%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP109^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 08:55:37 AM UTC 2026
% Result : Theorem 40.67s 7.35s
% Output : Refutation 40.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 25 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 658 ( 12 ~; 0 |; 0 &; 646 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 96 ( 94 usr; 9 con; 0-6 aty)
% Number of variables : 48 ( 30 ^; 18 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_b: $tType ).
thf(type_def_7,type,
real: $tType ).
thf(type_def_8,type,
set_real: $tType ).
thf(type_def_9,type,
set_a: $tType ).
thf(type_def_10,type,
a: $tType ).
thf(type_def_11,type,
b: $tType ).
thf(type_def_12,type,
nat: $tType ).
thf(type_def_13,type,
extended_ereal: $tType ).
thf(func_def_0,type,
set_real: $tType ).
thf(func_def_1,type,
extended_ereal: $tType ).
thf(func_def_2,type,
set_b: $tType ).
thf(func_def_3,type,
set_a: $tType ).
thf(func_def_4,type,
real: $tType ).
thf(func_def_5,type,
nat: $tType ).
thf(func_def_6,type,
b: $tType ).
thf(func_def_7,type,
a: $tType ).
thf(func_def_8,type,
convex_b: set_b > $o ).
thf(func_def_9,type,
inverse_inverse_real: real > real ).
thf(func_def_10,type,
finite_finite_real: set_real > $o ).
thf(func_def_11,type,
finite_finite_a: set_a > $o ).
thf(func_def_12,type,
finite_finite_b: set_b > $o ).
thf(func_def_13,type,
minus_minus_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
thf(func_def_14,type,
minus_minus_b_o: ( b > $o ) > ( b > $o ) > b > $o ).
thf(func_def_15,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_16,type,
minus_minus_real: real > real > real ).
thf(func_def_17,type,
minus_minus_set_a: set_a > set_a > set_a ).
thf(func_def_18,type,
minus_minus_set_b: set_b > set_b > set_b ).
thf(func_def_19,type,
minus_minus_b: b > b > b ).
thf(func_def_20,type,
one_one_real: real ).
thf(func_def_21,type,
plus_p2118002693_ereal: extended_ereal > extended_ereal > extended_ereal ).
thf(func_def_22,type,
plus_plus_real: real > real > real ).
thf(func_def_23,type,
plus_plus_set_b: set_b > set_b > set_b ).
thf(func_def_24,type,
plus_plus_b: b > b > b ).
thf(func_def_25,type,
times_times_real: real > real > real ).
thf(func_def_26,type,
groups1296524820l_real: ( real > real ) > set_real > real ).
thf(func_def_27,type,
groups769445524_a_nat: ( a > nat ) > set_a > nat ).
thf(func_def_28,type,
groups1862963056a_real: ( a > real ) > set_a > real ).
thf(func_def_29,type,
groups919362075_set_b: ( a > set_b ) > set_a > set_b ).
thf(func_def_30,type,
groups1199149371um_a_b: ( a > b ) > set_a > b ).
thf(func_def_31,type,
groups2098481813_b_nat: ( b > nat ) > set_b > nat ).
thf(func_def_32,type,
groups583146225b_real: ( b > real ) > set_b > real ).
thf(func_def_33,type,
groups448962650_set_b: ( b > set_b ) > set_b > set_b ).
thf(func_def_34,type,
groups2026918778um_b_b: ( b > b ) > set_b > b ).
thf(func_def_35,type,
if_real: $o > real > real > real ).
thf(func_def_36,type,
if_b: $o > b > b > b ).
thf(func_def_37,type,
lower_311861425x_on_b: set_b > ( b > extended_ereal ) > $o ).
thf(func_def_38,type,
bot_bot_set_a: set_a ).
thf(func_def_39,type,
bot_bot_set_b: set_b ).
thf(func_def_40,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_41,type,
real_V453051771R_real: real > real > real ).
thf(func_def_42,type,
real_V1035702896aleR_b: real > b > b ).
thf(func_def_43,type,
divide_divide_real: real > real > real ).
thf(func_def_44,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_45,type,
collect_b: ( b > $o ) > set_b ).
thf(func_def_46,type,
insert_real: real > set_real > set_real ).
thf(func_def_47,type,
insert_a: a > set_a > set_a ).
thf(func_def_48,type,
insert_b: b > set_b > set_b ).
thf(func_def_49,type,
member_a: a > set_a > $o ).
thf(func_def_50,type,
member_b: b > set_b > $o ).
thf(func_def_51,type,
c: set_b ).
thf(func_def_52,type,
a2: a > real ).
thf(func_def_53,type,
aa: a > real ).
thf(func_def_54,type,
f: b > extended_ereal ).
thf(func_def_55,type,
i: a ).
thf(func_def_56,type,
s: set_a ).
thf(func_def_57,type,
sa: set_a ).
thf(func_def_58,type,
y: a > b ).
thf(func_def_73,type,
sP0: set_a > ( a > real ) > ( a > a ) > ( a > real ) > $o ).
thf(func_def_74,type,
sP1: set_a > ( a > a ) > set_a > $o ).
thf(func_def_75,type,
sP2: ( a > b ) > ( a > b ) > ( a > a ) > set_a > $o ).
thf(func_def_76,type,
sP3: set_a > ( a > a ) > ( a > a ) > $o ).
thf(func_def_77,type,
sK4: set_a > set_a ).
thf(func_def_78,type,
sK5: set_a > a ).
thf(func_def_79,type,
sK6: ( set_a > $o ) > set_a ).
thf(func_def_80,type,
sK7: ( set_a > $o ) > a ).
thf(func_def_81,type,
sK8: ( set_a > $o ) > set_a ).
thf(func_def_82,type,
sK9: a > set_a > set_a ).
thf(func_def_83,type,
sK10: set_a > ( a > a ) > set_a > a ).
thf(func_def_84,type,
sK11: set_a > ( a > real ) > ( a > a ) > ( a > real ) > a ).
thf(func_def_85,type,
sK12: ( a > a ) > set_a > ( a > a ) > a ).
thf(func_def_86,type,
sK13: ( a > a ) > set_a > set_a > a ).
thf(func_def_87,type,
sK14: ( a > a ) > set_a > ( a > a ) > a ).
thf(func_def_88,type,
sK15: ( a > real ) > set_a > ( a > real ) > a ).
thf(func_def_89,type,
sK16: ( set_a > $o ) > a ).
thf(func_def_90,type,
sK17: ( set_a > $o ) > set_a ).
thf(func_def_91,type,
sK18: a > set_a > set_a ).
thf(func_def_92,type,
sK19: ( set_a > $o ) > a ).
thf(func_def_93,type,
sK20: ( set_a > $o ) > set_a ).
thf(func_def_94,type,
sK21: ( set_a > $o ) > a ).
thf(func_def_95,type,
sK22: set_a > a ).
thf(func_def_96,type,
sK23: set_a > ( a > a ) > ( a > a ) > a ).
thf(func_def_97,type,
sK24: ( a > b ) > ( a > b ) > ( a > a ) > set_a > a ).
thf(func_def_98,type,
sK25: set_a > set_a > ( a > a ) > a ).
thf(func_def_99,type,
sK26: set_a > set_a > ( a > a ) > a ).
thf(func_def_100,type,
sK27: set_a > ( a > a ) > ( a > a ) > a ).
thf(func_def_101,type,
sK28: ( a > b ) > set_a > ( a > b ) > a ).
thf(func_def_102,type,
sK29: set_a > ( a > b ) > ( a > b ) > ( a > a ) > set_a > ( a > a ) > a ).
thf(func_def_103,type,
sK30: set_a > ( a > a ) > set_a > ( a > a ) > a ).
thf(func_def_104,type,
sK31: ( set_a > $o ) > a ).
thf(func_def_105,type,
sK32: ( set_a > $o ) > set_a ).
thf(func_def_106,type,
sK33: set_a > set_a > ( a > a ) > a ).
thf(func_def_107,type,
sK34: a > set_a > set_a > ( a > a ) > a ).
thf(func_def_108,type,
sK35: set_a > ( a > real ) > set_a > ( a > real ) > ( a > a ) > a ).
thf(func_def_109,type,
sK36: ( a > real ) > set_a > set_a > ( a > real ) > ( a > a ) > ( a > a ) > a ).
thf(func_def_110,type,
sK37: set_a > set_a > ( a > a ) > ( a > a ) > a ).
thf(func_def_111,type,
sK38: ( a > a ) > set_a > set_a > a ).
thf(func_def_112,type,
sK39: a > ( a > a ) > set_a > set_a > a ).
thf(func_def_113,type,
sK40: ( a > a ) > set_a > ( a > b ) > set_a > ( a > b ) > a ).
thf(func_def_114,type,
ph41:
!>[X0: $tType] : X0 ).
thf(func_def_115,type,
sK42: a ).
thf(f2599,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f2598,f1283]) ).
thf(f1283,plain,
! [X2: real,X0: real,X1: b] :
( ( real_V1035702896aleR_b @ X0 @ ( real_V1035702896aleR_b @ X2 @ X1 ) )
= ( real_V1035702896aleR_b @ X2 @ ( real_V1035702896aleR_b @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f883]) ).
thf(f883,plain,
! [X0: real,X1: b,X2: real] :
( ( real_V1035702896aleR_b @ X0 @ ( real_V1035702896aleR_b @ X2 @ X1 ) )
= ( real_V1035702896aleR_b @ X2 @ ( real_V1035702896aleR_b @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,axiom,
! [X4: real,X5: b,X3: real] :
( ( real_V1035702896aleR_b @ X3 @ ( real_V1035702896aleR_b @ X4 @ X5 ) )
= ( real_V1035702896aleR_b @ X4 @ ( real_V1035702896aleR_b @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aJ622KHsm8/DTF2THF_14827.p',fact_35_scale__left__commute) ).
thf(f2598,plain,
( ( real_V1035702896aleR_b @ ( aa @ sK42 ) @ ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) ) @ ( y @ sK42 ) ) )
!= ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) ) @ ( real_V1035702896aleR_b @ ( aa @ sK42 ) @ ( y @ sK42 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2597,f1233]) ).
thf(f1233,plain,
! [X2: real,X0: real,X1: b] :
( ( real_V1035702896aleR_b @ X0 @ ( real_V1035702896aleR_b @ X2 @ X1 ) )
= ( real_V1035702896aleR_b @ ( times_times_real @ X0 @ X2 ) @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f884]) ).
thf(f884,plain,
! [X0: real,X1: b,X2: real] :
( ( real_V1035702896aleR_b @ X0 @ ( real_V1035702896aleR_b @ X2 @ X1 ) )
= ( real_V1035702896aleR_b @ ( times_times_real @ X0 @ X2 ) @ X1 ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
! [X3: real,X5: b,X4: real] :
( ( real_V1035702896aleR_b @ X3 @ ( real_V1035702896aleR_b @ X4 @ X5 ) )
= ( real_V1035702896aleR_b @ ( times_times_real @ X3 @ X4 ) @ X5 ) ),
file('/export/starexec/sandbox/tmp/tmp.aJ622KHsm8/DTF2THF_14827.p',fact_13_scaleR__scaleR) ).
thf(f2597,plain,
( ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) ) @ ( real_V1035702896aleR_b @ ( aa @ sK42 ) @ ( y @ sK42 ) ) )
!= ( real_V1035702896aleR_b @ ( times_times_real @ ( aa @ sK42 ) @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) ) ) @ ( y @ sK42 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2596]) ).
thf(f2596,plain,
( ( ^ [Y0: a] : ( real_V1035702896aleR_b @ ( times_times_real @ ( aa @ Y0 ) @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) ) ) @ ( y @ Y0 ) )
@ sK42 )
!= ( ^ [Y0: a] : ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) ) @ ( real_V1035702896aleR_b @ ( aa @ Y0 ) @ ( y @ Y0 ) ) )
@ sK42 ) ),
inference(negative_extensionality,[status(thm)],[f2589]) ).
thf(f2589,plain,
( ( ^ [Y0: a] : ( real_V1035702896aleR_b @ ( times_times_real @ ( aa @ Y0 ) @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) ) ) @ ( y @ Y0 ) ) )
!= ( ^ [Y0: a] : ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) ) @ ( real_V1035702896aleR_b @ ( aa @ Y0 ) @ ( y @ Y0 ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f2542]) ).
thf(f2542,plain,
( ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( groups1862963056a_real @ aa @ sa )
@ ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) ) @ ( real_V1035702896aleR_b @ ( aa @ Y0 ) @ ( y @ Y0 ) ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) )
!= ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( groups1862963056a_real @ aa @ sa )
@ ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( times_times_real @ ( aa @ Y0 ) @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) ) ) @ ( y @ Y0 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1639,f2541]) ).
thf(f2541,plain,
( ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) )
@ ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( aa @ Y0 ) @ ( y @ Y0 ) )
@ sa ) )
= ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) ) @ ( real_V1035702896aleR_b @ ( aa @ Y0 ) @ ( y @ Y0 ) ) )
@ sa ) ),
inference(forward_demodulation,[status(thm)],[f1266,f1138]) ).
thf(f1138,plain,
( ( minus_minus_real @ one_one_real @ ( aa @ i ) )
= ( groups1862963056a_real @ aa @ sa ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,axiom,
( ( minus_minus_real @ one_one_real @ ( aa @ i ) )
= ( groups1862963056a_real @ aa @ sa ) ),
file('/export/starexec/sandbox/tmp/tmp.aJ622KHsm8/DTF2THF_14827.p',fact_17__092_060open_062sum_Aa_As_A_061_A1_A_N_Aa_Ai_092_060close_062) ).
thf(f1266,plain,
( ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) )
@ ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( aa @ Y0 ) @ ( y @ Y0 ) )
@ sa ) )
= ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) @ ( real_V1035702896aleR_b @ ( aa @ Y0 ) @ ( y @ Y0 ) ) )
@ sa ) ),
inference(cnf_transformation,[status(thm)],[f516]) ).
thf(f516,plain,
( ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) )
@ ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( aa @ Y0 ) @ ( y @ Y0 ) )
@ sa ) )
= ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) @ ( real_V1035702896aleR_b @ ( aa @ Y0 ) @ ( y @ Y0 ) ) )
@ sa ) ),
inference(fool_elimination,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( groups1199149371um_a_b
@ ^ [X0: a] : ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) @ ( real_V1035702896aleR_b @ ( aa @ X0 ) @ ( y @ X0 ) ) )
@ sa )
= ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) )
@ ( groups1199149371um_a_b
@ ^ [X1: a] : ( real_V1035702896aleR_b @ ( aa @ X1 ) @ ( y @ X1 ) )
@ sa ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aJ622KHsm8/DTF2THF_14827.p',fact_2__092_060open_062_I_092_060Sum_062x_092_060in_062s_O_Aa_Ax_A_K_092_060_094sub_062R_Ay_Ax_A_P_092_060_094sub_062R_A_I1_A_N_Aa_Ai_J_J_A_061_A_I_092_060Sum_062j_092_060in_062s_O_Aa_Aj_A_K_092_060_094sub_062R_Ay_Aj_J_A_P_092_060_094sub_062R_A_I1_A_N_Aa_Ai_J_092_060close_062) ).
thf(f1639,plain,
( ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( groups1862963056a_real @ aa @ sa )
@ ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) )
@ ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( aa @ Y0 ) @ ( y @ Y0 ) )
@ sa ) ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) )
!= ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( groups1862963056a_real @ aa @ sa )
@ ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( times_times_real @ ( aa @ Y0 ) @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) ) ) @ ( y @ Y0 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1465,f1233]) ).
thf(f1465,plain,
( ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( groups1862963056a_real @ aa @ sa )
@ ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( times_times_real @ ( aa @ Y0 ) @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) ) ) @ ( y @ Y0 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) )
!= ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( times_times_real @ ( groups1862963056a_real @ aa @ sa ) @ ( inverse_inverse_real @ ( groups1862963056a_real @ aa @ sa ) ) )
@ ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( aa @ Y0 ) @ ( y @ Y0 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1120,f1138]) ).
thf(f1120,plain,
( ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( minus_minus_real @ one_one_real @ ( aa @ i ) )
@ ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( times_times_real @ ( aa @ Y0 ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) ) @ ( y @ Y0 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) )
!= ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( times_times_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) )
@ ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( aa @ Y0 ) @ ( y @ Y0 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f829]) ).
thf(f829,plain,
( ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( minus_minus_real @ one_one_real @ ( aa @ i ) )
@ ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( times_times_real @ ( aa @ Y0 ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) ) @ ( y @ Y0 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) )
!= ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( times_times_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) )
@ ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( aa @ Y0 ) @ ( y @ Y0 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ),
inference(flattening,[status(thm)],[f511]) ).
thf(f511,plain,
( ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( minus_minus_real @ one_one_real @ ( aa @ i ) )
@ ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( times_times_real @ ( aa @ Y0 ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) ) @ ( y @ Y0 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) )
!= ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( times_times_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) )
@ ( groups1199149371um_a_b
@ ^ [Y0: a] : ( real_V1035702896aleR_b @ ( aa @ Y0 ) @ ( y @ Y0 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f510]) ).
thf(f510,plain,
( ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( minus_minus_real @ one_one_real @ ( aa @ i ) )
@ ( groups1199149371um_a_b
@ ^ [X0: a] : ( real_V1035702896aleR_b @ ( times_times_real @ ( aa @ X0 ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) ) @ ( y @ X0 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) )
!= ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( times_times_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) )
@ ( groups1199149371um_a_b
@ ^ [X1: a] : ( real_V1035702896aleR_b @ ( aa @ X1 ) @ ( y @ X1 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ),
inference(rectify,[status(thm)],[f360]) ).
thf(f360,negated_conjecture,
( ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( minus_minus_real @ one_one_real @ ( aa @ i ) )
@ ( groups1199149371um_a_b
@ ^ [X1: a] : ( real_V1035702896aleR_b @ ( times_times_real @ ( aa @ X1 ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) ) @ ( y @ X1 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) )
!= ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( times_times_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) )
@ ( groups1199149371um_a_b
@ ^ [X1: a] : ( real_V1035702896aleR_b @ ( aa @ X1 ) @ ( y @ X1 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f359]) ).
thf(f359,conjecture,
( ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( minus_minus_real @ one_one_real @ ( aa @ i ) )
@ ( groups1199149371um_a_b
@ ^ [X1: a] : ( real_V1035702896aleR_b @ ( times_times_real @ ( aa @ X1 ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) ) @ ( y @ X1 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) )
= ( f
@ ( plus_plus_b
@ ( real_V1035702896aleR_b @ ( times_times_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) )
@ ( groups1199149371um_a_b
@ ^ [X1: a] : ( real_V1035702896aleR_b @ ( aa @ X1 ) @ ( y @ X1 ) )
@ sa ) )
@ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aJ622KHsm8/DTF2THF_14827.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP109^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.34 % Computer : n001.cluster.edu
% 0.19/0.34 % Model : x86_64 x86_64
% 0.19/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.34 % Memory : 8042.1875MB
% 0.19/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Tue Feb 24 08:26:50 EST 2026
% 0.19/0.35 % CPUTime :
% 0.19/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : ITP109^1 : TPTP v9.2.1. Released v7.5.0.
% 0.28/0.47 % Domain : Interactive Theorem Proving
% 0.28/0.47 % Problem : Sledgehammer Lower_Semicontinuous problem prob_1098__6259092_1
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Des21]
% 0.28/0.47 % Names : Lower_Semicontinuous/prob_1098__6259092_1 [Des21]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.67 v9.1.0, 0.62 v9.0.0, 0.80 v8.2.0, 0.69 v8.1.0, 0.82 v7.5.0
% 0.28/0.47 % Syntax : Number of formulae : 418 ( 209 unt; 59 typ; 0 def)
% 0.28/0.47 % Number of atoms : 942 ( 525 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 11 ( 2 avg)
% 0.28/0.47 % Number of connectives : 3880 ( 121 ~; 12 |; 114 &;3253 @)
% 0.28/0.47 % ( 0 <=>; 380 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 17 ( 6 avg)
% 0.28/0.47 % Number of types : 9 ( 8 usr)
% 0.28/0.47 % Number of type conns : 297 ( 297 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 54 ( 51 usr; 9 con; 0-3 aty)
% 0.28/0.47 % Number of variables : 1161 ( 141 ^; 993 !; 27 ?;1161 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:43:58.270
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % Could-be-implicit typings (8)
% 0.28/0.47 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 0.28/0.47 set_real: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Extended____Real__Oereal,type,
% 0.28/0.47 extended_ereal: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Set__Oset_Itf__b_J,type,
% 0.28/0.47 set_b: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.28/0.47 set_a: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Real__Oreal,type,
% 0.28/0.47 real: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_t__Nat__Onat,type,
% 0.28/0.47 nat: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_tf__b,type,
% 0.28/0.47 b: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_n_tf__a,type,
% 0.28/0.47 a: $tType ).
% 0.28/0.47
% 0.28/0.47 % Explicit typings (51)
% 0.28/0.47 thf(sy_c_Convex_Oconvex_001tf__b,type,
% 0.28/0.47 convex_b: set_b > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 0.28/0.47 inverse_inverse_real: real > real ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal,type,
% 0.28/0.47 finite_finite_real: set_real > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Finite__Set_Ofinite_001tf__a,type,
% 0.28/0.47 finite_finite_a: set_a > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Finite__Set_Ofinite_001tf__b,type,
% 0.28/0.47 finite_finite_b: set_b > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Ominus__class_Ominus_001_062_Itf__a_M_Eo_J,type,
% 0.28/0.47 minus_minus_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Ominus__class_Ominus_001_062_Itf__b_M_Eo_J,type,
% 0.28/0.47 minus_minus_b_o: ( b > $o ) > ( b > $o ) > b > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 0.28/0.47 minus_minus_nat: nat > nat > nat ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
% 0.28/0.47 minus_minus_real: real > real > real ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__a_J,type,
% 0.28/0.47 minus_minus_set_a: set_a > set_a > set_a ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__b_J,type,
% 0.28/0.47 minus_minus_set_b: set_b > set_b > set_b ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Ominus__class_Ominus_001tf__b,type,
% 0.28/0.47 minus_minus_b: b > b > b ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
% 0.28/0.47 one_one_real: real ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Oplus__class_Oplus_001t__Extended____Real__Oereal,type,
% 0.28/0.47 plus_p2118002693_ereal: extended_ereal > extended_ereal > extended_ereal ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
% 0.28/0.47 plus_plus_real: real > real > real ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Oplus__class_Oplus_001t__Set__Oset_Itf__b_J,type,
% 0.28/0.47 plus_plus_set_b: set_b > set_b > set_b ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Oplus__class_Oplus_001tf__b,type,
% 0.28/0.47 plus_plus_b: b > b > b ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal,type,
% 0.28/0.47 times_times_real: real > real > real ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.28/0.47 groups1296524820l_real: ( real > real ) > set_real > real ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__a_001t__Nat__Onat,type,
% 0.28/0.47 groups769445524_a_nat: ( a > nat ) > set_a > nat ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__a_001t__Real__Oreal,type,
% 0.28/0.47 groups1862963056a_real: ( a > real ) > set_a > real ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__a_001t__Set__Oset_Itf__b_J,type,
% 0.28/0.47 groups919362075_set_b: ( a > set_b ) > set_a > set_b ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__a_001tf__b,type,
% 0.28/0.47 groups1199149371um_a_b: ( a > b ) > set_a > b ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__b_001t__Nat__Onat,type,
% 0.28/0.47 groups2098481813_b_nat: ( b > nat ) > set_b > nat ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__b_001t__Real__Oreal,type,
% 0.28/0.47 groups583146225b_real: ( b > real ) > set_b > real ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__b_001t__Set__Oset_Itf__b_J,type,
% 0.28/0.47 groups448962650_set_b: ( b > set_b ) > set_b > set_b ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__b_001tf__b,type,
% 0.28/0.47 groups2026918778um_b_b: ( b > b ) > set_b > b ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_If_001t__Real__Oreal,type,
% 0.28/0.47 if_real: $o > real > real > real ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_If_001tf__b,type,
% 0.28/0.47 if_b: $o > b > b > b ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Lower__Semicontinuous__Mirabelle__mxyexokbxt_Oconvex__on_001tf__b,type,
% 0.28/0.47 lower_311861425x_on_b: set_b > ( b > extended_ereal ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 0.28/0.47 bot_bot_set_a: set_a ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__b_J,type,
% 0.28/0.47 bot_bot_set_b: set_b ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 0.28/0.47 ord_less_eq_real: real > real > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 0.28/0.47 real_V453051771R_real: real > real > real ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001tf__b,type,
% 0.28/0.47 real_V1035702896aleR_b: real > b > b ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 0.28/0.47 divide_divide_real: real > real > real ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.28/0.47 collect_a: ( a > $o ) > set_a ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_OCollect_001tf__b,type,
% 0.28/0.47 collect_b: ( b > $o ) > set_b ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 0.28/0.47 insert_real: real > set_real > set_real ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oinsert_001tf__a,type,
% 0.28/0.47 insert_a: a > set_a > set_a ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oinsert_001tf__b,type,
% 0.28/0.47 insert_b: b > set_b > set_b ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_member_001tf__a,type,
% 0.28/0.47 member_a: a > set_a > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_member_001tf__b,type,
% 0.28/0.47 member_b: b > set_b > $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_C,type,
% 0.28/0.47 c: set_b ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_a,type,
% 0.28/0.47 a2: a > real ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_aa____,type,
% 0.28/0.47 aa: a > real ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_f,type,
% 0.28/0.47 f: b > extended_ereal ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_i____,type,
% 0.28/0.47 i: a ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_s,type,
% 0.28/0.47 s: set_a ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_sa____,type,
% 0.28/0.47 sa: set_a ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_y,type,
% 0.28/0.47 y: a > b ).
% 0.28/0.47
% 0.28/0.47 % Relevant facts (353)
% 0.28/0.47 thf(fact_0_insert_Ohyps_I3_J,axiom,
% 0.28/0.47 ~ ( member_a @ i @ sa ) ).
% 0.28/0.47
% 0.28/0.47 % insert.hyps(3)
% 0.28/0.47 thf(fact_1_asm,axiom,
% 0.28/0.47 ( ( aa @ i )
% 0.28/0.47 != one_one_real ) ).
% 0.28/0.47
% 0.28/0.47 % asm
% 0.28/0.47 thf(fact_2__092_060open_062_I_092_060Sum_062x_092_060in_062s_O_Aa_Ax_A_K_092_060_094sub_062R_Ay_Ax_A_P_092_060_094sub_062R_A_I1_A_N_Aa_Ai_J_J_A_061_A_I_092_060Sum_062j_092_060in_062s_O_Aa_Aj_A_K_092_060_094sub_062R_Ay_Aj_J_A_P_092_060_094sub_062R_A_I1_A_N_Aa_Ai_J_092_060close_062,axiom,
% 0.28/0.47 ( ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [X: a] : ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) @ ( real_V1035702896aleR_b @ ( aa @ X ) @ ( y @ X ) ) )
% 0.28/0.47 @ sa )
% 0.28/0.47 = ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) )
% 0.28/0.47 @ ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 0.28/0.47 @ sa ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % \<open>(\<Sum>x\<in>s. a x *\<^sub>R y x /\<^sub>R (1 - a i)) = (\<Sum>j\<in>s. a j *\<^sub>R y j) /\<^sub>R (1 - a i)\<close>
% 0.28/0.47 thf(fact_3_insert_Ohyps_I2_J,axiom,
% 0.28/0.47 sa != bot_bot_set_a ).
% 0.28/0.47
% 0.28/0.47 % insert.hyps(2)
% 0.28/0.47 thf(fact_4_insert_Ohyps_I1_J,axiom,
% 0.28/0.47 finite_finite_a @ sa ).
% 0.28/0.47
% 0.28/0.47 % insert.hyps(1)
% 0.28/0.47 thf(fact_5__092_060open_062f_A_I_I_092_060Sum_062j_092_060in_062s_O_Aa_Aj_A_K_092_060_094sub_062R_Ay_Aj_J_A_L_Aa_Ai_A_K_092_060_094sub_062R_Ay_Ai_J_A_061_Af_A_I_I_I1_A_N_Aa_Ai_J_A_K_Ainverse_A_I1_A_N_Aa_Ai_J_J_A_K_092_060_094sub_062R_A_I_092_060Sum_062j_092_060in_062s_O_Aa_Aj_A_K_092_060_094sub_062R_Ay_Aj_J_A_L_Aa_Ai_A_K_092_060_094sub_062R_Ay_Ai_J_092_060close_062,axiom,
% 0.28/0.47 ( ( f
% 0.28/0.47 @ ( plus_plus_b
% 0.28/0.47 @ ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 0.28/0.47 @ sa )
% 0.28/0.47 @ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) )
% 0.28/0.47 = ( f
% 0.28/0.47 @ ( plus_plus_b
% 0.28/0.47 @ ( real_V1035702896aleR_b @ ( times_times_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) )
% 0.28/0.47 @ ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 0.28/0.47 @ sa ) )
% 0.28/0.47 @ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % \<open>f ((\<Sum>j\<in>s. a j *\<^sub>R y j) + a i *\<^sub>R y i) = f (((1 - a i) * inverse (1 - a i)) *\<^sub>R (\<Sum>j\<in>s. a j *\<^sub>R y j) + a i *\<^sub>R y i)\<close>
% 0.28/0.47 thf(fact_6_calculation,axiom,
% 0.28/0.47 ( ( f
% 0.28/0.47 @ ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 0.28/0.47 @ ( insert_a @ i @ sa ) ) )
% 0.28/0.47 = ( f
% 0.28/0.47 @ ( plus_plus_b
% 0.28/0.47 @ ( real_V1035702896aleR_b @ ( times_times_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) )
% 0.28/0.47 @ ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 0.28/0.47 @ sa ) )
% 0.28/0.47 @ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % calculation
% 0.28/0.47 thf(fact_7__092_060open_062f_A_I_092_060Sum_062j_092_060in_062insert_Ai_As_O_Aa_Aj_A_K_092_060_094sub_062R_Ay_Aj_J_A_061_Af_A_I_I_092_060Sum_062j_092_060in_062s_O_Aa_Aj_A_K_092_060_094sub_062R_Ay_Aj_J_A_L_Aa_Ai_A_K_092_060_094sub_062R_Ay_Ai_J_092_060close_062,axiom,
% 0.28/0.47 ( ( f
% 0.28/0.47 @ ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 0.28/0.47 @ ( insert_a @ i @ sa ) ) )
% 0.28/0.47 = ( f
% 0.28/0.47 @ ( plus_plus_b
% 0.28/0.47 @ ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 0.28/0.47 @ sa )
% 0.28/0.47 @ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % \<open>f (\<Sum>j\<in>insert i s. a j *\<^sub>R y j) = f ((\<Sum>j\<in>s. a j *\<^sub>R y j) + a i *\<^sub>R y i)\<close>
% 0.28/0.47 thf(fact_8_scaleR__collapse,axiom,
% 0.28/0.47 ! [U: real,A: b] :
% 0.28/0.47 ( ( plus_plus_b @ ( real_V1035702896aleR_b @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V1035702896aleR_b @ U @ A ) )
% 0.28/0.47 = A ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_collapse
% 0.28/0.47 thf(fact_9_scaleR__collapse,axiom,
% 0.28/0.47 ! [U: real,A: real] :
% 0.28/0.47 ( ( plus_plus_real @ ( real_V453051771R_real @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V453051771R_real @ U @ A ) )
% 0.28/0.47 = A ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_collapse
% 0.28/0.47 thf(fact_10_scaleR__eq__iff,axiom,
% 0.28/0.47 ! [B: b,U: real,A: b] :
% 0.28/0.47 ( ( ( plus_plus_b @ B @ ( real_V1035702896aleR_b @ U @ A ) )
% 0.28/0.47 = ( plus_plus_b @ A @ ( real_V1035702896aleR_b @ U @ B ) ) )
% 0.28/0.47 = ( ( A = B )
% 0.28/0.47 | ( U = one_one_real ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_eq_iff
% 0.28/0.47 thf(fact_11_scaleR__eq__iff,axiom,
% 0.28/0.47 ! [B: real,U: real,A: real] :
% 0.28/0.47 ( ( ( plus_plus_real @ B @ ( real_V453051771R_real @ U @ A ) )
% 0.28/0.47 = ( plus_plus_real @ A @ ( real_V453051771R_real @ U @ B ) ) )
% 0.28/0.47 = ( ( A = B )
% 0.28/0.47 | ( U = one_one_real ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_eq_iff
% 0.28/0.47 thf(fact_12_yai_I1_J,axiom,
% 0.28/0.47 member_b @ ( y @ i ) @ c ).
% 0.28/0.47
% 0.28/0.47 % yai(1)
% 0.28/0.47 thf(fact_13_scaleR__scaleR,axiom,
% 0.28/0.47 ! [A: real,B: real,X2: b] :
% 0.28/0.47 ( ( real_V1035702896aleR_b @ A @ ( real_V1035702896aleR_b @ B @ X2 ) )
% 0.28/0.47 = ( real_V1035702896aleR_b @ ( times_times_real @ A @ B ) @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_scaleR
% 0.28/0.47 thf(fact_14_scaleR__scaleR,axiom,
% 0.28/0.47 ! [A: real,B: real,X2: real] :
% 0.28/0.47 ( ( real_V453051771R_real @ A @ ( real_V453051771R_real @ B @ X2 ) )
% 0.28/0.47 = ( real_V453051771R_real @ ( times_times_real @ A @ B ) @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_scaleR
% 0.28/0.47 thf(fact_15_scaleR__one,axiom,
% 0.28/0.47 ! [X2: b] :
% 0.28/0.47 ( ( real_V1035702896aleR_b @ one_one_real @ X2 )
% 0.28/0.47 = X2 ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_one
% 0.28/0.47 thf(fact_16_scaleR__one,axiom,
% 0.28/0.47 ! [X2: real] :
% 0.28/0.47 ( ( real_V453051771R_real @ one_one_real @ X2 )
% 0.28/0.47 = X2 ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_one
% 0.28/0.47 thf(fact_17__092_060open_062sum_Aa_As_A_061_A1_A_N_Aa_Ai_092_060close_062,axiom,
% 0.28/0.47 ( ( groups1862963056a_real @ aa @ sa )
% 0.28/0.47 = ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % \<open>sum a s = 1 - a i\<close>
% 0.28/0.47 thf(fact_18_inverse__eq__1__iff,axiom,
% 0.28/0.47 ! [X2: real] :
% 0.28/0.47 ( ( ( inverse_inverse_real @ X2 )
% 0.28/0.47 = one_one_real )
% 0.28/0.47 = ( X2 = one_one_real ) ) ).
% 0.28/0.47
% 0.28/0.47 % inverse_eq_1_iff
% 0.28/0.47 thf(fact_19_inverse__1,axiom,
% 0.28/0.47 ( ( inverse_inverse_real @ one_one_real )
% 0.28/0.47 = one_one_real ) ).
% 0.28/0.47
% 0.28/0.47 % inverse_1
% 0.28/0.47 thf(fact_20_inverse__mult__distrib,axiom,
% 0.28/0.47 ! [A: real,B: real] :
% 0.28/0.47 ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 0.28/0.47 = ( times_times_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % inverse_mult_distrib
% 0.28/0.47 thf(fact_21_mult__scaleR__left,axiom,
% 0.28/0.47 ! [A: real,X2: real,Y: real] :
% 0.28/0.47 ( ( times_times_real @ ( real_V453051771R_real @ A @ X2 ) @ Y )
% 0.28/0.47 = ( real_V453051771R_real @ A @ ( times_times_real @ X2 @ Y ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_scaleR_left
% 0.28/0.47 thf(fact_22_assms_I1_J,axiom,
% 0.28/0.47 finite_finite_a @ s ).
% 0.28/0.47
% 0.28/0.47 % assms(1)
% 0.28/0.47 thf(fact_23_assms_I2_J,axiom,
% 0.28/0.47 s != bot_bot_set_a ).
% 0.28/0.47
% 0.28/0.47 % assms(2)
% 0.28/0.47 thf(fact_24_assms_I7_J,axiom,
% 0.28/0.47 ! [I: a] :
% 0.28/0.47 ( ( member_a @ I @ s )
% 0.28/0.47 => ( member_b @ ( y @ I ) @ c ) ) ).
% 0.28/0.47
% 0.28/0.47 % assms(7)
% 0.28/0.47 thf(fact_25_insert_Oprems_I3_J,axiom,
% 0.28/0.47 ! [I: a] :
% 0.28/0.47 ( ( member_a @ I @ ( insert_a @ i @ sa ) )
% 0.28/0.47 => ( member_b @ ( y @ I ) @ c ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert.prems(3)
% 0.28/0.47 thf(fact_26_inverse__inverse__eq,axiom,
% 0.28/0.47 ! [A: real] :
% 0.28/0.47 ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 0.28/0.47 = A ) ).
% 0.28/0.47
% 0.28/0.47 % inverse_inverse_eq
% 0.28/0.47 thf(fact_27_inverse__eq__iff__eq,axiom,
% 0.28/0.47 ! [A: real,B: real] :
% 0.28/0.47 ( ( ( inverse_inverse_real @ A )
% 0.28/0.47 = ( inverse_inverse_real @ B ) )
% 0.28/0.47 = ( A = B ) ) ).
% 0.28/0.47
% 0.28/0.47 % inverse_eq_iff_eq
% 0.28/0.47 thf(fact_28_insert_Oprems_I1_J,axiom,
% 0.28/0.47 ( ( groups1862963056a_real @ aa @ ( insert_a @ i @ sa ) )
% 0.28/0.47 = one_one_real ) ).
% 0.28/0.47
% 0.28/0.47 % insert.prems(1)
% 0.28/0.47 thf(fact_29_assms_I3_J,axiom,
% 0.28/0.47 lower_311861425x_on_b @ c @ f ).
% 0.28/0.47
% 0.28/0.47 % assms(3)
% 0.28/0.47 thf(fact_30_fis,axiom,
% 0.28/0.47 finite_finite_a @ ( insert_a @ i @ sa ) ).
% 0.28/0.47
% 0.28/0.47 % fis
% 0.28/0.47 thf(fact_31_mult__scaleR__right,axiom,
% 0.28/0.47 ! [X2: real,A: real,Y: real] :
% 0.28/0.47 ( ( times_times_real @ X2 @ ( real_V453051771R_real @ A @ Y ) )
% 0.28/0.47 = ( real_V453051771R_real @ A @ ( times_times_real @ X2 @ Y ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_scaleR_right
% 0.28/0.47 thf(fact_32_assms_I4_J,axiom,
% 0.28/0.47 convex_b @ c ).
% 0.28/0.47
% 0.28/0.47 % assms(4)
% 0.28/0.47 thf(fact_33_assms_I5_J,axiom,
% 0.28/0.47 ( ( groups1862963056a_real @ a2 @ s )
% 0.28/0.47 = one_one_real ) ).
% 0.28/0.47
% 0.28/0.47 % assms(5)
% 0.28/0.47 thf(fact_34_real__scaleR__def,axiom,
% 0.28/0.47 real_V453051771R_real = times_times_real ).
% 0.28/0.47
% 0.28/0.47 % real_scaleR_def
% 0.28/0.47 thf(fact_35_scale__left__commute,axiom,
% 0.28/0.47 ! [A: real,B: real,X2: b] :
% 0.28/0.47 ( ( real_V1035702896aleR_b @ A @ ( real_V1035702896aleR_b @ B @ X2 ) )
% 0.28/0.47 = ( real_V1035702896aleR_b @ B @ ( real_V1035702896aleR_b @ A @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_left_commute
% 0.28/0.47 thf(fact_36_scale__left__commute,axiom,
% 0.28/0.47 ! [A: real,B: real,X2: real] :
% 0.28/0.47 ( ( real_V453051771R_real @ A @ ( real_V453051771R_real @ B @ X2 ) )
% 0.28/0.47 = ( real_V453051771R_real @ B @ ( real_V453051771R_real @ A @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_left_commute
% 0.28/0.47 thf(fact_37_inverse__eq__imp__eq,axiom,
% 0.28/0.47 ! [A: real,B: real] :
% 0.28/0.47 ( ( ( inverse_inverse_real @ A )
% 0.28/0.47 = ( inverse_inverse_real @ B ) )
% 0.28/0.47 => ( A = B ) ) ).
% 0.28/0.47
% 0.28/0.47 % inverse_eq_imp_eq
% 0.28/0.47 thf(fact_38_scaleR__add__right,axiom,
% 0.28/0.47 ! [A: real,X2: b,Y: b] :
% 0.28/0.47 ( ( real_V1035702896aleR_b @ A @ ( plus_plus_b @ X2 @ Y ) )
% 0.28/0.47 = ( plus_plus_b @ ( real_V1035702896aleR_b @ A @ X2 ) @ ( real_V1035702896aleR_b @ A @ Y ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_add_right
% 0.28/0.47 thf(fact_39_scaleR__add__right,axiom,
% 0.28/0.47 ! [A: real,X2: real,Y: real] :
% 0.28/0.47 ( ( real_V453051771R_real @ A @ ( plus_plus_real @ X2 @ Y ) )
% 0.28/0.47 = ( plus_plus_real @ ( real_V453051771R_real @ A @ X2 ) @ ( real_V453051771R_real @ A @ Y ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_add_right
% 0.28/0.47 thf(fact_40_scaleR__add__left,axiom,
% 0.28/0.47 ! [A: real,B: real,X2: b] :
% 0.28/0.47 ( ( real_V1035702896aleR_b @ ( plus_plus_real @ A @ B ) @ X2 )
% 0.28/0.47 = ( plus_plus_b @ ( real_V1035702896aleR_b @ A @ X2 ) @ ( real_V1035702896aleR_b @ B @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_add_left
% 0.28/0.47 thf(fact_41_scaleR__add__left,axiom,
% 0.28/0.47 ! [A: real,B: real,X2: real] :
% 0.28/0.47 ( ( real_V453051771R_real @ ( plus_plus_real @ A @ B ) @ X2 )
% 0.28/0.47 = ( plus_plus_real @ ( real_V453051771R_real @ A @ X2 ) @ ( real_V453051771R_real @ B @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_add_left
% 0.28/0.47 thf(fact_42_scaleR__left_Oadd,axiom,
% 0.28/0.47 ! [X2: real,Y: real,Xa: b] :
% 0.28/0.47 ( ( real_V1035702896aleR_b @ ( plus_plus_real @ X2 @ Y ) @ Xa )
% 0.28/0.47 = ( plus_plus_b @ ( real_V1035702896aleR_b @ X2 @ Xa ) @ ( real_V1035702896aleR_b @ Y @ Xa ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_left.add
% 0.28/0.47 thf(fact_43_scaleR__left_Oadd,axiom,
% 0.28/0.47 ! [X2: real,Y: real,Xa: real] :
% 0.28/0.47 ( ( real_V453051771R_real @ ( plus_plus_real @ X2 @ Y ) @ Xa )
% 0.28/0.47 = ( plus_plus_real @ ( real_V453051771R_real @ X2 @ Xa ) @ ( real_V453051771R_real @ Y @ Xa ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_left.add
% 0.28/0.47 thf(fact_44_scale__right__diff__distrib,axiom,
% 0.28/0.47 ! [A: real,X2: b,Y: b] :
% 0.28/0.47 ( ( real_V1035702896aleR_b @ A @ ( minus_minus_b @ X2 @ Y ) )
% 0.28/0.47 = ( minus_minus_b @ ( real_V1035702896aleR_b @ A @ X2 ) @ ( real_V1035702896aleR_b @ A @ Y ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_right_diff_distrib
% 0.28/0.47 thf(fact_45_scale__right__diff__distrib,axiom,
% 0.28/0.47 ! [A: real,X2: real,Y: real] :
% 0.28/0.47 ( ( real_V453051771R_real @ A @ ( minus_minus_real @ X2 @ Y ) )
% 0.28/0.47 = ( minus_minus_real @ ( real_V453051771R_real @ A @ X2 ) @ ( real_V453051771R_real @ A @ Y ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_right_diff_distrib
% 0.28/0.47 thf(fact_46_mult__commute__imp__mult__inverse__commute,axiom,
% 0.28/0.47 ! [Y: real,X2: real] :
% 0.28/0.47 ( ( ( times_times_real @ Y @ X2 )
% 0.28/0.47 = ( times_times_real @ X2 @ Y ) )
% 0.28/0.47 => ( ( times_times_real @ ( inverse_inverse_real @ Y ) @ X2 )
% 0.28/0.47 = ( times_times_real @ X2 @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mult_commute_imp_mult_inverse_commute
% 0.28/0.47 thf(fact_47_scale__sum__right,axiom,
% 0.28/0.47 ! [A: real,F: a > b,A2: set_a] :
% 0.28/0.47 ( ( real_V1035702896aleR_b @ A @ ( groups1199149371um_a_b @ F @ A2 ) )
% 0.28/0.47 = ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [X: a] : ( real_V1035702896aleR_b @ A @ ( F @ X ) )
% 0.28/0.47 @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_sum_right
% 0.28/0.47 thf(fact_48_scale__sum__right,axiom,
% 0.28/0.47 ! [A: real,F: a > real,A2: set_a] :
% 0.28/0.47 ( ( real_V453051771R_real @ A @ ( groups1862963056a_real @ F @ A2 ) )
% 0.28/0.47 = ( groups1862963056a_real
% 0.28/0.47 @ ^ [X: a] : ( real_V453051771R_real @ A @ ( F @ X ) )
% 0.28/0.47 @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_sum_right
% 0.28/0.47 thf(fact_49_scale__sum__left,axiom,
% 0.28/0.47 ! [F: a > real,A2: set_a,X2: b] :
% 0.28/0.47 ( ( real_V1035702896aleR_b @ ( groups1862963056a_real @ F @ A2 ) @ X2 )
% 0.28/0.47 = ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [A3: a] : ( real_V1035702896aleR_b @ ( F @ A3 ) @ X2 )
% 0.28/0.47 @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_sum_left
% 0.28/0.47 thf(fact_50_scale__sum__left,axiom,
% 0.28/0.47 ! [F: a > real,A2: set_a,X2: real] :
% 0.28/0.47 ( ( real_V453051771R_real @ ( groups1862963056a_real @ F @ A2 ) @ X2 )
% 0.28/0.47 = ( groups1862963056a_real
% 0.28/0.47 @ ^ [A3: a] : ( real_V453051771R_real @ ( F @ A3 ) @ X2 )
% 0.28/0.47 @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_sum_left
% 0.28/0.47 thf(fact_51_scaleR__right_Osum,axiom,
% 0.28/0.47 ! [A: real,G: a > b,A2: set_a] :
% 0.28/0.47 ( ( real_V1035702896aleR_b @ A @ ( groups1199149371um_a_b @ G @ A2 ) )
% 0.28/0.47 = ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [X: a] : ( real_V1035702896aleR_b @ A @ ( G @ X ) )
% 0.28/0.47 @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_right.sum
% 0.28/0.47 thf(fact_52_scaleR__right_Osum,axiom,
% 0.28/0.47 ! [A: real,G: a > real,A2: set_a] :
% 0.28/0.47 ( ( real_V453051771R_real @ A @ ( groups1862963056a_real @ G @ A2 ) )
% 0.28/0.47 = ( groups1862963056a_real
% 0.28/0.47 @ ^ [X: a] : ( real_V453051771R_real @ A @ ( G @ X ) )
% 0.28/0.47 @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_right.sum
% 0.28/0.47 thf(fact_53_scaleR__left_Osum,axiom,
% 0.28/0.47 ! [G: a > real,A2: set_a,X2: b] :
% 0.28/0.47 ( ( real_V1035702896aleR_b @ ( groups1862963056a_real @ G @ A2 ) @ X2 )
% 0.28/0.47 = ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [X: a] : ( real_V1035702896aleR_b @ ( G @ X ) @ X2 )
% 0.28/0.47 @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_left.sum
% 0.28/0.47 thf(fact_54_scaleR__left_Osum,axiom,
% 0.28/0.47 ! [G: a > real,A2: set_a,X2: real] :
% 0.28/0.47 ( ( real_V453051771R_real @ ( groups1862963056a_real @ G @ A2 ) @ X2 )
% 0.28/0.47 = ( groups1862963056a_real
% 0.28/0.47 @ ^ [X: a] : ( real_V453051771R_real @ ( G @ X ) @ X2 )
% 0.28/0.47 @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_left.sum
% 0.28/0.47 thf(fact_55_inverse__unique,axiom,
% 0.28/0.47 ! [A: real,B: real] :
% 0.28/0.47 ( ( ( times_times_real @ A @ B )
% 0.28/0.47 = one_one_real )
% 0.28/0.47 => ( ( inverse_inverse_real @ A )
% 0.28/0.47 = B ) ) ).
% 0.28/0.47
% 0.28/0.47 % inverse_unique
% 0.28/0.47 thf(fact_56_scale__left__diff__distrib,axiom,
% 0.28/0.47 ! [A: real,B: real,X2: b] :
% 0.28/0.47 ( ( real_V1035702896aleR_b @ ( minus_minus_real @ A @ B ) @ X2 )
% 0.28/0.47 = ( minus_minus_b @ ( real_V1035702896aleR_b @ A @ X2 ) @ ( real_V1035702896aleR_b @ B @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_left_diff_distrib
% 0.28/0.47 thf(fact_57_scale__left__diff__distrib,axiom,
% 0.28/0.47 ! [A: real,B: real,X2: real] :
% 0.28/0.47 ( ( real_V453051771R_real @ ( minus_minus_real @ A @ B ) @ X2 )
% 0.28/0.47 = ( minus_minus_real @ ( real_V453051771R_real @ A @ X2 ) @ ( real_V453051771R_real @ B @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_left_diff_distrib
% 0.28/0.47 thf(fact_58_scaleR__left_Odiff,axiom,
% 0.28/0.47 ! [X2: real,Y: real,Xa: b] :
% 0.28/0.47 ( ( real_V1035702896aleR_b @ ( minus_minus_real @ X2 @ Y ) @ Xa )
% 0.28/0.47 = ( minus_minus_b @ ( real_V1035702896aleR_b @ X2 @ Xa ) @ ( real_V1035702896aleR_b @ Y @ Xa ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_left.diff
% 0.28/0.47 thf(fact_59_scaleR__left_Odiff,axiom,
% 0.28/0.47 ! [X2: real,Y: real,Xa: real] :
% 0.28/0.47 ( ( real_V453051771R_real @ ( minus_minus_real @ X2 @ Y ) @ Xa )
% 0.28/0.47 = ( minus_minus_real @ ( real_V453051771R_real @ X2 @ Xa ) @ ( real_V453051771R_real @ Y @ Xa ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_left.diff
% 0.28/0.47 thf(fact_60_mem__Collect__eq,axiom,
% 0.28/0.47 ! [A: a,P: a > $o] :
% 0.28/0.47 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.28/0.47 = ( P @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % mem_Collect_eq
% 0.28/0.47 thf(fact_61_mem__Collect__eq,axiom,
% 0.28/0.47 ! [A: b,P: b > $o] :
% 0.28/0.47 ( ( member_b @ A @ ( collect_b @ P ) )
% 0.28/0.47 = ( P @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % mem_Collect_eq
% 0.28/0.47 thf(fact_62_Collect__mem__eq,axiom,
% 0.28/0.47 ! [A2: set_a] :
% 0.28/0.47 ( ( collect_a
% 0.28/0.47 @ ^ [X: a] : ( member_a @ X @ A2 ) )
% 0.28/0.47 = A2 ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mem_eq
% 0.28/0.47 thf(fact_63_Collect__mem__eq,axiom,
% 0.28/0.47 ! [A2: set_b] :
% 0.28/0.47 ( ( collect_b
% 0.28/0.47 @ ^ [X: b] : ( member_b @ X @ A2 ) )
% 0.28/0.47 = A2 ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mem_eq
% 0.28/0.47 thf(fact_64_inverse__scaleR__distrib,axiom,
% 0.28/0.47 ! [A: real,X2: real] :
% 0.28/0.47 ( ( inverse_inverse_real @ ( real_V453051771R_real @ A @ X2 ) )
% 0.28/0.47 = ( real_V453051771R_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % inverse_scaleR_distrib
% 0.28/0.47 thf(fact_65_asum,axiom,
% 0.28/0.47 ( member_b
% 0.28/0.47 @ ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( divide_divide_real @ ( aa @ J ) @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) @ ( y @ J ) )
% 0.28/0.47 @ sa )
% 0.28/0.47 @ c ) ).
% 0.28/0.47
% 0.28/0.47 % asum
% 0.28/0.47 thf(fact_66_sum_Oinsert,axiom,
% 0.28/0.47 ! [A2: set_b,X2: b,G: b > b] :
% 0.28/0.47 ( ( finite_finite_b @ A2 )
% 0.28/0.47 => ( ~ ( member_b @ X2 @ A2 )
% 0.28/0.47 => ( ( groups2026918778um_b_b @ G @ ( insert_b @ X2 @ A2 ) )
% 0.28/0.47 = ( plus_plus_b @ ( G @ X2 ) @ ( groups2026918778um_b_b @ G @ A2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.insert
% 0.28/0.47 thf(fact_67_sum_Oinsert,axiom,
% 0.28/0.47 ! [A2: set_b,X2: b,G: b > real] :
% 0.28/0.47 ( ( finite_finite_b @ A2 )
% 0.28/0.47 => ( ~ ( member_b @ X2 @ A2 )
% 0.28/0.47 => ( ( groups583146225b_real @ G @ ( insert_b @ X2 @ A2 ) )
% 0.28/0.47 = ( plus_plus_real @ ( G @ X2 ) @ ( groups583146225b_real @ G @ A2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.insert
% 0.28/0.47 thf(fact_68_sum_Oinsert,axiom,
% 0.28/0.47 ! [A2: set_a,X2: a,G: a > b] :
% 0.28/0.47 ( ( finite_finite_a @ A2 )
% 0.28/0.47 => ( ~ ( member_a @ X2 @ A2 )
% 0.28/0.47 => ( ( groups1199149371um_a_b @ G @ ( insert_a @ X2 @ A2 ) )
% 0.28/0.47 = ( plus_plus_b @ ( G @ X2 ) @ ( groups1199149371um_a_b @ G @ A2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.insert
% 0.28/0.47 thf(fact_69_sum_Oinsert,axiom,
% 0.28/0.47 ! [A2: set_a,X2: a,G: a > real] :
% 0.28/0.47 ( ( finite_finite_a @ A2 )
% 0.28/0.47 => ( ~ ( member_a @ X2 @ A2 )
% 0.28/0.47 => ( ( groups1862963056a_real @ G @ ( insert_a @ X2 @ A2 ) )
% 0.28/0.47 = ( plus_plus_real @ ( G @ X2 ) @ ( groups1862963056a_real @ G @ A2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.insert
% 0.28/0.47 thf(fact_70_affine__hull__finite__step,axiom,
% 0.28/0.47 ! [S: set_b,A: b,W: real,Y: b] :
% 0.28/0.47 ( ( finite_finite_b @ S )
% 0.28/0.47 => ( ( ? [U2: b > real] :
% 0.28/0.47 ( ( ( groups583146225b_real @ U2 @ ( insert_b @ A @ S ) )
% 0.28/0.47 = W )
% 0.28/0.47 & ( ( groups2026918778um_b_b
% 0.28/0.47 @ ^ [X: b] : ( real_V1035702896aleR_b @ ( U2 @ X ) @ X )
% 0.28/0.47 @ ( insert_b @ A @ S ) )
% 0.28/0.47 = Y ) ) )
% 0.28/0.47 = ( ? [V: real,U2: b > real] :
% 0.28/0.47 ( ( ( groups583146225b_real @ U2 @ S )
% 0.28/0.47 = ( minus_minus_real @ W @ V ) )
% 0.28/0.47 & ( ( groups2026918778um_b_b
% 0.28/0.47 @ ^ [X: b] : ( real_V1035702896aleR_b @ ( U2 @ X ) @ X )
% 0.28/0.47 @ S )
% 0.28/0.47 = ( minus_minus_b @ Y @ ( real_V1035702896aleR_b @ V @ A ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % affine_hull_finite_step
% 0.28/0.47 thf(fact_71_affine__hull__finite__step,axiom,
% 0.28/0.47 ! [S: set_real,A: real,W: real,Y: real] :
% 0.28/0.47 ( ( finite_finite_real @ S )
% 0.28/0.47 => ( ( ? [U2: real > real] :
% 0.28/0.47 ( ( ( groups1296524820l_real @ U2 @ ( insert_real @ A @ S ) )
% 0.28/0.47 = W )
% 0.28/0.47 & ( ( groups1296524820l_real
% 0.28/0.47 @ ^ [X: real] : ( real_V453051771R_real @ ( U2 @ X ) @ X )
% 0.28/0.47 @ ( insert_real @ A @ S ) )
% 0.28/0.47 = Y ) ) )
% 0.28/0.47 = ( ? [V: real,U2: real > real] :
% 0.28/0.47 ( ( ( groups1296524820l_real @ U2 @ S )
% 0.28/0.47 = ( minus_minus_real @ W @ V ) )
% 0.28/0.47 & ( ( groups1296524820l_real
% 0.28/0.47 @ ^ [X: real] : ( real_V453051771R_real @ ( U2 @ X ) @ X )
% 0.28/0.47 @ S )
% 0.28/0.47 = ( minus_minus_real @ Y @ ( real_V453051771R_real @ V @ A ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % affine_hull_finite_step
% 0.28/0.47 thf(fact_72_a1,axiom,
% 0.28/0.47 ( ( groups1862963056a_real
% 0.28/0.47 @ ^ [J: a] : ( divide_divide_real @ ( aa @ J ) @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) )
% 0.28/0.47 @ sa )
% 0.28/0.47 = one_one_real ) ).
% 0.28/0.47
% 0.28/0.47 % a1
% 0.28/0.47 thf(fact_73__092_060open_062sum_Aa_As_A_P_A_I1_A_N_Aa_Ai_J_A_061_A1_092_060close_062,axiom,
% 0.28/0.47 ( ( divide_divide_real @ ( groups1862963056a_real @ aa @ sa ) @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) )
% 0.28/0.47 = one_one_real ) ).
% 0.28/0.47
% 0.28/0.47 % \<open>sum a s / (1 - a i) = 1\<close>
% 0.28/0.47 thf(fact_74_singleton__conv,axiom,
% 0.28/0.47 ! [A: a] :
% 0.28/0.47 ( ( collect_a
% 0.28/0.47 @ ^ [X: a] : ( X = A ) )
% 0.28/0.47 = ( insert_a @ A @ bot_bot_set_a ) ) ).
% 0.28/0.47
% 0.28/0.47 % singleton_conv
% 0.28/0.47 thf(fact_75_singleton__conv2,axiom,
% 0.28/0.47 ! [A: a] :
% 0.28/0.47 ( ( collect_a
% 0.28/0.47 @ ( ^ [Y2: a,Z: a] : ( Y2 = Z )
% 0.28/0.47 @ A ) )
% 0.28/0.47 = ( insert_a @ A @ bot_bot_set_a ) ) ).
% 0.28/0.47
% 0.28/0.47 % singleton_conv2
% 0.28/0.47 thf(fact_76_finite__insert,axiom,
% 0.28/0.47 ! [A: a,A2: set_a] :
% 0.28/0.47 ( ( finite_finite_a @ ( insert_a @ A @ A2 ) )
% 0.28/0.47 = ( finite_finite_a @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_insert
% 0.28/0.47 thf(fact_77_sum__diff1,axiom,
% 0.28/0.47 ! [A2: set_b,A: b,F: b > real] :
% 0.28/0.47 ( ( finite_finite_b @ A2 )
% 0.28/0.47 => ( ( ( member_b @ A @ A2 )
% 0.28/0.47 => ( ( groups583146225b_real @ F @ ( minus_minus_set_b @ A2 @ ( insert_b @ A @ bot_bot_set_b ) ) )
% 0.28/0.47 = ( minus_minus_real @ ( groups583146225b_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.28/0.47 & ( ~ ( member_b @ A @ A2 )
% 0.28/0.47 => ( ( groups583146225b_real @ F @ ( minus_minus_set_b @ A2 @ ( insert_b @ A @ bot_bot_set_b ) ) )
% 0.28/0.47 = ( groups583146225b_real @ F @ A2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum_diff1
% 0.28/0.47 thf(fact_78_sum__diff1,axiom,
% 0.28/0.47 ! [A2: set_a,A: a,F: a > b] :
% 0.28/0.47 ( ( finite_finite_a @ A2 )
% 0.28/0.47 => ( ( ( member_a @ A @ A2 )
% 0.28/0.47 => ( ( groups1199149371um_a_b @ F @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 0.28/0.47 = ( minus_minus_b @ ( groups1199149371um_a_b @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.28/0.47 & ( ~ ( member_a @ A @ A2 )
% 0.28/0.47 => ( ( groups1199149371um_a_b @ F @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 0.28/0.47 = ( groups1199149371um_a_b @ F @ A2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum_diff1
% 0.28/0.47 thf(fact_79_sum__diff1,axiom,
% 0.28/0.47 ! [A2: set_a,A: a,F: a > real] :
% 0.28/0.47 ( ( finite_finite_a @ A2 )
% 0.28/0.47 => ( ( ( member_a @ A @ A2 )
% 0.28/0.47 => ( ( groups1862963056a_real @ F @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 0.28/0.47 = ( minus_minus_real @ ( groups1862963056a_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.28/0.47 & ( ~ ( member_a @ A @ A2 )
% 0.28/0.47 => ( ( groups1862963056a_real @ F @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 0.28/0.47 = ( groups1862963056a_real @ F @ A2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum_diff1
% 0.28/0.47 thf(fact_80_singletonI,axiom,
% 0.28/0.47 ! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ) ).
% 0.28/0.47
% 0.28/0.47 % singletonI
% 0.28/0.47 thf(fact_81_singletonI,axiom,
% 0.28/0.47 ! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ) ).
% 0.28/0.47
% 0.28/0.47 % singletonI
% 0.28/0.47 thf(fact_82_empty__Collect__eq,axiom,
% 0.28/0.47 ! [P: a > $o] :
% 0.28/0.47 ( ( bot_bot_set_a
% 0.28/0.47 = ( collect_a @ P ) )
% 0.28/0.47 = ( ! [X: a] :
% 0.28/0.47 ~ ( P @ X ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % empty_Collect_eq
% 0.28/0.47 thf(fact_83_Collect__empty__eq,axiom,
% 0.28/0.47 ! [P: a > $o] :
% 0.28/0.47 ( ( ( collect_a @ P )
% 0.28/0.47 = bot_bot_set_a )
% 0.28/0.47 = ( ! [X: a] :
% 0.28/0.47 ~ ( P @ X ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_empty_eq
% 0.28/0.47 thf(fact_84_all__not__in__conv,axiom,
% 0.28/0.47 ! [A2: set_b] :
% 0.28/0.47 ( ( ! [X: b] :
% 0.28/0.47 ~ ( member_b @ X @ A2 ) )
% 0.28/0.47 = ( A2 = bot_bot_set_b ) ) ).
% 0.28/0.47
% 0.28/0.47 % all_not_in_conv
% 0.28/0.47 thf(fact_85_all__not__in__conv,axiom,
% 0.28/0.47 ! [A2: set_a] :
% 0.28/0.47 ( ( ! [X: a] :
% 0.28/0.47 ~ ( member_a @ X @ A2 ) )
% 0.28/0.47 = ( A2 = bot_bot_set_a ) ) ).
% 0.28/0.47
% 0.28/0.47 % all_not_in_conv
% 0.28/0.47 thf(fact_86_empty__iff,axiom,
% 0.28/0.47 ! [C: b] :
% 0.28/0.47 ~ ( member_b @ C @ bot_bot_set_b ) ).
