%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP150^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:57 AM UTC 2026
% Result : Theorem 7.02s 2.21s
% Output : Refutation 7.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 135 ( 79 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 500 ( 8 ~; 1 |; 0 &; 459 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 73 usr; 17 con; 0-3 aty)
% ( 32 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 106 ( 55 ^; 51 !; 0 ?; 106 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_8,type,
polyno1532895200ly_nat: $tType ).
thf(type_def_9,type,
polyno727731844poly_a: $tType ).
thf(type_def_10,type,
list_a: $tType ).
thf(type_def_11,type,
list_nat: $tType ).
thf(func_def_0,type,
polyno1532895200ly_nat: $tType ).
thf(func_def_1,type,
polyno727731844poly_a: $tType ).
thf(func_def_2,type,
list_nat: $tType ).
thf(func_def_3,type,
list_a: $tType ).
thf(func_def_4,type,
nat: $tType ).
thf(func_def_5,type,
a: $tType ).
thf(func_def_6,type,
one_one_nat: nat ).
thf(func_def_7,type,
one_one_a: a ).
thf(func_def_8,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_9,type,
plus_plus_a: a > a > a ).
thf(func_def_10,type,
times_times_nat: nat > nat > nat ).
thf(func_def_11,type,
times_times_a: a > a > a ).
thf(func_def_12,type,
zero_zero_nat: nat ).
thf(func_def_13,type,
zero_zero_a: a ).
thf(func_def_14,type,
if_nat: $o > nat > nat > nat ).
thf(func_def_15,type,
compow808008746ly_nat: nat > ( polyno1532895200ly_nat > polyno1532895200ly_nat ) > polyno1532895200ly_nat > polyno1532895200ly_nat ).
thf(func_def_16,type,
compow1114216044poly_a: nat > ( polyno727731844poly_a > polyno727731844poly_a ) > polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_17,type,
polyno422358502poly_a: list_a > polyno727731844poly_a > a ).
thf(func_def_18,type,
polyno587244178ad_nat: polyno1532895200ly_nat > polyno1532895200ly_nat ).
thf(func_def_19,type,
polyno1465139388head_a: polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_20,type,
polyno220183259ee_nat: polyno1532895200ly_nat > nat ).
thf(func_def_21,type,
polyno578545843gree_a: polyno727731844poly_a > nat ).
thf(func_def_22,type,
polyno1779722485en_nat: polyno1532895200ly_nat > nat > nat ).
thf(func_def_23,type,
polyno1674775833reen_a: polyno727731844poly_a > nat > nat ).
thf(func_def_24,type,
polyno1952548879ad_nat: polyno1532895200ly_nat > polyno1532895200ly_nat ).
thf(func_def_25,type,
polyno1884029055head_a: polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_26,type,
polyno524777654st_nat: polyno1532895200ly_nat > nat ).
thf(func_def_27,type,
polyno2115742616onst_a: polyno727731844poly_a > a ).
thf(func_def_28,type,
polyno544860353dn_nat: polyno1532895200ly_nat > nat > polyno1532895200ly_nat ).
thf(func_def_29,type,
polyno567601229eadn_a: polyno727731844poly_a > nat > polyno727731844poly_a ).
thf(func_def_30,type,
polyno1013235523ly_nat: polyno1532895200ly_nat > $o ).
thf(func_def_31,type,
polyno190918219poly_a: polyno727731844poly_a > $o ).
thf(func_def_32,type,
polyno892049031yh_nat: polyno1532895200ly_nat > nat > $o ).
thf(func_def_33,type,
polyno1372495879olyh_a: polyno727731844poly_a > nat > $o ).
thf(func_def_34,type,
polyno1222032024dd_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
thf(func_def_35,type,
polyno1623170614_Add_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_36,type,
polyno1999838549nd_nat: nat > polyno1532895200ly_nat ).
thf(func_def_37,type,
polyno2024845497ound_a: nat > polyno727731844poly_a ).
thf(func_def_38,type,
polyno720942678CN_nat: polyno1532895200ly_nat > nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
thf(func_def_39,type,
polyno1057396216e_CN_a: polyno727731844poly_a > nat > polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_40,type,
polyno2122022170_C_nat: nat > polyno1532895200ly_nat ).
thf(func_def_41,type,
polyno439679028le_C_a: a > polyno727731844poly_a ).
thf(func_def_42,type,
polyno1415441627ul_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
thf(func_def_43,type,
polyno1491482291_Mul_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_44,type,
polyno1366804583eg_nat: polyno1532895200ly_nat > polyno1532895200ly_nat ).
thf(func_def_45,type,
polyno96675367_Neg_a: polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_46,type,
polyno359287218Pw_nat: polyno1532895200ly_nat > nat > polyno1532895200ly_nat ).
thf(func_def_47,type,
polyno1538138524e_Pw_a: polyno727731844poly_a > nat > polyno727731844poly_a ).
thf(func_def_48,type,
polyno1921014231ub_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
thf(func_def_49,type,
polyno975704247_Sub_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_50,type,
polyno1467023772ul_nat: nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
thf(func_def_51,type,
polyno562434098cmul_a: a > polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_52,type,
polyno212464073eriv_a: polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_53,type,
polyno1006823949_aux_a: a > polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_54,type,
polyno929799083ul_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
thf(func_def_55,type,
polyno1934269411ymul_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_56,type,
polyno955999183nate_a: polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_57,type,
polyno1510045887ow_nat: nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
thf(func_def_58,type,
polyno1371724751ypow_a: nat > polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_59,type,
polyno1418491367ysub_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_60,type,
polyno336795754t0_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
thf(func_def_61,type,
polyno1397854436bst0_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_62,type,
polyno1964927358t1_nat: polyno1532895200ly_nat > polyno1532895200ly_nat ).
thf(func_def_63,type,
polyno784948432ift1_a: polyno727731844poly_a > polyno727731844poly_a ).
thf(func_def_64,type,
polyno1438831695bs_nat: list_nat > polyno1532895200ly_nat > $o ).
thf(func_def_65,type,
polyno896877631f_bs_a: list_a > polyno727731844poly_a > $o ).
thf(func_def_66,type,
n0: nat ).
thf(func_def_67,type,
n1: nat ).
thf(func_def_68,type,
p: polyno727731844poly_a ).
thf(func_def_69,type,
q: polyno727731844poly_a ).
thf(func_def_88,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_89,type,
sK2: list_a ).
thf(func_def_90,type,
sK3: list_a ).
thf(func_def_91,type,
sK4: nat ).
thf(func_def_92,type,
sK5: nat ).
thf(func_def_93,type,
sK6: nat ).
thf(func_def_94,type,
sK7: polyno727731844poly_a > list_a ).
thf(func_def_95,type,
sK8: nat ).
thf(func_def_96,type,
sK9: polyno727731844poly_a > list_a ).
thf(f1317,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1316,f1311]) ).
thf(f1311,plain,
! [X2: list_a,X1: polyno727731844poly_a] :
( $true
= ( !! @ polyno727731844poly_a
@ ^ [Y0: polyno727731844poly_a] :
( ( polyno422358502poly_a @ X2 @ ( polyno1491482291_Mul_a @ Y0 @ X1 ) )
= ( times_times_a @ ( polyno422358502poly_a @ X2 @ Y0 ) @ ( polyno422358502poly_a @ X2 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1308]) ).
thf(f1308,plain,
! [X2: list_a,X1: polyno727731844poly_a] :
( ( ^ [Y0: list_a] :
( !! @ polyno727731844poly_a
@ ^ [Y1: polyno727731844poly_a] :
( ( polyno422358502poly_a @ Y0 @ ( polyno1491482291_Mul_a @ Y1 @ X1 ) )
= ( times_times_a @ ( polyno422358502poly_a @ Y0 @ Y1 ) @ ( polyno422358502poly_a @ Y0 @ X1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f1305]) ).
thf(f1305,plain,
! [X1: polyno727731844poly_a] :
( $true
= ( !! @ list_a
@ ^ [Y0: list_a] :
( !! @ polyno727731844poly_a
@ ^ [Y1: polyno727731844poly_a] :
( ( polyno422358502poly_a @ Y0 @ ( polyno1491482291_Mul_a @ Y1 @ X1 ) )
= ( times_times_a @ ( polyno422358502poly_a @ Y0 @ Y1 ) @ ( polyno422358502poly_a @ Y0 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1304]) ).
thf(f1304,plain,
! [X1: polyno727731844poly_a] :
( ( ^ [Y0: polyno727731844poly_a] :
( !! @ list_a
@ ^ [Y1: list_a] :
( !! @ polyno727731844poly_a
@ ^ [Y2: polyno727731844poly_a] :
( ( polyno422358502poly_a @ Y1 @ ( polyno1491482291_Mul_a @ Y2 @ Y0 ) )
= ( times_times_a @ ( polyno422358502poly_a @ Y1 @ Y2 ) @ ( polyno422358502poly_a @ Y1 @ Y0 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1110]) ).
thf(f1110,plain,
( ( !! @ polyno727731844poly_a
@ ^ [Y0: polyno727731844poly_a] :
( !! @ list_a
@ ^ [Y1: list_a] :
( !! @ polyno727731844poly_a
@ ^ [Y2: polyno727731844poly_a] :
( ( polyno422358502poly_a @ Y1 @ ( polyno1491482291_Mul_a @ Y2 @ Y0 ) )
= ( times_times_a @ ( polyno422358502poly_a @ Y1 @ Y2 ) @ ( polyno422358502poly_a @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f449]) ).
thf(f449,plain,
( ( !! @ polyno727731844poly_a
@ ^ [Y0: polyno727731844poly_a] :
( !! @ list_a
@ ^ [Y1: list_a] :
( !! @ polyno727731844poly_a
@ ^ [Y2: polyno727731844poly_a] :
( ( polyno422358502poly_a @ Y1 @ ( polyno1491482291_Mul_a @ Y2 @ Y0 ) )
= ( times_times_a @ ( polyno422358502poly_a @ Y1 @ Y2 ) @ ( polyno422358502poly_a @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f448]) ).
thf(f448,plain,
! [X0: polyno727731844poly_a,X1: list_a,X2: polyno727731844poly_a] :
( ( polyno422358502poly_a @ X1 @ ( polyno1491482291_Mul_a @ X0 @ X2 ) )
= ( times_times_a @ ( polyno422358502poly_a @ X1 @ X0 ) @ ( polyno422358502poly_a @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,axiom,
! [X4: polyno727731844poly_a,X3: list_a,X7: polyno727731844poly_a] :
( ( polyno422358502poly_a @ X3 @ ( polyno1491482291_Mul_a @ X4 @ X7 ) )
= ( times_times_a @ ( polyno422358502poly_a @ X3 @ X4 ) @ ( polyno422358502poly_a @ X3 @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HVFAM8xlRw/DTF2THF_3593.p',fact_29_Ipoly_Osimps_I6_J) ).
thf(f1316,plain,
! [X0: polyno727731844poly_a] :
( ( !! @ polyno727731844poly_a
@ ^ [Y0: polyno727731844poly_a] :
( ( polyno422358502poly_a @ ( sK9 @ X0 ) @ ( polyno1491482291_Mul_a @ Y0 @ X0 ) )
= ( times_times_a @ ( polyno422358502poly_a @ ( sK9 @ X0 ) @ Y0 ) @ ( polyno422358502poly_a @ ( sK9 @ X0 ) @ X0 ) ) ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f1315,f1278]) ).
thf(f1278,plain,
! [X2: polyno727731844poly_a,X0: list_a,X1: polyno727731844poly_a] :
( $true
= ( ( polyno422358502poly_a @ X0 @ ( polyno1934269411ymul_a @ X2 @ X1 ) )
= ( polyno422358502poly_a @ X0 @ ( polyno1934269411ymul_a @ X1 @ X2 ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1277,f1271]) ).
thf(f1271,plain,
! [X2: list_a,X3: polyno727731844poly_a,X1: polyno727731844poly_a] :
( ( polyno422358502poly_a @ X2 @ ( polyno1934269411ymul_a @ X3 @ X1 ) )
= ( times_times_a @ ( polyno422358502poly_a @ X2 @ X3 ) @ ( polyno422358502poly_a @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f1269]) ).
thf(f1269,plain,
! [X2: list_a,X3: polyno727731844poly_a,X1: polyno727731844poly_a] :
( $true
= ( ( times_times_a @ ( polyno422358502poly_a @ X2 @ X3 ) @ ( polyno422358502poly_a @ X2 @ X1 ) )
= ( polyno422358502poly_a @ X2 @ ( polyno1934269411ymul_a @ X3 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1268]) ).
thf(f1268,plain,
! [X2: list_a,X3: polyno727731844poly_a,X1: polyno727731844poly_a] :
( $true
= ( ^ [Y0: polyno727731844poly_a] :
( ( times_times_a @ ( polyno422358502poly_a @ X2 @ Y0 ) @ ( polyno422358502poly_a @ X2 @ X1 ) )
= ( polyno422358502poly_a @ X2 @ ( polyno1934269411ymul_a @ Y0 @ X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f1263]) ).
thf(f1263,plain,
! [X2: list_a,X1: polyno727731844poly_a] :
( ( !! @ polyno727731844poly_a
@ ^ [Y0: polyno727731844poly_a] :
( ( times_times_a @ ( polyno422358502poly_a @ X2 @ Y0 ) @ ( polyno422358502poly_a @ X2 @ X1 ) )
= ( polyno422358502poly_a @ X2 @ ( polyno1934269411ymul_a @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1259]) ).
thf(f1259,plain,
! [X2: list_a,X1: polyno727731844poly_a] :
( ( ^ [Y0: list_a] :
( !! @ polyno727731844poly_a
@ ^ [Y1: polyno727731844poly_a] :
( ( times_times_a @ ( polyno422358502poly_a @ Y0 @ Y1 ) @ ( polyno422358502poly_a @ Y0 @ X1 ) )
= ( polyno422358502poly_a @ Y0 @ ( polyno1934269411ymul_a @ Y1 @ X1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f1258]) ).
thf(f1258,plain,
! [X1: polyno727731844poly_a] :
( $true
= ( !! @ list_a
@ ^ [Y0: list_a] :
( !! @ polyno727731844poly_a
@ ^ [Y1: polyno727731844poly_a] :
( ( times_times_a @ ( polyno422358502poly_a @ Y0 @ Y1 ) @ ( polyno422358502poly_a @ Y0 @ X1 ) )
= ( polyno422358502poly_a @ Y0 @ ( polyno1934269411ymul_a @ Y1 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1257]) ).
thf(f1257,plain,
! [X1: polyno727731844poly_a] :
( $true
= ( ^ [Y0: polyno727731844poly_a] :
( !! @ list_a
@ ^ [Y1: list_a] :
( !! @ polyno727731844poly_a
@ ^ [Y2: polyno727731844poly_a] :
( ( times_times_a @ ( polyno422358502poly_a @ Y1 @ Y2 ) @ ( polyno422358502poly_a @ Y1 @ Y0 ) )
= ( polyno422358502poly_a @ Y1 @ ( polyno1934269411ymul_a @ Y2 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1104]) ).
thf(f1104,plain,
( ( !! @ polyno727731844poly_a
@ ^ [Y0: polyno727731844poly_a] :
( !! @ list_a
@ ^ [Y1: list_a] :
( !! @ polyno727731844poly_a
@ ^ [Y2: polyno727731844poly_a] :
( ( times_times_a @ ( polyno422358502poly_a @ Y1 @ Y2 ) @ ( polyno422358502poly_a @ Y1 @ Y0 ) )
= ( polyno422358502poly_a @ Y1 @ ( polyno1934269411ymul_a @ Y2 @ Y0 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f485]) ).
thf(f485,plain,
( ( !! @ polyno727731844poly_a
@ ^ [Y0: polyno727731844poly_a] :
( !! @ list_a
@ ^ [Y1: list_a] :
( !! @ polyno727731844poly_a
@ ^ [Y2: polyno727731844poly_a] :
( ( times_times_a @ ( polyno422358502poly_a @ Y1 @ Y2 ) @ ( polyno422358502poly_a @ Y1 @ Y0 ) )
= ( polyno422358502poly_a @ Y1 @ ( polyno1934269411ymul_a @ Y2 @ Y0 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f484]) ).
thf(f484,plain,
! [X0: polyno727731844poly_a,X1: list_a,X2: polyno727731844poly_a] :
( ( times_times_a @ ( polyno422358502poly_a @ X1 @ X0 ) @ ( polyno422358502poly_a @ X1 @ X2 ) )
= ( polyno422358502poly_a @ X1 @ ( polyno1934269411ymul_a @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
! [X1: polyno727731844poly_a,X3: list_a,X2: polyno727731844poly_a] :
( ( polyno422358502poly_a @ X3 @ ( polyno1934269411ymul_a @ X1 @ X2 ) )
= ( times_times_a @ ( polyno422358502poly_a @ X3 @ X1 ) @ ( polyno422358502poly_a @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HVFAM8xlRw/DTF2THF_3593.p',fact_10_polymul) ).
thf(f1277,plain,
! [X2: polyno727731844poly_a,X0: list_a,X1: polyno727731844poly_a] :
( $true
= ( ( times_times_a @ ( polyno422358502poly_a @ X0 @ X2 ) @ ( polyno422358502poly_a @ X0 @ X1 ) )
= ( polyno422358502poly_a @ X0 @ ( polyno1934269411ymul_a @ X1 @ X2 ) ) ) ),
inference(superposition,[status(thm)],[f1269,f1180]) ).
thf(f1180,plain,
! [X2: a,X1: a] :
( ( times_times_a @ X2 @ X1 )
= ( times_times_a @ X1 @ X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f1178]) ).
thf(f1178,plain,
! [X2: a,X1: a] :
( ( times_times_a @ X1 @ X2 )
= ( ^ [Y0: a] : ( times_times_a @ Y0 @ X1 )
@ X2 ) ),
inference(argument_congruence,[status(thm)],[f1177]) ).
thf(f1177,plain,
! [X1: a] :
( ( ^ [Y0: a] : ( times_times_a @ Y0 @ X1 ) )
= ( times_times_a @ X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f1176]) ).
thf(f1176,plain,
! [X1: a] :
( ( ^ [Y0: a,Y1: a] : ( times_times_a @ Y1 @ Y0 )
@ X1 )
= ( times_times_a @ X1 ) ),
inference(argument_congruence,[status(thm)],[f1124]) ).
thf(f1124,plain,
( times_times_a
= ( ^ [Y0: a,Y1: a] : ( times_times_a @ Y1 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
thf(f431,plain,
( times_times_a
= ( ^ [Y0: a,Y1: a] : ( times_times_a @ Y1 @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f430]) ).
thf(f430,plain,
( times_times_a
= ( ^ [X0: a,X1: a] : ( times_times_a @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f133]) ).
thf(f133,axiom,
( times_times_a
= ( ^ [X41: a,X42: a] : ( times_times_a @ X42 @ X41 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HVFAM8xlRw/DTF2THF_3593.p',fact_132_mult_Ocommute) ).
thf(f1315,plain,
! [X0: polyno727731844poly_a] :
( ( !! @ polyno727731844poly_a
@ ^ [Y0: polyno727731844poly_a] :
( ( polyno422358502poly_a @ ( sK9 @ X0 ) @ ( polyno1491482291_Mul_a @ Y0 @ X0 ) )
= ( times_times_a @ ( polyno422358502poly_a @ ( sK9 @ X0 ) @ Y0 ) @ ( polyno422358502poly_a @ ( sK9 @ X0 ) @ X0 ) ) ) )
!= ( ( polyno422358502poly_a @ ( sK9 @ X0 ) @ ( polyno1934269411ymul_a @ p @ q ) )
= ( polyno422358502poly_a @ ( sK9 @ X0 ) @ ( polyno1934269411ymul_a @ q @ p ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1314]) ).
thf(f1314,plain,
! [X0: polyno727731844poly_a] :
( ( ^ [Y0: list_a] :
( ( polyno422358502poly_a @ Y0 @ ( polyno1934269411ymul_a @ p @ q ) )
= ( polyno422358502poly_a @ Y0 @ ( polyno1934269411ymul_a @ q @ p ) ) )
@ ( sK9 @ X0 ) )
!= ( ^ [Y0: list_a] :
( !! @ polyno727731844poly_a
@ ^ [Y1: polyno727731844poly_a] :
( ( polyno422358502poly_a @ Y0 @ ( polyno1491482291_Mul_a @ Y1 @ X0 ) )
= ( times_times_a @ ( polyno422358502poly_a @ Y0 @ Y1 ) @ ( polyno422358502poly_a @ Y0 @ X0 ) ) ) )
@ ( sK9 @ X0 ) ) ),
inference(negative_extensionality,[status(thm)],[f1313]) ).
thf(f1313,plain,
! [X0: polyno727731844poly_a] :
( ( ^ [Y0: list_a] :
( !! @ polyno727731844poly_a
@ ^ [Y1: polyno727731844poly_a] :
( ( polyno422358502poly_a @ Y0 @ ( polyno1491482291_Mul_a @ Y1 @ X0 ) )
= ( times_times_a @ ( polyno422358502poly_a @ Y0 @ Y1 ) @ ( polyno422358502poly_a @ Y0 @ X0 ) ) ) ) )
!= ( ^ [Y0: list_a] :
( ( polyno422358502poly_a @ Y0 @ ( polyno1934269411ymul_a @ p @ q ) )
= ( polyno422358502poly_a @ Y0 @ ( polyno1934269411ymul_a @ q @ p ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1309]) ).
thf(f1309,plain,
! [X0: polyno727731844poly_a] :
( ( ( ^ [Y0: list_a] :
( !! @ polyno727731844poly_a
@ ^ [Y1: polyno727731844poly_a] :
( ( polyno422358502poly_a @ Y0 @ ( polyno1491482291_Mul_a @ Y1 @ X0 ) )
= ( times_times_a @ ( polyno422358502poly_a @ Y0 @ Y1 ) @ ( polyno422358502poly_a @ Y0 @ X0 ) ) ) ) )
!= ( ^ [Y0: list_a] :
( ( polyno422358502poly_a @ Y0 @ ( polyno1934269411ymul_a @ p @ q ) )
= ( polyno422358502poly_a @ Y0 @ ( polyno1934269411ymul_a @ q @ p ) ) ) ) )
| ( $false = $true ) ),
inference(constrained_superposition,[status(thm)],[f1305,f1156]) ).
thf(f1156,plain,
( $false
= ( !! @ list_a
@ ^ [Y0: list_a] :
( ( polyno422358502poly_a @ Y0 @ ( polyno1934269411ymul_a @ p @ q ) )
= ( polyno422358502poly_a @ Y0 @ ( polyno1934269411ymul_a @ q @ p ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1091,f1154]) ).
thf(f1154,plain,
( $false
= ( ( polyno1934269411ymul_a @ p @ q )
= ( polyno1934269411ymul_a @ q @ p ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1068]) ).
thf(f1068,plain,
( $true
= ( ( polyno1934269411ymul_a @ p @ q )
!= ( polyno1934269411ymul_a @ q @ p ) ) ),
inference(cnf_transformation,[status(thm)],[f995]) ).
thf(f995,plain,
( $true
= ( ( polyno1934269411ymul_a @ p @ q )
!= ( polyno1934269411ymul_a @ q @ p ) ) ),
inference(fool_elimination,[status(thm)],[f357]) ).
thf(f357,negated_conjecture,
( ( polyno1934269411ymul_a @ p @ q )
!= ( polyno1934269411ymul_a @ q @ p ) ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f356,conjecture,
( ( polyno1934269411ymul_a @ p @ q )
= ( polyno1934269411ymul_a @ q @ p ) ),
file('/export/starexec/sandbox2/tmp/tmp.HVFAM8xlRw/DTF2THF_3593.p',conj_0) ).
thf(f1091,plain,
( ( !! @ list_a
@ ^ [Y0: list_a] :
( ( polyno422358502poly_a @ Y0 @ ( polyno1934269411ymul_a @ p @ q ) )
= ( polyno422358502poly_a @ Y0 @ ( polyno1934269411ymul_a @ q @ p ) ) ) )
= ( ( polyno1934269411ymul_a @ p @ q )
= ( polyno1934269411ymul_a @ q @ p ) ) ),
inference(cnf_transformation,[status(thm)],[f363]) ).
thf(f363,plain,
( ( !! @ list_a
@ ^ [Y0: list_a] :
( ( polyno422358502poly_a @ Y0 @ ( polyno1934269411ymul_a @ p @ q ) )
= ( polyno422358502poly_a @ Y0 @ ( polyno1934269411ymul_a @ q @ p ) ) ) )
= ( ( polyno1934269411ymul_a @ p @ q )
= ( polyno1934269411ymul_a @ q @ p ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: list_a] :
( ( ( polyno422358502poly_a @ X0 @ ( polyno1934269411ymul_a @ p @ q ) )
= ( polyno422358502poly_a @ X0 @ ( polyno1934269411ymul_a @ q @ p ) ) )
= ( ( polyno1934269411ymul_a @ p @ q )
= ( polyno1934269411ymul_a @ q @ p ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HVFAM8xlRw/DTF2THF_3593.p',fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP150^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n011.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:27:47 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.25/0.47 ---- Original DTF file ---
% 0.25/0.47 thf(spec,logic,$$dhol).
% 0.25/0.47 %------------------------------------------------------------------------------
% 0.25/0.47 % File : ITP150^1 : TPTP v9.2.1. Released v7.5.0.
% 0.25/0.47 % Domain : Interactive Theorem Proving
% 0.25/0.47 % Problem : Sledgehammer Polynomial_Expression problem prob_1319__8380132_1
% 0.25/0.47 % Version : Especial.
% 0.25/0.47 % English :
% 0.25/0.47
% 0.25/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.25/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.25/0.47 % Source : [Des21]
% 0.25/0.47 % Names : Polynomial_Expression/prob_1319__8380132_1 [Des21]
% 0.25/0.47
% 0.25/0.47 % Status : Theorem
% 0.25/0.47 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0
% 0.25/0.47 % Syntax : Number of formulae : 426 ( 287 unt; 70 typ; 0 def)
% 0.25/0.47 % Number of atoms : 681 ( 579 equ; 0 cnn)
% 0.25/0.47 % Maximal formula atoms : 17 ( 1 avg)
% 0.25/0.47 % Number of connectives : 2320 ( 91 ~; 21 |; 28 &;2044 @)
% 0.25/0.47 % ( 0 <=>; 136 =>; 0 <=; 0 <~>)
% 0.25/0.47 % Maximal formula depth : 15 ( 4 avg)
% 0.25/0.47 % Number of types : 7 ( 6 usr)
% 0.25/0.47 % Number of type conns : 111 ( 111 >; 0 *; 0 +; 0 <<)
% 0.25/0.47 % Number of symbols : 67 ( 64 usr; 10 con; 0-3 aty)
% 0.25/0.47 % Number of variables : 939 ( 53 ^; 864 !; 22 ?; 939 :)
% 0.25/0.47 % SPC : TH0_THM_EQU_NAR
% 0.25/0.47
% 0.25/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:33:11.258
% 0.25/0.47 %------------------------------------------------------------------------------
% 0.25/0.47 % Could-be-implicit typings (6)
% 0.25/0.47 thf(ty_n_t__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_It__Nat__Onat_J,type,
% 0.25/0.47 polyno1532895200ly_nat: $tType ).
% 0.25/0.47
% 0.25/0.47 thf(ty_n_t__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_Itf__a_J,type,
% 0.25/0.47 polyno727731844poly_a: $tType ).
% 0.25/0.47
% 0.25/0.47 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.25/0.47 list_nat: $tType ).
% 0.25/0.47
% 0.25/0.47 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.25/0.47 list_a: $tType ).
% 0.25/0.47
% 0.25/0.47 thf(ty_n_t__Nat__Onat,type,
% 0.25/0.47 nat: $tType ).
% 0.25/0.47
% 0.25/0.47 thf(ty_n_tf__a,type,
% 0.25/0.47 a: $tType ).
% 0.25/0.47
% 0.25/0.47 % Explicit typings (64)
% 0.25/0.47 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.25/0.47 one_one_nat: nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Groups_Oone__class_Oone_001tf__a,type,
% 0.25/0.47 one_one_a: a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 0.25/0.47 plus_plus_nat: nat > nat > nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Groups_Oplus__class_Oplus_001tf__a,type,
% 0.25/0.47 plus_plus_a: a > a > a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 0.25/0.47 times_times_nat: nat > nat > nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Groups_Otimes__class_Otimes_001tf__a,type,
% 0.25/0.47 times_times_a: a > a > a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.25/0.47 zero_zero_nat: nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Groups_Ozero__class_Ozero_001tf__a,type,
% 0.25/0.47 zero_zero_a: a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_If_001t__Nat__Onat,type,
% 0.25/0.47 if_nat: $o > nat > nat > nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Nat_Ocompow_001_062_It__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_It__Nat__Onat_J_Mt__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_It__Nat__Onat_J_J,type,
% 0.25/0.47 compow808008746ly_nat: nat > ( polyno1532895200ly_nat > polyno1532895200ly_nat ) > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Nat_Ocompow_001_062_It__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_Itf__a_J_Mt__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_Itf__a_J_J,type,
% 0.25/0.47 compow1114216044poly_a: nat > ( polyno727731844poly_a > polyno727731844poly_a ) > polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_OIpoly_001tf__a,type,
% 0.25/0.47 polyno422358502poly_a: list_a > polyno727731844poly_a > a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Obehead_001t__Nat__Onat,type,
% 0.25/0.47 polyno587244178ad_nat: polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Obehead_001tf__a,type,
% 0.25/0.47 polyno1465139388head_a: polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Odegree_001t__Nat__Onat,type,
% 0.25/0.47 polyno220183259ee_nat: polyno1532895200ly_nat > nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Odegree_001tf__a,type,
% 0.25/0.47 polyno578545843gree_a: polyno727731844poly_a > nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Odegreen_001t__Nat__Onat,type,
% 0.25/0.47 polyno1779722485en_nat: polyno1532895200ly_nat > nat > nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Odegreen_001tf__a,type,
% 0.25/0.47 polyno1674775833reen_a: polyno727731844poly_a > nat > nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Ohead_001t__Nat__Onat,type,
% 0.25/0.47 polyno1952548879ad_nat: polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Ohead_001tf__a,type,
% 0.25/0.47 polyno1884029055head_a: polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oheadconst_001t__Nat__Onat,type,
% 0.25/0.47 polyno524777654st_nat: polyno1532895200ly_nat > nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oheadconst_001tf__a,type,
% 0.25/0.47 polyno2115742616onst_a: polyno727731844poly_a > a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oheadn_001t__Nat__Onat,type,
% 0.25/0.47 polyno544860353dn_nat: polyno1532895200ly_nat > nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oheadn_001tf__a,type,
% 0.25/0.47 polyno567601229eadn_a: polyno727731844poly_a > nat > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oisnpoly_001t__Nat__Onat,type,
% 0.25/0.47 polyno1013235523ly_nat: polyno1532895200ly_nat > $o ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oisnpoly_001tf__a,type,
% 0.25/0.47 polyno190918219poly_a: polyno727731844poly_a > $o ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oisnpolyh_001t__Nat__Onat,type,
% 0.25/0.47 polyno892049031yh_nat: polyno1532895200ly_nat > nat > $o ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oisnpolyh_001tf__a,type,
% 0.25/0.47 polyno1372495879olyh_a: polyno727731844poly_a > nat > $o ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OAdd_001t__Nat__Onat,type,
% 0.25/0.47 polyno1222032024dd_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OAdd_001tf__a,type,
% 0.25/0.47 polyno1623170614_Add_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OBound_001t__Nat__Onat,type,
% 0.25/0.47 polyno1999838549nd_nat: nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OBound_001tf__a,type,
% 0.25/0.47 polyno2024845497ound_a: nat > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OCN_001t__Nat__Onat,type,
% 0.25/0.47 polyno720942678CN_nat: polyno1532895200ly_nat > nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OCN_001tf__a,type,
% 0.25/0.47 polyno1057396216e_CN_a: polyno727731844poly_a > nat > polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OC_001t__Nat__Onat,type,
% 0.25/0.47 polyno2122022170_C_nat: nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OC_001tf__a,type,
% 0.25/0.47 polyno439679028le_C_a: a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OMul_001t__Nat__Onat,type,
% 0.25/0.47 polyno1415441627ul_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OMul_001tf__a,type,
% 0.25/0.47 polyno1491482291_Mul_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_ONeg_001t__Nat__Onat,type,
% 0.25/0.47 polyno1366804583eg_nat: polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_ONeg_001tf__a,type,
% 0.25/0.47 polyno96675367_Neg_a: polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OPw_001t__Nat__Onat,type,
% 0.25/0.47 polyno359287218Pw_nat: polyno1532895200ly_nat > nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OPw_001tf__a,type,
% 0.25/0.47 polyno1538138524e_Pw_a: polyno727731844poly_a > nat > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OSub_001t__Nat__Onat,type,
% 0.25/0.47 polyno1921014231ub_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OSub_001tf__a,type,
% 0.25/0.47 polyno975704247_Sub_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly__cmul_001t__Nat__Onat,type,
% 0.25/0.47 polyno1467023772ul_nat: nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly__cmul_001tf__a,type,
% 0.25/0.47 polyno562434098cmul_a: a > polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly__deriv_001tf__a,type,
% 0.25/0.47 polyno212464073eriv_a: polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly__deriv__aux_001tf__a,type,
% 0.25/0.47 polyno1006823949_aux_a: a > polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolymul_001t__Nat__Onat,type,
% 0.25/0.47 polyno929799083ul_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolymul_001tf__a,type,
% 0.25/0.47 polyno1934269411ymul_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolynate_001tf__a,type,
% 0.25/0.47 polyno955999183nate_a: polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolypow_001t__Nat__Onat,type,
% 0.25/0.47 polyno1510045887ow_nat: nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolypow_001tf__a,type,
% 0.25/0.47 polyno1371724751ypow_a: nat > polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolysub_001tf__a,type,
% 0.25/0.47 polyno1418491367ysub_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolysubst0_001t__Nat__Onat,type,
% 0.25/0.47 polyno336795754t0_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolysubst0_001tf__a,type,
% 0.25/0.47 polyno1397854436bst0_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oshift1_001t__Nat__Onat,type,
% 0.25/0.47 polyno1964927358t1_nat: polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oshift1_001tf__a,type,
% 0.25/0.47 polyno784948432ift1_a: polyno727731844poly_a > polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Owf__bs_001t__Nat__Onat,type,
% 0.25/0.47 polyno1438831695bs_nat: list_nat > polyno1532895200ly_nat > $o ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Owf__bs_001tf__a,type,
% 0.25/0.47 polyno896877631f_bs_a: list_a > polyno727731844poly_a > $o ).
% 0.25/0.47
% 0.25/0.47 thf(sy_v_n0,type,
% 0.25/0.47 n0: nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_v_n1,type,
% 0.25/0.47 n1: nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_v_p,type,
% 0.25/0.47 p: polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_v_q,type,
% 0.25/0.47 q: polyno727731844poly_a ).
% 0.25/0.47
% 0.25/0.47 % Relevant facts (352)
% 0.25/0.47 thf(fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062,axiom,
% 0.25/0.47 ( ( ! [Bs: list_a] :
% 0.25/0.47 ( ( polyno422358502poly_a @ Bs @ ( polyno1934269411ymul_a @ p @ q ) )
% 0.25/0.47 = ( polyno422358502poly_a @ Bs @ ( polyno1934269411ymul_a @ q @ p ) ) ) )
% 0.25/0.47 = ( ( polyno1934269411ymul_a @ p @ q )
% 0.25/0.47 = ( polyno1934269411ymul_a @ q @ p ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % \<open>(\<forall>bs. Ipoly bs (p *\<^sub>p q) = Ipoly bs (q *\<^sub>p p)) = (p *\<^sub>p q = q *\<^sub>p p)\<close>
% 0.25/0.47 thf(fact_1_np,axiom,
% 0.25/0.47 polyno1372495879olyh_a @ p @ n0 ).
% 0.25/0.47
% 0.25/0.47 % np
% 0.25/0.47 thf(fact_2_nq,axiom,
% 0.25/0.47 polyno1372495879olyh_a @ q @ n1 ).
% 0.25/0.47
% 0.25/0.47 % nq
% 0.25/0.47 thf(fact_3_polymul__norm,axiom,
% 0.25/0.47 ! [P: polyno727731844poly_a,Q: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno190918219poly_a @ P )
% 0.25/0.47 => ( ( polyno190918219poly_a @ Q )
% 0.25/0.47 => ( polyno190918219poly_a @ ( polyno1934269411ymul_a @ P @ Q ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul_norm
% 0.25/0.47 thf(fact_4_wf__bs__polyul,axiom,
% 0.25/0.47 ! [Bs2: list_nat,P: polyno1532895200ly_nat,Q: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno1438831695bs_nat @ Bs2 @ P )
% 0.25/0.47 => ( ( polyno1438831695bs_nat @ Bs2 @ Q )
% 0.25/0.47 => ( polyno1438831695bs_nat @ Bs2 @ ( polyno929799083ul_nat @ P @ Q ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % wf_bs_polyul
% 0.25/0.47 thf(fact_5_wf__bs__polyul,axiom,
% 0.25/0.47 ! [Bs2: list_a,P: polyno727731844poly_a,Q: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno896877631f_bs_a @ Bs2 @ P )
% 0.25/0.47 => ( ( polyno896877631f_bs_a @ Bs2 @ Q )
% 0.25/0.47 => ( polyno896877631f_bs_a @ Bs2 @ ( polyno1934269411ymul_a @ P @ Q ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % wf_bs_polyul
% 0.25/0.47 thf(fact_6_polymul_Osimps_I20_J,axiom,
% 0.25/0.47 ! [A: polyno1532895200ly_nat,V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno929799083ul_nat @ A @ ( polyno1415441627ul_nat @ V @ Va ) )
% 0.25/0.47 = ( polyno1415441627ul_nat @ A @ ( polyno1415441627ul_nat @ V @ Va ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(20)
% 0.25/0.47 thf(fact_7_polymul_Osimps_I20_J,axiom,
% 0.25/0.47 ! [A: polyno727731844poly_a,V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno1934269411ymul_a @ A @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 0.25/0.47 = ( polyno1491482291_Mul_a @ A @ ( polyno1491482291_Mul_a @ V @ Va ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(20)
% 0.25/0.47 thf(fact_8_polymul_Osimps_I8_J,axiom,
% 0.25/0.47 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat,B: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno929799083ul_nat @ ( polyno1415441627ul_nat @ V @ Va ) @ B )
% 0.25/0.47 = ( polyno1415441627ul_nat @ ( polyno1415441627ul_nat @ V @ Va ) @ B ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(8)
% 0.25/0.47 thf(fact_9_polymul_Osimps_I8_J,axiom,
% 0.25/0.47 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a,B: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno1934269411ymul_a @ ( polyno1491482291_Mul_a @ V @ Va ) @ B )
% 0.25/0.47 = ( polyno1491482291_Mul_a @ ( polyno1491482291_Mul_a @ V @ Va ) @ B ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(8)
% 0.25/0.47 thf(fact_10_polymul,axiom,
% 0.25/0.47 ! [Bs2: list_a,P: polyno727731844poly_a,Q: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno422358502poly_a @ Bs2 @ ( polyno1934269411ymul_a @ P @ Q ) )
% 0.25/0.47 = ( times_times_a @ ( polyno422358502poly_a @ Bs2 @ P ) @ ( polyno422358502poly_a @ Bs2 @ Q ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul
% 0.25/0.47 thf(fact_11_polymul_Osimps_I1_J,axiom,
% 0.25/0.47 ! [C: nat,C2: nat] :
% 0.25/0.47 ( ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ C ) @ ( polyno2122022170_C_nat @ C2 ) )
% 0.25/0.47 = ( polyno2122022170_C_nat @ ( times_times_nat @ C @ C2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(1)
% 0.25/0.47 thf(fact_12_polymul_Osimps_I1_J,axiom,
% 0.25/0.47 ! [C: a,C2: a] :
% 0.25/0.47 ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ C ) @ ( polyno439679028le_C_a @ C2 ) )
% 0.25/0.47 = ( polyno439679028le_C_a @ ( times_times_a @ C @ C2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(1)
% 0.25/0.47 thf(fact_13_polynate_Osimps_I4_J,axiom,
% 0.25/0.47 ! [P: polyno727731844poly_a,Q: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno955999183nate_a @ ( polyno1491482291_Mul_a @ P @ Q ) )
% 0.25/0.47 = ( polyno1934269411ymul_a @ ( polyno955999183nate_a @ P ) @ ( polyno955999183nate_a @ Q ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polynate.simps(4)
% 0.25/0.47 thf(fact_14_polymul_Osimps_I26_J,axiom,
% 0.25/0.47 ! [Vc: polyno1532895200ly_nat,Vd: polyno1532895200ly_nat,V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno929799083ul_nat @ ( polyno1415441627ul_nat @ Vc @ Vd ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) )
% 0.25/0.47 = ( polyno1415441627ul_nat @ ( polyno1415441627ul_nat @ Vc @ Vd ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(26)
% 0.25/0.47 thf(fact_15_polymul_Osimps_I26_J,axiom,
% 0.25/0.47 ! [Vc: polyno727731844poly_a,Vd: polyno727731844poly_a,V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno1934269411ymul_a @ ( polyno1491482291_Mul_a @ Vc @ Vd ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) )
% 0.25/0.47 = ( polyno1491482291_Mul_a @ ( polyno1491482291_Mul_a @ Vc @ Vd ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(26)
% 0.25/0.47 thf(fact_16_polymul_Osimps_I14_J,axiom,
% 0.25/0.47 ! [V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat,Vc: polyno1532895200ly_nat,Vd: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno929799083ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno1415441627ul_nat @ Vc @ Vd ) )
% 0.25/0.47 = ( polyno1415441627ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno1415441627ul_nat @ Vc @ Vd ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(14)
% 0.25/0.47 thf(fact_17_polymul_Osimps_I14_J,axiom,
% 0.25/0.47 ! [V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a,Vc: polyno727731844poly_a,Vd: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno1491482291_Mul_a @ Vc @ Vd ) )
% 0.25/0.47 = ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno1491482291_Mul_a @ Vc @ Vd ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(14)
% 0.25/0.47 thf(fact_18_polymul_Osimps_I18_J,axiom,
% 0.25/0.47 ! [A: polyno1532895200ly_nat,V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno929799083ul_nat @ A @ ( polyno1222032024dd_nat @ V @ Va ) )
% 0.25/0.47 = ( polyno1415441627ul_nat @ A @ ( polyno1222032024dd_nat @ V @ Va ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(18)
% 0.25/0.47 thf(fact_19_polymul_Osimps_I18_J,axiom,
% 0.25/0.47 ! [A: polyno727731844poly_a,V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno1934269411ymul_a @ A @ ( polyno1623170614_Add_a @ V @ Va ) )
% 0.25/0.47 = ( polyno1491482291_Mul_a @ A @ ( polyno1623170614_Add_a @ V @ Va ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(18)
% 0.25/0.47 thf(fact_20_poly_Oinject_I8_J,axiom,
% 0.25/0.47 ! [X81: polyno727731844poly_a,X82: nat,X83: polyno727731844poly_a,Y81: polyno727731844poly_a,Y82: nat,Y83: polyno727731844poly_a] :
% 0.25/0.47 ( ( ( polyno1057396216e_CN_a @ X81 @ X82 @ X83 )
% 0.25/0.47 = ( polyno1057396216e_CN_a @ Y81 @ Y82 @ Y83 ) )
% 0.25/0.47 = ( ( X81 = Y81 )
% 0.25/0.47 & ( X82 = Y82 )
% 0.25/0.47 & ( X83 = Y83 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.inject(8)
% 0.25/0.47 thf(fact_21_poly_Oinject_I8_J,axiom,
% 0.25/0.47 ! [X81: polyno1532895200ly_nat,X82: nat,X83: polyno1532895200ly_nat,Y81: polyno1532895200ly_nat,Y82: nat,Y83: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( ( polyno720942678CN_nat @ X81 @ X82 @ X83 )
% 0.25/0.47 = ( polyno720942678CN_nat @ Y81 @ Y82 @ Y83 ) )
% 0.25/0.47 = ( ( X81 = Y81 )
% 0.25/0.47 & ( X82 = Y82 )
% 0.25/0.47 & ( X83 = Y83 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.inject(8)
% 0.25/0.47 thf(fact_22_poly_Oinject_I1_J,axiom,
% 0.25/0.47 ! [X1: a,Y1: a] :
% 0.25/0.47 ( ( ( polyno439679028le_C_a @ X1 )
% 0.25/0.47 = ( polyno439679028le_C_a @ Y1 ) )
% 0.25/0.47 = ( X1 = Y1 ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.inject(1)
% 0.25/0.47 thf(fact_23_poly_Oinject_I1_J,axiom,
% 0.25/0.47 ! [X1: nat,Y1: nat] :
% 0.25/0.47 ( ( ( polyno2122022170_C_nat @ X1 )
% 0.25/0.47 = ( polyno2122022170_C_nat @ Y1 ) )
% 0.25/0.47 = ( X1 = Y1 ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.inject(1)
% 0.25/0.47 thf(fact_24_poly_Oinject_I5_J,axiom,
% 0.25/0.47 ! [X51: polyno1532895200ly_nat,X52: polyno1532895200ly_nat,Y51: polyno1532895200ly_nat,Y52: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( ( polyno1415441627ul_nat @ X51 @ X52 )
% 0.25/0.47 = ( polyno1415441627ul_nat @ Y51 @ Y52 ) )
% 0.25/0.47 = ( ( X51 = Y51 )
% 0.25/0.47 & ( X52 = Y52 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.inject(5)
% 0.25/0.47 thf(fact_25_poly_Oinject_I5_J,axiom,
% 0.25/0.47 ! [X51: polyno727731844poly_a,X52: polyno727731844poly_a,Y51: polyno727731844poly_a,Y52: polyno727731844poly_a] :
% 0.25/0.47 ( ( ( polyno1491482291_Mul_a @ X51 @ X52 )
% 0.25/0.47 = ( polyno1491482291_Mul_a @ Y51 @ Y52 ) )
% 0.25/0.47 = ( ( X51 = Y51 )
% 0.25/0.47 & ( X52 = Y52 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.inject(5)
% 0.25/0.47 thf(fact_26_poly_Oinject_I3_J,axiom,
% 0.25/0.47 ! [X31: polyno727731844poly_a,X32: polyno727731844poly_a,Y31: polyno727731844poly_a,Y32: polyno727731844poly_a] :
% 0.25/0.47 ( ( ( polyno1623170614_Add_a @ X31 @ X32 )
% 0.25/0.47 = ( polyno1623170614_Add_a @ Y31 @ Y32 ) )
% 0.25/0.47 = ( ( X31 = Y31 )
% 0.25/0.47 & ( X32 = Y32 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.inject(3)
% 0.25/0.47 thf(fact_27_poly_Oinject_I3_J,axiom,
% 0.25/0.47 ! [X31: polyno1532895200ly_nat,X32: polyno1532895200ly_nat,Y31: polyno1532895200ly_nat,Y32: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( ( polyno1222032024dd_nat @ X31 @ X32 )
% 0.25/0.47 = ( polyno1222032024dd_nat @ Y31 @ Y32 ) )
% 0.25/0.47 = ( ( X31 = Y31 )
% 0.25/0.47 & ( X32 = Y32 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.inject(3)
% 0.25/0.47 thf(fact_28_polynate,axiom,
% 0.25/0.47 ! [Bs2: list_a,P: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno422358502poly_a @ Bs2 @ ( polyno955999183nate_a @ P ) )
% 0.25/0.47 = ( polyno422358502poly_a @ Bs2 @ P ) ) ).
