%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP044^1 : 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 : n018.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 08:55:06 AM UTC 2026
% Result : Theorem 6.29s 2.05s
% Output : Refutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 26 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 116 ( 11 ~; 3 |; 0 &; 100 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 162 ( 160 usr; 18 con; 0-3 aty)
% Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
list_nat: $tType ).
thf(type_def_7,type,
list_poly_a: $tType ).
thf(type_def_8,type,
list_a: $tType ).
thf(type_def_9,type,
poly_a: $tType ).
thf(type_def_10,type,
poly_poly_a: $tType ).
thf(type_def_11,type,
a: $tType ).
thf(type_def_12,type,
nat: $tType ).
thf(type_def_13,type,
poly_nat: $tType ).
thf(type_def_14,type,
list_list_a: $tType ).
thf(func_def_0,type,
poly_poly_a: $tType ).
thf(func_def_1,type,
list_poly_a: $tType ).
thf(func_def_2,type,
list_list_a: $tType ).
thf(func_def_3,type,
poly_nat: $tType ).
thf(func_def_4,type,
list_nat: $tType ).
thf(func_def_5,type,
poly_a: $tType ).
thf(func_def_6,type,
list_a: $tType ).
thf(func_def_7,type,
nat: $tType ).
thf(func_def_8,type,
a: $tType ).
thf(func_def_9,type,
descar226543321ms_nat: list_nat > list_nat ).
thf(func_def_10,type,
descar282223555poly_a: list_poly_a > list_poly_a ).
thf(func_def_11,type,
descar1375166517sums_a: list_a > list_a ).
thf(func_def_12,type,
descar434775507poly_a: poly_a > poly_poly_a > poly_poly_a ).
thf(func_def_13,type,
descar466059845root_a: a > poly_a > poly_a ).
thf(func_def_14,type,
descar357075861poly_a: list_poly_a > nat ).
thf(func_def_15,type,
descar2095969287nges_a: list_a > nat ).
thf(func_def_16,type,
one_one_nat: nat ).
thf(func_def_17,type,
one_one_poly_nat: poly_nat ).
thf(func_def_18,type,
one_one_poly_poly_a: poly_poly_a ).
thf(func_def_19,type,
one_one_poly_a: poly_a ).
thf(func_def_20,type,
one_one_a: a ).
thf(func_def_21,type,
times_times_nat: nat > nat > nat ).
thf(func_def_22,type,
times_times_poly_a: poly_a > poly_a > poly_a ).
thf(func_def_23,type,
times_times_a: a > a > a ).
thf(func_def_24,type,
uminus_uminus_poly_a: poly_a > poly_a ).
thf(func_def_25,type,
uminus_uminus_a: a > a ).
thf(func_def_26,type,
zero_zero_nat: nat ).
thf(func_def_27,type,
zero_zero_poly_nat: poly_nat ).
thf(func_def_28,type,
zero_z2096148049poly_a: poly_poly_a ).
thf(func_def_29,type,
zero_zero_poly_a: poly_a ).
thf(func_def_30,type,
zero_zero_a: a ).
thf(func_def_31,type,
append_nat: list_nat > list_nat > list_nat ).
thf(func_def_32,type,
append_poly_a: list_poly_a > list_poly_a > list_poly_a ).
thf(func_def_33,type,
append_a: list_a > list_a > list_a ).
thf(func_def_34,type,
cons_list_a: list_a > list_list_a > list_list_a ).
thf(func_def_35,type,
cons_nat: nat > list_nat > list_nat ).
thf(func_def_36,type,
cons_poly_a: poly_a > list_poly_a > list_poly_a ).
thf(func_def_37,type,
cons_a: a > list_a > list_a ).
thf(func_def_38,type,
nil_list_a: list_list_a ).
thf(func_def_39,type,
nil_nat: list_nat ).
thf(func_def_40,type,
nil_poly_a: list_poly_a ).
thf(func_def_41,type,
nil_a: list_a ).
thf(func_def_42,type,
null_poly_a: list_poly_a > $o ).
thf(func_def_43,type,
null_a: list_a > $o ).
thf(func_def_44,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_45,type,
ord_less_poly_a: poly_a > poly_a > $o ).
thf(func_def_46,type,
ord_less_a: a > a > $o ).
thf(func_def_47,type,
poly_nat2: list_nat > poly_nat ).
thf(func_def_48,type,
poly_poly_a2: list_poly_a > poly_poly_a ).
thf(func_def_49,type,
poly_a2: list_a > poly_a ).
thf(func_def_50,type,
coeffs_nat: poly_nat > list_nat ).
thf(func_def_51,type,
coeffs_poly_a: poly_poly_a > list_poly_a ).
thf(func_def_52,type,
coeffs_a: poly_a > list_a ).
thf(func_def_53,type,
is_zero_poly_a: poly_poly_a > $o ).
thf(func_def_54,type,
is_zero_a: poly_a > $o ).
thf(func_def_55,type,
pCons_nat: nat > poly_nat > poly_nat ).
thf(func_def_56,type,
pCons_poly_a: poly_a > poly_poly_a > poly_poly_a ).
thf(func_def_57,type,
pCons_a: a > poly_a > poly_a ).
thf(func_def_58,type,
smult_nat: nat > poly_nat > poly_nat ).
thf(func_def_59,type,
smult_poly_a: poly_a > poly_poly_a > poly_poly_a ).
thf(func_def_60,type,
smult_a: a > poly_a > poly_a ).
thf(func_def_61,type,
g: poly_a ).
thf(func_def_62,type,
v: poly_a > nat ).
thf(func_def_63,type,
xs: list_a ).
thf(func_def_64,type,
ys: list_a ).
thf(func_def_76,type,
sK0: ( list_a > list_a > $o ) > a ).
thf(func_def_77,type,
sK1: ( list_a > list_a > $o ) > list_a ).
thf(func_def_78,type,
sK2: ( list_a > list_a > $o ) > list_a ).
thf(func_def_79,type,
sK3: ( list_a > list_a > $o ) > a ).
thf(func_def_80,type,
sK4: ( list_a > list_a > $o ) > list_a ).
thf(func_def_81,type,
sK5: ( list_a > list_a > $o ) > list_a ).
thf(func_def_82,type,
sK6: ( list_a > list_a > $o ) > a ).
thf(func_def_83,type,
sK7: ( list_a > list_a > $o ) > a ).
thf(func_def_84,type,
sK8: ( list_a > list_a > $o ) > a ).
thf(func_def_85,type,
sK9: ( list_a > list_a > $o ) > list_a ).
thf(func_def_86,type,
sK10: ( list_a > list_a > $o ) > list_a ).
thf(func_def_87,type,
sK11: ( list_a > list_a > $o ) > list_a ).
thf(func_def_88,type,
sK12: ( list_a > $o ) > list_a ).
thf(func_def_89,type,
sK13: ( list_a > $o ) > a ).
thf(func_def_90,type,
sK14: list_list_a > list_list_a ).
thf(func_def_91,type,
sK15: list_list_a > a ).
thf(func_def_92,type,
sK16: list_list_a > list_a ).
thf(func_def_93,type,
sK17: list_list_a > list_list_a ).
thf(func_def_94,type,
sK18: poly_a > poly_a ).
thf(func_def_95,type,
sK19: poly_a > a ).
thf(func_def_96,type,
sK20: ( poly_a > $o ) > a ).
thf(func_def_97,type,
sK21: ( poly_a > $o ) > poly_a ).
thf(func_def_98,type,
sK22: ( ( a > a > $o ) > list_a > $o ) > a > a > $o ).
thf(func_def_99,type,
sK23: ( ( a > a > $o ) > list_a > $o ) > a ).
thf(func_def_100,type,
sK24: ( ( a > a > $o ) > list_a > $o ) > a > a > $o ).
thf(func_def_101,type,
sK25: ( ( a > a > $o ) > list_a > $o ) > a ).
thf(func_def_102,type,
sK26: ( ( a > a > $o ) > list_a > $o ) > a ).
thf(func_def_103,type,
sK27: ( ( a > a > $o ) > list_a > $o ) > list_a ).
thf(func_def_104,type,
sK28: ( ( a > a > $o ) > list_a > $o ) > a > a > $o ).
thf(func_def_105,type,
sK29: ( poly_a > poly_a > $o ) > poly_a ).
thf(func_def_106,type,
sK30: ( poly_a > poly_a > $o ) > a ).
thf(func_def_107,type,
sK31: ( poly_a > poly_a > $o ) > poly_a ).
thf(func_def_108,type,
sK32: ( poly_a > poly_a > $o ) > a ).
thf(func_def_109,type,
sK33: ( list_a > list_a > $o ) > list_a ).
thf(func_def_110,type,
sK34: ( list_a > list_a > $o ) > list_a ).
thf(func_def_111,type,
sK35: ( list_a > list_a > $o ) > a ).
thf(func_def_112,type,
sK36: ( list_a > list_a > $o ) > a ).
thf(func_def_113,type,
sK37: ( list_a > list_a > $o ) > list_a ).
thf(func_def_114,type,
sK38: ( list_a > list_a > $o ) > list_a ).
thf(func_def_115,type,
sK39: ( list_a > list_a > $o ) > a ).
thf(func_def_116,type,
sK40: ( nat > $o ) > nat ).
thf(func_def_117,type,
sK41: poly_a > a ).
thf(func_def_118,type,
sK42: poly_a > poly_a ).
thf(func_def_119,type,
sK43: ( ( a > a ) > list_a > list_a > $o ) > a > a ).
thf(func_def_120,type,
sK44: ( ( a > a ) > list_a > list_a > $o ) > list_a ).
thf(func_def_121,type,
sK45: ( ( a > a ) > list_a > list_a > $o ) > list_a ).
thf(func_def_122,type,
sK46: ( ( a > a ) > list_a > list_a > $o ) > a ).
thf(func_def_123,type,
sK47: ( ( a > a ) > list_a > list_a > $o ) > a > a ).
thf(func_def_124,type,
sK48: ( ( a > a ) > list_a > list_a > $o ) > list_a ).
thf(func_def_125,type,
sK49: ( list_a > $o ) > list_a ).
thf(func_def_126,type,
sK50: ( list_a > $o ) > a ).
thf(func_def_127,type,
sK51: ( poly_poly_a > $o ) > poly_poly_a ).
thf(func_def_128,type,
sK52: ( poly_poly_a > $o ) > poly_a ).
thf(func_def_129,type,
sK53: ( nat > $o ) > nat ).
thf(func_def_130,type,
sK54: ( list_a > $o ) > a ).
thf(func_def_131,type,
sK55: ( list_a > $o ) > a ).
thf(func_def_132,type,
sK56: ( list_a > $o ) > list_a ).
thf(func_def_133,type,
sK57: ( list_a > $o ) > a ).
thf(func_def_134,type,
sK58: list_a > list_a ).
thf(func_def_135,type,
sK59: list_a > a ).
thf(func_def_136,type,
sK60: list_a > list_a ).
thf(func_def_137,type,
sK61: list_a > a ).
thf(func_def_138,type,
sK62: ( ( a > a > $o ) > list_a > $o ) > list_a ).
thf(func_def_139,type,
sK63: ( ( a > a > $o ) > list_a > $o ) > a > a > $o ).
thf(func_def_140,type,
sK64: ( ( a > a > $o ) > list_a > $o ) > a ).
thf(func_def_141,type,
sK65: ( ( a > a > $o ) > list_a > $o ) > a > a > $o ).
thf(func_def_142,type,
sK66: list_a > a ).
thf(func_def_143,type,
sK67: list_a > list_a ).
thf(func_def_144,type,
sK68: ( nat > $o ) > nat ).
thf(func_def_145,type,
sK69: ( list_a > $o ) > a ).
thf(func_def_146,type,
sK70: ( list_a > $o ) > list_a ).
thf(func_def_147,type,
sK71: ( list_a > $o ) > a ).
thf(func_def_148,type,
sK72: ( list_a > $o ) > list_a ).
thf(func_def_149,type,
sK73: ( list_a > $o ) > a ).
thf(func_def_150,type,
sK74: list_a > a ).
thf(func_def_151,type,
sK75: list_a > list_a ).
thf(func_def_152,type,
sK76: list_a > a ).
thf(func_def_153,type,
sK77: list_a > a ).
thf(func_def_154,type,
sK78: ( list_a > list_a > $o ) > a ).
thf(func_def_155,type,
sK79: ( list_a > list_a > $o ) > list_a ).
thf(func_def_156,type,
sK80: ( list_a > list_a > $o ) > list_a ).
thf(func_def_157,type,
sK81: ( list_a > list_a > $o ) > a ).
thf(func_def_158,type,
sK82: ( list_a > list_a > $o ) > a ).
thf(func_def_159,type,
sK83: ( list_a > list_a > $o ) > list_a ).
thf(func_def_160,type,
sK84: ( list_a > list_a > $o ) > list_a ).
thf(func_def_161,type,
sK85: ( list_a > list_a > $o ) > list_a ).
thf(func_def_162,type,
sK86: ( list_a > list_a > $o ) > list_a ).
thf(func_def_163,type,
sK87: ( list_a > list_a > $o ) > a ).
thf(func_def_164,type,
sK88: ( list_a > list_a > $o ) > a ).
thf(func_def_165,type,
sK89: ( list_a > list_a > $o ) > list_a ).
thf(func_def_166,type,
sK90: ( list_a > list_a > $o ) > list_a ).
thf(func_def_167,type,
sK91: list_a > a ).
thf(func_def_168,type,
sK92: list_a > a ).
thf(func_def_169,type,
sK93: list_a > a ).
thf(func_def_170,type,
sK94: list_a > list_a ).
thf(func_def_171,type,
sK95: ( list_a > $o ) > a ).
thf(func_def_172,type,
sK96: ( list_a > $o ) > list_a ).
thf(func_def_173,type,
sK97: ( list_a > $o ) > a ).
thf(func_def_174,type,
sK98: ( list_a > $o ) > a ).
thf(func_def_175,type,
sK99: ( poly_a > $o ) > poly_a ).
thf(func_def_176,type,
sK100: ( poly_a > $o ) > a ).
thf(func_def_177,type,
sK101: ( poly_nat > $o ) > poly_nat ).
thf(func_def_178,type,
sK102: ( poly_nat > $o ) > nat ).
thf(func_def_180,type,
ph104:
!>[X0: $tType] : X0 ).
thf(f1742,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f1741]) ).
thf(f1741,plain,
( ( descar2095969287nges_a @ ( coeffs_a @ g ) )
!= ( descar2095969287nges_a @ ( coeffs_a @ g ) ) ),
inference(forward_demodulation,[status(thm)],[f1740,f1405]) ).
thf(f1405,plain,
! [X0: poly_a] :
( ( poly_a2 @ ( coeffs_a @ X0 ) )
= X0 ),
inference(cnf_transformation,[status(thm)],[f872]) ).
thf(f872,plain,
! [X0: poly_a] :
( ( poly_a2 @ ( coeffs_a @ X0 ) )
= X0 ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
! [X6: poly_a] :
( ( poly_a2 @ ( coeffs_a @ X6 ) )
= X6 ),
file('/export/starexec/sandbox2/tmp/tmp.t7mfK5zq2L/DTF2THF_27787.p',fact_13_Poly__coeffs) ).
thf(f1740,plain,
( ( descar2095969287nges_a @ ( coeffs_a @ g ) )
!= ( descar2095969287nges_a @ ( coeffs_a @ ( poly_a2 @ ( coeffs_a @ g ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1737,f1343]) ).
thf(f1343,plain,
! [X0: list_a] :
( ( poly_a2 @ ( append_a @ X0 @ ( cons_a @ zero_zero_a @ nil_a ) ) )
= ( poly_a2 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f821]) ).
thf(f821,plain,
! [X0: list_a] :
( ( poly_a2 @ ( append_a @ X0 @ ( cons_a @ zero_zero_a @ nil_a ) ) )
= ( poly_a2 @ X0 ) ),
inference(rectify,[status(thm)],[f67]) ).
thf(f67,axiom,
! [X11: list_a] :
( ( poly_a2 @ ( append_a @ X11 @ ( cons_a @ zero_zero_a @ nil_a ) ) )
= ( poly_a2 @ X11 ) ),
file('/export/starexec/sandbox2/tmp/tmp.t7mfK5zq2L/DTF2THF_27787.p',fact_66_Poly__snoc__zero) ).
thf(f1737,plain,
( ( descar2095969287nges_a @ ( coeffs_a @ g ) )
!= ( descar2095969287nges_a @ ( coeffs_a @ ( poly_a2 @ ( append_a @ ( coeffs_a @ g ) @ ( cons_a @ zero_zero_a @ nil_a ) ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f1716]) ).
thf(f1716,plain,
! [X0: poly_a] :
( ( ( poly_a2 @ ( append_a @ ( coeffs_a @ g ) @ ( cons_a @ zero_zero_a @ nil_a ) ) )
!= X0 )
| ( ( descar2095969287nges_a @ ( coeffs_a @ X0 ) )
!= ( descar2095969287nges_a @ ( coeffs_a @ g ) ) ) ),
inference(superposition,[status(thm)],[f1581,f1499]) ).
thf(f1499,plain,
! [X0: poly_a,X1: list_a] :
( ( ( descar2095969287nges_a @ ( coeffs_a @ X0 ) )
= ( descar2095969287nges_a @ X1 ) )
| ( ( poly_a2 @ X1 )
!= X0 ) ),
inference(cnf_transformation,[status(thm)],[f956]) ).
thf(f956,plain,
! [X0: poly_a,X1: list_a] :
( ( ( descar2095969287nges_a @ ( coeffs_a @ X0 ) )
= ( descar2095969287nges_a @ X1 ) )
| ( ( poly_a2 @ X1 )
!= X0 ) ),
inference(ennf_transformation,[status(thm)],[f787]) ).
thf(f787,plain,
! [X0: poly_a,X1: list_a] :
( ( ( poly_a2 @ X1 )
= X0 )
=> ( ( descar2095969287nges_a @ ( coeffs_a @ X0 ) )
= ( descar2095969287nges_a @ X1 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X6: poly_a,X5: list_a] :
( ( ( poly_a2 @ X5 )
= X6 )
=> ( ( descar2095969287nges_a @ X5 )
= ( descar2095969287nges_a @ ( coeffs_a @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.t7mfK5zq2L/DTF2THF_27787.p',fact_6_sign__changes__coeff__sign__changes) ).
thf(f1581,plain,
( ( descar2095969287nges_a @ ( coeffs_a @ g ) )
!= ( descar2095969287nges_a @ ( append_a @ ( coeffs_a @ g ) @ ( cons_a @ zero_zero_a @ nil_a ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1246,f1313]) ).
thf(f1313,plain,
( ys
= ( append_a @ ( coeffs_a @ g ) @ ( cons_a @ zero_zero_a @ nil_a ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,axiom,
( ys
= ( append_a @ ( coeffs_a @ g ) @ ( cons_a @ zero_zero_a @ nil_a ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.t7mfK5zq2L/DTF2THF_27787.p',fact_7_ys__def) ).
thf(f1246,plain,
( ( descar2095969287nges_a @ ys )
!= ( descar2095969287nges_a @ ( coeffs_a @ g ) ) ),
inference(cnf_transformation,[status(thm)],[f849]) ).
thf(f849,plain,
( ( descar2095969287nges_a @ ys )
!= ( descar2095969287nges_a @ ( coeffs_a @ g ) ) ),
inference(flattening,[status(thm)],[f348]) ).
thf(f348,negated_conjecture,
( ( descar2095969287nges_a @ ys )
!= ( descar2095969287nges_a @ ( coeffs_a @ g ) ) ),
inference(negated_conjecture,[status(cth)],[f347]) ).
thf(f347,conjecture,
( ( descar2095969287nges_a @ ys )
= ( descar2095969287nges_a @ ( coeffs_a @ g ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.t7mfK5zq2L/DTF2THF_27787.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP044^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n018.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 08:24:16 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : ITP044^1 : TPTP v9.2.1. Released v7.5.0.
% 0.18/0.45 % Domain : Interactive Theorem Proving
% 0.18/0.45 % Problem : Sledgehammer Descartes_Sign_Rule problem prob_761__5872108_1
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.18/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Des21]
% 0.18/0.45 % Names : Descartes_Sign_Rule/prob_761__5872108_1 [Des21]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0
% 0.18/0.45 % Syntax : Number of formulae : 412 ( 240 unt; 65 typ; 0 def)
% 0.18/0.45 % Number of atoms : 790 ( 531 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 10 ( 2 avg)
% 0.18/0.45 % Number of connectives : 2132 ( 114 ~; 47 |; 46 &;1703 @)
% 0.18/0.45 % ( 0 <=>; 222 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 17 ( 5 avg)
% 0.18/0.45 % Number of types : 10 ( 9 usr)
% 0.18/0.45 % Number of type conns : 114 ( 114 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 57 ( 56 usr; 17 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 718 ( 16 ^; 697 !; 5 ?; 718 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 15:42:44.488
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % Could-be-implicit typings (9)
% 0.18/0.45 thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J,type,
% 0.18/0.45 poly_poly_a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__List__Olist_It__Polynomial__Opoly_Itf__a_J_J,type,
% 0.18/0.45 list_poly_a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.45 list_list_a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 0.18/0.45 poly_nat: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.18/0.45 list_nat: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 poly_a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.18/0.45 list_a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Nat__Onat,type,
% 0.18/0.45 nat: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_tf__a,type,
% 0.18/0.45 a: $tType ).
% 0.18/0.45
% 0.18/0.45 % Explicit typings (56)
% 0.18/0.45 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Opsums_001t__Nat__Onat,type,
% 0.18/0.45 descar226543321ms_nat: list_nat > list_nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Opsums_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 descar282223555poly_a: list_poly_a > list_poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Opsums_001tf__a,type,
% 0.18/0.45 descar1375166517sums_a: list_a > list_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Oreduce__root_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 descar434775507poly_a: poly_a > poly_poly_a > poly_poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Oreduce__root_001tf__a,type,
% 0.18/0.45 descar466059845root_a: a > poly_a > poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Osign__changes_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 descar357075861poly_a: list_poly_a > nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Osign__changes_001tf__a,type,
% 0.18/0.45 descar2095969287nges_a: list_a > nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.18/0.45 one_one_nat: nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 0.18/0.45 one_one_poly_nat: poly_nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J,type,
% 0.18/0.45 one_one_poly_poly_a: poly_poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 one_one_poly_a: poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Oone__class_Oone_001tf__a,type,
% 0.18/0.45 one_one_a: a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 0.18/0.45 times_times_nat: nat > nat > nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 times_times_poly_a: poly_a > poly_a > poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Otimes__class_Otimes_001tf__a,type,
% 0.18/0.45 times_times_a: a > a > a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 uminus_uminus_poly_a: poly_a > poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001tf__a,type,
% 0.18/0.45 uminus_uminus_a: a > a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.18/0.45 zero_zero_nat: nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 0.18/0.45 zero_zero_poly_nat: poly_nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J,type,
% 0.18/0.45 zero_z2096148049poly_a: poly_poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 zero_zero_poly_a: poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Ozero__class_Ozero_001tf__a,type,
% 0.18/0.45 zero_zero_a: a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 0.18/0.45 append_nat: list_nat > list_nat > list_nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oappend_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 append_poly_a: list_poly_a > list_poly_a > list_poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Oappend_001tf__a,type,
% 0.18/0.45 append_a: list_a > list_a > list_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_OCons_001t__List__Olist_Itf__a_J,type,
% 0.18/0.45 cons_list_a: list_a > list_list_a > list_list_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 0.18/0.45 cons_nat: nat > list_nat > list_nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_OCons_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 cons_poly_a: poly_a > list_poly_a > list_poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_OCons_001tf__a,type,
% 0.18/0.45 cons_a: a > list_a > list_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__a_J,type,
% 0.18/0.45 nil_list_a: list_list_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 0.18/0.45 nil_nat: list_nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_ONil_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 nil_poly_a: list_poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Olist_ONil_001tf__a,type,
% 0.18/0.45 nil_a: list_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Onull_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 null_poly_a: list_poly_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_List_Onull_001tf__a,type,
% 0.18/0.45 null_a: list_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.18/0.45 ord_less_nat: nat > nat > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 ord_less_poly_a: poly_a > poly_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Oord__class_Oless_001tf__a,type,
% 0.18/0.45 ord_less_a: a > a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Polynomial_OPoly_001t__Nat__Onat,type,
% 0.18/0.45 poly_nat2: list_nat > poly_nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Polynomial_OPoly_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 poly_poly_a2: list_poly_a > poly_poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Polynomial_OPoly_001tf__a,type,
% 0.18/0.45 poly_a2: list_a > poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Polynomial_Ocoeffs_001t__Nat__Onat,type,
% 0.18/0.45 coeffs_nat: poly_nat > list_nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Polynomial_Ocoeffs_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 coeffs_poly_a: poly_poly_a > list_poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Polynomial_Ocoeffs_001tf__a,type,
% 0.18/0.45 coeffs_a: poly_a > list_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Polynomial_Ois__zero_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 is_zero_poly_a: poly_poly_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Polynomial_Ois__zero_001tf__a,type,
% 0.18/0.45 is_zero_a: poly_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Polynomial_OpCons_001t__Nat__Onat,type,
% 0.18/0.45 pCons_nat: nat > poly_nat > poly_nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 pCons_poly_a: poly_a > poly_poly_a > poly_poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Polynomial_OpCons_001tf__a,type,
% 0.18/0.45 pCons_a: a > poly_a > poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Polynomial_Osmult_001t__Nat__Onat,type,
% 0.18/0.45 smult_nat: nat > poly_nat > poly_nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Polynomial_Osmult_001t__Polynomial__Opoly_Itf__a_J,type,
% 0.18/0.45 smult_poly_a: poly_a > poly_poly_a > poly_poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Polynomial_Osmult_001tf__a,type,
% 0.18/0.45 smult_a: a > poly_a > poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_g,type,
% 0.18/0.45 g: poly_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_v,type,
% 0.18/0.45 v: poly_a > nat ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_xs____,type,
% 0.18/0.45 xs: list_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_ys____,type,
% 0.18/0.45 ys: list_a ).
% 0.18/0.45
% 0.18/0.45 % Relevant facts (346)
% 0.18/0.45 thf(fact_0_v__def,axiom,
% 0.18/0.45 ( v
% 0.18/0.45 = ( ^ [F: poly_a] : ( descar2095969287nges_a @ ( coeffs_a @ F ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % v_def
% 0.18/0.45 thf(fact_1_nz,axiom,
% 0.18/0.45 g != zero_zero_poly_a ).
% 0.18/0.45
% 0.18/0.45 % nz
% 0.18/0.45 thf(fact_2_coeffs__eq__iff,axiom,
% 0.18/0.45 ( ( ^ [Y: poly_poly_a,Z: poly_poly_a] : ( Y = Z ) )
% 0.18/0.45 = ( ^ [P: poly_poly_a,Q: poly_poly_a] :
% 0.18/0.45 ( ( coeffs_poly_a @ P )
% 0.18/0.45 = ( coeffs_poly_a @ Q ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % coeffs_eq_iff
% 0.18/0.45 thf(fact_3_coeffs__eq__iff,axiom,
% 0.18/0.45 ( ( ^ [Y: poly_a,Z: poly_a] : ( Y = Z ) )
% 0.18/0.45 = ( ^ [P: poly_a,Q: poly_a] :
% 0.18/0.45 ( ( coeffs_a @ P )
% 0.18/0.45 = ( coeffs_a @ Q ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % coeffs_eq_iff
% 0.18/0.45 thf(fact_4_ys,axiom,
% 0.18/0.45 ( ys
% 0.18/0.45 = ( descar1375166517sums_a @ xs ) ) ).
% 0.18/0.45
% 0.18/0.45 % ys
% 0.18/0.45 thf(fact_5_sign__changes__coeff__sign__changes,axiom,
% 0.18/0.45 ! [Xs: list_poly_a,P2: poly_poly_a] :
% 0.18/0.45 ( ( ( poly_poly_a2 @ Xs )
% 0.18/0.45 = P2 )
% 0.18/0.45 => ( ( descar357075861poly_a @ Xs )
% 0.18/0.45 = ( descar357075861poly_a @ ( coeffs_poly_a @ P2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sign_changes_coeff_sign_changes
% 0.18/0.45 thf(fact_6_sign__changes__coeff__sign__changes,axiom,
% 0.18/0.45 ! [Xs: list_a,P2: poly_a] :
% 0.18/0.45 ( ( ( poly_a2 @ Xs )
% 0.18/0.45 = P2 )
% 0.18/0.45 => ( ( descar2095969287nges_a @ Xs )
% 0.18/0.45 = ( descar2095969287nges_a @ ( coeffs_a @ P2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sign_changes_coeff_sign_changes
% 0.18/0.45 thf(fact_7_ys__def,axiom,
% 0.18/0.45 ( ys
% 0.18/0.45 = ( append_a @ ( coeffs_a @ g ) @ ( cons_a @ zero_zero_a @ nil_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ys_def
% 0.18/0.45 thf(fact_8_coeff__sign__changes__reduce__root,axiom,
% 0.18/0.45 ! [A: poly_a,P2: poly_poly_a] :
% 0.18/0.45 ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.18/0.45 => ( ( descar357075861poly_a @ ( coeffs_poly_a @ ( descar434775507poly_a @ A @ P2 ) ) )
% 0.18/0.45 = ( descar357075861poly_a @ ( coeffs_poly_a @ P2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % coeff_sign_changes_reduce_root
% 0.18/0.45 thf(fact_9_coeff__sign__changes__reduce__root,axiom,
% 0.18/0.45 ! [A: a,P2: poly_a] :
% 0.18/0.45 ( ( ord_less_a @ zero_zero_a @ A )
% 0.18/0.45 => ( ( descar2095969287nges_a @ ( coeffs_a @ ( descar466059845root_a @ A @ P2 ) ) )
% 0.18/0.45 = ( descar2095969287nges_a @ ( coeffs_a @ P2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % coeff_sign_changes_reduce_root
% 0.18/0.45 thf(fact_10_is__zero__def,axiom,
% 0.18/0.45 ( is_zero_poly_a
% 0.18/0.45 = ( ^ [P: poly_poly_a] : ( null_poly_a @ ( coeffs_poly_a @ P ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % is_zero_def
% 0.18/0.45 thf(fact_11_is__zero__def,axiom,
% 0.18/0.45 ( is_zero_a
% 0.18/0.45 = ( ^ [P: poly_a] : ( null_a @ ( coeffs_a @ P ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % is_zero_def
% 0.18/0.45 thf(fact_12_Poly__coeffs,axiom,
% 0.18/0.45 ! [P2: poly_poly_a] :
% 0.18/0.45 ( ( poly_poly_a2 @ ( coeffs_poly_a @ P2 ) )
% 0.18/0.45 = P2 ) ).
% 0.18/0.45
% 0.18/0.45 % Poly_coeffs
% 0.18/0.45 thf(fact_13_Poly__coeffs,axiom,
% 0.18/0.45 ! [P2: poly_a] :
% 0.18/0.45 ( ( poly_a2 @ ( coeffs_a @ P2 ) )
% 0.18/0.45 = P2 ) ).
% 0.18/0.45
% 0.18/0.45 % Poly_coeffs
% 0.18/0.45 thf(fact_14_sign__changes__Nil,axiom,
% 0.18/0.45 ( ( descar357075861poly_a @ nil_poly_a )
% 0.18/0.45 = zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % sign_changes_Nil
% 0.18/0.45 thf(fact_15_sign__changes__Nil,axiom,
% 0.18/0.45 ( ( descar2095969287nges_a @ nil_a )
% 0.18/0.45 = zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % sign_changes_Nil
% 0.18/0.45 thf(fact_16_xs__def,axiom,
% 0.18/0.45 ( xs
% 0.18/0.45 = ( coeffs_a @ ( times_times_poly_a @ ( pCons_a @ one_one_a @ ( pCons_a @ ( uminus_uminus_a @ one_one_a ) @ zero_zero_poly_a ) ) @ g ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % xs_def
% 0.18/0.45 thf(fact_17_coeff__sign__changes__smult,axiom,
% 0.18/0.45 ! [A: a,P2: poly_a] :
% 0.18/0.45 ( ( ord_less_a @ zero_zero_a @ A )
% 0.18/0.45 => ( ( descar2095969287nges_a @ ( coeffs_a @ ( smult_a @ A @ P2 ) ) )
% 0.18/0.45 = ( descar2095969287nges_a @ ( coeffs_a @ P2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % coeff_sign_changes_smult
% 0.18/0.45 thf(fact_18_coeff__sign__changes__smult,axiom,
% 0.18/0.45 ! [A: poly_a,P2: poly_poly_a] :
% 0.18/0.45 ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.18/0.45 => ( ( descar357075861poly_a @ ( coeffs_poly_a @ ( smult_poly_a @ A @ P2 ) ) )
% 0.18/0.45 = ( descar357075861poly_a @ ( coeffs_poly_a @ P2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % coeff_sign_changes_smult
% 0.18/0.45 thf(fact_19_sign__changes__0__Cons,axiom,
% 0.18/0.45 ! [Xs: list_a] :
% 0.18/0.45 ( ( descar2095969287nges_a @ ( cons_a @ zero_zero_a @ Xs ) )
% 0.18/0.45 = ( descar2095969287nges_a @ Xs ) ) ).
% 0.18/0.45
% 0.18/0.45 % sign_changes_0_Cons
% 0.18/0.45 thf(fact_20_sign__changes__0__Cons,axiom,
% 0.18/0.45 ! [Xs: list_poly_a] :
% 0.18/0.45 ( ( descar357075861poly_a @ ( cons_poly_a @ zero_zero_poly_a @ Xs ) )
% 0.18/0.45 = ( descar357075861poly_a @ Xs ) ) ).
% 0.18/0.45
% 0.18/0.45 % sign_changes_0_Cons
% 0.18/0.45 thf(fact_21_sign__changes__Cons__Cons__0,axiom,
% 0.18/0.45 ! [X: a,Xs: list_a] :
% 0.18/0.45 ( ( descar2095969287nges_a @ ( cons_a @ X @ ( cons_a @ zero_zero_a @ Xs ) ) )
% 0.18/0.45 = ( descar2095969287nges_a @ ( cons_a @ X @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sign_changes_Cons_Cons_0
% 0.18/0.45 thf(fact_22_sign__changes__Cons__Cons__0,axiom,
% 0.18/0.45 ! [X: poly_a,Xs: list_poly_a] :
% 0.18/0.45 ( ( descar357075861poly_a @ ( cons_poly_a @ X @ ( cons_poly_a @ zero_zero_poly_a @ Xs ) ) )
% 0.18/0.45 = ( descar357075861poly_a @ ( cons_poly_a @ X @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sign_changes_Cons_Cons_0
% 0.18/0.45 thf(fact_23_pCons__eq__iff,axiom,
% 0.18/0.45 ! [A: a,P2: poly_a,B: a,Q2: poly_a] :
% 0.18/0.45 ( ( ( pCons_a @ A @ P2 )
% 0.18/0.45 = ( pCons_a @ B @ Q2 ) )
% 0.18/0.45 = ( ( A = B )
% 0.18/0.45 & ( P2 = Q2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pCons_eq_iff
% 0.18/0.45 thf(fact_24_minus__pCons,axiom,
% 0.18/0.45 ! [A: a,P2: poly_a] :
% 0.18/0.45 ( ( uminus_uminus_poly_a @ ( pCons_a @ A @ P2 ) )
% 0.18/0.45 = ( pCons_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_poly_a @ P2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % minus_pCons
% 0.18/0.45 thf(fact_25_smult__smult,axiom,
% 0.18/0.45 ! [A: poly_a,B: poly_a,P2: poly_poly_a] :
% 0.18/0.45 ( ( smult_poly_a @ A @ ( smult_poly_a @ B @ P2 ) )
% 0.18/0.45 = ( smult_poly_a @ ( times_times_poly_a @ A @ B ) @ P2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % smult_smult
% 0.18/0.45 thf(fact_26_smult__smult,axiom,
% 0.18/0.45 ! [A: nat,B: nat,P2: poly_nat] :
% 0.18/0.45 ( ( smult_nat @ A @ ( smult_nat @ B @ P2 ) )
% 0.18/0.45 = ( smult_nat @ ( times_times_nat @ A @ B ) @ P2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % smult_smult
% 0.18/0.45 thf(fact_27_smult__1__left,axiom,
% 0.18/0.45 ! [P2: poly_a] :
% 0.18/0.45 ( ( smult_a @ one_one_a @ P2 )
% 0.18/0.45 = P2 ) ).
% 0.18/0.45
% 0.18/0.45 % smult_1_left
% 0.18/0.45 thf(fact_28_smult__1__left,axiom,
% 0.18/0.45 ! [P2: poly_nat] :
% 0.18/0.45 ( ( smult_nat @ one_one_nat @ P2 )
% 0.18/0.45 = P2 ) ).
% 0.18/0.45
% 0.18/0.45 % smult_1_left
% 0.18/0.45 thf(fact_29_smult__minus__left,axiom,
% 0.18/0.45 ! [A: a,P2: poly_a] :
% 0.18/0.45 ( ( smult_a @ ( uminus_uminus_a @ A ) @ P2 )
% 0.18/0.45 = ( uminus_uminus_poly_a @ ( smult_a @ A @ P2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % smult_minus_left
% 0.18/0.45 thf(fact_30_smult__0__right,axiom,
% 0.18/0.45 ! [A: a] :
% 0.18/0.45 ( ( smult_a @ A @ zero_zero_poly_a )
% 0.18/0.45 = zero_zero_poly_a ) ).
% 0.18/0.45
% 0.18/0.45 % smult_0_right
% 0.18/0.45 thf(fact_31_mult__smult__left,axiom,
% 0.18/0.45 ! [A: a,P2: poly_a,Q2: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ ( smult_a @ A @ P2 ) @ Q2 )
% 0.18/0.45 = ( smult_a @ A @ ( times_times_poly_a @ P2 @ Q2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_smult_left
% 0.18/0.45 thf(fact_32_mult__smult__right,axiom,
% 0.18/0.45 ! [P2: poly_a,A: a,Q2: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ P2 @ ( smult_a @ A @ Q2 ) )
% 0.18/0.45 = ( smult_a @ A @ ( times_times_poly_a @ P2 @ Q2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_smult_right
% 0.18/0.45 thf(fact_33_pCons__0__0,axiom,
% 0.18/0.45 ( ( pCons_poly_a @ zero_zero_poly_a @ zero_z2096148049poly_a )
% 0.18/0.45 = zero_z2096148049poly_a ) ).
% 0.18/0.45
% 0.18/0.45 % pCons_0_0
% 0.18/0.45 thf(fact_34_pCons__0__0,axiom,
% 0.18/0.45 ( ( pCons_a @ zero_zero_a @ zero_zero_poly_a )
% 0.18/0.45 = zero_zero_poly_a ) ).
% 0.18/0.45
% 0.18/0.45 % pCons_0_0
% 0.18/0.45 thf(fact_35_pCons__0__0,axiom,
% 0.18/0.45 ( ( pCons_nat @ zero_zero_nat @ zero_zero_poly_nat )
% 0.18/0.45 = zero_zero_poly_nat ) ).
% 0.18/0.45
% 0.18/0.45 % pCons_0_0
% 0.18/0.45 thf(fact_36_pCons__eq__0__iff,axiom,
% 0.18/0.45 ! [A: poly_a,P2: poly_poly_a] :
% 0.18/0.45 ( ( ( pCons_poly_a @ A @ P2 )
% 0.18/0.45 = zero_z2096148049poly_a )
% 0.18/0.45 = ( ( A = zero_zero_poly_a )
% 0.18/0.45 & ( P2 = zero_z2096148049poly_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pCons_eq_0_iff
% 0.18/0.45 thf(fact_37_pCons__eq__0__iff,axiom,
% 0.18/0.45 ! [A: nat,P2: poly_nat] :
% 0.18/0.45 ( ( ( pCons_nat @ A @ P2 )
% 0.18/0.45 = zero_zero_poly_nat )
% 0.18/0.45 = ( ( A = zero_zero_nat )
% 0.18/0.45 & ( P2 = zero_zero_poly_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pCons_eq_0_iff
% 0.18/0.45 thf(fact_38_pCons__eq__0__iff,axiom,
% 0.18/0.45 ! [A: a,P2: poly_a] :
% 0.18/0.45 ( ( ( pCons_a @ A @ P2 )
% 0.18/0.45 = zero_zero_poly_a )
% 0.18/0.45 = ( ( A = zero_zero_a )
% 0.18/0.45 & ( P2 = zero_zero_poly_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pCons_eq_0_iff
% 0.18/0.45 thf(fact_39_one__poly__eq__simps_I2_J,axiom,
% 0.18/0.45 ( ( pCons_nat @ one_one_nat @ zero_zero_poly_nat )
% 0.18/0.45 = one_one_poly_nat ) ).