% 0.28/0.47
% 0.28/0.47 % empty_iff
% 0.28/0.47 thf(fact_87_empty__iff,axiom,
% 0.28/0.47 ! [C: a] :
% 0.28/0.47 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 0.28/0.47
% 0.28/0.47 % empty_iff
% 0.28/0.47 thf(fact_88_insert__absorb2,axiom,
% 0.28/0.47 ! [X2: a,A2: set_a] :
% 0.28/0.47 ( ( insert_a @ X2 @ ( insert_a @ X2 @ A2 ) )
% 0.28/0.47 = ( insert_a @ X2 @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_absorb2
% 0.28/0.47 thf(fact_89_insert__iff,axiom,
% 0.28/0.47 ! [A: a,B: a,A2: set_a] :
% 0.28/0.47 ( ( member_a @ A @ ( insert_a @ B @ A2 ) )
% 0.28/0.47 = ( ( A = B )
% 0.28/0.47 | ( member_a @ A @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_iff
% 0.28/0.47 thf(fact_90_insert__iff,axiom,
% 0.28/0.47 ! [A: b,B: b,A2: set_b] :
% 0.28/0.47 ( ( member_b @ A @ ( insert_b @ B @ A2 ) )
% 0.28/0.47 = ( ( A = B )
% 0.28/0.47 | ( member_b @ A @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_iff
% 0.28/0.47 thf(fact_91_insertCI,axiom,
% 0.28/0.47 ! [A: a,B2: set_a,B: a] :
% 0.28/0.47 ( ( ~ ( member_a @ A @ B2 )
% 0.28/0.47 => ( A = B ) )
% 0.28/0.47 => ( member_a @ A @ ( insert_a @ B @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insertCI
% 0.28/0.47 thf(fact_92_insertCI,axiom,
% 0.28/0.47 ! [A: b,B2: set_b,B: b] :
% 0.28/0.47 ( ( ~ ( member_b @ A @ B2 )
% 0.28/0.47 => ( A = B ) )
% 0.28/0.47 => ( member_b @ A @ ( insert_b @ B @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insertCI
% 0.28/0.47 thf(fact_93_Diff__iff,axiom,
% 0.28/0.47 ! [C: a,A2: set_a,B2: set_a] :
% 0.28/0.47 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B2 ) )
% 0.28/0.47 = ( ( member_a @ C @ A2 )
% 0.28/0.47 & ~ ( member_a @ C @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Diff_iff
% 0.28/0.47 thf(fact_94_Diff__iff,axiom,
% 0.28/0.47 ! [C: b,A2: set_b,B2: set_b] :
% 0.28/0.47 ( ( member_b @ C @ ( minus_minus_set_b @ A2 @ B2 ) )
% 0.28/0.47 = ( ( member_b @ C @ A2 )
% 0.28/0.47 & ~ ( member_b @ C @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Diff_iff
% 0.28/0.47 thf(fact_95_DiffI,axiom,
% 0.28/0.47 ! [C: a,A2: set_a,B2: set_a] :
% 0.28/0.47 ( ( member_a @ C @ A2 )
% 0.28/0.47 => ( ~ ( member_a @ C @ B2 )
% 0.28/0.47 => ( member_a @ C @ ( minus_minus_set_a @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % DiffI
% 0.28/0.47 thf(fact_96_DiffI,axiom,
% 0.28/0.47 ! [C: b,A2: set_b,B2: set_b] :
% 0.28/0.47 ( ( member_b @ C @ A2 )
% 0.28/0.47 => ( ~ ( member_b @ C @ B2 )
% 0.28/0.47 => ( member_b @ C @ ( minus_minus_set_b @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % DiffI
% 0.28/0.47 thf(fact_97_finite__Collect__disjI,axiom,
% 0.28/0.47 ! [P: a > $o,Q: a > $o] :
% 0.28/0.47 ( ( finite_finite_a
% 0.28/0.47 @ ( collect_a
% 0.28/0.47 @ ^ [X: a] :
% 0.28/0.47 ( ( P @ X )
% 0.28/0.47 | ( Q @ X ) ) ) )
% 0.28/0.47 = ( ( finite_finite_a @ ( collect_a @ P ) )
% 0.28/0.47 & ( finite_finite_a @ ( collect_a @ Q ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_Collect_disjI
% 0.28/0.47 thf(fact_98_finite__Collect__conjI,axiom,
% 0.28/0.47 ! [P: a > $o,Q: a > $o] :
% 0.28/0.47 ( ( ( finite_finite_a @ ( collect_a @ P ) )
% 0.28/0.47 | ( finite_finite_a @ ( collect_a @ Q ) ) )
% 0.28/0.47 => ( finite_finite_a
% 0.28/0.47 @ ( collect_a
% 0.28/0.47 @ ^ [X: a] :
% 0.28/0.47 ( ( P @ X )
% 0.28/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_Collect_conjI
% 0.28/0.47 thf(fact_99_times__divide__eq__left,axiom,
% 0.28/0.47 ! [B: real,C: real,A: real] :
% 0.28/0.47 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.28/0.47 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 0.28/0.47
% 0.28/0.47 % times_divide_eq_left
% 0.28/0.47 thf(fact_100_divide__divide__eq__left,axiom,
% 0.28/0.47 ! [A: real,B: real,C: real] :
% 0.28/0.47 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 0.28/0.47 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % divide_divide_eq_left
% 0.28/0.47 thf(fact_101_divide__divide__eq__right,axiom,
% 0.28/0.47 ! [A: real,B: real,C: real] :
% 0.28/0.47 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.28/0.47 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 % divide_divide_eq_right
% 0.28/0.47 thf(fact_102_times__divide__eq__right,axiom,
% 0.28/0.47 ! [A: real,B: real,C: real] :
% 0.28/0.47 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.28/0.47 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 0.28/0.47
% 0.28/0.47 % times_divide_eq_right
% 0.28/0.47 thf(fact_103_Diff__cancel,axiom,
% 0.28/0.47 ! [A2: set_a] :
% 0.28/0.47 ( ( minus_minus_set_a @ A2 @ A2 )
% 0.28/0.47 = bot_bot_set_a ) ).
% 0.28/0.47
% 0.28/0.47 % Diff_cancel
% 0.28/0.47 thf(fact_104_empty__Diff,axiom,
% 0.28/0.47 ! [A2: set_a] :
% 0.28/0.47 ( ( minus_minus_set_a @ bot_bot_set_a @ A2 )
% 0.28/0.47 = bot_bot_set_a ) ).
% 0.28/0.47
% 0.28/0.47 % empty_Diff
% 0.28/0.47 thf(fact_105_Diff__empty,axiom,
% 0.28/0.47 ! [A2: set_a] :
% 0.28/0.47 ( ( minus_minus_set_a @ A2 @ bot_bot_set_a )
% 0.28/0.47 = A2 ) ).
% 0.28/0.47
% 0.28/0.47 % Diff_empty
% 0.28/0.47 thf(fact_106_finite__Diff2,axiom,
% 0.28/0.47 ! [B2: set_a,A2: set_a] :
% 0.28/0.47 ( ( finite_finite_a @ B2 )
% 0.28/0.47 => ( ( finite_finite_a @ ( minus_minus_set_a @ A2 @ B2 ) )
% 0.28/0.47 = ( finite_finite_a @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_Diff2
% 0.28/0.47 thf(fact_107_finite__Diff,axiom,
% 0.28/0.47 ! [A2: set_a,B2: set_a] :
% 0.28/0.47 ( ( finite_finite_a @ A2 )
% 0.28/0.47 => ( finite_finite_a @ ( minus_minus_set_a @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_Diff
% 0.28/0.47 thf(fact_108_insert__Diff1,axiom,
% 0.28/0.47 ! [X2: a,B2: set_a,A2: set_a] :
% 0.28/0.47 ( ( member_a @ X2 @ B2 )
% 0.28/0.47 => ( ( minus_minus_set_a @ ( insert_a @ X2 @ A2 ) @ B2 )
% 0.28/0.47 = ( minus_minus_set_a @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_Diff1
% 0.28/0.47 thf(fact_109_insert__Diff1,axiom,
% 0.28/0.47 ! [X2: b,B2: set_b,A2: set_b] :
% 0.28/0.47 ( ( member_b @ X2 @ B2 )
% 0.28/0.47 => ( ( minus_minus_set_b @ ( insert_b @ X2 @ A2 ) @ B2 )
% 0.28/0.47 = ( minus_minus_set_b @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_Diff1
% 0.28/0.47 thf(fact_110_Diff__insert0,axiom,
% 0.28/0.47 ! [X2: a,A2: set_a,B2: set_a] :
% 0.28/0.47 ( ~ ( member_a @ X2 @ A2 )
% 0.28/0.47 => ( ( minus_minus_set_a @ A2 @ ( insert_a @ X2 @ B2 ) )
% 0.28/0.47 = ( minus_minus_set_a @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Diff_insert0
% 0.28/0.47 thf(fact_111_Diff__insert0,axiom,
% 0.28/0.47 ! [X2: b,A2: set_b,B2: set_b] :
% 0.28/0.47 ( ~ ( member_b @ X2 @ A2 )
% 0.28/0.47 => ( ( minus_minus_set_b @ A2 @ ( insert_b @ X2 @ B2 ) )
% 0.28/0.47 = ( minus_minus_set_b @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Diff_insert0
% 0.28/0.47 thf(fact_112_inverse__divide,axiom,
% 0.28/0.47 ! [A: real,B: real] :
% 0.28/0.47 ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 0.28/0.47 = ( divide_divide_real @ B @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % inverse_divide
% 0.28/0.47 thf(fact_113_insert__Diff__single,axiom,
% 0.28/0.47 ! [A: a,A2: set_a] :
% 0.28/0.47 ( ( insert_a @ A @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 0.28/0.47 = ( insert_a @ A @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_Diff_single
% 0.28/0.47 thf(fact_114_finite__Diff__insert,axiom,
% 0.28/0.47 ! [A2: set_a,A: a,B2: set_a] :
% 0.28/0.47 ( ( finite_finite_a @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ B2 ) ) )
% 0.28/0.47 = ( finite_finite_a @ ( minus_minus_set_a @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_Diff_insert
% 0.28/0.47 thf(fact_115_sum__diff1__nat,axiom,
% 0.28/0.47 ! [A: b,A2: set_b,F: b > nat] :
% 0.28/0.47 ( ( ( member_b @ A @ A2 )
% 0.28/0.47 => ( ( groups2098481813_b_nat @ F @ ( minus_minus_set_b @ A2 @ ( insert_b @ A @ bot_bot_set_b ) ) )
% 0.28/0.47 = ( minus_minus_nat @ ( groups2098481813_b_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.28/0.47 & ( ~ ( member_b @ A @ A2 )
% 0.28/0.47 => ( ( groups2098481813_b_nat @ F @ ( minus_minus_set_b @ A2 @ ( insert_b @ A @ bot_bot_set_b ) ) )
% 0.28/0.47 = ( groups2098481813_b_nat @ F @ A2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum_diff1_nat
% 0.28/0.47 thf(fact_116_sum__diff1__nat,axiom,
% 0.28/0.47 ! [A: a,A2: set_a,F: a > nat] :
% 0.28/0.47 ( ( ( member_a @ A @ A2 )
% 0.28/0.47 => ( ( groups769445524_a_nat @ F @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 0.28/0.47 = ( minus_minus_nat @ ( groups769445524_a_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.28/0.47 & ( ~ ( member_a @ A @ A2 )
% 0.28/0.47 => ( ( groups769445524_a_nat @ F @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 0.28/0.47 = ( groups769445524_a_nat @ F @ A2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum_diff1_nat
% 0.28/0.47 thf(fact_117_minus__set__def,axiom,
% 0.28/0.47 ( minus_minus_set_a
% 0.28/0.47 = ( ^ [A4: set_a,B3: set_a] :
% 0.28/0.47 ( collect_a
% 0.28/0.47 @ ( minus_minus_a_o
% 0.28/0.47 @ ^ [X: a] : ( member_a @ X @ A4 )
% 0.28/0.47 @ ^ [X: a] : ( member_a @ X @ B3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % minus_set_def
% 0.28/0.47 thf(fact_118_minus__set__def,axiom,
% 0.28/0.47 ( minus_minus_set_b
% 0.28/0.47 = ( ^ [A4: set_b,B3: set_b] :
% 0.28/0.47 ( collect_b
% 0.28/0.47 @ ( minus_minus_b_o
% 0.28/0.47 @ ^ [X: b] : ( member_b @ X @ A4 )
% 0.28/0.47 @ ^ [X: b] : ( member_b @ X @ B3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % minus_set_def
% 0.28/0.47 thf(fact_119_set__diff__eq,axiom,
% 0.28/0.47 ( minus_minus_set_a
% 0.28/0.47 = ( ^ [A4: set_a,B3: set_a] :
% 0.28/0.47 ( collect_a
% 0.28/0.47 @ ^ [X: a] :
% 0.28/0.47 ( ( member_a @ X @ A4 )
% 0.28/0.47 & ~ ( member_a @ X @ B3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_diff_eq
% 0.28/0.47 thf(fact_120_set__diff__eq,axiom,
% 0.28/0.47 ( minus_minus_set_b
% 0.28/0.47 = ( ^ [A4: set_b,B3: set_b] :
% 0.28/0.47 ( collect_b
% 0.28/0.47 @ ^ [X: b] :
% 0.28/0.47 ( ( member_b @ X @ A4 )
% 0.28/0.47 & ~ ( member_b @ X @ B3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_diff_eq
% 0.28/0.47 thf(fact_121_DiffD2,axiom,
% 0.28/0.47 ! [C: a,A2: set_a,B2: set_a] :
% 0.28/0.47 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B2 ) )
% 0.28/0.47 => ~ ( member_a @ C @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % DiffD2
% 0.28/0.47 thf(fact_122_DiffD2,axiom,
% 0.28/0.47 ! [C: b,A2: set_b,B2: set_b] :
% 0.28/0.47 ( ( member_b @ C @ ( minus_minus_set_b @ A2 @ B2 ) )
% 0.28/0.47 => ~ ( member_b @ C @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % DiffD2
% 0.28/0.47 thf(fact_123_DiffD1,axiom,
% 0.28/0.47 ! [C: a,A2: set_a,B2: set_a] :
% 0.28/0.47 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B2 ) )
% 0.28/0.47 => ( member_a @ C @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % DiffD1
% 0.28/0.47 thf(fact_124_DiffD1,axiom,
% 0.28/0.47 ! [C: b,A2: set_b,B2: set_b] :
% 0.28/0.47 ( ( member_b @ C @ ( minus_minus_set_b @ A2 @ B2 ) )
% 0.28/0.47 => ( member_b @ C @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % DiffD1
% 0.28/0.47 thf(fact_125_DiffE,axiom,
% 0.28/0.47 ! [C: a,A2: set_a,B2: set_a] :
% 0.28/0.47 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B2 ) )
% 0.28/0.47 => ~ ( ( member_a @ C @ A2 )
% 0.28/0.47 => ( member_a @ C @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % DiffE
% 0.28/0.47 thf(fact_126_DiffE,axiom,
% 0.28/0.47 ! [C: b,A2: set_b,B2: set_b] :
% 0.28/0.47 ( ( member_b @ C @ ( minus_minus_set_b @ A2 @ B2 ) )
% 0.28/0.47 => ~ ( ( member_b @ C @ A2 )
% 0.28/0.47 => ( member_b @ C @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % DiffE
% 0.28/0.47 thf(fact_127_Diff__infinite__finite,axiom,
% 0.28/0.47 ! [T: set_a,S: set_a] :
% 0.28/0.47 ( ( finite_finite_a @ T )
% 0.28/0.47 => ( ~ ( finite_finite_a @ S )
% 0.28/0.47 => ~ ( finite_finite_a @ ( minus_minus_set_a @ S @ T ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Diff_infinite_finite
% 0.28/0.47 thf(fact_128_insert__Diff__if,axiom,
% 0.28/0.47 ! [X2: a,B2: set_a,A2: set_a] :
% 0.28/0.47 ( ( ( member_a @ X2 @ B2 )
% 0.28/0.47 => ( ( minus_minus_set_a @ ( insert_a @ X2 @ A2 ) @ B2 )
% 0.28/0.47 = ( minus_minus_set_a @ A2 @ B2 ) ) )
% 0.28/0.47 & ( ~ ( member_a @ X2 @ B2 )
% 0.28/0.47 => ( ( minus_minus_set_a @ ( insert_a @ X2 @ A2 ) @ B2 )
% 0.28/0.47 = ( insert_a @ X2 @ ( minus_minus_set_a @ A2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_Diff_if
% 0.28/0.47 thf(fact_129_insert__Diff__if,axiom,
% 0.28/0.47 ! [X2: b,B2: set_b,A2: set_b] :
% 0.28/0.47 ( ( ( member_b @ X2 @ B2 )
% 0.28/0.47 => ( ( minus_minus_set_b @ ( insert_b @ X2 @ A2 ) @ B2 )
% 0.28/0.47 = ( minus_minus_set_b @ A2 @ B2 ) ) )
% 0.28/0.47 & ( ~ ( member_b @ X2 @ B2 )
% 0.28/0.47 => ( ( minus_minus_set_b @ ( insert_b @ X2 @ A2 ) @ B2 )
% 0.28/0.47 = ( insert_b @ X2 @ ( minus_minus_set_b @ A2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_Diff_if
% 0.28/0.47 thf(fact_130_sum__divide__distrib,axiom,
% 0.28/0.47 ! [F: a > real,A2: set_a,R: real] :
% 0.28/0.47 ( ( divide_divide_real @ ( groups1862963056a_real @ F @ A2 ) @ R )
% 0.28/0.47 = ( groups1862963056a_real
% 0.28/0.47 @ ^ [N: a] : ( divide_divide_real @ ( F @ N ) @ R )
% 0.28/0.47 @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum_divide_distrib
% 0.28/0.47 thf(fact_131_convex__ereal__add,axiom,
% 0.28/0.47 ! [S2: set_b,F: b > extended_ereal,G: b > extended_ereal] :
% 0.28/0.47 ( ( lower_311861425x_on_b @ S2 @ F )
% 0.28/0.47 => ( ( lower_311861425x_on_b @ S2 @ G )
% 0.28/0.47 => ( lower_311861425x_on_b @ S2
% 0.28/0.47 @ ^ [X: b] : ( plus_p2118002693_ereal @ ( F @ X ) @ ( G @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % convex_ereal_add
% 0.28/0.47 thf(fact_132_times__divide__times__eq,axiom,
% 0.28/0.47 ! [X2: real,Y: real,Z2: real,W: real] :
% 0.28/0.47 ( ( times_times_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ Z2 @ W ) )
% 0.28/0.47 = ( divide_divide_real @ ( times_times_real @ X2 @ Z2 ) @ ( times_times_real @ Y @ W ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % times_divide_times_eq
% 0.28/0.47 thf(fact_133_divide__divide__times__eq,axiom,
% 0.28/0.47 ! [X2: real,Y: real,Z2: real,W: real] :
% 0.28/0.47 ( ( divide_divide_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ Z2 @ W ) )
% 0.28/0.47 = ( divide_divide_real @ ( times_times_real @ X2 @ W ) @ ( times_times_real @ Y @ Z2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % divide_divide_times_eq
% 0.28/0.47 thf(fact_134_divide__divide__eq__left_H,axiom,
% 0.28/0.47 ! [A: real,B: real,C: real] :
% 0.28/0.47 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 0.28/0.47 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % divide_divide_eq_left'
% 0.28/0.47 thf(fact_135_add__divide__distrib,axiom,
% 0.28/0.47 ! [A: real,B: real,C: real] :
% 0.28/0.47 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.28/0.47 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_divide_distrib
% 0.28/0.47 thf(fact_136_diff__divide__distrib,axiom,
% 0.28/0.47 ! [A: real,B: real,C: real] :
% 0.28/0.47 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.28/0.47 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % diff_divide_distrib
% 0.28/0.47 thf(fact_137_Diff__insert__absorb,axiom,
% 0.28/0.47 ! [X2: b,A2: set_b] :
% 0.28/0.47 ( ~ ( member_b @ X2 @ A2 )
% 0.28/0.47 => ( ( minus_minus_set_b @ ( insert_b @ X2 @ A2 ) @ ( insert_b @ X2 @ bot_bot_set_b ) )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Diff_insert_absorb
% 0.28/0.47 thf(fact_138_Diff__insert__absorb,axiom,
% 0.28/0.47 ! [X2: a,A2: set_a] :
% 0.28/0.47 ( ~ ( member_a @ X2 @ A2 )
% 0.28/0.47 => ( ( minus_minus_set_a @ ( insert_a @ X2 @ A2 ) @ ( insert_a @ X2 @ bot_bot_set_a ) )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Diff_insert_absorb
% 0.28/0.47 thf(fact_139_Diff__insert2,axiom,
% 0.28/0.47 ! [A2: set_a,A: a,B2: set_a] :
% 0.28/0.47 ( ( minus_minus_set_a @ A2 @ ( insert_a @ A @ B2 ) )
% 0.28/0.47 = ( minus_minus_set_a @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Diff_insert2
% 0.28/0.47 thf(fact_140_insert__Diff,axiom,
% 0.28/0.47 ! [A: b,A2: set_b] :
% 0.28/0.47 ( ( member_b @ A @ A2 )
% 0.28/0.47 => ( ( insert_b @ A @ ( minus_minus_set_b @ A2 @ ( insert_b @ A @ bot_bot_set_b ) ) )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_Diff
% 0.28/0.47 thf(fact_141_insert__Diff,axiom,
% 0.28/0.47 ! [A: a,A2: set_a] :
% 0.28/0.47 ( ( member_a @ A @ A2 )
% 0.28/0.47 => ( ( insert_a @ A @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_Diff
% 0.28/0.47 thf(fact_142_Diff__insert,axiom,
% 0.28/0.47 ! [A2: set_a,A: a,B2: set_a] :
% 0.28/0.47 ( ( minus_minus_set_a @ A2 @ ( insert_a @ A @ B2 ) )
% 0.28/0.47 = ( minus_minus_set_a @ ( minus_minus_set_a @ A2 @ B2 ) @ ( insert_a @ A @ bot_bot_set_a ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Diff_insert
% 0.28/0.47 thf(fact_143_finite__empty__induct,axiom,
% 0.28/0.47 ! [A2: set_b,P: set_b > $o] :
% 0.28/0.47 ( ( finite_finite_b @ A2 )
% 0.28/0.47 => ( ( P @ A2 )
% 0.28/0.47 => ( ! [A5: b,A6: set_b] :
% 0.28/0.47 ( ( finite_finite_b @ A6 )
% 0.28/0.47 => ( ( member_b @ A5 @ A6 )
% 0.28/0.47 => ( ( P @ A6 )
% 0.28/0.47 => ( P @ ( minus_minus_set_b @ A6 @ ( insert_b @ A5 @ bot_bot_set_b ) ) ) ) ) )
% 0.28/0.47 => ( P @ bot_bot_set_b ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_empty_induct
% 0.28/0.47 thf(fact_144_finite__empty__induct,axiom,
% 0.28/0.47 ! [A2: set_a,P: set_a > $o] :
% 0.28/0.47 ( ( finite_finite_a @ A2 )
% 0.28/0.47 => ( ( P @ A2 )
% 0.28/0.47 => ( ! [A5: a,A6: set_a] :
% 0.28/0.47 ( ( finite_finite_a @ A6 )
% 0.28/0.47 => ( ( member_a @ A5 @ A6 )
% 0.28/0.47 => ( ( P @ A6 )
% 0.28/0.47 => ( P @ ( minus_minus_set_a @ A6 @ ( insert_a @ A5 @ bot_bot_set_a ) ) ) ) ) )
% 0.28/0.47 => ( P @ bot_bot_set_a ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_empty_induct
% 0.28/0.47 thf(fact_145_infinite__coinduct,axiom,
% 0.28/0.47 ! [X3: set_a > $o,A2: set_a] :
% 0.28/0.47 ( ( X3 @ A2 )
% 0.28/0.47 => ( ! [A6: set_a] :
% 0.28/0.47 ( ( X3 @ A6 )
% 0.28/0.47 => ? [X4: a] :
% 0.28/0.47 ( ( member_a @ X4 @ A6 )
% 0.28/0.47 & ( ( X3 @ ( minus_minus_set_a @ A6 @ ( insert_a @ X4 @ bot_bot_set_a ) ) )
% 0.28/0.47 | ~ ( finite_finite_a @ ( minus_minus_set_a @ A6 @ ( insert_a @ X4 @ bot_bot_set_a ) ) ) ) ) )
% 0.28/0.47 => ~ ( finite_finite_a @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % infinite_coinduct
% 0.28/0.47 thf(fact_146_infinite__remove,axiom,
% 0.28/0.47 ! [S: set_a,A: a] :
% 0.28/0.47 ( ~ ( finite_finite_a @ S )
% 0.28/0.47 => ~ ( finite_finite_a @ ( minus_minus_set_a @ S @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % infinite_remove
% 0.28/0.47 thf(fact_147_field__class_Ofield__divide__inverse,axiom,
% 0.28/0.47 ( divide_divide_real
% 0.28/0.47 = ( ^ [A3: real,B4: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % field_class.field_divide_inverse
% 0.28/0.47 thf(fact_148_divide__inverse,axiom,
% 0.28/0.47 ( divide_divide_real
% 0.28/0.47 = ( ^ [A3: real,B4: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % divide_inverse
% 0.28/0.47 thf(fact_149_divide__inverse__commute,axiom,
% 0.28/0.47 ( divide_divide_real
% 0.28/0.47 = ( ^ [A3: real,B4: real] : ( times_times_real @ ( inverse_inverse_real @ B4 ) @ A3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % divide_inverse_commute
% 0.28/0.47 thf(fact_150_inverse__eq__divide,axiom,
% 0.28/0.47 ( inverse_inverse_real
% 0.28/0.47 = ( divide_divide_real @ one_one_real ) ) ).
% 0.28/0.47
% 0.28/0.47 % inverse_eq_divide
% 0.28/0.47 thf(fact_151_ex__in__conv,axiom,
% 0.28/0.47 ! [A2: set_b] :
% 0.28/0.47 ( ( ? [X: b] : ( member_b @ X @ A2 ) )
% 0.28/0.47 = ( A2 != bot_bot_set_b ) ) ).
% 0.28/0.47
% 0.28/0.47 % ex_in_conv
% 0.28/0.47 thf(fact_152_ex__in__conv,axiom,
% 0.28/0.47 ! [A2: set_a] :
% 0.28/0.47 ( ( ? [X: a] : ( member_a @ X @ A2 ) )
% 0.28/0.47 = ( A2 != bot_bot_set_a ) ) ).
% 0.28/0.47
% 0.28/0.47 % ex_in_conv
% 0.28/0.47 thf(fact_153_equals0I,axiom,
% 0.28/0.47 ! [A2: set_b] :
% 0.28/0.47 ( ! [Y3: b] :
% 0.28/0.47 ~ ( member_b @ Y3 @ A2 )
% 0.28/0.47 => ( A2 = bot_bot_set_b ) ) ).
% 0.28/0.47
% 0.28/0.47 % equals0I
% 0.28/0.47 thf(fact_154_equals0I,axiom,
% 0.28/0.47 ! [A2: set_a] :
% 0.28/0.47 ( ! [Y3: a] :
% 0.28/0.47 ~ ( member_a @ Y3 @ A2 )
% 0.28/0.47 => ( A2 = bot_bot_set_a ) ) ).
% 0.28/0.47
% 0.28/0.47 % equals0I
% 0.28/0.47 thf(fact_155_equals0D,axiom,
% 0.28/0.47 ! [A2: set_b,A: b] :
% 0.28/0.47 ( ( A2 = bot_bot_set_b )
% 0.28/0.47 => ~ ( member_b @ A @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % equals0D
% 0.28/0.47 thf(fact_156_equals0D,axiom,
% 0.28/0.47 ! [A2: set_a,A: a] :
% 0.28/0.47 ( ( A2 = bot_bot_set_a )
% 0.28/0.47 => ~ ( member_a @ A @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % equals0D
% 0.28/0.47 thf(fact_157_emptyE,axiom,
% 0.28/0.47 ! [A: b] :
% 0.28/0.47 ~ ( member_b @ A @ bot_bot_set_b ) ).
% 0.28/0.47
% 0.28/0.47 % emptyE
% 0.28/0.47 thf(fact_158_emptyE,axiom,
% 0.28/0.47 ! [A: a] :
% 0.28/0.47 ~ ( member_a @ A @ bot_bot_set_a ) ).
% 0.28/0.47
% 0.28/0.47 % emptyE
% 0.28/0.47 thf(fact_159_mk__disjoint__insert,axiom,
% 0.28/0.47 ! [A: a,A2: set_a] :
% 0.28/0.47 ( ( member_a @ A @ A2 )
% 0.28/0.47 => ? [B5: set_a] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 = ( insert_a @ A @ B5 ) )
% 0.28/0.47 & ~ ( member_a @ A @ B5 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mk_disjoint_insert
% 0.28/0.47 thf(fact_160_mk__disjoint__insert,axiom,
% 0.28/0.47 ! [A: b,A2: set_b] :
% 0.28/0.47 ( ( member_b @ A @ A2 )
% 0.28/0.47 => ? [B5: set_b] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 = ( insert_b @ A @ B5 ) )
% 0.28/0.47 & ~ ( member_b @ A @ B5 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % mk_disjoint_insert
% 0.28/0.47 thf(fact_161_insert__commute,axiom,
% 0.28/0.47 ! [X2: a,Y: a,A2: set_a] :
% 0.28/0.47 ( ( insert_a @ X2 @ ( insert_a @ Y @ A2 ) )
% 0.28/0.47 = ( insert_a @ Y @ ( insert_a @ X2 @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_commute
% 0.28/0.47 thf(fact_162_insert__eq__iff,axiom,
% 0.28/0.47 ! [A: a,A2: set_a,B: a,B2: set_a] :
% 0.28/0.47 ( ~ ( member_a @ A @ A2 )
% 0.28/0.47 => ( ~ ( member_a @ B @ B2 )
% 0.28/0.47 => ( ( ( insert_a @ A @ A2 )
% 0.28/0.47 = ( insert_a @ B @ B2 ) )
% 0.28/0.47 = ( ( ( A = B )
% 0.28/0.47 => ( A2 = B2 ) )
% 0.28/0.47 & ( ( A != B )
% 0.28/0.47 => ? [C2: set_a] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 = ( insert_a @ B @ C2 ) )
% 0.28/0.47 & ~ ( member_a @ B @ C2 )
% 0.28/0.47 & ( B2
% 0.28/0.47 = ( insert_a @ A @ C2 ) )
% 0.28/0.47 & ~ ( member_a @ A @ C2 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_eq_iff
% 0.28/0.47 thf(fact_163_insert__eq__iff,axiom,
% 0.28/0.47 ! [A: b,A2: set_b,B: b,B2: set_b] :
% 0.28/0.47 ( ~ ( member_b @ A @ A2 )
% 0.28/0.47 => ( ~ ( member_b @ B @ B2 )
% 0.28/0.47 => ( ( ( insert_b @ A @ A2 )
% 0.28/0.47 = ( insert_b @ B @ B2 ) )
% 0.28/0.47 = ( ( ( A = B )
% 0.28/0.47 => ( A2 = B2 ) )
% 0.28/0.47 & ( ( A != B )
% 0.28/0.47 => ? [C2: set_b] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 = ( insert_b @ B @ C2 ) )
% 0.28/0.47 & ~ ( member_b @ B @ C2 )
% 0.28/0.47 & ( B2
% 0.28/0.47 = ( insert_b @ A @ C2 ) )
% 0.28/0.47 & ~ ( member_b @ A @ C2 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_eq_iff
% 0.28/0.47 thf(fact_164_insert__absorb,axiom,
% 0.28/0.47 ! [A: a,A2: set_a] :
% 0.28/0.47 ( ( member_a @ A @ A2 )
% 0.28/0.47 => ( ( insert_a @ A @ A2 )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_absorb
% 0.28/0.47 thf(fact_165_insert__absorb,axiom,
% 0.28/0.47 ! [A: b,A2: set_b] :
% 0.28/0.47 ( ( member_b @ A @ A2 )
% 0.28/0.47 => ( ( insert_b @ A @ A2 )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_absorb
% 0.28/0.47 thf(fact_166_insert__ident,axiom,
% 0.28/0.47 ! [X2: a,A2: set_a,B2: set_a] :
% 0.28/0.47 ( ~ ( member_a @ X2 @ A2 )
% 0.28/0.47 => ( ~ ( member_a @ X2 @ B2 )
% 0.28/0.47 => ( ( ( insert_a @ X2 @ A2 )
% 0.28/0.47 = ( insert_a @ X2 @ B2 ) )
% 0.28/0.47 = ( A2 = B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_ident
% 0.28/0.47 thf(fact_167_insert__ident,axiom,
% 0.28/0.47 ! [X2: b,A2: set_b,B2: set_b] :
% 0.28/0.47 ( ~ ( member_b @ X2 @ A2 )
% 0.28/0.47 => ( ~ ( member_b @ X2 @ B2 )
% 0.28/0.47 => ( ( ( insert_b @ X2 @ A2 )
% 0.28/0.47 = ( insert_b @ X2 @ B2 ) )
% 0.28/0.47 = ( A2 = B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_ident
% 0.28/0.47 thf(fact_168_Set_Oset__insert,axiom,
% 0.28/0.47 ! [X2: a,A2: set_a] :
% 0.28/0.47 ( ( member_a @ X2 @ A2 )
% 0.28/0.47 => ~ ! [B5: set_a] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 = ( insert_a @ X2 @ B5 ) )
% 0.28/0.47 => ( member_a @ X2 @ B5 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Set.set_insert
% 0.28/0.47 thf(fact_169_Set_Oset__insert,axiom,
% 0.28/0.47 ! [X2: b,A2: set_b] :
% 0.28/0.47 ( ( member_b @ X2 @ A2 )
% 0.28/0.47 => ~ ! [B5: set_b] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 = ( insert_b @ X2 @ B5 ) )
% 0.28/0.47 => ( member_b @ X2 @ B5 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Set.set_insert
% 0.28/0.47 thf(fact_170_insertI2,axiom,
% 0.28/0.47 ! [A: a,B2: set_a,B: a] :
% 0.28/0.47 ( ( member_a @ A @ B2 )
% 0.28/0.47 => ( member_a @ A @ ( insert_a @ B @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insertI2
% 0.28/0.47 thf(fact_171_insertI2,axiom,
% 0.28/0.47 ! [A: b,B2: set_b,B: b] :
% 0.28/0.47 ( ( member_b @ A @ B2 )
% 0.28/0.47 => ( member_b @ A @ ( insert_b @ B @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insertI2
% 0.28/0.47 thf(fact_172_insertI1,axiom,
% 0.28/0.47 ! [A: a,B2: set_a] : ( member_a @ A @ ( insert_a @ A @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % insertI1
% 0.28/0.47 thf(fact_173_insertI1,axiom,
% 0.28/0.47 ! [A: b,B2: set_b] : ( member_b @ A @ ( insert_b @ A @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % insertI1
% 0.28/0.47 thf(fact_174_insertE,axiom,
% 0.28/0.47 ! [A: a,B: a,A2: set_a] :
% 0.28/0.47 ( ( member_a @ A @ ( insert_a @ B @ A2 ) )
% 0.28/0.47 => ( ( A != B )
% 0.28/0.47 => ( member_a @ A @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insertE
% 0.28/0.47 thf(fact_175_insertE,axiom,
% 0.28/0.47 ! [A: b,B: b,A2: set_b] :
% 0.28/0.47 ( ( member_b @ A @ ( insert_b @ B @ A2 ) )
% 0.28/0.47 => ( ( A != B )
% 0.28/0.47 => ( member_b @ A @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insertE
% 0.28/0.47 thf(fact_176_sum_Ocong,axiom,
% 0.28/0.47 ! [A2: set_a,B2: set_a,G: a > b,H: a > b] :
% 0.28/0.47 ( ( A2 = B2 )
% 0.28/0.47 => ( ! [X5: a] :
% 0.28/0.47 ( ( member_a @ X5 @ B2 )
% 0.28/0.47 => ( ( G @ X5 )
% 0.28/0.47 = ( H @ X5 ) ) )
% 0.28/0.47 => ( ( groups1199149371um_a_b @ G @ A2 )
% 0.28/0.47 = ( groups1199149371um_a_b @ H @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.cong
% 0.28/0.47 thf(fact_177_sum_Ocong,axiom,
% 0.28/0.47 ! [A2: set_a,B2: set_a,G: a > real,H: a > real] :
% 0.28/0.47 ( ( A2 = B2 )
% 0.28/0.47 => ( ! [X5: a] :
% 0.28/0.47 ( ( member_a @ X5 @ B2 )
% 0.28/0.47 => ( ( G @ X5 )
% 0.28/0.47 = ( H @ X5 ) ) )
% 0.28/0.47 => ( ( groups1862963056a_real @ G @ A2 )
% 0.28/0.47 = ( groups1862963056a_real @ H @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.cong
% 0.28/0.47 thf(fact_178_sum_Oeq__general,axiom,
% 0.28/0.47 ! [B2: set_a,A2: set_b,H: b > a,Gamma: a > b,Phi: b > b] :
% 0.28/0.47 ( ! [Y3: a] :
% 0.28/0.47 ( ( member_a @ Y3 @ B2 )
% 0.28/0.47 => ? [X4: b] :
% 0.28/0.47 ( ( member_b @ X4 @ A2 )
% 0.28/0.47 & ( ( H @ X4 )
% 0.28/0.47 = Y3 )
% 0.28/0.47 & ! [Ya: b] :
% 0.28/0.47 ( ( ( member_b @ Ya @ A2 )
% 0.28/0.47 & ( ( H @ Ya )
% 0.28/0.47 = Y3 ) )
% 0.28/0.47 => ( Ya = X4 ) ) ) )
% 0.28/0.47 => ( ! [X5: b] :
% 0.28/0.47 ( ( member_b @ X5 @ A2 )
% 0.28/0.47 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 0.28/0.47 & ( ( Gamma @ ( H @ X5 ) )
% 0.28/0.47 = ( Phi @ X5 ) ) ) )
% 0.28/0.47 => ( ( groups2026918778um_b_b @ Phi @ A2 )
% 0.28/0.47 = ( groups1199149371um_a_b @ Gamma @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.eq_general
% 0.28/0.47 thf(fact_179_sum_Oeq__general,axiom,
% 0.28/0.47 ! [B2: set_a,A2: set_b,H: b > a,Gamma: a > real,Phi: b > real] :
% 0.28/0.47 ( ! [Y3: a] :
% 0.28/0.47 ( ( member_a @ Y3 @ B2 )
% 0.28/0.47 => ? [X4: b] :
% 0.28/0.47 ( ( member_b @ X4 @ A2 )
% 0.28/0.47 & ( ( H @ X4 )
% 0.28/0.47 = Y3 )
% 0.28/0.47 & ! [Ya: b] :
% 0.28/0.47 ( ( ( member_b @ Ya @ A2 )
% 0.28/0.47 & ( ( H @ Ya )
% 0.28/0.47 = Y3 ) )
% 0.28/0.47 => ( Ya = X4 ) ) ) )
% 0.28/0.47 => ( ! [X5: b] :
% 0.28/0.47 ( ( member_b @ X5 @ A2 )
% 0.28/0.47 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 0.28/0.47 & ( ( Gamma @ ( H @ X5 ) )
% 0.28/0.47 = ( Phi @ X5 ) ) ) )
% 0.28/0.47 => ( ( groups583146225b_real @ Phi @ A2 )
% 0.28/0.47 = ( groups1862963056a_real @ Gamma @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.eq_general
% 0.28/0.47 thf(fact_180_sum_Oeq__general,axiom,
% 0.28/0.47 ! [B2: set_b,A2: set_a,H: a > b,Gamma: b > b,Phi: a > b] :
% 0.28/0.47 ( ! [Y3: b] :
% 0.28/0.47 ( ( member_b @ Y3 @ B2 )
% 0.28/0.47 => ? [X4: a] :
% 0.28/0.47 ( ( member_a @ X4 @ A2 )
% 0.28/0.47 & ( ( H @ X4 )
% 0.28/0.47 = Y3 )
% 0.28/0.47 & ! [Ya: a] :
% 0.28/0.47 ( ( ( member_a @ Ya @ A2 )
% 0.28/0.47 & ( ( H @ Ya )
% 0.28/0.47 = Y3 ) )
% 0.28/0.47 => ( Ya = X4 ) ) ) )
% 0.28/0.47 => ( ! [X5: a] :
% 0.28/0.47 ( ( member_a @ X5 @ A2 )
% 0.28/0.47 => ( ( member_b @ ( H @ X5 ) @ B2 )
% 0.28/0.47 & ( ( Gamma @ ( H @ X5 ) )
% 0.28/0.47 = ( Phi @ X5 ) ) ) )
% 0.28/0.47 => ( ( groups1199149371um_a_b @ Phi @ A2 )
% 0.28/0.47 = ( groups2026918778um_b_b @ Gamma @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.eq_general
% 0.28/0.47 thf(fact_181_sum_Oeq__general,axiom,
% 0.28/0.47 ! [B2: set_a,A2: set_a,H: a > a,Gamma: a > b,Phi: a > b] :
% 0.28/0.47 ( ! [Y3: a] :
% 0.28/0.47 ( ( member_a @ Y3 @ B2 )
% 0.28/0.47 => ? [X4: a] :
% 0.28/0.47 ( ( member_a @ X4 @ A2 )
% 0.28/0.47 & ( ( H @ X4 )
% 0.28/0.47 = Y3 )
% 0.28/0.47 & ! [Ya: a] :
% 0.28/0.47 ( ( ( member_a @ Ya @ A2 )
% 0.28/0.47 & ( ( H @ Ya )
% 0.28/0.47 = Y3 ) )
% 0.28/0.47 => ( Ya = X4 ) ) ) )
% 0.28/0.47 => ( ! [X5: a] :
% 0.28/0.47 ( ( member_a @ X5 @ A2 )
% 0.28/0.47 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 0.28/0.47 & ( ( Gamma @ ( H @ X5 ) )
% 0.28/0.47 = ( Phi @ X5 ) ) ) )
% 0.28/0.47 => ( ( groups1199149371um_a_b @ Phi @ A2 )
% 0.28/0.47 = ( groups1199149371um_a_b @ Gamma @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.eq_general
% 0.28/0.47 thf(fact_182_sum_Oeq__general,axiom,
% 0.28/0.47 ! [B2: set_b,A2: set_a,H: a > b,Gamma: b > real,Phi: a > real] :
% 0.28/0.47 ( ! [Y3: b] :
% 0.28/0.47 ( ( member_b @ Y3 @ B2 )
% 0.28/0.47 => ? [X4: a] :
% 0.28/0.47 ( ( member_a @ X4 @ A2 )
% 0.28/0.47 & ( ( H @ X4 )
% 0.28/0.47 = Y3 )
% 0.28/0.47 & ! [Ya: a] :
% 0.28/0.47 ( ( ( member_a @ Ya @ A2 )
% 0.28/0.47 & ( ( H @ Ya )
% 0.28/0.47 = Y3 ) )
% 0.28/0.47 => ( Ya = X4 ) ) ) )
% 0.28/0.47 => ( ! [X5: a] :
% 0.28/0.47 ( ( member_a @ X5 @ A2 )
% 0.28/0.47 => ( ( member_b @ ( H @ X5 ) @ B2 )
% 0.28/0.47 & ( ( Gamma @ ( H @ X5 ) )
% 0.28/0.47 = ( Phi @ X5 ) ) ) )
% 0.28/0.47 => ( ( groups1862963056a_real @ Phi @ A2 )
% 0.28/0.47 = ( groups583146225b_real @ Gamma @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.eq_general
% 0.28/0.47 thf(fact_183_sum_Oeq__general,axiom,
% 0.28/0.47 ! [B2: set_a,A2: set_a,H: a > a,Gamma: a > real,Phi: a > real] :
% 0.28/0.47 ( ! [Y3: a] :
% 0.28/0.47 ( ( member_a @ Y3 @ B2 )
% 0.28/0.47 => ? [X4: a] :
% 0.28/0.47 ( ( member_a @ X4 @ A2 )
% 0.28/0.47 & ( ( H @ X4 )
% 0.28/0.47 = Y3 )
% 0.28/0.47 & ! [Ya: a] :
% 0.28/0.47 ( ( ( member_a @ Ya @ A2 )
% 0.28/0.47 & ( ( H @ Ya )
% 0.28/0.47 = Y3 ) )
% 0.28/0.47 => ( Ya = X4 ) ) ) )
% 0.28/0.47 => ( ! [X5: a] :
% 0.28/0.47 ( ( member_a @ X5 @ A2 )
% 0.28/0.47 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 0.28/0.47 & ( ( Gamma @ ( H @ X5 ) )
% 0.28/0.47 = ( Phi @ X5 ) ) ) )
% 0.28/0.47 => ( ( groups1862963056a_real @ Phi @ A2 )
% 0.28/0.47 = ( groups1862963056a_real @ Gamma @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.eq_general
% 0.28/0.47 thf(fact_184_sum_Oeq__general__inverses,axiom,
% 0.28/0.47 ! [B2: set_a,K: a > b,A2: set_b,H: b > a,Gamma: a > b,Phi: b > b] :
% 0.28/0.47 ( ! [Y3: a] :
% 0.28/0.47 ( ( member_a @ Y3 @ B2 )
% 0.28/0.47 => ( ( member_b @ ( K @ Y3 ) @ A2 )
% 0.28/0.47 & ( ( H @ ( K @ Y3 ) )
% 0.28/0.47 = Y3 ) ) )
% 0.28/0.47 => ( ! [X5: b] :
% 0.28/0.47 ( ( member_b @ X5 @ A2 )
% 0.28/0.47 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 0.28/0.47 & ( ( K @ ( H @ X5 ) )
% 0.28/0.47 = X5 )
% 0.28/0.47 & ( ( Gamma @ ( H @ X5 ) )
% 0.28/0.47 = ( Phi @ X5 ) ) ) )
% 0.28/0.47 => ( ( groups2026918778um_b_b @ Phi @ A2 )
% 0.28/0.47 = ( groups1199149371um_a_b @ Gamma @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.eq_general_inverses
% 0.28/0.47 thf(fact_185_sum_Oeq__general__inverses,axiom,
% 0.28/0.47 ! [B2: set_a,K: a > b,A2: set_b,H: b > a,Gamma: a > real,Phi: b > real] :
% 0.28/0.47 ( ! [Y3: a] :
% 0.28/0.47 ( ( member_a @ Y3 @ B2 )
% 0.28/0.47 => ( ( member_b @ ( K @ Y3 ) @ A2 )
% 0.28/0.47 & ( ( H @ ( K @ Y3 ) )
% 0.28/0.47 = Y3 ) ) )
% 0.28/0.47 => ( ! [X5: b] :
% 0.28/0.47 ( ( member_b @ X5 @ A2 )
% 0.28/0.47 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 0.28/0.47 & ( ( K @ ( H @ X5 ) )
% 0.28/0.47 = X5 )
% 0.28/0.47 & ( ( Gamma @ ( H @ X5 ) )
% 0.28/0.47 = ( Phi @ X5 ) ) ) )
% 0.28/0.47 => ( ( groups583146225b_real @ Phi @ A2 )
% 0.28/0.47 = ( groups1862963056a_real @ Gamma @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.eq_general_inverses
% 0.28/0.47 thf(fact_186_sum_Oeq__general__inverses,axiom,
% 0.28/0.47 ! [B2: set_b,K: b > a,A2: set_a,H: a > b,Gamma: b > b,Phi: a > b] :
% 0.28/0.47 ( ! [Y3: b] :
% 0.28/0.47 ( ( member_b @ Y3 @ B2 )
% 0.28/0.47 => ( ( member_a @ ( K @ Y3 ) @ A2 )
% 0.28/0.47 & ( ( H @ ( K @ Y3 ) )
% 0.28/0.47 = Y3 ) ) )
% 0.28/0.47 => ( ! [X5: a] :
% 0.28/0.47 ( ( member_a @ X5 @ A2 )
% 0.28/0.47 => ( ( member_b @ ( H @ X5 ) @ B2 )
% 0.28/0.47 & ( ( K @ ( H @ X5 ) )
% 0.28/0.47 = X5 )
% 0.28/0.47 & ( ( Gamma @ ( H @ X5 ) )
% 0.28/0.47 = ( Phi @ X5 ) ) ) )
% 0.28/0.47 => ( ( groups1199149371um_a_b @ Phi @ A2 )
% 0.28/0.47 = ( groups2026918778um_b_b @ Gamma @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.eq_general_inverses
% 0.28/0.47 thf(fact_187_sum_Oeq__general__inverses,axiom,
% 0.28/0.47 ! [B2: set_a,K: a > a,A2: set_a,H: a > a,Gamma: a > b,Phi: a > b] :
% 0.28/0.47 ( ! [Y3: a] :
% 0.28/0.47 ( ( member_a @ Y3 @ B2 )
% 0.28/0.47 => ( ( member_a @ ( K @ Y3 ) @ A2 )
% 0.28/0.47 & ( ( H @ ( K @ Y3 ) )
% 0.28/0.47 = Y3 ) ) )
% 0.28/0.47 => ( ! [X5: a] :
% 0.28/0.47 ( ( member_a @ X5 @ A2 )
% 0.28/0.47 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 0.28/0.47 & ( ( K @ ( H @ X5 ) )
% 0.28/0.47 = X5 )
% 0.28/0.47 & ( ( Gamma @ ( H @ X5 ) )
% 0.28/0.47 = ( Phi @ X5 ) ) ) )
% 0.28/0.47 => ( ( groups1199149371um_a_b @ Phi @ A2 )
% 0.28/0.47 = ( groups1199149371um_a_b @ Gamma @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.eq_general_inverses
% 0.28/0.47 thf(fact_188_sum_Oeq__general__inverses,axiom,
% 0.28/0.47 ! [B2: set_b,K: b > a,A2: set_a,H: a > b,Gamma: b > real,Phi: a > real] :
% 0.28/0.47 ( ! [Y3: b] :
% 0.28/0.47 ( ( member_b @ Y3 @ B2 )
% 0.28/0.47 => ( ( member_a @ ( K @ Y3 ) @ A2 )
% 0.28/0.47 & ( ( H @ ( K @ Y3 ) )
% 0.28/0.47 = Y3 ) ) )
% 0.28/0.47 => ( ! [X5: a] :
% 0.28/0.47 ( ( member_a @ X5 @ A2 )
% 0.28/0.47 => ( ( member_b @ ( H @ X5 ) @ B2 )
% 0.28/0.47 & ( ( K @ ( H @ X5 ) )
% 0.28/0.47 = X5 )
% 0.28/0.47 & ( ( Gamma @ ( H @ X5 ) )
% 0.28/0.47 = ( Phi @ X5 ) ) ) )
% 0.28/0.47 => ( ( groups1862963056a_real @ Phi @ A2 )
% 0.28/0.47 = ( groups583146225b_real @ Gamma @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.eq_general_inverses
% 0.28/0.47 thf(fact_189_sum_Oeq__general__inverses,axiom,
% 0.28/0.47 ! [B2: set_a,K: a > a,A2: set_a,H: a > a,Gamma: a > real,Phi: a > real] :
% 0.28/0.47 ( ! [Y3: a] :
% 0.28/0.47 ( ( member_a @ Y3 @ B2 )
% 0.28/0.47 => ( ( member_a @ ( K @ Y3 ) @ A2 )
% 0.28/0.47 & ( ( H @ ( K @ Y3 ) )
% 0.28/0.47 = Y3 ) ) )
% 0.28/0.47 => ( ! [X5: a] :
% 0.28/0.47 ( ( member_a @ X5 @ A2 )
% 0.28/0.47 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 0.28/0.47 & ( ( K @ ( H @ X5 ) )
% 0.28/0.47 = X5 )
% 0.28/0.47 & ( ( Gamma @ ( H @ X5 ) )
% 0.28/0.47 = ( Phi @ X5 ) ) ) )
% 0.28/0.47 => ( ( groups1862963056a_real @ Phi @ A2 )
% 0.28/0.47 = ( groups1862963056a_real @ Gamma @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.eq_general_inverses
% 0.28/0.47 thf(fact_190_sum_Oreindex__bij__witness,axiom,
% 0.28/0.47 ! [S: set_b,I2: a > b,J2: b > a,T: set_a,H: a > b,G: b > b] :
% 0.28/0.47 ( ! [A5: b] :
% 0.28/0.47 ( ( member_b @ A5 @ S )
% 0.28/0.47 => ( ( I2 @ ( J2 @ A5 ) )
% 0.28/0.47 = A5 ) )
% 0.28/0.47 => ( ! [A5: b] :
% 0.28/0.47 ( ( member_b @ A5 @ S )
% 0.28/0.47 => ( member_a @ ( J2 @ A5 ) @ T ) )
% 0.28/0.47 => ( ! [B6: a] :
% 0.28/0.47 ( ( member_a @ B6 @ T )
% 0.28/0.47 => ( ( J2 @ ( I2 @ B6 ) )
% 0.28/0.47 = B6 ) )
% 0.28/0.47 => ( ! [B6: a] :
% 0.28/0.47 ( ( member_a @ B6 @ T )
% 0.28/0.47 => ( member_b @ ( I2 @ B6 ) @ S ) )
% 0.28/0.47 => ( ! [A5: b] :
% 0.28/0.47 ( ( member_b @ A5 @ S )
% 0.28/0.47 => ( ( H @ ( J2 @ A5 ) )
% 0.28/0.47 = ( G @ A5 ) ) )
% 0.28/0.47 => ( ( groups2026918778um_b_b @ G @ S )
% 0.28/0.47 = ( groups1199149371um_a_b @ H @ T ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.reindex_bij_witness
% 0.28/0.47 thf(fact_191_sum_Oreindex__bij__witness,axiom,
% 0.28/0.47 ! [S: set_b,I2: a > b,J2: b > a,T: set_a,H: a > real,G: b > real] :
% 0.28/0.47 ( ! [A5: b] :
% 0.28/0.47 ( ( member_b @ A5 @ S )
% 0.28/0.47 => ( ( I2 @ ( J2 @ A5 ) )
% 0.28/0.47 = A5 ) )
% 0.28/0.47 => ( ! [A5: b] :
% 0.28/0.47 ( ( member_b @ A5 @ S )
% 0.28/0.47 => ( member_a @ ( J2 @ A5 ) @ T ) )
% 0.28/0.47 => ( ! [B6: a] :
% 0.28/0.47 ( ( member_a @ B6 @ T )
% 0.28/0.47 => ( ( J2 @ ( I2 @ B6 ) )
% 0.28/0.47 = B6 ) )
% 0.28/0.47 => ( ! [B6: a] :
% 0.28/0.47 ( ( member_a @ B6 @ T )
% 0.28/0.47 => ( member_b @ ( I2 @ B6 ) @ S ) )
% 0.28/0.47 => ( ! [A5: b] :
% 0.28/0.47 ( ( member_b @ A5 @ S )
% 0.28/0.47 => ( ( H @ ( J2 @ A5 ) )
% 0.28/0.47 = ( G @ A5 ) ) )
% 0.28/0.47 => ( ( groups583146225b_real @ G @ S )
% 0.28/0.47 = ( groups1862963056a_real @ H @ T ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.reindex_bij_witness
% 0.28/0.47 thf(fact_192_sum_Oreindex__bij__witness,axiom,
% 0.28/0.47 ! [S: set_a,I2: b > a,J2: a > b,T: set_b,H: b > b,G: a > b] :
% 0.28/0.47 ( ! [A5: a] :
% 0.28/0.47 ( ( member_a @ A5 @ S )
% 0.28/0.47 => ( ( I2 @ ( J2 @ A5 ) )
% 0.28/0.47 = A5 ) )
% 0.28/0.47 => ( ! [A5: a] :
% 0.28/0.47 ( ( member_a @ A5 @ S )
% 0.28/0.47 => ( member_b @ ( J2 @ A5 ) @ T ) )
% 0.28/0.47 => ( ! [B6: b] :
% 0.28/0.47 ( ( member_b @ B6 @ T )
% 0.28/0.47 => ( ( J2 @ ( I2 @ B6 ) )
% 0.28/0.47 = B6 ) )
% 0.28/0.47 => ( ! [B6: b] :
% 0.28/0.47 ( ( member_b @ B6 @ T )
% 0.28/0.47 => ( member_a @ ( I2 @ B6 ) @ S ) )
% 0.28/0.47 => ( ! [A5: a] :
% 0.28/0.47 ( ( member_a @ A5 @ S )
% 0.28/0.47 => ( ( H @ ( J2 @ A5 ) )
% 0.28/0.47 = ( G @ A5 ) ) )
% 0.28/0.47 => ( ( groups1199149371um_a_b @ G @ S )
% 0.28/0.47 = ( groups2026918778um_b_b @ H @ T ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.reindex_bij_witness
% 0.28/0.47 thf(fact_193_sum_Oreindex__bij__witness,axiom,
% 0.28/0.47 ! [S: set_a,I2: a > a,J2: a > a,T: set_a,H: a > b,G: a > b] :
% 0.28/0.47 ( ! [A5: a] :
% 0.28/0.47 ( ( member_a @ A5 @ S )
% 0.28/0.47 => ( ( I2 @ ( J2 @ A5 ) )
% 0.28/0.47 = A5 ) )
% 0.28/0.47 => ( ! [A5: a] :
% 0.28/0.47 ( ( member_a @ A5 @ S )
% 0.28/0.47 => ( member_a @ ( J2 @ A5 ) @ T ) )
% 0.28/0.47 => ( ! [B6: a] :
% 0.28/0.47 ( ( member_a @ B6 @ T )
% 0.28/0.47 => ( ( J2 @ ( I2 @ B6 ) )
% 0.28/0.47 = B6 ) )
% 0.28/0.47 => ( ! [B6: a] :
% 0.28/0.47 ( ( member_a @ B6 @ T )
% 0.28/0.47 => ( member_a @ ( I2 @ B6 ) @ S ) )
% 0.28/0.47 => ( ! [A5: a] :
% 0.28/0.47 ( ( member_a @ A5 @ S )
% 0.28/0.47 => ( ( H @ ( J2 @ A5 ) )
% 0.28/0.47 = ( G @ A5 ) ) )
% 0.28/0.47 => ( ( groups1199149371um_a_b @ G @ S )
% 0.28/0.47 = ( groups1199149371um_a_b @ H @ T ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.reindex_bij_witness
% 0.28/0.47 thf(fact_194_sum_Oreindex__bij__witness,axiom,
% 0.28/0.47 ! [S: set_a,I2: b > a,J2: a > b,T: set_b,H: b > real,G: a > real] :
% 0.28/0.47 ( ! [A5: a] :
% 0.28/0.47 ( ( member_a @ A5 @ S )
% 0.28/0.47 => ( ( I2 @ ( J2 @ A5 ) )
% 0.28/0.47 = A5 ) )
% 0.28/0.47 => ( ! [A5: a] :
% 0.28/0.47 ( ( member_a @ A5 @ S )
% 0.28/0.47 => ( member_b @ ( J2 @ A5 ) @ T ) )
% 0.28/0.47 => ( ! [B6: b] :
% 0.28/0.47 ( ( member_b @ B6 @ T )
% 0.28/0.47 => ( ( J2 @ ( I2 @ B6 ) )
% 0.28/0.47 = B6 ) )
% 0.28/0.47 => ( ! [B6: b] :
% 0.28/0.47 ( ( member_b @ B6 @ T )
% 0.28/0.47 => ( member_a @ ( I2 @ B6 ) @ S ) )
% 0.28/0.47 => ( ! [A5: a] :
% 0.28/0.47 ( ( member_a @ A5 @ S )
% 0.28/0.47 => ( ( H @ ( J2 @ A5 ) )
% 0.28/0.47 = ( G @ A5 ) ) )
% 0.28/0.47 => ( ( groups1862963056a_real @ G @ S )
% 0.28/0.47 = ( groups583146225b_real @ H @ T ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.reindex_bij_witness
% 0.28/0.47 thf(fact_195_sum_Oreindex__bij__witness,axiom,
% 0.28/0.47 ! [S: set_a,I2: a > a,J2: a > a,T: set_a,H: a > real,G: a > real] :
% 0.28/0.47 ( ! [A5: a] :
% 0.28/0.47 ( ( member_a @ A5 @ S )
% 0.28/0.47 => ( ( I2 @ ( J2 @ A5 ) )
% 0.28/0.47 = A5 ) )
% 0.28/0.47 => ( ! [A5: a] :
% 0.28/0.47 ( ( member_a @ A5 @ S )
% 0.28/0.47 => ( member_a @ ( J2 @ A5 ) @ T ) )
% 0.28/0.47 => ( ! [B6: a] :
% 0.28/0.47 ( ( member_a @ B6 @ T )
% 0.28/0.47 => ( ( J2 @ ( I2 @ B6 ) )
% 0.28/0.47 = B6 ) )
% 0.28/0.47 => ( ! [B6: a] :
% 0.28/0.47 ( ( member_a @ B6 @ T )
% 0.28/0.47 => ( member_a @ ( I2 @ B6 ) @ S ) )
% 0.28/0.47 => ( ! [A5: a] :
% 0.28/0.47 ( ( member_a @ A5 @ S )
% 0.28/0.47 => ( ( H @ ( J2 @ A5 ) )
% 0.28/0.47 = ( G @ A5 ) ) )
% 0.28/0.47 => ( ( groups1862963056a_real @ G @ S )
% 0.28/0.47 = ( groups1862963056a_real @ H @ T ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.reindex_bij_witness
% 0.28/0.47 thf(fact_196_if__smult,axiom,
% 0.28/0.47 ! [P: $o,X2: real,Y: real,V2: b] :
% 0.28/0.47 ( ( P
% 0.28/0.47 => ( ( real_V1035702896aleR_b @ ( if_real @ P @ X2 @ Y ) @ V2 )
% 0.28/0.47 = ( real_V1035702896aleR_b @ X2 @ V2 ) ) )
% 0.28/0.47 & ( ~ P
% 0.28/0.47 => ( ( real_V1035702896aleR_b @ ( if_real @ P @ X2 @ Y ) @ V2 )
% 0.28/0.47 = ( real_V1035702896aleR_b @ Y @ V2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % if_smult
% 0.28/0.47 thf(fact_197_if__smult,axiom,
% 0.28/0.47 ! [P: $o,X2: real,Y: real,V2: real] :
% 0.28/0.47 ( ( P
% 0.28/0.47 => ( ( real_V453051771R_real @ ( if_real @ P @ X2 @ Y ) @ V2 )
% 0.28/0.47 = ( real_V453051771R_real @ X2 @ V2 ) ) )
% 0.28/0.47 & ( ~ P
% 0.28/0.47 => ( ( real_V453051771R_real @ ( if_real @ P @ X2 @ Y ) @ V2 )
% 0.28/0.47 = ( real_V453051771R_real @ Y @ V2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % if_smult
% 0.28/0.47 thf(fact_198_sum_Oinsert__remove,axiom,
% 0.28/0.47 ! [A2: set_a,G: a > b,X2: a] :
% 0.28/0.47 ( ( finite_finite_a @ A2 )
% 0.28/0.47 => ( ( groups1199149371um_a_b @ G @ ( insert_a @ X2 @ A2 ) )
% 0.28/0.47 = ( plus_plus_b @ ( G @ X2 ) @ ( groups1199149371um_a_b @ G @ ( minus_minus_set_a @ A2 @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.insert_remove
% 0.28/0.47 thf(fact_199_sum_Oinsert__remove,axiom,
% 0.28/0.47 ! [A2: set_a,G: a > real,X2: a] :
% 0.28/0.47 ( ( finite_finite_a @ A2 )
% 0.28/0.47 => ( ( groups1862963056a_real @ G @ ( insert_a @ X2 @ A2 ) )
% 0.28/0.47 = ( plus_plus_real @ ( G @ X2 ) @ ( groups1862963056a_real @ G @ ( minus_minus_set_a @ A2 @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.insert_remove
% 0.28/0.47 thf(fact_200_sum_Oremove,axiom,
% 0.28/0.47 ! [A2: set_b,X2: b,G: b > b] :
% 0.28/0.47 ( ( finite_finite_b @ A2 )
% 0.28/0.47 => ( ( member_b @ X2 @ A2 )
% 0.28/0.47 => ( ( groups2026918778um_b_b @ G @ A2 )
% 0.28/0.47 = ( plus_plus_b @ ( G @ X2 ) @ ( groups2026918778um_b_b @ G @ ( minus_minus_set_b @ A2 @ ( insert_b @ X2 @ bot_bot_set_b ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.remove
% 0.28/0.47 thf(fact_201_sum_Oremove,axiom,
% 0.28/0.47 ! [A2: set_b,X2: b,G: b > real] :
% 0.28/0.47 ( ( finite_finite_b @ A2 )
% 0.28/0.47 => ( ( member_b @ X2 @ A2 )
% 0.28/0.47 => ( ( groups583146225b_real @ G @ A2 )
% 0.28/0.47 = ( plus_plus_real @ ( G @ X2 ) @ ( groups583146225b_real @ G @ ( minus_minus_set_b @ A2 @ ( insert_b @ X2 @ bot_bot_set_b ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.remove
% 0.28/0.47 thf(fact_202_sum_Oremove,axiom,
% 0.28/0.47 ! [A2: set_a,X2: a,G: a > b] :
% 0.28/0.47 ( ( finite_finite_a @ A2 )
% 0.28/0.47 => ( ( member_a @ X2 @ A2 )
% 0.28/0.47 => ( ( groups1199149371um_a_b @ G @ A2 )
% 0.28/0.47 = ( plus_plus_b @ ( G @ X2 ) @ ( groups1199149371um_a_b @ G @ ( minus_minus_set_a @ A2 @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.remove
% 0.28/0.47 thf(fact_203_sum_Oremove,axiom,
% 0.28/0.47 ! [A2: set_a,X2: a,G: a > real] :
% 0.28/0.47 ( ( finite_finite_a @ A2 )
% 0.28/0.47 => ( ( member_a @ X2 @ A2 )
% 0.28/0.47 => ( ( groups1862963056a_real @ G @ A2 )
% 0.28/0.47 = ( plus_plus_real @ ( G @ X2 ) @ ( groups1862963056a_real @ G @ ( minus_minus_set_a @ A2 @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.remove
% 0.28/0.47 thf(fact_204_sum_Odelta__remove,axiom,
% 0.28/0.47 ! [S: set_b,A: b,B: b > b,C: b > b] :
% 0.28/0.47 ( ( finite_finite_b @ S )
% 0.28/0.47 => ( ( ( member_b @ A @ S )
% 0.28/0.47 => ( ( groups2026918778um_b_b
% 0.28/0.47 @ ^ [K2: b] : ( if_b @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.28/0.47 @ S )
% 0.28/0.47 = ( plus_plus_b @ ( B @ A ) @ ( groups2026918778um_b_b @ C @ ( minus_minus_set_b @ S @ ( insert_b @ A @ bot_bot_set_b ) ) ) ) ) )
% 0.28/0.47 & ( ~ ( member_b @ A @ S )
% 0.28/0.47 => ( ( groups2026918778um_b_b
% 0.28/0.47 @ ^ [K2: b] : ( if_b @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.28/0.47 @ S )
% 0.28/0.47 = ( groups2026918778um_b_b @ C @ ( minus_minus_set_b @ S @ ( insert_b @ A @ bot_bot_set_b ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.delta_remove
% 0.28/0.47 thf(fact_205_sum_Odelta__remove,axiom,
% 0.28/0.47 ! [S: set_b,A: b,B: b > real,C: b > real] :
% 0.28/0.47 ( ( finite_finite_b @ S )
% 0.28/0.47 => ( ( ( member_b @ A @ S )
% 0.28/0.47 => ( ( groups583146225b_real
% 0.28/0.47 @ ^ [K2: b] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.28/0.47 @ S )
% 0.28/0.47 = ( plus_plus_real @ ( B @ A ) @ ( groups583146225b_real @ C @ ( minus_minus_set_b @ S @ ( insert_b @ A @ bot_bot_set_b ) ) ) ) ) )
% 0.28/0.47 & ( ~ ( member_b @ A @ S )
% 0.28/0.47 => ( ( groups583146225b_real
% 0.28/0.47 @ ^ [K2: b] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.28/0.47 @ S )
% 0.28/0.47 = ( groups583146225b_real @ C @ ( minus_minus_set_b @ S @ ( insert_b @ A @ bot_bot_set_b ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.delta_remove
% 0.28/0.47 thf(fact_206_sum_Odelta__remove,axiom,
% 0.28/0.47 ! [S: set_a,A: a,B: a > b,C: a > b] :
% 0.28/0.47 ( ( finite_finite_a @ S )
% 0.28/0.47 => ( ( ( member_a @ A @ S )
% 0.28/0.47 => ( ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [K2: a] : ( if_b @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.28/0.47 @ S )
% 0.28/0.47 = ( plus_plus_b @ ( B @ A ) @ ( groups1199149371um_a_b @ C @ ( minus_minus_set_a @ S @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ) )
% 0.28/0.47 & ( ~ ( member_a @ A @ S )
% 0.28/0.47 => ( ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [K2: a] : ( if_b @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.28/0.47 @ S )
% 0.28/0.47 = ( groups1199149371um_a_b @ C @ ( minus_minus_set_a @ S @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.delta_remove
% 0.28/0.47 thf(fact_207_sum_Odelta__remove,axiom,
% 0.28/0.47 ! [S: set_a,A: a,B: a > real,C: a > real] :
% 0.28/0.47 ( ( finite_finite_a @ S )
% 0.28/0.47 => ( ( ( member_a @ A @ S )
% 0.28/0.47 => ( ( groups1862963056a_real
% 0.28/0.47 @ ^ [K2: a] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.28/0.47 @ S )
% 0.28/0.47 = ( plus_plus_real @ ( B @ A ) @ ( groups1862963056a_real @ C @ ( minus_minus_set_a @ S @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ) )
% 0.28/0.47 & ( ~ ( member_a @ A @ S )
% 0.28/0.47 => ( ( groups1862963056a_real
% 0.28/0.47 @ ^ [K2: a] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.28/0.47 @ S )
% 0.28/0.47 = ( groups1862963056a_real @ C @ ( minus_minus_set_a @ S @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.delta_remove
% 0.28/0.47 thf(fact_208_empty__def,axiom,
% 0.28/0.47 ( bot_bot_set_a
% 0.28/0.47 = ( collect_a
% 0.28/0.47 @ ^ [X: a] : $false ) ) ).
