%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP172^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:08 AM UTC 2026
% Result : Theorem 3.03s 1.68s
% Output : Refutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 45 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 162 ( 26 ~; 7 |; 3 &; 123 @)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 26 ( 25 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 149 ( 146 usr; 18 con; 0-5 aty)
% Number of variables : 26 ( 5 ^; 15 !; 6 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
product_unit: $tType ).
thf(type_def_6,type,
list_char: $tType ).
thf(type_def_7,type,
option_element_ptr_a: $tType ).
thf(type_def_8,type,
list_n282880152tr_b_c: $tType ).
thf(type_def_9,type,
option2026120038on_j_k: $tType ).
thf(type_def_10,type,
rDocum326988203on_j_k: $tType ).
thf(type_def_12,type,
rObjec1617416918on_j_k: $tType ).
thf(type_def_13,type,
rObjec1413572695_j_k_l: $tType ).
thf(type_def_14,type,
option841825948on_j_k: $tType ).
thf(type_def_15,type,
heap_S1465075775_j_k_l: $tType ).
thf(type_def_16,type,
fset_d1663890464tr_d_e: $tType ).
thf(type_def_17,type,
docume1935157360tr_d_e: $tType ).
thf(type_def_18,type,
object945351580_d_e_f: $tType ).
thf(type_def_19,type,
option1330818496tr_d_e: $tType ).
thf(type_def_20,type,
sum_su1576157353tr_d_e: $tType ).
thf(type_def_21,type,
nat: $tType ).
thf(type_def_22,type,
node_p1234578834tr_b_c: $tType ).
thf(type_def_23,type,
char: $tType ).
thf(type_def_24,type,
list_l118626078tr_b_c: $tType ).
thf(type_def_25,type,
list_list_char: $tType ).
thf(type_def_26,type,
set_nat: $tType ).
thf(type_def_27,type,
rObjec103300152t_unit: $tType ).
thf(type_def_28,type,
option1749760295_j_k_l: $tType ).
thf(type_def_29,type,
element_ptr_a: $tType ).
thf(type_def_30,type,
sum_su1221287958on_j_k: $tType ).
thf(func_def_0,type,
heap_S1465075775_j_k_l: $tType ).
thf(func_def_1,type,
option1749760295_j_k_l: $tType ).
thf(func_def_2,type,
rObjec1413572695_j_k_l: $tType ).
thf(func_def_3,type,
object945351580_d_e_f: $tType ).
thf(func_def_4,type,
option841825948on_j_k: $tType ).
thf(func_def_5,type,
rObjec1617416918on_j_k: $tType ).
thf(func_def_6,type,
rDocum326988203on_j_k: $tType ).
thf(func_def_7,type,
list_l118626078tr_b_c: $tType ).
thf(func_def_8,type,
list_n282880152tr_b_c: $tType ).
thf(func_def_9,type,
node_p1234578834tr_b_c: $tType ).
thf(func_def_10,type,
option2026120038on_j_k: $tType ).
thf(func_def_11,type,
option1330818496tr_d_e: $tType ).
thf(func_def_12,type,
fset_d1663890464tr_d_e: $tType ).
thf(func_def_13,type,
sum_su1221287958on_j_k: $tType ).
thf(func_def_14,type,
docume1935157360tr_d_e: $tType ).
thf(func_def_15,type,
sum_su1576157353tr_d_e: $tType ).
thf(func_def_16,type,
rObjec103300152t_unit: $tType ).
thf(func_def_17,type,
option_element_ptr_a: $tType ).
thf(func_def_18,type,
list_list_char: $tType ).
thf(func_def_19,type,
element_ptr_a: $tType ).
thf(func_def_20,type,
list_char: $tType ).
thf(func_def_21,type,
set_nat: $tType ).
thf(func_def_22,type,
product_unit: $tType ).
thf(func_def_23,type,
char: $tType ).
thf(func_def_24,type,
nat: $tType ).
thf(func_def_25,type,
rDocum427676485on_j_k: product_unit > list_char > option_element_ptr_a > list_n282880152tr_b_c > option2026120038on_j_k > rDocum326988203on_j_k ).
thf(func_def_26,type,
discon866287741on_j_k: rObjec1617416918on_j_k > list_n282880152tr_b_c ).
thf(func_def_27,type,
discon442323090on_j_k: ( list_n282880152tr_b_c > list_n282880152tr_b_c ) > rObjec1617416918on_j_k > rObjec1617416918on_j_k ).
thf(func_def_28,type,
doctyp814403297on_j_k: rObjec1617416918on_j_k > list_char ).
thf(func_def_29,type,
doctyp68000440on_j_k: ( list_char > list_char ) > rObjec1617416918on_j_k > rObjec1617416918on_j_k ).
thf(func_def_30,type,
docume1175131570on_j_k: rObjec1617416918on_j_k > option_element_ptr_a ).
thf(func_def_31,type,
docume244715269on_j_k: ( option_element_ptr_a > option_element_ptr_a ) > rObjec1617416918on_j_k > rObjec1617416918on_j_k ).
thf(func_def_32,type,
more_c1453068134on_j_k: rObjec1617416918on_j_k > option2026120038on_j_k ).
thf(func_def_33,type,
more_u1044474223_c_a_b: ( option2026120038on_j_k > option2026120038on_j_k ) > rObjec1617416918on_j_k > rObjec1617416918on_j_k ).
thf(func_def_34,type,
nothin757132294on_j_k: rObjec1617416918on_j_k > product_unit ).
thf(func_def_35,type,
nothin1105341917on_j_k: ( product_unit > product_unit ) > rObjec1617416918on_j_k > rObjec1617416918on_j_k ).
thf(func_def_36,type,
cast_D1252964113_h_i_l: rObjec1617416918on_j_k > rObjec1413572695_j_k_l ).
thf(func_def_37,type,
cast_O1034441233_j_k_l: rObjec1413572695_j_k_l > option841825948on_j_k ).
thf(func_def_38,type,
docume1070804385_j_k_l: heap_S1465075775_j_k_l > fset_d1663890464tr_d_e ).
thf(func_def_39,type,
get_D_1192261494_j_k_l: docume1935157360tr_d_e > heap_S1465075775_j_k_l > option841825948on_j_k ).
thf(func_def_40,type,
is_doc1417632087_j_k_l: rObjec1413572695_j_k_l > $o ).
thf(func_def_41,type,
put_D_2126422573_h_i_l: docume1935157360tr_d_e > rObjec1617416918on_j_k > heap_S1465075775_j_k_l > heap_S1465075775_j_k_l ).
thf(func_def_42,type,
cast_d1608273229_b_c_f: docume1935157360tr_d_e > object945351580_d_e_f ).
thf(func_def_43,type,
cast_o761049241_d_e_f: object945351580_d_e_f > option1330818496tr_d_e ).
thf(func_def_44,type,
docume1825929374tr_d_e: sum_su1576157353tr_d_e > docume1935157360tr_d_e ).
thf(func_def_45,type,
docume1511108976tr_d_e: nat > docume1935157360tr_d_e ).
thf(func_def_46,type,
docume1799427087tr_d_e: ( sum_su1576157353tr_d_e > nat ) > docume1935157360tr_d_e > nat ).
thf(func_def_47,type,
is_doc2037328342tr_d_e: docume1935157360tr_d_e > $o ).
thf(func_def_48,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_49,type,
zero_zero_nat: nat ).
thf(func_def_50,type,
append846395565tr_b_c: list_n282880152tr_b_c > list_n282880152tr_b_c > list_n282880152tr_b_c ).
thf(func_def_51,type,
append_char: list_char > list_char > list_char ).
thf(func_def_52,type,
count_2128515342tr_b_c: list_n282880152tr_b_c > node_p1234578834tr_b_c > nat ).
thf(func_def_53,type,
count_list_char: list_char > char > nat ).
thf(func_def_54,type,
gen_le170886571tr_b_c: nat > list_l118626078tr_b_c > nat ).
thf(func_def_55,type,
gen_length_list_char: nat > list_list_char > nat ).
thf(func_def_56,type,
gen_le955068453tr_b_c: nat > list_n282880152tr_b_c > nat ).
thf(func_def_57,type,
gen_length_char: nat > list_char > nat ).
thf(func_def_58,type,
insert678865070tr_b_c: node_p1234578834tr_b_c > list_n282880152tr_b_c > list_n282880152tr_b_c ).
thf(func_def_59,type,
insert_char: char > list_char > list_char ).
thf(func_def_60,type,
cons_l1809994318tr_b_c: list_n282880152tr_b_c > list_l118626078tr_b_c > list_l118626078tr_b_c ).
thf(func_def_61,type,
cons_list_char: list_char > list_list_char > list_list_char ).
thf(func_def_62,type,
cons_n413985352tr_b_c: node_p1234578834tr_b_c > list_n282880152tr_b_c > list_n282880152tr_b_c ).
thf(func_def_63,type,
cons_char: char > list_char > list_char ).
thf(func_def_64,type,
nil_li198338206tr_b_c: list_l118626078tr_b_c ).
thf(func_def_65,type,
nil_list_char: list_list_char ).
thf(func_def_66,type,
nil_no279930520tr_b_c: list_n282880152tr_b_c ).
thf(func_def_67,type,
nil_char: list_char ).
thf(func_def_68,type,
list_e529904353tr_b_c: ( list_n282880152tr_b_c > $o ) > list_l118626078tr_b_c > $o ).
thf(func_def_69,type,
list_ex1_list_char: ( list_char > $o ) > list_list_char > $o ).
thf(func_def_70,type,
list_e469495899tr_b_c: ( node_p1234578834tr_b_c > $o ) > list_n282880152tr_b_c > $o ).
thf(func_def_71,type,
list_ex1_char: ( char > $o ) > list_char > $o ).
thf(func_def_72,type,
n_list1807568544tr_b_c: nat > list_n282880152tr_b_c > list_l118626078tr_b_c ).
thf(func_def_73,type,
n_lists_char: nat > list_char > list_list_char ).
thf(func_def_74,type,
nths_n1256675478tr_b_c: list_n282880152tr_b_c > set_nat > list_n282880152tr_b_c ).
thf(func_def_75,type,
nths_char: list_char > set_nat > list_char ).
thf(func_def_76,type,
produc1509350401tr_b_c: list_l118626078tr_b_c > list_l118626078tr_b_c ).
thf(func_def_77,type,
product_lists_char: list_list_char > list_list_char ).
thf(func_def_78,type,
splice1294941035tr_b_c: list_n282880152tr_b_c > list_n282880152tr_b_c > list_n282880152tr_b_c ).
thf(func_def_79,type,
splice_char: list_char > list_char > list_char ).
thf(func_def_80,type,
subseq1828679783tr_b_c: list_n282880152tr_b_c > list_l118626078tr_b_c ).
thf(func_def_81,type,
subseqs_char: list_char > list_list_char ).
thf(func_def_82,type,
suc: nat > nat ).
thf(func_def_83,type,
size_s724035844tr_d_e: docume1935157360tr_d_e > nat ).
thf(func_def_84,type,
size_s9369994tr_b_c: list_l118626078tr_b_c > nat ).
thf(func_def_85,type,
size_s2008079621t_char: list_list_char > nat ).
thf(func_def_86,type,
size_s2106487044tr_b_c: list_n282880152tr_b_c > nat ).
thf(func_def_87,type,
size_size_list_char: list_char > nat ).
thf(func_def_88,type,
size_s1129684517_ptr_a: option_element_ptr_a > nat ).
thf(func_def_89,type,
size_s7667464on_j_k: option841825948on_j_k > nat ).
thf(func_def_90,type,
size_s1129069050on_j_k: option2026120038on_j_k > nat ).
thf(func_def_91,type,
nat_set_decode: nat > set_nat ).
thf(func_def_92,type,
nat_set_encode: set_nat > nat ).
thf(func_def_93,type,
nat_triangle: nat > nat ).
thf(func_def_94,type,
rObjec1303043984on_j_k: product_unit > rDocum326988203on_j_k > rObjec1617416918on_j_k ).
thf(func_def_95,type,
rObjec730108904t_unit: product_unit > product_unit > rObjec103300152t_unit ).
thf(func_def_96,type,
extend1066431834on_j_k: rObjec103300152t_unit > rDocum326988203on_j_k > rObjec1617416918on_j_k ).
thf(func_def_97,type,
extend_Product_unit: rObjec103300152t_unit > product_unit > rObjec103300152t_unit ).
thf(func_def_98,type,
more_R1625109589on_j_k: rObjec1617416918on_j_k > rDocum326988203on_j_k ).
thf(func_def_99,type,
more_Product_unit: rObjec103300152t_unit > product_unit ).
thf(func_def_100,type,
nothin1567949605on_j_k: rObjec1617416918on_j_k > product_unit ).
thf(func_def_101,type,
nothing_Product_unit: rObjec103300152t_unit > product_unit ).
thf(func_def_102,type,
get_O_623850005_j_k_l: object945351580_d_e_f > heap_S1465075775_j_k_l > option1749760295_j_k_l ).
thf(func_def_103,type,
put_O_834343516_j_k_l: object945351580_d_e_f > rObjec1413572695_j_k_l > heap_S1465075775_j_k_l > heap_S1465075775_j_k_l ).
thf(func_def_104,type,
bind_e22036734_ptr_a: option_element_ptr_a > ( element_ptr_a > option_element_ptr_a ) > option_element_ptr_a ).
thf(func_def_105,type,
bind_e1012152651on_j_k: option_element_ptr_a > ( element_ptr_a > option2026120038on_j_k ) > option2026120038on_j_k ).
thf(func_def_106,type,
bind_S287509021_ptr_a: option2026120038on_j_k > ( sum_su1221287958on_j_k > option_element_ptr_a ) > option_element_ptr_a ).
thf(func_def_107,type,
bind_S607117548on_j_k: option2026120038on_j_k > ( sum_su1221287958on_j_k > option2026120038on_j_k ) > option2026120038on_j_k ).
thf(func_def_108,type,
none_d1458959567tr_d_e: option1330818496tr_d_e ).
thf(func_def_109,type,
none_element_ptr_a: option_element_ptr_a ).
thf(func_def_110,type,
none_R1587534007on_j_k: option841825948on_j_k ).
thf(func_def_111,type,
none_R1773662646_j_k_l: option1749760295_j_k_l ).
thf(func_def_112,type,
none_S1393028981on_j_k: option2026120038on_j_k ).
thf(func_def_113,type,
some_d1631029323tr_d_e: docume1935157360tr_d_e > option1330818496tr_d_e ).
thf(func_def_114,type,
some_element_ptr_a: element_ptr_a > option_element_ptr_a ).
thf(func_def_115,type,
some_R67702331on_j_k: rObjec1617416918on_j_k > option841825948on_j_k ).
thf(func_def_116,type,
some_R1598191922_j_k_l: rObjec1413572695_j_k_l > option1749760295_j_k_l ).
thf(func_def_117,type,
some_S1960742641on_j_k: sum_su1221287958on_j_k > option2026120038on_j_k ).
thf(func_def_118,type,
size_o1635055885tr_d_e: ( docume1935157360tr_d_e > nat ) > option1330818496tr_d_e > nat ).
thf(func_def_119,type,
size_o1591053974_ptr_a: ( element_ptr_a > nat ) > option_element_ptr_a > nat ).
thf(func_def_120,type,
size_o26122489on_j_k: ( rObjec1617416918on_j_k > nat ) > option841825948on_j_k > nat ).
thf(func_def_121,type,
size_o310046708_j_k_l: ( rObjec1413572695_j_k_l > nat ) > option1749760295_j_k_l > nat ).
thf(func_def_122,type,
size_o1777465779on_j_k: ( sum_su1221287958on_j_k > nat ) > option2026120038on_j_k > nat ).
thf(func_def_123,type,
bot_bo1111241908tr_d_e: fset_d1663890464tr_d_e ).
thf(func_def_124,type,
bot_bot_nat: nat ).
thf(func_def_125,type,
bot_bot_set_nat: set_nat ).
thf(func_def_126,type,
product_Unity: product_unit ).
thf(func_def_127,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_128,type,
type_w92696601_j_k_l: heap_S1465075775_j_k_l > $o ).
thf(func_def_129,type,
member_nat: nat > set_nat > $o ).
thf(func_def_130,type,
h: heap_S1465075775_j_k_l ).
thf(func_def_131,type,
h2: heap_S1465075775_j_k_l ).
thf(func_def_144,type,
sK0: nat > nat ).
thf(func_def_145,type,
sK1: rObjec1413572695_j_k_l > rObjec1617416918on_j_k ).
thf(func_def_146,type,
sK2: nat > nat ).
thf(func_def_147,type,
sK3: ( rObjec103300152t_unit > $o ) > product_unit ).
thf(func_def_148,type,
sK4: ( nat > $o ) > nat ).
thf(func_def_149,type,
sK5: ( nat > $o ) > nat ).
thf(func_def_150,type,
sK6: ( rObjec1617416918on_j_k > $o ) > product_unit ).
thf(func_def_151,type,
sK7: ( rObjec1617416918on_j_k > $o ) > list_char ).
thf(func_def_152,type,
sK8: ( rObjec1617416918on_j_k > $o ) > list_n282880152tr_b_c ).
thf(func_def_153,type,
sK9: ( rObjec1617416918on_j_k > $o ) > option2026120038on_j_k ).
thf(func_def_154,type,
sK10: ( rObjec1617416918on_j_k > $o ) > option_element_ptr_a ).
thf(func_def_155,type,
sK11: ( rObjec1617416918on_j_k > $o ) > product_unit ).
thf(func_def_156,type,
sK12: rObjec103300152t_unit > product_unit ).
thf(func_def_157,type,
sK13: docume1935157360tr_d_e > sum_su1576157353tr_d_e ).
thf(func_def_158,type,
sK14: docume1935157360tr_d_e > nat ).
thf(func_def_159,type,
sK15: rObjec1617416918on_j_k > product_unit ).
thf(func_def_160,type,
sK16: rObjec1617416918on_j_k > rDocum326988203on_j_k ).
thf(func_def_161,type,
sK17: ( nat > $o ) > nat ).
thf(func_def_162,type,
sK18: ( rDocum326988203on_j_k > $o ) > list_char ).
thf(func_def_163,type,
sK19: ( rDocum326988203on_j_k > $o ) > list_n282880152tr_b_c ).
thf(func_def_164,type,
sK20: ( rDocum326988203on_j_k > $o ) > option_element_ptr_a ).
thf(func_def_165,type,
sK21: ( rDocum326988203on_j_k > $o ) > option2026120038on_j_k ).
thf(func_def_166,type,
sK22: ( rDocum326988203on_j_k > $o ) > product_unit ).
thf(func_def_167,type,
sK23: ( nat > $o ) > nat ).
thf(func_def_168,type,
sK24: ( docume1935157360tr_d_e > $o ) > nat ).
thf(func_def_169,type,
sK25: ( docume1935157360tr_d_e > $o ) > sum_su1576157353tr_d_e ).
thf(func_def_170,type,
sK26: ( rObjec1617416918on_j_k > $o ) > product_unit ).
thf(func_def_171,type,
sK27: ( rObjec1617416918on_j_k > $o ) > rDocum326988203on_j_k ).
thf(func_def_172,type,
sK28: rObjec1617416918on_j_k > option2026120038on_j_k ).
thf(func_def_173,type,
sK29: rObjec1617416918on_j_k > product_unit ).
thf(func_def_174,type,
sK30: rObjec1617416918on_j_k > list_char ).
thf(func_def_175,type,
sK31: rObjec1617416918on_j_k > list_n282880152tr_b_c ).
thf(func_def_176,type,
sK32: rObjec1617416918on_j_k > product_unit ).
thf(func_def_177,type,
sK33: rObjec1617416918on_j_k > option_element_ptr_a ).
thf(func_def_178,type,
sK34: nat > nat ).
thf(func_def_179,type,
sK35: ( nat > nat > $o ) > nat ).
thf(func_def_180,type,
sK36: ( nat > nat > $o ) > nat ).
thf(func_def_181,type,
sK37: ( nat > nat > $o ) > nat ).
thf(func_def_182,type,
sK38: ( nat > nat > $o ) > nat ).
thf(f870,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f869,f847]) ).
thf(f847,plain,
! [X1: rObjec1617416918on_j_k] :
( none_R1587534007on_j_k
!= ( cast_O1034441233_j_k_l @ ( cast_D1252964113_h_i_l @ X1 ) ) ),
inference(equality_resolution,[status(thm)],[f775]) ).
thf(f775,plain,
! [X0: rObjec1413572695_j_k_l,X1: rObjec1617416918on_j_k] :
( ( ( cast_D1252964113_h_i_l @ X1 )
!= X0 )
| ( none_R1587534007on_j_k
!= ( cast_O1034441233_j_k_l @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f717]) ).
thf(f717,plain,
! [X0: rObjec1413572695_j_k_l] :
( ( ! [X1: rObjec1617416918on_j_k] :
( ( cast_D1252964113_h_i_l @ X1 )
!= X0 )
| ( none_R1587534007on_j_k
!= ( cast_O1034441233_j_k_l @ X0 ) ) )
& ( ( none_R1587534007on_j_k
= ( cast_O1034441233_j_k_l @ X0 ) )
| ( ( cast_D1252964113_h_i_l @ ( sK1 @ X0 ) )
= X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f715,f716]) ).