% 0.18/0.45
% 0.18/0.45 % one_poly_eq_simps(2)
% 0.18/0.45 thf(fact_40_one__poly__eq__simps_I2_J,axiom,
% 0.18/0.45 ( ( pCons_a @ one_one_a @ zero_zero_poly_a )
% 0.18/0.45 = one_one_poly_a ) ).
% 0.18/0.45
% 0.18/0.45 % one_poly_eq_simps(2)
% 0.18/0.45 thf(fact_41_one__poly__eq__simps_I1_J,axiom,
% 0.18/0.45 ( one_one_poly_nat
% 0.18/0.45 = ( pCons_nat @ one_one_nat @ zero_zero_poly_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % one_poly_eq_simps(1)
% 0.18/0.45 thf(fact_42_one__poly__eq__simps_I1_J,axiom,
% 0.18/0.45 ( one_one_poly_a
% 0.18/0.45 = ( pCons_a @ one_one_a @ zero_zero_poly_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % one_poly_eq_simps(1)
% 0.18/0.45 thf(fact_43_smult__0__left,axiom,
% 0.18/0.45 ! [P2: poly_poly_a] :
% 0.18/0.45 ( ( smult_poly_a @ zero_zero_poly_a @ P2 )
% 0.18/0.45 = zero_z2096148049poly_a ) ).
% 0.18/0.45
% 0.18/0.45 % smult_0_left
% 0.18/0.45 thf(fact_44_smult__0__left,axiom,
% 0.18/0.45 ! [P2: poly_a] :
% 0.18/0.45 ( ( smult_a @ zero_zero_a @ P2 )
% 0.18/0.45 = zero_zero_poly_a ) ).
% 0.18/0.45
% 0.18/0.45 % smult_0_left
% 0.18/0.45 thf(fact_45_smult__0__left,axiom,
% 0.18/0.45 ! [P2: poly_nat] :
% 0.18/0.45 ( ( smult_nat @ zero_zero_nat @ P2 )
% 0.18/0.45 = zero_zero_poly_nat ) ).
% 0.18/0.45
% 0.18/0.45 % smult_0_left
% 0.18/0.45 thf(fact_46_smult__eq__0__iff,axiom,
% 0.18/0.45 ! [A: poly_a,P2: poly_poly_a] :
% 0.18/0.45 ( ( ( smult_poly_a @ A @ P2 )
% 0.18/0.45 = zero_z2096148049poly_a )
% 0.18/0.45 = ( ( A = zero_zero_poly_a )
% 0.18/0.45 | ( P2 = zero_z2096148049poly_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % smult_eq_0_iff
% 0.18/0.45 thf(fact_47_smult__eq__0__iff,axiom,
% 0.18/0.45 ! [A: nat,P2: poly_nat] :
% 0.18/0.45 ( ( ( smult_nat @ A @ P2 )
% 0.18/0.45 = zero_zero_poly_nat )
% 0.18/0.45 = ( ( A = zero_zero_nat )
% 0.18/0.45 | ( P2 = zero_zero_poly_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % smult_eq_0_iff
% 0.18/0.45 thf(fact_48_smult__eq__0__iff,axiom,
% 0.18/0.45 ! [A: a,P2: poly_a] :
% 0.18/0.45 ( ( ( smult_a @ A @ P2 )
% 0.18/0.45 = zero_zero_poly_a )
% 0.18/0.45 = ( ( A = zero_zero_a )
% 0.18/0.45 | ( P2 = zero_zero_poly_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % smult_eq_0_iff
% 0.18/0.45 thf(fact_49_smult__pCons,axiom,
% 0.18/0.45 ! [A: a,B: a,P2: poly_a] :
% 0.18/0.45 ( ( smult_a @ A @ ( pCons_a @ B @ P2 ) )
% 0.18/0.45 = ( pCons_a @ ( times_times_a @ A @ B ) @ ( smult_a @ A @ P2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % smult_pCons
% 0.18/0.45 thf(fact_50_smult__pCons,axiom,
% 0.18/0.45 ! [A: poly_a,B: poly_a,P2: poly_poly_a] :
% 0.18/0.45 ( ( smult_poly_a @ A @ ( pCons_poly_a @ B @ P2 ) )
% 0.18/0.45 = ( pCons_poly_a @ ( times_times_poly_a @ A @ B ) @ ( smult_poly_a @ A @ P2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % smult_pCons
% 0.18/0.45 thf(fact_51_smult__pCons,axiom,
% 0.18/0.45 ! [A: nat,B: nat,P2: poly_nat] :
% 0.18/0.45 ( ( smult_nat @ A @ ( pCons_nat @ B @ P2 ) )
% 0.18/0.45 = ( pCons_nat @ ( times_times_nat @ A @ B ) @ ( smult_nat @ A @ P2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % smult_pCons
% 0.18/0.45 thf(fact_52_coeffs__eq__Nil,axiom,
% 0.18/0.45 ! [P2: poly_poly_a] :
% 0.18/0.45 ( ( ( coeffs_poly_a @ P2 )
% 0.18/0.45 = nil_poly_a )
% 0.18/0.45 = ( P2 = zero_z2096148049poly_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % coeffs_eq_Nil
% 0.18/0.45 thf(fact_53_coeffs__eq__Nil,axiom,
% 0.18/0.45 ! [P2: poly_a] :
% 0.18/0.45 ( ( ( coeffs_a @ P2 )
% 0.18/0.45 = nil_a )
% 0.18/0.45 = ( P2 = zero_zero_poly_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % coeffs_eq_Nil
% 0.18/0.45 thf(fact_54_coeffs__0__eq__Nil,axiom,
% 0.18/0.45 ( ( coeffs_poly_a @ zero_z2096148049poly_a )
% 0.18/0.45 = nil_poly_a ) ).
% 0.18/0.45
% 0.18/0.45 % coeffs_0_eq_Nil
% 0.18/0.45 thf(fact_55_coeffs__0__eq__Nil,axiom,
% 0.18/0.45 ( ( coeffs_a @ zero_zero_poly_a )
% 0.18/0.45 = nil_a ) ).
% 0.18/0.45
% 0.18/0.45 % coeffs_0_eq_Nil
% 0.18/0.45 thf(fact_56_psums__0__Cons,axiom,
% 0.18/0.45 ! [Xs: list_poly_a] :
% 0.18/0.45 ( ( descar282223555poly_a @ ( cons_poly_a @ zero_zero_poly_a @ Xs ) )
% 0.18/0.45 = ( cons_poly_a @ zero_zero_poly_a @ ( descar282223555poly_a @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % psums_0_Cons
% 0.18/0.45 thf(fact_57_psums__0__Cons,axiom,
% 0.18/0.45 ! [Xs: list_nat] :
% 0.18/0.45 ( ( descar226543321ms_nat @ ( cons_nat @ zero_zero_nat @ Xs ) )
% 0.18/0.45 = ( cons_nat @ zero_zero_nat @ ( descar226543321ms_nat @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % psums_0_Cons
% 0.18/0.45 thf(fact_58_psums__0__Cons,axiom,
% 0.18/0.45 ! [Xs: list_a] :
% 0.18/0.45 ( ( descar1375166517sums_a @ ( cons_a @ zero_zero_a @ Xs ) )
% 0.18/0.45 = ( cons_a @ zero_zero_a @ ( descar1375166517sums_a @ Xs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % psums_0_Cons
% 0.18/0.45 thf(fact_59_coeffs__1__eq,axiom,
% 0.18/0.45 ( ( coeffs_poly_a @ one_one_poly_poly_a )
% 0.18/0.45 = ( cons_poly_a @ one_one_poly_a @ nil_poly_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % coeffs_1_eq
% 0.18/0.45 thf(fact_60_coeffs__1__eq,axiom,
% 0.18/0.45 ( ( coeffs_a @ one_one_poly_a )
% 0.18/0.45 = ( cons_a @ one_one_a @ nil_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % coeffs_1_eq
% 0.18/0.45 thf(fact_61_coeffs__1__eq,axiom,
% 0.18/0.45 ( ( coeffs_nat @ one_one_poly_nat )
% 0.18/0.45 = ( cons_nat @ one_one_nat @ nil_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % coeffs_1_eq
% 0.18/0.45 thf(fact_62_sign__changes__singleton,axiom,
% 0.18/0.45 ! [X: a] :
% 0.18/0.45 ( ( descar2095969287nges_a @ ( cons_a @ X @ nil_a ) )
% 0.18/0.45 = zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % sign_changes_singleton
% 0.18/0.45 thf(fact_63_sign__changes__singleton,axiom,
% 0.18/0.45 ! [X: poly_a] :
% 0.18/0.45 ( ( descar357075861poly_a @ ( cons_poly_a @ X @ nil_poly_a ) )
% 0.18/0.45 = zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % sign_changes_singleton
% 0.18/0.45 thf(fact_64__092_060open_062sign__changes_Axs_A_061_Av_A_I_091_0581_058_058_Ha_M_A_N_A_I1_058_058_Ha_J_058_093_A_K_Ag_J_092_060close_062,axiom,
% 0.18/0.45 ( ( descar2095969287nges_a @ xs )
% 0.18/0.45 = ( v @ ( times_times_poly_a @ ( pCons_a @ one_one_a @ ( pCons_a @ ( uminus_uminus_a @ one_one_a ) @ zero_zero_poly_a ) ) @ g ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % \<open>sign_changes xs = v ([:1::'a, - (1::'a):] * g)\<close>
% 0.18/0.45 thf(fact_65_Poly__snoc__zero,axiom,
% 0.18/0.45 ! [As: list_poly_a] :
% 0.18/0.45 ( ( poly_poly_a2 @ ( append_poly_a @ As @ ( cons_poly_a @ zero_zero_poly_a @ nil_poly_a ) ) )
% 0.18/0.45 = ( poly_poly_a2 @ As ) ) ).
% 0.18/0.45
% 0.18/0.45 % Poly_snoc_zero
% 0.18/0.45 thf(fact_66_Poly__snoc__zero,axiom,
% 0.18/0.45 ! [As: list_a] :
% 0.18/0.45 ( ( poly_a2 @ ( append_a @ As @ ( cons_a @ zero_zero_a @ nil_a ) ) )
% 0.18/0.45 = ( poly_a2 @ As ) ) ).
% 0.18/0.45
% 0.18/0.45 % Poly_snoc_zero
% 0.18/0.45 thf(fact_67_Poly__snoc__zero,axiom,
% 0.18/0.45 ! [As: list_nat] :
% 0.18/0.45 ( ( poly_nat2 @ ( append_nat @ As @ ( cons_nat @ zero_zero_nat @ nil_nat ) ) )
% 0.18/0.45 = ( poly_nat2 @ As ) ) ).
% 0.18/0.45
% 0.18/0.45 % Poly_snoc_zero
% 0.18/0.45 thf(fact_68_Poly_Osimps_I2_J,axiom,
% 0.18/0.45 ! [A: a,As: list_a] :
% 0.18/0.45 ( ( poly_a2 @ ( cons_a @ A @ As ) )
% 0.18/0.45 = ( pCons_a @ A @ ( poly_a2 @ As ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Poly.simps(2)
% 0.18/0.45 thf(fact_69_Poly_Osimps_I1_J,axiom,
% 0.18/0.45 ( ( poly_a2 @ nil_a )
% 0.18/0.45 = zero_zero_poly_a ) ).
% 0.18/0.45
% 0.18/0.45 % Poly.simps(1)
% 0.18/0.45 thf(fact_70_psums_Osimps_I2_J,axiom,
% 0.18/0.45 ! [X: a] :
% 0.18/0.45 ( ( descar1375166517sums_a @ ( cons_a @ X @ nil_a ) )
% 0.18/0.45 = ( cons_a @ X @ nil_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % psums.simps(2)
% 0.18/0.45 thf(fact_71_psums_Osimps_I1_J,axiom,
% 0.18/0.45 ( ( descar1375166517sums_a @ nil_a )
% 0.18/0.45 = nil_a ) ).
% 0.18/0.45
% 0.18/0.45 % psums.simps(1)
% 0.18/0.45 thf(fact_72_pCons__one,axiom,
% 0.18/0.45 ( ( pCons_nat @ one_one_nat @ zero_zero_poly_nat )
% 0.18/0.45 = one_one_poly_nat ) ).
% 0.18/0.45
% 0.18/0.45 % pCons_one
% 0.18/0.45 thf(fact_73_pCons__one,axiom,
% 0.18/0.45 ( ( pCons_a @ one_one_a @ zero_zero_poly_a )
% 0.18/0.45 = one_one_poly_a ) ).
% 0.18/0.45
% 0.18/0.45 % pCons_one
% 0.18/0.45 thf(fact_74_pCons__cases,axiom,
% 0.18/0.45 ! [P2: poly_a] :
% 0.18/0.45 ~ ! [A2: a,Q3: poly_a] :
% 0.18/0.45 ( P2
% 0.18/0.45 != ( pCons_a @ A2 @ Q3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % pCons_cases
% 0.18/0.45 thf(fact_75_is__zero__null,axiom,
% 0.18/0.45 ( is_zero_a
% 0.18/0.45 = ( ^ [P: poly_a] : ( P = zero_zero_poly_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % is_zero_null
% 0.18/0.45 thf(fact_76_pCons__induct,axiom,
% 0.18/0.45 ! [P3: poly_poly_a > $o,P2: poly_poly_a] :
% 0.18/0.45 ( ( P3 @ zero_z2096148049poly_a )
% 0.18/0.45 => ( ! [A2: poly_a,P4: poly_poly_a] :
% 0.18/0.45 ( ( ( A2 != zero_zero_poly_a )
% 0.18/0.45 | ( P4 != zero_z2096148049poly_a ) )
% 0.18/0.45 => ( ( P3 @ P4 )
% 0.18/0.45 => ( P3 @ ( pCons_poly_a @ A2 @ P4 ) ) ) )
% 0.18/0.45 => ( P3 @ P2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pCons_induct
% 0.18/0.45 thf(fact_77_pCons__induct,axiom,
% 0.18/0.45 ! [P3: poly_nat > $o,P2: poly_nat] :
% 0.18/0.45 ( ( P3 @ zero_zero_poly_nat )
% 0.18/0.45 => ( ! [A2: nat,P4: poly_nat] :
% 0.18/0.45 ( ( ( A2 != zero_zero_nat )
% 0.18/0.45 | ( P4 != zero_zero_poly_nat ) )
% 0.18/0.45 => ( ( P3 @ P4 )
% 0.18/0.45 => ( P3 @ ( pCons_nat @ A2 @ P4 ) ) ) )
% 0.18/0.45 => ( P3 @ P2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pCons_induct
% 0.18/0.45 thf(fact_78_pCons__induct,axiom,
% 0.18/0.45 ! [P3: poly_a > $o,P2: poly_a] :
% 0.18/0.45 ( ( P3 @ zero_zero_poly_a )
% 0.18/0.45 => ( ! [A2: a,P4: poly_a] :
% 0.18/0.45 ( ( ( A2 != zero_zero_a )
% 0.18/0.45 | ( P4 != zero_zero_poly_a ) )
% 0.18/0.45 => ( ( P3 @ P4 )
% 0.18/0.45 => ( P3 @ ( pCons_a @ A2 @ P4 ) ) ) )
% 0.18/0.45 => ( P3 @ P2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pCons_induct
% 0.18/0.45 thf(fact_79_pderiv_Ocases,axiom,
% 0.18/0.45 ! [X: poly_a] :
% 0.18/0.45 ~ ! [A2: a,P4: poly_a] :
% 0.18/0.45 ( X
% 0.18/0.45 != ( pCons_a @ A2 @ P4 ) ) ).
% 0.18/0.45
% 0.18/0.45 % pderiv.cases
% 0.18/0.45 thf(fact_80_poly__induct2,axiom,
% 0.18/0.45 ! [P3: poly_a > poly_a > $o,P2: poly_a,Q2: poly_a] :
% 0.18/0.45 ( ( P3 @ zero_zero_poly_a @ zero_zero_poly_a )
% 0.18/0.45 => ( ! [A2: a,P4: poly_a,B2: a,Q3: poly_a] :
% 0.18/0.45 ( ( P3 @ P4 @ Q3 )
% 0.18/0.45 => ( P3 @ ( pCons_a @ A2 @ P4 ) @ ( pCons_a @ B2 @ Q3 ) ) )
% 0.18/0.45 => ( P3 @ P2 @ Q2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % poly_induct2
% 0.18/0.45 thf(fact_81_pderiv_Oinduct,axiom,
% 0.18/0.45 ! [P3: poly_a > $o,A0: poly_a] :
% 0.18/0.45 ( ! [A2: a,P4: poly_a] :
% 0.18/0.45 ( ( ( P4 != zero_zero_poly_a )
% 0.18/0.45 => ( P3 @ P4 ) )
% 0.18/0.45 => ( P3 @ ( pCons_a @ A2 @ P4 ) ) )
% 0.18/0.45 => ( P3 @ A0 ) ) ).
% 0.18/0.45
% 0.18/0.45 % pderiv.induct
% 0.18/0.45 thf(fact_82_mult__poly__0__left,axiom,
% 0.18/0.45 ! [Q2: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ zero_zero_poly_a @ Q2 )
% 0.18/0.45 = zero_zero_poly_a ) ).
% 0.18/0.45
% 0.18/0.45 % mult_poly_0_left
% 0.18/0.45 thf(fact_83_mult__poly__0__right,axiom,
% 0.18/0.45 ! [P2: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ P2 @ zero_zero_poly_a )
% 0.18/0.45 = zero_zero_poly_a ) ).
% 0.18/0.45
% 0.18/0.45 % mult_poly_0_right
% 0.18/0.45 thf(fact_84_plus__coeffs_Oinduct,axiom,
% 0.18/0.45 ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 0.18/0.45 ( ! [Xs2: list_a] : ( P3 @ Xs2 @ nil_a )
% 0.18/0.45 => ( ! [V: a,Va: list_a] : ( P3 @ nil_a @ ( cons_a @ V @ Va ) )
% 0.18/0.45 => ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
% 0.18/0.45 ( ( P3 @ Xs2 @ Ys )
% 0.18/0.45 => ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) )
% 0.18/0.45 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % plus_coeffs.induct
% 0.18/0.45 thf(fact_85_not__0__coeffs__not__Nil,axiom,
% 0.18/0.45 ! [P2: poly_poly_a] :
% 0.18/0.45 ( ( P2 != zero_z2096148049poly_a )
% 0.18/0.45 => ( ( coeffs_poly_a @ P2 )
% 0.18/0.45 != nil_poly_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % not_0_coeffs_not_Nil
% 0.18/0.45 thf(fact_86_not__0__coeffs__not__Nil,axiom,
% 0.18/0.45 ! [P2: poly_a] :
% 0.18/0.45 ( ( P2 != zero_zero_poly_a )
% 0.18/0.45 => ( ( coeffs_a @ P2 )
% 0.18/0.45 != nil_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % not_0_coeffs_not_Nil
% 0.18/0.45 thf(fact_87_minus__poly__rev__list_Oinduct,axiom,
% 0.18/0.45 ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 0.18/0.45 ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
% 0.18/0.45 ( ( P3 @ Xs2 @ Ys )
% 0.18/0.45 => ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) )
% 0.18/0.45 => ( ! [Xs2: list_a] : ( P3 @ Xs2 @ nil_a )
% 0.18/0.45 => ( ! [Y2: a,Ys: list_a] : ( P3 @ nil_a @ ( cons_a @ Y2 @ Ys ) )
% 0.18/0.45 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % minus_poly_rev_list.induct
% 0.18/0.45 thf(fact_88_synthetic__div__unique__lemma,axiom,
% 0.18/0.45 ! [C: a,P2: poly_a,A: a] :
% 0.18/0.45 ( ( ( smult_a @ C @ P2 )
% 0.18/0.45 = ( pCons_a @ A @ P2 ) )
% 0.18/0.45 => ( P2 = zero_zero_poly_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % synthetic_div_unique_lemma
% 0.18/0.45 thf(fact_89_psums_Ocases,axiom,
% 0.18/0.45 ! [X: list_a] :
% 0.18/0.45 ( ( X != nil_a )
% 0.18/0.45 => ( ! [X2: a] :
% 0.18/0.45 ( X
% 0.18/0.45 != ( cons_a @ X2 @ nil_a ) )
% 0.18/0.45 => ~ ! [X2: a,Y2: a,Xs2: list_a] :
% 0.18/0.45 ( X
% 0.18/0.45 != ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % psums.cases
% 0.18/0.45 thf(fact_90_reduce__root__pCons,axiom,
% 0.18/0.45 ! [A: a,C: a,P2: poly_a] :
% 0.18/0.45 ( ( descar466059845root_a @ A @ ( pCons_a @ C @ P2 ) )
% 0.18/0.45 = ( pCons_a @ C @ ( smult_a @ A @ ( descar466059845root_a @ A @ P2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % reduce_root_pCons
% 0.18/0.45 thf(fact_91_reduce__root__pCons,axiom,
% 0.18/0.45 ! [A: poly_a,C: poly_a,P2: poly_poly_a] :
% 0.18/0.45 ( ( descar434775507poly_a @ A @ ( pCons_poly_a @ C @ P2 ) )
% 0.18/0.45 = ( pCons_poly_a @ C @ ( smult_poly_a @ A @ ( descar434775507poly_a @ A @ P2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % reduce_root_pCons
% 0.18/0.45 thf(fact_92_reduce__root__nonzero,axiom,
% 0.18/0.45 ! [A: a,P2: poly_a] :
% 0.18/0.45 ( ( A != zero_zero_a )
% 0.18/0.45 => ( ( P2 != zero_zero_poly_a )
% 0.18/0.45 => ( ( descar466059845root_a @ A @ P2 )
% 0.18/0.45 != zero_zero_poly_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % reduce_root_nonzero
% 0.18/0.45 thf(fact_93_reduce__root__nonzero,axiom,
% 0.18/0.45 ! [A: poly_a,P2: poly_poly_a] :
% 0.18/0.45 ( ( A != zero_zero_poly_a )
% 0.18/0.45 => ( ( P2 != zero_z2096148049poly_a )
% 0.18/0.45 => ( ( descar434775507poly_a @ A @ P2 )
% 0.18/0.45 != zero_z2096148049poly_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % reduce_root_nonzero
% 0.18/0.45 thf(fact_94_sign__changes__Cons__Cons__same,axiom,
% 0.18/0.45 ! [X: a,Y3: a,Xs: list_a] :
% 0.18/0.45 ( ( ord_less_a @ zero_zero_a @ ( times_times_a @ X @ Y3 ) )
% 0.18/0.45 => ( ( descar2095969287nges_a @ ( cons_a @ X @ ( cons_a @ Y3 @ Xs ) ) )
% 0.18/0.45 = ( descar2095969287nges_a @ ( cons_a @ Y3 @ Xs ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sign_changes_Cons_Cons_same
% 0.18/0.45 thf(fact_95_sign__changes__Cons__Cons__same,axiom,
% 0.18/0.45 ! [X: poly_a,Y3: poly_a,Xs: list_poly_a] :
% 0.18/0.45 ( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ X @ Y3 ) )
% 0.18/0.45 => ( ( descar357075861poly_a @ ( cons_poly_a @ X @ ( cons_poly_a @ Y3 @ Xs ) ) )
% 0.18/0.45 = ( descar357075861poly_a @ ( cons_poly_a @ Y3 @ Xs ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sign_changes_Cons_Cons_same
% 0.18/0.45 thf(fact_96_append1__eq__conv,axiom,
% 0.18/0.45 ! [Xs: list_a,X: a,Ys2: list_a,Y3: a] :
% 0.18/0.45 ( ( ( append_a @ Xs @ ( cons_a @ X @ nil_a ) )
% 0.18/0.45 = ( append_a @ Ys2 @ ( cons_a @ Y3 @ nil_a ) ) )
% 0.18/0.45 = ( ( Xs = Ys2 )
% 0.18/0.45 & ( X = Y3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append1_eq_conv
% 0.18/0.45 thf(fact_97_mult__minus1,axiom,
% 0.18/0.45 ! [Z2: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ ( uminus_uminus_poly_a @ one_one_poly_a ) @ Z2 )
% 0.18/0.45 = ( uminus_uminus_poly_a @ Z2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_minus1
% 0.18/0.45 thf(fact_98_mult__minus1,axiom,
% 0.18/0.45 ! [Z2: a] :
% 0.18/0.45 ( ( times_times_a @ ( uminus_uminus_a @ one_one_a ) @ Z2 )
% 0.18/0.45 = ( uminus_uminus_a @ Z2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_minus1
% 0.18/0.45 thf(fact_99_mult__minus1__right,axiom,
% 0.18/0.45 ! [Z2: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ Z2 @ ( uminus_uminus_poly_a @ one_one_poly_a ) )
% 0.18/0.45 = ( uminus_uminus_poly_a @ Z2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_minus1_right
% 0.18/0.45 thf(fact_100_mult__minus1__right,axiom,
% 0.18/0.45 ! [Z2: a] :
% 0.18/0.45 ( ( times_times_a @ Z2 @ ( uminus_uminus_a @ one_one_a ) )
% 0.18/0.45 = ( uminus_uminus_a @ Z2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_minus1_right
% 0.18/0.45 thf(fact_101_less__neg__neg,axiom,
% 0.18/0.45 ! [A: poly_a] :
% 0.18/0.45 ( ( ord_less_poly_a @ A @ ( uminus_uminus_poly_a @ A ) )
% 0.18/0.45 = ( ord_less_poly_a @ A @ zero_zero_poly_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_neg_neg
% 0.18/0.45 thf(fact_102_less__neg__neg,axiom,
% 0.18/0.45 ! [A: a] :
% 0.18/0.45 ( ( ord_less_a @ A @ ( uminus_uminus_a @ A ) )
% 0.18/0.45 = ( ord_less_a @ A @ zero_zero_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_neg_neg
% 0.18/0.45 thf(fact_103_neg__less__pos,axiom,
% 0.18/0.45 ! [A: poly_a] :
% 0.18/0.45 ( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ A )
% 0.18/0.45 = ( ord_less_poly_a @ zero_zero_poly_a @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_less_pos
% 0.18/0.45 thf(fact_104_neg__less__pos,axiom,
% 0.18/0.45 ! [A: a] :
% 0.18/0.45 ( ( ord_less_a @ ( uminus_uminus_a @ A ) @ A )
% 0.18/0.45 = ( ord_less_a @ zero_zero_a @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_less_pos
% 0.18/0.45 thf(fact_105_neg__0__less__iff__less,axiom,
% 0.18/0.45 ! [A: poly_a] :
% 0.18/0.45 ( ( ord_less_poly_a @ zero_zero_poly_a @ ( uminus_uminus_poly_a @ A ) )
% 0.18/0.45 = ( ord_less_poly_a @ A @ zero_zero_poly_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_0_less_iff_less
% 0.18/0.45 thf(fact_106_neg__0__less__iff__less,axiom,
% 0.18/0.45 ! [A: a] :
% 0.18/0.45 ( ( ord_less_a @ zero_zero_a @ ( uminus_uminus_a @ A ) )
% 0.18/0.45 = ( ord_less_a @ A @ zero_zero_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_0_less_iff_less
% 0.18/0.45 thf(fact_107_neg__less__0__iff__less,axiom,
% 0.18/0.45 ! [A: poly_a] :
% 0.18/0.45 ( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ zero_zero_poly_a )
% 0.18/0.45 = ( ord_less_poly_a @ zero_zero_poly_a @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_less_0_iff_less
% 0.18/0.45 thf(fact_108_neg__less__0__iff__less,axiom,
% 0.18/0.45 ! [A: a] :
% 0.18/0.45 ( ( ord_less_a @ ( uminus_uminus_a @ A ) @ zero_zero_a )
% 0.18/0.45 = ( ord_less_a @ zero_zero_a @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_less_0_iff_less
% 0.18/0.45 thf(fact_109_mult__cancel__left1,axiom,
% 0.18/0.45 ! [C: a,B: a] :
% 0.18/0.45 ( ( C
% 0.18/0.45 = ( times_times_a @ C @ B ) )
% 0.18/0.45 = ( ( C = zero_zero_a )
% 0.18/0.45 | ( B = one_one_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_cancel_left1
% 0.18/0.45 thf(fact_110_mult__cancel__left1,axiom,
% 0.18/0.45 ! [C: poly_a,B: poly_a] :
% 0.18/0.45 ( ( C
% 0.18/0.45 = ( times_times_poly_a @ C @ B ) )
% 0.18/0.45 = ( ( C = zero_zero_poly_a )
% 0.18/0.45 | ( B = one_one_poly_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_cancel_left1
% 0.18/0.45 thf(fact_111_mult__cancel__left2,axiom,
% 0.18/0.45 ! [C: a,A: a] :
% 0.18/0.45 ( ( ( times_times_a @ C @ A )
% 0.18/0.45 = C )
% 0.18/0.45 = ( ( C = zero_zero_a )
% 0.18/0.45 | ( A = one_one_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_cancel_left2
% 0.18/0.45 thf(fact_112_mult__cancel__left2,axiom,
% 0.18/0.45 ! [C: poly_a,A: poly_a] :
% 0.18/0.45 ( ( ( times_times_poly_a @ C @ A )
% 0.18/0.45 = C )
% 0.18/0.45 = ( ( C = zero_zero_poly_a )
% 0.18/0.45 | ( A = one_one_poly_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_cancel_left2
% 0.18/0.45 thf(fact_113_mult__cancel__right1,axiom,
% 0.18/0.45 ! [C: a,B: a] :
% 0.18/0.45 ( ( C
% 0.18/0.45 = ( times_times_a @ B @ C ) )
% 0.18/0.45 = ( ( C = zero_zero_a )
% 0.18/0.45 | ( B = one_one_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_cancel_right1
% 0.18/0.45 thf(fact_114_mult__cancel__right1,axiom,
% 0.18/0.45 ! [C: poly_a,B: poly_a] :
% 0.18/0.45 ( ( C
% 0.18/0.45 = ( times_times_poly_a @ B @ C ) )
% 0.18/0.45 = ( ( C = zero_zero_poly_a )
% 0.18/0.45 | ( B = one_one_poly_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_cancel_right1
% 0.18/0.45 thf(fact_115_mult__cancel__right2,axiom,
% 0.18/0.45 ! [A: a,C: a] :
% 0.18/0.45 ( ( ( times_times_a @ A @ C )
% 0.18/0.45 = C )
% 0.18/0.45 = ( ( C = zero_zero_a )
% 0.18/0.45 | ( A = one_one_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_cancel_right2
% 0.18/0.45 thf(fact_116_mult__cancel__right2,axiom,
% 0.18/0.45 ! [A: poly_a,C: poly_a] :
% 0.18/0.45 ( ( ( times_times_poly_a @ A @ C )
% 0.18/0.45 = C )
% 0.18/0.45 = ( ( C = zero_zero_poly_a )
% 0.18/0.45 | ( A = one_one_poly_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_cancel_right2
% 0.18/0.45 thf(fact_117_neg__equal__iff__equal,axiom,
% 0.18/0.45 ! [A: a,B: a] :
% 0.18/0.45 ( ( ( uminus_uminus_a @ A )
% 0.18/0.45 = ( uminus_uminus_a @ B ) )
% 0.18/0.45 = ( A = B ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_equal_iff_equal
% 0.18/0.45 thf(fact_118_add_Oinverse__inverse,axiom,
% 0.18/0.45 ! [A: a] :
% 0.18/0.45 ( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % add.inverse_inverse
% 0.18/0.45 thf(fact_119_list_Oinject,axiom,
% 0.18/0.45 ! [X21: a,X22: list_a,Y21: a,Y22: list_a] :
% 0.18/0.45 ( ( ( cons_a @ X21 @ X22 )
% 0.18/0.45 = ( cons_a @ Y21 @ Y22 ) )
% 0.18/0.45 = ( ( X21 = Y21 )
% 0.18/0.45 & ( X22 = Y22 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list.inject
% 0.18/0.45 thf(fact_120_same__append__eq,axiom,
% 0.18/0.45 ! [Xs: list_a,Ys2: list_a,Zs: list_a] :
% 0.18/0.45 ( ( ( append_a @ Xs @ Ys2 )
% 0.18/0.45 = ( append_a @ Xs @ Zs ) )
% 0.18/0.45 = ( Ys2 = Zs ) ) ).
% 0.18/0.45
% 0.18/0.45 % same_append_eq
% 0.18/0.45 thf(fact_121_append__same__eq,axiom,
% 0.18/0.45 ! [Ys2: list_a,Xs: list_a,Zs: list_a] :
% 0.18/0.45 ( ( ( append_a @ Ys2 @ Xs )
% 0.18/0.45 = ( append_a @ Zs @ Xs ) )
% 0.18/0.45 = ( Ys2 = Zs ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_same_eq
% 0.18/0.45 thf(fact_122_append__assoc,axiom,
% 0.18/0.45 ! [Xs: list_a,Ys2: list_a,Zs: list_a] :
% 0.18/0.45 ( ( append_a @ ( append_a @ Xs @ Ys2 ) @ Zs )
% 0.18/0.45 = ( append_a @ Xs @ ( append_a @ Ys2 @ Zs ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_assoc
% 0.18/0.45 thf(fact_123_append_Oassoc,axiom,
% 0.18/0.45 ! [A: list_a,B: list_a,C: list_a] :
% 0.18/0.45 ( ( append_a @ ( append_a @ A @ B ) @ C )
% 0.18/0.45 = ( append_a @ A @ ( append_a @ B @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append.assoc
% 0.18/0.45 thf(fact_124_not__gr__zero,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.18/0.45 = ( N = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % not_gr_zero
% 0.18/0.45 thf(fact_125_mult__cancel__right,axiom,
% 0.18/0.45 ! [A: a,C: a,B: a] :
% 0.18/0.45 ( ( ( times_times_a @ A @ C )
% 0.18/0.45 = ( times_times_a @ B @ C ) )
% 0.18/0.45 = ( ( C = zero_zero_a )
% 0.18/0.45 | ( A = B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_cancel_right
% 0.18/0.45 thf(fact_126_mult__cancel__right,axiom,
% 0.18/0.45 ! [A: poly_a,C: poly_a,B: poly_a] :
% 0.18/0.45 ( ( ( times_times_poly_a @ A @ C )
% 0.18/0.45 = ( times_times_poly_a @ B @ C ) )
% 0.18/0.45 = ( ( C = zero_zero_poly_a )
% 0.18/0.45 | ( A = B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_cancel_right
% 0.18/0.45 thf(fact_127_mult__cancel__right,axiom,
% 0.18/0.45 ! [A: nat,C: nat,B: nat] :
% 0.18/0.45 ( ( ( times_times_nat @ A @ C )
% 0.18/0.45 = ( times_times_nat @ B @ C ) )
% 0.18/0.45 = ( ( C = zero_zero_nat )
% 0.18/0.45 | ( A = B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_cancel_right
% 0.18/0.45 thf(fact_128_mult__cancel__left,axiom,
% 0.18/0.45 ! [C: a,A: a,B: a] :
% 0.18/0.45 ( ( ( times_times_a @ C @ A )
% 0.18/0.45 = ( times_times_a @ C @ B ) )
% 0.18/0.45 = ( ( C = zero_zero_a )
% 0.18/0.45 | ( A = B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_cancel_left
% 0.18/0.45 thf(fact_129_mult__cancel__left,axiom,
% 0.18/0.45 ! [C: poly_a,A: poly_a,B: poly_a] :
% 0.18/0.45 ( ( ( times_times_poly_a @ C @ A )
% 0.18/0.45 = ( times_times_poly_a @ C @ B ) )
% 0.18/0.45 = ( ( C = zero_zero_poly_a )
% 0.18/0.45 | ( A = B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_cancel_left
% 0.18/0.45 thf(fact_130_mult__cancel__left,axiom,
% 0.18/0.45 ! [C: nat,A: nat,B: nat] :
% 0.18/0.45 ( ( ( times_times_nat @ C @ A )
% 0.18/0.45 = ( times_times_nat @ C @ B ) )
% 0.18/0.45 = ( ( C = zero_zero_nat )
% 0.18/0.45 | ( A = B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_cancel_left
% 0.18/0.45 thf(fact_131_mult__eq__0__iff,axiom,
% 0.18/0.45 ! [A: a,B: a] :
% 0.18/0.45 ( ( ( times_times_a @ A @ B )
% 0.18/0.45 = zero_zero_a )
% 0.18/0.45 = ( ( A = zero_zero_a )
% 0.18/0.45 | ( B = zero_zero_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_eq_0_iff
% 0.18/0.45 thf(fact_132_mult__eq__0__iff,axiom,
% 0.18/0.45 ! [A: poly_a,B: poly_a] :
% 0.18/0.45 ( ( ( times_times_poly_a @ A @ B )
% 0.18/0.45 = zero_zero_poly_a )
% 0.18/0.45 = ( ( A = zero_zero_poly_a )
% 0.18/0.45 | ( B = zero_zero_poly_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_eq_0_iff
% 0.18/0.45 thf(fact_133_mult__eq__0__iff,axiom,
% 0.18/0.45 ! [A: nat,B: nat] :
% 0.18/0.45 ( ( ( times_times_nat @ A @ B )
% 0.18/0.45 = zero_zero_nat )
% 0.18/0.45 = ( ( A = zero_zero_nat )
% 0.18/0.45 | ( B = zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_eq_0_iff
% 0.18/0.45 thf(fact_134_mult__zero__right,axiom,
% 0.18/0.45 ! [A: a] :
% 0.18/0.45 ( ( times_times_a @ A @ zero_zero_a )
% 0.18/0.45 = zero_zero_a ) ).
% 0.18/0.45
% 0.18/0.45 % mult_zero_right
% 0.18/0.45 thf(fact_135_mult__zero__right,axiom,
% 0.18/0.45 ! [A: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ A @ zero_zero_poly_a )
% 0.18/0.45 = zero_zero_poly_a ) ).
% 0.18/0.45
% 0.18/0.45 % mult_zero_right
% 0.18/0.45 thf(fact_136_mult__zero__right,axiom,
% 0.18/0.45 ! [A: nat] :
% 0.18/0.45 ( ( times_times_nat @ A @ zero_zero_nat )
% 0.18/0.45 = zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % mult_zero_right
% 0.18/0.45 thf(fact_137_mult__zero__left,axiom,
% 0.18/0.45 ! [A: a] :
% 0.18/0.45 ( ( times_times_a @ zero_zero_a @ A )
% 0.18/0.45 = zero_zero_a ) ).
% 0.18/0.45
% 0.18/0.45 % mult_zero_left
% 0.18/0.45 thf(fact_138_mult__zero__left,axiom,
% 0.18/0.45 ! [A: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ zero_zero_poly_a @ A )
% 0.18/0.45 = zero_zero_poly_a ) ).
% 0.18/0.45
% 0.18/0.45 % mult_zero_left
% 0.18/0.45 thf(fact_139_mult__zero__left,axiom,
% 0.18/0.45 ! [A: nat] :
% 0.18/0.45 ( ( times_times_nat @ zero_zero_nat @ A )
% 0.18/0.45 = zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % mult_zero_left
% 0.18/0.45 thf(fact_140_neg__equal__zero,axiom,
% 0.18/0.45 ! [A: poly_a] :
% 0.18/0.45 ( ( ( uminus_uminus_poly_a @ A )
% 0.18/0.45 = A )
% 0.18/0.45 = ( A = zero_zero_poly_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_equal_zero
% 0.18/0.45 thf(fact_141_neg__equal__zero,axiom,
% 0.18/0.45 ! [A: a] :
% 0.18/0.45 ( ( ( uminus_uminus_a @ A )
% 0.18/0.45 = A )
% 0.18/0.45 = ( A = zero_zero_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_equal_zero
% 0.18/0.45 thf(fact_142_equal__neg__zero,axiom,
% 0.18/0.45 ! [A: poly_a] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( uminus_uminus_poly_a @ A ) )
% 0.18/0.45 = ( A = zero_zero_poly_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % equal_neg_zero
% 0.18/0.45 thf(fact_143_equal__neg__zero,axiom,
% 0.18/0.45 ! [A: a] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( uminus_uminus_a @ A ) )
% 0.18/0.45 = ( A = zero_zero_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % equal_neg_zero
% 0.18/0.45 thf(fact_144_neg__equal__0__iff__equal,axiom,
% 0.18/0.45 ! [A: poly_a] :
% 0.18/0.45 ( ( ( uminus_uminus_poly_a @ A )
% 0.18/0.45 = zero_zero_poly_a )
% 0.18/0.45 = ( A = zero_zero_poly_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_equal_0_iff_equal
% 0.18/0.45 thf(fact_145_neg__equal__0__iff__equal,axiom,
% 0.18/0.45 ! [A: a] :
% 0.18/0.45 ( ( ( uminus_uminus_a @ A )
% 0.18/0.45 = zero_zero_a )
% 0.18/0.45 = ( A = zero_zero_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_equal_0_iff_equal
% 0.18/0.45 thf(fact_146_neg__0__equal__iff__equal,axiom,
% 0.18/0.45 ! [A: poly_a] :
% 0.18/0.45 ( ( zero_zero_poly_a
% 0.18/0.45 = ( uminus_uminus_poly_a @ A ) )
% 0.18/0.45 = ( zero_zero_poly_a = A ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_0_equal_iff_equal
% 0.18/0.45 thf(fact_147_neg__0__equal__iff__equal,axiom,
% 0.18/0.45 ! [A: a] :
% 0.18/0.45 ( ( zero_zero_a
% 0.18/0.45 = ( uminus_uminus_a @ A ) )
% 0.18/0.45 = ( zero_zero_a = A ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_0_equal_iff_equal
% 0.18/0.45 thf(fact_148_add_Oinverse__neutral,axiom,
% 0.18/0.45 ( ( uminus_uminus_poly_a @ zero_zero_poly_a )
% 0.18/0.45 = zero_zero_poly_a ) ).