% 0.28/0.47
% 0.28/0.47 % empty_def
% 0.28/0.47 thf(fact_209_pigeonhole__infinite__rel,axiom,
% 0.28/0.47 ! [A2: set_b,B2: set_a,R2: b > a > $o] :
% 0.28/0.47 ( ~ ( finite_finite_b @ A2 )
% 0.28/0.47 => ( ( finite_finite_a @ B2 )
% 0.28/0.47 => ( ! [X5: b] :
% 0.28/0.47 ( ( member_b @ X5 @ A2 )
% 0.28/0.47 => ? [Xa2: a] :
% 0.28/0.47 ( ( member_a @ Xa2 @ B2 )
% 0.28/0.47 & ( R2 @ X5 @ Xa2 ) ) )
% 0.28/0.47 => ? [X5: a] :
% 0.28/0.47 ( ( member_a @ X5 @ B2 )
% 0.28/0.47 & ~ ( finite_finite_b
% 0.28/0.47 @ ( collect_b
% 0.28/0.47 @ ^ [A3: b] :
% 0.28/0.47 ( ( member_b @ A3 @ A2 )
% 0.28/0.47 & ( R2 @ A3 @ X5 ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pigeonhole_infinite_rel
% 0.28/0.47 thf(fact_210_pigeonhole__infinite__rel,axiom,
% 0.28/0.47 ! [A2: set_a,B2: set_a,R2: a > a > $o] :
% 0.28/0.47 ( ~ ( finite_finite_a @ A2 )
% 0.28/0.47 => ( ( finite_finite_a @ B2 )
% 0.28/0.47 => ( ! [X5: a] :
% 0.28/0.47 ( ( member_a @ X5 @ A2 )
% 0.28/0.47 => ? [Xa2: a] :
% 0.28/0.47 ( ( member_a @ Xa2 @ B2 )
% 0.28/0.47 & ( R2 @ X5 @ Xa2 ) ) )
% 0.28/0.47 => ? [X5: a] :
% 0.28/0.47 ( ( member_a @ X5 @ B2 )
% 0.28/0.47 & ~ ( finite_finite_a
% 0.28/0.47 @ ( collect_a
% 0.28/0.47 @ ^ [A3: a] :
% 0.28/0.47 ( ( member_a @ A3 @ A2 )
% 0.28/0.47 & ( R2 @ A3 @ X5 ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pigeonhole_infinite_rel
% 0.28/0.47 thf(fact_211_not__finite__existsD,axiom,
% 0.28/0.47 ! [P: a > $o] :
% 0.28/0.47 ( ~ ( finite_finite_a @ ( collect_a @ P ) )
% 0.28/0.47 => ? [X_1: a] : ( P @ X_1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_finite_existsD
% 0.28/0.47 thf(fact_212_insert__Collect,axiom,
% 0.28/0.47 ! [A: a,P: a > $o] :
% 0.28/0.47 ( ( insert_a @ A @ ( collect_a @ P ) )
% 0.28/0.47 = ( collect_a
% 0.28/0.47 @ ^ [U2: a] :
% 0.28/0.47 ( ( U2 != A )
% 0.28/0.47 => ( P @ U2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_Collect
% 0.28/0.47 thf(fact_213_insert__compr,axiom,
% 0.28/0.47 ( insert_a
% 0.28/0.47 = ( ^ [A3: a,B3: set_a] :
% 0.28/0.47 ( collect_a
% 0.28/0.47 @ ^ [X: a] :
% 0.28/0.47 ( ( X = A3 )
% 0.28/0.47 | ( member_a @ X @ B3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_compr
% 0.28/0.47 thf(fact_214_insert__compr,axiom,
% 0.28/0.47 ( insert_b
% 0.28/0.47 = ( ^ [A3: b,B3: set_b] :
% 0.28/0.47 ( collect_b
% 0.28/0.47 @ ^ [X: b] :
% 0.28/0.47 ( ( X = A3 )
% 0.28/0.47 | ( member_b @ X @ B3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_compr
% 0.28/0.47 thf(fact_215_sum__delta__notmem_I4_J,axiom,
% 0.28/0.47 ! [X2: a,S2: set_a,P: a > b,Q: a > b] :
% 0.28/0.47 ( ~ ( member_a @ X2 @ S2 )
% 0.28/0.47 => ( ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [Y4: a] : ( if_b @ ( X2 = Y4 ) @ ( P @ Y4 ) @ ( Q @ Y4 ) )
% 0.28/0.47 @ S2 )
% 0.28/0.47 = ( groups1199149371um_a_b @ Q @ S2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum_delta_notmem(4)
% 0.28/0.47 thf(fact_216_sum__delta__notmem_I4_J,axiom,
% 0.28/0.47 ! [X2: a,S2: set_a,P: a > real,Q: a > real] :
% 0.28/0.47 ( ~ ( member_a @ X2 @ S2 )
% 0.28/0.47 => ( ( groups1862963056a_real
% 0.28/0.47 @ ^ [Y4: a] : ( if_real @ ( X2 = Y4 ) @ ( P @ Y4 ) @ ( Q @ Y4 ) )
% 0.28/0.47 @ S2 )
% 0.28/0.47 = ( groups1862963056a_real @ Q @ S2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum_delta_notmem(4)
% 0.28/0.47 thf(fact_217_sum__delta__notmem_I3_J,axiom,
% 0.28/0.47 ! [X2: a,S2: set_a,P: a > b,Q: a > b] :
% 0.28/0.47 ( ~ ( member_a @ X2 @ S2 )
% 0.28/0.47 => ( ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [Y4: a] : ( if_b @ ( Y4 = X2 ) @ ( P @ Y4 ) @ ( Q @ Y4 ) )
% 0.28/0.47 @ S2 )
% 0.28/0.47 = ( groups1199149371um_a_b @ Q @ S2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum_delta_notmem(3)
% 0.28/0.47 thf(fact_218_sum__delta__notmem_I3_J,axiom,
% 0.28/0.47 ! [X2: a,S2: set_a,P: a > real,Q: a > real] :
% 0.28/0.47 ( ~ ( member_a @ X2 @ S2 )
% 0.28/0.47 => ( ( groups1862963056a_real
% 0.28/0.47 @ ^ [Y4: a] : ( if_real @ ( Y4 = X2 ) @ ( P @ Y4 ) @ ( Q @ Y4 ) )
% 0.28/0.47 @ S2 )
% 0.28/0.47 = ( groups1862963056a_real @ Q @ S2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum_delta_notmem(3)
% 0.28/0.47 thf(fact_219_sum__delta__notmem_I2_J,axiom,
% 0.28/0.47 ! [X2: a,S2: set_a,P: a > b,Q: a > b] :
% 0.28/0.47 ( ~ ( member_a @ X2 @ S2 )
% 0.28/0.47 => ( ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [Y4: a] : ( if_b @ ( X2 = Y4 ) @ ( P @ X2 ) @ ( Q @ Y4 ) )
% 0.28/0.47 @ S2 )
% 0.28/0.47 = ( groups1199149371um_a_b @ Q @ S2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum_delta_notmem(2)
% 0.28/0.47 thf(fact_220_sum__delta__notmem_I2_J,axiom,
% 0.28/0.47 ! [X2: a,S2: set_a,P: a > real,Q: a > real] :
% 0.28/0.47 ( ~ ( member_a @ X2 @ S2 )
% 0.28/0.47 => ( ( groups1862963056a_real
% 0.28/0.47 @ ^ [Y4: a] : ( if_real @ ( X2 = Y4 ) @ ( P @ X2 ) @ ( Q @ Y4 ) )
% 0.28/0.47 @ S2 )
% 0.28/0.47 = ( groups1862963056a_real @ Q @ S2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum_delta_notmem(2)
% 0.28/0.47 thf(fact_221_sum__delta__notmem_I1_J,axiom,
% 0.28/0.47 ! [X2: a,S2: set_a,P: a > b,Q: a > b] :
% 0.28/0.47 ( ~ ( member_a @ X2 @ S2 )
% 0.28/0.47 => ( ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [Y4: a] : ( if_b @ ( Y4 = X2 ) @ ( P @ X2 ) @ ( Q @ Y4 ) )
% 0.28/0.47 @ S2 )
% 0.28/0.47 = ( groups1199149371um_a_b @ Q @ S2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum_delta_notmem(1)
% 0.28/0.47 thf(fact_222_sum__delta__notmem_I1_J,axiom,
% 0.28/0.47 ! [X2: a,S2: set_a,P: a > real,Q: a > real] :
% 0.28/0.47 ( ~ ( member_a @ X2 @ S2 )
% 0.28/0.47 => ( ( groups1862963056a_real
% 0.28/0.47 @ ^ [Y4: a] : ( if_real @ ( Y4 = X2 ) @ ( P @ X2 ) @ ( Q @ Y4 ) )
% 0.28/0.47 @ S2 )
% 0.28/0.47 = ( groups1862963056a_real @ Q @ S2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum_delta_notmem(1)
% 0.28/0.47 thf(fact_223_sum_Oswap,axiom,
% 0.28/0.47 ! [G: a > a > b,B2: set_a,A2: set_a] :
% 0.28/0.47 ( ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [I3: a] : ( groups1199149371um_a_b @ ( G @ I3 ) @ B2 )
% 0.28/0.47 @ A2 )
% 0.28/0.47 = ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [J: a] :
% 0.28/0.47 ( groups1199149371um_a_b
% 0.28/0.47 @ ^ [I3: a] : ( G @ I3 @ J )
% 0.28/0.47 @ A2 )
% 0.28/0.47 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.swap
% 0.28/0.47 thf(fact_224_sum_Oswap,axiom,
% 0.28/0.47 ! [G: a > a > real,B2: set_a,A2: set_a] :
% 0.28/0.47 ( ( groups1862963056a_real
% 0.28/0.47 @ ^ [I3: a] : ( groups1862963056a_real @ ( G @ I3 ) @ B2 )
% 0.28/0.47 @ A2 )
% 0.28/0.47 = ( groups1862963056a_real
% 0.28/0.47 @ ^ [J: a] :
% 0.28/0.47 ( groups1862963056a_real
% 0.28/0.47 @ ^ [I3: a] : ( G @ I3 @ J )
% 0.28/0.47 @ A2 )
% 0.28/0.47 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sum.swap
% 0.28/0.47 thf(fact_225_infinite__imp__nonempty,axiom,
% 0.28/0.47 ! [S: set_a] :
% 0.28/0.47 ( ~ ( finite_finite_a @ S )
% 0.28/0.47 => ( S != bot_bot_set_a ) ) ).
% 0.28/0.47
% 0.28/0.47 % infinite_imp_nonempty
% 0.28/0.47 thf(fact_226_finite_OemptyI,axiom,
% 0.28/0.47 finite_finite_a @ bot_bot_set_a ).
% 0.28/0.47
% 0.28/0.47 % finite.emptyI
% 0.28/0.47 thf(fact_227_singleton__inject,axiom,
% 0.28/0.47 ! [A: a,B: a] :
% 0.28/0.47 ( ( ( insert_a @ A @ bot_bot_set_a )
% 0.28/0.47 = ( insert_a @ B @ bot_bot_set_a ) )
% 0.28/0.47 => ( A = B ) ) ).
% 0.28/0.47
% 0.28/0.47 % singleton_inject
% 0.28/0.47 thf(fact_228_insert__not__empty,axiom,
% 0.28/0.47 ! [A: a,A2: set_a] :
% 0.28/0.47 ( ( insert_a @ A @ A2 )
% 0.28/0.47 != bot_bot_set_a ) ).
% 0.28/0.48
% 0.28/0.48 % insert_not_empty
% 0.28/0.48 thf(fact_229_doubleton__eq__iff,axiom,
% 0.28/0.48 ! [A: a,B: a,C: a,D: a] :
% 0.28/0.48 ( ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
% 0.28/0.48 = ( insert_a @ C @ ( insert_a @ D @ bot_bot_set_a ) ) )
% 0.28/0.48 = ( ( ( A = C )
% 0.28/0.48 & ( B = D ) )
% 0.28/0.48 | ( ( A = D )
% 0.28/0.48 & ( B = C ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % doubleton_eq_iff
% 0.28/0.48 thf(fact_230_singleton__iff,axiom,
% 0.28/0.48 ! [B: b,A: b] :
% 0.28/0.48 ( ( member_b @ B @ ( insert_b @ A @ bot_bot_set_b ) )
% 0.28/0.48 = ( B = A ) ) ).
% 0.28/0.48
% 0.28/0.48 % singleton_iff
% 0.28/0.48 thf(fact_231_singleton__iff,axiom,
% 0.28/0.48 ! [B: a,A: a] :
% 0.28/0.48 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 0.28/0.48 = ( B = A ) ) ).
% 0.28/0.48
% 0.28/0.48 % singleton_iff
% 0.28/0.48 thf(fact_232_singletonD,axiom,
% 0.28/0.48 ! [B: b,A: b] :
% 0.28/0.48 ( ( member_b @ B @ ( insert_b @ A @ bot_bot_set_b ) )
% 0.28/0.48 => ( B = A ) ) ).
% 0.28/0.48
% 0.28/0.48 % singletonD
% 0.28/0.48 thf(fact_233_singletonD,axiom,
% 0.28/0.48 ! [B: a,A: a] :
% 0.28/0.48 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 0.28/0.48 => ( B = A ) ) ).
% 0.28/0.48
% 0.28/0.48 % singletonD
% 0.28/0.48 thf(fact_234_finite_OinsertI,axiom,
% 0.28/0.48 ! [A2: set_a,A: a] :
% 0.28/0.48 ( ( finite_finite_a @ A2 )
% 0.28/0.48 => ( finite_finite_a @ ( insert_a @ A @ A2 ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % finite.insertI
% 0.28/0.48 thf(fact_235_sum__product,axiom,
% 0.28/0.48 ! [F: a > real,A2: set_a,G: a > real,B2: set_a] :
% 0.28/0.48 ( ( times_times_real @ ( groups1862963056a_real @ F @ A2 ) @ ( groups1862963056a_real @ G @ B2 ) )
% 0.28/0.48 = ( groups1862963056a_real
% 0.28/0.48 @ ^ [I3: a] :
% 0.28/0.48 ( groups1862963056a_real
% 0.28/0.48 @ ^ [J: a] : ( times_times_real @ ( F @ I3 ) @ ( G @ J ) )
% 0.28/0.48 @ B2 )
% 0.28/0.48 @ A2 ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum_product
% 0.28/0.48 thf(fact_236_sum__distrib__left,axiom,
% 0.28/0.48 ! [R: real,F: a > real,A2: set_a] :
% 0.28/0.48 ( ( times_times_real @ R @ ( groups1862963056a_real @ F @ A2 ) )
% 0.28/0.48 = ( groups1862963056a_real
% 0.28/0.48 @ ^ [N: a] : ( times_times_real @ R @ ( F @ N ) )
% 0.28/0.48 @ A2 ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum_distrib_left
% 0.28/0.48 thf(fact_237_sum__distrib__right,axiom,
% 0.28/0.48 ! [F: a > real,A2: set_a,R: real] :
% 0.28/0.48 ( ( times_times_real @ ( groups1862963056a_real @ F @ A2 ) @ R )
% 0.28/0.48 = ( groups1862963056a_real
% 0.28/0.48 @ ^ [N: a] : ( times_times_real @ ( F @ N ) @ R )
% 0.28/0.48 @ A2 ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum_distrib_right
% 0.28/0.48 thf(fact_238_sum_Odistrib,axiom,
% 0.28/0.48 ! [G: a > b,H: a > b,A2: set_a] :
% 0.28/0.48 ( ( groups1199149371um_a_b
% 0.28/0.48 @ ^ [X: a] : ( plus_plus_b @ ( G @ X ) @ ( H @ X ) )
% 0.28/0.48 @ A2 )
% 0.28/0.48 = ( plus_plus_b @ ( groups1199149371um_a_b @ G @ A2 ) @ ( groups1199149371um_a_b @ H @ A2 ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum.distrib
% 0.28/0.48 thf(fact_239_sum_Odistrib,axiom,
% 0.28/0.48 ! [G: a > real,H: a > real,A2: set_a] :
% 0.28/0.48 ( ( groups1862963056a_real
% 0.28/0.48 @ ^ [X: a] : ( plus_plus_real @ ( G @ X ) @ ( H @ X ) )
% 0.28/0.48 @ A2 )
% 0.28/0.48 = ( plus_plus_real @ ( groups1862963056a_real @ G @ A2 ) @ ( groups1862963056a_real @ H @ A2 ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum.distrib
% 0.28/0.48 thf(fact_240_Collect__conv__if2,axiom,
% 0.28/0.48 ! [P: a > $o,A: a] :
% 0.28/0.48 ( ( ( P @ A )
% 0.28/0.48 => ( ( collect_a
% 0.28/0.48 @ ^ [X: a] :
% 0.28/0.48 ( ( A = X )
% 0.28/0.48 & ( P @ X ) ) )
% 0.28/0.48 = ( insert_a @ A @ bot_bot_set_a ) ) )
% 0.28/0.48 & ( ~ ( P @ A )
% 0.28/0.48 => ( ( collect_a
% 0.28/0.48 @ ^ [X: a] :
% 0.28/0.48 ( ( A = X )
% 0.28/0.48 & ( P @ X ) ) )
% 0.28/0.48 = bot_bot_set_a ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % Collect_conv_if2
% 0.28/0.48 thf(fact_241_Collect__conv__if,axiom,
% 0.28/0.48 ! [P: a > $o,A: a] :
% 0.28/0.48 ( ( ( P @ A )
% 0.28/0.48 => ( ( collect_a
% 0.28/0.48 @ ^ [X: a] :
% 0.28/0.48 ( ( X = A )
% 0.28/0.48 & ( P @ X ) ) )
% 0.28/0.48 = ( insert_a @ A @ bot_bot_set_a ) ) )
% 0.28/0.48 & ( ~ ( P @ A )
% 0.28/0.48 => ( ( collect_a
% 0.28/0.48 @ ^ [X: a] :
% 0.28/0.48 ( ( X = A )
% 0.28/0.48 & ( P @ X ) ) )
% 0.28/0.48 = bot_bot_set_a ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % Collect_conv_if
% 0.28/0.48 thf(fact_242_sum__subtractf,axiom,
% 0.28/0.48 ! [F: a > b,G: a > b,A2: set_a] :
% 0.28/0.48 ( ( groups1199149371um_a_b
% 0.28/0.48 @ ^ [X: a] : ( minus_minus_b @ ( F @ X ) @ ( G @ X ) )
% 0.28/0.48 @ A2 )
% 0.28/0.48 = ( minus_minus_b @ ( groups1199149371um_a_b @ F @ A2 ) @ ( groups1199149371um_a_b @ G @ A2 ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum_subtractf
% 0.28/0.48 thf(fact_243_sum__subtractf,axiom,
% 0.28/0.48 ! [F: a > real,G: a > real,A2: set_a] :
% 0.28/0.48 ( ( groups1862963056a_real
% 0.28/0.48 @ ^ [X: a] : ( minus_minus_real @ ( F @ X ) @ ( G @ X ) )
% 0.28/0.48 @ A2 )
% 0.28/0.48 = ( minus_minus_real @ ( groups1862963056a_real @ F @ A2 ) @ ( groups1862963056a_real @ G @ A2 ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum_subtractf
% 0.28/0.48 thf(fact_244_sum_Oswap__restrict,axiom,
% 0.28/0.48 ! [A2: set_b,B2: set_a,G: b > a > b,R2: b > a > $o] :
% 0.28/0.48 ( ( finite_finite_b @ A2 )
% 0.28/0.48 => ( ( finite_finite_a @ B2 )
% 0.28/0.48 => ( ( groups2026918778um_b_b
% 0.28/0.48 @ ^ [X: b] :
% 0.28/0.48 ( groups1199149371um_a_b @ ( G @ X )
% 0.28/0.48 @ ( collect_a
% 0.28/0.48 @ ^ [Y4: a] :
% 0.28/0.48 ( ( member_a @ Y4 @ B2 )
% 0.28/0.48 & ( R2 @ X @ Y4 ) ) ) )
% 0.28/0.48 @ A2 )
% 0.28/0.48 = ( groups1199149371um_a_b
% 0.28/0.48 @ ^ [Y4: a] :
% 0.28/0.48 ( groups2026918778um_b_b
% 0.28/0.48 @ ^ [X: b] : ( G @ X @ Y4 )
% 0.28/0.48 @ ( collect_b
% 0.28/0.48 @ ^ [X: b] :
% 0.28/0.48 ( ( member_b @ X @ A2 )
% 0.28/0.48 & ( R2 @ X @ Y4 ) ) ) )
% 0.28/0.48 @ B2 ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum.swap_restrict
% 0.28/0.48 thf(fact_245_sum_Oswap__restrict,axiom,
% 0.28/0.48 ! [A2: set_b,B2: set_a,G: b > a > real,R2: b > a > $o] :
% 0.28/0.48 ( ( finite_finite_b @ A2 )
% 0.28/0.48 => ( ( finite_finite_a @ B2 )
% 0.28/0.48 => ( ( groups583146225b_real
% 0.28/0.48 @ ^ [X: b] :
% 0.28/0.48 ( groups1862963056a_real @ ( G @ X )
% 0.28/0.48 @ ( collect_a
% 0.28/0.48 @ ^ [Y4: a] :
% 0.28/0.48 ( ( member_a @ Y4 @ B2 )
% 0.28/0.48 & ( R2 @ X @ Y4 ) ) ) )
% 0.28/0.48 @ A2 )
% 0.28/0.48 = ( groups1862963056a_real
% 0.28/0.48 @ ^ [Y4: a] :
% 0.28/0.48 ( groups583146225b_real
% 0.28/0.48 @ ^ [X: b] : ( G @ X @ Y4 )
% 0.28/0.48 @ ( collect_b
% 0.28/0.48 @ ^ [X: b] :
% 0.28/0.48 ( ( member_b @ X @ A2 )
% 0.28/0.48 & ( R2 @ X @ Y4 ) ) ) )
% 0.28/0.48 @ B2 ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum.swap_restrict
% 0.28/0.48 thf(fact_246_sum_Oswap__restrict,axiom,
% 0.28/0.48 ! [A2: set_a,B2: set_b,G: a > b > b,R2: a > b > $o] :
% 0.28/0.48 ( ( finite_finite_a @ A2 )
% 0.28/0.48 => ( ( finite_finite_b @ B2 )
% 0.28/0.48 => ( ( groups1199149371um_a_b
% 0.28/0.48 @ ^ [X: a] :
% 0.28/0.48 ( groups2026918778um_b_b @ ( G @ X )
% 0.28/0.48 @ ( collect_b
% 0.28/0.48 @ ^ [Y4: b] :
% 0.28/0.48 ( ( member_b @ Y4 @ B2 )
% 0.28/0.48 & ( R2 @ X @ Y4 ) ) ) )
% 0.28/0.48 @ A2 )
% 0.28/0.48 = ( groups2026918778um_b_b
% 0.28/0.48 @ ^ [Y4: b] :
% 0.28/0.48 ( groups1199149371um_a_b
% 0.28/0.48 @ ^ [X: a] : ( G @ X @ Y4 )
% 0.28/0.48 @ ( collect_a
% 0.28/0.48 @ ^ [X: a] :
% 0.28/0.48 ( ( member_a @ X @ A2 )
% 0.28/0.48 & ( R2 @ X @ Y4 ) ) ) )
% 0.28/0.48 @ B2 ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum.swap_restrict
% 0.28/0.48 thf(fact_247_sum_Oswap__restrict,axiom,
% 0.28/0.48 ! [A2: set_a,B2: set_a,G: a > a > b,R2: a > a > $o] :
% 0.28/0.48 ( ( finite_finite_a @ A2 )
% 0.28/0.48 => ( ( finite_finite_a @ B2 )
% 0.28/0.48 => ( ( groups1199149371um_a_b
% 0.28/0.48 @ ^ [X: a] :
% 0.28/0.48 ( groups1199149371um_a_b @ ( G @ X )
% 0.28/0.48 @ ( collect_a
% 0.28/0.48 @ ^ [Y4: a] :
% 0.28/0.48 ( ( member_a @ Y4 @ B2 )
% 0.28/0.48 & ( R2 @ X @ Y4 ) ) ) )
% 0.28/0.48 @ A2 )
% 0.28/0.48 = ( groups1199149371um_a_b
% 0.28/0.48 @ ^ [Y4: a] :
% 0.28/0.48 ( groups1199149371um_a_b
% 0.28/0.48 @ ^ [X: a] : ( G @ X @ Y4 )
% 0.28/0.48 @ ( collect_a
% 0.28/0.48 @ ^ [X: a] :
% 0.28/0.48 ( ( member_a @ X @ A2 )
% 0.28/0.48 & ( R2 @ X @ Y4 ) ) ) )
% 0.28/0.48 @ B2 ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum.swap_restrict
% 0.28/0.48 thf(fact_248_sum_Oswap__restrict,axiom,
% 0.28/0.48 ! [A2: set_a,B2: set_b,G: a > b > real,R2: a > b > $o] :
% 0.28/0.48 ( ( finite_finite_a @ A2 )
% 0.28/0.48 => ( ( finite_finite_b @ B2 )
% 0.28/0.48 => ( ( groups1862963056a_real
% 0.28/0.48 @ ^ [X: a] :
% 0.28/0.48 ( groups583146225b_real @ ( G @ X )
% 0.28/0.48 @ ( collect_b
% 0.28/0.48 @ ^ [Y4: b] :
% 0.28/0.48 ( ( member_b @ Y4 @ B2 )
% 0.28/0.48 & ( R2 @ X @ Y4 ) ) ) )
% 0.28/0.48 @ A2 )
% 0.28/0.48 = ( groups583146225b_real
% 0.28/0.48 @ ^ [Y4: b] :
% 0.28/0.48 ( groups1862963056a_real
% 0.28/0.48 @ ^ [X: a] : ( G @ X @ Y4 )
% 0.28/0.48 @ ( collect_a
% 0.28/0.48 @ ^ [X: a] :
% 0.28/0.48 ( ( member_a @ X @ A2 )
% 0.28/0.48 & ( R2 @ X @ Y4 ) ) ) )
% 0.28/0.48 @ B2 ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum.swap_restrict
% 0.28/0.48 thf(fact_249_sum_Oswap__restrict,axiom,
% 0.28/0.48 ! [A2: set_a,B2: set_a,G: a > a > real,R2: a > a > $o] :
% 0.28/0.48 ( ( finite_finite_a @ A2 )
% 0.28/0.48 => ( ( finite_finite_a @ B2 )
% 0.28/0.48 => ( ( groups1862963056a_real
% 0.28/0.48 @ ^ [X: a] :
% 0.28/0.48 ( groups1862963056a_real @ ( G @ X )
% 0.28/0.48 @ ( collect_a
% 0.28/0.48 @ ^ [Y4: a] :
% 0.28/0.48 ( ( member_a @ Y4 @ B2 )
% 0.28/0.48 & ( R2 @ X @ Y4 ) ) ) )
% 0.28/0.48 @ A2 )
% 0.28/0.48 = ( groups1862963056a_real
% 0.28/0.48 @ ^ [Y4: a] :
% 0.28/0.48 ( groups1862963056a_real
% 0.28/0.48 @ ^ [X: a] : ( G @ X @ Y4 )
% 0.28/0.48 @ ( collect_a
% 0.28/0.48 @ ^ [X: a] :
% 0.28/0.48 ( ( member_a @ X @ A2 )
% 0.28/0.48 & ( R2 @ X @ Y4 ) ) ) )
% 0.28/0.48 @ B2 ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum.swap_restrict
% 0.28/0.48 thf(fact_250_infinite__finite__induct,axiom,
% 0.28/0.48 ! [P: set_b > $o,A2: set_b] :
% 0.28/0.48 ( ! [A6: set_b] :
% 0.28/0.48 ( ~ ( finite_finite_b @ A6 )
% 0.28/0.48 => ( P @ A6 ) )
% 0.28/0.48 => ( ( P @ bot_bot_set_b )
% 0.28/0.48 => ( ! [X5: b,F2: set_b] :
% 0.28/0.48 ( ( finite_finite_b @ F2 )
% 0.28/0.48 => ( ~ ( member_b @ X5 @ F2 )
% 0.28/0.48 => ( ( P @ F2 )
% 0.28/0.48 => ( P @ ( insert_b @ X5 @ F2 ) ) ) ) )
% 0.28/0.48 => ( P @ A2 ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % infinite_finite_induct
% 0.28/0.48 thf(fact_251_infinite__finite__induct,axiom,
% 0.28/0.48 ! [P: set_a > $o,A2: set_a] :
% 0.28/0.48 ( ! [A6: set_a] :
% 0.28/0.48 ( ~ ( finite_finite_a @ A6 )
% 0.28/0.48 => ( P @ A6 ) )
% 0.28/0.48 => ( ( P @ bot_bot_set_a )
% 0.28/0.48 => ( ! [X5: a,F2: set_a] :
% 0.28/0.48 ( ( finite_finite_a @ F2 )
% 0.28/0.48 => ( ~ ( member_a @ X5 @ F2 )
% 0.28/0.48 => ( ( P @ F2 )
% 0.28/0.48 => ( P @ ( insert_a @ X5 @ F2 ) ) ) ) )
% 0.28/0.48 => ( P @ A2 ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % infinite_finite_induct
% 0.28/0.48 thf(fact_252_finite__ne__induct,axiom,
% 0.28/0.48 ! [F3: set_b,P: set_b > $o] :
% 0.28/0.48 ( ( finite_finite_b @ F3 )
% 0.28/0.48 => ( ( F3 != bot_bot_set_b )
% 0.28/0.48 => ( ! [X5: b] : ( P @ ( insert_b @ X5 @ bot_bot_set_b ) )
% 0.28/0.48 => ( ! [X5: b,F2: set_b] :
% 0.28/0.48 ( ( finite_finite_b @ F2 )
% 0.28/0.48 => ( ( F2 != bot_bot_set_b )
% 0.28/0.48 => ( ~ ( member_b @ X5 @ F2 )
% 0.28/0.48 => ( ( P @ F2 )
% 0.28/0.48 => ( P @ ( insert_b @ X5 @ F2 ) ) ) ) ) )
% 0.28/0.48 => ( P @ F3 ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % finite_ne_induct
% 0.28/0.48 thf(fact_253_finite__ne__induct,axiom,
% 0.28/0.48 ! [F3: set_a,P: set_a > $o] :
% 0.28/0.48 ( ( finite_finite_a @ F3 )
% 0.28/0.48 => ( ( F3 != bot_bot_set_a )
% 0.28/0.48 => ( ! [X5: a] : ( P @ ( insert_a @ X5 @ bot_bot_set_a ) )
% 0.28/0.48 => ( ! [X5: a,F2: set_a] :
% 0.28/0.48 ( ( finite_finite_a @ F2 )
% 0.28/0.48 => ( ( F2 != bot_bot_set_a )
% 0.28/0.48 => ( ~ ( member_a @ X5 @ F2 )
% 0.28/0.48 => ( ( P @ F2 )
% 0.28/0.48 => ( P @ ( insert_a @ X5 @ F2 ) ) ) ) ) )
% 0.28/0.48 => ( P @ F3 ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % finite_ne_induct
% 0.28/0.48 thf(fact_254_finite_Oinducts,axiom,
% 0.28/0.48 ! [X2: set_a,P: set_a > $o] :
% 0.28/0.48 ( ( finite_finite_a @ X2 )
% 0.28/0.48 => ( ( P @ bot_bot_set_a )
% 0.28/0.48 => ( ! [A6: set_a,A5: a] :
% 0.28/0.48 ( ( finite_finite_a @ A6 )
% 0.28/0.48 => ( ( P @ A6 )
% 0.28/0.48 => ( P @ ( insert_a @ A5 @ A6 ) ) ) )
% 0.28/0.48 => ( P @ X2 ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % finite.inducts
% 0.28/0.48 thf(fact_255_finite__induct,axiom,
% 0.28/0.48 ! [F3: set_b,P: set_b > $o] :
% 0.28/0.48 ( ( finite_finite_b @ F3 )
% 0.28/0.48 => ( ( P @ bot_bot_set_b )
% 0.28/0.48 => ( ! [X5: b,F2: set_b] :
% 0.28/0.48 ( ( finite_finite_b @ F2 )
% 0.28/0.48 => ( ~ ( member_b @ X5 @ F2 )
% 0.28/0.48 => ( ( P @ F2 )
% 0.28/0.48 => ( P @ ( insert_b @ X5 @ F2 ) ) ) ) )
% 0.28/0.48 => ( P @ F3 ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % finite_induct
% 0.28/0.48 thf(fact_256_finite__induct,axiom,
% 0.28/0.48 ! [F3: set_a,P: set_a > $o] :
% 0.28/0.48 ( ( finite_finite_a @ F3 )
% 0.28/0.48 => ( ( P @ bot_bot_set_a )
% 0.28/0.48 => ( ! [X5: a,F2: set_a] :
% 0.28/0.48 ( ( finite_finite_a @ F2 )
% 0.28/0.48 => ( ~ ( member_a @ X5 @ F2 )
% 0.28/0.48 => ( ( P @ F2 )
% 0.28/0.48 => ( P @ ( insert_a @ X5 @ F2 ) ) ) ) )
% 0.28/0.48 => ( P @ F3 ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % finite_induct
% 0.28/0.48 thf(fact_257_finite_Osimps,axiom,
% 0.28/0.48 ( finite_finite_a
% 0.28/0.48 = ( ^ [A3: set_a] :
% 0.28/0.48 ( ( A3 = bot_bot_set_a )
% 0.28/0.48 | ? [A4: set_a,B4: a] :
% 0.28/0.48 ( ( A3
% 0.28/0.48 = ( insert_a @ B4 @ A4 ) )
% 0.28/0.48 & ( finite_finite_a @ A4 ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % finite.simps
% 0.28/0.48 thf(fact_258_finite_Ocases,axiom,
% 0.28/0.48 ! [A: set_a] :
% 0.28/0.48 ( ( finite_finite_a @ A )
% 0.28/0.48 => ( ( A != bot_bot_set_a )
% 0.28/0.48 => ~ ! [A6: set_a] :
% 0.28/0.48 ( ? [A5: a] :
% 0.28/0.48 ( A
% 0.28/0.48 = ( insert_a @ A5 @ A6 ) )
% 0.28/0.48 => ~ ( finite_finite_a @ A6 ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % finite.cases
% 0.28/0.48 thf(fact_259_prod_Ofinite__Collect__op,axiom,
% 0.28/0.48 ! [I4: set_b,X2: b > real,Y: b > real] :
% 0.28/0.48 ( ( finite_finite_b
% 0.28/0.48 @ ( collect_b
% 0.28/0.48 @ ^ [I3: b] :
% 0.28/0.48 ( ( member_b @ I3 @ I4 )
% 0.28/0.48 & ( ( X2 @ I3 )
% 0.28/0.48 != one_one_real ) ) ) )
% 0.28/0.48 => ( ( finite_finite_b
% 0.28/0.48 @ ( collect_b
% 0.28/0.48 @ ^ [I3: b] :
% 0.28/0.48 ( ( member_b @ I3 @ I4 )
% 0.28/0.48 & ( ( Y @ I3 )
% 0.28/0.48 != one_one_real ) ) ) )
% 0.28/0.48 => ( finite_finite_b
% 0.28/0.48 @ ( collect_b
% 0.28/0.48 @ ^ [I3: b] :
% 0.28/0.48 ( ( member_b @ I3 @ I4 )
% 0.28/0.48 & ( ( times_times_real @ ( X2 @ I3 ) @ ( Y @ I3 ) )
% 0.28/0.48 != one_one_real ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % prod.finite_Collect_op
% 0.28/0.48 thf(fact_260_prod_Ofinite__Collect__op,axiom,
% 0.28/0.48 ! [I4: set_a,X2: a > real,Y: a > real] :
% 0.28/0.48 ( ( finite_finite_a
% 0.28/0.48 @ ( collect_a
% 0.28/0.48 @ ^ [I3: a] :
% 0.28/0.48 ( ( member_a @ I3 @ I4 )
% 0.28/0.48 & ( ( X2 @ I3 )
% 0.28/0.48 != one_one_real ) ) ) )
% 0.28/0.48 => ( ( finite_finite_a
% 0.28/0.48 @ ( collect_a
% 0.28/0.48 @ ^ [I3: a] :
% 0.28/0.48 ( ( member_a @ I3 @ I4 )
% 0.28/0.48 & ( ( Y @ I3 )
% 0.28/0.48 != one_one_real ) ) ) )
% 0.28/0.48 => ( finite_finite_a
% 0.28/0.48 @ ( collect_a
% 0.28/0.48 @ ^ [I3: a] :
% 0.28/0.48 ( ( member_a @ I3 @ I4 )
% 0.28/0.48 & ( ( times_times_real @ ( X2 @ I3 ) @ ( Y @ I3 ) )
% 0.28/0.48 != one_one_real ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % prod.finite_Collect_op
% 0.28/0.48 thf(fact_261_sum_Oinsert__if,axiom,
% 0.28/0.48 ! [A2: set_b,X2: b,G: b > b] :
% 0.28/0.48 ( ( finite_finite_b @ A2 )
% 0.28/0.48 => ( ( ( member_b @ X2 @ A2 )
% 0.28/0.48 => ( ( groups2026918778um_b_b @ G @ ( insert_b @ X2 @ A2 ) )
% 0.28/0.48 = ( groups2026918778um_b_b @ G @ A2 ) ) )
% 0.28/0.48 & ( ~ ( member_b @ X2 @ A2 )
% 0.28/0.48 => ( ( groups2026918778um_b_b @ G @ ( insert_b @ X2 @ A2 ) )
% 0.28/0.48 = ( plus_plus_b @ ( G @ X2 ) @ ( groups2026918778um_b_b @ G @ A2 ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum.insert_if
% 0.28/0.48 thf(fact_262_sum_Oinsert__if,axiom,
% 0.28/0.48 ! [A2: set_b,X2: b,G: b > real] :
% 0.28/0.48 ( ( finite_finite_b @ A2 )
% 0.28/0.48 => ( ( ( member_b @ X2 @ A2 )
% 0.28/0.48 => ( ( groups583146225b_real @ G @ ( insert_b @ X2 @ A2 ) )
% 0.28/0.48 = ( groups583146225b_real @ G @ A2 ) ) )
% 0.28/0.48 & ( ~ ( member_b @ X2 @ A2 )
% 0.28/0.48 => ( ( groups583146225b_real @ G @ ( insert_b @ X2 @ A2 ) )
% 0.28/0.48 = ( plus_plus_real @ ( G @ X2 ) @ ( groups583146225b_real @ G @ A2 ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum.insert_if
% 0.28/0.48 thf(fact_263_sum_Oinsert__if,axiom,
% 0.28/0.48 ! [A2: set_a,X2: a,G: a > b] :
% 0.28/0.48 ( ( finite_finite_a @ A2 )
% 0.28/0.48 => ( ( ( member_a @ X2 @ A2 )
% 0.28/0.48 => ( ( groups1199149371um_a_b @ G @ ( insert_a @ X2 @ A2 ) )
% 0.28/0.48 = ( groups1199149371um_a_b @ G @ A2 ) ) )
% 0.28/0.48 & ( ~ ( member_a @ X2 @ A2 )
% 0.28/0.48 => ( ( groups1199149371um_a_b @ G @ ( insert_a @ X2 @ A2 ) )
% 0.28/0.48 = ( plus_plus_b @ ( G @ X2 ) @ ( groups1199149371um_a_b @ G @ A2 ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum.insert_if
% 0.28/0.48 thf(fact_264_sum_Oinsert__if,axiom,
% 0.28/0.48 ! [A2: set_a,X2: a,G: a > real] :
% 0.28/0.48 ( ( finite_finite_a @ A2 )
% 0.28/0.48 => ( ( ( member_a @ X2 @ A2 )
% 0.28/0.48 => ( ( groups1862963056a_real @ G @ ( insert_a @ X2 @ A2 ) )
% 0.28/0.48 = ( groups1862963056a_real @ G @ A2 ) ) )
% 0.28/0.48 & ( ~ ( member_a @ X2 @ A2 )
% 0.28/0.48 => ( ( groups1862963056a_real @ G @ ( insert_a @ X2 @ A2 ) )
% 0.28/0.48 = ( plus_plus_real @ ( G @ X2 ) @ ( groups1862963056a_real @ G @ A2 ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % sum.insert_if
% 0.28/0.48 thf(fact_265_convex__singleton,axiom,
% 0.28/0.48 ! [A: b] : ( convex_b @ ( insert_b @ A @ bot_bot_set_b ) ) ).
% 0.28/0.48
% 0.28/0.48 % convex_singleton
% 0.28/0.48 thf(fact_266_real__divide__square__eq,axiom,
% 0.28/0.48 ! [R: real,A: real] :
% 0.28/0.48 ( ( divide_divide_real @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ R ) )
% 0.28/0.48 = ( divide_divide_real @ A @ R ) ) ).
% 0.28/0.48
% 0.28/0.48 % real_divide_square_eq
% 0.28/0.48 thf(fact_267_convex__empty,axiom,
% 0.28/0.48 convex_b @ bot_bot_set_b ).
% 0.28/0.48
% 0.28/0.48 % convex_empty
% 0.28/0.48 thf(fact_268_div__by__1,axiom,
% 0.28/0.48 ! [A: real] :
% 0.28/0.48 ( ( divide_divide_real @ A @ one_one_real )
% 0.28/0.48 = A ) ).
% 0.28/0.48
% 0.28/0.48 % div_by_1
% 0.28/0.48 thf(fact_269_add__diff__cancel,axiom,
% 0.28/0.48 ! [A: b,B: b] :
% 0.28/0.48 ( ( minus_minus_b @ ( plus_plus_b @ A @ B ) @ B )
% 0.28/0.48 = A ) ).
% 0.28/0.48
% 0.28/0.48 % add_diff_cancel
% 0.28/0.48 thf(fact_270_add__diff__cancel,axiom,
% 0.28/0.48 ! [A: real,B: real] :
% 0.28/0.48 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.28/0.48 = A ) ).
% 0.28/0.48
% 0.28/0.48 % add_diff_cancel
% 0.28/0.48 thf(fact_271_diff__add__cancel,axiom,
% 0.28/0.48 ! [A: b,B: b] :
% 0.28/0.48 ( ( plus_plus_b @ ( minus_minus_b @ A @ B ) @ B )
% 0.28/0.48 = A ) ).
% 0.28/0.48
% 0.28/0.48 % diff_add_cancel
% 0.28/0.48 thf(fact_272_diff__add__cancel,axiom,
% 0.28/0.48 ! [A: real,B: real] :
% 0.28/0.48 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.28/0.48 = A ) ).
% 0.28/0.48
% 0.28/0.48 % diff_add_cancel
% 0.28/0.48 thf(fact_273_add__right__cancel,axiom,
% 0.28/0.48 ! [B: b,A: b,C: b] :
% 0.28/0.48 ( ( ( plus_plus_b @ B @ A )
% 0.28/0.48 = ( plus_plus_b @ C @ A ) )
% 0.28/0.48 = ( B = C ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_right_cancel
% 0.28/0.48 thf(fact_274_add__right__cancel,axiom,
% 0.28/0.48 ! [B: real,A: real,C: real] :
% 0.28/0.48 ( ( ( plus_plus_real @ B @ A )
% 0.28/0.48 = ( plus_plus_real @ C @ A ) )
% 0.28/0.48 = ( B = C ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_right_cancel
% 0.28/0.48 thf(fact_275_add__left__cancel,axiom,
% 0.28/0.48 ! [A: b,B: b,C: b] :
% 0.28/0.48 ( ( ( plus_plus_b @ A @ B )
% 0.28/0.48 = ( plus_plus_b @ A @ C ) )
% 0.28/0.48 = ( B = C ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_left_cancel
% 0.28/0.48 thf(fact_276_add__left__cancel,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( ( plus_plus_real @ A @ B )
% 0.28/0.48 = ( plus_plus_real @ A @ C ) )
% 0.28/0.48 = ( B = C ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_left_cancel
% 0.28/0.48 thf(fact_277_mult_Oright__neutral,axiom,
% 0.28/0.48 ! [A: real] :
% 0.28/0.48 ( ( times_times_real @ A @ one_one_real )
% 0.28/0.48 = A ) ).
% 0.28/0.48
% 0.28/0.48 % mult.right_neutral
% 0.28/0.48 thf(fact_278_mult_Oleft__neutral,axiom,
% 0.28/0.48 ! [A: real] :
% 0.28/0.48 ( ( times_times_real @ one_one_real @ A )
% 0.28/0.48 = A ) ).
% 0.28/0.48
% 0.28/0.48 % mult.left_neutral
% 0.28/0.48 thf(fact_279_add__diff__cancel__right_H,axiom,
% 0.28/0.48 ! [A: b,B: b] :
% 0.28/0.48 ( ( minus_minus_b @ ( plus_plus_b @ A @ B ) @ B )
% 0.28/0.48 = A ) ).
% 0.28/0.48
% 0.28/0.48 % add_diff_cancel_right'
% 0.28/0.48 thf(fact_280_add__diff__cancel__right_H,axiom,
% 0.28/0.48 ! [A: real,B: real] :
% 0.28/0.48 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.28/0.48 = A ) ).
% 0.28/0.48
% 0.28/0.48 % add_diff_cancel_right'
% 0.28/0.48 thf(fact_281_add__diff__cancel__right,axiom,
% 0.28/0.48 ! [A: b,C: b,B: b] :
% 0.28/0.48 ( ( minus_minus_b @ ( plus_plus_b @ A @ C ) @ ( plus_plus_b @ B @ C ) )
% 0.28/0.48 = ( minus_minus_b @ A @ B ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_diff_cancel_right
% 0.28/0.48 thf(fact_282_add__diff__cancel__right,axiom,
% 0.28/0.48 ! [A: real,C: real,B: real] :
% 0.28/0.48 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.28/0.48 = ( minus_minus_real @ A @ B ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_diff_cancel_right
% 0.28/0.48 thf(fact_283_add__diff__cancel__left_H,axiom,
% 0.28/0.48 ! [A: b,B: b] :
% 0.28/0.48 ( ( minus_minus_b @ ( plus_plus_b @ A @ B ) @ A )
% 0.28/0.48 = B ) ).
% 0.28/0.48
% 0.28/0.48 % add_diff_cancel_left'
% 0.28/0.48 thf(fact_284_add__diff__cancel__left_H,axiom,
% 0.28/0.48 ! [A: real,B: real] :
% 0.28/0.48 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 0.28/0.48 = B ) ).
% 0.28/0.48
% 0.28/0.48 % add_diff_cancel_left'
% 0.28/0.48 thf(fact_285_add__diff__cancel__left,axiom,
% 0.28/0.48 ! [C: b,A: b,B: b] :
% 0.28/0.48 ( ( minus_minus_b @ ( plus_plus_b @ C @ A ) @ ( plus_plus_b @ C @ B ) )
% 0.28/0.48 = ( minus_minus_b @ A @ B ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_diff_cancel_left
% 0.28/0.48 thf(fact_286_add__diff__cancel__left,axiom,
% 0.28/0.48 ! [C: real,A: real,B: real] :
% 0.28/0.48 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.28/0.48 = ( minus_minus_real @ A @ B ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_diff_cancel_left
% 0.28/0.48 thf(fact_287_mult_Oleft__commute,axiom,
% 0.28/0.48 ! [B: real,A: real,C: real] :
% 0.28/0.48 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 0.28/0.48 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % mult.left_commute
% 0.28/0.48 thf(fact_288_mult_Ocommute,axiom,
% 0.28/0.48 ( times_times_real
% 0.28/0.48 = ( ^ [A3: real,B4: real] : ( times_times_real @ B4 @ A3 ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % mult.commute
% 0.28/0.48 thf(fact_289_mult_Oassoc,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 0.28/0.48 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % mult.assoc
% 0.28/0.48 thf(fact_290_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 0.28/0.48 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % ab_semigroup_mult_class.mult_ac(1)
% 0.28/0.48 thf(fact_291_add__right__imp__eq,axiom,
% 0.28/0.48 ! [B: b,A: b,C: b] :
% 0.28/0.48 ( ( ( plus_plus_b @ B @ A )
% 0.28/0.48 = ( plus_plus_b @ C @ A ) )
% 0.28/0.48 => ( B = C ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_right_imp_eq
% 0.28/0.48 thf(fact_292_add__right__imp__eq,axiom,
% 0.28/0.48 ! [B: real,A: real,C: real] :
% 0.28/0.48 ( ( ( plus_plus_real @ B @ A )
% 0.28/0.48 = ( plus_plus_real @ C @ A ) )
% 0.28/0.48 => ( B = C ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_right_imp_eq
% 0.28/0.48 thf(fact_293_add__left__imp__eq,axiom,
% 0.28/0.48 ! [A: b,B: b,C: b] :
% 0.28/0.48 ( ( ( plus_plus_b @ A @ B )
% 0.28/0.48 = ( plus_plus_b @ A @ C ) )
% 0.28/0.48 => ( B = C ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_left_imp_eq
% 0.28/0.48 thf(fact_294_add__left__imp__eq,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( ( plus_plus_real @ A @ B )
% 0.28/0.48 = ( plus_plus_real @ A @ C ) )
% 0.28/0.48 => ( B = C ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_left_imp_eq
% 0.28/0.48 thf(fact_295_add_Oleft__commute,axiom,
% 0.28/0.48 ! [B: b,A: b,C: b] :
% 0.28/0.48 ( ( plus_plus_b @ B @ ( plus_plus_b @ A @ C ) )
% 0.28/0.48 = ( plus_plus_b @ A @ ( plus_plus_b @ B @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % add.left_commute
% 0.28/0.48 thf(fact_296_add_Oleft__commute,axiom,
% 0.28/0.48 ! [B: real,A: real,C: real] :
% 0.28/0.48 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 0.28/0.48 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % add.left_commute
% 0.28/0.48 thf(fact_297_add_Ocommute,axiom,
% 0.28/0.48 ( plus_plus_b
% 0.28/0.48 = ( ^ [A3: b,B4: b] : ( plus_plus_b @ B4 @ A3 ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % add.commute
% 0.28/0.48 thf(fact_298_add_Ocommute,axiom,
% 0.28/0.48 ( plus_plus_real
% 0.28/0.48 = ( ^ [A3: real,B4: real] : ( plus_plus_real @ B4 @ A3 ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % add.commute
% 0.28/0.48 thf(fact_299_add_Oright__cancel,axiom,
% 0.28/0.48 ! [B: b,A: b,C: b] :
% 0.28/0.48 ( ( ( plus_plus_b @ B @ A )
% 0.28/0.48 = ( plus_plus_b @ C @ A ) )
% 0.28/0.48 = ( B = C ) ) ).
% 0.28/0.48
% 0.28/0.48 % add.right_cancel
% 0.28/0.48 thf(fact_300_add_Oright__cancel,axiom,
% 0.28/0.48 ! [B: real,A: real,C: real] :
% 0.28/0.48 ( ( ( plus_plus_real @ B @ A )
% 0.28/0.48 = ( plus_plus_real @ C @ A ) )
% 0.28/0.48 = ( B = C ) ) ).
% 0.28/0.48
% 0.28/0.48 % add.right_cancel
% 0.28/0.48 thf(fact_301_add_Oleft__cancel,axiom,
% 0.28/0.48 ! [A: b,B: b,C: b] :
% 0.28/0.48 ( ( ( plus_plus_b @ A @ B )
% 0.28/0.48 = ( plus_plus_b @ A @ C ) )
% 0.28/0.48 = ( B = C ) ) ).
% 0.28/0.48
% 0.28/0.48 % add.left_cancel
% 0.28/0.48 thf(fact_302_add_Oleft__cancel,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( ( plus_plus_real @ A @ B )
% 0.28/0.48 = ( plus_plus_real @ A @ C ) )
% 0.28/0.48 = ( B = C ) ) ).
% 0.28/0.48
% 0.28/0.48 % add.left_cancel
% 0.28/0.48 thf(fact_303_add_Oassoc,axiom,
% 0.28/0.48 ! [A: b,B: b,C: b] :
% 0.28/0.48 ( ( plus_plus_b @ ( plus_plus_b @ A @ B ) @ C )
% 0.28/0.48 = ( plus_plus_b @ A @ ( plus_plus_b @ B @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % add.assoc
% 0.28/0.48 thf(fact_304_add_Oassoc,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.28/0.48 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % add.assoc
% 0.28/0.48 thf(fact_305_group__cancel_Oadd2,axiom,
% 0.28/0.48 ! [B2: b,K: b,B: b,A: b] :
% 0.28/0.48 ( ( B2
% 0.28/0.48 = ( plus_plus_b @ K @ B ) )
% 0.28/0.48 => ( ( plus_plus_b @ A @ B2 )
% 0.28/0.48 = ( plus_plus_b @ K @ ( plus_plus_b @ A @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % group_cancel.add2
% 0.28/0.48 thf(fact_306_group__cancel_Oadd2,axiom,
% 0.28/0.48 ! [B2: real,K: real,B: real,A: real] :
% 0.28/0.48 ( ( B2
% 0.28/0.48 = ( plus_plus_real @ K @ B ) )
% 0.28/0.48 => ( ( plus_plus_real @ A @ B2 )
% 0.28/0.48 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % group_cancel.add2
% 0.28/0.48 thf(fact_307_group__cancel_Oadd1,axiom,
% 0.28/0.48 ! [A2: b,K: b,A: b,B: b] :
% 0.28/0.48 ( ( A2
% 0.28/0.48 = ( plus_plus_b @ K @ A ) )
% 0.28/0.48 => ( ( plus_plus_b @ A2 @ B )
% 0.28/0.48 = ( plus_plus_b @ K @ ( plus_plus_b @ A @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % group_cancel.add1
% 0.28/0.48 thf(fact_308_group__cancel_Oadd1,axiom,
% 0.28/0.48 ! [A2: real,K: real,A: real,B: real] :
% 0.28/0.48 ( ( A2
% 0.28/0.48 = ( plus_plus_real @ K @ A ) )
% 0.28/0.48 => ( ( plus_plus_real @ A2 @ B )
% 0.28/0.48 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % group_cancel.add1
% 0.28/0.48 thf(fact_309_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.28/0.48 ! [I2: real,J2: real,K: real,L: real] :
% 0.28/0.48 ( ( ( I2 = J2 )
% 0.28/0.48 & ( K = L ) )
% 0.28/0.48 => ( ( plus_plus_real @ I2 @ K )
% 0.28/0.48 = ( plus_plus_real @ J2 @ L ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_mono_thms_linordered_semiring(4)
% 0.28/0.48 thf(fact_310_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.28/0.48 ! [A: b,B: b,C: b] :
% 0.28/0.48 ( ( plus_plus_b @ ( plus_plus_b @ A @ B ) @ C )
% 0.28/0.48 = ( plus_plus_b @ A @ ( plus_plus_b @ B @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % ab_semigroup_add_class.add_ac(1)
% 0.28/0.48 thf(fact_311_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.28/0.48 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % ab_semigroup_add_class.add_ac(1)
% 0.28/0.48 thf(fact_312_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.28/0.48 ! [A: real,C: real,B: real] :
% 0.28/0.48 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 0.28/0.48 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 0.28/0.48
% 0.28/0.48 % cancel_ab_semigroup_add_class.diff_right_commute
% 0.28/0.48 thf(fact_313_diff__eq__diff__eq,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real,D: real] :
% 0.28/0.48 ( ( ( minus_minus_real @ A @ B )
% 0.28/0.48 = ( minus_minus_real @ C @ D ) )
% 0.28/0.48 => ( ( A = B )
% 0.28/0.48 = ( C = D ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % diff_eq_diff_eq
% 0.28/0.48 thf(fact_314_one__reorient,axiom,
% 0.28/0.48 ! [X2: real] :
% 0.28/0.48 ( ( one_one_real = X2 )
% 0.28/0.48 = ( X2 = one_one_real ) ) ).
% 0.28/0.48
% 0.28/0.48 % one_reorient
% 0.28/0.48 thf(fact_315_convex__set__plus,axiom,
% 0.28/0.48 ! [S: set_b,T: set_b] :
% 0.28/0.48 ( ( convex_b @ S )
% 0.28/0.48 => ( ( convex_b @ T )
% 0.28/0.48 => ( convex_b @ ( plus_plus_set_b @ S @ T ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % convex_set_plus
% 0.28/0.48 thf(fact_316_convex__set__sum,axiom,
% 0.28/0.48 ! [A2: set_a,B2: a > set_b] :
% 0.28/0.48 ( ! [I5: a] :
% 0.28/0.48 ( ( member_a @ I5 @ A2 )
% 0.28/0.48 => ( convex_b @ ( B2 @ I5 ) ) )
% 0.28/0.48 => ( convex_b @ ( groups919362075_set_b @ B2 @ A2 ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % convex_set_sum
% 0.28/0.48 thf(fact_317_convex__set__sum,axiom,
% 0.28/0.48 ! [A2: set_b,B2: b > set_b] :
% 0.28/0.48 ( ! [I5: b] :
% 0.28/0.48 ( ( member_b @ I5 @ A2 )
% 0.28/0.48 => ( convex_b @ ( B2 @ I5 ) ) )
% 0.28/0.48 => ( convex_b @ ( groups448962650_set_b @ B2 @ A2 ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % convex_set_sum
% 0.28/0.48 thf(fact_318_combine__common__factor,axiom,
% 0.28/0.48 ! [A: real,E: real,B: real,C: real] :
% 0.28/0.48 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 0.28/0.48 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 0.28/0.48
% 0.28/0.48 % combine_common_factor
% 0.28/0.48 thf(fact_319_distrib__right,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.28/0.48 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % distrib_right
% 0.28/0.48 thf(fact_320_distrib__left,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.28/0.48 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % distrib_left
% 0.28/0.48 thf(fact_321_comm__semiring__class_Odistrib,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.28/0.48 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % comm_semiring_class.distrib
% 0.28/0.48 thf(fact_322_ring__class_Oring__distribs_I1_J,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.28/0.48 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % ring_class.ring_distribs(1)
% 0.28/0.48 thf(fact_323_ring__class_Oring__distribs_I2_J,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.28/0.48 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % ring_class.ring_distribs(2)
% 0.28/0.48 thf(fact_324_right__diff__distrib_H,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.28/0.48 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % right_diff_distrib'
% 0.28/0.48 thf(fact_325_left__diff__distrib_H,axiom,
% 0.28/0.48 ! [B: real,C: real,A: real] :
% 0.28/0.48 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 0.28/0.48 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % left_diff_distrib'
% 0.28/0.48 thf(fact_326_right__diff__distrib,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.28/0.48 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % right_diff_distrib
% 0.28/0.48 thf(fact_327_left__diff__distrib,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.28/0.48 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % left_diff_distrib
% 0.28/0.48 thf(fact_328_mult_Ocomm__neutral,axiom,
% 0.28/0.48 ! [A: real] :
% 0.28/0.48 ( ( times_times_real @ A @ one_one_real )
% 0.28/0.48 = A ) ).
% 0.28/0.48
% 0.28/0.48 % mult.comm_neutral
% 0.28/0.48 thf(fact_329_comm__monoid__mult__class_Omult__1,axiom,
% 0.28/0.48 ! [A: real] :
% 0.28/0.48 ( ( times_times_real @ one_one_real @ A )
% 0.28/0.48 = A ) ).