thf(f716,plain,
! [X0: rObjec1413572695_j_k_l] :
( ? [X2: rObjec1617416918on_j_k] :
( ( cast_D1252964113_h_i_l @ X2 )
= X0 )
=> ( ( cast_D1252964113_h_i_l @ ( sK1 @ X0 ) )
= X0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f715,plain,
! [X0: rObjec1413572695_j_k_l] :
( ( ! [X1: rObjec1617416918on_j_k] :
( ( cast_D1252964113_h_i_l @ X1 )
!= X0 )
| ( none_R1587534007on_j_k
!= ( cast_O1034441233_j_k_l @ X0 ) ) )
& ( ( none_R1587534007on_j_k
= ( cast_O1034441233_j_k_l @ X0 ) )
| ? [X2: rObjec1617416918on_j_k] :
( ( cast_D1252964113_h_i_l @ X2 )
= X0 ) ) ),
inference(rectify,[status(thm)],[f714]) ).
thf(f714,plain,
! [X0: rObjec1413572695_j_k_l] :
( ( ! [X1: rObjec1617416918on_j_k] :
( ( cast_D1252964113_h_i_l @ X1 )
!= X0 )
| ( none_R1587534007on_j_k
!= ( cast_O1034441233_j_k_l @ X0 ) ) )
& ( ( none_R1587534007on_j_k
= ( cast_O1034441233_j_k_l @ X0 ) )
| ? [X1: rObjec1617416918on_j_k] :
( ( cast_D1252964113_h_i_l @ X1 )
= X0 ) ) ),
inference(nnf_transformation,[status(thm)],[f702]) ).
thf(f702,plain,
! [X0: rObjec1413572695_j_k_l] :
( ! [X1: rObjec1617416918on_j_k] :
( ( cast_D1252964113_h_i_l @ X1 )
!= X0 )
<=> ( none_R1587534007on_j_k
= ( cast_O1034441233_j_k_l @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f651]) ).
thf(f651,plain,
! [X0: rObjec1413572695_j_k_l] :
( ( none_R1587534007on_j_k
= ( cast_O1034441233_j_k_l @ X0 ) )
<=> ~ ? [X1: rObjec1617416918on_j_k] :
( ( cast_D1252964113_h_i_l @ X1 )
= X0 ) ),
inference(fool_elimination,[status(thm)],[f650]) ).
thf(f650,plain,
! [X0: rObjec1413572695_j_k_l] :
~ ? [X1: rObjec1617416918on_j_k] :
( ( ( cast_D1252964113_h_i_l @ X1 )
= X0 )
= ( none_R1587534007on_j_k
= ( cast_O1034441233_j_k_l @ X0 ) ) ),
inference(rectify,[status(thm)],[f111]) ).
thf(f111,axiom,
! [X53: rObjec1413572695_j_k_l] :
~ ? [X37: rObjec1617416918on_j_k] :
( ( ( cast_D1252964113_h_i_l @ X37 )
= X53 )
= ( none_R1587534007on_j_k
= ( cast_O1034441233_j_k_l @ X53 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YeJj9WbkkZ/DTF2THF_6811.p',fact_110_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__none) ).
thf(f869,plain,
( none_R1587534007on_j_k
= ( cast_O1034441233_j_k_l @ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f868]) ).
thf(f868,plain,
( ( none_R1587534007on_j_k
= ( cast_O1034441233_j_k_l @ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[status(thm)],[f867]) ).
thf(f867,plain,
( ( none_R1587534007on_j_k
!= ( cast_O1034441233_j_k_l @ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f846]) ).
thf(f846,plain,
( $true
!= ( ^ [Y0: rObjec1413572695_j_k_l] :
( none_R1587534007on_j_k
!= ( cast_O1034441233_j_k_l @ Y0 ) )
@ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f808,f805]) ).
thf(f805,plain,
( is_doc1417632087_j_k_l
= ( ^ [Y0: rObjec1413572695_j_k_l] :
( none_R1587534007on_j_k
!= ( cast_O1034441233_j_k_l @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f503]) ).
thf(f503,plain,
( is_doc1417632087_j_k_l
= ( ^ [Y0: rObjec1413572695_j_k_l] :
( none_R1587534007on_j_k
!= ( cast_O1034441233_j_k_l @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f502]) ).
thf(f502,plain,
( ( ^ [X0: rObjec1413572695_j_k_l] :
( none_R1587534007on_j_k
!= ( cast_O1034441233_j_k_l @ X0 ) ) )
= is_doc1417632087_j_k_l ),
inference(rectify,[status(thm)],[f116]) ).
thf(f116,axiom,
( ( ^ [X54: rObjec1413572695_j_k_l] :
( none_R1587534007on_j_k
!= ( cast_O1034441233_j_k_l @ X54 ) ) )
= is_doc1417632087_j_k_l ),
file('/export/starexec/sandbox2/tmp/tmp.YeJj9WbkkZ/DTF2THF_6811.p',fact_115_is__document__kind__def) ).
thf(f808,plain,
( ( is_doc1417632087_j_k_l @ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f656]) ).
thf(f656,plain,
( ( is_doc1417632087_j_k_l @ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f371]) ).
thf(f371,plain,
( ( is_doc1417632087_j_k_l @ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f370]) ).
thf(f370,plain,
~ ( is_doc1417632087_j_k_l @ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ) ),
inference(rectify,[status(thm)],[f344]) ).
thf(f344,negated_conjecture,
~ ( is_doc1417632087_j_k_l @ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ) ),
inference(negated_conjecture,[status(cth)],[f343]) ).
thf(f343,conjecture,
is_doc1417632087_j_k_l @ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YeJj9WbkkZ/DTF2THF_6811.p',conj_3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP172^1 : 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
% 0.16/0.34 % Computer : n011.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:28:32 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : ITP172^1 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.46 % Domain : Interactive Theorem Proving
% 0.31/0.46 % Problem : Sledgehammer ShadowRootMonad problem prob_623__5857930_1
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Des21]
% 0.31/0.46 % Names : ShadowRootMonad/prob_623__5857930_1 [Des21]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0
% 0.31/0.46 % Syntax : Number of formulae : 475 ( 219 unt; 132 typ; 0 def)
% 0.31/0.46 % Number of atoms : 716 ( 702 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 7 ( 2 avg)
% 0.31/0.46 % Number of connectives : 2795 ( 147 ~; 12 |; 51 &;2133 @)
% 0.31/0.46 % ( 0 <=>; 452 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 29 ( 6 avg)
% 0.31/0.46 % Number of types : 26 ( 25 usr)
% 0.31/0.46 % Number of type conns : 402 ( 402 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 108 ( 107 usr; 16 con; 0-5 aty)
% 0.31/0.46 % Number of variables : 1120 ( 18 ^;1075 !; 27 ?;1120 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:33:17.461
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % Could-be-implicit typings (25)
% 0.31/0.46 thf(ty_n_t__ObjectClass__Oheap_It__Sum____Type__Osum_It__NodePointer__Onode____ptr_It__Sum____Type__Osum_It__ElementPointer__Oelement____ptr_Itf__a_J_Mt__Sum____Type__Osum_It__CharacterDataPointer__Ocharacter____data____ptr_Itf__b_J_Mtf__c_J_J_J_Mt__Sum____Type__Osum_It__DocumentPointer__Odocument____ptr_It__Sum____Type__Osum_It__ShadowRootPointer__Oshadow____root____ptr_Itf__d_J_Mtf__e_J_J_Mtf__f_J_J_Mt__Sum____Type__Osum_It__NodeClass__ORNode__ORNode____ext_It__Sum____Type__Osum_It__ElementClass__ORElement__ORElement____ext_Itf__c_Mtf__a_Mtf__b_Mtf__d_Mt__Option__Ooption_Itf__g_J_J_Mt__Sum____Type__Osum_It__CharacterDataClass__ORCharacterData__ORCharacterData____ext_It__Option__Ooption_Itf__h_J_J_Mtf__i_J_J_J_Mt__Sum____Type__Osum_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_Mtf__l_J_J_J,type,
% 0.31/0.46 heap_S1465075775_j_k_l: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Option__Ooption_It__ObjectClass__ORObject__ORObject____ext_It__Sum____Type__Osum_It__NodeClass__ORNode__ORNode____ext_It__Sum____Type__Osum_It__ElementClass__ORElement__ORElement____ext_Itf__c_Mtf__a_Mtf__b_Mtf__d_Mt__Option__Ooption_Itf__g_J_J_Mt__Sum____Type__Osum_It__CharacterDataClass__ORCharacterData__ORCharacterData____ext_It__Option__Ooption_Itf__h_J_J_Mtf__i_J_J_J_Mt__Sum____Type__Osum_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_Mtf__l_J_J_J_J,type,
% 0.31/0.46 option1749760295_j_k_l: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__ObjectClass__ORObject__ORObject____ext_It__Sum____Type__Osum_It__NodeClass__ORNode__ORNode____ext_It__Sum____Type__Osum_It__ElementClass__ORElement__ORElement____ext_Itf__c_Mtf__a_Mtf__b_Mtf__d_Mt__Option__Ooption_Itf__g_J_J_Mt__Sum____Type__Osum_It__CharacterDataClass__ORCharacterData__ORCharacterData____ext_It__Option__Ooption_Itf__h_J_J_Mtf__i_J_J_J_Mt__Sum____Type__Osum_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_Mtf__l_J_J_J,type,
% 0.31/0.46 rObjec1413572695_j_k_l: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__ObjectPointer__Oobject____ptr_It__Sum____Type__Osum_It__NodePointer__Onode____ptr_It__Sum____Type__Osum_It__ElementPointer__Oelement____ptr_Itf__a_J_Mt__Sum____Type__Osum_It__CharacterDataPointer__Ocharacter____data____ptr_Itf__b_J_Mtf__c_J_J_J_Mt__Sum____Type__Osum_It__DocumentPointer__Odocument____ptr_It__Sum____Type__Osum_It__ShadowRootPointer__Oshadow____root____ptr_Itf__d_J_Mtf__e_J_J_Mtf__f_J_J_J,type,
% 0.31/0.46 object945351580_d_e_f: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Option__Ooption_It__ObjectClass__ORObject__ORObject____ext_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_J_J,type,
% 0.31/0.46 option841825948on_j_k: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__ObjectClass__ORObject__ORObject____ext_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_J,type,
% 0.31/0.46 rObjec1617416918on_j_k: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J,type,
% 0.31/0.46 rDocum326988203on_j_k: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__NodePointer__Onode____ptr_It__Sum____Type__Osum_It__ElementPointer__Oelement____ptr_Itf__a_J_Mt__Sum____Type__Osum_It__CharacterDataPointer__Ocharacter____data____ptr_Itf__b_J_Mtf__c_J_J_J_J_J,type,
% 0.31/0.46 list_l118626078tr_b_c: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__List__Olist_It__NodePointer__Onode____ptr_It__Sum____Type__Osum_It__ElementPointer__Oelement____ptr_Itf__a_J_Mt__Sum____Type__Osum_It__CharacterDataPointer__Ocharacter____data____ptr_Itf__b_J_Mtf__c_J_J_J_J,type,
% 0.31/0.46 list_n282880152tr_b_c: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__NodePointer__Onode____ptr_It__Sum____Type__Osum_It__ElementPointer__Oelement____ptr_Itf__a_J_Mt__Sum____Type__Osum_It__CharacterDataPointer__Ocharacter____data____ptr_Itf__b_J_Mtf__c_J_J_J,type,
% 0.31/0.46 node_p1234578834tr_b_c: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J,type,
% 0.31/0.46 option2026120038on_j_k: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Option__Ooption_It__DocumentPointer__Odocument____ptr_It__Sum____Type__Osum_It__ShadowRootPointer__Oshadow____root____ptr_Itf__d_J_Mtf__e_J_J_J,type,
% 0.31/0.46 option1330818496tr_d_e: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__FSet__Ofset_It__DocumentPointer__Odocument____ptr_It__Sum____Type__Osum_It__ShadowRootPointer__Oshadow____root____ptr_Itf__d_J_Mtf__e_J_J_J,type,
% 0.31/0.46 fset_d1663890464tr_d_e: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J,type,
% 0.31/0.46 sum_su1221287958on_j_k: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__DocumentPointer__Odocument____ptr_It__Sum____Type__Osum_It__ShadowRootPointer__Oshadow____root____ptr_Itf__d_J_Mtf__e_J_J,type,
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% 0.31/0.46 size_o1591053974_ptr_a: ( element_ptr_a > nat ) > option_element_ptr_a > nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Option_Ooption_Osize__option_001t__ObjectClass__ORObject__ORObject____ext_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_J,type,
% 0.31/0.46 size_o26122489on_j_k: ( rObjec1617416918on_j_k > nat ) > option841825948on_j_k > nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Option_Ooption_Osize__option_001t__ObjectClass__ORObject__ORObject____ext_It__Sum____Type__Osum_It__NodeClass__ORNode__ORNode____ext_It__Sum____Type__Osum_It__ElementClass__ORElement__ORElement____ext_Itf__c_Mtf__a_Mtf__b_Mtf__d_Mt__Option__Ooption_Itf__g_J_J_Mt__Sum____Type__Osum_It__CharacterDataClass__ORCharacterData__ORCharacterData____ext_It__Option__Ooption_Itf__h_J_J_Mtf__i_J_J_J_Mt__Sum____Type__Osum_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_Mtf__l_J_J_J,type,
% 0.31/0.46 size_o310046708_j_k_l: ( rObjec1413572695_j_k_l > nat ) > option1749760295_j_k_l > nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Option_Ooption_Osize__option_001t__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J,type,
% 0.31/0.46 size_o1777465779on_j_k: ( sum_su1221287958on_j_k > nat ) > option2026120038on_j_k > nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__DocumentPointer__Odocument____ptr_It__Sum____Type__Osum_It__ShadowRootPointer__Oshadow____root____ptr_Itf__d_J_Mtf__e_J_J_J,type,
% 0.31/0.46 bot_bo1111241908tr_d_e: fset_d1663890464tr_d_e ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 0.31/0.46 bot_bot_nat: nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.31/0.46 bot_bot_set_nat: set_nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Product__Type_OUnity,type,
% 0.31/0.46 product_Unity: product_unit ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.31/0.46 collect_nat: ( nat > $o ) > set_nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_ShadowRootClass_Otype__wf_001tf__a_001tf__b_001tf__c_001tf__d_001tf__e_001tf__f_001tf__g_001tf__h_001tf__i_001tf__j_001tf__k_001tf__l,type,
% 0.31/0.46 type_w92696601_j_k_l: heap_S1465075775_j_k_l > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Nat__Onat,type,
% 0.31/0.46 member_nat: nat > set_nat > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_h,type,
% 0.31/0.46 h: heap_S1465075775_j_k_l ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_h_H,type,
% 0.31/0.46 h2: heap_S1465075775_j_k_l ).
% 0.31/0.46
% 0.31/0.46 % Relevant facts (339)
% 0.31/0.46 thf(fact_0_cast_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t__inject,axiom,
% 0.31/0.46 ! [X: rObjec1617416918on_j_k,Y: rObjec1617416918on_j_k] :
% 0.31/0.46 ( ( ( cast_D1252964113_h_i_l @ X )
% 0.31/0.46 = ( cast_D1252964113_h_i_l @ Y ) )
% 0.31/0.46 = ( X = Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % cast\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_inject
% 0.31/0.46 thf(fact_1_cast_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r_092_060_094sub_0622_092_060_094sub_062o_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r__inject,axiom,
% 0.31/0.46 ! [X: docume1935157360tr_d_e,Y: docume1935157360tr_d_e] :
% 0.31/0.46 ( ( ( cast_d1608273229_b_c_f @ X )
% 0.31/0.46 = ( cast_d1608273229_b_c_f @ Y ) )
% 0.31/0.46 = ( X = Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_inject
% 0.31/0.46 thf(fact_2_document__ptr_Oinject_I1_J,axiom,
% 0.31/0.46 ! [X1: nat,Y1: nat] :
% 0.31/0.46 ( ( ( docume1511108976tr_d_e @ X1 )
% 0.31/0.46 = ( docume1511108976tr_d_e @ Y1 ) )
% 0.31/0.46 = ( X1 = Y1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % document_ptr.inject(1)
% 0.31/0.46 thf(fact_3_RDocument_Oext__inject,axiom,
% 0.31/0.46 ! [Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k,Nothinga2: product_unit,Doctype2: list_char,Document_element2: option_element_ptr_a,Disconnected_nodes2: list_n282880152tr_b_c,More2: option2026120038on_j_k] :
% 0.31/0.46 ( ( ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More )
% 0.31/0.46 = ( rDocum427676485on_j_k @ Nothinga2 @ Doctype2 @ Document_element2 @ Disconnected_nodes2 @ More2 ) )
% 0.31/0.46 = ( ( Nothinga = Nothinga2 )
% 0.31/0.46 & ( Doctype = Doctype2 )
% 0.31/0.46 & ( Document_element = Document_element2 )
% 0.31/0.46 & ( Disconnected_nodes = Disconnected_nodes2 )
% 0.31/0.46 & ( More = More2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.ext_inject
% 0.31/0.46 thf(fact_4_RObject_Oext__inject,axiom,
% 0.31/0.46 ! [Nothing: product_unit,More: rDocum326988203on_j_k,Nothing2: product_unit,More2: rDocum326988203on_j_k] :
% 0.31/0.46 ( ( ( rObjec1303043984on_j_k @ Nothing @ More )
% 0.31/0.46 = ( rObjec1303043984on_j_k @ Nothing2 @ More2 ) )
% 0.31/0.46 = ( ( Nothing = Nothing2 )
% 0.31/0.46 & ( More = More2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.ext_inject
% 0.31/0.46 thf(fact_5_RObject_Oext__inject,axiom,
% 0.31/0.46 ! [Nothing: product_unit,More: product_unit,Nothing2: product_unit,More2: product_unit] :
% 0.31/0.46 ( ( ( rObjec730108904t_unit @ Nothing @ More )
% 0.31/0.46 = ( rObjec730108904t_unit @ Nothing2 @ More2 ) )
% 0.31/0.46 = ( ( Nothing = Nothing2 )
% 0.31/0.46 & ( More = More2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.ext_inject
% 0.31/0.46 thf(fact_6_nat_Oinject,axiom,
% 0.31/0.46 ! [X2: nat,Y2: nat] :
% 0.31/0.46 ( ( ( suc @ X2 )
% 0.31/0.46 = ( suc @ Y2 ) )
% 0.31/0.46 = ( X2 = Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % nat.inject
% 0.31/0.46 thf(fact_7_old_Onat_Oinject,axiom,
% 0.31/0.46 ! [Nat: nat,Nat2: nat] :
% 0.31/0.46 ( ( ( suc @ Nat )
% 0.31/0.46 = ( suc @ Nat2 ) )
% 0.31/0.46 = ( Nat = Nat2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.nat.inject
% 0.31/0.46 thf(fact_8_RDocument_Ocases__scheme,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k] :
% 0.31/0.46 ~ ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list_char,Document_element3: option_element_ptr_a,Disconnected_nodes3: list_n282880152tr_b_c,More3: option2026120038on_j_k] :
% 0.31/0.46 ( R
% 0.31/0.46 != ( rObjec1303043984on_j_k @ Nothing3 @ ( rDocum427676485on_j_k @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.cases_scheme
% 0.31/0.46 thf(fact_9_RDocument_Oinduct__scheme,axiom,
% 0.31/0.46 ! [P: rObjec1617416918on_j_k > $o,R: rObjec1617416918on_j_k] :
% 0.31/0.46 ( ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list_char,Document_element3: option_element_ptr_a,Disconnected_nodes3: list_n282880152tr_b_c,More3: option2026120038on_j_k] : ( P @ ( rObjec1303043984on_j_k @ Nothing3 @ ( rDocum427676485on_j_k @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) ) )
% 0.31/0.46 => ( P @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.induct_scheme
% 0.31/0.46 thf(fact_10_bot__nat__def,axiom,
% 0.31/0.46 bot_bot_nat = zero_zero_nat ).
% 0.31/0.46
% 0.31/0.46 % bot_nat_def
% 0.31/0.46 thf(fact_11_RObject_Oinduct,axiom,
% 0.31/0.46 ! [P: rObjec103300152t_unit > $o,R: rObjec103300152t_unit] :
% 0.31/0.46 ( ! [Nothing3: product_unit] : ( P @ ( rObjec730108904t_unit @ Nothing3 @ product_Unity ) )
% 0.31/0.46 => ( P @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.induct
% 0.31/0.46 thf(fact_12_RObject_Ocases,axiom,
% 0.31/0.46 ! [R: rObjec103300152t_unit] :
% 0.31/0.46 ~ ! [Nothing3: product_unit] :
% 0.31/0.46 ( R
% 0.31/0.46 != ( rObjec730108904t_unit @ Nothing3 @ product_Unity ) ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.cases
% 0.31/0.46 thf(fact_13_zero__reorient,axiom,
% 0.31/0.46 ! [X: nat] :
% 0.31/0.46 ( ( zero_zero_nat = X )
% 0.31/0.46 = ( X = zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % zero_reorient
% 0.31/0.46 thf(fact_14_n__not__Suc__n,axiom,
% 0.31/0.46 ! [N: nat] :
% 0.31/0.46 ( N
% 0.31/0.46 != ( suc @ N ) ) ).