% 0.18/0.45
% 0.18/0.45 % add.inverse_neutral
% 0.18/0.45 thf(fact_149_add_Oinverse__neutral,axiom,
% 0.18/0.45 ( ( uminus_uminus_a @ zero_zero_a )
% 0.18/0.45 = zero_zero_a ) ).
% 0.18/0.45
% 0.18/0.45 % add.inverse_neutral
% 0.18/0.45 thf(fact_150_mult_Oright__neutral,axiom,
% 0.18/0.45 ! [A: a] :
% 0.18/0.45 ( ( times_times_a @ A @ one_one_a )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % mult.right_neutral
% 0.18/0.45 thf(fact_151_mult_Oright__neutral,axiom,
% 0.18/0.45 ! [A: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ A @ one_one_poly_a )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % mult.right_neutral
% 0.18/0.45 thf(fact_152_mult_Oright__neutral,axiom,
% 0.18/0.45 ! [A: nat] :
% 0.18/0.45 ( ( times_times_nat @ A @ one_one_nat )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % mult.right_neutral
% 0.18/0.45 thf(fact_153_mult_Oleft__neutral,axiom,
% 0.18/0.45 ! [A: a] :
% 0.18/0.45 ( ( times_times_a @ one_one_a @ A )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % mult.left_neutral
% 0.18/0.45 thf(fact_154_mult_Oleft__neutral,axiom,
% 0.18/0.45 ! [A: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ one_one_poly_a @ A )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % mult.left_neutral
% 0.18/0.45 thf(fact_155_mult_Oleft__neutral,axiom,
% 0.18/0.45 ! [A: nat] :
% 0.18/0.45 ( ( times_times_nat @ one_one_nat @ A )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % mult.left_neutral
% 0.18/0.45 thf(fact_156_neg__less__iff__less,axiom,
% 0.18/0.45 ! [B: poly_a,A: poly_a] :
% 0.18/0.45 ( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ B ) @ ( uminus_uminus_poly_a @ A ) )
% 0.18/0.45 = ( ord_less_poly_a @ A @ B ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_less_iff_less
% 0.18/0.45 thf(fact_157_neg__less__iff__less,axiom,
% 0.18/0.45 ! [B: a,A: a] :
% 0.18/0.45 ( ( ord_less_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) )
% 0.18/0.45 = ( ord_less_a @ A @ B ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_less_iff_less
% 0.18/0.45 thf(fact_158_mult__minus__right,axiom,
% 0.18/0.45 ! [A: poly_a,B: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ A @ ( uminus_uminus_poly_a @ B ) )
% 0.18/0.45 = ( uminus_uminus_poly_a @ ( times_times_poly_a @ A @ B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_minus_right
% 0.18/0.45 thf(fact_159_mult__minus__right,axiom,
% 0.18/0.45 ! [A: a,B: a] :
% 0.18/0.45 ( ( times_times_a @ A @ ( uminus_uminus_a @ B ) )
% 0.18/0.45 = ( uminus_uminus_a @ ( times_times_a @ A @ B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_minus_right
% 0.18/0.45 thf(fact_160_minus__mult__minus,axiom,
% 0.18/0.45 ! [A: poly_a,B: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ ( uminus_uminus_poly_a @ A ) @ ( uminus_uminus_poly_a @ B ) )
% 0.18/0.45 = ( times_times_poly_a @ A @ B ) ) ).
% 0.18/0.45
% 0.18/0.45 % minus_mult_minus
% 0.18/0.45 thf(fact_161_minus__mult__minus,axiom,
% 0.18/0.45 ! [A: a,B: a] :
% 0.18/0.45 ( ( times_times_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_a @ B ) )
% 0.18/0.45 = ( times_times_a @ A @ B ) ) ).
% 0.18/0.45
% 0.18/0.45 % minus_mult_minus
% 0.18/0.45 thf(fact_162_mult__minus__left,axiom,
% 0.18/0.45 ! [A: poly_a,B: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ ( uminus_uminus_poly_a @ A ) @ B )
% 0.18/0.45 = ( uminus_uminus_poly_a @ ( times_times_poly_a @ A @ B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_minus_left
% 0.18/0.45 thf(fact_163_mult__minus__left,axiom,
% 0.18/0.45 ! [A: a,B: a] :
% 0.18/0.45 ( ( times_times_a @ ( uminus_uminus_a @ A ) @ B )
% 0.18/0.45 = ( uminus_uminus_a @ ( times_times_a @ A @ B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_minus_left
% 0.18/0.45 thf(fact_164_append_Oright__neutral,axiom,
% 0.18/0.45 ! [A: list_a] :
% 0.18/0.45 ( ( append_a @ A @ nil_a )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % append.right_neutral
% 0.18/0.45 thf(fact_165_append__is__Nil__conv,axiom,
% 0.18/0.45 ! [Xs: list_a,Ys2: list_a] :
% 0.18/0.45 ( ( ( append_a @ Xs @ Ys2 )
% 0.18/0.45 = nil_a )
% 0.18/0.45 = ( ( Xs = nil_a )
% 0.18/0.45 & ( Ys2 = nil_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_is_Nil_conv
% 0.18/0.45 thf(fact_166_Nil__is__append__conv,axiom,
% 0.18/0.45 ! [Xs: list_a,Ys2: list_a] :
% 0.18/0.45 ( ( nil_a
% 0.18/0.45 = ( append_a @ Xs @ Ys2 ) )
% 0.18/0.45 = ( ( Xs = nil_a )
% 0.18/0.45 & ( Ys2 = nil_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Nil_is_append_conv
% 0.18/0.45 thf(fact_167_self__append__conv2,axiom,
% 0.18/0.45 ! [Ys2: list_a,Xs: list_a] :
% 0.18/0.45 ( ( Ys2
% 0.18/0.45 = ( append_a @ Xs @ Ys2 ) )
% 0.18/0.45 = ( Xs = nil_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % self_append_conv2
% 0.18/0.45 thf(fact_168_append__self__conv2,axiom,
% 0.18/0.45 ! [Xs: list_a,Ys2: list_a] :
% 0.18/0.45 ( ( ( append_a @ Xs @ Ys2 )
% 0.18/0.45 = Ys2 )
% 0.18/0.45 = ( Xs = nil_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_self_conv2
% 0.18/0.45 thf(fact_169_self__append__conv,axiom,
% 0.18/0.45 ! [Xs: list_a,Ys2: list_a] :
% 0.18/0.45 ( ( Xs
% 0.18/0.45 = ( append_a @ Xs @ Ys2 ) )
% 0.18/0.45 = ( Ys2 = nil_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % self_append_conv
% 0.18/0.45 thf(fact_170_append__self__conv,axiom,
% 0.18/0.45 ! [Xs: list_a,Ys2: list_a] :
% 0.18/0.45 ( ( ( append_a @ Xs @ Ys2 )
% 0.18/0.45 = Xs )
% 0.18/0.45 = ( Ys2 = nil_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_self_conv
% 0.18/0.45 thf(fact_171_append__Nil2,axiom,
% 0.18/0.45 ! [Xs: list_a] :
% 0.18/0.45 ( ( append_a @ Xs @ nil_a )
% 0.18/0.45 = Xs ) ).
% 0.18/0.45
% 0.18/0.45 % append_Nil2
% 0.18/0.45 thf(fact_172_smult__one,axiom,
% 0.18/0.45 ! [C: a] :
% 0.18/0.45 ( ( smult_a @ C @ one_one_poly_a )
% 0.18/0.45 = ( pCons_a @ C @ zero_zero_poly_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % smult_one
% 0.18/0.45 thf(fact_173_zero__reorient,axiom,
% 0.18/0.45 ! [X: poly_a] :
% 0.18/0.45 ( ( zero_zero_poly_a = X )
% 0.18/0.45 = ( X = zero_zero_poly_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_reorient
% 0.18/0.45 thf(fact_174_zero__reorient,axiom,
% 0.18/0.45 ! [X: a] :
% 0.18/0.45 ( ( zero_zero_a = X )
% 0.18/0.45 = ( X = zero_zero_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_reorient
% 0.18/0.45 thf(fact_175_zero__reorient,axiom,
% 0.18/0.45 ! [X: nat] :
% 0.18/0.45 ( ( zero_zero_nat = X )
% 0.18/0.45 = ( X = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_reorient
% 0.18/0.45 thf(fact_176_linorder__neqE__linordered__idom,axiom,
% 0.18/0.45 ! [X: a,Y3: a] :
% 0.18/0.45 ( ( X != Y3 )
% 0.18/0.45 => ( ~ ( ord_less_a @ X @ Y3 )
% 0.18/0.45 => ( ord_less_a @ Y3 @ X ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % linorder_neqE_linordered_idom
% 0.18/0.45 thf(fact_177_linorder__neqE__linordered__idom,axiom,
% 0.18/0.45 ! [X: poly_a,Y3: poly_a] :
% 0.18/0.45 ( ( X != Y3 )
% 0.18/0.45 => ( ~ ( ord_less_poly_a @ X @ Y3 )
% 0.18/0.45 => ( ord_less_poly_a @ Y3 @ X ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % linorder_neqE_linordered_idom
% 0.18/0.45 thf(fact_178_mult_Oleft__commute,axiom,
% 0.18/0.45 ! [B: poly_a,A: poly_a,C: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ B @ ( times_times_poly_a @ A @ C ) )
% 0.18/0.45 = ( times_times_poly_a @ A @ ( times_times_poly_a @ B @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult.left_commute
% 0.18/0.45 thf(fact_179_mult_Oleft__commute,axiom,
% 0.18/0.45 ! [B: nat,A: nat,C: nat] :
% 0.18/0.45 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 0.18/0.45 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult.left_commute
% 0.18/0.45 thf(fact_180_mult_Ocommute,axiom,
% 0.18/0.45 ( times_times_poly_a
% 0.18/0.45 = ( ^ [A3: poly_a,B3: poly_a] : ( times_times_poly_a @ B3 @ A3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult.commute
% 0.18/0.45 thf(fact_181_mult_Ocommute,axiom,
% 0.18/0.45 ( times_times_nat
% 0.18/0.45 = ( ^ [A3: nat,B3: nat] : ( times_times_nat @ B3 @ A3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult.commute
% 0.18/0.45 thf(fact_182_mult_Oassoc,axiom,
% 0.18/0.45 ! [A: poly_a,B: poly_a,C: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ ( times_times_poly_a @ A @ B ) @ C )
% 0.18/0.45 = ( times_times_poly_a @ A @ ( times_times_poly_a @ B @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult.assoc
% 0.18/0.45 thf(fact_183_mult_Oassoc,axiom,
% 0.18/0.45 ! [A: nat,B: nat,C: nat] :
% 0.18/0.45 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.18/0.45 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult.assoc
% 0.18/0.45 thf(fact_184_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.18/0.45 ! [A: poly_a,B: poly_a,C: poly_a] :
% 0.18/0.45 ( ( times_times_poly_a @ ( times_times_poly_a @ A @ B ) @ C )
% 0.18/0.45 = ( times_times_poly_a @ A @ ( times_times_poly_a @ B @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ab_semigroup_mult_class.mult_ac(1)
% 0.18/0.45 thf(fact_185_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.18/0.45 ! [A: nat,B: nat,C: nat] :
% 0.18/0.45 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.18/0.45 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ab_semigroup_mult_class.mult_ac(1)
% 0.18/0.45 thf(fact_186_one__reorient,axiom,
% 0.18/0.45 ! [X: a] :
% 0.18/0.45 ( ( one_one_a = X )
% 0.18/0.45 = ( X = one_one_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % one_reorient
% 0.18/0.45 thf(fact_187_one__reorient,axiom,
% 0.18/0.45 ! [X: nat] :
% 0.18/0.45 ( ( one_one_nat = X )
% 0.18/0.45 = ( X = one_one_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % one_reorient
% 0.18/0.45 thf(fact_188_minus__equation__iff,axiom,
% 0.18/0.45 ! [A: a,B: a] :
% 0.18/0.45 ( ( ( uminus_uminus_a @ A )
% 0.18/0.45 = B )
% 0.18/0.45 = ( ( uminus_uminus_a @ B )
% 0.18/0.45 = A ) ) ).
% 0.18/0.45
% 0.18/0.45 % minus_equation_iff
% 0.18/0.45 thf(fact_189_equation__minus__iff,axiom,
% 0.18/0.45 ! [A: a,B: a] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( uminus_uminus_a @ B ) )
% 0.18/0.45 = ( B
% 0.18/0.45 = ( uminus_uminus_a @ A ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % equation_minus_iff
% 0.18/0.45 thf(fact_190_not__Cons__self2,axiom,
% 0.18/0.45 ! [X: a,Xs: list_a] :
% 0.18/0.45 ( ( cons_a @ X @ Xs )
% 0.18/0.45 != Xs ) ).
% 0.18/0.45
% 0.18/0.45 % not_Cons_self2
% 0.18/0.45 thf(fact_191_append__eq__append__conv2,axiom,
% 0.18/0.45 ! [Xs: list_a,Ys2: list_a,Zs: list_a,Ts: list_a] :
% 0.18/0.45 ( ( ( append_a @ Xs @ Ys2 )
% 0.18/0.45 = ( append_a @ Zs @ Ts ) )
% 0.18/0.45 = ( ? [Us: list_a] :
% 0.18/0.45 ( ( ( Xs
% 0.18/0.45 = ( append_a @ Zs @ Us ) )
% 0.18/0.45 & ( ( append_a @ Us @ Ys2 )
% 0.18/0.45 = Ts ) )
% 0.18/0.45 | ( ( ( append_a @ Xs @ Us )
% 0.18/0.45 = Zs )
% 0.18/0.45 & ( Ys2
% 0.18/0.45 = ( append_a @ Us @ Ts ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_eq_append_conv2
% 0.18/0.45 thf(fact_192_append__eq__appendI,axiom,
% 0.18/0.45 ! [Xs: list_a,Xs1: list_a,Zs: list_a,Ys2: list_a,Us2: list_a] :
% 0.18/0.45 ( ( ( append_a @ Xs @ Xs1 )
% 0.18/0.45 = Zs )
% 0.18/0.45 => ( ( Ys2
% 0.18/0.45 = ( append_a @ Xs1 @ Us2 ) )
% 0.18/0.45 => ( ( append_a @ Xs @ Ys2 )
% 0.18/0.45 = ( append_a @ Zs @ Us2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % append_eq_appendI
% 0.18/0.45 thf(fact_193_sign__changes__two,axiom,
% 0.18/0.45 ! [X: a,Y3: a] :
% 0.18/0.45 ( ( ( ( ( ord_less_a @ zero_zero_a @ X )
% 0.18/0.45 & ( ord_less_a @ Y3 @ zero_zero_a ) )
% 0.18/0.45 | ( ( ord_less_a @ X @ zero_zero_a )
% 0.18/0.45 & ( ord_less_a @ zero_zero_a @ Y3 ) ) )
% 0.18/0.45 => ( ( descar2095969287nges_a @ ( cons_a @ X @ ( cons_a @ Y3 @ nil_a ) ) )
% 0.18/0.45 = one_one_nat ) )
% 0.18/0.45 & ( ~ ( ( ( ord_less_a @ zero_zero_a @ X )
% 0.18/0.45 & ( ord_less_a @ Y3 @ zero_zero_a ) )
% 0.18/0.45 | ( ( ord_less_a @ X @ zero_zero_a )
% 0.18/0.45 & ( ord_less_a @ zero_zero_a @ Y3 ) ) )
% 0.18/0.45 => ( ( descar2095969287nges_a @ ( cons_a @ X @ ( cons_a @ Y3 @ nil_a ) ) )
% 0.18/0.45 = zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sign_changes_two
% 0.18/0.45 thf(fact_194_sign__changes__two,axiom,
% 0.18/0.45 ! [X: poly_a,Y3: poly_a] :
% 0.18/0.45 ( ( ( ( ( ord_less_poly_a @ zero_zero_poly_a @ X )
% 0.18/0.45 & ( ord_less_poly_a @ Y3 @ zero_zero_poly_a ) )
% 0.18/0.45 | ( ( ord_less_poly_a @ X @ zero_zero_poly_a )
% 0.18/0.45 & ( ord_less_poly_a @ zero_zero_poly_a @ Y3 ) ) )
% 0.18/0.45 => ( ( descar357075861poly_a @ ( cons_poly_a @ X @ ( cons_poly_a @ Y3 @ nil_poly_a ) ) )
% 0.18/0.45 = one_one_nat ) )
% 0.18/0.45 & ( ~ ( ( ( ord_less_poly_a @ zero_zero_poly_a @ X )
% 0.18/0.45 & ( ord_less_poly_a @ Y3 @ zero_zero_poly_a ) )
% 0.18/0.45 | ( ( ord_less_poly_a @ X @ zero_zero_poly_a )
% 0.18/0.45 & ( ord_less_poly_a @ zero_zero_poly_a @ Y3 ) ) )
% 0.18/0.45 => ( ( descar357075861poly_a @ ( cons_poly_a @ X @ ( cons_poly_a @ Y3 @ nil_poly_a ) ) )
% 0.18/0.45 = zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sign_changes_two
% 0.18/0.45 thf(fact_195_zero__less__iff__neq__zero,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 = ( N != zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_less_iff_neq_zero
% 0.18/0.45 thf(fact_196_gr__implies__not__zero,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ M @ N )
% 0.18/0.45 => ( N != zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % gr_implies_not_zero
% 0.18/0.45 thf(fact_197_not__less__zero,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % not_less_zero
% 0.18/0.45 thf(fact_198_gr__zeroI,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( N != zero_zero_nat )
% 0.18/0.45 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % gr_zeroI
% 0.18/0.45 thf(fact_199_less__numeral__extra_I3_J,axiom,
% 0.18/0.45 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % less_numeral_extra(3)
% 0.18/0.45 thf(fact_200_less__numeral__extra_I3_J,axiom,
% 0.18/0.45 ~ ( ord_less_a @ zero_zero_a @ zero_zero_a ) ).
% 0.18/0.45
% 0.18/0.45 % less_numeral_extra(3)
% 0.18/0.45 thf(fact_201_less__numeral__extra_I3_J,axiom,
% 0.18/0.45 ~ ( ord_less_poly_a @ zero_zero_poly_a @ zero_zero_poly_a ) ).
% 0.18/0.45
% 0.18/0.45 % less_numeral_extra(3)
% 0.18/0.45 thf(fact_202_mult__right__cancel,axiom,
% 0.18/0.45 ! [C: a,A: a,B: a] :
% 0.18/0.45 ( ( C != zero_zero_a )
% 0.18/0.45 => ( ( ( times_times_a @ A @ C )
% 0.18/0.45 = ( times_times_a @ B @ C ) )
% 0.18/0.45 = ( A = B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_right_cancel
% 0.18/0.45 thf(fact_203_mult__right__cancel,axiom,
% 0.18/0.45 ! [C: poly_a,A: poly_a,B: poly_a] :
% 0.18/0.45 ( ( C != zero_zero_poly_a )
% 0.18/0.45 => ( ( ( times_times_poly_a @ A @ C )
% 0.18/0.45 = ( times_times_poly_a @ B @ C ) )
% 0.18/0.45 = ( A = B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_right_cancel
% 0.18/0.45 thf(fact_204_mult__right__cancel,axiom,
% 0.18/0.45 ! [C: nat,A: nat,B: nat] :
% 0.18/0.45 ( ( C != zero_zero_nat )
% 0.18/0.45 => ( ( ( times_times_nat @ A @ C )
% 0.18/0.45 = ( times_times_nat @ B @ C ) )
% 0.18/0.45 = ( A = B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_right_cancel
% 0.18/0.45 thf(fact_205_mult__left__cancel,axiom,
% 0.18/0.45 ! [C: a,A: a,B: a] :
% 0.18/0.45 ( ( C != zero_zero_a )
% 0.18/0.45 => ( ( ( times_times_a @ C @ A )
% 0.18/0.45 = ( times_times_a @ C @ B ) )
% 0.18/0.45 = ( A = B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_left_cancel
% 0.18/0.45 thf(fact_206_mult__left__cancel,axiom,
% 0.18/0.45 ! [C: poly_a,A: poly_a,B: poly_a] :
% 0.18/0.45 ( ( C != zero_zero_poly_a )
% 0.18/0.45 => ( ( ( times_times_poly_a @ C @ A )
% 0.18/0.45 = ( times_times_poly_a @ C @ B ) )
% 0.18/0.45 = ( A = B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_left_cancel
% 0.18/0.45 thf(fact_207_mult__left__cancel,axiom,
% 0.18/0.45 ! [C: nat,A: nat,B: nat] :
% 0.18/0.45 ( ( C != zero_zero_nat )
% 0.18/0.45 => ( ( ( times_times_nat @ C @ A )
% 0.18/0.45 = ( times_times_nat @ C @ B ) )
% 0.18/0.45 = ( A = B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_left_cancel
% 0.18/0.45 thf(fact_208_no__zero__divisors,axiom,
% 0.18/0.45 ! [A: a,B: a] :
% 0.18/0.45 ( ( A != zero_zero_a )
% 0.18/0.45 => ( ( B != zero_zero_a )
% 0.18/0.45 => ( ( times_times_a @ A @ B )
% 0.18/0.45 != zero_zero_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % no_zero_divisors
% 0.18/0.45 thf(fact_209_no__zero__divisors,axiom,
% 0.18/0.45 ! [A: poly_a,B: poly_a] :
% 0.18/0.45 ( ( A != zero_zero_poly_a )
% 0.18/0.45 => ( ( B != zero_zero_poly_a )
% 0.18/0.45 => ( ( times_times_poly_a @ A @ B )
% 0.18/0.45 != zero_zero_poly_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % no_zero_divisors
% 0.18/0.45 thf(fact_210_no__zero__divisors,axiom,
% 0.18/0.45 ! [A: nat,B: nat] :
% 0.18/0.45 ( ( A != zero_zero_nat )
% 0.18/0.45 => ( ( B != zero_zero_nat )
% 0.18/0.45 => ( ( times_times_nat @ A @ B )
% 0.18/0.45 != zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % no_zero_divisors
% 0.18/0.45 thf(fact_211_divisors__zero,axiom,
% 0.18/0.45 ! [A: a,B: a] :
% 0.18/0.45 ( ( ( times_times_a @ A @ B )
% 0.18/0.45 = zero_zero_a )
% 0.18/0.45 => ( ( A = zero_zero_a )
% 0.18/0.45 | ( B = zero_zero_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divisors_zero
% 0.18/0.45 thf(fact_212_divisors__zero,axiom,
% 0.18/0.45 ! [A: poly_a,B: poly_a] :
% 0.18/0.45 ( ( ( times_times_poly_a @ A @ B )
% 0.18/0.45 = zero_zero_poly_a )
% 0.18/0.45 => ( ( A = zero_zero_poly_a )
% 0.18/0.45 | ( B = zero_zero_poly_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divisors_zero
% 0.18/0.45 thf(fact_213_divisors__zero,axiom,
% 0.18/0.45 ! [A: nat,B: nat] :
% 0.18/0.45 ( ( ( times_times_nat @ A @ B )
% 0.18/0.45 = zero_zero_nat )
% 0.18/0.45 => ( ( A = zero_zero_nat )
% 0.18/0.45 | ( B = zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divisors_zero
% 0.18/0.45 thf(fact_214_mult__not__zero,axiom,
% 0.18/0.45 ! [A: a,B: a] :
% 0.18/0.45 ( ( ( times_times_a @ A @ B )
% 0.18/0.45 != zero_zero_a )
% 0.18/0.45 => ( ( A != zero_zero_a )
% 0.18/0.45 & ( B != zero_zero_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mult_not_zero
% 0.18/0.45 thf(fact_215_mult__not__zero,axiom,
% 0.18/0.45 ! [A: poly_a,B: poly_a] :
% 0.18/0.45 ( ( ( times_times_poly_a @ A @ B )
% 0.18/0.46 != zero_zero_poly_a )
% 0.18/0.46 => ( ( A != zero_zero_poly_a )
% 0.18/0.46 & ( B != zero_zero_poly_a ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % mult_not_zero
% 0.18/0.46 thf(fact_216_mult__not__zero,axiom,
% 0.18/0.46 ! [A: nat,B: nat] :
% 0.18/0.46 ( ( ( times_times_nat @ A @ B )
% 0.18/0.46 != zero_zero_nat )
% 0.18/0.46 => ( ( A != zero_zero_nat )
% 0.18/0.46 & ( B != zero_zero_nat ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % mult_not_zero
% 0.18/0.46 thf(fact_217_zero__neq__one,axiom,
% 0.18/0.46 zero_zero_poly_a != one_one_poly_a ).
% 0.18/0.46
% 0.18/0.46 % zero_neq_one
% 0.18/0.46 thf(fact_218_zero__neq__one,axiom,
% 0.18/0.46 zero_zero_a != one_one_a ).
% 0.18/0.46
% 0.18/0.46 % zero_neq_one
% 0.18/0.46 thf(fact_219_zero__neq__one,axiom,
% 0.18/0.46 zero_zero_nat != one_one_nat ).
% 0.18/0.46
% 0.18/0.46 % zero_neq_one
% 0.18/0.46 thf(fact_220_less__numeral__extra_I4_J,axiom,
% 0.18/0.46 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.18/0.46
% 0.18/0.46 % less_numeral_extra(4)
% 0.18/0.46 thf(fact_221_less__numeral__extra_I4_J,axiom,
% 0.18/0.46 ~ ( ord_less_a @ one_one_a @ one_one_a ) ).
% 0.18/0.46
% 0.18/0.46 % less_numeral_extra(4)
% 0.18/0.46 thf(fact_222_less__numeral__extra_I4_J,axiom,
% 0.18/0.46 ~ ( ord_less_poly_a @ one_one_poly_a @ one_one_poly_a ) ).
% 0.18/0.46
% 0.18/0.46 % less_numeral_extra(4)
% 0.18/0.46 thf(fact_223_mult_Ocomm__neutral,axiom,
% 0.30/0.46 ! [A: a] :
% 0.30/0.46 ( ( times_times_a @ A @ one_one_a )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % mult.comm_neutral
% 0.30/0.46 thf(fact_224_mult_Ocomm__neutral,axiom,
% 0.30/0.46 ! [A: poly_a] :
% 0.30/0.46 ( ( times_times_poly_a @ A @ one_one_poly_a )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % mult.comm_neutral
% 0.30/0.46 thf(fact_225_mult_Ocomm__neutral,axiom,
% 0.30/0.46 ! [A: nat] :
% 0.30/0.46 ( ( times_times_nat @ A @ one_one_nat )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % mult.comm_neutral
% 0.30/0.46 thf(fact_226_comm__monoid__mult__class_Omult__1,axiom,
% 0.30/0.46 ! [A: a] :
% 0.30/0.46 ( ( times_times_a @ one_one_a @ A )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % comm_monoid_mult_class.mult_1
% 0.30/0.46 thf(fact_227_comm__monoid__mult__class_Omult__1,axiom,
% 0.30/0.46 ! [A: poly_a] :
% 0.30/0.46 ( ( times_times_poly_a @ one_one_poly_a @ A )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % comm_monoid_mult_class.mult_1
% 0.30/0.46 thf(fact_228_comm__monoid__mult__class_Omult__1,axiom,
% 0.30/0.46 ! [A: nat] :
% 0.30/0.46 ( ( times_times_nat @ one_one_nat @ A )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % comm_monoid_mult_class.mult_1
% 0.30/0.46 thf(fact_229_minus__less__iff,axiom,
% 0.30/0.46 ! [A: poly_a,B: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ B )
% 0.30/0.46 = ( ord_less_poly_a @ ( uminus_uminus_poly_a @ B ) @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % minus_less_iff
% 0.30/0.46 thf(fact_230_minus__less__iff,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ord_less_a @ ( uminus_uminus_a @ A ) @ B )
% 0.30/0.46 = ( ord_less_a @ ( uminus_uminus_a @ B ) @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % minus_less_iff
% 0.30/0.46 thf(fact_231_less__minus__iff,axiom,
% 0.30/0.46 ! [A: poly_a,B: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ A @ ( uminus_uminus_poly_a @ B ) )
% 0.30/0.46 = ( ord_less_poly_a @ B @ ( uminus_uminus_poly_a @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_minus_iff
% 0.30/0.46 thf(fact_232_less__minus__iff,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ord_less_a @ A @ ( uminus_uminus_a @ B ) )
% 0.30/0.46 = ( ord_less_a @ B @ ( uminus_uminus_a @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_minus_iff
% 0.30/0.46 thf(fact_233_minus__mult__commute,axiom,
% 0.30/0.46 ! [A: poly_a,B: poly_a] :
% 0.30/0.46 ( ( times_times_poly_a @ ( uminus_uminus_poly_a @ A ) @ B )
% 0.30/0.46 = ( times_times_poly_a @ A @ ( uminus_uminus_poly_a @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minus_mult_commute
% 0.30/0.46 thf(fact_234_minus__mult__commute,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( times_times_a @ ( uminus_uminus_a @ A ) @ B )
% 0.30/0.46 = ( times_times_a @ A @ ( uminus_uminus_a @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minus_mult_commute
% 0.30/0.46 thf(fact_235_square__eq__iff,axiom,
% 0.30/0.46 ! [A: poly_a,B: poly_a] :
% 0.30/0.46 ( ( ( times_times_poly_a @ A @ A )
% 0.30/0.46 = ( times_times_poly_a @ B @ B ) )
% 0.30/0.46 = ( ( A = B )
% 0.30/0.46 | ( A
% 0.30/0.46 = ( uminus_uminus_poly_a @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % square_eq_iff
% 0.30/0.46 thf(fact_236_square__eq__iff,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ( times_times_a @ A @ A )
% 0.30/0.46 = ( times_times_a @ B @ B ) )
% 0.30/0.46 = ( ( A = B )
% 0.30/0.46 | ( A
% 0.30/0.46 = ( uminus_uminus_a @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % square_eq_iff
% 0.30/0.46 thf(fact_237_one__neq__neg__one,axiom,
% 0.30/0.46 ( one_one_a
% 0.30/0.46 != ( uminus_uminus_a @ one_one_a ) ) ).
% 0.30/0.46
% 0.30/0.46 % one_neq_neg_one
% 0.30/0.46 thf(fact_238_strict__sorted_Oinduct,axiom,
% 0.30/0.46 ! [P3: list_a > $o,A0: list_a] :
% 0.30/0.46 ( ( P3 @ nil_a )
% 0.30/0.46 => ( ! [X2: a,Ys: list_a] :
% 0.30/0.46 ( ( P3 @ Ys )
% 0.30/0.46 => ( P3 @ ( cons_a @ X2 @ Ys ) ) )
% 0.30/0.46 => ( P3 @ A0 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % strict_sorted.induct
% 0.30/0.46 thf(fact_239_strict__sorted_Ocases,axiom,
% 0.30/0.46 ! [X: list_a] :
% 0.30/0.46 ( ( X != nil_a )
% 0.30/0.46 => ~ ! [X2: a,Ys: list_a] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons_a @ X2 @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % strict_sorted.cases
% 0.30/0.46 thf(fact_240_map__tailrec__rev_Oinduct,axiom,
% 0.30/0.46 ! [P3: ( a > a ) > list_a > list_a > $o,A0: a > a,A1: list_a,A22: list_a] :
% 0.30/0.46 ( ! [F2: a > a,X_1: list_a] : ( P3 @ F2 @ nil_a @ X_1 )
% 0.30/0.46 => ( ! [F2: a > a,A2: a,As2: list_a,Bs: list_a] :
% 0.30/0.46 ( ( P3 @ F2 @ As2 @ ( cons_a @ ( F2 @ A2 ) @ Bs ) )
% 0.30/0.46 => ( P3 @ F2 @ ( cons_a @ A2 @ As2 ) @ Bs ) )
% 0.30/0.46 => ( P3 @ A0 @ A1 @ A22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_tailrec_rev.induct
% 0.30/0.46 thf(fact_241_list__nonempty__induct,axiom,
% 0.30/0.46 ! [Xs: list_a,P3: list_a > $o] :
% 0.30/0.46 ( ( Xs != nil_a )
% 0.30/0.46 => ( ! [X2: a] : ( P3 @ ( cons_a @ X2 @ nil_a ) )
% 0.30/0.46 => ( ! [X2: a,Xs2: list_a] :
% 0.30/0.46 ( ( Xs2 != nil_a )
% 0.30/0.46 => ( ( P3 @ Xs2 )
% 0.30/0.46 => ( P3 @ ( cons_a @ X2 @ Xs2 ) ) ) )
% 0.30/0.46 => ( P3 @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_nonempty_induct
% 0.30/0.46 thf(fact_242_successively_Oinduct,axiom,
% 0.30/0.46 ! [P3: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
% 0.30/0.46 ( ! [P5: a > a > $o] : ( P3 @ P5 @ nil_a )
% 0.30/0.46 => ( ! [P5: a > a > $o,X2: a] : ( P3 @ P5 @ ( cons_a @ X2 @ nil_a ) )
% 0.30/0.46 => ( ! [P5: a > a > $o,X2: a,Y2: a,Xs2: list_a] :
% 0.30/0.46 ( ( P3 @ P5 @ ( cons_a @ Y2 @ Xs2 ) )
% 0.30/0.46 => ( P3 @ P5 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) )
% 0.30/0.46 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % successively.induct
% 0.30/0.46 thf(fact_243_remdups__adj_Oinduct,axiom,
% 0.30/0.46 ! [P3: list_a > $o,A0: list_a] :
% 0.30/0.46 ( ( P3 @ nil_a )
% 0.30/0.46 => ( ! [X2: a] : ( P3 @ ( cons_a @ X2 @ nil_a ) )
% 0.30/0.46 => ( ! [X2: a,Y2: a,Xs2: list_a] :
% 0.30/0.46 ( ( ( X2 = Y2 )
% 0.30/0.46 => ( P3 @ ( cons_a @ X2 @ Xs2 ) ) )
% 0.30/0.46 => ( ( ( X2 != Y2 )
% 0.30/0.46 => ( P3 @ ( cons_a @ Y2 @ Xs2 ) ) )
% 0.30/0.46 => ( P3 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) ) )
% 0.30/0.46 => ( P3 @ A0 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % remdups_adj.induct
% 0.30/0.46 thf(fact_244_sorted__wrt_Oinduct,axiom,
% 0.30/0.46 ! [P3: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
% 0.30/0.46 ( ! [P5: a > a > $o] : ( P3 @ P5 @ nil_a )
% 0.30/0.46 => ( ! [P5: a > a > $o,X2: a,Ys: list_a] :
% 0.30/0.46 ( ( P3 @ P5 @ Ys )
% 0.30/0.46 => ( P3 @ P5 @ ( cons_a @ X2 @ Ys ) ) )
% 0.30/0.46 => ( P3 @ A0 @ A1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sorted_wrt.induct
% 0.30/0.46 thf(fact_245_remdups__adj_Ocases,axiom,
% 0.30/0.46 ! [X: list_a] :
% 0.30/0.46 ( ( X != nil_a )
% 0.30/0.46 => ( ! [X2: a] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons_a @ X2 @ nil_a ) )
% 0.30/0.46 => ~ ! [X2: a,Y2: a,Xs2: list_a] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % remdups_adj.cases
% 0.30/0.46 thf(fact_246_transpose_Ocases,axiom,
% 0.30/0.46 ! [X: list_list_a] :
% 0.30/0.46 ( ( X != nil_list_a )
% 0.30/0.46 => ( ! [Xss: list_list_a] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons_list_a @ nil_a @ Xss ) )
% 0.30/0.46 => ~ ! [X2: a,Xs2: list_a,Xss: list_list_a] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons_list_a @ ( cons_a @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % transpose.cases
% 0.30/0.46 thf(fact_247_shuffles_Oinduct,axiom,
% 0.30/0.46 ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 0.30/0.46 ( ! [X_1: list_a] : ( P3 @ nil_a @ X_1 )
% 0.30/0.46 => ( ! [Xs2: list_a] : ( P3 @ Xs2 @ nil_a )
% 0.30/0.46 => ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
% 0.30/0.46 ( ( P3 @ Xs2 @ ( cons_a @ Y2 @ Ys ) )
% 0.30/0.46 => ( ( P3 @ ( cons_a @ X2 @ Xs2 ) @ Ys )
% 0.30/0.46 => ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) ) )
% 0.30/0.46 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % shuffles.induct
% 0.30/0.46 thf(fact_248_min__list_Oinduct,axiom,
% 0.30/0.46 ! [P3: list_a > $o,A0: list_a] :
% 0.30/0.46 ( ! [X2: a,Xs2: list_a] :
% 0.30/0.46 ( ! [X212: a,X222: list_a] :
% 0.30/0.46 ( ( Xs2
% 0.30/0.46 = ( cons_a @ X212 @ X222 ) )
% 0.30/0.46 => ( P3 @ Xs2 ) )
% 0.30/0.46 => ( P3 @ ( cons_a @ X2 @ Xs2 ) ) )
% 0.30/0.46 => ( ( P3 @ nil_a )
% 0.30/0.46 => ( P3 @ A0 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % min_list.induct
% 0.30/0.46 thf(fact_249_min__list_Ocases,axiom,
% 0.30/0.46 ! [X: list_a] :
% 0.30/0.46 ( ! [X2: a,Xs2: list_a] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons_a @ X2 @ Xs2 ) )
% 0.30/0.46 => ( X = nil_a ) ) ).