% 0.28/0.48
% 0.28/0.48 % comm_monoid_mult_class.mult_1
% 0.28/0.48 thf(fact_330_add__implies__diff,axiom,
% 0.28/0.48 ! [C: b,B: b,A: b] :
% 0.28/0.48 ( ( ( plus_plus_b @ C @ B )
% 0.28/0.48 = A )
% 0.28/0.48 => ( C
% 0.28/0.48 = ( minus_minus_b @ A @ B ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_implies_diff
% 0.28/0.48 thf(fact_331_add__implies__diff,axiom,
% 0.28/0.48 ! [C: real,B: real,A: real] :
% 0.28/0.48 ( ( ( plus_plus_real @ C @ B )
% 0.28/0.48 = A )
% 0.28/0.48 => ( C
% 0.28/0.48 = ( minus_minus_real @ A @ B ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_implies_diff
% 0.28/0.48 thf(fact_332_diff__diff__add,axiom,
% 0.28/0.48 ! [A: b,B: b,C: b] :
% 0.28/0.48 ( ( minus_minus_b @ ( minus_minus_b @ A @ B ) @ C )
% 0.28/0.48 = ( minus_minus_b @ A @ ( plus_plus_b @ B @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % diff_diff_add
% 0.28/0.48 thf(fact_333_diff__diff__add,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.28/0.48 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % diff_diff_add
% 0.28/0.48 thf(fact_334_diff__add__eq__diff__diff__swap,axiom,
% 0.28/0.48 ! [A: b,B: b,C: b] :
% 0.28/0.48 ( ( minus_minus_b @ A @ ( plus_plus_b @ B @ C ) )
% 0.28/0.48 = ( minus_minus_b @ ( minus_minus_b @ A @ C ) @ B ) ) ).
% 0.28/0.48
% 0.28/0.48 % diff_add_eq_diff_diff_swap
% 0.28/0.48 thf(fact_335_diff__add__eq__diff__diff__swap,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.28/0.48 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 0.28/0.48
% 0.28/0.48 % diff_add_eq_diff_diff_swap
% 0.28/0.48 thf(fact_336_diff__add__eq,axiom,
% 0.28/0.48 ! [A: b,B: b,C: b] :
% 0.28/0.48 ( ( plus_plus_b @ ( minus_minus_b @ A @ B ) @ C )
% 0.28/0.48 = ( minus_minus_b @ ( plus_plus_b @ A @ C ) @ B ) ) ).
% 0.28/0.48
% 0.28/0.48 % diff_add_eq
% 0.28/0.48 thf(fact_337_diff__add__eq,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.28/0.48 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.28/0.48
% 0.28/0.48 % diff_add_eq
% 0.28/0.48 thf(fact_338_diff__diff__eq2,axiom,
% 0.28/0.48 ! [A: b,B: b,C: b] :
% 0.28/0.48 ( ( minus_minus_b @ A @ ( minus_minus_b @ B @ C ) )
% 0.28/0.48 = ( minus_minus_b @ ( plus_plus_b @ A @ C ) @ B ) ) ).
% 0.28/0.48
% 0.28/0.48 % diff_diff_eq2
% 0.28/0.48 thf(fact_339_diff__diff__eq2,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.28/0.48 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.28/0.48
% 0.28/0.48 % diff_diff_eq2
% 0.28/0.48 thf(fact_340_add__diff__eq,axiom,
% 0.28/0.48 ! [A: b,B: b,C: b] :
% 0.28/0.48 ( ( plus_plus_b @ A @ ( minus_minus_b @ B @ C ) )
% 0.28/0.48 = ( minus_minus_b @ ( plus_plus_b @ A @ B ) @ C ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_diff_eq
% 0.28/0.48 thf(fact_341_add__diff__eq,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.28/0.48 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.28/0.48
% 0.28/0.48 % add_diff_eq
% 0.28/0.48 thf(fact_342_eq__diff__eq,axiom,
% 0.28/0.48 ! [A: b,C: b,B: b] :
% 0.28/0.48 ( ( A
% 0.28/0.48 = ( minus_minus_b @ C @ B ) )
% 0.28/0.48 = ( ( plus_plus_b @ A @ B )
% 0.28/0.48 = C ) ) ).
% 0.28/0.48
% 0.28/0.48 % eq_diff_eq
% 0.28/0.48 thf(fact_343_eq__diff__eq,axiom,
% 0.28/0.48 ! [A: real,C: real,B: real] :
% 0.28/0.48 ( ( A
% 0.28/0.48 = ( minus_minus_real @ C @ B ) )
% 0.28/0.48 = ( ( plus_plus_real @ A @ B )
% 0.28/0.48 = C ) ) ).
% 0.28/0.48
% 0.28/0.48 % eq_diff_eq
% 0.28/0.48 thf(fact_344_diff__eq__eq,axiom,
% 0.28/0.48 ! [A: b,B: b,C: b] :
% 0.28/0.48 ( ( ( minus_minus_b @ A @ B )
% 0.28/0.48 = C )
% 0.28/0.48 = ( A
% 0.28/0.48 = ( plus_plus_b @ C @ B ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % diff_eq_eq
% 0.28/0.48 thf(fact_345_diff__eq__eq,axiom,
% 0.28/0.48 ! [A: real,B: real,C: real] :
% 0.28/0.48 ( ( ( minus_minus_real @ A @ B )
% 0.28/0.48 = C )
% 0.28/0.48 = ( A
% 0.28/0.48 = ( plus_plus_real @ C @ B ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % diff_eq_eq
% 0.28/0.48 thf(fact_346_group__cancel_Osub1,axiom,
% 0.28/0.48 ! [A2: b,K: b,A: b,B: b] :
% 0.28/0.48 ( ( A2
% 0.28/0.48 = ( plus_plus_b @ K @ A ) )
% 0.28/0.48 => ( ( minus_minus_b @ A2 @ B )
% 0.28/0.48 = ( plus_plus_b @ K @ ( minus_minus_b @ A @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % group_cancel.sub1
% 0.28/0.48 thf(fact_347_group__cancel_Osub1,axiom,
% 0.28/0.48 ! [A2: real,K: real,A: real,B: real] :
% 0.28/0.48 ( ( A2
% 0.28/0.48 = ( plus_plus_real @ K @ A ) )
% 0.28/0.48 => ( ( minus_minus_real @ A2 @ B )
% 0.28/0.48 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % group_cancel.sub1
% 0.28/0.48 thf(fact_348_lambda__one,axiom,
% 0.28/0.48 ( ( ^ [X: real] : X )
% 0.28/0.48 = ( times_times_real @ one_one_real ) ) ).
% 0.28/0.48
% 0.28/0.48 % lambda_one
% 0.28/0.48 thf(fact_349_square__diff__square__factored,axiom,
% 0.28/0.48 ! [X2: real,Y: real] :
% 0.28/0.48 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) )
% 0.28/0.48 = ( times_times_real @ ( plus_plus_real @ X2 @ Y ) @ ( minus_minus_real @ X2 @ Y ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % square_diff_square_factored
% 0.28/0.48 thf(fact_350_eq__add__iff2,axiom,
% 0.28/0.48 ! [A: real,E: real,C: real,B: real,D: real] :
% 0.28/0.48 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 0.28/0.48 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.28/0.48 = ( C
% 0.28/0.48 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 0.28/0.48
% 0.28/0.48 % eq_add_iff2
% 0.28/0.48 thf(fact_351_eq__add__iff1,axiom,
% 0.28/0.48 ! [A: real,E: real,C: real,B: real,D: real] :
% 0.28/0.48 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 0.28/0.48 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.28/0.48 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 0.28/0.48 = D ) ) ).
% 0.28/0.48
% 0.28/0.48 % eq_add_iff1
% 0.28/0.48 thf(fact_352_ai1,axiom,
% 0.28/0.48 ord_less_eq_real @ ( aa @ i ) @ one_one_real ).
% 0.28/0.48
% 0.28/0.48 % ai1
% 0.28/0.48
% 0.28/0.48 % Helper facts (5)
% 0.28/0.48 thf(help_If_2_1_If_001tf__b_T,axiom,
% 0.28/0.48 ! [X2: b,Y: b] :
% 0.28/0.48 ( ( if_b @ $false @ X2 @ Y )
% 0.28/0.48 = Y ) ).
% 0.28/0.48
% 0.28/0.48 thf(help_If_1_1_If_001tf__b_T,axiom,
% 0.28/0.48 ! [X2: b,Y: b] :
% 0.28/0.48 ( ( if_b @ $true @ X2 @ Y )
% 0.28/0.48 = X2 ) ).
% 0.28/0.48
% 0.28/0.48 thf(help_If_3_1_If_001t__Real__Oreal_T,axiom,
% 0.28/0.48 ! [P: $o] :
% 0.28/0.48 ( ( P = $true )
% 0.28/0.48 | ( P = $false ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 0.28/0.48 ! [X2: real,Y: real] :
% 0.28/0.48 ( ( if_real @ $false @ X2 @ Y )
% 0.28/0.48 = Y ) ).
% 0.28/0.48
% 0.28/0.48 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 0.28/0.48 ! [X2: real,Y: real] :
% 0.28/0.48 ( ( if_real @ $true @ X2 @ Y )
% 0.28/0.48 = X2 ) ).
% 0.28/0.48
% 0.28/0.48 % Conjectures (1)
% 0.28/0.48 thf(conj_0,conjecture,
% 0.28/0.48 ( ( f
% 0.28/0.48 @ ( plus_plus_b
% 0.28/0.48 @ ( real_V1035702896aleR_b @ ( times_times_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) )
% 0.28/0.48 @ ( groups1199149371um_a_b
% 0.28/0.48 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 0.28/0.48 @ sa ) )
% 0.28/0.48 @ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) )
% 0.28/0.48 = ( f
% 0.28/0.48 @ ( plus_plus_b
% 0.28/0.48 @ ( real_V1035702896aleR_b @ ( minus_minus_real @ one_one_real @ ( aa @ i ) )
% 0.28/0.48 @ ( groups1199149371um_a_b
% 0.28/0.48 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( times_times_real @ ( aa @ J ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) ) @ ( y @ J ) )
% 0.28/0.48 @ sa ) )
% 0.28/0.48 @ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 %------------------------------------------------------------------------------
% 0.28/0.48 ------------------------
% 2.89/1.79 ---- Embedded in THF ---
% 2.89/1.79 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.89/1.79 %%% Generated on Tue Feb 24 08:26:51 EST 2026
% 2.89/1.79 %%% using '$$dhol' embedding, version 1.3.0.
% 2.89/1.79 %%% Logic specification used:
% 2.89/1.79 %%% thf(spec, logic, $$dhol).
% 2.89/1.79
% 2.89/1.79 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.aJ622KHsm8/DTF2DTF14827.p
% See solution above
% 2.89/1.80 ------------------------
% 3.19/1.82 ---- Cleaned THF ---
% 3.19/1.82 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 3.19/1.82 set_real: $tType ).
% 3.19/1.82
% 3.19/1.82 thf(ty_n_t__Extended____Real__Oereal,type,
% 3.19/1.82 extended_ereal: $tType ).
% 3.19/1.82
% 3.19/1.82 thf(ty_n_t__Set__Oset_Itf__b_J,type,
% 3.19/1.82 set_b: $tType ).
% 3.19/1.82
% 3.19/1.82 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 3.19/1.82 set_a: $tType ).
% 3.19/1.82
% 3.19/1.82 thf(ty_n_t__Real__Oreal,type,
% 3.19/1.82 real: $tType ).
% 3.19/1.82
% 3.19/1.82 thf(ty_n_t__Nat__Onat,type,
% 3.19/1.82 nat: $tType ).
% 3.19/1.82
% 3.19/1.82 thf(ty_n_tf__b,type,
% 3.19/1.82 b: $tType ).
% 3.19/1.82
% 3.19/1.82 thf(ty_n_tf__a,type,
% 3.19/1.82 a: $tType ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Convex_Oconvex_001tf__b,type,
% 3.19/1.82 convex_b: set_b > $o ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 3.19/1.82 inverse_inverse_real: real > real ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal,type,
% 3.19/1.82 finite_finite_real: set_real > $o ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Finite__Set_Ofinite_001tf__a,type,
% 3.19/1.82 finite_finite_a: set_a > $o ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Finite__Set_Ofinite_001tf__b,type,
% 3.19/1.82 finite_finite_b: set_b > $o ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups_Ominus__class_Ominus_001_062_Itf__a_M_Eo_J,type,
% 3.19/1.82 minus_minus_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups_Ominus__class_Ominus_001_062_Itf__b_M_Eo_J,type,
% 3.19/1.82 minus_minus_b_o: ( b > $o ) > ( b > $o ) > b > $o ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 3.19/1.82 minus_minus_nat: nat > nat > nat ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
% 3.19/1.82 minus_minus_real: real > real > real ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__a_J,type,
% 3.19/1.82 minus_minus_set_a: set_a > set_a > set_a ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__b_J,type,
% 3.19/1.82 minus_minus_set_b: set_b > set_b > set_b ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups_Ominus__class_Ominus_001tf__b,type,
% 3.19/1.82 minus_minus_b: b > b > b ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
% 3.19/1.82 one_one_real: real ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups_Oplus__class_Oplus_001t__Extended____Real__Oereal,type,
% 3.19/1.82 plus_p2118002693_ereal: extended_ereal > extended_ereal > extended_ereal ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
% 3.19/1.82 plus_plus_real: real > real > real ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups_Oplus__class_Oplus_001t__Set__Oset_Itf__b_J,type,
% 3.19/1.82 plus_plus_set_b: set_b > set_b > set_b ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups_Oplus__class_Oplus_001tf__b,type,
% 3.19/1.82 plus_plus_b: b > b > b ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal,type,
% 3.19/1.82 times_times_real: real > real > real ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Real__Oreal,type,
% 3.19/1.82 groups1296524820l_real: ( real > real ) > set_real > real ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__a_001t__Nat__Onat,type,
% 3.19/1.82 groups769445524_a_nat: ( a > nat ) > set_a > nat ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__a_001t__Real__Oreal,type,
% 3.19/1.82 groups1862963056a_real: ( a > real ) > set_a > real ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__a_001t__Set__Oset_Itf__b_J,type,
% 3.19/1.82 groups919362075_set_b: ( a > set_b ) > set_a > set_b ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__a_001tf__b,type,
% 3.19/1.82 groups1199149371um_a_b: ( a > b ) > set_a > b ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__b_001t__Nat__Onat,type,
% 3.19/1.82 groups2098481813_b_nat: ( b > nat ) > set_b > nat ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__b_001t__Real__Oreal,type,
% 3.19/1.82 groups583146225b_real: ( b > real ) > set_b > real ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__b_001t__Set__Oset_Itf__b_J,type,
% 3.19/1.82 groups448962650_set_b: ( b > set_b ) > set_b > set_b ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001tf__b_001tf__b,type,
% 3.19/1.82 groups2026918778um_b_b: ( b > b ) > set_b > b ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_If_001t__Real__Oreal,type,
% 3.19/1.82 if_real: $o > real > real > real ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_If_001tf__b,type,
% 3.19/1.82 if_b: $o > b > b > b ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Lower__Semicontinuous__Mirabelle__mxyexokbxt_Oconvex__on_001tf__b,type,
% 3.19/1.82 lower_311861425x_on_b: set_b > ( b > extended_ereal ) > $o ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 3.19/1.82 bot_bot_set_a: set_a ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__b_J,type,
% 3.19/1.82 bot_bot_set_b: set_b ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 3.19/1.82 ord_less_eq_real: real > real > $o ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 3.19/1.82 real_V453051771R_real: real > real > real ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001tf__b,type,
% 3.19/1.82 real_V1035702896aleR_b: real > b > b ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 3.19/1.82 divide_divide_real: real > real > real ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Set_OCollect_001tf__a,type,
% 3.19/1.82 collect_a: ( a > $o ) > set_a ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Set_OCollect_001tf__b,type,
% 3.19/1.82 collect_b: ( b > $o ) > set_b ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 3.19/1.82 insert_real: real > set_real > set_real ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Set_Oinsert_001tf__a,type,
% 3.19/1.82 insert_a: a > set_a > set_a ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_Set_Oinsert_001tf__b,type,
% 3.19/1.82 insert_b: b > set_b > set_b ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_member_001tf__a,type,
% 3.19/1.82 member_a: a > set_a > $o ).
% 3.19/1.82
% 3.19/1.82 thf(sy_c_member_001tf__b,type,
% 3.19/1.82 member_b: b > set_b > $o ).
% 3.19/1.82
% 3.19/1.82 thf(sy_v_C,type,
% 3.19/1.82 c: set_b ).
% 3.19/1.82
% 3.19/1.82 thf(sy_v_a,type,
% 3.19/1.82 a2: a > real ).
% 3.19/1.82
% 3.19/1.82 thf(sy_v_aa____,type,
% 3.19/1.82 aa: a > real ).
% 3.19/1.82
% 3.19/1.82 thf(sy_v_f,type,
% 3.19/1.82 f: b > extended_ereal ).
% 3.19/1.82
% 3.19/1.82 thf(sy_v_i____,type,
% 3.19/1.82 i: a ).
% 3.19/1.82
% 3.19/1.82 thf(sy_v_s,type,
% 3.19/1.82 s: set_a ).
% 3.19/1.82
% 3.19/1.82 thf(sy_v_sa____,type,
% 3.19/1.82 sa: set_a ).
% 3.19/1.82
% 3.19/1.82 thf(sy_v_y,type,
% 3.19/1.82 y: a > b ).
% 3.19/1.82
% 3.19/1.82 thf(fact_0_insert_Ohyps_I3_J,axiom,
% 3.19/1.82 ~ ( member_a @ i @ sa ) ).
% 3.19/1.82
% 3.19/1.82 thf(fact_1_asm,axiom,
% 3.19/1.82 ( ( aa @ i )
% 3.19/1.82 != one_one_real ) ).
% 3.19/1.82
% 3.19/1.82 thf(fact_2__092_060open_062_I_092_060Sum_062x_092_060in_062s_O_Aa_Ax_A_K_092_060_094sub_062R_Ay_Ax_A_P_092_060_094sub_062R_A_I1_A_N_Aa_Ai_J_J_A_061_A_I_092_060Sum_062j_092_060in_062s_O_Aa_Aj_A_K_092_060_094sub_062R_Ay_Aj_J_A_P_092_060_094sub_062R_A_I1_A_N_Aa_Ai_J_092_060close_062,axiom,
% 3.19/1.82 ( ( groups1199149371um_a_b
% 3.19/1.82 @ ^ [X: a] : ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) @ ( real_V1035702896aleR_b @ ( aa @ X ) @ ( y @ X ) ) )
% 3.19/1.82 @ sa )
% 3.19/1.82 = ( real_V1035702896aleR_b @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) )
% 3.19/1.82 @ ( groups1199149371um_a_b
% 3.19/1.82 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 3.19/1.82 @ sa ) ) ) ).
% 3.19/1.82
% 3.19/1.82 thf(fact_3_insert_Ohyps_I2_J,axiom,
% 3.19/1.82 sa != bot_bot_set_a ).
% 3.19/1.82
% 3.19/1.82 thf(fact_4_insert_Ohyps_I1_J,axiom,
% 3.19/1.82 finite_finite_a @ sa ).
% 3.19/1.82
% 3.19/1.82 thf(fact_5__092_060open_062f_A_I_I_092_060Sum_062j_092_060in_062s_O_Aa_Aj_A_K_092_060_094sub_062R_Ay_Aj_J_A_L_Aa_Ai_A_K_092_060_094sub_062R_Ay_Ai_J_A_061_Af_A_I_I_I1_A_N_Aa_Ai_J_A_K_Ainverse_A_I1_A_N_Aa_Ai_J_J_A_K_092_060_094sub_062R_A_I_092_060Sum_062j_092_060in_062s_O_Aa_Aj_A_K_092_060_094sub_062R_Ay_Aj_J_A_L_Aa_Ai_A_K_092_060_094sub_062R_Ay_Ai_J_092_060close_062,axiom,
% 3.19/1.82 ( ( f
% 3.19/1.82 @ ( plus_plus_b
% 3.19/1.82 @ ( groups1199149371um_a_b
% 3.19/1.82 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 3.19/1.82 @ sa )
% 3.19/1.82 @ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) )
% 3.19/1.82 = ( f
% 3.19/1.82 @ ( plus_plus_b
% 3.19/1.82 @ ( real_V1035702896aleR_b @ ( times_times_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) )
% 3.19/1.82 @ ( groups1199149371um_a_b
% 3.19/1.82 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 3.19/1.82 @ sa ) )
% 3.19/1.82 @ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ) ).
% 3.19/1.82
% 3.19/1.82 thf(fact_6_calculation,axiom,
% 3.19/1.82 ( ( f
% 3.19/1.82 @ ( groups1199149371um_a_b
% 3.19/1.82 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 3.19/1.82 @ ( insert_a @ i @ sa ) ) )
% 3.19/1.82 = ( f
% 3.19/1.82 @ ( plus_plus_b
% 3.19/1.82 @ ( real_V1035702896aleR_b @ ( times_times_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) )
% 3.19/1.82 @ ( groups1199149371um_a_b
% 3.19/1.82 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 3.19/1.82 @ sa ) )
% 3.19/1.82 @ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ) ).
% 3.19/1.82
% 3.19/1.82 thf(fact_7__092_060open_062f_A_I_092_060Sum_062j_092_060in_062insert_Ai_As_O_Aa_Aj_A_K_092_060_094sub_062R_Ay_Aj_J_A_061_Af_A_I_I_092_060Sum_062j_092_060in_062s_O_Aa_Aj_A_K_092_060_094sub_062R_Ay_Aj_J_A_L_Aa_Ai_A_K_092_060_094sub_062R_Ay_Ai_J_092_060close_062,axiom,
% 3.19/1.83 ( ( f
% 3.19/1.83 @ ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 3.19/1.83 @ ( insert_a @ i @ sa ) ) )
% 3.19/1.83 = ( f
% 3.19/1.83 @ ( plus_plus_b
% 3.19/1.83 @ ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 3.19/1.83 @ sa )
% 3.19/1.83 @ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_8_scaleR__collapse,axiom,
% 3.19/1.83 ! [U: real,A: b] :
% 3.19/1.83 ( ( plus_plus_b @ ( real_V1035702896aleR_b @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V1035702896aleR_b @ U @ A ) )
% 3.19/1.83 = A ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_9_scaleR__collapse,axiom,
% 3.19/1.83 ! [U: real,A: real] :
% 3.19/1.83 ( ( plus_plus_real @ ( real_V453051771R_real @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V453051771R_real @ U @ A ) )
% 3.19/1.83 = A ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_10_scaleR__eq__iff,axiom,
% 3.19/1.83 ! [B: b,U: real,A: b] :
% 3.19/1.83 ( ( ( plus_plus_b @ B @ ( real_V1035702896aleR_b @ U @ A ) )
% 3.19/1.83 = ( plus_plus_b @ A @ ( real_V1035702896aleR_b @ U @ B ) ) )
% 3.19/1.83 = ( ( A = B )
% 3.19/1.83 | ( U = one_one_real ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_11_scaleR__eq__iff,axiom,
% 3.19/1.83 ! [B: real,U: real,A: real] :
% 3.19/1.83 ( ( ( plus_plus_real @ B @ ( real_V453051771R_real @ U @ A ) )
% 3.19/1.83 = ( plus_plus_real @ A @ ( real_V453051771R_real @ U @ B ) ) )
% 3.19/1.83 = ( ( A = B )
% 3.19/1.83 | ( U = one_one_real ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_12_yai_I1_J,axiom,
% 3.19/1.83 member_b @ ( y @ i ) @ c ).
% 3.19/1.83
% 3.19/1.83 thf(fact_13_scaleR__scaleR,axiom,
% 3.19/1.83 ! [A: real,B: real,X2: b] :
% 3.19/1.83 ( ( real_V1035702896aleR_b @ A @ ( real_V1035702896aleR_b @ B @ X2 ) )
% 3.19/1.83 = ( real_V1035702896aleR_b @ ( times_times_real @ A @ B ) @ X2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_14_scaleR__scaleR,axiom,
% 3.19/1.83 ! [A: real,B: real,X2: real] :
% 3.19/1.83 ( ( real_V453051771R_real @ A @ ( real_V453051771R_real @ B @ X2 ) )
% 3.19/1.83 = ( real_V453051771R_real @ ( times_times_real @ A @ B ) @ X2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_15_scaleR__one,axiom,
% 3.19/1.83 ! [X2: b] :
% 3.19/1.83 ( ( real_V1035702896aleR_b @ one_one_real @ X2 )
% 3.19/1.83 = X2 ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_16_scaleR__one,axiom,
% 3.19/1.83 ! [X2: real] :
% 3.19/1.83 ( ( real_V453051771R_real @ one_one_real @ X2 )
% 3.19/1.83 = X2 ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_17__092_060open_062sum_Aa_As_A_061_A1_A_N_Aa_Ai_092_060close_062,axiom,
% 3.19/1.83 ( ( groups1862963056a_real @ aa @ sa )
% 3.19/1.83 = ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_18_inverse__eq__1__iff,axiom,
% 3.19/1.83 ! [X2: real] :
% 3.19/1.83 ( ( ( inverse_inverse_real @ X2 )
% 3.19/1.83 = one_one_real )
% 3.19/1.83 = ( X2 = one_one_real ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_19_inverse__1,axiom,
% 3.19/1.83 ( ( inverse_inverse_real @ one_one_real )
% 3.19/1.83 = one_one_real ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_20_inverse__mult__distrib,axiom,
% 3.19/1.83 ! [A: real,B: real] :
% 3.19/1.83 ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 3.19/1.83 = ( times_times_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_21_mult__scaleR__left,axiom,
% 3.19/1.83 ! [A: real,X2: real,Y: real] :
% 3.19/1.83 ( ( times_times_real @ ( real_V453051771R_real @ A @ X2 ) @ Y )
% 3.19/1.83 = ( real_V453051771R_real @ A @ ( times_times_real @ X2 @ Y ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_22_assms_I1_J,axiom,
% 3.19/1.83 finite_finite_a @ s ).
% 3.19/1.83
% 3.19/1.83 thf(fact_23_assms_I2_J,axiom,
% 3.19/1.83 s != bot_bot_set_a ).
% 3.19/1.83
% 3.19/1.83 thf(fact_24_assms_I7_J,axiom,
% 3.19/1.83 ! [I: a] :
% 3.19/1.83 ( ( member_a @ I @ s )
% 3.19/1.83 => ( member_b @ ( y @ I ) @ c ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_25_insert_Oprems_I3_J,axiom,
% 3.19/1.83 ! [I: a] :
% 3.19/1.83 ( ( member_a @ I @ ( insert_a @ i @ sa ) )
% 3.19/1.83 => ( member_b @ ( y @ I ) @ c ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_26_inverse__inverse__eq,axiom,
% 3.19/1.83 ! [A: real] :
% 3.19/1.83 ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 3.19/1.83 = A ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_27_inverse__eq__iff__eq,axiom,
% 3.19/1.83 ! [A: real,B: real] :
% 3.19/1.83 ( ( ( inverse_inverse_real @ A )
% 3.19/1.83 = ( inverse_inverse_real @ B ) )
% 3.19/1.83 = ( A = B ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_28_insert_Oprems_I1_J,axiom,
% 3.19/1.83 ( ( groups1862963056a_real @ aa @ ( insert_a @ i @ sa ) )
% 3.19/1.83 = one_one_real ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_29_assms_I3_J,axiom,
% 3.19/1.83 lower_311861425x_on_b @ c @ f ).
% 3.19/1.83
% 3.19/1.83 thf(fact_30_fis,axiom,
% 3.19/1.83 finite_finite_a @ ( insert_a @ i @ sa ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_31_mult__scaleR__right,axiom,
% 3.19/1.83 ! [X2: real,A: real,Y: real] :
% 3.19/1.83 ( ( times_times_real @ X2 @ ( real_V453051771R_real @ A @ Y ) )
% 3.19/1.83 = ( real_V453051771R_real @ A @ ( times_times_real @ X2 @ Y ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_32_assms_I4_J,axiom,
% 3.19/1.83 convex_b @ c ).
% 3.19/1.83
% 3.19/1.83 thf(fact_33_assms_I5_J,axiom,
% 3.19/1.83 ( ( groups1862963056a_real @ a2 @ s )
% 3.19/1.83 = one_one_real ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_34_real__scaleR__def,axiom,
% 3.19/1.83 real_V453051771R_real = times_times_real ).
% 3.19/1.83
% 3.19/1.83 thf(fact_35_scale__left__commute,axiom,
% 3.19/1.83 ! [A: real,B: real,X2: b] :
% 3.19/1.83 ( ( real_V1035702896aleR_b @ A @ ( real_V1035702896aleR_b @ B @ X2 ) )
% 3.19/1.83 = ( real_V1035702896aleR_b @ B @ ( real_V1035702896aleR_b @ A @ X2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_36_scale__left__commute,axiom,
% 3.19/1.83 ! [A: real,B: real,X2: real] :
% 3.19/1.83 ( ( real_V453051771R_real @ A @ ( real_V453051771R_real @ B @ X2 ) )
% 3.19/1.83 = ( real_V453051771R_real @ B @ ( real_V453051771R_real @ A @ X2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_37_inverse__eq__imp__eq,axiom,
% 3.19/1.83 ! [A: real,B: real] :
% 3.19/1.83 ( ( ( inverse_inverse_real @ A )
% 3.19/1.83 = ( inverse_inverse_real @ B ) )
% 3.19/1.83 => ( A = B ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_38_scaleR__add__right,axiom,
% 3.19/1.83 ! [A: real,X2: b,Y: b] :
% 3.19/1.83 ( ( real_V1035702896aleR_b @ A @ ( plus_plus_b @ X2 @ Y ) )
% 3.19/1.83 = ( plus_plus_b @ ( real_V1035702896aleR_b @ A @ X2 ) @ ( real_V1035702896aleR_b @ A @ Y ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_39_scaleR__add__right,axiom,
% 3.19/1.83 ! [A: real,X2: real,Y: real] :
% 3.19/1.83 ( ( real_V453051771R_real @ A @ ( plus_plus_real @ X2 @ Y ) )
% 3.19/1.83 = ( plus_plus_real @ ( real_V453051771R_real @ A @ X2 ) @ ( real_V453051771R_real @ A @ Y ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_40_scaleR__add__left,axiom,
% 3.19/1.83 ! [A: real,B: real,X2: b] :
% 3.19/1.83 ( ( real_V1035702896aleR_b @ ( plus_plus_real @ A @ B ) @ X2 )
% 3.19/1.83 = ( plus_plus_b @ ( real_V1035702896aleR_b @ A @ X2 ) @ ( real_V1035702896aleR_b @ B @ X2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_41_scaleR__add__left,axiom,
% 3.19/1.83 ! [A: real,B: real,X2: real] :
% 3.19/1.83 ( ( real_V453051771R_real @ ( plus_plus_real @ A @ B ) @ X2 )
% 3.19/1.83 = ( plus_plus_real @ ( real_V453051771R_real @ A @ X2 ) @ ( real_V453051771R_real @ B @ X2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_42_scaleR__left_Oadd,axiom,
% 3.19/1.83 ! [X2: real,Y: real,Xa: b] :
% 3.19/1.83 ( ( real_V1035702896aleR_b @ ( plus_plus_real @ X2 @ Y ) @ Xa )
% 3.19/1.83 = ( plus_plus_b @ ( real_V1035702896aleR_b @ X2 @ Xa ) @ ( real_V1035702896aleR_b @ Y @ Xa ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_43_scaleR__left_Oadd,axiom,
% 3.19/1.83 ! [X2: real,Y: real,Xa: real] :
% 3.19/1.83 ( ( real_V453051771R_real @ ( plus_plus_real @ X2 @ Y ) @ Xa )
% 3.19/1.83 = ( plus_plus_real @ ( real_V453051771R_real @ X2 @ Xa ) @ ( real_V453051771R_real @ Y @ Xa ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_44_scale__right__diff__distrib,axiom,
% 3.19/1.83 ! [A: real,X2: b,Y: b] :
% 3.19/1.83 ( ( real_V1035702896aleR_b @ A @ ( minus_minus_b @ X2 @ Y ) )
% 3.19/1.83 = ( minus_minus_b @ ( real_V1035702896aleR_b @ A @ X2 ) @ ( real_V1035702896aleR_b @ A @ Y ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_45_scale__right__diff__distrib,axiom,
% 3.19/1.83 ! [A: real,X2: real,Y: real] :
% 3.19/1.83 ( ( real_V453051771R_real @ A @ ( minus_minus_real @ X2 @ Y ) )
% 3.19/1.83 = ( minus_minus_real @ ( real_V453051771R_real @ A @ X2 ) @ ( real_V453051771R_real @ A @ Y ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_46_mult__commute__imp__mult__inverse__commute,axiom,
% 3.19/1.83 ! [Y: real,X2: real] :
% 3.19/1.83 ( ( ( times_times_real @ Y @ X2 )
% 3.19/1.83 = ( times_times_real @ X2 @ Y ) )
% 3.19/1.83 => ( ( times_times_real @ ( inverse_inverse_real @ Y ) @ X2 )
% 3.19/1.83 = ( times_times_real @ X2 @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_47_scale__sum__right,axiom,
% 3.19/1.83 ! [A: real,F: a > b,A2: set_a] :
% 3.19/1.83 ( ( real_V1035702896aleR_b @ A @ ( groups1199149371um_a_b @ F @ A2 ) )
% 3.19/1.83 = ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [X: a] : ( real_V1035702896aleR_b @ A @ ( F @ X ) )
% 3.19/1.83 @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_48_scale__sum__right,axiom,
% 3.19/1.83 ! [A: real,F: a > real,A2: set_a] :
% 3.19/1.83 ( ( real_V453051771R_real @ A @ ( groups1862963056a_real @ F @ A2 ) )
% 3.19/1.83 = ( groups1862963056a_real
% 3.19/1.83 @ ^ [X: a] : ( real_V453051771R_real @ A @ ( F @ X ) )
% 3.19/1.83 @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_49_scale__sum__left,axiom,
% 3.19/1.83 ! [F: a > real,A2: set_a,X2: b] :
% 3.19/1.83 ( ( real_V1035702896aleR_b @ ( groups1862963056a_real @ F @ A2 ) @ X2 )
% 3.19/1.83 = ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [A3: a] : ( real_V1035702896aleR_b @ ( F @ A3 ) @ X2 )
% 3.19/1.83 @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_50_scale__sum__left,axiom,
% 3.19/1.83 ! [F: a > real,A2: set_a,X2: real] :
% 3.19/1.83 ( ( real_V453051771R_real @ ( groups1862963056a_real @ F @ A2 ) @ X2 )
% 3.19/1.83 = ( groups1862963056a_real
% 3.19/1.83 @ ^ [A3: a] : ( real_V453051771R_real @ ( F @ A3 ) @ X2 )
% 3.19/1.83 @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_51_scaleR__right_Osum,axiom,
% 3.19/1.83 ! [A: real,G: a > b,A2: set_a] :
% 3.19/1.83 ( ( real_V1035702896aleR_b @ A @ ( groups1199149371um_a_b @ G @ A2 ) )
% 3.19/1.83 = ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [X: a] : ( real_V1035702896aleR_b @ A @ ( G @ X ) )
% 3.19/1.83 @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_52_scaleR__right_Osum,axiom,
% 3.19/1.83 ! [A: real,G: a > real,A2: set_a] :
% 3.19/1.83 ( ( real_V453051771R_real @ A @ ( groups1862963056a_real @ G @ A2 ) )
% 3.19/1.83 = ( groups1862963056a_real
% 3.19/1.83 @ ^ [X: a] : ( real_V453051771R_real @ A @ ( G @ X ) )
% 3.19/1.83 @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_53_scaleR__left_Osum,axiom,
% 3.19/1.83 ! [G: a > real,A2: set_a,X2: b] :
% 3.19/1.83 ( ( real_V1035702896aleR_b @ ( groups1862963056a_real @ G @ A2 ) @ X2 )
% 3.19/1.83 = ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [X: a] : ( real_V1035702896aleR_b @ ( G @ X ) @ X2 )
% 3.19/1.83 @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_54_scaleR__left_Osum,axiom,
% 3.19/1.83 ! [G: a > real,A2: set_a,X2: real] :
% 3.19/1.83 ( ( real_V453051771R_real @ ( groups1862963056a_real @ G @ A2 ) @ X2 )
% 3.19/1.83 = ( groups1862963056a_real
% 3.19/1.83 @ ^ [X: a] : ( real_V453051771R_real @ ( G @ X ) @ X2 )
% 3.19/1.83 @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_55_inverse__unique,axiom,
% 3.19/1.83 ! [A: real,B: real] :
% 3.19/1.83 ( ( ( times_times_real @ A @ B )
% 3.19/1.83 = one_one_real )
% 3.19/1.83 => ( ( inverse_inverse_real @ A )
% 3.19/1.83 = B ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_56_scale__left__diff__distrib,axiom,
% 3.19/1.83 ! [A: real,B: real,X2: b] :
% 3.19/1.83 ( ( real_V1035702896aleR_b @ ( minus_minus_real @ A @ B ) @ X2 )
% 3.19/1.83 = ( minus_minus_b @ ( real_V1035702896aleR_b @ A @ X2 ) @ ( real_V1035702896aleR_b @ B @ X2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_57_scale__left__diff__distrib,axiom,
% 3.19/1.83 ! [A: real,B: real,X2: real] :
% 3.19/1.83 ( ( real_V453051771R_real @ ( minus_minus_real @ A @ B ) @ X2 )
% 3.19/1.83 = ( minus_minus_real @ ( real_V453051771R_real @ A @ X2 ) @ ( real_V453051771R_real @ B @ X2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_58_scaleR__left_Odiff,axiom,
% 3.19/1.83 ! [X2: real,Y: real,Xa: b] :
% 3.19/1.83 ( ( real_V1035702896aleR_b @ ( minus_minus_real @ X2 @ Y ) @ Xa )
% 3.19/1.83 = ( minus_minus_b @ ( real_V1035702896aleR_b @ X2 @ Xa ) @ ( real_V1035702896aleR_b @ Y @ Xa ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_59_scaleR__left_Odiff,axiom,
% 3.19/1.83 ! [X2: real,Y: real,Xa: real] :
% 3.19/1.83 ( ( real_V453051771R_real @ ( minus_minus_real @ X2 @ Y ) @ Xa )
% 3.19/1.83 = ( minus_minus_real @ ( real_V453051771R_real @ X2 @ Xa ) @ ( real_V453051771R_real @ Y @ Xa ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_60_mem__Collect__eq,axiom,
% 3.19/1.83 ! [A: a,P: a > $o] :
% 3.19/1.83 ( ( member_a @ A @ ( collect_a @ P ) )
% 3.19/1.83 = ( P @ A ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_61_mem__Collect__eq,axiom,
% 3.19/1.83 ! [A: b,P: b > $o] :
% 3.19/1.83 ( ( member_b @ A @ ( collect_b @ P ) )
% 3.19/1.83 = ( P @ A ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_62_Collect__mem__eq,axiom,
% 3.19/1.83 ! [A2: set_a] :
% 3.19/1.83 ( ( collect_a
% 3.19/1.83 @ ^ [X: a] : ( member_a @ X @ A2 ) )
% 3.19/1.83 = A2 ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_63_Collect__mem__eq,axiom,
% 3.19/1.83 ! [A2: set_b] :
% 3.19/1.83 ( ( collect_b
% 3.19/1.83 @ ^ [X: b] : ( member_b @ X @ A2 ) )
% 3.19/1.83 = A2 ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_64_inverse__scaleR__distrib,axiom,
% 3.19/1.83 ! [A: real,X2: real] :
% 3.19/1.83 ( ( inverse_inverse_real @ ( real_V453051771R_real @ A @ X2 ) )
% 3.19/1.83 = ( real_V453051771R_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ X2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_65_asum,axiom,
% 3.19/1.83 ( member_b
% 3.19/1.83 @ ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( divide_divide_real @ ( aa @ J ) @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) @ ( y @ J ) )
% 3.19/1.83 @ sa )
% 3.19/1.83 @ c ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_66_sum_Oinsert,axiom,
% 3.19/1.83 ! [A2: set_b,X2: b,G: b > b] :
% 3.19/1.83 ( ( finite_finite_b @ A2 )
% 3.19/1.83 => ( ~ ( member_b @ X2 @ A2 )
% 3.19/1.83 => ( ( groups2026918778um_b_b @ G @ ( insert_b @ X2 @ A2 ) )
% 3.19/1.83 = ( plus_plus_b @ ( G @ X2 ) @ ( groups2026918778um_b_b @ G @ A2 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_67_sum_Oinsert,axiom,
% 3.19/1.83 ! [A2: set_b,X2: b,G: b > real] :
% 3.19/1.83 ( ( finite_finite_b @ A2 )
% 3.19/1.83 => ( ~ ( member_b @ X2 @ A2 )
% 3.19/1.83 => ( ( groups583146225b_real @ G @ ( insert_b @ X2 @ A2 ) )
% 3.19/1.83 = ( plus_plus_real @ ( G @ X2 ) @ ( groups583146225b_real @ G @ A2 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_68_sum_Oinsert,axiom,
% 3.19/1.83 ! [A2: set_a,X2: a,G: a > b] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ~ ( member_a @ X2 @ A2 )
% 3.19/1.83 => ( ( groups1199149371um_a_b @ G @ ( insert_a @ X2 @ A2 ) )
% 3.19/1.83 = ( plus_plus_b @ ( G @ X2 ) @ ( groups1199149371um_a_b @ G @ A2 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_69_sum_Oinsert,axiom,
% 3.19/1.83 ! [A2: set_a,X2: a,G: a > real] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ~ ( member_a @ X2 @ A2 )
% 3.19/1.83 => ( ( groups1862963056a_real @ G @ ( insert_a @ X2 @ A2 ) )
% 3.19/1.83 = ( plus_plus_real @ ( G @ X2 ) @ ( groups1862963056a_real @ G @ A2 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_70_affine__hull__finite__step,axiom,
% 3.19/1.83 ! [S: set_b,A: b,W: real,Y: b] :
% 3.19/1.83 ( ( finite_finite_b @ S )
% 3.19/1.83 => ( ( ? [U2: b > real] :
% 3.19/1.83 ( ( ( groups583146225b_real @ U2 @ ( insert_b @ A @ S ) )
% 3.19/1.83 = W )
% 3.19/1.83 & ( ( groups2026918778um_b_b
% 3.19/1.83 @ ^ [X: b] : ( real_V1035702896aleR_b @ ( U2 @ X ) @ X )
% 3.19/1.83 @ ( insert_b @ A @ S ) )
% 3.19/1.83 = Y ) ) )
% 3.19/1.83 = ( ? [V: real,U2: b > real] :
% 3.19/1.83 ( ( ( groups583146225b_real @ U2 @ S )
% 3.19/1.83 = ( minus_minus_real @ W @ V ) )
% 3.19/1.83 & ( ( groups2026918778um_b_b
% 3.19/1.83 @ ^ [X: b] : ( real_V1035702896aleR_b @ ( U2 @ X ) @ X )
% 3.19/1.83 @ S )
% 3.19/1.83 = ( minus_minus_b @ Y @ ( real_V1035702896aleR_b @ V @ A ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_71_affine__hull__finite__step,axiom,
% 3.19/1.83 ! [S: set_real,A: real,W: real,Y: real] :
% 3.19/1.83 ( ( finite_finite_real @ S )
% 3.19/1.83 => ( ( ? [U2: real > real] :
% 3.19/1.83 ( ( ( groups1296524820l_real @ U2 @ ( insert_real @ A @ S ) )
% 3.19/1.83 = W )
% 3.19/1.83 & ( ( groups1296524820l_real
% 3.19/1.83 @ ^ [X: real] : ( real_V453051771R_real @ ( U2 @ X ) @ X )
% 3.19/1.83 @ ( insert_real @ A @ S ) )
% 3.19/1.83 = Y ) ) )
% 3.19/1.83 = ( ? [V: real,U2: real > real] :
% 3.19/1.83 ( ( ( groups1296524820l_real @ U2 @ S )
% 3.19/1.83 = ( minus_minus_real @ W @ V ) )
% 3.19/1.83 & ( ( groups1296524820l_real
% 3.19/1.83 @ ^ [X: real] : ( real_V453051771R_real @ ( U2 @ X ) @ X )
% 3.19/1.83 @ S )
% 3.19/1.83 = ( minus_minus_real @ Y @ ( real_V453051771R_real @ V @ A ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_72_a1,axiom,
% 3.19/1.83 ( ( groups1862963056a_real
% 3.19/1.83 @ ^ [J: a] : ( divide_divide_real @ ( aa @ J ) @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) )
% 3.19/1.83 @ sa )
% 3.19/1.83 = one_one_real ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_73__092_060open_062sum_Aa_As_A_P_A_I1_A_N_Aa_Ai_J_A_061_A1_092_060close_062,axiom,
% 3.19/1.83 ( ( divide_divide_real @ ( groups1862963056a_real @ aa @ sa ) @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) )
% 3.19/1.83 = one_one_real ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_74_singleton__conv,axiom,
% 3.19/1.83 ! [A: a] :
% 3.19/1.83 ( ( collect_a
% 3.19/1.83 @ ^ [X: a] : ( X = A ) )
% 3.19/1.83 = ( insert_a @ A @ bot_bot_set_a ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_75_singleton__conv2,axiom,
% 3.19/1.83 ! [A: a] :
% 3.19/1.83 ( ( collect_a
% 3.19/1.83 @ ( ^ [Y2: a,Z: a] : ( Y2 = Z )
% 3.19/1.83 @ A ) )
% 3.19/1.83 = ( insert_a @ A @ bot_bot_set_a ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_76_finite__insert,axiom,
% 3.19/1.83 ! [A: a,A2: set_a] :
% 3.19/1.83 ( ( finite_finite_a @ ( insert_a @ A @ A2 ) )
% 3.19/1.83 = ( finite_finite_a @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_77_sum__diff1,axiom,
% 3.19/1.83 ! [A2: set_b,A: b,F: b > real] :
% 3.19/1.83 ( ( finite_finite_b @ A2 )
% 3.19/1.83 => ( ( ( member_b @ A @ A2 )
% 3.19/1.83 => ( ( groups583146225b_real @ F @ ( minus_minus_set_b @ A2 @ ( insert_b @ A @ bot_bot_set_b ) ) )
% 3.19/1.83 = ( minus_minus_real @ ( groups583146225b_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.19/1.83 & ( ~ ( member_b @ A @ A2 )
% 3.19/1.83 => ( ( groups583146225b_real @ F @ ( minus_minus_set_b @ A2 @ ( insert_b @ A @ bot_bot_set_b ) ) )
% 3.19/1.83 = ( groups583146225b_real @ F @ A2 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_78_sum__diff1,axiom,
% 3.19/1.83 ! [A2: set_a,A: a,F: a > b] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ( ( member_a @ A @ A2 )
% 3.19/1.83 => ( ( groups1199149371um_a_b @ F @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 3.19/1.83 = ( minus_minus_b @ ( groups1199149371um_a_b @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.19/1.83 & ( ~ ( member_a @ A @ A2 )
% 3.19/1.83 => ( ( groups1199149371um_a_b @ F @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 3.19/1.83 = ( groups1199149371um_a_b @ F @ A2 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_79_sum__diff1,axiom,
% 3.19/1.83 ! [A2: set_a,A: a,F: a > real] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ( ( member_a @ A @ A2 )
% 3.19/1.83 => ( ( groups1862963056a_real @ F @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 3.19/1.83 = ( minus_minus_real @ ( groups1862963056a_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.19/1.83 & ( ~ ( member_a @ A @ A2 )
% 3.19/1.83 => ( ( groups1862963056a_real @ F @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 3.19/1.83 = ( groups1862963056a_real @ F @ A2 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_80_singletonI,axiom,
% 3.19/1.83 ! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_81_singletonI,axiom,
% 3.19/1.83 ! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_82_empty__Collect__eq,axiom,
% 3.19/1.83 ! [P: a > $o] :
% 3.19/1.83 ( ( bot_bot_set_a
% 3.19/1.83 = ( collect_a @ P ) )
% 3.19/1.83 = ( ! [X: a] :
% 3.19/1.83 ~ ( P @ X ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_83_Collect__empty__eq,axiom,
% 3.19/1.83 ! [P: a > $o] :
% 3.19/1.83 ( ( ( collect_a @ P )
% 3.19/1.83 = bot_bot_set_a )
% 3.19/1.83 = ( ! [X: a] :
% 3.19/1.83 ~ ( P @ X ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_84_all__not__in__conv,axiom,
% 3.19/1.83 ! [A2: set_b] :
% 3.19/1.83 ( ( ! [X: b] :
% 3.19/1.83 ~ ( member_b @ X @ A2 ) )
% 3.19/1.83 = ( A2 = bot_bot_set_b ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_85_all__not__in__conv,axiom,
% 3.19/1.83 ! [A2: set_a] :
% 3.19/1.83 ( ( ! [X: a] :
% 3.19/1.83 ~ ( member_a @ X @ A2 ) )
% 3.19/1.83 = ( A2 = bot_bot_set_a ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_86_empty__iff,axiom,
% 3.19/1.83 ! [C: b] :
% 3.19/1.83 ~ ( member_b @ C @ bot_bot_set_b ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_87_empty__iff,axiom,
% 3.19/1.83 ! [C: a] :
% 3.19/1.83 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_88_insert__absorb2,axiom,
% 3.19/1.83 ! [X2: a,A2: set_a] :
% 3.19/1.83 ( ( insert_a @ X2 @ ( insert_a @ X2 @ A2 ) )
% 3.19/1.83 = ( insert_a @ X2 @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_89_insert__iff,axiom,
% 3.19/1.83 ! [A: a,B: a,A2: set_a] :
% 3.19/1.83 ( ( member_a @ A @ ( insert_a @ B @ A2 ) )
% 3.19/1.83 = ( ( A = B )
% 3.19/1.83 | ( member_a @ A @ A2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_90_insert__iff,axiom,
% 3.19/1.83 ! [A: b,B: b,A2: set_b] :
% 3.19/1.83 ( ( member_b @ A @ ( insert_b @ B @ A2 ) )
% 3.19/1.83 = ( ( A = B )
% 3.19/1.83 | ( member_b @ A @ A2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_91_insertCI,axiom,
% 3.19/1.83 ! [A: a,B2: set_a,B: a] :
% 3.19/1.83 ( ( ~ ( member_a @ A @ B2 )
% 3.19/1.83 => ( A = B ) )
% 3.19/1.83 => ( member_a @ A @ ( insert_a @ B @ B2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_92_insertCI,axiom,
% 3.19/1.83 ! [A: b,B2: set_b,B: b] :
% 3.19/1.83 ( ( ~ ( member_b @ A @ B2 )
% 3.19/1.83 => ( A = B ) )
% 3.19/1.83 => ( member_b @ A @ ( insert_b @ B @ B2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_93_Diff__iff,axiom,
% 3.19/1.83 ! [C: a,A2: set_a,B2: set_a] :
% 3.19/1.83 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B2 ) )
% 3.19/1.83 = ( ( member_a @ C @ A2 )
% 3.19/1.83 & ~ ( member_a @ C @ B2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_94_Diff__iff,axiom,
% 3.19/1.83 ! [C: b,A2: set_b,B2: set_b] :
% 3.19/1.83 ( ( member_b @ C @ ( minus_minus_set_b @ A2 @ B2 ) )
% 3.19/1.83 = ( ( member_b @ C @ A2 )
% 3.19/1.83 & ~ ( member_b @ C @ B2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_95_DiffI,axiom,
% 3.19/1.83 ! [C: a,A2: set_a,B2: set_a] :
% 3.19/1.83 ( ( member_a @ C @ A2 )
% 3.19/1.83 => ( ~ ( member_a @ C @ B2 )
% 3.19/1.83 => ( member_a @ C @ ( minus_minus_set_a @ A2 @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_96_DiffI,axiom,
% 3.19/1.83 ! [C: b,A2: set_b,B2: set_b] :
% 3.19/1.83 ( ( member_b @ C @ A2 )
% 3.19/1.83 => ( ~ ( member_b @ C @ B2 )
% 3.19/1.83 => ( member_b @ C @ ( minus_minus_set_b @ A2 @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_97_finite__Collect__disjI,axiom,
% 3.19/1.83 ! [P: a > $o,Q: a > $o] :
% 3.19/1.83 ( ( finite_finite_a
% 3.19/1.83 @ ( collect_a
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( ( P @ X )
% 3.19/1.83 | ( Q @ X ) ) ) )
% 3.19/1.83 = ( ( finite_finite_a @ ( collect_a @ P ) )
% 3.19/1.83 & ( finite_finite_a @ ( collect_a @ Q ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_98_finite__Collect__conjI,axiom,
% 3.19/1.83 ! [P: a > $o,Q: a > $o] :
% 3.19/1.83 ( ( ( finite_finite_a @ ( collect_a @ P ) )
% 3.19/1.83 | ( finite_finite_a @ ( collect_a @ Q ) ) )
% 3.19/1.83 => ( finite_finite_a
% 3.19/1.83 @ ( collect_a
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( ( P @ X )
% 3.19/1.83 & ( Q @ X ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_99_times__divide__eq__left,axiom,
% 3.19/1.83 ! [B: real,C: real,A: real] :
% 3.19/1.83 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 3.19/1.83 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_100_divide__divide__eq__left,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 3.19/1.83 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_101_divide__divide__eq__right,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 3.19/1.83 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_102_times__divide__eq__right,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 3.19/1.83 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_103_Diff__cancel,axiom,
% 3.19/1.83 ! [A2: set_a] :
% 3.19/1.83 ( ( minus_minus_set_a @ A2 @ A2 )
% 3.19/1.83 = bot_bot_set_a ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_104_empty__Diff,axiom,
% 3.19/1.83 ! [A2: set_a] :
% 3.19/1.83 ( ( minus_minus_set_a @ bot_bot_set_a @ A2 )
% 3.19/1.83 = bot_bot_set_a ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_105_Diff__empty,axiom,
% 3.19/1.83 ! [A2: set_a] :
% 3.19/1.83 ( ( minus_minus_set_a @ A2 @ bot_bot_set_a )
% 3.19/1.83 = A2 ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_106_finite__Diff2,axiom,
% 3.19/1.83 ! [B2: set_a,A2: set_a] :
% 3.19/1.83 ( ( finite_finite_a @ B2 )
% 3.19/1.83 => ( ( finite_finite_a @ ( minus_minus_set_a @ A2 @ B2 ) )
% 3.19/1.83 = ( finite_finite_a @ A2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_107_finite__Diff,axiom,
% 3.19/1.83 ! [A2: set_a,B2: set_a] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( finite_finite_a @ ( minus_minus_set_a @ A2 @ B2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_108_insert__Diff1,axiom,
% 3.19/1.83 ! [X2: a,B2: set_a,A2: set_a] :
% 3.19/1.83 ( ( member_a @ X2 @ B2 )
% 3.19/1.83 => ( ( minus_minus_set_a @ ( insert_a @ X2 @ A2 ) @ B2 )
% 3.19/1.83 = ( minus_minus_set_a @ A2 @ B2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_109_insert__Diff1,axiom,
% 3.19/1.83 ! [X2: b,B2: set_b,A2: set_b] :
% 3.19/1.83 ( ( member_b @ X2 @ B2 )
% 3.19/1.83 => ( ( minus_minus_set_b @ ( insert_b @ X2 @ A2 ) @ B2 )
% 3.19/1.83 = ( minus_minus_set_b @ A2 @ B2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_110_Diff__insert0,axiom,
% 3.19/1.83 ! [X2: a,A2: set_a,B2: set_a] :
% 3.19/1.83 ( ~ ( member_a @ X2 @ A2 )
% 3.19/1.83 => ( ( minus_minus_set_a @ A2 @ ( insert_a @ X2 @ B2 ) )
% 3.19/1.83 = ( minus_minus_set_a @ A2 @ B2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_111_Diff__insert0,axiom,
% 3.19/1.83 ! [X2: b,A2: set_b,B2: set_b] :