% 0.31/0.46
% 0.31/0.46 % n_not_Suc_n
% 0.31/0.46 thf(fact_15_Suc__inject,axiom,
% 0.31/0.46 ! [X: nat,Y: nat] :
% 0.31/0.46 ( ( ( suc @ X )
% 0.31/0.46 = ( suc @ Y ) )
% 0.31/0.46 => ( X = Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % Suc_inject
% 0.31/0.46 thf(fact_16_RObject_Oinduct__scheme,axiom,
% 0.31/0.46 ! [P: rObjec1617416918on_j_k > $o,R: rObjec1617416918on_j_k] :
% 0.31/0.46 ( ! [Nothing3: product_unit,More3: rDocum326988203on_j_k] : ( P @ ( rObjec1303043984on_j_k @ Nothing3 @ More3 ) )
% 0.31/0.46 => ( P @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.induct_scheme
% 0.31/0.46 thf(fact_17_RObject_Oinduct__scheme,axiom,
% 0.31/0.46 ! [P: rObjec103300152t_unit > $o,R: rObjec103300152t_unit] :
% 0.31/0.46 ( ! [Nothing3: product_unit,More3: product_unit] : ( P @ ( rObjec730108904t_unit @ Nothing3 @ More3 ) )
% 0.31/0.46 => ( P @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.induct_scheme
% 0.31/0.46 thf(fact_18_RObject_Ocases__scheme,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k] :
% 0.31/0.46 ~ ! [Nothing3: product_unit,More3: rDocum326988203on_j_k] :
% 0.31/0.46 ( R
% 0.31/0.46 != ( rObjec1303043984on_j_k @ Nothing3 @ More3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.cases_scheme
% 0.31/0.46 thf(fact_19_RObject_Ocases__scheme,axiom,
% 0.31/0.46 ! [R: rObjec103300152t_unit] :
% 0.31/0.46 ~ ! [Nothing3: product_unit,More3: product_unit] :
% 0.31/0.46 ( R
% 0.31/0.46 != ( rObjec730108904t_unit @ Nothing3 @ More3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.cases_scheme
% 0.31/0.46 thf(fact_20_RDocument_Oext__induct,axiom,
% 0.31/0.46 ! [P: rDocum326988203on_j_k > $o,R: rDocum326988203on_j_k] :
% 0.31/0.46 ( ! [Nothinga3: product_unit,Doctype3: list_char,Document_element3: option_element_ptr_a,Disconnected_nodes3: list_n282880152tr_b_c,More3: option2026120038on_j_k] : ( P @ ( rDocum427676485on_j_k @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) )
% 0.31/0.46 => ( P @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.ext_induct
% 0.31/0.46 thf(fact_21_not0__implies__Suc,axiom,
% 0.31/0.46 ! [N: nat] :
% 0.31/0.46 ( ( N != zero_zero_nat )
% 0.31/0.46 => ? [M: nat] :
% 0.31/0.46 ( N
% 0.31/0.46 = ( suc @ M ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % not0_implies_Suc
% 0.31/0.46 thf(fact_22_old_Onat_Oinducts,axiom,
% 0.31/0.46 ! [P: nat > $o,Nat: nat] :
% 0.31/0.46 ( ( P @ zero_zero_nat )
% 0.31/0.46 => ( ! [Nat3: nat] :
% 0.31/0.46 ( ( P @ Nat3 )
% 0.31/0.46 => ( P @ ( suc @ Nat3 ) ) )
% 0.31/0.46 => ( P @ Nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.nat.inducts
% 0.31/0.46 thf(fact_23_old_Onat_Oexhaust,axiom,
% 0.31/0.46 ! [Y: nat] :
% 0.31/0.46 ( ( Y != zero_zero_nat )
% 0.31/0.46 => ~ ! [Nat3: nat] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( suc @ Nat3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.nat.exhaust
% 0.31/0.46 thf(fact_24_Zero__not__Suc,axiom,
% 0.31/0.46 ! [M2: nat] :
% 0.31/0.46 ( zero_zero_nat
% 0.31/0.46 != ( suc @ M2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Zero_not_Suc
% 0.31/0.46 thf(fact_25_Zero__neq__Suc,axiom,
% 0.31/0.46 ! [M2: nat] :
% 0.31/0.46 ( zero_zero_nat
% 0.31/0.46 != ( suc @ M2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Zero_neq_Suc
% 0.31/0.46 thf(fact_26_Suc__neq__Zero,axiom,
% 0.31/0.46 ! [M2: nat] :
% 0.31/0.46 ( ( suc @ M2 )
% 0.31/0.46 != zero_zero_nat ) ).
% 0.31/0.46
% 0.31/0.46 % Suc_neq_Zero
% 0.31/0.46 thf(fact_27_zero__induct,axiom,
% 0.31/0.46 ! [P: nat > $o,K: nat] :
% 0.31/0.46 ( ( P @ K )
% 0.31/0.46 => ( ! [N2: nat] :
% 0.31/0.46 ( ( P @ ( suc @ N2 ) )
% 0.31/0.46 => ( P @ N2 ) )
% 0.31/0.46 => ( P @ zero_zero_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % zero_induct
% 0.31/0.46 thf(fact_28_diff__induct,axiom,
% 0.31/0.46 ! [P: nat > nat > $o,M2: nat,N: nat] :
% 0.31/0.46 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 0.31/0.46 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 0.31/0.46 => ( ! [X3: nat,Y3: nat] :
% 0.31/0.46 ( ( P @ X3 @ Y3 )
% 0.31/0.46 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 0.31/0.46 => ( P @ M2 @ N ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % diff_induct
% 0.31/0.46 thf(fact_29_nat__induct,axiom,
% 0.31/0.46 ! [P: nat > $o,N: nat] :
% 0.31/0.46 ( ( P @ zero_zero_nat )
% 0.31/0.46 => ( ! [N2: nat] :
% 0.31/0.46 ( ( P @ N2 )
% 0.31/0.46 => ( P @ ( suc @ N2 ) ) )
% 0.31/0.46 => ( P @ N ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % nat_induct
% 0.31/0.46 thf(fact_30_nat_OdiscI,axiom,
% 0.31/0.46 ! [Nat: nat,X2: nat] :
% 0.31/0.46 ( ( Nat
% 0.31/0.46 = ( suc @ X2 ) )
% 0.31/0.46 => ( Nat != zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % nat.discI
% 0.31/0.46 thf(fact_31_old_Onat_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [Nat2: nat] :
% 0.31/0.46 ( zero_zero_nat
% 0.31/0.46 != ( suc @ Nat2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.nat.distinct(1)
% 0.31/0.46 thf(fact_32_old_Onat_Odistinct_I2_J,axiom,
% 0.31/0.46 ! [Nat2: nat] :
% 0.31/0.46 ( ( suc @ Nat2 )
% 0.31/0.46 != zero_zero_nat ) ).
% 0.31/0.46
% 0.31/0.46 % old.nat.distinct(2)
% 0.31/0.46 thf(fact_33_nat_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [X2: nat] :
% 0.31/0.46 ( zero_zero_nat
% 0.31/0.46 != ( suc @ X2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % nat.distinct(1)
% 0.31/0.46 thf(fact_34_document__ptr_Osize__gen_I1_J,axiom,
% 0.31/0.46 ! [X: sum_su1576157353tr_d_e > nat,X1: nat] :
% 0.31/0.46 ( ( docume1799427087tr_d_e @ X @ ( docume1511108976tr_d_e @ X1 ) )
% 0.31/0.46 = ( suc @ zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % document_ptr.size_gen(1)
% 0.31/0.46 thf(fact_35_document__ptr_Osize_I3_J,axiom,
% 0.31/0.46 ! [X1: nat] :
% 0.31/0.46 ( ( size_s724035844tr_d_e @ ( docume1511108976tr_d_e @ X1 ) )
% 0.31/0.46 = ( suc @ zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % document_ptr.size(3)
% 0.31/0.46 thf(fact_36_put_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__def,axiom,
% 0.31/0.46 ( put_D_2126422573_h_i_l
% 0.31/0.46 = ( ^ [Document_ptr: docume1935157360tr_d_e,Document: rObjec1617416918on_j_k] : ( put_O_834343516_j_k_l @ ( cast_d1608273229_b_c_f @ Document_ptr ) @ ( cast_D1252964113_h_i_l @ Document ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % put\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def
% 0.31/0.46 thf(fact_37_exists__least__lemma,axiom,
% 0.31/0.46 ! [P: nat > $o] :
% 0.31/0.46 ( ~ ( P @ zero_zero_nat )
% 0.31/0.46 => ( ? [X_1: nat] : ( P @ X_1 )
% 0.31/0.46 => ? [N2: nat] :
% 0.31/0.46 ( ~ ( P @ N2 )
% 0.31/0.46 & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % exists_least_lemma
% 0.31/0.46 thf(fact_38_list__decode_Ocases,axiom,
% 0.31/0.46 ! [X: nat] :
% 0.31/0.46 ( ( X != zero_zero_nat )
% 0.31/0.46 => ~ ! [N2: nat] :
% 0.31/0.46 ( X
% 0.31/0.46 != ( suc @ N2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % list_decode.cases
% 0.31/0.46 thf(fact_39_object__empty,axiom,
% 0.31/0.46 ! [X: rObjec1617416918on_j_k] :
% 0.31/0.46 ( ( rObjec1303043984on_j_k @ product_Unity @ ( more_R1625109589on_j_k @ X ) )
% 0.31/0.46 = X ) ).
% 0.31/0.46
% 0.31/0.46 % object_empty
% 0.31/0.46 thf(fact_40_object__empty,axiom,
% 0.31/0.46 ! [X: rObjec103300152t_unit] :
% 0.31/0.46 ( ( rObjec730108904t_unit @ product_Unity @ ( more_Product_unit @ X ) )
% 0.31/0.46 = X ) ).
% 0.31/0.46
% 0.31/0.46 % object_empty
% 0.31/0.46 thf(fact_41_mem__Collect__eq,axiom,
% 0.31/0.46 ! [A: nat,P: nat > $o] :
% 0.31/0.46 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.31/0.46 = ( P @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_Collect_eq
% 0.31/0.46 thf(fact_42_Collect__mem__eq,axiom,
% 0.31/0.46 ! [A2: set_nat] :
% 0.31/0.46 ( ( collect_nat
% 0.31/0.46 @ ^ [X4: nat] : ( member_nat @ X4 @ A2 ) )
% 0.31/0.46 = A2 ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mem_eq
% 0.31/0.46 thf(fact_43_RDocument_Oupdate__convs_I1_J,axiom,
% 0.31/0.46 ! [Nothing2: product_unit > product_unit,Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 0.31/0.46 ( ( nothin1105341917on_j_k @ Nothing2 @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.31/0.46 = ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ ( Nothing2 @ Nothinga ) @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.update_convs(1)
% 0.31/0.46 thf(fact_44_RDocument_Oupdate__convs_I2_J,axiom,
% 0.31/0.46 ! [Doctype2: list_char > list_char,Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 0.31/0.46 ( ( doctyp68000440on_j_k @ Doctype2 @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.31/0.46 = ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ ( Doctype2 @ Doctype ) @ Document_element @ Disconnected_nodes @ More ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.update_convs(2)
% 0.31/0.46 thf(fact_45_RDocument_Oupdate__convs_I3_J,axiom,
% 0.31/0.46 ! [Document_element2: option_element_ptr_a > option_element_ptr_a,Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 0.31/0.46 ( ( docume244715269on_j_k @ Document_element2 @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.31/0.46 = ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ ( Document_element2 @ Document_element ) @ Disconnected_nodes @ More ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.update_convs(3)
% 0.31/0.46 thf(fact_46_RDocument_Oupdate__convs_I4_J,axiom,
% 0.31/0.46 ! [Disconnected_nodes2: list_n282880152tr_b_c > list_n282880152tr_b_c,Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 0.31/0.46 ( ( discon442323090on_j_k @ Disconnected_nodes2 @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.31/0.46 = ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ ( Disconnected_nodes2 @ Disconnected_nodes ) @ More ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.update_convs(4)
% 0.31/0.46 thf(fact_47_size__neq__size__imp__neq,axiom,
% 0.31/0.46 ! [X: docume1935157360tr_d_e,Y: docume1935157360tr_d_e] :
% 0.31/0.46 ( ( ( size_s724035844tr_d_e @ X )
% 0.31/0.46 != ( size_s724035844tr_d_e @ Y ) )
% 0.31/0.46 => ( X != Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % size_neq_size_imp_neq
% 0.31/0.46 thf(fact_48_size__neq__size__imp__neq,axiom,
% 0.31/0.46 ! [X: list_n282880152tr_b_c,Y: list_n282880152tr_b_c] :
% 0.31/0.46 ( ( ( size_s2106487044tr_b_c @ X )
% 0.31/0.46 != ( size_s2106487044tr_b_c @ Y ) )
% 0.31/0.46 => ( X != Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % size_neq_size_imp_neq
% 0.31/0.46 thf(fact_49_size__neq__size__imp__neq,axiom,
% 0.31/0.46 ! [X: list_char,Y: list_char] :
% 0.31/0.46 ( ( ( size_size_list_char @ X )
% 0.31/0.46 != ( size_size_list_char @ Y ) )
% 0.31/0.46 => ( X != Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % size_neq_size_imp_neq
% 0.31/0.46 thf(fact_50_size__neq__size__imp__neq,axiom,
% 0.31/0.46 ! [X: option2026120038on_j_k,Y: option2026120038on_j_k] :
% 0.31/0.46 ( ( ( size_s1129069050on_j_k @ X )
% 0.31/0.46 != ( size_s1129069050on_j_k @ Y ) )
% 0.31/0.46 => ( X != Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % size_neq_size_imp_neq
% 0.31/0.46 thf(fact_51_size__neq__size__imp__neq,axiom,
% 0.31/0.46 ! [X: option_element_ptr_a,Y: option_element_ptr_a] :
% 0.31/0.46 ( ( ( size_s1129684517_ptr_a @ X )
% 0.31/0.46 != ( size_s1129684517_ptr_a @ Y ) )
% 0.31/0.46 => ( X != Y ) ) ).
% 0.31/0.46
% 0.31/0.46 % size_neq_size_imp_neq
% 0.31/0.46 thf(fact_52_RObject_Oselect__convs_I2_J,axiom,
% 0.31/0.46 ! [Nothing: product_unit,More: rDocum326988203on_j_k] :
% 0.31/0.46 ( ( more_R1625109589on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ More ) )
% 0.31/0.46 = More ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.select_convs(2)
% 0.31/0.46 thf(fact_53_RObject_Oselect__convs_I2_J,axiom,
% 0.31/0.46 ! [Nothing: product_unit,More: product_unit] :
% 0.31/0.46 ( ( more_Product_unit @ ( rObjec730108904t_unit @ Nothing @ More ) )
% 0.31/0.46 = More ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.select_convs(2)
% 0.31/0.46 thf(fact_54_document__ptr_Osize__neq,axiom,
% 0.31/0.46 ! [X: docume1935157360tr_d_e] :
% 0.31/0.46 ( ( size_s724035844tr_d_e @ X )
% 0.31/0.46 != zero_zero_nat ) ).
% 0.31/0.46
% 0.31/0.46 % document_ptr.size_neq
% 0.31/0.46 thf(fact_55_object__more__extend__id,axiom,
% 0.31/0.46 ! [X: rObjec103300152t_unit,Y: product_unit] :
% 0.31/0.46 ( ( more_Product_unit @ ( extend_Product_unit @ X @ Y ) )
% 0.31/0.46 = Y ) ).
% 0.31/0.46
% 0.31/0.46 % object_more_extend_id
% 0.31/0.46 thf(fact_56_object__more__extend__id,axiom,
% 0.31/0.46 ! [X: rObjec103300152t_unit,Y: rDocum326988203on_j_k] :
% 0.31/0.46 ( ( more_R1625109589on_j_k @ ( extend1066431834on_j_k @ X @ Y ) )
% 0.31/0.46 = Y ) ).