% 0.30/0.46
% 0.30/0.46 % min_list.cases
% 0.30/0.46 thf(fact_250_induct__list012,axiom,
% 0.30/0.46 ! [P3: list_a > $o,Xs: list_a] :
% 0.30/0.46 ( ( P3 @ nil_a )
% 0.30/0.46 => ( ! [X2: a] : ( P3 @ ( cons_a @ X2 @ nil_a ) )
% 0.30/0.46 => ( ! [X2: a,Y2: a,Zs2: list_a] :
% 0.30/0.46 ( ( P3 @ Zs2 )
% 0.30/0.46 => ( ( P3 @ ( cons_a @ Y2 @ Zs2 ) )
% 0.30/0.46 => ( P3 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Zs2 ) ) ) ) )
% 0.30/0.46 => ( P3 @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % induct_list012
% 0.30/0.46 thf(fact_251_splice_Oinduct,axiom,
% 0.30/0.46 ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 0.30/0.46 ( ! [X_1: list_a] : ( P3 @ nil_a @ X_1 )
% 0.30/0.46 => ( ! [X2: a,Xs2: list_a,Ys: list_a] :
% 0.30/0.46 ( ( P3 @ Ys @ Xs2 )
% 0.30/0.46 => ( P3 @ ( cons_a @ X2 @ Xs2 ) @ Ys ) )
% 0.30/0.46 => ( P3 @ A0 @ A1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % splice.induct
% 0.30/0.46 thf(fact_252_list__induct2_H,axiom,
% 0.30/0.46 ! [P3: list_a > list_a > $o,Xs: list_a,Ys2: list_a] :
% 0.30/0.46 ( ( P3 @ nil_a @ nil_a )
% 0.30/0.46 => ( ! [X2: a,Xs2: list_a] : ( P3 @ ( cons_a @ X2 @ Xs2 ) @ nil_a )
% 0.30/0.46 => ( ! [Y2: a,Ys: list_a] : ( P3 @ nil_a @ ( cons_a @ Y2 @ Ys ) )
% 0.30/0.46 => ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
% 0.30/0.46 ( ( P3 @ Xs2 @ Ys )
% 0.30/0.46 => ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) )
% 0.30/0.46 => ( P3 @ Xs @ Ys2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_induct2'
% 0.30/0.46 thf(fact_253_neq__Nil__conv,axiom,
% 0.30/0.46 ! [Xs: list_a] :
% 0.30/0.46 ( ( Xs != nil_a )
% 0.30/0.46 = ( ? [Y4: a,Ys3: list_a] :
% 0.30/0.46 ( Xs
% 0.30/0.46 = ( cons_a @ Y4 @ Ys3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % neq_Nil_conv
% 0.30/0.46 thf(fact_254_list_Oinducts,axiom,
% 0.30/0.46 ! [P3: list_a > $o,List: list_a] :
% 0.30/0.46 ( ( P3 @ nil_a )
% 0.30/0.46 => ( ! [X1: a,X23: list_a] :
% 0.30/0.46 ( ( P3 @ X23 )
% 0.30/0.46 => ( P3 @ ( cons_a @ X1 @ X23 ) ) )
% 0.30/0.46 => ( P3 @ List ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.inducts
% 0.30/0.46 thf(fact_255_list_Oexhaust,axiom,
% 0.30/0.46 ! [Y3: list_a] :
% 0.30/0.46 ( ( Y3 != nil_a )
% 0.30/0.46 => ~ ! [X213: a,X223: list_a] :
% 0.30/0.46 ( Y3
% 0.30/0.46 != ( cons_a @ X213 @ X223 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.exhaust
% 0.30/0.46 thf(fact_256_list_OdiscI,axiom,
% 0.30/0.46 ! [List: list_a,X21: a,X22: list_a] :
% 0.30/0.46 ( ( List
% 0.30/0.46 = ( cons_a @ X21 @ X22 ) )
% 0.30/0.46 => ( List != nil_a ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.discI
% 0.30/0.46 thf(fact_257_list_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [X21: a,X22: list_a] :
% 0.30/0.46 ( nil_a
% 0.30/0.46 != ( cons_a @ X21 @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.distinct(1)
% 0.30/0.46 thf(fact_258_append__Cons,axiom,
% 0.30/0.46 ! [X: a,Xs: list_a,Ys2: list_a] :
% 0.30/0.46 ( ( append_a @ ( cons_a @ X @ Xs ) @ Ys2 )
% 0.30/0.46 = ( cons_a @ X @ ( append_a @ Xs @ Ys2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_Cons
% 0.30/0.46 thf(fact_259_Cons__eq__appendI,axiom,
% 0.30/0.46 ! [X: a,Xs1: list_a,Ys2: list_a,Xs: list_a,Zs: list_a] :
% 0.30/0.46 ( ( ( cons_a @ X @ Xs1 )
% 0.30/0.46 = Ys2 )
% 0.30/0.46 => ( ( Xs
% 0.30/0.46 = ( append_a @ Xs1 @ Zs ) )
% 0.30/0.46 => ( ( cons_a @ X @ Xs )
% 0.30/0.46 = ( append_a @ Ys2 @ Zs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Cons_eq_appendI
% 0.30/0.46 thf(fact_260_append_Oleft__neutral,axiom,
% 0.30/0.46 ! [A: list_a] :
% 0.30/0.46 ( ( append_a @ nil_a @ A )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % append.left_neutral
% 0.30/0.46 thf(fact_261_append__Nil,axiom,
% 0.30/0.46 ! [Ys2: list_a] :
% 0.30/0.46 ( ( append_a @ nil_a @ Ys2 )
% 0.30/0.46 = Ys2 ) ).
% 0.30/0.46
% 0.30/0.46 % append_Nil
% 0.30/0.46 thf(fact_262_eq__Nil__appendI,axiom,
% 0.30/0.46 ! [Xs: list_a,Ys2: list_a] :
% 0.30/0.46 ( ( Xs = Ys2 )
% 0.30/0.46 => ( Xs
% 0.30/0.46 = ( append_a @ nil_a @ Ys2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_Nil_appendI
% 0.30/0.46 thf(fact_263_null__rec_I1_J,axiom,
% 0.30/0.46 ! [X: a,Xs: list_a] :
% 0.30/0.46 ~ ( null_a @ ( cons_a @ X @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % null_rec(1)
% 0.30/0.46 thf(fact_264_eq__Nil__null,axiom,
% 0.30/0.46 ! [Xs: list_a] :
% 0.30/0.46 ( ( Xs = nil_a )
% 0.30/0.46 = ( null_a @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_Nil_null
% 0.30/0.46 thf(fact_265_null__rec_I2_J,axiom,
% 0.30/0.46 null_a @ nil_a ).
% 0.30/0.46
% 0.30/0.46 % null_rec(2)
% 0.30/0.46 thf(fact_266_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.30/0.46 ! [A: nat,B: nat,C: nat] :
% 0.30/0.46 ( ( ord_less_nat @ A @ B )
% 0.30/0.46 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.30/0.46 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.30/0.46 thf(fact_267_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( ord_less_a @ A @ B )
% 0.30/0.46 => ( ( ord_less_a @ zero_zero_a @ C )
% 0.30/0.46 => ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.30/0.46 thf(fact_268_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.30/0.46 ! [A: poly_a,B: poly_a,C: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ A @ B )
% 0.30/0.46 => ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 0.30/0.46 => ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.30/0.46 thf(fact_269_mult__less__cancel__right__disj,axiom,
% 0.30/0.46 ! [A: a,C: a,B: a] :
% 0.30/0.46 ( ( ord_less_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) )
% 0.30/0.46 = ( ( ( ord_less_a @ zero_zero_a @ C )
% 0.30/0.46 & ( ord_less_a @ A @ B ) )
% 0.30/0.46 | ( ( ord_less_a @ C @ zero_zero_a )
% 0.30/0.46 & ( ord_less_a @ B @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_right_disj
% 0.30/0.46 thf(fact_270_mult__less__cancel__right__disj,axiom,
% 0.30/0.46 ! [A: poly_a,C: poly_a,B: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ ( times_times_poly_a @ A @ C ) @ ( times_times_poly_a @ B @ C ) )
% 0.30/0.46 = ( ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 0.30/0.46 & ( ord_less_poly_a @ A @ B ) )
% 0.30/0.46 | ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
% 0.30/0.46 & ( ord_less_poly_a @ B @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_right_disj
% 0.30/0.46 thf(fact_271_mult__strict__right__mono,axiom,
% 0.30/0.46 ! [A: nat,B: nat,C: nat] :
% 0.30/0.46 ( ( ord_less_nat @ A @ B )
% 0.30/0.46 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.30/0.46 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_right_mono
% 0.30/0.46 thf(fact_272_mult__strict__right__mono,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( ord_less_a @ A @ B )
% 0.30/0.46 => ( ( ord_less_a @ zero_zero_a @ C )
% 0.30/0.46 => ( ord_less_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_right_mono
% 0.30/0.46 thf(fact_273_mult__strict__right__mono,axiom,
% 0.30/0.46 ! [A: poly_a,B: poly_a,C: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ A @ B )
% 0.30/0.46 => ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 0.30/0.46 => ( ord_less_poly_a @ ( times_times_poly_a @ A @ C ) @ ( times_times_poly_a @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_right_mono
% 0.30/0.46 thf(fact_274_mult__strict__right__mono__neg,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( ord_less_a @ B @ A )
% 0.30/0.46 => ( ( ord_less_a @ C @ zero_zero_a )
% 0.30/0.46 => ( ord_less_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_right_mono_neg
% 0.30/0.46 thf(fact_275_mult__strict__right__mono__neg,axiom,
% 0.30/0.46 ! [B: poly_a,A: poly_a,C: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ B @ A )
% 0.30/0.46 => ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
% 0.30/0.46 => ( ord_less_poly_a @ ( times_times_poly_a @ A @ C ) @ ( times_times_poly_a @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_right_mono_neg
% 0.30/0.46 thf(fact_276_mult__less__cancel__left__disj,axiom,
% 0.30/0.46 ! [C: a,A: a,B: a] :
% 0.30/0.46 ( ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) )
% 0.30/0.46 = ( ( ( ord_less_a @ zero_zero_a @ C )
% 0.30/0.46 & ( ord_less_a @ A @ B ) )
% 0.30/0.46 | ( ( ord_less_a @ C @ zero_zero_a )
% 0.30/0.46 & ( ord_less_a @ B @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_left_disj
% 0.30/0.46 thf(fact_277_mult__less__cancel__left__disj,axiom,
% 0.30/0.46 ! [C: poly_a,A: poly_a,B: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) )
% 0.30/0.46 = ( ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 0.30/0.46 & ( ord_less_poly_a @ A @ B ) )
% 0.30/0.46 | ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
% 0.30/0.46 & ( ord_less_poly_a @ B @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_left_disj
% 0.30/0.46 thf(fact_278_mult__strict__left__mono,axiom,
% 0.30/0.46 ! [A: nat,B: nat,C: nat] :
% 0.30/0.46 ( ( ord_less_nat @ A @ B )
% 0.30/0.46 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.30/0.46 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_left_mono
% 0.30/0.46 thf(fact_279_mult__strict__left__mono,axiom,
% 0.30/0.46 ! [A: a,B: a,C: a] :
% 0.30/0.46 ( ( ord_less_a @ A @ B )
% 0.30/0.46 => ( ( ord_less_a @ zero_zero_a @ C )
% 0.30/0.46 => ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_left_mono
% 0.30/0.46 thf(fact_280_mult__strict__left__mono,axiom,
% 0.30/0.46 ! [A: poly_a,B: poly_a,C: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ A @ B )
% 0.30/0.46 => ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 0.30/0.46 => ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_left_mono
% 0.30/0.46 thf(fact_281_mult__strict__left__mono__neg,axiom,
% 0.30/0.46 ! [B: a,A: a,C: a] :
% 0.30/0.46 ( ( ord_less_a @ B @ A )
% 0.30/0.46 => ( ( ord_less_a @ C @ zero_zero_a )
% 0.30/0.46 => ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_left_mono_neg
% 0.30/0.46 thf(fact_282_mult__strict__left__mono__neg,axiom,
% 0.30/0.46 ! [B: poly_a,A: poly_a,C: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ B @ A )
% 0.30/0.46 => ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
% 0.30/0.46 => ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_left_mono_neg
% 0.30/0.46 thf(fact_283_mult__less__cancel__left__pos,axiom,
% 0.30/0.46 ! [C: a,A: a,B: a] :
% 0.30/0.46 ( ( ord_less_a @ zero_zero_a @ C )
% 0.30/0.46 => ( ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) )
% 0.30/0.46 = ( ord_less_a @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_left_pos
% 0.30/0.46 thf(fact_284_mult__less__cancel__left__pos,axiom,
% 0.30/0.46 ! [C: poly_a,A: poly_a,B: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 0.30/0.46 => ( ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) )
% 0.30/0.46 = ( ord_less_poly_a @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_left_pos
% 0.30/0.46 thf(fact_285_mult__less__cancel__left__neg,axiom,
% 0.30/0.46 ! [C: a,A: a,B: a] :
% 0.30/0.46 ( ( ord_less_a @ C @ zero_zero_a )
% 0.30/0.46 => ( ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) )
% 0.30/0.46 = ( ord_less_a @ B @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_left_neg
% 0.30/0.46 thf(fact_286_mult__less__cancel__left__neg,axiom,
% 0.30/0.46 ! [C: poly_a,A: poly_a,B: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
% 0.30/0.46 => ( ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) )
% 0.30/0.46 = ( ord_less_poly_a @ B @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_left_neg
% 0.30/0.46 thf(fact_287_zero__less__mult__pos2,axiom,
% 0.30/0.46 ! [B: nat,A: nat] :
% 0.30/0.46 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 0.30/0.46 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.46 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_mult_pos2
% 0.30/0.46 thf(fact_288_zero__less__mult__pos2,axiom,
% 0.30/0.46 ! [B: a,A: a] :
% 0.30/0.46 ( ( ord_less_a @ zero_zero_a @ ( times_times_a @ B @ A ) )
% 0.30/0.46 => ( ( ord_less_a @ zero_zero_a @ A )
% 0.30/0.46 => ( ord_less_a @ zero_zero_a @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_mult_pos2
% 0.30/0.46 thf(fact_289_zero__less__mult__pos2,axiom,
% 0.30/0.46 ! [B: poly_a,A: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ B @ A ) )
% 0.30/0.46 => ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.30/0.46 => ( ord_less_poly_a @ zero_zero_poly_a @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_mult_pos2
% 0.30/0.46 thf(fact_290_zero__less__mult__pos,axiom,
% 0.30/0.46 ! [A: nat,B: nat] :
% 0.30/0.46 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 0.30/0.46 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.46 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_mult_pos
% 0.30/0.46 thf(fact_291_zero__less__mult__pos,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) )
% 0.30/0.46 => ( ( ord_less_a @ zero_zero_a @ A )
% 0.30/0.46 => ( ord_less_a @ zero_zero_a @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_mult_pos
% 0.30/0.46 thf(fact_292_zero__less__mult__pos,axiom,
% 0.30/0.46 ! [A: poly_a,B: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) )
% 0.30/0.46 => ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.30/0.46 => ( ord_less_poly_a @ zero_zero_poly_a @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_mult_pos
% 0.30/0.46 thf(fact_293_zero__less__mult__iff,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) )
% 0.30/0.46 = ( ( ( ord_less_a @ zero_zero_a @ A )
% 0.30/0.46 & ( ord_less_a @ zero_zero_a @ B ) )
% 0.30/0.46 | ( ( ord_less_a @ A @ zero_zero_a )
% 0.30/0.46 & ( ord_less_a @ B @ zero_zero_a ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_mult_iff
% 0.30/0.46 thf(fact_294_zero__less__mult__iff,axiom,
% 0.30/0.46 ! [A: poly_a,B: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) )
% 0.30/0.46 = ( ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.30/0.46 & ( ord_less_poly_a @ zero_zero_poly_a @ B ) )
% 0.30/0.46 | ( ( ord_less_poly_a @ A @ zero_zero_poly_a )
% 0.30/0.46 & ( ord_less_poly_a @ B @ zero_zero_poly_a ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_mult_iff
% 0.30/0.46 thf(fact_295_mult__pos__neg2,axiom,
% 0.30/0.46 ! [A: nat,B: nat] :
% 0.30/0.46 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.46 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.30/0.46 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_pos_neg2
% 0.30/0.46 thf(fact_296_mult__pos__neg2,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ord_less_a @ zero_zero_a @ A )
% 0.30/0.46 => ( ( ord_less_a @ B @ zero_zero_a )
% 0.30/0.46 => ( ord_less_a @ ( times_times_a @ B @ A ) @ zero_zero_a ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_pos_neg2
% 0.30/0.46 thf(fact_297_mult__pos__neg2,axiom,
% 0.30/0.46 ! [A: poly_a,B: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.30/0.46 => ( ( ord_less_poly_a @ B @ zero_zero_poly_a )
% 0.30/0.46 => ( ord_less_poly_a @ ( times_times_poly_a @ B @ A ) @ zero_zero_poly_a ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_pos_neg2
% 0.30/0.46 thf(fact_298_mult__pos__pos,axiom,
% 0.30/0.46 ! [A: nat,B: nat] :
% 0.30/0.46 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.46 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.46 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_pos_pos
% 0.30/0.46 thf(fact_299_mult__pos__pos,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ord_less_a @ zero_zero_a @ A )
% 0.30/0.46 => ( ( ord_less_a @ zero_zero_a @ B )
% 0.30/0.46 => ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_pos_pos
% 0.30/0.46 thf(fact_300_mult__pos__pos,axiom,
% 0.30/0.46 ! [A: poly_a,B: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.30/0.46 => ( ( ord_less_poly_a @ zero_zero_poly_a @ B )
% 0.30/0.46 => ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_pos_pos
% 0.30/0.46 thf(fact_301_mult__pos__neg,axiom,
% 0.30/0.46 ! [A: nat,B: nat] :
% 0.30/0.46 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.46 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.30/0.46 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_pos_neg
% 0.30/0.46 thf(fact_302_mult__pos__neg,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ord_less_a @ zero_zero_a @ A )
% 0.30/0.46 => ( ( ord_less_a @ B @ zero_zero_a )
% 0.30/0.46 => ( ord_less_a @ ( times_times_a @ A @ B ) @ zero_zero_a ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_pos_neg
% 0.30/0.46 thf(fact_303_mult__pos__neg,axiom,
% 0.30/0.46 ! [A: poly_a,B: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.30/0.46 => ( ( ord_less_poly_a @ B @ zero_zero_poly_a )
% 0.30/0.46 => ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ zero_zero_poly_a ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_pos_neg
% 0.30/0.46 thf(fact_304_mult__neg__pos,axiom,
% 0.30/0.46 ! [A: nat,B: nat] :
% 0.30/0.46 ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.30/0.46 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.46 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_neg_pos
% 0.30/0.46 thf(fact_305_mult__neg__pos,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ord_less_a @ A @ zero_zero_a )
% 0.30/0.46 => ( ( ord_less_a @ zero_zero_a @ B )
% 0.30/0.46 => ( ord_less_a @ ( times_times_a @ A @ B ) @ zero_zero_a ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_neg_pos
% 0.30/0.46 thf(fact_306_mult__neg__pos,axiom,
% 0.30/0.46 ! [A: poly_a,B: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ A @ zero_zero_poly_a )
% 0.30/0.46 => ( ( ord_less_poly_a @ zero_zero_poly_a @ B )
% 0.30/0.46 => ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ zero_zero_poly_a ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_neg_pos
% 0.30/0.46 thf(fact_307_mult__less__0__iff,axiom,
% 0.30/0.46 ! [A: a,B: a] :
% 0.30/0.46 ( ( ord_less_a @ ( times_times_a @ A @ B ) @ zero_zero_a )
% 0.30/0.46 = ( ( ( ord_less_a @ zero_zero_a @ A )
% 0.30/0.46 & ( ord_less_a @ B @ zero_zero_a ) )
% 0.30/0.46 | ( ( ord_less_a @ A @ zero_zero_a )
% 0.30/0.46 & ( ord_less_a @ zero_zero_a @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_0_iff
% 0.30/0.46 thf(fact_308_mult__less__0__iff,axiom,
% 0.30/0.46 ! [A: poly_a,B: poly_a] :
% 0.30/0.46 ( ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ zero_zero_poly_a )
% 0.30/0.46 = ( ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 0.30/0.46 & ( ord_less_poly_a @ B @ zero_zero_poly_a ) )
% 0.30/0.46 | ( ( ord_less_poly_a @ A @ zero_zero_poly_a )
% 0.30/0.46 & ( ord_less_poly_a @ zero_zero_poly_a @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_0_iff
% 0.30/0.46 thf(fact_309_nat__mult__less__cancel__disj,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.30/0.46 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.30/0.46 & ( ord_less_nat @ M @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_mult_less_cancel_disj
% 0.30/0.46 thf(fact_310_nat__0__less__mult__iff,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 0.30/0.46 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.30/0.46 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_0_less_mult_iff
% 0.30/0.46 thf(fact_311_mult__less__cancel2,axiom,
% 0.30/0.46 ! [M: nat,K: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.30/0.46 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.30/0.46 & ( ord_less_nat @ M @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel2
% 0.30/0.46 thf(fact_312_mult__cancel2,axiom,
% 0.30/0.46 ! [M: nat,K: nat,N: nat] :
% 0.30/0.46 ( ( ( times_times_nat @ M @ K )
% 0.30/0.46 = ( times_times_nat @ N @ K ) )
% 0.30/0.46 = ( ( M = N )
% 0.30/0.46 | ( K = zero_zero_nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_cancel2
% 0.30/0.46 thf(fact_313_neq0__conv,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( N != zero_zero_nat )
% 0.30/0.46 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % neq0_conv
% 0.30/0.46 thf(fact_314_less__nat__zero__code,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.30/0.46
% 0.30/0.46 % less_nat_zero_code
% 0.30/0.46 thf(fact_315_bot__nat__0_Onot__eq__extremum,axiom,
% 0.30/0.46 ! [A: nat] :
% 0.30/0.46 ( ( A != zero_zero_nat )
% 0.30/0.46 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_nat_0.not_eq_extremum
% 0.30/0.46 thf(fact_316_mult__is__0,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ( times_times_nat @ M @ N )
% 0.30/0.46 = zero_zero_nat )
% 0.30/0.46 = ( ( M = zero_zero_nat )
% 0.30/0.46 | ( N = zero_zero_nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_is_0
% 0.30/0.46 thf(fact_317_mult__0__right,axiom,
% 0.30/0.46 ! [M: nat] :
% 0.30/0.46 ( ( times_times_nat @ M @ zero_zero_nat )
% 0.30/0.46 = zero_zero_nat ) ).
% 0.30/0.46
% 0.30/0.46 % mult_0_right
% 0.30/0.46 thf(fact_318_mult__cancel1,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ( times_times_nat @ K @ M )
% 0.30/0.46 = ( times_times_nat @ K @ N ) )
% 0.30/0.46 = ( ( M = N )
% 0.30/0.46 | ( K = zero_zero_nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_cancel1
% 0.30/0.46 thf(fact_319_nat__1__eq__mult__iff,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( one_one_nat
% 0.30/0.46 = ( times_times_nat @ M @ N ) )
% 0.30/0.46 = ( ( M = one_one_nat )
% 0.30/0.46 & ( N = one_one_nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_1_eq_mult_iff
% 0.30/0.46 thf(fact_320_nat__mult__eq__1__iff,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ( times_times_nat @ M @ N )
% 0.30/0.46 = one_one_nat )
% 0.30/0.46 = ( ( M = one_one_nat )
% 0.30/0.46 & ( N = one_one_nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_mult_eq_1_iff
% 0.30/0.46 thf(fact_321_less__one,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( ord_less_nat @ N @ one_one_nat )
% 0.30/0.46 = ( N = zero_zero_nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_one
% 0.30/0.46 thf(fact_322_nat__mult__1,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( times_times_nat @ one_one_nat @ N )
% 0.30/0.46 = N ) ).
% 0.30/0.46
% 0.30/0.46 % nat_mult_1
% 0.30/0.46 thf(fact_323_nat__mult__1__right,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( times_times_nat @ N @ one_one_nat )
% 0.30/0.46 = N ) ).
% 0.30/0.46
% 0.30/0.46 % nat_mult_1_right
% 0.30/0.46 thf(fact_324_linorder__neqE__nat,axiom,
% 0.30/0.46 ! [X: nat,Y3: nat] :
% 0.30/0.46 ( ( X != Y3 )
% 0.30/0.46 => ( ~ ( ord_less_nat @ X @ Y3 )
% 0.30/0.46 => ( ord_less_nat @ Y3 @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_neqE_nat
% 0.30/0.46 thf(fact_325_infinite__descent,axiom,
% 0.30/0.46 ! [P3: nat > $o,N: nat] :
% 0.30/0.46 ( ! [N2: nat] :
% 0.30/0.46 ( ~ ( P3 @ N2 )
% 0.30/0.46 => ? [M2: nat] :
% 0.30/0.46 ( ( ord_less_nat @ M2 @ N2 )
% 0.30/0.46 & ~ ( P3 @ M2 ) ) )
% 0.30/0.46 => ( P3 @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % infinite_descent
% 0.30/0.46 thf(fact_326_nat__less__induct,axiom,
% 0.30/0.46 ! [P3: nat > $o,N: nat] :
% 0.30/0.46 ( ! [N2: nat] :
% 0.30/0.46 ( ! [M2: nat] :
% 0.30/0.46 ( ( ord_less_nat @ M2 @ N2 )
% 0.30/0.46 => ( P3 @ M2 ) )
% 0.30/0.46 => ( P3 @ N2 ) )
% 0.30/0.46 => ( P3 @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_less_induct
% 0.30/0.46 thf(fact_327_less__irrefl__nat,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ~ ( ord_less_nat @ N @ N ) ).
% 0.30/0.46
% 0.30/0.46 % less_irrefl_nat
% 0.30/0.46 thf(fact_328_less__not__refl3,axiom,
% 0.30/0.46 ! [S: nat,T: nat] :
% 0.30/0.46 ( ( ord_less_nat @ S @ T )
% 0.30/0.46 => ( S != T ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_not_refl3
% 0.30/0.46 thf(fact_329_less__not__refl2,axiom,
% 0.30/0.46 ! [N: nat,M: nat] :
% 0.30/0.46 ( ( ord_less_nat @ N @ M )
% 0.30/0.46 => ( M != N ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_not_refl2
% 0.30/0.46 thf(fact_330_less__not__refl,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ~ ( ord_less_nat @ N @ N ) ).
% 0.30/0.46
% 0.30/0.46 % less_not_refl
% 0.30/0.46 thf(fact_331_nat__neq__iff,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( M != N )
% 0.30/0.46 = ( ( ord_less_nat @ M @ N )
% 0.30/0.46 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_neq_iff
% 0.30/0.46 thf(fact_332_gr0I,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( N != zero_zero_nat )
% 0.30/0.46 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr0I
% 0.30/0.46 thf(fact_333_not__gr0,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.30/0.46 = ( N = zero_zero_nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_gr0
% 0.30/0.46 thf(fact_334_not__less0,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.30/0.46
% 0.30/0.46 % not_less0
% 0.30/0.46 thf(fact_335_less__zeroE,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.30/0.46
% 0.30/0.46 % less_zeroE
% 0.30/0.46 thf(fact_336_gr__implies__not0,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_nat @ M @ N )
% 0.30/0.46 => ( N != zero_zero_nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr_implies_not0
% 0.30/0.46 thf(fact_337_infinite__descent0,axiom,
% 0.30/0.46 ! [P3: nat > $o,N: nat] :
% 0.30/0.46 ( ( P3 @ zero_zero_nat )
% 0.30/0.46 => ( ! [N2: nat] :
% 0.30/0.46 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.30/0.46 => ( ~ ( P3 @ N2 )
% 0.30/0.46 => ? [M2: nat] :
% 0.30/0.46 ( ( ord_less_nat @ M2 @ N2 )
% 0.30/0.46 & ~ ( P3 @ M2 ) ) ) )
% 0.30/0.46 => ( P3 @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % infinite_descent0
% 0.30/0.46 thf(fact_338_bot__nat__0_Oextremum__strict,axiom,
% 0.30/0.46 ! [A: nat] :
% 0.30/0.46 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.30/0.46
% 0.30/0.46 % bot_nat_0.extremum_strict
% 0.30/0.46 thf(fact_339_mult__less__mono1,axiom,
% 0.30/0.46 ! [I: nat,J: nat,K: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I @ J )
% 0.30/0.46 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.30/0.46 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_mono1
% 0.30/0.46 thf(fact_340_mult__less__mono2,axiom,
% 0.30/0.46 ! [I: nat,J: nat,K: nat] :
% 0.30/0.46 ( ( ord_less_nat @ I @ J )
% 0.30/0.46 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.30/0.46 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_mono2
% 0.30/0.46 thf(fact_341_mult__0,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( times_times_nat @ zero_zero_nat @ N )
% 0.30/0.46 = zero_zero_nat ) ).
% 0.30/0.46
% 0.30/0.46 % mult_0
% 0.30/0.46 thf(fact_342_nat__mult__eq__cancel1,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.30/0.46 => ( ( ( times_times_nat @ K @ M )
% 0.30/0.46 = ( times_times_nat @ K @ N ) )
% 0.30/0.46 = ( M = N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_mult_eq_cancel1
% 0.30/0.46 thf(fact_343_nat__mult__less__cancel1,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.30/0.46 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.30/0.46 = ( ord_less_nat @ M @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_mult_less_cancel1
% 0.30/0.46 thf(fact_344_nat__mult__eq__cancel__disj,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ( times_times_nat @ K @ M )
% 0.30/0.46 = ( times_times_nat @ K @ N ) )
% 0.30/0.46 = ( ( K = zero_zero_nat )
% 0.30/0.46 | ( M = N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_mult_eq_cancel_disj
% 0.30/0.46 thf(fact_345_mult__eq__self__implies__10,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( M
% 0.30/0.46 = ( times_times_nat @ M @ N ) )
% 0.30/0.46 => ( ( N = one_one_nat )
% 0.30/0.46 | ( M = zero_zero_nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_eq_self_implies_10
% 0.30/0.46
% 0.30/0.46 % Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 ( ( descar2095969287nges_a @ ys )
% 0.30/0.46 = ( descar2095969287nges_a @ ( coeffs_a @ g ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 2.56/1.44 ---- Embedded in THF ---
% 2.56/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.56/1.44 %%% Generated on Tue Feb 24 08:24:17 EST 2026
% 2.56/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 2.56/1.44 %%% Logic specification used:
% 2.56/1.44 %%% thf(spec, logic, $$dhol).
% 2.56/1.44
% 2.56/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.t7mfK5zq2L/DTF2DTF27787.p
% See solution above
% 2.56/1.44 ------------------------
% 2.56/1.46 ---- Cleaned THF ---
% 2.56/1.46 thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J,type,
% 2.56/1.46 poly_poly_a: $tType ).
% 2.56/1.46
% 2.56/1.46 thf(ty_n_t__List__Olist_It__Polynomial__Opoly_Itf__a_J_J,type,
% 2.56/1.46 list_poly_a: $tType ).
% 2.56/1.46
% 2.56/1.46 thf(ty_n_t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 2.56/1.46 list_list_a: $tType ).
% 2.56/1.46
% 2.56/1.46 thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 2.56/1.46 poly_nat: $tType ).
% 2.56/1.46
% 2.56/1.46 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 2.56/1.46 list_nat: $tType ).
% 2.56/1.46
% 2.56/1.46 thf(ty_n_t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 poly_a: $tType ).
% 2.56/1.46
% 2.56/1.46 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 2.56/1.46 list_a: $tType ).
% 2.56/1.46
% 2.56/1.46 thf(ty_n_t__Nat__Onat,type,
% 2.56/1.46 nat: $tType ).
% 2.56/1.46
% 2.56/1.46 thf(ty_n_tf__a,type,
% 2.56/1.46 a: $tType ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Opsums_001t__Nat__Onat,type,
% 2.56/1.46 descar226543321ms_nat: list_nat > list_nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Opsums_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 descar282223555poly_a: list_poly_a > list_poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Opsums_001tf__a,type,
% 2.56/1.46 descar1375166517sums_a: list_a > list_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Oreduce__root_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 descar434775507poly_a: poly_a > poly_poly_a > poly_poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Oreduce__root_001tf__a,type,
% 2.56/1.46 descar466059845root_a: a > poly_a > poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Osign__changes_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 descar357075861poly_a: list_poly_a > nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Descartes__Sign__Rule__Mirabelle__gwrulepwnb_Osign__changes_001tf__a,type,
% 2.56/1.46 descar2095969287nges_a: list_a > nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 2.56/1.46 one_one_nat: nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 2.56/1.46 one_one_poly_nat: poly_nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J,type,
% 2.56/1.46 one_one_poly_poly_a: poly_poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 one_one_poly_a: poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Groups_Oone__class_Oone_001tf__a,type,
% 2.56/1.46 one_one_a: a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 2.56/1.46 times_times_nat: nat > nat > nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 times_times_poly_a: poly_a > poly_a > poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Groups_Otimes__class_Otimes_001tf__a,type,
% 2.56/1.46 times_times_a: a > a > a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 uminus_uminus_poly_a: poly_a > poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Groups_Ouminus__class_Ouminus_001tf__a,type,
% 2.56/1.46 uminus_uminus_a: a > a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 2.56/1.46 zero_zero_nat: nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Nat__Onat_J,type,
% 2.56/1.46 zero_zero_poly_nat: poly_nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J,type,
% 2.56/1.46 zero_z2096148049poly_a: poly_poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 zero_zero_poly_a: poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Groups_Ozero__class_Ozero_001tf__a,type,
% 2.56/1.46 zero_zero_a: a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 2.56/1.46 append_nat: list_nat > list_nat > list_nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_List_Oappend_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 append_poly_a: list_poly_a > list_poly_a > list_poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_List_Oappend_001tf__a,type,
% 2.56/1.46 append_a: list_a > list_a > list_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_List_Olist_OCons_001t__List__Olist_Itf__a_J,type,
% 2.56/1.46 cons_list_a: list_a > list_list_a > list_list_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 2.56/1.46 cons_nat: nat > list_nat > list_nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_List_Olist_OCons_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 cons_poly_a: poly_a > list_poly_a > list_poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_List_Olist_OCons_001tf__a,type,
% 2.56/1.46 cons_a: a > list_a > list_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__a_J,type,
% 2.56/1.46 nil_list_a: list_list_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 2.56/1.46 nil_nat: list_nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_List_Olist_ONil_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 nil_poly_a: list_poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_List_Olist_ONil_001tf__a,type,
% 2.56/1.46 nil_a: list_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_List_Onull_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 null_poly_a: list_poly_a > $o ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_List_Onull_001tf__a,type,
% 2.56/1.46 null_a: list_a > $o ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 2.56/1.46 ord_less_nat: nat > nat > $o ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 ord_less_poly_a: poly_a > poly_a > $o ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Orderings_Oord__class_Oless_001tf__a,type,
% 2.56/1.46 ord_less_a: a > a > $o ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Polynomial_OPoly_001t__Nat__Onat,type,
% 2.56/1.46 poly_nat2: list_nat > poly_nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Polynomial_OPoly_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 poly_poly_a2: list_poly_a > poly_poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Polynomial_OPoly_001tf__a,type,
% 2.56/1.46 poly_a2: list_a > poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Polynomial_Ocoeffs_001t__Nat__Onat,type,
% 2.56/1.46 coeffs_nat: poly_nat > list_nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Polynomial_Ocoeffs_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 coeffs_poly_a: poly_poly_a > list_poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Polynomial_Ocoeffs_001tf__a,type,
% 2.56/1.46 coeffs_a: poly_a > list_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Polynomial_Ois__zero_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 is_zero_poly_a: poly_poly_a > $o ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Polynomial_Ois__zero_001tf__a,type,
% 2.56/1.46 is_zero_a: poly_a > $o ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Polynomial_OpCons_001t__Nat__Onat,type,
% 2.56/1.46 pCons_nat: nat > poly_nat > poly_nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 pCons_poly_a: poly_a > poly_poly_a > poly_poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Polynomial_OpCons_001tf__a,type,
% 2.56/1.46 pCons_a: a > poly_a > poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Polynomial_Osmult_001t__Nat__Onat,type,
% 2.56/1.46 smult_nat: nat > poly_nat > poly_nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Polynomial_Osmult_001t__Polynomial__Opoly_Itf__a_J,type,
% 2.56/1.46 smult_poly_a: poly_a > poly_poly_a > poly_poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_c_Polynomial_Osmult_001tf__a,type,
% 2.56/1.46 smult_a: a > poly_a > poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_v_g,type,
% 2.56/1.46 g: poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_v_v,type,
% 2.56/1.46 v: poly_a > nat ).
% 2.56/1.46
% 2.56/1.46 thf(sy_v_xs____,type,
% 2.56/1.46 xs: list_a ).
% 2.56/1.46
% 2.56/1.46 thf(sy_v_ys____,type,
% 2.56/1.46 ys: list_a ).
% 2.56/1.46
% 2.56/1.46 thf(fact_0_v__def,axiom,
% 2.56/1.46 ( v
% 2.56/1.46 = ( ^ [F: poly_a] : ( descar2095969287nges_a @ ( coeffs_a @ F ) ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_1_nz,axiom,
% 2.56/1.46 g != zero_zero_poly_a ).
% 2.56/1.46
% 2.56/1.46 thf(fact_2_coeffs__eq__iff,axiom,
% 2.56/1.46 ( ( ^ [Y: poly_poly_a,Z: poly_poly_a] : ( Y = Z ) )
% 2.56/1.46 = ( ^ [P: poly_poly_a,Q: poly_poly_a] :
% 2.56/1.46 ( ( coeffs_poly_a @ P )
% 2.56/1.46 = ( coeffs_poly_a @ Q ) ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_3_coeffs__eq__iff,axiom,
% 2.56/1.46 ( ( ^ [Y: poly_a,Z: poly_a] : ( Y = Z ) )
% 2.56/1.46 = ( ^ [P: poly_a,Q: poly_a] :
% 2.56/1.46 ( ( coeffs_a @ P )
% 2.56/1.46 = ( coeffs_a @ Q ) ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_4_ys,axiom,
% 2.56/1.46 ( ys
% 2.56/1.46 = ( descar1375166517sums_a @ xs ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_5_sign__changes__coeff__sign__changes,axiom,
% 2.56/1.46 ! [Xs: list_poly_a,P2: poly_poly_a] :
% 2.56/1.46 ( ( ( poly_poly_a2 @ Xs )
% 2.56/1.46 = P2 )
% 2.56/1.46 => ( ( descar357075861poly_a @ Xs )
% 2.56/1.46 = ( descar357075861poly_a @ ( coeffs_poly_a @ P2 ) ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_6_sign__changes__coeff__sign__changes,axiom,
% 2.56/1.46 ! [Xs: list_a,P2: poly_a] :
% 2.56/1.46 ( ( ( poly_a2 @ Xs )
% 2.56/1.46 = P2 )
% 2.56/1.46 => ( ( descar2095969287nges_a @ Xs )
% 2.56/1.46 = ( descar2095969287nges_a @ ( coeffs_a @ P2 ) ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_7_ys__def,axiom,
% 2.56/1.46 ( ys
% 2.56/1.46 = ( append_a @ ( coeffs_a @ g ) @ ( cons_a @ zero_zero_a @ nil_a ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_8_coeff__sign__changes__reduce__root,axiom,
% 2.56/1.46 ! [A: poly_a,P2: poly_poly_a] :
% 2.56/1.46 ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 2.56/1.46 => ( ( descar357075861poly_a @ ( coeffs_poly_a @ ( descar434775507poly_a @ A @ P2 ) ) )
% 2.56/1.46 = ( descar357075861poly_a @ ( coeffs_poly_a @ P2 ) ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_9_coeff__sign__changes__reduce__root,axiom,
% 2.56/1.46 ! [A: a,P2: poly_a] :
% 2.56/1.46 ( ( ord_less_a @ zero_zero_a @ A )
% 2.56/1.46 => ( ( descar2095969287nges_a @ ( coeffs_a @ ( descar466059845root_a @ A @ P2 ) ) )
% 2.56/1.46 = ( descar2095969287nges_a @ ( coeffs_a @ P2 ) ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_10_is__zero__def,axiom,
% 2.56/1.46 ( is_zero_poly_a
% 2.56/1.46 = ( ^ [P: poly_poly_a] : ( null_poly_a @ ( coeffs_poly_a @ P ) ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_11_is__zero__def,axiom,
% 2.56/1.46 ( is_zero_a
% 2.56/1.46 = ( ^ [P: poly_a] : ( null_a @ ( coeffs_a @ P ) ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_12_Poly__coeffs,axiom,
% 2.56/1.46 ! [P2: poly_poly_a] :
% 2.56/1.46 ( ( poly_poly_a2 @ ( coeffs_poly_a @ P2 ) )
% 2.56/1.46 = P2 ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_13_Poly__coeffs,axiom,
% 2.56/1.46 ! [P2: poly_a] :
% 2.56/1.46 ( ( poly_a2 @ ( coeffs_a @ P2 ) )
% 2.56/1.46 = P2 ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_14_sign__changes__Nil,axiom,
% 2.56/1.46 ( ( descar357075861poly_a @ nil_poly_a )
% 2.56/1.46 = zero_zero_nat ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_15_sign__changes__Nil,axiom,
% 2.56/1.46 ( ( descar2095969287nges_a @ nil_a )
% 2.56/1.46 = zero_zero_nat ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_16_xs__def,axiom,
% 2.56/1.46 ( xs
% 2.56/1.46 = ( coeffs_a @ ( times_times_poly_a @ ( pCons_a @ one_one_a @ ( pCons_a @ ( uminus_uminus_a @ one_one_a ) @ zero_zero_poly_a ) ) @ g ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_17_coeff__sign__changes__smult,axiom,
% 2.56/1.46 ! [A: a,P2: poly_a] :
% 2.56/1.46 ( ( ord_less_a @ zero_zero_a @ A )
% 2.56/1.46 => ( ( descar2095969287nges_a @ ( coeffs_a @ ( smult_a @ A @ P2 ) ) )
% 2.56/1.46 = ( descar2095969287nges_a @ ( coeffs_a @ P2 ) ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_18_coeff__sign__changes__smult,axiom,
% 2.56/1.46 ! [A: poly_a,P2: poly_poly_a] :
% 2.56/1.46 ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 2.56/1.46 => ( ( descar357075861poly_a @ ( coeffs_poly_a @ ( smult_poly_a @ A @ P2 ) ) )
% 2.56/1.46 = ( descar357075861poly_a @ ( coeffs_poly_a @ P2 ) ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_19_sign__changes__0__Cons,axiom,
% 2.56/1.46 ! [Xs: list_a] :
% 2.56/1.46 ( ( descar2095969287nges_a @ ( cons_a @ zero_zero_a @ Xs ) )
% 2.56/1.46 = ( descar2095969287nges_a @ Xs ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_20_sign__changes__0__Cons,axiom,
% 2.56/1.46 ! [Xs: list_poly_a] :
% 2.56/1.46 ( ( descar357075861poly_a @ ( cons_poly_a @ zero_zero_poly_a @ Xs ) )
% 2.56/1.46 = ( descar357075861poly_a @ Xs ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_21_sign__changes__Cons__Cons__0,axiom,
% 2.56/1.46 ! [X: a,Xs: list_a] :
% 2.56/1.46 ( ( descar2095969287nges_a @ ( cons_a @ X @ ( cons_a @ zero_zero_a @ Xs ) ) )
% 2.56/1.46 = ( descar2095969287nges_a @ ( cons_a @ X @ Xs ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_22_sign__changes__Cons__Cons__0,axiom,
% 2.56/1.46 ! [X: poly_a,Xs: list_poly_a] :
% 2.56/1.46 ( ( descar357075861poly_a @ ( cons_poly_a @ X @ ( cons_poly_a @ zero_zero_poly_a @ Xs ) ) )
% 2.56/1.46 = ( descar357075861poly_a @ ( cons_poly_a @ X @ Xs ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_23_pCons__eq__iff,axiom,
% 2.56/1.46 ! [A: a,P2: poly_a,B: a,Q2: poly_a] :
% 2.56/1.46 ( ( ( pCons_a @ A @ P2 )
% 2.56/1.46 = ( pCons_a @ B @ Q2 ) )
% 2.56/1.46 = ( ( A = B )
% 2.56/1.46 & ( P2 = Q2 ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_24_minus__pCons,axiom,
% 2.56/1.46 ! [A: a,P2: poly_a] :
% 2.56/1.46 ( ( uminus_uminus_poly_a @ ( pCons_a @ A @ P2 ) )
% 2.56/1.46 = ( pCons_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_poly_a @ P2 ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_25_smult__smult,axiom,
% 2.56/1.46 ! [A: poly_a,B: poly_a,P2: poly_poly_a] :
% 2.56/1.46 ( ( smult_poly_a @ A @ ( smult_poly_a @ B @ P2 ) )
% 2.56/1.46 = ( smult_poly_a @ ( times_times_poly_a @ A @ B ) @ P2 ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_26_smult__smult,axiom,
% 2.56/1.46 ! [A: nat,B: nat,P2: poly_nat] :
% 2.56/1.46 ( ( smult_nat @ A @ ( smult_nat @ B @ P2 ) )
% 2.56/1.46 = ( smult_nat @ ( times_times_nat @ A @ B ) @ P2 ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_27_smult__1__left,axiom,
% 2.56/1.46 ! [P2: poly_a] :
% 2.56/1.46 ( ( smult_a @ one_one_a @ P2 )
% 2.56/1.46 = P2 ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_28_smult__1__left,axiom,
% 2.56/1.46 ! [P2: poly_nat] :
% 2.56/1.46 ( ( smult_nat @ one_one_nat @ P2 )
% 2.56/1.46 = P2 ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_29_smult__minus__left,axiom,
% 2.56/1.46 ! [A: a,P2: poly_a] :
% 2.56/1.46 ( ( smult_a @ ( uminus_uminus_a @ A ) @ P2 )
% 2.56/1.46 = ( uminus_uminus_poly_a @ ( smult_a @ A @ P2 ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_30_smult__0__right,axiom,
% 2.56/1.46 ! [A: a] :
% 2.56/1.46 ( ( smult_a @ A @ zero_zero_poly_a )
% 2.56/1.46 = zero_zero_poly_a ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_31_mult__smult__left,axiom,
% 2.56/1.46 ! [A: a,P2: poly_a,Q2: poly_a] :
% 2.56/1.46 ( ( times_times_poly_a @ ( smult_a @ A @ P2 ) @ Q2 )
% 2.56/1.46 = ( smult_a @ A @ ( times_times_poly_a @ P2 @ Q2 ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_32_mult__smult__right,axiom,
% 2.56/1.46 ! [P2: poly_a,A: a,Q2: poly_a] :
% 2.56/1.46 ( ( times_times_poly_a @ P2 @ ( smult_a @ A @ Q2 ) )
% 2.56/1.46 = ( smult_a @ A @ ( times_times_poly_a @ P2 @ Q2 ) ) ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_33_pCons__0__0,axiom,
% 2.56/1.46 ( ( pCons_poly_a @ zero_zero_poly_a @ zero_z2096148049poly_a )
% 2.56/1.46 = zero_z2096148049poly_a ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_34_pCons__0__0,axiom,
% 2.56/1.46 ( ( pCons_a @ zero_zero_a @ zero_zero_poly_a )
% 2.56/1.46 = zero_zero_poly_a ) ).