% 3.19/1.83 ( ~ ( member_b @ X2 @ A2 )
% 3.19/1.83 => ( ( minus_minus_set_b @ A2 @ ( insert_b @ X2 @ B2 ) )
% 3.19/1.83 = ( minus_minus_set_b @ A2 @ B2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_112_inverse__divide,axiom,
% 3.19/1.83 ! [A: real,B: real] :
% 3.19/1.83 ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 3.19/1.83 = ( divide_divide_real @ B @ A ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_113_insert__Diff__single,axiom,
% 3.19/1.83 ! [A: a,A2: set_a] :
% 3.19/1.83 ( ( insert_a @ A @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 3.19/1.83 = ( insert_a @ A @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_114_finite__Diff__insert,axiom,
% 3.19/1.83 ! [A2: set_a,A: a,B2: set_a] :
% 3.19/1.83 ( ( finite_finite_a @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ B2 ) ) )
% 3.19/1.83 = ( finite_finite_a @ ( minus_minus_set_a @ A2 @ B2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_115_sum__diff1__nat,axiom,
% 3.19/1.83 ! [A: b,A2: set_b,F: b > nat] :
% 3.19/1.83 ( ( ( member_b @ A @ A2 )
% 3.19/1.83 => ( ( groups2098481813_b_nat @ F @ ( minus_minus_set_b @ A2 @ ( insert_b @ A @ bot_bot_set_b ) ) )
% 3.19/1.83 = ( minus_minus_nat @ ( groups2098481813_b_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.19/1.83 & ( ~ ( member_b @ A @ A2 )
% 3.19/1.83 => ( ( groups2098481813_b_nat @ F @ ( minus_minus_set_b @ A2 @ ( insert_b @ A @ bot_bot_set_b ) ) )
% 3.19/1.83 = ( groups2098481813_b_nat @ F @ A2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_116_sum__diff1__nat,axiom,
% 3.19/1.83 ! [A: a,A2: set_a,F: a > nat] :
% 3.19/1.83 ( ( ( member_a @ A @ A2 )
% 3.19/1.83 => ( ( groups769445524_a_nat @ F @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 3.19/1.83 = ( minus_minus_nat @ ( groups769445524_a_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.19/1.83 & ( ~ ( member_a @ A @ A2 )
% 3.19/1.83 => ( ( groups769445524_a_nat @ F @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 3.19/1.83 = ( groups769445524_a_nat @ F @ A2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_117_minus__set__def,axiom,
% 3.19/1.83 ( minus_minus_set_a
% 3.19/1.83 = ( ^ [A4: set_a,B3: set_a] :
% 3.19/1.83 ( collect_a
% 3.19/1.83 @ ( minus_minus_a_o
% 3.19/1.83 @ ^ [X: a] : ( member_a @ X @ A4 )
% 3.19/1.83 @ ^ [X: a] : ( member_a @ X @ B3 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_118_minus__set__def,axiom,
% 3.19/1.83 ( minus_minus_set_b
% 3.19/1.83 = ( ^ [A4: set_b,B3: set_b] :
% 3.19/1.83 ( collect_b
% 3.19/1.83 @ ( minus_minus_b_o
% 3.19/1.83 @ ^ [X: b] : ( member_b @ X @ A4 )
% 3.19/1.83 @ ^ [X: b] : ( member_b @ X @ B3 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_119_set__diff__eq,axiom,
% 3.19/1.83 ( minus_minus_set_a
% 3.19/1.83 = ( ^ [A4: set_a,B3: set_a] :
% 3.19/1.83 ( collect_a
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( ( member_a @ X @ A4 )
% 3.19/1.83 & ~ ( member_a @ X @ B3 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_120_set__diff__eq,axiom,
% 3.19/1.83 ( minus_minus_set_b
% 3.19/1.83 = ( ^ [A4: set_b,B3: set_b] :
% 3.19/1.83 ( collect_b
% 3.19/1.83 @ ^ [X: b] :
% 3.19/1.83 ( ( member_b @ X @ A4 )
% 3.19/1.83 & ~ ( member_b @ X @ B3 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_121_DiffD2,axiom,
% 3.19/1.83 ! [C: a,A2: set_a,B2: set_a] :
% 3.19/1.83 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B2 ) )
% 3.19/1.83 => ~ ( member_a @ C @ B2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_122_DiffD2,axiom,
% 3.19/1.83 ! [C: b,A2: set_b,B2: set_b] :
% 3.19/1.83 ( ( member_b @ C @ ( minus_minus_set_b @ A2 @ B2 ) )
% 3.19/1.83 => ~ ( member_b @ C @ B2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_123_DiffD1,axiom,
% 3.19/1.83 ! [C: a,A2: set_a,B2: set_a] :
% 3.19/1.83 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B2 ) )
% 3.19/1.83 => ( member_a @ C @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_124_DiffD1,axiom,
% 3.19/1.83 ! [C: b,A2: set_b,B2: set_b] :
% 3.19/1.83 ( ( member_b @ C @ ( minus_minus_set_b @ A2 @ B2 ) )
% 3.19/1.83 => ( member_b @ C @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_125_DiffE,axiom,
% 3.19/1.83 ! [C: a,A2: set_a,B2: set_a] :
% 3.19/1.83 ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B2 ) )
% 3.19/1.83 => ~ ( ( member_a @ C @ A2 )
% 3.19/1.83 => ( member_a @ C @ B2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_126_DiffE,axiom,
% 3.19/1.83 ! [C: b,A2: set_b,B2: set_b] :
% 3.19/1.83 ( ( member_b @ C @ ( minus_minus_set_b @ A2 @ B2 ) )
% 3.19/1.83 => ~ ( ( member_b @ C @ A2 )
% 3.19/1.83 => ( member_b @ C @ B2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_127_Diff__infinite__finite,axiom,
% 3.19/1.83 ! [T: set_a,S: set_a] :
% 3.19/1.83 ( ( finite_finite_a @ T )
% 3.19/1.83 => ( ~ ( finite_finite_a @ S )
% 3.19/1.83 => ~ ( finite_finite_a @ ( minus_minus_set_a @ S @ T ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_128_insert__Diff__if,axiom,
% 3.19/1.83 ! [X2: a,B2: set_a,A2: set_a] :
% 3.19/1.83 ( ( ( member_a @ X2 @ B2 )
% 3.19/1.83 => ( ( minus_minus_set_a @ ( insert_a @ X2 @ A2 ) @ B2 )
% 3.19/1.83 = ( minus_minus_set_a @ A2 @ B2 ) ) )
% 3.19/1.83 & ( ~ ( member_a @ X2 @ B2 )
% 3.19/1.83 => ( ( minus_minus_set_a @ ( insert_a @ X2 @ A2 ) @ B2 )
% 3.19/1.83 = ( insert_a @ X2 @ ( minus_minus_set_a @ A2 @ B2 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_129_insert__Diff__if,axiom,
% 3.19/1.83 ! [X2: b,B2: set_b,A2: set_b] :
% 3.19/1.83 ( ( ( member_b @ X2 @ B2 )
% 3.19/1.83 => ( ( minus_minus_set_b @ ( insert_b @ X2 @ A2 ) @ B2 )
% 3.19/1.83 = ( minus_minus_set_b @ A2 @ B2 ) ) )
% 3.19/1.83 & ( ~ ( member_b @ X2 @ B2 )
% 3.19/1.83 => ( ( minus_minus_set_b @ ( insert_b @ X2 @ A2 ) @ B2 )
% 3.19/1.83 = ( insert_b @ X2 @ ( minus_minus_set_b @ A2 @ B2 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_130_sum__divide__distrib,axiom,
% 3.19/1.83 ! [F: a > real,A2: set_a,R: real] :
% 3.19/1.83 ( ( divide_divide_real @ ( groups1862963056a_real @ F @ A2 ) @ R )
% 3.19/1.83 = ( groups1862963056a_real
% 3.19/1.83 @ ^ [N: a] : ( divide_divide_real @ ( F @ N ) @ R )
% 3.19/1.83 @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_131_convex__ereal__add,axiom,
% 3.19/1.83 ! [S2: set_b,F: b > extended_ereal,G: b > extended_ereal] :
% 3.19/1.83 ( ( lower_311861425x_on_b @ S2 @ F )
% 3.19/1.83 => ( ( lower_311861425x_on_b @ S2 @ G )
% 3.19/1.83 => ( lower_311861425x_on_b @ S2
% 3.19/1.83 @ ^ [X: b] : ( plus_p2118002693_ereal @ ( F @ X ) @ ( G @ X ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_132_times__divide__times__eq,axiom,
% 3.19/1.83 ! [X2: real,Y: real,Z2: real,W: real] :
% 3.19/1.83 ( ( times_times_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ Z2 @ W ) )
% 3.19/1.83 = ( divide_divide_real @ ( times_times_real @ X2 @ Z2 ) @ ( times_times_real @ Y @ W ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_133_divide__divide__times__eq,axiom,
% 3.19/1.83 ! [X2: real,Y: real,Z2: real,W: real] :
% 3.19/1.83 ( ( divide_divide_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ Z2 @ W ) )
% 3.19/1.83 = ( divide_divide_real @ ( times_times_real @ X2 @ W ) @ ( times_times_real @ Y @ Z2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_134_divide__divide__eq__left_H,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 3.19/1.83 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_135_add__divide__distrib,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 3.19/1.83 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_136_diff__divide__distrib,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 3.19/1.83 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_137_Diff__insert__absorb,axiom,
% 3.19/1.83 ! [X2: b,A2: set_b] :
% 3.19/1.83 ( ~ ( member_b @ X2 @ A2 )
% 3.19/1.83 => ( ( minus_minus_set_b @ ( insert_b @ X2 @ A2 ) @ ( insert_b @ X2 @ bot_bot_set_b ) )
% 3.19/1.83 = A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_138_Diff__insert__absorb,axiom,
% 3.19/1.83 ! [X2: a,A2: set_a] :
% 3.19/1.83 ( ~ ( member_a @ X2 @ A2 )
% 3.19/1.83 => ( ( minus_minus_set_a @ ( insert_a @ X2 @ A2 ) @ ( insert_a @ X2 @ bot_bot_set_a ) )
% 3.19/1.83 = A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_139_Diff__insert2,axiom,
% 3.19/1.83 ! [A2: set_a,A: a,B2: set_a] :
% 3.19/1.83 ( ( minus_minus_set_a @ A2 @ ( insert_a @ A @ B2 ) )
% 3.19/1.83 = ( minus_minus_set_a @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) @ B2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_140_insert__Diff,axiom,
% 3.19/1.83 ! [A: b,A2: set_b] :
% 3.19/1.83 ( ( member_b @ A @ A2 )
% 3.19/1.83 => ( ( insert_b @ A @ ( minus_minus_set_b @ A2 @ ( insert_b @ A @ bot_bot_set_b ) ) )
% 3.19/1.83 = A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_141_insert__Diff,axiom,
% 3.19/1.83 ! [A: a,A2: set_a] :
% 3.19/1.83 ( ( member_a @ A @ A2 )
% 3.19/1.83 => ( ( insert_a @ A @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
% 3.19/1.83 = A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_142_Diff__insert,axiom,
% 3.19/1.83 ! [A2: set_a,A: a,B2: set_a] :
% 3.19/1.83 ( ( minus_minus_set_a @ A2 @ ( insert_a @ A @ B2 ) )
% 3.19/1.83 = ( minus_minus_set_a @ ( minus_minus_set_a @ A2 @ B2 ) @ ( insert_a @ A @ bot_bot_set_a ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_143_finite__empty__induct,axiom,
% 3.19/1.83 ! [A2: set_b,P: set_b > $o] :
% 3.19/1.83 ( ( finite_finite_b @ A2 )
% 3.19/1.83 => ( ( P @ A2 )
% 3.19/1.83 => ( ! [A5: b,A6: set_b] :
% 3.19/1.83 ( ( finite_finite_b @ A6 )
% 3.19/1.83 => ( ( member_b @ A5 @ A6 )
% 3.19/1.83 => ( ( P @ A6 )
% 3.19/1.83 => ( P @ ( minus_minus_set_b @ A6 @ ( insert_b @ A5 @ bot_bot_set_b ) ) ) ) ) )
% 3.19/1.83 => ( P @ bot_bot_set_b ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_144_finite__empty__induct,axiom,
% 3.19/1.83 ! [A2: set_a,P: set_a > $o] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ( P @ A2 )
% 3.19/1.83 => ( ! [A5: a,A6: set_a] :
% 3.19/1.83 ( ( finite_finite_a @ A6 )
% 3.19/1.83 => ( ( member_a @ A5 @ A6 )
% 3.19/1.83 => ( ( P @ A6 )
% 3.19/1.83 => ( P @ ( minus_minus_set_a @ A6 @ ( insert_a @ A5 @ bot_bot_set_a ) ) ) ) ) )
% 3.19/1.83 => ( P @ bot_bot_set_a ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_145_infinite__coinduct,axiom,
% 3.19/1.83 ! [X3: set_a > $o,A2: set_a] :
% 3.19/1.83 ( ( X3 @ A2 )
% 3.19/1.83 => ( ! [A6: set_a] :
% 3.19/1.83 ( ( X3 @ A6 )
% 3.19/1.83 => ? [X4: a] :
% 3.19/1.83 ( ( member_a @ X4 @ A6 )
% 3.19/1.83 & ( ( X3 @ ( minus_minus_set_a @ A6 @ ( insert_a @ X4 @ bot_bot_set_a ) ) )
% 3.19/1.83 | ~ ( finite_finite_a @ ( minus_minus_set_a @ A6 @ ( insert_a @ X4 @ bot_bot_set_a ) ) ) ) ) )
% 3.19/1.83 => ~ ( finite_finite_a @ A2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_146_infinite__remove,axiom,
% 3.19/1.83 ! [S: set_a,A: a] :
% 3.19/1.83 ( ~ ( finite_finite_a @ S )
% 3.19/1.83 => ~ ( finite_finite_a @ ( minus_minus_set_a @ S @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_147_field__class_Ofield__divide__inverse,axiom,
% 3.19/1.83 ( divide_divide_real
% 3.19/1.83 = ( ^ [A3: real,B4: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B4 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_148_divide__inverse,axiom,
% 3.19/1.83 ( divide_divide_real
% 3.19/1.83 = ( ^ [A3: real,B4: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B4 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_149_divide__inverse__commute,axiom,
% 3.19/1.83 ( divide_divide_real
% 3.19/1.83 = ( ^ [A3: real,B4: real] : ( times_times_real @ ( inverse_inverse_real @ B4 ) @ A3 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_150_inverse__eq__divide,axiom,
% 3.19/1.83 ( inverse_inverse_real
% 3.19/1.83 = ( divide_divide_real @ one_one_real ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_151_ex__in__conv,axiom,
% 3.19/1.83 ! [A2: set_b] :
% 3.19/1.83 ( ( ? [X: b] : ( member_b @ X @ A2 ) )
% 3.19/1.83 = ( A2 != bot_bot_set_b ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_152_ex__in__conv,axiom,
% 3.19/1.83 ! [A2: set_a] :
% 3.19/1.83 ( ( ? [X: a] : ( member_a @ X @ A2 ) )
% 3.19/1.83 = ( A2 != bot_bot_set_a ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_153_equals0I,axiom,
% 3.19/1.83 ! [A2: set_b] :
% 3.19/1.83 ( ! [Y3: b] :
% 3.19/1.83 ~ ( member_b @ Y3 @ A2 )
% 3.19/1.83 => ( A2 = bot_bot_set_b ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_154_equals0I,axiom,
% 3.19/1.83 ! [A2: set_a] :
% 3.19/1.83 ( ! [Y3: a] :
% 3.19/1.83 ~ ( member_a @ Y3 @ A2 )
% 3.19/1.83 => ( A2 = bot_bot_set_a ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_155_equals0D,axiom,
% 3.19/1.83 ! [A2: set_b,A: b] :
% 3.19/1.83 ( ( A2 = bot_bot_set_b )
% 3.19/1.83 => ~ ( member_b @ A @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_156_equals0D,axiom,
% 3.19/1.83 ! [A2: set_a,A: a] :
% 3.19/1.83 ( ( A2 = bot_bot_set_a )
% 3.19/1.83 => ~ ( member_a @ A @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_157_emptyE,axiom,
% 3.19/1.83 ! [A: b] :
% 3.19/1.83 ~ ( member_b @ A @ bot_bot_set_b ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_158_emptyE,axiom,
% 3.19/1.83 ! [A: a] :
% 3.19/1.83 ~ ( member_a @ A @ bot_bot_set_a ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_159_mk__disjoint__insert,axiom,
% 3.19/1.83 ! [A: a,A2: set_a] :
% 3.19/1.83 ( ( member_a @ A @ A2 )
% 3.19/1.83 => ? [B5: set_a] :
% 3.19/1.83 ( ( A2
% 3.19/1.83 = ( insert_a @ A @ B5 ) )
% 3.19/1.83 & ~ ( member_a @ A @ B5 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_160_mk__disjoint__insert,axiom,
% 3.19/1.83 ! [A: b,A2: set_b] :
% 3.19/1.83 ( ( member_b @ A @ A2 )
% 3.19/1.83 => ? [B5: set_b] :
% 3.19/1.83 ( ( A2
% 3.19/1.83 = ( insert_b @ A @ B5 ) )
% 3.19/1.83 & ~ ( member_b @ A @ B5 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_161_insert__commute,axiom,
% 3.19/1.83 ! [X2: a,Y: a,A2: set_a] :
% 3.19/1.83 ( ( insert_a @ X2 @ ( insert_a @ Y @ A2 ) )
% 3.19/1.83 = ( insert_a @ Y @ ( insert_a @ X2 @ A2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_162_insert__eq__iff,axiom,
% 3.19/1.83 ! [A: a,A2: set_a,B: a,B2: set_a] :
% 3.19/1.83 ( ~ ( member_a @ A @ A2 )
% 3.19/1.83 => ( ~ ( member_a @ B @ B2 )
% 3.19/1.83 => ( ( ( insert_a @ A @ A2 )
% 3.19/1.83 = ( insert_a @ B @ B2 ) )
% 3.19/1.83 = ( ( ( A = B )
% 3.19/1.83 => ( A2 = B2 ) )
% 3.19/1.83 & ( ( A != B )
% 3.19/1.83 => ? [C2: set_a] :
% 3.19/1.83 ( ( A2
% 3.19/1.83 = ( insert_a @ B @ C2 ) )
% 3.19/1.83 & ~ ( member_a @ B @ C2 )
% 3.19/1.83 & ( B2
% 3.19/1.83 = ( insert_a @ A @ C2 ) )
% 3.19/1.83 & ~ ( member_a @ A @ C2 ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_163_insert__eq__iff,axiom,
% 3.19/1.83 ! [A: b,A2: set_b,B: b,B2: set_b] :
% 3.19/1.83 ( ~ ( member_b @ A @ A2 )
% 3.19/1.83 => ( ~ ( member_b @ B @ B2 )
% 3.19/1.83 => ( ( ( insert_b @ A @ A2 )
% 3.19/1.83 = ( insert_b @ B @ B2 ) )
% 3.19/1.83 = ( ( ( A = B )
% 3.19/1.83 => ( A2 = B2 ) )
% 3.19/1.83 & ( ( A != B )
% 3.19/1.83 => ? [C2: set_b] :
% 3.19/1.83 ( ( A2
% 3.19/1.83 = ( insert_b @ B @ C2 ) )
% 3.19/1.83 & ~ ( member_b @ B @ C2 )
% 3.19/1.83 & ( B2
% 3.19/1.83 = ( insert_b @ A @ C2 ) )
% 3.19/1.83 & ~ ( member_b @ A @ C2 ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_164_insert__absorb,axiom,
% 3.19/1.83 ! [A: a,A2: set_a] :
% 3.19/1.83 ( ( member_a @ A @ A2 )
% 3.19/1.83 => ( ( insert_a @ A @ A2 )
% 3.19/1.83 = A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_165_insert__absorb,axiom,
% 3.19/1.83 ! [A: b,A2: set_b] :
% 3.19/1.83 ( ( member_b @ A @ A2 )
% 3.19/1.83 => ( ( insert_b @ A @ A2 )
% 3.19/1.83 = A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_166_insert__ident,axiom,
% 3.19/1.83 ! [X2: a,A2: set_a,B2: set_a] :
% 3.19/1.83 ( ~ ( member_a @ X2 @ A2 )
% 3.19/1.83 => ( ~ ( member_a @ X2 @ B2 )
% 3.19/1.83 => ( ( ( insert_a @ X2 @ A2 )
% 3.19/1.83 = ( insert_a @ X2 @ B2 ) )
% 3.19/1.83 = ( A2 = B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_167_insert__ident,axiom,
% 3.19/1.83 ! [X2: b,A2: set_b,B2: set_b] :
% 3.19/1.83 ( ~ ( member_b @ X2 @ A2 )
% 3.19/1.83 => ( ~ ( member_b @ X2 @ B2 )
% 3.19/1.83 => ( ( ( insert_b @ X2 @ A2 )
% 3.19/1.83 = ( insert_b @ X2 @ B2 ) )
% 3.19/1.83 = ( A2 = B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_168_Set_Oset__insert,axiom,
% 3.19/1.83 ! [X2: a,A2: set_a] :
% 3.19/1.83 ( ( member_a @ X2 @ A2 )
% 3.19/1.83 => ~ ! [B5: set_a] :
% 3.19/1.83 ( ( A2
% 3.19/1.83 = ( insert_a @ X2 @ B5 ) )
% 3.19/1.83 => ( member_a @ X2 @ B5 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_169_Set_Oset__insert,axiom,
% 3.19/1.83 ! [X2: b,A2: set_b] :
% 3.19/1.83 ( ( member_b @ X2 @ A2 )
% 3.19/1.83 => ~ ! [B5: set_b] :
% 3.19/1.83 ( ( A2
% 3.19/1.83 = ( insert_b @ X2 @ B5 ) )
% 3.19/1.83 => ( member_b @ X2 @ B5 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_170_insertI2,axiom,
% 3.19/1.83 ! [A: a,B2: set_a,B: a] :
% 3.19/1.83 ( ( member_a @ A @ B2 )
% 3.19/1.83 => ( member_a @ A @ ( insert_a @ B @ B2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_171_insertI2,axiom,
% 3.19/1.83 ! [A: b,B2: set_b,B: b] :
% 3.19/1.83 ( ( member_b @ A @ B2 )
% 3.19/1.83 => ( member_b @ A @ ( insert_b @ B @ B2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_172_insertI1,axiom,
% 3.19/1.83 ! [A: a,B2: set_a] : ( member_a @ A @ ( insert_a @ A @ B2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_173_insertI1,axiom,
% 3.19/1.83 ! [A: b,B2: set_b] : ( member_b @ A @ ( insert_b @ A @ B2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_174_insertE,axiom,
% 3.19/1.83 ! [A: a,B: a,A2: set_a] :
% 3.19/1.83 ( ( member_a @ A @ ( insert_a @ B @ A2 ) )
% 3.19/1.83 => ( ( A != B )
% 3.19/1.83 => ( member_a @ A @ A2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_175_insertE,axiom,
% 3.19/1.83 ! [A: b,B: b,A2: set_b] :
% 3.19/1.83 ( ( member_b @ A @ ( insert_b @ B @ A2 ) )
% 3.19/1.83 => ( ( A != B )
% 3.19/1.83 => ( member_b @ A @ A2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_176_sum_Ocong,axiom,
% 3.19/1.83 ! [A2: set_a,B2: set_a,G: a > b,H: a > b] :
% 3.19/1.83 ( ( A2 = B2 )
% 3.19/1.83 => ( ! [X5: a] :
% 3.19/1.83 ( ( member_a @ X5 @ B2 )
% 3.19/1.83 => ( ( G @ X5 )
% 3.19/1.83 = ( H @ X5 ) ) )
% 3.19/1.83 => ( ( groups1199149371um_a_b @ G @ A2 )
% 3.19/1.83 = ( groups1199149371um_a_b @ H @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_177_sum_Ocong,axiom,
% 3.19/1.83 ! [A2: set_a,B2: set_a,G: a > real,H: a > real] :
% 3.19/1.83 ( ( A2 = B2 )
% 3.19/1.83 => ( ! [X5: a] :
% 3.19/1.83 ( ( member_a @ X5 @ B2 )
% 3.19/1.83 => ( ( G @ X5 )
% 3.19/1.83 = ( H @ X5 ) ) )
% 3.19/1.83 => ( ( groups1862963056a_real @ G @ A2 )
% 3.19/1.83 = ( groups1862963056a_real @ H @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_178_sum_Oeq__general,axiom,
% 3.19/1.83 ! [B2: set_a,A2: set_b,H: b > a,Gamma: a > b,Phi: b > b] :
% 3.19/1.83 ( ! [Y3: a] :
% 3.19/1.83 ( ( member_a @ Y3 @ B2 )
% 3.19/1.83 => ? [X4: b] :
% 3.19/1.83 ( ( member_b @ X4 @ A2 )
% 3.19/1.83 & ( ( H @ X4 )
% 3.19/1.83 = Y3 )
% 3.19/1.83 & ! [Ya: b] :
% 3.19/1.83 ( ( ( member_b @ Ya @ A2 )
% 3.19/1.83 & ( ( H @ Ya )
% 3.19/1.83 = Y3 ) )
% 3.19/1.83 => ( Ya = X4 ) ) ) )
% 3.19/1.83 => ( ! [X5: b] :
% 3.19/1.83 ( ( member_b @ X5 @ A2 )
% 3.19/1.83 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 3.19/1.83 & ( ( Gamma @ ( H @ X5 ) )
% 3.19/1.83 = ( Phi @ X5 ) ) ) )
% 3.19/1.83 => ( ( groups2026918778um_b_b @ Phi @ A2 )
% 3.19/1.83 = ( groups1199149371um_a_b @ Gamma @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_179_sum_Oeq__general,axiom,
% 3.19/1.83 ! [B2: set_a,A2: set_b,H: b > a,Gamma: a > real,Phi: b > real] :
% 3.19/1.83 ( ! [Y3: a] :
% 3.19/1.83 ( ( member_a @ Y3 @ B2 )
% 3.19/1.83 => ? [X4: b] :
% 3.19/1.83 ( ( member_b @ X4 @ A2 )
% 3.19/1.83 & ( ( H @ X4 )
% 3.19/1.83 = Y3 )
% 3.19/1.83 & ! [Ya: b] :
% 3.19/1.83 ( ( ( member_b @ Ya @ A2 )
% 3.19/1.83 & ( ( H @ Ya )
% 3.19/1.83 = Y3 ) )
% 3.19/1.83 => ( Ya = X4 ) ) ) )
% 3.19/1.83 => ( ! [X5: b] :
% 3.19/1.83 ( ( member_b @ X5 @ A2 )
% 3.19/1.83 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 3.19/1.83 & ( ( Gamma @ ( H @ X5 ) )
% 3.19/1.83 = ( Phi @ X5 ) ) ) )
% 3.19/1.83 => ( ( groups583146225b_real @ Phi @ A2 )
% 3.19/1.83 = ( groups1862963056a_real @ Gamma @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_180_sum_Oeq__general,axiom,
% 3.19/1.83 ! [B2: set_b,A2: set_a,H: a > b,Gamma: b > b,Phi: a > b] :
% 3.19/1.83 ( ! [Y3: b] :
% 3.19/1.83 ( ( member_b @ Y3 @ B2 )
% 3.19/1.83 => ? [X4: a] :
% 3.19/1.83 ( ( member_a @ X4 @ A2 )
% 3.19/1.83 & ( ( H @ X4 )
% 3.19/1.83 = Y3 )
% 3.19/1.83 & ! [Ya: a] :
% 3.19/1.83 ( ( ( member_a @ Ya @ A2 )
% 3.19/1.83 & ( ( H @ Ya )
% 3.19/1.83 = Y3 ) )
% 3.19/1.83 => ( Ya = X4 ) ) ) )
% 3.19/1.83 => ( ! [X5: a] :
% 3.19/1.83 ( ( member_a @ X5 @ A2 )
% 3.19/1.83 => ( ( member_b @ ( H @ X5 ) @ B2 )
% 3.19/1.83 & ( ( Gamma @ ( H @ X5 ) )
% 3.19/1.83 = ( Phi @ X5 ) ) ) )
% 3.19/1.83 => ( ( groups1199149371um_a_b @ Phi @ A2 )
% 3.19/1.83 = ( groups2026918778um_b_b @ Gamma @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_181_sum_Oeq__general,axiom,
% 3.19/1.83 ! [B2: set_a,A2: set_a,H: a > a,Gamma: a > b,Phi: a > b] :
% 3.19/1.83 ( ! [Y3: a] :
% 3.19/1.83 ( ( member_a @ Y3 @ B2 )
% 3.19/1.83 => ? [X4: a] :
% 3.19/1.83 ( ( member_a @ X4 @ A2 )
% 3.19/1.83 & ( ( H @ X4 )
% 3.19/1.83 = Y3 )
% 3.19/1.83 & ! [Ya: a] :
% 3.19/1.83 ( ( ( member_a @ Ya @ A2 )
% 3.19/1.83 & ( ( H @ Ya )
% 3.19/1.83 = Y3 ) )
% 3.19/1.83 => ( Ya = X4 ) ) ) )
% 3.19/1.83 => ( ! [X5: a] :
% 3.19/1.83 ( ( member_a @ X5 @ A2 )
% 3.19/1.83 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 3.19/1.83 & ( ( Gamma @ ( H @ X5 ) )
% 3.19/1.83 = ( Phi @ X5 ) ) ) )
% 3.19/1.83 => ( ( groups1199149371um_a_b @ Phi @ A2 )
% 3.19/1.83 = ( groups1199149371um_a_b @ Gamma @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_182_sum_Oeq__general,axiom,
% 3.19/1.83 ! [B2: set_b,A2: set_a,H: a > b,Gamma: b > real,Phi: a > real] :
% 3.19/1.83 ( ! [Y3: b] :
% 3.19/1.83 ( ( member_b @ Y3 @ B2 )
% 3.19/1.83 => ? [X4: a] :
% 3.19/1.83 ( ( member_a @ X4 @ A2 )
% 3.19/1.83 & ( ( H @ X4 )
% 3.19/1.83 = Y3 )
% 3.19/1.83 & ! [Ya: a] :
% 3.19/1.83 ( ( ( member_a @ Ya @ A2 )
% 3.19/1.83 & ( ( H @ Ya )
% 3.19/1.83 = Y3 ) )
% 3.19/1.83 => ( Ya = X4 ) ) ) )
% 3.19/1.83 => ( ! [X5: a] :
% 3.19/1.83 ( ( member_a @ X5 @ A2 )
% 3.19/1.83 => ( ( member_b @ ( H @ X5 ) @ B2 )
% 3.19/1.83 & ( ( Gamma @ ( H @ X5 ) )
% 3.19/1.83 = ( Phi @ X5 ) ) ) )
% 3.19/1.83 => ( ( groups1862963056a_real @ Phi @ A2 )
% 3.19/1.83 = ( groups583146225b_real @ Gamma @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_183_sum_Oeq__general,axiom,
% 3.19/1.83 ! [B2: set_a,A2: set_a,H: a > a,Gamma: a > real,Phi: a > real] :
% 3.19/1.83 ( ! [Y3: a] :
% 3.19/1.83 ( ( member_a @ Y3 @ B2 )
% 3.19/1.83 => ? [X4: a] :
% 3.19/1.83 ( ( member_a @ X4 @ A2 )
% 3.19/1.83 & ( ( H @ X4 )
% 3.19/1.83 = Y3 )
% 3.19/1.83 & ! [Ya: a] :
% 3.19/1.83 ( ( ( member_a @ Ya @ A2 )
% 3.19/1.83 & ( ( H @ Ya )
% 3.19/1.83 = Y3 ) )
% 3.19/1.83 => ( Ya = X4 ) ) ) )
% 3.19/1.83 => ( ! [X5: a] :
% 3.19/1.83 ( ( member_a @ X5 @ A2 )
% 3.19/1.83 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 3.19/1.83 & ( ( Gamma @ ( H @ X5 ) )
% 3.19/1.83 = ( Phi @ X5 ) ) ) )
% 3.19/1.83 => ( ( groups1862963056a_real @ Phi @ A2 )
% 3.19/1.83 = ( groups1862963056a_real @ Gamma @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_184_sum_Oeq__general__inverses,axiom,
% 3.19/1.83 ! [B2: set_a,K: a > b,A2: set_b,H: b > a,Gamma: a > b,Phi: b > b] :
% 3.19/1.83 ( ! [Y3: a] :
% 3.19/1.83 ( ( member_a @ Y3 @ B2 )
% 3.19/1.83 => ( ( member_b @ ( K @ Y3 ) @ A2 )
% 3.19/1.83 & ( ( H @ ( K @ Y3 ) )
% 3.19/1.83 = Y3 ) ) )
% 3.19/1.83 => ( ! [X5: b] :
% 3.19/1.83 ( ( member_b @ X5 @ A2 )
% 3.19/1.83 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 3.19/1.83 & ( ( K @ ( H @ X5 ) )
% 3.19/1.83 = X5 )
% 3.19/1.83 & ( ( Gamma @ ( H @ X5 ) )
% 3.19/1.83 = ( Phi @ X5 ) ) ) )
% 3.19/1.83 => ( ( groups2026918778um_b_b @ Phi @ A2 )
% 3.19/1.83 = ( groups1199149371um_a_b @ Gamma @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_185_sum_Oeq__general__inverses,axiom,
% 3.19/1.83 ! [B2: set_a,K: a > b,A2: set_b,H: b > a,Gamma: a > real,Phi: b > real] :
% 3.19/1.83 ( ! [Y3: a] :
% 3.19/1.83 ( ( member_a @ Y3 @ B2 )
% 3.19/1.83 => ( ( member_b @ ( K @ Y3 ) @ A2 )
% 3.19/1.83 & ( ( H @ ( K @ Y3 ) )
% 3.19/1.83 = Y3 ) ) )
% 3.19/1.83 => ( ! [X5: b] :
% 3.19/1.83 ( ( member_b @ X5 @ A2 )
% 3.19/1.83 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 3.19/1.83 & ( ( K @ ( H @ X5 ) )
% 3.19/1.83 = X5 )
% 3.19/1.83 & ( ( Gamma @ ( H @ X5 ) )
% 3.19/1.83 = ( Phi @ X5 ) ) ) )
% 3.19/1.83 => ( ( groups583146225b_real @ Phi @ A2 )
% 3.19/1.83 = ( groups1862963056a_real @ Gamma @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_186_sum_Oeq__general__inverses,axiom,
% 3.19/1.83 ! [B2: set_b,K: b > a,A2: set_a,H: a > b,Gamma: b > b,Phi: a > b] :
% 3.19/1.83 ( ! [Y3: b] :
% 3.19/1.83 ( ( member_b @ Y3 @ B2 )
% 3.19/1.83 => ( ( member_a @ ( K @ Y3 ) @ A2 )
% 3.19/1.83 & ( ( H @ ( K @ Y3 ) )
% 3.19/1.83 = Y3 ) ) )
% 3.19/1.83 => ( ! [X5: a] :
% 3.19/1.83 ( ( member_a @ X5 @ A2 )
% 3.19/1.83 => ( ( member_b @ ( H @ X5 ) @ B2 )
% 3.19/1.83 & ( ( K @ ( H @ X5 ) )
% 3.19/1.83 = X5 )
% 3.19/1.83 & ( ( Gamma @ ( H @ X5 ) )
% 3.19/1.83 = ( Phi @ X5 ) ) ) )
% 3.19/1.83 => ( ( groups1199149371um_a_b @ Phi @ A2 )
% 3.19/1.83 = ( groups2026918778um_b_b @ Gamma @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_187_sum_Oeq__general__inverses,axiom,
% 3.19/1.83 ! [B2: set_a,K: a > a,A2: set_a,H: a > a,Gamma: a > b,Phi: a > b] :
% 3.19/1.83 ( ! [Y3: a] :
% 3.19/1.83 ( ( member_a @ Y3 @ B2 )
% 3.19/1.83 => ( ( member_a @ ( K @ Y3 ) @ A2 )
% 3.19/1.83 & ( ( H @ ( K @ Y3 ) )
% 3.19/1.83 = Y3 ) ) )
% 3.19/1.83 => ( ! [X5: a] :
% 3.19/1.83 ( ( member_a @ X5 @ A2 )
% 3.19/1.83 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 3.19/1.83 & ( ( K @ ( H @ X5 ) )
% 3.19/1.83 = X5 )
% 3.19/1.83 & ( ( Gamma @ ( H @ X5 ) )
% 3.19/1.83 = ( Phi @ X5 ) ) ) )
% 3.19/1.83 => ( ( groups1199149371um_a_b @ Phi @ A2 )
% 3.19/1.83 = ( groups1199149371um_a_b @ Gamma @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_188_sum_Oeq__general__inverses,axiom,
% 3.19/1.83 ! [B2: set_b,K: b > a,A2: set_a,H: a > b,Gamma: b > real,Phi: a > real] :
% 3.19/1.83 ( ! [Y3: b] :
% 3.19/1.83 ( ( member_b @ Y3 @ B2 )
% 3.19/1.83 => ( ( member_a @ ( K @ Y3 ) @ A2 )
% 3.19/1.83 & ( ( H @ ( K @ Y3 ) )
% 3.19/1.83 = Y3 ) ) )
% 3.19/1.83 => ( ! [X5: a] :
% 3.19/1.83 ( ( member_a @ X5 @ A2 )
% 3.19/1.83 => ( ( member_b @ ( H @ X5 ) @ B2 )
% 3.19/1.83 & ( ( K @ ( H @ X5 ) )
% 3.19/1.83 = X5 )
% 3.19/1.83 & ( ( Gamma @ ( H @ X5 ) )
% 3.19/1.83 = ( Phi @ X5 ) ) ) )
% 3.19/1.83 => ( ( groups1862963056a_real @ Phi @ A2 )
% 3.19/1.83 = ( groups583146225b_real @ Gamma @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_189_sum_Oeq__general__inverses,axiom,
% 3.19/1.83 ! [B2: set_a,K: a > a,A2: set_a,H: a > a,Gamma: a > real,Phi: a > real] :
% 3.19/1.83 ( ! [Y3: a] :
% 3.19/1.83 ( ( member_a @ Y3 @ B2 )
% 3.19/1.83 => ( ( member_a @ ( K @ Y3 ) @ A2 )
% 3.19/1.83 & ( ( H @ ( K @ Y3 ) )
% 3.19/1.83 = Y3 ) ) )
% 3.19/1.83 => ( ! [X5: a] :
% 3.19/1.83 ( ( member_a @ X5 @ A2 )
% 3.19/1.83 => ( ( member_a @ ( H @ X5 ) @ B2 )
% 3.19/1.83 & ( ( K @ ( H @ X5 ) )
% 3.19/1.83 = X5 )
% 3.19/1.83 & ( ( Gamma @ ( H @ X5 ) )
% 3.19/1.83 = ( Phi @ X5 ) ) ) )
% 3.19/1.83 => ( ( groups1862963056a_real @ Phi @ A2 )
% 3.19/1.83 = ( groups1862963056a_real @ Gamma @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_190_sum_Oreindex__bij__witness,axiom,
% 3.19/1.83 ! [S: set_b,I2: a > b,J2: b > a,T: set_a,H: a > b,G: b > b] :
% 3.19/1.83 ( ! [A5: b] :
% 3.19/1.83 ( ( member_b @ A5 @ S )
% 3.19/1.83 => ( ( I2 @ ( J2 @ A5 ) )
% 3.19/1.83 = A5 ) )
% 3.19/1.83 => ( ! [A5: b] :
% 3.19/1.83 ( ( member_b @ A5 @ S )
% 3.19/1.83 => ( member_a @ ( J2 @ A5 ) @ T ) )
% 3.19/1.83 => ( ! [B6: a] :
% 3.19/1.83 ( ( member_a @ B6 @ T )
% 3.19/1.83 => ( ( J2 @ ( I2 @ B6 ) )
% 3.19/1.83 = B6 ) )
% 3.19/1.83 => ( ! [B6: a] :
% 3.19/1.83 ( ( member_a @ B6 @ T )
% 3.19/1.83 => ( member_b @ ( I2 @ B6 ) @ S ) )
% 3.19/1.83 => ( ! [A5: b] :
% 3.19/1.83 ( ( member_b @ A5 @ S )
% 3.19/1.83 => ( ( H @ ( J2 @ A5 ) )
% 3.19/1.83 = ( G @ A5 ) ) )
% 3.19/1.83 => ( ( groups2026918778um_b_b @ G @ S )
% 3.19/1.83 = ( groups1199149371um_a_b @ H @ T ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_191_sum_Oreindex__bij__witness,axiom,
% 3.19/1.83 ! [S: set_b,I2: a > b,J2: b > a,T: set_a,H: a > real,G: b > real] :
% 3.19/1.83 ( ! [A5: b] :
% 3.19/1.83 ( ( member_b @ A5 @ S )
% 3.19/1.83 => ( ( I2 @ ( J2 @ A5 ) )
% 3.19/1.83 = A5 ) )
% 3.19/1.83 => ( ! [A5: b] :
% 3.19/1.83 ( ( member_b @ A5 @ S )
% 3.19/1.83 => ( member_a @ ( J2 @ A5 ) @ T ) )
% 3.19/1.83 => ( ! [B6: a] :
% 3.19/1.83 ( ( member_a @ B6 @ T )
% 3.19/1.83 => ( ( J2 @ ( I2 @ B6 ) )
% 3.19/1.83 = B6 ) )
% 3.19/1.83 => ( ! [B6: a] :
% 3.19/1.83 ( ( member_a @ B6 @ T )
% 3.19/1.83 => ( member_b @ ( I2 @ B6 ) @ S ) )
% 3.19/1.83 => ( ! [A5: b] :
% 3.19/1.83 ( ( member_b @ A5 @ S )
% 3.19/1.83 => ( ( H @ ( J2 @ A5 ) )
% 3.19/1.83 = ( G @ A5 ) ) )
% 3.19/1.83 => ( ( groups583146225b_real @ G @ S )
% 3.19/1.83 = ( groups1862963056a_real @ H @ T ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_192_sum_Oreindex__bij__witness,axiom,
% 3.19/1.83 ! [S: set_a,I2: b > a,J2: a > b,T: set_b,H: b > b,G: a > b] :
% 3.19/1.83 ( ! [A5: a] :
% 3.19/1.83 ( ( member_a @ A5 @ S )
% 3.19/1.83 => ( ( I2 @ ( J2 @ A5 ) )
% 3.19/1.83 = A5 ) )
% 3.19/1.83 => ( ! [A5: a] :
% 3.19/1.83 ( ( member_a @ A5 @ S )
% 3.19/1.83 => ( member_b @ ( J2 @ A5 ) @ T ) )
% 3.19/1.83 => ( ! [B6: b] :
% 3.19/1.83 ( ( member_b @ B6 @ T )
% 3.19/1.83 => ( ( J2 @ ( I2 @ B6 ) )
% 3.19/1.83 = B6 ) )
% 3.19/1.83 => ( ! [B6: b] :
% 3.19/1.83 ( ( member_b @ B6 @ T )
% 3.19/1.83 => ( member_a @ ( I2 @ B6 ) @ S ) )
% 3.19/1.83 => ( ! [A5: a] :
% 3.19/1.83 ( ( member_a @ A5 @ S )
% 3.19/1.83 => ( ( H @ ( J2 @ A5 ) )
% 3.19/1.83 = ( G @ A5 ) ) )
% 3.19/1.83 => ( ( groups1199149371um_a_b @ G @ S )
% 3.19/1.83 = ( groups2026918778um_b_b @ H @ T ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_193_sum_Oreindex__bij__witness,axiom,
% 3.19/1.83 ! [S: set_a,I2: a > a,J2: a > a,T: set_a,H: a > b,G: a > b] :
% 3.19/1.83 ( ! [A5: a] :
% 3.19/1.83 ( ( member_a @ A5 @ S )
% 3.19/1.83 => ( ( I2 @ ( J2 @ A5 ) )
% 3.19/1.83 = A5 ) )
% 3.19/1.83 => ( ! [A5: a] :
% 3.19/1.83 ( ( member_a @ A5 @ S )
% 3.19/1.83 => ( member_a @ ( J2 @ A5 ) @ T ) )
% 3.19/1.83 => ( ! [B6: a] :
% 3.19/1.83 ( ( member_a @ B6 @ T )
% 3.19/1.83 => ( ( J2 @ ( I2 @ B6 ) )
% 3.19/1.83 = B6 ) )
% 3.19/1.83 => ( ! [B6: a] :
% 3.19/1.83 ( ( member_a @ B6 @ T )
% 3.19/1.83 => ( member_a @ ( I2 @ B6 ) @ S ) )
% 3.19/1.83 => ( ! [A5: a] :
% 3.19/1.83 ( ( member_a @ A5 @ S )
% 3.19/1.83 => ( ( H @ ( J2 @ A5 ) )
% 3.19/1.83 = ( G @ A5 ) ) )
% 3.19/1.83 => ( ( groups1199149371um_a_b @ G @ S )
% 3.19/1.83 = ( groups1199149371um_a_b @ H @ T ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_194_sum_Oreindex__bij__witness,axiom,
% 3.19/1.83 ! [S: set_a,I2: b > a,J2: a > b,T: set_b,H: b > real,G: a > real] :
% 3.19/1.83 ( ! [A5: a] :
% 3.19/1.83 ( ( member_a @ A5 @ S )
% 3.19/1.83 => ( ( I2 @ ( J2 @ A5 ) )
% 3.19/1.83 = A5 ) )
% 3.19/1.83 => ( ! [A5: a] :
% 3.19/1.83 ( ( member_a @ A5 @ S )
% 3.19/1.83 => ( member_b @ ( J2 @ A5 ) @ T ) )
% 3.19/1.83 => ( ! [B6: b] :
% 3.19/1.83 ( ( member_b @ B6 @ T )
% 3.19/1.83 => ( ( J2 @ ( I2 @ B6 ) )
% 3.19/1.83 = B6 ) )
% 3.19/1.83 => ( ! [B6: b] :
% 3.19/1.83 ( ( member_b @ B6 @ T )
% 3.19/1.83 => ( member_a @ ( I2 @ B6 ) @ S ) )
% 3.19/1.83 => ( ! [A5: a] :
% 3.19/1.83 ( ( member_a @ A5 @ S )
% 3.19/1.83 => ( ( H @ ( J2 @ A5 ) )
% 3.19/1.83 = ( G @ A5 ) ) )
% 3.19/1.83 => ( ( groups1862963056a_real @ G @ S )
% 3.19/1.83 = ( groups583146225b_real @ H @ T ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_195_sum_Oreindex__bij__witness,axiom,
% 3.19/1.83 ! [S: set_a,I2: a > a,J2: a > a,T: set_a,H: a > real,G: a > real] :
% 3.19/1.83 ( ! [A5: a] :
% 3.19/1.83 ( ( member_a @ A5 @ S )
% 3.19/1.83 => ( ( I2 @ ( J2 @ A5 ) )
% 3.19/1.83 = A5 ) )
% 3.19/1.83 => ( ! [A5: a] :
% 3.19/1.83 ( ( member_a @ A5 @ S )
% 3.19/1.83 => ( member_a @ ( J2 @ A5 ) @ T ) )
% 3.19/1.83 => ( ! [B6: a] :
% 3.19/1.83 ( ( member_a @ B6 @ T )
% 3.19/1.83 => ( ( J2 @ ( I2 @ B6 ) )
% 3.19/1.83 = B6 ) )
% 3.19/1.83 => ( ! [B6: a] :
% 3.19/1.83 ( ( member_a @ B6 @ T )
% 3.19/1.83 => ( member_a @ ( I2 @ B6 ) @ S ) )
% 3.19/1.83 => ( ! [A5: a] :
% 3.19/1.83 ( ( member_a @ A5 @ S )
% 3.19/1.83 => ( ( H @ ( J2 @ A5 ) )
% 3.19/1.83 = ( G @ A5 ) ) )
% 3.19/1.83 => ( ( groups1862963056a_real @ G @ S )
% 3.19/1.83 = ( groups1862963056a_real @ H @ T ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_196_if__smult,axiom,
% 3.19/1.83 ! [P: $o,X2: real,Y: real,V2: b] :
% 3.19/1.83 ( ( P
% 3.19/1.83 => ( ( real_V1035702896aleR_b @ ( if_real @ P @ X2 @ Y ) @ V2 )
% 3.19/1.83 = ( real_V1035702896aleR_b @ X2 @ V2 ) ) )
% 3.19/1.83 & ( ~ P
% 3.19/1.83 => ( ( real_V1035702896aleR_b @ ( if_real @ P @ X2 @ Y ) @ V2 )
% 3.19/1.83 = ( real_V1035702896aleR_b @ Y @ V2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_197_if__smult,axiom,
% 3.19/1.83 ! [P: $o,X2: real,Y: real,V2: real] :
% 3.19/1.83 ( ( P
% 3.19/1.83 => ( ( real_V453051771R_real @ ( if_real @ P @ X2 @ Y ) @ V2 )
% 3.19/1.83 = ( real_V453051771R_real @ X2 @ V2 ) ) )
% 3.19/1.83 & ( ~ P
% 3.19/1.83 => ( ( real_V453051771R_real @ ( if_real @ P @ X2 @ Y ) @ V2 )
% 3.19/1.83 = ( real_V453051771R_real @ Y @ V2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_198_sum_Oinsert__remove,axiom,
% 3.19/1.83 ! [A2: set_a,G: a > b,X2: a] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ( groups1199149371um_a_b @ G @ ( insert_a @ X2 @ A2 ) )
% 3.19/1.83 = ( plus_plus_b @ ( G @ X2 ) @ ( groups1199149371um_a_b @ G @ ( minus_minus_set_a @ A2 @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_199_sum_Oinsert__remove,axiom,
% 3.19/1.83 ! [A2: set_a,G: a > real,X2: a] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ( groups1862963056a_real @ G @ ( insert_a @ X2 @ A2 ) )
% 3.19/1.83 = ( plus_plus_real @ ( G @ X2 ) @ ( groups1862963056a_real @ G @ ( minus_minus_set_a @ A2 @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_200_sum_Oremove,axiom,
% 3.19/1.83 ! [A2: set_b,X2: b,G: b > b] :
% 3.19/1.83 ( ( finite_finite_b @ A2 )
% 3.19/1.83 => ( ( member_b @ X2 @ A2 )
% 3.19/1.83 => ( ( groups2026918778um_b_b @ G @ A2 )
% 3.19/1.83 = ( plus_plus_b @ ( G @ X2 ) @ ( groups2026918778um_b_b @ G @ ( minus_minus_set_b @ A2 @ ( insert_b @ X2 @ bot_bot_set_b ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_201_sum_Oremove,axiom,
% 3.19/1.83 ! [A2: set_b,X2: b,G: b > real] :
% 3.19/1.83 ( ( finite_finite_b @ A2 )
% 3.19/1.83 => ( ( member_b @ X2 @ A2 )
% 3.19/1.83 => ( ( groups583146225b_real @ G @ A2 )
% 3.19/1.83 = ( plus_plus_real @ ( G @ X2 ) @ ( groups583146225b_real @ G @ ( minus_minus_set_b @ A2 @ ( insert_b @ X2 @ bot_bot_set_b ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_202_sum_Oremove,axiom,
% 3.19/1.83 ! [A2: set_a,X2: a,G: a > b] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ( member_a @ X2 @ A2 )
% 3.19/1.83 => ( ( groups1199149371um_a_b @ G @ A2 )
% 3.19/1.83 = ( plus_plus_b @ ( G @ X2 ) @ ( groups1199149371um_a_b @ G @ ( minus_minus_set_a @ A2 @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_203_sum_Oremove,axiom,
% 3.19/1.83 ! [A2: set_a,X2: a,G: a > real] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ( member_a @ X2 @ A2 )
% 3.19/1.83 => ( ( groups1862963056a_real @ G @ A2 )
% 3.19/1.83 = ( plus_plus_real @ ( G @ X2 ) @ ( groups1862963056a_real @ G @ ( minus_minus_set_a @ A2 @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_204_sum_Odelta__remove,axiom,
% 3.19/1.83 ! [S: set_b,A: b,B: b > b,C: b > b] :
% 3.19/1.83 ( ( finite_finite_b @ S )
% 3.19/1.83 => ( ( ( member_b @ A @ S )
% 3.19/1.83 => ( ( groups2026918778um_b_b
% 3.19/1.83 @ ^ [K2: b] : ( if_b @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 3.19/1.83 @ S )
% 3.19/1.83 = ( plus_plus_b @ ( B @ A ) @ ( groups2026918778um_b_b @ C @ ( minus_minus_set_b @ S @ ( insert_b @ A @ bot_bot_set_b ) ) ) ) ) )
% 3.19/1.83 & ( ~ ( member_b @ A @ S )
% 3.19/1.83 => ( ( groups2026918778um_b_b
% 3.19/1.83 @ ^ [K2: b] : ( if_b @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 3.19/1.83 @ S )
% 3.19/1.83 = ( groups2026918778um_b_b @ C @ ( minus_minus_set_b @ S @ ( insert_b @ A @ bot_bot_set_b ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_205_sum_Odelta__remove,axiom,
% 3.19/1.83 ! [S: set_b,A: b,B: b > real,C: b > real] :
% 3.19/1.83 ( ( finite_finite_b @ S )
% 3.19/1.83 => ( ( ( member_b @ A @ S )
% 3.19/1.83 => ( ( groups583146225b_real
% 3.19/1.83 @ ^ [K2: b] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 3.19/1.83 @ S )
% 3.19/1.83 = ( plus_plus_real @ ( B @ A ) @ ( groups583146225b_real @ C @ ( minus_minus_set_b @ S @ ( insert_b @ A @ bot_bot_set_b ) ) ) ) ) )
% 3.19/1.83 & ( ~ ( member_b @ A @ S )
% 3.19/1.83 => ( ( groups583146225b_real
% 3.19/1.83 @ ^ [K2: b] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 3.19/1.83 @ S )
% 3.19/1.83 = ( groups583146225b_real @ C @ ( minus_minus_set_b @ S @ ( insert_b @ A @ bot_bot_set_b ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_206_sum_Odelta__remove,axiom,
% 3.19/1.83 ! [S: set_a,A: a,B: a > b,C: a > b] :
% 3.19/1.83 ( ( finite_finite_a @ S )
% 3.19/1.83 => ( ( ( member_a @ A @ S )
% 3.19/1.83 => ( ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [K2: a] : ( if_b @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 3.19/1.83 @ S )
% 3.19/1.83 = ( plus_plus_b @ ( B @ A ) @ ( groups1199149371um_a_b @ C @ ( minus_minus_set_a @ S @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ) )
% 3.19/1.83 & ( ~ ( member_a @ A @ S )
% 3.19/1.83 => ( ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [K2: a] : ( if_b @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 3.19/1.83 @ S )
% 3.19/1.83 = ( groups1199149371um_a_b @ C @ ( minus_minus_set_a @ S @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_207_sum_Odelta__remove,axiom,
% 3.19/1.83 ! [S: set_a,A: a,B: a > real,C: a > real] :
% 3.19/1.83 ( ( finite_finite_a @ S )
% 3.19/1.83 => ( ( ( member_a @ A @ S )
% 3.19/1.83 => ( ( groups1862963056a_real
% 3.19/1.83 @ ^ [K2: a] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 3.19/1.83 @ S )
% 3.19/1.83 = ( plus_plus_real @ ( B @ A ) @ ( groups1862963056a_real @ C @ ( minus_minus_set_a @ S @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ) )
% 3.19/1.83 & ( ~ ( member_a @ A @ S )
% 3.19/1.83 => ( ( groups1862963056a_real
% 3.19/1.83 @ ^ [K2: a] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 3.19/1.83 @ S )
% 3.19/1.83 = ( groups1862963056a_real @ C @ ( minus_minus_set_a @ S @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_208_empty__def,axiom,
% 3.19/1.83 ( bot_bot_set_a
% 3.19/1.83 = ( collect_a
% 3.19/1.83 @ ^ [X: a] : $false ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_209_pigeonhole__infinite__rel,axiom,
% 3.19/1.83 ! [A2: set_b,B2: set_a,R2: b > a > $o] :
% 3.19/1.83 ( ~ ( finite_finite_b @ A2 )
% 3.19/1.83 => ( ( finite_finite_a @ B2 )
% 3.19/1.83 => ( ! [X5: b] :
% 3.19/1.83 ( ( member_b @ X5 @ A2 )
% 3.19/1.83 => ? [Xa2: a] :
% 3.19/1.83 ( ( member_a @ Xa2 @ B2 )
% 3.19/1.83 & ( R2 @ X5 @ Xa2 ) ) )
% 3.19/1.83 => ? [X5: a] :
% 3.19/1.83 ( ( member_a @ X5 @ B2 )
% 3.19/1.83 & ~ ( finite_finite_b
% 3.19/1.83 @ ( collect_b
% 3.19/1.83 @ ^ [A3: b] :
% 3.19/1.83 ( ( member_b @ A3 @ A2 )
% 3.19/1.83 & ( R2 @ A3 @ X5 ) ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_210_pigeonhole__infinite__rel,axiom,
% 3.19/1.83 ! [A2: set_a,B2: set_a,R2: a > a > $o] :
% 3.19/1.83 ( ~ ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ( finite_finite_a @ B2 )
% 3.19/1.83 => ( ! [X5: a] :
% 3.19/1.83 ( ( member_a @ X5 @ A2 )
% 3.19/1.83 => ? [Xa2: a] :
% 3.19/1.83 ( ( member_a @ Xa2 @ B2 )
% 3.19/1.83 & ( R2 @ X5 @ Xa2 ) ) )
% 3.19/1.83 => ? [X5: a] :
% 3.19/1.83 ( ( member_a @ X5 @ B2 )
% 3.19/1.83 & ~ ( finite_finite_a
% 3.19/1.83 @ ( collect_a
% 3.19/1.83 @ ^ [A3: a] :
% 3.19/1.83 ( ( member_a @ A3 @ A2 )
% 3.19/1.83 & ( R2 @ A3 @ X5 ) ) ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_211_not__finite__existsD,axiom,
% 3.19/1.83 ! [P: a > $o] :
% 3.19/1.83 ( ~ ( finite_finite_a @ ( collect_a @ P ) )
% 3.19/1.83 => ? [X_1: a] : ( P @ X_1 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_212_insert__Collect,axiom,
% 3.19/1.83 ! [A: a,P: a > $o] :
% 3.19/1.83 ( ( insert_a @ A @ ( collect_a @ P ) )
% 3.19/1.83 = ( collect_a
% 3.19/1.83 @ ^ [U2: a] :
% 3.19/1.83 ( ( U2 != A )
% 3.19/1.83 => ( P @ U2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_213_insert__compr,axiom,
% 3.19/1.83 ( insert_a
% 3.19/1.83 = ( ^ [A3: a,B3: set_a] :
% 3.19/1.83 ( collect_a
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( ( X = A3 )
% 3.19/1.83 | ( member_a @ X @ B3 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_214_insert__compr,axiom,
% 3.19/1.83 ( insert_b
% 3.19/1.83 = ( ^ [A3: b,B3: set_b] :
% 3.19/1.83 ( collect_b
% 3.19/1.83 @ ^ [X: b] :
% 3.19/1.83 ( ( X = A3 )
% 3.19/1.83 | ( member_b @ X @ B3 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_215_sum__delta__notmem_I4_J,axiom,
% 3.19/1.83 ! [X2: a,S2: set_a,P: a > b,Q: a > b] :
% 3.19/1.83 ( ~ ( member_a @ X2 @ S2 )
% 3.19/1.83 => ( ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [Y4: a] : ( if_b @ ( X2 = Y4 ) @ ( P @ Y4 ) @ ( Q @ Y4 ) )
% 3.19/1.83 @ S2 )
% 3.19/1.83 = ( groups1199149371um_a_b @ Q @ S2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_216_sum__delta__notmem_I4_J,axiom,
% 3.19/1.83 ! [X2: a,S2: set_a,P: a > real,Q: a > real] :
% 3.19/1.83 ( ~ ( member_a @ X2 @ S2 )
% 3.19/1.83 => ( ( groups1862963056a_real
% 3.19/1.83 @ ^ [Y4: a] : ( if_real @ ( X2 = Y4 ) @ ( P @ Y4 ) @ ( Q @ Y4 ) )
% 3.19/1.83 @ S2 )
% 3.19/1.83 = ( groups1862963056a_real @ Q @ S2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_217_sum__delta__notmem_I3_J,axiom,
% 3.19/1.83 ! [X2: a,S2: set_a,P: a > b,Q: a > b] :
% 3.19/1.83 ( ~ ( member_a @ X2 @ S2 )
% 3.19/1.83 => ( ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [Y4: a] : ( if_b @ ( Y4 = X2 ) @ ( P @ Y4 ) @ ( Q @ Y4 ) )
% 3.19/1.83 @ S2 )
% 3.19/1.83 = ( groups1199149371um_a_b @ Q @ S2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_218_sum__delta__notmem_I3_J,axiom,
% 3.19/1.83 ! [X2: a,S2: set_a,P: a > real,Q: a > real] :
% 3.19/1.83 ( ~ ( member_a @ X2 @ S2 )
% 3.19/1.83 => ( ( groups1862963056a_real
% 3.19/1.83 @ ^ [Y4: a] : ( if_real @ ( Y4 = X2 ) @ ( P @ Y4 ) @ ( Q @ Y4 ) )
% 3.19/1.83 @ S2 )
% 3.19/1.83 = ( groups1862963056a_real @ Q @ S2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_219_sum__delta__notmem_I2_J,axiom,
% 3.19/1.83 ! [X2: a,S2: set_a,P: a > b,Q: a > b] :
% 3.19/1.83 ( ~ ( member_a @ X2 @ S2 )
% 3.19/1.83 => ( ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [Y4: a] : ( if_b @ ( X2 = Y4 ) @ ( P @ X2 ) @ ( Q @ Y4 ) )
% 3.19/1.83 @ S2 )
% 3.19/1.83 = ( groups1199149371um_a_b @ Q @ S2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_220_sum__delta__notmem_I2_J,axiom,
% 3.19/1.83 ! [X2: a,S2: set_a,P: a > real,Q: a > real] :
% 3.19/1.83 ( ~ ( member_a @ X2 @ S2 )
% 3.19/1.83 => ( ( groups1862963056a_real
% 3.19/1.83 @ ^ [Y4: a] : ( if_real @ ( X2 = Y4 ) @ ( P @ X2 ) @ ( Q @ Y4 ) )
% 3.19/1.83 @ S2 )
% 3.19/1.83 = ( groups1862963056a_real @ Q @ S2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_221_sum__delta__notmem_I1_J,axiom,
% 3.19/1.83 ! [X2: a,S2: set_a,P: a > b,Q: a > b] :
% 3.19/1.83 ( ~ ( member_a @ X2 @ S2 )
% 3.19/1.83 => ( ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [Y4: a] : ( if_b @ ( Y4 = X2 ) @ ( P @ X2 ) @ ( Q @ Y4 ) )
% 3.19/1.83 @ S2 )
% 3.19/1.83 = ( groups1199149371um_a_b @ Q @ S2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_222_sum__delta__notmem_I1_J,axiom,
% 3.19/1.83 ! [X2: a,S2: set_a,P: a > real,Q: a > real] :
% 3.19/1.83 ( ~ ( member_a @ X2 @ S2 )
% 3.19/1.83 => ( ( groups1862963056a_real
% 3.19/1.83 @ ^ [Y4: a] : ( if_real @ ( Y4 = X2 ) @ ( P @ X2 ) @ ( Q @ Y4 ) )
% 3.19/1.83 @ S2 )
% 3.19/1.83 = ( groups1862963056a_real @ Q @ S2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_223_sum_Oswap,axiom,
% 3.19/1.83 ! [G: a > a > b,B2: set_a,A2: set_a] :
% 3.19/1.83 ( ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [I3: a] : ( groups1199149371um_a_b @ ( G @ I3 ) @ B2 )
% 3.19/1.83 @ A2 )
% 3.19/1.83 = ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [J: a] :
% 3.19/1.83 ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [I3: a] : ( G @ I3 @ J )
% 3.19/1.83 @ A2 )
% 3.19/1.83 @ B2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_224_sum_Oswap,axiom,
% 3.19/1.83 ! [G: a > a > real,B2: set_a,A2: set_a] :
% 3.19/1.83 ( ( groups1862963056a_real
% 3.19/1.83 @ ^ [I3: a] : ( groups1862963056a_real @ ( G @ I3 ) @ B2 )
% 3.19/1.83 @ A2 )
% 3.19/1.83 = ( groups1862963056a_real
% 3.19/1.83 @ ^ [J: a] :
% 3.19/1.83 ( groups1862963056a_real
% 3.19/1.83 @ ^ [I3: a] : ( G @ I3 @ J )
% 3.19/1.83 @ A2 )
% 3.19/1.83 @ B2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_225_infinite__imp__nonempty,axiom,
% 3.19/1.83 ! [S: set_a] :
% 3.19/1.83 ( ~ ( finite_finite_a @ S )
% 3.19/1.83 => ( S != bot_bot_set_a ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_226_finite_OemptyI,axiom,
% 3.19/1.83 finite_finite_a @ bot_bot_set_a ).