% 0.31/0.46
% 0.31/0.46 % object_more_extend_id
% 0.31/0.46 thf(fact_57_RDocument_Oupdate__convs_I5_J,axiom,
% 0.31/0.46 ! [More2: option2026120038on_j_k > option2026120038on_j_k,Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 0.31/0.46 ( ( more_u1044474223_c_a_b @ More2 @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.31/0.46 = ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ ( More2 @ More ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.update_convs(5)
% 0.31/0.46 thf(fact_58_is__document__ptr__ref,axiom,
% 0.31/0.46 ! [N: nat] : ( is_doc2037328342tr_d_e @ ( docume1511108976tr_d_e @ N ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_document_ptr_ref
% 0.31/0.46 thf(fact_59_RDocument_Oselect__convs_I5_J,axiom,
% 0.31/0.46 ! [Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 0.31/0.46 ( ( more_c1453068134on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.31/0.46 = More ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.select_convs(5)
% 0.31/0.46 thf(fact_60_RDocument_Oselect__convs_I4_J,axiom,
% 0.31/0.46 ! [Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 0.31/0.46 ( ( discon866287741on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.31/0.46 = Disconnected_nodes ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.select_convs(4)
% 0.31/0.46 thf(fact_61_RDocument_Oselect__convs_I3_J,axiom,
% 0.31/0.46 ! [Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 0.31/0.46 ( ( docume1175131570on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.31/0.46 = Document_element ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.select_convs(3)
% 0.31/0.46 thf(fact_62_RDocument_Oselect__convs_I2_J,axiom,
% 0.31/0.46 ! [Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 0.31/0.46 ( ( doctyp814403297on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.31/0.46 = Doctype ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.select_convs(2)
% 0.31/0.46 thf(fact_63_RDocument_Oselect__convs_I1_J,axiom,
% 0.31/0.46 ! [Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 0.31/0.46 ( ( nothin757132294on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.31/0.46 = Nothinga ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.select_convs(1)
% 0.31/0.46 thf(fact_64_RDocument_Ounfold__congs_I6_J,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: option2026120038on_j_k,F: option2026120038on_j_k > option2026120038on_j_k,F2: option2026120038on_j_k > option2026120038on_j_k] :
% 0.31/0.46 ( ( R = R2 )
% 0.31/0.46 => ( ( ( more_c1453068134on_j_k @ R2 )
% 0.31/0.46 = V )
% 0.31/0.46 => ( ! [V2: option2026120038on_j_k] :
% 0.31/0.46 ( ( V2 = V )
% 0.31/0.46 => ( ( F @ V2 )
% 0.31/0.46 = ( F2 @ V2 ) ) )
% 0.31/0.46 => ( ( more_u1044474223_c_a_b @ F @ R )
% 0.31/0.46 = ( more_u1044474223_c_a_b @ F2 @ R2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.unfold_congs(6)
% 0.31/0.46 thf(fact_65_RDocument_Ofold__congs_I6_J,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: option2026120038on_j_k,F: option2026120038on_j_k > option2026120038on_j_k,F2: option2026120038on_j_k > option2026120038on_j_k] :
% 0.31/0.46 ( ( R = R2 )
% 0.31/0.46 => ( ( ( more_c1453068134on_j_k @ R2 )
% 0.31/0.46 = V )
% 0.31/0.46 => ( ! [V2: option2026120038on_j_k] :
% 0.31/0.46 ( ( V = V2 )
% 0.31/0.46 => ( ( F @ V2 )
% 0.31/0.46 = ( F2 @ V2 ) ) )
% 0.31/0.46 => ( ( more_u1044474223_c_a_b @ F @ R )
% 0.31/0.46 = ( more_u1044474223_c_a_b @ F2 @ R2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.fold_congs(6)
% 0.31/0.46 thf(fact_66_RDocument_Ounfold__congs_I3_J,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: list_char,F: list_char > list_char,F2: list_char > list_char] :
% 0.31/0.46 ( ( R = R2 )
% 0.31/0.46 => ( ( ( doctyp814403297on_j_k @ R2 )
% 0.31/0.46 = V )
% 0.31/0.46 => ( ! [V2: list_char] :
% 0.31/0.46 ( ( V2 = V )
% 0.31/0.46 => ( ( F @ V2 )
% 0.31/0.46 = ( F2 @ V2 ) ) )
% 0.31/0.46 => ( ( doctyp68000440on_j_k @ F @ R )
% 0.31/0.46 = ( doctyp68000440on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.unfold_congs(3)
% 0.31/0.46 thf(fact_67_RDocument_Ounfold__congs_I4_J,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: option_element_ptr_a,F: option_element_ptr_a > option_element_ptr_a,F2: option_element_ptr_a > option_element_ptr_a] :
% 0.31/0.46 ( ( R = R2 )
% 0.31/0.46 => ( ( ( docume1175131570on_j_k @ R2 )
% 0.31/0.46 = V )
% 0.31/0.46 => ( ! [V2: option_element_ptr_a] :
% 0.31/0.46 ( ( V2 = V )
% 0.31/0.46 => ( ( F @ V2 )
% 0.31/0.46 = ( F2 @ V2 ) ) )
% 0.31/0.46 => ( ( docume244715269on_j_k @ F @ R )
% 0.31/0.46 = ( docume244715269on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.unfold_congs(4)
% 0.31/0.46 thf(fact_68_RDocument_Ounfold__congs_I5_J,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: list_n282880152tr_b_c,F: list_n282880152tr_b_c > list_n282880152tr_b_c,F2: list_n282880152tr_b_c > list_n282880152tr_b_c] :
% 0.31/0.46 ( ( R = R2 )
% 0.31/0.46 => ( ( ( discon866287741on_j_k @ R2 )
% 0.31/0.46 = V )
% 0.31/0.46 => ( ! [V2: list_n282880152tr_b_c] :
% 0.31/0.46 ( ( V2 = V )
% 0.31/0.46 => ( ( F @ V2 )
% 0.31/0.46 = ( F2 @ V2 ) ) )
% 0.31/0.46 => ( ( discon442323090on_j_k @ F @ R )
% 0.31/0.46 = ( discon442323090on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.unfold_congs(5)
% 0.31/0.46 thf(fact_69_RDocument_Ofold__congs_I3_J,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: list_char,F: list_char > list_char,F2: list_char > list_char] :
% 0.31/0.46 ( ( R = R2 )
% 0.31/0.46 => ( ( ( doctyp814403297on_j_k @ R2 )
% 0.31/0.46 = V )
% 0.31/0.46 => ( ! [V2: list_char] :
% 0.31/0.46 ( ( V = V2 )
% 0.31/0.46 => ( ( F @ V2 )
% 0.31/0.46 = ( F2 @ V2 ) ) )
% 0.31/0.46 => ( ( doctyp68000440on_j_k @ F @ R )
% 0.31/0.46 = ( doctyp68000440on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.fold_congs(3)
% 0.31/0.46 thf(fact_70_RDocument_Ofold__congs_I4_J,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: option_element_ptr_a,F: option_element_ptr_a > option_element_ptr_a,F2: option_element_ptr_a > option_element_ptr_a] :
% 0.31/0.46 ( ( R = R2 )
% 0.31/0.46 => ( ( ( docume1175131570on_j_k @ R2 )
% 0.31/0.46 = V )
% 0.31/0.46 => ( ! [V2: option_element_ptr_a] :
% 0.31/0.46 ( ( V = V2 )
% 0.31/0.46 => ( ( F @ V2 )
% 0.31/0.46 = ( F2 @ V2 ) ) )
% 0.31/0.46 => ( ( docume244715269on_j_k @ F @ R )
% 0.31/0.46 = ( docume244715269on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.fold_congs(4)
% 0.31/0.46 thf(fact_71_RDocument_Ofold__congs_I5_J,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: list_n282880152tr_b_c,F: list_n282880152tr_b_c > list_n282880152tr_b_c,F2: list_n282880152tr_b_c > list_n282880152tr_b_c] :
% 0.31/0.46 ( ( R = R2 )
% 0.31/0.46 => ( ( ( discon866287741on_j_k @ R2 )
% 0.31/0.46 = V )
% 0.31/0.46 => ( ! [V2: list_n282880152tr_b_c] :
% 0.31/0.46 ( ( V = V2 )
% 0.31/0.46 => ( ( F @ V2 )
% 0.31/0.46 = ( F2 @ V2 ) ) )
% 0.31/0.46 => ( ( discon442323090on_j_k @ F @ R )
% 0.31/0.46 = ( discon442323090on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.fold_congs(5)
% 0.31/0.46 thf(fact_72_RDocument_Ounfold__congs_I2_J,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: product_unit,F: product_unit > product_unit,F2: product_unit > product_unit] :
% 0.31/0.46 ( ( R = R2 )
% 0.31/0.46 => ( ( ( nothin757132294on_j_k @ R2 )
% 0.31/0.46 = V )
% 0.31/0.46 => ( ! [V2: product_unit] :
% 0.31/0.46 ( ( V2 = V )
% 0.31/0.46 => ( ( F @ V2 )
% 0.31/0.46 = ( F2 @ V2 ) ) )
% 0.31/0.46 => ( ( nothin1105341917on_j_k @ F @ R )
% 0.31/0.46 = ( nothin1105341917on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.unfold_congs(2)
% 0.31/0.46 thf(fact_73_RDocument_Ofold__congs_I2_J,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: product_unit,F: product_unit > product_unit,F2: product_unit > product_unit] :
% 0.31/0.46 ( ( R = R2 )
% 0.31/0.46 => ( ( ( nothin757132294on_j_k @ R2 )
% 0.31/0.46 = V )
% 0.31/0.46 => ( ! [V2: product_unit] :
% 0.31/0.46 ( ( V = V2 )
% 0.31/0.46 => ( ( F @ V2 )
% 0.31/0.46 = ( F2 @ V2 ) ) )
% 0.31/0.46 => ( ( nothin1105341917on_j_k @ F @ R )
% 0.31/0.46 = ( nothin1105341917on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.fold_congs(2)
% 0.31/0.46 thf(fact_74_length__0__conv,axiom,
% 0.31/0.46 ! [Xs: list_l118626078tr_b_c] :
% 0.31/0.46 ( ( ( size_s9369994tr_b_c @ Xs )
% 0.31/0.46 = zero_zero_nat )
% 0.31/0.46 = ( Xs = nil_li198338206tr_b_c ) ) ).
% 0.31/0.46
% 0.31/0.46 % length_0_conv
% 0.31/0.46 thf(fact_75_length__0__conv,axiom,
% 0.31/0.46 ! [Xs: list_list_char] :
% 0.31/0.46 ( ( ( size_s2008079621t_char @ Xs )
% 0.31/0.46 = zero_zero_nat )
% 0.31/0.46 = ( Xs = nil_list_char ) ) ).
% 0.31/0.46
% 0.31/0.46 % length_0_conv
% 0.31/0.46 thf(fact_76_length__0__conv,axiom,
% 0.31/0.46 ! [Xs: list_char] :
% 0.31/0.46 ( ( ( size_size_list_char @ Xs )
% 0.31/0.46 = zero_zero_nat )
% 0.31/0.46 = ( Xs = nil_char ) ) ).
% 0.31/0.46
% 0.31/0.46 % length_0_conv
% 0.31/0.46 thf(fact_77_length__0__conv,axiom,
% 0.31/0.46 ! [Xs: list_n282880152tr_b_c] :
% 0.31/0.46 ( ( ( size_s2106487044tr_b_c @ Xs )
% 0.31/0.46 = zero_zero_nat )
% 0.31/0.46 = ( Xs = nil_no279930520tr_b_c ) ) ).
% 0.31/0.46
% 0.31/0.46 % length_0_conv
% 0.31/0.46 thf(fact_78_RDocument_Osurjective,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k] :
% 0.31/0.46 ( R
% 0.31/0.46 = ( rObjec1303043984on_j_k @ ( nothin1567949605on_j_k @ R ) @ ( rDocum427676485on_j_k @ ( nothin757132294on_j_k @ R ) @ ( doctyp814403297on_j_k @ R ) @ ( docume1175131570on_j_k @ R ) @ ( discon866287741on_j_k @ R ) @ ( more_c1453068134on_j_k @ R ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.surjective
% 0.31/0.46 thf(fact_79_RDocument_Oequality,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k] :
% 0.31/0.46 ( ( ( nothin1567949605on_j_k @ R )
% 0.31/0.46 = ( nothin1567949605on_j_k @ R2 ) )
% 0.31/0.46 => ( ( ( nothin757132294on_j_k @ R )
% 0.31/0.46 = ( nothin757132294on_j_k @ R2 ) )
% 0.31/0.46 => ( ( ( doctyp814403297on_j_k @ R )
% 0.31/0.46 = ( doctyp814403297on_j_k @ R2 ) )
% 0.31/0.46 => ( ( ( docume1175131570on_j_k @ R )
% 0.31/0.46 = ( docume1175131570on_j_k @ R2 ) )
% 0.31/0.46 => ( ( ( discon866287741on_j_k @ R )
% 0.31/0.46 = ( discon866287741on_j_k @ R2 ) )
% 0.31/0.46 => ( ( ( more_c1453068134on_j_k @ R )
% 0.31/0.46 = ( more_c1453068134on_j_k @ R2 ) )
% 0.31/0.46 => ( R = R2 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RDocument.equality
% 0.31/0.46 thf(fact_80_option_Osize_I3_J,axiom,
% 0.31/0.46 ( ( size_s7667464on_j_k @ none_R1587534007on_j_k )
% 0.31/0.46 = ( suc @ zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.size(3)
% 0.31/0.46 thf(fact_81_option_Osize_I3_J,axiom,
% 0.31/0.46 ( ( size_s1129684517_ptr_a @ none_element_ptr_a )
% 0.31/0.46 = ( suc @ zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.size(3)
% 0.31/0.46 thf(fact_82_option_Osize_I3_J,axiom,
% 0.31/0.46 ( ( size_s1129069050on_j_k @ none_S1393028981on_j_k )
% 0.31/0.46 = ( suc @ zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.size(3)
% 0.31/0.46 thf(fact_83_list_Osize_I3_J,axiom,
% 0.31/0.46 ( ( size_s9369994tr_b_c @ nil_li198338206tr_b_c )
% 0.31/0.46 = zero_zero_nat ) ).
% 0.31/0.46
% 0.31/0.46 % list.size(3)
% 0.31/0.46 thf(fact_84_list_Osize_I3_J,axiom,
% 0.31/0.46 ( ( size_s2008079621t_char @ nil_list_char )
% 0.31/0.46 = zero_zero_nat ) ).
% 0.31/0.46
% 0.31/0.46 % list.size(3)
% 0.31/0.46 thf(fact_85_list_Osize_I3_J,axiom,
% 0.31/0.46 ( ( size_size_list_char @ nil_char )
% 0.31/0.46 = zero_zero_nat ) ).
% 0.31/0.46
% 0.31/0.46 % list.size(3)
% 0.31/0.46 thf(fact_86_list_Osize_I3_J,axiom,
% 0.31/0.46 ( ( size_s2106487044tr_b_c @ nil_no279930520tr_b_c )
% 0.31/0.46 = zero_zero_nat ) ).
% 0.31/0.46
% 0.31/0.46 % list.size(3)
% 0.31/0.46 thf(fact_87_document__ptr_Osize_I4_J,axiom,
% 0.31/0.46 ! [X2: sum_su1576157353tr_d_e] :
% 0.31/0.46 ( ( size_s724035844tr_d_e @ ( docume1825929374tr_d_e @ X2 ) )
% 0.31/0.46 = ( suc @ zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % document_ptr.size(4)
% 0.31/0.46 thf(fact_88_RObject_Osurjective,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k] :
% 0.31/0.46 ( R
% 0.31/0.46 = ( rObjec1303043984on_j_k @ ( nothin1567949605on_j_k @ R ) @ ( more_R1625109589on_j_k @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.surjective
% 0.31/0.46 thf(fact_89_RObject_Osurjective,axiom,
% 0.31/0.46 ! [R: rObjec103300152t_unit] :
% 0.31/0.46 ( R
% 0.31/0.46 = ( rObjec730108904t_unit @ ( nothing_Product_unit @ R ) @ ( more_Product_unit @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.surjective
% 0.31/0.46 thf(fact_90_document__ptr_Oinject_I2_J,axiom,
% 0.31/0.46 ! [X2: sum_su1576157353tr_d_e,Y2: sum_su1576157353tr_d_e] :
% 0.31/0.46 ( ( ( docume1825929374tr_d_e @ X2 )
% 0.31/0.46 = ( docume1825929374tr_d_e @ Y2 ) )
% 0.31/0.46 = ( X2 = Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % document_ptr.inject(2)
% 0.31/0.46 thf(fact_91_neq__if__length__neq,axiom,
% 0.31/0.46 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 0.31/0.46 ( ( ( size_s2106487044tr_b_c @ Xs )
% 0.31/0.46 != ( size_s2106487044tr_b_c @ Ys ) )
% 0.31/0.46 => ( Xs != Ys ) ) ).
% 0.31/0.46
% 0.31/0.46 % neq_if_length_neq
% 0.31/0.46 thf(fact_92_neq__if__length__neq,axiom,
% 0.31/0.46 ! [Xs: list_char,Ys: list_char] :
% 0.31/0.46 ( ( ( size_size_list_char @ Xs )
% 0.31/0.46 != ( size_size_list_char @ Ys ) )
% 0.31/0.46 => ( Xs != Ys ) ) ).
% 0.31/0.46
% 0.31/0.46 % neq_if_length_neq
% 0.31/0.46 thf(fact_93_Ex__list__of__length,axiom,
% 0.31/0.46 ! [N: nat] :
% 0.31/0.46 ? [Xs2: list_n282880152tr_b_c] :
% 0.31/0.46 ( ( size_s2106487044tr_b_c @ Xs2 )
% 0.31/0.46 = N ) ).
% 0.31/0.46
% 0.31/0.46 % Ex_list_of_length
% 0.31/0.46 thf(fact_94_Ex__list__of__length,axiom,
% 0.31/0.46 ! [N: nat] :
% 0.31/0.46 ? [Xs2: list_char] :
% 0.31/0.46 ( ( size_size_list_char @ Xs2 )
% 0.31/0.46 = N ) ).
% 0.31/0.46
% 0.31/0.46 % Ex_list_of_length
% 0.31/0.46 thf(fact_95_document__ptr_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [X1: nat,X2: sum_su1576157353tr_d_e] :
% 0.31/0.46 ( ( docume1511108976tr_d_e @ X1 )
% 0.31/0.46 != ( docume1825929374tr_d_e @ X2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % document_ptr.distinct(1)
% 0.31/0.46 thf(fact_96_document__ptr_Oinduct,axiom,
% 0.31/0.46 ! [P: docume1935157360tr_d_e > $o,Document_ptr2: docume1935157360tr_d_e] :
% 0.31/0.46 ( ! [X3: nat] : ( P @ ( docume1511108976tr_d_e @ X3 ) )
% 0.31/0.46 => ( ! [X3: sum_su1576157353tr_d_e] : ( P @ ( docume1825929374tr_d_e @ X3 ) )
% 0.31/0.46 => ( P @ Document_ptr2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % document_ptr.induct
% 0.31/0.46 thf(fact_97_document__ptr_Oexhaust,axiom,
% 0.31/0.46 ! [Y: docume1935157360tr_d_e] :
% 0.31/0.46 ( ! [X12: nat] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( docume1511108976tr_d_e @ X12 ) )
% 0.31/0.46 => ~ ! [X22: sum_su1576157353tr_d_e] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( docume1825929374tr_d_e @ X22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % document_ptr.exhaust
% 0.31/0.46 thf(fact_98_RObject_Oselect__convs_I1_J,axiom,
% 0.31/0.46 ! [Nothing: product_unit,More: rDocum326988203on_j_k] :
% 0.31/0.46 ( ( nothin1567949605on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ More ) )
% 0.31/0.46 = Nothing ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.select_convs(1)
% 0.31/0.46 thf(fact_99_RObject_Oselect__convs_I1_J,axiom,
% 0.31/0.46 ! [Nothing: product_unit,More: product_unit] :
% 0.31/0.46 ( ( nothing_Product_unit @ ( rObjec730108904t_unit @ Nothing @ More ) )
% 0.31/0.46 = Nothing ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.select_convs(1)
% 0.31/0.46 thf(fact_100_RObject_Oequality,axiom,
% 0.31/0.46 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k] :
% 0.31/0.46 ( ( ( nothin1567949605on_j_k @ R )
% 0.31/0.46 = ( nothin1567949605on_j_k @ R2 ) )
% 0.31/0.46 => ( ( ( more_R1625109589on_j_k @ R )
% 0.31/0.46 = ( more_R1625109589on_j_k @ R2 ) )
% 0.31/0.46 => ( R = R2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.equality
% 0.31/0.46 thf(fact_101_RObject_Oequality,axiom,
% 0.31/0.46 ! [R: rObjec103300152t_unit,R2: rObjec103300152t_unit] :
% 0.31/0.46 ( ( ( nothing_Product_unit @ R )
% 0.31/0.46 = ( nothing_Product_unit @ R2 ) )
% 0.31/0.46 => ( ( ( more_Product_unit @ R )
% 0.31/0.46 = ( more_Product_unit @ R2 ) )
% 0.31/0.46 => ( R = R2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % RObject.equality
% 0.31/0.46 thf(fact_102_option_Osize__neq,axiom,
% 0.31/0.46 ! [X: option2026120038on_j_k] :
% 0.31/0.46 ( ( size_s1129069050on_j_k @ X )
% 0.31/0.46 != zero_zero_nat ) ).
% 0.31/0.46
% 0.31/0.46 % option.size_neq
% 0.31/0.46 thf(fact_103_option_Osize__neq,axiom,
% 0.31/0.46 ! [X: option_element_ptr_a] :
% 0.31/0.46 ( ( size_s1129684517_ptr_a @ X )
% 0.31/0.46 != zero_zero_nat ) ).
% 0.31/0.46
% 0.31/0.46 % option.size_neq
% 0.31/0.46 thf(fact_104_option_Osize__gen_I1_J,axiom,
% 0.31/0.46 ! [X: rObjec1617416918on_j_k > nat] :
% 0.31/0.46 ( ( size_o26122489on_j_k @ X @ none_R1587534007on_j_k )
% 0.31/0.46 = ( suc @ zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.size_gen(1)
% 0.31/0.46 thf(fact_105_option_Osize__gen_I1_J,axiom,
% 0.31/0.46 ! [X: element_ptr_a > nat] :
% 0.31/0.46 ( ( size_o1591053974_ptr_a @ X @ none_element_ptr_a )
% 0.31/0.46 = ( suc @ zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.size_gen(1)
% 0.31/0.46 thf(fact_106_option_Osize__gen_I1_J,axiom,
% 0.31/0.46 ! [X: sum_su1221287958on_j_k > nat] :
% 0.31/0.46 ( ( size_o1777465779on_j_k @ X @ none_S1393028981on_j_k )
% 0.31/0.46 = ( suc @ zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.size_gen(1)
% 0.31/0.46 thf(fact_107_length__code,axiom,
% 0.31/0.46 ( size_s2106487044tr_b_c
% 0.31/0.46 = ( gen_le955068453tr_b_c @ zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % length_code
% 0.31/0.46 thf(fact_108_length__code,axiom,
% 0.31/0.46 ( size_size_list_char
% 0.31/0.46 = ( gen_length_char @ zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % length_code
% 0.31/0.46 thf(fact_109_document__ptr_Osize__gen_I2_J,axiom,
% 0.31/0.46 ! [X: sum_su1576157353tr_d_e > nat,X2: sum_su1576157353tr_d_e] :
% 0.31/0.46 ( ( docume1799427087tr_d_e @ X @ ( docume1825929374tr_d_e @ X2 ) )
% 0.31/0.46 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % document_ptr.size_gen(2)
% 0.31/0.46 thf(fact_110_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__none,axiom,
% 0.31/0.46 ! [Obj: rObjec1413572695_j_k_l] :
% 0.31/0.46 ( ( ( cast_O1034441233_j_k_l @ Obj )
% 0.31/0.46 = none_R1587534007on_j_k )
% 0.31/0.46 = ( ~ ? [Document: rObjec1617416918on_j_k] :
% 0.31/0.46 ( ( cast_D1252964113_h_i_l @ Document )
% 0.31/0.46 = Obj ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_none
% 0.31/0.46 thf(fact_111_list__ex1__simps_I1_J,axiom,
% 0.31/0.46 ! [P: list_n282880152tr_b_c > $o] :
% 0.31/0.46 ~ ( list_e529904353tr_b_c @ P @ nil_li198338206tr_b_c ) ).
% 0.31/0.46
% 0.31/0.46 % list_ex1_simps(1)
% 0.31/0.46 thf(fact_112_list__ex1__simps_I1_J,axiom,
% 0.31/0.46 ! [P: list_char > $o] :
% 0.31/0.46 ~ ( list_ex1_list_char @ P @ nil_list_char ) ).
% 0.31/0.46
% 0.31/0.46 % list_ex1_simps(1)
% 0.31/0.46 thf(fact_113_list__ex1__simps_I1_J,axiom,
% 0.31/0.46 ! [P: char > $o] :
% 0.31/0.46 ~ ( list_ex1_char @ P @ nil_char ) ).
% 0.31/0.46
% 0.31/0.46 % list_ex1_simps(1)
% 0.31/0.46 thf(fact_114_list__ex1__simps_I1_J,axiom,
% 0.31/0.46 ! [P: node_p1234578834tr_b_c > $o] :
% 0.31/0.46 ~ ( list_e469495899tr_b_c @ P @ nil_no279930520tr_b_c ) ).