% 0.25/0.47
% 0.25/0.47 % polynate
% 0.25/0.47 thf(fact_29_Ipoly_Osimps_I6_J,axiom,
% 0.25/0.47 ! [Bs2: list_a,A: polyno727731844poly_a,B: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno422358502poly_a @ Bs2 @ ( polyno1491482291_Mul_a @ A @ B ) )
% 0.25/0.47 = ( times_times_a @ ( polyno422358502poly_a @ Bs2 @ A ) @ ( polyno422358502poly_a @ Bs2 @ B ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % Ipoly.simps(6)
% 0.25/0.47 thf(fact_30_Ipoly_Osimps_I1_J,axiom,
% 0.25/0.47 ! [Bs2: list_a,C: a] :
% 0.25/0.47 ( ( polyno422358502poly_a @ Bs2 @ ( polyno439679028le_C_a @ C ) )
% 0.25/0.47 = C ) ).
% 0.25/0.47
% 0.25/0.47 % Ipoly.simps(1)
% 0.25/0.47 thf(fact_31_poly_Odistinct_I49_J,axiom,
% 0.25/0.47 ! [X51: polyno1532895200ly_nat,X52: polyno1532895200ly_nat,X81: polyno1532895200ly_nat,X82: nat,X83: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno1415441627ul_nat @ X51 @ X52 )
% 0.25/0.47 != ( polyno720942678CN_nat @ X81 @ X82 @ X83 ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.distinct(49)
% 0.25/0.47 thf(fact_32_poly_Odistinct_I49_J,axiom,
% 0.25/0.47 ! [X51: polyno727731844poly_a,X52: polyno727731844poly_a,X81: polyno727731844poly_a,X82: nat,X83: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno1491482291_Mul_a @ X51 @ X52 )
% 0.25/0.47 != ( polyno1057396216e_CN_a @ X81 @ X82 @ X83 ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.distinct(49)
% 0.25/0.47 thf(fact_33_poly_Odistinct_I35_J,axiom,
% 0.25/0.47 ! [X31: polyno727731844poly_a,X32: polyno727731844poly_a,X81: polyno727731844poly_a,X82: nat,X83: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno1623170614_Add_a @ X31 @ X32 )
% 0.25/0.47 != ( polyno1057396216e_CN_a @ X81 @ X82 @ X83 ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.distinct(35)
% 0.25/0.47 thf(fact_34_poly_Odistinct_I35_J,axiom,
% 0.25/0.47 ! [X31: polyno1532895200ly_nat,X32: polyno1532895200ly_nat,X81: polyno1532895200ly_nat,X82: nat,X83: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno1222032024dd_nat @ X31 @ X32 )
% 0.25/0.47 != ( polyno720942678CN_nat @ X81 @ X82 @ X83 ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.distinct(35)
% 0.25/0.47 thf(fact_35_poly_Odistinct_I29_J,axiom,
% 0.25/0.47 ! [X31: polyno1532895200ly_nat,X32: polyno1532895200ly_nat,X51: polyno1532895200ly_nat,X52: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno1222032024dd_nat @ X31 @ X32 )
% 0.25/0.47 != ( polyno1415441627ul_nat @ X51 @ X52 ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.distinct(29)
% 0.25/0.47 thf(fact_36_poly_Odistinct_I29_J,axiom,
% 0.25/0.47 ! [X31: polyno727731844poly_a,X32: polyno727731844poly_a,X51: polyno727731844poly_a,X52: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno1623170614_Add_a @ X31 @ X32 )
% 0.25/0.47 != ( polyno1491482291_Mul_a @ X51 @ X52 ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.distinct(29)
% 0.25/0.47 thf(fact_37_poly_Odistinct_I13_J,axiom,
% 0.25/0.47 ! [X1: a,X81: polyno727731844poly_a,X82: nat,X83: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno439679028le_C_a @ X1 )
% 0.25/0.47 != ( polyno1057396216e_CN_a @ X81 @ X82 @ X83 ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.distinct(13)
% 0.25/0.47 thf(fact_38_poly_Odistinct_I13_J,axiom,
% 0.25/0.47 ! [X1: nat,X81: polyno1532895200ly_nat,X82: nat,X83: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno2122022170_C_nat @ X1 )
% 0.25/0.47 != ( polyno720942678CN_nat @ X81 @ X82 @ X83 ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.distinct(13)
% 0.25/0.47 thf(fact_39_poly_Odistinct_I7_J,axiom,
% 0.25/0.47 ! [X1: nat,X51: polyno1532895200ly_nat,X52: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno2122022170_C_nat @ X1 )
% 0.25/0.47 != ( polyno1415441627ul_nat @ X51 @ X52 ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.distinct(7)
% 0.25/0.47 thf(fact_40_poly_Odistinct_I7_J,axiom,
% 0.25/0.47 ! [X1: a,X51: polyno727731844poly_a,X52: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno439679028le_C_a @ X1 )
% 0.25/0.47 != ( polyno1491482291_Mul_a @ X51 @ X52 ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.distinct(7)
% 0.25/0.47 thf(fact_41_poly_Odistinct_I3_J,axiom,
% 0.25/0.47 ! [X1: a,X31: polyno727731844poly_a,X32: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno439679028le_C_a @ X1 )
% 0.25/0.47 != ( polyno1623170614_Add_a @ X31 @ X32 ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.distinct(3)
% 0.25/0.47 thf(fact_42_poly_Odistinct_I3_J,axiom,
% 0.25/0.47 ! [X1: nat,X31: polyno1532895200ly_nat,X32: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno2122022170_C_nat @ X1 )
% 0.25/0.47 != ( polyno1222032024dd_nat @ X31 @ X32 ) ) ).
% 0.25/0.47
% 0.25/0.47 % poly.distinct(3)
% 0.25/0.47 thf(fact_43_polymul_Osimps_I24_J,axiom,
% 0.25/0.47 ! [Vc: polyno1532895200ly_nat,Vd: polyno1532895200ly_nat,V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno929799083ul_nat @ ( polyno1222032024dd_nat @ Vc @ Vd ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) )
% 0.25/0.47 = ( polyno1415441627ul_nat @ ( polyno1222032024dd_nat @ Vc @ Vd ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(24)
% 0.25/0.47 thf(fact_44_polymul_Osimps_I24_J,axiom,
% 0.25/0.47 ! [Vc: polyno727731844poly_a,Vd: polyno727731844poly_a,V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno1934269411ymul_a @ ( polyno1623170614_Add_a @ Vc @ Vd ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) )
% 0.25/0.47 = ( polyno1491482291_Mul_a @ ( polyno1623170614_Add_a @ Vc @ Vd ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(24)
% 0.25/0.47 thf(fact_45_polymul_Osimps_I12_J,axiom,
% 0.25/0.47 ! [V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat,Vc: polyno1532895200ly_nat,Vd: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno929799083ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno1222032024dd_nat @ Vc @ Vd ) )
% 0.25/0.47 = ( polyno1415441627ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno1222032024dd_nat @ Vc @ Vd ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(12)
% 0.25/0.47 thf(fact_46_polymul_Osimps_I12_J,axiom,
% 0.25/0.47 ! [V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a,Vc: polyno727731844poly_a,Vd: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno1623170614_Add_a @ Vc @ Vd ) )
% 0.25/0.47 = ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno1623170614_Add_a @ Vc @ Vd ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % polymul.simps(12)
% 0.25/0.47 thf(fact_47_isnpolyh_Osimps_I6_J,axiom,
% 0.25/0.47 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno892049031yh_nat @ ( polyno1415441627ul_nat @ V @ Va ) )
% 0.25/0.47 = ( ^ [K: nat] : $false ) ) ).
% 0.25/0.47
% 0.25/0.47 % isnpolyh.simps(6)
% 0.25/0.47 thf(fact_48_isnpolyh_Osimps_I6_J,axiom,
% 0.25/0.47 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.47 ( ( polyno1372495879olyh_a @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 0.25/0.47 = ( ^ [K: nat] : $false ) ) ).
% 0.25/0.47
% 0.25/0.47 % isnpolyh.simps(6)
% 0.25/0.47 thf(fact_49_isnpolyh_Osimps_I4_J,axiom,
% 0.25/0.47 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.47 ( ( polyno892049031yh_nat @ ( polyno1222032024dd_nat @ V @ Va ) )
% 0.25/0.47 = ( ^ [K: nat] : $false ) ) ).
% 0.25/0.47
% 0.25/0.47 % isnpolyh.simps(4)
% 0.25/0.47 thf(fact_50_isnpolyh_Osimps_I4_J,axiom,
% 0.25/0.47 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ ( polyno1623170614_Add_a @ V @ Va ) )
% 0.25/0.48 = ( ^ [K: nat] : $false ) ) ).
% 0.25/0.48
% 0.25/0.48 % isnpolyh.simps(4)
% 0.25/0.48 thf(fact_51_isnpolyh_Osimps_I1_J,axiom,
% 0.25/0.48 ! [C: nat] :
% 0.25/0.48 ( ( polyno892049031yh_nat @ ( polyno2122022170_C_nat @ C ) )
% 0.25/0.48 = ( ^ [K: nat] : $true ) ) ).
% 0.25/0.48
% 0.25/0.48 % isnpolyh.simps(1)
% 0.25/0.48 thf(fact_52_isnpolyh_Osimps_I1_J,axiom,
% 0.25/0.48 ! [C: a] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ ( polyno439679028le_C_a @ C ) )
% 0.25/0.48 = ( ^ [K: nat] : $true ) ) ).
% 0.25/0.48
% 0.25/0.48 % isnpolyh.simps(1)
% 0.25/0.48 thf(fact_53_polynate_Osimps_I8_J,axiom,
% 0.25/0.48 ! [C: a] :
% 0.25/0.48 ( ( polyno955999183nate_a @ ( polyno439679028le_C_a @ C ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ C ) ) ).
% 0.25/0.48
% 0.25/0.48 % polynate.simps(8)
% 0.25/0.48 thf(fact_54_polynate__norm,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a] : ( polyno190918219poly_a @ ( polyno955999183nate_a @ P ) ) ).
% 0.25/0.48
% 0.25/0.48 % polynate_norm
% 0.25/0.48 thf(fact_55_isnpolyh__unique,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N0: nat,Q: polyno727731844poly_a,N1: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N0 )
% 0.25/0.48 => ( ( polyno1372495879olyh_a @ Q @ N1 )
% 0.25/0.48 => ( ( ! [Bs: list_a] :
% 0.25/0.48 ( ( polyno422358502poly_a @ Bs @ P )
% 0.25/0.48 = ( polyno422358502poly_a @ Bs @ Q ) ) )
% 0.25/0.48 = ( P = Q ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % isnpolyh_unique
% 0.25/0.48 thf(fact_56_polymul_Osimps_I6_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat,B: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno929799083ul_nat @ ( polyno1222032024dd_nat @ V @ Va ) @ B )
% 0.25/0.48 = ( polyno1415441627ul_nat @ ( polyno1222032024dd_nat @ V @ Va ) @ B ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(6)
% 0.25/0.48 thf(fact_57_polymul_Osimps_I6_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a,B: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1934269411ymul_a @ ( polyno1623170614_Add_a @ V @ Va ) @ B )
% 0.25/0.48 = ( polyno1491482291_Mul_a @ ( polyno1623170614_Add_a @ V @ Va ) @ B ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(6)
% 0.25/0.48 thf(fact_58_isnpolyh__zero__iff,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N0: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N0 )
% 0.25/0.48 => ( ! [Bs3: list_a] :
% 0.25/0.48 ( ( polyno896877631f_bs_a @ Bs3 @ P )
% 0.25/0.48 => ( ( polyno422358502poly_a @ Bs3 @ P )
% 0.25/0.48 = zero_zero_a ) )
% 0.25/0.48 => ( P
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % isnpolyh_zero_iff
% 0.25/0.48 thf(fact_59_poly__cmul,axiom,
% 0.25/0.48 ! [Bs2: list_a,C: a,P: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno422358502poly_a @ Bs2 @ ( polyno562434098cmul_a @ C @ P ) )
% 0.25/0.48 = ( polyno422358502poly_a @ Bs2 @ ( polyno1491482291_Mul_a @ ( polyno439679028le_C_a @ C ) @ P ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul
% 0.25/0.48 thf(fact_60_polymul__0_I2_J,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N0: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N0 )
% 0.25/0.48 => ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ P )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul_0(2)
% 0.25/0.48 thf(fact_61_polymul__0_I1_J,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N0: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N0 )
% 0.25/0.48 => ( ( polyno1934269411ymul_a @ P @ ( polyno439679028le_C_a @ zero_zero_a ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul_0(1)
% 0.25/0.48 thf(fact_62_polymul__1_I2_J,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N0: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N0 )
% 0.25/0.48 => ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ one_one_a ) @ P )
% 0.25/0.48 = P ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul_1(2)
% 0.25/0.48 thf(fact_63_polymul__1_I1_J,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N0: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N0 )
% 0.25/0.48 => ( ( polyno1934269411ymul_a @ P @ ( polyno439679028le_C_a @ one_one_a ) )
% 0.25/0.48 = P ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul_1(1)
% 0.25/0.48 thf(fact_64_polynate_Osimps_I7_J,axiom,
% 0.25/0.48 ! [C: polyno727731844poly_a,N: nat,P: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno955999183nate_a @ ( polyno1057396216e_CN_a @ C @ N @ P ) )
% 0.25/0.48 = ( polyno955999183nate_a @ ( polyno1623170614_Add_a @ C @ ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ N ) @ P ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polynate.simps(7)
% 0.25/0.48 thf(fact_65_polymul__eq0__iff,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N0: nat,Q: polyno727731844poly_a,N1: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N0 )
% 0.25/0.48 => ( ( polyno1372495879olyh_a @ Q @ N1 )
% 0.25/0.48 => ( ( ( polyno1934269411ymul_a @ P @ Q )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) )
% 0.25/0.48 = ( ( P
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) )
% 0.25/0.48 | ( Q
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul_eq0_iff
% 0.25/0.48 thf(fact_66_poly__cmul_Osimps_I4_J,axiom,
% 0.25/0.48 ! [Y: a,V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno562434098cmul_a @ Y @ ( polyno1623170614_Add_a @ V @ Va ) )
% 0.25/0.48 = ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ Y ) @ ( polyno1623170614_Add_a @ V @ Va ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(4)
% 0.25/0.48 thf(fact_67_poly__cmul_Osimps_I4_J,axiom,
% 0.25/0.48 ! [Y: nat,V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno1467023772ul_nat @ Y @ ( polyno1222032024dd_nat @ V @ Va ) )
% 0.25/0.48 = ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ Y ) @ ( polyno1222032024dd_nat @ V @ Va ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(4)
% 0.25/0.48 thf(fact_68_poly__cmul_Osimps_I6_J,axiom,
% 0.25/0.48 ! [Y: nat,V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno1467023772ul_nat @ Y @ ( polyno1415441627ul_nat @ V @ Va ) )
% 0.25/0.48 = ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ Y ) @ ( polyno1415441627ul_nat @ V @ Va ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(6)
% 0.25/0.48 thf(fact_69_poly__cmul_Osimps_I6_J,axiom,
% 0.25/0.48 ! [Y: a,V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno562434098cmul_a @ Y @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 0.25/0.48 = ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ Y ) @ ( polyno1491482291_Mul_a @ V @ Va ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(6)
% 0.25/0.48 thf(fact_70_polymul_Osimps_I3_J,axiom,
% 0.25/0.48 ! [C2: a,C: polyno727731844poly_a,N: nat,P: polyno727731844poly_a] :
% 0.25/0.48 ( ( ( C2 = zero_zero_a )
% 0.25/0.48 => ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ C @ N @ P ) @ ( polyno439679028le_C_a @ C2 ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) )
% 0.25/0.48 & ( ( C2 != zero_zero_a )
% 0.25/0.48 => ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ C @ N @ P ) @ ( polyno439679028le_C_a @ C2 ) )
% 0.25/0.48 = ( polyno1057396216e_CN_a @ ( polyno1934269411ymul_a @ C @ ( polyno439679028le_C_a @ C2 ) ) @ N @ ( polyno1934269411ymul_a @ P @ ( polyno439679028le_C_a @ C2 ) ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(3)
% 0.25/0.48 thf(fact_71_polymul_Osimps_I3_J,axiom,
% 0.25/0.48 ! [C2: nat,C: polyno1532895200ly_nat,N: nat,P: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( ( C2 = zero_zero_nat )
% 0.25/0.48 => ( ( polyno929799083ul_nat @ ( polyno720942678CN_nat @ C @ N @ P ) @ ( polyno2122022170_C_nat @ C2 ) )
% 0.25/0.48 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) )
% 0.25/0.48 & ( ( C2 != zero_zero_nat )
% 0.25/0.48 => ( ( polyno929799083ul_nat @ ( polyno720942678CN_nat @ C @ N @ P ) @ ( polyno2122022170_C_nat @ C2 ) )
% 0.25/0.48 = ( polyno720942678CN_nat @ ( polyno929799083ul_nat @ C @ ( polyno2122022170_C_nat @ C2 ) ) @ N @ ( polyno929799083ul_nat @ P @ ( polyno2122022170_C_nat @ C2 ) ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(3)
% 0.25/0.48 thf(fact_72_poly_Oinject_I2_J,axiom,
% 0.25/0.48 ! [X2: nat,Y2: nat] :
% 0.25/0.48 ( ( ( polyno2024845497ound_a @ X2 )
% 0.25/0.48 = ( polyno2024845497ound_a @ Y2 ) )
% 0.25/0.48 = ( X2 = Y2 ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly.inject(2)
% 0.25/0.48 thf(fact_73_poly_Oinject_I2_J,axiom,
% 0.25/0.48 ! [X2: nat,Y2: nat] :
% 0.25/0.48 ( ( ( polyno1999838549nd_nat @ X2 )
% 0.25/0.48 = ( polyno1999838549nd_nat @ Y2 ) )
% 0.25/0.48 = ( X2 = Y2 ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly.inject(2)
% 0.25/0.48 thf(fact_74_polynate_Osimps_I1_J,axiom,
% 0.25/0.48 ! [N: nat] :
% 0.25/0.48 ( ( polyno955999183nate_a @ ( polyno2024845497ound_a @ N ) )
% 0.25/0.48 = ( polyno1057396216e_CN_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ N @ ( polyno439679028le_C_a @ one_one_a ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polynate.simps(1)
% 0.25/0.48 thf(fact_75_poly__cmul_Osimps_I3_J,axiom,
% 0.25/0.48 ! [Y: a,V: nat] :
% 0.25/0.48 ( ( polyno562434098cmul_a @ Y @ ( polyno2024845497ound_a @ V ) )
% 0.25/0.48 = ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ Y ) @ ( polyno2024845497ound_a @ V ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(3)
% 0.25/0.48 thf(fact_76_poly__cmul_Osimps_I3_J,axiom,
% 0.25/0.48 ! [Y: nat,V: nat] :
% 0.25/0.48 ( ( polyno1467023772ul_nat @ Y @ ( polyno1999838549nd_nat @ V ) )
% 0.25/0.48 = ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ Y ) @ ( polyno1999838549nd_nat @ V ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(3)
% 0.25/0.48 thf(fact_77_poly_Odistinct_I25_J,axiom,
% 0.25/0.48 ! [X2: nat,X81: polyno727731844poly_a,X82: nat,X83: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno2024845497ound_a @ X2 )
% 0.25/0.48 != ( polyno1057396216e_CN_a @ X81 @ X82 @ X83 ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly.distinct(25)
% 0.25/0.48 thf(fact_78_poly_Odistinct_I25_J,axiom,
% 0.25/0.48 ! [X2: nat,X81: polyno1532895200ly_nat,X82: nat,X83: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno1999838549nd_nat @ X2 )
% 0.25/0.48 != ( polyno720942678CN_nat @ X81 @ X82 @ X83 ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly.distinct(25)
% 0.25/0.48 thf(fact_79_poly_Odistinct_I1_J,axiom,
% 0.25/0.48 ! [X1: a,X2: nat] :
% 0.25/0.48 ( ( polyno439679028le_C_a @ X1 )
% 0.25/0.48 != ( polyno2024845497ound_a @ X2 ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly.distinct(1)
% 0.25/0.48 thf(fact_80_poly_Odistinct_I1_J,axiom,
% 0.25/0.48 ! [X1: nat,X2: nat] :
% 0.25/0.48 ( ( polyno2122022170_C_nat @ X1 )
% 0.25/0.48 != ( polyno1999838549nd_nat @ X2 ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly.distinct(1)
% 0.25/0.48 thf(fact_81_poly_Odistinct_I19_J,axiom,
% 0.25/0.48 ! [X2: nat,X51: polyno1532895200ly_nat,X52: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno1999838549nd_nat @ X2 )
% 0.25/0.48 != ( polyno1415441627ul_nat @ X51 @ X52 ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly.distinct(19)
% 0.25/0.48 thf(fact_82_poly_Odistinct_I19_J,axiom,
% 0.25/0.48 ! [X2: nat,X51: polyno727731844poly_a,X52: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno2024845497ound_a @ X2 )
% 0.25/0.48 != ( polyno1491482291_Mul_a @ X51 @ X52 ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly.distinct(19)
% 0.25/0.48 thf(fact_83_poly_Odistinct_I15_J,axiom,
% 0.25/0.48 ! [X2: nat,X31: polyno727731844poly_a,X32: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno2024845497ound_a @ X2 )
% 0.25/0.48 != ( polyno1623170614_Add_a @ X31 @ X32 ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly.distinct(15)
% 0.25/0.48 thf(fact_84_poly_Odistinct_I15_J,axiom,
% 0.25/0.48 ! [X2: nat,X31: polyno1532895200ly_nat,X32: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno1999838549nd_nat @ X2 )
% 0.25/0.48 != ( polyno1222032024dd_nat @ X31 @ X32 ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly.distinct(15)
% 0.25/0.48 thf(fact_85_isnpolyh_Osimps_I3_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno892049031yh_nat @ ( polyno1999838549nd_nat @ V ) )
% 0.25/0.48 = ( ^ [K: nat] : $false ) ) ).
% 0.25/0.48
% 0.25/0.48 % isnpolyh.simps(3)
% 0.25/0.48 thf(fact_86_isnpolyh_Osimps_I3_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ ( polyno2024845497ound_a @ V ) )
% 0.25/0.48 = ( ^ [K: nat] : $false ) ) ).
% 0.25/0.48
% 0.25/0.48 % isnpolyh.simps(3)
% 0.25/0.48 thf(fact_87_poly__cmul_Osimps_I2_J,axiom,
% 0.25/0.48 ! [Y: a,C: polyno727731844poly_a,N: nat,P: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno562434098cmul_a @ Y @ ( polyno1057396216e_CN_a @ C @ N @ P ) )
% 0.25/0.48 = ( polyno1057396216e_CN_a @ ( polyno562434098cmul_a @ Y @ C ) @ N @ ( polyno562434098cmul_a @ Y @ P ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(2)
% 0.25/0.48 thf(fact_88_poly__cmul_Osimps_I2_J,axiom,
% 0.25/0.48 ! [Y: nat,C: polyno1532895200ly_nat,N: nat,P: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno1467023772ul_nat @ Y @ ( polyno720942678CN_nat @ C @ N @ P ) )
% 0.25/0.48 = ( polyno720942678CN_nat @ ( polyno1467023772ul_nat @ Y @ C ) @ N @ ( polyno1467023772ul_nat @ Y @ P ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(2)
% 0.25/0.48 thf(fact_89_polymul_Osimps_I17_J,axiom,
% 0.25/0.48 ! [A: polyno1532895200ly_nat,V: nat] :
% 0.25/0.48 ( ( polyno929799083ul_nat @ A @ ( polyno1999838549nd_nat @ V ) )
% 0.25/0.48 = ( polyno1415441627ul_nat @ A @ ( polyno1999838549nd_nat @ V ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(17)
% 0.25/0.48 thf(fact_90_polymul_Osimps_I17_J,axiom,
% 0.25/0.48 ! [A: polyno727731844poly_a,V: nat] :
% 0.25/0.48 ( ( polyno1934269411ymul_a @ A @ ( polyno2024845497ound_a @ V ) )
% 0.25/0.48 = ( polyno1491482291_Mul_a @ A @ ( polyno2024845497ound_a @ V ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(17)
% 0.25/0.48 thf(fact_91_polymul_Osimps_I5_J,axiom,
% 0.25/0.48 ! [V: nat,B: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno929799083ul_nat @ ( polyno1999838549nd_nat @ V ) @ B )
% 0.25/0.48 = ( polyno1415441627ul_nat @ ( polyno1999838549nd_nat @ V ) @ B ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(5)
% 0.25/0.48 thf(fact_92_polymul_Osimps_I5_J,axiom,
% 0.25/0.48 ! [V: nat,B: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1934269411ymul_a @ ( polyno2024845497ound_a @ V ) @ B )
% 0.25/0.48 = ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ V ) @ B ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(5)
% 0.25/0.48 thf(fact_93_poly__cmul_Osimps_I1_J,axiom,
% 0.25/0.48 ! [Y: a,X: a] :
% 0.25/0.48 ( ( polyno562434098cmul_a @ Y @ ( polyno439679028le_C_a @ X ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ ( times_times_a @ Y @ X ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(1)
% 0.25/0.48 thf(fact_94_poly__cmul_Osimps_I1_J,axiom,
% 0.25/0.48 ! [Y: nat,X: nat] :
% 0.25/0.48 ( ( polyno1467023772ul_nat @ Y @ ( polyno2122022170_C_nat @ X ) )
% 0.25/0.48 = ( polyno2122022170_C_nat @ ( times_times_nat @ Y @ X ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(1)
% 0.25/0.48 thf(fact_95_one__normh,axiom,
% 0.25/0.48 ! [N: nat] : ( polyno892049031yh_nat @ ( polyno2122022170_C_nat @ one_one_nat ) @ N ) ).
% 0.25/0.48
% 0.25/0.48 % one_normh
% 0.25/0.48 thf(fact_96_one__normh,axiom,
% 0.25/0.48 ! [N: nat] : ( polyno1372495879olyh_a @ ( polyno439679028le_C_a @ one_one_a ) @ N ) ).
% 0.25/0.48
% 0.25/0.48 % one_normh
% 0.25/0.48 thf(fact_97_zero__normh,axiom,
% 0.25/0.48 ! [N: nat] : ( polyno892049031yh_nat @ ( polyno2122022170_C_nat @ zero_zero_nat ) @ N ) ).
% 0.25/0.48
% 0.25/0.48 % zero_normh
% 0.25/0.48 thf(fact_98_zero__normh,axiom,
% 0.25/0.48 ! [N: nat] : ( polyno1372495879olyh_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ N ) ).
% 0.25/0.48
% 0.25/0.48 % zero_normh
% 0.25/0.48 thf(fact_99_isnpoly__def,axiom,
% 0.25/0.48 ( polyno1013235523ly_nat
% 0.25/0.48 = ( ^ [P2: polyno1532895200ly_nat] : ( polyno892049031yh_nat @ P2 @ zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % isnpoly_def
% 0.25/0.48 thf(fact_100_isnpoly__def,axiom,
% 0.25/0.48 ( polyno190918219poly_a
% 0.25/0.48 = ( ^ [P2: polyno727731844poly_a] : ( polyno1372495879olyh_a @ P2 @ zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % isnpoly_def
% 0.25/0.48 thf(fact_101_polymul_Osimps_I11_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat,Vc: nat] :
% 0.25/0.48 ( ( polyno929799083ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno1999838549nd_nat @ Vc ) )
% 0.25/0.48 = ( polyno1415441627ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno1999838549nd_nat @ Vc ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(11)
% 0.25/0.48 thf(fact_102_polymul_Osimps_I11_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a,Vc: nat] :
% 0.25/0.48 ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno2024845497ound_a @ Vc ) )
% 0.25/0.48 = ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno2024845497ound_a @ Vc ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(11)
% 0.25/0.48 thf(fact_103_polymul_Osimps_I23_J,axiom,
% 0.25/0.48 ! [Vc: nat,V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno929799083ul_nat @ ( polyno1999838549nd_nat @ Vc ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) )
% 0.25/0.48 = ( polyno1415441627ul_nat @ ( polyno1999838549nd_nat @ Vc ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(23)
% 0.25/0.48 thf(fact_104_polymul_Osimps_I23_J,axiom,
% 0.25/0.48 ! [Vc: nat,V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1934269411ymul_a @ ( polyno2024845497ound_a @ Vc ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) )
% 0.25/0.48 = ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ Vc ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(23)
% 0.25/0.48 thf(fact_105_polymul_Osimps_I2_J,axiom,
% 0.25/0.48 ! [C: a,C2: polyno727731844poly_a,N2: nat,P3: polyno727731844poly_a] :
% 0.25/0.48 ( ( ( C = zero_zero_a )
% 0.25/0.48 => ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ C ) @ ( polyno1057396216e_CN_a @ C2 @ N2 @ P3 ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) )
% 0.25/0.48 & ( ( C != zero_zero_a )
% 0.25/0.48 => ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ C ) @ ( polyno1057396216e_CN_a @ C2 @ N2 @ P3 ) )
% 0.25/0.48 = ( polyno1057396216e_CN_a @ ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ C ) @ C2 ) @ N2 @ ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ C ) @ P3 ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(2)
% 0.25/0.48 thf(fact_106_polymul_Osimps_I2_J,axiom,
% 0.25/0.48 ! [C: nat,C2: polyno1532895200ly_nat,N2: nat,P3: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( ( C = zero_zero_nat )
% 0.25/0.48 => ( ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ C ) @ ( polyno720942678CN_nat @ C2 @ N2 @ P3 ) )
% 0.25/0.48 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) )
% 0.25/0.48 & ( ( C != zero_zero_nat )
% 0.25/0.48 => ( ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ C ) @ ( polyno720942678CN_nat @ C2 @ N2 @ P3 ) )
% 0.25/0.48 = ( polyno720942678CN_nat @ ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ C ) @ C2 ) @ N2 @ ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ C ) @ P3 ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(2)
% 0.25/0.48 thf(fact_107_mult__cancel__left1,axiom,
% 0.25/0.48 ! [C: a,B: a] :
% 0.25/0.48 ( ( C
% 0.25/0.48 = ( times_times_a @ C @ B ) )
% 0.25/0.48 = ( ( C = zero_zero_a )
% 0.25/0.48 | ( B = one_one_a ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_cancel_left1
% 0.25/0.48 thf(fact_108_mult__cancel__left2,axiom,
% 0.25/0.48 ! [C: a,A: a] :
% 0.25/0.48 ( ( ( times_times_a @ C @ A )
% 0.25/0.48 = C )
% 0.25/0.48 = ( ( C = zero_zero_a )
% 0.25/0.48 | ( A = one_one_a ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_cancel_left2
% 0.25/0.48 thf(fact_109_mult__cancel__right1,axiom,
% 0.25/0.48 ! [C: a,B: a] :
% 0.25/0.48 ( ( C
% 0.25/0.48 = ( times_times_a @ B @ C ) )
% 0.25/0.48 = ( ( C = zero_zero_a )
% 0.25/0.48 | ( B = one_one_a ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_cancel_right1
% 0.25/0.48 thf(fact_110_mult__cancel__right2,axiom,
% 0.25/0.48 ! [A: a,C: a] :
% 0.25/0.48 ( ( ( times_times_a @ A @ C )
% 0.25/0.48 = C )
% 0.25/0.48 = ( ( C = zero_zero_a )
% 0.25/0.48 | ( A = one_one_a ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_cancel_right2
% 0.25/0.48 thf(fact_111_mult_Oright__neutral,axiom,
% 0.25/0.48 ! [A: nat] :
% 0.25/0.48 ( ( times_times_nat @ A @ one_one_nat )
% 0.25/0.48 = A ) ).
% 0.25/0.48
% 0.25/0.48 % mult.right_neutral
% 0.25/0.48 thf(fact_112_mult_Oright__neutral,axiom,
% 0.25/0.48 ! [A: a] :
% 0.25/0.48 ( ( times_times_a @ A @ one_one_a )
% 0.25/0.48 = A ) ).
% 0.25/0.48
% 0.25/0.48 % mult.right_neutral
% 0.25/0.48 thf(fact_113_mult_Oleft__neutral,axiom,
% 0.25/0.48 ! [A: nat] :
% 0.25/0.48 ( ( times_times_nat @ one_one_nat @ A )
% 0.25/0.48 = A ) ).
% 0.25/0.48
% 0.25/0.48 % mult.left_neutral
% 0.25/0.48 thf(fact_114_mult_Oleft__neutral,axiom,
% 0.25/0.48 ! [A: a] :
% 0.25/0.48 ( ( times_times_a @ one_one_a @ A )
% 0.25/0.48 = A ) ).
% 0.25/0.48
% 0.25/0.48 % mult.left_neutral
% 0.25/0.48 thf(fact_115_mult__cancel__right,axiom,
% 0.25/0.48 ! [A: nat,C: nat,B: nat] :
% 0.25/0.48 ( ( ( times_times_nat @ A @ C )
% 0.25/0.48 = ( times_times_nat @ B @ C ) )
% 0.25/0.48 = ( ( C = zero_zero_nat )
% 0.25/0.48 | ( A = B ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_cancel_right
% 0.25/0.48 thf(fact_116_mult__cancel__right,axiom,
% 0.25/0.48 ! [A: a,C: a,B: a] :
% 0.25/0.48 ( ( ( times_times_a @ A @ C )
% 0.25/0.48 = ( times_times_a @ B @ C ) )
% 0.25/0.48 = ( ( C = zero_zero_a )
% 0.25/0.48 | ( A = B ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_cancel_right
% 0.25/0.48 thf(fact_117_mult__cancel__left,axiom,
% 0.25/0.48 ! [C: nat,A: nat,B: nat] :
% 0.25/0.48 ( ( ( times_times_nat @ C @ A )
% 0.25/0.48 = ( times_times_nat @ C @ B ) )
% 0.25/0.48 = ( ( C = zero_zero_nat )
% 0.25/0.48 | ( A = B ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_cancel_left
% 0.25/0.48 thf(fact_118_mult__cancel__left,axiom,
% 0.25/0.48 ! [C: a,A: a,B: a] :
% 0.25/0.48 ( ( ( times_times_a @ C @ A )
% 0.25/0.48 = ( times_times_a @ C @ B ) )
% 0.25/0.48 = ( ( C = zero_zero_a )
% 0.25/0.48 | ( A = B ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_cancel_left
% 0.25/0.48 thf(fact_119_mult__zero__left,axiom,
% 0.25/0.48 ! [A: nat] :
% 0.25/0.48 ( ( times_times_nat @ zero_zero_nat @ A )
% 0.25/0.48 = zero_zero_nat ) ).
% 0.25/0.48
% 0.25/0.48 % mult_zero_left
% 0.25/0.48 thf(fact_120_mult__zero__left,axiom,
% 0.25/0.48 ! [A: a] :
% 0.25/0.48 ( ( times_times_a @ zero_zero_a @ A )
% 0.25/0.48 = zero_zero_a ) ).
% 0.25/0.48
% 0.25/0.48 % mult_zero_left
% 0.25/0.48 thf(fact_121_mult__zero__right,axiom,
% 0.25/0.48 ! [A: nat] :
% 0.25/0.48 ( ( times_times_nat @ A @ zero_zero_nat )
% 0.25/0.48 = zero_zero_nat ) ).
% 0.25/0.48
% 0.25/0.48 % mult_zero_right
% 0.25/0.48 thf(fact_122_mult__zero__right,axiom,
% 0.25/0.48 ! [A: a] :
% 0.25/0.48 ( ( times_times_a @ A @ zero_zero_a )
% 0.25/0.48 = zero_zero_a ) ).
% 0.25/0.48
% 0.25/0.48 % mult_zero_right
% 0.25/0.48 thf(fact_123_mult__eq__0__iff,axiom,
% 0.25/0.48 ! [A: nat,B: nat] :
% 0.25/0.48 ( ( ( times_times_nat @ A @ B )
% 0.25/0.48 = zero_zero_nat )
% 0.25/0.48 = ( ( A = zero_zero_nat )
% 0.25/0.48 | ( B = zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_eq_0_iff
% 0.25/0.48 thf(fact_124_mult__eq__0__iff,axiom,
% 0.25/0.48 ! [A: a,B: a] :
% 0.25/0.48 ( ( ( times_times_a @ A @ B )
% 0.25/0.48 = zero_zero_a )
% 0.25/0.48 = ( ( A = zero_zero_a )
% 0.25/0.48 | ( B = zero_zero_a ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_eq_0_iff
% 0.25/0.48 thf(fact_125_zero__reorient,axiom,
% 0.25/0.48 ! [X: a] :
% 0.25/0.48 ( ( zero_zero_a = X )
% 0.25/0.48 = ( X = zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % zero_reorient
% 0.25/0.48 thf(fact_126_zero__reorient,axiom,
% 0.25/0.48 ! [X: nat] :
% 0.25/0.48 ( ( zero_zero_nat = X )
% 0.25/0.48 = ( X = zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % zero_reorient
% 0.25/0.48 thf(fact_127_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.25/0.48 ! [A: nat,B: nat,C: nat] :
% 0.25/0.48 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.25/0.48 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % ab_semigroup_mult_class.mult_ac(1)
% 0.25/0.48 thf(fact_128_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.25/0.48 ! [A: a,B: a,C: a] :
% 0.25/0.48 ( ( times_times_a @ ( times_times_a @ A @ B ) @ C )
% 0.25/0.48 = ( times_times_a @ A @ ( times_times_a @ B @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % ab_semigroup_mult_class.mult_ac(1)
% 0.25/0.48 thf(fact_129_mult_Oassoc,axiom,
% 0.25/0.48 ! [A: nat,B: nat,C: nat] :
% 0.25/0.48 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.25/0.48 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult.assoc
% 0.25/0.48 thf(fact_130_mult_Oassoc,axiom,
% 0.25/0.48 ! [A: a,B: a,C: a] :
% 0.25/0.48 ( ( times_times_a @ ( times_times_a @ A @ B ) @ C )
% 0.25/0.48 = ( times_times_a @ A @ ( times_times_a @ B @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult.assoc
% 0.25/0.48 thf(fact_131_mult_Ocommute,axiom,
% 0.25/0.48 ( times_times_nat
% 0.25/0.48 = ( ^ [A2: nat,B2: nat] : ( times_times_nat @ B2 @ A2 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult.commute
% 0.25/0.48 thf(fact_132_mult_Ocommute,axiom,
% 0.25/0.48 ( times_times_a
% 0.25/0.48 = ( ^ [A2: a,B2: a] : ( times_times_a @ B2 @ A2 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult.commute
% 0.25/0.48 thf(fact_133_mult_Oleft__commute,axiom,
% 0.25/0.48 ! [B: nat,A: nat,C: nat] :
% 0.25/0.48 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 0.25/0.48 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult.left_commute
% 0.25/0.48 thf(fact_134_mult_Oleft__commute,axiom,
% 0.25/0.48 ! [B: a,A: a,C: a] :
% 0.25/0.48 ( ( times_times_a @ B @ ( times_times_a @ A @ C ) )
% 0.25/0.48 = ( times_times_a @ A @ ( times_times_a @ B @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult.left_commute
% 0.25/0.48 thf(fact_135_one__reorient,axiom,
% 0.25/0.48 ! [X: a] :
% 0.25/0.48 ( ( one_one_a = X )
% 0.25/0.48 = ( X = one_one_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % one_reorient
% 0.25/0.48 thf(fact_136_one__reorient,axiom,
% 0.25/0.48 ! [X: nat] :
% 0.25/0.48 ( ( one_one_nat = X )
% 0.25/0.48 = ( X = one_one_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % one_reorient
% 0.25/0.48 thf(fact_137_mult__not__zero,axiom,
% 0.25/0.48 ! [A: nat,B: nat] :
% 0.25/0.48 ( ( ( times_times_nat @ A @ B )
% 0.25/0.48 != zero_zero_nat )
% 0.25/0.48 => ( ( A != zero_zero_nat )
% 0.25/0.48 & ( B != zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_not_zero
% 0.25/0.48 thf(fact_138_mult__not__zero,axiom,
% 0.25/0.48 ! [A: a,B: a] :
% 0.25/0.48 ( ( ( times_times_a @ A @ B )
% 0.25/0.48 != zero_zero_a )
% 0.25/0.48 => ( ( A != zero_zero_a )
% 0.25/0.48 & ( B != zero_zero_a ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_not_zero
% 0.25/0.48 thf(fact_139_divisors__zero,axiom,
% 0.25/0.48 ! [A: nat,B: nat] :
% 0.25/0.48 ( ( ( times_times_nat @ A @ B )
% 0.25/0.48 = zero_zero_nat )
% 0.25/0.48 => ( ( A = zero_zero_nat )
% 0.25/0.48 | ( B = zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % divisors_zero
% 0.25/0.48 thf(fact_140_divisors__zero,axiom,
% 0.25/0.48 ! [A: a,B: a] :
% 0.25/0.48 ( ( ( times_times_a @ A @ B )
% 0.25/0.48 = zero_zero_a )
% 0.25/0.48 => ( ( A = zero_zero_a )
% 0.25/0.48 | ( B = zero_zero_a ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % divisors_zero
% 0.25/0.48 thf(fact_141_no__zero__divisors,axiom,
% 0.25/0.48 ! [A: nat,B: nat] :
% 0.25/0.48 ( ( A != zero_zero_nat )
% 0.25/0.48 => ( ( B != zero_zero_nat )
% 0.25/0.48 => ( ( times_times_nat @ A @ B )
% 0.25/0.48 != zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % no_zero_divisors
% 0.25/0.48 thf(fact_142_no__zero__divisors,axiom,
% 0.25/0.48 ! [A: a,B: a] :
% 0.25/0.48 ( ( A != zero_zero_a )
% 0.25/0.48 => ( ( B != zero_zero_a )
% 0.25/0.48 => ( ( times_times_a @ A @ B )
% 0.25/0.48 != zero_zero_a ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % no_zero_divisors
% 0.25/0.48 thf(fact_143_mult__left__cancel,axiom,
% 0.25/0.48 ! [C: nat,A: nat,B: nat] :
% 0.25/0.48 ( ( C != zero_zero_nat )
% 0.25/0.48 => ( ( ( times_times_nat @ C @ A )
% 0.25/0.48 = ( times_times_nat @ C @ B ) )
% 0.25/0.48 = ( A = B ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_left_cancel
% 0.25/0.48 thf(fact_144_mult__left__cancel,axiom,
% 0.25/0.48 ! [C: a,A: a,B: a] :
% 0.25/0.48 ( ( C != zero_zero_a )
% 0.25/0.48 => ( ( ( times_times_a @ C @ A )
% 0.25/0.48 = ( times_times_a @ C @ B ) )
% 0.25/0.48 = ( A = B ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_left_cancel
% 0.25/0.48 thf(fact_145_mult__right__cancel,axiom,
% 0.25/0.48 ! [C: nat,A: nat,B: nat] :
% 0.25/0.48 ( ( C != zero_zero_nat )
% 0.25/0.48 => ( ( ( times_times_nat @ A @ C )
% 0.25/0.48 = ( times_times_nat @ B @ C ) )
% 0.25/0.48 = ( A = B ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_right_cancel
% 0.25/0.48 thf(fact_146_mult__right__cancel,axiom,
% 0.25/0.48 ! [C: a,A: a,B: a] :
% 0.25/0.48 ( ( C != zero_zero_a )
% 0.25/0.48 => ( ( ( times_times_a @ A @ C )
% 0.25/0.48 = ( times_times_a @ B @ C ) )
% 0.25/0.48 = ( A = B ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_right_cancel
% 0.25/0.48 thf(fact_147_zero__neq__one,axiom,
% 0.25/0.48 zero_zero_a != one_one_a ).
% 0.25/0.48
% 0.25/0.48 % zero_neq_one
% 0.25/0.48 thf(fact_148_zero__neq__one,axiom,
% 0.25/0.48 zero_zero_nat != one_one_nat ).
% 0.25/0.48
% 0.25/0.48 % zero_neq_one
% 0.25/0.48 thf(fact_149_comm__monoid__mult__class_Omult__1,axiom,
% 0.25/0.48 ! [A: nat] :
% 0.25/0.48 ( ( times_times_nat @ one_one_nat @ A )
% 0.25/0.48 = A ) ).
% 0.25/0.48
% 0.25/0.48 % comm_monoid_mult_class.mult_1
% 0.25/0.48 thf(fact_150_comm__monoid__mult__class_Omult__1,axiom,
% 0.25/0.48 ! [A: a] :
% 0.25/0.48 ( ( times_times_a @ one_one_a @ A )
% 0.25/0.48 = A ) ).
% 0.25/0.48
% 0.25/0.48 % comm_monoid_mult_class.mult_1
% 0.25/0.48 thf(fact_151_mult_Ocomm__neutral,axiom,
% 0.25/0.48 ! [A: nat] :
% 0.25/0.48 ( ( times_times_nat @ A @ one_one_nat )
% 0.25/0.48 = A ) ).