% 3.19/1.83
% 3.19/1.83 thf(fact_227_singleton__inject,axiom,
% 3.19/1.83 ! [A: a,B: a] :
% 3.19/1.83 ( ( ( insert_a @ A @ bot_bot_set_a )
% 3.19/1.83 = ( insert_a @ B @ bot_bot_set_a ) )
% 3.19/1.83 => ( A = B ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_228_insert__not__empty,axiom,
% 3.19/1.83 ! [A: a,A2: set_a] :
% 3.19/1.83 ( ( insert_a @ A @ A2 )
% 3.19/1.83 != bot_bot_set_a ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_229_doubleton__eq__iff,axiom,
% 3.19/1.83 ! [A: a,B: a,C: a,D: a] :
% 3.19/1.83 ( ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
% 3.19/1.83 = ( insert_a @ C @ ( insert_a @ D @ bot_bot_set_a ) ) )
% 3.19/1.83 = ( ( ( A = C )
% 3.19/1.83 & ( B = D ) )
% 3.19/1.83 | ( ( A = D )
% 3.19/1.83 & ( B = C ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_230_singleton__iff,axiom,
% 3.19/1.83 ! [B: b,A: b] :
% 3.19/1.83 ( ( member_b @ B @ ( insert_b @ A @ bot_bot_set_b ) )
% 3.19/1.83 = ( B = A ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_231_singleton__iff,axiom,
% 3.19/1.83 ! [B: a,A: a] :
% 3.19/1.83 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 3.19/1.83 = ( B = A ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_232_singletonD,axiom,
% 3.19/1.83 ! [B: b,A: b] :
% 3.19/1.83 ( ( member_b @ B @ ( insert_b @ A @ bot_bot_set_b ) )
% 3.19/1.83 => ( B = A ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_233_singletonD,axiom,
% 3.19/1.83 ! [B: a,A: a] :
% 3.19/1.83 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 3.19/1.83 => ( B = A ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_234_finite_OinsertI,axiom,
% 3.19/1.83 ! [A2: set_a,A: a] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( finite_finite_a @ ( insert_a @ A @ A2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_235_sum__product,axiom,
% 3.19/1.83 ! [F: a > real,A2: set_a,G: a > real,B2: set_a] :
% 3.19/1.83 ( ( times_times_real @ ( groups1862963056a_real @ F @ A2 ) @ ( groups1862963056a_real @ G @ B2 ) )
% 3.19/1.83 = ( groups1862963056a_real
% 3.19/1.83 @ ^ [I3: a] :
% 3.19/1.83 ( groups1862963056a_real
% 3.19/1.83 @ ^ [J: a] : ( times_times_real @ ( F @ I3 ) @ ( G @ J ) )
% 3.19/1.83 @ B2 )
% 3.19/1.83 @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_236_sum__distrib__left,axiom,
% 3.19/1.83 ! [R: real,F: a > real,A2: set_a] :
% 3.19/1.83 ( ( times_times_real @ R @ ( groups1862963056a_real @ F @ A2 ) )
% 3.19/1.83 = ( groups1862963056a_real
% 3.19/1.83 @ ^ [N: a] : ( times_times_real @ R @ ( F @ N ) )
% 3.19/1.83 @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_237_sum__distrib__right,axiom,
% 3.19/1.83 ! [F: a > real,A2: set_a,R: real] :
% 3.19/1.83 ( ( times_times_real @ ( groups1862963056a_real @ F @ A2 ) @ R )
% 3.19/1.83 = ( groups1862963056a_real
% 3.19/1.83 @ ^ [N: a] : ( times_times_real @ ( F @ N ) @ R )
% 3.19/1.83 @ A2 ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_238_sum_Odistrib,axiom,
% 3.19/1.83 ! [G: a > b,H: a > b,A2: set_a] :
% 3.19/1.83 ( ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [X: a] : ( plus_plus_b @ ( G @ X ) @ ( H @ X ) )
% 3.19/1.83 @ A2 )
% 3.19/1.83 = ( plus_plus_b @ ( groups1199149371um_a_b @ G @ A2 ) @ ( groups1199149371um_a_b @ H @ A2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_239_sum_Odistrib,axiom,
% 3.19/1.83 ! [G: a > real,H: a > real,A2: set_a] :
% 3.19/1.83 ( ( groups1862963056a_real
% 3.19/1.83 @ ^ [X: a] : ( plus_plus_real @ ( G @ X ) @ ( H @ X ) )
% 3.19/1.83 @ A2 )
% 3.19/1.83 = ( plus_plus_real @ ( groups1862963056a_real @ G @ A2 ) @ ( groups1862963056a_real @ H @ A2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_240_Collect__conv__if2,axiom,
% 3.19/1.83 ! [P: a > $o,A: a] :
% 3.19/1.83 ( ( ( P @ A )
% 3.19/1.83 => ( ( collect_a
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( ( A = X )
% 3.19/1.83 & ( P @ X ) ) )
% 3.19/1.83 = ( insert_a @ A @ bot_bot_set_a ) ) )
% 3.19/1.83 & ( ~ ( P @ A )
% 3.19/1.83 => ( ( collect_a
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( ( A = X )
% 3.19/1.83 & ( P @ X ) ) )
% 3.19/1.83 = bot_bot_set_a ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_241_Collect__conv__if,axiom,
% 3.19/1.83 ! [P: a > $o,A: a] :
% 3.19/1.83 ( ( ( P @ A )
% 3.19/1.83 => ( ( collect_a
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( ( X = A )
% 3.19/1.83 & ( P @ X ) ) )
% 3.19/1.83 = ( insert_a @ A @ bot_bot_set_a ) ) )
% 3.19/1.83 & ( ~ ( P @ A )
% 3.19/1.83 => ( ( collect_a
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( ( X = A )
% 3.19/1.83 & ( P @ X ) ) )
% 3.19/1.83 = bot_bot_set_a ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_242_sum__subtractf,axiom,
% 3.19/1.83 ! [F: a > b,G: a > b,A2: set_a] :
% 3.19/1.83 ( ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [X: a] : ( minus_minus_b @ ( F @ X ) @ ( G @ X ) )
% 3.19/1.83 @ A2 )
% 3.19/1.83 = ( minus_minus_b @ ( groups1199149371um_a_b @ F @ A2 ) @ ( groups1199149371um_a_b @ G @ A2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_243_sum__subtractf,axiom,
% 3.19/1.83 ! [F: a > real,G: a > real,A2: set_a] :
% 3.19/1.83 ( ( groups1862963056a_real
% 3.19/1.83 @ ^ [X: a] : ( minus_minus_real @ ( F @ X ) @ ( G @ X ) )
% 3.19/1.83 @ A2 )
% 3.19/1.83 = ( minus_minus_real @ ( groups1862963056a_real @ F @ A2 ) @ ( groups1862963056a_real @ G @ A2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_244_sum_Oswap__restrict,axiom,
% 3.19/1.83 ! [A2: set_b,B2: set_a,G: b > a > b,R2: b > a > $o] :
% 3.19/1.83 ( ( finite_finite_b @ A2 )
% 3.19/1.83 => ( ( finite_finite_a @ B2 )
% 3.19/1.83 => ( ( groups2026918778um_b_b
% 3.19/1.83 @ ^ [X: b] :
% 3.19/1.83 ( groups1199149371um_a_b @ ( G @ X )
% 3.19/1.83 @ ( collect_a
% 3.19/1.83 @ ^ [Y4: a] :
% 3.19/1.83 ( ( member_a @ Y4 @ B2 )
% 3.19/1.83 & ( R2 @ X @ Y4 ) ) ) )
% 3.19/1.83 @ A2 )
% 3.19/1.83 = ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [Y4: a] :
% 3.19/1.83 ( groups2026918778um_b_b
% 3.19/1.83 @ ^ [X: b] : ( G @ X @ Y4 )
% 3.19/1.83 @ ( collect_b
% 3.19/1.83 @ ^ [X: b] :
% 3.19/1.83 ( ( member_b @ X @ A2 )
% 3.19/1.83 & ( R2 @ X @ Y4 ) ) ) )
% 3.19/1.83 @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_245_sum_Oswap__restrict,axiom,
% 3.19/1.83 ! [A2: set_b,B2: set_a,G: b > a > real,R2: b > a > $o] :
% 3.19/1.83 ( ( finite_finite_b @ A2 )
% 3.19/1.83 => ( ( finite_finite_a @ B2 )
% 3.19/1.83 => ( ( groups583146225b_real
% 3.19/1.83 @ ^ [X: b] :
% 3.19/1.83 ( groups1862963056a_real @ ( G @ X )
% 3.19/1.83 @ ( collect_a
% 3.19/1.83 @ ^ [Y4: a] :
% 3.19/1.83 ( ( member_a @ Y4 @ B2 )
% 3.19/1.83 & ( R2 @ X @ Y4 ) ) ) )
% 3.19/1.83 @ A2 )
% 3.19/1.83 = ( groups1862963056a_real
% 3.19/1.83 @ ^ [Y4: a] :
% 3.19/1.83 ( groups583146225b_real
% 3.19/1.83 @ ^ [X: b] : ( G @ X @ Y4 )
% 3.19/1.83 @ ( collect_b
% 3.19/1.83 @ ^ [X: b] :
% 3.19/1.83 ( ( member_b @ X @ A2 )
% 3.19/1.83 & ( R2 @ X @ Y4 ) ) ) )
% 3.19/1.83 @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_246_sum_Oswap__restrict,axiom,
% 3.19/1.83 ! [A2: set_a,B2: set_b,G: a > b > b,R2: a > b > $o] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ( finite_finite_b @ B2 )
% 3.19/1.83 => ( ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( groups2026918778um_b_b @ ( G @ X )
% 3.19/1.83 @ ( collect_b
% 3.19/1.83 @ ^ [Y4: b] :
% 3.19/1.83 ( ( member_b @ Y4 @ B2 )
% 3.19/1.83 & ( R2 @ X @ Y4 ) ) ) )
% 3.19/1.83 @ A2 )
% 3.19/1.83 = ( groups2026918778um_b_b
% 3.19/1.83 @ ^ [Y4: b] :
% 3.19/1.83 ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [X: a] : ( G @ X @ Y4 )
% 3.19/1.83 @ ( collect_a
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( ( member_a @ X @ A2 )
% 3.19/1.83 & ( R2 @ X @ Y4 ) ) ) )
% 3.19/1.83 @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_247_sum_Oswap__restrict,axiom,
% 3.19/1.83 ! [A2: set_a,B2: set_a,G: a > a > b,R2: a > a > $o] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ( finite_finite_a @ B2 )
% 3.19/1.83 => ( ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( groups1199149371um_a_b @ ( G @ X )
% 3.19/1.83 @ ( collect_a
% 3.19/1.83 @ ^ [Y4: a] :
% 3.19/1.83 ( ( member_a @ Y4 @ B2 )
% 3.19/1.83 & ( R2 @ X @ Y4 ) ) ) )
% 3.19/1.83 @ A2 )
% 3.19/1.83 = ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [Y4: a] :
% 3.19/1.83 ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [X: a] : ( G @ X @ Y4 )
% 3.19/1.83 @ ( collect_a
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( ( member_a @ X @ A2 )
% 3.19/1.83 & ( R2 @ X @ Y4 ) ) ) )
% 3.19/1.83 @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_248_sum_Oswap__restrict,axiom,
% 3.19/1.83 ! [A2: set_a,B2: set_b,G: a > b > real,R2: a > b > $o] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ( finite_finite_b @ B2 )
% 3.19/1.83 => ( ( groups1862963056a_real
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( groups583146225b_real @ ( G @ X )
% 3.19/1.83 @ ( collect_b
% 3.19/1.83 @ ^ [Y4: b] :
% 3.19/1.83 ( ( member_b @ Y4 @ B2 )
% 3.19/1.83 & ( R2 @ X @ Y4 ) ) ) )
% 3.19/1.83 @ A2 )
% 3.19/1.83 = ( groups583146225b_real
% 3.19/1.83 @ ^ [Y4: b] :
% 3.19/1.83 ( groups1862963056a_real
% 3.19/1.83 @ ^ [X: a] : ( G @ X @ Y4 )
% 3.19/1.83 @ ( collect_a
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( ( member_a @ X @ A2 )
% 3.19/1.83 & ( R2 @ X @ Y4 ) ) ) )
% 3.19/1.83 @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_249_sum_Oswap__restrict,axiom,
% 3.19/1.83 ! [A2: set_a,B2: set_a,G: a > a > real,R2: a > a > $o] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ( finite_finite_a @ B2 )
% 3.19/1.83 => ( ( groups1862963056a_real
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( groups1862963056a_real @ ( G @ X )
% 3.19/1.83 @ ( collect_a
% 3.19/1.83 @ ^ [Y4: a] :
% 3.19/1.83 ( ( member_a @ Y4 @ B2 )
% 3.19/1.83 & ( R2 @ X @ Y4 ) ) ) )
% 3.19/1.83 @ A2 )
% 3.19/1.83 = ( groups1862963056a_real
% 3.19/1.83 @ ^ [Y4: a] :
% 3.19/1.83 ( groups1862963056a_real
% 3.19/1.83 @ ^ [X: a] : ( G @ X @ Y4 )
% 3.19/1.83 @ ( collect_a
% 3.19/1.83 @ ^ [X: a] :
% 3.19/1.83 ( ( member_a @ X @ A2 )
% 3.19/1.83 & ( R2 @ X @ Y4 ) ) ) )
% 3.19/1.83 @ B2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_250_infinite__finite__induct,axiom,
% 3.19/1.83 ! [P: set_b > $o,A2: set_b] :
% 3.19/1.83 ( ! [A6: set_b] :
% 3.19/1.83 ( ~ ( finite_finite_b @ A6 )
% 3.19/1.83 => ( P @ A6 ) )
% 3.19/1.83 => ( ( P @ bot_bot_set_b )
% 3.19/1.83 => ( ! [X5: b,F2: set_b] :
% 3.19/1.83 ( ( finite_finite_b @ F2 )
% 3.19/1.83 => ( ~ ( member_b @ X5 @ F2 )
% 3.19/1.83 => ( ( P @ F2 )
% 3.19/1.83 => ( P @ ( insert_b @ X5 @ F2 ) ) ) ) )
% 3.19/1.83 => ( P @ A2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_251_infinite__finite__induct,axiom,
% 3.19/1.83 ! [P: set_a > $o,A2: set_a] :
% 3.19/1.83 ( ! [A6: set_a] :
% 3.19/1.83 ( ~ ( finite_finite_a @ A6 )
% 3.19/1.83 => ( P @ A6 ) )
% 3.19/1.83 => ( ( P @ bot_bot_set_a )
% 3.19/1.83 => ( ! [X5: a,F2: set_a] :
% 3.19/1.83 ( ( finite_finite_a @ F2 )
% 3.19/1.83 => ( ~ ( member_a @ X5 @ F2 )
% 3.19/1.83 => ( ( P @ F2 )
% 3.19/1.83 => ( P @ ( insert_a @ X5 @ F2 ) ) ) ) )
% 3.19/1.83 => ( P @ A2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_252_finite__ne__induct,axiom,
% 3.19/1.83 ! [F3: set_b,P: set_b > $o] :
% 3.19/1.83 ( ( finite_finite_b @ F3 )
% 3.19/1.83 => ( ( F3 != bot_bot_set_b )
% 3.19/1.83 => ( ! [X5: b] : ( P @ ( insert_b @ X5 @ bot_bot_set_b ) )
% 3.19/1.83 => ( ! [X5: b,F2: set_b] :
% 3.19/1.83 ( ( finite_finite_b @ F2 )
% 3.19/1.83 => ( ( F2 != bot_bot_set_b )
% 3.19/1.83 => ( ~ ( member_b @ X5 @ F2 )
% 3.19/1.83 => ( ( P @ F2 )
% 3.19/1.83 => ( P @ ( insert_b @ X5 @ F2 ) ) ) ) ) )
% 3.19/1.83 => ( P @ F3 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_253_finite__ne__induct,axiom,
% 3.19/1.83 ! [F3: set_a,P: set_a > $o] :
% 3.19/1.83 ( ( finite_finite_a @ F3 )
% 3.19/1.83 => ( ( F3 != bot_bot_set_a )
% 3.19/1.83 => ( ! [X5: a] : ( P @ ( insert_a @ X5 @ bot_bot_set_a ) )
% 3.19/1.83 => ( ! [X5: a,F2: set_a] :
% 3.19/1.83 ( ( finite_finite_a @ F2 )
% 3.19/1.83 => ( ( F2 != bot_bot_set_a )
% 3.19/1.83 => ( ~ ( member_a @ X5 @ F2 )
% 3.19/1.83 => ( ( P @ F2 )
% 3.19/1.83 => ( P @ ( insert_a @ X5 @ F2 ) ) ) ) ) )
% 3.19/1.83 => ( P @ F3 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_254_finite_Oinducts,axiom,
% 3.19/1.83 ! [X2: set_a,P: set_a > $o] :
% 3.19/1.83 ( ( finite_finite_a @ X2 )
% 3.19/1.83 => ( ( P @ bot_bot_set_a )
% 3.19/1.83 => ( ! [A6: set_a,A5: a] :
% 3.19/1.83 ( ( finite_finite_a @ A6 )
% 3.19/1.83 => ( ( P @ A6 )
% 3.19/1.83 => ( P @ ( insert_a @ A5 @ A6 ) ) ) )
% 3.19/1.83 => ( P @ X2 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_255_finite__induct,axiom,
% 3.19/1.83 ! [F3: set_b,P: set_b > $o] :
% 3.19/1.83 ( ( finite_finite_b @ F3 )
% 3.19/1.83 => ( ( P @ bot_bot_set_b )
% 3.19/1.83 => ( ! [X5: b,F2: set_b] :
% 3.19/1.83 ( ( finite_finite_b @ F2 )
% 3.19/1.83 => ( ~ ( member_b @ X5 @ F2 )
% 3.19/1.83 => ( ( P @ F2 )
% 3.19/1.83 => ( P @ ( insert_b @ X5 @ F2 ) ) ) ) )
% 3.19/1.83 => ( P @ F3 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_256_finite__induct,axiom,
% 3.19/1.83 ! [F3: set_a,P: set_a > $o] :
% 3.19/1.83 ( ( finite_finite_a @ F3 )
% 3.19/1.83 => ( ( P @ bot_bot_set_a )
% 3.19/1.83 => ( ! [X5: a,F2: set_a] :
% 3.19/1.83 ( ( finite_finite_a @ F2 )
% 3.19/1.83 => ( ~ ( member_a @ X5 @ F2 )
% 3.19/1.83 => ( ( P @ F2 )
% 3.19/1.83 => ( P @ ( insert_a @ X5 @ F2 ) ) ) ) )
% 3.19/1.83 => ( P @ F3 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_257_finite_Osimps,axiom,
% 3.19/1.83 ( finite_finite_a
% 3.19/1.83 = ( ^ [A3: set_a] :
% 3.19/1.83 ( ( A3 = bot_bot_set_a )
% 3.19/1.83 | ? [A4: set_a,B4: a] :
% 3.19/1.83 ( ( A3
% 3.19/1.83 = ( insert_a @ B4 @ A4 ) )
% 3.19/1.83 & ( finite_finite_a @ A4 ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_258_finite_Ocases,axiom,
% 3.19/1.83 ! [A: set_a] :
% 3.19/1.83 ( ( finite_finite_a @ A )
% 3.19/1.83 => ( ( A != bot_bot_set_a )
% 3.19/1.83 => ~ ! [A6: set_a] :
% 3.19/1.83 ( ? [A5: a] :
% 3.19/1.83 ( A
% 3.19/1.83 = ( insert_a @ A5 @ A6 ) )
% 3.19/1.83 => ~ ( finite_finite_a @ A6 ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_259_prod_Ofinite__Collect__op,axiom,
% 3.19/1.83 ! [I4: set_b,X2: b > real,Y: b > real] :
% 3.19/1.83 ( ( finite_finite_b
% 3.19/1.83 @ ( collect_b
% 3.19/1.83 @ ^ [I3: b] :
% 3.19/1.83 ( ( member_b @ I3 @ I4 )
% 3.19/1.83 & ( ( X2 @ I3 )
% 3.19/1.83 != one_one_real ) ) ) )
% 3.19/1.83 => ( ( finite_finite_b
% 3.19/1.83 @ ( collect_b
% 3.19/1.83 @ ^ [I3: b] :
% 3.19/1.83 ( ( member_b @ I3 @ I4 )
% 3.19/1.83 & ( ( Y @ I3 )
% 3.19/1.83 != one_one_real ) ) ) )
% 3.19/1.83 => ( finite_finite_b
% 3.19/1.83 @ ( collect_b
% 3.19/1.83 @ ^ [I3: b] :
% 3.19/1.83 ( ( member_b @ I3 @ I4 )
% 3.19/1.83 & ( ( times_times_real @ ( X2 @ I3 ) @ ( Y @ I3 ) )
% 3.19/1.83 != one_one_real ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_260_prod_Ofinite__Collect__op,axiom,
% 3.19/1.83 ! [I4: set_a,X2: a > real,Y: a > real] :
% 3.19/1.83 ( ( finite_finite_a
% 3.19/1.83 @ ( collect_a
% 3.19/1.83 @ ^ [I3: a] :
% 3.19/1.83 ( ( member_a @ I3 @ I4 )
% 3.19/1.83 & ( ( X2 @ I3 )
% 3.19/1.83 != one_one_real ) ) ) )
% 3.19/1.83 => ( ( finite_finite_a
% 3.19/1.83 @ ( collect_a
% 3.19/1.83 @ ^ [I3: a] :
% 3.19/1.83 ( ( member_a @ I3 @ I4 )
% 3.19/1.83 & ( ( Y @ I3 )
% 3.19/1.83 != one_one_real ) ) ) )
% 3.19/1.83 => ( finite_finite_a
% 3.19/1.83 @ ( collect_a
% 3.19/1.83 @ ^ [I3: a] :
% 3.19/1.83 ( ( member_a @ I3 @ I4 )
% 3.19/1.83 & ( ( times_times_real @ ( X2 @ I3 ) @ ( Y @ I3 ) )
% 3.19/1.83 != one_one_real ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_261_sum_Oinsert__if,axiom,
% 3.19/1.83 ! [A2: set_b,X2: b,G: b > b] :
% 3.19/1.83 ( ( finite_finite_b @ A2 )
% 3.19/1.83 => ( ( ( member_b @ X2 @ A2 )
% 3.19/1.83 => ( ( groups2026918778um_b_b @ G @ ( insert_b @ X2 @ A2 ) )
% 3.19/1.83 = ( groups2026918778um_b_b @ G @ A2 ) ) )
% 3.19/1.83 & ( ~ ( member_b @ X2 @ A2 )
% 3.19/1.83 => ( ( groups2026918778um_b_b @ G @ ( insert_b @ X2 @ A2 ) )
% 3.19/1.83 = ( plus_plus_b @ ( G @ X2 ) @ ( groups2026918778um_b_b @ G @ A2 ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_262_sum_Oinsert__if,axiom,
% 3.19/1.83 ! [A2: set_b,X2: b,G: b > real] :
% 3.19/1.83 ( ( finite_finite_b @ A2 )
% 3.19/1.83 => ( ( ( member_b @ X2 @ A2 )
% 3.19/1.83 => ( ( groups583146225b_real @ G @ ( insert_b @ X2 @ A2 ) )
% 3.19/1.83 = ( groups583146225b_real @ G @ A2 ) ) )
% 3.19/1.83 & ( ~ ( member_b @ X2 @ A2 )
% 3.19/1.83 => ( ( groups583146225b_real @ G @ ( insert_b @ X2 @ A2 ) )
% 3.19/1.83 = ( plus_plus_real @ ( G @ X2 ) @ ( groups583146225b_real @ G @ A2 ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_263_sum_Oinsert__if,axiom,
% 3.19/1.83 ! [A2: set_a,X2: a,G: a > b] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ( ( member_a @ X2 @ A2 )
% 3.19/1.83 => ( ( groups1199149371um_a_b @ G @ ( insert_a @ X2 @ A2 ) )
% 3.19/1.83 = ( groups1199149371um_a_b @ G @ A2 ) ) )
% 3.19/1.83 & ( ~ ( member_a @ X2 @ A2 )
% 3.19/1.83 => ( ( groups1199149371um_a_b @ G @ ( insert_a @ X2 @ A2 ) )
% 3.19/1.83 = ( plus_plus_b @ ( G @ X2 ) @ ( groups1199149371um_a_b @ G @ A2 ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_264_sum_Oinsert__if,axiom,
% 3.19/1.83 ! [A2: set_a,X2: a,G: a > real] :
% 3.19/1.83 ( ( finite_finite_a @ A2 )
% 3.19/1.83 => ( ( ( member_a @ X2 @ A2 )
% 3.19/1.83 => ( ( groups1862963056a_real @ G @ ( insert_a @ X2 @ A2 ) )
% 3.19/1.83 = ( groups1862963056a_real @ G @ A2 ) ) )
% 3.19/1.83 & ( ~ ( member_a @ X2 @ A2 )
% 3.19/1.83 => ( ( groups1862963056a_real @ G @ ( insert_a @ X2 @ A2 ) )
% 3.19/1.83 = ( plus_plus_real @ ( G @ X2 ) @ ( groups1862963056a_real @ G @ A2 ) ) ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_265_convex__singleton,axiom,
% 3.19/1.83 ! [A: b] : ( convex_b @ ( insert_b @ A @ bot_bot_set_b ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_266_real__divide__square__eq,axiom,
% 3.19/1.83 ! [R: real,A: real] :
% 3.19/1.83 ( ( divide_divide_real @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ R ) )
% 3.19/1.83 = ( divide_divide_real @ A @ R ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_267_convex__empty,axiom,
% 3.19/1.83 convex_b @ bot_bot_set_b ).
% 3.19/1.83
% 3.19/1.83 thf(fact_268_div__by__1,axiom,
% 3.19/1.83 ! [A: real] :
% 3.19/1.83 ( ( divide_divide_real @ A @ one_one_real )
% 3.19/1.83 = A ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_269_add__diff__cancel,axiom,
% 3.19/1.83 ! [A: b,B: b] :
% 3.19/1.83 ( ( minus_minus_b @ ( plus_plus_b @ A @ B ) @ B )
% 3.19/1.83 = A ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_270_add__diff__cancel,axiom,
% 3.19/1.83 ! [A: real,B: real] :
% 3.19/1.83 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 3.19/1.83 = A ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_271_diff__add__cancel,axiom,
% 3.19/1.83 ! [A: b,B: b] :
% 3.19/1.83 ( ( plus_plus_b @ ( minus_minus_b @ A @ B ) @ B )
% 3.19/1.83 = A ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_272_diff__add__cancel,axiom,
% 3.19/1.83 ! [A: real,B: real] :
% 3.19/1.83 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 3.19/1.83 = A ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_273_add__right__cancel,axiom,
% 3.19/1.83 ! [B: b,A: b,C: b] :
% 3.19/1.83 ( ( ( plus_plus_b @ B @ A )
% 3.19/1.83 = ( plus_plus_b @ C @ A ) )
% 3.19/1.83 = ( B = C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_274_add__right__cancel,axiom,
% 3.19/1.83 ! [B: real,A: real,C: real] :
% 3.19/1.83 ( ( ( plus_plus_real @ B @ A )
% 3.19/1.83 = ( plus_plus_real @ C @ A ) )
% 3.19/1.83 = ( B = C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_275_add__left__cancel,axiom,
% 3.19/1.83 ! [A: b,B: b,C: b] :
% 3.19/1.83 ( ( ( plus_plus_b @ A @ B )
% 3.19/1.83 = ( plus_plus_b @ A @ C ) )
% 3.19/1.83 = ( B = C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_276_add__left__cancel,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( ( plus_plus_real @ A @ B )
% 3.19/1.83 = ( plus_plus_real @ A @ C ) )
% 3.19/1.83 = ( B = C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_277_mult_Oright__neutral,axiom,
% 3.19/1.83 ! [A: real] :
% 3.19/1.83 ( ( times_times_real @ A @ one_one_real )
% 3.19/1.83 = A ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_278_mult_Oleft__neutral,axiom,
% 3.19/1.83 ! [A: real] :
% 3.19/1.83 ( ( times_times_real @ one_one_real @ A )
% 3.19/1.83 = A ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_279_add__diff__cancel__right_H,axiom,
% 3.19/1.83 ! [A: b,B: b] :
% 3.19/1.83 ( ( minus_minus_b @ ( plus_plus_b @ A @ B ) @ B )
% 3.19/1.83 = A ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_280_add__diff__cancel__right_H,axiom,
% 3.19/1.83 ! [A: real,B: real] :
% 3.19/1.83 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 3.19/1.83 = A ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_281_add__diff__cancel__right,axiom,
% 3.19/1.83 ! [A: b,C: b,B: b] :
% 3.19/1.83 ( ( minus_minus_b @ ( plus_plus_b @ A @ C ) @ ( plus_plus_b @ B @ C ) )
% 3.19/1.83 = ( minus_minus_b @ A @ B ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_282_add__diff__cancel__right,axiom,
% 3.19/1.83 ! [A: real,C: real,B: real] :
% 3.19/1.83 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 3.19/1.83 = ( minus_minus_real @ A @ B ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_283_add__diff__cancel__left_H,axiom,
% 3.19/1.83 ! [A: b,B: b] :
% 3.19/1.83 ( ( minus_minus_b @ ( plus_plus_b @ A @ B ) @ A )
% 3.19/1.83 = B ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_284_add__diff__cancel__left_H,axiom,
% 3.19/1.83 ! [A: real,B: real] :
% 3.19/1.83 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 3.19/1.83 = B ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_285_add__diff__cancel__left,axiom,
% 3.19/1.83 ! [C: b,A: b,B: b] :
% 3.19/1.83 ( ( minus_minus_b @ ( plus_plus_b @ C @ A ) @ ( plus_plus_b @ C @ B ) )
% 3.19/1.83 = ( minus_minus_b @ A @ B ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_286_add__diff__cancel__left,axiom,
% 3.19/1.83 ! [C: real,A: real,B: real] :
% 3.19/1.83 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 3.19/1.83 = ( minus_minus_real @ A @ B ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_287_mult_Oleft__commute,axiom,
% 3.19/1.83 ! [B: real,A: real,C: real] :
% 3.19/1.83 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 3.19/1.83 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_288_mult_Ocommute,axiom,
% 3.19/1.83 ( times_times_real
% 3.19/1.83 = ( ^ [A3: real,B4: real] : ( times_times_real @ B4 @ A3 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_289_mult_Oassoc,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 3.19/1.83 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_290_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 3.19/1.83 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_291_add__right__imp__eq,axiom,
% 3.19/1.83 ! [B: b,A: b,C: b] :
% 3.19/1.83 ( ( ( plus_plus_b @ B @ A )
% 3.19/1.83 = ( plus_plus_b @ C @ A ) )
% 3.19/1.83 => ( B = C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_292_add__right__imp__eq,axiom,
% 3.19/1.83 ! [B: real,A: real,C: real] :
% 3.19/1.83 ( ( ( plus_plus_real @ B @ A )
% 3.19/1.83 = ( plus_plus_real @ C @ A ) )
% 3.19/1.83 => ( B = C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_293_add__left__imp__eq,axiom,
% 3.19/1.83 ! [A: b,B: b,C: b] :
% 3.19/1.83 ( ( ( plus_plus_b @ A @ B )
% 3.19/1.83 = ( plus_plus_b @ A @ C ) )
% 3.19/1.83 => ( B = C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_294_add__left__imp__eq,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( ( plus_plus_real @ A @ B )
% 3.19/1.83 = ( plus_plus_real @ A @ C ) )
% 3.19/1.83 => ( B = C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_295_add_Oleft__commute,axiom,
% 3.19/1.83 ! [B: b,A: b,C: b] :
% 3.19/1.83 ( ( plus_plus_b @ B @ ( plus_plus_b @ A @ C ) )
% 3.19/1.83 = ( plus_plus_b @ A @ ( plus_plus_b @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_296_add_Oleft__commute,axiom,
% 3.19/1.83 ! [B: real,A: real,C: real] :
% 3.19/1.83 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 3.19/1.83 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_297_add_Ocommute,axiom,
% 3.19/1.83 ( plus_plus_b
% 3.19/1.83 = ( ^ [A3: b,B4: b] : ( plus_plus_b @ B4 @ A3 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_298_add_Ocommute,axiom,
% 3.19/1.83 ( plus_plus_real
% 3.19/1.83 = ( ^ [A3: real,B4: real] : ( plus_plus_real @ B4 @ A3 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_299_add_Oright__cancel,axiom,
% 3.19/1.83 ! [B: b,A: b,C: b] :
% 3.19/1.83 ( ( ( plus_plus_b @ B @ A )
% 3.19/1.83 = ( plus_plus_b @ C @ A ) )
% 3.19/1.83 = ( B = C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_300_add_Oright__cancel,axiom,
% 3.19/1.83 ! [B: real,A: real,C: real] :
% 3.19/1.83 ( ( ( plus_plus_real @ B @ A )
% 3.19/1.83 = ( plus_plus_real @ C @ A ) )
% 3.19/1.83 = ( B = C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_301_add_Oleft__cancel,axiom,
% 3.19/1.83 ! [A: b,B: b,C: b] :
% 3.19/1.83 ( ( ( plus_plus_b @ A @ B )
% 3.19/1.83 = ( plus_plus_b @ A @ C ) )
% 3.19/1.83 = ( B = C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_302_add_Oleft__cancel,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( ( plus_plus_real @ A @ B )
% 3.19/1.83 = ( plus_plus_real @ A @ C ) )
% 3.19/1.83 = ( B = C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_303_add_Oassoc,axiom,
% 3.19/1.83 ! [A: b,B: b,C: b] :
% 3.19/1.83 ( ( plus_plus_b @ ( plus_plus_b @ A @ B ) @ C )
% 3.19/1.83 = ( plus_plus_b @ A @ ( plus_plus_b @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_304_add_Oassoc,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 3.19/1.83 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_305_group__cancel_Oadd2,axiom,
% 3.19/1.83 ! [B2: b,K: b,B: b,A: b] :
% 3.19/1.83 ( ( B2
% 3.19/1.83 = ( plus_plus_b @ K @ B ) )
% 3.19/1.83 => ( ( plus_plus_b @ A @ B2 )
% 3.19/1.83 = ( plus_plus_b @ K @ ( plus_plus_b @ A @ B ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_306_group__cancel_Oadd2,axiom,
% 3.19/1.83 ! [B2: real,K: real,B: real,A: real] :
% 3.19/1.83 ( ( B2
% 3.19/1.83 = ( plus_plus_real @ K @ B ) )
% 3.19/1.83 => ( ( plus_plus_real @ A @ B2 )
% 3.19/1.83 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_307_group__cancel_Oadd1,axiom,
% 3.19/1.83 ! [A2: b,K: b,A: b,B: b] :
% 3.19/1.83 ( ( A2
% 3.19/1.83 = ( plus_plus_b @ K @ A ) )
% 3.19/1.83 => ( ( plus_plus_b @ A2 @ B )
% 3.19/1.83 = ( plus_plus_b @ K @ ( plus_plus_b @ A @ B ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_308_group__cancel_Oadd1,axiom,
% 3.19/1.83 ! [A2: real,K: real,A: real,B: real] :
% 3.19/1.83 ( ( A2
% 3.19/1.83 = ( plus_plus_real @ K @ A ) )
% 3.19/1.83 => ( ( plus_plus_real @ A2 @ B )
% 3.19/1.83 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_309_add__mono__thms__linordered__semiring_I4_J,axiom,
% 3.19/1.83 ! [I2: real,J2: real,K: real,L: real] :
% 3.19/1.83 ( ( ( I2 = J2 )
% 3.19/1.83 & ( K = L ) )
% 3.19/1.83 => ( ( plus_plus_real @ I2 @ K )
% 3.19/1.83 = ( plus_plus_real @ J2 @ L ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_310_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 3.19/1.83 ! [A: b,B: b,C: b] :
% 3.19/1.83 ( ( plus_plus_b @ ( plus_plus_b @ A @ B ) @ C )
% 3.19/1.83 = ( plus_plus_b @ A @ ( plus_plus_b @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_311_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 3.19/1.83 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_312_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 3.19/1.83 ! [A: real,C: real,B: real] :
% 3.19/1.83 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 3.19/1.83 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_313_diff__eq__diff__eq,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real,D: real] :
% 3.19/1.83 ( ( ( minus_minus_real @ A @ B )
% 3.19/1.83 = ( minus_minus_real @ C @ D ) )
% 3.19/1.83 => ( ( A = B )
% 3.19/1.83 = ( C = D ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_314_one__reorient,axiom,
% 3.19/1.83 ! [X2: real] :
% 3.19/1.83 ( ( one_one_real = X2 )
% 3.19/1.83 = ( X2 = one_one_real ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_315_convex__set__plus,axiom,
% 3.19/1.83 ! [S: set_b,T: set_b] :
% 3.19/1.83 ( ( convex_b @ S )
% 3.19/1.83 => ( ( convex_b @ T )
% 3.19/1.83 => ( convex_b @ ( plus_plus_set_b @ S @ T ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_316_convex__set__sum,axiom,
% 3.19/1.83 ! [A2: set_a,B2: a > set_b] :
% 3.19/1.83 ( ! [I5: a] :
% 3.19/1.83 ( ( member_a @ I5 @ A2 )
% 3.19/1.83 => ( convex_b @ ( B2 @ I5 ) ) )
% 3.19/1.83 => ( convex_b @ ( groups919362075_set_b @ B2 @ A2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_317_convex__set__sum,axiom,
% 3.19/1.83 ! [A2: set_b,B2: b > set_b] :
% 3.19/1.83 ( ! [I5: b] :
% 3.19/1.83 ( ( member_b @ I5 @ A2 )
% 3.19/1.83 => ( convex_b @ ( B2 @ I5 ) ) )
% 3.19/1.83 => ( convex_b @ ( groups448962650_set_b @ B2 @ A2 ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_318_combine__common__factor,axiom,
% 3.19/1.83 ! [A: real,E: real,B: real,C: real] :
% 3.19/1.83 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 3.19/1.83 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_319_distrib__right,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 3.19/1.83 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_320_distrib__left,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 3.19/1.83 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_321_comm__semiring__class_Odistrib,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 3.19/1.83 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_322_ring__class_Oring__distribs_I1_J,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 3.19/1.83 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_323_ring__class_Oring__distribs_I2_J,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 3.19/1.83 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_324_right__diff__distrib_H,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 3.19/1.83 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_325_left__diff__distrib_H,axiom,
% 3.19/1.83 ! [B: real,C: real,A: real] :
% 3.19/1.83 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 3.19/1.83 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_326_right__diff__distrib,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 3.19/1.83 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_327_left__diff__distrib,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 3.19/1.83 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_328_mult_Ocomm__neutral,axiom,
% 3.19/1.83 ! [A: real] :
% 3.19/1.83 ( ( times_times_real @ A @ one_one_real )
% 3.19/1.83 = A ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_329_comm__monoid__mult__class_Omult__1,axiom,
% 3.19/1.83 ! [A: real] :
% 3.19/1.83 ( ( times_times_real @ one_one_real @ A )
% 3.19/1.83 = A ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_330_add__implies__diff,axiom,
% 3.19/1.83 ! [C: b,B: b,A: b] :
% 3.19/1.83 ( ( ( plus_plus_b @ C @ B )
% 3.19/1.83 = A )
% 3.19/1.83 => ( C
% 3.19/1.83 = ( minus_minus_b @ A @ B ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_331_add__implies__diff,axiom,
% 3.19/1.83 ! [C: real,B: real,A: real] :
% 3.19/1.83 ( ( ( plus_plus_real @ C @ B )
% 3.19/1.83 = A )
% 3.19/1.83 => ( C
% 3.19/1.83 = ( minus_minus_real @ A @ B ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_332_diff__diff__add,axiom,
% 3.19/1.83 ! [A: b,B: b,C: b] :
% 3.19/1.83 ( ( minus_minus_b @ ( minus_minus_b @ A @ B ) @ C )
% 3.19/1.83 = ( minus_minus_b @ A @ ( plus_plus_b @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_333_diff__diff__add,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 3.19/1.83 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_334_diff__add__eq__diff__diff__swap,axiom,
% 3.19/1.83 ! [A: b,B: b,C: b] :
% 3.19/1.83 ( ( minus_minus_b @ A @ ( plus_plus_b @ B @ C ) )
% 3.19/1.83 = ( minus_minus_b @ ( minus_minus_b @ A @ C ) @ B ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_335_diff__add__eq__diff__diff__swap,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 3.19/1.83 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_336_diff__add__eq,axiom,
% 3.19/1.83 ! [A: b,B: b,C: b] :
% 3.19/1.83 ( ( plus_plus_b @ ( minus_minus_b @ A @ B ) @ C )
% 3.19/1.83 = ( minus_minus_b @ ( plus_plus_b @ A @ C ) @ B ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_337_diff__add__eq,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 3.19/1.83 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_338_diff__diff__eq2,axiom,
% 3.19/1.83 ! [A: b,B: b,C: b] :
% 3.19/1.83 ( ( minus_minus_b @ A @ ( minus_minus_b @ B @ C ) )
% 3.19/1.83 = ( minus_minus_b @ ( plus_plus_b @ A @ C ) @ B ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_339_diff__diff__eq2,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 3.19/1.83 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_340_add__diff__eq,axiom,
% 3.19/1.83 ! [A: b,B: b,C: b] :
% 3.19/1.83 ( ( plus_plus_b @ A @ ( minus_minus_b @ B @ C ) )
% 3.19/1.83 = ( minus_minus_b @ ( plus_plus_b @ A @ B ) @ C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_341_add__diff__eq,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 3.19/1.83 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_342_eq__diff__eq,axiom,
% 3.19/1.83 ! [A: b,C: b,B: b] :
% 3.19/1.83 ( ( A
% 3.19/1.83 = ( minus_minus_b @ C @ B ) )
% 3.19/1.83 = ( ( plus_plus_b @ A @ B )
% 3.19/1.83 = C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_343_eq__diff__eq,axiom,
% 3.19/1.83 ! [A: real,C: real,B: real] :
% 3.19/1.83 ( ( A
% 3.19/1.83 = ( minus_minus_real @ C @ B ) )
% 3.19/1.83 = ( ( plus_plus_real @ A @ B )
% 3.19/1.83 = C ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_344_diff__eq__eq,axiom,
% 3.19/1.83 ! [A: b,B: b,C: b] :
% 3.19/1.83 ( ( ( minus_minus_b @ A @ B )
% 3.19/1.83 = C )
% 3.19/1.83 = ( A
% 3.19/1.83 = ( plus_plus_b @ C @ B ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_345_diff__eq__eq,axiom,
% 3.19/1.83 ! [A: real,B: real,C: real] :
% 3.19/1.83 ( ( ( minus_minus_real @ A @ B )
% 3.19/1.83 = C )
% 3.19/1.83 = ( A
% 3.19/1.83 = ( plus_plus_real @ C @ B ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_346_group__cancel_Osub1,axiom,
% 3.19/1.83 ! [A2: b,K: b,A: b,B: b] :
% 3.19/1.83 ( ( A2
% 3.19/1.83 = ( plus_plus_b @ K @ A ) )
% 3.19/1.83 => ( ( minus_minus_b @ A2 @ B )
% 3.19/1.83 = ( plus_plus_b @ K @ ( minus_minus_b @ A @ B ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_347_group__cancel_Osub1,axiom,
% 3.19/1.83 ! [A2: real,K: real,A: real,B: real] :
% 3.19/1.83 ( ( A2
% 3.19/1.83 = ( plus_plus_real @ K @ A ) )
% 3.19/1.83 => ( ( minus_minus_real @ A2 @ B )
% 3.19/1.83 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_348_lambda__one,axiom,
% 3.19/1.83 ( ( ^ [X: real] : X )
% 3.19/1.83 = ( times_times_real @ one_one_real ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_349_square__diff__square__factored,axiom,
% 3.19/1.83 ! [X2: real,Y: real] :
% 3.19/1.83 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) )
% 3.19/1.83 = ( times_times_real @ ( plus_plus_real @ X2 @ Y ) @ ( minus_minus_real @ X2 @ Y ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_350_eq__add__iff2,axiom,
% 3.19/1.83 ! [A: real,E: real,C: real,B: real,D: real] :
% 3.19/1.83 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 3.19/1.83 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 3.19/1.83 = ( C
% 3.19/1.83 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_351_eq__add__iff1,axiom,
% 3.19/1.83 ! [A: real,E: real,C: real,B: real,D: real] :
% 3.19/1.83 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 3.19/1.83 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 3.19/1.83 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 3.19/1.83 = D ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(fact_352_ai1,axiom,
% 3.19/1.83 ord_less_eq_real @ ( aa @ i ) @ one_one_real ).
% 3.19/1.83
% 3.19/1.83 thf(help_If_2_1_If_001tf__b_T,axiom,
% 3.19/1.83 ! [X2: b,Y: b] :
% 3.19/1.83 ( ( if_b @ $false @ X2 @ Y )
% 3.19/1.83 = Y ) ).
% 3.19/1.83
% 3.19/1.83 thf(help_If_1_1_If_001tf__b_T,axiom,
% 3.19/1.83 ! [X2: b,Y: b] :
% 3.19/1.83 ( ( if_b @ $true @ X2 @ Y )
% 3.19/1.83 = X2 ) ).
% 3.19/1.83
% 3.19/1.83 thf(help_If_3_1_If_001t__Real__Oreal_T,axiom,
% 3.19/1.83 ! [P: $o] :
% 3.19/1.83 ( ( P = $true )
% 3.19/1.83 | ( P = $false ) ) ).
% 3.19/1.83
% 3.19/1.83 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 3.19/1.83 ! [X2: real,Y: real] :
% 3.19/1.83 ( ( if_real @ $false @ X2 @ Y )
% 3.19/1.83 = Y ) ).
% 3.19/1.83
% 3.19/1.83 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 3.19/1.83 ! [X2: real,Y: real] :
% 3.19/1.83 ( ( if_real @ $true @ X2 @ Y )
% 3.19/1.83 = X2 ) ).
% 3.19/1.83
% 3.19/1.83 thf(conj_0,conjecture,
% 3.19/1.83 ( ( f
% 3.19/1.83 @ ( plus_plus_b
% 3.19/1.83 @ ( real_V1035702896aleR_b @ ( times_times_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) )
% 3.19/1.83 @ ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( aa @ J ) @ ( y @ J ) )
% 3.19/1.83 @ sa ) )
% 3.19/1.83 @ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) )
% 3.19/1.83 = ( f
% 3.19/1.83 @ ( plus_plus_b
% 3.19/1.83 @ ( real_V1035702896aleR_b @ ( minus_minus_real @ one_one_real @ ( aa @ i ) )
% 3.19/1.83 @ ( groups1199149371um_a_b
% 3.19/1.83 @ ^ [J: a] : ( real_V1035702896aleR_b @ ( times_times_real @ ( aa @ J ) @ ( inverse_inverse_real @ ( minus_minus_real @ one_one_real @ ( aa @ i ) ) ) ) @ ( y @ J ) )
% 3.19/1.83 @ sa ) )
% 3.19/1.83 @ ( real_V1035702896aleR_b @ ( aa @ i ) @ ( y @ i ) ) ) ) ) ).
% 3.19/1.83 ------------------------
% 3.19/1.85 % (14954)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_14827 for (2999ds/27Mi)
% 3.19/1.85 % (14958)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14827 for (2999ds/18Mi)
% 3.19/1.85 % (14957)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_14827 for (2999ds/275Mi)
% 3.19/1.85 % (14956)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_14827 for (2999ds/2Mi)
% 3.19/1.85 % (14956)Instruction limit reached!
% 3.19/1.85 % (14956)------------------------------
% 3.19/1.85 % (14956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.85 % (14956)Termination reason: Unknown
% 3.19/1.85 % (14956)Termination phase: shuffling
% 3.19/1.85
% 3.19/1.85 % (14956)Memory used [KB]: 1535
% 3.19/1.85 % (14956)Time elapsed: 0.002 s
% 3.19/1.85 % (14956)Instructions burned: 3 (million)
% 3.19/1.85 % (14956)------------------------------
% 3.19/1.85 % (14956)------------------------------
% 3.19/1.86 % (14952)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14827 for (2999ds/183Mi)
% 3.19/1.86 % (14958)Instruction limit reached!
% 3.19/1.86 % (14958)------------------------------
% 3.19/1.86 % (14958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.86 % (14958)Termination reason: Unknown
% 3.19/1.86 % (14958)Termination phase: shuffling
% 3.19/1.86
% 3.19/1.86 % (14958)Memory used [KB]: 1791
% 3.19/1.86 % (14958)Time elapsed: 0.007 s
% 3.19/1.86 % (14958)Instructions burned: 18 (million)
% 3.19/1.86 % (14958)------------------------------
% 3.19/1.86 % (14958)------------------------------
% 3.19/1.86 % (14953)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_14827 for (2999ds/4Mi)
% 3.19/1.86 % (14953)Instruction limit reached!
% 3.19/1.86 % (14953)------------------------------
% 3.19/1.86 % (14953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.86 % (14953)Termination reason: Unknown
% 3.19/1.86 % (14953)Termination phase: shuffling
% 3.19/1.86
% 3.19/1.86 % (14953)Memory used [KB]: 1535
% 3.19/1.86 % (14953)Time elapsed: 0.003 s
% 3.19/1.86 % (14953)Instructions burned: 5 (million)
% 3.19/1.86 % (14953)------------------------------
% 3.19/1.86 % (14953)------------------------------
% 3.19/1.86 % (14954)Instruction limit reached!
% 3.19/1.86 % (14954)------------------------------
% 3.19/1.86 % (14954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.86 % (14954)Termination reason: Unknown
% 3.19/1.86 % (14954)Termination phase: shuffling
% 3.19/1.86
% 3.19/1.86 % (14954)Memory used [KB]: 2046
% 3.19/1.86 % (14954)Time elapsed: 0.011 s
% 3.19/1.86 % (14954)Instructions burned: 29 (million)
% 3.19/1.86 % (14954)------------------------------
% 3.19/1.86 % (14954)------------------------------
% 3.19/1.87 % (14960)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_14827 for (2999ds/37Mi)
% 3.19/1.87 % (14962)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_14827 for (2999ds/3Mi)
% 3.19/1.87 % (14962)Instruction limit reached!
% 3.19/1.87 % (14962)------------------------------
% 3.19/1.87 % (14962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.87 % (14962)Termination reason: Unknown
% 3.19/1.87 % (14962)Termination phase: shuffling
% 3.19/1.87
% 3.19/1.87 % (14962)Memory used [KB]: 1535
% 3.19/1.87 % (14962)Time elapsed: 0.002 s
% 3.19/1.87 % (14962)Instructions burned: 3 (million)
% 3.19/1.87 % (14962)------------------------------
% 3.19/1.87 % (14962)------------------------------
% 3.19/1.87 % (14961)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_14827 for (2999ds/15Mi)
% 3.19/1.88 % (14959)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14827 for (2999ds/3Mi)
% 3.19/1.88 % (14961)Instruction limit reached!
% 3.19/1.88 % (14961)------------------------------
% 3.19/1.88 % (14961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.88 % (14961)Termination reason: Unknown
% 3.19/1.88 % (14961)Termination phase: shuffling
% 3.19/1.88
% 3.19/1.88 % (14961)Memory used [KB]: 1791
% 3.19/1.88 % (14961)Time elapsed: 0.006 s
% 3.19/1.88 % (14961)Instructions burned: 15 (million)
% 3.19/1.88 % (14961)------------------------------
% 3.19/1.88 % (14961)------------------------------
% 3.19/1.88 % (14959)Instruction limit reached!
% 3.19/1.88 % (14959)------------------------------
% 3.19/1.88 % (14959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.88 % (14960)Instruction limit reached!
% 3.19/1.88 % (14960)------------------------------
% 3.19/1.88 % (14960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.88 % (14959)Termination reason: Unknown
% 3.19/1.88 % (14959)Termination phase: shuffling
% 3.19/1.88
% 3.19/1.88 % (14959)Memory used [KB]: 1535
% 3.19/1.88 % (14959)Time elapsed: 0.004 s
% 3.19/1.88 % (14959)Instructions burned: 4 (million)
% 3.19/1.88 % (14959)------------------------------
% 3.19/1.88 % (14959)------------------------------
% 3.19/1.88 % (14960)Termination reason: Unknown
% 3.19/1.88 % (14960)Termination phase: shuffling
% 3.19/1.88
% 3.19/1.88 % (14960)Memory used [KB]: 2302
% 3.19/1.88 % (14960)Time elapsed: 0.011 s
% 3.19/1.88 % (14960)Instructions burned: 37 (million)
% 3.19/1.88 % (14960)------------------------------
% 3.19/1.88 % (14960)------------------------------
% 3.19/1.88 % (14955)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14827 for (2999ds/2Mi)
% 3.19/1.88 % (14955)Instruction limit reached!
% 3.19/1.88 % (14955)------------------------------
% 3.19/1.88 % (14955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.88 % (14955)Termination reason: Unknown
% 3.19/1.88 % (14955)Termination phase: shuffling
% 3.19/1.88
% 3.19/1.88 % (14955)Memory used [KB]: 1535
% 3.19/1.88 % (14955)Time elapsed: 0.003 s
% 3.19/1.88 % (14955)Instructions burned: 3 (million)
% 3.19/1.88 % (14955)------------------------------
% 3.19/1.88 % (14955)------------------------------
% 3.19/1.88 % (14963)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_14827 for (2999ds/1041Mi)
% 3.19/1.89 % (14964)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14827 for (2999ds/7Mi)
% 3.19/1.89 % (14965)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14827 for (2999ds/16Mi)
% 3.19/1.89 % (14964)Instruction limit reached!
% 3.19/1.89 % (14964)------------------------------
% 3.19/1.89 % (14964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.89 % (14964)Termination reason: Unknown
% 3.19/1.89 % (14964)Termination phase: shuffling
% 3.19/1.89
% 3.19/1.89 % (14964)Memory used [KB]: 1663
% 3.19/1.89 % (14964)Time elapsed: 0.004 s
% 3.19/1.89 % (14964)Instructions burned: 9 (million)
% 3.19/1.89 % (14964)------------------------------
% 3.19/1.89 % (14964)------------------------------
% 3.19/1.89 % (14965)Instruction limit reached!
% 3.19/1.89 % (14965)------------------------------
% 3.19/1.89 % (14965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.89 % (14965)Termination reason: Unknown
% 3.19/1.89 % (14965)Termination phase: shuffling
% 3.19/1.89
% 3.19/1.89 % (14965)Memory used [KB]: 1791
% 3.19/1.89 % (14965)Time elapsed: 0.006 s
% 3.19/1.89 % (14965)Instructions burned: 16 (million)
% 3.19/1.89 % (14965)------------------------------
% 3.19/1.89 % (14965)------------------------------
% 3.22/1.90 % (14966)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_14827 for (2999ds/3Mi)
% 3.22/1.90 % (14968)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14827 for (2999ds/7Mi)
% 3.22/1.90 % (14966)Instruction limit reached!
% 3.22/1.90 % (14966)------------------------------
% 3.22/1.90 % (14966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.90 % (14966)Termination reason: Unknown
% 3.22/1.90 % (14966)Termination phase: shuffling
% 3.22/1.90
% 3.22/1.90 % (14966)Memory used [KB]: 1535
% 3.22/1.90 % (14966)Time elapsed: 0.004 s
% 3.22/1.90 % (14966)Instructions burned: 4 (million)
% 3.22/1.90 % (14966)------------------------------
% 3.22/1.90 % (14966)------------------------------
% 3.22/1.90 % (14969)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14827 for (2999ds/3Mi)
% 3.22/1.90 % (14968)Instruction limit reached!
% 3.22/1.90 % (14968)------------------------------
% 3.22/1.90 % (14968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.90 % (14968)Termination reason: Unknown
% 3.22/1.90 % (14968)Termination phase: shuffling
% 3.22/1.90
% 3.22/1.90 % (14968)Memory used [KB]: 1663
% 3.22/1.90 % (14968)Time elapsed: 0.004 s
% 3.22/1.90 % (14968)Instructions burned: 9 (million)
% 3.22/1.90 % (14968)------------------------------
% 3.22/1.90 % (14968)------------------------------
% 3.22/1.90 % (14969)Instruction limit reached!
% 3.22/1.90 % (14969)------------------------------
% 3.22/1.90 % (14969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.90 % (14969)Termination reason: Unknown
% 3.22/1.90 % (14969)Termination phase: shuffling
% 3.22/1.90
% 3.22/1.90 % (14969)Memory used [KB]: 1535
% 3.22/1.90 % (14969)Time elapsed: 0.002 s
% 3.22/1.90 % (14969)Instructions burned: 3 (million)
% 3.22/1.90 % (14969)------------------------------
% 3.22/1.90 % (14969)------------------------------
% 3.22/1.91 % (14952)Instruction limit reached!
% 3.22/1.91 % (14952)------------------------------
% 3.22/1.91 % (14952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.91 % (14952)Termination reason: Unknown
% 3.22/1.91 % (14952)Termination phase: Saturation
% 3.22/1.91
% 3.22/1.91 % (14952)Memory used [KB]: 7291
% 3.22/1.91 % (14952)Time elapsed: 0.051 s
% 3.22/1.91 % (14952)Instructions burned: 186 (million)
% 3.22/1.91 % (14952)------------------------------
% 3.22/1.91 % (14952)------------------------------
% 3.22/1.91 % (14967)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_14827 for (2999ds/3Mi)
% 3.22/1.91 % (14967)Instruction limit reached!
% 3.22/1.91 % (14967)------------------------------
% 3.22/1.91 % (14967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.91 % (14967)Termination reason: Unknown
% 3.22/1.91 % (14967)Termination phase: shuffling
% 3.22/1.91
% 3.22/1.91 % (14967)Memory used [KB]: 1535
% 3.22/1.91 % (14967)Time elapsed: 0.003 s
% 3.22/1.91 % (14967)Instructions burned: 3 (million)
% 3.22/1.91 % (14967)------------------------------
% 3.22/1.91 % (14967)------------------------------
% 3.22/1.91 % (14971)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14827 for (2999ds/18Mi)
% 3.22/1.91 % (14972)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_14827 for (2999ds/710Mi)
% 3.22/1.92 % (14973)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14827 for (2999ds/6Mi)
% 3.22/1.92 % (14973)Instruction limit reached!
% 3.22/1.92 % (14973)------------------------------
% 3.22/1.92 % (14973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.92 % (14973)Termination reason: Unknown
% 3.22/1.92 % (14973)Termination phase: shuffling
% 3.22/1.92
% 3.22/1.92 % (14973)Memory used [KB]: 1535
% 3.22/1.92 % (14973)Time elapsed: 0.003 s
% 3.22/1.92 % (14973)Instructions burned: 6 (million)
% 3.22/1.92 % (14973)------------------------------
% 3.22/1.92 % (14973)------------------------------
% 3.22/1.92 % (14971)Instruction limit reached!
% 3.22/1.92 % (14971)------------------------------
% 3.22/1.92 % (14971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.92 % (14971)Termination reason: Unknown
% 3.22/1.92 % (14971)Termination phase: shuffling
% 3.22/1.92
% 3.22/1.92 % (14971)Memory used [KB]: 1791
% 3.22/1.92 % (14971)Time elapsed: 0.008 s
% 3.22/1.92 % (14971)Instructions burned: 18 (million)
% 3.22/1.92 % (14971)------------------------------
% 3.22/1.92 % (14971)------------------------------
% 3.22/1.92 % (14970)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14827 for (2999ds/4Mi)
% 3.22/1.92 % (14974)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_14827 for (2999ds/902Mi)
% 3.22/1.92 % (14970)Instruction limit reached!
% 3.22/1.92 % (14970)------------------------------
% 3.22/1.92 % (14970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.92 % (14970)Termination reason: Unknown
% 3.22/1.92 % (14970)Termination phase: shuffling
% 3.22/1.92
% 3.22/1.92 % (14970)Memory used [KB]: 1535
% 3.22/1.92 % (14970)Time elapsed: 0.004 s
% 3.22/1.92 % (14970)Instructions burned: 5 (million)
% 3.22/1.92 % (14970)------------------------------
% 3.22/1.92 % (14970)------------------------------
% 3.22/1.93 % (14976)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_14827 for (2999ds/5Mi)
% 3.22/1.93 % (14976)Instruction limit reached!
% 3.22/1.93 % (14976)------------------------------
% 3.22/1.93 % (14976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.93 % (14976)Termination reason: Unknown
% 3.22/1.93 % (14976)Termination phase: shuffling
% 3.22/1.93
% 3.22/1.93 % (14976)Memory used [KB]: 1663
% 3.22/1.93 % (14976)Time elapsed: 0.003 s
% 3.22/1.93 % (14976)Instructions burned: 7 (million)
% 3.22/1.93 % (14976)------------------------------
% 3.22/1.93 % (14976)------------------------------
% 3.22/1.93 % (14957)Instruction limit reached!
% 3.22/1.93 % (14957)------------------------------
% 3.22/1.93 % (14957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.93 % (14957)Termination reason: Unknown
% 3.22/1.93 % (14957)Termination phase: Saturation
% 3.22/1.93
% 3.22/1.93 % (14957)Memory used [KB]: 7675
% 3.22/1.93 % (14957)Time elapsed: 0.081 s
% 3.22/1.93 % (14957)Instructions burned: 275 (million)
% 3.22/1.93 % (14957)------------------------------
% 3.22/1.93 % (14957)------------------------------
% 3.22/1.94 % (14975)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_14827 for (2999ds/21Mi)
% 3.22/1.94 % (14978)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_14827 for (2998ds/377Mi)
% 3.22/1.94 % (14979)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_14827 for (2998ds/779Mi)
% 3.22/1.94 % (14977)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_14827 for (2999ds/6Mi)
% 3.22/1.95 % (14977)Instruction limit reached!
% 3.22/1.95 % (14977)------------------------------
% 3.22/1.95 % (14977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.95 % (14977)Termination reason: Unknown
% 3.22/1.95 % (14977)Termination phase: shuffling
% 3.22/1.95
% 3.22/1.95 % (14977)Memory used [KB]: 1663
% 3.22/1.95 % (14977)Time elapsed: 0.005 s
% 3.22/1.95 % (14977)Instructions burned: 6 (million)
% 3.22/1.95 % (14977)------------------------------
% 3.22/1.95 % (14977)------------------------------
% 3.22/1.95 % (14975)Instruction limit reached!
% 3.22/1.95 % (14975)------------------------------
% 3.22/1.95 % (14975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.95 % (14975)Termination reason: Unknown
% 3.22/1.95 % (14975)Termination phase: shuffling
% 3.22/1.95
% 3.22/1.95 % (14975)Memory used [KB]: 1918
% 3.22/1.95 % (14975)Time elapsed: 0.013 s
% 3.22/1.95 % (14975)Instructions burned: 21 (million)
% 3.22/1.95 % (14975)------------------------------
% 3.22/1.95 % (14975)------------------------------
% 3.22/1.97 % (14980)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_14827 for (2998ds/19Mi)
% 3.22/1.97 % (14981)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_14827 for (2998ds/879Mi)
% 3.22/1.98 % (14980)Instruction limit reached!
% 3.22/1.98 % (14980)------------------------------
% 3.22/1.98 % (14980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.98 % (14980)Termination reason: Unknown
% 3.22/1.98 % (14980)Termination phase: shuffling
% 3.22/1.98
% 3.22/1.98 % (14980)Memory used [KB]: 1918
% 3.22/1.98 % (14980)Time elapsed: 0.012 s
% 3.22/1.98 % (14980)Instructions burned: 20 (million)
% 3.22/1.98 % (14980)------------------------------
% 3.22/1.98 % (14980)------------------------------
% 3.22/2.00 % (14982)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_14827 for (2998ds/17Mi)
% 3.22/2.00 % (14982)Instruction limit reached!
% 3.22/2.00 % (14982)------------------------------
% 3.22/2.00 % (14982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/2.00 % (14982)Termination reason: Unknown
% 3.22/2.00 % (14982)Termination phase: shuffling
% 3.22/2.00
% 3.22/2.00 % (14982)Memory used [KB]: 1791
% 3.22/2.00 % (14982)Time elapsed: 0.008 s
% 3.22/2.00 % (14982)Instructions burned: 20 (million)
% 3.22/2.00 % (14982)------------------------------
% 3.22/2.00 % (14982)------------------------------
% 3.22/2.01 % (14983)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_14827 for (2998ds/3Mi)
% 4.27/2.01 % (14983)Instruction limit reached!
% 4.27/2.01 % (14983)------------------------------
% 4.27/2.01 % (14983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.27/2.01 % (14983)Termination reason: Unknown
% 4.27/2.01 % (14983)Termination phase: shuffling
% 4.27/2.01
% 4.27/2.01 % (14983)Memory used [KB]: 1535
% 4.27/2.01 % (14983)Time elapsed: 0.003 s
% 4.27/2.01 % (14983)Instructions burned: 5 (million)
% 4.27/2.01 % (14983)------------------------------
% 4.27/2.01 % (14983)------------------------------
% 4.27/2.02 % (14984)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_14827 for (2998ds/30Mi)
% 4.27/2.04 % (14984)Instruction limit reached!
% 4.27/2.04 % (14984)------------------------------
% 4.27/2.04 % (14984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.27/2.04 % (14984)Termination reason: Unknown
% 4.27/2.04 % (14984)Termination phase: shuffling
% 4.27/2.04
% 4.27/2.04 % (14984)Memory used [KB]: 1918
% 4.27/2.04 % (14984)Time elapsed: 0.016 s
% 4.27/2.04 % (14984)Instructions burned: 30 (million)
% 4.27/2.04 % (14984)------------------------------
% 4.27/2.04 % (14984)------------------------------
% 4.27/2.05 % (14978)Instruction limit reached!
% 4.27/2.05 % (14978)------------------------------
% 4.27/2.05 % (14978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.27/2.05 % (14978)Termination reason: Unknown
% 4.27/2.05 % (14978)Termination phase: Saturation
% 4.27/2.05
% 4.27/2.05 % (14978)Memory used [KB]: 8571
% 4.27/2.05 % (14978)Time elapsed: 0.109 s
% 4.27/2.05 % (14978)Instructions burned: 379 (million)
% 4.27/2.05 % (14978)------------------------------
% 4.27/2.05 % (14978)------------------------------
% 4.27/2.05 % (14985)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_14827 for (2997ds/127Mi)
% 4.27/2.06 % (14986)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_14827 for (2997ds/100Mi)
% 4.27/2.08 % (14986)Instruction limit reached!
% 4.27/2.08 % (14986)------------------------------
% 4.27/2.08 % (14986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.27/2.08 % (14986)Termination reason: Unknown
% 4.27/2.08 % (14986)Termination phase: Property scanning
% 4.27/2.08
% 4.27/2.08 % (14986)Memory used [KB]: 2814
% 4.27/2.08 % (14986)Time elapsed: 0.028 s
% 4.27/2.08 % (14986)Instructions burned: 102 (million)
% 4.27/2.08 % (14986)------------------------------
% 4.27/2.08 % (14986)------------------------------
% 4.27/2.08 % (14985)Instruction limit reached!
% 4.27/2.08 % (14985)------------------------------
% 4.27/2.08 % (14985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.27/2.08 % (14985)Termination reason: Unknown
% 4.27/2.08 % (14985)Termination phase: Function definition elimination
% 4.27/2.08
% 4.27/2.08 % (14985)Memory used [KB]: 2814
% 4.27/2.08 % (14985)Time elapsed: 0.037 s
% 4.27/2.08 % (14985)Instructions burned: 129 (million)
% 4.27/2.08 % (14985)------------------------------
% 4.27/2.08 % (14985)------------------------------
% 4.27/2.09 % (14972)Refutation not found, non-redundant clauses discarded% (14972)------------------------------
% 4.27/2.09 % (14972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.27/2.09 % (14972)Termination reason: Refutation not found, non-redundant clauses discarded
% 4.27/2.09
% 4.27/2.09 % (14972)Memory used [KB]: 7291
% 4.27/2.09 % (14972)Time elapsed: 0.179 s
% 4.27/2.09 % (14972)Instructions burned: 590 (million)
% 4.27/2.09 % (14972)------------------------------
% 4.27/2.09 % (14972)------------------------------
% 4.27/2.09 % (14987)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_14827 for (2997ds/3Mi)
% 4.27/2.09 % (14988)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_14827 for (2997ds/20Mi)
% 4.27/2.10 % (14987)Instruction limit reached!
% 4.27/2.10 % (14987)------------------------------
% 4.27/2.10 % (14987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.27/2.10 % (14987)Termination reason: Unknown
% 4.27/2.10 % (14987)Termination phase: shuffling
% 4.27/2.10
% 4.27/2.10 % (14987)Memory used [KB]: 1663
% 4.27/2.10 % (14987)Time elapsed: 0.003 s
% 4.27/2.10 % (14987)Instructions burned: 5 (million)
% 4.27/2.10 % (14987)------------------------------
% 4.27/2.10 % (14987)------------------------------
% 4.27/2.10 % (14989)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_14827 for (2997ds/86Mi)
% 4.27/2.10 % (14988)Instruction limit reached!
% 4.27/2.10 % (14988)------------------------------
% 4.27/2.10 % (14988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.27/2.10 % (14988)Termination reason: Unknown
% 4.27/2.10 % (14988)Termination phase: shuffling
% 4.27/2.10
% 4.27/2.10 % (14988)Memory used [KB]: 1918
% 4.27/2.10 % (14988)Time elapsed: 0.008 s
% 4.27/2.10 % (14988)Instructions burned: 22 (million)
% 4.27/2.10 % (14988)------------------------------
% 4.27/2.10 % (14988)------------------------------
% 4.27/2.11 % (14990)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_14827 for (2997ds/107Mi)
% 4.27/2.11 % (14991)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_14827 for (2997ds/39Mi)
% 4.96/2.13 % (14989)Instruction limit reached!
% 4.96/2.13 % (14989)------------------------------
% 4.96/2.13 % (14989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.96/2.13 % (14989)Termination reason: Unknown
% 4.96/2.13 % (14989)Termination phase: Property scanning
% 4.96/2.13
% 4.96/2.13 % (14989)Memory used [KB]: 2686
% 4.96/2.13 % (14989)Time elapsed: 0.026 s
% 4.96/2.13 % (14989)Instructions burned: 86 (million)
% 4.96/2.13 % (14989)------------------------------
% 4.96/2.13 % (14989)------------------------------
% 4.96/2.13 % (14991)Instruction limit reached!
% 4.96/2.13 % (14991)------------------------------
% 4.96/2.13 % (14991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.96/2.13 % (14991)Termination reason: Unknown
% 4.96/2.13 % (14991)Termination phase: shuffling
% 4.96/2.13
% 4.96/2.13 % (14991)Memory used [KB]: 2302
% 4.96/2.13 % (14991)Time elapsed: 0.022 s
% 4.96/2.13 % (14991)Instructions burned: 40 (million)
% 4.96/2.13 % (14991)------------------------------
% 4.96/2.13 % (14991)------------------------------
% 4.96/2.14 % (14992)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_14827 for (2997ds/448Mi)
% 4.96/2.14 % (14990)Instruction limit reached!
% 4.96/2.14 % (14990)------------------------------
% 4.96/2.14 % (14990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.96/2.14 % (14990)Termination reason: Unknown
% 4.96/2.14 % (14990)Termination phase: Property scanning
% 4.96/2.14
% 4.96/2.14 % (14990)Memory used [KB]: 2814
% 4.96/2.14 % (14990)Time elapsed: 0.032 s
% 4.96/2.14 % (14990)Instructions burned: 110 (million)
% 4.96/2.14 % (14990)------------------------------
% 4.96/2.14 % (14990)------------------------------
% 4.96/2.15 % (14994)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_14827 for (2996ds/98Mi)
% 4.96/2.15 % (14993)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_14827 for (2997ds/46Mi)
% 4.96/2.15 % (14979)Instruction limit reached!
