00 (x != (divide_divide_int @ (plus_plus_int @ x @ (divide_divide_int @ (times_times_int @ x @ (power_power_int @ x @ pm)) @ (power_power_int @ x @ pm))) @ (semiri2019852685at_int @ (plus_plus_nat @ one_one_nat @ pm)))) | ~spl9_3),
% 44.45/8.00 inference(backward_demodulation,[status(thm)],[f1737,f2373])).
% 44.45/8.00 % SZS output end Proof for DTF2THF_29722
% 44.45/8.00 % (30178)------------------------------
% 44.45/8.00 % (30178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.45/8.00 % (30178)Termination reason: Refutation
% 44.45/8.00
% 44.45/8.00 % (30178)Memory used [KB]: 7675
% 44.45/8.00 % (30178)Time elapsed: 0.233 s
% 44.45/8.00 % (30178)Instructions burned: 728 (million)
% 44.45/8.00 % (30178)------------------------------
% 44.45/8.00 % (30178)------------------------------
% 44.45/8.00 % (29819)Success in time 6.11 s
%------------------------------------------------------------------------------