% 0.25/0.48
% 0.25/0.48 % mult.comm_neutral
% 0.25/0.48 thf(fact_152_mult_Ocomm__neutral,axiom,
% 0.25/0.48 ! [A: a] :
% 0.25/0.48 ( ( times_times_a @ A @ one_one_a )
% 0.25/0.48 = A ) ).
% 0.25/0.48
% 0.25/0.48 % mult.comm_neutral
% 0.25/0.48 thf(fact_153_mult__is__0,axiom,
% 0.25/0.48 ! [M: nat,N: nat] :
% 0.25/0.48 ( ( ( times_times_nat @ M @ N )
% 0.25/0.48 = zero_zero_nat )
% 0.25/0.48 = ( ( M = zero_zero_nat )
% 0.25/0.48 | ( N = zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_is_0
% 0.25/0.48 thf(fact_154_mult__0__right,axiom,
% 0.25/0.48 ! [M: nat] :
% 0.25/0.48 ( ( times_times_nat @ M @ zero_zero_nat )
% 0.25/0.48 = zero_zero_nat ) ).
% 0.25/0.48
% 0.25/0.48 % mult_0_right
% 0.25/0.48 thf(fact_155_mult__cancel1,axiom,
% 0.25/0.48 ! [K2: nat,M: nat,N: nat] :
% 0.25/0.48 ( ( ( times_times_nat @ K2 @ M )
% 0.25/0.48 = ( times_times_nat @ K2 @ N ) )
% 0.25/0.48 = ( ( M = N )
% 0.25/0.48 | ( K2 = zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_cancel1
% 0.25/0.48 thf(fact_156_mult__cancel2,axiom,
% 0.25/0.48 ! [M: nat,K2: nat,N: nat] :
% 0.25/0.48 ( ( ( times_times_nat @ M @ K2 )
% 0.25/0.48 = ( times_times_nat @ N @ K2 ) )
% 0.25/0.48 = ( ( M = N )
% 0.25/0.48 | ( K2 = zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_cancel2
% 0.25/0.48 thf(fact_157_shift1,axiom,
% 0.25/0.48 ! [Bs2: list_a,P: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno422358502poly_a @ Bs2 @ ( polyno784948432ift1_a @ P ) )
% 0.25/0.48 = ( polyno422358502poly_a @ Bs2 @ ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ zero_zero_nat ) @ P ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % shift1
% 0.25/0.48 thf(fact_158_shift1__isnpolyh,axiom,
% 0.25/0.48 ! [P: polyno1532895200ly_nat,N0: nat] :
% 0.25/0.48 ( ( polyno892049031yh_nat @ P @ N0 )
% 0.25/0.48 => ( ( P
% 0.25/0.48 != ( polyno2122022170_C_nat @ zero_zero_nat ) )
% 0.25/0.48 => ( polyno892049031yh_nat @ ( polyno1964927358t1_nat @ P ) @ zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % shift1_isnpolyh
% 0.25/0.48 thf(fact_159_shift1__isnpolyh,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N0: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N0 )
% 0.25/0.48 => ( ( P
% 0.25/0.48 != ( polyno439679028le_C_a @ zero_zero_a ) )
% 0.25/0.48 => ( polyno1372495879olyh_a @ ( polyno784948432ift1_a @ P ) @ zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % shift1_isnpolyh
% 0.25/0.48 thf(fact_160_nat__mult__eq__1__iff,axiom,
% 0.25/0.48 ! [M: nat,N: nat] :
% 0.25/0.48 ( ( ( times_times_nat @ M @ N )
% 0.25/0.48 = one_one_nat )
% 0.25/0.48 = ( ( M = one_one_nat )
% 0.25/0.48 & ( N = one_one_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % nat_mult_eq_1_iff
% 0.25/0.48 thf(fact_161_nat__1__eq__mult__iff,axiom,
% 0.25/0.48 ! [M: nat,N: nat] :
% 0.25/0.48 ( ( one_one_nat
% 0.25/0.48 = ( times_times_nat @ M @ N ) )
% 0.25/0.48 = ( ( M = one_one_nat )
% 0.25/0.48 & ( N = one_one_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % nat_1_eq_mult_iff
% 0.25/0.48 thf(fact_162_nat__mult__1__right,axiom,
% 0.25/0.48 ! [N: nat] :
% 0.25/0.48 ( ( times_times_nat @ N @ one_one_nat )
% 0.25/0.48 = N ) ).
% 0.25/0.48
% 0.25/0.48 % nat_mult_1_right
% 0.25/0.48 thf(fact_163_nat__mult__1,axiom,
% 0.25/0.48 ! [N: nat] :
% 0.25/0.48 ( ( times_times_nat @ one_one_nat @ N )
% 0.25/0.48 = N ) ).
% 0.25/0.48
% 0.25/0.48 % nat_mult_1
% 0.25/0.48 thf(fact_164_mult__eq__self__implies__10,axiom,
% 0.25/0.48 ! [M: nat,N: nat] :
% 0.25/0.48 ( ( M
% 0.25/0.48 = ( times_times_nat @ M @ N ) )
% 0.25/0.48 => ( ( N = one_one_nat )
% 0.25/0.48 | ( M = zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_eq_self_implies_10
% 0.25/0.48 thf(fact_165_mult__0,axiom,
% 0.25/0.48 ! [N: nat] :
% 0.25/0.48 ( ( times_times_nat @ zero_zero_nat @ N )
% 0.25/0.48 = zero_zero_nat ) ).
% 0.25/0.48
% 0.25/0.48 % mult_0
% 0.25/0.48 thf(fact_166_shift1__nz,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno784948432ift1_a @ P )
% 0.25/0.48 != ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % shift1_nz
% 0.25/0.48 thf(fact_167_shift1__nz,axiom,
% 0.25/0.48 ! [P: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno1964927358t1_nat @ P )
% 0.25/0.48 != ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % shift1_nz
% 0.25/0.48 thf(fact_168_shift1__isnpoly,axiom,
% 0.25/0.48 ! [P: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno1013235523ly_nat @ P )
% 0.25/0.48 => ( ( P
% 0.25/0.48 != ( polyno2122022170_C_nat @ zero_zero_nat ) )
% 0.25/0.48 => ( polyno1013235523ly_nat @ ( polyno1964927358t1_nat @ P ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % shift1_isnpoly
% 0.25/0.48 thf(fact_169_shift1__isnpoly,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno190918219poly_a @ P )
% 0.25/0.48 => ( ( P
% 0.25/0.48 != ( polyno439679028le_C_a @ zero_zero_a ) )
% 0.25/0.48 => ( polyno190918219poly_a @ ( polyno784948432ift1_a @ P ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % shift1_isnpoly
% 0.25/0.48 thf(fact_170_shift1__def,axiom,
% 0.25/0.48 ( polyno784948432ift1_a
% 0.25/0.48 = ( polyno1057396216e_CN_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % shift1_def
% 0.25/0.48 thf(fact_171_shift1__def,axiom,
% 0.25/0.48 ( polyno1964927358t1_nat
% 0.25/0.48 = ( polyno720942678CN_nat @ ( polyno2122022170_C_nat @ zero_zero_nat ) @ zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % shift1_def
% 0.25/0.48 thf(fact_172_nat__mult__eq__cancel__disj,axiom,
% 0.25/0.48 ! [K2: nat,M: nat,N: nat] :
% 0.25/0.48 ( ( ( times_times_nat @ K2 @ M )
% 0.25/0.48 = ( times_times_nat @ K2 @ N ) )
% 0.25/0.48 = ( ( K2 = zero_zero_nat )
% 0.25/0.48 | ( M = N ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % nat_mult_eq_cancel_disj
% 0.25/0.48 thf(fact_173_headn__nz,axiom,
% 0.25/0.48 ! [P: polyno1532895200ly_nat,N0: nat,M: nat] :
% 0.25/0.48 ( ( polyno892049031yh_nat @ P @ N0 )
% 0.25/0.48 => ( ( ( polyno544860353dn_nat @ P @ M )
% 0.25/0.48 = ( polyno2122022170_C_nat @ zero_zero_nat ) )
% 0.25/0.48 = ( P
% 0.25/0.48 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % headn_nz
% 0.25/0.48 thf(fact_174_headn__nz,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N0: nat,M: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N0 )
% 0.25/0.48 => ( ( ( polyno567601229eadn_a @ P @ M )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) )
% 0.25/0.48 = ( P
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % headn_nz
% 0.25/0.48 thf(fact_175_headconst__zero,axiom,
% 0.25/0.48 ! [P: polyno1532895200ly_nat,N0: nat] :
% 0.25/0.48 ( ( polyno892049031yh_nat @ P @ N0 )
% 0.25/0.48 => ( ( ( polyno524777654st_nat @ P )
% 0.25/0.48 = zero_zero_nat )
% 0.25/0.48 = ( P
% 0.25/0.48 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % headconst_zero
% 0.25/0.48 thf(fact_176_headconst__zero,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N0: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N0 )
% 0.25/0.48 => ( ( ( polyno2115742616onst_a @ P )
% 0.25/0.48 = zero_zero_a )
% 0.25/0.48 = ( P
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % headconst_zero
% 0.25/0.48 thf(fact_177_polysub__same__0,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N0: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N0 )
% 0.25/0.48 => ( ( polyno1418491367ysub_a @ P @ P )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polysub_same_0
% 0.25/0.48 thf(fact_178_polysubst0_Osimps_I8_J,axiom,
% 0.25/0.48 ! [N: nat,T: polyno1532895200ly_nat,C: polyno1532895200ly_nat,P: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( ( N = zero_zero_nat )
% 0.25/0.48 => ( ( polyno336795754t0_nat @ T @ ( polyno720942678CN_nat @ C @ N @ P ) )
% 0.25/0.48 = ( polyno1222032024dd_nat @ ( polyno336795754t0_nat @ T @ C ) @ ( polyno1415441627ul_nat @ T @ ( polyno336795754t0_nat @ T @ P ) ) ) ) )
% 0.25/0.48 & ( ( N != zero_zero_nat )
% 0.25/0.48 => ( ( polyno336795754t0_nat @ T @ ( polyno720942678CN_nat @ C @ N @ P ) )
% 0.25/0.48 = ( polyno720942678CN_nat @ ( polyno336795754t0_nat @ T @ C ) @ N @ ( polyno336795754t0_nat @ T @ P ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polysubst0.simps(8)
% 0.25/0.48 thf(fact_179_polysubst0_Osimps_I8_J,axiom,
% 0.25/0.48 ! [N: nat,T: polyno727731844poly_a,C: polyno727731844poly_a,P: polyno727731844poly_a] :
% 0.25/0.48 ( ( ( N = zero_zero_nat )
% 0.25/0.48 => ( ( polyno1397854436bst0_a @ T @ ( polyno1057396216e_CN_a @ C @ N @ P ) )
% 0.25/0.48 = ( polyno1623170614_Add_a @ ( polyno1397854436bst0_a @ T @ C ) @ ( polyno1491482291_Mul_a @ T @ ( polyno1397854436bst0_a @ T @ P ) ) ) ) )
% 0.25/0.48 & ( ( N != zero_zero_nat )
% 0.25/0.48 => ( ( polyno1397854436bst0_a @ T @ ( polyno1057396216e_CN_a @ C @ N @ P ) )
% 0.25/0.48 = ( polyno1057396216e_CN_a @ ( polyno1397854436bst0_a @ T @ C ) @ N @ ( polyno1397854436bst0_a @ T @ P ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polysubst0.simps(8)
% 0.25/0.48 thf(fact_180_polysubst0_Osimps_I1_J,axiom,
% 0.25/0.48 ! [T: polyno727731844poly_a,C: a] :
% 0.25/0.48 ( ( polyno1397854436bst0_a @ T @ ( polyno439679028le_C_a @ C ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ C ) ) ).
% 0.25/0.48
% 0.25/0.48 % polysubst0.simps(1)
% 0.25/0.48 thf(fact_181_polysubst0_Osimps_I1_J,axiom,
% 0.25/0.48 ! [T: polyno1532895200ly_nat,C: nat] :
% 0.25/0.48 ( ( polyno336795754t0_nat @ T @ ( polyno2122022170_C_nat @ C ) )
% 0.25/0.48 = ( polyno2122022170_C_nat @ C ) ) ).
% 0.25/0.48
% 0.25/0.48 % polysubst0.simps(1)
% 0.25/0.48 thf(fact_182_polysubst0_Osimps_I6_J,axiom,
% 0.25/0.48 ! [T: polyno1532895200ly_nat,A: polyno1532895200ly_nat,B: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno336795754t0_nat @ T @ ( polyno1415441627ul_nat @ A @ B ) )
% 0.25/0.48 = ( polyno1415441627ul_nat @ ( polyno336795754t0_nat @ T @ A ) @ ( polyno336795754t0_nat @ T @ B ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polysubst0.simps(6)
% 0.25/0.48 thf(fact_183_polysubst0_Osimps_I6_J,axiom,
% 0.25/0.48 ! [T: polyno727731844poly_a,A: polyno727731844poly_a,B: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1397854436bst0_a @ T @ ( polyno1491482291_Mul_a @ A @ B ) )
% 0.25/0.48 = ( polyno1491482291_Mul_a @ ( polyno1397854436bst0_a @ T @ A ) @ ( polyno1397854436bst0_a @ T @ B ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polysubst0.simps(6)
% 0.25/0.48 thf(fact_184_polysubst0_Osimps_I4_J,axiom,
% 0.25/0.48 ! [T: polyno727731844poly_a,A: polyno727731844poly_a,B: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1397854436bst0_a @ T @ ( polyno1623170614_Add_a @ A @ B ) )
% 0.25/0.48 = ( polyno1623170614_Add_a @ ( polyno1397854436bst0_a @ T @ A ) @ ( polyno1397854436bst0_a @ T @ B ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polysubst0.simps(4)
% 0.25/0.48 thf(fact_185_polysubst0_Osimps_I4_J,axiom,
% 0.25/0.48 ! [T: polyno1532895200ly_nat,A: polyno1532895200ly_nat,B: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno336795754t0_nat @ T @ ( polyno1222032024dd_nat @ A @ B ) )
% 0.25/0.48 = ( polyno1222032024dd_nat @ ( polyno336795754t0_nat @ T @ A ) @ ( polyno336795754t0_nat @ T @ B ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polysubst0.simps(4)
% 0.25/0.48 thf(fact_186_headn_Osimps_I2_J,axiom,
% 0.25/0.48 ! [V: a] :
% 0.25/0.48 ( ( polyno567601229eadn_a @ ( polyno439679028le_C_a @ V ) )
% 0.25/0.48 = ( ^ [M2: nat] : ( polyno439679028le_C_a @ V ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % headn.simps(2)
% 0.25/0.48 thf(fact_187_headn_Osimps_I2_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno544860353dn_nat @ ( polyno2122022170_C_nat @ V ) )
% 0.25/0.48 = ( ^ [M2: nat] : ( polyno2122022170_C_nat @ V ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % headn.simps(2)
% 0.25/0.48 thf(fact_188_headn_Osimps_I6_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno544860353dn_nat @ ( polyno1415441627ul_nat @ V @ Va ) )
% 0.25/0.48 = ( ^ [M2: nat] : ( polyno1415441627ul_nat @ V @ Va ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % headn.simps(6)
% 0.25/0.48 thf(fact_189_headn_Osimps_I6_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno567601229eadn_a @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 0.25/0.48 = ( ^ [M2: nat] : ( polyno1491482291_Mul_a @ V @ Va ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % headn.simps(6)
% 0.25/0.48 thf(fact_190_headn_Osimps_I4_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno567601229eadn_a @ ( polyno1623170614_Add_a @ V @ Va ) )
% 0.25/0.48 = ( ^ [M2: nat] : ( polyno1623170614_Add_a @ V @ Va ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % headn.simps(4)
% 0.25/0.48 thf(fact_191_headn_Osimps_I4_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno544860353dn_nat @ ( polyno1222032024dd_nat @ V @ Va ) )
% 0.25/0.48 = ( ^ [M2: nat] : ( polyno1222032024dd_nat @ V @ Va ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % headn.simps(4)
% 0.25/0.48 thf(fact_192_headn_Osimps_I3_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno567601229eadn_a @ ( polyno2024845497ound_a @ V ) )
% 0.25/0.48 = ( ^ [M2: nat] : ( polyno2024845497ound_a @ V ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % headn.simps(3)
% 0.25/0.48 thf(fact_193_headn_Osimps_I3_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno544860353dn_nat @ ( polyno1999838549nd_nat @ V ) )
% 0.25/0.48 = ( ^ [M2: nat] : ( polyno1999838549nd_nat @ V ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % headn.simps(3)
% 0.25/0.48 thf(fact_194_wf__bs__polysub,axiom,
% 0.25/0.48 ! [Bs2: list_a,P: polyno727731844poly_a,Q: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno896877631f_bs_a @ Bs2 @ P )
% 0.25/0.48 => ( ( polyno896877631f_bs_a @ Bs2 @ Q )
% 0.25/0.48 => ( polyno896877631f_bs_a @ Bs2 @ ( polyno1418491367ysub_a @ P @ Q ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % wf_bs_polysub
% 0.25/0.48 thf(fact_195_polysub__norm,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,Q: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno190918219poly_a @ P )
% 0.25/0.48 => ( ( polyno190918219poly_a @ Q )
% 0.25/0.48 => ( polyno190918219poly_a @ ( polyno1418491367ysub_a @ P @ Q ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polysub_norm
% 0.25/0.48 thf(fact_196_headconst_Osimps_I1_J,axiom,
% 0.25/0.48 ! [C: polyno727731844poly_a,N: nat,P: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno2115742616onst_a @ ( polyno1057396216e_CN_a @ C @ N @ P ) )
% 0.25/0.48 = ( polyno2115742616onst_a @ P ) ) ).
% 0.25/0.48
% 0.25/0.48 % headconst.simps(1)
% 0.25/0.48 thf(fact_197_headconst_Osimps_I1_J,axiom,
% 0.25/0.48 ! [C: polyno1532895200ly_nat,N: nat,P: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno524777654st_nat @ ( polyno720942678CN_nat @ C @ N @ P ) )
% 0.25/0.48 = ( polyno524777654st_nat @ P ) ) ).
% 0.25/0.48
% 0.25/0.48 % headconst.simps(1)
% 0.25/0.48 thf(fact_198_headconst_Osimps_I2_J,axiom,
% 0.25/0.48 ! [N: a] :
% 0.25/0.48 ( ( polyno2115742616onst_a @ ( polyno439679028le_C_a @ N ) )
% 0.25/0.48 = N ) ).
% 0.25/0.48
% 0.25/0.48 % headconst.simps(2)
% 0.25/0.48 thf(fact_199_headconst_Osimps_I2_J,axiom,
% 0.25/0.48 ! [N: nat] :
% 0.25/0.48 ( ( polyno524777654st_nat @ ( polyno2122022170_C_nat @ N ) )
% 0.25/0.48 = N ) ).
% 0.25/0.48
% 0.25/0.48 % headconst.simps(2)
% 0.25/0.48 thf(fact_200_polysubst0_Osimps_I2_J,axiom,
% 0.25/0.48 ! [N: nat,T: polyno727731844poly_a] :
% 0.25/0.48 ( ( ( N = zero_zero_nat )
% 0.25/0.48 => ( ( polyno1397854436bst0_a @ T @ ( polyno2024845497ound_a @ N ) )
% 0.25/0.48 = T ) )
% 0.25/0.48 & ( ( N != zero_zero_nat )
% 0.25/0.48 => ( ( polyno1397854436bst0_a @ T @ ( polyno2024845497ound_a @ N ) )
% 0.25/0.48 = ( polyno2024845497ound_a @ N ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polysubst0.simps(2)
% 0.25/0.48 thf(fact_201_polysubst0_Osimps_I2_J,axiom,
% 0.25/0.48 ! [N: nat,T: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( ( N = zero_zero_nat )
% 0.25/0.48 => ( ( polyno336795754t0_nat @ T @ ( polyno1999838549nd_nat @ N ) )
% 0.25/0.48 = T ) )
% 0.25/0.48 & ( ( N != zero_zero_nat )
% 0.25/0.48 => ( ( polyno336795754t0_nat @ T @ ( polyno1999838549nd_nat @ N ) )
% 0.25/0.48 = ( polyno1999838549nd_nat @ N ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polysubst0.simps(2)
% 0.25/0.48 thf(fact_202_polysub__0,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N0: nat,Q: polyno727731844poly_a,N1: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N0 )
% 0.25/0.48 => ( ( polyno1372495879olyh_a @ Q @ N1 )
% 0.25/0.48 => ( ( ( polyno1418491367ysub_a @ P @ Q )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) )
% 0.25/0.48 = ( P = Q ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polysub_0
% 0.25/0.48 thf(fact_203_headnz,axiom,
% 0.25/0.48 ! [P: polyno1532895200ly_nat,N: nat,M: nat] :
% 0.25/0.48 ( ( polyno892049031yh_nat @ P @ N )
% 0.25/0.48 => ( ( P
% 0.25/0.48 != ( polyno2122022170_C_nat @ zero_zero_nat ) )
% 0.25/0.48 => ( ( polyno544860353dn_nat @ P @ M )
% 0.25/0.48 != ( polyno2122022170_C_nat @ zero_zero_nat ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % headnz
% 0.25/0.48 thf(fact_204_headnz,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N: nat,M: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N )
% 0.25/0.48 => ( ( P
% 0.25/0.48 != ( polyno439679028le_C_a @ zero_zero_a ) )
% 0.25/0.48 => ( ( polyno567601229eadn_a @ P @ M )
% 0.25/0.48 != ( polyno439679028le_C_a @ zero_zero_a ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % headnz
% 0.25/0.48 thf(fact_205_degree__npolyhCN,axiom,
% 0.25/0.48 ! [C: polyno1532895200ly_nat,N: nat,P: polyno1532895200ly_nat,N0: nat] :
% 0.25/0.48 ( ( polyno892049031yh_nat @ ( polyno720942678CN_nat @ C @ N @ P ) @ N0 )
% 0.25/0.48 => ( ( polyno220183259ee_nat @ C )
% 0.25/0.48 = zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % degree_npolyhCN
% 0.25/0.48 thf(fact_206_degree__npolyhCN,axiom,
% 0.25/0.48 ! [C: polyno727731844poly_a,N: nat,P: polyno727731844poly_a,N0: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ ( polyno1057396216e_CN_a @ C @ N @ P ) @ N0 )
% 0.25/0.48 => ( ( polyno578545843gree_a @ C )
% 0.25/0.48 = zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % degree_npolyhCN
% 0.25/0.48 thf(fact_207_poly__deriv_Osimps_I3_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno212464073eriv_a @ ( polyno2024845497ound_a @ V ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_deriv.simps(3)
% 0.25/0.48 thf(fact_208_poly__deriv_Osimps_I4_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno212464073eriv_a @ ( polyno1623170614_Add_a @ V @ Va ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_deriv.simps(4)
% 0.25/0.48 thf(fact_209_poly__deriv_Osimps_I6_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno212464073eriv_a @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_deriv.simps(6)
% 0.25/0.48 thf(fact_210_degree_Osimps_I2_J,axiom,
% 0.25/0.48 ! [V: a] :
% 0.25/0.48 ( ( polyno578545843gree_a @ ( polyno439679028le_C_a @ V ) )
% 0.25/0.48 = zero_zero_nat ) ).
% 0.25/0.48
% 0.25/0.48 % degree.simps(2)
% 0.25/0.48 thf(fact_211_degree_Osimps_I2_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno220183259ee_nat @ ( polyno2122022170_C_nat @ V ) )
% 0.25/0.48 = zero_zero_nat ) ).
% 0.25/0.48
% 0.25/0.48 % degree.simps(2)
% 0.25/0.48 thf(fact_212_degree_Osimps_I6_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno220183259ee_nat @ ( polyno1415441627ul_nat @ V @ Va ) )
% 0.25/0.48 = zero_zero_nat ) ).
% 0.25/0.48
% 0.25/0.48 % degree.simps(6)
% 0.25/0.48 thf(fact_213_degree_Osimps_I6_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno578545843gree_a @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 0.25/0.48 = zero_zero_nat ) ).
% 0.25/0.48
% 0.25/0.48 % degree.simps(6)
% 0.25/0.48 thf(fact_214_degree_Osimps_I4_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno578545843gree_a @ ( polyno1623170614_Add_a @ V @ Va ) )
% 0.25/0.48 = zero_zero_nat ) ).
% 0.25/0.48
% 0.25/0.48 % degree.simps(4)
% 0.25/0.48 thf(fact_215_degree_Osimps_I4_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno220183259ee_nat @ ( polyno1222032024dd_nat @ V @ Va ) )
% 0.25/0.48 = zero_zero_nat ) ).
% 0.25/0.48
% 0.25/0.48 % degree.simps(4)
% 0.25/0.48 thf(fact_216_degree_Osimps_I3_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno578545843gree_a @ ( polyno2024845497ound_a @ V ) )
% 0.25/0.48 = zero_zero_nat ) ).
% 0.25/0.48
% 0.25/0.48 % degree.simps(3)
% 0.25/0.48 thf(fact_217_degree_Osimps_I3_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno220183259ee_nat @ ( polyno1999838549nd_nat @ V ) )
% 0.25/0.48 = zero_zero_nat ) ).
% 0.25/0.48
% 0.25/0.48 % degree.simps(3)
% 0.25/0.48 thf(fact_218_poly__deriv_Osimps_I2_J,axiom,
% 0.25/0.48 ! [V: a] :
% 0.25/0.48 ( ( polyno212464073eriv_a @ ( polyno439679028le_C_a @ V ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_deriv.simps(2)
% 0.25/0.48 thf(fact_219_poly__deriv_Osimps_I1_J,axiom,
% 0.25/0.48 ! [C: polyno727731844poly_a,P: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno212464073eriv_a @ ( polyno1057396216e_CN_a @ C @ zero_zero_nat @ P ) )
% 0.25/0.48 = ( polyno1006823949_aux_a @ one_one_a @ P ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_deriv.simps(1)
% 0.25/0.48 thf(fact_220_funpow__shift1__1,axiom,
% 0.25/0.48 ! [Bs2: list_a,N: nat,P: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno422358502poly_a @ Bs2 @ ( compow1114216044poly_a @ N @ polyno784948432ift1_a @ P ) )
% 0.25/0.48 = ( polyno422358502poly_a @ Bs2 @ ( polyno1934269411ymul_a @ ( compow1114216044poly_a @ N @ polyno784948432ift1_a @ ( polyno439679028le_C_a @ one_one_a ) ) @ P ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % funpow_shift1_1
% 0.25/0.48 thf(fact_221_head__nz,axiom,
% 0.25/0.48 ! [P: polyno1532895200ly_nat,N0: nat] :
% 0.25/0.48 ( ( polyno892049031yh_nat @ P @ N0 )
% 0.25/0.48 => ( ( ( polyno1952548879ad_nat @ P )
% 0.25/0.48 = ( polyno2122022170_C_nat @ zero_zero_nat ) )
% 0.25/0.48 = ( P
% 0.25/0.48 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % head_nz
% 0.25/0.48 thf(fact_222_head__nz,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N0: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N0 )
% 0.25/0.48 => ( ( ( polyno1884029055head_a @ P )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) )
% 0.25/0.48 = ( P
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % head_nz
% 0.25/0.48 thf(fact_223_degreen__npolyhCN,axiom,
% 0.25/0.48 ! [C: polyno1532895200ly_nat,N: nat,P: polyno1532895200ly_nat,N0: nat] :
% 0.25/0.48 ( ( polyno892049031yh_nat @ ( polyno720942678CN_nat @ C @ N @ P ) @ N0 )
% 0.25/0.48 => ( ( polyno1779722485en_nat @ C @ N )
% 0.25/0.48 = zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % degreen_npolyhCN
% 0.25/0.48 thf(fact_224_degreen__npolyhCN,axiom,
% 0.25/0.48 ! [C: polyno727731844poly_a,N: nat,P: polyno727731844poly_a,N0: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ ( polyno1057396216e_CN_a @ C @ N @ P ) @ N0 )
% 0.25/0.48 => ( ( polyno1674775833reen_a @ C @ N )
% 0.25/0.48 = zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % degreen_npolyhCN
% 0.25/0.48 thf(fact_225_funpow__0,axiom,
% 0.25/0.48 ! [F: polyno727731844poly_a > polyno727731844poly_a,X: polyno727731844poly_a] :
% 0.25/0.48 ( ( compow1114216044poly_a @ zero_zero_nat @ F @ X )
% 0.25/0.48 = X ) ).
% 0.25/0.48
% 0.25/0.48 % funpow_0
% 0.25/0.48 thf(fact_226_funpow__0,axiom,
% 0.25/0.48 ! [F: polyno1532895200ly_nat > polyno1532895200ly_nat,X: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( compow808008746ly_nat @ zero_zero_nat @ F @ X )
% 0.25/0.48 = X ) ).
% 0.25/0.48
% 0.25/0.48 % funpow_0
% 0.25/0.48 thf(fact_227_funpow__swap1,axiom,
% 0.25/0.48 ! [F: polyno727731844poly_a > polyno727731844poly_a,N: nat,X: polyno727731844poly_a] :
% 0.25/0.48 ( ( F @ ( compow1114216044poly_a @ N @ F @ X ) )
% 0.25/0.48 = ( compow1114216044poly_a @ N @ F @ ( F @ X ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % funpow_swap1
% 0.25/0.48 thf(fact_228_funpow__swap1,axiom,
% 0.25/0.48 ! [F: polyno1532895200ly_nat > polyno1532895200ly_nat,N: nat,X: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( F @ ( compow808008746ly_nat @ N @ F @ X ) )
% 0.25/0.48 = ( compow808008746ly_nat @ N @ F @ ( F @ X ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % funpow_swap1
% 0.25/0.48 thf(fact_229_funpow__isnpolyh,axiom,
% 0.25/0.48 ! [N: nat,F: polyno1532895200ly_nat > polyno1532895200ly_nat,P: polyno1532895200ly_nat,K2: nat] :
% 0.25/0.48 ( ! [P4: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno892049031yh_nat @ P4 @ N )
% 0.25/0.48 => ( polyno892049031yh_nat @ ( F @ P4 ) @ N ) )
% 0.25/0.48 => ( ( polyno892049031yh_nat @ P @ N )
% 0.25/0.48 => ( polyno892049031yh_nat @ ( compow808008746ly_nat @ K2 @ F @ P ) @ N ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % funpow_isnpolyh
% 0.25/0.48 thf(fact_230_funpow__isnpolyh,axiom,
% 0.25/0.48 ! [N: nat,F: polyno727731844poly_a > polyno727731844poly_a,P: polyno727731844poly_a,K2: nat] :
% 0.25/0.48 ( ! [P4: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P4 @ N )
% 0.25/0.48 => ( polyno1372495879olyh_a @ ( F @ P4 ) @ N ) )
% 0.25/0.48 => ( ( polyno1372495879olyh_a @ P @ N )
% 0.25/0.48 => ( polyno1372495879olyh_a @ ( compow1114216044poly_a @ K2 @ F @ P ) @ N ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % funpow_isnpolyh
% 0.25/0.48 thf(fact_231_funpow__mult,axiom,
% 0.25/0.48 ! [N: nat,M: nat,F: polyno727731844poly_a > polyno727731844poly_a] :
% 0.25/0.48 ( ( compow1114216044poly_a @ N @ ( compow1114216044poly_a @ M @ F ) )
% 0.25/0.48 = ( compow1114216044poly_a @ ( times_times_nat @ M @ N ) @ F ) ) ).
% 0.25/0.48
% 0.25/0.48 % funpow_mult
% 0.25/0.48 thf(fact_232_funpow__mult,axiom,
% 0.25/0.48 ! [N: nat,M: nat,F: polyno1532895200ly_nat > polyno1532895200ly_nat] :
% 0.25/0.48 ( ( compow808008746ly_nat @ N @ ( compow808008746ly_nat @ M @ F ) )
% 0.25/0.48 = ( compow808008746ly_nat @ ( times_times_nat @ M @ N ) @ F ) ) ).
% 0.25/0.48
% 0.25/0.48 % funpow_mult
% 0.25/0.48 thf(fact_233_head_Osimps_I2_J,axiom,
% 0.25/0.48 ! [V: a] :
% 0.25/0.48 ( ( polyno1884029055head_a @ ( polyno439679028le_C_a @ V ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ V ) ) ).
% 0.25/0.48
% 0.25/0.48 % head.simps(2)
% 0.25/0.48 thf(fact_234_head_Osimps_I2_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno1952548879ad_nat @ ( polyno2122022170_C_nat @ V ) )
% 0.25/0.48 = ( polyno2122022170_C_nat @ V ) ) ).
% 0.25/0.48
% 0.25/0.48 % head.simps(2)
% 0.25/0.48 thf(fact_235_head_Osimps_I6_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno1952548879ad_nat @ ( polyno1415441627ul_nat @ V @ Va ) )
% 0.25/0.48 = ( polyno1415441627ul_nat @ V @ Va ) ) ).
% 0.25/0.48
% 0.25/0.48 % head.simps(6)
% 0.25/0.48 thf(fact_236_head_Osimps_I6_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1884029055head_a @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 0.25/0.48 = ( polyno1491482291_Mul_a @ V @ Va ) ) ).
% 0.25/0.48
% 0.25/0.48 % head.simps(6)
% 0.25/0.48 thf(fact_237_head_Osimps_I4_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1884029055head_a @ ( polyno1623170614_Add_a @ V @ Va ) )
% 0.25/0.48 = ( polyno1623170614_Add_a @ V @ Va ) ) ).
% 0.25/0.48
% 0.25/0.48 % head.simps(4)
% 0.25/0.48 thf(fact_238_head_Osimps_I4_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno1952548879ad_nat @ ( polyno1222032024dd_nat @ V @ Va ) )
% 0.25/0.48 = ( polyno1222032024dd_nat @ V @ Va ) ) ).
% 0.25/0.48
% 0.25/0.48 % head.simps(4)
% 0.25/0.48 thf(fact_239_head_Osimps_I3_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno1884029055head_a @ ( polyno2024845497ound_a @ V ) )
% 0.25/0.48 = ( polyno2024845497ound_a @ V ) ) ).
% 0.25/0.48
% 0.25/0.48 % head.simps(3)
% 0.25/0.48 thf(fact_240_head_Osimps_I3_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno1952548879ad_nat @ ( polyno1999838549nd_nat @ V ) )
% 0.25/0.48 = ( polyno1999838549nd_nat @ V ) ) ).
% 0.25/0.48
% 0.25/0.48 % head.simps(3)
% 0.25/0.48 thf(fact_241_head__isnpolyh,axiom,
% 0.25/0.48 ! [P: polyno1532895200ly_nat,N0: nat] :
% 0.25/0.48 ( ( polyno892049031yh_nat @ P @ N0 )
% 0.25/0.48 => ( polyno892049031yh_nat @ ( polyno1952548879ad_nat @ P ) @ N0 ) ) ).
% 0.25/0.48
% 0.25/0.48 % head_isnpolyh
% 0.25/0.48 thf(fact_242_head__isnpolyh,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N0: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N0 )
% 0.25/0.48 => ( polyno1372495879olyh_a @ ( polyno1884029055head_a @ P ) @ N0 ) ) ).
% 0.25/0.48
% 0.25/0.48 % head_isnpolyh
% 0.25/0.48 thf(fact_243_degreen_Osimps_I2_J,axiom,
% 0.25/0.48 ! [V: a] :
% 0.25/0.48 ( ( polyno1674775833reen_a @ ( polyno439679028le_C_a @ V ) )
% 0.25/0.48 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % degreen.simps(2)
% 0.25/0.48 thf(fact_244_degreen_Osimps_I2_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno1779722485en_nat @ ( polyno2122022170_C_nat @ V ) )
% 0.25/0.48 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % degreen.simps(2)
% 0.25/0.48 thf(fact_245_degreen_Osimps_I6_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno1779722485en_nat @ ( polyno1415441627ul_nat @ V @ Va ) )
% 0.25/0.48 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % degreen.simps(6)
% 0.25/0.48 thf(fact_246_degreen_Osimps_I6_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1674775833reen_a @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 0.25/0.48 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % degreen.simps(6)
% 0.25/0.48 thf(fact_247_degreen_Osimps_I4_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1674775833reen_a @ ( polyno1623170614_Add_a @ V @ Va ) )
% 0.25/0.48 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % degreen.simps(4)
% 0.25/0.48 thf(fact_248_degreen_Osimps_I4_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno1779722485en_nat @ ( polyno1222032024dd_nat @ V @ Va ) )
% 0.25/0.48 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % degreen.simps(4)
% 0.25/0.48 thf(fact_249_degreen_Osimps_I3_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno1674775833reen_a @ ( polyno2024845497ound_a @ V ) )
% 0.25/0.48 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % degreen.simps(3)
% 0.25/0.48 thf(fact_250_degreen_Osimps_I3_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno1779722485en_nat @ ( polyno1999838549nd_nat @ V ) )
% 0.25/0.48 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % degreen.simps(3)
% 0.25/0.48 thf(fact_251_head_Osimps_I1_J,axiom,
% 0.25/0.48 ! [C: polyno727731844poly_a,P: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1884029055head_a @ ( polyno1057396216e_CN_a @ C @ zero_zero_nat @ P ) )
% 0.25/0.48 = ( polyno1884029055head_a @ P ) ) ).
% 0.25/0.48
% 0.25/0.48 % head.simps(1)
% 0.25/0.48 thf(fact_252_head_Osimps_I1_J,axiom,
% 0.25/0.48 ! [C: polyno1532895200ly_nat,P: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno1952548879ad_nat @ ( polyno720942678CN_nat @ C @ zero_zero_nat @ P ) )
% 0.25/0.48 = ( polyno1952548879ad_nat @ P ) ) ).
% 0.25/0.48
% 0.25/0.48 % head.simps(1)
% 0.25/0.48 thf(fact_253_head__eq__headn0,axiom,
% 0.25/0.48 ( polyno1884029055head_a
% 0.25/0.48 = ( ^ [P2: polyno727731844poly_a] : ( polyno567601229eadn_a @ P2 @ zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % head_eq_headn0
% 0.25/0.48 thf(fact_254_head__eq__headn0,axiom,
% 0.25/0.48 ( polyno1952548879ad_nat
% 0.25/0.48 = ( ^ [P2: polyno1532895200ly_nat] : ( polyno544860353dn_nat @ P2 @ zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % head_eq_headn0
% 0.25/0.48 thf(fact_255_poly__deriv__aux_Osimps_I2_J,axiom,
% 0.25/0.48 ! [N: a,V: a] :
% 0.25/0.48 ( ( polyno1006823949_aux_a @ N @ ( polyno439679028le_C_a @ V ) )
% 0.25/0.48 = ( polyno562434098cmul_a @ N @ ( polyno439679028le_C_a @ V ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_deriv_aux.simps(2)
% 0.25/0.48 thf(fact_256_poly__deriv__aux_Osimps_I6_J,axiom,
% 0.25/0.48 ! [N: a,V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1006823949_aux_a @ N @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 0.25/0.48 = ( polyno562434098cmul_a @ N @ ( polyno1491482291_Mul_a @ V @ Va ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_deriv_aux.simps(6)
% 0.25/0.48 thf(fact_257_funpow__shift1__isnpoly,axiom,
% 0.25/0.48 ! [P: polyno1532895200ly_nat,N: nat] :
% 0.25/0.48 ( ( polyno1013235523ly_nat @ P )
% 0.25/0.48 => ( ( P
% 0.25/0.48 != ( polyno2122022170_C_nat @ zero_zero_nat ) )
% 0.25/0.48 => ( polyno1013235523ly_nat @ ( compow808008746ly_nat @ N @ polyno1964927358t1_nat @ P ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % funpow_shift1_isnpoly
% 0.25/0.48 thf(fact_258_funpow__shift1__isnpoly,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N: nat] :
% 0.25/0.48 ( ( polyno190918219poly_a @ P )
% 0.25/0.48 => ( ( P
% 0.25/0.48 != ( polyno439679028le_C_a @ zero_zero_a ) )
% 0.25/0.48 => ( polyno190918219poly_a @ ( compow1114216044poly_a @ N @ polyno784948432ift1_a @ P ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % funpow_shift1_isnpoly
% 0.25/0.48 thf(fact_259_funpow__shift1,axiom,
% 0.25/0.48 ! [Bs2: list_a,N: nat,P: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno422358502poly_a @ Bs2 @ ( compow1114216044poly_a @ N @ polyno784948432ift1_a @ P ) )
% 0.25/0.48 = ( polyno422358502poly_a @ Bs2 @ ( polyno1491482291_Mul_a @ ( polyno1538138524e_Pw_a @ ( polyno2024845497ound_a @ zero_zero_nat ) @ N ) @ P ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % funpow_shift1
% 0.25/0.48 thf(fact_260_add__left__cancel,axiom,
% 0.25/0.48 ! [A: nat,B: nat,C: nat] :
% 0.25/0.48 ( ( ( plus_plus_nat @ A @ B )
% 0.25/0.48 = ( plus_plus_nat @ A @ C ) )
% 0.25/0.48 = ( B = C ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_left_cancel
% 0.25/0.48 thf(fact_261_add__right__cancel,axiom,
% 0.25/0.48 ! [B: nat,A: nat,C: nat] :
% 0.25/0.48 ( ( ( plus_plus_nat @ B @ A )
% 0.25/0.48 = ( plus_plus_nat @ C @ A ) )
% 0.25/0.48 = ( B = C ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_right_cancel
% 0.25/0.48 thf(fact_262_add__is__0,axiom,
% 0.25/0.48 ! [M: nat,N: nat] :
% 0.25/0.48 ( ( ( plus_plus_nat @ M @ N )
% 0.25/0.48 = zero_zero_nat )
% 0.25/0.48 = ( ( M = zero_zero_nat )
% 0.25/0.48 & ( N = zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_is_0
% 0.25/0.48 thf(fact_263_Nat_Oadd__0__right,axiom,
% 0.25/0.48 ! [M: nat] :
% 0.25/0.48 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.25/0.48 = M ) ).
% 0.25/0.48
% 0.25/0.48 % Nat.add_0_right
% 0.25/0.48 thf(fact_264_zero__eq__add__iff__both__eq__0,axiom,
% 0.25/0.48 ! [X: nat,Y: nat] :
% 0.25/0.48 ( ( zero_zero_nat
% 0.25/0.48 = ( plus_plus_nat @ X @ Y ) )
% 0.25/0.48 = ( ( X = zero_zero_nat )
% 0.25/0.48 & ( Y = zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % zero_eq_add_iff_both_eq_0
% 0.25/0.48 thf(fact_265_add__eq__0__iff__both__eq__0,axiom,
% 0.25/0.48 ! [X: nat,Y: nat] :
% 0.25/0.48 ( ( ( plus_plus_nat @ X @ Y )
% 0.25/0.48 = zero_zero_nat )
% 0.25/0.48 = ( ( X = zero_zero_nat )
% 0.25/0.48 & ( Y = zero_zero_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_eq_0_iff_both_eq_0
% 0.25/0.48 thf(fact_266_add__cancel__right__right,axiom,
% 0.25/0.48 ! [A: nat,B: nat] :
% 0.25/0.48 ( ( A
% 0.25/0.48 = ( plus_plus_nat @ A @ B ) )
% 0.25/0.48 = ( B = zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_cancel_right_right
% 0.25/0.48 thf(fact_267_add__cancel__right__left,axiom,
% 0.25/0.48 ! [A: nat,B: nat] :
% 0.25/0.48 ( ( A
% 0.25/0.48 = ( plus_plus_nat @ B @ A ) )
% 0.25/0.48 = ( B = zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_cancel_right_left
% 0.25/0.48 thf(fact_268_add__cancel__left__right,axiom,
% 0.25/0.48 ! [A: nat,B: nat] :
% 0.25/0.48 ( ( ( plus_plus_nat @ A @ B )
% 0.25/0.48 = A )
% 0.25/0.48 = ( B = zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_cancel_left_right
% 0.25/0.48 thf(fact_269_add__cancel__left__left,axiom,
% 0.25/0.48 ! [B: nat,A: nat] :
% 0.25/0.48 ( ( ( plus_plus_nat @ B @ A )
% 0.25/0.48 = A )
% 0.25/0.48 = ( B = zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_cancel_left_left
% 0.25/0.48 thf(fact_270_add_Oright__neutral,axiom,
% 0.25/0.48 ! [A: nat] :
% 0.25/0.48 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.25/0.48 = A ) ).
% 0.25/0.48
% 0.25/0.48 % add.right_neutral
% 0.25/0.48 thf(fact_271_add_Oleft__neutral,axiom,
% 0.25/0.48 ! [A: nat] :
% 0.25/0.48 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.25/0.48 = A ) ).
% 0.25/0.48
% 0.25/0.48 % add.left_neutral
% 0.25/0.48 thf(fact_272_left__add__mult__distrib,axiom,
% 0.25/0.48 ! [I: nat,U: nat,J: nat,K2: nat] :
% 0.25/0.48 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K2 ) )
% 0.25/0.48 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K2 ) ) ).
% 0.25/0.48
% 0.25/0.48 % left_add_mult_distrib
% 0.25/0.48 thf(fact_273_plus__nat_Oadd__0,axiom,
% 0.25/0.48 ! [N: nat] :
% 0.25/0.48 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.25/0.48 = N ) ).
% 0.25/0.48
% 0.25/0.48 % plus_nat.add_0
% 0.25/0.48 thf(fact_274_add__eq__self__zero,axiom,
% 0.25/0.48 ! [M: nat,N: nat] :
% 0.25/0.48 ( ( ( plus_plus_nat @ M @ N )
% 0.25/0.48 = M )
% 0.25/0.48 => ( N = zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_eq_self_zero
% 0.25/0.48 thf(fact_275_isnpolyh_Osimps_I8_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ ( polyno1538138524e_Pw_a @ V @ Va ) )
% 0.25/0.48 = ( ^ [K: nat] : $false ) ) ).