% 4.96/2.15 % (14979)------------------------------
% 4.96/2.15 % (14979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.96/2.15 % (14979)Termination reason: Unknown
% 4.96/2.15 % (14979)Termination phase: Saturation
% 4.96/2.15
% 4.96/2.15 % (14979)Memory used [KB]: 10106
% 4.96/2.15 % (14979)Time elapsed: 0.212 s
% 4.96/2.15 % (14979)Instructions burned: 782 (million)
% 4.96/2.15 % (14979)------------------------------
% 4.96/2.15 % (14979)------------------------------
% 4.96/2.16 % (14995)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_14827 for (2996ds/507Mi)
% 4.96/2.17 % (14994)Instruction limit reached!
% 4.96/2.17 % (14994)------------------------------
% 4.96/2.17 % (14994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.96/2.17 % (14994)Termination reason: Unknown
% 4.96/2.17 % (14994)Termination phase: Property scanning
% 4.96/2.17
% 4.96/2.17 % (14994)Memory used [KB]: 2814
% 4.96/2.17 % (14994)Time elapsed: 0.027 s
% 4.96/2.17 % (14994)Instructions burned: 98 (million)
% 4.96/2.17 % (14994)------------------------------
% 4.96/2.17 % (14994)------------------------------
% 4.96/2.18 % (14993)Instruction limit reached!
% 4.96/2.18 % (14993)------------------------------
% 4.96/2.18 % (14993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.96/2.18 % (14993)Termination reason: Unknown
% 4.96/2.18 % (14993)Termination phase: Property scanning
% 4.96/2.18
% 4.96/2.18 % (14993)Memory used [KB]: 2046
% 4.96/2.18 % (14993)Time elapsed: 0.027 s
% 4.96/2.18 % (14993)Instructions burned: 47 (million)
% 4.96/2.18 % (14993)------------------------------
% 4.96/2.18 % (14993)------------------------------
% 4.96/2.18 % (14996)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_14827 for (2996ds/149Mi)
% 4.96/2.20 % (14997)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_14827 for (2996ds/39Mi)
% 5.44/2.20 % (14963)Instruction limit reached!
% 5.44/2.20 % (14963)------------------------------
% 5.44/2.20 % (14963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.20 % (14963)Termination reason: Unknown
% 5.44/2.20 % (14963)Termination phase: Saturation
% 5.44/2.20
% 5.44/2.20 % (14963)Memory used [KB]: 10234
% 5.44/2.20 % (14963)Time elapsed: 0.333 s
% 5.44/2.20 % (14963)Instructions burned: 1042 (million)
% 5.44/2.20 % (14963)------------------------------
% 5.44/2.20 % (14963)------------------------------
% 5.44/2.22 % (14998)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_14827 for (2996ds/6Mi)
% 5.44/2.22 % (14997)Instruction limit reached!
% 5.44/2.22 % (14997)------------------------------
% 5.44/2.22 % (14997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.22 % (14997)Termination reason: Unknown
% 5.44/2.22 % (14997)Termination phase: Property scanning
% 5.44/2.22
% 5.44/2.22 % (14997)Memory used [KB]: 2046
% 5.44/2.22 % (14997)Time elapsed: 0.023 s
% 5.44/2.22 % (14997)Instructions burned: 39 (million)
% 5.44/2.22 % (14997)------------------------------
% 5.44/2.22 % (14997)------------------------------
% 5.44/2.22 % (14998)Instruction limit reached!
% 5.44/2.22 % (14998)------------------------------
% 5.44/2.22 % (14998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.22 % (14998)Termination reason: Unknown
% 5.44/2.22 % (14998)Termination phase: shuffling
% 5.44/2.22
% 5.44/2.22 % (14998)Memory used [KB]: 1663
% 5.44/2.22 % (14998)Time elapsed: 0.004 s
% 5.44/2.22 % (14998)Instructions burned: 9 (million)
% 5.44/2.22 % (14998)------------------------------
% 5.44/2.22 % (14998)------------------------------
% 5.44/2.22 % (14996)Instruction limit reached!
% 5.44/2.22 % (14996)------------------------------
% 5.44/2.22 % (14996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.22 % (14996)Termination reason: Unknown
% 5.44/2.22 % (14996)Termination phase: Function definition elimination
% 5.44/2.22
% 5.44/2.22 % (14996)Memory used [KB]: 2814
% 5.44/2.22 % (14996)Time elapsed: 0.041 s
% 5.44/2.22 % (14996)Instructions burned: 149 (million)
% 5.44/2.22 % (14996)------------------------------
% 5.44/2.22 % (14996)------------------------------
% 5.44/2.23 % (15000)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_14827 for (2996ds/47Mi)
% 5.44/2.23 % (14974)Instruction limit reached!
% 5.44/2.23 % (14974)------------------------------
% 5.44/2.23 % (14974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.23 % (14974)Termination reason: Unknown
% 5.44/2.23 % (14974)Termination phase: Saturation
% 5.44/2.23
% 5.44/2.23 % (14974)Memory used [KB]: 9338
% 5.44/2.23 % (14974)Time elapsed: 0.310 s
% 5.44/2.23 % (14974)Instructions burned: 902 (million)
% 5.44/2.23 % (14974)------------------------------
% 5.44/2.23 % (14974)------------------------------
% 5.44/2.23 % (15001)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_14827 for (2996ds/44Mi)
% 5.44/2.24 % (14999)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_14827 for (2996ds/1087Mi)
% 5.44/2.24 % (15002)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_14827 for (2996ds/432Mi)
% 5.44/2.24 % (15000)Instruction limit reached!
% 5.44/2.24 % (15000)------------------------------
% 5.44/2.24 % (15000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.24 % (15000)Termination reason: Unknown
% 5.44/2.24 % (15000)Termination phase: Property scanning
% 5.44/2.24
% 5.44/2.24 % (15000)Memory used [KB]: 2046
% 5.44/2.24 % (15000)Time elapsed: 0.015 s
% 5.44/2.24 % (15000)Instructions burned: 47 (million)
% 5.44/2.24 % (15000)------------------------------
% 5.44/2.24 % (15000)------------------------------
% 5.44/2.24 % (15001)Instruction limit reached!
% 5.44/2.24 % (15001)------------------------------
% 5.44/2.24 % (15001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.24 % (15001)Termination reason: Unknown
% 5.44/2.24 % (15001)Termination phase: shuffling
% 5.44/2.24
% 5.44/2.24 % (15001)Memory used [KB]: 2302
% 5.44/2.24 % (15001)Time elapsed: 0.013 s
% 5.44/2.24 % (15001)Instructions burned: 44 (million)
% 5.44/2.24 % (15001)------------------------------
% 5.44/2.24 % (15001)------------------------------
% 5.44/2.25 % (15003)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_14827 for (2996ds/62Mi)
% 5.44/2.25 % (15004)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_14827 for (2996ds/31Mi)
% 5.44/2.25 % (14992)Instruction limit reached!
% 5.44/2.25 % (14992)------------------------------
% 5.44/2.25 % (14992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.25 % (14992)Termination reason: Unknown
% 5.44/2.25 % (14992)Termination phase: Saturation
% 5.44/2.25
% 5.44/2.25 % (14992)Memory used [KB]: 8827
% 5.44/2.25 % (14992)Time elapsed: 0.120 s
% 5.44/2.25 % (14992)Instructions burned: 451 (million)
% 5.44/2.25 % (14992)------------------------------
% 5.44/2.25 % (14992)------------------------------
% 5.44/2.26 % (15004)Instruction limit reached!
% 5.44/2.26 % (15004)------------------------------
% 5.44/2.26 % (15004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.26 % (15004)Termination reason: Unknown
% 5.44/2.26 % (15004)Termination phase: Property scanning
% 5.44/2.26
% 5.44/2.26 % (15004)Memory used [KB]: 2046
% 5.44/2.26 % (15004)Time elapsed: 0.011 s
% 5.44/2.26 % (15004)Instructions burned: 31 (million)
% 5.44/2.26 % (15004)------------------------------
% 5.44/2.26 % (15004)------------------------------
% 5.44/2.26 % (15005)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_14827 for (2995ds/96Mi)
% 5.44/2.27 % (15006)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_14827 for (2995ds/453Mi)
% 5.44/2.28 % (15003)Instruction limit reached!
% 5.44/2.28 % (15003)------------------------------
% 5.44/2.28 % (15003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.28 % (15003)Termination reason: Unknown
% 5.44/2.28 % (15003)Termination phase: shuffling
% 5.44/2.28
% 5.44/2.28 % (15003)Memory used [KB]: 2814
% 5.44/2.28 % (15003)Time elapsed: 0.028 s
% 5.44/2.28 % (15003)Instructions burned: 62 (million)
% 5.44/2.28 % (15003)------------------------------
% 5.44/2.28 % (15003)------------------------------
% 5.44/2.29 % (15005)Instruction limit reached!
% 5.44/2.29 % (15005)------------------------------
% 5.44/2.29 % (15005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.29 % (15005)Termination reason: Unknown
% 5.44/2.29 % (15005)Termination phase: Property scanning
% 5.44/2.29
% 5.44/2.29 % (15005)Memory used [KB]: 2686
% 5.44/2.29 % (15005)Time elapsed: 0.029 s
% 5.44/2.29 % (15005)Instructions burned: 97 (million)
% 5.44/2.29 % (15005)------------------------------
% 5.44/2.29 % (15005)------------------------------
% 5.96/2.30 % (15007)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_14827 for (2995ds/71Mi)
% 5.96/2.30 % (15008)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_14827 for (2995ds/83Mi)
% 5.96/2.31 % (14995)Instruction limit reached!
% 5.96/2.31 % (14995)------------------------------
% 5.96/2.31 % (14995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.31 % (14995)Termination reason: Unknown
% 5.96/2.31 % (14995)Termination phase: Saturation
% 5.96/2.31
% 5.96/2.31 % (14995)Memory used [KB]: 8955
% 5.96/2.31 % (14995)Time elapsed: 0.149 s
% 5.96/2.31 % (14995)Instructions burned: 509 (million)
% 5.96/2.31 % (14995)------------------------------
% 5.96/2.31 % (14995)------------------------------
% 5.96/2.32 % (15009)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_14827 for (2995ds/11Mi)
% 5.96/2.33 % (15009)Instruction limit reached!
% 5.96/2.33 % (15009)------------------------------
% 5.96/2.33 % (15009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.33 % (15009)Termination reason: Unknown
% 5.96/2.33 % (15009)Termination phase: shuffling
% 5.96/2.33
% 5.96/2.33 % (15009)Memory used [KB]: 1791
% 5.96/2.33 % (15009)Time elapsed: 0.005 s
% 5.96/2.33 % (15009)Instructions burned: 13 (million)
% 5.96/2.33 % (15009)------------------------------
% 5.96/2.33 % (15009)------------------------------
% 5.96/2.33 % (15008)Instruction limit reached!
% 5.96/2.33 % (15008)------------------------------
% 5.96/2.33 % (15008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.33 % (15008)Termination reason: Unknown
% 5.96/2.33 % (15008)Termination phase: Property scanning
% 5.96/2.33
% 5.96/2.33 % (15008)Memory used [KB]: 2430
% 5.96/2.33 % (15008)Time elapsed: 0.027 s
% 5.96/2.33 % (15008)Instructions burned: 86 (million)
% 5.96/2.33 % (15008)------------------------------
% 5.96/2.33 % (15008)------------------------------
% 5.96/2.33 % (15007)Instruction limit reached!
% 5.96/2.33 % (15007)------------------------------
% 5.96/2.33 % (15007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.33 % (15007)Termination reason: Unknown
% 5.96/2.33 % (15007)Termination phase: Preprocessing 3
% 5.96/2.33
% 5.96/2.33 % (15007)Memory used [KB]: 2558
% 5.96/2.33 % (15007)Time elapsed: 0.037 s
% 5.96/2.33 % (15007)Instructions burned: 72 (million)
% 5.96/2.33 % (15007)------------------------------
% 5.96/2.33 % (15007)------------------------------
% 5.96/2.34 % (15010)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_14827 for (2995ds/41Mi)
% 5.96/2.34 % (15011)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14827 for (2994ds/6Mi)
% 5.96/2.34 % (15011)Instruction limit reached!
% 5.96/2.34 % (15011)------------------------------
% 5.96/2.34 % (15011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.34 % (15011)Termination reason: Unknown
% 5.96/2.34 % (15011)Termination phase: shuffling
% 5.96/2.34
% 5.96/2.34 % (15011)Memory used [KB]: 1535
% 5.96/2.34 % (15011)Time elapsed: 0.003 s
% 5.96/2.34 % (15011)Instructions burned: 6 (million)
% 5.96/2.34 % (15011)------------------------------
% 5.96/2.34 % (15011)------------------------------
% 5.96/2.34 % (15012)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_14827 for (2994ds/150Mi)
% 5.96/2.35 % (15010)Instruction limit reached!
% 5.96/2.35 % (15010)------------------------------
% 5.96/2.35 % (15010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.35 % (15010)Termination reason: Unknown
% 5.96/2.35 % (15010)Termination phase: shuffling
% 5.96/2.35
% 5.96/2.35 % (15010)Memory used [KB]: 2302
% 5.96/2.35 % (15010)Time elapsed: 0.013 s
% 5.96/2.35 % (15010)Instructions burned: 44 (million)
% 5.96/2.35 % (15010)------------------------------
% 5.96/2.35 % (15010)------------------------------
% 5.96/2.35 % (15013)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_14827 for (2994ds/343Mi)
% 5.96/2.36 % (15014)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_14827 for (2994ds/109Mi)
% 5.96/2.36 % (15002)Instruction limit reached!
% 5.96/2.36 % (15002)------------------------------
% 5.96/2.36 % (15002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.36 % (15002)Termination reason: Unknown
% 5.96/2.36 % (15002)Termination phase: Saturation
% 5.96/2.36
% 5.96/2.36 % (15002)Memory used [KB]: 3709
% 5.96/2.36 % (15002)Time elapsed: 0.123 s
% 5.96/2.36 % (15002)Instructions burned: 434 (million)
% 5.96/2.36 % (15002)------------------------------
% 5.96/2.36 % (15002)------------------------------
% 5.96/2.37 % (15015)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_14827 for (2994ds/253Mi)
% 5.96/2.38 % (15012)Instruction limit reached!
% 5.96/2.38 % (15012)------------------------------
% 5.96/2.38 % (15012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.38 % (15012)Termination reason: Unknown
% 5.96/2.38 % (15012)Termination phase: Function definition elimination
% 5.96/2.38
% 5.96/2.38 % (15012)Memory used [KB]: 2814
% 5.96/2.38 % (15012)Time elapsed: 0.042 s
% 5.96/2.38 % (15012)Instructions burned: 152 (million)
% 5.96/2.38 % (15012)------------------------------
% 5.96/2.38 % (15012)------------------------------
% 5.96/2.39 % (15014)Instruction limit reached!
% 5.96/2.39 % (15014)------------------------------
% 5.96/2.39 % (15014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.39 % (15014)Termination reason: Unknown
% 5.96/2.39 % (15014)Termination phase: Property scanning
% 5.96/2.39
% 5.96/2.39 % (15014)Memory used [KB]: 2686
% 5.96/2.39 % (15014)Time elapsed: 0.032 s
% 5.96/2.39 % (15014)Instructions burned: 110 (million)
% 5.96/2.39 % (15014)------------------------------
% 5.96/2.39 % (15014)------------------------------
% 5.96/2.39 % (15016)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_14827 for (2994ds/140Mi)
% 6.57/2.40 % (15006)Instruction limit reached!
% 6.57/2.40 % (15006)------------------------------
% 6.57/2.40 % (15006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.40 % (15006)Termination reason: Unknown
% 6.57/2.40 % (15006)Termination phase: Saturation
% 6.57/2.40
% 6.57/2.40 % (15006)Memory used [KB]: 8315
% 6.57/2.40 % (15006)Time elapsed: 0.147 s
% 6.57/2.40 % (15006)Instructions burned: 454 (million)
% 6.57/2.40 % (15006)------------------------------
% 6.57/2.40 % (15006)------------------------------
% 6.57/2.40 % (15017)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_14827 for (2994ds/614Mi)
% 6.57/2.41 % (15018)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_14827 for (2994ds/202Mi)
% 6.57/2.43 % (15016)Instruction limit reached!
% 6.57/2.43 % (15016)------------------------------
% 6.57/2.43 % (15016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.43 % (15016)Termination reason: Unknown
% 6.57/2.43 % (15016)Termination phase: Saturation
% 6.57/2.43
% 6.57/2.43 % (15016)Memory used [KB]: 7164
% 6.57/2.43 % (15016)Time elapsed: 0.043 s
% 6.57/2.43 % (15016)Instructions burned: 140 (million)
% 6.57/2.43 % (15016)------------------------------
% 6.57/2.43 % (15016)------------------------------
% 6.57/2.45 % (15019)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_14827 for (2993ds/339Mi)
% 6.57/2.45 % (15013)Instruction limit reached!
% 6.57/2.45 % (15013)------------------------------
% 6.57/2.45 % (15013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.45 % (15013)Termination reason: Unknown
% 6.57/2.45 % (15013)Termination phase: Saturation
% 6.57/2.45
% 6.57/2.45 % (15013)Memory used [KB]: 8315
% 6.57/2.45 % (15013)Time elapsed: 0.101 s
% 6.57/2.45 % (15013)Instructions burned: 343 (million)
% 6.57/2.45 % (15013)------------------------------
% 6.57/2.45 % (15013)------------------------------
% 6.57/2.45 % (15018)Refutation not found, incomplete strategy
% 6.57/2.45 % (15018)------------------------------
% 6.57/2.45 % (15018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.45 % (15018)Termination reason: Refutation not found, incomplete strategy
% 6.57/2.45
% 6.57/2.45
% 6.57/2.45 % (15018)Memory used [KB]: 7419
% 6.57/2.45 % (15018)Time elapsed: 0.048 s
% 6.57/2.45 % (15018)Instructions burned: 154 (million)
% 6.57/2.45 % (15018)------------------------------
% 6.57/2.45 % (15018)------------------------------
% 6.57/2.45 % (14981)Instruction limit reached!
% 6.57/2.45 % (14981)------------------------------
% 6.57/2.45 % (14981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.45 % (14981)Termination reason: Unknown
% 6.57/2.45 % (14981)Termination phase: Saturation
% 6.57/2.45
% 6.57/2.45 % (14981)Memory used [KB]: 8059
% 6.57/2.45 % (14981)Time elapsed: 0.488 s
% 6.57/2.45 % (14981)Instructions burned: 879 (million)
% 6.57/2.45 % (14981)------------------------------
% 6.57/2.45 % (14981)------------------------------
% 6.57/2.45 % (15015)Instruction limit reached!
% 6.57/2.45 % (15015)------------------------------
% 6.57/2.45 % (15015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.45 % (15015)Termination reason: Unknown
% 6.57/2.45 % (15015)Termination phase: Saturation
% 6.57/2.45
% 6.57/2.45 % (15015)Memory used [KB]: 7931
% 6.57/2.45 % (15015)Time elapsed: 0.083 s
% 6.57/2.45 % (15015)Instructions burned: 254 (million)
% 6.57/2.45 % (15015)------------------------------
% 6.57/2.45 % (15015)------------------------------
% 6.57/2.46 % (15021)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_14827 for (2993ds/283Mi)
% 6.57/2.46 % (15022)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_14827 for (2993ds/134Mi)
% 6.57/2.46 % (15023)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_14827 for (2993ds/298Mi)
% 6.57/2.47 % (15024)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_14827 for (2993ds/192Mi)
% 7.09/2.50 % (15022)Instruction limit reached!
% 7.09/2.50 % (15022)------------------------------
% 7.09/2.50 % (15022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.50 % (15022)Termination reason: Unknown
% 7.09/2.50 % (15022)Termination phase: Property scanning
% 7.09/2.50
% 7.09/2.50 % (15022)Memory used [KB]: 2814
% 7.09/2.50 % (15022)Time elapsed: 0.039 s
% 7.09/2.50 % (15022)Instructions burned: 136 (million)
% 7.09/2.50 % (15022)------------------------------
% 7.09/2.50 % (15022)------------------------------
% 7.09/2.51 % (15025)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_14827 for (2993ds/258Mi)
% 7.09/2.53 % (15021)Instruction limit reached!
% 7.09/2.53 % (15021)------------------------------
% 7.09/2.53 % (15021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.53 % (15021)Termination reason: Unknown
% 7.09/2.53 % (15021)Termination phase: Saturation
% 7.09/2.53
% 7.09/2.53 % (15021)Memory used [KB]: 7675
% 7.09/2.53 % (15021)Time elapsed: 0.074 s
% 7.09/2.53 % (15021)Instructions burned: 286 (million)
% 7.09/2.53 % (15021)------------------------------
% 7.09/2.53 % (15021)------------------------------
% 7.09/2.54 % (15019)Instruction limit reached!
% 7.09/2.54 % (15019)------------------------------
% 7.09/2.54 % (15019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.54 % (15019)Termination reason: Unknown
% 7.09/2.54 % (15019)Termination phase: Saturation
% 7.09/2.54
% 7.09/2.54 % (15019)Memory used [KB]: 7547
% 7.09/2.54 % (15019)Time elapsed: 0.096 s
% 7.09/2.54 % (15019)Instructions burned: 342 (million)
% 7.09/2.54 % (15019)------------------------------
% 7.09/2.54 % (15019)------------------------------
% 7.09/2.54 % (15023)Instruction limit reached!
% 7.09/2.54 % (15023)------------------------------
% 7.09/2.54 % (15023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.54 % (15023)Termination reason: Unknown
% 7.09/2.54 % (15023)Termination phase: Saturation
% 7.09/2.54
% 7.09/2.54 % (15023)Memory used [KB]: 7803
% 7.09/2.54 % (15023)Time elapsed: 0.077 s
% 7.09/2.54 % (15023)Instructions burned: 298 (million)
% 7.09/2.54 % (15023)------------------------------
% 7.09/2.54 % (15023)------------------------------
% 7.09/2.54 % (15026)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_14827 for (2993ds/90Mi)
% 7.09/2.55 % (15027)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_14827 for (2992ds/231Mi)
% 7.09/2.55 % (15028)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_14827 for (2992ds/458Mi)
% 7.09/2.57 % (15026)Instruction limit reached!
% 7.09/2.57 % (15026)------------------------------
% 7.09/2.57 % (15026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.57 % (15026)Termination reason: Unknown
% 7.09/2.57 % (15026)Termination phase: Property scanning
% 7.09/2.57
% 7.09/2.57 % (15026)Memory used [KB]: 2686
% 7.09/2.57 % (15026)Time elapsed: 0.027 s
% 7.09/2.57 % (15026)Instructions burned: 90 (million)
% 7.09/2.57 % (15026)------------------------------
% 7.09/2.57 % (15026)------------------------------
% 7.09/2.57 % (15024)Instruction limit reached!
% 7.09/2.57 % (15024)------------------------------
% 7.09/2.57 % (15024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.57 % (15024)Termination reason: Unknown
% 7.09/2.57 % (15024)Termination phase: Saturation
% 7.09/2.57
% 7.09/2.57 % (15024)Memory used [KB]: 3198
% 7.09/2.57 % (15024)Time elapsed: 0.099 s
% 7.09/2.57 % (15024)Instructions burned: 192 (million)
% 7.09/2.57 % (15024)------------------------------
% 7.09/2.57 % (15024)------------------------------
% 7.09/2.58 % (15017)Instruction limit reached!
% 7.09/2.58 % (15017)------------------------------
% 7.09/2.58 % (15017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.58 % (15017)Termination reason: Unknown
% 7.09/2.58 % (15017)Termination phase: Saturation
% 7.09/2.58
% 7.09/2.58 % (15017)Memory used [KB]: 9338
% 7.09/2.58 % (15017)Time elapsed: 0.180 s
% 7.09/2.58 % (15017)Instructions burned: 615 (million)
% 7.09/2.58 % (15017)------------------------------
% 7.09/2.58 % (15017)------------------------------
% 7.09/2.58 % (15029)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_14827 for (2992ds/31Mi)
% 7.09/2.58 % (15025)Instruction limit reached!
% 7.09/2.58 % (15025)------------------------------
% 7.09/2.58 % (15025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.58 % (15025)Termination reason: Unknown
% 7.09/2.58 % (15025)Termination phase: Saturation
% 7.09/2.58
% 7.09/2.58 % (15025)Memory used [KB]: 3198
% 7.09/2.58 % (15025)Time elapsed: 0.070 s
% 7.09/2.58 % (15025)Instructions burned: 260 (million)
% 7.09/2.58 % (15025)------------------------------
% 7.09/2.58 % (15025)------------------------------
% 7.09/2.59 % (15031)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_14827 for (2992ds/987Mi)
% 7.09/2.59 % (15029)Instruction limit reached!
% 7.09/2.59 % (15029)------------------------------
% 7.09/2.59 % (15029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.59 % (15029)Termination reason: Unknown
% 7.09/2.59 % (15029)Termination phase: shuffling
% 7.09/2.59
% 7.09/2.59 % (15029)Memory used [KB]: 2046
% 7.09/2.59 % (15029)Time elapsed: 0.011 s
% 7.09/2.59 % (15029)Instructions burned: 31 (million)
% 7.09/2.59 % (15029)------------------------------
% 7.09/2.59 % (15029)------------------------------
% 7.09/2.59 % (15032)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_14827 for (2992ds/182Mi)
% 7.09/2.59 % (15030)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_14827 for (2992ds/297Mi)
% 7.85/2.60 % (15033)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_14827 for (2992ds/182Mi)
% 7.85/2.61 % (15027)Instruction limit reached!
% 7.85/2.61 % (15027)------------------------------
% 7.85/2.61 % (15027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.61 % (15027)Termination reason: Unknown
% 7.85/2.61 % (15027)Termination phase: Saturation
% 7.85/2.61
% 7.85/2.61 % (15027)Memory used [KB]: 7675
% 7.85/2.61 % (15027)Time elapsed: 0.061 s
% 7.85/2.61 % (15027)Instructions burned: 234 (million)
% 7.85/2.61 % (15027)------------------------------
% 7.85/2.61 % (15027)------------------------------
% 7.85/2.62 % (15034)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_14827 for (2992ds/154Mi)
% 7.85/2.64 % (15032)Instruction limit reached!
% 7.85/2.64 % (15032)------------------------------
% 7.85/2.64 % (15032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.64 % (15032)Termination reason: Unknown
% 7.85/2.64 % (15032)Termination phase: Property scanning
% 7.85/2.64
% 7.85/2.64 % (15032)Memory used [KB]: 2814
% 7.85/2.64 % (15032)Time elapsed: 0.049 s
% 7.85/2.64 % (15032)Instructions burned: 182 (million)
% 7.85/2.64 % (15032)------------------------------
% 7.85/2.64 % (15032)------------------------------
% 7.85/2.65 % (15033)Instruction limit reached!
% 7.85/2.65 % (15033)------------------------------
% 7.85/2.65 % (15033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.65 % (15033)Termination reason: Unknown
% 7.85/2.65 % (15033)Termination phase: Saturation
% 7.85/2.65
% 7.85/2.65 % (15033)Memory used [KB]: 7291
% 7.85/2.65 % (15033)Time elapsed: 0.051 s
% 7.85/2.65 % (15033)Instructions burned: 185 (million)
% 7.85/2.65 % (15033)------------------------------
% 7.85/2.65 % (15033)------------------------------
% 7.85/2.65 % (15035)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_14827 for (2992ds/79Mi)
% 7.85/2.66 % (15036)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_14827 for (2991ds/216Mi)
% 7.85/2.66 % (15034)Instruction limit reached!
% 7.85/2.66 % (15034)------------------------------
% 7.85/2.66 % (15034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.66 % (15034)Termination reason: Unknown
% 7.85/2.66 % (15034)Termination phase: Function definition elimination
% 7.85/2.66
% 7.85/2.66 % (15034)Memory used [KB]: 2942
% 7.85/2.66 % (15034)Time elapsed: 0.042 s
% 7.85/2.66 % (15034)Instructions burned: 155 (million)
% 7.85/2.66 % (15034)------------------------------
% 7.85/2.66 % (15034)------------------------------
% 7.85/2.67 % (15037)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_14827 for (2991ds/114Mi)
% 7.85/2.67 % (15035)Instruction limit reached!
% 7.85/2.67 % (15035)------------------------------
% 7.85/2.67 % (15035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.67 % (15035)Termination reason: Unknown
% 7.85/2.67 % (15035)Termination phase: Property scanning
% 7.85/2.67
% 7.85/2.67 % (15035)Memory used [KB]: 2686
% 7.85/2.67 % (15035)Time elapsed: 0.025 s
% 7.85/2.67 % (15035)Instructions burned: 80 (million)
% 7.85/2.67 % (15035)------------------------------
% 7.85/2.67 % (15035)------------------------------
% 7.85/2.68 % (15038)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_14827 for (2991ds/922Mi)
% 7.85/2.68 % (15028)Instruction limit reached!
% 7.85/2.68 % (15028)------------------------------
% 7.85/2.68 % (15028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.68 % (15028)Termination reason: Unknown
% 7.85/2.68 % (15028)Termination phase: Saturation
% 7.85/2.68
% 7.85/2.68 % (15028)Memory used [KB]: 8571
% 7.85/2.68 % (15028)Time elapsed: 0.134 s
% 7.85/2.68 % (15028)Instructions burned: 458 (million)
% 7.85/2.68 % (15028)------------------------------
% 7.85/2.68 % (15028)------------------------------
% 7.85/2.69 % (15039)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_14827 for (2991ds/182Mi)
% 8.26/2.70 % (15037)Instruction limit reached!
% 8.26/2.70 % (15037)------------------------------
% 8.26/2.70 % (15037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.70 % (15037)Termination reason: Unknown
% 8.26/2.70 % (15037)Termination phase: Function definition elimination
% 8.26/2.70
% 8.26/2.70 % (15037)Memory used [KB]: 2686
% 8.26/2.70 % (15037)Time elapsed: 0.034 s
% 8.26/2.70 % (15037)Instructions burned: 116 (million)
% 8.26/2.70 % (15037)------------------------------
% 8.26/2.70 % (15037)------------------------------
% 8.26/2.71 % (15040)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_14827 for (2991ds/164Mi)
% 8.26/2.71 % (15036)Instruction limit reached!
% 8.26/2.71 % (15036)------------------------------
% 8.26/2.71 % (15036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.71 % (15036)Termination reason: Unknown
% 8.26/2.71 % (15036)Termination phase: Property scanning
% 8.26/2.71
% 8.26/2.71 % (15036)Memory used [KB]: 3070
% 8.26/2.71 % (15036)Time elapsed: 0.058 s
% 8.26/2.71 % (15036)Instructions burned: 218 (million)
% 8.26/2.71 % (15036)------------------------------
% 8.26/2.71 % (15036)------------------------------
% 8.26/2.72 % (15041)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_14827 for (2991ds/50Mi)
% 8.26/2.74 % (15041)Instruction limit reached!
% 8.26/2.74 % (15041)------------------------------
% 8.26/2.74 % (15041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.74 % (15041)Termination reason: Unknown
% 8.26/2.74 % (15041)Termination phase: shuffling
% 8.26/2.74
% 8.26/2.74 % (15041)Memory used [KB]: 2430
% 8.26/2.74 % (15041)Time elapsed: 0.015 s
% 8.26/2.74 % (15041)Instructions burned: 50 (million)
% 8.26/2.74 % (15041)------------------------------
% 8.26/2.74 % (15041)------------------------------
% 8.26/2.74 % (15039)Instruction limit reached!
% 8.26/2.74 % (15039)------------------------------
% 8.26/2.74 % (15039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.74 % (15039)Termination reason: Unknown
% 8.26/2.74 % (15039)Termination phase: Property scanning
% 8.26/2.74
% 8.26/2.74 % (15039)Memory used [KB]: 3070
% 8.26/2.74 % (15039)Time elapsed: 0.049 s
% 8.26/2.74 % (15039)Instructions burned: 182 (million)
% 8.26/2.74 % (15039)------------------------------
% 8.26/2.74 % (15039)------------------------------
% 8.26/2.75 % (15042)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_14827 for (2991ds/368Mi)
% 8.26/2.75 % (15043)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_14827 for (2991ds/1021Mi)
% 8.26/2.75 % (15030)Instruction limit reached!
% 8.26/2.75 % (15030)------------------------------
% 8.26/2.75 % (15030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.75 % (15030)Termination reason: Unknown
% 8.26/2.75 % (15030)Termination phase: Saturation
% 8.26/2.75
% 8.26/2.75 % (15030)Memory used [KB]: 7803
% 8.26/2.75 % (15030)Time elapsed: 0.162 s
% 8.26/2.75 % (15030)Instructions burned: 297 (million)
% 8.26/2.75 % (15030)------------------------------
% 8.26/2.75 % (15030)------------------------------
% 8.26/2.76 % (15040)Instruction limit reached!
% 8.26/2.76 % (15040)------------------------------
% 8.26/2.76 % (15040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.76 % (15040)Termination reason: Unknown
% 8.26/2.76 % (15040)Termination phase: Property scanning
% 8.26/2.76
% 8.26/2.76 % (15040)Memory used [KB]: 2942
% 8.26/2.76 % (15040)Time elapsed: 0.045 s
% 8.26/2.76 % (15040)Instructions burned: 164 (million)
% 8.26/2.76 % (15040)------------------------------
% 8.26/2.76 % (15040)------------------------------
% 8.26/2.77 % (15045)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_14827 for (2990ds/204Mi)
% 8.26/2.77 % (15044)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_14827 for (2990ds/267Mi)
% 8.68/2.81 % (14999)Instruction limit reached!
% 8.68/2.81 % (14999)------------------------------
% 8.68/2.81 % (14999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.68/2.81 % (14999)Termination reason: Unknown
% 8.68/2.81 % (14999)Termination phase: Saturation
% 8.68/2.81
% 8.68/2.81 % (14999)Memory used [KB]: 7547
% 8.68/2.81 % (14999)Time elapsed: 0.581 s
% 8.68/2.81 % (14999)Instructions burned: 1087 (million)
% 8.68/2.81 % (14999)------------------------------
% 8.68/2.81 % (14999)------------------------------
% 8.68/2.82 % (15045)Instruction limit reached!
% 8.68/2.82 % (15045)------------------------------
% 8.68/2.82 % (15045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.68/2.82 % (15045)Termination reason: Unknown
% 8.68/2.82 % (15045)Termination phase: Saturation
% 8.68/2.82
% 8.68/2.82 % (15045)Memory used [KB]: 7291
% 8.68/2.82 % (15045)Time elapsed: 0.059 s
% 8.68/2.82 % (15045)Instructions burned: 204 (million)
% 8.68/2.82 % (15045)------------------------------
% 8.68/2.82 % (15045)------------------------------
% 8.68/2.83 % (15046)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_14827 for (2990ds/26Mi)
% 8.68/2.84 % (15046)Instruction limit reached!
% 8.68/2.84 % (15046)------------------------------
% 8.68/2.84 % (15046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.68/2.84 % (15046)Termination reason: Unknown
% 8.68/2.84 % (15046)Termination phase: shuffling
% 8.68/2.84
% 8.68/2.84 % (15046)Memory used [KB]: 2174
% 8.68/2.84 % (15046)Time elapsed: 0.009 s
% 8.68/2.84 % (15046)Instructions burned: 28 (million)
% 8.68/2.84 % (15046)------------------------------
% 8.68/2.84 % (15046)------------------------------
% 8.68/2.84 % (15047)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_14827 for (2990ds/53Mi)
% 8.68/2.85 % (15048)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_14827 for (2989ds/4436Mi)
% 8.68/2.85 % (15042)Instruction limit reached!
% 8.68/2.85 % (15042)------------------------------
% 8.68/2.85 % (15042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.68/2.85 % (15042)Termination reason: Unknown
% 8.68/2.85 % (15042)Termination phase: Saturation
% 8.68/2.85
% 8.68/2.85 % (15042)Memory used [KB]: 8571
% 8.68/2.85 % (15042)Time elapsed: 0.128 s
% 8.68/2.85 % (15042)Instructions burned: 369 (million)
% 8.68/2.85 % (15042)------------------------------
% 8.68/2.85 % (15042)------------------------------
% 8.68/2.86 % (15049)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_14827 for (2989ds/1539Mi)
% 8.68/2.87 % (15047)Instruction limit reached!
% 8.68/2.87 % (15047)------------------------------
% 8.68/2.87 % (15047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.68/2.87 % (15047)Termination reason: Unknown
% 8.68/2.87 % (15047)Termination phase: shuffling
% 8.68/2.87
% 8.68/2.87 % (15047)Memory used [KB]: 2430
% 8.68/2.87 % (15047)Time elapsed: 0.029 s
% 8.68/2.87 % (15047)Instructions burned: 53 (million)
% 8.68/2.87 % (15047)------------------------------
% 8.68/2.87 % (15047)------------------------------
% 8.68/2.90 % (15031)Instruction limit reached!
% 8.68/2.90 % (15031)------------------------------
% 8.68/2.90 % (15031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.68/2.90 % (15031)Termination reason: Unknown
% 8.68/2.90 % (15031)Termination phase: Saturation
% 8.68/2.90
% 8.68/2.90 % (15031)Memory used [KB]: 9594
% 8.68/2.90 % (15031)Time elapsed: 0.310 s
% 8.68/2.90 % (15031)Instructions burned: 987 (million)
% 8.68/2.90 % (15031)------------------------------
% 8.68/2.90 % (15031)------------------------------
% 9.84/2.90 % (15050)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_14827 for (2989ds/408Mi)
% 9.84/2.91 % (15051)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_14827 for (2989ds/5205Mi)
% 9.84/2.91 % (15044)Instruction limit reached!
% 9.84/2.91 % (15044)------------------------------
% 9.84/2.91 % (15044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.91 % (15044)Termination reason: Unknown
% 9.84/2.91 % (15044)Termination phase: Saturation
% 9.84/2.91
% 9.84/2.91 % (15044)Memory used [KB]: 7675
% 9.84/2.91 % (15044)Time elapsed: 0.140 s
% 9.84/2.91 % (15044)Instructions burned: 268 (million)
% 9.84/2.91 % (15044)------------------------------
% 9.84/2.91 % (15044)------------------------------
% 9.84/2.93 % (15052)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_14827 for (2989ds/1913Mi)
% 9.84/2.96 % (15038)Instruction limit reached!
% 9.84/2.96 % (15038)------------------------------
% 9.84/2.96 % (15038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.96 % (15038)Termination reason: Unknown
% 9.84/2.96 % (15038)Termination phase: Saturation
% 9.84/2.96
% 9.84/2.96 % (15038)Memory used [KB]: 7675
% 9.84/2.96 % (15038)Time elapsed: 0.278 s
% 9.84/2.96 % (15038)Instructions burned: 923 (million)
% 9.84/2.96 % (15038)------------------------------
% 9.84/2.96 % (15038)------------------------------
% 9.84/2.97 % (15053)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_14827 for (2988ds/4350Mi)
% 11.25/3.06 % (15043)Instruction limit reached!
% 11.25/3.06 % (15043)------------------------------
% 11.25/3.06 % (15043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.25/3.06 % (15043)Termination reason: Unknown
% 11.25/3.06 % (15043)Termination phase: Saturation
% 11.25/3.06
% 11.25/3.06 % (15043)Memory used [KB]: 8955
% 11.25/3.06 % (15043)Time elapsed: 0.329 s
% 11.25/3.06 % (15043)Instructions burned: 1022 (million)
% 11.25/3.06 % (15043)------------------------------
% 11.25/3.06 % (15043)------------------------------
% 11.25/3.07 % (15054)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_14827 for (2987ds/68Mi)
% 11.25/3.09 % (15054)Instruction limit reached!
% 11.25/3.09 % (15054)------------------------------
% 11.25/3.09 % (15054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.25/3.09 % (15054)Termination reason: Unknown
% 11.25/3.09 % (15054)Termination phase: Preprocessing 1
% 11.25/3.09
% 11.25/3.09 % (15054)Memory used [KB]: 2174
% 11.25/3.09 % (15054)Time elapsed: 0.022 s
% 11.25/3.09 % (15054)Instructions burned: 69 (million)
% 11.25/3.09 % (15054)------------------------------
% 11.25/3.09 % (15054)------------------------------
% 11.25/3.10 % (15055)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_14827 for (2987ds/358Mi)
% 11.93/3.12 % (15050)Instruction limit reached!
% 11.93/3.12 % (15050)------------------------------
% 11.93/3.12 % (15050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.93/3.12 % (15050)Termination reason: Unknown
% 11.93/3.12 % (15050)Termination phase: Saturation
% 11.93/3.12
% 11.93/3.12 % (15050)Memory used [KB]: 8955
% 11.93/3.12 % (15050)Time elapsed: 0.225 s
% 11.93/3.12 % (15050)Instructions burned: 408 (million)
% 11.93/3.12 % (15050)------------------------------
% 11.93/3.12 % (15050)------------------------------
% 11.93/3.14 % (15056)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_14827 for (2987ds/31Mi)
% 11.93/3.16 % (15056)Instruction limit reached!
% 11.93/3.16 % (15056)------------------------------
% 11.93/3.16 % (15056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.93/3.16 % (15056)Termination reason: Unknown
% 11.93/3.16 % (15056)Termination phase: Property scanning
% 11.93/3.16
% 11.93/3.16 % (15056)Memory used [KB]: 2046
% 11.93/3.16 % (15056)Time elapsed: 0.019 s
% 11.93/3.16 % (15056)Instructions burned: 31 (million)
% 11.93/3.16 % (15056)------------------------------
% 11.93/3.16 % (15056)------------------------------
% 11.93/3.18 % (15057)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_14827 for (2986ds/279Mi)
% 12.37/3.20 % (15055)Instruction limit reached!
% 12.37/3.20 % (15055)------------------------------
% 12.37/3.20 % (15055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.37/3.20 % (15055)Termination reason: Unknown
% 12.37/3.20 % (15055)Termination phase: Saturation
% 12.37/3.20
% 12.37/3.20 % (15055)Memory used [KB]: 7931
% 12.37/3.20 % (15055)Time elapsed: 0.103 s
% 12.37/3.20 % (15055)Instructions burned: 360 (million)
% 12.37/3.20 % (15055)------------------------------
% 12.37/3.20 % (15055)------------------------------
% 12.37/3.21 % (15058)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_14827 for (2986ds/258Mi)
% 12.37/3.27 % (15057)Refutation not found, incomplete strategy
% 12.37/3.27 % (15057)------------------------------
% 12.37/3.27 % (15057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.37/3.27 % (15057)Termination reason: Refutation not found, incomplete strategy
% 12.37/3.27
% 12.37/3.27
% 12.37/3.27 % (15057)Memory used [KB]: 7675
% 12.37/3.27 % (15057)Time elapsed: 0.096 s
% 12.37/3.27 % (15057)Instructions burned: 195 (million)
% 12.37/3.27 % (15057)------------------------------
% 12.37/3.27 % (15057)------------------------------
% 12.37/3.28 % (15058)Instruction limit reached!
% 12.37/3.28 % (15058)------------------------------
% 12.37/3.28 % (15058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.37/3.28 % (15058)Termination reason: Unknown
% 12.37/3.28 % (15058)Termination phase: Saturation
% 12.37/3.28
% 12.37/3.28 % (15058)Memory used [KB]: 7803
% 12.37/3.28 % (15058)Time elapsed: 0.074 s
% 12.37/3.28 % (15058)Instructions burned: 258 (million)
% 12.37/3.28 % (15058)------------------------------
% 12.37/3.28 % (15058)------------------------------
% 12.37/3.28 % (15059)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_14827 for (2985ds/26Mi)
% 12.37/3.29 % (15059)Instruction limit reached!
% 12.37/3.29 % (15059)------------------------------
% 12.37/3.29 % (15059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.37/3.29 % (15059)Termination reason: Unknown
% 12.37/3.29 % (15059)Termination phase: shuffling
% 12.37/3.29
% 12.37/3.29 % (15059)Memory used [KB]: 2174
% 12.37/3.29 % (15059)Time elapsed: 0.010 s
% 12.37/3.29 % (15059)Instructions burned: 29 (million)
% 12.37/3.29 % (15059)------------------------------
% 12.37/3.29 % (15059)------------------------------
% 12.37/3.29 % (15060)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_14827 for (2985ds/995Mi)
% 13.19/3.30 % (15061)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_14827 for (2985ds/373Mi)
% 13.19/3.31 % (15049)Instruction limit reached!
% 13.19/3.31 % (15049)------------------------------
% 13.19/3.31 % (15049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.19/3.31 % (15049)Termination reason: Unknown
% 13.19/3.31 % (15049)Termination phase: Saturation
% 13.19/3.31
% 13.19/3.31 % (15049)Memory used [KB]: 9978
% 13.19/3.31 % (15049)Time elapsed: 0.452 s
% 13.19/3.31 % (15049)Instructions burned: 1540 (million)
% 13.19/3.31 % (15049)------------------------------
% 13.19/3.31 % (15049)------------------------------
% 13.19/3.32 % (15062)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_14827 for (2985ds/253Mi)
% 13.19/3.39 % (15062)Instruction limit reached!
% 13.19/3.39 % (15062)------------------------------
% 13.19/3.39 % (15062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.19/3.39 % (15062)Termination reason: Unknown
% 13.19/3.39 % (15062)Termination phase: Saturation
% 13.19/3.39
% 13.19/3.39 % (15062)Memory used [KB]: 7675
% 13.19/3.39 % (15062)Time elapsed: 0.067 s
% 13.19/3.39 % (15062)Instructions burned: 256 (million)
% 13.19/3.39 % (15062)------------------------------
% 13.19/3.39 % (15062)------------------------------
% 13.70/3.40 % (15063)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_14827 for (2984ds/832Mi)
% 13.70/3.41 % (15061)Instruction limit reached!
% 13.70/3.41 % (15061)------------------------------
% 13.70/3.41 % (15061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.70/3.41 % (15061)Termination reason: Unknown
% 13.70/3.41 % (15061)Termination phase: Saturation
% 13.70/3.41
% 13.70/3.41 % (15061)Memory used [KB]: 8443
% 13.70/3.41 % (15061)Time elapsed: 0.110 s
% 13.70/3.41 % (15061)Instructions burned: 376 (million)
% 13.70/3.41 % (15061)------------------------------
% 13.70/3.41 % (15061)------------------------------
% 13.70/3.42 % (15064)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_14827 for (2984ds/668Mi)
% 14.20/3.55 % (15052)Instruction limit reached!
% 14.20/3.55 % (15052)------------------------------
% 14.20/3.55 % (15052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.20/3.55 % (15052)Termination reason: Unknown
% 14.20/3.55 % (15052)Termination phase: Saturation
% 14.20/3.55
% 14.20/3.55 % (15052)Memory used [KB]: 4477
% 14.20/3.55 % (15052)Time elapsed: 0.615 s
% 14.20/3.55 % (15052)Instructions burned: 1915 (million)
% 14.20/3.55 % (15052)------------------------------
% 14.20/3.55 % (15052)------------------------------
% 14.20/3.56 % (15065)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_14827 for (2982ds/40Mi)
% 14.20/3.57 % (15065)Instruction limit reached!
% 14.20/3.57 % (15065)------------------------------
% 14.20/3.57 % (15065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.20/3.57 % (15065)Termination reason: Unknown
% 14.20/3.57 % (15065)Termination phase: shuffling
% 14.20/3.57
% 14.20/3.57 % (15065)Memory used [KB]: 2302
% 14.20/3.57 % (15065)Time elapsed: 0.013 s
% 14.20/3.57 % (15065)Instructions burned: 42 (million)
% 14.20/3.57 % (15065)------------------------------
% 14.20/3.57 % (15065)------------------------------
% 14.20/3.57 % (15060)Instruction limit reached!
% 14.20/3.57 % (15060)------------------------------
% 14.20/3.57 % (15060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.20/3.57 % (15060)Termination reason: Unknown
% 14.20/3.57 % (15060)Termination phase: Saturation
% 14.20/3.57
% 14.20/3.57 % (15060)Memory used [KB]: 9850
% 14.20/3.57 % (15060)Time elapsed: 0.285 s
% 14.20/3.57 % (15060)Instructions burned: 996 (million)
% 14.20/3.57 % (15060)------------------------------
% 14.20/3.57 % (15060)------------------------------
% 14.20/3.58 % (15066)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_14827 for (2982ds/294Mi)
% 14.20/3.58 % (15067)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_14827 for (2982ds/187Mi)
% 14.88/3.61 % (15064)Instruction limit reached!
% 14.88/3.61 % (15064)------------------------------
% 14.88/3.61 % (15064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.88/3.61 % (15064)Termination reason: Unknown
% 14.88/3.61 % (15064)Termination phase: Saturation
% 14.88/3.61
% 14.88/3.61 % (15064)Memory used [KB]: 14072
% 14.88/3.61 % (15064)Time elapsed: 0.193 s
% 14.88/3.61 % (15064)Instructions burned: 670 (million)
% 14.88/3.61 % (15064)------------------------------
% 14.88/3.61 % (15064)------------------------------
% 14.88/3.62 % (15068)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_14827 for (2982ds/371Mi)
% 14.88/3.62 % (15066)Refutation not found, incomplete strategy
% 14.88/3.62 % (15066)------------------------------
% 14.88/3.62 % (15066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.88/3.62 % (15066)Termination reason: Refutation not found, incomplete strategy
% 14.88/3.62
% 14.88/3.62
% 14.88/3.62 % (15066)Memory used [KB]: 7675
% 14.88/3.62 % (15066)Time elapsed: 0.048 s
% 14.88/3.62 % (15066)Instructions burned: 172 (million)
% 14.88/3.62 % (15066)------------------------------
% 14.88/3.62 % (15066)------------------------------
% 14.88/3.63 % (15069)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_14827 for (2982ds/1827Mi)
% 14.88/3.63 % (15067)Instruction limit reached!
% 14.88/3.63 % (15067)------------------------------
% 14.88/3.63 % (15067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.88/3.63 % (15067)Termination reason: Unknown
% 14.88/3.63 % (15067)Termination phase: Saturation
% 14.88/3.63
% 14.88/3.63 % (15067)Memory used [KB]: 7291
% 14.88/3.63 % (15067)Time elapsed: 0.051 s
% 14.88/3.63 % (15067)Instructions burned: 187 (million)
% 14.88/3.63 % (15067)------------------------------
% 14.88/3.63 % (15067)------------------------------
% 14.88/3.64 % (15063)Instruction limit reached!
% 14.88/3.64 % (15063)------------------------------
% 14.88/3.64 % (15063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.88/3.64 % (15063)Termination reason: Unknown
% 14.88/3.64 % (15063)Termination phase: Saturation
% 14.88/3.64
% 14.88/3.64 % (15063)Memory used [KB]: 8955
% 14.88/3.64 % (15063)Time elapsed: 0.242 s
% 14.88/3.64 % (15063)Instructions burned: 834 (million)
% 14.88/3.64 % (15063)------------------------------
% 14.88/3.64 % (15063)------------------------------
% 14.88/3.64 % (15070)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_14827 for (2982ds/70Mi)
% 14.88/3.65 % (15071)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_14827 for (2981ds/316Mi)
% 14.88/3.66 % (15070)Instruction limit reached!
% 14.88/3.66 % (15070)------------------------------
% 14.88/3.66 % (15070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.88/3.66 % (15070)Termination reason: Unknown
% 14.88/3.66 % (15070)Termination phase: Property scanning
% 14.88/3.66
% 14.88/3.66 % (15070)Memory used [KB]: 2814
% 14.88/3.66 % (15070)Time elapsed: 0.020 s
% 14.88/3.66 % (15070)Instructions burned: 72 (million)
% 14.88/3.66 % (15070)------------------------------
% 14.88/3.66 % (15070)------------------------------
% 14.88/3.67 % (15072)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_14827 for (2981ds/932Mi)
% 15.77/3.73 % (15071)Refutation not found, incomplete strategy
% 15.77/3.73 % (15071)------------------------------
% 15.77/3.73 % (15071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.77/3.73 % (15071)Termination reason: Refutation not found, incomplete strategy
% 15.77/3.73
% 15.77/3.73
% 15.77/3.73 % (15071)Memory used [KB]: 8059
% 15.77/3.73 % (15071)Time elapsed: 0.082 s
% 15.77/3.73 % (15071)Instructions burned: 305 (million)
% 15.77/3.73 % (15071)------------------------------
% 15.77/3.73 % (15071)------------------------------
% 15.77/3.73 % (15068)Instruction limit reached!
% 15.77/3.73 % (15068)------------------------------
% 15.77/3.73 % (15068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.77/3.73 % (15068)Termination reason: Unknown
% 15.77/3.73 % (15068)Termination phase: Saturation
% 15.77/3.73
% 15.77/3.73 % (15068)Memory used [KB]: 8187
% 15.77/3.73 % (15068)Time elapsed: 0.115 s
% 15.77/3.73 % (15068)Instructions burned: 372 (million)
% 15.77/3.73 % (15068)------------------------------
% 15.77/3.73 % (15068)------------------------------
% 15.77/3.74 % (15074)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_14827 for (2981ds/4714Mi)
% 15.77/3.74 % (15075)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_14827 for (2981ds/8250Mi)
% 16.29/3.82 % (15074)Refutation not found, incomplete strategy
% 16.29/3.82 % (15074)------------------------------
% 16.29/3.82 % (15074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/3.82 % (15074)Termination reason: Refutation not found, incomplete strategy
% 16.29/3.82
% 16.29/3.82
% 16.29/3.82 % (15074)Memory used [KB]: 8187
% 16.29/3.82 % (15074)Time elapsed: 0.083 s
% 16.29/3.82 % (15074)Instructions burned: 313 (million)
% 16.29/3.82 % (15074)------------------------------
% 16.29/3.82 % (15074)------------------------------
% 16.29/3.83 % (15076)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_14827 for (2980ds/770Mi)
% 16.69/3.94 % (15072)Instruction limit reached!
% 16.69/3.94 % (15072)------------------------------
% 16.69/3.94 % (15072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.69/3.94 % (15072)Termination reason: Unknown
% 16.69/3.94 % (15072)Termination phase: Saturation
% 16.69/3.94
% 16.69/3.94 % (15072)Memory used [KB]: 9338
% 16.69/3.94 % (15072)Time elapsed: 0.269 s
% 16.69/3.94 % (15072)Instructions burned: 932 (million)
% 16.69/3.94 % (15072)------------------------------
% 16.69/3.94 % (15072)------------------------------
% 16.69/3.95 % (15077)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_14827 for (2978ds/794Mi)
% 18.23/4.06 % (15076)Instruction limit reached!
% 18.23/4.06 % (15076)------------------------------
% 18.23/4.06 % (15076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.23/4.06 % (15076)Termination reason: Unknown
% 18.23/4.06 % (15076)Termination phase: Saturation
% 18.23/4.06
% 18.23/4.06 % (15076)Memory used [KB]: 8827
% 18.23/4.06 % (15076)Time elapsed: 0.230 s
% 18.23/4.06 % (15076)Instructions burned: 772 (million)
% 18.23/4.06 % (15076)------------------------------
% 18.23/4.06 % (15076)------------------------------
% 18.23/4.07 % (15078)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_14827 for (2977ds/464Mi)
% 18.89/4.15 % (15053)Instruction limit reached!
% 18.89/4.15 % (15053)------------------------------
% 18.89/4.15 % (15053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.89/4.15 % (15053)Termination reason: Unknown
% 18.89/4.15 % (15053)Termination phase: Saturation
% 18.89/4.15
% 18.89/4.15 % (15053)Memory used [KB]: 8443
% 18.89/4.15 % (15053)Time elapsed: 1.184 s
% 18.89/4.15 % (15053)Instructions burned: 4354 (million)
% 18.89/4.15 % (15053)------------------------------
% 18.89/4.15 % (15053)------------------------------
% 18.89/4.16 % (15079)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_14827 for (2976ds/1376Mi)
% 18.89/4.19 % (15069)Instruction limit reached!
% 18.89/4.19 % (15069)------------------------------
% 18.89/4.19 % (15069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.89/4.19 % (15069)Termination reason: Unknown
% 18.89/4.19 % (15069)Termination phase: Saturation
% 18.89/4.19
% 18.89/4.19 % (15069)Memory used [KB]: 9210
% 18.89/4.19 % (15069)Time elapsed: 0.557 s
% 18.89/4.19 % (15069)Instructions burned: 1828 (million)
% 18.89/4.19 % (15069)------------------------------
% 18.89/4.19 % (15069)------------------------------
% 18.89/4.19 % (15077)Instruction limit reached!
% 18.89/4.19 % (15077)------------------------------
% 18.89/4.19 % (15077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.89/4.19 % (15077)Termination reason: Unknown
% 18.89/4.19 % (15077)Termination phase: Saturation
% 18.89/4.19
% 18.89/4.19 % (15077)Memory used [KB]: 6396
% 18.89/4.19 % (15077)Time elapsed: 0.242 s
% 18.89/4.19 % (15077)Instructions burned: 794 (million)
% 18.89/4.19 % (15077)------------------------------
% 18.89/4.19 % (15077)------------------------------
% 19.33/4.20 % (15080)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_14827 for (2976ds/906Mi)
% 19.33/4.20 % (15081)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_14827 for (2976ds/434Mi)
% 19.33/4.21 % (15078)Instruction limit reached!
% 19.33/4.21 % (15078)------------------------------
% 19.33/4.21 % (15078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.33/4.21 % (15078)Termination reason: Unknown
% 19.33/4.21 % (15078)Termination phase: Saturation
% 19.33/4.21
% 19.33/4.21 % (15078)Memory used [KB]: 8187
% 19.33/4.21 % (15078)Time elapsed: 0.137 s
% 19.33/4.21 % (15078)Instructions burned: 464 (million)
% 19.33/4.21 % (15078)------------------------------
% 19.33/4.21 % (15078)------------------------------
% 19.33/4.21 % (15048)Instruction limit reached!
% 19.33/4.21 % (15048)------------------------------
% 19.33/4.21 % (15048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.33/4.21 % (15048)Termination reason: Unknown
% 19.33/4.21 % (15048)Termination phase: Saturation
% 19.33/4.21
% 19.33/4.21 % (15048)Memory used [KB]: 8571
% 19.33/4.21 % (15048)Time elapsed: 1.344 s
% 19.33/4.21 % (15048)Instructions burned: 4439 (million)
% 19.33/4.21 % (15048)------------------------------
% 19.33/4.21 % (15048)------------------------------
% 19.33/4.22 % (15082)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_14827 for (2976ds/865Mi)
% 19.33/4.22 % (15083)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_14827 for (2976ds/593Mi)
% 19.68/4.33 % (15081)Instruction limit reached!
% 19.68/4.33 % (15081)------------------------------
% 19.68/4.33 % (15081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.68/4.33 % (15081)Termination reason: Unknown
% 19.68/4.33 % (15081)Termination phase: Saturation
% 19.68/4.33
% 19.68/4.33 % (15081)Memory used [KB]: 8059
% 19.68/4.33 % (15081)Time elapsed: 0.126 s
% 19.68/4.33 % (15081)Instructions burned: 436 (million)
% 19.68/4.33 % (15081)------------------------------
% 19.68/4.33 % (15081)------------------------------
% 19.68/4.34 % (15084)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_14827 for (2975ds/443Mi)
% 19.68/4.38 % (15083)Instruction limit reached!
% 19.68/4.38 % (15083)------------------------------
% 19.68/4.38 % (15083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.68/4.38 % (15083)Termination reason: Unknown
% 19.68/4.38 % (15083)Termination phase: Saturation
% 19.68/4.38
% 19.68/4.38 % (15083)Memory used [KB]: 9594
% 19.68/4.38 % (15083)Time elapsed: 0.160 s
% 19.68/4.38 % (15083)Instructions burned: 595 (million)
% 19.68/4.38 % (15083)------------------------------
% 19.68/4.38 % (15083)------------------------------
% 19.68/4.39 % (15085)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_14827 for (2974ds/594Mi)
% 20.18/4.45 % (15051)Instruction limit reached!
% 20.18/4.45 % (15051)------------------------------
% 20.18/4.45 % (15051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.18/4.45 % (15051)Termination reason: Unknown
% 20.18/4.45 % (15051)Termination phase: Saturation
% 20.18/4.45
% 20.18/4.45 % (15051)Memory used [KB]: 15223
% 20.18/4.45 % (15051)Time elapsed: 1.550 s
% 20.18/4.45 % (15051)Instructions burned: 5205 (million)
% 20.18/4.45 % (15051)------------------------------
% 20.18/4.45 % (15051)------------------------------
% 20.18/4.47 % (15086)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_14827 for (2973ds/327Mi)
% 20.18/4.47 % (15084)Instruction limit reached!
% 20.18/4.47 % (15084)------------------------------
% 20.18/4.47 % (15084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.18/4.47 % (15084)Termination reason: Unknown
% 20.18/4.47 % (15084)Termination phase: Saturation
% 20.18/4.47
% 20.18/4.47 % (15084)Memory used [KB]: 8187
% 20.18/4.47 % (15084)Time elapsed: 0.151 s
% 20.18/4.47 % (15084)Instructions burned: 443 (million)
% 20.18/4.47 % (15084)------------------------------
% 20.18/4.47 % (15084)------------------------------
% 20.18/4.47 % (15082)Instruction limit reached!
% 20.18/4.47 % (15082)------------------------------
% 20.18/4.47 % (15082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.18/4.47 % (15082)Termination reason: Unknown
% 20.18/4.47 % (15082)Termination phase: Saturation
% 20.18/4.47
% 20.18/4.47 % (15082)Memory used [KB]: 9722
% 20.18/4.47 % (15082)Time elapsed: 0.254 s
% 20.18/4.47 % (15082)Instructions burned: 865 (million)
% 20.18/4.47 % (15082)------------------------------
% 20.18/4.47 % (15082)------------------------------
% 20.18/4.48 % (15087)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_14827 for (2973ds/5411Mi)
% 20.18/4.48 % (15088)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_14827 for (2973ds/1762Mi)
% 20.18/4.49 % (15080)Instruction limit reached!
% 20.18/4.49 % (15080)------------------------------
% 20.18/4.49 % (15080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.18/4.49 % (15080)Termination reason: Unknown
% 20.18/4.49 % (15080)Termination phase: Saturation
% 20.18/4.49
% 20.18/4.49 % (15080)Memory used [KB]: 12537
% 20.18/4.49 % (15080)Time elapsed: 0.292 s
% 20.18/4.49 % (15080)Instructions burned: 908 (million)
% 20.18/4.49 % (15080)------------------------------
% 20.18/4.49 % (15080)------------------------------
% 21.06/4.50 % (15089)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_14827 for (2973ds/96Mi)
% 21.06/4.53 % (15089)Instruction limit reached!
% 21.06/4.53 % (15089)------------------------------
% 21.06/4.53 % (15089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.06/4.53 % (15089)Termination reason: Unknown
% 21.06/4.53 % (15089)Termination phase: Property scanning
% 21.06/4.53
% 21.06/4.53 % (15089)Memory used [KB]: 2814
% 21.06/4.53 % (15089)Time elapsed: 0.027 s
% 21.06/4.53 % (15089)Instructions burned: 97 (million)
% 21.06/4.53 % (15089)------------------------------
% 21.06/4.53 % (15089)------------------------------
% 21.06/4.54 % (15090)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_14827 for (2973ds/503Mi)
% 21.06/4.56 % (15086)Instruction limit reached!
% 21.06/4.56 % (15086)------------------------------
% 21.06/4.56 % (15086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.06/4.56 % (15086)Termination reason: Unknown
% 21.06/4.56 % (15086)Termination phase: Saturation
% 21.06/4.56
% 21.06/4.56 % (15086)Memory used [KB]: 8187
% 21.06/4.56 % (15086)Time elapsed: 0.097 s
% 21.06/4.56 % (15086)Instructions burned: 327 (million)
% 21.06/4.56 % (15086)------------------------------
% 21.06/4.56 % (15086)------------------------------
% 21.06/4.57 % (15079)Instruction limit reached!
% 21.06/4.57 % (15079)------------------------------
% 21.06/4.57 % (15079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.06/4.57 % (15079)Termination reason: Unknown
% 21.06/4.57 % (15079)Termination phase: Saturation
% 21.06/4.57
% 21.06/4.57 % (15079)Memory used [KB]: 11257
% 21.06/4.57 % (15079)Time elapsed: 0.409 s
% 21.06/4.57 % (15079)Instructions burned: 1378 (million)
% 21.06/4.57 % (15079)------------------------------
% 21.06/4.57 % (15079)------------------------------
% 21.06/4.57 % (15091)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_14827 for (2972ds/90Mi)
% 21.06/4.57 % (15085)Instruction limit reached!