% 2.56/1.46
% 2.56/1.46 thf(fact_35_pCons__0__0,axiom,
% 2.56/1.46 ( ( pCons_nat @ zero_zero_nat @ zero_zero_poly_nat )
% 2.56/1.46 = zero_zero_poly_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_36_pCons__eq__0__iff,axiom,
% 2.56/1.47 ! [A: poly_a,P2: poly_poly_a] :
% 2.56/1.47 ( ( ( pCons_poly_a @ A @ P2 )
% 2.56/1.47 = zero_z2096148049poly_a )
% 2.56/1.47 = ( ( A = zero_zero_poly_a )
% 2.56/1.47 & ( P2 = zero_z2096148049poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_37_pCons__eq__0__iff,axiom,
% 2.56/1.47 ! [A: nat,P2: poly_nat] :
% 2.56/1.47 ( ( ( pCons_nat @ A @ P2 )
% 2.56/1.47 = zero_zero_poly_nat )
% 2.56/1.47 = ( ( A = zero_zero_nat )
% 2.56/1.47 & ( P2 = zero_zero_poly_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_38_pCons__eq__0__iff,axiom,
% 2.56/1.47 ! [A: a,P2: poly_a] :
% 2.56/1.47 ( ( ( pCons_a @ A @ P2 )
% 2.56/1.47 = zero_zero_poly_a )
% 2.56/1.47 = ( ( A = zero_zero_a )
% 2.56/1.47 & ( P2 = zero_zero_poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_39_one__poly__eq__simps_I2_J,axiom,
% 2.56/1.47 ( ( pCons_nat @ one_one_nat @ zero_zero_poly_nat )
% 2.56/1.47 = one_one_poly_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_40_one__poly__eq__simps_I2_J,axiom,
% 2.56/1.47 ( ( pCons_a @ one_one_a @ zero_zero_poly_a )
% 2.56/1.47 = one_one_poly_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_41_one__poly__eq__simps_I1_J,axiom,
% 2.56/1.47 ( one_one_poly_nat
% 2.56/1.47 = ( pCons_nat @ one_one_nat @ zero_zero_poly_nat ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_42_one__poly__eq__simps_I1_J,axiom,
% 2.56/1.47 ( one_one_poly_a
% 2.56/1.47 = ( pCons_a @ one_one_a @ zero_zero_poly_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_43_smult__0__left,axiom,
% 2.56/1.47 ! [P2: poly_poly_a] :
% 2.56/1.47 ( ( smult_poly_a @ zero_zero_poly_a @ P2 )
% 2.56/1.47 = zero_z2096148049poly_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_44_smult__0__left,axiom,
% 2.56/1.47 ! [P2: poly_a] :
% 2.56/1.47 ( ( smult_a @ zero_zero_a @ P2 )
% 2.56/1.47 = zero_zero_poly_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_45_smult__0__left,axiom,
% 2.56/1.47 ! [P2: poly_nat] :
% 2.56/1.47 ( ( smult_nat @ zero_zero_nat @ P2 )
% 2.56/1.47 = zero_zero_poly_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_46_smult__eq__0__iff,axiom,
% 2.56/1.47 ! [A: poly_a,P2: poly_poly_a] :
% 2.56/1.47 ( ( ( smult_poly_a @ A @ P2 )
% 2.56/1.47 = zero_z2096148049poly_a )
% 2.56/1.47 = ( ( A = zero_zero_poly_a )
% 2.56/1.47 | ( P2 = zero_z2096148049poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_47_smult__eq__0__iff,axiom,
% 2.56/1.47 ! [A: nat,P2: poly_nat] :
% 2.56/1.47 ( ( ( smult_nat @ A @ P2 )
% 2.56/1.47 = zero_zero_poly_nat )
% 2.56/1.47 = ( ( A = zero_zero_nat )
% 2.56/1.47 | ( P2 = zero_zero_poly_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_48_smult__eq__0__iff,axiom,
% 2.56/1.47 ! [A: a,P2: poly_a] :
% 2.56/1.47 ( ( ( smult_a @ A @ P2 )
% 2.56/1.47 = zero_zero_poly_a )
% 2.56/1.47 = ( ( A = zero_zero_a )
% 2.56/1.47 | ( P2 = zero_zero_poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_49_smult__pCons,axiom,
% 2.56/1.47 ! [A: a,B: a,P2: poly_a] :
% 2.56/1.47 ( ( smult_a @ A @ ( pCons_a @ B @ P2 ) )
% 2.56/1.47 = ( pCons_a @ ( times_times_a @ A @ B ) @ ( smult_a @ A @ P2 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_50_smult__pCons,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a,P2: poly_poly_a] :
% 2.56/1.47 ( ( smult_poly_a @ A @ ( pCons_poly_a @ B @ P2 ) )
% 2.56/1.47 = ( pCons_poly_a @ ( times_times_poly_a @ A @ B ) @ ( smult_poly_a @ A @ P2 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_51_smult__pCons,axiom,
% 2.56/1.47 ! [A: nat,B: nat,P2: poly_nat] :
% 2.56/1.47 ( ( smult_nat @ A @ ( pCons_nat @ B @ P2 ) )
% 2.56/1.47 = ( pCons_nat @ ( times_times_nat @ A @ B ) @ ( smult_nat @ A @ P2 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_52_coeffs__eq__Nil,axiom,
% 2.56/1.47 ! [P2: poly_poly_a] :
% 2.56/1.47 ( ( ( coeffs_poly_a @ P2 )
% 2.56/1.47 = nil_poly_a )
% 2.56/1.47 = ( P2 = zero_z2096148049poly_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_53_coeffs__eq__Nil,axiom,
% 2.56/1.47 ! [P2: poly_a] :
% 2.56/1.47 ( ( ( coeffs_a @ P2 )
% 2.56/1.47 = nil_a )
% 2.56/1.47 = ( P2 = zero_zero_poly_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_54_coeffs__0__eq__Nil,axiom,
% 2.56/1.47 ( ( coeffs_poly_a @ zero_z2096148049poly_a )
% 2.56/1.47 = nil_poly_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_55_coeffs__0__eq__Nil,axiom,
% 2.56/1.47 ( ( coeffs_a @ zero_zero_poly_a )
% 2.56/1.47 = nil_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_56_psums__0__Cons,axiom,
% 2.56/1.47 ! [Xs: list_poly_a] :
% 2.56/1.47 ( ( descar282223555poly_a @ ( cons_poly_a @ zero_zero_poly_a @ Xs ) )
% 2.56/1.47 = ( cons_poly_a @ zero_zero_poly_a @ ( descar282223555poly_a @ Xs ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_57_psums__0__Cons,axiom,
% 2.56/1.47 ! [Xs: list_nat] :
% 2.56/1.47 ( ( descar226543321ms_nat @ ( cons_nat @ zero_zero_nat @ Xs ) )
% 2.56/1.47 = ( cons_nat @ zero_zero_nat @ ( descar226543321ms_nat @ Xs ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_58_psums__0__Cons,axiom,
% 2.56/1.47 ! [Xs: list_a] :
% 2.56/1.47 ( ( descar1375166517sums_a @ ( cons_a @ zero_zero_a @ Xs ) )
% 2.56/1.47 = ( cons_a @ zero_zero_a @ ( descar1375166517sums_a @ Xs ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_59_coeffs__1__eq,axiom,
% 2.56/1.47 ( ( coeffs_poly_a @ one_one_poly_poly_a )
% 2.56/1.47 = ( cons_poly_a @ one_one_poly_a @ nil_poly_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_60_coeffs__1__eq,axiom,
% 2.56/1.47 ( ( coeffs_a @ one_one_poly_a )
% 2.56/1.47 = ( cons_a @ one_one_a @ nil_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_61_coeffs__1__eq,axiom,
% 2.56/1.47 ( ( coeffs_nat @ one_one_poly_nat )
% 2.56/1.47 = ( cons_nat @ one_one_nat @ nil_nat ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_62_sign__changes__singleton,axiom,
% 2.56/1.47 ! [X: a] :
% 2.56/1.47 ( ( descar2095969287nges_a @ ( cons_a @ X @ nil_a ) )
% 2.56/1.47 = zero_zero_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_63_sign__changes__singleton,axiom,
% 2.56/1.47 ! [X: poly_a] :
% 2.56/1.47 ( ( descar357075861poly_a @ ( cons_poly_a @ X @ nil_poly_a ) )
% 2.56/1.47 = zero_zero_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_64__092_060open_062sign__changes_Axs_A_061_Av_A_I_091_0581_058_058_Ha_M_A_N_A_I1_058_058_Ha_J_058_093_A_K_Ag_J_092_060close_062,axiom,
% 2.56/1.47 ( ( descar2095969287nges_a @ xs )
% 2.56/1.47 = ( v @ ( times_times_poly_a @ ( pCons_a @ one_one_a @ ( pCons_a @ ( uminus_uminus_a @ one_one_a ) @ zero_zero_poly_a ) ) @ g ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_65_Poly__snoc__zero,axiom,
% 2.56/1.47 ! [As: list_poly_a] :
% 2.56/1.47 ( ( poly_poly_a2 @ ( append_poly_a @ As @ ( cons_poly_a @ zero_zero_poly_a @ nil_poly_a ) ) )
% 2.56/1.47 = ( poly_poly_a2 @ As ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_66_Poly__snoc__zero,axiom,
% 2.56/1.47 ! [As: list_a] :
% 2.56/1.47 ( ( poly_a2 @ ( append_a @ As @ ( cons_a @ zero_zero_a @ nil_a ) ) )
% 2.56/1.47 = ( poly_a2 @ As ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_67_Poly__snoc__zero,axiom,
% 2.56/1.47 ! [As: list_nat] :
% 2.56/1.47 ( ( poly_nat2 @ ( append_nat @ As @ ( cons_nat @ zero_zero_nat @ nil_nat ) ) )
% 2.56/1.47 = ( poly_nat2 @ As ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_68_Poly_Osimps_I2_J,axiom,
% 2.56/1.47 ! [A: a,As: list_a] :
% 2.56/1.47 ( ( poly_a2 @ ( cons_a @ A @ As ) )
% 2.56/1.47 = ( pCons_a @ A @ ( poly_a2 @ As ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_69_Poly_Osimps_I1_J,axiom,
% 2.56/1.47 ( ( poly_a2 @ nil_a )
% 2.56/1.47 = zero_zero_poly_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_70_psums_Osimps_I2_J,axiom,
% 2.56/1.47 ! [X: a] :
% 2.56/1.47 ( ( descar1375166517sums_a @ ( cons_a @ X @ nil_a ) )
% 2.56/1.47 = ( cons_a @ X @ nil_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_71_psums_Osimps_I1_J,axiom,
% 2.56/1.47 ( ( descar1375166517sums_a @ nil_a )
% 2.56/1.47 = nil_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_72_pCons__one,axiom,
% 2.56/1.47 ( ( pCons_nat @ one_one_nat @ zero_zero_poly_nat )
% 2.56/1.47 = one_one_poly_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_73_pCons__one,axiom,
% 2.56/1.47 ( ( pCons_a @ one_one_a @ zero_zero_poly_a )
% 2.56/1.47 = one_one_poly_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_74_pCons__cases,axiom,
% 2.56/1.47 ! [P2: poly_a] :
% 2.56/1.47 ~ ! [A2: a,Q3: poly_a] :
% 2.56/1.47 ( P2
% 2.56/1.47 != ( pCons_a @ A2 @ Q3 ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_75_is__zero__null,axiom,
% 2.56/1.47 ( is_zero_a
% 2.56/1.47 = ( ^ [P: poly_a] : ( P = zero_zero_poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_76_pCons__induct,axiom,
% 2.56/1.47 ! [P3: poly_poly_a > $o,P2: poly_poly_a] :
% 2.56/1.47 ( ( P3 @ zero_z2096148049poly_a )
% 2.56/1.47 => ( ! [A2: poly_a,P4: poly_poly_a] :
% 2.56/1.47 ( ( ( A2 != zero_zero_poly_a )
% 2.56/1.47 | ( P4 != zero_z2096148049poly_a ) )
% 2.56/1.47 => ( ( P3 @ P4 )
% 2.56/1.47 => ( P3 @ ( pCons_poly_a @ A2 @ P4 ) ) ) )
% 2.56/1.47 => ( P3 @ P2 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_77_pCons__induct,axiom,
% 2.56/1.47 ! [P3: poly_nat > $o,P2: poly_nat] :
% 2.56/1.47 ( ( P3 @ zero_zero_poly_nat )
% 2.56/1.47 => ( ! [A2: nat,P4: poly_nat] :
% 2.56/1.47 ( ( ( A2 != zero_zero_nat )
% 2.56/1.47 | ( P4 != zero_zero_poly_nat ) )
% 2.56/1.47 => ( ( P3 @ P4 )
% 2.56/1.47 => ( P3 @ ( pCons_nat @ A2 @ P4 ) ) ) )
% 2.56/1.47 => ( P3 @ P2 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_78_pCons__induct,axiom,
% 2.56/1.47 ! [P3: poly_a > $o,P2: poly_a] :
% 2.56/1.47 ( ( P3 @ zero_zero_poly_a )
% 2.56/1.47 => ( ! [A2: a,P4: poly_a] :
% 2.56/1.47 ( ( ( A2 != zero_zero_a )
% 2.56/1.47 | ( P4 != zero_zero_poly_a ) )
% 2.56/1.47 => ( ( P3 @ P4 )
% 2.56/1.47 => ( P3 @ ( pCons_a @ A2 @ P4 ) ) ) )
% 2.56/1.47 => ( P3 @ P2 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_79_pderiv_Ocases,axiom,
% 2.56/1.47 ! [X: poly_a] :
% 2.56/1.47 ~ ! [A2: a,P4: poly_a] :
% 2.56/1.47 ( X
% 2.56/1.47 != ( pCons_a @ A2 @ P4 ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_80_poly__induct2,axiom,
% 2.56/1.47 ! [P3: poly_a > poly_a > $o,P2: poly_a,Q2: poly_a] :
% 2.56/1.47 ( ( P3 @ zero_zero_poly_a @ zero_zero_poly_a )
% 2.56/1.47 => ( ! [A2: a,P4: poly_a,B2: a,Q3: poly_a] :
% 2.56/1.47 ( ( P3 @ P4 @ Q3 )
% 2.56/1.47 => ( P3 @ ( pCons_a @ A2 @ P4 ) @ ( pCons_a @ B2 @ Q3 ) ) )
% 2.56/1.47 => ( P3 @ P2 @ Q2 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_81_pderiv_Oinduct,axiom,
% 2.56/1.47 ! [P3: poly_a > $o,A0: poly_a] :
% 2.56/1.47 ( ! [A2: a,P4: poly_a] :
% 2.56/1.47 ( ( ( P4 != zero_zero_poly_a )
% 2.56/1.47 => ( P3 @ P4 ) )
% 2.56/1.47 => ( P3 @ ( pCons_a @ A2 @ P4 ) ) )
% 2.56/1.47 => ( P3 @ A0 ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_82_mult__poly__0__left,axiom,
% 2.56/1.47 ! [Q2: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ zero_zero_poly_a @ Q2 )
% 2.56/1.47 = zero_zero_poly_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_83_mult__poly__0__right,axiom,
% 2.56/1.47 ! [P2: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ P2 @ zero_zero_poly_a )
% 2.56/1.47 = zero_zero_poly_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_84_plus__coeffs_Oinduct,axiom,
% 2.56/1.47 ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 2.56/1.47 ( ! [Xs2: list_a] : ( P3 @ Xs2 @ nil_a )
% 2.56/1.47 => ( ! [V: a,Va: list_a] : ( P3 @ nil_a @ ( cons_a @ V @ Va ) )
% 2.56/1.47 => ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
% 2.56/1.47 ( ( P3 @ Xs2 @ Ys )
% 2.56/1.47 => ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) )
% 2.56/1.47 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_85_not__0__coeffs__not__Nil,axiom,
% 2.56/1.47 ! [P2: poly_poly_a] :
% 2.56/1.47 ( ( P2 != zero_z2096148049poly_a )
% 2.56/1.47 => ( ( coeffs_poly_a @ P2 )
% 2.56/1.47 != nil_poly_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_86_not__0__coeffs__not__Nil,axiom,
% 2.56/1.47 ! [P2: poly_a] :
% 2.56/1.47 ( ( P2 != zero_zero_poly_a )
% 2.56/1.47 => ( ( coeffs_a @ P2 )
% 2.56/1.47 != nil_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_87_minus__poly__rev__list_Oinduct,axiom,
% 2.56/1.47 ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 2.56/1.47 ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
% 2.56/1.47 ( ( P3 @ Xs2 @ Ys )
% 2.56/1.47 => ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) )
% 2.56/1.47 => ( ! [Xs2: list_a] : ( P3 @ Xs2 @ nil_a )
% 2.56/1.47 => ( ! [Y2: a,Ys: list_a] : ( P3 @ nil_a @ ( cons_a @ Y2 @ Ys ) )
% 2.56/1.47 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_88_synthetic__div__unique__lemma,axiom,
% 2.56/1.47 ! [C: a,P2: poly_a,A: a] :
% 2.56/1.47 ( ( ( smult_a @ C @ P2 )
% 2.56/1.47 = ( pCons_a @ A @ P2 ) )
% 2.56/1.47 => ( P2 = zero_zero_poly_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_89_psums_Ocases,axiom,
% 2.56/1.47 ! [X: list_a] :
% 2.56/1.47 ( ( X != nil_a )
% 2.56/1.47 => ( ! [X2: a] :
% 2.56/1.47 ( X
% 2.56/1.47 != ( cons_a @ X2 @ nil_a ) )
% 2.56/1.47 => ~ ! [X2: a,Y2: a,Xs2: list_a] :
% 2.56/1.47 ( X
% 2.56/1.47 != ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_90_reduce__root__pCons,axiom,
% 2.56/1.47 ! [A: a,C: a,P2: poly_a] :
% 2.56/1.47 ( ( descar466059845root_a @ A @ ( pCons_a @ C @ P2 ) )
% 2.56/1.47 = ( pCons_a @ C @ ( smult_a @ A @ ( descar466059845root_a @ A @ P2 ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_91_reduce__root__pCons,axiom,
% 2.56/1.47 ! [A: poly_a,C: poly_a,P2: poly_poly_a] :
% 2.56/1.47 ( ( descar434775507poly_a @ A @ ( pCons_poly_a @ C @ P2 ) )
% 2.56/1.47 = ( pCons_poly_a @ C @ ( smult_poly_a @ A @ ( descar434775507poly_a @ A @ P2 ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_92_reduce__root__nonzero,axiom,
% 2.56/1.47 ! [A: a,P2: poly_a] :
% 2.56/1.47 ( ( A != zero_zero_a )
% 2.56/1.47 => ( ( P2 != zero_zero_poly_a )
% 2.56/1.47 => ( ( descar466059845root_a @ A @ P2 )
% 2.56/1.47 != zero_zero_poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_93_reduce__root__nonzero,axiom,
% 2.56/1.47 ! [A: poly_a,P2: poly_poly_a] :
% 2.56/1.47 ( ( A != zero_zero_poly_a )
% 2.56/1.47 => ( ( P2 != zero_z2096148049poly_a )
% 2.56/1.47 => ( ( descar434775507poly_a @ A @ P2 )
% 2.56/1.47 != zero_z2096148049poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_94_sign__changes__Cons__Cons__same,axiom,
% 2.56/1.47 ! [X: a,Y3: a,Xs: list_a] :
% 2.56/1.47 ( ( ord_less_a @ zero_zero_a @ ( times_times_a @ X @ Y3 ) )
% 2.56/1.47 => ( ( descar2095969287nges_a @ ( cons_a @ X @ ( cons_a @ Y3 @ Xs ) ) )
% 2.56/1.47 = ( descar2095969287nges_a @ ( cons_a @ Y3 @ Xs ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_95_sign__changes__Cons__Cons__same,axiom,
% 2.56/1.47 ! [X: poly_a,Y3: poly_a,Xs: list_poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ X @ Y3 ) )
% 2.56/1.47 => ( ( descar357075861poly_a @ ( cons_poly_a @ X @ ( cons_poly_a @ Y3 @ Xs ) ) )
% 2.56/1.47 = ( descar357075861poly_a @ ( cons_poly_a @ Y3 @ Xs ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_96_append1__eq__conv,axiom,
% 2.56/1.47 ! [Xs: list_a,X: a,Ys2: list_a,Y3: a] :
% 2.56/1.47 ( ( ( append_a @ Xs @ ( cons_a @ X @ nil_a ) )
% 2.56/1.47 = ( append_a @ Ys2 @ ( cons_a @ Y3 @ nil_a ) ) )
% 2.56/1.47 = ( ( Xs = Ys2 )
% 2.56/1.47 & ( X = Y3 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_97_mult__minus1,axiom,
% 2.56/1.47 ! [Z2: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ ( uminus_uminus_poly_a @ one_one_poly_a ) @ Z2 )
% 2.56/1.47 = ( uminus_uminus_poly_a @ Z2 ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_98_mult__minus1,axiom,
% 2.56/1.47 ! [Z2: a] :
% 2.56/1.47 ( ( times_times_a @ ( uminus_uminus_a @ one_one_a ) @ Z2 )
% 2.56/1.47 = ( uminus_uminus_a @ Z2 ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_99_mult__minus1__right,axiom,
% 2.56/1.47 ! [Z2: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ Z2 @ ( uminus_uminus_poly_a @ one_one_poly_a ) )
% 2.56/1.47 = ( uminus_uminus_poly_a @ Z2 ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_100_mult__minus1__right,axiom,
% 2.56/1.47 ! [Z2: a] :
% 2.56/1.47 ( ( times_times_a @ Z2 @ ( uminus_uminus_a @ one_one_a ) )
% 2.56/1.47 = ( uminus_uminus_a @ Z2 ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_101_less__neg__neg,axiom,
% 2.56/1.47 ! [A: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ A @ ( uminus_uminus_poly_a @ A ) )
% 2.56/1.47 = ( ord_less_poly_a @ A @ zero_zero_poly_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_102_less__neg__neg,axiom,
% 2.56/1.47 ! [A: a] :
% 2.56/1.47 ( ( ord_less_a @ A @ ( uminus_uminus_a @ A ) )
% 2.56/1.47 = ( ord_less_a @ A @ zero_zero_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_103_neg__less__pos,axiom,
% 2.56/1.47 ! [A: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ A )
% 2.56/1.47 = ( ord_less_poly_a @ zero_zero_poly_a @ A ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_104_neg__less__pos,axiom,
% 2.56/1.47 ! [A: a] :
% 2.56/1.47 ( ( ord_less_a @ ( uminus_uminus_a @ A ) @ A )
% 2.56/1.47 = ( ord_less_a @ zero_zero_a @ A ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_105_neg__0__less__iff__less,axiom,
% 2.56/1.47 ! [A: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ zero_zero_poly_a @ ( uminus_uminus_poly_a @ A ) )
% 2.56/1.47 = ( ord_less_poly_a @ A @ zero_zero_poly_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_106_neg__0__less__iff__less,axiom,
% 2.56/1.47 ! [A: a] :
% 2.56/1.47 ( ( ord_less_a @ zero_zero_a @ ( uminus_uminus_a @ A ) )
% 2.56/1.47 = ( ord_less_a @ A @ zero_zero_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_107_neg__less__0__iff__less,axiom,
% 2.56/1.47 ! [A: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ zero_zero_poly_a )
% 2.56/1.47 = ( ord_less_poly_a @ zero_zero_poly_a @ A ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_108_neg__less__0__iff__less,axiom,
% 2.56/1.47 ! [A: a] :
% 2.56/1.47 ( ( ord_less_a @ ( uminus_uminus_a @ A ) @ zero_zero_a )
% 2.56/1.47 = ( ord_less_a @ zero_zero_a @ A ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_109_mult__cancel__left1,axiom,
% 2.56/1.47 ! [C: a,B: a] :
% 2.56/1.47 ( ( C
% 2.56/1.47 = ( times_times_a @ C @ B ) )
% 2.56/1.47 = ( ( C = zero_zero_a )
% 2.56/1.47 | ( B = one_one_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_110_mult__cancel__left1,axiom,
% 2.56/1.47 ! [C: poly_a,B: poly_a] :
% 2.56/1.47 ( ( C
% 2.56/1.47 = ( times_times_poly_a @ C @ B ) )
% 2.56/1.47 = ( ( C = zero_zero_poly_a )
% 2.56/1.47 | ( B = one_one_poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_111_mult__cancel__left2,axiom,
% 2.56/1.47 ! [C: a,A: a] :
% 2.56/1.47 ( ( ( times_times_a @ C @ A )
% 2.56/1.47 = C )
% 2.56/1.47 = ( ( C = zero_zero_a )
% 2.56/1.47 | ( A = one_one_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_112_mult__cancel__left2,axiom,
% 2.56/1.47 ! [C: poly_a,A: poly_a] :
% 2.56/1.47 ( ( ( times_times_poly_a @ C @ A )
% 2.56/1.47 = C )
% 2.56/1.47 = ( ( C = zero_zero_poly_a )
% 2.56/1.47 | ( A = one_one_poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_113_mult__cancel__right1,axiom,
% 2.56/1.47 ! [C: a,B: a] :
% 2.56/1.47 ( ( C
% 2.56/1.47 = ( times_times_a @ B @ C ) )
% 2.56/1.47 = ( ( C = zero_zero_a )
% 2.56/1.47 | ( B = one_one_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_114_mult__cancel__right1,axiom,
% 2.56/1.47 ! [C: poly_a,B: poly_a] :
% 2.56/1.47 ( ( C
% 2.56/1.47 = ( times_times_poly_a @ B @ C ) )
% 2.56/1.47 = ( ( C = zero_zero_poly_a )
% 2.56/1.47 | ( B = one_one_poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_115_mult__cancel__right2,axiom,
% 2.56/1.47 ! [A: a,C: a] :
% 2.56/1.47 ( ( ( times_times_a @ A @ C )
% 2.56/1.47 = C )
% 2.56/1.47 = ( ( C = zero_zero_a )
% 2.56/1.47 | ( A = one_one_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_116_mult__cancel__right2,axiom,
% 2.56/1.47 ! [A: poly_a,C: poly_a] :
% 2.56/1.47 ( ( ( times_times_poly_a @ A @ C )
% 2.56/1.47 = C )
% 2.56/1.47 = ( ( C = zero_zero_poly_a )
% 2.56/1.47 | ( A = one_one_poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_117_neg__equal__iff__equal,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( ( uminus_uminus_a @ A )
% 2.56/1.47 = ( uminus_uminus_a @ B ) )
% 2.56/1.47 = ( A = B ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_118_add_Oinverse__inverse,axiom,
% 2.56/1.47 ! [A: a] :
% 2.56/1.47 ( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) )
% 2.56/1.47 = A ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_119_list_Oinject,axiom,
% 2.56/1.47 ! [X21: a,X22: list_a,Y21: a,Y22: list_a] :
% 2.56/1.47 ( ( ( cons_a @ X21 @ X22 )
% 2.56/1.47 = ( cons_a @ Y21 @ Y22 ) )
% 2.56/1.47 = ( ( X21 = Y21 )
% 2.56/1.47 & ( X22 = Y22 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_120_same__append__eq,axiom,
% 2.56/1.47 ! [Xs: list_a,Ys2: list_a,Zs: list_a] :
% 2.56/1.47 ( ( ( append_a @ Xs @ Ys2 )
% 2.56/1.47 = ( append_a @ Xs @ Zs ) )
% 2.56/1.47 = ( Ys2 = Zs ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_121_append__same__eq,axiom,
% 2.56/1.47 ! [Ys2: list_a,Xs: list_a,Zs: list_a] :
% 2.56/1.47 ( ( ( append_a @ Ys2 @ Xs )
% 2.56/1.47 = ( append_a @ Zs @ Xs ) )
% 2.56/1.47 = ( Ys2 = Zs ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_122_append__assoc,axiom,
% 2.56/1.47 ! [Xs: list_a,Ys2: list_a,Zs: list_a] :
% 2.56/1.47 ( ( append_a @ ( append_a @ Xs @ Ys2 ) @ Zs )
% 2.56/1.47 = ( append_a @ Xs @ ( append_a @ Ys2 @ Zs ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_123_append_Oassoc,axiom,
% 2.56/1.47 ! [A: list_a,B: list_a,C: list_a] :
% 2.56/1.47 ( ( append_a @ ( append_a @ A @ B ) @ C )
% 2.56/1.47 = ( append_a @ A @ ( append_a @ B @ C ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_124_not__gr__zero,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 2.56/1.47 = ( N = zero_zero_nat ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_125_mult__cancel__right,axiom,
% 2.56/1.47 ! [A: a,C: a,B: a] :
% 2.56/1.47 ( ( ( times_times_a @ A @ C )
% 2.56/1.47 = ( times_times_a @ B @ C ) )
% 2.56/1.47 = ( ( C = zero_zero_a )
% 2.56/1.47 | ( A = B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_126_mult__cancel__right,axiom,
% 2.56/1.47 ! [A: poly_a,C: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ( times_times_poly_a @ A @ C )
% 2.56/1.47 = ( times_times_poly_a @ B @ C ) )
% 2.56/1.47 = ( ( C = zero_zero_poly_a )
% 2.56/1.47 | ( A = B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_127_mult__cancel__right,axiom,
% 2.56/1.47 ! [A: nat,C: nat,B: nat] :
% 2.56/1.47 ( ( ( times_times_nat @ A @ C )
% 2.56/1.47 = ( times_times_nat @ B @ C ) )
% 2.56/1.47 = ( ( C = zero_zero_nat )
% 2.56/1.47 | ( A = B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_128_mult__cancel__left,axiom,
% 2.56/1.47 ! [C: a,A: a,B: a] :
% 2.56/1.47 ( ( ( times_times_a @ C @ A )
% 2.56/1.47 = ( times_times_a @ C @ B ) )
% 2.56/1.47 = ( ( C = zero_zero_a )
% 2.56/1.47 | ( A = B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_129_mult__cancel__left,axiom,
% 2.56/1.47 ! [C: poly_a,A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ( times_times_poly_a @ C @ A )
% 2.56/1.47 = ( times_times_poly_a @ C @ B ) )
% 2.56/1.47 = ( ( C = zero_zero_poly_a )
% 2.56/1.47 | ( A = B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_130_mult__cancel__left,axiom,
% 2.56/1.47 ! [C: nat,A: nat,B: nat] :
% 2.56/1.47 ( ( ( times_times_nat @ C @ A )
% 2.56/1.47 = ( times_times_nat @ C @ B ) )
% 2.56/1.47 = ( ( C = zero_zero_nat )
% 2.56/1.47 | ( A = B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_131_mult__eq__0__iff,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( ( times_times_a @ A @ B )
% 2.56/1.47 = zero_zero_a )
% 2.56/1.47 = ( ( A = zero_zero_a )
% 2.56/1.47 | ( B = zero_zero_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_132_mult__eq__0__iff,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ( times_times_poly_a @ A @ B )
% 2.56/1.47 = zero_zero_poly_a )
% 2.56/1.47 = ( ( A = zero_zero_poly_a )
% 2.56/1.47 | ( B = zero_zero_poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_133_mult__eq__0__iff,axiom,
% 2.56/1.47 ! [A: nat,B: nat] :
% 2.56/1.47 ( ( ( times_times_nat @ A @ B )
% 2.56/1.47 = zero_zero_nat )
% 2.56/1.47 = ( ( A = zero_zero_nat )
% 2.56/1.47 | ( B = zero_zero_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_134_mult__zero__right,axiom,
% 2.56/1.47 ! [A: a] :
% 2.56/1.47 ( ( times_times_a @ A @ zero_zero_a )
% 2.56/1.47 = zero_zero_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_135_mult__zero__right,axiom,
% 2.56/1.47 ! [A: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ A @ zero_zero_poly_a )
% 2.56/1.47 = zero_zero_poly_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_136_mult__zero__right,axiom,
% 2.56/1.47 ! [A: nat] :
% 2.56/1.47 ( ( times_times_nat @ A @ zero_zero_nat )
% 2.56/1.47 = zero_zero_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_137_mult__zero__left,axiom,
% 2.56/1.47 ! [A: a] :
% 2.56/1.47 ( ( times_times_a @ zero_zero_a @ A )
% 2.56/1.47 = zero_zero_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_138_mult__zero__left,axiom,
% 2.56/1.47 ! [A: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ zero_zero_poly_a @ A )
% 2.56/1.47 = zero_zero_poly_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_139_mult__zero__left,axiom,
% 2.56/1.47 ! [A: nat] :
% 2.56/1.47 ( ( times_times_nat @ zero_zero_nat @ A )
% 2.56/1.47 = zero_zero_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_140_neg__equal__zero,axiom,
% 2.56/1.47 ! [A: poly_a] :
% 2.56/1.47 ( ( ( uminus_uminus_poly_a @ A )
% 2.56/1.47 = A )
% 2.56/1.47 = ( A = zero_zero_poly_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_141_neg__equal__zero,axiom,
% 2.56/1.47 ! [A: a] :
% 2.56/1.47 ( ( ( uminus_uminus_a @ A )
% 2.56/1.47 = A )
% 2.56/1.47 = ( A = zero_zero_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_142_equal__neg__zero,axiom,
% 2.56/1.47 ! [A: poly_a] :
% 2.56/1.47 ( ( A
% 2.56/1.47 = ( uminus_uminus_poly_a @ A ) )
% 2.56/1.47 = ( A = zero_zero_poly_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_143_equal__neg__zero,axiom,
% 2.56/1.47 ! [A: a] :
% 2.56/1.47 ( ( A
% 2.56/1.47 = ( uminus_uminus_a @ A ) )
% 2.56/1.47 = ( A = zero_zero_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_144_neg__equal__0__iff__equal,axiom,
% 2.56/1.47 ! [A: poly_a] :
% 2.56/1.47 ( ( ( uminus_uminus_poly_a @ A )
% 2.56/1.47 = zero_zero_poly_a )
% 2.56/1.47 = ( A = zero_zero_poly_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_145_neg__equal__0__iff__equal,axiom,
% 2.56/1.47 ! [A: a] :
% 2.56/1.47 ( ( ( uminus_uminus_a @ A )
% 2.56/1.47 = zero_zero_a )
% 2.56/1.47 = ( A = zero_zero_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_146_neg__0__equal__iff__equal,axiom,
% 2.56/1.47 ! [A: poly_a] :
% 2.56/1.47 ( ( zero_zero_poly_a
% 2.56/1.47 = ( uminus_uminus_poly_a @ A ) )
% 2.56/1.47 = ( zero_zero_poly_a = A ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_147_neg__0__equal__iff__equal,axiom,
% 2.56/1.47 ! [A: a] :
% 2.56/1.47 ( ( zero_zero_a
% 2.56/1.47 = ( uminus_uminus_a @ A ) )
% 2.56/1.47 = ( zero_zero_a = A ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_148_add_Oinverse__neutral,axiom,
% 2.56/1.47 ( ( uminus_uminus_poly_a @ zero_zero_poly_a )
% 2.56/1.47 = zero_zero_poly_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_149_add_Oinverse__neutral,axiom,
% 2.56/1.47 ( ( uminus_uminus_a @ zero_zero_a )
% 2.56/1.47 = zero_zero_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_150_mult_Oright__neutral,axiom,
% 2.56/1.47 ! [A: a] :
% 2.56/1.47 ( ( times_times_a @ A @ one_one_a )
% 2.56/1.47 = A ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_151_mult_Oright__neutral,axiom,
% 2.56/1.47 ! [A: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ A @ one_one_poly_a )
% 2.56/1.47 = A ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_152_mult_Oright__neutral,axiom,
% 2.56/1.47 ! [A: nat] :
% 2.56/1.47 ( ( times_times_nat @ A @ one_one_nat )
% 2.56/1.47 = A ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_153_mult_Oleft__neutral,axiom,
% 2.56/1.47 ! [A: a] :