% 0.25/0.48
% 0.25/0.48 % isnpolyh.simps(8)
% 0.25/0.48 thf(fact_276_add__mult__distrib2,axiom,
% 0.25/0.48 ! [K2: nat,M: nat,N: nat] :
% 0.25/0.48 ( ( times_times_nat @ K2 @ ( plus_plus_nat @ M @ N ) )
% 0.25/0.48 = ( plus_plus_nat @ ( times_times_nat @ K2 @ M ) @ ( times_times_nat @ K2 @ N ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_mult_distrib2
% 0.25/0.48 thf(fact_277_add__mult__distrib,axiom,
% 0.25/0.48 ! [M: nat,N: nat,K2: nat] :
% 0.25/0.48 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K2 )
% 0.25/0.48 = ( plus_plus_nat @ ( times_times_nat @ M @ K2 ) @ ( times_times_nat @ N @ K2 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_mult_distrib
% 0.25/0.48 thf(fact_278_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.25/0.48 ! [A: nat,B: nat,C: nat] :
% 0.25/0.48 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.25/0.48 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % ab_semigroup_add_class.add_ac(1)
% 0.25/0.48 thf(fact_279_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.25/0.48 ! [I: nat,J: nat,K2: nat,L: nat] :
% 0.25/0.48 ( ( ( I = J )
% 0.25/0.48 & ( K2 = L ) )
% 0.25/0.48 => ( ( plus_plus_nat @ I @ K2 )
% 0.25/0.48 = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_mono_thms_linordered_semiring(4)
% 0.25/0.48 thf(fact_280_group__cancel_Oadd1,axiom,
% 0.25/0.48 ! [A3: nat,K2: nat,A: nat,B: nat] :
% 0.25/0.48 ( ( A3
% 0.25/0.48 = ( plus_plus_nat @ K2 @ A ) )
% 0.25/0.48 => ( ( plus_plus_nat @ A3 @ B )
% 0.25/0.48 = ( plus_plus_nat @ K2 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % group_cancel.add1
% 0.25/0.48 thf(fact_281_group__cancel_Oadd2,axiom,
% 0.25/0.48 ! [B3: nat,K2: nat,B: nat,A: nat] :
% 0.25/0.48 ( ( B3
% 0.25/0.48 = ( plus_plus_nat @ K2 @ B ) )
% 0.25/0.48 => ( ( plus_plus_nat @ A @ B3 )
% 0.25/0.48 = ( plus_plus_nat @ K2 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % group_cancel.add2
% 0.25/0.48 thf(fact_282_add_Oassoc,axiom,
% 0.25/0.48 ! [A: nat,B: nat,C: nat] :
% 0.25/0.48 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.25/0.48 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % add.assoc
% 0.25/0.48 thf(fact_283_add_Ocommute,axiom,
% 0.25/0.48 ( plus_plus_nat
% 0.25/0.48 = ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % add.commute
% 0.25/0.48 thf(fact_284_add_Oleft__commute,axiom,
% 0.25/0.48 ! [B: nat,A: nat,C: nat] :
% 0.25/0.48 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 0.25/0.48 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % add.left_commute
% 0.25/0.48 thf(fact_285_add__left__imp__eq,axiom,
% 0.25/0.48 ! [A: nat,B: nat,C: nat] :
% 0.25/0.48 ( ( ( plus_plus_nat @ A @ B )
% 0.25/0.48 = ( plus_plus_nat @ A @ C ) )
% 0.25/0.48 => ( B = C ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_left_imp_eq
% 0.25/0.48 thf(fact_286_add__right__imp__eq,axiom,
% 0.25/0.48 ! [B: nat,A: nat,C: nat] :
% 0.25/0.48 ( ( ( plus_plus_nat @ B @ A )
% 0.25/0.48 = ( plus_plus_nat @ C @ A ) )
% 0.25/0.48 => ( B = C ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_right_imp_eq
% 0.25/0.48 thf(fact_287_combine__common__factor,axiom,
% 0.25/0.48 ! [A: nat,E: nat,B: nat,C: nat] :
% 0.25/0.48 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 0.25/0.48 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 0.25/0.48
% 0.25/0.48 % combine_common_factor
% 0.25/0.48 thf(fact_288_combine__common__factor,axiom,
% 0.25/0.48 ! [A: a,E: a,B: a,C: a] :
% 0.25/0.48 ( ( plus_plus_a @ ( times_times_a @ A @ E ) @ ( plus_plus_a @ ( times_times_a @ B @ E ) @ C ) )
% 0.25/0.48 = ( plus_plus_a @ ( times_times_a @ ( plus_plus_a @ A @ B ) @ E ) @ C ) ) ).
% 0.25/0.48
% 0.25/0.48 % combine_common_factor
% 0.25/0.48 thf(fact_289_distrib__right,axiom,
% 0.25/0.48 ! [A: nat,B: nat,C: nat] :
% 0.25/0.48 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.25/0.48 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % distrib_right
% 0.25/0.48 thf(fact_290_distrib__right,axiom,
% 0.25/0.48 ! [A: a,B: a,C: a] :
% 0.25/0.48 ( ( times_times_a @ ( plus_plus_a @ A @ B ) @ C )
% 0.25/0.48 = ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % distrib_right
% 0.25/0.48 thf(fact_291_distrib__left,axiom,
% 0.25/0.48 ! [A: nat,B: nat,C: nat] :
% 0.25/0.48 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.25/0.48 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % distrib_left
% 0.25/0.48 thf(fact_292_distrib__left,axiom,
% 0.25/0.48 ! [A: a,B: a,C: a] :
% 0.25/0.48 ( ( times_times_a @ A @ ( plus_plus_a @ B @ C ) )
% 0.25/0.48 = ( plus_plus_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ A @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % distrib_left
% 0.25/0.48 thf(fact_293_comm__semiring__class_Odistrib,axiom,
% 0.25/0.48 ! [A: nat,B: nat,C: nat] :
% 0.25/0.48 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.25/0.48 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % comm_semiring_class.distrib
% 0.25/0.48 thf(fact_294_comm__semiring__class_Odistrib,axiom,
% 0.25/0.48 ! [A: a,B: a,C: a] :
% 0.25/0.48 ( ( times_times_a @ ( plus_plus_a @ A @ B ) @ C )
% 0.25/0.48 = ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % comm_semiring_class.distrib
% 0.25/0.48 thf(fact_295_ring__class_Oring__distribs_I1_J,axiom,
% 0.25/0.48 ! [A: a,B: a,C: a] :
% 0.25/0.48 ( ( times_times_a @ A @ ( plus_plus_a @ B @ C ) )
% 0.25/0.48 = ( plus_plus_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ A @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % ring_class.ring_distribs(1)
% 0.25/0.48 thf(fact_296_ring__class_Oring__distribs_I2_J,axiom,
% 0.25/0.48 ! [A: a,B: a,C: a] :
% 0.25/0.48 ( ( times_times_a @ ( plus_plus_a @ A @ B ) @ C )
% 0.25/0.48 = ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % ring_class.ring_distribs(2)
% 0.25/0.48 thf(fact_297_poly_Odistinct_I47_J,axiom,
% 0.25/0.48 ! [X51: polyno727731844poly_a,X52: polyno727731844poly_a,X71: polyno727731844poly_a,X72: nat] :
% 0.25/0.48 ( ( polyno1491482291_Mul_a @ X51 @ X52 )
% 0.25/0.48 != ( polyno1538138524e_Pw_a @ X71 @ X72 ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly.distinct(47)
% 0.25/0.48 thf(fact_298_add_Ocomm__neutral,axiom,
% 0.25/0.48 ! [A: nat] :
% 0.25/0.48 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.25/0.48 = A ) ).
% 0.25/0.48
% 0.25/0.48 % add.comm_neutral
% 0.25/0.48 thf(fact_299_comm__monoid__add__class_Oadd__0,axiom,
% 0.25/0.48 ! [A: nat] :
% 0.25/0.48 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.25/0.48 = A ) ).
% 0.25/0.48
% 0.25/0.48 % comm_monoid_add_class.add_0
% 0.25/0.48 thf(fact_300_poly_Odistinct_I11_J,axiom,
% 0.25/0.48 ! [X1: a,X71: polyno727731844poly_a,X72: nat] :
% 0.25/0.48 ( ( polyno439679028le_C_a @ X1 )
% 0.25/0.48 != ( polyno1538138524e_Pw_a @ X71 @ X72 ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly.distinct(11)
% 0.25/0.48 thf(fact_301_poly_Odistinct_I11_J,axiom,
% 0.25/0.48 ! [X1: nat,X71: polyno1532895200ly_nat,X72: nat] :
% 0.25/0.48 ( ( polyno2122022170_C_nat @ X1 )
% 0.25/0.48 != ( polyno359287218Pw_nat @ X71 @ X72 ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly.distinct(11)
% 0.25/0.48 thf(fact_302_polymul_Osimps_I22_J,axiom,
% 0.25/0.48 ! [A: polyno1532895200ly_nat,V: polyno1532895200ly_nat,Va: nat] :
% 0.25/0.48 ( ( polyno929799083ul_nat @ A @ ( polyno359287218Pw_nat @ V @ Va ) )
% 0.25/0.48 = ( polyno1415441627ul_nat @ A @ ( polyno359287218Pw_nat @ V @ Va ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(22)
% 0.25/0.48 thf(fact_303_polymul_Osimps_I22_J,axiom,
% 0.25/0.48 ! [A: polyno727731844poly_a,V: polyno727731844poly_a,Va: nat] :
% 0.25/0.48 ( ( polyno1934269411ymul_a @ A @ ( polyno1538138524e_Pw_a @ V @ Va ) )
% 0.25/0.48 = ( polyno1491482291_Mul_a @ A @ ( polyno1538138524e_Pw_a @ V @ Va ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(22)
% 0.25/0.48 thf(fact_304_polymul_Osimps_I10_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: nat,B: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno929799083ul_nat @ ( polyno359287218Pw_nat @ V @ Va ) @ B )
% 0.25/0.48 = ( polyno1415441627ul_nat @ ( polyno359287218Pw_nat @ V @ Va ) @ B ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(10)
% 0.25/0.48 thf(fact_305_polymul_Osimps_I10_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: nat,B: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1934269411ymul_a @ ( polyno1538138524e_Pw_a @ V @ Va ) @ B )
% 0.25/0.48 = ( polyno1491482291_Mul_a @ ( polyno1538138524e_Pw_a @ V @ Va ) @ B ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(10)
% 0.25/0.48 thf(fact_306_Ipoly_Osimps_I4_J,axiom,
% 0.25/0.48 ! [Bs2: list_a,A: polyno727731844poly_a,B: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno422358502poly_a @ Bs2 @ ( polyno1623170614_Add_a @ A @ B ) )
% 0.25/0.48 = ( plus_plus_a @ ( polyno422358502poly_a @ Bs2 @ A ) @ ( polyno422358502poly_a @ Bs2 @ B ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % Ipoly.simps(4)
% 0.25/0.48 thf(fact_307_polymul_Osimps_I16_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat,Vc: polyno1532895200ly_nat,Vd: nat] :
% 0.25/0.48 ( ( polyno929799083ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno359287218Pw_nat @ Vc @ Vd ) )
% 0.25/0.48 = ( polyno1415441627ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno359287218Pw_nat @ Vc @ Vd ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(16)
% 0.25/0.48 thf(fact_308_polymul_Osimps_I16_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a,Vc: polyno727731844poly_a,Vd: nat] :
% 0.25/0.48 ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno1538138524e_Pw_a @ Vc @ Vd ) )
% 0.25/0.48 = ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno1538138524e_Pw_a @ Vc @ Vd ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(16)
% 0.25/0.48 thf(fact_309_polymul_Osimps_I28_J,axiom,
% 0.25/0.48 ! [Vc: polyno1532895200ly_nat,Vd: nat,V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno929799083ul_nat @ ( polyno359287218Pw_nat @ Vc @ Vd ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) )
% 0.25/0.48 = ( polyno1415441627ul_nat @ ( polyno359287218Pw_nat @ Vc @ Vd ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(28)
% 0.25/0.48 thf(fact_310_polymul_Osimps_I28_J,axiom,
% 0.25/0.48 ! [Vc: polyno727731844poly_a,Vd: nat,V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1934269411ymul_a @ ( polyno1538138524e_Pw_a @ Vc @ Vd ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) )
% 0.25/0.48 = ( polyno1491482291_Mul_a @ ( polyno1538138524e_Pw_a @ Vc @ Vd ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(28)
% 0.25/0.48 thf(fact_311_poly__cmul_Osimps_I8_J,axiom,
% 0.25/0.48 ! [Y: a,V: polyno727731844poly_a,Va: nat] :
% 0.25/0.48 ( ( polyno562434098cmul_a @ Y @ ( polyno1538138524e_Pw_a @ V @ Va ) )
% 0.25/0.48 = ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ Y ) @ ( polyno1538138524e_Pw_a @ V @ Va ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(8)
% 0.25/0.48 thf(fact_312_poly__cmul_Osimps_I8_J,axiom,
% 0.25/0.48 ! [Y: nat,V: polyno1532895200ly_nat,Va: nat] :
% 0.25/0.48 ( ( polyno1467023772ul_nat @ Y @ ( polyno359287218Pw_nat @ V @ Va ) )
% 0.25/0.48 = ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ Y ) @ ( polyno359287218Pw_nat @ V @ Va ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(8)
% 0.25/0.48 thf(fact_313_poly__deriv_Osimps_I8_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: nat] :
% 0.25/0.48 ( ( polyno212464073eriv_a @ ( polyno1538138524e_Pw_a @ V @ Va ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_deriv.simps(8)
% 0.25/0.48 thf(fact_314_behead,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N: nat,Bs2: list_a] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N )
% 0.25/0.48 => ( ( polyno422358502poly_a @ Bs2 @ ( polyno1623170614_Add_a @ ( polyno1491482291_Mul_a @ ( polyno1884029055head_a @ P ) @ ( polyno1538138524e_Pw_a @ ( polyno2024845497ound_a @ zero_zero_nat ) @ ( polyno578545843gree_a @ P ) ) ) @ ( polyno1465139388head_a @ P ) ) )
% 0.25/0.48 = ( polyno422358502poly_a @ Bs2 @ P ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead
% 0.25/0.48 thf(fact_315_behead__isnpolyh,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N )
% 0.25/0.48 => ( polyno1372495879olyh_a @ ( polyno1465139388head_a @ P ) @ N ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead_isnpolyh
% 0.25/0.48 thf(fact_316_behead_Osimps_I2_J,axiom,
% 0.25/0.48 ! [V: a] :
% 0.25/0.48 ( ( polyno1465139388head_a @ ( polyno439679028le_C_a @ V ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead.simps(2)
% 0.25/0.48 thf(fact_317_behead_Osimps_I2_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno587244178ad_nat @ ( polyno2122022170_C_nat @ V ) )
% 0.25/0.48 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead.simps(2)
% 0.25/0.48 thf(fact_318_behead_Osimps_I6_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno587244178ad_nat @ ( polyno1415441627ul_nat @ V @ Va ) )
% 0.25/0.48 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead.simps(6)
% 0.25/0.48 thf(fact_319_behead_Osimps_I6_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1465139388head_a @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead.simps(6)
% 0.25/0.48 thf(fact_320_behead_Osimps_I4_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1465139388head_a @ ( polyno1623170614_Add_a @ V @ Va ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead.simps(4)
% 0.25/0.48 thf(fact_321_behead_Osimps_I4_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno587244178ad_nat @ ( polyno1222032024dd_nat @ V @ Va ) )
% 0.25/0.48 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead.simps(4)
% 0.25/0.48 thf(fact_322_behead_Osimps_I3_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno1465139388head_a @ ( polyno2024845497ound_a @ V ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead.simps(3)
% 0.25/0.48 thf(fact_323_behead_Osimps_I3_J,axiom,
% 0.25/0.48 ! [V: nat] :
% 0.25/0.48 ( ( polyno587244178ad_nat @ ( polyno1999838549nd_nat @ V ) )
% 0.25/0.48 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead.simps(3)
% 0.25/0.48 thf(fact_324_behead_Osimps_I8_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: nat] :
% 0.25/0.48 ( ( polyno1465139388head_a @ ( polyno1538138524e_Pw_a @ V @ Va ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead.simps(8)
% 0.25/0.48 thf(fact_325_behead_Osimps_I8_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: nat] :
% 0.25/0.48 ( ( polyno587244178ad_nat @ ( polyno359287218Pw_nat @ V @ Va ) )
% 0.25/0.48 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead.simps(8)
% 0.25/0.48 thf(fact_326_add__scale__eq__noteq,axiom,
% 0.25/0.48 ! [R: nat,A: nat,B: nat,C: nat,D: nat] :
% 0.25/0.48 ( ( R != zero_zero_nat )
% 0.25/0.48 => ( ( ( A = B )
% 0.25/0.48 & ( C != D ) )
% 0.25/0.48 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
% 0.25/0.48 != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_scale_eq_noteq
% 0.25/0.48 thf(fact_327_add__scale__eq__noteq,axiom,
% 0.25/0.48 ! [R: a,A: a,B: a,C: a,D: a] :
% 0.25/0.48 ( ( R != zero_zero_a )
% 0.25/0.48 => ( ( ( A = B )
% 0.25/0.48 & ( C != D ) )
% 0.25/0.48 => ( ( plus_plus_a @ A @ ( times_times_a @ R @ C ) )
% 0.25/0.48 != ( plus_plus_a @ B @ ( times_times_a @ R @ D ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_scale_eq_noteq
% 0.25/0.48 thf(fact_328_add__0__iff,axiom,
% 0.25/0.48 ! [B: nat,A: nat] :
% 0.25/0.48 ( ( B
% 0.25/0.48 = ( plus_plus_nat @ B @ A ) )
% 0.25/0.48 = ( A = zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_0_iff
% 0.25/0.48 thf(fact_329_crossproduct__noteq,axiom,
% 0.25/0.48 ! [A: nat,B: nat,C: nat,D: nat] :
% 0.25/0.48 ( ( ( A != B )
% 0.25/0.48 & ( C != D ) )
% 0.25/0.48 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 0.25/0.48 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % crossproduct_noteq
% 0.25/0.48 thf(fact_330_crossproduct__noteq,axiom,
% 0.25/0.48 ! [A: a,B: a,C: a,D: a] :
% 0.25/0.48 ( ( ( A != B )
% 0.25/0.48 & ( C != D ) )
% 0.25/0.48 = ( ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ D ) )
% 0.25/0.48 != ( plus_plus_a @ ( times_times_a @ A @ D ) @ ( times_times_a @ B @ C ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % crossproduct_noteq
% 0.25/0.48 thf(fact_331_crossproduct__eq,axiom,
% 0.25/0.48 ! [W: nat,Y: nat,X: nat,Z: nat] :
% 0.25/0.48 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 0.25/0.48 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 0.25/0.48 = ( ( W = X )
% 0.25/0.48 | ( Y = Z ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % crossproduct_eq
% 0.25/0.48 thf(fact_332_crossproduct__eq,axiom,
% 0.25/0.48 ! [W: a,Y: a,X: a,Z: a] :
% 0.25/0.48 ( ( ( plus_plus_a @ ( times_times_a @ W @ Y ) @ ( times_times_a @ X @ Z ) )
% 0.25/0.48 = ( plus_plus_a @ ( times_times_a @ W @ Z ) @ ( times_times_a @ X @ Y ) ) )
% 0.25/0.48 = ( ( W = X )
% 0.25/0.48 | ( Y = Z ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % crossproduct_eq
% 0.25/0.48 thf(fact_333_Euclid__induct,axiom,
% 0.25/0.48 ! [P5: nat > nat > $o,A: nat,B: nat] :
% 0.25/0.48 ( ! [A4: nat,B4: nat] :
% 0.25/0.48 ( ( P5 @ A4 @ B4 )
% 0.25/0.48 = ( P5 @ B4 @ A4 ) )
% 0.25/0.48 => ( ! [A4: nat] : ( P5 @ A4 @ zero_zero_nat )
% 0.25/0.48 => ( ! [A4: nat,B4: nat] :
% 0.25/0.48 ( ( P5 @ A4 @ B4 )
% 0.25/0.48 => ( P5 @ A4 @ ( plus_plus_nat @ A4 @ B4 ) ) )
% 0.25/0.48 => ( P5 @ A @ B ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % Euclid_induct
% 0.25/0.48 thf(fact_334_verit__sum__simplify,axiom,
% 0.25/0.48 ! [A: nat] :
% 0.25/0.48 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.25/0.48 = A ) ).
% 0.25/0.48
% 0.25/0.48 % verit_sum_simplify
% 0.25/0.48 thf(fact_335_polypow_Osimps_I1_J,axiom,
% 0.25/0.48 ( ( polyno1371724751ypow_a @ zero_zero_nat )
% 0.25/0.48 = ( ^ [P2: polyno727731844poly_a] : ( polyno439679028le_C_a @ one_one_a ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polypow.simps(1)
% 0.25/0.48 thf(fact_336_polypow_Osimps_I1_J,axiom,
% 0.25/0.48 ( ( polyno1510045887ow_nat @ zero_zero_nat )
% 0.25/0.48 = ( ^ [P2: polyno1532895200ly_nat] : ( polyno2122022170_C_nat @ one_one_nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % polypow.simps(1)
% 0.25/0.48 thf(fact_337_degreen_Oelims,axiom,
% 0.25/0.48 ! [X: polyno1532895200ly_nat,Y: nat > nat] :
% 0.25/0.48 ( ( ( polyno1779722485en_nat @ X )
% 0.25/0.48 = Y )
% 0.25/0.48 => ( ! [C3: polyno1532895200ly_nat,N3: nat,P4: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( X
% 0.25/0.48 = ( polyno720942678CN_nat @ C3 @ N3 @ P4 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : ( if_nat @ ( N3 = M2 ) @ ( plus_plus_nat @ one_one_nat @ ( polyno1779722485en_nat @ P4 @ N3 ) ) @ zero_zero_nat ) ) ) )
% 0.25/0.48 => ( ( ? [V2: nat] :
% 0.25/0.48 ( X
% 0.25/0.48 = ( polyno2122022170_C_nat @ V2 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 0.25/0.48 => ( ( ? [V2: nat] :
% 0.25/0.48 ( X
% 0.25/0.48 = ( polyno1999838549nd_nat @ V2 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 0.25/0.48 => ( ( ? [V2: polyno1532895200ly_nat,Va2: polyno1532895200ly_nat] :
% 0.25/0.48 ( X
% 0.25/0.48 = ( polyno1222032024dd_nat @ V2 @ Va2 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 0.25/0.48 => ( ( ? [V2: polyno1532895200ly_nat,Va2: polyno1532895200ly_nat] :
% 0.25/0.48 ( X
% 0.25/0.48 = ( polyno1921014231ub_nat @ V2 @ Va2 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 0.25/0.48 => ( ( ? [V2: polyno1532895200ly_nat,Va2: polyno1532895200ly_nat] :
% 0.25/0.48 ( X
% 0.25/0.48 = ( polyno1415441627ul_nat @ V2 @ Va2 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 0.25/0.48 => ( ( ? [V2: polyno1532895200ly_nat] :
% 0.25/0.48 ( X
% 0.25/0.48 = ( polyno1366804583eg_nat @ V2 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 0.25/0.48 => ~ ( ? [V2: polyno1532895200ly_nat,Va2: nat] :
% 0.25/0.48 ( X
% 0.25/0.48 = ( polyno359287218Pw_nat @ V2 @ Va2 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % degreen.elims
% 0.25/0.48 thf(fact_338_degreen_Oelims,axiom,
% 0.25/0.48 ! [X: polyno727731844poly_a,Y: nat > nat] :
% 0.25/0.48 ( ( ( polyno1674775833reen_a @ X )
% 0.25/0.48 = Y )
% 0.25/0.48 => ( ! [C3: polyno727731844poly_a,N3: nat,P4: polyno727731844poly_a] :
% 0.25/0.48 ( ( X
% 0.25/0.48 = ( polyno1057396216e_CN_a @ C3 @ N3 @ P4 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : ( if_nat @ ( N3 = M2 ) @ ( plus_plus_nat @ one_one_nat @ ( polyno1674775833reen_a @ P4 @ N3 ) ) @ zero_zero_nat ) ) ) )
% 0.25/0.48 => ( ( ? [V2: a] :
% 0.25/0.48 ( X
% 0.25/0.48 = ( polyno439679028le_C_a @ V2 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 0.25/0.48 => ( ( ? [V2: nat] :
% 0.25/0.48 ( X
% 0.25/0.48 = ( polyno2024845497ound_a @ V2 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 0.25/0.48 => ( ( ? [V2: polyno727731844poly_a,Va2: polyno727731844poly_a] :
% 0.25/0.48 ( X
% 0.25/0.48 = ( polyno1623170614_Add_a @ V2 @ Va2 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 0.25/0.48 => ( ( ? [V2: polyno727731844poly_a,Va2: polyno727731844poly_a] :
% 0.25/0.48 ( X
% 0.25/0.48 = ( polyno975704247_Sub_a @ V2 @ Va2 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 0.25/0.48 => ( ( ? [V2: polyno727731844poly_a,Va2: polyno727731844poly_a] :
% 0.25/0.48 ( X
% 0.25/0.48 = ( polyno1491482291_Mul_a @ V2 @ Va2 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 0.25/0.48 => ( ( ? [V2: polyno727731844poly_a] :
% 0.25/0.48 ( X
% 0.25/0.48 = ( polyno96675367_Neg_a @ V2 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 0.25/0.48 => ~ ( ? [V2: polyno727731844poly_a,Va2: nat] :
% 0.25/0.48 ( X
% 0.25/0.48 = ( polyno1538138524e_Pw_a @ V2 @ Va2 ) )
% 0.25/0.48 => ( Y
% 0.25/0.48 != ( ^ [M2: nat] : zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % degreen.elims
% 0.25/0.48 thf(fact_339_behead_Osimps_I5_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1465139388head_a @ ( polyno975704247_Sub_a @ V @ Va ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead.simps(5)
% 0.25/0.48 thf(fact_340_behead_Osimps_I5_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno587244178ad_nat @ ( polyno1921014231ub_nat @ V @ Va ) )
% 0.25/0.48 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead.simps(5)
% 0.25/0.48 thf(fact_341_poly__cmul_Osimps_I5_J,axiom,
% 0.25/0.48 ! [Y: a,V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno562434098cmul_a @ Y @ ( polyno975704247_Sub_a @ V @ Va ) )
% 0.25/0.48 = ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ Y ) @ ( polyno975704247_Sub_a @ V @ Va ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(5)
% 0.25/0.48 thf(fact_342_poly__cmul_Osimps_I5_J,axiom,
% 0.25/0.48 ! [Y: nat,V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno1467023772ul_nat @ Y @ ( polyno1921014231ub_nat @ V @ Va ) )
% 0.25/0.48 = ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ Y ) @ ( polyno1921014231ub_nat @ V @ Va ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(5)
% 0.25/0.48 thf(fact_343_behead_Osimps_I7_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1465139388head_a @ ( polyno96675367_Neg_a @ V ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead.simps(7)
% 0.25/0.48 thf(fact_344_behead_Osimps_I7_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno587244178ad_nat @ ( polyno1366804583eg_nat @ V ) )
% 0.25/0.48 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 0.25/0.48
% 0.25/0.48 % behead.simps(7)
% 0.25/0.48 thf(fact_345_poly__cmul_Osimps_I7_J,axiom,
% 0.25/0.48 ! [Y: a,V: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno562434098cmul_a @ Y @ ( polyno96675367_Neg_a @ V ) )
% 0.25/0.48 = ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ Y ) @ ( polyno96675367_Neg_a @ V ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(7)
% 0.25/0.48 thf(fact_346_poly__cmul_Osimps_I7_J,axiom,
% 0.25/0.48 ! [Y: nat,V: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno1467023772ul_nat @ Y @ ( polyno1366804583eg_nat @ V ) )
% 0.25/0.48 = ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ Y ) @ ( polyno1366804583eg_nat @ V ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_cmul.simps(7)
% 0.25/0.48 thf(fact_347_poly__deriv_Osimps_I5_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno212464073eriv_a @ ( polyno975704247_Sub_a @ V @ Va ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_deriv.simps(5)
% 0.25/0.48 thf(fact_348_poly__deriv_Osimps_I7_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno212464073eriv_a @ ( polyno96675367_Neg_a @ V ) )
% 0.25/0.48 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 0.25/0.48
% 0.25/0.48 % poly_deriv.simps(7)
% 0.25/0.48 thf(fact_349_polypow__normh,axiom,
% 0.25/0.48 ! [P: polyno727731844poly_a,N: nat,K2: nat] :
% 0.25/0.48 ( ( polyno1372495879olyh_a @ P @ N )
% 0.25/0.48 => ( polyno1372495879olyh_a @ ( polyno1371724751ypow_a @ K2 @ P ) @ N ) ) ).
% 0.25/0.48
% 0.25/0.48 % polypow_normh
% 0.25/0.48 thf(fact_350_polymul_Osimps_I7_J,axiom,
% 0.25/0.48 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat,B: polyno1532895200ly_nat] :
% 0.25/0.48 ( ( polyno929799083ul_nat @ ( polyno1921014231ub_nat @ V @ Va ) @ B )
% 0.25/0.48 = ( polyno1415441627ul_nat @ ( polyno1921014231ub_nat @ V @ Va ) @ B ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(7)
% 0.25/0.48 thf(fact_351_polymul_Osimps_I7_J,axiom,
% 0.25/0.48 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a,B: polyno727731844poly_a] :
% 0.25/0.48 ( ( polyno1934269411ymul_a @ ( polyno975704247_Sub_a @ V @ Va ) @ B )
% 0.25/0.48 = ( polyno1491482291_Mul_a @ ( polyno975704247_Sub_a @ V @ Va ) @ B ) ) ).
% 0.25/0.48
% 0.25/0.48 % polymul.simps(7)
% 0.25/0.48
% 0.25/0.48 % Helper facts (3)
% 0.25/0.48 thf(help_If_3_1_If_001t__Nat__Onat_T,axiom,
% 0.25/0.48 ! [P5: $o] :
% 0.25/0.48 ( ( P5 = $true )
% 0.25/0.48 | ( P5 = $false ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.25/0.48 ! [X: nat,Y: nat] :
% 0.25/0.48 ( ( if_nat @ $false @ X @ Y )
% 0.25/0.48 = Y ) ).
% 0.25/0.48
% 0.25/0.48 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.25/0.48 ! [X: nat,Y: nat] :
% 0.25/0.48 ( ( if_nat @ $true @ X @ Y )
% 0.25/0.48 = X ) ).
% 0.25/0.48
% 0.25/0.48 % Conjectures (1)
% 0.25/0.48 thf(conj_0,conjecture,
% 0.25/0.48 ( ( polyno1934269411ymul_a @ p @ q )
% 0.25/0.48 = ( polyno1934269411ymul_a @ q @ p ) ) ).
% 0.25/0.48
% 0.25/0.48 %------------------------------------------------------------------------------
% 0.25/0.48 ------------------------
% 2.87/1.53 ---- Embedded in THF ---
% 2.87/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.87/1.53 %%% Generated on Tue Feb 24 08:27:48 EST 2026
% 2.87/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.87/1.53 %%% Logic specification used:
% 2.87/1.53 %%% thf(spec, logic, $$dhol).
% 2.87/1.53
% 2.87/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.HVFAM8xlRw/DTF2DTF3593.p
% See solution above
% 2.87/1.53 ------------------------
% 2.87/1.55 ---- Cleaned THF ---
% 2.87/1.55 thf(ty_n_t__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_It__Nat__Onat_J,type,
% 2.87/1.55 polyno1532895200ly_nat: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_n_t__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_Itf__a_J,type,
% 2.87/1.55 polyno727731844poly_a: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 2.87/1.55 list_nat: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 2.87/1.55 list_a: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_n_t__Nat__Onat,type,
% 2.87/1.55 nat: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_n_tf__a,type,
% 2.87/1.55 a: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 2.87/1.55 one_one_nat: nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Groups_Oone__class_Oone_001tf__a,type,
% 2.87/1.55 one_one_a: a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 2.87/1.55 plus_plus_nat: nat > nat > nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Groups_Oplus__class_Oplus_001tf__a,type,
% 2.87/1.55 plus_plus_a: a > a > a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 2.87/1.55 times_times_nat: nat > nat > nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Groups_Otimes__class_Otimes_001tf__a,type,
% 2.87/1.55 times_times_a: a > a > a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 2.87/1.55 zero_zero_nat: nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Groups_Ozero__class_Ozero_001tf__a,type,
% 2.87/1.55 zero_zero_a: a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_If_001t__Nat__Onat,type,
% 2.87/1.55 if_nat: $o > nat > nat > nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Nat_Ocompow_001_062_It__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_It__Nat__Onat_J_Mt__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_It__Nat__Onat_J_J,type,
% 2.87/1.55 compow808008746ly_nat: nat > ( polyno1532895200ly_nat > polyno1532895200ly_nat ) > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Nat_Ocompow_001_062_It__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_Itf__a_J_Mt__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_Itf__a_J_J,type,
% 2.87/1.55 compow1114216044poly_a: nat > ( polyno727731844poly_a > polyno727731844poly_a ) > polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_OIpoly_001tf__a,type,
% 2.87/1.55 polyno422358502poly_a: list_a > polyno727731844poly_a > a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Obehead_001t__Nat__Onat,type,
% 2.87/1.55 polyno587244178ad_nat: polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Obehead_001tf__a,type,
% 2.87/1.55 polyno1465139388head_a: polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Odegree_001t__Nat__Onat,type,
% 2.87/1.55 polyno220183259ee_nat: polyno1532895200ly_nat > nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Odegree_001tf__a,type,
% 2.87/1.55 polyno578545843gree_a: polyno727731844poly_a > nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Odegreen_001t__Nat__Onat,type,
% 2.87/1.55 polyno1779722485en_nat: polyno1532895200ly_nat > nat > nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Odegreen_001tf__a,type,
% 2.87/1.55 polyno1674775833reen_a: polyno727731844poly_a > nat > nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Ohead_001t__Nat__Onat,type,
% 2.87/1.55 polyno1952548879ad_nat: polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Ohead_001tf__a,type,
% 2.87/1.55 polyno1884029055head_a: polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oheadconst_001t__Nat__Onat,type,
% 2.87/1.55 polyno524777654st_nat: polyno1532895200ly_nat > nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oheadconst_001tf__a,type,
% 2.87/1.55 polyno2115742616onst_a: polyno727731844poly_a > a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oheadn_001t__Nat__Onat,type,
% 2.87/1.55 polyno544860353dn_nat: polyno1532895200ly_nat > nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oheadn_001tf__a,type,
% 2.87/1.55 polyno567601229eadn_a: polyno727731844poly_a > nat > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oisnpoly_001t__Nat__Onat,type,
% 2.87/1.55 polyno1013235523ly_nat: polyno1532895200ly_nat > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oisnpoly_001tf__a,type,
% 2.87/1.55 polyno190918219poly_a: polyno727731844poly_a > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oisnpolyh_001t__Nat__Onat,type,
% 2.87/1.55 polyno892049031yh_nat: polyno1532895200ly_nat > nat > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oisnpolyh_001tf__a,type,
% 2.87/1.55 polyno1372495879olyh_a: polyno727731844poly_a > nat > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OAdd_001t__Nat__Onat,type,
% 2.87/1.55 polyno1222032024dd_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OAdd_001tf__a,type,
% 2.87/1.55 polyno1623170614_Add_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OBound_001t__Nat__Onat,type,
% 2.87/1.55 polyno1999838549nd_nat: nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OBound_001tf__a,type,
% 2.87/1.55 polyno2024845497ound_a: nat > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OCN_001t__Nat__Onat,type,
% 2.87/1.55 polyno720942678CN_nat: polyno1532895200ly_nat > nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OCN_001tf__a,type,
% 2.87/1.55 polyno1057396216e_CN_a: polyno727731844poly_a > nat > polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OC_001t__Nat__Onat,type,
% 2.87/1.55 polyno2122022170_C_nat: nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OC_001tf__a,type,
% 2.87/1.55 polyno439679028le_C_a: a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OMul_001t__Nat__Onat,type,
% 2.87/1.55 polyno1415441627ul_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OMul_001tf__a,type,
% 2.87/1.55 polyno1491482291_Mul_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_ONeg_001t__Nat__Onat,type,
% 2.87/1.55 polyno1366804583eg_nat: polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_ONeg_001tf__a,type,
% 2.87/1.55 polyno96675367_Neg_a: polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OPw_001t__Nat__Onat,type,
% 2.87/1.55 polyno359287218Pw_nat: polyno1532895200ly_nat > nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OPw_001tf__a,type,
% 2.87/1.55 polyno1538138524e_Pw_a: polyno727731844poly_a > nat > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OSub_001t__Nat__Onat,type,
% 2.87/1.55 polyno1921014231ub_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OSub_001tf__a,type,
% 2.87/1.55 polyno975704247_Sub_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly__cmul_001t__Nat__Onat,type,
% 2.87/1.55 polyno1467023772ul_nat: nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly__cmul_001tf__a,type,
% 2.87/1.55 polyno562434098cmul_a: a > polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly__deriv_001tf__a,type,
% 2.87/1.55 polyno212464073eriv_a: polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly__deriv__aux_001tf__a,type,
% 2.87/1.55 polyno1006823949_aux_a: a > polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolymul_001t__Nat__Onat,type,
% 2.87/1.55 polyno929799083ul_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolymul_001tf__a,type,
% 2.87/1.55 polyno1934269411ymul_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolynate_001tf__a,type,
% 2.87/1.55 polyno955999183nate_a: polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolypow_001t__Nat__Onat,type,
% 2.87/1.55 polyno1510045887ow_nat: nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolypow_001tf__a,type,
% 2.87/1.55 polyno1371724751ypow_a: nat > polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolysub_001tf__a,type,
% 2.87/1.55 polyno1418491367ysub_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolysubst0_001t__Nat__Onat,type,
% 2.87/1.55 polyno336795754t0_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolysubst0_001tf__a,type,
% 2.87/1.55 polyno1397854436bst0_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oshift1_001t__Nat__Onat,type,
% 2.87/1.55 polyno1964927358t1_nat: polyno1532895200ly_nat > polyno1532895200ly_nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oshift1_001tf__a,type,
% 2.87/1.55 polyno784948432ift1_a: polyno727731844poly_a > polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Owf__bs_001t__Nat__Onat,type,
% 2.87/1.55 polyno1438831695bs_nat: list_nat > polyno1532895200ly_nat > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Owf__bs_001tf__a,type,
% 2.87/1.55 polyno896877631f_bs_a: list_a > polyno727731844poly_a > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_n0,type,
% 2.87/1.55 n0: nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_n1,type,
% 2.87/1.55 n1: nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_p,type,
% 2.87/1.55 p: polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_q,type,
% 2.87/1.55 q: polyno727731844poly_a ).
% 2.87/1.55
% 2.87/1.55 thf(fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062,axiom,
% 2.87/1.55 ( ( ! [Bs: list_a] :
% 2.87/1.55 ( ( polyno422358502poly_a @ Bs @ ( polyno1934269411ymul_a @ p @ q ) )
% 2.87/1.55 = ( polyno422358502poly_a @ Bs @ ( polyno1934269411ymul_a @ q @ p ) ) ) )
% 2.87/1.55 = ( ( polyno1934269411ymul_a @ p @ q )
% 2.87/1.55 = ( polyno1934269411ymul_a @ q @ p ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_1_np,axiom,
% 2.87/1.55 polyno1372495879olyh_a @ p @ n0 ).
% 2.87/1.55
% 2.87/1.55 thf(fact_2_nq,axiom,
% 2.87/1.55 polyno1372495879olyh_a @ q @ n1 ).