% 0.31/0.46
% 0.31/0.46 % list_ex1_simps(1)
% 0.31/0.46 thf(fact_115_is__document__kind__def,axiom,
% 0.31/0.46 ( is_doc1417632087_j_k_l
% 0.31/0.46 = ( ^ [Ptr: rObjec1413572695_j_k_l] :
% 0.31/0.46 ( ( cast_O1034441233_j_k_l @ Ptr )
% 0.31/0.46 != none_R1587534007on_j_k ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_document_kind_def
% 0.31/0.46 thf(fact_116_add__right__cancel,axiom,
% 0.31/0.46 ! [B: nat,A: nat,C: nat] :
% 0.31/0.46 ( ( ( plus_plus_nat @ B @ A )
% 0.31/0.46 = ( plus_plus_nat @ C @ A ) )
% 0.31/0.46 = ( B = C ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_right_cancel
% 0.31/0.46 thf(fact_117_add__left__cancel,axiom,
% 0.31/0.46 ! [A: nat,B: nat,C: nat] :
% 0.31/0.46 ( ( ( plus_plus_nat @ A @ B )
% 0.31/0.46 = ( plus_plus_nat @ A @ C ) )
% 0.31/0.46 = ( B = C ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_left_cancel
% 0.31/0.46 thf(fact_118_zero__eq__add__iff__both__eq__0,axiom,
% 0.31/0.46 ! [X: nat,Y: nat] :
% 0.31/0.46 ( ( zero_zero_nat
% 0.31/0.46 = ( plus_plus_nat @ X @ Y ) )
% 0.31/0.46 = ( ( X = zero_zero_nat )
% 0.31/0.46 & ( Y = zero_zero_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % zero_eq_add_iff_both_eq_0
% 0.31/0.46 thf(fact_119_add__eq__0__iff__both__eq__0,axiom,
% 0.31/0.46 ! [X: nat,Y: nat] :
% 0.31/0.46 ( ( ( plus_plus_nat @ X @ Y )
% 0.31/0.46 = zero_zero_nat )
% 0.31/0.46 = ( ( X = zero_zero_nat )
% 0.31/0.46 & ( Y = zero_zero_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_eq_0_iff_both_eq_0
% 0.31/0.46 thf(fact_120_add__cancel__right__right,axiom,
% 0.31/0.46 ! [A: nat,B: nat] :
% 0.31/0.46 ( ( A
% 0.31/0.46 = ( plus_plus_nat @ A @ B ) )
% 0.31/0.46 = ( B = zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_cancel_right_right
% 0.31/0.46 thf(fact_121_add__cancel__right__left,axiom,
% 0.31/0.46 ! [A: nat,B: nat] :
% 0.31/0.46 ( ( A
% 0.31/0.46 = ( plus_plus_nat @ B @ A ) )
% 0.31/0.46 = ( B = zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_cancel_right_left
% 0.31/0.46 thf(fact_122_add__cancel__left__right,axiom,
% 0.31/0.46 ! [A: nat,B: nat] :
% 0.31/0.46 ( ( ( plus_plus_nat @ A @ B )
% 0.31/0.46 = A )
% 0.31/0.46 = ( B = zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_cancel_left_right
% 0.31/0.46 thf(fact_123_add__cancel__left__left,axiom,
% 0.31/0.46 ! [B: nat,A: nat] :
% 0.31/0.46 ( ( ( plus_plus_nat @ B @ A )
% 0.31/0.46 = A )
% 0.31/0.46 = ( B = zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_cancel_left_left
% 0.31/0.46 thf(fact_124_add_Oright__neutral,axiom,
% 0.31/0.46 ! [A: nat] :
% 0.31/0.46 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.31/0.46 = A ) ).
% 0.31/0.46
% 0.31/0.46 % add.right_neutral
% 0.31/0.46 thf(fact_125_add_Oleft__neutral,axiom,
% 0.31/0.46 ! [A: nat] :
% 0.31/0.46 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.31/0.46 = A ) ).
% 0.31/0.46
% 0.31/0.46 % add.left_neutral
% 0.31/0.46 thf(fact_126_add__Suc__right,axiom,
% 0.31/0.46 ! [M2: nat,N: nat] :
% 0.31/0.46 ( ( plus_plus_nat @ M2 @ ( suc @ N ) )
% 0.31/0.46 = ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_Suc_right
% 0.31/0.46 thf(fact_127_Nat_Oadd__0__right,axiom,
% 0.31/0.46 ! [M2: nat] :
% 0.31/0.46 ( ( plus_plus_nat @ M2 @ zero_zero_nat )
% 0.31/0.46 = M2 ) ).
% 0.31/0.46
% 0.31/0.46 % Nat.add_0_right
% 0.31/0.46 thf(fact_128_add__is__0,axiom,
% 0.31/0.46 ! [M2: nat,N: nat] :
% 0.31/0.46 ( ( ( plus_plus_nat @ M2 @ N )
% 0.31/0.46 = zero_zero_nat )
% 0.31/0.46 = ( ( M2 = zero_zero_nat )
% 0.31/0.46 & ( N = zero_zero_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_is_0
% 0.31/0.46 thf(fact_129_gen__length__def,axiom,
% 0.31/0.46 ( gen_le955068453tr_b_c
% 0.31/0.46 = ( ^ [N3: nat,Xs3: list_n282880152tr_b_c] : ( plus_plus_nat @ N3 @ ( size_s2106487044tr_b_c @ Xs3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % gen_length_def
% 0.31/0.46 thf(fact_130_gen__length__def,axiom,
% 0.31/0.46 ( gen_length_char
% 0.31/0.46 = ( ^ [N3: nat,Xs3: list_char] : ( plus_plus_nat @ N3 @ ( size_size_list_char @ Xs3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % gen_length_def
% 0.31/0.46 thf(fact_131_add__right__imp__eq,axiom,
% 0.31/0.46 ! [B: nat,A: nat,C: nat] :
% 0.31/0.46 ( ( ( plus_plus_nat @ B @ A )
% 0.31/0.46 = ( plus_plus_nat @ C @ A ) )
% 0.31/0.46 => ( B = C ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_right_imp_eq
% 0.31/0.46 thf(fact_132_add__left__imp__eq,axiom,
% 0.31/0.46 ! [A: nat,B: nat,C: nat] :
% 0.31/0.46 ( ( ( plus_plus_nat @ A @ B )
% 0.31/0.46 = ( plus_plus_nat @ A @ C ) )
% 0.31/0.46 => ( B = C ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_left_imp_eq
% 0.31/0.46 thf(fact_133_add_Oleft__commute,axiom,
% 0.31/0.46 ! [B: nat,A: nat,C: nat] :
% 0.31/0.46 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 0.31/0.46 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % add.left_commute
% 0.31/0.46 thf(fact_134_add_Ocommute,axiom,
% 0.31/0.46 ( plus_plus_nat
% 0.31/0.46 = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % add.commute
% 0.31/0.46 thf(fact_135_add_Oassoc,axiom,
% 0.31/0.46 ! [A: nat,B: nat,C: nat] :
% 0.31/0.46 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.31/0.46 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % add.assoc
% 0.31/0.46 thf(fact_136_group__cancel_Oadd2,axiom,
% 0.31/0.46 ! [B3: nat,K: nat,B: nat,A: nat] :
% 0.31/0.46 ( ( B3
% 0.31/0.46 = ( plus_plus_nat @ K @ B ) )
% 0.31/0.46 => ( ( plus_plus_nat @ A @ B3 )
% 0.31/0.46 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % group_cancel.add2
% 0.31/0.46 thf(fact_137_group__cancel_Oadd1,axiom,
% 0.31/0.46 ! [A2: nat,K: nat,A: nat,B: nat] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( plus_plus_nat @ K @ A ) )
% 0.31/0.46 => ( ( plus_plus_nat @ A2 @ B )
% 0.31/0.46 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % group_cancel.add1
% 0.31/0.46 thf(fact_138_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.31/0.46 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/0.46 ( ( ( I = J )
% 0.31/0.46 & ( K = L ) )
% 0.31/0.46 => ( ( plus_plus_nat @ I @ K )
% 0.31/0.46 = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_mono_thms_linordered_semiring(4)
% 0.31/0.46 thf(fact_139_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.31/0.46 ! [A: nat,B: nat,C: nat] :
% 0.31/0.46 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.31/0.46 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ab_semigroup_add_class.add_ac(1)
% 0.31/0.46 thf(fact_140_add_Ocomm__neutral,axiom,
% 0.31/0.46 ! [A: nat] :
% 0.31/0.46 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.31/0.46 = A ) ).
% 0.31/0.46
% 0.31/0.46 % add.comm_neutral
% 0.31/0.46 thf(fact_141_comm__monoid__add__class_Oadd__0,axiom,
% 0.31/0.46 ! [A: nat] :
% 0.31/0.46 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.31/0.46 = A ) ).
% 0.31/0.46
% 0.31/0.46 % comm_monoid_add_class.add_0
% 0.31/0.46 thf(fact_142_add__Suc,axiom,
% 0.31/0.46 ! [M2: nat,N: nat] :
% 0.31/0.46 ( ( plus_plus_nat @ ( suc @ M2 ) @ N )
% 0.31/0.46 = ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_Suc
% 0.31/0.46 thf(fact_143_nat__arith_Osuc1,axiom,
% 0.31/0.46 ! [A2: nat,K: nat,A: nat] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( plus_plus_nat @ K @ A ) )
% 0.31/0.46 => ( ( suc @ A2 )
% 0.31/0.46 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % nat_arith.suc1
% 0.31/0.46 thf(fact_144_add__Suc__shift,axiom,
% 0.31/0.46 ! [M2: nat,N: nat] :
% 0.31/0.46 ( ( plus_plus_nat @ ( suc @ M2 ) @ N )
% 0.31/0.46 = ( plus_plus_nat @ M2 @ ( suc @ N ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_Suc_shift
% 0.31/0.46 thf(fact_145_add__eq__self__zero,axiom,
% 0.31/0.46 ! [M2: nat,N: nat] :
% 0.31/0.46 ( ( ( plus_plus_nat @ M2 @ N )
% 0.31/0.46 = M2 )
% 0.31/0.46 => ( N = zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_eq_self_zero
% 0.31/0.46 thf(fact_146_plus__nat_Oadd__0,axiom,
% 0.31/0.46 ! [N: nat] :
% 0.31/0.46 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.31/0.46 = N ) ).
% 0.31/0.46
% 0.31/0.46 % plus_nat.add_0
% 0.31/0.46 thf(fact_147_one__is__add,axiom,
% 0.31/0.46 ! [M2: nat,N: nat] :
% 0.31/0.46 ( ( ( suc @ zero_zero_nat )
% 0.31/0.46 = ( plus_plus_nat @ M2 @ N ) )
% 0.31/0.46 = ( ( ( M2
% 0.31/0.46 = ( suc @ zero_zero_nat ) )
% 0.31/0.46 & ( N = zero_zero_nat ) )
% 0.31/0.46 | ( ( M2 = zero_zero_nat )
% 0.31/0.46 & ( N
% 0.31/0.46 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % one_is_add
% 0.31/0.46 thf(fact_148_add__is__1,axiom,
% 0.31/0.46 ! [M2: nat,N: nat] :
% 0.31/0.46 ( ( ( plus_plus_nat @ M2 @ N )
% 0.31/0.46 = ( suc @ zero_zero_nat ) )
% 0.31/0.46 = ( ( ( M2
% 0.31/0.46 = ( suc @ zero_zero_nat ) )
% 0.31/0.46 & ( N = zero_zero_nat ) )
% 0.31/0.46 | ( ( M2 = zero_zero_nat )
% 0.31/0.46 & ( N
% 0.31/0.46 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_is_1
% 0.31/0.46 thf(fact_149_gen__length__code_I1_J,axiom,
% 0.31/0.46 ! [N: nat] :
% 0.31/0.46 ( ( gen_le170886571tr_b_c @ N @ nil_li198338206tr_b_c )
% 0.31/0.46 = N ) ).
% 0.31/0.46
% 0.31/0.46 % gen_length_code(1)
% 0.31/0.46 thf(fact_150_gen__length__code_I1_J,axiom,
% 0.31/0.46 ! [N: nat] :
% 0.31/0.46 ( ( gen_length_list_char @ N @ nil_list_char )
% 0.31/0.46 = N ) ).
% 0.31/0.46
% 0.31/0.46 % gen_length_code(1)
% 0.31/0.46 thf(fact_151_gen__length__code_I1_J,axiom,
% 0.31/0.46 ! [N: nat] :
% 0.31/0.46 ( ( gen_length_char @ N @ nil_char )
% 0.31/0.46 = N ) ).
% 0.31/0.46
% 0.31/0.46 % gen_length_code(1)
% 0.31/0.46 thf(fact_152_gen__length__code_I1_J,axiom,
% 0.31/0.46 ! [N: nat] :
% 0.31/0.46 ( ( gen_le955068453tr_b_c @ N @ nil_no279930520tr_b_c )
% 0.31/0.46 = N ) ).
% 0.31/0.46
% 0.31/0.46 % gen_length_code(1)
% 0.31/0.46 thf(fact_153_Euclid__induct,axiom,
% 0.31/0.46 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.31/0.46 ( ! [A4: nat,B4: nat] :
% 0.31/0.46 ( ( P @ A4 @ B4 )
% 0.31/0.46 = ( P @ B4 @ A4 ) )
% 0.31/0.46 => ( ! [A4: nat] : ( P @ A4 @ zero_zero_nat )
% 0.31/0.46 => ( ! [A4: nat,B4: nat] :
% 0.31/0.46 ( ( P @ A4 @ B4 )
% 0.31/0.46 => ( P @ A4 @ ( plus_plus_nat @ A4 @ B4 ) ) )
% 0.31/0.46 => ( P @ A @ B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Euclid_induct
% 0.31/0.46 thf(fact_154_triangle__Suc,axiom,
% 0.31/0.46 ! [N: nat] :
% 0.31/0.46 ( ( nat_triangle @ ( suc @ N ) )
% 0.31/0.46 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % triangle_Suc
% 0.31/0.46 thf(fact_155_verit__sum__simplify,axiom,
% 0.31/0.46 ! [A: nat] :
% 0.31/0.46 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.31/0.46 = A ) ).
% 0.31/0.46
% 0.31/0.46 % verit_sum_simplify
% 0.31/0.46 thf(fact_156_add__0__iff,axiom,
% 0.31/0.46 ! [B: nat,A: nat] :
% 0.31/0.46 ( ( B
% 0.31/0.46 = ( plus_plus_nat @ B @ A ) )
% 0.31/0.46 = ( A = zero_zero_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % add_0_iff
% 0.31/0.46 thf(fact_157_option_Osize__gen_I2_J,axiom,
% 0.31/0.46 ! [X: rObjec1617416918on_j_k > nat,X2: rObjec1617416918on_j_k] :
% 0.31/0.46 ( ( size_o26122489on_j_k @ X @ ( some_R67702331on_j_k @ X2 ) )
% 0.31/0.46 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.size_gen(2)
% 0.31/0.46 thf(fact_158_option_Osize__gen_I2_J,axiom,
% 0.31/0.46 ! [X: docume1935157360tr_d_e > nat,X2: docume1935157360tr_d_e] :
% 0.31/0.46 ( ( size_o1635055885tr_d_e @ X @ ( some_d1631029323tr_d_e @ X2 ) )
% 0.31/0.46 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.size_gen(2)
% 0.31/0.46 thf(fact_159_option_Osize__gen_I2_J,axiom,
% 0.31/0.46 ! [X: rObjec1413572695_j_k_l > nat,X2: rObjec1413572695_j_k_l] :
% 0.31/0.46 ( ( size_o310046708_j_k_l @ X @ ( some_R1598191922_j_k_l @ X2 ) )
% 0.31/0.46 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.size_gen(2)
% 0.31/0.46 thf(fact_160_option_Osize__gen_I2_J,axiom,
% 0.31/0.46 ! [X: sum_su1221287958on_j_k > nat,X2: sum_su1221287958on_j_k] :
% 0.31/0.46 ( ( size_o1777465779on_j_k @ X @ ( some_S1960742641on_j_k @ X2 ) )
% 0.31/0.46 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.size_gen(2)
% 0.31/0.46 thf(fact_161_option_Osize__gen_I2_J,axiom,
% 0.31/0.46 ! [X: element_ptr_a > nat,X2: element_ptr_a] :
% 0.31/0.46 ( ( size_o1591053974_ptr_a @ X @ ( some_element_ptr_a @ X2 ) )
% 0.31/0.46 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.size_gen(2)
% 0.31/0.46 thf(fact_162_option_Oinject,axiom,
% 0.31/0.46 ! [X2: sum_su1221287958on_j_k,Y2: sum_su1221287958on_j_k] :
% 0.31/0.46 ( ( ( some_S1960742641on_j_k @ X2 )
% 0.31/0.46 = ( some_S1960742641on_j_k @ Y2 ) )
% 0.31/0.46 = ( X2 = Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.inject
% 0.31/0.46 thf(fact_163_option_Oinject,axiom,
% 0.31/0.46 ! [X2: element_ptr_a,Y2: element_ptr_a] :
% 0.31/0.46 ( ( ( some_element_ptr_a @ X2 )
% 0.31/0.46 = ( some_element_ptr_a @ Y2 ) )
% 0.31/0.46 = ( X2 = Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.inject
% 0.31/0.46 thf(fact_164_option_Oinject,axiom,
% 0.31/0.46 ! [X2: rObjec1617416918on_j_k,Y2: rObjec1617416918on_j_k] :
% 0.31/0.46 ( ( ( some_R67702331on_j_k @ X2 )
% 0.31/0.46 = ( some_R67702331on_j_k @ Y2 ) )
% 0.31/0.46 = ( X2 = Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.inject
% 0.31/0.46 thf(fact_165_option_Oinject,axiom,
% 0.31/0.46 ! [X2: docume1935157360tr_d_e,Y2: docume1935157360tr_d_e] :
% 0.31/0.46 ( ( ( some_d1631029323tr_d_e @ X2 )
% 0.31/0.46 = ( some_d1631029323tr_d_e @ Y2 ) )
% 0.31/0.46 = ( X2 = Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.inject
% 0.31/0.46 thf(fact_166_option_Oinject,axiom,
% 0.31/0.46 ! [X2: rObjec1413572695_j_k_l,Y2: rObjec1413572695_j_k_l] :
% 0.31/0.46 ( ( ( some_R1598191922_j_k_l @ X2 )
% 0.31/0.46 = ( some_R1598191922_j_k_l @ Y2 ) )
% 0.31/0.46 = ( X2 = Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.inject
% 0.31/0.46 thf(fact_167_not__Some__eq,axiom,
% 0.31/0.46 ! [X: option841825948on_j_k] :
% 0.31/0.46 ( ( ! [Y4: rObjec1617416918on_j_k] :
% 0.31/0.46 ( X
% 0.31/0.46 != ( some_R67702331on_j_k @ Y4 ) ) )
% 0.31/0.46 = ( X = none_R1587534007on_j_k ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_Some_eq
% 0.31/0.46 thf(fact_168_not__Some__eq,axiom,
% 0.31/0.46 ! [X: option1330818496tr_d_e] :
% 0.31/0.46 ( ( ! [Y4: docume1935157360tr_d_e] :
% 0.31/0.46 ( X
% 0.31/0.46 != ( some_d1631029323tr_d_e @ Y4 ) ) )
% 0.31/0.46 = ( X = none_d1458959567tr_d_e ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_Some_eq
% 0.31/0.46 thf(fact_169_not__Some__eq,axiom,
% 0.31/0.46 ! [X: option1749760295_j_k_l] :
% 0.31/0.46 ( ( ! [Y4: rObjec1413572695_j_k_l] :
% 0.31/0.46 ( X
% 0.31/0.46 != ( some_R1598191922_j_k_l @ Y4 ) ) )
% 0.31/0.46 = ( X = none_R1773662646_j_k_l ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_Some_eq
% 0.31/0.46 thf(fact_170_not__Some__eq,axiom,
% 0.31/0.46 ! [X: option_element_ptr_a] :
% 0.31/0.46 ( ( ! [Y4: element_ptr_a] :
% 0.31/0.46 ( X
% 0.31/0.46 != ( some_element_ptr_a @ Y4 ) ) )
% 0.31/0.46 = ( X = none_element_ptr_a ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_Some_eq
% 0.31/0.46 thf(fact_171_not__Some__eq,axiom,
% 0.31/0.46 ! [X: option2026120038on_j_k] :
% 0.31/0.46 ( ( ! [Y4: sum_su1221287958on_j_k] :
% 0.31/0.46 ( X
% 0.31/0.46 != ( some_S1960742641on_j_k @ Y4 ) ) )
% 0.31/0.46 = ( X = none_S1393028981on_j_k ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_Some_eq
% 0.31/0.46 thf(fact_172_not__None__eq,axiom,
% 0.31/0.46 ! [X: option841825948on_j_k] :
% 0.31/0.46 ( ( X != none_R1587534007on_j_k )
% 0.31/0.46 = ( ? [Y4: rObjec1617416918on_j_k] :
% 0.31/0.46 ( X
% 0.31/0.46 = ( some_R67702331on_j_k @ Y4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_None_eq
% 0.31/0.46 thf(fact_173_not__None__eq,axiom,
% 0.31/0.46 ! [X: option1330818496tr_d_e] :
% 0.31/0.46 ( ( X != none_d1458959567tr_d_e )
% 0.31/0.46 = ( ? [Y4: docume1935157360tr_d_e] :
% 0.31/0.46 ( X
% 0.31/0.46 = ( some_d1631029323tr_d_e @ Y4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_None_eq
% 0.31/0.46 thf(fact_174_not__None__eq,axiom,
% 0.31/0.46 ! [X: option1749760295_j_k_l] :
% 0.31/0.46 ( ( X != none_R1773662646_j_k_l )
% 0.31/0.46 = ( ? [Y4: rObjec1413572695_j_k_l] :
% 0.31/0.46 ( X
% 0.31/0.46 = ( some_R1598191922_j_k_l @ Y4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_None_eq
% 0.31/0.46 thf(fact_175_not__None__eq,axiom,
% 0.31/0.46 ! [X: option_element_ptr_a] :
% 0.31/0.46 ( ( X != none_element_ptr_a )
% 0.31/0.46 = ( ? [Y4: element_ptr_a] :
% 0.31/0.46 ( X
% 0.31/0.46 = ( some_element_ptr_a @ Y4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_None_eq
% 0.31/0.46 thf(fact_176_not__None__eq,axiom,
% 0.31/0.46 ! [X: option2026120038on_j_k] :
% 0.31/0.46 ( ( X != none_S1393028981on_j_k )
% 0.31/0.46 = ( ? [Y4: sum_su1221287958on_j_k] :
% 0.31/0.46 ( X
% 0.31/0.46 = ( some_S1960742641on_j_k @ Y4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_None_eq
% 0.31/0.46 thf(fact_177_triangle__0,axiom,
% 0.31/0.46 ( ( nat_triangle @ zero_zero_nat )
% 0.31/0.46 = zero_zero_nat ) ).