% 2.56/1.47 ( ( times_times_a @ one_one_a @ A )
% 2.56/1.47 = A ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_154_mult_Oleft__neutral,axiom,
% 2.56/1.47 ! [A: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ one_one_poly_a @ A )
% 2.56/1.47 = A ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_155_mult_Oleft__neutral,axiom,
% 2.56/1.47 ! [A: nat] :
% 2.56/1.47 ( ( times_times_nat @ one_one_nat @ A )
% 2.56/1.47 = A ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_156_neg__less__iff__less,axiom,
% 2.56/1.47 ! [B: poly_a,A: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ B ) @ ( uminus_uminus_poly_a @ A ) )
% 2.56/1.47 = ( ord_less_poly_a @ A @ B ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_157_neg__less__iff__less,axiom,
% 2.56/1.47 ! [B: a,A: a] :
% 2.56/1.47 ( ( ord_less_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) )
% 2.56/1.47 = ( ord_less_a @ A @ B ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_158_mult__minus__right,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ A @ ( uminus_uminus_poly_a @ B ) )
% 2.56/1.47 = ( uminus_uminus_poly_a @ ( times_times_poly_a @ A @ B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_159_mult__minus__right,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( times_times_a @ A @ ( uminus_uminus_a @ B ) )
% 2.56/1.47 = ( uminus_uminus_a @ ( times_times_a @ A @ B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_160_minus__mult__minus,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ ( uminus_uminus_poly_a @ A ) @ ( uminus_uminus_poly_a @ B ) )
% 2.56/1.47 = ( times_times_poly_a @ A @ B ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_161_minus__mult__minus,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( times_times_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_a @ B ) )
% 2.56/1.47 = ( times_times_a @ A @ B ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_162_mult__minus__left,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ ( uminus_uminus_poly_a @ A ) @ B )
% 2.56/1.47 = ( uminus_uminus_poly_a @ ( times_times_poly_a @ A @ B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_163_mult__minus__left,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( times_times_a @ ( uminus_uminus_a @ A ) @ B )
% 2.56/1.47 = ( uminus_uminus_a @ ( times_times_a @ A @ B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_164_append_Oright__neutral,axiom,
% 2.56/1.47 ! [A: list_a] :
% 2.56/1.47 ( ( append_a @ A @ nil_a )
% 2.56/1.47 = A ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_165_append__is__Nil__conv,axiom,
% 2.56/1.47 ! [Xs: list_a,Ys2: list_a] :
% 2.56/1.47 ( ( ( append_a @ Xs @ Ys2 )
% 2.56/1.47 = nil_a )
% 2.56/1.47 = ( ( Xs = nil_a )
% 2.56/1.47 & ( Ys2 = nil_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_166_Nil__is__append__conv,axiom,
% 2.56/1.47 ! [Xs: list_a,Ys2: list_a] :
% 2.56/1.47 ( ( nil_a
% 2.56/1.47 = ( append_a @ Xs @ Ys2 ) )
% 2.56/1.47 = ( ( Xs = nil_a )
% 2.56/1.47 & ( Ys2 = nil_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_167_self__append__conv2,axiom,
% 2.56/1.47 ! [Ys2: list_a,Xs: list_a] :
% 2.56/1.47 ( ( Ys2
% 2.56/1.47 = ( append_a @ Xs @ Ys2 ) )
% 2.56/1.47 = ( Xs = nil_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_168_append__self__conv2,axiom,
% 2.56/1.47 ! [Xs: list_a,Ys2: list_a] :
% 2.56/1.47 ( ( ( append_a @ Xs @ Ys2 )
% 2.56/1.47 = Ys2 )
% 2.56/1.47 = ( Xs = nil_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_169_self__append__conv,axiom,
% 2.56/1.47 ! [Xs: list_a,Ys2: list_a] :
% 2.56/1.47 ( ( Xs
% 2.56/1.47 = ( append_a @ Xs @ Ys2 ) )
% 2.56/1.47 = ( Ys2 = nil_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_170_append__self__conv,axiom,
% 2.56/1.47 ! [Xs: list_a,Ys2: list_a] :
% 2.56/1.47 ( ( ( append_a @ Xs @ Ys2 )
% 2.56/1.47 = Xs )
% 2.56/1.47 = ( Ys2 = nil_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_171_append__Nil2,axiom,
% 2.56/1.47 ! [Xs: list_a] :
% 2.56/1.47 ( ( append_a @ Xs @ nil_a )
% 2.56/1.47 = Xs ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_172_smult__one,axiom,
% 2.56/1.47 ! [C: a] :
% 2.56/1.47 ( ( smult_a @ C @ one_one_poly_a )
% 2.56/1.47 = ( pCons_a @ C @ zero_zero_poly_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_173_zero__reorient,axiom,
% 2.56/1.47 ! [X: poly_a] :
% 2.56/1.47 ( ( zero_zero_poly_a = X )
% 2.56/1.47 = ( X = zero_zero_poly_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_174_zero__reorient,axiom,
% 2.56/1.47 ! [X: a] :
% 2.56/1.47 ( ( zero_zero_a = X )
% 2.56/1.47 = ( X = zero_zero_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_175_zero__reorient,axiom,
% 2.56/1.47 ! [X: nat] :
% 2.56/1.47 ( ( zero_zero_nat = X )
% 2.56/1.47 = ( X = zero_zero_nat ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_176_linorder__neqE__linordered__idom,axiom,
% 2.56/1.47 ! [X: a,Y3: a] :
% 2.56/1.47 ( ( X != Y3 )
% 2.56/1.47 => ( ~ ( ord_less_a @ X @ Y3 )
% 2.56/1.47 => ( ord_less_a @ Y3 @ X ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_177_linorder__neqE__linordered__idom,axiom,
% 2.56/1.47 ! [X: poly_a,Y3: poly_a] :
% 2.56/1.47 ( ( X != Y3 )
% 2.56/1.47 => ( ~ ( ord_less_poly_a @ X @ Y3 )
% 2.56/1.47 => ( ord_less_poly_a @ Y3 @ X ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_178_mult_Oleft__commute,axiom,
% 2.56/1.47 ! [B: poly_a,A: poly_a,C: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ B @ ( times_times_poly_a @ A @ C ) )
% 2.56/1.47 = ( times_times_poly_a @ A @ ( times_times_poly_a @ B @ C ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_179_mult_Oleft__commute,axiom,
% 2.56/1.47 ! [B: nat,A: nat,C: nat] :
% 2.56/1.47 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 2.56/1.47 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_180_mult_Ocommute,axiom,
% 2.56/1.47 ( times_times_poly_a
% 2.56/1.47 = ( ^ [A3: poly_a,B3: poly_a] : ( times_times_poly_a @ B3 @ A3 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_181_mult_Ocommute,axiom,
% 2.56/1.47 ( times_times_nat
% 2.56/1.47 = ( ^ [A3: nat,B3: nat] : ( times_times_nat @ B3 @ A3 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_182_mult_Oassoc,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a,C: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ ( times_times_poly_a @ A @ B ) @ C )
% 2.56/1.47 = ( times_times_poly_a @ A @ ( times_times_poly_a @ B @ C ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_183_mult_Oassoc,axiom,
% 2.56/1.47 ! [A: nat,B: nat,C: nat] :
% 2.56/1.47 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 2.56/1.47 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_184_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a,C: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ ( times_times_poly_a @ A @ B ) @ C )
% 2.56/1.47 = ( times_times_poly_a @ A @ ( times_times_poly_a @ B @ C ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_185_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 2.56/1.47 ! [A: nat,B: nat,C: nat] :
% 2.56/1.47 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 2.56/1.47 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_186_one__reorient,axiom,
% 2.56/1.47 ! [X: a] :
% 2.56/1.47 ( ( one_one_a = X )
% 2.56/1.47 = ( X = one_one_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_187_one__reorient,axiom,
% 2.56/1.47 ! [X: nat] :
% 2.56/1.47 ( ( one_one_nat = X )
% 2.56/1.47 = ( X = one_one_nat ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_188_minus__equation__iff,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( ( uminus_uminus_a @ A )
% 2.56/1.47 = B )
% 2.56/1.47 = ( ( uminus_uminus_a @ B )
% 2.56/1.47 = A ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_189_equation__minus__iff,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( A
% 2.56/1.47 = ( uminus_uminus_a @ B ) )
% 2.56/1.47 = ( B
% 2.56/1.47 = ( uminus_uminus_a @ A ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_190_not__Cons__self2,axiom,
% 2.56/1.47 ! [X: a,Xs: list_a] :
% 2.56/1.47 ( ( cons_a @ X @ Xs )
% 2.56/1.47 != Xs ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_191_append__eq__append__conv2,axiom,
% 2.56/1.47 ! [Xs: list_a,Ys2: list_a,Zs: list_a,Ts: list_a] :
% 2.56/1.47 ( ( ( append_a @ Xs @ Ys2 )
% 2.56/1.47 = ( append_a @ Zs @ Ts ) )
% 2.56/1.47 = ( ? [Us: list_a] :
% 2.56/1.47 ( ( ( Xs
% 2.56/1.47 = ( append_a @ Zs @ Us ) )
% 2.56/1.47 & ( ( append_a @ Us @ Ys2 )
% 2.56/1.47 = Ts ) )
% 2.56/1.47 | ( ( ( append_a @ Xs @ Us )
% 2.56/1.47 = Zs )
% 2.56/1.47 & ( Ys2
% 2.56/1.47 = ( append_a @ Us @ Ts ) ) ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_192_append__eq__appendI,axiom,
% 2.56/1.47 ! [Xs: list_a,Xs1: list_a,Zs: list_a,Ys2: list_a,Us2: list_a] :
% 2.56/1.47 ( ( ( append_a @ Xs @ Xs1 )
% 2.56/1.47 = Zs )
% 2.56/1.47 => ( ( Ys2
% 2.56/1.47 = ( append_a @ Xs1 @ Us2 ) )
% 2.56/1.47 => ( ( append_a @ Xs @ Ys2 )
% 2.56/1.47 = ( append_a @ Zs @ Us2 ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_193_sign__changes__two,axiom,
% 2.56/1.47 ! [X: a,Y3: a] :
% 2.56/1.47 ( ( ( ( ( ord_less_a @ zero_zero_a @ X )
% 2.56/1.47 & ( ord_less_a @ Y3 @ zero_zero_a ) )
% 2.56/1.47 | ( ( ord_less_a @ X @ zero_zero_a )
% 2.56/1.47 & ( ord_less_a @ zero_zero_a @ Y3 ) ) )
% 2.56/1.47 => ( ( descar2095969287nges_a @ ( cons_a @ X @ ( cons_a @ Y3 @ nil_a ) ) )
% 2.56/1.47 = one_one_nat ) )
% 2.56/1.47 & ( ~ ( ( ( ord_less_a @ zero_zero_a @ X )
% 2.56/1.47 & ( ord_less_a @ Y3 @ zero_zero_a ) )
% 2.56/1.47 | ( ( ord_less_a @ X @ zero_zero_a )
% 2.56/1.47 & ( ord_less_a @ zero_zero_a @ Y3 ) ) )
% 2.56/1.47 => ( ( descar2095969287nges_a @ ( cons_a @ X @ ( cons_a @ Y3 @ nil_a ) ) )
% 2.56/1.47 = zero_zero_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_194_sign__changes__two,axiom,
% 2.56/1.47 ! [X: poly_a,Y3: poly_a] :
% 2.56/1.47 ( ( ( ( ( ord_less_poly_a @ zero_zero_poly_a @ X )
% 2.56/1.47 & ( ord_less_poly_a @ Y3 @ zero_zero_poly_a ) )
% 2.56/1.47 | ( ( ord_less_poly_a @ X @ zero_zero_poly_a )
% 2.56/1.47 & ( ord_less_poly_a @ zero_zero_poly_a @ Y3 ) ) )
% 2.56/1.47 => ( ( descar357075861poly_a @ ( cons_poly_a @ X @ ( cons_poly_a @ Y3 @ nil_poly_a ) ) )
% 2.56/1.47 = one_one_nat ) )
% 2.56/1.47 & ( ~ ( ( ( ord_less_poly_a @ zero_zero_poly_a @ X )
% 2.56/1.47 & ( ord_less_poly_a @ Y3 @ zero_zero_poly_a ) )
% 2.56/1.47 | ( ( ord_less_poly_a @ X @ zero_zero_poly_a )
% 2.56/1.47 & ( ord_less_poly_a @ zero_zero_poly_a @ Y3 ) ) )
% 2.56/1.47 => ( ( descar357075861poly_a @ ( cons_poly_a @ X @ ( cons_poly_a @ Y3 @ nil_poly_a ) ) )
% 2.56/1.47 = zero_zero_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_195_zero__less__iff__neq__zero,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.56/1.47 = ( N != zero_zero_nat ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_196_gr__implies__not__zero,axiom,
% 2.56/1.47 ! [M: nat,N: nat] :
% 2.56/1.47 ( ( ord_less_nat @ M @ N )
% 2.56/1.47 => ( N != zero_zero_nat ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_197_not__less__zero,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_198_gr__zeroI,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ( ( N != zero_zero_nat )
% 2.56/1.47 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_199_less__numeral__extra_I3_J,axiom,
% 2.56/1.47 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_200_less__numeral__extra_I3_J,axiom,
% 2.56/1.47 ~ ( ord_less_a @ zero_zero_a @ zero_zero_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_201_less__numeral__extra_I3_J,axiom,
% 2.56/1.47 ~ ( ord_less_poly_a @ zero_zero_poly_a @ zero_zero_poly_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_202_mult__right__cancel,axiom,
% 2.56/1.47 ! [C: a,A: a,B: a] :
% 2.56/1.47 ( ( C != zero_zero_a )
% 2.56/1.47 => ( ( ( times_times_a @ A @ C )
% 2.56/1.47 = ( times_times_a @ B @ C ) )
% 2.56/1.47 = ( A = B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_203_mult__right__cancel,axiom,
% 2.56/1.47 ! [C: poly_a,A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( C != zero_zero_poly_a )
% 2.56/1.47 => ( ( ( times_times_poly_a @ A @ C )
% 2.56/1.47 = ( times_times_poly_a @ B @ C ) )
% 2.56/1.47 = ( A = B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_204_mult__right__cancel,axiom,
% 2.56/1.47 ! [C: nat,A: nat,B: nat] :
% 2.56/1.47 ( ( C != zero_zero_nat )
% 2.56/1.47 => ( ( ( times_times_nat @ A @ C )
% 2.56/1.47 = ( times_times_nat @ B @ C ) )
% 2.56/1.47 = ( A = B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_205_mult__left__cancel,axiom,
% 2.56/1.47 ! [C: a,A: a,B: a] :
% 2.56/1.47 ( ( C != zero_zero_a )
% 2.56/1.47 => ( ( ( times_times_a @ C @ A )
% 2.56/1.47 = ( times_times_a @ C @ B ) )
% 2.56/1.47 = ( A = B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_206_mult__left__cancel,axiom,
% 2.56/1.47 ! [C: poly_a,A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( C != zero_zero_poly_a )
% 2.56/1.47 => ( ( ( times_times_poly_a @ C @ A )
% 2.56/1.47 = ( times_times_poly_a @ C @ B ) )
% 2.56/1.47 = ( A = B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_207_mult__left__cancel,axiom,
% 2.56/1.47 ! [C: nat,A: nat,B: nat] :
% 2.56/1.47 ( ( C != zero_zero_nat )
% 2.56/1.47 => ( ( ( times_times_nat @ C @ A )
% 2.56/1.47 = ( times_times_nat @ C @ B ) )
% 2.56/1.47 = ( A = B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_208_no__zero__divisors,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( A != zero_zero_a )
% 2.56/1.47 => ( ( B != zero_zero_a )
% 2.56/1.47 => ( ( times_times_a @ A @ B )
% 2.56/1.47 != zero_zero_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_209_no__zero__divisors,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( A != zero_zero_poly_a )
% 2.56/1.47 => ( ( B != zero_zero_poly_a )
% 2.56/1.47 => ( ( times_times_poly_a @ A @ B )
% 2.56/1.47 != zero_zero_poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_210_no__zero__divisors,axiom,
% 2.56/1.47 ! [A: nat,B: nat] :
% 2.56/1.47 ( ( A != zero_zero_nat )
% 2.56/1.47 => ( ( B != zero_zero_nat )
% 2.56/1.47 => ( ( times_times_nat @ A @ B )
% 2.56/1.47 != zero_zero_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_211_divisors__zero,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( ( times_times_a @ A @ B )
% 2.56/1.47 = zero_zero_a )
% 2.56/1.47 => ( ( A = zero_zero_a )
% 2.56/1.47 | ( B = zero_zero_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_212_divisors__zero,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ( times_times_poly_a @ A @ B )
% 2.56/1.47 = zero_zero_poly_a )
% 2.56/1.47 => ( ( A = zero_zero_poly_a )
% 2.56/1.47 | ( B = zero_zero_poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_213_divisors__zero,axiom,
% 2.56/1.47 ! [A: nat,B: nat] :
% 2.56/1.47 ( ( ( times_times_nat @ A @ B )
% 2.56/1.47 = zero_zero_nat )
% 2.56/1.47 => ( ( A = zero_zero_nat )
% 2.56/1.47 | ( B = zero_zero_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_214_mult__not__zero,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( ( times_times_a @ A @ B )
% 2.56/1.47 != zero_zero_a )
% 2.56/1.47 => ( ( A != zero_zero_a )
% 2.56/1.47 & ( B != zero_zero_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_215_mult__not__zero,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ( times_times_poly_a @ A @ B )
% 2.56/1.47 != zero_zero_poly_a )
% 2.56/1.47 => ( ( A != zero_zero_poly_a )
% 2.56/1.47 & ( B != zero_zero_poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_216_mult__not__zero,axiom,
% 2.56/1.47 ! [A: nat,B: nat] :
% 2.56/1.47 ( ( ( times_times_nat @ A @ B )
% 2.56/1.47 != zero_zero_nat )
% 2.56/1.47 => ( ( A != zero_zero_nat )
% 2.56/1.47 & ( B != zero_zero_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_217_zero__neq__one,axiom,
% 2.56/1.47 zero_zero_poly_a != one_one_poly_a ).
% 2.56/1.47
% 2.56/1.47 thf(fact_218_zero__neq__one,axiom,
% 2.56/1.47 zero_zero_a != one_one_a ).
% 2.56/1.47
% 2.56/1.47 thf(fact_219_zero__neq__one,axiom,
% 2.56/1.47 zero_zero_nat != one_one_nat ).
% 2.56/1.47
% 2.56/1.47 thf(fact_220_less__numeral__extra_I4_J,axiom,
% 2.56/1.47 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_221_less__numeral__extra_I4_J,axiom,
% 2.56/1.47 ~ ( ord_less_a @ one_one_a @ one_one_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_222_less__numeral__extra_I4_J,axiom,
% 2.56/1.47 ~ ( ord_less_poly_a @ one_one_poly_a @ one_one_poly_a ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_223_mult_Ocomm__neutral,axiom,
% 2.56/1.47 ! [A: a] :
% 2.56/1.47 ( ( times_times_a @ A @ one_one_a )
% 2.56/1.47 = A ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_224_mult_Ocomm__neutral,axiom,
% 2.56/1.47 ! [A: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ A @ one_one_poly_a )
% 2.56/1.47 = A ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_225_mult_Ocomm__neutral,axiom,
% 2.56/1.47 ! [A: nat] :
% 2.56/1.47 ( ( times_times_nat @ A @ one_one_nat )
% 2.56/1.47 = A ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_226_comm__monoid__mult__class_Omult__1,axiom,
% 2.56/1.47 ! [A: a] :
% 2.56/1.47 ( ( times_times_a @ one_one_a @ A )
% 2.56/1.47 = A ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_227_comm__monoid__mult__class_Omult__1,axiom,
% 2.56/1.47 ! [A: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ one_one_poly_a @ A )
% 2.56/1.47 = A ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_228_comm__monoid__mult__class_Omult__1,axiom,
% 2.56/1.47 ! [A: nat] :
% 2.56/1.47 ( ( times_times_nat @ one_one_nat @ A )
% 2.56/1.47 = A ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_229_minus__less__iff,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ B )
% 2.56/1.47 = ( ord_less_poly_a @ ( uminus_uminus_poly_a @ B ) @ A ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_230_minus__less__iff,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( ord_less_a @ ( uminus_uminus_a @ A ) @ B )
% 2.56/1.47 = ( ord_less_a @ ( uminus_uminus_a @ B ) @ A ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_231_less__minus__iff,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ A @ ( uminus_uminus_poly_a @ B ) )
% 2.56/1.47 = ( ord_less_poly_a @ B @ ( uminus_uminus_poly_a @ A ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_232_less__minus__iff,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( ord_less_a @ A @ ( uminus_uminus_a @ B ) )
% 2.56/1.47 = ( ord_less_a @ B @ ( uminus_uminus_a @ A ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_233_minus__mult__commute,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( times_times_poly_a @ ( uminus_uminus_poly_a @ A ) @ B )
% 2.56/1.47 = ( times_times_poly_a @ A @ ( uminus_uminus_poly_a @ B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_234_minus__mult__commute,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( times_times_a @ ( uminus_uminus_a @ A ) @ B )
% 2.56/1.47 = ( times_times_a @ A @ ( uminus_uminus_a @ B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_235_square__eq__iff,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ( times_times_poly_a @ A @ A )
% 2.56/1.47 = ( times_times_poly_a @ B @ B ) )
% 2.56/1.47 = ( ( A = B )
% 2.56/1.47 | ( A
% 2.56/1.47 = ( uminus_uminus_poly_a @ B ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_236_square__eq__iff,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( ( times_times_a @ A @ A )
% 2.56/1.47 = ( times_times_a @ B @ B ) )
% 2.56/1.47 = ( ( A = B )
% 2.56/1.47 | ( A
% 2.56/1.47 = ( uminus_uminus_a @ B ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_237_one__neq__neg__one,axiom,
% 2.56/1.47 ( one_one_a
% 2.56/1.47 != ( uminus_uminus_a @ one_one_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_238_strict__sorted_Oinduct,axiom,
% 2.56/1.47 ! [P3: list_a > $o,A0: list_a] :
% 2.56/1.47 ( ( P3 @ nil_a )
% 2.56/1.47 => ( ! [X2: a,Ys: list_a] :
% 2.56/1.47 ( ( P3 @ Ys )
% 2.56/1.47 => ( P3 @ ( cons_a @ X2 @ Ys ) ) )
% 2.56/1.47 => ( P3 @ A0 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_239_strict__sorted_Ocases,axiom,
% 2.56/1.47 ! [X: list_a] :
% 2.56/1.47 ( ( X != nil_a )
% 2.56/1.47 => ~ ! [X2: a,Ys: list_a] :
% 2.56/1.47 ( X
% 2.56/1.47 != ( cons_a @ X2 @ Ys ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_240_map__tailrec__rev_Oinduct,axiom,
% 2.56/1.47 ! [P3: ( a > a ) > list_a > list_a > $o,A0: a > a,A1: list_a,A22: list_a] :
% 2.56/1.47 ( ! [F2: a > a,X_1: list_a] : ( P3 @ F2 @ nil_a @ X_1 )
% 2.56/1.47 => ( ! [F2: a > a,A2: a,As2: list_a,Bs: list_a] :
% 2.56/1.47 ( ( P3 @ F2 @ As2 @ ( cons_a @ ( F2 @ A2 ) @ Bs ) )
% 2.56/1.47 => ( P3 @ F2 @ ( cons_a @ A2 @ As2 ) @ Bs ) )
% 2.56/1.47 => ( P3 @ A0 @ A1 @ A22 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_241_list__nonempty__induct,axiom,
% 2.56/1.47 ! [Xs: list_a,P3: list_a > $o] :
% 2.56/1.47 ( ( Xs != nil_a )
% 2.56/1.47 => ( ! [X2: a] : ( P3 @ ( cons_a @ X2 @ nil_a ) )
% 2.56/1.47 => ( ! [X2: a,Xs2: list_a] :
% 2.56/1.47 ( ( Xs2 != nil_a )
% 2.56/1.47 => ( ( P3 @ Xs2 )
% 2.56/1.47 => ( P3 @ ( cons_a @ X2 @ Xs2 ) ) ) )
% 2.56/1.47 => ( P3 @ Xs ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_242_successively_Oinduct,axiom,
% 2.56/1.47 ! [P3: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
% 2.56/1.47 ( ! [P5: a > a > $o] : ( P3 @ P5 @ nil_a )
% 2.56/1.47 => ( ! [P5: a > a > $o,X2: a] : ( P3 @ P5 @ ( cons_a @ X2 @ nil_a ) )
% 2.56/1.47 => ( ! [P5: a > a > $o,X2: a,Y2: a,Xs2: list_a] :
% 2.56/1.47 ( ( P3 @ P5 @ ( cons_a @ Y2 @ Xs2 ) )
% 2.56/1.47 => ( P3 @ P5 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) )
% 2.56/1.47 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_243_remdups__adj_Oinduct,axiom,
% 2.56/1.47 ! [P3: list_a > $o,A0: list_a] :
% 2.56/1.47 ( ( P3 @ nil_a )
% 2.56/1.47 => ( ! [X2: a] : ( P3 @ ( cons_a @ X2 @ nil_a ) )
% 2.56/1.47 => ( ! [X2: a,Y2: a,Xs2: list_a] :
% 2.56/1.47 ( ( ( X2 = Y2 )
% 2.56/1.47 => ( P3 @ ( cons_a @ X2 @ Xs2 ) ) )
% 2.56/1.47 => ( ( ( X2 != Y2 )
% 2.56/1.47 => ( P3 @ ( cons_a @ Y2 @ Xs2 ) ) )
% 2.56/1.47 => ( P3 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) ) )
% 2.56/1.47 => ( P3 @ A0 ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_244_sorted__wrt_Oinduct,axiom,
% 2.56/1.47 ! [P3: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
% 2.56/1.47 ( ! [P5: a > a > $o] : ( P3 @ P5 @ nil_a )
% 2.56/1.47 => ( ! [P5: a > a > $o,X2: a,Ys: list_a] :
% 2.56/1.47 ( ( P3 @ P5 @ Ys )
% 2.56/1.47 => ( P3 @ P5 @ ( cons_a @ X2 @ Ys ) ) )
% 2.56/1.47 => ( P3 @ A0 @ A1 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_245_remdups__adj_Ocases,axiom,
% 2.56/1.47 ! [X: list_a] :
% 2.56/1.47 ( ( X != nil_a )
% 2.56/1.47 => ( ! [X2: a] :
% 2.56/1.47 ( X
% 2.56/1.47 != ( cons_a @ X2 @ nil_a ) )
% 2.56/1.47 => ~ ! [X2: a,Y2: a,Xs2: list_a] :
% 2.56/1.47 ( X
% 2.56/1.47 != ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_246_transpose_Ocases,axiom,
% 2.56/1.47 ! [X: list_list_a] :
% 2.56/1.47 ( ( X != nil_list_a )
% 2.56/1.47 => ( ! [Xss: list_list_a] :
% 2.56/1.47 ( X
% 2.56/1.47 != ( cons_list_a @ nil_a @ Xss ) )
% 2.56/1.47 => ~ ! [X2: a,Xs2: list_a,Xss: list_list_a] :
% 2.56/1.47 ( X
% 2.56/1.47 != ( cons_list_a @ ( cons_a @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_247_shuffles_Oinduct,axiom,
% 2.56/1.47 ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 2.56/1.47 ( ! [X_1: list_a] : ( P3 @ nil_a @ X_1 )
% 2.56/1.47 => ( ! [Xs2: list_a] : ( P3 @ Xs2 @ nil_a )
% 2.56/1.47 => ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
% 2.56/1.47 ( ( P3 @ Xs2 @ ( cons_a @ Y2 @ Ys ) )
% 2.56/1.47 => ( ( P3 @ ( cons_a @ X2 @ Xs2 ) @ Ys )
% 2.56/1.47 => ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) ) )
% 2.56/1.47 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_248_min__list_Oinduct,axiom,
% 2.56/1.47 ! [P3: list_a > $o,A0: list_a] :
% 2.56/1.47 ( ! [X2: a,Xs2: list_a] :
% 2.56/1.47 ( ! [X212: a,X222: list_a] :
% 2.56/1.47 ( ( Xs2
% 2.56/1.47 = ( cons_a @ X212 @ X222 ) )
% 2.56/1.47 => ( P3 @ Xs2 ) )
% 2.56/1.47 => ( P3 @ ( cons_a @ X2 @ Xs2 ) ) )
% 2.56/1.47 => ( ( P3 @ nil_a )
% 2.56/1.47 => ( P3 @ A0 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_249_min__list_Ocases,axiom,
% 2.56/1.47 ! [X: list_a] :
% 2.56/1.47 ( ! [X2: a,Xs2: list_a] :
% 2.56/1.47 ( X
% 2.56/1.47 != ( cons_a @ X2 @ Xs2 ) )
% 2.56/1.47 => ( X = nil_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_250_induct__list012,axiom,
% 2.56/1.47 ! [P3: list_a > $o,Xs: list_a] :
% 2.56/1.47 ( ( P3 @ nil_a )
% 2.56/1.47 => ( ! [X2: a] : ( P3 @ ( cons_a @ X2 @ nil_a ) )
% 2.56/1.47 => ( ! [X2: a,Y2: a,Zs2: list_a] :
% 2.56/1.47 ( ( P3 @ Zs2 )
% 2.56/1.47 => ( ( P3 @ ( cons_a @ Y2 @ Zs2 ) )
% 2.56/1.47 => ( P3 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Zs2 ) ) ) ) )
% 2.56/1.47 => ( P3 @ Xs ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_251_splice_Oinduct,axiom,
% 2.56/1.47 ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 2.56/1.47 ( ! [X_1: list_a] : ( P3 @ nil_a @ X_1 )
% 2.56/1.47 => ( ! [X2: a,Xs2: list_a,Ys: list_a] :
% 2.56/1.47 ( ( P3 @ Ys @ Xs2 )
% 2.56/1.47 => ( P3 @ ( cons_a @ X2 @ Xs2 ) @ Ys ) )
% 2.56/1.47 => ( P3 @ A0 @ A1 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_252_list__induct2_H,axiom,
% 2.56/1.47 ! [P3: list_a > list_a > $o,Xs: list_a,Ys2: list_a] :
% 2.56/1.47 ( ( P3 @ nil_a @ nil_a )
% 2.56/1.47 => ( ! [X2: a,Xs2: list_a] : ( P3 @ ( cons_a @ X2 @ Xs2 ) @ nil_a )
% 2.56/1.47 => ( ! [Y2: a,Ys: list_a] : ( P3 @ nil_a @ ( cons_a @ Y2 @ Ys ) )
% 2.56/1.47 => ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
% 2.56/1.47 ( ( P3 @ Xs2 @ Ys )
% 2.56/1.47 => ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) )
% 2.56/1.47 => ( P3 @ Xs @ Ys2 ) ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_253_neq__Nil__conv,axiom,
% 2.56/1.47 ! [Xs: list_a] :
% 2.56/1.47 ( ( Xs != nil_a )
% 2.56/1.47 = ( ? [Y4: a,Ys3: list_a] :
% 2.56/1.47 ( Xs
% 2.56/1.47 = ( cons_a @ Y4 @ Ys3 ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_254_list_Oinducts,axiom,
% 2.56/1.47 ! [P3: list_a > $o,List: list_a] :
% 2.56/1.47 ( ( P3 @ nil_a )
% 2.56/1.47 => ( ! [X1: a,X23: list_a] :
% 2.56/1.47 ( ( P3 @ X23 )
% 2.56/1.47 => ( P3 @ ( cons_a @ X1 @ X23 ) ) )
% 2.56/1.47 => ( P3 @ List ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_255_list_Oexhaust,axiom,
% 2.56/1.47 ! [Y3: list_a] :
% 2.56/1.47 ( ( Y3 != nil_a )
% 2.56/1.47 => ~ ! [X213: a,X223: list_a] :
% 2.56/1.47 ( Y3
% 2.56/1.47 != ( cons_a @ X213 @ X223 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_256_list_OdiscI,axiom,
% 2.56/1.47 ! [List: list_a,X21: a,X22: list_a] :
% 2.56/1.47 ( ( List
% 2.56/1.47 = ( cons_a @ X21 @ X22 ) )
% 2.56/1.47 => ( List != nil_a ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_257_list_Odistinct_I1_J,axiom,
% 2.56/1.47 ! [X21: a,X22: list_a] :
% 2.56/1.47 ( nil_a
% 2.56/1.47 != ( cons_a @ X21 @ X22 ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_258_append__Cons,axiom,
% 2.56/1.47 ! [X: a,Xs: list_a,Ys2: list_a] :
% 2.56/1.47 ( ( append_a @ ( cons_a @ X @ Xs ) @ Ys2 )
% 2.56/1.47 = ( cons_a @ X @ ( append_a @ Xs @ Ys2 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_259_Cons__eq__appendI,axiom,
% 2.56/1.47 ! [X: a,Xs1: list_a,Ys2: list_a,Xs: list_a,Zs: list_a] :
% 2.56/1.47 ( ( ( cons_a @ X @ Xs1 )
% 2.56/1.47 = Ys2 )
% 2.56/1.47 => ( ( Xs
% 2.56/1.47 = ( append_a @ Xs1 @ Zs ) )
% 2.56/1.47 => ( ( cons_a @ X @ Xs )
% 2.56/1.47 = ( append_a @ Ys2 @ Zs ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_260_append_Oleft__neutral,axiom,
% 2.56/1.47 ! [A: list_a] :
% 2.56/1.47 ( ( append_a @ nil_a @ A )
% 2.56/1.47 = A ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_261_append__Nil,axiom,
% 2.56/1.47 ! [Ys2: list_a] :
% 2.56/1.47 ( ( append_a @ nil_a @ Ys2 )
% 2.56/1.47 = Ys2 ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_262_eq__Nil__appendI,axiom,
% 2.56/1.47 ! [Xs: list_a,Ys2: list_a] :
% 2.56/1.47 ( ( Xs = Ys2 )
% 2.56/1.47 => ( Xs
% 2.56/1.47 = ( append_a @ nil_a @ Ys2 ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_263_null__rec_I1_J,axiom,
% 2.56/1.47 ! [X: a,Xs: list_a] :
% 2.56/1.47 ~ ( null_a @ ( cons_a @ X @ Xs ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_264_eq__Nil__null,axiom,
% 2.56/1.47 ! [Xs: list_a] :
% 2.56/1.47 ( ( Xs = nil_a )
% 2.56/1.47 = ( null_a @ Xs ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_265_null__rec_I2_J,axiom,
% 2.56/1.47 null_a @ nil_a ).