% 2.87/1.55
% 2.87/1.55 thf(fact_3_polymul__norm,axiom,
% 2.87/1.55 ! [P: polyno727731844poly_a,Q: polyno727731844poly_a] :
% 2.87/1.55 ( ( polyno190918219poly_a @ P )
% 2.87/1.55 => ( ( polyno190918219poly_a @ Q )
% 2.87/1.55 => ( polyno190918219poly_a @ ( polyno1934269411ymul_a @ P @ Q ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_4_wf__bs__polyul,axiom,
% 2.87/1.55 ! [Bs2: list_nat,P: polyno1532895200ly_nat,Q: polyno1532895200ly_nat] :
% 2.87/1.55 ( ( polyno1438831695bs_nat @ Bs2 @ P )
% 2.87/1.55 => ( ( polyno1438831695bs_nat @ Bs2 @ Q )
% 2.87/1.55 => ( polyno1438831695bs_nat @ Bs2 @ ( polyno929799083ul_nat @ P @ Q ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_5_wf__bs__polyul,axiom,
% 2.87/1.55 ! [Bs2: list_a,P: polyno727731844poly_a,Q: polyno727731844poly_a] :
% 2.87/1.55 ( ( polyno896877631f_bs_a @ Bs2 @ P )
% 2.87/1.55 => ( ( polyno896877631f_bs_a @ Bs2 @ Q )
% 2.87/1.55 => ( polyno896877631f_bs_a @ Bs2 @ ( polyno1934269411ymul_a @ P @ Q ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_6_polymul_Osimps_I20_J,axiom,
% 2.87/1.55 ! [A: polyno1532895200ly_nat,V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.55 ( ( polyno929799083ul_nat @ A @ ( polyno1415441627ul_nat @ V @ Va ) )
% 2.87/1.55 = ( polyno1415441627ul_nat @ A @ ( polyno1415441627ul_nat @ V @ Va ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_7_polymul_Osimps_I20_J,axiom,
% 2.87/1.55 ! [A: polyno727731844poly_a,V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.55 ( ( polyno1934269411ymul_a @ A @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 2.87/1.55 = ( polyno1491482291_Mul_a @ A @ ( polyno1491482291_Mul_a @ V @ Va ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_8_polymul_Osimps_I8_J,axiom,
% 2.87/1.55 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat,B: polyno1532895200ly_nat] :
% 2.87/1.55 ( ( polyno929799083ul_nat @ ( polyno1415441627ul_nat @ V @ Va ) @ B )
% 2.87/1.55 = ( polyno1415441627ul_nat @ ( polyno1415441627ul_nat @ V @ Va ) @ B ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_9_polymul_Osimps_I8_J,axiom,
% 2.87/1.55 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a,B: polyno727731844poly_a] :
% 2.87/1.55 ( ( polyno1934269411ymul_a @ ( polyno1491482291_Mul_a @ V @ Va ) @ B )
% 2.87/1.55 = ( polyno1491482291_Mul_a @ ( polyno1491482291_Mul_a @ V @ Va ) @ B ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_10_polymul,axiom,
% 2.87/1.55 ! [Bs2: list_a,P: polyno727731844poly_a,Q: polyno727731844poly_a] :
% 2.87/1.55 ( ( polyno422358502poly_a @ Bs2 @ ( polyno1934269411ymul_a @ P @ Q ) )
% 2.87/1.55 = ( times_times_a @ ( polyno422358502poly_a @ Bs2 @ P ) @ ( polyno422358502poly_a @ Bs2 @ Q ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_11_polymul_Osimps_I1_J,axiom,
% 2.87/1.55 ! [C: nat,C2: nat] :
% 2.87/1.55 ( ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ C ) @ ( polyno2122022170_C_nat @ C2 ) )
% 2.87/1.55 = ( polyno2122022170_C_nat @ ( times_times_nat @ C @ C2 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_12_polymul_Osimps_I1_J,axiom,
% 2.87/1.55 ! [C: a,C2: a] :
% 2.87/1.55 ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ C ) @ ( polyno439679028le_C_a @ C2 ) )
% 2.87/1.55 = ( polyno439679028le_C_a @ ( times_times_a @ C @ C2 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_13_polynate_Osimps_I4_J,axiom,
% 2.87/1.55 ! [P: polyno727731844poly_a,Q: polyno727731844poly_a] :
% 2.87/1.55 ( ( polyno955999183nate_a @ ( polyno1491482291_Mul_a @ P @ Q ) )
% 2.87/1.55 = ( polyno1934269411ymul_a @ ( polyno955999183nate_a @ P ) @ ( polyno955999183nate_a @ Q ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_14_polymul_Osimps_I26_J,axiom,
% 2.87/1.55 ! [Vc: polyno1532895200ly_nat,Vd: polyno1532895200ly_nat,V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat] :
% 2.87/1.55 ( ( polyno929799083ul_nat @ ( polyno1415441627ul_nat @ Vc @ Vd ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) )
% 2.87/1.55 = ( polyno1415441627ul_nat @ ( polyno1415441627ul_nat @ Vc @ Vd ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_15_polymul_Osimps_I26_J,axiom,
% 2.87/1.55 ! [Vc: polyno727731844poly_a,Vd: polyno727731844poly_a,V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a] :
% 2.87/1.55 ( ( polyno1934269411ymul_a @ ( polyno1491482291_Mul_a @ Vc @ Vd ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) )
% 2.87/1.55 = ( polyno1491482291_Mul_a @ ( polyno1491482291_Mul_a @ Vc @ Vd ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_16_polymul_Osimps_I14_J,axiom,
% 2.87/1.55 ! [V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat,Vc: polyno1532895200ly_nat,Vd: polyno1532895200ly_nat] :
% 2.87/1.55 ( ( polyno929799083ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno1415441627ul_nat @ Vc @ Vd ) )
% 2.87/1.55 = ( polyno1415441627ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno1415441627ul_nat @ Vc @ Vd ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_17_polymul_Osimps_I14_J,axiom,
% 2.87/1.55 ! [V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a,Vc: polyno727731844poly_a,Vd: polyno727731844poly_a] :
% 2.87/1.55 ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno1491482291_Mul_a @ Vc @ Vd ) )
% 2.87/1.55 = ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno1491482291_Mul_a @ Vc @ Vd ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_18_polymul_Osimps_I18_J,axiom,
% 2.87/1.55 ! [A: polyno1532895200ly_nat,V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.55 ( ( polyno929799083ul_nat @ A @ ( polyno1222032024dd_nat @ V @ Va ) )
% 2.87/1.55 = ( polyno1415441627ul_nat @ A @ ( polyno1222032024dd_nat @ V @ Va ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_19_polymul_Osimps_I18_J,axiom,
% 2.87/1.55 ! [A: polyno727731844poly_a,V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.55 ( ( polyno1934269411ymul_a @ A @ ( polyno1623170614_Add_a @ V @ Va ) )
% 2.87/1.55 = ( polyno1491482291_Mul_a @ A @ ( polyno1623170614_Add_a @ V @ Va ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_20_poly_Oinject_I8_J,axiom,
% 2.87/1.55 ! [X81: polyno727731844poly_a,X82: nat,X83: polyno727731844poly_a,Y81: polyno727731844poly_a,Y82: nat,Y83: polyno727731844poly_a] :
% 2.87/1.55 ( ( ( polyno1057396216e_CN_a @ X81 @ X82 @ X83 )
% 2.87/1.55 = ( polyno1057396216e_CN_a @ Y81 @ Y82 @ Y83 ) )
% 2.87/1.55 = ( ( X81 = Y81 )
% 2.87/1.55 & ( X82 = Y82 )
% 2.87/1.55 & ( X83 = Y83 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_21_poly_Oinject_I8_J,axiom,
% 2.87/1.55 ! [X81: polyno1532895200ly_nat,X82: nat,X83: polyno1532895200ly_nat,Y81: polyno1532895200ly_nat,Y82: nat,Y83: polyno1532895200ly_nat] :
% 2.87/1.55 ( ( ( polyno720942678CN_nat @ X81 @ X82 @ X83 )
% 2.87/1.55 = ( polyno720942678CN_nat @ Y81 @ Y82 @ Y83 ) )
% 2.87/1.55 = ( ( X81 = Y81 )
% 2.87/1.55 & ( X82 = Y82 )
% 2.87/1.55 & ( X83 = Y83 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_22_poly_Oinject_I1_J,axiom,
% 2.87/1.55 ! [X1: a,Y1: a] :
% 2.87/1.55 ( ( ( polyno439679028le_C_a @ X1 )
% 2.87/1.55 = ( polyno439679028le_C_a @ Y1 ) )
% 2.87/1.55 = ( X1 = Y1 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_23_poly_Oinject_I1_J,axiom,
% 2.87/1.55 ! [X1: nat,Y1: nat] :
% 2.87/1.55 ( ( ( polyno2122022170_C_nat @ X1 )
% 2.87/1.55 = ( polyno2122022170_C_nat @ Y1 ) )
% 2.87/1.55 = ( X1 = Y1 ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_24_poly_Oinject_I5_J,axiom,
% 2.87/1.55 ! [X51: polyno1532895200ly_nat,X52: polyno1532895200ly_nat,Y51: polyno1532895200ly_nat,Y52: polyno1532895200ly_nat] :
% 2.87/1.55 ( ( ( polyno1415441627ul_nat @ X51 @ X52 )
% 2.87/1.55 = ( polyno1415441627ul_nat @ Y51 @ Y52 ) )
% 2.87/1.55 = ( ( X51 = Y51 )
% 2.87/1.55 & ( X52 = Y52 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_25_poly_Oinject_I5_J,axiom,
% 2.87/1.55 ! [X51: polyno727731844poly_a,X52: polyno727731844poly_a,Y51: polyno727731844poly_a,Y52: polyno727731844poly_a] :
% 2.87/1.55 ( ( ( polyno1491482291_Mul_a @ X51 @ X52 )
% 2.87/1.55 = ( polyno1491482291_Mul_a @ Y51 @ Y52 ) )
% 2.87/1.55 = ( ( X51 = Y51 )
% 2.87/1.55 & ( X52 = Y52 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_26_poly_Oinject_I3_J,axiom,
% 2.87/1.55 ! [X31: polyno727731844poly_a,X32: polyno727731844poly_a,Y31: polyno727731844poly_a,Y32: polyno727731844poly_a] :
% 2.87/1.55 ( ( ( polyno1623170614_Add_a @ X31 @ X32 )
% 2.87/1.55 = ( polyno1623170614_Add_a @ Y31 @ Y32 ) )
% 2.87/1.55 = ( ( X31 = Y31 )
% 2.87/1.55 & ( X32 = Y32 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_27_poly_Oinject_I3_J,axiom,
% 2.87/1.55 ! [X31: polyno1532895200ly_nat,X32: polyno1532895200ly_nat,Y31: polyno1532895200ly_nat,Y32: polyno1532895200ly_nat] :
% 2.87/1.55 ( ( ( polyno1222032024dd_nat @ X31 @ X32 )
% 2.87/1.55 = ( polyno1222032024dd_nat @ Y31 @ Y32 ) )
% 2.87/1.55 = ( ( X31 = Y31 )
% 2.87/1.55 & ( X32 = Y32 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_28_polynate,axiom,
% 2.87/1.55 ! [Bs2: list_a,P: polyno727731844poly_a] :
% 2.87/1.55 ( ( polyno422358502poly_a @ Bs2 @ ( polyno955999183nate_a @ P ) )
% 2.87/1.55 = ( polyno422358502poly_a @ Bs2 @ P ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_29_Ipoly_Osimps_I6_J,axiom,
% 2.87/1.56 ! [Bs2: list_a,A: polyno727731844poly_a,B: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno422358502poly_a @ Bs2 @ ( polyno1491482291_Mul_a @ A @ B ) )
% 2.87/1.56 = ( times_times_a @ ( polyno422358502poly_a @ Bs2 @ A ) @ ( polyno422358502poly_a @ Bs2 @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_30_Ipoly_Osimps_I1_J,axiom,
% 2.87/1.56 ! [Bs2: list_a,C: a] :
% 2.87/1.56 ( ( polyno422358502poly_a @ Bs2 @ ( polyno439679028le_C_a @ C ) )
% 2.87/1.56 = C ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_31_poly_Odistinct_I49_J,axiom,
% 2.87/1.56 ! [X51: polyno1532895200ly_nat,X52: polyno1532895200ly_nat,X81: polyno1532895200ly_nat,X82: nat,X83: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1415441627ul_nat @ X51 @ X52 )
% 2.87/1.56 != ( polyno720942678CN_nat @ X81 @ X82 @ X83 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_32_poly_Odistinct_I49_J,axiom,
% 2.87/1.56 ! [X51: polyno727731844poly_a,X52: polyno727731844poly_a,X81: polyno727731844poly_a,X82: nat,X83: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1491482291_Mul_a @ X51 @ X52 )
% 2.87/1.56 != ( polyno1057396216e_CN_a @ X81 @ X82 @ X83 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_33_poly_Odistinct_I35_J,axiom,
% 2.87/1.56 ! [X31: polyno727731844poly_a,X32: polyno727731844poly_a,X81: polyno727731844poly_a,X82: nat,X83: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1623170614_Add_a @ X31 @ X32 )
% 2.87/1.56 != ( polyno1057396216e_CN_a @ X81 @ X82 @ X83 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_34_poly_Odistinct_I35_J,axiom,
% 2.87/1.56 ! [X31: polyno1532895200ly_nat,X32: polyno1532895200ly_nat,X81: polyno1532895200ly_nat,X82: nat,X83: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1222032024dd_nat @ X31 @ X32 )
% 2.87/1.56 != ( polyno720942678CN_nat @ X81 @ X82 @ X83 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_35_poly_Odistinct_I29_J,axiom,
% 2.87/1.56 ! [X31: polyno1532895200ly_nat,X32: polyno1532895200ly_nat,X51: polyno1532895200ly_nat,X52: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1222032024dd_nat @ X31 @ X32 )
% 2.87/1.56 != ( polyno1415441627ul_nat @ X51 @ X52 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_36_poly_Odistinct_I29_J,axiom,
% 2.87/1.56 ! [X31: polyno727731844poly_a,X32: polyno727731844poly_a,X51: polyno727731844poly_a,X52: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1623170614_Add_a @ X31 @ X32 )
% 2.87/1.56 != ( polyno1491482291_Mul_a @ X51 @ X52 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_37_poly_Odistinct_I13_J,axiom,
% 2.87/1.56 ! [X1: a,X81: polyno727731844poly_a,X82: nat,X83: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno439679028le_C_a @ X1 )
% 2.87/1.56 != ( polyno1057396216e_CN_a @ X81 @ X82 @ X83 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_38_poly_Odistinct_I13_J,axiom,
% 2.87/1.56 ! [X1: nat,X81: polyno1532895200ly_nat,X82: nat,X83: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno2122022170_C_nat @ X1 )
% 2.87/1.56 != ( polyno720942678CN_nat @ X81 @ X82 @ X83 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_39_poly_Odistinct_I7_J,axiom,
% 2.87/1.56 ! [X1: nat,X51: polyno1532895200ly_nat,X52: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno2122022170_C_nat @ X1 )
% 2.87/1.56 != ( polyno1415441627ul_nat @ X51 @ X52 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_40_poly_Odistinct_I7_J,axiom,
% 2.87/1.56 ! [X1: a,X51: polyno727731844poly_a,X52: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno439679028le_C_a @ X1 )
% 2.87/1.56 != ( polyno1491482291_Mul_a @ X51 @ X52 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_41_poly_Odistinct_I3_J,axiom,
% 2.87/1.56 ! [X1: a,X31: polyno727731844poly_a,X32: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno439679028le_C_a @ X1 )
% 2.87/1.56 != ( polyno1623170614_Add_a @ X31 @ X32 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_42_poly_Odistinct_I3_J,axiom,
% 2.87/1.56 ! [X1: nat,X31: polyno1532895200ly_nat,X32: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno2122022170_C_nat @ X1 )
% 2.87/1.56 != ( polyno1222032024dd_nat @ X31 @ X32 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_43_polymul_Osimps_I24_J,axiom,
% 2.87/1.56 ! [Vc: polyno1532895200ly_nat,Vd: polyno1532895200ly_nat,V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno929799083ul_nat @ ( polyno1222032024dd_nat @ Vc @ Vd ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) )
% 2.87/1.56 = ( polyno1415441627ul_nat @ ( polyno1222032024dd_nat @ Vc @ Vd ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_44_polymul_Osimps_I24_J,axiom,
% 2.87/1.56 ! [Vc: polyno727731844poly_a,Vd: polyno727731844poly_a,V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1934269411ymul_a @ ( polyno1623170614_Add_a @ Vc @ Vd ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) )
% 2.87/1.56 = ( polyno1491482291_Mul_a @ ( polyno1623170614_Add_a @ Vc @ Vd ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_45_polymul_Osimps_I12_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat,Vc: polyno1532895200ly_nat,Vd: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno929799083ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno1222032024dd_nat @ Vc @ Vd ) )
% 2.87/1.56 = ( polyno1415441627ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno1222032024dd_nat @ Vc @ Vd ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_46_polymul_Osimps_I12_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a,Vc: polyno727731844poly_a,Vd: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno1623170614_Add_a @ Vc @ Vd ) )
% 2.87/1.56 = ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno1623170614_Add_a @ Vc @ Vd ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_47_isnpolyh_Osimps_I6_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno892049031yh_nat @ ( polyno1415441627ul_nat @ V @ Va ) )
% 2.87/1.56 = ( ^ [K: nat] : $false ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_48_isnpolyh_Osimps_I6_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 2.87/1.56 = ( ^ [K: nat] : $false ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_49_isnpolyh_Osimps_I4_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno892049031yh_nat @ ( polyno1222032024dd_nat @ V @ Va ) )
% 2.87/1.56 = ( ^ [K: nat] : $false ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_50_isnpolyh_Osimps_I4_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ ( polyno1623170614_Add_a @ V @ Va ) )
% 2.87/1.56 = ( ^ [K: nat] : $false ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_51_isnpolyh_Osimps_I1_J,axiom,
% 2.87/1.56 ! [C: nat] :
% 2.87/1.56 ( ( polyno892049031yh_nat @ ( polyno2122022170_C_nat @ C ) )
% 2.87/1.56 = ( ^ [K: nat] : $true ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_52_isnpolyh_Osimps_I1_J,axiom,
% 2.87/1.56 ! [C: a] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ ( polyno439679028le_C_a @ C ) )
% 2.87/1.56 = ( ^ [K: nat] : $true ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_53_polynate_Osimps_I8_J,axiom,
% 2.87/1.56 ! [C: a] :
% 2.87/1.56 ( ( polyno955999183nate_a @ ( polyno439679028le_C_a @ C ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ C ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_54_polynate__norm,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a] : ( polyno190918219poly_a @ ( polyno955999183nate_a @ P ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_55_isnpolyh__unique,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N0: nat,Q: polyno727731844poly_a,N1: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N0 )
% 2.87/1.56 => ( ( polyno1372495879olyh_a @ Q @ N1 )
% 2.87/1.56 => ( ( ! [Bs: list_a] :
% 2.87/1.56 ( ( polyno422358502poly_a @ Bs @ P )
% 2.87/1.56 = ( polyno422358502poly_a @ Bs @ Q ) ) )
% 2.87/1.56 = ( P = Q ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_56_polymul_Osimps_I6_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat,B: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno929799083ul_nat @ ( polyno1222032024dd_nat @ V @ Va ) @ B )
% 2.87/1.56 = ( polyno1415441627ul_nat @ ( polyno1222032024dd_nat @ V @ Va ) @ B ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_57_polymul_Osimps_I6_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a,B: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1934269411ymul_a @ ( polyno1623170614_Add_a @ V @ Va ) @ B )
% 2.87/1.56 = ( polyno1491482291_Mul_a @ ( polyno1623170614_Add_a @ V @ Va ) @ B ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_58_isnpolyh__zero__iff,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N0: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N0 )
% 2.87/1.56 => ( ! [Bs3: list_a] :
% 2.87/1.56 ( ( polyno896877631f_bs_a @ Bs3 @ P )
% 2.87/1.56 => ( ( polyno422358502poly_a @ Bs3 @ P )
% 2.87/1.56 = zero_zero_a ) )
% 2.87/1.56 => ( P
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_59_poly__cmul,axiom,
% 2.87/1.56 ! [Bs2: list_a,C: a,P: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno422358502poly_a @ Bs2 @ ( polyno562434098cmul_a @ C @ P ) )
% 2.87/1.56 = ( polyno422358502poly_a @ Bs2 @ ( polyno1491482291_Mul_a @ ( polyno439679028le_C_a @ C ) @ P ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_60_polymul__0_I2_J,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N0: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N0 )
% 2.87/1.56 => ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ P )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_61_polymul__0_I1_J,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N0: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N0 )
% 2.87/1.56 => ( ( polyno1934269411ymul_a @ P @ ( polyno439679028le_C_a @ zero_zero_a ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_62_polymul__1_I2_J,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N0: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N0 )
% 2.87/1.56 => ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ one_one_a ) @ P )
% 2.87/1.56 = P ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_63_polymul__1_I1_J,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N0: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N0 )
% 2.87/1.56 => ( ( polyno1934269411ymul_a @ P @ ( polyno439679028le_C_a @ one_one_a ) )
% 2.87/1.56 = P ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_64_polynate_Osimps_I7_J,axiom,
% 2.87/1.56 ! [C: polyno727731844poly_a,N: nat,P: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno955999183nate_a @ ( polyno1057396216e_CN_a @ C @ N @ P ) )
% 2.87/1.56 = ( polyno955999183nate_a @ ( polyno1623170614_Add_a @ C @ ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ N ) @ P ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_65_polymul__eq0__iff,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N0: nat,Q: polyno727731844poly_a,N1: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N0 )
% 2.87/1.56 => ( ( polyno1372495879olyh_a @ Q @ N1 )
% 2.87/1.56 => ( ( ( polyno1934269411ymul_a @ P @ Q )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) )
% 2.87/1.56 = ( ( P
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) )
% 2.87/1.56 | ( Q
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_66_poly__cmul_Osimps_I4_J,axiom,
% 2.87/1.56 ! [Y: a,V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno562434098cmul_a @ Y @ ( polyno1623170614_Add_a @ V @ Va ) )
% 2.87/1.56 = ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ Y ) @ ( polyno1623170614_Add_a @ V @ Va ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_67_poly__cmul_Osimps_I4_J,axiom,
% 2.87/1.56 ! [Y: nat,V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1467023772ul_nat @ Y @ ( polyno1222032024dd_nat @ V @ Va ) )
% 2.87/1.56 = ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ Y ) @ ( polyno1222032024dd_nat @ V @ Va ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_68_poly__cmul_Osimps_I6_J,axiom,
% 2.87/1.56 ! [Y: nat,V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1467023772ul_nat @ Y @ ( polyno1415441627ul_nat @ V @ Va ) )
% 2.87/1.56 = ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ Y ) @ ( polyno1415441627ul_nat @ V @ Va ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_69_poly__cmul_Osimps_I6_J,axiom,
% 2.87/1.56 ! [Y: a,V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno562434098cmul_a @ Y @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 2.87/1.56 = ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ Y ) @ ( polyno1491482291_Mul_a @ V @ Va ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_70_polymul_Osimps_I3_J,axiom,
% 2.87/1.56 ! [C2: a,C: polyno727731844poly_a,N: nat,P: polyno727731844poly_a] :
% 2.87/1.56 ( ( ( C2 = zero_zero_a )
% 2.87/1.56 => ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ C @ N @ P ) @ ( polyno439679028le_C_a @ C2 ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) )
% 2.87/1.56 & ( ( C2 != zero_zero_a )
% 2.87/1.56 => ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ C @ N @ P ) @ ( polyno439679028le_C_a @ C2 ) )
% 2.87/1.56 = ( polyno1057396216e_CN_a @ ( polyno1934269411ymul_a @ C @ ( polyno439679028le_C_a @ C2 ) ) @ N @ ( polyno1934269411ymul_a @ P @ ( polyno439679028le_C_a @ C2 ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_71_polymul_Osimps_I3_J,axiom,
% 2.87/1.56 ! [C2: nat,C: polyno1532895200ly_nat,N: nat,P: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( ( C2 = zero_zero_nat )
% 2.87/1.56 => ( ( polyno929799083ul_nat @ ( polyno720942678CN_nat @ C @ N @ P ) @ ( polyno2122022170_C_nat @ C2 ) )
% 2.87/1.56 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) )
% 2.87/1.56 & ( ( C2 != zero_zero_nat )
% 2.87/1.56 => ( ( polyno929799083ul_nat @ ( polyno720942678CN_nat @ C @ N @ P ) @ ( polyno2122022170_C_nat @ C2 ) )
% 2.87/1.56 = ( polyno720942678CN_nat @ ( polyno929799083ul_nat @ C @ ( polyno2122022170_C_nat @ C2 ) ) @ N @ ( polyno929799083ul_nat @ P @ ( polyno2122022170_C_nat @ C2 ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_72_poly_Oinject_I2_J,axiom,
% 2.87/1.56 ! [X2: nat,Y2: nat] :
% 2.87/1.56 ( ( ( polyno2024845497ound_a @ X2 )
% 2.87/1.56 = ( polyno2024845497ound_a @ Y2 ) )
% 2.87/1.56 = ( X2 = Y2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_73_poly_Oinject_I2_J,axiom,
% 2.87/1.56 ! [X2: nat,Y2: nat] :
% 2.87/1.56 ( ( ( polyno1999838549nd_nat @ X2 )
% 2.87/1.56 = ( polyno1999838549nd_nat @ Y2 ) )
% 2.87/1.56 = ( X2 = Y2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_74_polynate_Osimps_I1_J,axiom,
% 2.87/1.56 ! [N: nat] :
% 2.87/1.56 ( ( polyno955999183nate_a @ ( polyno2024845497ound_a @ N ) )
% 2.87/1.56 = ( polyno1057396216e_CN_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ N @ ( polyno439679028le_C_a @ one_one_a ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_75_poly__cmul_Osimps_I3_J,axiom,
% 2.87/1.56 ! [Y: a,V: nat] :
% 2.87/1.56 ( ( polyno562434098cmul_a @ Y @ ( polyno2024845497ound_a @ V ) )
% 2.87/1.56 = ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ Y ) @ ( polyno2024845497ound_a @ V ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_76_poly__cmul_Osimps_I3_J,axiom,
% 2.87/1.56 ! [Y: nat,V: nat] :
% 2.87/1.56 ( ( polyno1467023772ul_nat @ Y @ ( polyno1999838549nd_nat @ V ) )
% 2.87/1.56 = ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ Y ) @ ( polyno1999838549nd_nat @ V ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_77_poly_Odistinct_I25_J,axiom,
% 2.87/1.56 ! [X2: nat,X81: polyno727731844poly_a,X82: nat,X83: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno2024845497ound_a @ X2 )
% 2.87/1.56 != ( polyno1057396216e_CN_a @ X81 @ X82 @ X83 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_78_poly_Odistinct_I25_J,axiom,
% 2.87/1.56 ! [X2: nat,X81: polyno1532895200ly_nat,X82: nat,X83: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1999838549nd_nat @ X2 )
% 2.87/1.56 != ( polyno720942678CN_nat @ X81 @ X82 @ X83 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_79_poly_Odistinct_I1_J,axiom,
% 2.87/1.56 ! [X1: a,X2: nat] :
% 2.87/1.56 ( ( polyno439679028le_C_a @ X1 )
% 2.87/1.56 != ( polyno2024845497ound_a @ X2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_80_poly_Odistinct_I1_J,axiom,
% 2.87/1.56 ! [X1: nat,X2: nat] :
% 2.87/1.56 ( ( polyno2122022170_C_nat @ X1 )
% 2.87/1.56 != ( polyno1999838549nd_nat @ X2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_81_poly_Odistinct_I19_J,axiom,
% 2.87/1.56 ! [X2: nat,X51: polyno1532895200ly_nat,X52: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1999838549nd_nat @ X2 )
% 2.87/1.56 != ( polyno1415441627ul_nat @ X51 @ X52 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_82_poly_Odistinct_I19_J,axiom,
% 2.87/1.56 ! [X2: nat,X51: polyno727731844poly_a,X52: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno2024845497ound_a @ X2 )
% 2.87/1.56 != ( polyno1491482291_Mul_a @ X51 @ X52 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_83_poly_Odistinct_I15_J,axiom,
% 2.87/1.56 ! [X2: nat,X31: polyno727731844poly_a,X32: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno2024845497ound_a @ X2 )
% 2.87/1.56 != ( polyno1623170614_Add_a @ X31 @ X32 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_84_poly_Odistinct_I15_J,axiom,
% 2.87/1.56 ! [X2: nat,X31: polyno1532895200ly_nat,X32: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1999838549nd_nat @ X2 )
% 2.87/1.56 != ( polyno1222032024dd_nat @ X31 @ X32 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_85_isnpolyh_Osimps_I3_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno892049031yh_nat @ ( polyno1999838549nd_nat @ V ) )
% 2.87/1.56 = ( ^ [K: nat] : $false ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_86_isnpolyh_Osimps_I3_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ ( polyno2024845497ound_a @ V ) )
% 2.87/1.56 = ( ^ [K: nat] : $false ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_87_poly__cmul_Osimps_I2_J,axiom,
% 2.87/1.56 ! [Y: a,C: polyno727731844poly_a,N: nat,P: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno562434098cmul_a @ Y @ ( polyno1057396216e_CN_a @ C @ N @ P ) )
% 2.87/1.56 = ( polyno1057396216e_CN_a @ ( polyno562434098cmul_a @ Y @ C ) @ N @ ( polyno562434098cmul_a @ Y @ P ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_88_poly__cmul_Osimps_I2_J,axiom,
% 2.87/1.56 ! [Y: nat,C: polyno1532895200ly_nat,N: nat,P: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1467023772ul_nat @ Y @ ( polyno720942678CN_nat @ C @ N @ P ) )
% 2.87/1.56 = ( polyno720942678CN_nat @ ( polyno1467023772ul_nat @ Y @ C ) @ N @ ( polyno1467023772ul_nat @ Y @ P ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_89_polymul_Osimps_I17_J,axiom,
% 2.87/1.56 ! [A: polyno1532895200ly_nat,V: nat] :
% 2.87/1.56 ( ( polyno929799083ul_nat @ A @ ( polyno1999838549nd_nat @ V ) )
% 2.87/1.56 = ( polyno1415441627ul_nat @ A @ ( polyno1999838549nd_nat @ V ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_90_polymul_Osimps_I17_J,axiom,
% 2.87/1.56 ! [A: polyno727731844poly_a,V: nat] :
% 2.87/1.56 ( ( polyno1934269411ymul_a @ A @ ( polyno2024845497ound_a @ V ) )
% 2.87/1.56 = ( polyno1491482291_Mul_a @ A @ ( polyno2024845497ound_a @ V ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_91_polymul_Osimps_I5_J,axiom,
% 2.87/1.56 ! [V: nat,B: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno929799083ul_nat @ ( polyno1999838549nd_nat @ V ) @ B )
% 2.87/1.56 = ( polyno1415441627ul_nat @ ( polyno1999838549nd_nat @ V ) @ B ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_92_polymul_Osimps_I5_J,axiom,
% 2.87/1.56 ! [V: nat,B: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1934269411ymul_a @ ( polyno2024845497ound_a @ V ) @ B )
% 2.87/1.56 = ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ V ) @ B ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_93_poly__cmul_Osimps_I1_J,axiom,
% 2.87/1.56 ! [Y: a,X: a] :
% 2.87/1.56 ( ( polyno562434098cmul_a @ Y @ ( polyno439679028le_C_a @ X ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ ( times_times_a @ Y @ X ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_94_poly__cmul_Osimps_I1_J,axiom,
% 2.87/1.56 ! [Y: nat,X: nat] :
% 2.87/1.56 ( ( polyno1467023772ul_nat @ Y @ ( polyno2122022170_C_nat @ X ) )
% 2.87/1.56 = ( polyno2122022170_C_nat @ ( times_times_nat @ Y @ X ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_95_one__normh,axiom,
% 2.87/1.56 ! [N: nat] : ( polyno892049031yh_nat @ ( polyno2122022170_C_nat @ one_one_nat ) @ N ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_96_one__normh,axiom,
% 2.87/1.56 ! [N: nat] : ( polyno1372495879olyh_a @ ( polyno439679028le_C_a @ one_one_a ) @ N ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_97_zero__normh,axiom,
% 2.87/1.56 ! [N: nat] : ( polyno892049031yh_nat @ ( polyno2122022170_C_nat @ zero_zero_nat ) @ N ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_98_zero__normh,axiom,
% 2.87/1.56 ! [N: nat] : ( polyno1372495879olyh_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ N ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_99_isnpoly__def,axiom,
% 2.87/1.56 ( polyno1013235523ly_nat
% 2.87/1.56 = ( ^ [P2: polyno1532895200ly_nat] : ( polyno892049031yh_nat @ P2 @ zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_100_isnpoly__def,axiom,
% 2.87/1.56 ( polyno190918219poly_a
% 2.87/1.56 = ( ^ [P2: polyno727731844poly_a] : ( polyno1372495879olyh_a @ P2 @ zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_101_polymul_Osimps_I11_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat,Vc: nat] :
% 2.87/1.56 ( ( polyno929799083ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno1999838549nd_nat @ Vc ) )
% 2.87/1.56 = ( polyno1415441627ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno1999838549nd_nat @ Vc ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_102_polymul_Osimps_I11_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a,Vc: nat] :
% 2.87/1.56 ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno2024845497ound_a @ Vc ) )
% 2.87/1.56 = ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno2024845497ound_a @ Vc ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_103_polymul_Osimps_I23_J,axiom,
% 2.87/1.56 ! [Vc: nat,V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno929799083ul_nat @ ( polyno1999838549nd_nat @ Vc ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) )
% 2.87/1.56 = ( polyno1415441627ul_nat @ ( polyno1999838549nd_nat @ Vc ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_104_polymul_Osimps_I23_J,axiom,
% 2.87/1.56 ! [Vc: nat,V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1934269411ymul_a @ ( polyno2024845497ound_a @ Vc ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) )
% 2.87/1.56 = ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ Vc ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_105_polymul_Osimps_I2_J,axiom,
% 2.87/1.56 ! [C: a,C2: polyno727731844poly_a,N2: nat,P3: polyno727731844poly_a] :
% 2.87/1.56 ( ( ( C = zero_zero_a )
% 2.87/1.56 => ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ C ) @ ( polyno1057396216e_CN_a @ C2 @ N2 @ P3 ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) )
% 2.87/1.56 & ( ( C != zero_zero_a )
% 2.87/1.56 => ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ C ) @ ( polyno1057396216e_CN_a @ C2 @ N2 @ P3 ) )
% 2.87/1.56 = ( polyno1057396216e_CN_a @ ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ C ) @ C2 ) @ N2 @ ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ C ) @ P3 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_106_polymul_Osimps_I2_J,axiom,
% 2.87/1.56 ! [C: nat,C2: polyno1532895200ly_nat,N2: nat,P3: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( ( C = zero_zero_nat )
% 2.87/1.56 => ( ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ C ) @ ( polyno720942678CN_nat @ C2 @ N2 @ P3 ) )
% 2.87/1.56 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) )
% 2.87/1.56 & ( ( C != zero_zero_nat )
% 2.87/1.56 => ( ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ C ) @ ( polyno720942678CN_nat @ C2 @ N2 @ P3 ) )
% 2.87/1.56 = ( polyno720942678CN_nat @ ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ C ) @ C2 ) @ N2 @ ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ C ) @ P3 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_107_mult__cancel__left1,axiom,
% 2.87/1.56 ! [C: a,B: a] :
% 2.87/1.56 ( ( C
% 2.87/1.56 = ( times_times_a @ C @ B ) )
% 2.87/1.56 = ( ( C = zero_zero_a )
% 2.87/1.56 | ( B = one_one_a ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_108_mult__cancel__left2,axiom,
% 2.87/1.56 ! [C: a,A: a] :
% 2.87/1.56 ( ( ( times_times_a @ C @ A )
% 2.87/1.56 = C )
% 2.87/1.56 = ( ( C = zero_zero_a )
% 2.87/1.56 | ( A = one_one_a ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_109_mult__cancel__right1,axiom,
% 2.87/1.56 ! [C: a,B: a] :
% 2.87/1.56 ( ( C
% 2.87/1.56 = ( times_times_a @ B @ C ) )
% 2.87/1.56 = ( ( C = zero_zero_a )
% 2.87/1.56 | ( B = one_one_a ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_110_mult__cancel__right2,axiom,
% 2.87/1.56 ! [A: a,C: a] :
% 2.87/1.56 ( ( ( times_times_a @ A @ C )
% 2.87/1.56 = C )
% 2.87/1.56 = ( ( C = zero_zero_a )
% 2.87/1.56 | ( A = one_one_a ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_111_mult_Oright__neutral,axiom,
% 2.87/1.56 ! [A: nat] :
% 2.87/1.56 ( ( times_times_nat @ A @ one_one_nat )
% 2.87/1.56 = A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_112_mult_Oright__neutral,axiom,
% 2.87/1.56 ! [A: a] :
% 2.87/1.56 ( ( times_times_a @ A @ one_one_a )
% 2.87/1.56 = A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_113_mult_Oleft__neutral,axiom,
% 2.87/1.56 ! [A: nat] :
% 2.87/1.56 ( ( times_times_nat @ one_one_nat @ A )
% 2.87/1.56 = A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_114_mult_Oleft__neutral,axiom,
% 2.87/1.56 ! [A: a] :
% 2.87/1.56 ( ( times_times_a @ one_one_a @ A )
% 2.87/1.56 = A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_115_mult__cancel__right,axiom,
% 2.87/1.56 ! [A: nat,C: nat,B: nat] :
% 2.87/1.56 ( ( ( times_times_nat @ A @ C )
% 2.87/1.56 = ( times_times_nat @ B @ C ) )
% 2.87/1.56 = ( ( C = zero_zero_nat )
% 2.87/1.56 | ( A = B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_116_mult__cancel__right,axiom,
% 2.87/1.56 ! [A: a,C: a,B: a] :
% 2.87/1.56 ( ( ( times_times_a @ A @ C )
% 2.87/1.56 = ( times_times_a @ B @ C ) )
% 2.87/1.56 = ( ( C = zero_zero_a )
% 2.87/1.56 | ( A = B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_117_mult__cancel__left,axiom,
% 2.87/1.56 ! [C: nat,A: nat,B: nat] :
% 2.87/1.56 ( ( ( times_times_nat @ C @ A )
% 2.87/1.56 = ( times_times_nat @ C @ B ) )
% 2.87/1.56 = ( ( C = zero_zero_nat )
% 2.87/1.56 | ( A = B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_118_mult__cancel__left,axiom,
% 2.87/1.56 ! [C: a,A: a,B: a] :
% 2.87/1.56 ( ( ( times_times_a @ C @ A )
% 2.87/1.56 = ( times_times_a @ C @ B ) )
% 2.87/1.56 = ( ( C = zero_zero_a )
% 2.87/1.56 | ( A = B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_119_mult__zero__left,axiom,
% 2.87/1.56 ! [A: nat] :
% 2.87/1.56 ( ( times_times_nat @ zero_zero_nat @ A )
% 2.87/1.56 = zero_zero_nat ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_120_mult__zero__left,axiom,
% 2.87/1.56 ! [A: a] :
% 2.87/1.56 ( ( times_times_a @ zero_zero_a @ A )
% 2.87/1.56 = zero_zero_a ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_121_mult__zero__right,axiom,
% 2.87/1.56 ! [A: nat] :
% 2.87/1.56 ( ( times_times_nat @ A @ zero_zero_nat )
% 2.87/1.56 = zero_zero_nat ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_122_mult__zero__right,axiom,
% 2.87/1.56 ! [A: a] :
% 2.87/1.56 ( ( times_times_a @ A @ zero_zero_a )
% 2.87/1.56 = zero_zero_a ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_123_mult__eq__0__iff,axiom,
% 2.87/1.56 ! [A: nat,B: nat] :
% 2.87/1.56 ( ( ( times_times_nat @ A @ B )
% 2.87/1.56 = zero_zero_nat )
% 2.87/1.56 = ( ( A = zero_zero_nat )
% 2.87/1.56 | ( B = zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_124_mult__eq__0__iff,axiom,
% 2.87/1.56 ! [A: a,B: a] :
% 2.87/1.56 ( ( ( times_times_a @ A @ B )
% 2.87/1.56 = zero_zero_a )
% 2.87/1.56 = ( ( A = zero_zero_a )
% 2.87/1.56 | ( B = zero_zero_a ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_125_zero__reorient,axiom,
% 2.87/1.56 ! [X: a] :
% 2.87/1.56 ( ( zero_zero_a = X )
% 2.87/1.56 = ( X = zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_126_zero__reorient,axiom,
% 2.87/1.56 ! [X: nat] :
% 2.87/1.56 ( ( zero_zero_nat = X )
% 2.87/1.56 = ( X = zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_127_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 2.87/1.56 ! [A: nat,B: nat,C: nat] :
% 2.87/1.56 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 2.87/1.56 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_128_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 2.87/1.56 ! [A: a,B: a,C: a] :
% 2.87/1.56 ( ( times_times_a @ ( times_times_a @ A @ B ) @ C )
% 2.87/1.56 = ( times_times_a @ A @ ( times_times_a @ B @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_129_mult_Oassoc,axiom,
% 2.87/1.56 ! [A: nat,B: nat,C: nat] :
% 2.87/1.56 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 2.87/1.56 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_130_mult_Oassoc,axiom,
% 2.87/1.56 ! [A: a,B: a,C: a] :
% 2.87/1.56 ( ( times_times_a @ ( times_times_a @ A @ B ) @ C )
% 2.87/1.56 = ( times_times_a @ A @ ( times_times_a @ B @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_131_mult_Ocommute,axiom,
% 2.87/1.56 ( times_times_nat
% 2.87/1.56 = ( ^ [A2: nat,B2: nat] : ( times_times_nat @ B2 @ A2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_132_mult_Ocommute,axiom,
% 2.87/1.56 ( times_times_a
% 2.87/1.56 = ( ^ [A2: a,B2: a] : ( times_times_a @ B2 @ A2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_133_mult_Oleft__commute,axiom,
% 2.87/1.56 ! [B: nat,A: nat,C: nat] :
% 2.87/1.56 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 2.87/1.56 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_134_mult_Oleft__commute,axiom,
% 2.87/1.56 ! [B: a,A: a,C: a] :
% 2.87/1.56 ( ( times_times_a @ B @ ( times_times_a @ A @ C ) )
% 2.87/1.56 = ( times_times_a @ A @ ( times_times_a @ B @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_135_one__reorient,axiom,
% 2.87/1.56 ! [X: a] :
% 2.87/1.56 ( ( one_one_a = X )
% 2.87/1.56 = ( X = one_one_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_136_one__reorient,axiom,
% 2.87/1.56 ! [X: nat] :
% 2.87/1.56 ( ( one_one_nat = X )
% 2.87/1.56 = ( X = one_one_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_137_mult__not__zero,axiom,
% 2.87/1.56 ! [A: nat,B: nat] :
% 2.87/1.56 ( ( ( times_times_nat @ A @ B )
% 2.87/1.56 != zero_zero_nat )
% 2.87/1.56 => ( ( A != zero_zero_nat )
% 2.87/1.56 & ( B != zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_138_mult__not__zero,axiom,
% 2.87/1.56 ! [A: a,B: a] :
% 2.87/1.56 ( ( ( times_times_a @ A @ B )
% 2.87/1.56 != zero_zero_a )
% 2.87/1.56 => ( ( A != zero_zero_a )
% 2.87/1.56 & ( B != zero_zero_a ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_139_divisors__zero,axiom,
% 2.87/1.56 ! [A: nat,B: nat] :
% 2.87/1.56 ( ( ( times_times_nat @ A @ B )
% 2.87/1.56 = zero_zero_nat )
% 2.87/1.56 => ( ( A = zero_zero_nat )
% 2.87/1.56 | ( B = zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_140_divisors__zero,axiom,
% 2.87/1.56 ! [A: a,B: a] :
% 2.87/1.56 ( ( ( times_times_a @ A @ B )
% 2.87/1.56 = zero_zero_a )
% 2.87/1.56 => ( ( A = zero_zero_a )
% 2.87/1.56 | ( B = zero_zero_a ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_141_no__zero__divisors,axiom,
% 2.87/1.56 ! [A: nat,B: nat] :
% 2.87/1.56 ( ( A != zero_zero_nat )
% 2.87/1.56 => ( ( B != zero_zero_nat )
% 2.87/1.56 => ( ( times_times_nat @ A @ B )
% 2.87/1.56 != zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_142_no__zero__divisors,axiom,
% 2.87/1.56 ! [A: a,B: a] :
% 2.87/1.56 ( ( A != zero_zero_a )
% 2.87/1.56 => ( ( B != zero_zero_a )
% 2.87/1.56 => ( ( times_times_a @ A @ B )
% 2.87/1.56 != zero_zero_a ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_143_mult__left__cancel,axiom,
% 2.87/1.56 ! [C: nat,A: nat,B: nat] :
% 2.87/1.56 ( ( C != zero_zero_nat )
% 2.87/1.56 => ( ( ( times_times_nat @ C @ A )
% 2.87/1.56 = ( times_times_nat @ C @ B ) )
% 2.87/1.56 = ( A = B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_144_mult__left__cancel,axiom,
% 2.87/1.56 ! [C: a,A: a,B: a] :
% 2.87/1.56 ( ( C != zero_zero_a )
% 2.87/1.56 => ( ( ( times_times_a @ C @ A )
% 2.87/1.56 = ( times_times_a @ C @ B ) )
% 2.87/1.56 = ( A = B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_145_mult__right__cancel,axiom,
% 2.87/1.56 ! [C: nat,A: nat,B: nat] :
% 2.87/1.56 ( ( C != zero_zero_nat )
% 2.87/1.56 => ( ( ( times_times_nat @ A @ C )
% 2.87/1.56 = ( times_times_nat @ B @ C ) )
% 2.87/1.56 = ( A = B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_146_mult__right__cancel,axiom,
% 2.87/1.56 ! [C: a,A: a,B: a] :
% 2.87/1.56 ( ( C != zero_zero_a )
% 2.87/1.56 => ( ( ( times_times_a @ A @ C )
% 2.87/1.56 = ( times_times_a @ B @ C ) )
% 2.87/1.56 = ( A = B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_147_zero__neq__one,axiom,
% 2.87/1.56 zero_zero_a != one_one_a ).
% 2.87/1.56
% 2.87/1.56 thf(fact_148_zero__neq__one,axiom,
% 2.87/1.56 zero_zero_nat != one_one_nat ).