% 0.31/0.46
% 0.31/0.46 % triangle_0
% 0.31/0.46 thf(fact_178_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__inv,axiom,
% 0.31/0.46 ! [Document2: rObjec1617416918on_j_k] :
% 0.31/0.46 ( ( cast_O1034441233_j_k_l @ ( cast_D1252964113_h_i_l @ Document2 ) )
% 0.31/0.46 = ( some_R67702331on_j_k @ Document2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_inv
% 0.31/0.46 thf(fact_179_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__some,axiom,
% 0.31/0.46 ! [Obj: rObjec1413572695_j_k_l,Document2: rObjec1617416918on_j_k] :
% 0.31/0.46 ( ( ( cast_O1034441233_j_k_l @ Obj )
% 0.31/0.46 = ( some_R67702331on_j_k @ Document2 ) )
% 0.31/0.46 = ( ( cast_D1252964113_h_i_l @ Document2 )
% 0.31/0.46 = Obj ) ) ).
% 0.31/0.46
% 0.31/0.46 % cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_some
% 0.31/0.46 thf(fact_180_option_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [X2: rObjec1617416918on_j_k] :
% 0.31/0.46 ( none_R1587534007on_j_k
% 0.31/0.46 != ( some_R67702331on_j_k @ X2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.distinct(1)
% 0.31/0.46 thf(fact_181_option_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [X2: docume1935157360tr_d_e] :
% 0.31/0.46 ( none_d1458959567tr_d_e
% 0.31/0.46 != ( some_d1631029323tr_d_e @ X2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.distinct(1)
% 0.31/0.46 thf(fact_182_option_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [X2: rObjec1413572695_j_k_l] :
% 0.31/0.46 ( none_R1773662646_j_k_l
% 0.31/0.46 != ( some_R1598191922_j_k_l @ X2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.distinct(1)
% 0.31/0.46 thf(fact_183_option_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [X2: element_ptr_a] :
% 0.31/0.46 ( none_element_ptr_a
% 0.31/0.46 != ( some_element_ptr_a @ X2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.distinct(1)
% 0.31/0.46 thf(fact_184_option_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [X2: sum_su1221287958on_j_k] :
% 0.31/0.46 ( none_S1393028981on_j_k
% 0.31/0.46 != ( some_S1960742641on_j_k @ X2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.distinct(1)
% 0.31/0.46 thf(fact_185_option_OdiscI,axiom,
% 0.31/0.46 ! [Option: option841825948on_j_k,X2: rObjec1617416918on_j_k] :
% 0.31/0.46 ( ( Option
% 0.31/0.46 = ( some_R67702331on_j_k @ X2 ) )
% 0.31/0.46 => ( Option != none_R1587534007on_j_k ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.discI
% 0.31/0.46 thf(fact_186_option_OdiscI,axiom,
% 0.31/0.46 ! [Option: option1330818496tr_d_e,X2: docume1935157360tr_d_e] :
% 0.31/0.46 ( ( Option
% 0.31/0.46 = ( some_d1631029323tr_d_e @ X2 ) )
% 0.31/0.46 => ( Option != none_d1458959567tr_d_e ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.discI
% 0.31/0.46 thf(fact_187_option_OdiscI,axiom,
% 0.31/0.46 ! [Option: option1749760295_j_k_l,X2: rObjec1413572695_j_k_l] :
% 0.31/0.46 ( ( Option
% 0.31/0.46 = ( some_R1598191922_j_k_l @ X2 ) )
% 0.31/0.46 => ( Option != none_R1773662646_j_k_l ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.discI
% 0.31/0.46 thf(fact_188_option_OdiscI,axiom,
% 0.31/0.46 ! [Option: option_element_ptr_a,X2: element_ptr_a] :
% 0.31/0.46 ( ( Option
% 0.31/0.46 = ( some_element_ptr_a @ X2 ) )
% 0.31/0.46 => ( Option != none_element_ptr_a ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.discI
% 0.31/0.46 thf(fact_189_option_OdiscI,axiom,
% 0.31/0.46 ! [Option: option2026120038on_j_k,X2: sum_su1221287958on_j_k] :
% 0.31/0.46 ( ( Option
% 0.31/0.46 = ( some_S1960742641on_j_k @ X2 ) )
% 0.31/0.46 => ( Option != none_S1393028981on_j_k ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.discI
% 0.31/0.46 thf(fact_190_option_Oexhaust,axiom,
% 0.31/0.46 ! [Y: option_element_ptr_a] :
% 0.31/0.46 ( ( Y != none_element_ptr_a )
% 0.31/0.46 => ~ ! [X22: element_ptr_a] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( some_element_ptr_a @ X22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.exhaust
% 0.31/0.46 thf(fact_191_option_Oexhaust,axiom,
% 0.31/0.46 ! [Y: option2026120038on_j_k] :
% 0.31/0.46 ( ( Y != none_S1393028981on_j_k )
% 0.31/0.46 => ~ ! [X22: sum_su1221287958on_j_k] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( some_S1960742641on_j_k @ X22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.exhaust
% 0.31/0.46 thf(fact_192_option_Oinducts,axiom,
% 0.31/0.46 ! [P: option_element_ptr_a > $o,Option: option_element_ptr_a] :
% 0.31/0.46 ( ( P @ none_element_ptr_a )
% 0.31/0.46 => ( ! [X3: element_ptr_a] : ( P @ ( some_element_ptr_a @ X3 ) )
% 0.31/0.46 => ( P @ Option ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.inducts
% 0.31/0.46 thf(fact_193_option_Oinducts,axiom,
% 0.31/0.46 ! [P: option2026120038on_j_k > $o,Option: option2026120038on_j_k] :
% 0.31/0.46 ( ( P @ none_S1393028981on_j_k )
% 0.31/0.46 => ( ! [X3: sum_su1221287958on_j_k] : ( P @ ( some_S1960742641on_j_k @ X3 ) )
% 0.31/0.46 => ( P @ Option ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % option.inducts
% 0.31/0.46 thf(fact_194_split__option__ex,axiom,
% 0.31/0.46 ( ( ^ [P2: option_element_ptr_a > $o] :
% 0.31/0.46 ? [X5: option_element_ptr_a] : ( P2 @ X5 ) )
% 0.31/0.46 = ( ^ [P3: option_element_ptr_a > $o] :
% 0.31/0.46 ( ( P3 @ none_element_ptr_a )
% 0.31/0.46 | ? [X4: element_ptr_a] : ( P3 @ ( some_element_ptr_a @ X4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_option_ex
% 0.31/0.46 thf(fact_195_split__option__ex,axiom,
% 0.31/0.46 ( ( ^ [P2: option2026120038on_j_k > $o] :
% 0.31/0.46 ? [X5: option2026120038on_j_k] : ( P2 @ X5 ) )
% 0.31/0.46 = ( ^ [P3: option2026120038on_j_k > $o] :
% 0.31/0.46 ( ( P3 @ none_S1393028981on_j_k )
% 0.31/0.46 | ? [X4: sum_su1221287958on_j_k] : ( P3 @ ( some_S1960742641on_j_k @ X4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_option_ex
% 0.31/0.46 thf(fact_196_split__option__all,axiom,
% 0.31/0.46 ( ( ^ [P2: option_element_ptr_a > $o] :
% 0.31/0.46 ! [X5: option_element_ptr_a] : ( P2 @ X5 ) )
% 0.31/0.46 = ( ^ [P3: option_element_ptr_a > $o] :
% 0.31/0.46 ( ( P3 @ none_element_ptr_a )
% 0.31/0.46 & ! [X4: element_ptr_a] : ( P3 @ ( some_element_ptr_a @ X4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_option_all
% 0.31/0.46 thf(fact_197_split__option__all,axiom,
% 0.31/0.46 ( ( ^ [P2: option2026120038on_j_k > $o] :
% 0.31/0.46 ! [X5: option2026120038on_j_k] : ( P2 @ X5 ) )
% 0.31/0.46 = ( ^ [P3: option2026120038on_j_k > $o] :
% 0.31/0.46 ( ( P3 @ none_S1393028981on_j_k )
% 0.31/0.46 & ! [X4: sum_su1221287958on_j_k] : ( P3 @ ( some_S1960742641on_j_k @ X4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_option_all
% 0.31/0.46 thf(fact_198_combine__options__cases,axiom,
% 0.31/0.46 ! [X: option_element_ptr_a,P: option_element_ptr_a > option_element_ptr_a > $o,Y: option_element_ptr_a] :
% 0.31/0.46 ( ( ( X = none_element_ptr_a )
% 0.31/0.46 => ( P @ X @ Y ) )
% 0.31/0.46 => ( ( ( Y = none_element_ptr_a )
% 0.31/0.46 => ( P @ X @ Y ) )
% 0.31/0.46 => ( ! [A4: element_ptr_a,B4: element_ptr_a] :
% 0.31/0.46 ( ( X
% 0.31/0.46 = ( some_element_ptr_a @ A4 ) )
% 0.31/0.46 => ( ( Y
% 0.31/0.46 = ( some_element_ptr_a @ B4 ) )
% 0.31/0.46 => ( P @ X @ Y ) ) )
% 0.31/0.46 => ( P @ X @ Y ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % combine_options_cases
% 0.31/0.46 thf(fact_199_combine__options__cases,axiom,
% 0.31/0.46 ! [X: option_element_ptr_a,P: option_element_ptr_a > option2026120038on_j_k > $o,Y: option2026120038on_j_k] :
% 0.31/0.46 ( ( ( X = none_element_ptr_a )
% 0.31/0.46 => ( P @ X @ Y ) )
% 0.31/0.46 => ( ( ( Y = none_S1393028981on_j_k )
% 0.31/0.46 => ( P @ X @ Y ) )
% 0.31/0.46 => ( ! [A4: element_ptr_a,B4: sum_su1221287958on_j_k] :
% 0.31/0.46 ( ( X
% 0.31/0.46 = ( some_element_ptr_a @ A4 ) )
% 0.31/0.46 => ( ( Y
% 0.31/0.46 = ( some_S1960742641on_j_k @ B4 ) )
% 0.31/0.46 => ( P @ X @ Y ) ) )
% 0.31/0.46 => ( P @ X @ Y ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % combine_options_cases
% 0.31/0.46 thf(fact_200_combine__options__cases,axiom,
% 0.31/0.46 ! [X: option2026120038on_j_k,P: option2026120038on_j_k > option_element_ptr_a > $o,Y: option_element_ptr_a] :
% 0.31/0.46 ( ( ( X = none_S1393028981on_j_k )
% 0.31/0.46 => ( P @ X @ Y ) )
% 0.31/0.46 => ( ( ( Y = none_element_ptr_a )
% 0.31/0.46 => ( P @ X @ Y ) )
% 0.31/0.46 => ( ! [A4: sum_su1221287958on_j_k,B4: element_ptr_a] :
% 0.31/0.46 ( ( X
% 0.31/0.46 = ( some_S1960742641on_j_k @ A4 ) )
% 0.31/0.46 => ( ( Y
% 0.31/0.46 = ( some_element_ptr_a @ B4 ) )
% 0.31/0.46 => ( P @ X @ Y ) ) )
% 0.31/0.46 => ( P @ X @ Y ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % combine_options_cases
% 0.31/0.46 thf(fact_201_combine__options__cases,axiom,
% 0.31/0.46 ! [X: option2026120038on_j_k,P: option2026120038on_j_k > option2026120038on_j_k > $o,Y: option2026120038on_j_k] :
% 0.31/0.46 ( ( ( X = none_S1393028981on_j_k )
% 0.31/0.46 => ( P @ X @ Y ) )
% 0.31/0.46 => ( ( ( Y = none_S1393028981on_j_k )
% 0.31/0.46 => ( P @ X @ Y ) )
% 0.31/0.46 => ( ! [A4: sum_su1221287958on_j_k,B4: sum_su1221287958on_j_k] :
% 0.31/0.46 ( ( X
% 0.31/0.46 = ( some_S1960742641on_j_k @ A4 ) )
% 0.31/0.46 => ( ( Y
% 0.31/0.46 = ( some_S1960742641on_j_k @ B4 ) )
% 0.31/0.46 => ( P @ X @ Y ) ) )
% 0.31/0.46 => ( P @ X @ Y ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % combine_options_cases
% 0.31/0.46 thf(fact_202_document__ptr__casts__commute2,axiom,
% 0.31/0.46 ! [Document_ptr2: docume1935157360tr_d_e] :
% 0.31/0.46 ( ( cast_o761049241_d_e_f @ ( cast_d1608273229_b_c_f @ Document_ptr2 ) )
% 0.31/0.46 = ( some_d1631029323tr_d_e @ Document_ptr2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % document_ptr_casts_commute2
% 0.31/0.46 thf(fact_203_document__ptr__casts__commute,axiom,
% 0.31/0.46 ! [Ptr2: object945351580_d_e_f,Document_ptr2: docume1935157360tr_d_e] :
% 0.31/0.46 ( ( ( cast_o761049241_d_e_f @ Ptr2 )
% 0.31/0.46 = ( some_d1631029323tr_d_e @ Document_ptr2 ) )
% 0.31/0.46 = ( ( cast_d1608273229_b_c_f @ Document_ptr2 )
% 0.31/0.46 = Ptr2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % document_ptr_casts_commute
% 0.31/0.46 thf(fact_204_get__document__ptr__simp,axiom,
% 0.31/0.46 ! [Ptr2: object945351580_d_e_f,Document_ptr2: docume1935157360tr_d_e,Obj: rObjec1413572695_j_k_l,H: heap_S1465075775_j_k_l] :
% 0.31/0.46 ( ( ( Ptr2
% 0.31/0.46 = ( cast_d1608273229_b_c_f @ Document_ptr2 ) )
% 0.31/0.46 => ( ( get_D_1192261494_j_k_l @ Document_ptr2 @ ( put_O_834343516_j_k_l @ Ptr2 @ Obj @ H ) )
% 0.31/0.46 = ( cast_O1034441233_j_k_l @ Obj ) ) )
% 0.31/0.46 & ( ( Ptr2
% 0.31/0.46 != ( cast_d1608273229_b_c_f @ Document_ptr2 ) )
% 0.31/0.46 => ( ( get_D_1192261494_j_k_l @ Document_ptr2 @ ( put_O_834343516_j_k_l @ Ptr2 @ Obj @ H ) )
% 0.31/0.46 = ( get_D_1192261494_j_k_l @ Document_ptr2 @ H ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % get_document_ptr_simp
% 0.31/0.46 thf(fact_205_split__Nil__iff,axiom,
% 0.31/0.46 ! [Xs: list_char,Ys: list_char] :
% 0.31/0.46 ( ( ( splice_char @ Xs @ Ys )
% 0.31/0.46 = nil_char )
% 0.31/0.46 = ( ( Xs = nil_char )
% 0.31/0.46 & ( Ys = nil_char ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_Nil_iff
% 0.31/0.46 thf(fact_206_split__Nil__iff,axiom,
% 0.31/0.46 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 0.31/0.46 ( ( ( splice1294941035tr_b_c @ Xs @ Ys )
% 0.31/0.46 = nil_no279930520tr_b_c )
% 0.31/0.46 = ( ( Xs = nil_no279930520tr_b_c )
% 0.31/0.46 & ( Ys = nil_no279930520tr_b_c ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_Nil_iff
% 0.31/0.46 thf(fact_207_splice__Nil2,axiom,
% 0.31/0.46 ! [Xs: list_char] :
% 0.31/0.46 ( ( splice_char @ Xs @ nil_char )
% 0.31/0.46 = Xs ) ).
% 0.31/0.46
% 0.31/0.46 % splice_Nil2
% 0.31/0.46 thf(fact_208_splice__Nil2,axiom,
% 0.31/0.46 ! [Xs: list_n282880152tr_b_c] :
% 0.31/0.46 ( ( splice1294941035tr_b_c @ Xs @ nil_no279930520tr_b_c )
% 0.31/0.46 = Xs ) ).
% 0.31/0.46
% 0.31/0.46 % splice_Nil2
% 0.31/0.46 thf(fact_209_splice_Osimps_I1_J,axiom,
% 0.31/0.46 ! [Ys: list_char] :
% 0.31/0.46 ( ( splice_char @ nil_char @ Ys )
% 0.31/0.46 = Ys ) ).
% 0.31/0.46
% 0.31/0.46 % splice.simps(1)
% 0.31/0.46 thf(fact_210_splice_Osimps_I1_J,axiom,
% 0.31/0.46 ! [Ys: list_n282880152tr_b_c] :
% 0.31/0.46 ( ( splice1294941035tr_b_c @ nil_no279930520tr_b_c @ Ys )
% 0.31/0.46 = Ys ) ).
% 0.31/0.46
% 0.31/0.46 % splice.simps(1)
% 0.31/0.46 thf(fact_211_get__object__ptr__simp1,axiom,
% 0.31/0.46 ! [Object_ptr: object945351580_d_e_f,Object: rObjec1413572695_j_k_l,H: heap_S1465075775_j_k_l] :
% 0.31/0.47 ( ( get_O_623850005_j_k_l @ Object_ptr @ ( put_O_834343516_j_k_l @ Object_ptr @ Object @ H ) )
% 0.31/0.47 = ( some_R1598191922_j_k_l @ Object ) ) ).
% 0.31/0.47
% 0.31/0.47 % get_object_ptr_simp1
% 0.31/0.47 thf(fact_212_count__list_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Y: char] :
% 0.31/0.47 ( ( count_list_char @ nil_char @ Y )
% 0.31/0.47 = zero_zero_nat ) ).
% 0.31/0.47
% 0.31/0.47 % count_list.simps(1)
% 0.31/0.47 thf(fact_213_count__list_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Y: node_p1234578834tr_b_c] :
% 0.31/0.47 ( ( count_2128515342tr_b_c @ nil_no279930520tr_b_c @ Y )
% 0.31/0.47 = zero_zero_nat ) ).