% 2.56/1.47
% 2.56/1.47 thf(fact_266_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 2.56/1.47 ! [A: nat,B: nat,C: nat] :
% 2.56/1.47 ( ( ord_less_nat @ A @ B )
% 2.56/1.47 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 2.56/1.47 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_267_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 2.56/1.47 ! [A: a,B: a,C: a] :
% 2.56/1.47 ( ( ord_less_a @ A @ B )
% 2.56/1.47 => ( ( ord_less_a @ zero_zero_a @ C )
% 2.56/1.47 => ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_268_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a,C: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ A @ B )
% 2.56/1.47 => ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 2.56/1.47 => ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_269_mult__less__cancel__right__disj,axiom,
% 2.56/1.47 ! [A: a,C: a,B: a] :
% 2.56/1.47 ( ( ord_less_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) )
% 2.56/1.47 = ( ( ( ord_less_a @ zero_zero_a @ C )
% 2.56/1.47 & ( ord_less_a @ A @ B ) )
% 2.56/1.47 | ( ( ord_less_a @ C @ zero_zero_a )
% 2.56/1.47 & ( ord_less_a @ B @ A ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_270_mult__less__cancel__right__disj,axiom,
% 2.56/1.47 ! [A: poly_a,C: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ ( times_times_poly_a @ A @ C ) @ ( times_times_poly_a @ B @ C ) )
% 2.56/1.47 = ( ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 2.56/1.47 & ( ord_less_poly_a @ A @ B ) )
% 2.56/1.47 | ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
% 2.56/1.47 & ( ord_less_poly_a @ B @ A ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_271_mult__strict__right__mono,axiom,
% 2.56/1.47 ! [A: nat,B: nat,C: nat] :
% 2.56/1.47 ( ( ord_less_nat @ A @ B )
% 2.56/1.47 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 2.56/1.47 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_272_mult__strict__right__mono,axiom,
% 2.56/1.47 ! [A: a,B: a,C: a] :
% 2.56/1.47 ( ( ord_less_a @ A @ B )
% 2.56/1.47 => ( ( ord_less_a @ zero_zero_a @ C )
% 2.56/1.47 => ( ord_less_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_273_mult__strict__right__mono,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a,C: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ A @ B )
% 2.56/1.47 => ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 2.56/1.47 => ( ord_less_poly_a @ ( times_times_poly_a @ A @ C ) @ ( times_times_poly_a @ B @ C ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_274_mult__strict__right__mono__neg,axiom,
% 2.56/1.47 ! [B: a,A: a,C: a] :
% 2.56/1.47 ( ( ord_less_a @ B @ A )
% 2.56/1.47 => ( ( ord_less_a @ C @ zero_zero_a )
% 2.56/1.47 => ( ord_less_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_275_mult__strict__right__mono__neg,axiom,
% 2.56/1.47 ! [B: poly_a,A: poly_a,C: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ B @ A )
% 2.56/1.47 => ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
% 2.56/1.47 => ( ord_less_poly_a @ ( times_times_poly_a @ A @ C ) @ ( times_times_poly_a @ B @ C ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_276_mult__less__cancel__left__disj,axiom,
% 2.56/1.47 ! [C: a,A: a,B: a] :
% 2.56/1.47 ( ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) )
% 2.56/1.47 = ( ( ( ord_less_a @ zero_zero_a @ C )
% 2.56/1.47 & ( ord_less_a @ A @ B ) )
% 2.56/1.47 | ( ( ord_less_a @ C @ zero_zero_a )
% 2.56/1.47 & ( ord_less_a @ B @ A ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_277_mult__less__cancel__left__disj,axiom,
% 2.56/1.47 ! [C: poly_a,A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) )
% 2.56/1.47 = ( ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 2.56/1.47 & ( ord_less_poly_a @ A @ B ) )
% 2.56/1.47 | ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
% 2.56/1.47 & ( ord_less_poly_a @ B @ A ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_278_mult__strict__left__mono,axiom,
% 2.56/1.47 ! [A: nat,B: nat,C: nat] :
% 2.56/1.47 ( ( ord_less_nat @ A @ B )
% 2.56/1.47 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 2.56/1.47 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_279_mult__strict__left__mono,axiom,
% 2.56/1.47 ! [A: a,B: a,C: a] :
% 2.56/1.47 ( ( ord_less_a @ A @ B )
% 2.56/1.47 => ( ( ord_less_a @ zero_zero_a @ C )
% 2.56/1.47 => ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_280_mult__strict__left__mono,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a,C: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ A @ B )
% 2.56/1.47 => ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 2.56/1.47 => ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_281_mult__strict__left__mono__neg,axiom,
% 2.56/1.47 ! [B: a,A: a,C: a] :
% 2.56/1.47 ( ( ord_less_a @ B @ A )
% 2.56/1.47 => ( ( ord_less_a @ C @ zero_zero_a )
% 2.56/1.47 => ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_282_mult__strict__left__mono__neg,axiom,
% 2.56/1.47 ! [B: poly_a,A: poly_a,C: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ B @ A )
% 2.56/1.47 => ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
% 2.56/1.47 => ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_283_mult__less__cancel__left__pos,axiom,
% 2.56/1.47 ! [C: a,A: a,B: a] :
% 2.56/1.47 ( ( ord_less_a @ zero_zero_a @ C )
% 2.56/1.47 => ( ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) )
% 2.56/1.47 = ( ord_less_a @ A @ B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_284_mult__less__cancel__left__pos,axiom,
% 2.56/1.47 ! [C: poly_a,A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
% 2.56/1.47 => ( ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) )
% 2.56/1.47 = ( ord_less_poly_a @ A @ B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_285_mult__less__cancel__left__neg,axiom,
% 2.56/1.47 ! [C: a,A: a,B: a] :
% 2.56/1.47 ( ( ord_less_a @ C @ zero_zero_a )
% 2.56/1.47 => ( ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) )
% 2.56/1.47 = ( ord_less_a @ B @ A ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_286_mult__less__cancel__left__neg,axiom,
% 2.56/1.47 ! [C: poly_a,A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
% 2.56/1.47 => ( ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) )
% 2.56/1.47 = ( ord_less_poly_a @ B @ A ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_287_zero__less__mult__pos2,axiom,
% 2.56/1.47 ! [B: nat,A: nat] :
% 2.56/1.47 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 2.56/1.47 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.56/1.47 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_288_zero__less__mult__pos2,axiom,
% 2.56/1.47 ! [B: a,A: a] :
% 2.56/1.47 ( ( ord_less_a @ zero_zero_a @ ( times_times_a @ B @ A ) )
% 2.56/1.47 => ( ( ord_less_a @ zero_zero_a @ A )
% 2.56/1.47 => ( ord_less_a @ zero_zero_a @ B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_289_zero__less__mult__pos2,axiom,
% 2.56/1.47 ! [B: poly_a,A: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ B @ A ) )
% 2.56/1.47 => ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 2.56/1.47 => ( ord_less_poly_a @ zero_zero_poly_a @ B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_290_zero__less__mult__pos,axiom,
% 2.56/1.47 ! [A: nat,B: nat] :
% 2.56/1.47 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 2.56/1.47 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.56/1.47 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_291_zero__less__mult__pos,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) )
% 2.56/1.47 => ( ( ord_less_a @ zero_zero_a @ A )
% 2.56/1.47 => ( ord_less_a @ zero_zero_a @ B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_292_zero__less__mult__pos,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) )
% 2.56/1.47 => ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 2.56/1.47 => ( ord_less_poly_a @ zero_zero_poly_a @ B ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_293_zero__less__mult__iff,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) )
% 2.56/1.47 = ( ( ( ord_less_a @ zero_zero_a @ A )
% 2.56/1.47 & ( ord_less_a @ zero_zero_a @ B ) )
% 2.56/1.47 | ( ( ord_less_a @ A @ zero_zero_a )
% 2.56/1.47 & ( ord_less_a @ B @ zero_zero_a ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_294_zero__less__mult__iff,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) )
% 2.56/1.47 = ( ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 2.56/1.47 & ( ord_less_poly_a @ zero_zero_poly_a @ B ) )
% 2.56/1.47 | ( ( ord_less_poly_a @ A @ zero_zero_poly_a )
% 2.56/1.47 & ( ord_less_poly_a @ B @ zero_zero_poly_a ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_295_mult__pos__neg2,axiom,
% 2.56/1.47 ! [A: nat,B: nat] :
% 2.56/1.47 ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.56/1.47 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 2.56/1.47 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_296_mult__pos__neg2,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( ord_less_a @ zero_zero_a @ A )
% 2.56/1.47 => ( ( ord_less_a @ B @ zero_zero_a )
% 2.56/1.47 => ( ord_less_a @ ( times_times_a @ B @ A ) @ zero_zero_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_297_mult__pos__neg2,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 2.56/1.47 => ( ( ord_less_poly_a @ B @ zero_zero_poly_a )
% 2.56/1.47 => ( ord_less_poly_a @ ( times_times_poly_a @ B @ A ) @ zero_zero_poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_298_mult__pos__pos,axiom,
% 2.56/1.47 ! [A: nat,B: nat] :
% 2.56/1.47 ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.56/1.47 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 2.56/1.47 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_299_mult__pos__pos,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( ord_less_a @ zero_zero_a @ A )
% 2.56/1.47 => ( ( ord_less_a @ zero_zero_a @ B )
% 2.56/1.47 => ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_300_mult__pos__pos,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 2.56/1.47 => ( ( ord_less_poly_a @ zero_zero_poly_a @ B )
% 2.56/1.47 => ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_301_mult__pos__neg,axiom,
% 2.56/1.47 ! [A: nat,B: nat] :
% 2.56/1.47 ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.56/1.47 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 2.56/1.47 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_302_mult__pos__neg,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( ord_less_a @ zero_zero_a @ A )
% 2.56/1.47 => ( ( ord_less_a @ B @ zero_zero_a )
% 2.56/1.47 => ( ord_less_a @ ( times_times_a @ A @ B ) @ zero_zero_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_303_mult__pos__neg,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 2.56/1.47 => ( ( ord_less_poly_a @ B @ zero_zero_poly_a )
% 2.56/1.47 => ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ zero_zero_poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_304_mult__neg__pos,axiom,
% 2.56/1.47 ! [A: nat,B: nat] :
% 2.56/1.47 ( ( ord_less_nat @ A @ zero_zero_nat )
% 2.56/1.47 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 2.56/1.47 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_305_mult__neg__pos,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( ord_less_a @ A @ zero_zero_a )
% 2.56/1.47 => ( ( ord_less_a @ zero_zero_a @ B )
% 2.56/1.47 => ( ord_less_a @ ( times_times_a @ A @ B ) @ zero_zero_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_306_mult__neg__pos,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ A @ zero_zero_poly_a )
% 2.56/1.47 => ( ( ord_less_poly_a @ zero_zero_poly_a @ B )
% 2.56/1.47 => ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ zero_zero_poly_a ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_307_mult__less__0__iff,axiom,
% 2.56/1.47 ! [A: a,B: a] :
% 2.56/1.47 ( ( ord_less_a @ ( times_times_a @ A @ B ) @ zero_zero_a )
% 2.56/1.47 = ( ( ( ord_less_a @ zero_zero_a @ A )
% 2.56/1.47 & ( ord_less_a @ B @ zero_zero_a ) )
% 2.56/1.47 | ( ( ord_less_a @ A @ zero_zero_a )
% 2.56/1.47 & ( ord_less_a @ zero_zero_a @ B ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_308_mult__less__0__iff,axiom,
% 2.56/1.47 ! [A: poly_a,B: poly_a] :
% 2.56/1.47 ( ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ zero_zero_poly_a )
% 2.56/1.47 = ( ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
% 2.56/1.47 & ( ord_less_poly_a @ B @ zero_zero_poly_a ) )
% 2.56/1.47 | ( ( ord_less_poly_a @ A @ zero_zero_poly_a )
% 2.56/1.47 & ( ord_less_poly_a @ zero_zero_poly_a @ B ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_309_nat__mult__less__cancel__disj,axiom,
% 2.56/1.47 ! [K: nat,M: nat,N: nat] :
% 2.56/1.47 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 2.56/1.47 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 2.56/1.47 & ( ord_less_nat @ M @ N ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_310_nat__0__less__mult__iff,axiom,
% 2.56/1.47 ! [M: nat,N: nat] :
% 2.56/1.47 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 2.56/1.47 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 2.56/1.47 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_311_mult__less__cancel2,axiom,
% 2.56/1.47 ! [M: nat,K: nat,N: nat] :
% 2.56/1.47 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 2.56/1.47 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 2.56/1.47 & ( ord_less_nat @ M @ N ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_312_mult__cancel2,axiom,
% 2.56/1.47 ! [M: nat,K: nat,N: nat] :
% 2.56/1.47 ( ( ( times_times_nat @ M @ K )
% 2.56/1.47 = ( times_times_nat @ N @ K ) )
% 2.56/1.47 = ( ( M = N )
% 2.56/1.47 | ( K = zero_zero_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_313_neq0__conv,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ( ( N != zero_zero_nat )
% 2.56/1.47 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_314_less__nat__zero__code,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_315_bot__nat__0_Onot__eq__extremum,axiom,
% 2.56/1.47 ! [A: nat] :
% 2.56/1.47 ( ( A != zero_zero_nat )
% 2.56/1.47 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_316_mult__is__0,axiom,
% 2.56/1.47 ! [M: nat,N: nat] :
% 2.56/1.47 ( ( ( times_times_nat @ M @ N )
% 2.56/1.47 = zero_zero_nat )
% 2.56/1.47 = ( ( M = zero_zero_nat )
% 2.56/1.47 | ( N = zero_zero_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_317_mult__0__right,axiom,
% 2.56/1.47 ! [M: nat] :
% 2.56/1.47 ( ( times_times_nat @ M @ zero_zero_nat )
% 2.56/1.47 = zero_zero_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_318_mult__cancel1,axiom,
% 2.56/1.47 ! [K: nat,M: nat,N: nat] :
% 2.56/1.47 ( ( ( times_times_nat @ K @ M )
% 2.56/1.47 = ( times_times_nat @ K @ N ) )
% 2.56/1.47 = ( ( M = N )
% 2.56/1.47 | ( K = zero_zero_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_319_nat__1__eq__mult__iff,axiom,
% 2.56/1.47 ! [M: nat,N: nat] :
% 2.56/1.47 ( ( one_one_nat
% 2.56/1.47 = ( times_times_nat @ M @ N ) )
% 2.56/1.47 = ( ( M = one_one_nat )
% 2.56/1.47 & ( N = one_one_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_320_nat__mult__eq__1__iff,axiom,
% 2.56/1.47 ! [M: nat,N: nat] :
% 2.56/1.47 ( ( ( times_times_nat @ M @ N )
% 2.56/1.47 = one_one_nat )
% 2.56/1.47 = ( ( M = one_one_nat )
% 2.56/1.47 & ( N = one_one_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_321_less__one,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ( ( ord_less_nat @ N @ one_one_nat )
% 2.56/1.47 = ( N = zero_zero_nat ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_322_nat__mult__1,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ( ( times_times_nat @ one_one_nat @ N )
% 2.56/1.47 = N ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_323_nat__mult__1__right,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ( ( times_times_nat @ N @ one_one_nat )
% 2.56/1.47 = N ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_324_linorder__neqE__nat,axiom,
% 2.56/1.47 ! [X: nat,Y3: nat] :
% 2.56/1.47 ( ( X != Y3 )
% 2.56/1.47 => ( ~ ( ord_less_nat @ X @ Y3 )
% 2.56/1.47 => ( ord_less_nat @ Y3 @ X ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_325_infinite__descent,axiom,
% 2.56/1.47 ! [P3: nat > $o,N: nat] :
% 2.56/1.47 ( ! [N2: nat] :
% 2.56/1.47 ( ~ ( P3 @ N2 )
% 2.56/1.47 => ? [M2: nat] :
% 2.56/1.47 ( ( ord_less_nat @ M2 @ N2 )
% 2.56/1.47 & ~ ( P3 @ M2 ) ) )
% 2.56/1.47 => ( P3 @ N ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_326_nat__less__induct,axiom,
% 2.56/1.47 ! [P3: nat > $o,N: nat] :
% 2.56/1.47 ( ! [N2: nat] :
% 2.56/1.47 ( ! [M2: nat] :
% 2.56/1.47 ( ( ord_less_nat @ M2 @ N2 )
% 2.56/1.47 => ( P3 @ M2 ) )
% 2.56/1.47 => ( P3 @ N2 ) )
% 2.56/1.47 => ( P3 @ N ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_327_less__irrefl__nat,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ~ ( ord_less_nat @ N @ N ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_328_less__not__refl3,axiom,
% 2.56/1.47 ! [S: nat,T: nat] :
% 2.56/1.47 ( ( ord_less_nat @ S @ T )
% 2.56/1.47 => ( S != T ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_329_less__not__refl2,axiom,
% 2.56/1.47 ! [N: nat,M: nat] :
% 2.56/1.47 ( ( ord_less_nat @ N @ M )
% 2.56/1.47 => ( M != N ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_330_less__not__refl,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ~ ( ord_less_nat @ N @ N ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_331_nat__neq__iff,axiom,
% 2.56/1.47 ! [M: nat,N: nat] :
% 2.56/1.47 ( ( M != N )
% 2.56/1.47 = ( ( ord_less_nat @ M @ N )
% 2.56/1.47 | ( ord_less_nat @ N @ M ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_332_gr0I,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ( ( N != zero_zero_nat )
% 2.56/1.47 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_333_not__gr0,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 2.56/1.47 = ( N = zero_zero_nat ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_334_not__less0,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_335_less__zeroE,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_336_gr__implies__not0,axiom,
% 2.56/1.47 ! [M: nat,N: nat] :
% 2.56/1.47 ( ( ord_less_nat @ M @ N )
% 2.56/1.47 => ( N != zero_zero_nat ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_337_infinite__descent0,axiom,
% 2.56/1.47 ! [P3: nat > $o,N: nat] :
% 2.56/1.47 ( ( P3 @ zero_zero_nat )
% 2.56/1.47 => ( ! [N2: nat] :
% 2.56/1.47 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 2.56/1.47 => ( ~ ( P3 @ N2 )
% 2.56/1.47 => ? [M2: nat] :
% 2.56/1.47 ( ( ord_less_nat @ M2 @ N2 )
% 2.56/1.47 & ~ ( P3 @ M2 ) ) ) )
% 2.56/1.47 => ( P3 @ N ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_338_bot__nat__0_Oextremum__strict,axiom,
% 2.56/1.47 ! [A: nat] :
% 2.56/1.47 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_339_mult__less__mono1,axiom,
% 2.56/1.47 ! [I: nat,J: nat,K: nat] :
% 2.56/1.47 ( ( ord_less_nat @ I @ J )
% 2.56/1.47 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 2.56/1.47 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_340_mult__less__mono2,axiom,
% 2.56/1.47 ! [I: nat,J: nat,K: nat] :
% 2.56/1.47 ( ( ord_less_nat @ I @ J )
% 2.56/1.47 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 2.56/1.47 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_341_mult__0,axiom,
% 2.56/1.47 ! [N: nat] :
% 2.56/1.47 ( ( times_times_nat @ zero_zero_nat @ N )
% 2.56/1.47 = zero_zero_nat ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_342_nat__mult__eq__cancel1,axiom,
% 2.56/1.47 ! [K: nat,M: nat,N: nat] :
% 2.56/1.47 ( ( ord_less_nat @ zero_zero_nat @ K )
% 2.56/1.47 => ( ( ( times_times_nat @ K @ M )
% 2.56/1.47 = ( times_times_nat @ K @ N ) )
% 2.56/1.47 = ( M = N ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_343_nat__mult__less__cancel1,axiom,
% 2.56/1.47 ! [K: nat,M: nat,N: nat] :
% 2.56/1.47 ( ( ord_less_nat @ zero_zero_nat @ K )
% 2.56/1.47 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 2.56/1.47 = ( ord_less_nat @ M @ N ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_344_nat__mult__eq__cancel__disj,axiom,
% 2.56/1.47 ! [K: nat,M: nat,N: nat] :
% 2.56/1.47 ( ( ( times_times_nat @ K @ M )
% 2.56/1.47 = ( times_times_nat @ K @ N ) )
% 2.56/1.47 = ( ( K = zero_zero_nat )
% 2.56/1.47 | ( M = N ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(fact_345_mult__eq__self__implies__10,axiom,
% 2.56/1.47 ! [M: nat,N: nat] :
% 2.56/1.47 ( ( M
% 2.56/1.47 = ( times_times_nat @ M @ N ) )
% 2.56/1.47 => ( ( N = one_one_nat )
% 2.56/1.47 | ( M = zero_zero_nat ) ) ) ).
% 2.56/1.47
% 2.56/1.47 thf(conj_0,conjecture,
% 2.56/1.47 ( ( descar2095969287nges_a @ ys )
% 2.56/1.47 = ( descar2095969287nges_a @ ( coeffs_a @ g ) ) ) ).
% 2.56/1.47 ------------------------
% 2.56/1.50 % (27961)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_27787 for (2999ds/4Mi)
% 2.56/1.50 % (27963)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/2Mi)
% 2.56/1.50 % (27962)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_27787 for (2999ds/27Mi)
% 2.56/1.50 % (27966)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/18Mi)
% 2.67/1.50 % (27965)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_27787 for (2999ds/275Mi)
% 2.67/1.50 % (27963)Instruction limit reached!
% 2.67/1.50 % (27963)------------------------------
% 2.67/1.50 % (27963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.50 % (27963)Termination reason: Unknown
% 2.67/1.50 % (27963)Termination phase: shuffling
% 2.67/1.50
% 2.67/1.50 % (27963)Memory used [KB]: 1407
% 2.67/1.50 % (27963)Time elapsed: 0.003 s
% 2.67/1.50 % (27963)Instructions burned: 3 (million)
% 2.67/1.50 % (27963)------------------------------
% 2.67/1.50 % (27963)------------------------------
% 2.67/1.50 % (27960)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/183Mi)
% 2.67/1.50 % (27961)Instruction limit reached!
% 2.67/1.50 % (27961)------------------------------
% 2.67/1.50 % (27961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.50 % (27961)Termination reason: Unknown
% 2.67/1.50 % (27961)Termination phase: shuffling
% 2.67/1.50
% 2.67/1.50 % (27961)Memory used [KB]: 1407
% 2.67/1.50 % (27961)Time elapsed: 0.004 s
% 2.67/1.50 % (27961)Instructions burned: 7 (million)
% 2.67/1.50 % (27961)------------------------------
% 2.67/1.50 % (27961)------------------------------
% 2.67/1.50 % (27964)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_27787 for (2999ds/2Mi)
% 2.67/1.50 % (27964)Instruction limit reached!
% 2.67/1.50 % (27964)------------------------------
% 2.67/1.50 % (27964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.50 % (27964)Termination reason: Unknown
% 2.67/1.50 % (27964)Termination phase: shuffling
% 2.67/1.50
% 2.67/1.50 % (27964)Memory used [KB]: 1279
% 2.67/1.50 % (27964)Time elapsed: 0.003 s
% 2.67/1.50 % (27964)Instructions burned: 2 (million)
% 2.67/1.50 % (27964)------------------------------
% 2.67/1.50 % (27964)------------------------------
% 2.67/1.50 % (27966)Instruction limit reached!
% 2.67/1.50 % (27966)------------------------------
% 2.67/1.50 % (27966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.50 % (27966)Termination reason: Unknown
% 2.67/1.50 % (27966)Termination phase: Property scanning
% 2.67/1.50
% 2.67/1.50 % (27966)Memory used [KB]: 1535
% 2.67/1.50 % (27966)Time elapsed: 0.008 s
% 2.67/1.50 % (27966)Instructions burned: 21 (million)
% 2.67/1.50 % (27966)------------------------------
% 2.67/1.50 % (27966)------------------------------
% 2.67/1.50 % (27962)Instruction limit reached!
% 2.67/1.50 % (27962)------------------------------
% 2.67/1.50 % (27962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.50 % (27962)Termination reason: Unknown
% 2.67/1.50 % (27962)Termination phase: Property scanning
% 2.67/1.50
% 2.67/1.50 % (27962)Memory used [KB]: 1663
% 2.67/1.50 % (27962)Time elapsed: 0.010 s
% 2.67/1.50 % (27962)Instructions burned: 28 (million)
% 2.67/1.50 % (27962)------------------------------
% 2.67/1.50 % (27962)------------------------------
% 2.67/1.51 % (27967)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/3Mi)
% 2.67/1.51 % (27968)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_27787 for (2999ds/37Mi)
% 2.67/1.51 % (27967)Instruction limit reached!
% 2.67/1.51 % (27967)------------------------------
% 2.67/1.51 % (27967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.51 % (27967)Termination reason: Unknown
% 2.67/1.51 % (27967)Termination phase: shuffling
% 2.67/1.51
% 2.67/1.51 % (27967)Memory used [KB]: 1407
% 2.67/1.51 % (27967)Time elapsed: 0.002 s
% 2.67/1.51 % (27967)Instructions burned: 3 (million)
% 2.67/1.51 % (27967)------------------------------
% 2.67/1.51 % (27967)------------------------------
% 2.67/1.51 % (27970)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_27787 for (2999ds/3Mi)
% 2.67/1.51 % (27971)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_27787 for (2999ds/1041Mi)
% 2.67/1.51 % (27970)Instruction limit reached!
% 2.67/1.51 % (27970)------------------------------
% 2.67/1.51 % (27970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.51 % (27970)Termination reason: Unknown
% 2.67/1.51 % (27970)Termination phase: shuffling
% 2.67/1.51
% 2.67/1.51 % (27970)Memory used [KB]: 1407
% 2.67/1.51 % (27970)Time elapsed: 0.003 s
% 2.67/1.51 % (27970)Instructions burned: 5 (million)
% 2.67/1.51 % (27970)------------------------------
% 2.67/1.51 % (27970)------------------------------
% 2.67/1.52 % (27969)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_27787 for (2999ds/15Mi)
% 2.67/1.52 % (27972)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/7Mi)
% 2.67/1.52 % (27968)Instruction limit reached!
% 2.67/1.52 % (27968)------------------------------
% 2.67/1.52 % (27968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.52 % (27968)Termination reason: Unknown
% 2.67/1.52 % (27968)Termination phase: shuffling
% 2.67/1.52
% 2.67/1.52 % (27968)Memory used [KB]: 2046
% 2.67/1.52 % (27968)Time elapsed: 0.011 s
% 2.67/1.52 % (27968)Instructions burned: 37 (million)
% 2.67/1.52 % (27968)------------------------------
% 2.67/1.52 % (27968)------------------------------
% 2.67/1.52 % (27972)Instruction limit reached!
% 2.67/1.52 % (27972)------------------------------
% 2.67/1.52 % (27972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.52 % (27972)Termination reason: Unknown
% 2.67/1.52 % (27972)Termination phase: shuffling
% 2.67/1.52
% 2.67/1.52 % (27972)Memory used [KB]: 1535
% 2.67/1.52 % (27972)Time elapsed: 0.004 s
% 2.67/1.52 % (27972)Instructions burned: 9 (million)
% 2.67/1.52 % (27972)------------------------------
% 2.67/1.52 % (27972)------------------------------
% 2.67/1.52 % (27965)Refutation not found, incomplete strategy
% 2.67/1.52 % (27965)------------------------------
% 2.67/1.52 % (27965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.52 % (27965)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.52
% 2.67/1.52
% 2.67/1.52 % (27965)Memory used [KB]: 6652
% 2.67/1.52 % (27965)Time elapsed: 0.024 s
% 2.67/1.52 % (27965)Instructions burned: 71 (million)
% 2.67/1.52 % (27965)------------------------------
% 2.67/1.52 % (27965)------------------------------
% 2.67/1.53 % (27974)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_27787 for (2999ds/3Mi)
% 2.67/1.53 % (27969)Instruction limit reached!
% 2.67/1.53 % (27969)------------------------------
% 2.67/1.53 % (27969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.53 % (27969)Termination reason: Unknown
% 2.67/1.53 % (27969)Termination phase: Property scanning
% 2.67/1.53
% 2.67/1.53 % (27969)Memory used [KB]: 1535
% 2.67/1.53 % (27969)Time elapsed: 0.012 s
% 2.67/1.53 % (27969)Instructions burned: 16 (million)
% 2.67/1.53 % (27969)------------------------------
% 2.67/1.53 % (27969)------------------------------
% 2.67/1.53 % (27973)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/16Mi)
% 2.67/1.53 % (27974)Instruction limit reached!
% 2.67/1.53 % (27974)------------------------------
% 2.67/1.53 % (27974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.53 % (27974)Termination reason: Unknown
% 2.67/1.53 % (27974)Termination phase: shuffling
% 2.67/1.53
% 2.67/1.53 % (27974)Memory used [KB]: 1407
% 2.67/1.53 % (27974)Time elapsed: 0.002 s
% 2.67/1.53 % (27974)Instructions burned: 3 (million)
% 2.67/1.53 % (27974)------------------------------
% 2.67/1.53 % (27974)------------------------------
% 2.67/1.53 % (27975)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_27787 for (2999ds/3Mi)
% 2.67/1.53 % (27975)Instruction limit reached!
% 2.67/1.53 % (27975)------------------------------
% 2.67/1.53 % (27975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.53 % (27975)Termination reason: Unknown
% 2.67/1.53 % (27975)Termination phase: shuffling
% 2.67/1.53
% 2.67/1.53 % (27975)Memory used [KB]: 1407
% 2.67/1.53 % (27975)Time elapsed: 0.002 s
% 2.67/1.53 % (27975)Instructions burned: 3 (million)
% 2.67/1.53 % (27975)------------------------------
% 2.67/1.53 % (27975)------------------------------
% 2.67/1.54 % (27973)Instruction limit reached!
% 2.67/1.54 % (27973)------------------------------
% 2.67/1.54 % (27973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.54 % (27973)Termination reason: Unknown
% 2.67/1.54 % (27973)Termination phase: Property scanning
% 2.67/1.54
% 2.67/1.54 % (27973)Memory used [KB]: 1663
% 2.67/1.54 % (27973)Time elapsed: 0.011 s
% 2.67/1.54 % (27973)Instructions burned: 17 (million)
% 2.67/1.54 % (27973)------------------------------
% 2.67/1.54 % (27973)------------------------------
% 2.67/1.54 % (27978)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/4Mi)
% 2.67/1.54 % (27976)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/7Mi)
% 2.67/1.54 % (27978)Instruction limit reached!
% 2.67/1.54 % (27978)------------------------------
% 2.67/1.54 % (27978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.54 % (27978)Termination reason: Unknown
% 2.67/1.54 % (27978)Termination phase: shuffling
% 2.67/1.54
% 2.67/1.54 % (27978)Memory used [KB]: 1407
% 2.67/1.54 % (27978)Time elapsed: 0.003 s
% 2.67/1.54 % (27978)Instructions burned: 6 (million)
% 2.67/1.54 % (27978)------------------------------
% 2.67/1.54 % (27978)------------------------------
% 2.67/1.54 % (27979)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/18Mi)
% 2.67/1.54 % (27976)Instruction limit reached!
% 2.67/1.54 % (27976)------------------------------
% 2.67/1.54 % (27976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.54 % (27976)Termination reason: Unknown
% 2.67/1.54 % (27976)Termination phase: shuffling
% 2.67/1.54
% 2.67/1.54 % (27976)Memory used [KB]: 1407
% 2.67/1.54 % (27976)Time elapsed: 0.006 s
% 2.67/1.54 % (27976)Instructions burned: 8 (million)
% 2.67/1.54 % (27976)------------------------------
% 2.67/1.54 % (27976)------------------------------
% 2.67/1.54 % (27977)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/3Mi)
% 2.67/1.55 % (27979)Instruction limit reached!
% 2.67/1.55 % (27979)------------------------------
% 2.67/1.55 % (27979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.55 % (27979)Termination reason: Unknown
% 2.67/1.55 % (27979)Termination phase: Property scanning
% 2.67/1.55
% 2.67/1.55 % (27979)Memory used [KB]: 1663
% 2.67/1.55 % (27979)Time elapsed: 0.007 s
% 2.67/1.55 % (27979)Instructions burned: 20 (million)
% 2.67/1.55 % (27979)------------------------------
% 2.67/1.55 % (27979)------------------------------
% 2.67/1.55 % (27977)Instruction limit reached!
% 2.67/1.55 % (27977)------------------------------
% 2.67/1.55 % (27977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.55 % (27977)Termination reason: Unknown
% 2.67/1.55 % (27977)Termination phase: shuffling
% 2.67/1.55
% 2.67/1.55 % (27977)Memory used [KB]: 1407
% 2.67/1.55 % (27977)Time elapsed: 0.004 s
% 2.67/1.55 % (27977)Instructions burned: 3 (million)
% 2.67/1.55 % (27977)------------------------------
% 2.67/1.55 % (27977)------------------------------
% 2.67/1.55 % (27981)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/6Mi)
% 2.67/1.55 % (27980)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/710Mi)
% 2.67/1.55 % (27981)Instruction limit reached!
% 2.67/1.55 % (27981)------------------------------
% 2.67/1.55 % (27981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.55 % (27981)Termination reason: Unknown
% 2.67/1.55 % (27981)Termination phase: shuffling
% 2.67/1.55
% 2.67/1.55 % (27981)Memory used [KB]: 1407
% 2.67/1.55 % (27981)Time elapsed: 0.003 s
% 2.67/1.55 % (27981)Instructions burned: 6 (million)
% 2.67/1.55 % (27981)------------------------------
% 2.67/1.55 % (27981)------------------------------
% 2.67/1.56 % (27983)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_27787 for (2999ds/21Mi)
% 2.67/1.56 % (27985)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_27787 for (2999ds/6Mi)
% 2.67/1.56 % (27982)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_27787 for (2999ds/902Mi)
% 2.67/1.56 % (27985)Instruction limit reached!
% 2.67/1.56 % (27985)------------------------------
% 2.67/1.56 % (27985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.56 % (27985)Termination reason: Unknown
% 2.67/1.56 % (27985)Termination phase: shuffling
% 2.67/1.56
% 2.67/1.56 % (27985)Memory used [KB]: 1407
% 2.67/1.56 % (27985)Time elapsed: 0.003 s
% 2.67/1.56 % (27985)Instructions burned: 7 (million)
% 2.67/1.56 % (27985)------------------------------
% 2.67/1.56 % (27985)------------------------------
% 2.67/1.56 % (27984)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/5Mi)
% 2.67/1.56 % (27960)Instruction limit reached!
% 2.67/1.56 % (27960)------------------------------
% 2.67/1.56 % (27960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.56 % (27960)Termination reason: Unknown
% 2.67/1.56 % (27960)Termination phase: Saturation
% 2.67/1.56
% 2.67/1.56 % (27960)Memory used [KB]: 7164
% 2.67/1.56 % (27960)Time elapsed: 0.070 s
% 2.67/1.56 % (27960)Instructions burned: 184 (million)
% 2.67/1.56 % (27960)------------------------------
% 2.67/1.56 % (27960)------------------------------
% 2.67/1.57 % (27984)Instruction limit reached!
% 2.67/1.57 % (27984)------------------------------
% 2.67/1.57 % (27984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.57 % (27984)Termination reason: Unknown
% 2.67/1.57 % (27984)Termination phase: shuffling
% 2.67/1.57
% 2.67/1.57 % (27984)Memory used [KB]: 1407
% 2.67/1.57 % (27984)Time elapsed: 0.005 s
% 2.67/1.57 % (27984)Instructions burned: 5 (million)
% 2.67/1.57 % (27984)------------------------------
% 2.67/1.57 % (27984)------------------------------
% 2.67/1.57 % (27983)Instruction limit reached!
% 2.67/1.57 % (27983)------------------------------
% 2.67/1.57 % (27983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.57 % (27983)Termination reason: Unknown
% 2.67/1.57 % (27983)Termination phase: shuffling
% 2.67/1.57
% 2.67/1.57 % (27983)Memory used [KB]: 1663
% 2.67/1.57 % (27983)Time elapsed: 0.012 s
% 2.67/1.57 % (27983)Instructions burned: 21 (million)
% 2.67/1.57 % (27983)------------------------------
% 2.67/1.57 % (27983)------------------------------
% 2.67/1.57 % (27980)Refutation not found, incomplete strategy
% 2.67/1.57 % (27980)------------------------------
% 2.67/1.57 % (27980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.57 % (27980)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.57
% 2.67/1.57
% 2.67/1.57 % (27980)Memory used [KB]: 6268
% 2.67/1.57 % (27980)Time elapsed: 0.018 s
% 2.67/1.57 % (27980)Instructions burned: 52 (million)
% 2.67/1.57 % (27980)------------------------------
% 2.67/1.57 % (27980)------------------------------
% 2.67/1.57 % (27986)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/377Mi)
% 2.67/1.57 % (27987)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_27787 for (2999ds/779Mi)
% 2.67/1.58 % (27989)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/879Mi)
% 2.67/1.58 % (27990)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/17Mi)
% 2.67/1.58 % (27990)Instruction limit reached!
% 2.67/1.58 % (27990)------------------------------
% 2.67/1.58 % (27990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.58 % (27990)Termination reason: Unknown
% 2.67/1.58 % (27990)Termination phase: Property scanning
% 2.67/1.58
% 2.67/1.58 % (27990)Memory used [KB]: 1663
% 2.67/1.58 % (27990)Time elapsed: 0.007 s
% 2.67/1.58 % (27990)Instructions burned: 19 (million)
% 2.67/1.58 % (27990)------------------------------
% 2.67/1.58 % (27990)------------------------------
% 2.67/1.58 % (27988)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_27787 for (2999ds/19Mi)
% 2.67/1.59 % (27992)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27787 for (2999ds/3Mi)
% 2.67/1.59 % (27992)Instruction limit reached!
% 2.67/1.59 % (27992)------------------------------
% 2.67/1.59 % (27992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.59 % (27992)Termination reason: Unknown
% 2.67/1.59 % (27992)Termination phase: shuffling
% 2.67/1.59
% 2.67/1.59 % (27992)Memory used [KB]: 1407
% 2.67/1.59 % (27992)Time elapsed: 0.003 s
% 2.67/1.59 % (27992)Instructions burned: 5 (million)
% 2.67/1.59 % (27992)------------------------------
% 2.67/1.59 % (27992)------------------------------
% 2.67/1.59 % (27988)Instruction limit reached!
% 2.67/1.59 % (27988)------------------------------
% 2.67/1.59 % (27988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.59 % (27988)Termination reason: Unknown
% 2.67/1.59 % (27988)Termination phase: shuffling
% 2.67/1.59
% 2.67/1.59 % (27988)Memory used [KB]: 1663
% 2.67/1.59 % (27988)Time elapsed: 0.012 s
% 2.67/1.59 % (27988)Instructions burned: 19 (million)
% 2.67/1.59 % (27988)------------------------------
% 2.67/1.59 % (27988)------------------------------
% 2.67/1.60 % (27997)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_27787 for (2998ds/30Mi)
% 2.67/1.61 % (27998)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_27787 for (2998ds/127Mi)
% 2.67/1.61 % (27997)Instruction limit reached!
% 2.67/1.61 % (27997)------------------------------
% 2.67/1.61 % (27997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.61 % (27997)Termination reason: Unknown
% 2.67/1.61 % (27997)Termination phase: Property scanning
% 2.67/1.61
% 2.67/1.61 % (27997)Memory used [KB]: 1663
% 2.67/1.61 % (27997)Time elapsed: 0.010 s
% 2.67/1.61 % (27997)Instructions burned: 30 (million)
% 2.67/1.61 % (27997)------------------------------
% 2.67/1.61 % (27997)------------------------------
% 2.67/1.61 % (27982)Refutation not found, incomplete strategy
% 2.67/1.61 % (27982)------------------------------
% 2.67/1.61 % (27982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.61 % (27982)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.61
% 2.67/1.61
% 2.67/1.61 % (27982)Memory used [KB]: 7036
% 2.67/1.61 % (27982)Time elapsed: 0.056 s
% 2.67/1.61 % (27982)Instructions burned: 100 (million)
% 2.67/1.61 % (27982)------------------------------
% 2.67/1.61 % (27982)------------------------------
% 2.67/1.62 % (28007)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_27787 for (2998ds/100Mi)
% 2.67/1.62 % (28009)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_27787 for (2998ds/3Mi)
% 2.67/1.63 % (28009)Instruction limit reached!
% 2.67/1.63 % (28009)------------------------------
% 2.67/1.63 % (28009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.63 % (28009)Termination reason: Unknown
% 2.67/1.63 % (28009)Termination phase: shuffling
% 2.67/1.63
% 2.67/1.63 % (28009)Memory used [KB]: 1407
% 2.67/1.63 % (28009)Time elapsed: 0.002 s
% 2.67/1.63 % (28009)Instructions burned: 3 (million)
% 2.67/1.63 % (28009)------------------------------
% 2.67/1.63 % (28009)------------------------------
% 2.67/1.64 % (28015)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_27787 for (2998ds/20Mi)
% 2.67/1.64 % (28015)Instruction limit reached!
% 2.67/1.64 % (28015)------------------------------
% 2.67/1.64 % (28015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.64 % (28015)Termination reason: Unknown
% 2.67/1.64 % (28015)Termination phase: Property scanning
% 2.67/1.64
% 2.67/1.64 % (28015)Memory used [KB]: 1535
% 2.67/1.64 % (28015)Time elapsed: 0.009 s
% 2.67/1.64 % (28015)Instructions burned: 21 (million)
% 2.67/1.64 % (28015)------------------------------
% 2.67/1.64 % (28015)------------------------------
% 2.67/1.65 % (28007)Instruction limit reached!
% 2.67/1.65 % (28007)------------------------------
% 2.67/1.65 % (28007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.65 % (28007)Termination reason: Unknown
% 2.67/1.65 % (28007)Termination phase: Function definition elimination
% 2.67/1.65
% 2.67/1.65 % (28007)Memory used [KB]: 2302
% 2.67/1.65 % (28007)Time elapsed: 0.028 s
% 2.67/1.65 % (28007)Instructions burned: 103 (million)
% 2.67/1.65 % (28007)------------------------------
% 2.67/1.65 % (28007)------------------------------
% 2.67/1.65 % (28023)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_27787 for (2998ds/86Mi)
% 2.67/1.65 % (27998)Instruction limit reached!
% 2.67/1.65 % (27998)------------------------------
% 2.67/1.65 % (27998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.65 % (27998)Termination reason: Unknown
% 2.67/1.65 % (27998)Termination phase: Saturation
% 2.67/1.65
% 2.67/1.65 % (27998)Memory used [KB]: 6908
% 2.67/1.65 % (27998)Time elapsed: 0.044 s
% 2.67/1.65 % (27998)Instructions burned: 129 (million)
% 2.67/1.65 % (27998)------------------------------
% 2.67/1.65 % (27998)------------------------------
% 2.67/1.66 % (28026)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_27787 for (2998ds/107Mi)
% 2.67/1.66 % (28032)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_27787 for (2998ds/39Mi)
% 2.67/1.68 % (28032)Instruction limit reached!
% 2.67/1.68 % (28032)------------------------------
% 2.67/1.68 % (28032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.68 % (28032)Termination reason: Unknown
% 2.67/1.68 % (28032)Termination phase: shuffling
% 2.67/1.68
% 2.67/1.68 % (28032)Memory used [KB]: 2174
% 2.67/1.68 % (28032)Time elapsed: 0.014 s
% 2.67/1.68 % (28032)Instructions burned: 40 (million)
% 2.67/1.68 % (28032)------------------------------
% 2.67/1.68 % (28032)------------------------------
% 2.67/1.68 % (28023)Instruction limit reached!
% 2.67/1.68 % (28023)------------------------------
% 2.67/1.68 % (28023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.68 % (28023)Termination reason: Unknown
% 2.67/1.68 % (28023)Termination phase: Saturation
% 2.67/1.68
% 2.67/1.68 % (28023)Memory used [KB]: 6652
% 2.67/1.68 % (28023)Time elapsed: 0.028 s
% 2.67/1.68 % (28023)Instructions burned: 86 (million)
% 2.67/1.68 % (28023)------------------------------
% 2.67/1.68 % (28023)------------------------------
% 2.67/1.69 % (28040)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_27787 for (2997ds/448Mi)
% 2.67/1.69 % (28043)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_27787 for (2997ds/46Mi)
% 2.67/1.69 % (28026)Instruction limit reached!
% 2.67/1.69 % (28026)------------------------------
% 2.67/1.69 % (28026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.69 % (28026)Termination reason: Unknown
% 2.67/1.69 % (28026)Termination phase: Saturation
% 2.67/1.69
% 2.67/1.69 % (28026)Memory used [KB]: 6908
% 2.67/1.69 % (28026)Time elapsed: 0.033 s
% 2.67/1.69 % (28026)Instructions burned: 108 (million)
% 2.67/1.69 % (28026)------------------------------
% 2.67/1.69 % (28026)------------------------------
% 2.67/1.69 % (27986)Instruction limit reached!
% 2.67/1.69 % (27986)------------------------------
% 2.67/1.69 % (27986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.69 % (27986)Termination reason: Unknown
% 2.67/1.69 % (27986)Termination phase: Saturation
% 2.67/1.69
% 2.67/1.69 % (27986)Memory used [KB]: 7803
% 2.67/1.69 % (27986)Time elapsed: 0.121 s
% 2.67/1.69 % (27986)Instructions burned: 377 (million)
% 2.67/1.69 % (27986)------------------------------
% 2.67/1.69 % (27986)------------------------------
% 2.67/1.70 % (28048)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_27787 for (2997ds/98Mi)
% 2.67/1.70 % (28050)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_27787 for (2997ds/507Mi)
% 2.67/1.70 % (28043)Instruction limit reached!
% 2.67/1.70 % (28043)------------------------------
% 2.67/1.70 % (28043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.70 % (28043)Termination reason: Unknown
% 2.67/1.70 % (28043)Termination phase: Preprocessing 3
% 2.67/1.70
% 2.67/1.70 % (28043)Memory used [KB]: 1918
% 2.67/1.70 % (28043)Time elapsed: 0.017 s
% 2.67/1.70 % (28043)Instructions burned: 47 (million)
% 2.67/1.70 % (28043)------------------------------
% 2.67/1.70 % (28043)------------------------------
% 2.67/1.71 % (28056)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_27787 for (2997ds/149Mi)
% 2.67/1.73 % (28048)Instruction limit reached!
% 2.67/1.73 % (28048)------------------------------
% 2.67/1.73 % (28048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.73 % (28048)Termination reason: Unknown
% 2.67/1.73 % (28048)Termination phase: Function definition elimination
% 2.67/1.73
% 2.67/1.73 % (28048)Memory used [KB]: 2302
% 2.67/1.73 % (28048)Time elapsed: 0.027 s
% 2.67/1.73 % (28048)Instructions burned: 100 (million)
% 2.67/1.73 % (28048)------------------------------
% 2.67/1.73 % (28048)------------------------------
% 2.67/1.73 % (28050)Refutation not found, incomplete strategy
% 2.67/1.73 % (28050)------------------------------
% 2.67/1.73 % (28050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.73 % (28050)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.73
% 2.67/1.73
% 2.67/1.73 % (28050)Memory used [KB]: 7291
% 2.67/1.73 % (28050)Time elapsed: 0.034 s
% 2.67/1.73 % (28050)Instructions burned: 113 (million)
% 2.67/1.73 % (28050)------------------------------
% 2.67/1.73 % (28050)------------------------------
% 2.67/1.74 % (28062)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_27787 for (2997ds/39Mi)
% 2.67/1.75 % (28062)Instruction limit reached!