% 2.87/1.56
% 2.87/1.56 thf(fact_149_comm__monoid__mult__class_Omult__1,axiom,
% 2.87/1.56 ! [A: nat] :
% 2.87/1.56 ( ( times_times_nat @ one_one_nat @ A )
% 2.87/1.56 = A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_150_comm__monoid__mult__class_Omult__1,axiom,
% 2.87/1.56 ! [A: a] :
% 2.87/1.56 ( ( times_times_a @ one_one_a @ A )
% 2.87/1.56 = A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_151_mult_Ocomm__neutral,axiom,
% 2.87/1.56 ! [A: nat] :
% 2.87/1.56 ( ( times_times_nat @ A @ one_one_nat )
% 2.87/1.56 = A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_152_mult_Ocomm__neutral,axiom,
% 2.87/1.56 ! [A: a] :
% 2.87/1.56 ( ( times_times_a @ A @ one_one_a )
% 2.87/1.56 = A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_153_mult__is__0,axiom,
% 2.87/1.56 ! [M: nat,N: nat] :
% 2.87/1.56 ( ( ( times_times_nat @ M @ N )
% 2.87/1.56 = zero_zero_nat )
% 2.87/1.56 = ( ( M = zero_zero_nat )
% 2.87/1.56 | ( N = zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_154_mult__0__right,axiom,
% 2.87/1.56 ! [M: nat] :
% 2.87/1.56 ( ( times_times_nat @ M @ zero_zero_nat )
% 2.87/1.56 = zero_zero_nat ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_155_mult__cancel1,axiom,
% 2.87/1.56 ! [K2: nat,M: nat,N: nat] :
% 2.87/1.56 ( ( ( times_times_nat @ K2 @ M )
% 2.87/1.56 = ( times_times_nat @ K2 @ N ) )
% 2.87/1.56 = ( ( M = N )
% 2.87/1.56 | ( K2 = zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_156_mult__cancel2,axiom,
% 2.87/1.56 ! [M: nat,K2: nat,N: nat] :
% 2.87/1.56 ( ( ( times_times_nat @ M @ K2 )
% 2.87/1.56 = ( times_times_nat @ N @ K2 ) )
% 2.87/1.56 = ( ( M = N )
% 2.87/1.56 | ( K2 = zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_157_shift1,axiom,
% 2.87/1.56 ! [Bs2: list_a,P: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno422358502poly_a @ Bs2 @ ( polyno784948432ift1_a @ P ) )
% 2.87/1.56 = ( polyno422358502poly_a @ Bs2 @ ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ zero_zero_nat ) @ P ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_158_shift1__isnpolyh,axiom,
% 2.87/1.56 ! [P: polyno1532895200ly_nat,N0: nat] :
% 2.87/1.56 ( ( polyno892049031yh_nat @ P @ N0 )
% 2.87/1.56 => ( ( P
% 2.87/1.56 != ( polyno2122022170_C_nat @ zero_zero_nat ) )
% 2.87/1.56 => ( polyno892049031yh_nat @ ( polyno1964927358t1_nat @ P ) @ zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_159_shift1__isnpolyh,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N0: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N0 )
% 2.87/1.56 => ( ( P
% 2.87/1.56 != ( polyno439679028le_C_a @ zero_zero_a ) )
% 2.87/1.56 => ( polyno1372495879olyh_a @ ( polyno784948432ift1_a @ P ) @ zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_160_nat__mult__eq__1__iff,axiom,
% 2.87/1.56 ! [M: nat,N: nat] :
% 2.87/1.56 ( ( ( times_times_nat @ M @ N )
% 2.87/1.56 = one_one_nat )
% 2.87/1.56 = ( ( M = one_one_nat )
% 2.87/1.56 & ( N = one_one_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_161_nat__1__eq__mult__iff,axiom,
% 2.87/1.56 ! [M: nat,N: nat] :
% 2.87/1.56 ( ( one_one_nat
% 2.87/1.56 = ( times_times_nat @ M @ N ) )
% 2.87/1.56 = ( ( M = one_one_nat )
% 2.87/1.56 & ( N = one_one_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_162_nat__mult__1__right,axiom,
% 2.87/1.56 ! [N: nat] :
% 2.87/1.56 ( ( times_times_nat @ N @ one_one_nat )
% 2.87/1.56 = N ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_163_nat__mult__1,axiom,
% 2.87/1.56 ! [N: nat] :
% 2.87/1.56 ( ( times_times_nat @ one_one_nat @ N )
% 2.87/1.56 = N ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_164_mult__eq__self__implies__10,axiom,
% 2.87/1.56 ! [M: nat,N: nat] :
% 2.87/1.56 ( ( M
% 2.87/1.56 = ( times_times_nat @ M @ N ) )
% 2.87/1.56 => ( ( N = one_one_nat )
% 2.87/1.56 | ( M = zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_165_mult__0,axiom,
% 2.87/1.56 ! [N: nat] :
% 2.87/1.56 ( ( times_times_nat @ zero_zero_nat @ N )
% 2.87/1.56 = zero_zero_nat ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_166_shift1__nz,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno784948432ift1_a @ P )
% 2.87/1.56 != ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_167_shift1__nz,axiom,
% 2.87/1.56 ! [P: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1964927358t1_nat @ P )
% 2.87/1.56 != ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_168_shift1__isnpoly,axiom,
% 2.87/1.56 ! [P: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1013235523ly_nat @ P )
% 2.87/1.56 => ( ( P
% 2.87/1.56 != ( polyno2122022170_C_nat @ zero_zero_nat ) )
% 2.87/1.56 => ( polyno1013235523ly_nat @ ( polyno1964927358t1_nat @ P ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_169_shift1__isnpoly,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno190918219poly_a @ P )
% 2.87/1.56 => ( ( P
% 2.87/1.56 != ( polyno439679028le_C_a @ zero_zero_a ) )
% 2.87/1.56 => ( polyno190918219poly_a @ ( polyno784948432ift1_a @ P ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_170_shift1__def,axiom,
% 2.87/1.56 ( polyno784948432ift1_a
% 2.87/1.56 = ( polyno1057396216e_CN_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_171_shift1__def,axiom,
% 2.87/1.56 ( polyno1964927358t1_nat
% 2.87/1.56 = ( polyno720942678CN_nat @ ( polyno2122022170_C_nat @ zero_zero_nat ) @ zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_172_nat__mult__eq__cancel__disj,axiom,
% 2.87/1.56 ! [K2: nat,M: nat,N: nat] :
% 2.87/1.56 ( ( ( times_times_nat @ K2 @ M )
% 2.87/1.56 = ( times_times_nat @ K2 @ N ) )
% 2.87/1.56 = ( ( K2 = zero_zero_nat )
% 2.87/1.56 | ( M = N ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_173_headn__nz,axiom,
% 2.87/1.56 ! [P: polyno1532895200ly_nat,N0: nat,M: nat] :
% 2.87/1.56 ( ( polyno892049031yh_nat @ P @ N0 )
% 2.87/1.56 => ( ( ( polyno544860353dn_nat @ P @ M )
% 2.87/1.56 = ( polyno2122022170_C_nat @ zero_zero_nat ) )
% 2.87/1.56 = ( P
% 2.87/1.56 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_174_headn__nz,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N0: nat,M: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N0 )
% 2.87/1.56 => ( ( ( polyno567601229eadn_a @ P @ M )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) )
% 2.87/1.56 = ( P
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_175_headconst__zero,axiom,
% 2.87/1.56 ! [P: polyno1532895200ly_nat,N0: nat] :
% 2.87/1.56 ( ( polyno892049031yh_nat @ P @ N0 )
% 2.87/1.56 => ( ( ( polyno524777654st_nat @ P )
% 2.87/1.56 = zero_zero_nat )
% 2.87/1.56 = ( P
% 2.87/1.56 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_176_headconst__zero,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N0: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N0 )
% 2.87/1.56 => ( ( ( polyno2115742616onst_a @ P )
% 2.87/1.56 = zero_zero_a )
% 2.87/1.56 = ( P
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_177_polysub__same__0,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N0: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N0 )
% 2.87/1.56 => ( ( polyno1418491367ysub_a @ P @ P )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_178_polysubst0_Osimps_I8_J,axiom,
% 2.87/1.56 ! [N: nat,T: polyno1532895200ly_nat,C: polyno1532895200ly_nat,P: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( ( N = zero_zero_nat )
% 2.87/1.56 => ( ( polyno336795754t0_nat @ T @ ( polyno720942678CN_nat @ C @ N @ P ) )
% 2.87/1.56 = ( polyno1222032024dd_nat @ ( polyno336795754t0_nat @ T @ C ) @ ( polyno1415441627ul_nat @ T @ ( polyno336795754t0_nat @ T @ P ) ) ) ) )
% 2.87/1.56 & ( ( N != zero_zero_nat )
% 2.87/1.56 => ( ( polyno336795754t0_nat @ T @ ( polyno720942678CN_nat @ C @ N @ P ) )
% 2.87/1.56 = ( polyno720942678CN_nat @ ( polyno336795754t0_nat @ T @ C ) @ N @ ( polyno336795754t0_nat @ T @ P ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_179_polysubst0_Osimps_I8_J,axiom,
% 2.87/1.56 ! [N: nat,T: polyno727731844poly_a,C: polyno727731844poly_a,P: polyno727731844poly_a] :
% 2.87/1.56 ( ( ( N = zero_zero_nat )
% 2.87/1.56 => ( ( polyno1397854436bst0_a @ T @ ( polyno1057396216e_CN_a @ C @ N @ P ) )
% 2.87/1.56 = ( polyno1623170614_Add_a @ ( polyno1397854436bst0_a @ T @ C ) @ ( polyno1491482291_Mul_a @ T @ ( polyno1397854436bst0_a @ T @ P ) ) ) ) )
% 2.87/1.56 & ( ( N != zero_zero_nat )
% 2.87/1.56 => ( ( polyno1397854436bst0_a @ T @ ( polyno1057396216e_CN_a @ C @ N @ P ) )
% 2.87/1.56 = ( polyno1057396216e_CN_a @ ( polyno1397854436bst0_a @ T @ C ) @ N @ ( polyno1397854436bst0_a @ T @ P ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_180_polysubst0_Osimps_I1_J,axiom,
% 2.87/1.56 ! [T: polyno727731844poly_a,C: a] :
% 2.87/1.56 ( ( polyno1397854436bst0_a @ T @ ( polyno439679028le_C_a @ C ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ C ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_181_polysubst0_Osimps_I1_J,axiom,
% 2.87/1.56 ! [T: polyno1532895200ly_nat,C: nat] :
% 2.87/1.56 ( ( polyno336795754t0_nat @ T @ ( polyno2122022170_C_nat @ C ) )
% 2.87/1.56 = ( polyno2122022170_C_nat @ C ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_182_polysubst0_Osimps_I6_J,axiom,
% 2.87/1.56 ! [T: polyno1532895200ly_nat,A: polyno1532895200ly_nat,B: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno336795754t0_nat @ T @ ( polyno1415441627ul_nat @ A @ B ) )
% 2.87/1.56 = ( polyno1415441627ul_nat @ ( polyno336795754t0_nat @ T @ A ) @ ( polyno336795754t0_nat @ T @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_183_polysubst0_Osimps_I6_J,axiom,
% 2.87/1.56 ! [T: polyno727731844poly_a,A: polyno727731844poly_a,B: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1397854436bst0_a @ T @ ( polyno1491482291_Mul_a @ A @ B ) )
% 2.87/1.56 = ( polyno1491482291_Mul_a @ ( polyno1397854436bst0_a @ T @ A ) @ ( polyno1397854436bst0_a @ T @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_184_polysubst0_Osimps_I4_J,axiom,
% 2.87/1.56 ! [T: polyno727731844poly_a,A: polyno727731844poly_a,B: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1397854436bst0_a @ T @ ( polyno1623170614_Add_a @ A @ B ) )
% 2.87/1.56 = ( polyno1623170614_Add_a @ ( polyno1397854436bst0_a @ T @ A ) @ ( polyno1397854436bst0_a @ T @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_185_polysubst0_Osimps_I4_J,axiom,
% 2.87/1.56 ! [T: polyno1532895200ly_nat,A: polyno1532895200ly_nat,B: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno336795754t0_nat @ T @ ( polyno1222032024dd_nat @ A @ B ) )
% 2.87/1.56 = ( polyno1222032024dd_nat @ ( polyno336795754t0_nat @ T @ A ) @ ( polyno336795754t0_nat @ T @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_186_headn_Osimps_I2_J,axiom,
% 2.87/1.56 ! [V: a] :
% 2.87/1.56 ( ( polyno567601229eadn_a @ ( polyno439679028le_C_a @ V ) )
% 2.87/1.56 = ( ^ [M2: nat] : ( polyno439679028le_C_a @ V ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_187_headn_Osimps_I2_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno544860353dn_nat @ ( polyno2122022170_C_nat @ V ) )
% 2.87/1.56 = ( ^ [M2: nat] : ( polyno2122022170_C_nat @ V ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_188_headn_Osimps_I6_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno544860353dn_nat @ ( polyno1415441627ul_nat @ V @ Va ) )
% 2.87/1.56 = ( ^ [M2: nat] : ( polyno1415441627ul_nat @ V @ Va ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_189_headn_Osimps_I6_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno567601229eadn_a @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 2.87/1.56 = ( ^ [M2: nat] : ( polyno1491482291_Mul_a @ V @ Va ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_190_headn_Osimps_I4_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno567601229eadn_a @ ( polyno1623170614_Add_a @ V @ Va ) )
% 2.87/1.56 = ( ^ [M2: nat] : ( polyno1623170614_Add_a @ V @ Va ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_191_headn_Osimps_I4_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno544860353dn_nat @ ( polyno1222032024dd_nat @ V @ Va ) )
% 2.87/1.56 = ( ^ [M2: nat] : ( polyno1222032024dd_nat @ V @ Va ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_192_headn_Osimps_I3_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno567601229eadn_a @ ( polyno2024845497ound_a @ V ) )
% 2.87/1.56 = ( ^ [M2: nat] : ( polyno2024845497ound_a @ V ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_193_headn_Osimps_I3_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno544860353dn_nat @ ( polyno1999838549nd_nat @ V ) )
% 2.87/1.56 = ( ^ [M2: nat] : ( polyno1999838549nd_nat @ V ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_194_wf__bs__polysub,axiom,
% 2.87/1.56 ! [Bs2: list_a,P: polyno727731844poly_a,Q: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno896877631f_bs_a @ Bs2 @ P )
% 2.87/1.56 => ( ( polyno896877631f_bs_a @ Bs2 @ Q )
% 2.87/1.56 => ( polyno896877631f_bs_a @ Bs2 @ ( polyno1418491367ysub_a @ P @ Q ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_195_polysub__norm,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,Q: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno190918219poly_a @ P )
% 2.87/1.56 => ( ( polyno190918219poly_a @ Q )
% 2.87/1.56 => ( polyno190918219poly_a @ ( polyno1418491367ysub_a @ P @ Q ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_196_headconst_Osimps_I1_J,axiom,
% 2.87/1.56 ! [C: polyno727731844poly_a,N: nat,P: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno2115742616onst_a @ ( polyno1057396216e_CN_a @ C @ N @ P ) )
% 2.87/1.56 = ( polyno2115742616onst_a @ P ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_197_headconst_Osimps_I1_J,axiom,
% 2.87/1.56 ! [C: polyno1532895200ly_nat,N: nat,P: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno524777654st_nat @ ( polyno720942678CN_nat @ C @ N @ P ) )
% 2.87/1.56 = ( polyno524777654st_nat @ P ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_198_headconst_Osimps_I2_J,axiom,
% 2.87/1.56 ! [N: a] :
% 2.87/1.56 ( ( polyno2115742616onst_a @ ( polyno439679028le_C_a @ N ) )
% 2.87/1.56 = N ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_199_headconst_Osimps_I2_J,axiom,
% 2.87/1.56 ! [N: nat] :
% 2.87/1.56 ( ( polyno524777654st_nat @ ( polyno2122022170_C_nat @ N ) )
% 2.87/1.56 = N ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_200_polysubst0_Osimps_I2_J,axiom,
% 2.87/1.56 ! [N: nat,T: polyno727731844poly_a] :
% 2.87/1.56 ( ( ( N = zero_zero_nat )
% 2.87/1.56 => ( ( polyno1397854436bst0_a @ T @ ( polyno2024845497ound_a @ N ) )
% 2.87/1.56 = T ) )
% 2.87/1.56 & ( ( N != zero_zero_nat )
% 2.87/1.56 => ( ( polyno1397854436bst0_a @ T @ ( polyno2024845497ound_a @ N ) )
% 2.87/1.56 = ( polyno2024845497ound_a @ N ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_201_polysubst0_Osimps_I2_J,axiom,
% 2.87/1.56 ! [N: nat,T: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( ( N = zero_zero_nat )
% 2.87/1.56 => ( ( polyno336795754t0_nat @ T @ ( polyno1999838549nd_nat @ N ) )
% 2.87/1.56 = T ) )
% 2.87/1.56 & ( ( N != zero_zero_nat )
% 2.87/1.56 => ( ( polyno336795754t0_nat @ T @ ( polyno1999838549nd_nat @ N ) )
% 2.87/1.56 = ( polyno1999838549nd_nat @ N ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_202_polysub__0,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N0: nat,Q: polyno727731844poly_a,N1: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N0 )
% 2.87/1.56 => ( ( polyno1372495879olyh_a @ Q @ N1 )
% 2.87/1.56 => ( ( ( polyno1418491367ysub_a @ P @ Q )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) )
% 2.87/1.56 = ( P = Q ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_203_headnz,axiom,
% 2.87/1.56 ! [P: polyno1532895200ly_nat,N: nat,M: nat] :
% 2.87/1.56 ( ( polyno892049031yh_nat @ P @ N )
% 2.87/1.56 => ( ( P
% 2.87/1.56 != ( polyno2122022170_C_nat @ zero_zero_nat ) )
% 2.87/1.56 => ( ( polyno544860353dn_nat @ P @ M )
% 2.87/1.56 != ( polyno2122022170_C_nat @ zero_zero_nat ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_204_headnz,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N: nat,M: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N )
% 2.87/1.56 => ( ( P
% 2.87/1.56 != ( polyno439679028le_C_a @ zero_zero_a ) )
% 2.87/1.56 => ( ( polyno567601229eadn_a @ P @ M )
% 2.87/1.56 != ( polyno439679028le_C_a @ zero_zero_a ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_205_degree__npolyhCN,axiom,
% 2.87/1.56 ! [C: polyno1532895200ly_nat,N: nat,P: polyno1532895200ly_nat,N0: nat] :
% 2.87/1.56 ( ( polyno892049031yh_nat @ ( polyno720942678CN_nat @ C @ N @ P ) @ N0 )
% 2.87/1.56 => ( ( polyno220183259ee_nat @ C )
% 2.87/1.56 = zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_206_degree__npolyhCN,axiom,
% 2.87/1.56 ! [C: polyno727731844poly_a,N: nat,P: polyno727731844poly_a,N0: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ ( polyno1057396216e_CN_a @ C @ N @ P ) @ N0 )
% 2.87/1.56 => ( ( polyno578545843gree_a @ C )
% 2.87/1.56 = zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_207_poly__deriv_Osimps_I3_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno212464073eriv_a @ ( polyno2024845497ound_a @ V ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_208_poly__deriv_Osimps_I4_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno212464073eriv_a @ ( polyno1623170614_Add_a @ V @ Va ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_209_poly__deriv_Osimps_I6_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno212464073eriv_a @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_210_degree_Osimps_I2_J,axiom,
% 2.87/1.56 ! [V: a] :
% 2.87/1.56 ( ( polyno578545843gree_a @ ( polyno439679028le_C_a @ V ) )
% 2.87/1.56 = zero_zero_nat ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_211_degree_Osimps_I2_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno220183259ee_nat @ ( polyno2122022170_C_nat @ V ) )
% 2.87/1.56 = zero_zero_nat ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_212_degree_Osimps_I6_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno220183259ee_nat @ ( polyno1415441627ul_nat @ V @ Va ) )
% 2.87/1.56 = zero_zero_nat ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_213_degree_Osimps_I6_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno578545843gree_a @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 2.87/1.56 = zero_zero_nat ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_214_degree_Osimps_I4_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno578545843gree_a @ ( polyno1623170614_Add_a @ V @ Va ) )
% 2.87/1.56 = zero_zero_nat ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_215_degree_Osimps_I4_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno220183259ee_nat @ ( polyno1222032024dd_nat @ V @ Va ) )
% 2.87/1.56 = zero_zero_nat ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_216_degree_Osimps_I3_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno578545843gree_a @ ( polyno2024845497ound_a @ V ) )
% 2.87/1.56 = zero_zero_nat ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_217_degree_Osimps_I3_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno220183259ee_nat @ ( polyno1999838549nd_nat @ V ) )
% 2.87/1.56 = zero_zero_nat ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_218_poly__deriv_Osimps_I2_J,axiom,
% 2.87/1.56 ! [V: a] :
% 2.87/1.56 ( ( polyno212464073eriv_a @ ( polyno439679028le_C_a @ V ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_219_poly__deriv_Osimps_I1_J,axiom,
% 2.87/1.56 ! [C: polyno727731844poly_a,P: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno212464073eriv_a @ ( polyno1057396216e_CN_a @ C @ zero_zero_nat @ P ) )
% 2.87/1.56 = ( polyno1006823949_aux_a @ one_one_a @ P ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_220_funpow__shift1__1,axiom,
% 2.87/1.56 ! [Bs2: list_a,N: nat,P: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno422358502poly_a @ Bs2 @ ( compow1114216044poly_a @ N @ polyno784948432ift1_a @ P ) )
% 2.87/1.56 = ( polyno422358502poly_a @ Bs2 @ ( polyno1934269411ymul_a @ ( compow1114216044poly_a @ N @ polyno784948432ift1_a @ ( polyno439679028le_C_a @ one_one_a ) ) @ P ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_221_head__nz,axiom,
% 2.87/1.56 ! [P: polyno1532895200ly_nat,N0: nat] :
% 2.87/1.56 ( ( polyno892049031yh_nat @ P @ N0 )
% 2.87/1.56 => ( ( ( polyno1952548879ad_nat @ P )
% 2.87/1.56 = ( polyno2122022170_C_nat @ zero_zero_nat ) )
% 2.87/1.56 = ( P
% 2.87/1.56 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_222_head__nz,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N0: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N0 )
% 2.87/1.56 => ( ( ( polyno1884029055head_a @ P )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) )
% 2.87/1.56 = ( P
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_223_degreen__npolyhCN,axiom,
% 2.87/1.56 ! [C: polyno1532895200ly_nat,N: nat,P: polyno1532895200ly_nat,N0: nat] :
% 2.87/1.56 ( ( polyno892049031yh_nat @ ( polyno720942678CN_nat @ C @ N @ P ) @ N0 )
% 2.87/1.56 => ( ( polyno1779722485en_nat @ C @ N )
% 2.87/1.56 = zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_224_degreen__npolyhCN,axiom,
% 2.87/1.56 ! [C: polyno727731844poly_a,N: nat,P: polyno727731844poly_a,N0: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ ( polyno1057396216e_CN_a @ C @ N @ P ) @ N0 )
% 2.87/1.56 => ( ( polyno1674775833reen_a @ C @ N )
% 2.87/1.56 = zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_225_funpow__0,axiom,
% 2.87/1.56 ! [F: polyno727731844poly_a > polyno727731844poly_a,X: polyno727731844poly_a] :
% 2.87/1.56 ( ( compow1114216044poly_a @ zero_zero_nat @ F @ X )
% 2.87/1.56 = X ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_226_funpow__0,axiom,
% 2.87/1.56 ! [F: polyno1532895200ly_nat > polyno1532895200ly_nat,X: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( compow808008746ly_nat @ zero_zero_nat @ F @ X )
% 2.87/1.56 = X ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_227_funpow__swap1,axiom,
% 2.87/1.56 ! [F: polyno727731844poly_a > polyno727731844poly_a,N: nat,X: polyno727731844poly_a] :
% 2.87/1.56 ( ( F @ ( compow1114216044poly_a @ N @ F @ X ) )
% 2.87/1.56 = ( compow1114216044poly_a @ N @ F @ ( F @ X ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_228_funpow__swap1,axiom,
% 2.87/1.56 ! [F: polyno1532895200ly_nat > polyno1532895200ly_nat,N: nat,X: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( F @ ( compow808008746ly_nat @ N @ F @ X ) )
% 2.87/1.56 = ( compow808008746ly_nat @ N @ F @ ( F @ X ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_229_funpow__isnpolyh,axiom,
% 2.87/1.56 ! [N: nat,F: polyno1532895200ly_nat > polyno1532895200ly_nat,P: polyno1532895200ly_nat,K2: nat] :
% 2.87/1.56 ( ! [P4: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno892049031yh_nat @ P4 @ N )
% 2.87/1.56 => ( polyno892049031yh_nat @ ( F @ P4 ) @ N ) )
% 2.87/1.56 => ( ( polyno892049031yh_nat @ P @ N )
% 2.87/1.56 => ( polyno892049031yh_nat @ ( compow808008746ly_nat @ K2 @ F @ P ) @ N ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_230_funpow__isnpolyh,axiom,
% 2.87/1.56 ! [N: nat,F: polyno727731844poly_a > polyno727731844poly_a,P: polyno727731844poly_a,K2: nat] :
% 2.87/1.56 ( ! [P4: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P4 @ N )
% 2.87/1.56 => ( polyno1372495879olyh_a @ ( F @ P4 ) @ N ) )
% 2.87/1.56 => ( ( polyno1372495879olyh_a @ P @ N )
% 2.87/1.56 => ( polyno1372495879olyh_a @ ( compow1114216044poly_a @ K2 @ F @ P ) @ N ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_231_funpow__mult,axiom,
% 2.87/1.56 ! [N: nat,M: nat,F: polyno727731844poly_a > polyno727731844poly_a] :
% 2.87/1.56 ( ( compow1114216044poly_a @ N @ ( compow1114216044poly_a @ M @ F ) )
% 2.87/1.56 = ( compow1114216044poly_a @ ( times_times_nat @ M @ N ) @ F ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_232_funpow__mult,axiom,
% 2.87/1.56 ! [N: nat,M: nat,F: polyno1532895200ly_nat > polyno1532895200ly_nat] :
% 2.87/1.56 ( ( compow808008746ly_nat @ N @ ( compow808008746ly_nat @ M @ F ) )
% 2.87/1.56 = ( compow808008746ly_nat @ ( times_times_nat @ M @ N ) @ F ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_233_head_Osimps_I2_J,axiom,
% 2.87/1.56 ! [V: a] :
% 2.87/1.56 ( ( polyno1884029055head_a @ ( polyno439679028le_C_a @ V ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ V ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_234_head_Osimps_I2_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno1952548879ad_nat @ ( polyno2122022170_C_nat @ V ) )
% 2.87/1.56 = ( polyno2122022170_C_nat @ V ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_235_head_Osimps_I6_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1952548879ad_nat @ ( polyno1415441627ul_nat @ V @ Va ) )
% 2.87/1.56 = ( polyno1415441627ul_nat @ V @ Va ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_236_head_Osimps_I6_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1884029055head_a @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 2.87/1.56 = ( polyno1491482291_Mul_a @ V @ Va ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_237_head_Osimps_I4_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1884029055head_a @ ( polyno1623170614_Add_a @ V @ Va ) )
% 2.87/1.56 = ( polyno1623170614_Add_a @ V @ Va ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_238_head_Osimps_I4_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1952548879ad_nat @ ( polyno1222032024dd_nat @ V @ Va ) )
% 2.87/1.56 = ( polyno1222032024dd_nat @ V @ Va ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_239_head_Osimps_I3_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno1884029055head_a @ ( polyno2024845497ound_a @ V ) )
% 2.87/1.56 = ( polyno2024845497ound_a @ V ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_240_head_Osimps_I3_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno1952548879ad_nat @ ( polyno1999838549nd_nat @ V ) )
% 2.87/1.56 = ( polyno1999838549nd_nat @ V ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_241_head__isnpolyh,axiom,
% 2.87/1.56 ! [P: polyno1532895200ly_nat,N0: nat] :
% 2.87/1.56 ( ( polyno892049031yh_nat @ P @ N0 )
% 2.87/1.56 => ( polyno892049031yh_nat @ ( polyno1952548879ad_nat @ P ) @ N0 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_242_head__isnpolyh,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N0: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N0 )
% 2.87/1.56 => ( polyno1372495879olyh_a @ ( polyno1884029055head_a @ P ) @ N0 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_243_degreen_Osimps_I2_J,axiom,
% 2.87/1.56 ! [V: a] :
% 2.87/1.56 ( ( polyno1674775833reen_a @ ( polyno439679028le_C_a @ V ) )
% 2.87/1.56 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_244_degreen_Osimps_I2_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno1779722485en_nat @ ( polyno2122022170_C_nat @ V ) )
% 2.87/1.56 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_245_degreen_Osimps_I6_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1779722485en_nat @ ( polyno1415441627ul_nat @ V @ Va ) )
% 2.87/1.56 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_246_degreen_Osimps_I6_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1674775833reen_a @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 2.87/1.56 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_247_degreen_Osimps_I4_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1674775833reen_a @ ( polyno1623170614_Add_a @ V @ Va ) )
% 2.87/1.56 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_248_degreen_Osimps_I4_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1779722485en_nat @ ( polyno1222032024dd_nat @ V @ Va ) )
% 2.87/1.56 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_249_degreen_Osimps_I3_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno1674775833reen_a @ ( polyno2024845497ound_a @ V ) )
% 2.87/1.56 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_250_degreen_Osimps_I3_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno1779722485en_nat @ ( polyno1999838549nd_nat @ V ) )
% 2.87/1.56 = ( ^ [M2: nat] : zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_251_head_Osimps_I1_J,axiom,
% 2.87/1.56 ! [C: polyno727731844poly_a,P: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1884029055head_a @ ( polyno1057396216e_CN_a @ C @ zero_zero_nat @ P ) )
% 2.87/1.56 = ( polyno1884029055head_a @ P ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_252_head_Osimps_I1_J,axiom,
% 2.87/1.56 ! [C: polyno1532895200ly_nat,P: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1952548879ad_nat @ ( polyno720942678CN_nat @ C @ zero_zero_nat @ P ) )
% 2.87/1.56 = ( polyno1952548879ad_nat @ P ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_253_head__eq__headn0,axiom,
% 2.87/1.56 ( polyno1884029055head_a
% 2.87/1.56 = ( ^ [P2: polyno727731844poly_a] : ( polyno567601229eadn_a @ P2 @ zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_254_head__eq__headn0,axiom,
% 2.87/1.56 ( polyno1952548879ad_nat
% 2.87/1.56 = ( ^ [P2: polyno1532895200ly_nat] : ( polyno544860353dn_nat @ P2 @ zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_255_poly__deriv__aux_Osimps_I2_J,axiom,
% 2.87/1.56 ! [N: a,V: a] :
% 2.87/1.56 ( ( polyno1006823949_aux_a @ N @ ( polyno439679028le_C_a @ V ) )
% 2.87/1.56 = ( polyno562434098cmul_a @ N @ ( polyno439679028le_C_a @ V ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_256_poly__deriv__aux_Osimps_I6_J,axiom,
% 2.87/1.56 ! [N: a,V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1006823949_aux_a @ N @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 2.87/1.56 = ( polyno562434098cmul_a @ N @ ( polyno1491482291_Mul_a @ V @ Va ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_257_funpow__shift1__isnpoly,axiom,
% 2.87/1.56 ! [P: polyno1532895200ly_nat,N: nat] :
% 2.87/1.56 ( ( polyno1013235523ly_nat @ P )
% 2.87/1.56 => ( ( P
% 2.87/1.56 != ( polyno2122022170_C_nat @ zero_zero_nat ) )
% 2.87/1.56 => ( polyno1013235523ly_nat @ ( compow808008746ly_nat @ N @ polyno1964927358t1_nat @ P ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_258_funpow__shift1__isnpoly,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N: nat] :
% 2.87/1.56 ( ( polyno190918219poly_a @ P )
% 2.87/1.56 => ( ( P
% 2.87/1.56 != ( polyno439679028le_C_a @ zero_zero_a ) )
% 2.87/1.56 => ( polyno190918219poly_a @ ( compow1114216044poly_a @ N @ polyno784948432ift1_a @ P ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_259_funpow__shift1,axiom,
% 2.87/1.56 ! [Bs2: list_a,N: nat,P: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno422358502poly_a @ Bs2 @ ( compow1114216044poly_a @ N @ polyno784948432ift1_a @ P ) )
% 2.87/1.56 = ( polyno422358502poly_a @ Bs2 @ ( polyno1491482291_Mul_a @ ( polyno1538138524e_Pw_a @ ( polyno2024845497ound_a @ zero_zero_nat ) @ N ) @ P ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_260_add__left__cancel,axiom,
% 2.87/1.56 ! [A: nat,B: nat,C: nat] :
% 2.87/1.56 ( ( ( plus_plus_nat @ A @ B )
% 2.87/1.56 = ( plus_plus_nat @ A @ C ) )
% 2.87/1.56 = ( B = C ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_261_add__right__cancel,axiom,
% 2.87/1.56 ! [B: nat,A: nat,C: nat] :
% 2.87/1.56 ( ( ( plus_plus_nat @ B @ A )
% 2.87/1.56 = ( plus_plus_nat @ C @ A ) )
% 2.87/1.56 = ( B = C ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_262_add__is__0,axiom,
% 2.87/1.56 ! [M: nat,N: nat] :
% 2.87/1.56 ( ( ( plus_plus_nat @ M @ N )
% 2.87/1.56 = zero_zero_nat )
% 2.87/1.56 = ( ( M = zero_zero_nat )
% 2.87/1.56 & ( N = zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_263_Nat_Oadd__0__right,axiom,
% 2.87/1.56 ! [M: nat] :
% 2.87/1.56 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 2.87/1.56 = M ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_264_zero__eq__add__iff__both__eq__0,axiom,
% 2.87/1.56 ! [X: nat,Y: nat] :
% 2.87/1.56 ( ( zero_zero_nat
% 2.87/1.56 = ( plus_plus_nat @ X @ Y ) )
% 2.87/1.56 = ( ( X = zero_zero_nat )
% 2.87/1.56 & ( Y = zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_265_add__eq__0__iff__both__eq__0,axiom,
% 2.87/1.56 ! [X: nat,Y: nat] :
% 2.87/1.56 ( ( ( plus_plus_nat @ X @ Y )
% 2.87/1.56 = zero_zero_nat )
% 2.87/1.56 = ( ( X = zero_zero_nat )
% 2.87/1.56 & ( Y = zero_zero_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_266_add__cancel__right__right,axiom,
% 2.87/1.56 ! [A: nat,B: nat] :
% 2.87/1.56 ( ( A
% 2.87/1.56 = ( plus_plus_nat @ A @ B ) )
% 2.87/1.56 = ( B = zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_267_add__cancel__right__left,axiom,
% 2.87/1.56 ! [A: nat,B: nat] :
% 2.87/1.56 ( ( A
% 2.87/1.56 = ( plus_plus_nat @ B @ A ) )
% 2.87/1.56 = ( B = zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_268_add__cancel__left__right,axiom,
% 2.87/1.56 ! [A: nat,B: nat] :
% 2.87/1.56 ( ( ( plus_plus_nat @ A @ B )
% 2.87/1.56 = A )
% 2.87/1.56 = ( B = zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_269_add__cancel__left__left,axiom,
% 2.87/1.56 ! [B: nat,A: nat] :
% 2.87/1.56 ( ( ( plus_plus_nat @ B @ A )
% 2.87/1.56 = A )
% 2.87/1.56 = ( B = zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_270_add_Oright__neutral,axiom,
% 2.87/1.56 ! [A: nat] :
% 2.87/1.56 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 2.87/1.56 = A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_271_add_Oleft__neutral,axiom,
% 2.87/1.56 ! [A: nat] :
% 2.87/1.56 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 2.87/1.56 = A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_272_left__add__mult__distrib,axiom,
% 2.87/1.56 ! [I: nat,U: nat,J: nat,K2: nat] :
% 2.87/1.56 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K2 ) )
% 2.87/1.56 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_273_plus__nat_Oadd__0,axiom,
% 2.87/1.56 ! [N: nat] :
% 2.87/1.56 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 2.87/1.56 = N ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_274_add__eq__self__zero,axiom,
% 2.87/1.56 ! [M: nat,N: nat] :
% 2.87/1.56 ( ( ( plus_plus_nat @ M @ N )
% 2.87/1.56 = M )
% 2.87/1.56 => ( N = zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_275_isnpolyh_Osimps_I8_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ ( polyno1538138524e_Pw_a @ V @ Va ) )
% 2.87/1.56 = ( ^ [K: nat] : $false ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_276_add__mult__distrib2,axiom,
% 2.87/1.56 ! [K2: nat,M: nat,N: nat] :
% 2.87/1.56 ( ( times_times_nat @ K2 @ ( plus_plus_nat @ M @ N ) )
% 2.87/1.56 = ( plus_plus_nat @ ( times_times_nat @ K2 @ M ) @ ( times_times_nat @ K2 @ N ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_277_add__mult__distrib,axiom,
% 2.87/1.56 ! [M: nat,N: nat,K2: nat] :
% 2.87/1.56 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K2 )
% 2.87/1.56 = ( plus_plus_nat @ ( times_times_nat @ M @ K2 ) @ ( times_times_nat @ N @ K2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_278_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.87/1.56 ! [A: nat,B: nat,C: nat] :
% 2.87/1.56 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.87/1.56 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_279_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.87/1.56 ! [I: nat,J: nat,K2: nat,L: nat] :
% 2.87/1.56 ( ( ( I = J )
% 2.87/1.56 & ( K2 = L ) )
% 2.87/1.56 => ( ( plus_plus_nat @ I @ K2 )
% 2.87/1.56 = ( plus_plus_nat @ J @ L ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_280_group__cancel_Oadd1,axiom,
% 2.87/1.56 ! [A3: nat,K2: nat,A: nat,B: nat] :
% 2.87/1.56 ( ( A3
% 2.87/1.56 = ( plus_plus_nat @ K2 @ A ) )
% 2.87/1.56 => ( ( plus_plus_nat @ A3 @ B )
% 2.87/1.56 = ( plus_plus_nat @ K2 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_281_group__cancel_Oadd2,axiom,
% 2.87/1.56 ! [B3: nat,K2: nat,B: nat,A: nat] :
% 2.87/1.56 ( ( B3
% 2.87/1.56 = ( plus_plus_nat @ K2 @ B ) )
% 2.87/1.56 => ( ( plus_plus_nat @ A @ B3 )
% 2.87/1.56 = ( plus_plus_nat @ K2 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_282_add_Oassoc,axiom,
% 2.87/1.56 ! [A: nat,B: nat,C: nat] :
% 2.87/1.56 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.87/1.56 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_283_add_Ocommute,axiom,
% 2.87/1.56 ( plus_plus_nat
% 2.87/1.56 = ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_284_add_Oleft__commute,axiom,
% 2.87/1.56 ! [B: nat,A: nat,C: nat] :
% 2.87/1.56 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 2.87/1.56 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_285_add__left__imp__eq,axiom,
% 2.87/1.56 ! [A: nat,B: nat,C: nat] :
% 2.87/1.56 ( ( ( plus_plus_nat @ A @ B )
% 2.87/1.56 = ( plus_plus_nat @ A @ C ) )
% 2.87/1.56 => ( B = C ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_286_add__right__imp__eq,axiom,
% 2.87/1.56 ! [B: nat,A: nat,C: nat] :
% 2.87/1.56 ( ( ( plus_plus_nat @ B @ A )
% 2.87/1.56 = ( plus_plus_nat @ C @ A ) )
% 2.87/1.56 => ( B = C ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_287_combine__common__factor,axiom,
% 2.87/1.56 ! [A: nat,E: nat,B: nat,C: nat] :
% 2.87/1.56 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 2.87/1.56 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_288_combine__common__factor,axiom,
% 2.87/1.56 ! [A: a,E: a,B: a,C: a] :
% 2.87/1.56 ( ( plus_plus_a @ ( times_times_a @ A @ E ) @ ( plus_plus_a @ ( times_times_a @ B @ E ) @ C ) )
% 2.87/1.56 = ( plus_plus_a @ ( times_times_a @ ( plus_plus_a @ A @ B ) @ E ) @ C ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_289_distrib__right,axiom,
% 2.87/1.56 ! [A: nat,B: nat,C: nat] :
% 2.87/1.56 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.87/1.56 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_290_distrib__right,axiom,
% 2.87/1.56 ! [A: a,B: a,C: a] :
% 2.87/1.56 ( ( times_times_a @ ( plus_plus_a @ A @ B ) @ C )
% 2.87/1.56 = ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_291_distrib__left,axiom,
% 2.87/1.56 ! [A: nat,B: nat,C: nat] :
% 2.87/1.56 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 2.87/1.56 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_292_distrib__left,axiom,
% 2.87/1.56 ! [A: a,B: a,C: a] :
% 2.87/1.56 ( ( times_times_a @ A @ ( plus_plus_a @ B @ C ) )
% 2.87/1.56 = ( plus_plus_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ A @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_293_comm__semiring__class_Odistrib,axiom,
% 2.87/1.56 ! [A: nat,B: nat,C: nat] :
% 2.87/1.56 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.87/1.56 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_294_comm__semiring__class_Odistrib,axiom,
% 2.87/1.56 ! [A: a,B: a,C: a] :
% 2.87/1.56 ( ( times_times_a @ ( plus_plus_a @ A @ B ) @ C )
% 2.87/1.56 = ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_295_ring__class_Oring__distribs_I1_J,axiom,
% 2.87/1.56 ! [A: a,B: a,C: a] :
% 2.87/1.56 ( ( times_times_a @ A @ ( plus_plus_a @ B @ C ) )
% 2.87/1.56 = ( plus_plus_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ A @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_296_ring__class_Oring__distribs_I2_J,axiom,
% 2.87/1.56 ! [A: a,B: a,C: a] :
% 2.87/1.56 ( ( times_times_a @ ( plus_plus_a @ A @ B ) @ C )
% 2.87/1.56 = ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_297_poly_Odistinct_I47_J,axiom,
% 2.87/1.56 ! [X51: polyno727731844poly_a,X52: polyno727731844poly_a,X71: polyno727731844poly_a,X72: nat] :
% 2.87/1.56 ( ( polyno1491482291_Mul_a @ X51 @ X52 )
% 2.87/1.56 != ( polyno1538138524e_Pw_a @ X71 @ X72 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_298_add_Ocomm__neutral,axiom,
% 2.87/1.56 ! [A: nat] :
% 2.87/1.56 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 2.87/1.56 = A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_299_comm__monoid__add__class_Oadd__0,axiom,
% 2.87/1.56 ! [A: nat] :
% 2.87/1.56 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 2.87/1.56 = A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_300_poly_Odistinct_I11_J,axiom,
% 2.87/1.56 ! [X1: a,X71: polyno727731844poly_a,X72: nat] :
% 2.87/1.56 ( ( polyno439679028le_C_a @ X1 )
% 2.87/1.56 != ( polyno1538138524e_Pw_a @ X71 @ X72 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_301_poly_Odistinct_I11_J,axiom,
% 2.87/1.56 ! [X1: nat,X71: polyno1532895200ly_nat,X72: nat] :
% 2.87/1.56 ( ( polyno2122022170_C_nat @ X1 )
% 2.87/1.56 != ( polyno359287218Pw_nat @ X71 @ X72 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_302_polymul_Osimps_I22_J,axiom,
% 2.87/1.56 ! [A: polyno1532895200ly_nat,V: polyno1532895200ly_nat,Va: nat] :
% 2.87/1.56 ( ( polyno929799083ul_nat @ A @ ( polyno359287218Pw_nat @ V @ Va ) )
% 2.87/1.56 = ( polyno1415441627ul_nat @ A @ ( polyno359287218Pw_nat @ V @ Va ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_303_polymul_Osimps_I22_J,axiom,
% 2.87/1.56 ! [A: polyno727731844poly_a,V: polyno727731844poly_a,Va: nat] :
% 2.87/1.56 ( ( polyno1934269411ymul_a @ A @ ( polyno1538138524e_Pw_a @ V @ Va ) )
% 2.87/1.56 = ( polyno1491482291_Mul_a @ A @ ( polyno1538138524e_Pw_a @ V @ Va ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_304_polymul_Osimps_I10_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: nat,B: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno929799083ul_nat @ ( polyno359287218Pw_nat @ V @ Va ) @ B )
% 2.87/1.56 = ( polyno1415441627ul_nat @ ( polyno359287218Pw_nat @ V @ Va ) @ B ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_305_polymul_Osimps_I10_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: nat,B: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1934269411ymul_a @ ( polyno1538138524e_Pw_a @ V @ Va ) @ B )
% 2.87/1.56 = ( polyno1491482291_Mul_a @ ( polyno1538138524e_Pw_a @ V @ Va ) @ B ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_306_Ipoly_Osimps_I4_J,axiom,
% 2.87/1.56 ! [Bs2: list_a,A: polyno727731844poly_a,B: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno422358502poly_a @ Bs2 @ ( polyno1623170614_Add_a @ A @ B ) )
% 2.87/1.56 = ( plus_plus_a @ ( polyno422358502poly_a @ Bs2 @ A ) @ ( polyno422358502poly_a @ Bs2 @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_307_polymul_Osimps_I16_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat,Vc: polyno1532895200ly_nat,Vd: nat] :
% 2.87/1.56 ( ( polyno929799083ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno359287218Pw_nat @ Vc @ Vd ) )
% 2.87/1.56 = ( polyno1415441627ul_nat @ ( polyno720942678CN_nat @ V @ Va @ Vb ) @ ( polyno359287218Pw_nat @ Vc @ Vd ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_308_polymul_Osimps_I16_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a,Vc: polyno727731844poly_a,Vd: nat] :
% 2.87/1.56 ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno1538138524e_Pw_a @ Vc @ Vd ) )
% 2.87/1.56 = ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) @ ( polyno1538138524e_Pw_a @ Vc @ Vd ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_309_polymul_Osimps_I28_J,axiom,
% 2.87/1.56 ! [Vc: polyno1532895200ly_nat,Vd: nat,V: polyno1532895200ly_nat,Va: nat,Vb: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno929799083ul_nat @ ( polyno359287218Pw_nat @ Vc @ Vd ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) )
% 2.87/1.56 = ( polyno1415441627ul_nat @ ( polyno359287218Pw_nat @ Vc @ Vd ) @ ( polyno720942678CN_nat @ V @ Va @ Vb ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_310_polymul_Osimps_I28_J,axiom,
% 2.87/1.56 ! [Vc: polyno727731844poly_a,Vd: nat,V: polyno727731844poly_a,Va: nat,Vb: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1934269411ymul_a @ ( polyno1538138524e_Pw_a @ Vc @ Vd ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) )
% 2.87/1.56 = ( polyno1491482291_Mul_a @ ( polyno1538138524e_Pw_a @ Vc @ Vd ) @ ( polyno1057396216e_CN_a @ V @ Va @ Vb ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_311_poly__cmul_Osimps_I8_J,axiom,
% 2.87/1.56 ! [Y: a,V: polyno727731844poly_a,Va: nat] :
% 2.87/1.56 ( ( polyno562434098cmul_a @ Y @ ( polyno1538138524e_Pw_a @ V @ Va ) )
% 2.87/1.56 = ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ Y ) @ ( polyno1538138524e_Pw_a @ V @ Va ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_312_poly__cmul_Osimps_I8_J,axiom,
% 2.87/1.56 ! [Y: nat,V: polyno1532895200ly_nat,Va: nat] :
% 2.87/1.56 ( ( polyno1467023772ul_nat @ Y @ ( polyno359287218Pw_nat @ V @ Va ) )
% 2.87/1.56 = ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ Y ) @ ( polyno359287218Pw_nat @ V @ Va ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_313_poly__deriv_Osimps_I8_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: nat] :
% 2.87/1.56 ( ( polyno212464073eriv_a @ ( polyno1538138524e_Pw_a @ V @ Va ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_314_behead,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N: nat,Bs2: list_a] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N )
% 2.87/1.56 => ( ( polyno422358502poly_a @ Bs2 @ ( polyno1623170614_Add_a @ ( polyno1491482291_Mul_a @ ( polyno1884029055head_a @ P ) @ ( polyno1538138524e_Pw_a @ ( polyno2024845497ound_a @ zero_zero_nat ) @ ( polyno578545843gree_a @ P ) ) ) @ ( polyno1465139388head_a @ P ) ) )
% 2.87/1.56 = ( polyno422358502poly_a @ Bs2 @ P ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_315_behead__isnpolyh,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N )
% 2.87/1.56 => ( polyno1372495879olyh_a @ ( polyno1465139388head_a @ P ) @ N ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_316_behead_Osimps_I2_J,axiom,
% 2.87/1.56 ! [V: a] :
% 2.87/1.56 ( ( polyno1465139388head_a @ ( polyno439679028le_C_a @ V ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_317_behead_Osimps_I2_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno587244178ad_nat @ ( polyno2122022170_C_nat @ V ) )
% 2.87/1.56 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_318_behead_Osimps_I6_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno587244178ad_nat @ ( polyno1415441627ul_nat @ V @ Va ) )
% 2.87/1.56 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_319_behead_Osimps_I6_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1465139388head_a @ ( polyno1491482291_Mul_a @ V @ Va ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_320_behead_Osimps_I4_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1465139388head_a @ ( polyno1623170614_Add_a @ V @ Va ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_321_behead_Osimps_I4_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno587244178ad_nat @ ( polyno1222032024dd_nat @ V @ Va ) )
% 2.87/1.56 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_322_behead_Osimps_I3_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno1465139388head_a @ ( polyno2024845497ound_a @ V ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_323_behead_Osimps_I3_J,axiom,
% 2.87/1.56 ! [V: nat] :
% 2.87/1.56 ( ( polyno587244178ad_nat @ ( polyno1999838549nd_nat @ V ) )
% 2.87/1.56 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_324_behead_Osimps_I8_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: nat] :
% 2.87/1.56 ( ( polyno1465139388head_a @ ( polyno1538138524e_Pw_a @ V @ Va ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_325_behead_Osimps_I8_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: nat] :
% 2.87/1.56 ( ( polyno587244178ad_nat @ ( polyno359287218Pw_nat @ V @ Va ) )
% 2.87/1.56 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_326_add__scale__eq__noteq,axiom,
% 2.87/1.56 ! [R: nat,A: nat,B: nat,C: nat,D: nat] :
% 2.87/1.56 ( ( R != zero_zero_nat )
% 2.87/1.56 => ( ( ( A = B )
% 2.87/1.56 & ( C != D ) )
% 2.87/1.56 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
% 2.87/1.56 != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_327_add__scale__eq__noteq,axiom,
% 2.87/1.56 ! [R: a,A: a,B: a,C: a,D: a] :
% 2.87/1.56 ( ( R != zero_zero_a )
% 2.87/1.56 => ( ( ( A = B )
% 2.87/1.56 & ( C != D ) )
% 2.87/1.56 => ( ( plus_plus_a @ A @ ( times_times_a @ R @ C ) )
% 2.87/1.56 != ( plus_plus_a @ B @ ( times_times_a @ R @ D ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_328_add__0__iff,axiom,
% 2.87/1.56 ! [B: nat,A: nat] :
% 2.87/1.56 ( ( B
% 2.87/1.56 = ( plus_plus_nat @ B @ A ) )
% 2.87/1.56 = ( A = zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_329_crossproduct__noteq,axiom,
% 2.87/1.56 ! [A: nat,B: nat,C: nat,D: nat] :
% 2.87/1.56 ( ( ( A != B )
% 2.87/1.56 & ( C != D ) )
% 2.87/1.56 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 2.87/1.56 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_330_crossproduct__noteq,axiom,
% 2.87/1.56 ! [A: a,B: a,C: a,D: a] :
% 2.87/1.56 ( ( ( A != B )
% 2.87/1.56 & ( C != D ) )
% 2.87/1.56 = ( ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ D ) )
% 2.87/1.56 != ( plus_plus_a @ ( times_times_a @ A @ D ) @ ( times_times_a @ B @ C ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_331_crossproduct__eq,axiom,
% 2.87/1.56 ! [W: nat,Y: nat,X: nat,Z: nat] :
% 2.87/1.56 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 2.87/1.56 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 2.87/1.56 = ( ( W = X )
% 2.87/1.56 | ( Y = Z ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_332_crossproduct__eq,axiom,
% 2.87/1.56 ! [W: a,Y: a,X: a,Z: a] :
% 2.87/1.56 ( ( ( plus_plus_a @ ( times_times_a @ W @ Y ) @ ( times_times_a @ X @ Z ) )
% 2.87/1.56 = ( plus_plus_a @ ( times_times_a @ W @ Z ) @ ( times_times_a @ X @ Y ) ) )
% 2.87/1.56 = ( ( W = X )
% 2.87/1.56 | ( Y = Z ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_333_Euclid__induct,axiom,
% 2.87/1.56 ! [P5: nat > nat > $o,A: nat,B: nat] :
% 2.87/1.56 ( ! [A4: nat,B4: nat] :
% 2.87/1.56 ( ( P5 @ A4 @ B4 )
% 2.87/1.56 = ( P5 @ B4 @ A4 ) )
% 2.87/1.56 => ( ! [A4: nat] : ( P5 @ A4 @ zero_zero_nat )
% 2.87/1.56 => ( ! [A4: nat,B4: nat] :
% 2.87/1.56 ( ( P5 @ A4 @ B4 )
% 2.87/1.56 => ( P5 @ A4 @ ( plus_plus_nat @ A4 @ B4 ) ) )
% 2.87/1.56 => ( P5 @ A @ B ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_334_verit__sum__simplify,axiom,
% 2.87/1.56 ! [A: nat] :
% 2.87/1.56 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 2.87/1.56 = A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_335_polypow_Osimps_I1_J,axiom,
% 2.87/1.56 ( ( polyno1371724751ypow_a @ zero_zero_nat )
% 2.87/1.56 = ( ^ [P2: polyno727731844poly_a] : ( polyno439679028le_C_a @ one_one_a ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_336_polypow_Osimps_I1_J,axiom,
% 2.87/1.56 ( ( polyno1510045887ow_nat @ zero_zero_nat )
% 2.87/1.56 = ( ^ [P2: polyno1532895200ly_nat] : ( polyno2122022170_C_nat @ one_one_nat ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_337_degreen_Oelims,axiom,
% 2.87/1.56 ! [X: polyno1532895200ly_nat,Y: nat > nat] :
% 2.87/1.56 ( ( ( polyno1779722485en_nat @ X )
% 2.87/1.56 = Y )
% 2.87/1.56 => ( ! [C3: polyno1532895200ly_nat,N3: nat,P4: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( X
% 2.87/1.56 = ( polyno720942678CN_nat @ C3 @ N3 @ P4 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : ( if_nat @ ( N3 = M2 ) @ ( plus_plus_nat @ one_one_nat @ ( polyno1779722485en_nat @ P4 @ N3 ) ) @ zero_zero_nat ) ) ) )
% 2.87/1.56 => ( ( ? [V2: nat] :
% 2.87/1.56 ( X
% 2.87/1.56 = ( polyno2122022170_C_nat @ V2 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 2.87/1.56 => ( ( ? [V2: nat] :
% 2.87/1.56 ( X
% 2.87/1.56 = ( polyno1999838549nd_nat @ V2 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 2.87/1.56 => ( ( ? [V2: polyno1532895200ly_nat,Va2: polyno1532895200ly_nat] :
% 2.87/1.56 ( X
% 2.87/1.56 = ( polyno1222032024dd_nat @ V2 @ Va2 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 2.87/1.56 => ( ( ? [V2: polyno1532895200ly_nat,Va2: polyno1532895200ly_nat] :
% 2.87/1.56 ( X
% 2.87/1.56 = ( polyno1921014231ub_nat @ V2 @ Va2 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 2.87/1.56 => ( ( ? [V2: polyno1532895200ly_nat,Va2: polyno1532895200ly_nat] :
% 2.87/1.56 ( X
% 2.87/1.56 = ( polyno1415441627ul_nat @ V2 @ Va2 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 2.87/1.56 => ( ( ? [V2: polyno1532895200ly_nat] :
% 2.87/1.56 ( X
% 2.87/1.56 = ( polyno1366804583eg_nat @ V2 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 2.87/1.56 => ~ ( ? [V2: polyno1532895200ly_nat,Va2: nat] :
% 2.87/1.56 ( X
% 2.87/1.56 = ( polyno359287218Pw_nat @ V2 @ Va2 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_338_degreen_Oelims,axiom,
% 2.87/1.56 ! [X: polyno727731844poly_a,Y: nat > nat] :
% 2.87/1.56 ( ( ( polyno1674775833reen_a @ X )
% 2.87/1.56 = Y )
% 2.87/1.56 => ( ! [C3: polyno727731844poly_a,N3: nat,P4: polyno727731844poly_a] :
% 2.87/1.56 ( ( X
% 2.87/1.56 = ( polyno1057396216e_CN_a @ C3 @ N3 @ P4 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : ( if_nat @ ( N3 = M2 ) @ ( plus_plus_nat @ one_one_nat @ ( polyno1674775833reen_a @ P4 @ N3 ) ) @ zero_zero_nat ) ) ) )
% 2.87/1.56 => ( ( ? [V2: a] :
% 2.87/1.56 ( X
% 2.87/1.56 = ( polyno439679028le_C_a @ V2 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 2.87/1.56 => ( ( ? [V2: nat] :
% 2.87/1.56 ( X
% 2.87/1.56 = ( polyno2024845497ound_a @ V2 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 2.87/1.56 => ( ( ? [V2: polyno727731844poly_a,Va2: polyno727731844poly_a] :
% 2.87/1.56 ( X
% 2.87/1.56 = ( polyno1623170614_Add_a @ V2 @ Va2 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 2.87/1.56 => ( ( ? [V2: polyno727731844poly_a,Va2: polyno727731844poly_a] :
% 2.87/1.56 ( X
% 2.87/1.56 = ( polyno975704247_Sub_a @ V2 @ Va2 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 2.87/1.56 => ( ( ? [V2: polyno727731844poly_a,Va2: polyno727731844poly_a] :
% 2.87/1.56 ( X
% 2.87/1.56 = ( polyno1491482291_Mul_a @ V2 @ Va2 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 2.87/1.56 => ( ( ? [V2: polyno727731844poly_a] :
% 2.87/1.56 ( X
% 2.87/1.56 = ( polyno96675367_Neg_a @ V2 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : zero_zero_nat ) ) )
% 2.87/1.56 => ~ ( ? [V2: polyno727731844poly_a,Va2: nat] :
% 2.87/1.56 ( X
% 2.87/1.56 = ( polyno1538138524e_Pw_a @ V2 @ Va2 ) )
% 2.87/1.56 => ( Y
% 2.87/1.56 != ( ^ [M2: nat] : zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_339_behead_Osimps_I5_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1465139388head_a @ ( polyno975704247_Sub_a @ V @ Va ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_340_behead_Osimps_I5_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno587244178ad_nat @ ( polyno1921014231ub_nat @ V @ Va ) )
% 2.87/1.56 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_341_poly__cmul_Osimps_I5_J,axiom,
% 2.87/1.56 ! [Y: a,V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno562434098cmul_a @ Y @ ( polyno975704247_Sub_a @ V @ Va ) )
% 2.87/1.56 = ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ Y ) @ ( polyno975704247_Sub_a @ V @ Va ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_342_poly__cmul_Osimps_I5_J,axiom,
% 2.87/1.56 ! [Y: nat,V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1467023772ul_nat @ Y @ ( polyno1921014231ub_nat @ V @ Va ) )
% 2.87/1.56 = ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ Y ) @ ( polyno1921014231ub_nat @ V @ Va ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_343_behead_Osimps_I7_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1465139388head_a @ ( polyno96675367_Neg_a @ V ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_344_behead_Osimps_I7_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno587244178ad_nat @ ( polyno1366804583eg_nat @ V ) )
% 2.87/1.56 = ( polyno2122022170_C_nat @ zero_zero_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_345_poly__cmul_Osimps_I7_J,axiom,
% 2.87/1.56 ! [Y: a,V: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno562434098cmul_a @ Y @ ( polyno96675367_Neg_a @ V ) )
% 2.87/1.56 = ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ Y ) @ ( polyno96675367_Neg_a @ V ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_346_poly__cmul_Osimps_I7_J,axiom,
% 2.87/1.56 ! [Y: nat,V: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno1467023772ul_nat @ Y @ ( polyno1366804583eg_nat @ V ) )
% 2.87/1.56 = ( polyno929799083ul_nat @ ( polyno2122022170_C_nat @ Y ) @ ( polyno1366804583eg_nat @ V ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_347_poly__deriv_Osimps_I5_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno212464073eriv_a @ ( polyno975704247_Sub_a @ V @ Va ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_348_poly__deriv_Osimps_I7_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno212464073eriv_a @ ( polyno96675367_Neg_a @ V ) )
% 2.87/1.56 = ( polyno439679028le_C_a @ zero_zero_a ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_349_polypow__normh,axiom,
% 2.87/1.56 ! [P: polyno727731844poly_a,N: nat,K2: nat] :
% 2.87/1.56 ( ( polyno1372495879olyh_a @ P @ N )
% 2.87/1.56 => ( polyno1372495879olyh_a @ ( polyno1371724751ypow_a @ K2 @ P ) @ N ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_350_polymul_Osimps_I7_J,axiom,
% 2.87/1.56 ! [V: polyno1532895200ly_nat,Va: polyno1532895200ly_nat,B: polyno1532895200ly_nat] :
% 2.87/1.56 ( ( polyno929799083ul_nat @ ( polyno1921014231ub_nat @ V @ Va ) @ B )
% 2.87/1.56 = ( polyno1415441627ul_nat @ ( polyno1921014231ub_nat @ V @ Va ) @ B ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_351_polymul_Osimps_I7_J,axiom,
% 2.87/1.56 ! [V: polyno727731844poly_a,Va: polyno727731844poly_a,B: polyno727731844poly_a] :
% 2.87/1.56 ( ( polyno1934269411ymul_a @ ( polyno975704247_Sub_a @ V @ Va ) @ B )
% 2.87/1.56 = ( polyno1491482291_Mul_a @ ( polyno975704247_Sub_a @ V @ Va ) @ B ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(help_If_3_1_If_001t__Nat__Onat_T,axiom,
% 2.87/1.56 ! [P5: $o] :
% 2.87/1.56 ( ( P5 = $true )
% 2.87/1.56 | ( P5 = $false ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 2.87/1.56 ! [X: nat,Y: nat] :
% 2.87/1.56 ( ( if_nat @ $false @ X @ Y )
% 2.87/1.56 = Y ) ).