% 0.31/0.47
% 0.31/0.47 % count_list.simps(1)
% 0.31/0.47 thf(fact_214_get__object__ptr__simp2,axiom,
% 0.31/0.47 ! [Object_ptr: object945351580_d_e_f,Object_ptr2: object945351580_d_e_f,Object: rObjec1413572695_j_k_l,H: heap_S1465075775_j_k_l] :
% 0.31/0.47 ( ( Object_ptr != Object_ptr2 )
% 0.31/0.47 => ( ( get_O_623850005_j_k_l @ Object_ptr @ ( put_O_834343516_j_k_l @ Object_ptr2 @ Object @ H ) )
% 0.31/0.47 = ( get_O_623850005_j_k_l @ Object_ptr @ H ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % get_object_ptr_simp2
% 0.31/0.47 thf(fact_215_transpose_Ocases,axiom,
% 0.31/0.47 ! [X: list_list_char] :
% 0.31/0.47 ( ( X != nil_list_char )
% 0.31/0.47 => ( ! [Xss: list_list_char] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_list_char @ nil_char @ Xss ) )
% 0.31/0.47 => ~ ! [X3: char,Xs2: list_char,Xss: list_list_char] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_list_char @ ( cons_char @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % transpose.cases
% 0.31/0.47 thf(fact_216_transpose_Ocases,axiom,
% 0.31/0.47 ! [X: list_l118626078tr_b_c] :
% 0.31/0.47 ( ( X != nil_li198338206tr_b_c )
% 0.31/0.47 => ( ! [Xss: list_l118626078tr_b_c] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ Xss ) )
% 0.31/0.47 => ~ ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Xss: list_l118626078tr_b_c] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_l1809994318tr_b_c @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % transpose.cases
% 0.31/0.47 thf(fact_217_list_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X21: char,X222: list_char] :
% 0.31/0.47 ( nil_char
% 0.31/0.47 != ( cons_char @ X21 @ X222 ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.distinct(1)
% 0.31/0.47 thf(fact_218_list_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X21: node_p1234578834tr_b_c,X222: list_n282880152tr_b_c] :
% 0.31/0.47 ( nil_no279930520tr_b_c
% 0.31/0.47 != ( cons_n413985352tr_b_c @ X21 @ X222 ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.distinct(1)
% 0.31/0.47 thf(fact_219_list_OdiscI,axiom,
% 0.31/0.47 ! [List: list_char,X21: char,X222: list_char] :
% 0.31/0.47 ( ( List
% 0.31/0.47 = ( cons_char @ X21 @ X222 ) )
% 0.31/0.47 => ( List != nil_char ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.discI
% 0.31/0.47 thf(fact_220_list_OdiscI,axiom,
% 0.31/0.47 ! [List: list_n282880152tr_b_c,X21: node_p1234578834tr_b_c,X222: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( List
% 0.31/0.47 = ( cons_n413985352tr_b_c @ X21 @ X222 ) )
% 0.31/0.47 => ( List != nil_no279930520tr_b_c ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.discI
% 0.31/0.47 thf(fact_221_list_Oexhaust,axiom,
% 0.31/0.47 ! [Y: list_char] :
% 0.31/0.47 ( ( Y != nil_char )
% 0.31/0.47 => ~ ! [X212: char,X223: list_char] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( cons_char @ X212 @ X223 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.exhaust
% 0.31/0.47 thf(fact_222_list_Oexhaust,axiom,
% 0.31/0.47 ! [Y: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( Y != nil_no279930520tr_b_c )
% 0.31/0.47 => ~ ! [X212: node_p1234578834tr_b_c,X223: list_n282880152tr_b_c] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( cons_n413985352tr_b_c @ X212 @ X223 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.exhaust
% 0.31/0.47 thf(fact_223_list_Oinducts,axiom,
% 0.31/0.47 ! [P: list_char > $o,List: list_char] :
% 0.31/0.47 ( ( P @ nil_char )
% 0.31/0.47 => ( ! [X12: char,X22: list_char] :
% 0.31/0.47 ( ( P @ X22 )
% 0.31/0.47 => ( P @ ( cons_char @ X12 @ X22 ) ) )
% 0.31/0.47 => ( P @ List ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.inducts
% 0.31/0.47 thf(fact_224_list_Oinducts,axiom,
% 0.31/0.47 ! [P: list_n282880152tr_b_c > $o,List: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( P @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X12: node_p1234578834tr_b_c,X22: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( P @ X22 )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X12 @ X22 ) ) )
% 0.31/0.47 => ( P @ List ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.inducts
% 0.31/0.47 thf(fact_225_neq__Nil__conv,axiom,
% 0.31/0.47 ! [Xs: list_char] :
% 0.31/0.47 ( ( Xs != nil_char )
% 0.31/0.47 = ( ? [Y4: char,Ys2: list_char] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( cons_char @ Y4 @ Ys2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_Nil_conv
% 0.31/0.47 thf(fact_226_neq__Nil__conv,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( Xs != nil_no279930520tr_b_c )
% 0.31/0.47 = ( ? [Y4: node_p1234578834tr_b_c,Ys2: list_n282880152tr_b_c] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( cons_n413985352tr_b_c @ Y4 @ Ys2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_Nil_conv
% 0.31/0.47 thf(fact_227_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_char > list_char > $o,Xs: list_char,Ys: list_char] :
% 0.31/0.47 ( ( P @ nil_char @ nil_char )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char] : ( P @ ( cons_char @ X3 @ Xs2 ) @ nil_char )
% 0.31/0.47 => ( ! [Y3: char,Ys3: list_char] : ( P @ nil_char @ ( cons_char @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_228_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_char > list_n282880152tr_b_c > $o,Xs: list_char,Ys: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( P @ nil_char @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char] : ( P @ ( cons_char @ X3 @ Xs2 ) @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] : ( P @ nil_char @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_229_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_n282880152tr_b_c > list_char > $o,Xs: list_n282880152tr_b_c,Ys: list_char] :
% 0.31/0.47 ( ( P @ nil_no279930520tr_b_c @ nil_char )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ nil_char )
% 0.31/0.47 => ( ! [Y3: char,Ys3: list_char] : ( P @ nil_no279930520tr_b_c @ ( cons_char @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_230_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_n282880152tr_b_c > list_n282880152tr_b_c > $o,Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( P @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] : ( P @ nil_no279930520tr_b_c @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_231_splice_Oinduct,axiom,
% 0.31/0.47 ! [P: list_char > list_char > $o,A0: list_char,A1: list_char] :
% 0.31/0.47 ( ! [X_12: list_char] : ( P @ nil_char @ X_12 )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Ys3: list_char] :
% 0.31/0.47 ( ( P @ Ys3 @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ Ys3 ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % splice.induct
% 0.31/0.47 thf(fact_232_splice_Oinduct,axiom,
% 0.31/0.47 ! [P: list_n282880152tr_b_c > list_n282880152tr_b_c > $o,A0: list_n282880152tr_b_c,A1: list_n282880152tr_b_c] :
% 0.31/0.47 ( ! [X_12: list_n282880152tr_b_c] : ( P @ nil_no279930520tr_b_c @ X_12 )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Ys3: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( P @ Ys3 @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ Ys3 ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % splice.induct
% 0.31/0.47 thf(fact_233_induct__list012,axiom,
% 0.31/0.47 ! [P: list_char > $o,Xs: list_char] :
% 0.31/0.47 ( ( P @ nil_char )
% 0.31/0.47 => ( ! [X3: char] : ( P @ ( cons_char @ X3 @ nil_char ) )
% 0.31/0.47 => ( ! [X3: char,Y3: char,Zs: list_char] :
% 0.31/0.47 ( ( P @ Zs )
% 0.31/0.47 => ( ( P @ ( cons_char @ Y3 @ Zs ) )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ ( cons_char @ Y3 @ Zs ) ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % induct_list012
% 0.31/0.47 thf(fact_234_induct__list012,axiom,
% 0.31/0.47 ! [P: list_n282880152tr_b_c > $o,Xs: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( P @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Y3: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( P @ Zs )
% 0.31/0.47 => ( ( P @ ( cons_n413985352tr_b_c @ Y3 @ Zs ) )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ ( cons_n413985352tr_b_c @ Y3 @ Zs ) ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % induct_list012
% 0.31/0.47 thf(fact_235_shuffles_Oinduct,axiom,
% 0.31/0.47 ! [P: list_char > list_char > $o,A0: list_char,A1: list_char] :
% 0.31/0.47 ( ! [X_12: list_char] : ( P @ nil_char @ X_12 )
% 0.31/0.47 => ( ! [Xs2: list_char] : ( P @ Xs2 @ nil_char )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char] :
% 0.31/0.47 ( ( P @ Xs2 @ ( cons_char @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ( P @ ( cons_char @ X3 @ Xs2 ) @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % shuffles.induct
% 0.31/0.47 thf(fact_236_shuffles_Oinduct,axiom,
% 0.31/0.47 ! [P: list_n282880152tr_b_c > list_n282880152tr_b_c > $o,A0: list_n282880152tr_b_c,A1: list_n282880152tr_b_c] :
% 0.31/0.47 ( ! [X_12: list_n282880152tr_b_c] : ( P @ nil_no279930520tr_b_c @ X_12 )
% 0.31/0.47 => ( ! [Xs2: list_n282880152tr_b_c] : ( P @ Xs2 @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( P @ Xs2 @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % shuffles.induct
% 0.31/0.47 thf(fact_237_remdups__adj_Ocases,axiom,
% 0.31/0.47 ! [X: list_char] :
% 0.31/0.47 ( ( X != nil_char )
% 0.31/0.47 => ( ! [X3: char] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_char @ X3 @ nil_char ) )
% 0.31/0.47 => ~ ! [X3: char,Y3: char,Xs2: list_char] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_char @ X3 @ ( cons_char @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.cases
% 0.31/0.47 thf(fact_238_remdups__adj_Ocases,axiom,
% 0.31/0.47 ! [X: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( X != nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
% 0.31/0.47 => ~ ! [X3: node_p1234578834tr_b_c,Y3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_n413985352tr_b_c @ X3 @ ( cons_n413985352tr_b_c @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.cases
% 0.31/0.47 thf(fact_239_sorted__wrt_Oinduct,axiom,
% 0.31/0.47 ! [P: ( char > char > $o ) > list_char > $o,A0: char > char > $o,A1: list_char] :
% 0.31/0.47 ( ! [P4: char > char > $o] : ( P @ P4 @ nil_char )
% 0.31/0.47 => ( ! [P4: char > char > $o,X3: char,Ys3: list_char] :
% 0.31/0.47 ( ( P @ P4 @ Ys3 )
% 0.31/0.47 => ( P @ P4 @ ( cons_char @ X3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sorted_wrt.induct
% 0.31/0.47 thf(fact_240_sorted__wrt_Oinduct,axiom,
% 0.31/0.47 ! [P: ( node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o ) > list_n282880152tr_b_c > $o,A0: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o,A1: list_n282880152tr_b_c] :
% 0.31/0.47 ( ! [P4: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o] : ( P @ P4 @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [P4: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o,X3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( P @ P4 @ Ys3 )
% 0.31/0.47 => ( P @ P4 @ ( cons_n413985352tr_b_c @ X3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sorted_wrt.induct
% 0.31/0.47 thf(fact_241_remdups__adj_Oinduct,axiom,
% 0.31/0.47 ! [P: list_char > $o,A0: list_char] :
% 0.31/0.47 ( ( P @ nil_char )
% 0.31/0.47 => ( ! [X3: char] : ( P @ ( cons_char @ X3 @ nil_char ) )
% 0.31/0.47 => ( ! [X3: char,Y3: char,Xs2: list_char] :
% 0.31/0.47 ( ( ( X3 = Y3 )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) ) )
% 0.31/0.47 => ( ( ( X3 != Y3 )
% 0.31/0.47 => ( P @ ( cons_char @ Y3 @ Xs2 ) ) )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ ( cons_char @ Y3 @ Xs2 ) ) ) ) )
% 0.31/0.47 => ( P @ A0 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.induct
% 0.31/0.47 thf(fact_242_remdups__adj_Oinduct,axiom,
% 0.31/0.47 ! [P: list_n282880152tr_b_c > $o,A0: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( P @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Y3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( X3 = Y3 )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) ) )
% 0.31/0.47 => ( ( ( X3 != Y3 )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ Y3 @ Xs2 ) ) )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ ( cons_n413985352tr_b_c @ Y3 @ Xs2 ) ) ) ) )
% 0.31/0.47 => ( P @ A0 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.induct
% 0.31/0.47 thf(fact_243_successively_Oinduct,axiom,
% 0.31/0.47 ! [P: ( char > char > $o ) > list_char > $o,A0: char > char > $o,A1: list_char] :
% 0.31/0.47 ( ! [P4: char > char > $o] : ( P @ P4 @ nil_char )
% 0.31/0.47 => ( ! [P4: char > char > $o,X3: char] : ( P @ P4 @ ( cons_char @ X3 @ nil_char ) )
% 0.31/0.47 => ( ! [P4: char > char > $o,X3: char,Y3: char,Xs2: list_char] :
% 0.31/0.47 ( ( P @ P4 @ ( cons_char @ Y3 @ Xs2 ) )
% 0.31/0.47 => ( P @ P4 @ ( cons_char @ X3 @ ( cons_char @ Y3 @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % successively.induct
% 0.31/0.47 thf(fact_244_successively_Oinduct,axiom,
% 0.31/0.47 ! [P: ( node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o ) > list_n282880152tr_b_c > $o,A0: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o,A1: list_n282880152tr_b_c] :
% 0.31/0.47 ( ! [P4: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o] : ( P @ P4 @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [P4: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o,X3: node_p1234578834tr_b_c] : ( P @ P4 @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
% 0.31/0.47 => ( ! [P4: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o,X3: node_p1234578834tr_b_c,Y3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( P @ P4 @ ( cons_n413985352tr_b_c @ Y3 @ Xs2 ) )
% 0.31/0.47 => ( P @ P4 @ ( cons_n413985352tr_b_c @ X3 @ ( cons_n413985352tr_b_c @ Y3 @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % successively.induct
% 0.31/0.47 thf(fact_245_list__nonempty__induct,axiom,
% 0.31/0.47 ! [Xs: list_char,P: list_char > $o] :
% 0.31/0.47 ( ( Xs != nil_char )
% 0.31/0.47 => ( ! [X3: char] : ( P @ ( cons_char @ X3 @ nil_char ) )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char] :
% 0.31/0.47 ( ( Xs2 != nil_char )
% 0.31/0.47 => ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_nonempty_induct
% 0.31/0.47 thf(fact_246_list__nonempty__induct,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,P: list_n282880152tr_b_c > $o] :
% 0.31/0.47 ( ( Xs != nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( Xs2 != nil_no279930520tr_b_c )
% 0.31/0.47 => ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_nonempty_induct
% 0.31/0.47 thf(fact_247_list__induct4,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_char,Zs2: list_char,Ws: list_char,P: list_char > list_char > list_char > list_char > $o] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs )
% 0.31/0.47 = ( size_size_list_char @ Ys ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys )
% 0.31/0.47 = ( size_size_list_char @ Zs2 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Zs2 )
% 0.31/0.47 = ( size_size_list_char @ Ws ) )
% 0.31/0.47 => ( ( P @ nil_char @ nil_char @ nil_char @ nil_char )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: char,Zs: list_char,W: char,Ws2: list_char] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs2 )
% 0.31/0.47 = ( size_size_list_char @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys3 )
% 0.31/0.47 = ( size_size_list_char @ Zs ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Zs )
% 0.31/0.47 = ( size_size_list_char @ Ws2 ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct4
% 0.31/0.47 thf(fact_248_list__induct4,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_char,Zs2: list_char,Ws: list_n282880152tr_b_c,P: list_char > list_char > list_char > list_n282880152tr_b_c > $o] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs )
% 0.31/0.47 = ( size_size_list_char @ Ys ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys )
% 0.31/0.47 = ( size_size_list_char @ Zs2 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Zs2 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ws ) )
% 0.31/0.47 => ( ( P @ nil_char @ nil_char @ nil_char @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: char,Zs: list_char,W: node_p1234578834tr_b_c,Ws2: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs2 )
% 0.31/0.47 = ( size_size_list_char @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys3 )
% 0.31/0.47 = ( size_size_list_char @ Zs ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Zs )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ws2 ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_n413985352tr_b_c @ W @ Ws2 ) ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct4
% 0.31/0.47 thf(fact_249_list__induct4,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_char,Zs2: list_n282880152tr_b_c,Ws: list_char,P: list_char > list_char > list_n282880152tr_b_c > list_char > $o] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs )
% 0.31/0.47 = ( size_size_list_char @ Ys ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Zs2 )
% 0.31/0.47 = ( size_size_list_char @ Ws ) )
% 0.31/0.47 => ( ( P @ nil_char @ nil_char @ nil_no279930520tr_b_c @ nil_char )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c,W: char,Ws2: list_char] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs2 )
% 0.31/0.47 = ( size_size_list_char @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys3 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Zs )
% 0.31/0.47 = ( size_size_list_char @ Ws2 ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct4
% 0.31/0.47 thf(fact_250_list__induct4,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_n282880152tr_b_c,Zs2: list_char,Ws: list_char,P: list_char > list_n282880152tr_b_c > list_char > list_char > $o] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Ys )
% 0.31/0.47 = ( size_size_list_char @ Zs2 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Zs2 )
% 0.31/0.47 = ( size_size_list_char @ Ws ) )
% 0.31/0.47 => ( ( P @ nil_char @ nil_no279930520tr_b_c @ nil_char @ nil_char )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: char,Zs: list_char,W: char,Ws2: list_char] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs2 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Ys3 )
% 0.31/0.47 = ( size_size_list_char @ Zs ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Zs )
% 0.31/0.47 = ( size_size_list_char @ Ws2 ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct4
% 0.31/0.47 thf(fact_251_list__induct4,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,Ys: list_char,Zs2: list_char,Ws: list_char,P: list_n282880152tr_b_c > list_char > list_char > list_char > $o] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs )
% 0.31/0.47 = ( size_size_list_char @ Ys ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys )
% 0.31/0.47 = ( size_size_list_char @ Zs2 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Zs2 )
% 0.31/0.47 = ( size_size_list_char @ Ws ) )
% 0.31/0.47 => ( ( P @ nil_no279930520tr_b_c @ nil_char @ nil_char @ nil_char )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char,Z: char,Zs: list_char,W: char,Ws2: list_char] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 0.31/0.47 = ( size_size_list_char @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys3 )
% 0.31/0.47 = ( size_size_list_char @ Zs ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Zs )
% 0.31/0.47 = ( size_size_list_char @ Ws2 ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct4
% 0.31/0.47 thf(fact_252_list__induct4,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_char,Zs2: list_n282880152tr_b_c,Ws: list_n282880152tr_b_c,P: list_char > list_char > list_n282880152tr_b_c > list_n282880152tr_b_c > $o] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs )
% 0.31/0.47 = ( size_size_list_char @ Ys ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Zs2 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ws ) )
% 0.31/0.47 => ( ( P @ nil_char @ nil_char @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c,W: node_p1234578834tr_b_c,Ws2: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs2 )
% 0.31/0.47 = ( size_size_list_char @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys3 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Zs )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ws2 ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) @ ( cons_n413985352tr_b_c @ W @ Ws2 ) ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct4
% 0.31/0.47 thf(fact_253_list__induct4,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_n282880152tr_b_c,Zs2: list_char,Ws: list_n282880152tr_b_c,P: list_char > list_n282880152tr_b_c > list_char > list_n282880152tr_b_c > $o] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Ys )
% 0.31/0.47 = ( size_size_list_char @ Zs2 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Zs2 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ws ) )
% 0.31/0.47 => ( ( P @ nil_char @ nil_no279930520tr_b_c @ nil_char @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: char,Zs: list_char,W: node_p1234578834tr_b_c,Ws2: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs2 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Ys3 )
% 0.31/0.47 = ( size_size_list_char @ Zs ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Zs )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ws2 ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_n413985352tr_b_c @ W @ Ws2 ) ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct4