% 2.67/1.75 % (28062)------------------------------
% 2.67/1.75 % (28062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.75 % (28062)Termination reason: Unknown
% 2.67/1.75 % (28062)Termination phase: Preprocessing 3
% 2.67/1.75
% 2.67/1.75 % (28062)Memory used [KB]: 1918
% 2.67/1.75 % (28062)Time elapsed: 0.013 s
% 2.67/1.75 % (28062)Instructions burned: 41 (million)
% 2.67/1.75 % (28062)------------------------------
% 2.67/1.75 % (28062)------------------------------
% 2.67/1.75 % (28067)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_27787 for (2997ds/6Mi)
% 2.67/1.76 % (28067)Instruction limit reached!
% 2.67/1.76 % (28067)------------------------------
% 2.67/1.76 % (28067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.76 % (28067)Termination reason: Unknown
% 2.67/1.76 % (28067)Termination phase: shuffling
% 2.67/1.76
% 2.67/1.76 % (28067)Memory used [KB]: 1407
% 2.67/1.76 % (28067)Time elapsed: 0.006 s
% 2.67/1.76 % (28067)Instructions burned: 7 (million)
% 2.67/1.76 % (28067)------------------------------
% 2.67/1.76 % (28067)------------------------------
% 2.67/1.76 % (28073)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_27787 for (2997ds/1087Mi)
% 2.67/1.76 % (28056)Instruction limit reached!
% 2.67/1.76 % (28056)------------------------------
% 2.67/1.76 % (28056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.76 % (28056)Termination reason: Unknown
% 2.67/1.76 % (28056)Termination phase: Saturation
% 2.67/1.76
% 2.67/1.76 % (28056)Memory used [KB]: 7036
% 2.67/1.76 % (28056)Time elapsed: 0.051 s
% 2.67/1.76 % (28056)Instructions burned: 150 (million)
% 2.67/1.76 % (28056)------------------------------
% 2.67/1.76 % (28056)------------------------------
% 2.67/1.77 % (28074)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_27787 for (2997ds/47Mi)
% 2.67/1.77 % (28085)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_27787 for (2997ds/44Mi)
% 2.67/1.79 % (28085)Instruction limit reached!
% 2.67/1.79 % (28085)------------------------------
% 2.67/1.79 % (28085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.79 % (28085)Termination reason: Unknown
% 2.67/1.79 % (28085)Termination phase: Property scanning
% 2.67/1.79
% 2.67/1.79 % (28085)Memory used [KB]: 2174
% 2.67/1.79 % (28085)Time elapsed: 0.015 s
% 2.67/1.79 % (28085)Instructions burned: 45 (million)
% 2.67/1.79 % (28085)------------------------------
% 2.67/1.79 % (28085)------------------------------
% 2.67/1.79 % (28074)Instruction limit reached!
% 2.67/1.79 % (28074)------------------------------
% 2.67/1.79 % (28074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.79 % (28074)Termination reason: Unknown
% 2.67/1.79 % (28074)Termination phase: Property scanning
% 2.67/1.79
% 2.67/1.79 % (28074)Memory used [KB]: 2046
% 2.67/1.79 % (28074)Time elapsed: 0.023 s
% 2.67/1.79 % (28074)Instructions burned: 47 (million)
% 2.67/1.79 % (28074)------------------------------
% 2.67/1.79 % (28074)------------------------------
% 2.67/1.80 % (28096)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_27787 for (2996ds/432Mi)
% 2.67/1.80 % (28097)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_27787 for (2996ds/62Mi)
% 2.67/1.81 % (27987)Instruction limit reached!
% 2.67/1.81 % (27987)------------------------------
% 2.67/1.81 % (27987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.81 % (27987)Termination reason: Unknown
% 2.67/1.81 % (27987)Termination phase: Saturation
% 2.67/1.81
% 2.67/1.81 % (27987)Memory used [KB]: 8187
% 2.67/1.81 % (27987)Time elapsed: 0.241 s
% 2.67/1.81 % (27987)Instructions burned: 779 (million)
% 2.67/1.81 % (27987)------------------------------
% 2.67/1.81 % (27987)------------------------------
% 2.67/1.82 % (28097)Instruction limit reached!
% 2.67/1.82 % (28097)------------------------------
% 2.67/1.82 % (28097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.82 % (28097)Termination reason: Unknown
% 2.67/1.82 % (28097)Termination phase: Property scanning
% 2.67/1.82
% 2.67/1.82 % (28097)Memory used [KB]: 2174
% 2.67/1.82 % (28097)Time elapsed: 0.018 s
% 2.67/1.82 % (28097)Instructions burned: 63 (million)
% 2.67/1.82 % (28097)------------------------------
% 2.67/1.82 % (28097)------------------------------
% 2.67/1.82 % (28113)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_27787 for (2996ds/31Mi)
% 2.67/1.83 % (28040)Instruction limit reached!
% 2.67/1.83 % (28040)------------------------------
% 2.67/1.83 % (28040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.83 % (28040)Termination reason: Unknown
% 2.67/1.83 % (28040)Termination phase: Saturation
% 2.67/1.83
% 2.67/1.83 % (28040)Memory used [KB]: 8187
% 2.67/1.83 % (28040)Time elapsed: 0.144 s
% 2.67/1.83 % (28040)Instructions burned: 448 (million)
% 2.67/1.83 % (28040)------------------------------
% 2.67/1.83 % (28040)------------------------------
% 2.67/1.83 % (28117)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_27787 for (2996ds/96Mi)
% 2.67/1.83 % (28113)Instruction limit reached!
% 2.67/1.83 % (28113)------------------------------
% 2.67/1.83 % (28113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.83 % (28113)Termination reason: Unknown
% 2.67/1.83 % (28113)Termination phase: Preprocessing 1
% 2.67/1.83
% 2.67/1.83 % (28113)Memory used [KB]: 1663
% 2.67/1.83 % (28113)Time elapsed: 0.011 s
% 2.67/1.83 % (28113)Instructions burned: 32 (million)
% 2.67/1.83 % (28113)------------------------------
% 2.67/1.83 % (28113)------------------------------
% 2.67/1.84 % (27971)Instruction limit reached!
% 2.67/1.84 % (27971)------------------------------
% 2.67/1.84 % (27971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.84 % (27971)Termination reason: Unknown
% 2.67/1.84 % (27971)Termination phase: Saturation
% 2.67/1.84
% 2.67/1.84 % (27971)Memory used [KB]: 8571
% 2.67/1.84 % (27971)Time elapsed: 0.326 s
% 2.67/1.84 % (27971)Instructions burned: 1041 (million)
% 2.67/1.84 % (27971)------------------------------
% 2.67/1.84 % (27971)------------------------------
% 2.67/1.84 % (28123)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_27787 for (2996ds/453Mi)
% 2.67/1.84 % (28125)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_27787 for (2996ds/71Mi)
% 2.67/1.85 % (28126)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_27787 for (2996ds/83Mi)
% 2.67/1.85 % (27989)Instruction limit reached!
% 2.67/1.85 % (27989)------------------------------
% 2.67/1.85 % (27989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.85 % (27989)Termination reason: Unknown
% 2.67/1.85 % (27989)Termination phase: Saturation
% 2.67/1.85
% 2.67/1.85 % (27989)Memory used [KB]: 6652
% 2.67/1.85 % (27989)Time elapsed: 0.276 s
% 2.67/1.85 % (27989)Instructions burned: 879 (million)
% 2.67/1.85 % (27989)------------------------------
% 2.67/1.85 % (27989)------------------------------
% 2.67/1.86 % (28117)Instruction limit reached!
% 2.67/1.86 % (28117)------------------------------
% 2.67/1.86 % (28117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.86 % (28117)Termination reason: Unknown
% 2.67/1.86 % (28117)Termination phase: Saturation
% 2.67/1.86
% 2.67/1.86 % (28117)Memory used [KB]: 6780
% 2.67/1.86 % (28117)Time elapsed: 0.029 s
% 2.67/1.86 % (28117)Instructions burned: 98 (million)
% 2.67/1.86 % (28117)------------------------------
% 2.67/1.86 % (28117)------------------------------
% 2.67/1.86 % (28133)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_27787 for (2996ds/11Mi)
% 2.67/1.86 % (28125)Instruction limit reached!
% 2.67/1.86 % (28125)------------------------------
% 2.67/1.86 % (28125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.86 % (28125)Termination reason: Unknown
% 2.67/1.86 % (28125)Termination phase: Property scanning
% 2.67/1.86
% 2.67/1.86 % (28125)Memory used [KB]: 2174
% 2.67/1.86 % (28125)Time elapsed: 0.021 s
% 2.67/1.86 % (28125)Instructions burned: 71 (million)
% 2.67/1.86 % (28125)------------------------------
% 2.67/1.86 % (28125)------------------------------
% 2.67/1.86 % (28133)Instruction limit reached!
% 2.67/1.86 % (28133)------------------------------
% 2.67/1.86 % (28133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.86 % (28133)Termination reason: Unknown
% 2.67/1.87 % (28133)Termination phase: shuffling
% 2.67/1.87
% 2.67/1.87 % (28133)Memory used [KB]: 1663
% 2.67/1.87 % (28133)Time elapsed: 0.005 s
% 2.67/1.87 % (28133)Instructions burned: 14 (million)
% 2.67/1.87 % (28133)------------------------------
% 2.67/1.87 % (28133)------------------------------
% 2.67/1.87 % (28140)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_27787 for (2996ds/41Mi)
% 2.67/1.87 % (28126)Instruction limit reached!
% 2.67/1.87 % (28126)------------------------------
% 2.67/1.87 % (28126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.87 % (28126)Termination reason: Unknown
% 2.67/1.87 % (28126)Termination phase: Saturation
% 2.67/1.87
% 2.67/1.87 % (28126)Memory used [KB]: 6652
% 2.67/1.87 % (28126)Time elapsed: 0.025 s
% 2.67/1.87 % (28126)Instructions burned: 84 (million)
% 2.67/1.87 % (28126)------------------------------
% 2.67/1.87 % (28126)------------------------------
% 2.67/1.87 % (28144)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27787 for (2996ds/6Mi)
% 2.67/1.87 % (28145)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_27787 for (2996ds/150Mi)
% 2.67/1.87 % (28144)Instruction limit reached!
% 2.67/1.87 % (28144)------------------------------
% 2.67/1.87 % (28144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.87 % (28144)Termination reason: Unknown
% 2.67/1.87 % (28144)Termination phase: shuffling
% 2.67/1.87
% 2.67/1.87 % (28144)Memory used [KB]: 1407
% 2.67/1.87 % (28144)Time elapsed: 0.003 s
% 2.67/1.87 % (28144)Instructions burned: 6 (million)
% 2.67/1.87 % (28144)------------------------------
% 2.67/1.87 % (28144)------------------------------
% 2.67/1.88 % (28140)Instruction limit reached!
% 2.67/1.88 % (28140)------------------------------
% 2.67/1.88 % (28140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.88 % (28140)Termination reason: Unknown
% 2.67/1.88 % (28140)Termination phase: Property scanning
% 2.67/1.88
% 2.67/1.88 % (28140)Memory used [KB]: 2174
% 2.67/1.88 % (28140)Time elapsed: 0.013 s
% 2.67/1.88 % (28140)Instructions burned: 43 (million)
% 2.67/1.88 % (28140)------------------------------
% 2.67/1.88 % (28140)------------------------------
% 2.67/1.88 % (28147)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_27787 for (2996ds/343Mi)
% 2.67/1.88 % (28149)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_27787 for (2996ds/109Mi)
% 2.67/1.89 % (28152)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_27787 for (2996ds/253Mi)
% 2.67/1.92 % (28149)Instruction limit reached!
% 2.67/1.92 % (28149)------------------------------
% 2.67/1.92 % (28149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.92 % (28149)Termination reason: Unknown
% 2.67/1.92 % (28149)Termination phase: Saturation
% 2.67/1.92
% 2.67/1.92 % (28149)Memory used [KB]: 6908
% 2.67/1.92 % (28149)Time elapsed: 0.032 s
% 2.67/1.92 % (28149)Instructions burned: 109 (million)
% 2.67/1.92 % (28149)------------------------------
% 2.67/1.92 % (28149)------------------------------
% 2.67/1.92 % (28145)Instruction limit reached!
% 2.67/1.92 % (28145)------------------------------
% 2.67/1.92 % (28145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.92 % (28145)Termination reason: Unknown
% 2.67/1.92 % (28145)Termination phase: Saturation
% 2.67/1.92
% 2.67/1.92 % (28145)Memory used [KB]: 6908
% 2.67/1.92 % (28145)Time elapsed: 0.047 s
% 2.67/1.92 % (28145)Instructions burned: 150 (million)
% 2.67/1.92 % (28145)------------------------------
% 2.67/1.92 % (28145)------------------------------
% 2.67/1.92 % (28169)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_27787 for (2995ds/140Mi)
% 2.67/1.93 % (28172)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_27787 for (2995ds/614Mi)
% 2.67/1.94 % (28096)Instruction limit reached!
% 2.67/1.94 % (28096)------------------------------
% 2.67/1.94 % (28096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.94 % (28096)Termination reason: Unknown
% 2.67/1.94 % (28096)Termination phase: Saturation
% 2.67/1.94
% 2.67/1.94 % (28096)Memory used [KB]: 3454
% 2.67/1.94 % (28096)Time elapsed: 0.143 s
% 2.67/1.94 % (28096)Instructions burned: 433 (million)
% 2.67/1.94 % (28096)------------------------------
% 2.67/1.94 % (28096)------------------------------
% 2.67/1.94 % (28169)Refutation not found, incomplete strategy
% 2.67/1.94 % (28169)------------------------------
% 2.67/1.94 % (28169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.94 % (28169)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.94
% 2.67/1.94
% 2.67/1.94 % (28169)Memory used [KB]: 6396
% 2.67/1.94 % (28169)Time elapsed: 0.020 s
% 2.67/1.94 % (28169)Instructions burned: 61 (million)
% 2.67/1.94 % (28169)------------------------------
% 2.67/1.94 % (28169)------------------------------
% 2.67/1.95 % (28178)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_27787 for (2995ds/202Mi)
% 2.67/1.95 % (28181)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_27787 for (2995ds/339Mi)
% 2.67/1.96 % (28178)Refutation not found, incomplete strategy
% 2.67/1.96 % (28178)------------------------------
% 2.67/1.96 % (28178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.96 % (28178)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.96
% 2.67/1.96
% 2.67/1.96 % (28178)Memory used [KB]: 6524
% 2.67/1.96 % (28178)Time elapsed: 0.017 s
% 2.67/1.96 % (28178)Instructions burned: 50 (million)
% 2.67/1.96 % (28178)------------------------------
% 2.67/1.96 % (28178)------------------------------
% 2.67/1.97 % (28152)Instruction limit reached!
% 2.67/1.97 % (28152)------------------------------
% 2.67/1.97 % (28152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.97 % (28152)Termination reason: Unknown
% 2.67/1.97 % (28152)Termination phase: Saturation
% 2.67/1.97
% 2.67/1.97 % (28152)Memory used [KB]: 7547
% 2.67/1.97 % (28152)Time elapsed: 0.081 s
% 2.67/1.97 % (28152)Instructions burned: 255 (million)
% 2.67/1.97 % (28152)------------------------------
% 2.67/1.97 % (28152)------------------------------
% 2.67/1.97 % (28123)Instruction limit reached!
% 2.67/1.97 % (28123)------------------------------
% 2.67/1.97 % (28123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.97 % (28123)Termination reason: Unknown
% 2.67/1.97 % (28123)Termination phase: Saturation
% 2.67/1.97
% 2.67/1.97 % (28123)Memory used [KB]: 7419
% 2.67/1.97 % (28123)Time elapsed: 0.133 s
% 2.67/1.97 % (28123)Instructions burned: 454 (million)
% 2.67/1.97 % (28123)------------------------------
% 2.67/1.97 % (28123)------------------------------
% 2.67/1.97 % (28188)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_27787 for (2995ds/283Mi)
% 2.67/1.98 % (28191)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_27787 for (2995ds/134Mi)
% 2.67/1.98 % (28193)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_27787 for (2995ds/298Mi)
% 2.67/1.99 % (28147)Instruction limit reached!
% 2.67/1.99 % (28147)------------------------------
% 2.67/1.99 % (28147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.99 % (28147)Termination reason: Unknown
% 2.67/1.99 % (28147)Termination phase: Saturation
% 2.67/1.99
% 2.67/1.99 % (28147)Memory used [KB]: 7547
% 2.67/1.99 % (28147)Time elapsed: 0.108 s
% 2.67/1.99 % (28147)Instructions burned: 346 (million)
% 2.67/1.99 % (28147)------------------------------
% 2.67/1.99 % (28147)------------------------------
% 2.67/2.00 % (28199)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_27787 for (2994ds/192Mi)
% 6.29/2.04 % (28199)First to succeed.
% 6.29/2.04 % (28191)Instruction limit reached!
% 6.29/2.04 % (28191)------------------------------
% 6.29/2.04 % (28191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.04 % (28191)Termination reason: Unknown
% 6.29/2.04 % (28191)Termination phase: Saturation
% 6.29/2.04
% 6.29/2.04 % (28191)Memory used [KB]: 6908
% 6.29/2.04 % (28191)Time elapsed: 0.084 s
% 6.29/2.04 % (28191)Instructions burned: 134 (million)
% 6.29/2.04 % (28191)------------------------------
% 6.29/2.04 % (28191)------------------------------
% 6.29/2.05 % (28199)Refutation found. Thanks to Tanya!
% 6.29/2.05 % SZS status Theorem for DTF2THF_27787
% 6.29/2.05 % SZS output start Proof for DTF2THF_27787
% 6.29/2.05 thf(type_def_5, type, list_nat: $tType).
% 6.29/2.05 thf(type_def_7, type, list_poly_a: $tType).
% 6.29/2.05 thf(type_def_8, type, list_a: $tType).
% 6.29/2.05 thf(type_def_9, type, poly_a: $tType).
% 6.29/2.05 thf(type_def_10, type, poly_poly_a: $tType).
% 6.29/2.05 thf(type_def_11, type, a: $tType).
% 6.29/2.05 thf(type_def_12, type, nat: $tType).
% 6.29/2.05 thf(type_def_13, type, poly_nat: $tType).
% 6.29/2.05 thf(type_def_14, type, list_list_a: $tType).
% 6.29/2.05 thf(func_def_0, type, poly_poly_a: $tType).
% 6.29/2.05 thf(func_def_1, type, list_poly_a: $tType).
% 6.29/2.05 thf(func_def_2, type, list_list_a: $tType).
% 6.29/2.05 thf(func_def_3, type, poly_nat: $tType).
% 6.29/2.05 thf(func_def_4, type, list_nat: $tType).
% 6.29/2.05 thf(func_def_5, type, poly_a: $tType).
% 6.29/2.05 thf(func_def_6, type, list_a: $tType).
% 6.29/2.05 thf(func_def_7, type, nat: $tType).
% 6.29/2.05 thf(func_def_8, type, a: $tType).
% 6.29/2.05 thf(func_def_9, type, descar226543321ms_nat: list_nat > list_nat).
% 6.29/2.05 thf(func_def_10, type, descar282223555poly_a: list_poly_a > list_poly_a).
% 6.29/2.05 thf(func_def_11, type, descar1375166517sums_a: list_a > list_a).
% 6.29/2.05 thf(func_def_12, type, descar434775507poly_a: poly_a > poly_poly_a > poly_poly_a).
% 6.29/2.05 thf(func_def_13, type, descar466059845root_a: a > poly_a > poly_a).
% 6.29/2.05 thf(func_def_14, type, descar357075861poly_a: list_poly_a > nat).
% 6.29/2.05 thf(func_def_15, type, descar2095969287nges_a: list_a > nat).
% 6.29/2.05 thf(func_def_16, type, one_one_nat: nat).
% 6.29/2.05 thf(func_def_17, type, one_one_poly_nat: poly_nat).
% 6.29/2.05 thf(func_def_18, type, one_one_poly_poly_a: poly_poly_a).
% 6.29/2.05 thf(func_def_19, type, one_one_poly_a: poly_a).
% 6.29/2.05 thf(func_def_20, type, one_one_a: a).
% 6.29/2.05 thf(func_def_21, type, times_times_nat: nat > nat > nat).
% 6.29/2.05 thf(func_def_22, type, times_times_poly_a: poly_a > poly_a > poly_a).
% 6.29/2.05 thf(func_def_23, type, times_times_a: a > a > a).
% 6.29/2.05 thf(func_def_24, type, uminus_uminus_poly_a: poly_a > poly_a).
% 6.29/2.05 thf(func_def_25, type, uminus_uminus_a: a > a).
% 6.29/2.05 thf(func_def_26, type, zero_zero_nat: nat).
% 6.29/2.05 thf(func_def_27, type, zero_zero_poly_nat: poly_nat).
% 6.29/2.05 thf(func_def_28, type, zero_z2096148049poly_a: poly_poly_a).
% 6.29/2.05 thf(func_def_29, type, zero_zero_poly_a: poly_a).
% 6.29/2.05 thf(func_def_30, type, zero_zero_a: a).
% 6.29/2.05 thf(func_def_31, type, append_nat: list_nat > list_nat > list_nat).
% 6.29/2.05 thf(func_def_32, type, append_poly_a: list_poly_a > list_poly_a > list_poly_a).
% 6.29/2.05 thf(func_def_33, type, append_a: list_a > list_a > list_a).
% 6.29/2.05 thf(func_def_34, type, cons_list_a: list_a > list_list_a > list_list_a).
% 6.29/2.05 thf(func_def_35, type, cons_nat: nat > list_nat > list_nat).
% 6.29/2.05 thf(func_def_36, type, cons_poly_a: poly_a > list_poly_a > list_poly_a).
% 6.29/2.05 thf(func_def_37, type, cons_a: a > list_a > list_a).
% 6.29/2.05 thf(func_def_38, type, nil_list_a: list_list_a).
% 6.29/2.05 thf(func_def_39, type, nil_nat: list_nat).
% 6.29/2.05 thf(func_def_40, type, nil_poly_a: list_poly_a).
% 6.29/2.05 thf(func_def_41, type, nil_a: list_a).
% 6.29/2.05 thf(func_def_42, type, null_poly_a: list_poly_a > $o).
% 6.29/2.05 thf(func_def_43, type, null_a: list_a > $o).
% 6.29/2.05 thf(func_def_44, type, ord_less_nat: nat > nat > $o).
% 6.29/2.05 thf(func_def_45, type, ord_less_poly_a: poly_a > poly_a > $o).
% 6.29/2.05 thf(func_def_46, type, ord_less_a: a > a > $o).
% 6.29/2.05 thf(func_def_47, type, poly_nat2: list_nat > poly_nat).
% 6.29/2.05 thf(func_def_48, type, poly_poly_a2: list_poly_a > poly_poly_a).
% 6.29/2.05 thf(func_def_49, type, poly_a2: list_a > poly_a).
% 6.29/2.05 thf(func_def_50, type, coeffs_nat: poly_nat > list_nat).
% 6.29/2.05 thf(func_def_51, type, coeffs_poly_a: poly_poly_a > list_poly_a).
% 6.29/2.05 thf(func_def_52, type, coeffs_a: poly_a > list_a).
% 6.29/2.05 thf(func_def_53, type, is_zero_poly_a: poly_poly_a > $o).
% 6.29/2.05 thf(func_def_54, type, is_zero_a: poly_a > $o).
% 6.29/2.05 thf(func_def_55, type, pCons_nat: nat > poly_nat > poly_nat).
% 6.29/2.05 thf(func_def_56, type, pCons_poly_a: poly_a > poly_poly_a > poly_poly_a).
% 6.29/2.05 thf(func_def_57, type, pCons_a: a > poly_a > poly_a).
% 6.29/2.05 thf(func_def_58, type, smult_nat: nat > poly_nat > poly_nat).
% 6.29/2.05 thf(func_def_59, type, smult_poly_a: poly_a > poly_poly_a > poly_poly_a).
% 6.29/2.05 thf(func_def_60, type, smult_a: a > poly_a > poly_a).
% 6.29/2.05 thf(func_def_61, type, g: poly_a).
% 6.29/2.05 thf(func_def_62, type, v: poly_a > nat).
% 6.29/2.05 thf(func_def_63, type, xs: list_a).
% 6.29/2.05 thf(func_def_64, type, ys: list_a).
% 6.29/2.05 thf(func_def_76, type, sK0: (list_a > list_a > $o) > a).
% 6.29/2.05 thf(func_def_77, type, sK1: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_78, type, sK2: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_79, type, sK3: (list_a > list_a > $o) > a).
% 6.29/2.05 thf(func_def_80, type, sK4: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_81, type, sK5: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_82, type, sK6: (list_a > list_a > $o) > a).
% 6.29/2.05 thf(func_def_83, type, sK7: (list_a > list_a > $o) > a).
% 6.29/2.05 thf(func_def_84, type, sK8: (list_a > list_a > $o) > a).
% 6.29/2.05 thf(func_def_85, type, sK9: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_86, type, sK10: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_87, type, sK11: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_88, type, sK12: (list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_89, type, sK13: (list_a > $o) > a).
% 6.29/2.05 thf(func_def_90, type, sK14: list_list_a > list_list_a).
% 6.29/2.05 thf(func_def_91, type, sK15: list_list_a > a).
% 6.29/2.05 thf(func_def_92, type, sK16: list_list_a > list_a).
% 6.29/2.05 thf(func_def_93, type, sK17: list_list_a > list_list_a).
% 6.29/2.05 thf(func_def_94, type, sK18: poly_a > poly_a).
% 6.29/2.05 thf(func_def_95, type, sK19: poly_a > a).
% 6.29/2.05 thf(func_def_96, type, sK20: (poly_a > $o) > a).
% 6.29/2.05 thf(func_def_97, type, sK21: (poly_a > $o) > poly_a).
% 6.29/2.05 thf(func_def_98, type, sK22: ((a > a > $o) > list_a > $o) > a > a > $o).
% 6.29/2.05 thf(func_def_99, type, sK23: ((a > a > $o) > list_a > $o) > a).
% 6.29/2.05 thf(func_def_100, type, sK24: ((a > a > $o) > list_a > $o) > a > a > $o).
% 6.29/2.05 thf(func_def_101, type, sK25: ((a > a > $o) > list_a > $o) > a).
% 6.29/2.05 thf(func_def_102, type, sK26: ((a > a > $o) > list_a > $o) > a).
% 6.29/2.05 thf(func_def_103, type, sK27: ((a > a > $o) > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_104, type, sK28: ((a > a > $o) > list_a > $o) > a > a > $o).
% 6.29/2.05 thf(func_def_105, type, sK29: (poly_a > poly_a > $o) > poly_a).
% 6.29/2.05 thf(func_def_106, type, sK30: (poly_a > poly_a > $o) > a).
% 6.29/2.05 thf(func_def_107, type, sK31: (poly_a > poly_a > $o) > poly_a).
% 6.29/2.05 thf(func_def_108, type, sK32: (poly_a > poly_a > $o) > a).
% 6.29/2.05 thf(func_def_109, type, sK33: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_110, type, sK34: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_111, type, sK35: (list_a > list_a > $o) > a).
% 6.29/2.05 thf(func_def_112, type, sK36: (list_a > list_a > $o) > a).
% 6.29/2.05 thf(func_def_113, type, sK37: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_114, type, sK38: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_115, type, sK39: (list_a > list_a > $o) > a).
% 6.29/2.05 thf(func_def_116, type, sK40: (nat > $o) > nat).
% 6.29/2.05 thf(func_def_117, type, sK41: poly_a > a).
% 6.29/2.05 thf(func_def_118, type, sK42: poly_a > poly_a).
% 6.29/2.05 thf(func_def_119, type, sK43: ((a > a) > list_a > list_a > $o) > a > a).
% 6.29/2.05 thf(func_def_120, type, sK44: ((a > a) > list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_121, type, sK45: ((a > a) > list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_122, type, sK46: ((a > a) > list_a > list_a > $o) > a).
% 6.29/2.05 thf(func_def_123, type, sK47: ((a > a) > list_a > list_a > $o) > a > a).
% 6.29/2.05 thf(func_def_124, type, sK48: ((a > a) > list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_125, type, sK49: (list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_126, type, sK50: (list_a > $o) > a).
% 6.29/2.05 thf(func_def_127, type, sK51: (poly_poly_a > $o) > poly_poly_a).
% 6.29/2.05 thf(func_def_128, type, sK52: (poly_poly_a > $o) > poly_a).
% 6.29/2.05 thf(func_def_129, type, sK53: (nat > $o) > nat).
% 6.29/2.05 thf(func_def_130, type, sK54: (list_a > $o) > a).
% 6.29/2.05 thf(func_def_131, type, sK55: (list_a > $o) > a).
% 6.29/2.05 thf(func_def_132, type, sK56: (list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_133, type, sK57: (list_a > $o) > a).
% 6.29/2.05 thf(func_def_134, type, sK58: list_a > list_a).
% 6.29/2.05 thf(func_def_135, type, sK59: list_a > a).
% 6.29/2.05 thf(func_def_136, type, sK60: list_a > list_a).
% 6.29/2.05 thf(func_def_137, type, sK61: list_a > a).
% 6.29/2.05 thf(func_def_138, type, sK62: ((a > a > $o) > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_139, type, sK63: ((a > a > $o) > list_a > $o) > a > a > $o).
% 6.29/2.05 thf(func_def_140, type, sK64: ((a > a > $o) > list_a > $o) > a).
% 6.29/2.05 thf(func_def_141, type, sK65: ((a > a > $o) > list_a > $o) > a > a > $o).
% 6.29/2.05 thf(func_def_142, type, sK66: list_a > a).
% 6.29/2.05 thf(func_def_143, type, sK67: list_a > list_a).
% 6.29/2.05 thf(func_def_144, type, sK68: (nat > $o) > nat).
% 6.29/2.05 thf(func_def_145, type, sK69: (list_a > $o) > a).
% 6.29/2.05 thf(func_def_146, type, sK70: (list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_147, type, sK71: (list_a > $o) > a).
% 6.29/2.05 thf(func_def_148, type, sK72: (list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_149, type, sK73: (list_a > $o) > a).
% 6.29/2.05 thf(func_def_150, type, sK74: list_a > a).
% 6.29/2.05 thf(func_def_151, type, sK75: list_a > list_a).
% 6.29/2.05 thf(func_def_152, type, sK76: list_a > a).
% 6.29/2.05 thf(func_def_153, type, sK77: list_a > a).
% 6.29/2.05 thf(func_def_154, type, sK78: (list_a > list_a > $o) > a).
% 6.29/2.05 thf(func_def_155, type, sK79: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_156, type, sK80: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_157, type, sK81: (list_a > list_a > $o) > a).
% 6.29/2.05 thf(func_def_158, type, sK82: (list_a > list_a > $o) > a).
% 6.29/2.05 thf(func_def_159, type, sK83: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_160, type, sK84: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_161, type, sK85: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_162, type, sK86: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_163, type, sK87: (list_a > list_a > $o) > a).
% 6.29/2.05 thf(func_def_164, type, sK88: (list_a > list_a > $o) > a).
% 6.29/2.05 thf(func_def_165, type, sK89: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_166, type, sK90: (list_a > list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_167, type, sK91: list_a > a).
% 6.29/2.05 thf(func_def_168, type, sK92: list_a > a).
% 6.29/2.05 thf(func_def_169, type, sK93: list_a > a).
% 6.29/2.05 thf(func_def_170, type, sK94: list_a > list_a).
% 6.29/2.05 thf(func_def_171, type, sK95: (list_a > $o) > a).
% 6.29/2.05 thf(func_def_172, type, sK96: (list_a > $o) > list_a).
% 6.29/2.05 thf(func_def_173, type, sK97: (list_a > $o) > a).
% 6.29/2.05 thf(func_def_174, type, sK98: (list_a > $o) > a).
% 6.29/2.05 thf(func_def_175, type, sK99: (poly_a > $o) > poly_a).
% 6.29/2.05 thf(func_def_176, type, sK100: (poly_a > $o) > a).
% 6.29/2.05 thf(func_def_177, type, sK101: (poly_nat > $o) > poly_nat).
% 6.29/2.05 thf(func_def_178, type, sK102: (poly_nat > $o) > nat).
% 6.29/2.05 thf(func_def_180, type, ph104: !>[X0: $tType]:(X0)).
% 6.29/2.05 thf(f1742,plain,(
% 6.29/2.05 $false),
% 6.29/2.05 inference(trivial_inequality_removal,[status(thm)],[f1741])).
% 6.29/2.05 thf(f1741,plain,(
% 6.29/2.05 ((descar2095969287nges_a @ (coeffs_a @ g)) != (descar2095969287nges_a @ (coeffs_a @ g)))),
% 6.29/2.05 inference(forward_demodulation,[status(thm)],[f1740,f1405])).
% 6.29/2.05 thf(f1405,plain,(
% 6.29/2.05 ( ! [X0 : poly_a] : (((poly_a2 @ (coeffs_a @ X0)) = X0)) )),
% 6.29/2.05 inference(cnf_transformation,[status(thm)],[f872])).
% 6.29/2.05 thf(f872,plain,(
% 6.29/2.05 ! [X0 : poly_a] : ((poly_a2 @ (coeffs_a @ X0)) = X0)),
% 6.29/2.05 inference(rectify,[status(thm)],[f14])).
% 6.29/2.05 thf(f14,axiom,(
% 6.29/2.05 ! [X6 : poly_a] : ((poly_a2 @ (coeffs_a @ X6)) = X6)),
% 6.29/2.05 file('/export/starexec/sandbox2/tmp/tmp.t7mfK5zq2L/DTF2THF_27787.p',fact_13_Poly__coeffs)).
% 6.29/2.05 thf(f1740,plain,(
% 6.29/2.05 ((descar2095969287nges_a @ (coeffs_a @ g)) != (descar2095969287nges_a @ (coeffs_a @ (poly_a2 @ (coeffs_a @ g)))))),
% 6.29/2.05 inference(forward_demodulation,[status(thm)],[f1737,f1343])).
% 6.29/2.05 thf(f1343,plain,(
% 6.29/2.05 ( ! [X0 : list_a] : (((poly_a2 @ (append_a @ X0 @ (cons_a @ zero_zero_a @ nil_a))) = (poly_a2 @ X0))) )),
% 6.29/2.05 inference(cnf_transformation,[status(thm)],[f821])).
% 6.29/2.05 thf(f821,plain,(
% 6.29/2.05 ! [X0 : list_a] : ((poly_a2 @ (append_a @ X0 @ (cons_a @ zero_zero_a @ nil_a))) = (poly_a2 @ X0))),
% 6.29/2.05 inference(rectify,[status(thm)],[f67])).
% 6.29/2.05 thf(f67,axiom,(
% 6.29/2.05 ! [X11 : list_a] : ((poly_a2 @ (append_a @ X11 @ (cons_a @ zero_zero_a @ nil_a))) = (poly_a2 @ X11))),
% 6.29/2.05 file('/export/starexec/sandbox2/tmp/tmp.t7mfK5zq2L/DTF2THF_27787.p',fact_66_Poly__snoc__zero)).
% 6.29/2.05 thf(f1737,plain,(
% 6.29/2.05 ((descar2095969287nges_a @ (coeffs_a @ g)) != (descar2095969287nges_a @ (coeffs_a @ (poly_a2 @ (append_a @ (coeffs_a @ g) @ (cons_a @ zero_zero_a @ nil_a))))))),
% 6.29/2.05 inference(equality_resolution,[status(thm)],[f1716])).
% 6.29/2.05 thf(f1716,plain,(
% 6.29/2.05 ( ! [X0 : poly_a] : (((poly_a2 @ (append_a @ (coeffs_a @ g) @ (cons_a @ zero_zero_a @ nil_a))) != X0) | ((descar2095969287nges_a @ (coeffs_a @ X0)) != (descar2095969287nges_a @ (coeffs_a @ g)))) )),
% 6.29/2.05 inference(superposition,[status(thm)],[f1581,f1499])).
% 6.29/2.05 thf(f1499,plain,(
% 6.29/2.05 ( ! [X0 : poly_a,X1 : list_a] : (((descar2095969287nges_a @ (coeffs_a @ X0)) = (descar2095969287nges_a @ X1)) | ((poly_a2 @ X1) != X0)) )),
% 6.29/2.05 inference(cnf_transformation,[status(thm)],[f956])).
% 6.29/2.05 thf(f956,plain,(
% 6.29/2.05 ! [X0 : poly_a,X1 : list_a] : (((descar2095969287nges_a @ (coeffs_a @ X0)) = (descar2095969287nges_a @ X1)) | ((poly_a2 @ X1) != X0))),
% 6.29/2.05 inference(ennf_transformation,[status(thm)],[f787])).
% 6.29/2.05 thf(f787,plain,(
% 6.29/2.05 ! [X0 : poly_a,X1 : list_a] : (((poly_a2 @ X1) = X0) => ((descar2095969287nges_a @ (coeffs_a @ X0)) = (descar2095969287nges_a @ X1)))),
% 6.29/2.05 inference(rectify,[status(thm)],[f7])).
% 6.29/2.05 thf(f7,axiom,(
% 6.29/2.05 ! [X6 : poly_a,X5 : list_a] : (((poly_a2 @ X5) = X6) => ((descar2095969287nges_a @ X5) = (descar2095969287nges_a @ (coeffs_a @ X6))))),
% 6.29/2.05 file('/export/starexec/sandbox2/tmp/tmp.t7mfK5zq2L/DTF2THF_27787.p',fact_6_sign__changes__coeff__sign__changes)).
% 6.29/2.05 thf(f1581,plain,(
% 6.29/2.05 ((descar2095969287nges_a @ (coeffs_a @ g)) != (descar2095969287nges_a @ (append_a @ (coeffs_a @ g) @ (cons_a @ zero_zero_a @ nil_a))))),
% 6.29/2.05 inference(definition_unfolding,[status(thm)],[f1246,f1313])).
% 6.29/2.05 thf(f1313,plain,(
% 6.29/2.05 (ys = (append_a @ (coeffs_a @ g) @ (cons_a @ zero_zero_a @ nil_a)))),
% 6.29/2.05 inference(cnf_transformation,[status(thm)],[f8])).
% 6.29/2.05 thf(f8,axiom,(
% 6.29/2.05 (ys = (append_a @ (coeffs_a @ g) @ (cons_a @ zero_zero_a @ nil_a)))),
% 6.29/2.05 file('/export/starexec/sandbox2/tmp/tmp.t7mfK5zq2L/DTF2THF_27787.p',fact_7_ys__def)).
% 6.29/2.05 thf(f1246,plain,(
% 6.29/2.05 ((descar2095969287nges_a @ ys) != (descar2095969287nges_a @ (coeffs_a @ g)))),
% 6.29/2.05 inference(cnf_transformation,[status(thm)],[f849])).
% 6.29/2.05 thf(f849,plain,(
% 6.29/2.05 ((descar2095969287nges_a @ ys) != (descar2095969287nges_a @ (coeffs_a @ g)))),
% 6.29/2.05 inference(flattening,[status(thm)],[f348])).
% 6.29/2.05 thf(f348,negated_conjecture,(
% 6.29/2.05 ~((descar2095969287nges_a @ ys) = (descar2095969287nges_a @ (coeffs_a @ g)))),
% 6.29/2.05 inference(negated_conjecture,[status(cth)],[f347])).
% 6.29/2.05 thf(f347,conjecture,(
% 6.29/2.05 ((descar2095969287nges_a @ ys) = (descar2095969287nges_a @ (coeffs_a @ g)))),
% 6.29/2.05 file('/export/starexec/sandbox2/tmp/tmp.t7mfK5zq2L/DTF2THF_27787.p',conj_0)).
% 6.29/2.05 % SZS output end Proof for DTF2THF_27787
% 6.29/2.05 % (28199)------------------------------
% 6.29/2.05 % (28199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.05 % (28199)Termination reason: Refutation
% 6.29/2.05
% 6.29/2.05 % (28199)Memory used [KB]: 7803
% 6.29/2.05 % (28199)Time elapsed: 0.046 s
% 6.29/2.05 % (28199)Instructions burned: 145 (million)
% 6.29/2.05 % (28199)------------------------------
% 6.29/2.05 % (28199)------------------------------
% 6.29/2.05 % (27959)Success in time 0.553 s
%------------------------------------------------------------------------------