% 21.06/4.57 % (15085)------------------------------
% 21.06/4.57 % (15085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.06/4.57 % (15085)Termination reason: Unknown
% 21.06/4.57 % (15085)Termination phase: Saturation
% 21.06/4.57
% 21.06/4.57 % (15085)Memory used [KB]: 7931
% 21.06/4.57 % (15085)Time elapsed: 0.204 s
% 21.06/4.57 % (15085)Instructions burned: 594 (million)
% 21.06/4.57 % (15085)------------------------------
% 21.06/4.57 % (15085)------------------------------
% 21.06/4.58 % (15092)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_14827 for (2972ds/593Mi)
% 21.06/4.58 % (15093)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_14827 for (2972ds/1512Mi)
% 21.91/4.60 % (15091)Instruction limit reached!
% 21.91/4.60 % (15091)------------------------------
% 21.91/4.60 % (15091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.91/4.60 % (15091)Termination reason: Unknown
% 21.91/4.60 % (15091)Termination phase: Property scanning
% 21.91/4.60
% 21.91/4.60 % (15091)Memory used [KB]: 2686
% 21.91/4.60 % (15091)Time elapsed: 0.027 s
% 21.91/4.60 % (15091)Instructions burned: 92 (million)
% 21.91/4.60 % (15091)------------------------------
% 21.91/4.60 % (15091)------------------------------
% 21.91/4.61 % (15094)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_14827 for (2972ds/569Mi)
% 21.91/4.69 % (15090)Instruction limit reached!
% 21.91/4.69 % (15090)------------------------------
% 21.91/4.69 % (15090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.91/4.69 % (15090)Termination reason: Unknown
% 21.91/4.69 % (15090)Termination phase: Saturation
% 21.91/4.69
% 21.91/4.69 % (15090)Memory used [KB]: 8571
% 21.91/4.69 % (15090)Time elapsed: 0.171 s
% 21.91/4.69 % (15090)Instructions burned: 504 (million)
% 21.91/4.69 % (15090)------------------------------
% 21.91/4.69 % (15090)------------------------------
% 21.91/4.70 % (15095)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_14827 for (2971ds/501Mi)
% 22.21/4.75 % (15092)Instruction limit reached!
% 22.21/4.75 % (15092)------------------------------
% 22.21/4.75 % (15092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.21/4.75 % (15092)Termination reason: Unknown
% 22.21/4.75 % (15092)Termination phase: Saturation
% 22.21/4.75
% 22.21/4.75 % (15092)Memory used [KB]: 9083
% 22.21/4.75 % (15092)Time elapsed: 0.176 s
% 22.21/4.75 % (15092)Instructions burned: 595 (million)
% 22.21/4.75 % (15092)------------------------------
% 22.21/4.75 % (15092)------------------------------
% 22.21/4.76 % (15094)Instruction limit reached!
% 22.21/4.76 % (15094)------------------------------
% 22.21/4.76 % (15094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.21/4.76 % (15094)Termination reason: Unknown
% 22.21/4.76 % (15094)Termination phase: Saturation
% 22.21/4.76
% 22.21/4.76 % (15094)Memory used [KB]: 8827
% 22.21/4.76 % (15094)Time elapsed: 0.158 s
% 22.21/4.76 % (15094)Instructions burned: 571 (million)
% 22.21/4.76 % (15094)------------------------------
% 22.21/4.76 % (15094)------------------------------
% 22.21/4.76 % (15096)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_14827 for (2970ds/562Mi)
% 22.21/4.77 % (15097)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_14827 for (2970ds/406Mi)
% 22.67/4.84 % (15095)Instruction limit reached!
% 22.67/4.84 % (15095)------------------------------
% 22.67/4.84 % (15095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.67/4.84 % (15095)Termination reason: Unknown
% 22.67/4.84 % (15095)Termination phase: Saturation
% 22.67/4.84
% 22.67/4.84 % (15095)Memory used [KB]: 9083
% 22.67/4.84 % (15095)Time elapsed: 0.144 s
% 22.67/4.84 % (15095)Instructions burned: 502 (million)
% 22.67/4.84 % (15095)------------------------------
% 22.67/4.84 % (15095)------------------------------
% 22.67/4.85 % (15098)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_14827 for (2969ds/582Mi)
% 22.67/4.89 % (15097)Instruction limit reached!
% 22.67/4.89 % (15097)------------------------------
% 22.67/4.89 % (15097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.67/4.89 % (15097)Termination reason: Unknown
% 22.67/4.89 % (15097)Termination phase: Saturation
% 22.67/4.89
% 22.67/4.89 % (15097)Memory used [KB]: 8571
% 22.67/4.89 % (15097)Time elapsed: 0.121 s
% 22.67/4.89 % (15097)Instructions burned: 407 (million)
% 22.67/4.89 % (15097)------------------------------
% 22.67/4.89 % (15097)------------------------------
% 23.04/4.90 % (15099)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_14827 for (2969ds/456Mi)
% 23.04/4.93 % (15096)Instruction limit reached!
% 23.04/4.93 % (15096)------------------------------
% 23.04/4.93 % (15096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.04/4.93 % (15096)Termination reason: Unknown
% 23.04/4.93 % (15096)Termination phase: Saturation
% 23.04/4.93
% 23.04/4.93 % (15096)Memory used [KB]: 9210
% 23.04/4.93 % (15096)Time elapsed: 0.165 s
% 23.04/4.93 % (15096)Instructions burned: 562 (million)
% 23.04/4.93 % (15096)------------------------------
% 23.04/4.93 % (15096)------------------------------
% 23.04/4.94 % (15100)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_14827 for (2969ds/393Mi)
% 23.04/4.98 % (15088)Instruction limit reached!
% 23.04/4.98 % (15088)------------------------------
% 23.04/4.98 % (15088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.04/4.98 % (15088)Termination reason: Unknown
% 23.04/4.98 % (15088)Termination phase: Saturation
% 23.04/4.98
% 23.04/4.98 % (15088)Memory used [KB]: 9466
% 23.04/4.98 % (15088)Time elapsed: 0.526 s
% 23.04/4.98 % (15088)Instructions burned: 1763 (million)
% 23.04/4.98 % (15088)------------------------------
% 23.04/4.98 % (15088)------------------------------
% 23.04/4.99 % (15102)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_14827 for (2968ds/1335Mi)
% 25.17/5.02 % (15098)Instruction limit reached!
% 25.17/5.02 % (15098)------------------------------
% 25.17/5.02 % (15098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.17/5.02 % (15098)Termination reason: Unknown
% 25.17/5.02 % (15098)Termination phase: Saturation
% 25.17/5.02
% 25.17/5.02 % (15098)Memory used [KB]: 8315
% 25.17/5.02 % (15098)Time elapsed: 0.173 s
% 25.17/5.02 % (15098)Instructions burned: 582 (million)
% 25.17/5.02 % (15098)------------------------------
% 25.17/5.02 % (15098)------------------------------
% 25.17/5.02 % (15093)Instruction limit reached!
% 25.17/5.02 % (15093)------------------------------
% 25.17/5.02 % (15093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.17/5.02 % (15093)Termination reason: Unknown
% 25.17/5.02 % (15093)Termination phase: Saturation
% 25.17/5.02
% 25.17/5.02 % (15093)Memory used [KB]: 9210
% 25.17/5.02 % (15093)Time elapsed: 0.468 s
% 25.17/5.02 % (15093)Instructions burned: 1512 (million)
% 25.17/5.02 % (15093)------------------------------
% 25.17/5.02 % (15093)------------------------------
% 25.17/5.03 % (15103)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_14827 for (2968ds/3373Mi)
% 25.17/5.03 % (15104)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_14827 for (2968ds/474Mi)
% 25.17/5.04 % (15099)Instruction limit reached!
% 25.17/5.04 % (15099)------------------------------
% 25.17/5.04 % (15099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.17/5.04 % (15099)Termination reason: Unknown
% 25.17/5.04 % (15099)Termination phase: Saturation
% 25.17/5.04
% 25.17/5.04 % (15099)Memory used [KB]: 9466
% 25.17/5.04 % (15099)Time elapsed: 0.133 s
% 25.17/5.04 % (15099)Instructions burned: 458 (million)
% 25.17/5.04 % (15099)------------------------------
% 25.17/5.04 % (15099)------------------------------
% 25.17/5.04 % (15100)Instruction limit reached!
% 25.17/5.04 % (15100)------------------------------
% 25.17/5.04 % (15100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.17/5.04 % (15100)Termination reason: Unknown
% 25.17/5.04 % (15100)Termination phase: Saturation
% 25.17/5.04
% 25.17/5.04 % (15100)Memory used [KB]: 8571
% 25.17/5.04 % (15100)Time elapsed: 0.106 s
% 25.17/5.04 % (15100)Instructions burned: 393 (million)
% 25.17/5.04 % (15100)------------------------------
% 25.17/5.04 % (15100)------------------------------
% 25.17/5.05 % (15105)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_14827 for (2967ds/157Mi)
% 25.17/5.05 % (15106)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_14827 for (2967ds/590Mi)
% 25.17/5.09 % (15105)Instruction limit reached!
% 25.17/5.09 % (15105)------------------------------
% 25.17/5.09 % (15105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.17/5.09 % (15105)Termination reason: Unknown
% 25.17/5.09 % (15105)Termination phase: Property scanning
% 25.17/5.09
% 25.17/5.09 % (15105)Memory used [KB]: 2942
% 25.17/5.09 % (15105)Time elapsed: 0.042 s
% 25.17/5.09 % (15105)Instructions burned: 158 (million)
% 25.17/5.09 % (15105)------------------------------
% 25.17/5.09 % (15105)------------------------------
% 25.17/5.10 % (15107)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_14827 for (2967ds/104Mi)
% 25.64/5.13 % (15107)Instruction limit reached!
% 25.64/5.13 % (15107)------------------------------
% 25.64/5.13 % (15107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.64/5.13 % (15107)Termination reason: Unknown
% 25.64/5.13 % (15107)Termination phase: Property scanning
% 25.64/5.13
% 25.64/5.13 % (15107)Memory used [KB]: 2686
% 25.64/5.13 % (15107)Time elapsed: 0.032 s
% 25.64/5.13 % (15107)Instructions burned: 106 (million)
% 25.64/5.13 % (15107)------------------------------
% 25.64/5.13 % (15107)------------------------------
% 25.64/5.14 % (15108)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_14827 for (2967ds/414Mi)
% 25.64/5.16 % (15104)Instruction limit reached!
% 25.64/5.16 % (15104)------------------------------
% 25.64/5.16 % (15104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.64/5.16 % (15104)Termination reason: Unknown
% 25.64/5.16 % (15104)Termination phase: Saturation
% 25.64/5.16
% 25.64/5.16 % (15104)Memory used [KB]: 8827
% 25.64/5.16 % (15104)Time elapsed: 0.134 s
% 25.64/5.16 % (15104)Instructions burned: 475 (million)
% 25.64/5.16 % (15104)------------------------------
% 25.64/5.16 % (15104)------------------------------
% 25.64/5.17 % (15109)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_14827 for (2966ds/715Mi)
% 26.06/5.21 % (15106)Instruction limit reached!
% 26.06/5.21 % (15106)------------------------------
% 26.06/5.21 % (15106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.06/5.21 % (15106)Termination reason: Unknown
% 26.06/5.21 % (15106)Termination phase: Saturation
% 26.06/5.21
% 26.06/5.21 % (15106)Memory used [KB]: 7931
% 26.06/5.21 % (15106)Time elapsed: 0.162 s
% 26.06/5.21 % (15106)Instructions burned: 592 (million)
% 26.06/5.21 % (15106)------------------------------
% 26.06/5.21 % (15106)------------------------------
% 26.06/5.22 % (15110)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_14827 for (2966ds/961Mi)
% 26.06/5.25 % (15108)Instruction limit reached!
% 26.06/5.25 % (15108)------------------------------
% 26.06/5.25 % (15108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.06/5.25 % (15108)Termination reason: Unknown
% 26.06/5.25 % (15108)Termination phase: Saturation
% 26.06/5.25
% 26.06/5.25 % (15108)Memory used [KB]: 8187
% 26.06/5.25 % (15108)Time elapsed: 0.113 s
% 26.06/5.25 % (15108)Instructions burned: 416 (million)
% 26.06/5.25 % (15108)------------------------------
% 26.06/5.25 % (15108)------------------------------
% 26.06/5.27 % (15111)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_14827 for (2965ds/1213Mi)
% 26.65/5.37 % (15102)Instruction limit reached!
% 26.65/5.37 % (15102)------------------------------
% 26.65/5.37 % (15102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.65/5.37 % (15102)Termination reason: Unknown
% 26.65/5.37 % (15102)Termination phase: Saturation
% 26.65/5.37
% 26.65/5.37 % (15102)Memory used [KB]: 9594
% 26.65/5.37 % (15102)Time elapsed: 0.381 s
% 26.65/5.37 % (15102)Instructions burned: 1336 (million)
% 26.65/5.37 % (15102)------------------------------
% 26.65/5.37 % (15102)------------------------------
% 26.65/5.38 % (15112)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_14827 for (2964ds/1979Mi)
% 26.65/5.38 % (15109)Instruction limit reached!
% 26.65/5.38 % (15109)------------------------------
% 26.65/5.38 % (15109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.65/5.38 % (15109)Termination reason: Unknown
% 26.65/5.38 % (15109)Termination phase: Saturation
% 26.65/5.38
% 26.65/5.38 % (15109)Memory used [KB]: 4349
% 26.65/5.38 % (15109)Time elapsed: 0.210 s
% 26.65/5.38 % (15109)Instructions burned: 716 (million)
% 26.65/5.38 % (15109)------------------------------
% 26.65/5.38 % (15109)------------------------------
% 26.65/5.39 % (15113)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_14827 for (2964ds/481Mi)
% 27.36/5.51 % (15110)Instruction limit reached!
% 27.36/5.51 % (15110)------------------------------
% 27.36/5.51 % (15110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.36/5.51 % (15110)Termination reason: Unknown
% 27.36/5.51 % (15110)Termination phase: Saturation
% 27.36/5.51
% 27.36/5.51 % (15110)Memory used [KB]: 8443
% 27.36/5.51 % (15110)Time elapsed: 0.287 s
% 27.36/5.51 % (15110)Instructions burned: 961 (million)
% 27.36/5.51 % (15110)------------------------------
% 27.36/5.51 % (15110)------------------------------
% 27.36/5.52 % (15114)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_14827 for (2963ds/783Mi)
% 27.36/5.53 % (15113)Instruction limit reached!
% 27.36/5.53 % (15113)------------------------------
% 27.36/5.53 % (15113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.36/5.53 % (15113)Termination reason: Unknown
% 27.36/5.53 % (15113)Termination phase: Saturation
% 27.36/5.53
% 27.36/5.53 % (15113)Memory used [KB]: 8187
% 27.36/5.53 % (15113)Time elapsed: 0.138 s
% 27.36/5.53 % (15113)Instructions burned: 483 (million)
% 27.36/5.53 % (15113)------------------------------
% 27.36/5.53 % (15113)------------------------------
% 27.36/5.54 % (15115)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_14827 for (2963ds/432Mi)
% 28.00/5.65 % (15111)Instruction limit reached!
% 28.00/5.65 % (15111)------------------------------
% 28.00/5.65 % (15111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.00/5.65 % (15111)Termination reason: Unknown
% 28.00/5.65 % (15111)Termination phase: Saturation
% 28.00/5.65
% 28.00/5.65 % (15111)Memory used [KB]: 9850
% 28.00/5.65 % (15111)Time elapsed: 0.380 s
% 28.00/5.65 % (15111)Instructions burned: 1214 (million)
% 28.00/5.65 % (15111)------------------------------
% 28.00/5.65 % (15111)------------------------------
% 28.00/5.66 % (15116)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_14827 for (2961ds/1670Mi)
% 28.00/5.67 % (15115)Instruction limit reached!
% 28.00/5.67 % (15115)------------------------------
% 28.00/5.67 % (15115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.00/5.67 % (15115)Termination reason: Unknown
% 28.00/5.67 % (15115)Termination phase: Saturation
% 28.00/5.67
% 28.00/5.67 % (15115)Memory used [KB]: 7291
% 28.00/5.67 % (15115)Time elapsed: 0.136 s
% 28.00/5.67 % (15115)Instructions burned: 435 (million)
% 28.00/5.67 % (15115)------------------------------
% 28.00/5.67 % (15115)------------------------------
% 28.00/5.68 % (15117)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_14827 for (2961ds/90Mi)
% 28.73/5.71 % (15117)Instruction limit reached!
% 28.73/5.71 % (15117)------------------------------
% 28.73/5.71 % (15117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.73/5.71 % (15117)Termination reason: Unknown
% 28.73/5.71 % (15117)Termination phase: Property scanning
% 28.73/5.71
% 28.73/5.71 % (15117)Memory used [KB]: 2686
% 28.73/5.71 % (15117)Time elapsed: 0.028 s
% 28.73/5.71 % (15117)Instructions burned: 92 (million)
% 28.73/5.71 % (15117)------------------------------
% 28.73/5.71 % (15117)------------------------------
% 28.73/5.72 % (15118)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_14827 for (2961ds/346Mi)
% 28.73/5.76 % (15114)Instruction limit reached!
% 28.73/5.76 % (15114)------------------------------
% 28.73/5.76 % (15114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.73/5.76 % (15114)Termination reason: Unknown
% 28.73/5.76 % (15114)Termination phase: Saturation
% 28.73/5.76
% 28.73/5.76 % (15114)Memory used [KB]: 8187
% 28.73/5.76 % (15114)Time elapsed: 0.241 s
% 28.73/5.76 % (15114)Instructions burned: 785 (million)
% 28.73/5.76 % (15114)------------------------------
% 28.73/5.76 % (15114)------------------------------
% 28.73/5.77 % (15119)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_14827 for (2960ds/401Mi)
% 29.22/5.82 % (15118)Instruction limit reached!
% 29.22/5.82 % (15118)------------------------------
% 29.22/5.82 % (15118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.22/5.82 % (15118)Termination reason: Unknown
% 29.22/5.82 % (15118)Termination phase: Saturation
% 29.22/5.82
% 29.22/5.82 % (15118)Memory used [KB]: 8059
% 29.22/5.82 % (15118)Time elapsed: 0.096 s
% 29.22/5.82 % (15118)Instructions burned: 348 (million)
% 29.22/5.82 % (15118)------------------------------
% 29.22/5.82 % (15118)------------------------------
% 29.22/5.83 % (15120)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_14827 for (2960ds/6454Mi)
% 29.22/5.87 % (15119)Instruction limit reached!
% 29.22/5.87 % (15119)------------------------------
% 29.22/5.87 % (15119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.22/5.87 % (15119)Termination reason: Unknown
% 29.22/5.87 % (15119)Termination phase: Saturation
% 29.22/5.87
% 29.22/5.87 % (15119)Memory used [KB]: 8699
% 29.22/5.87 % (15119)Time elapsed: 0.107 s
% 29.22/5.87 % (15119)Instructions burned: 404 (million)
% 29.22/5.87 % (15119)------------------------------
% 29.22/5.87 % (15119)------------------------------
% 29.22/5.88 % (15121)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_14827 for (2959ds/283Mi)
% 29.64/5.96 % (15121)Instruction limit reached!
% 29.64/5.96 % (15121)------------------------------
% 29.64/5.96 % (15121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.64/5.96 % (15121)Termination reason: Unknown
% 29.64/5.96 % (15121)Termination phase: Saturation
% 29.64/5.96
% 29.64/5.96 % (15121)Memory used [KB]: 7931
% 29.64/5.96 % (15121)Time elapsed: 0.081 s
% 29.64/5.96 % (15121)Instructions burned: 284 (million)
% 29.64/5.96 % (15121)------------------------------
% 29.64/5.96 % (15121)------------------------------
% 29.64/5.97 % (15122)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_14827 for (2958ds/865Mi)
% 29.64/5.98 % (15112)Instruction limit reached!
% 29.64/5.98 % (15112)------------------------------
% 29.64/5.98 % (15112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.64/5.98 % (15112)Termination reason: Unknown
% 29.64/5.98 % (15112)Termination phase: Saturation
% 29.64/5.98
% 29.64/5.98 % (15112)Memory used [KB]: 9210
% 29.64/5.98 % (15112)Time elapsed: 0.600 s
% 29.64/5.98 % (15112)Instructions burned: 1980 (million)
% 29.64/5.98 % (15112)------------------------------
% 29.64/5.98 % (15112)------------------------------
% 29.64/5.99 % (15123)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_14827 for (2958ds/4528Mi)
% 32.13/6.01 % (15087)Instruction limit reached!
% 32.13/6.01 % (15087)------------------------------
% 32.13/6.01 % (15087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.13/6.01 % (15087)Termination reason: Unknown
% 32.13/6.01 % (15087)Termination phase: Saturation
% 32.13/6.01
% 32.13/6.01 % (15087)Memory used [KB]: 12281
% 32.13/6.01 % (15087)Time elapsed: 1.559 s
% 32.13/6.01 % (15087)Instructions burned: 5411 (million)
% 32.13/6.01 % (15087)------------------------------
% 32.13/6.01 % (15087)------------------------------
% 32.13/6.03 % (15124)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_14827 for (2958ds/1001Mi)
% 32.13/6.03 % (15103)Instruction limit reached!
% 32.13/6.03 % (15103)------------------------------
% 32.13/6.03 % (15103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.13/6.03 % (15103)Termination reason: Unknown
% 32.13/6.03 % (15103)Termination phase: Saturation
% 32.13/6.03
% 32.13/6.03 % (15103)Memory used [KB]: 13048
% 32.13/6.03 % (15103)Time elapsed: 0.998 s
% 32.13/6.03 % (15103)Instructions burned: 3374 (million)
% 32.13/6.03 % (15103)------------------------------
% 32.13/6.03 % (15103)------------------------------
% 32.13/6.04 % (15125)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_14827 for (2958ds/102Mi)
% 32.13/6.06 % (15123)Refutation not found, incomplete strategy
% 32.13/6.06 % (15123)------------------------------
% 32.13/6.06 % (15123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.13/6.06 % (15123)Termination reason: Refutation not found, incomplete strategy
% 32.13/6.06
% 32.13/6.06
% 32.13/6.06 % (15123)Memory used [KB]: 3198
% 32.13/6.06 % (15123)Time elapsed: 0.069 s
% 32.13/6.06 % (15123)Instructions burned: 229 (million)
% 32.13/6.06 % (15123)------------------------------
% 32.13/6.06 % (15123)------------------------------
% 32.13/6.07 % (15125)Instruction limit reached!
% 32.13/6.07 % (15125)------------------------------
% 32.13/6.07 % (15125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.13/6.07 % (15125)Termination reason: Unknown
% 32.13/6.07 % (15125)Termination phase: Property scanning
% 32.13/6.07
% 32.13/6.07 % (15125)Memory used [KB]: 2814
% 32.13/6.07 % (15125)Time elapsed: 0.029 s
% 32.13/6.07 % (15125)Instructions burned: 104 (million)
% 32.13/6.07 % (15125)------------------------------
% 32.13/6.07 % (15125)------------------------------
% 32.13/6.07 % (15126)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_14827 for (2957ds/952Mi)
% 32.13/6.07 % (15127)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_14827 for (2957ds/578Mi)
% 32.68/6.15 % (15116)Instruction limit reached!
% 32.68/6.15 % (15116)------------------------------
% 32.68/6.15 % (15116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.68/6.15 % (15116)Termination reason: Unknown
% 32.68/6.15 % (15116)Termination phase: Saturation
% 32.68/6.15
% 32.68/6.15 % (15116)Memory used [KB]: 10618
% 32.68/6.15 % (15116)Time elapsed: 0.490 s
% 32.68/6.15 % (15116)Instructions burned: 1673 (million)
% 32.68/6.15 % (15116)------------------------------
% 32.68/6.15 % (15116)------------------------------
% 32.68/6.16 % (15128)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_14827 for (2956ds/643Mi)
% 32.97/6.23 % (15122)Instruction limit reached!
% 32.97/6.23 % (15122)------------------------------
% 32.97/6.23 % (15122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.97/6.23 % (15122)Termination reason: Unknown
% 32.97/6.23 % (15122)Termination phase: Saturation
% 32.97/6.23
% 32.97/6.23 % (15122)Memory used [KB]: 10874
% 32.97/6.23 % (15122)Time elapsed: 0.257 s
% 32.97/6.23 % (15122)Instructions burned: 865 (million)
% 32.97/6.23 % (15122)------------------------------
% 32.97/6.23 % (15122)------------------------------
% 32.97/6.24 % (15130)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_14827 for (2956ds/865Mi)
% 32.97/6.25 % (15127)Instruction limit reached!
% 32.97/6.25 % (15127)------------------------------
% 32.97/6.25 % (15127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.97/6.25 % (15127)Termination reason: Unknown
% 32.97/6.25 % (15127)Termination phase: Saturation
% 32.97/6.25
% 32.97/6.25 % (15127)Memory used [KB]: 8443
% 32.97/6.25 % (15127)Time elapsed: 0.175 s
% 32.97/6.25 % (15127)Instructions burned: 581 (million)
% 32.97/6.25 % (15127)------------------------------
% 32.97/6.25 % (15127)------------------------------
% 32.97/6.26 % (15131)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_14827 for (2955ds/1174Mi)
% 32.97/6.28 % (15075)Instruction limit reached!
% 32.97/6.28 % (15075)------------------------------
% 32.97/6.28 % (15075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.97/6.28 % (15075)Termination reason: Unknown
% 32.97/6.28 % (15075)Termination phase: Saturation
% 32.97/6.28
% 32.97/6.28 % (15075)Memory used [KB]: 12665
% 32.97/6.28 % (15075)Time elapsed: 2.538 s
% 32.97/6.28 % (15075)Instructions burned: 8251 (million)
% 32.97/6.28 % (15075)------------------------------
% 32.97/6.28 % (15075)------------------------------
% 32.97/6.30 % (15132)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_14827 for (2955ds/644Mi)
% 33.41/6.32 % (15124)Instruction limit reached!
% 33.41/6.32 % (15124)------------------------------
% 33.41/6.32 % (15124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.41/6.32 % (15124)Termination reason: Unknown
% 33.41/6.32 % (15124)Termination phase: Saturation
% 33.41/6.32
% 33.41/6.32 % (15124)Memory used [KB]: 11385
% 33.41/6.32 % (15124)Time elapsed: 0.300 s
% 33.41/6.32 % (15124)Instructions burned: 1001 (million)
% 33.41/6.32 % (15124)------------------------------
% 33.41/6.32 % (15124)------------------------------
% 33.41/6.33 % (15128)Instruction limit reached!
% 33.41/6.33 % (15128)------------------------------
% 33.41/6.33 % (15128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.41/6.33 % (15128)Termination reason: Unknown
% 33.41/6.33 % (15128)Termination phase: Saturation
% 33.41/6.33
% 33.41/6.33 % (15128)Memory used [KB]: 9722
% 33.41/6.33 % (15128)Time elapsed: 0.173 s
% 33.41/6.33 % (15128)Instructions burned: 643 (million)
% 33.41/6.33 % (15128)------------------------------
% 33.41/6.33 % (15128)------------------------------
% 33.41/6.33 % (15133)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_14827 for (2955ds/1201Mi)
% 33.41/6.34 % (15134)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_14827 for (2955ds/1046Mi)
% 33.41/6.36 % (15126)Instruction limit reached!
% 33.41/6.36 % (15126)------------------------------
% 33.41/6.36 % (15126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.41/6.36 % (15126)Termination reason: Unknown
% 33.41/6.36 % (15126)Termination phase: Saturation
% 33.41/6.36
% 33.41/6.36 % (15126)Memory used [KB]: 9594
% 33.41/6.36 % (15126)Time elapsed: 0.288 s
% 33.41/6.36 % (15126)Instructions burned: 953 (million)
% 33.41/6.36 % (15126)------------------------------
% 33.41/6.36 % (15126)------------------------------
% 33.41/6.37 % (15135)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_14827 for (2954ds/222Mi)
% 34.29/6.42 % (15135)Instruction limit reached!
% 34.29/6.42 % (15135)------------------------------
% 34.29/6.42 % (15135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.29/6.42 % (15135)Termination reason: Unknown
% 34.29/6.42 % (15135)Termination phase: Saturation
% 34.29/6.42
% 34.29/6.42 % (15135)Memory used [KB]: 7547
% 34.29/6.42 % (15135)Time elapsed: 0.059 s
% 34.29/6.42 % (15135)Instructions burned: 225 (million)
% 34.29/6.42 % (15135)------------------------------
% 34.29/6.42 % (15135)------------------------------
% 34.29/6.43 % (15136)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_14827 for (2954ds/68Mi)
% 34.29/6.45 % (15136)Instruction limit reached!
% 34.29/6.45 % (15136)------------------------------
% 34.29/6.45 % (15136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.29/6.46 % (15136)Termination reason: Unknown
% 34.29/6.46 % (15136)Termination phase: Preprocessing 1
% 34.29/6.46
% 34.29/6.46 % (15136)Memory used [KB]: 2174
% 34.29/6.46 % (15136)Time elapsed: 0.022 s
% 34.29/6.46 % (15136)Instructions burned: 69 (million)
% 34.29/6.46 % (15136)------------------------------
% 34.29/6.46 % (15136)------------------------------
% 34.29/6.47 % (15137)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_14827 for (2953ds/454Mi)
% 34.29/6.48 % (15132)Instruction limit reached!
% 34.29/6.48 % (15132)------------------------------
% 34.29/6.48 % (15132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.29/6.48 % (15132)Termination reason: Unknown
% 34.29/6.48 % (15132)Termination phase: Saturation
% 34.29/6.48
% 34.29/6.48 % (15132)Memory used [KB]: 9978
% 34.29/6.48 % (15132)Time elapsed: 0.190 s
% 34.29/6.48 % (15132)Instructions burned: 646 (million)
% 34.29/6.48 % (15132)------------------------------
% 34.29/6.48 % (15132)------------------------------
% 34.29/6.49 % (15138)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_14827 for (2953ds/360Mi)
% 34.68/6.50 % (15130)Instruction limit reached!
% 34.68/6.50 % (15130)------------------------------
% 34.68/6.50 % (15130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.68/6.50 % (15130)Termination reason: Unknown
% 34.68/6.50 % (15130)Termination phase: Saturation
% 34.68/6.50
% 34.68/6.50 % (15130)Memory used [KB]: 9722
% 34.68/6.50 % (15130)Time elapsed: 0.285 s
% 34.68/6.50 % (15130)Instructions burned: 865 (million)
% 34.68/6.50 % (15130)------------------------------
% 34.68/6.50 % (15130)------------------------------
% 34.68/6.51 % (15139)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_14827 for (2953ds/157Mi)
% 34.68/6.56 % (15139)Instruction limit reached!
% 34.68/6.56 % (15139)------------------------------
% 34.68/6.56 % (15139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.68/6.56 % (15139)Termination reason: Unknown
% 34.68/6.56 % (15139)Termination phase: Function definition elimination
% 34.68/6.56
% 34.68/6.56 % (15139)Memory used [KB]: 2814
% 34.68/6.56 % (15139)Time elapsed: 0.044 s
% 34.68/6.56 % (15139)Instructions burned: 160 (million)
% 34.68/6.56 % (15139)------------------------------
% 34.68/6.56 % (15139)------------------------------
% 34.68/6.57 % (15140)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_14827 for (2952ds/5061Mi)
% 34.68/6.59 % (15138)Instruction limit reached!
% 34.68/6.59 % (15138)------------------------------
% 34.68/6.59 % (15138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.68/6.59 % (15138)Termination reason: Unknown
% 34.68/6.59 % (15138)Termination phase: Saturation
% 34.68/6.59
% 34.68/6.59 % (15138)Memory used [KB]: 8571
% 34.68/6.59 % (15138)Time elapsed: 0.095 s
% 34.68/6.59 % (15138)Instructions burned: 361 (million)
% 34.68/6.59 % (15138)------------------------------
% 34.68/6.59 % (15138)------------------------------
% 34.68/6.59 % (15137)Instruction limit reached!
% 34.68/6.59 % (15137)------------------------------
% 34.68/6.59 % (15137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.68/6.59 % (15137)Termination reason: Unknown
% 34.68/6.59 % (15137)Termination phase: Saturation
% 34.68/6.59
% 34.68/6.59 % (15137)Memory used [KB]: 13432
% 34.68/6.59 % (15137)Time elapsed: 0.125 s
% 34.68/6.59 % (15137)Instructions burned: 456 (million)
% 34.68/6.59 % (15137)------------------------------
% 34.68/6.59 % (15137)------------------------------
% 35.34/6.60 % (15141)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_14827 for (2952ds/2401Mi)
% 35.34/6.60 % (15142)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_14827 for (2952ds/5798Mi)
% 35.34/6.60 % (15131)Instruction limit reached!
% 35.34/6.60 % (15131)------------------------------
% 35.34/6.60 % (15131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.34/6.60 % (15131)Termination reason: Unknown
% 35.34/6.60 % (15131)Termination phase: Saturation
% 35.34/6.60
% 35.34/6.60 % (15131)Memory used [KB]: 11385
% 35.34/6.60 % (15131)Time elapsed: 0.342 s
% 35.34/6.60 % (15131)Instructions burned: 1175 (million)
% 35.34/6.60 % (15131)------------------------------
% 35.34/6.60 % (15131)------------------------------
% 35.34/6.61 % (15143)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_14827 for (2952ds/346Mi)
% 35.34/6.64 % (15134)Instruction limit reached!
% 35.34/6.64 % (15134)------------------------------
% 35.34/6.64 % (15134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.34/6.64 % (15134)Termination reason: Unknown
% 35.34/6.64 % (15134)Termination phase: Saturation
% 35.34/6.64
% 35.34/6.64 % (15134)Memory used [KB]: 9722
% 35.34/6.64 % (15134)Time elapsed: 0.298 s
% 35.34/6.64 % (15134)Instructions burned: 1046 (million)
% 35.34/6.64 % (15134)------------------------------
% 35.34/6.64 % (15134)------------------------------
% 35.34/6.65 % (15144)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_14827 for (2951ds/1321Mi)
% 35.34/6.66 % (15133)Instruction limit reached!
% 35.34/6.66 % (15133)------------------------------
% 35.34/6.66 % (15133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.34/6.66 % (15133)Termination reason: Unknown
% 35.34/6.66 % (15133)Termination phase: Saturation
% 35.34/6.66
% 35.34/6.66 % (15133)Memory used [KB]: 8699
% 35.34/6.66 % (15133)Time elapsed: 0.328 s
% 35.34/6.66 % (15133)Instructions burned: 1201 (million)
% 35.34/6.66 % (15133)------------------------------
% 35.34/6.66 % (15133)------------------------------
% 35.34/6.67 % (15145)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_14827 for (2951ds/1312Mi)
% 36.44/6.70 % (15143)Instruction limit reached!
% 36.44/6.70 % (15143)------------------------------
% 36.44/6.70 % (15143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.44/6.70 % (15143)Termination reason: Unknown
% 36.44/6.70 % (15143)Termination phase: Saturation
% 36.44/6.70
% 36.44/6.70 % (15143)Memory used [KB]: 8059
% 36.44/6.70 % (15143)Time elapsed: 0.095 s
% 36.44/6.70 % (15143)Instructions burned: 346 (million)
% 36.44/6.70 % (15143)------------------------------
% 36.44/6.70 % (15143)------------------------------
% 36.44/6.71 % (15146)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_14827 for (2951ds/672Mi)
% 36.74/6.90 % (15146)Instruction limit reached!
% 36.74/6.90 % (15146)------------------------------
% 36.74/6.90 % (15146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.74/6.90 % (15146)Termination reason: Unknown
% 36.74/6.90 % (15146)Termination phase: Saturation
% 36.74/6.90
% 36.74/6.90 % (15146)Memory used [KB]: 9338
% 36.74/6.90 % (15146)Time elapsed: 0.192 s
% 36.74/6.90 % (15146)Instructions burned: 672 (million)
% 36.74/6.90 % (15146)------------------------------
% 36.74/6.90 % (15146)------------------------------
% 36.74/6.91 % (15147)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_14827 for (2949ds/1897Mi)
% 39.11/7.02 % (15144)Instruction limit reached!
% 39.11/7.02 % (15144)------------------------------
% 39.11/7.02 % (15144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.11/7.02 % (15144)Termination reason: Unknown
% 39.11/7.02 % (15144)Termination phase: Saturation
% 39.11/7.02
% 39.11/7.02 % (15144)Memory used [KB]: 6012
% 39.11/7.02 % (15144)Time elapsed: 0.373 s
% 39.11/7.02 % (15144)Instructions burned: 1322 (million)
% 39.11/7.02 % (15144)------------------------------
% 39.11/7.02 % (15144)------------------------------
% 39.11/7.03 % (15148)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_14827 for (2948ds/1202Mi)
% 39.11/7.05 % (15145)Instruction limit reached!
% 39.11/7.05 % (15145)------------------------------
% 39.11/7.05 % (15145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.11/7.05 % (15145)Termination reason: Unknown
% 39.11/7.05 % (15145)Termination phase: Saturation
% 39.11/7.05
% 39.11/7.05 % (15145)Memory used [KB]: 9338
% 39.11/7.05 % (15145)Time elapsed: 0.373 s
% 39.11/7.05 % (15145)Instructions burned: 1312 (million)
% 39.11/7.05 % (15145)------------------------------
% 39.11/7.05 % (15145)------------------------------
% 39.11/7.06 % (15149)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_14827 for (2947ds/1493Mi)
% 39.11/7.11 % (15149)Refutation not found, incomplete strategy
% 39.11/7.11 % (15149)------------------------------
% 39.11/7.11 % (15149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.11/7.11 % (15149)Termination reason: Refutation not found, incomplete strategy
% 39.11/7.11
% 39.11/7.11
% 39.11/7.11 % (15149)Memory used [KB]: 7675
% 39.11/7.11 % (15149)Time elapsed: 0.052 s
% 39.11/7.11 % (15149)Instructions burned: 188 (million)
% 39.11/7.11 % (15149)------------------------------
% 39.11/7.11 % (15149)------------------------------
% 39.75/7.12 % (15150)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_14827 for (2947ds/7679Mi)
% 40.67/7.31 % (15141)Instruction limit reached!
% 40.67/7.31 % (15141)------------------------------
% 40.67/7.31 % (15141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.67/7.31 % (15141)Termination reason: Unknown
% 40.67/7.31 % (15141)Termination phase: Saturation
% 40.67/7.31
% 40.67/7.31 % (15141)Memory used [KB]: 6396
% 40.67/7.31 % (15141)Time elapsed: 0.713 s
% 40.67/7.31 % (15141)Instructions burned: 2401 (million)
% 40.67/7.31 % (15141)------------------------------
% 40.67/7.31 % (15141)------------------------------
% 40.67/7.32 % (15151)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_14827 for (2945ds/340Mi)
% 40.67/7.35 % (15150)First to succeed.
% 40.67/7.35 % (15150)Refutation found. Thanks to Tanya!
% 40.67/7.35 % SZS status Theorem for DTF2THF_14827
% 40.67/7.35 % SZS output start Proof for DTF2THF_14827
% 40.67/7.35 thf(type_def_5, type, set_b: $tType).
% 40.67/7.35 thf(type_def_7, type, real: $tType).
% 40.67/7.35 thf(type_def_8, type, set_real: $tType).
% 40.67/7.35 thf(type_def_9, type, set_a: $tType).
% 40.67/7.35 thf(type_def_10, type, a: $tType).
% 40.67/7.35 thf(type_def_11, type, b: $tType).
% 40.67/7.35 thf(type_def_12, type, nat: $tType).
% 40.67/7.35 thf(type_def_13, type, extended_ereal: $tType).
% 40.67/7.35 thf(func_def_0, type, set_real: $tType).
% 40.67/7.35 thf(func_def_1, type, extended_ereal: $tType).
% 40.67/7.35 thf(func_def_2, type, set_b: $tType).
% 40.67/7.35 thf(func_def_3, type, set_a: $tType).
% 40.67/7.35 thf(func_def_4, type, real: $tType).
% 40.67/7.35 thf(func_def_5, type, nat: $tType).
% 40.67/7.35 thf(func_def_6, type, b: $tType).
% 40.67/7.35 thf(func_def_7, type, a: $tType).
% 40.67/7.35 thf(func_def_8, type, convex_b: set_b > $o).
% 40.67/7.35 thf(func_def_9, type, inverse_inverse_real: real > real).
% 40.67/7.35 thf(func_def_10, type, finite_finite_real: set_real > $o).
% 40.67/7.35 thf(func_def_11, type, finite_finite_a: set_a > $o).
% 40.67/7.35 thf(func_def_12, type, finite_finite_b: set_b > $o).
% 40.67/7.35 thf(func_def_13, type, minus_minus_a_o: (a > $o) > (a > $o) > a > $o).
% 40.67/7.35 thf(func_def_14, type, minus_minus_b_o: (b > $o) > (b > $o) > b > $o).
% 40.67/7.35 thf(func_def_15, type, minus_minus_nat: nat > nat > nat).
% 40.67/7.35 thf(func_def_16, type, minus_minus_real: real > real > real).
% 40.67/7.35 thf(func_def_17, type, minus_minus_set_a: set_a > set_a > set_a).
% 40.67/7.35 thf(func_def_18, type, minus_minus_set_b: set_b > set_b > set_b).
% 40.67/7.35 thf(func_def_19, type, minus_minus_b: b > b > b).
% 40.67/7.35 thf(func_def_20, type, one_one_real: real).
% 40.67/7.35 thf(func_def_21, type, plus_p2118002693_ereal: extended_ereal > extended_ereal > extended_ereal).
% 40.67/7.35 thf(func_def_22, type, plus_plus_real: real > real > real).
% 40.67/7.35 thf(func_def_23, type, plus_plus_set_b: set_b > set_b > set_b).
% 40.67/7.35 thf(func_def_24, type, plus_plus_b: b > b > b).
% 40.67/7.35 thf(func_def_25, type, times_times_real: real > real > real).
% 40.67/7.35 thf(func_def_26, type, groups1296524820l_real: (real > real) > set_real > real).
% 40.67/7.35 thf(func_def_27, type, groups769445524_a_nat: (a > nat) > set_a > nat).
% 40.67/7.35 thf(func_def_28, type, groups1862963056a_real: (a > real) > set_a > real).
% 40.67/7.35 thf(func_def_29, type, groups919362075_set_b: (a > set_b) > set_a > set_b).
% 40.67/7.35 thf(func_def_30, type, groups1199149371um_a_b: (a > b) > set_a > b).
% 40.67/7.35 thf(func_def_31, type, groups2098481813_b_nat: (b > nat) > set_b > nat).
% 40.67/7.35 thf(func_def_32, type, groups583146225b_real: (b > real) > set_b > real).
% 40.67/7.35 thf(func_def_33, type, groups448962650_set_b: (b > set_b) > set_b > set_b).
% 40.67/7.35 thf(func_def_34, type, groups2026918778um_b_b: (b > b) > set_b > b).
% 40.67/7.35 thf(func_def_35, type, if_real: $o > real > real > real).
% 40.67/7.35 thf(func_def_36, type, if_b: $o > b > b > b).
% 40.67/7.35 thf(func_def_37, type, lower_311861425x_on_b: set_b > (b > extended_ereal) > $o).
% 40.67/7.35 thf(func_def_38, type, bot_bot_set_a: set_a).
% 40.67/7.35 thf(func_def_39, type, bot_bot_set_b: set_b).
% 40.67/7.35 thf(func_def_40, type, ord_less_eq_real: real > real > $o).
% 40.67/7.35 thf(func_def_41, type, real_V453051771R_real: real > real > real).
% 40.67/7.35 thf(func_def_42, type, real_V1035702896aleR_b: real > b > b).
% 40.67/7.35 thf(func_def_43, type, divide_divide_real: real > real > real).
% 40.67/7.35 thf(func_def_44, type, collect_a: (a > $o) > set_a).
% 40.67/7.35 thf(func_def_45, type, collect_b: (b > $o) > set_b).
% 40.67/7.35 thf(func_def_46, type, insert_real: real > set_real > set_real).
% 40.67/7.35 thf(func_def_47, type, insert_a: a > set_a > set_a).
% 40.67/7.35 thf(func_def_48, type, insert_b: b > set_b > set_b).
% 40.67/7.35 thf(func_def_49, type, member_a: a > set_a > $o).
% 40.67/7.35 thf(func_def_50, type, member_b: b > set_b > $o).
% 40.67/7.35 thf(func_def_51, type, c: set_b).
% 40.67/7.35 thf(func_def_52, type, a2: a > real).
% 40.67/7.35 thf(func_def_53, type, aa: a > real).
% 40.67/7.35 thf(func_def_54, type, f: b > extended_ereal).
% 40.67/7.35 thf(func_def_55, type, i: a).
% 40.67/7.35 thf(func_def_56, type, s: set_a).
% 40.67/7.35 thf(func_def_57, type, sa: set_a).
% 40.67/7.35 thf(func_def_58, type, y: a > b).
% 40.67/7.35 thf(func_def_73, type, sP0: set_a > (a > real) > (a > a) > (a > real) > $o).
% 40.67/7.35 thf(func_def_74, type, sP1: set_a > (a > a) > set_a > $o).
% 40.67/7.35 thf(func_def_75, type, sP2: (a > b) > (a > b) > (a > a) > set_a > $o).
% 40.67/7.35 thf(func_def_76, type, sP3: set_a > (a > a) > (a > a) > $o).
% 40.67/7.35 thf(func_def_77, type, sK4: set_a > set_a).
% 40.67/7.35 thf(func_def_78, type, sK5: set_a > a).
% 40.67/7.35 thf(func_def_79, type, sK6: (set_a > $o) > set_a).
% 40.67/7.35 thf(func_def_80, type, sK7: (set_a > $o) > a).
% 40.67/7.35 thf(func_def_81, type, sK8: (set_a > $o) > set_a).
% 40.67/7.35 thf(func_def_82, type, sK9: a > set_a > set_a).
% 40.67/7.35 thf(func_def_83, type, sK10: set_a > (a > a) > set_a > a).
% 40.67/7.35 thf(func_def_84, type, sK11: set_a > (a > real) > (a > a) > (a > real) > a).
% 40.67/7.35 thf(func_def_85, type, sK12: (a > a) > set_a > (a > a) > a).
% 40.67/7.35 thf(func_def_86, type, sK13: (a > a) > set_a > set_a > a).
% 40.67/7.35 thf(func_def_87, type, sK14: (a > a) > set_a > (a > a) > a).
% 40.67/7.35 thf(func_def_88, type, sK15: (a > real) > set_a > (a > real) > a).
% 40.67/7.35 thf(func_def_89, type, sK16: (set_a > $o) > a).
% 40.67/7.35 thf(func_def_90, type, sK17: (set_a > $o) > set_a).
% 40.67/7.35 thf(func_def_91, type, sK18: a > set_a > set_a).
% 40.67/7.35 thf(func_def_92, type, sK19: (set_a > $o) > a).
% 40.67/7.35 thf(func_def_93, type, sK20: (set_a > $o) > set_a).
% 40.67/7.35 thf(func_def_94, type, sK21: (set_a > $o) > a).
% 40.67/7.35 thf(func_def_95, type, sK22: set_a > a).
% 40.67/7.35 thf(func_def_96, type, sK23: set_a > (a > a) > (a > a) > a).
% 40.67/7.35 thf(func_def_97, type, sK24: (a > b) > (a > b) > (a > a) > set_a > a).
% 40.67/7.35 thf(func_def_98, type, sK25: set_a > set_a > (a > a) > a).
% 40.67/7.35 thf(func_def_99, type, sK26: set_a > set_a > (a > a) > a).
% 40.67/7.35 thf(func_def_100, type, sK27: set_a > (a > a) > (a > a) > a).
% 40.67/7.35 thf(func_def_101, type, sK28: (a > b) > set_a > (a > b) > a).
% 40.67/7.35 thf(func_def_102, type, sK29: set_a > (a > b) > (a > b) > (a > a) > set_a > (a > a) > a).
% 40.67/7.35 thf(func_def_103, type, sK30: set_a > (a > a) > set_a > (a > a) > a).
% 40.67/7.35 thf(func_def_104, type, sK31: (set_a > $o) > a).
% 40.67/7.35 thf(func_def_105, type, sK32: (set_a > $o) > set_a).
% 40.67/7.35 thf(func_def_106, type, sK33: set_a > set_a > (a > a) > a).
% 40.67/7.35 thf(func_def_107, type, sK34: a > set_a > set_a > (a > a) > a).
% 40.67/7.35 thf(func_def_108, type, sK35: set_a > (a > real) > set_a > (a > real) > (a > a) > a).
% 40.67/7.35 thf(func_def_109, type, sK36: (a > real) > set_a > set_a > (a > real) > (a > a) > (a > a) > a).
% 40.67/7.35 thf(func_def_110, type, sK37: set_a > set_a > (a > a) > (a > a) > a).
% 40.67/7.35 thf(func_def_111, type, sK38: (a > a) > set_a > set_a > a).
% 40.67/7.35 thf(func_def_112, type, sK39: a > (a > a) > set_a > set_a > a).
% 40.67/7.35 thf(func_def_113, type, sK40: (a > a) > set_a > (a > b) > set_a > (a > b) > a).
% 40.67/7.35 thf(func_def_114, type, ph41: !>[X0: $tType]:(X0)).
% 40.67/7.35 thf(func_def_115, type, sK42: a).
% 40.67/7.35 thf(f2599,plain,(
% 40.67/7.35 $false),
% 40.67/7.35 inference(subsumption_resolution,[status(thm)],[f2598,f1283])).
% 40.67/7.35 thf(f1283,plain,(
% 40.67/7.35 ( ! [X2 : real,X0 : real,X1 : b] : (((real_V1035702896aleR_b @ X0 @ (real_V1035702896aleR_b @ X2 @ X1)) = (real_V1035702896aleR_b @ X2 @ (real_V1035702896aleR_b @ X0 @ X1)))) )),
% 40.67/7.35 inference(cnf_transformation,[status(thm)],[f883])).
% 40.67/7.35 thf(f883,plain,(
% 40.67/7.35 ! [X0 : real,X1 : b,X2 : real] : ((real_V1035702896aleR_b @ X0 @ (real_V1035702896aleR_b @ X2 @ X1)) = (real_V1035702896aleR_b @ X2 @ (real_V1035702896aleR_b @ X0 @ X1)))),
% 40.67/7.35 inference(rectify,[status(thm)],[f36])).
% 40.67/7.35 thf(f36,axiom,(
% 40.67/7.35 ! [X4 : real,X5 : b,X3 : real] : ((real_V1035702896aleR_b @ X3 @ (real_V1035702896aleR_b @ X4 @ X5)) = (real_V1035702896aleR_b @ X4 @ (real_V1035702896aleR_b @ X3 @ X5)))),
% 40.67/7.35 file('/export/starexec/sandbox/tmp/tmp.aJ622KHsm8/DTF2THF_14827.p',fact_35_scale__left__commute)).
% 40.67/7.35 thf(f2598,plain,(
% 40.67/7.35 ((real_V1035702896aleR_b @ (aa @ sK42) @ (real_V1035702896aleR_b @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa)) @ (y @ sK42))) != (real_V1035702896aleR_b @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa)) @ (real_V1035702896aleR_b @ (aa @ sK42) @ (y @ sK42))))),
% 40.67/7.35 inference(forward_demodulation,[status(thm)],[f2597,f1233])).
% 40.67/7.35 thf(f1233,plain,(
% 40.67/7.35 ( ! [X2 : real,X0 : real,X1 : b] : (((real_V1035702896aleR_b @ X0 @ (real_V1035702896aleR_b @ X2 @ X1)) = (real_V1035702896aleR_b @ (times_times_real @ X0 @ X2) @ X1))) )),
% 40.67/7.35 inference(cnf_transformation,[status(thm)],[f884])).
% 40.67/7.35 thf(f884,plain,(
% 40.67/7.35 ! [X0 : real,X1 : b,X2 : real] : ((real_V1035702896aleR_b @ X0 @ (real_V1035702896aleR_b @ X2 @ X1)) = (real_V1035702896aleR_b @ (times_times_real @ X0 @ X2) @ X1))),
% 40.67/7.35 inference(rectify,[status(thm)],[f14])).
% 40.67/7.35 thf(f14,axiom,(
% 40.67/7.35 ! [X3 : real,X5 : b,X4 : real] : ((real_V1035702896aleR_b @ X3 @ (real_V1035702896aleR_b @ X4 @ X5)) = (real_V1035702896aleR_b @ (times_times_real @ X3 @ X4) @ X5))),
% 40.67/7.35 file('/export/starexec/sandbox/tmp/tmp.aJ622KHsm8/DTF2THF_14827.p',fact_13_scaleR__scaleR)).
% 40.67/7.35 thf(f2597,plain,(
% 40.67/7.35 ((real_V1035702896aleR_b @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa)) @ (real_V1035702896aleR_b @ (aa @ sK42) @ (y @ sK42))) != (real_V1035702896aleR_b @ (times_times_real @ (aa @ sK42) @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa))) @ (y @ sK42)))),
% 40.67/7.35 inference(beta_eta_normalization,[status(thm)],[f2596])).
% 40.67/7.35 thf(f2596,plain,(
% 40.67/7.35 (((^[Y0 : a]: (real_V1035702896aleR_b @ (times_times_real @ (aa @ Y0) @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa))) @ (y @ Y0))) @ sK42) != ((^[Y0 : a]: (real_V1035702896aleR_b @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa)) @ (real_V1035702896aleR_b @ (aa @ Y0) @ (y @ Y0)))) @ sK42))),
% 40.67/7.35 inference(negative_extensionality,[status(thm)],[f2589])).
% 40.67/7.35 thf(f2589,plain,(
% 40.67/7.35 ((^[Y0 : a]: (real_V1035702896aleR_b @ (times_times_real @ (aa @ Y0) @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa))) @ (y @ Y0))) != (^[Y0 : a]: (real_V1035702896aleR_b @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa)) @ (real_V1035702896aleR_b @ (aa @ Y0) @ (y @ Y0)))))),
% 40.67/7.35 inference(equality_resolution,[status(thm)],[f2542])).
% 40.67/7.35 thf(f2542,plain,(
% 40.67/7.35 ((f @ (plus_plus_b @ (real_V1035702896aleR_b @ (groups1862963056a_real @ aa @ sa) @ (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa)) @ (real_V1035702896aleR_b @ (aa @ Y0) @ (y @ Y0)))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))) != (f @ (plus_plus_b @ (real_V1035702896aleR_b @ (groups1862963056a_real @ aa @ sa) @ (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (times_times_real @ (aa @ Y0) @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa))) @ (y @ Y0))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))))),
% 40.67/7.35 inference(backward_demodulation,[status(thm)],[f1639,f2541])).
% 40.67/7.35 thf(f2541,plain,(
% 40.67/7.35 ((real_V1035702896aleR_b @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa)) @ (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (aa @ Y0) @ (y @ Y0))) @ sa)) = (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa)) @ (real_V1035702896aleR_b @ (aa @ Y0) @ (y @ Y0)))) @ sa))),
% 40.67/7.35 inference(forward_demodulation,[status(thm)],[f1266,f1138])).
% 40.67/7.35 thf(f1138,plain,(
% 40.67/7.35 ((minus_minus_real @ one_one_real @ (aa @ i)) = (groups1862963056a_real @ aa @ sa))),
% 40.67/7.35 inference(cnf_transformation,[status(thm)],[f18])).
% 40.67/7.35 thf(f18,axiom,(
% 40.67/7.35 ((minus_minus_real @ one_one_real @ (aa @ i)) = (groups1862963056a_real @ aa @ sa))),
% 40.67/7.35 file('/export/starexec/sandbox/tmp/tmp.aJ622KHsm8/DTF2THF_14827.p',fact_17__092_060open_062sum_Aa_As_A_061_A1_A_N_Aa_Ai_092_060close_062)).
% 40.67/7.35 thf(f1266,plain,(
% 40.67/7.35 ((real_V1035702896aleR_b @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i))) @ (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (aa @ Y0) @ (y @ Y0))) @ sa)) = (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i))) @ (real_V1035702896aleR_b @ (aa @ Y0) @ (y @ Y0)))) @ sa))),
% 40.67/7.35 inference(cnf_transformation,[status(thm)],[f516])).
% 40.67/7.35 thf(f516,plain,(
% 40.67/7.35 ((real_V1035702896aleR_b @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i))) @ (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (aa @ Y0) @ (y @ Y0))) @ sa)) = (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i))) @ (real_V1035702896aleR_b @ (aa @ Y0) @ (y @ Y0)))) @ sa))),
% 40.67/7.35 inference(fool_elimination,[status(thm)],[f3])).
% 40.67/7.35 thf(f3,axiom,(
% 40.67/7.35 ((groups1199149371um_a_b @ (^[X0 : a] : (real_V1035702896aleR_b @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i))) @ (real_V1035702896aleR_b @ (aa @ X0) @ (y @ X0)))) @ sa) = (real_V1035702896aleR_b @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i))) @ (groups1199149371um_a_b @ (^[X1 : a] : (real_V1035702896aleR_b @ (aa @ X1) @ (y @ X1))) @ sa)))),
% 40.67/7.35 file('/export/starexec/sandbox/tmp/tmp.aJ622KHsm8/DTF2THF_14827.p',fact_2__092_060open_062_I_092_060Sum_062x_092_060in_062s_O_Aa_Ax_A_K_092_060_094sub_062R_Ay_Ax_A_P_092_060_094sub_062R_A_I1_A_N_Aa_Ai_J_J_A_061_A_I_092_060Sum_062j_092_060in_062s_O_Aa_Aj_A_K_092_060_094sub_062R_Ay_Aj_J_A_P_092_060_094sub_062R_A_I1_A_N_Aa_Ai_J_092_060close_062)).
% 40.67/7.35 thf(f1639,plain,(
% 40.67/7.35 ((f @ (plus_plus_b @ (real_V1035702896aleR_b @ (groups1862963056a_real @ aa @ sa) @ (real_V1035702896aleR_b @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa)) @ (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (aa @ Y0) @ (y @ Y0))) @ sa))) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))) != (f @ (plus_plus_b @ (real_V1035702896aleR_b @ (groups1862963056a_real @ aa @ sa) @ (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (times_times_real @ (aa @ Y0) @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa))) @ (y @ Y0))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))))),
% 40.67/7.35 inference(backward_demodulation,[status(thm)],[f1465,f1233])).
% 40.67/7.35 thf(f1465,plain,(
% 40.67/7.35 ((f @ (plus_plus_b @ (real_V1035702896aleR_b @ (groups1862963056a_real @ aa @ sa) @ (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (times_times_real @ (aa @ Y0) @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa))) @ (y @ Y0))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))) != (f @ (plus_plus_b @ (real_V1035702896aleR_b @ (times_times_real @ (groups1862963056a_real @ aa @ sa) @ (inverse_inverse_real @ (groups1862963056a_real @ aa @ sa))) @ (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (aa @ Y0) @ (y @ Y0))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))))),
% 40.67/7.35 inference(backward_demodulation,[status(thm)],[f1120,f1138])).
% 40.67/7.35 thf(f1120,plain,(
% 40.67/7.35 ((f @ (plus_plus_b @ (real_V1035702896aleR_b @ (minus_minus_real @ one_one_real @ (aa @ i)) @ (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (times_times_real @ (aa @ Y0) @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i)))) @ (y @ Y0))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))) != (f @ (plus_plus_b @ (real_V1035702896aleR_b @ (times_times_real @ (minus_minus_real @ one_one_real @ (aa @ i)) @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i)))) @ (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (aa @ Y0) @ (y @ Y0))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))))),
% 40.67/7.35 inference(cnf_transformation,[status(thm)],[f829])).
% 40.67/7.35 thf(f829,plain,(
% 40.67/7.35 ((f @ (plus_plus_b @ (real_V1035702896aleR_b @ (minus_minus_real @ one_one_real @ (aa @ i)) @ (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (times_times_real @ (aa @ Y0) @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i)))) @ (y @ Y0))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))) != (f @ (plus_plus_b @ (real_V1035702896aleR_b @ (times_times_real @ (minus_minus_real @ one_one_real @ (aa @ i)) @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i)))) @ (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (aa @ Y0) @ (y @ Y0))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))))),
% 40.67/7.35 inference(flattening,[status(thm)],[f511])).
% 40.67/7.35 thf(f511,plain,(
% 40.67/7.35 ~((f @ (plus_plus_b @ (real_V1035702896aleR_b @ (minus_minus_real @ one_one_real @ (aa @ i)) @ (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (times_times_real @ (aa @ Y0) @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i)))) @ (y @ Y0))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))) = (f @ (plus_plus_b @ (real_V1035702896aleR_b @ (times_times_real @ (minus_minus_real @ one_one_real @ (aa @ i)) @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i)))) @ (groups1199149371um_a_b @ (^[Y0 : a]: (real_V1035702896aleR_b @ (aa @ Y0) @ (y @ Y0))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))))),
% 40.67/7.35 inference(fool_elimination,[status(thm)],[f510])).
% 40.67/7.35 thf(f510,plain,(
% 40.67/7.35 ~((f @ (plus_plus_b @ (real_V1035702896aleR_b @ (minus_minus_real @ one_one_real @ (aa @ i)) @ (groups1199149371um_a_b @ (^[X0 : a] : (real_V1035702896aleR_b @ (times_times_real @ (aa @ X0) @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i)))) @ (y @ X0))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))) = (f @ (plus_plus_b @ (real_V1035702896aleR_b @ (times_times_real @ (minus_minus_real @ one_one_real @ (aa @ i)) @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i)))) @ (groups1199149371um_a_b @ (^[X1 : a] : (real_V1035702896aleR_b @ (aa @ X1) @ (y @ X1))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))))),
% 40.67/7.35 inference(rectify,[status(thm)],[f360])).
% 40.67/7.35 thf(f360,negated_conjecture,(
% 40.67/7.35 ~((f @ (plus_plus_b @ (real_V1035702896aleR_b @ (minus_minus_real @ one_one_real @ (aa @ i)) @ (groups1199149371um_a_b @ (^[X1 : a] : (real_V1035702896aleR_b @ (times_times_real @ (aa @ X1) @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i)))) @ (y @ X1))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))) = (f @ (plus_plus_b @ (real_V1035702896aleR_b @ (times_times_real @ (minus_minus_real @ one_one_real @ (aa @ i)) @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i)))) @ (groups1199149371um_a_b @ (^[X1 : a] : (real_V1035702896aleR_b @ (aa @ X1) @ (y @ X1))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))))),
% 40.67/7.35 inference(negated_conjecture,[status(cth)],[f359])).
% 40.67/7.35 thf(f359,conjecture,(
% 40.67/7.35 ((f @ (plus_plus_b @ (real_V1035702896aleR_b @ (minus_minus_real @ one_one_real @ (aa @ i)) @ (groups1199149371um_a_b @ (^[X1 : a] : (real_V1035702896aleR_b @ (times_times_real @ (aa @ X1) @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i)))) @ (y @ X1))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))) = (f @ (plus_plus_b @ (real_V1035702896aleR_b @ (times_times_real @ (minus_minus_real @ one_one_real @ (aa @ i)) @ (inverse_inverse_real @ (minus_minus_real @ one_one_real @ (aa @ i)))) @ (groups1199149371um_a_b @ (^[X1 : a] : (real_V1035702896aleR_b @ (aa @ X1) @ (y @ X1))) @ sa)) @ (real_V1035702896aleR_b @ (aa @ i) @ (y @ i)))))),
% 40.67/7.35 file('/export/starexec/sandbox/tmp/tmp.aJ622KHsm8/DTF2THF_14827.p',conj_0)).
% 40.67/7.35 % SZS output end Proof for DTF2THF_14827
% 40.67/7.35 % (15150)------------------------------
% 40.67/7.35 % (15150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.67/7.35 % (15150)Termination reason: Refutation
% 40.67/7.35
% 40.67/7.35 % (15150)Memory used [KB]: 3582
% 40.67/7.35 % (15150)Time elapsed: 0.233 s
% 40.67/7.35 % (15150)Instructions burned: 757 (million)
% 40.67/7.35 % (15150)------------------------------
% 40.67/7.35 % (15150)------------------------------
% 40.67/7.35 % (14951)Success in time 5.518 s
%------------------------------------------------------------------------------