% 2.87/1.56
% 2.87/1.56 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 2.87/1.56 ! [X: nat,Y: nat] :
% 2.87/1.56 ( ( if_nat @ $true @ X @ Y )
% 2.87/1.56 = X ) ).
% 2.87/1.56
% 2.87/1.56 thf(conj_0,conjecture,
% 2.87/1.56 ( ( polyno1934269411ymul_a @ p @ q )
% 2.87/1.56 = ( polyno1934269411ymul_a @ q @ p ) ) ).
% 2.87/1.56 ------------------------
% 2.87/1.58 % (3692)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/183Mi)
% 2.87/1.58 % (3698)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/18Mi)
% 2.87/1.58 % (3693)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_3593 for (2999ds/4Mi)
% 2.87/1.58 % (3693)Instruction limit reached!
% 2.87/1.58 % (3693)------------------------------
% 2.87/1.58 % (3693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.58 % (3693)Termination reason: Unknown
% 2.87/1.58 % (3693)Termination phase: shuffling
% 2.87/1.58
% 2.87/1.58 % (3693)Memory used [KB]: 1407
% 2.87/1.58 % (3693)Time elapsed: 0.003 s
% 2.87/1.58 % (3693)Instructions burned: 7 (million)
% 2.87/1.58 % (3693)------------------------------
% 2.87/1.58 % (3693)------------------------------
% 2.87/1.58 % (3698)Instruction limit reached!
% 2.87/1.58 % (3698)------------------------------
% 2.87/1.58 % (3698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.58 % (3698)Termination reason: Unknown
% 2.87/1.58 % (3698)Termination phase: Property scanning
% 2.87/1.58
% 2.87/1.58 % (3698)Memory used [KB]: 1535
% 2.87/1.58 % (3698)Time elapsed: 0.007 s
% 2.87/1.58 % (3698)Instructions burned: 20 (million)
% 2.87/1.58 % (3698)------------------------------
% 2.87/1.58 % (3698)------------------------------
% 2.87/1.59 % (3697)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_3593 for (2999ds/275Mi)
% 2.87/1.59 % (3695)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/2Mi)
% 2.87/1.59 % (3694)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_3593 for (2999ds/27Mi)
% 2.87/1.59 % (3696)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_3593 for (2999ds/2Mi)
% 2.87/1.59 % (3695)Instruction limit reached!
% 2.87/1.59 % (3695)------------------------------
% 2.87/1.59 % (3695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.59 % (3695)Termination reason: Unknown
% 2.87/1.59 % (3695)Termination phase: shuffling
% 2.87/1.59
% 2.87/1.59 % (3696)Instruction limit reached!
% 2.87/1.59 % (3696)------------------------------
% 2.87/1.59 % (3696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.59 % (3695)Memory used [KB]: 1407
% 2.87/1.59 % (3695)Time elapsed: 0.004 s
% 2.87/1.59 % (3695)Instructions burned: 3 (million)
% 2.87/1.59 % (3695)------------------------------
% 2.87/1.59 % (3695)------------------------------
% 2.87/1.59 % (3696)Termination reason: Unknown
% 2.87/1.59 % (3696)Termination phase: shuffling
% 2.87/1.59
% 2.87/1.59 % (3696)Memory used [KB]: 1407
% 2.87/1.59 % (3696)Time elapsed: 0.004 s
% 2.87/1.59 % (3696)Instructions burned: 3 (million)
% 2.87/1.59 % (3696)------------------------------
% 2.87/1.59 % (3696)------------------------------
% 2.87/1.59 % (3699)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/3Mi)
% 2.87/1.59 % (3699)Instruction limit reached!
% 2.87/1.59 % (3699)------------------------------
% 2.87/1.59 % (3699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.59 % (3699)Termination reason: Unknown
% 2.87/1.59 % (3699)Termination phase: shuffling
% 2.87/1.59
% 2.87/1.59 % (3699)Memory used [KB]: 1407
% 2.87/1.59 % (3699)Time elapsed: 0.003 s
% 2.87/1.59 % (3699)Instructions burned: 4 (million)
% 2.87/1.59 % (3699)------------------------------
% 2.87/1.59 % (3699)------------------------------
% 2.87/1.59 % (3700)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_3593 for (2999ds/37Mi)
% 2.93/1.60 % (3694)Instruction limit reached!
% 2.93/1.60 % (3694)------------------------------
% 2.93/1.60 % (3694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.60 % (3694)Termination reason: Unknown
% 2.93/1.60 % (3694)Termination phase: Preprocessing 1
% 2.93/1.60
% 2.93/1.60 % (3694)Memory used [KB]: 1663
% 2.93/1.60 % (3694)Time elapsed: 0.017 s
% 2.93/1.60 % (3694)Instructions burned: 27 (million)
% 2.93/1.60 % (3694)------------------------------
% 2.93/1.60 % (3694)------------------------------
% 2.93/1.60 % (3697)Refutation not found, incomplete strategy
% 2.93/1.60 % (3697)------------------------------
% 2.93/1.60 % (3697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.60 % (3697)Termination reason: Refutation not found, incomplete strategy
% 2.93/1.60
% 2.93/1.60
% 2.93/1.60 % (3697)Memory used [KB]: 6012
% 2.93/1.60 % (3697)Time elapsed: 0.018 s
% 2.93/1.60 % (3697)Instructions burned: 28 (million)
% 2.93/1.60 % (3697)------------------------------
% 2.93/1.60 % (3697)------------------------------
% 2.93/1.60 % (3703)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_3593 for (2999ds/1041Mi)
% 2.93/1.60 % (3700)Instruction limit reached!
% 2.93/1.60 % (3700)------------------------------
% 2.93/1.60 % (3700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.60 % (3700)Termination reason: Unknown
% 2.93/1.60 % (3700)Termination phase: shuffling
% 2.93/1.60
% 2.93/1.60 % (3700)Memory used [KB]: 2174
% 2.93/1.60 % (3700)Time elapsed: 0.011 s
% 2.93/1.60 % (3700)Instructions burned: 38 (million)
% 2.93/1.60 % (3700)------------------------------
% 2.93/1.60 % (3700)------------------------------
% 2.93/1.61 % (3701)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_3593 for (2999ds/15Mi)
% 2.93/1.61 % (3702)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_3593 for (2999ds/3Mi)
% 2.93/1.61 % (3702)Instruction limit reached!
% 2.93/1.61 % (3702)------------------------------
% 2.93/1.61 % (3702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.61 % (3702)Termination reason: Unknown
% 2.93/1.61 % (3702)Termination phase: shuffling
% 2.93/1.61
% 2.93/1.61 % (3702)Memory used [KB]: 1407
% 2.93/1.61 % (3702)Time elapsed: 0.004 s
% 2.93/1.61 % (3702)Instructions burned: 3 (million)
% 2.93/1.61 % (3702)------------------------------
% 2.93/1.61 % (3702)------------------------------
% 2.93/1.61 % (3706)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_3593 for (2999ds/3Mi)
% 2.93/1.61 % (3706)Instruction limit reached!
% 2.93/1.61 % (3706)------------------------------
% 2.93/1.61 % (3706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.61 % (3706)Termination reason: Unknown
% 2.93/1.61 % (3706)Termination phase: shuffling
% 2.93/1.61
% 2.93/1.61 % (3706)Memory used [KB]: 1407
% 2.93/1.61 % (3706)Time elapsed: 0.002 s
% 2.93/1.61 % (3706)Instructions burned: 3 (million)
% 2.93/1.61 % (3706)------------------------------
% 2.93/1.61 % (3706)------------------------------
% 2.93/1.61 % (3701)Instruction limit reached!
% 2.93/1.61 % (3701)------------------------------
% 2.93/1.61 % (3701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.61 % (3701)Termination reason: Unknown
% 2.93/1.61 % (3701)Termination phase: Property scanning
% 2.93/1.61
% 2.93/1.61 % (3701)Memory used [KB]: 1535
% 2.93/1.61 % (3705)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/16Mi)
% 2.93/1.61 % (3701)Time elapsed: 0.011 s
% 2.93/1.61 % (3701)Instructions burned: 16 (million)
% 2.93/1.61 % (3701)------------------------------
% 2.93/1.61 % (3701)------------------------------
% 2.93/1.62 % (3704)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/7Mi)
% 2.93/1.62 % (3705)Instruction limit reached!
% 2.93/1.62 % (3705)------------------------------
% 2.93/1.62 % (3705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.62 % (3705)Termination reason: Unknown
% 2.93/1.62 % (3705)Termination phase: Property scanning
% 2.93/1.62
% 2.93/1.62 % (3705)Memory used [KB]: 1535
% 2.93/1.62 % (3705)Time elapsed: 0.007 s
% 2.93/1.62 % (3705)Instructions burned: 17 (million)
% 2.93/1.62 % (3705)------------------------------
% 2.93/1.62 % (3705)------------------------------
% 2.93/1.62 % (3704)Instruction limit reached!
% 2.93/1.62 % (3704)------------------------------
% 2.93/1.62 % (3704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.62 % (3704)Termination reason: Unknown
% 2.93/1.62 % (3704)Termination phase: shuffling
% 2.93/1.62
% 2.93/1.62 % (3704)Memory used [KB]: 1407
% 2.93/1.62 % (3704)Time elapsed: 0.005 s
% 2.93/1.62 % (3704)Instructions burned: 7 (million)
% 2.93/1.62 % (3704)------------------------------
% 2.93/1.62 % (3704)------------------------------
% 2.93/1.62 % (3708)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/7Mi)
% 2.93/1.63 % (3708)Instruction limit reached!
% 2.93/1.63 % (3708)------------------------------
% 2.93/1.63 % (3708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.63 % (3708)Termination reason: Unknown
% 2.93/1.63 % (3708)Termination phase: shuffling
% 2.93/1.63
% 2.93/1.63 % (3708)Memory used [KB]: 1407
% 2.93/1.63 % (3708)Time elapsed: 0.003 s
% 2.93/1.63 % (3708)Instructions burned: 7 (million)
% 2.93/1.63 % (3707)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_3593 for (2999ds/3Mi)
% 2.93/1.63 % (3708)------------------------------
% 2.93/1.63 % (3708)------------------------------
% 2.93/1.63 % (3707)Instruction limit reached!
% 2.93/1.63 % (3707)------------------------------
% 2.93/1.63 % (3707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.63 % (3707)Termination reason: Unknown
% 2.93/1.63 % (3707)Termination phase: shuffling
% 2.93/1.63
% 2.93/1.63 % (3707)Memory used [KB]: 1407
% 2.93/1.63 % (3707)Time elapsed: 0.004 s
% 2.93/1.63 % (3707)Instructions burned: 3 (million)
% 2.93/1.63 % (3707)------------------------------
% 2.93/1.63 % (3707)------------------------------
% 2.93/1.63 % (3710)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/4Mi)
% 2.93/1.63 % (3710)Instruction limit reached!
% 2.93/1.63 % (3710)------------------------------
% 2.93/1.63 % (3710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.63 % (3710)Termination reason: Unknown
% 2.93/1.63 % (3710)Termination phase: shuffling
% 2.93/1.63
% 2.93/1.63 % (3710)Memory used [KB]: 1407
% 2.93/1.63 % (3710)Time elapsed: 0.003 s
% 2.93/1.63 % (3710)Instructions burned: 4 (million)
% 2.93/1.63 % (3710)------------------------------
% 2.93/1.63 % (3710)------------------------------
% 2.93/1.63 % (3709)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/3Mi)
% 2.93/1.63 % (3711)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/18Mi)
% 2.93/1.63 % (3692)Instruction limit reached!
% 2.93/1.63 % (3692)------------------------------
% 2.93/1.63 % (3692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.63 % (3692)Termination reason: Unknown
% 2.93/1.63 % (3692)Termination phase: Saturation
% 2.93/1.63
% 2.93/1.63 % (3692)Memory used [KB]: 7164
% 2.93/1.63 % (3692)Time elapsed: 0.055 s
% 2.93/1.63 % (3692)Instructions burned: 185 (million)
% 2.93/1.63 % (3692)------------------------------
% 2.93/1.63 % (3692)------------------------------
% 2.93/1.63 % (3709)Instruction limit reached!
% 2.93/1.63 % (3709)------------------------------
% 2.93/1.63 % (3709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.63 % (3709)Termination reason: Unknown
% 2.93/1.63 % (3709)Termination phase: shuffling
% 2.93/1.63
% 2.93/1.63 % (3709)Memory used [KB]: 1407
% 2.93/1.63 % (3709)Time elapsed: 0.004 s
% 2.93/1.63 % (3709)Instructions burned: 3 (million)
% 2.93/1.63 % (3709)------------------------------
% 2.93/1.63 % (3709)------------------------------
% 2.93/1.63 % (3712)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/710Mi)
% 2.93/1.64 % (3711)Instruction limit reached!
% 2.93/1.64 % (3711)------------------------------
% 2.93/1.64 % (3711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.64 % (3711)Termination reason: Unknown
% 2.93/1.64 % (3711)Termination phase: Property scanning
% 2.93/1.64
% 2.93/1.64 % (3711)Memory used [KB]: 1535
% 2.93/1.64 % (3711)Time elapsed: 0.008 s
% 2.93/1.64 % (3711)Instructions burned: 21 (million)
% 2.93/1.64 % (3711)------------------------------
% 2.93/1.64 % (3711)------------------------------
% 2.93/1.64 % (3715)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_3593 for (2999ds/21Mi)
% 2.93/1.64 % (3714)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_3593 for (2999ds/902Mi)
% 2.93/1.64 % (3712)Refutation not found, incomplete strategy
% 2.93/1.64 % (3712)------------------------------
% 2.93/1.64 % (3712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.64 % (3712)Termination reason: Refutation not found, incomplete strategy
% 2.93/1.64
% 2.93/1.64
% 2.93/1.64 % (3712)Memory used [KB]: 6140
% 2.93/1.64 % (3712)Time elapsed: 0.009 s
% 2.93/1.64 % (3712)Instructions burned: 27 (million)
% 2.93/1.64 % (3712)------------------------------
% 2.93/1.64 % (3712)------------------------------
% 2.93/1.64 % (3713)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/6Mi)
% 2.93/1.65 % (3716)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/5Mi)
% 2.93/1.65 % (3715)Instruction limit reached!
% 2.93/1.65 % (3715)------------------------------
% 2.93/1.65 % (3715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.65 % (3715)Termination reason: Unknown
% 2.93/1.65 % (3715)Termination phase: shuffling
% 2.93/1.65
% 2.93/1.65 % (3715)Memory used [KB]: 1791
% 2.93/1.65 % (3715)Time elapsed: 0.008 s
% 2.93/1.65 % (3715)Instructions burned: 23 (million)
% 2.93/1.65 % (3715)------------------------------
% 2.93/1.65 % (3715)------------------------------
% 2.93/1.65 % (3717)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_3593 for (2999ds/6Mi)
% 2.93/1.65 % (3716)Instruction limit reached!
% 2.93/1.65 % (3716)------------------------------
% 2.93/1.65 % (3716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.65 % (3716)Termination reason: Unknown
% 2.93/1.65 % (3716)Termination phase: shuffling
% 2.93/1.65
% 2.93/1.65 % (3716)Memory used [KB]: 1535
% 2.93/1.65 % (3716)Time elapsed: 0.003 s
% 2.93/1.65 % (3716)Instructions burned: 7 (million)
% 2.93/1.65 % (3716)------------------------------
% 2.93/1.65 % (3716)------------------------------
% 2.93/1.65 % (3713)Instruction limit reached!
% 2.93/1.65 % (3713)------------------------------
% 2.93/1.65 % (3713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.65 % (3713)Termination reason: Unknown
% 2.93/1.65 % (3713)Termination phase: shuffling
% 2.93/1.65
% 2.93/1.65 % (3713)Memory used [KB]: 1407
% 2.93/1.65 % (3713)Time elapsed: 0.006 s
% 2.93/1.65 % (3713)Instructions burned: 7 (million)
% 2.93/1.65 % (3713)------------------------------
% 2.93/1.65 % (3713)------------------------------
% 2.93/1.65 % (3717)Instruction limit reached!
% 2.93/1.65 % (3717)------------------------------
% 2.93/1.65 % (3717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.65 % (3717)Termination reason: Unknown
% 2.93/1.65 % (3717)Termination phase: shuffling
% 2.93/1.65
% 2.93/1.65 % (3717)Memory used [KB]: 1535
% 2.93/1.65 % (3717)Time elapsed: 0.004 s
% 2.93/1.65 % (3717)Instructions burned: 7 (million)
% 2.93/1.65 % (3717)------------------------------
% 2.93/1.65 % (3717)------------------------------
% 2.93/1.65 % (3718)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/377Mi)
% 2.93/1.66 % (3719)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_3593 for (2999ds/779Mi)
% 2.93/1.66 % (3720)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_3593 for (2999ds/19Mi)
% 2.93/1.66 % (3722)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/17Mi)
% 2.93/1.66 % (3720)Instruction limit reached!
% 2.93/1.66 % (3720)------------------------------
% 2.93/1.66 % (3720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.66 % (3720)Termination reason: Unknown
% 2.93/1.66 % (3720)Termination phase: shuffling
% 2.93/1.66
% 2.93/1.66 % (3720)Memory used [KB]: 1663
% 2.93/1.66 % (3720)Time elapsed: 0.006 s
% 2.93/1.66 % (3720)Instructions burned: 19 (million)
% 2.93/1.66 % (3720)------------------------------
% 2.93/1.66 % (3720)------------------------------
% 2.93/1.67 % (3721)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3593 for (2999ds/879Mi)
% 2.93/1.67 % (3722)Instruction limit reached!
% 2.93/1.67 % (3722)------------------------------
% 2.93/1.67 % (3722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.67 % (3722)Termination reason: Unknown
% 2.93/1.67 % (3722)Termination phase: Property scanning
% 2.93/1.67
% 2.93/1.67 % (3722)Memory used [KB]: 1535
% 2.93/1.67 % (3722)Time elapsed: 0.008 s
% 2.93/1.67 % (3722)Instructions burned: 19 (million)
% 2.93/1.67 % (3722)------------------------------
% 2.93/1.67 % (3722)------------------------------
% 2.93/1.67 % (3714)Refutation not found, incomplete strategy
% 2.93/1.67 % (3714)------------------------------
% 2.93/1.67 % (3714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.67 % (3714)Termination reason: Refutation not found, incomplete strategy
% 2.93/1.67
% 2.93/1.67
% 2.93/1.67 % (3714)Memory used [KB]: 6908
% 2.93/1.67 % (3714)Time elapsed: 0.031 s
% 2.93/1.67 % (3714)Instructions burned: 96 (million)
% 2.93/1.67 % (3714)------------------------------
% 2.93/1.67 % (3714)------------------------------
% 2.93/1.67 % (3723)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3593 for (2998ds/3Mi)
% 2.93/1.67 % (3723)Instruction limit reached!
% 2.93/1.67 % (3723)------------------------------
% 2.93/1.67 % (3723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.67 % (3723)Termination reason: Unknown
% 2.93/1.67 % (3723)Termination phase: shuffling
% 2.93/1.67
% 2.93/1.67 % (3723)Memory used [KB]: 1407
% 2.93/1.67 % (3723)Time elapsed: 0.002 s
% 2.93/1.67 % (3723)Instructions burned: 3 (million)
% 2.93/1.67 % (3723)------------------------------
% 2.93/1.67 % (3723)------------------------------
% 2.93/1.68 % (3724)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3593 for (2998ds/30Mi)
% 2.93/1.68 % (3725)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3593 for (2998ds/127Mi)
% 2.93/1.68 % (3726)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3593 for (2998ds/100Mi)
% 2.93/1.69 % (3724)Instruction limit reached!
% 2.93/1.69 % (3724)------------------------------
% 2.93/1.69 % (3724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.69 % (3724)Termination reason: Unknown
% 2.93/1.69 % (3724)Termination phase: Property scanning
% 2.93/1.69
% 2.93/1.69 % (3724)Memory used [KB]: 1791
% 2.93/1.69 % (3724)Time elapsed: 0.012 s
% 2.93/1.69 % (3724)Instructions burned: 31 (million)
% 2.93/1.69 % (3724)------------------------------
% 2.93/1.69 % (3724)------------------------------
% 2.93/1.70 % (3727)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_3593 for (2998ds/3Mi)
% 2.93/1.70 % (3727)Instruction limit reached!
% 2.93/1.70 % (3727)------------------------------
% 2.93/1.70 % (3727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.70 % (3727)Termination reason: Unknown
% 2.93/1.70 % (3727)Termination phase: shuffling
% 2.93/1.70
% 2.93/1.70 % (3727)Memory used [KB]: 1407
% 2.93/1.70 % (3727)Time elapsed: 0.002 s
% 2.93/1.70 % (3727)Instructions burned: 3 (million)
% 2.93/1.70 % (3727)------------------------------
% 2.93/1.70 % (3727)------------------------------
% 2.93/1.71 % (3726)Instruction limit reached!
% 2.93/1.71 % (3726)------------------------------
% 2.93/1.71 % (3726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.71 % (3726)Termination reason: Unknown
% 2.93/1.71 % (3726)Termination phase: Property scanning
% 2.93/1.71
% 2.93/1.71 % (3726)Memory used [KB]: 2430
% 2.93/1.71 % (3726)Time elapsed: 0.027 s
% 2.93/1.71 % (3726)Instructions burned: 103 (million)
% 2.93/1.71 % (3726)------------------------------
% 2.93/1.71 % (3726)------------------------------
% 2.93/1.71 % (3728)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_3593 for (2998ds/20Mi)
% 2.93/1.72 % (3728)Instruction limit reached!
% 2.93/1.72 % (3728)------------------------------
% 2.93/1.72 % (3728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.72 % (3728)Termination reason: Unknown
% 2.93/1.72 % (3728)Termination phase: Property scanning
% 2.93/1.72
% 2.93/1.72 % (3728)Memory used [KB]: 1535
% 2.93/1.72 % (3728)Time elapsed: 0.009 s
% 2.93/1.72 % (3728)Instructions burned: 23 (million)
% 2.93/1.72 % (3728)------------------------------
% 2.93/1.72 % (3728)------------------------------
% 2.93/1.72 % (3729)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_3593 for (2998ds/86Mi)
% 2.93/1.72 % (3725)Instruction limit reached!
% 2.93/1.72 % (3725)------------------------------
% 2.93/1.72 % (3725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.72 % (3725)Termination reason: Unknown
% 2.93/1.72 % (3725)Termination phase: Saturation
% 2.93/1.72
% 2.93/1.72 % (3725)Memory used [KB]: 6780
% 2.93/1.72 % (3725)Time elapsed: 0.042 s
% 2.93/1.72 % (3725)Instructions burned: 127 (million)
% 2.93/1.72 % (3725)------------------------------
% 2.93/1.72 % (3725)------------------------------
% 2.93/1.73 % (3730)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_3593 for (2998ds/107Mi)
% 2.93/1.73 % (3731)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_3593 for (2998ds/39Mi)
% 2.93/1.74 % (3729)Instruction limit reached!
% 2.93/1.74 % (3729)------------------------------
% 2.93/1.74 % (3729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.74 % (3729)Termination reason: Unknown
% 2.93/1.74 % (3729)Termination phase: Saturation
% 2.93/1.74
% 2.93/1.74 % (3729)Memory used [KB]: 6524
% 2.93/1.74 % (3729)Time elapsed: 0.025 s
% 2.93/1.74 % (3729)Instructions burned: 88 (million)
% 2.93/1.74 % (3729)------------------------------
% 2.93/1.74 % (3729)------------------------------
% 2.93/1.74 % (3731)Instruction limit reached!
% 2.93/1.74 % (3731)------------------------------
% 2.93/1.74 % (3731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.74 % (3731)Termination reason: Unknown
% 2.93/1.74 % (3731)Termination phase: shuffling
% 2.93/1.74
% 2.93/1.74 % (3731)Memory used [KB]: 2174
% 2.93/1.74 % (3731)Time elapsed: 0.014 s
% 2.93/1.74 % (3731)Instructions burned: 41 (million)
% 2.93/1.74 % (3731)------------------------------
% 2.93/1.74 % (3731)------------------------------
% 2.93/1.75 % (3732)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_3593 for (2998ds/448Mi)
% 2.93/1.76 % (3733)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_3593 for (2998ds/46Mi)
% 2.93/1.76 % (3730)Instruction limit reached!
% 2.93/1.76 % (3730)------------------------------
% 2.93/1.76 % (3730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.76 % (3730)Termination reason: Unknown
% 2.93/1.76 % (3730)Termination phase: Saturation
% 2.93/1.76
% 2.93/1.76 % (3730)Memory used [KB]: 6652
% 2.93/1.76 % (3730)Time elapsed: 0.036 s
% 2.93/1.76 % (3730)Instructions burned: 108 (million)
% 2.93/1.76 % (3730)------------------------------
% 2.93/1.76 % (3730)------------------------------
% 2.93/1.77 % (3733)Instruction limit reached!
% 2.93/1.77 % (3733)------------------------------
% 2.93/1.77 % (3733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.77 % (3733)Termination reason: Unknown
% 2.93/1.77 % (3733)Termination phase: Property scanning
% 2.93/1.77
% 2.93/1.77 % (3733)Memory used [KB]: 1918
% 2.93/1.77 % (3733)Time elapsed: 0.016 s
% 2.93/1.77 % (3733)Instructions burned: 46 (million)
% 2.93/1.77 % (3733)------------------------------
% 2.93/1.77 % (3733)------------------------------
% 2.93/1.77 % (3718)Instruction limit reached!
% 2.93/1.77 % (3718)------------------------------
% 2.93/1.77 % (3718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.77 % (3718)Termination reason: Unknown
% 2.93/1.77 % (3718)Termination phase: Saturation
% 2.93/1.77
% 2.93/1.77 % (3718)Memory used [KB]: 7675
% 2.93/1.77 % (3718)Time elapsed: 0.118 s
% 2.93/1.77 % (3718)Instructions burned: 379 (million)
% 2.93/1.77 % (3718)------------------------------
% 2.93/1.77 % (3718)------------------------------
% 2.93/1.77 % (3734)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_3593 for (2998ds/98Mi)
% 2.93/1.78 % (3735)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_3593 for (2997ds/507Mi)
% 2.93/1.78 % (3736)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_3593 for (2997ds/149Mi)
% 2.93/1.80 % (3734)Instruction limit reached!
% 2.93/1.80 % (3734)------------------------------
% 2.93/1.80 % (3734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.80 % (3734)Termination reason: Unknown
% 2.93/1.80 % (3734)Termination phase: Property scanning
% 2.93/1.80
% 2.93/1.80 % (3734)Memory used [KB]: 2430
% 2.93/1.80 % (3734)Time elapsed: 0.029 s
% 2.93/1.80 % (3734)Instructions burned: 98 (million)
% 2.93/1.80 % (3734)------------------------------
% 2.93/1.80 % (3734)------------------------------
% 2.93/1.81 % (3737)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_3593 for (2997ds/39Mi)
% 2.93/1.82 % (3735)Refutation not found, incomplete strategy
% 2.93/1.82 % (3735)------------------------------
% 2.93/1.82 % (3735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.82 % (3735)Termination reason: Refutation not found, incomplete strategy
% 2.93/1.82
% 2.93/1.82
% 2.93/1.82 % (3735)Memory used [KB]: 7419
% 2.93/1.82 % (3735)Time elapsed: 0.038 s
% 2.93/1.82 % (3735)Instructions burned: 116 (million)
% 2.93/1.82 % (3735)------------------------------
% 2.93/1.82 % (3735)------------------------------
% 2.93/1.82 % (3736)Instruction limit reached!
% 2.93/1.82 % (3736)------------------------------
% 2.93/1.82 % (3736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.82 % (3736)Termination reason: Unknown
% 2.93/1.82 % (3736)Termination phase: Property scanning
% 2.93/1.82
% 2.93/1.82 % (3736)Memory used [KB]: 2174
% 2.93/1.82 % (3736)Time elapsed: 0.039 s
% 2.93/1.82 % (3736)Instructions burned: 150 (million)
% 2.93/1.82 % (3736)------------------------------
% 2.93/1.82 % (3736)------------------------------
% 2.93/1.82 % (3737)Instruction limit reached!
% 2.93/1.82 % (3737)------------------------------
% 2.93/1.82 % (3737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.82 % (3737)Termination reason: Unknown
% 2.93/1.82 % (3737)Termination phase: Property scanning
% 2.93/1.82
% 2.93/1.82 % (3737)Memory used [KB]: 1918
% 2.93/1.82 % (3737)Time elapsed: 0.014 s
% 2.93/1.82 % (3737)Instructions burned: 42 (million)
% 2.93/1.82 % (3737)------------------------------
% 2.93/1.82 % (3737)------------------------------
% 2.93/1.83 % (3739)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_3593 for (2997ds/1087Mi)
% 2.93/1.83 % (3738)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_3593 for (2997ds/6Mi)
% 2.93/1.83 % (3738)Instruction limit reached!
% 2.93/1.83 % (3738)------------------------------
% 2.93/1.83 % (3738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.83 % (3738)Termination reason: Unknown
% 2.93/1.83 % (3738)Termination phase: shuffling
% 2.93/1.83
% 2.93/1.83 % (3738)Memory used [KB]: 1535
% 2.93/1.83 % (3738)Time elapsed: 0.004 s
% 2.93/1.83 % (3738)Instructions burned: 7 (million)
% 2.93/1.83 % (3738)------------------------------
% 2.93/1.83 % (3738)------------------------------
% 2.93/1.83 % (3740)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_3593 for (2997ds/47Mi)
% 2.93/1.84 % (3741)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_3593 for (2997ds/44Mi)
% 2.93/1.85 % (3740)Instruction limit reached!
% 2.93/1.85 % (3740)------------------------------
% 2.93/1.85 % (3740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.85 % (3740)Termination reason: Unknown
% 2.93/1.85 % (3740)Termination phase: Property scanning
% 2.93/1.85
% 2.93/1.85 % (3740)Memory used [KB]: 1918
% 2.93/1.85 % (3740)Time elapsed: 0.016 s
% 2.93/1.85 % (3740)Instructions burned: 47 (million)
% 2.93/1.85 % (3740)------------------------------
% 2.93/1.85 % (3740)------------------------------
% 2.93/1.85 % (3741)Instruction limit reached!
% 2.93/1.85 % (3741)------------------------------
% 2.93/1.85 % (3741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.85 % (3741)Termination reason: Unknown
% 2.93/1.85 % (3741)Termination phase: shuffling
% 2.93/1.85
% 2.93/1.85 % (3741)Memory used [KB]: 2174
% 2.93/1.85 % (3741)Time elapsed: 0.015 s
% 2.93/1.85 % (3741)Instructions burned: 45 (million)
% 2.93/1.85 % (3741)------------------------------
% 2.93/1.85 % (3741)------------------------------
% 2.93/1.86 % (3742)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_3593 for (2997ds/432Mi)
% 2.93/1.86 % (3743)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_3593 for (2997ds/62Mi)
% 2.93/1.88 % (3732)Instruction limit reached!
% 2.93/1.88 % (3732)------------------------------
% 2.93/1.88 % (3732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.88 % (3732)Termination reason: Unknown
% 2.93/1.88 % (3732)Termination phase: Saturation
% 2.93/1.88
% 2.93/1.88 % (3732)Memory used [KB]: 8315
% 2.93/1.88 % (3732)Time elapsed: 0.130 s
% 2.93/1.88 % (3732)Instructions burned: 450 (million)
% 2.93/1.88 % (3732)------------------------------
% 2.93/1.88 % (3732)------------------------------
% 2.93/1.88 % (3743)Instruction limit reached!
% 2.93/1.88 % (3743)------------------------------
% 2.93/1.88 % (3743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.88 % (3743)Termination reason: Unknown
% 2.93/1.88 % (3743)Termination phase: Property scanning
% 2.93/1.88
% 2.93/1.88 % (3743)Memory used [KB]: 2302
% 2.93/1.88 % (3743)Time elapsed: 0.020 s
% 2.93/1.88 % (3743)Instructions burned: 63 (million)
% 2.93/1.88 % (3743)------------------------------
% 2.93/1.88 % (3743)------------------------------
% 2.93/1.89 % (3744)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_3593 for (2996ds/31Mi)
% 2.93/1.89 % (3719)Instruction limit reached!
% 2.93/1.89 % (3719)------------------------------
% 2.93/1.89 % (3719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.89 % (3719)Termination reason: Unknown
% 2.93/1.89 % (3719)Termination phase: Saturation
% 2.93/1.89
% 2.93/1.89 % (3719)Memory used [KB]: 8443
% 2.93/1.89 % (3719)Time elapsed: 0.235 s
% 2.93/1.89 % (3719)Instructions burned: 781 (million)
% 2.93/1.89 % (3719)------------------------------
% 2.93/1.89 % (3719)------------------------------
% 2.93/1.89 % (3745)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_3593 for (2996ds/96Mi)
% 2.93/1.90 % (3744)Instruction limit reached!
% 2.93/1.90 % (3744)------------------------------
% 2.93/1.90 % (3744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.90 % (3744)Termination reason: Unknown
% 2.93/1.90 % (3744)Termination phase: shuffling
% 2.93/1.90
% 2.93/1.90 % (3744)Memory used [KB]: 1791
% 2.93/1.90 % (3744)Time elapsed: 0.010 s
% 2.93/1.90 % (3744)Instructions burned: 32 (million)
% 2.93/1.90 % (3744)------------------------------
% 2.93/1.90 % (3744)------------------------------
% 2.93/1.90 % (3746)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_3593 for (2996ds/453Mi)
% 2.93/1.91 % (3747)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_3593 for (2996ds/71Mi)
% 2.93/1.92 % (3745)Instruction limit reached!
% 2.93/1.92 % (3745)------------------------------
% 2.93/1.92 % (3745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.92 % (3745)Termination reason: Unknown
% 2.93/1.92 % (3745)Termination phase: Saturation
% 2.93/1.92
% 2.93/1.92 % (3745)Memory used [KB]: 6652
% 2.93/1.92 % (3745)Time elapsed: 0.031 s
% 2.93/1.92 % (3745)Instructions burned: 97 (million)
% 2.93/1.92 % (3745)------------------------------
% 2.93/1.92 % (3745)------------------------------
% 2.93/1.93 % (3747)Instruction limit reached!
% 2.93/1.93 % (3747)------------------------------
% 2.93/1.93 % (3747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.93 % (3747)Termination reason: Unknown
% 2.93/1.93 % (3747)Termination phase: Property scanning
% 2.93/1.93
% 2.93/1.93 % (3747)Memory used [KB]: 2046
% 2.93/1.93 % (3747)Time elapsed: 0.021 s
% 2.93/1.93 % (3747)Instructions burned: 72 (million)
% 2.93/1.93 % (3747)------------------------------
% 2.93/1.93 % (3747)------------------------------
% 2.93/1.93 % (3703)Instruction limit reached!
% 2.93/1.93 % (3703)------------------------------
% 2.93/1.93 % (3703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.93 % (3703)Termination reason: Unknown
% 2.93/1.93 % (3703)Termination phase: Saturation
% 2.93/1.93
% 2.93/1.93 % (3703)Memory used [KB]: 9722
% 2.93/1.93 % (3703)Time elapsed: 0.348 s
% 2.93/1.93 % (3703)Instructions burned: 1043 (million)
% 2.93/1.93 % (3703)------------------------------
% 2.93/1.93 % (3703)------------------------------
% 2.93/1.93 % (3748)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_3593 for (2996ds/83Mi)
% 2.93/1.94 % (3749)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_3593 for (2996ds/11Mi)
% 2.93/1.94 % (3750)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_3593 for (2996ds/41Mi)
% 2.93/1.94 % (3749)Instruction limit reached!
% 2.93/1.94 % (3749)------------------------------
% 2.93/1.94 % (3749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.94 % (3749)Termination reason: Unknown
% 2.93/1.94 % (3749)Termination phase: shuffling
% 2.93/1.94
% 2.93/1.94 % (3749)Memory used [KB]: 1535
% 2.93/1.94 % (3749)Time elapsed: 0.004 s
% 2.93/1.94 % (3749)Instructions burned: 11 (million)
% 2.93/1.94 % (3749)------------------------------
% 2.93/1.94 % (3749)------------------------------
% 2.93/1.94 % (3748)Refutation not found, incomplete strategy
% 2.93/1.94 % (3748)------------------------------
% 2.93/1.94 % (3748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.94 % (3748)Termination reason: Refutation not found, incomplete strategy
% 2.93/1.94
% 2.93/1.94
% 2.93/1.94 % (3748)Memory used [KB]: 6012
% 2.93/1.94 % (3748)Time elapsed: 0.011 s
% 2.93/1.94 % (3748)Instructions burned: 34 (million)
% 2.93/1.94 % (3748)------------------------------
% 2.93/1.94 % (3748)------------------------------
% 2.93/1.95 % (3750)Instruction limit reached!
% 2.93/1.95 % (3750)------------------------------
% 2.93/1.95 % (3750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.95 % (3750)Termination reason: Unknown
% 2.93/1.95 % (3750)Termination phase: shuffling
% 2.93/1.95
% 2.93/1.95 % (3750)Memory used [KB]: 2174
% 2.93/1.95 % (3750)Time elapsed: 0.012 s
% 2.93/1.95 % (3750)Instructions burned: 41 (million)
% 2.93/1.95 % (3750)------------------------------
% 2.93/1.95 % (3750)------------------------------
% 2.93/1.95 % (3751)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3593 for (2996ds/6Mi)
% 2.93/1.95 % (3752)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_3593 for (2996ds/150Mi)
% 2.93/1.95 % (3751)Instruction limit reached!
% 2.93/1.95 % (3751)------------------------------
% 2.93/1.95 % (3751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.95 % (3751)Termination reason: Unknown
% 2.93/1.95 % (3751)Termination phase: shuffling
% 2.93/1.95
% 2.93/1.95 % (3751)Memory used [KB]: 1407
% 2.93/1.95 % (3751)Time elapsed: 0.003 s
% 2.93/1.95 % (3751)Instructions burned: 7 (million)
% 2.93/1.95 % (3751)------------------------------
% 2.93/1.95 % (3751)------------------------------
% 2.93/1.96 % (3753)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_3593 for (2996ds/343Mi)
% 2.93/1.96 % (3754)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_3593 for (2996ds/109Mi)
% 2.93/1.97 % (3721)Instruction limit reached!
% 2.93/1.97 % (3721)------------------------------
% 2.93/1.97 % (3721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.97 % (3721)Termination reason: Unknown
% 2.93/1.97 % (3721)Termination phase: Saturation
% 2.93/1.97
% 2.93/1.97 % (3721)Memory used [KB]: 8443
% 2.93/1.97 % (3721)Time elapsed: 0.306 s
% 2.93/1.97 % (3721)Instructions burned: 881 (million)
% 2.93/1.97 % (3721)------------------------------
% 2.93/1.97 % (3721)------------------------------
% 2.93/1.98 % (3755)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_3593 for (2995ds/253Mi)
% 2.93/1.99 % (3742)Instruction limit reached!
% 2.93/1.99 % (3742)------------------------------
% 2.93/1.99 % (3742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.99 % (3742)Termination reason: Unknown
% 2.93/1.99 % (3742)Termination phase: Saturation
% 2.93/1.99
% 2.93/1.99 % (3742)Memory used [KB]: 3582
% 2.93/1.99 % (3742)Time elapsed: 0.158 s
% 2.93/1.99 % (3742)Instructions burned: 433 (million)
% 2.93/1.99 % (3742)------------------------------
% 2.93/1.99 % (3742)------------------------------
% 2.93/1.99 % (3754)Instruction limit reached!
% 2.93/1.99 % (3754)------------------------------
% 2.93/1.99 % (3754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.99 % (3754)Termination reason: Unknown
% 2.93/1.99 % (3754)Termination phase: Saturation
% 2.93/1.99
% 2.93/1.99 % (3754)Memory used [KB]: 6652
% 2.93/1.99 % (3754)Time elapsed: 0.032 s
% 2.93/1.99 % (3754)Instructions burned: 111 (million)
% 2.93/1.99 % (3754)------------------------------
% 2.93/1.99 % (3754)------------------------------
% 2.93/1.99 % (3755)Refutation not found, incomplete strategy
% 2.93/1.99 % (3755)------------------------------
% 2.93/1.99 % (3755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.99 % (3755)Termination reason: Refutation not found, incomplete strategy
% 2.93/1.99
% 2.93/1.99
% 2.93/1.99 % (3755)Memory used [KB]: 6140
% 2.93/1.99 % (3755)Time elapsed: 0.013 s
% 2.93/1.99 % (3755)Instructions burned: 36 (million)
% 2.93/1.99 % (3755)------------------------------
% 2.93/1.99 % (3755)------------------------------
% 2.93/2.00 % (3752)Instruction limit reached!
% 2.93/2.00 % (3752)------------------------------
% 2.93/2.00 % (3752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/2.00 % (3752)Termination reason: Unknown
% 2.93/2.00 % (3752)Termination phase: Saturation
% 2.93/2.00
% 2.93/2.00 % (3752)Memory used [KB]: 6908
% 2.93/2.00 % (3752)Time elapsed: 0.045 s
% 2.93/2.00 % (3752)Instructions burned: 151 (million)
% 2.93/2.00 % (3752)------------------------------
% 2.93/2.00 % (3752)------------------------------
% 2.93/2.00 % (3756)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_3593 for (2995ds/140Mi)
% 2.93/2.00 % (3757)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_3593 for (2995ds/614Mi)
% 2.93/2.01 % (3759)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_3593 for (2995ds/339Mi)
% 5.94/2.02 % (3756)Refutation not found, incomplete strategy
% 5.94/2.02 % (3756)------------------------------
% 5.94/2.02 % (3756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.02 % (3758)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_3593 for (2995ds/202Mi)
% 5.94/2.02 % (3756)Termination reason: Refutation not found, incomplete strategy
% 5.94/2.02
% 5.94/2.02
% 5.94/2.02 % (3756)Memory used [KB]: 6396
% 5.94/2.02 % (3756)Time elapsed: 0.015 s
% 5.94/2.02 % (3756)Instructions burned: 46 (million)
% 5.94/2.02 % (3756)------------------------------
% 5.94/2.02 % (3756)------------------------------
% 5.94/2.03 % (3760)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_3593 for (2995ds/283Mi)
% 5.94/2.03 % (3758)Refutation not found, incomplete strategy
% 5.94/2.03 % (3758)------------------------------
% 5.94/2.03 % (3758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.03 % (3758)Termination reason: Refutation not found, incomplete strategy
% 5.94/2.03
% 5.94/2.03
% 5.94/2.03 % (3758)Memory used [KB]: 6140
% 5.94/2.03 % (3758)Time elapsed: 0.011 s
% 5.94/2.03 % (3758)Instructions burned: 34 (million)
% 5.94/2.03 % (3758)------------------------------
% 5.94/2.03 % (3758)------------------------------
% 5.94/2.03 % (3746)Instruction limit reached!
% 5.94/2.03 % (3746)------------------------------
% 5.94/2.03 % (3746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.03 % (3746)Termination reason: Unknown
% 5.94/2.03 % (3746)Termination phase: Saturation
% 5.94/2.03
% 5.94/2.03 % (3746)Memory used [KB]: 7803
% 5.94/2.03 % (3746)Time elapsed: 0.130 s
% 5.94/2.03 % (3746)Instructions burned: 456 (million)
% 5.94/2.03 % (3746)------------------------------
% 5.94/2.03 % (3746)------------------------------
% 5.94/2.04 % (3761)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_3593 for (2995ds/134Mi)
% 5.94/2.04 % (3762)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_3593 for (2995ds/298Mi)
% 5.94/2.08 % (3761)Instruction limit reached!
% 5.94/2.08 % (3761)------------------------------
% 5.94/2.08 % (3761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.08 % (3761)Termination reason: Unknown
% 5.94/2.08 % (3761)Termination phase: Saturation
% 5.94/2.08
% 5.94/2.08 % (3761)Memory used [KB]: 6780
% 5.94/2.08 % (3761)Time elapsed: 0.041 s
% 5.94/2.08 % (3761)Instructions burned: 136 (million)
% 5.94/2.08 % (3761)------------------------------
% 5.94/2.08 % (3761)------------------------------
% 5.94/2.08 % (3753)Instruction limit reached!
% 5.94/2.08 % (3753)------------------------------
% 5.94/2.08 % (3753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.08 % (3753)Termination reason: Unknown
% 5.94/2.08 % (3753)Termination phase: Saturation
% 5.94/2.08
% 5.94/2.08 % (3753)Memory used [KB]: 7291
% 5.94/2.08 % (3753)Time elapsed: 0.123 s
% 5.94/2.08 % (3753)Instructions burned: 343 (million)
% 5.94/2.08 % (3753)------------------------------
% 5.94/2.08 % (3753)------------------------------
% 5.94/2.09 % (3763)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_3593 for (2994ds/192Mi)
% 5.94/2.09 % (3764)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_3593 for (2994ds/258Mi)
% 5.94/2.11 % (3760)Instruction limit reached!
% 5.94/2.11 % (3760)------------------------------
% 5.94/2.11 % (3760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.11 % (3760)Termination reason: Unknown
% 5.94/2.11 % (3760)Termination phase: Saturation
% 5.94/2.11
% 5.94/2.11 % (3760)Memory used [KB]: 7419
% 5.94/2.11 % (3760)Time elapsed: 0.083 s
% 5.94/2.11 % (3760)Instructions burned: 284 (million)
% 5.94/2.11 % (3760)------------------------------
% 5.94/2.11 % (3760)------------------------------
% 5.94/2.11 % (3759)Instruction limit reached!
% 5.94/2.11 % (3759)------------------------------
% 5.94/2.11 % (3759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.94/2.11 % (3759)Termination reason: Unknown
% 5.94/2.11 % (3759)Termination phase: Saturation
% 5.94/2.11
% 5.94/2.11 % (3759)Memory used [KB]: 7419
% 5.94/2.11 % (3759)Time elapsed: 0.106 s
% 5.94/2.11 % (3759)Instructions burned: 340 (million)
% 5.94/2.11 % (3759)------------------------------
% 5.94/2.11 % (3759)------------------------------
% 6.54/2.12 % (3765)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_3593 for (2994ds/90Mi)
% 6.54/2.12 % (3762)Instruction limit reached!
% 6.54/2.12 % (3762)------------------------------
% 6.54/2.12 % (3762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.12 % (3762)Termination reason: Unknown
% 6.54/2.12 % (3762)Termination phase: Saturation
% 6.54/2.12
% 6.54/2.12 % (3762)Memory used [KB]: 7419
% 6.54/2.12 % (3762)Time elapsed: 0.081 s
% 6.54/2.12 % (3762)Instructions burned: 300 (million)
% 6.54/2.12 % (3762)------------------------------
% 6.54/2.12 % (3762)------------------------------
% 6.54/2.12 % (3766)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_3593 for (2994ds/231Mi)
% 6.54/2.13 % (3763)Refutation not found, incomplete strategy
% 6.54/2.13 % (3763)------------------------------
% 6.54/2.13 % (3763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.13 % (3763)Termination reason: Refutation not found, incomplete strategy
% 6.54/2.13
% 6.54/2.13
% 6.54/2.13 % (3763)Memory used [KB]: 7675
% 6.54/2.13 % (3763)Time elapsed: 0.039 s
% 6.54/2.13 % (3763)Instructions burned: 132 (million)
% 6.54/2.13 % (3763)------------------------------
% 6.54/2.13 % (3763)------------------------------
% 6.54/2.13 % (3767)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_3593 for (2994ds/458Mi)
% 6.54/2.14 % (3768)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_3593 for (2994ds/31Mi)
% 6.54/2.14 % (3765)Instruction limit reached!
% 6.54/2.14 % (3765)------------------------------
% 6.54/2.14 % (3765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.14 % (3765)Termination reason: Unknown
% 6.54/2.14 % (3765)Termination phase: Saturation
% 6.54/2.14
% 6.54/2.14 % (3765)Memory used [KB]: 6524
% 6.54/2.14 % (3765)Time elapsed: 0.026 s
% 6.54/2.14 % (3765)Instructions burned: 91 (million)
% 6.54/2.14 % (3765)------------------------------
% 6.54/2.14 % (3765)------------------------------
% 6.54/2.14 % (3768)Instruction limit reached!
% 6.54/2.14 % (3768)------------------------------
% 6.54/2.14 % (3768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.14 % (3768)Termination reason: Unknown
% 6.54/2.14 % (3768)Termination phase: shuffling
% 6.54/2.14
% 6.54/2.14 % (3768)Memory used [KB]: 1791
% 6.54/2.14 % (3768)Time elapsed: 0.010 s
% 6.54/2.14 % (3768)Instructions burned: 31 (million)
% 6.54/2.14 % (3768)------------------------------
% 6.54/2.14 % (3768)------------------------------
% 6.54/2.15 % (3769)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_3593 for (2994ds/297Mi)
% 6.54/2.15 % (3770)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_3593 for (2994ds/987Mi)
% 6.54/2.16 % (3764)Instruction limit reached!
% 6.54/2.16 % (3764)------------------------------
% 6.54/2.16 % (3764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.16 % (3764)Termination reason: Unknown
% 6.54/2.16 % (3764)Termination phase: Saturation
% 6.54/2.16
% 6.54/2.16 % (3764)Memory used [KB]: 2174
% 6.54/2.16 % (3764)Time elapsed: 0.067 s
% 6.54/2.16 % (3764)Instructions burned: 260 (million)
% 6.54/2.16 % (3764)------------------------------
% 6.54/2.16 % (3764)------------------------------
% 6.54/2.17 % (3739)Instruction limit reached!
% 6.54/2.17 % (3739)------------------------------
% 6.54/2.17 % (3739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.17 % (3739)Termination reason: Unknown
% 6.54/2.17 % (3739)Termination phase: Saturation
% 6.54/2.17
% 6.54/2.17 % (3739)Memory used [KB]: 7675
% 6.54/2.17 % (3739)Time elapsed: 0.339 s
% 6.54/2.17 % (3739)Instructions burned: 1089 (million)
% 6.54/2.17 % (3739)------------------------------
% 6.54/2.17 % (3739)------------------------------
% 6.54/2.17 % (3771)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_3593 for (2994ds/182Mi)
% 6.54/2.17 % (3772)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_3593 for (2994ds/182Mi)
% 6.54/2.19 % (3766)Instruction limit reached!
% 6.54/2.19 % (3766)------------------------------
% 6.54/2.19 % (3766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.19 % (3766)Termination reason: Unknown
% 6.54/2.19 % (3766)Termination phase: Saturation
% 6.54/2.19
% 6.54/2.19 % (3766)Memory used [KB]: 7419
% 6.54/2.19 % (3766)Time elapsed: 0.066 s
% 6.54/2.19 % (3766)Instructions burned: 231 (million)
% 6.54/2.19 % (3766)------------------------------
% 6.54/2.19 % (3766)------------------------------
% 6.54/2.19 % (3757)Instruction limit reached!
% 6.54/2.19 % (3757)------------------------------
% 6.54/2.19 % (3757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.19 % (3757)Termination reason: Unknown
% 6.54/2.19 % (3757)Termination phase: Saturation
% 6.54/2.19
% 6.54/2.19 % (3757)Memory used [KB]: 7931
% 6.54/2.19 % (3757)Time elapsed: 0.186 s
% 6.54/2.19 % (3757)Instructions burned: 615 (million)
% 6.54/2.19 % (3757)------------------------------
% 6.54/2.19 % (3757)------------------------------
% 6.54/2.19 % (3773)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_3593 for (2993ds/154Mi)
% 7.02/2.20 % (3774)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_3593 for (2993ds/79Mi)
% 7.02/2.21 % (3769)First to succeed.
% 7.02/2.21 % (3769)Refutation found. Thanks to Tanya!
% 7.02/2.21 % SZS status Theorem for DTF2THF_3593
% 7.02/2.21 % SZS output start Proof for DTF2THF_3593
% 7.02/2.21 thf(type_def_5, type, nat: $tType).
% 7.02/2.21 thf(type_def_6, type, a: $tType).
% 7.02/2.21 thf(type_def_8, type, polyno1532895200ly_nat: $tType).
% 7.02/2.21 thf(type_def_9, type, polyno727731844poly_a: $tType).
% 7.02/2.21 thf(type_def_10, type, list_a: $tType).
% 7.02/2.21 thf(type_def_11, type, list_nat: $tType).
% 7.02/2.21 thf(func_def_0, type, polyno1532895200ly_nat: $tType).
% 7.02/2.21 thf(func_def_1, type, polyno727731844poly_a: $tType).
% 7.02/2.21 thf(func_def_2, type, list_nat: $tType).
% 7.02/2.21 thf(func_def_3, type, list_a: $tType).
% 7.02/2.21 thf(func_def_4, type, nat: $tType).
% 7.02/2.21 thf(func_def_5, type, a: $tType).
% 7.02/2.21 thf(func_def_6, type, one_one_nat: nat).
% 7.02/2.21 thf(func_def_7, type, one_one_a: a).
% 7.02/2.21 thf(func_def_8, type, plus_plus_nat: nat > nat > nat).
% 7.02/2.21 thf(func_def_9, type, plus_plus_a: a > a > a).
% 7.02/2.21 thf(func_def_10, type, times_times_nat: nat > nat > nat).
% 7.02/2.21 thf(func_def_11, type, times_times_a: a > a > a).
% 7.02/2.21 thf(func_def_12, type, zero_zero_nat: nat).
% 7.02/2.21 thf(func_def_13, type, zero_zero_a: a).
% 7.02/2.21 thf(func_def_14, type, if_nat: $o > nat > nat > nat).
% 7.02/2.21 thf(func_def_15, type, compow808008746ly_nat: nat > (polyno1532895200ly_nat > polyno1532895200ly_nat) > polyno1532895200ly_nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_16, type, compow1114216044poly_a: nat > (polyno727731844poly_a > polyno727731844poly_a) > polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_17, type, polyno422358502poly_a: list_a > polyno727731844poly_a > a).
% 7.02/2.21 thf(func_def_18, type, polyno587244178ad_nat: polyno1532895200ly_nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_19, type, polyno1465139388head_a: polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_20, type, polyno220183259ee_nat: polyno1532895200ly_nat > nat).
% 7.02/2.21 thf(func_def_21, type, polyno578545843gree_a: polyno727731844poly_a > nat).
% 7.02/2.21 thf(func_def_22, type, polyno1779722485en_nat: polyno1532895200ly_nat > nat > nat).
% 7.02/2.21 thf(func_def_23, type, polyno1674775833reen_a: polyno727731844poly_a > nat > nat).
% 7.02/2.21 thf(func_def_24, type, polyno1952548879ad_nat: polyno1532895200ly_nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_25, type, polyno1884029055head_a: polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_26, type, polyno524777654st_nat: polyno1532895200ly_nat > nat).
% 7.02/2.21 thf(func_def_27, type, polyno2115742616onst_a: polyno727731844poly_a > a).
% 7.02/2.21 thf(func_def_28, type, polyno544860353dn_nat: polyno1532895200ly_nat > nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_29, type, polyno567601229eadn_a: polyno727731844poly_a > nat > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_30, type, polyno1013235523ly_nat: polyno1532895200ly_nat > $o).
% 7.02/2.21 thf(func_def_31, type, polyno190918219poly_a: polyno727731844poly_a > $o).
% 7.02/2.21 thf(func_def_32, type, polyno892049031yh_nat: polyno1532895200ly_nat > nat > $o).
% 7.02/2.21 thf(func_def_33, type, polyno1372495879olyh_a: polyno727731844poly_a > nat > $o).
% 7.02/2.21 thf(func_def_34, type, polyno1222032024dd_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_35, type, polyno1623170614_Add_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_36, type, polyno1999838549nd_nat: nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_37, type, polyno2024845497ound_a: nat > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_38, type, polyno720942678CN_nat: polyno1532895200ly_nat > nat > polyno1532895200ly_nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_39, type, polyno1057396216e_CN_a: polyno727731844poly_a > nat > polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_40, type, polyno2122022170_C_nat: nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_41, type, polyno439679028le_C_a: a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_42, type, polyno1415441627ul_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_43, type, polyno1491482291_Mul_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_44, type, polyno1366804583eg_nat: polyno1532895200ly_nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_45, type, polyno96675367_Neg_a: polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_46, type, polyno359287218Pw_nat: polyno1532895200ly_nat > nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_47, type, polyno1538138524e_Pw_a: polyno727731844poly_a > nat > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_48, type, polyno1921014231ub_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_49, type, polyno975704247_Sub_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_50, type, polyno1467023772ul_nat: nat > polyno1532895200ly_nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_51, type, polyno562434098cmul_a: a > polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_52, type, polyno212464073eriv_a: polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_53, type, polyno1006823949_aux_a: a > polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_54, type, polyno929799083ul_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_55, type, polyno1934269411ymul_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_56, type, polyno955999183nate_a: polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_57, type, polyno1510045887ow_nat: nat > polyno1532895200ly_nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_58, type, polyno1371724751ypow_a: nat > polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_59, type, polyno1418491367ysub_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_60, type, polyno336795754t0_nat: polyno1532895200ly_nat > polyno1532895200ly_nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_61, type, polyno1397854436bst0_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_62, type, polyno1964927358t1_nat: polyno1532895200ly_nat > polyno1532895200ly_nat).
% 7.02/2.21 thf(func_def_63, type, polyno784948432ift1_a: polyno727731844poly_a > polyno727731844poly_a).
% 7.02/2.21 thf(func_def_64, type, polyno1438831695bs_nat: list_nat > polyno1532895200ly_nat > $o).
% 7.02/2.21 thf(func_def_65, type, polyno896877631f_bs_a: list_a > polyno727731844poly_a > $o).
% 7.02/2.21 thf(func_def_66, type, n0: nat).
% 7.02/2.21 thf(func_def_67, type, n1: nat).
% 7.02/2.21 thf(func_def_68, type, p: polyno727731844poly_a).
% 7.02/2.21 thf(func_def_69, type, q: polyno727731844poly_a).
% 7.02/2.21 thf(func_def_88, type, ph1: !>[X0: $tType]:(X0)).
% 7.02/2.21 thf(func_def_89, type, sK2: list_a).
% 7.02/2.21 thf(func_def_90, type, sK3: list_a).
% 7.02/2.21 thf(func_def_91, type, sK4: nat).
% 7.02/2.21 thf(func_def_92, type, sK5: nat).
% 7.02/2.21 thf(func_def_93, type, sK6: nat).
% 7.02/2.21 thf(func_def_94, type, sK7: polyno727731844poly_a > list_a).
% 7.02/2.21 thf(func_def_95, type, sK8: nat).
% 7.02/2.21 thf(func_def_96, type, sK9: polyno727731844poly_a > list_a).
% 7.02/2.21 thf(f1317,plain,(
% 7.02/2.21 $false),
% 7.02/2.21 inference(subsumption_resolution,[status(thm)],[f1316,f1311])).
% 7.02/2.21 thf(f1311,plain,(
% 7.02/2.21 ( ! [X2 : list_a,X1 : polyno727731844poly_a] : (($true = (!! @ polyno727731844poly_a @ (^[Y0 : polyno727731844poly_a]: ((polyno422358502poly_a @ X2 @ (polyno1491482291_Mul_a @ Y0 @ X1)) = (times_times_a @ (polyno422358502poly_a @ X2 @ Y0) @ (polyno422358502poly_a @ X2 @ X1))))))) )),
% 7.02/2.21 inference(beta_eta_normalization,[status(thm)],[f1308])).
% 7.02/2.21 thf(f1308,plain,(
% 7.02/2.21 ( ! [X2 : list_a,X1 : polyno727731844poly_a] : ((((^[Y0 : list_a]: (!! @ polyno727731844poly_a @ (^[Y1 : polyno727731844poly_a]: ((polyno422358502poly_a @ Y0 @ (polyno1491482291_Mul_a @ Y1 @ X1)) = (times_times_a @ (polyno422358502poly_a @ Y0 @ Y1) @ (polyno422358502poly_a @ Y0 @ X1)))))) @ X2) = $true)) )),
% 7.02/2.21 inference(pi_clausification,[status(thm)],[f1305])).
% 7.02/2.21 thf(f1305,plain,(
% 7.02/2.21 ( ! [X1 : polyno727731844poly_a] : (($true = (!! @ list_a @ (^[Y0 : list_a]: (!! @ polyno727731844poly_a @ (^[Y1 : polyno727731844poly_a]: ((polyno422358502poly_a @ Y0 @ (polyno1491482291_Mul_a @ Y1 @ X1)) = (times_times_a @ (polyno422358502poly_a @ Y0 @ Y1) @ (polyno422358502poly_a @ Y0 @ X1))))))))) )),
% 7.02/2.21 inference(beta_eta_normalization,[status(thm)],[f1304])).
% 7.02/2.21 thf(f1304,plain,(
% 7.02/2.21 ( ! [X1 : polyno727731844poly_a] : ((((^[Y0 : polyno727731844poly_a]: (!! @ list_a @ (^[Y1 : list_a]: (!! @ polyno727731844poly_a @ (^[Y2 : polyno727731844poly_a]: ((polyno422358502poly_a @ Y1 @ (polyno1491482291_Mul_a @ Y2 @ Y0)) = (times_times_a @ (polyno422358502poly_a @ Y1 @ Y2) @ (polyno422358502poly_a @ Y1 @ Y0)))))))) @ X1) = $true)) )),
% 7.02/2.21 inference(pi_clausification,[status(thm)],[f1110])).
% 7.02/2.21 thf(f1110,plain,(
% 7.02/2.21 ((!! @ polyno727731844poly_a @ (^[Y0 : polyno727731844poly_a]: (!! @ list_a @ (^[Y1 : list_a]: (!! @ polyno727731844poly_a @ (^[Y2 : polyno727731844poly_a]: ((polyno422358502poly_a @ Y1 @ (polyno1491482291_Mul_a @ Y2 @ Y0)) = (times_times_a @ (polyno422358502poly_a @ Y1 @ Y2) @ (polyno422358502poly_a @ Y1 @ Y0))))))))) = $true)),
% 7.02/2.21 inference(cnf_transformation,[status(thm)],[f449])).
% 7.02/2.21 thf(f449,plain,(
% 7.02/2.21 ((!! @ polyno727731844poly_a @ (^[Y0 : polyno727731844poly_a]: (!! @ list_a @ (^[Y1 : list_a]: (!! @ polyno727731844poly_a @ (^[Y2 : polyno727731844poly_a]: ((polyno422358502poly_a @ Y1 @ (polyno1491482291_Mul_a @ Y2 @ Y0)) = (times_times_a @ (polyno422358502poly_a @ Y1 @ Y2) @ (polyno422358502poly_a @ Y1 @ Y0))))))))) = $true)),
% 7.02/2.21 inference(fool_elimination,[status(thm)],[f448])).
% 7.02/2.21 thf(f448,plain,(
% 7.02/2.21 ! [X0 : polyno727731844poly_a,X1 : list_a,X2 : polyno727731844poly_a] : ((polyno422358502poly_a @ X1 @ (polyno1491482291_Mul_a @ X0 @ X2)) = (times_times_a @ (polyno422358502poly_a @ X1 @ X0) @ (polyno422358502poly_a @ X1 @ X2)))),
% 7.02/2.21 inference(rectify,[status(thm)],[f30])).
% 7.02/2.21 thf(f30,axiom,(
% 7.02/2.21 ! [X4 : polyno727731844poly_a,X3 : list_a,X7 : polyno727731844poly_a] : ((polyno422358502poly_a @ X3 @ (polyno1491482291_Mul_a @ X4 @ X7)) = (times_times_a @ (polyno422358502poly_a @ X3 @ X4) @ (polyno422358502poly_a @ X3 @ X7)))),
% 7.02/2.21 file('/export/starexec/sandbox2/tmp/tmp.HVFAM8xlRw/DTF2THF_3593.p',fact_29_Ipoly_Osimps_I6_J)).
% 7.02/2.21 thf(f1316,plain,(
% 7.02/2.21 ( ! [X0 : polyno727731844poly_a] : (((!! @ polyno727731844poly_a @ (^[Y0 : polyno727731844poly_a]: ((polyno422358502poly_a @ (sK9 @ X0) @ (polyno1491482291_Mul_a @ Y0 @ X0)) = (times_times_a @ (polyno422358502poly_a @ (sK9 @ X0) @ Y0) @ (polyno422358502poly_a @ (sK9 @ X0) @ X0))))) != $true)) )),
% 7.02/2.21 inference(forward_demodulation,[status(thm)],[f1315,f1278])).
% 7.02/2.21 thf(f1278,plain,(
% 7.02/2.21 ( ! [X2 : polyno727731844poly_a,X0 : list_a,X1 : polyno727731844poly_a] : (($true = ((polyno422358502poly_a @ X0 @ (polyno1934269411ymul_a @ X2 @ X1)) = (polyno422358502poly_a @ X0 @ (polyno1934269411ymul_a @ X1 @ X2))))) )),
% 7.02/2.21 inference(backward_demodulation,[status(thm)],[f1277,f1271])).
% 7.02/2.21 thf(f1271,plain,(
% 7.02/2.21 ( ! [X2 : list_a,X3 : polyno727731844poly_a,X1 : polyno727731844poly_a] : (((polyno422358502poly_a @ X2 @ (polyno1934269411ymul_a @ X3 @ X1)) = (times_times_a @ (polyno422358502poly_a @ X2 @ X3) @ (polyno422358502poly_a @ X2 @ X1)))) )),
% 7.02/2.21 inference(equality_proxy_clausification,[status(thm)],[f1269])).
% 7.02/2.21 thf(f1269,plain,(
% 7.02/2.21 ( ! [X2 : list_a,X3 : polyno727731844poly_a,X1 : polyno727731844poly_a] : (($true = ((times_times_a @ (polyno422358502poly_a @ X2 @ X3) @ (polyno422358502poly_a @ X2 @ X1)) = (polyno422358502poly_a @ X2 @ (polyno1934269411ymul_a @ X3 @ X1))))) )),
% 7.02/2.21 inference(beta_eta_normalization,[status(thm)],[f1268])).
% 7.02/2.21 thf(f1268,plain,(
% 7.02/2.21 ( ! [X2 : list_a,X3 : polyno727731844poly_a,X1 : polyno727731844poly_a] : (($true = ((^[Y0 : polyno727731844poly_a]: ((times_times_a @ (polyno422358502poly_a @ X2 @ Y0) @ (polyno422358502poly_a @ X2 @ X1)) = (polyno422358502poly_a @ X2 @ (polyno1934269411ymul_a @ Y0 @ X1)))) @ X3))) )),
% 7.02/2.21 inference(pi_clausification,[status(thm)],[f1263])).
% 7.02/2.21 thf(f1263,plain,(
% 7.02/2.21 ( ! [X2 : list_a,X1 : polyno727731844poly_a] : (((!! @ polyno727731844poly_a @ (^[Y0 : polyno727731844poly_a]: ((times_times_a @ (polyno422358502poly_a @ X2 @ Y0) @ (polyno422358502poly_a @ X2 @ X1)) = (polyno422358502poly_a @ X2 @ (polyno1934269411ymul_a @ Y0 @ X1))))) = $true)) )),
% 7.02/2.21 inference(beta_eta_normalization,[status(thm)],[f1259])).
% 7.02/2.21 thf(f1259,plain,(
% 7.02/2.21 ( ! [X2 : list_a,X1 : polyno727731844poly_a] : ((((^[Y0 : list_a]: (!! @ polyno727731844poly_a @ (^[Y1 : polyno727731844poly_a]: ((times_times_a @ (polyno422358502poly_a @ Y0 @ Y1) @ (polyno422358502poly_a @ Y0 @ X1)) = (polyno422358502poly_a @ Y0 @ (polyno1934269411ymul_a @ Y1 @ X1)))))) @ X2) = $true)) )),
% 7.02/2.21 inference(pi_clausification,[status(thm)],[f1258])).
% 7.02/2.21 thf(f1258,plain,(
% 7.02/2.21 ( ! [X1 : polyno727731844poly_a] : (($true = (!! @ list_a @ (^[Y0 : list_a]: (!! @ polyno727731844poly_a @ (^[Y1 : polyno727731844poly_a]: ((times_times_a @ (polyno422358502poly_a @ Y0 @ Y1) @ (polyno422358502poly_a @ Y0 @ X1)) = (polyno422358502poly_a @ Y0 @ (polyno1934269411ymul_a @ Y1 @ X1))))))))) )),
% 7.02/2.21 inference(beta_eta_normalization,[status(thm)],[f1257])).
% 7.02/2.21 thf(f1257,plain,(
% 7.02/2.21 ( ! [X1 : polyno727731844poly_a] : (($true = ((^[Y0 : polyno727731844poly_a]: (!! @ list_a @ (^[Y1 : list_a]: (!! @ polyno727731844poly_a @ (^[Y2 : polyno727731844poly_a]: ((times_times_a @ (polyno422358502poly_a @ Y1 @ Y2) @ (polyno422358502poly_a @ Y1 @ Y0)) = (polyno422358502poly_a @ Y1 @ (polyno1934269411ymul_a @ Y2 @ Y0)))))))) @ X1))) )),
% 7.02/2.21 inference(pi_clausification,[status(thm)],[f1104])).
% 7.02/2.21 thf(f1104,plain,(
% 7.02/2.21 ((!! @ polyno727731844poly_a @ (^[Y0 : polyno727731844poly_a]: (!! @ list_a @ (^[Y1 : list_a]: (!! @ polyno727731844poly_a @ (^[Y2 : polyno727731844poly_a]: ((times_times_a @ (polyno422358502poly_a @ Y1 @ Y2) @ (polyno422358502poly_a @ Y1 @ Y0)) = (polyno422358502poly_a @ Y1 @ (polyno1934269411ymul_a @ Y2 @ Y0))))))))) = $true)),
% 7.02/2.21 inference(cnf_transformation,[status(thm)],[f485])).
% 7.02/2.21 thf(f485,plain,(
% 7.02/2.21 ((!! @ polyno727731844poly_a @ (^[Y0 : polyno727731844poly_a]: (!! @ list_a @ (^[Y1 : list_a]: (!! @ polyno727731844poly_a @ (^[Y2 : polyno727731844poly_a]: ((times_times_a @ (polyno422358502poly_a @ Y1 @ Y2) @ (polyno422358502poly_a @ Y1 @ Y0)) = (polyno422358502poly_a @ Y1 @ (polyno1934269411ymul_a @ Y2 @ Y0))))))))) = $true)),
% 7.02/2.21 inference(fool_elimination,[status(thm)],[f484])).
% 7.02/2.21 thf(f484,plain,(
% 7.02/2.21 ! [X0 : polyno727731844poly_a,X1 : list_a,X2 : polyno727731844poly_a] : ((times_times_a @ (polyno422358502poly_a @ X1 @ X0) @ (polyno422358502poly_a @ X1 @ X2)) = (polyno422358502poly_a @ X1 @ (polyno1934269411ymul_a @ X0 @ X2)))),
% 7.02/2.21 inference(rectify,[status(thm)],[f11])).
% 7.02/2.21 thf(f11,axiom,(
% 7.02/2.21 ! [X1 : polyno727731844poly_a,X3 : list_a,X2 : polyno727731844poly_a] : ((polyno422358502poly_a @ X3 @ (polyno1934269411ymul_a @ X1 @ X2)) = (times_times_a @ (polyno422358502poly_a @ X3 @ X1) @ (polyno422358502poly_a @ X3 @ X2)))),
% 7.02/2.21 file('/export/starexec/sandbox2/tmp/tmp.HVFAM8xlRw/DTF2THF_3593.p',fact_10_polymul)).
% 7.02/2.21 thf(f1277,plain,(
% 7.02/2.21 ( ! [X2 : polyno727731844poly_a,X0 : list_a,X1 : polyno727731844poly_a] : (($true = ((times_times_a @ (polyno422358502poly_a @ X0 @ X2) @ (polyno422358502poly_a @ X0 @ X1)) = (polyno422358502poly_a @ X0 @ (polyno1934269411ymul_a @ X1 @ X2))))) )),
% 7.02/2.21 inference(superposition,[status(thm)],[f1269,f1180])).
% 7.02/2.21 thf(f1180,plain,(
% 7.02/2.21 ( ! [X2 : a,X1 : a] : (((times_times_a @ X2 @ X1) = (times_times_a @ X1 @ X2))) )),
% 7.02/2.21 inference(beta_eta_normalization,[status(thm)],[f1178])).
% 7.02/2.21 thf(f1178,plain,(
% 7.02/2.21 ( ! [X2 : a,X1 : a] : (((times_times_a @ X1 @ X2) = ((^[Y0 : a]: (times_times_a @ Y0 @ X1)) @ X2))) )),
% 7.02/2.21 inference(argument_congruence,[status(thm)],[f1177])).
% 7.02/2.21 thf(f1177,plain,(
% 7.02/2.21 ( ! [X1 : a] : (((^[Y0 : a]: (times_times_a @ Y0 @ X1)) = (times_times_a @ X1))) )),
% 7.02/2.21 inference(beta_eta_normalization,[status(thm)],[f1176])).
% 7.02/2.21 thf(f1176,plain,(
% 7.02/2.21 ( ! [X1 : a] : ((((^[Y0 : a]: ((^[Y1 : a]: (times_times_a @ Y1 @ Y0)))) @ X1) = (times_times_a @ X1))) )),
% 7.02/2.21 inference(argument_congruence,[status(thm)],[f1124])).
% 7.02/2.21 thf(f1124,plain,(
% 7.02/2.21 (times_times_a = (^[Y0 : a]: ((^[Y1 : a]: (times_times_a @ Y1 @ Y0)))))),
% 7.02/2.21 inference(cnf_transformation,[status(thm)],[f431])).
% 7.02/2.21 thf(f431,plain,(
% 7.02/2.21 (times_times_a = (^[Y0 : a]: ((^[Y1 : a]: (times_times_a @ Y1 @ Y0)))))),
% 7.02/2.21 inference(fool_elimination,[status(thm)],[f430])).
% 7.02/2.21 thf(f430,plain,(
% 7.02/2.21 (times_times_a = (^[X0 : a, X1 : a] : (times_times_a @ X1 @ X0)))),
% 7.02/2.21 inference(rectify,[status(thm)],[f133])).
% 7.02/2.21 thf(f133,axiom,(
% 7.02/2.21 (times_times_a = (^[X41 : a, X42 : a] : (times_times_a @ X42 @ X41)))),
% 7.02/2.21 file('/export/starexec/sandbox2/tmp/tmp.HVFAM8xlRw/DTF2THF_3593.p',fact_132_mult_Ocommute)).
% 7.02/2.21 thf(f1315,plain,(
% 7.02/2.21 ( ! [X0 : polyno727731844poly_a] : (((!! @ polyno727731844poly_a @ (^[Y0 : polyno727731844poly_a]: ((polyno422358502poly_a @ (sK9 @ X0) @ (polyno1491482291_Mul_a @ Y0 @ X0)) = (times_times_a @ (polyno422358502poly_a @ (sK9 @ X0) @ Y0) @ (polyno422358502poly_a @ (sK9 @ X0) @ X0))))) != ((polyno422358502poly_a @ (sK9 @ X0) @ (polyno1934269411ymul_a @ p @ q)) = (polyno422358502poly_a @ (sK9 @ X0) @ (polyno1934269411ymul_a @ q @ p))))) )),
% 7.02/2.21 inference(beta_eta_normalization,[status(thm)],[f1314])).
% 7.02/2.21 thf(f1314,plain,(
% 7.02/2.21 ( ! [X0 : polyno727731844poly_a] : ((((^[Y0 : list_a]: ((polyno422358502poly_a @ Y0 @ (polyno1934269411ymul_a @ p @ q)) = (polyno422358502poly_a @ Y0 @ (polyno1934269411ymul_a @ q @ p)))) @ (sK9 @ X0)) != ((^[Y0 : list_a]: (!! @ polyno727731844poly_a @ (^[Y1 : polyno727731844poly_a]: ((polyno422358502poly_a @ Y0 @ (polyno1491482291_Mul_a @ Y1 @ X0)) = (times_times_a @ (polyno422358502poly_a @ Y0 @ Y1) @ (polyno422358502poly_a @ Y0 @ X0)))))) @ (sK9 @ X0)))) )),
% 7.02/2.21 inference(negative_extensionality,[status(thm)],[f1313])).
% 7.02/2.21 thf(f1313,plain,(
% 7.02/2.21 ( ! [X0 : polyno727731844poly_a] : (((^[Y0 : list_a]: (!! @ polyno727731844poly_a @ (^[Y1 : polyno727731844poly_a]: ((polyno422358502poly_a @ Y0 @ (polyno1491482291_Mul_a @ Y1 @ X0)) = (times_times_a @ (polyno422358502poly_a @ Y0 @ Y1) @ (polyno422358502poly_a @ Y0 @ X0)))))) != (^[Y0 : list_a]: ((polyno422358502poly_a @ Y0 @ (polyno1934269411ymul_a @ p @ q)) = (polyno422358502poly_a @ Y0 @ (polyno1934269411ymul_a @ q @ p)))))) )),
% 7.02/2.21 inference(trivial_inequality_removal,[status(thm)],[f1309])).
% 7.02/2.21 thf(f1309,plain,(
% 7.02/2.21 ( ! [X0 : polyno727731844poly_a] : (((^[Y0 : list_a]: (!! @ polyno727731844poly_a @ (^[Y1 : polyno727731844poly_a]: ((polyno422358502poly_a @ Y0 @ (polyno1491482291_Mul_a @ Y1 @ X0)) = (times_times_a @ (polyno422358502poly_a @ Y0 @ Y1) @ (polyno422358502poly_a @ Y0 @ X0)))))) != (^[Y0 : list_a]: ((polyno422358502poly_a @ Y0 @ (polyno1934269411ymul_a @ p @ q)) = (polyno422358502poly_a @ Y0 @ (polyno1934269411ymul_a @ q @ p))))) | ($false = $true)) )),
% 7.02/2.21 inference(constrained_superposition,[status(thm)],[f1305,f1156])).
% 7.02/2.21 thf(f1156,plain,(
% 7.02/2.21 ($false = (!! @ list_a @ (^[Y0 : list_a]: ((polyno422358502poly_a @ Y0 @ (polyno1934269411ymul_a @ p @ q)) = (polyno422358502poly_a @ Y0 @ (polyno1934269411ymul_a @ q @ p))))))),
% 7.02/2.21 inference(backward_demodulation,[status(thm)],[f1091,f1154])).
% 7.02/2.21 thf(f1154,plain,(
% 7.02/2.21 ($false = ((polyno1934269411ymul_a @ p @ q) = (polyno1934269411ymul_a @ q @ p)))),
% 7.02/2.21 inference(not_proxy_clausification,[status(thm)],[f1068])).
% 7.02/2.21 thf(f1068,plain,(
% 7.02/2.21 ($true = (~ ((polyno1934269411ymul_a @ p @ q) = (polyno1934269411ymul_a @ q @ p))))),
% 7.02/2.21 inference(cnf_transformation,[status(thm)],[f995])).
% 7.02/2.21 thf(f995,plain,(
% 7.02/2.21 ($true = (~ ((polyno1934269411ymul_a @ p @ q) = (polyno1934269411ymul_a @ q @ p))))),
% 7.02/2.21 inference(fool_elimination,[status(thm)],[f357])).
% 7.02/2.21 thf(f357,negated_conjecture,(
% 7.02/2.21 ~((polyno1934269411ymul_a @ p @ q) = (polyno1934269411ymul_a @ q @ p))),
% 7.02/2.21 inference(negated_conjecture,[status(cth)],[f356])).
% 7.02/2.21 thf(f356,conjecture,(
% 7.02/2.21 ((polyno1934269411ymul_a @ p @ q) = (polyno1934269411ymul_a @ q @ p))),
% 7.02/2.21 file('/export/starexec/sandbox2/tmp/tmp.HVFAM8xlRw/DTF2THF_3593.p',conj_0)).
% 7.02/2.21 thf(f1091,plain,(
% 7.02/2.21 ((!! @ list_a @ (^[Y0 : list_a]: ((polyno422358502poly_a @ Y0 @ (polyno1934269411ymul_a @ p @ q)) = (polyno422358502poly_a @ Y0 @ (polyno1934269411ymul_a @ q @ p))))) = ((polyno1934269411ymul_a @ p @ q) = (polyno1934269411ymul_a @ q @ p)))),
% 7.02/2.21 inference(cnf_transformation,[status(thm)],[f363])).
% 7.02/2.21 thf(f363,plain,(
% 7.02/2.21 ((!! @ list_a @ (^[Y0 : list_a]: ((polyno422358502poly_a @ Y0 @ (polyno1934269411ymul_a @ p @ q)) = (polyno422358502poly_a @ Y0 @ (polyno1934269411ymul_a @ q @ p))))) = ((polyno1934269411ymul_a @ p @ q) = (polyno1934269411ymul_a @ q @ p)))),
% 7.02/2.21 inference(fool_elimination,[status(thm)],[f1])).
% 7.02/2.21 thf(f1,axiom,(
% 7.02/2.21 (! [X0 : list_a] : ((polyno422358502poly_a @ X0 @ (polyno1934269411ymul_a @ p @ q)) = (polyno422358502poly_a @ X0 @ (polyno1934269411ymul_a @ q @ p))) = ((polyno1934269411ymul_a @ p @ q) = (polyno1934269411ymul_a @ q @ p)))),
% 7.02/2.21 file('/export/starexec/sandbox2/tmp/tmp.HVFAM8xlRw/DTF2THF_3593.p',fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062)).
% 7.02/2.21 % SZS output end Proof for DTF2THF_3593
% 7.02/2.21 % (3769)------------------------------
% 7.02/2.21 % (3769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.21 % (3769)Termination reason: Refutation
% 7.02/2.21
% 7.02/2.21 % (3769)Memory used [KB]: 7419
% 7.02/2.21 % (3769)Time elapsed: 0.056 s
% 7.02/2.21 % (3769)Instructions burned: 187 (million)
% 7.02/2.21 % (3769)------------------------------
% 7.02/2.21 % (3769)------------------------------
% 7.02/2.21 % (3691)Success in time 0.639 s
%------------------------------------------------------------------------------