% 0.31/0.47 thf(fact_254_list__induct4,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_n282880152tr_b_c,Zs2: list_n282880152tr_b_c,Ws: list_char,P: list_char > list_n282880152tr_b_c > list_n282880152tr_b_c > list_char > $o] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Ys )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Zs2 )
% 0.31/0.47 = ( size_size_list_char @ Ws ) )
% 0.31/0.47 => ( ( P @ nil_char @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c @ nil_char )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c,W: char,Ws2: list_char] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs2 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Ys3 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Zs )
% 0.31/0.47 = ( size_size_list_char @ Ws2 ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct4
% 0.31/0.47 thf(fact_255_list__induct4,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,Ys: list_char,Zs2: list_char,Ws: list_n282880152tr_b_c,P: list_n282880152tr_b_c > list_char > list_char > list_n282880152tr_b_c > $o] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs )
% 0.31/0.47 = ( size_size_list_char @ Ys ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys )
% 0.31/0.47 = ( size_size_list_char @ Zs2 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Zs2 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ws ) )
% 0.31/0.47 => ( ( P @ nil_no279930520tr_b_c @ nil_char @ nil_char @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char,Z: char,Zs: list_char,W: node_p1234578834tr_b_c,Ws2: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 0.31/0.47 = ( size_size_list_char @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys3 )
% 0.31/0.47 = ( size_size_list_char @ Zs ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Zs )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ws2 ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_n413985352tr_b_c @ W @ Ws2 ) ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct4
% 0.31/0.47 thf(fact_256_list__induct4,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,Ys: list_char,Zs2: list_n282880152tr_b_c,Ws: list_char,P: list_n282880152tr_b_c > list_char > list_n282880152tr_b_c > list_char > $o] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs )
% 0.31/0.47 = ( size_size_list_char @ Ys ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Zs2 )
% 0.31/0.47 = ( size_size_list_char @ Ws ) )
% 0.31/0.47 => ( ( P @ nil_no279930520tr_b_c @ nil_char @ nil_no279930520tr_b_c @ nil_char )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c,W: char,Ws2: list_char] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 0.31/0.47 = ( size_size_list_char @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys3 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Zs )
% 0.31/0.47 = ( size_size_list_char @ Ws2 ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct4
% 0.31/0.47 thf(fact_257_list__induct3,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_char,Zs2: list_char,P: list_char > list_char > list_char > $o] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs )
% 0.31/0.47 = ( size_size_list_char @ Ys ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys )
% 0.31/0.47 = ( size_size_list_char @ Zs2 ) )
% 0.31/0.47 => ( ( P @ nil_char @ nil_char @ nil_char )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: char,Zs: list_char] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs2 )
% 0.31/0.47 = ( size_size_list_char @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys3 )
% 0.31/0.47 = ( size_size_list_char @ Zs ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct3
% 0.31/0.47 thf(fact_258_list__induct3,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_char,Zs2: list_n282880152tr_b_c,P: list_char > list_char > list_n282880152tr_b_c > $o] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs )
% 0.31/0.47 = ( size_size_list_char @ Ys ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 0.31/0.47 => ( ( P @ nil_char @ nil_char @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs2 )
% 0.31/0.47 = ( size_size_list_char @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys3 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct3
% 0.31/0.47 thf(fact_259_list__induct3,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_n282880152tr_b_c,Zs2: list_char,P: list_char > list_n282880152tr_b_c > list_char > $o] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Ys )
% 0.31/0.47 = ( size_size_list_char @ Zs2 ) )
% 0.31/0.47 => ( ( P @ nil_char @ nil_no279930520tr_b_c @ nil_char )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: char,Zs: list_char] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs2 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Ys3 )
% 0.31/0.47 = ( size_size_list_char @ Zs ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct3
% 0.31/0.47 thf(fact_260_list__induct3,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_n282880152tr_b_c,Zs2: list_n282880152tr_b_c,P: list_char > list_n282880152tr_b_c > list_n282880152tr_b_c > $o] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Ys )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 0.31/0.47 => ( ( P @ nil_char @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs2 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Ys3 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct3
% 0.31/0.47 thf(fact_261_list__induct3,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,Ys: list_char,Zs2: list_char,P: list_n282880152tr_b_c > list_char > list_char > $o] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs )
% 0.31/0.47 = ( size_size_list_char @ Ys ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys )
% 0.31/0.47 = ( size_size_list_char @ Zs2 ) )
% 0.31/0.47 => ( ( P @ nil_no279930520tr_b_c @ nil_char @ nil_char )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char,Z: char,Zs: list_char] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 0.31/0.47 = ( size_size_list_char @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys3 )
% 0.31/0.47 = ( size_size_list_char @ Zs ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct3
% 0.31/0.47 thf(fact_262_list__induct3,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,Ys: list_char,Zs2: list_n282880152tr_b_c,P: list_n282880152tr_b_c > list_char > list_n282880152tr_b_c > $o] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs )
% 0.31/0.47 = ( size_size_list_char @ Ys ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 0.31/0.47 => ( ( P @ nil_no279930520tr_b_c @ nil_char @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 0.31/0.47 = ( size_size_list_char @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_size_list_char @ Ys3 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct3
% 0.31/0.47 thf(fact_263_list__induct3,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c,Zs2: list_char,P: list_n282880152tr_b_c > list_n282880152tr_b_c > list_char > $o] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Ys )
% 0.31/0.47 = ( size_size_list_char @ Zs2 ) )
% 0.31/0.47 => ( ( P @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c @ nil_char )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: char,Zs: list_char] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Ys3 )
% 0.31/0.47 = ( size_size_list_char @ Zs ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct3
% 0.31/0.47 thf(fact_264_list__induct3,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c,Zs2: list_n282880152tr_b_c,P: list_n282880152tr_b_c > list_n282880152tr_b_c > list_n282880152tr_b_c > $o] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Ys )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 0.31/0.47 => ( ( P @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 0.31/0.47 => ( ( ( size_s2106487044tr_b_c @ Ys3 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Zs ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct3
% 0.31/0.47 thf(fact_265_list__induct2,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_char,P: list_char > list_char > $o] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs )
% 0.31/0.47 = ( size_size_list_char @ Ys ) )
% 0.31/0.47 => ( ( P @ nil_char @ nil_char )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs2 )
% 0.31/0.47 = ( size_size_list_char @ Ys3 ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2
% 0.31/0.47 thf(fact_266_list__induct2,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_n282880152tr_b_c,P: list_char > list_n282880152tr_b_c > $o] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys ) )
% 0.31/0.47 => ( ( P @ nil_char @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( size_size_list_char @ Xs2 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2
% 0.31/0.47 thf(fact_267_list__induct2,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,Ys: list_char,P: list_n282880152tr_b_c > list_char > $o] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs )
% 0.31/0.47 = ( size_size_list_char @ Ys ) )
% 0.31/0.47 => ( ( P @ nil_no279930520tr_b_c @ nil_char )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 0.31/0.47 = ( size_size_list_char @ Ys3 ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2
% 0.31/0.47 thf(fact_268_list__induct2,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c,P: list_n282880152tr_b_c > list_n282880152tr_b_c > $o] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys ) )
% 0.31/0.47 => ( ( P @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 0.31/0.47 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2
% 0.31/0.47 thf(fact_269_splice_Oelims,axiom,
% 0.31/0.47 ! [X: list_char,Xa: list_char,Y: list_char] :
% 0.31/0.47 ( ( ( splice_char @ X @ Xa )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( ( X = nil_char )
% 0.31/0.47 => ( Y != Xa ) )
% 0.31/0.47 => ~ ! [X3: char,Xs2: list_char] :
% 0.31/0.47 ( ( X
% 0.31/0.47 = ( cons_char @ X3 @ Xs2 ) )
% 0.31/0.47 => ( Y
% 0.31/0.47 != ( cons_char @ X3 @ ( splice_char @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % splice.elims
% 0.31/0.47 thf(fact_270_splice_Oelims,axiom,
% 0.31/0.47 ! [X: list_n282880152tr_b_c,Xa: list_n282880152tr_b_c,Y: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( splice1294941035tr_b_c @ X @ Xa )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( ( X = nil_no279930520tr_b_c )
% 0.31/0.47 => ( Y != Xa ) )
% 0.31/0.47 => ~ ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( X
% 0.31/0.47 = ( cons_n413985352tr_b_c @ X3 @ Xs2 ) )
% 0.31/0.47 => ( Y
% 0.31/0.47 != ( cons_n413985352tr_b_c @ X3 @ ( splice1294941035tr_b_c @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % splice.elims
% 0.31/0.47 thf(fact_271_get__object__ptr__simp,axiom,
% 0.31/0.47 ! [Ptr2: object945351580_d_e_f,Object_ptr: object945351580_d_e_f,Obj: rObjec1413572695_j_k_l,H: heap_S1465075775_j_k_l] :
% 0.31/0.47 ( ( ( Ptr2 = Object_ptr )
% 0.31/0.47 => ( ( get_O_623850005_j_k_l @ Object_ptr @ ( put_O_834343516_j_k_l @ Ptr2 @ Obj @ H ) )
% 0.31/0.47 = ( some_R1598191922_j_k_l @ Obj ) ) )
% 0.31/0.47 & ( ( Ptr2 != Object_ptr )
% 0.31/0.47 => ( ( get_O_623850005_j_k_l @ Object_ptr @ ( put_O_834343516_j_k_l @ Ptr2 @ Obj @ H ) )
% 0.31/0.47 = ( get_O_623850005_j_k_l @ Object_ptr @ H ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % get_object_ptr_simp
% 0.31/0.47 thf(fact_272_n__lists__Nil,axiom,
% 0.31/0.47 ! [N: nat] :
% 0.31/0.47 ( ( ( N = zero_zero_nat )
% 0.31/0.47 => ( ( n_lists_char @ N @ nil_char )
% 0.31/0.47 = ( cons_list_char @ nil_char @ nil_list_char ) ) )
% 0.31/0.47 & ( ( N != zero_zero_nat )
% 0.31/0.47 => ( ( n_lists_char @ N @ nil_char )
% 0.31/0.47 = nil_list_char ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % n_lists_Nil
% 0.31/0.47 thf(fact_273_n__lists__Nil,axiom,
% 0.31/0.47 ! [N: nat] :
% 0.31/0.47 ( ( ( N = zero_zero_nat )
% 0.31/0.47 => ( ( n_list1807568544tr_b_c @ N @ nil_no279930520tr_b_c )
% 0.31/0.47 = ( cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c ) ) )
% 0.31/0.47 & ( ( N != zero_zero_nat )
% 0.31/0.47 => ( ( n_list1807568544tr_b_c @ N @ nil_no279930520tr_b_c )
% 0.31/0.47 = nil_li198338206tr_b_c ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % n_lists_Nil
% 0.31/0.47 thf(fact_274_n__lists_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Xs: list_char] :
% 0.31/0.47 ( ( n_lists_char @ zero_zero_nat @ Xs )
% 0.31/0.47 = ( cons_list_char @ nil_char @ nil_list_char ) ) ).
% 0.31/0.47
% 0.31/0.47 % n_lists.simps(1)
% 0.31/0.47 thf(fact_275_n__lists_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( n_list1807568544tr_b_c @ zero_zero_nat @ Xs )
% 0.31/0.47 = ( cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c ) ) ).
% 0.31/0.47
% 0.31/0.47 % n_lists.simps(1)
% 0.31/0.47 thf(fact_276_product__lists_Osimps_I1_J,axiom,
% 0.31/0.47 ( ( product_lists_char @ nil_list_char )
% 0.31/0.47 = ( cons_list_char @ nil_char @ nil_list_char ) ) ).
% 0.31/0.47
% 0.31/0.47 % product_lists.simps(1)
% 0.31/0.47 thf(fact_277_product__lists_Osimps_I1_J,axiom,
% 0.31/0.47 ( ( produc1509350401tr_b_c @ nil_li198338206tr_b_c )
% 0.31/0.47 = ( cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c ) ) ).
% 0.31/0.47
% 0.31/0.47 % product_lists.simps(1)
% 0.31/0.47 thf(fact_278_subseqs_Osimps_I1_J,axiom,
% 0.31/0.47 ( ( subseqs_char @ nil_char )
% 0.31/0.47 = ( cons_list_char @ nil_char @ nil_list_char ) ) ).
% 0.31/0.47
% 0.31/0.47 % subseqs.simps(1)
% 0.31/0.47 thf(fact_279_subseqs_Osimps_I1_J,axiom,
% 0.31/0.47 ( ( subseq1828679783tr_b_c @ nil_no279930520tr_b_c )
% 0.31/0.47 = ( cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c ) ) ).
% 0.31/0.47
% 0.31/0.47 % subseqs.simps(1)
% 0.31/0.47 thf(fact_280_insert__Nil,axiom,
% 0.31/0.47 ! [X: char] :
% 0.31/0.47 ( ( insert_char @ X @ nil_char )
% 0.31/0.47 = ( cons_char @ X @ nil_char ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_Nil
% 0.31/0.47 thf(fact_281_insert__Nil,axiom,
% 0.31/0.47 ! [X: node_p1234578834tr_b_c] :
% 0.31/0.47 ( ( insert678865070tr_b_c @ X @ nil_no279930520tr_b_c )
% 0.31/0.47 = ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_Nil
% 0.31/0.47 thf(fact_282_nths__singleton,axiom,
% 0.31/0.47 ! [A2: set_nat,X: char] :
% 0.31/0.47 ( ( ( member_nat @ zero_zero_nat @ A2 )
% 0.31/0.47 => ( ( nths_char @ ( cons_char @ X @ nil_char ) @ A2 )
% 0.31/0.47 = ( cons_char @ X @ nil_char ) ) )
% 0.31/0.47 & ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 0.31/0.47 => ( ( nths_char @ ( cons_char @ X @ nil_char ) @ A2 )
% 0.31/0.47 = nil_char ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nths_singleton
% 0.31/0.47 thf(fact_283_nths__singleton,axiom,
% 0.31/0.47 ! [A2: set_nat,X: node_p1234578834tr_b_c] :
% 0.31/0.47 ( ( ( member_nat @ zero_zero_nat @ A2 )
% 0.31/0.47 => ( ( nths_n1256675478tr_b_c @ ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) @ A2 )
% 0.31/0.47 = ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) ) )
% 0.31/0.47 & ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 0.31/0.47 => ( ( nths_n1256675478tr_b_c @ ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) @ A2 )
% 0.31/0.47 = nil_no279930520tr_b_c ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nths_singleton
% 0.31/0.47 thf(fact_284_nths__nil,axiom,
% 0.31/0.47 ! [A2: set_nat] :
% 0.31/0.47 ( ( nths_char @ nil_char @ A2 )
% 0.31/0.47 = nil_char ) ).
% 0.31/0.47
% 0.31/0.47 % nths_nil
% 0.31/0.47 thf(fact_285_nths__nil,axiom,
% 0.31/0.47 ! [A2: set_nat] :
% 0.31/0.47 ( ( nths_n1256675478tr_b_c @ nil_no279930520tr_b_c @ A2 )
% 0.31/0.47 = nil_no279930520tr_b_c ) ).
% 0.31/0.47
% 0.31/0.47 % nths_nil
% 0.31/0.47 thf(fact_286_nths__empty,axiom,
% 0.31/0.47 ! [Xs: list_char] :
% 0.31/0.47 ( ( nths_char @ Xs @ bot_bot_set_nat )
% 0.31/0.47 = nil_char ) ).
% 0.31/0.47
% 0.31/0.47 % nths_empty
% 0.31/0.47 thf(fact_287_nths__empty,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( nths_n1256675478tr_b_c @ Xs @ bot_bot_set_nat )
% 0.31/0.47 = nil_no279930520tr_b_c ) ).
% 0.31/0.47
% 0.31/0.47 % nths_empty
% 0.31/0.47 thf(fact_288_bind__split__asm,axiom,
% 0.31/0.47 ! [P: option_element_ptr_a > $o,M2: option_element_ptr_a,F: element_ptr_a > option_element_ptr_a] :
% 0.31/0.47 ( ( P @ ( bind_e22036734_ptr_a @ M2 @ F ) )
% 0.31/0.47 = ( ~ ( ( ( M2 = none_element_ptr_a )
% 0.31/0.47 & ~ ( P @ none_element_ptr_a ) )
% 0.31/0.47 | ? [X4: element_ptr_a] :
% 0.31/0.47 ( ( M2
% 0.31/0.47 = ( some_element_ptr_a @ X4 ) )
% 0.31/0.47 & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bind_split_asm
% 0.31/0.47 thf(fact_289_bind__split__asm,axiom,
% 0.31/0.47 ! [P: option2026120038on_j_k > $o,M2: option_element_ptr_a,F: element_ptr_a > option2026120038on_j_k] :
% 0.31/0.47 ( ( P @ ( bind_e1012152651on_j_k @ M2 @ F ) )
% 0.31/0.47 = ( ~ ( ( ( M2 = none_element_ptr_a )
% 0.31/0.47 & ~ ( P @ none_S1393028981on_j_k ) )
% 0.31/0.47 | ? [X4: element_ptr_a] :
% 0.31/0.47 ( ( M2
% 0.31/0.47 = ( some_element_ptr_a @ X4 ) )
% 0.31/0.47 & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bind_split_asm
% 0.31/0.47 thf(fact_290_bind__split__asm,axiom,
% 0.31/0.47 ! [P: option_element_ptr_a > $o,M2: option2026120038on_j_k,F: sum_su1221287958on_j_k > option_element_ptr_a] :
% 0.31/0.47 ( ( P @ ( bind_S287509021_ptr_a @ M2 @ F ) )
% 0.31/0.47 = ( ~ ( ( ( M2 = none_S1393028981on_j_k )
% 0.31/0.47 & ~ ( P @ none_element_ptr_a ) )
% 0.31/0.47 | ? [X4: sum_su1221287958on_j_k] :
% 0.31/0.47 ( ( M2
% 0.31/0.47 = ( some_S1960742641on_j_k @ X4 ) )
% 0.31/0.47 & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bind_split_asm
% 0.31/0.47 thf(fact_291_bind__split__asm,axiom,
% 0.31/0.47 ! [P: option2026120038on_j_k > $o,M2: option2026120038on_j_k,F: sum_su1221287958on_j_k > option2026120038on_j_k] :
% 0.31/0.47 ( ( P @ ( bind_S607117548on_j_k @ M2 @ F ) )
% 0.31/0.47 = ( ~ ( ( ( M2 = none_S1393028981on_j_k )
% 0.31/0.47 & ~ ( P @ none_S1393028981on_j_k ) )
% 0.31/0.47 | ? [X4: sum_su1221287958on_j_k] :
% 0.31/0.47 ( ( M2
% 0.31/0.47 = ( some_S1960742641on_j_k @ X4 ) )
% 0.31/0.47 & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bind_split_asm
% 0.31/0.47 thf(fact_292_bind__split,axiom,
% 0.31/0.47 ! [P: option_element_ptr_a > $o,M2: option_element_ptr_a,F: element_ptr_a > option_element_ptr_a] :
% 0.31/0.47 ( ( P @ ( bind_e22036734_ptr_a @ M2 @ F ) )
% 0.31/0.47 = ( ( ( M2 = none_element_ptr_a )
% 0.31/0.47 => ( P @ none_element_ptr_a ) )
% 0.31/0.47 & ! [V3: element_ptr_a] :
% 0.31/0.47 ( ( M2
% 0.31/0.47 = ( some_element_ptr_a @ V3 ) )
% 0.31/0.47 => ( P @ ( F @ V3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bind_split
% 0.31/0.47 thf(fact_293_bind__split,axiom,
% 0.31/0.47 ! [P: option2026120038on_j_k > $o,M2: option_element_ptr_a,F: element_ptr_a > option2026120038on_j_k] :
% 0.31/0.47 ( ( P @ ( bind_e1012152651on_j_k @ M2 @ F ) )
% 0.31/0.47 = ( ( ( M2 = none_element_ptr_a )
% 0.31/0.47 => ( P @ none_S1393028981on_j_k ) )
% 0.31/0.47 & ! [V3: element_ptr_a] :
% 0.31/0.47 ( ( M2
% 0.31/0.47 = ( some_element_ptr_a @ V3 ) )
% 0.31/0.47 => ( P @ ( F @ V3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bind_split
% 0.31/0.47 thf(fact_294_bind__split,axiom,
% 0.31/0.47 ! [P: option_element_ptr_a > $o,M2: option2026120038on_j_k,F: sum_su1221287958on_j_k > option_element_ptr_a] :
% 0.31/0.47 ( ( P @ ( bind_S287509021_ptr_a @ M2 @ F ) )
% 0.31/0.47 = ( ( ( M2 = none_S1393028981on_j_k )
% 0.31/0.47 => ( P @ none_element_ptr_a ) )
% 0.31/0.47 & ! [V3: sum_su1221287958on_j_k] :
% 0.31/0.47 ( ( M2
% 0.31/0.47 = ( some_S1960742641on_j_k @ V3 ) )
% 0.31/0.47 => ( P @ ( F @ V3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bind_split
% 0.31/0.47 thf(fact_295_bind__split,axiom,
% 0.31/0.47 ! [P: option2026120038on_j_k > $o,M2: option2026120038on_j_k,F: sum_su1221287958on_j_k > option2026120038on_j_k] :
% 0.31/0.47 ( ( P @ ( bind_S607117548on_j_k @ M2 @ F ) )
% 0.31/0.47 = ( ( ( M2 = none_S1393028981on_j_k )
% 0.31/0.47 => ( P @ none_S1393028981on_j_k ) )
% 0.31/0.47 & ! [V3: sum_su1221287958on_j_k] :
% 0.31/0.47 ( ( M2
% 0.31/0.47 = ( some_S1960742641on_j_k @ V3 ) )
% 0.31/0.47 => ( P @ ( F @ V3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bind_split
% 0.31/0.47 thf(fact_296_bind_Obind__lzero,axiom,
% 0.31/0.47 ! [F: element_ptr_a > option_element_ptr_a] :
% 0.31/0.47 ( ( bind_e22036734_ptr_a @ none_element_ptr_a @ F )
% 0.31/0.47 = none_element_ptr_a ) ).
% 0.31/0.47
% 0.31/0.47 % bind.bind_lzero
% 0.31/0.47 thf(fact_297_bind_Obind__lzero,axiom,
% 0.31/0.47 ! [F: element_ptr_a > option2026120038on_j_k] :
% 0.31/0.47 ( ( bind_e1012152651on_j_k @ none_element_ptr_a @ F )
% 0.31/0.47 = none_S1393028981on_j_k ) ).
% 0.31/0.47
% 0.31/0.47 % bind.bind_lzero
% 0.31/0.47 thf(fact_298_bind_Obind__lzero,axiom,
% 0.31/0.47 ! [F: sum_su1221287958on_j_k > option_element_ptr_a] :
% 0.31/0.47 ( ( bind_S287509021_ptr_a @ none_S1393028981on_j_k @ F )
% 0.31/0.47 = none_element_ptr_a ) ).
% 0.31/0.47
% 0.31/0.47 % bind.bind_lzero
% 0.31/0.47 thf(fact_299_bind_Obind__lzero,axiom,
% 0.31/0.47 ! [F: sum_su1221287958on_j_k > option2026120038on_j_k] :
% 0.31/0.47 ( ( bind_S607117548on_j_k @ none_S1393028981on_j_k @ F )
% 0.31/0.47 = none_S1393028981on_j_k ) ).
% 0.31/0.47
% 0.31/0.47 % bind.bind_lzero
% 0.31/0.47 thf(fact_300_set__encode__empty,axiom,
% 0.31/0.47 ( ( nat_set_encode @ bot_bot_set_nat )
% 0.31/0.47 = zero_zero_nat ) ).
% 0.31/0.47
% 0.31/0.47 % set_encode_empty
% 0.31/0.47 thf(fact_301_set__decode__zero,axiom,
% 0.31/0.47 ( ( nat_set_decode @ zero_zero_nat )
% 0.31/0.47 = bot_bot_set_nat ) ).
% 0.31/0.47
% 0.31/0.47 % set_decode_zero
% 0.31/0.47 thf(fact_302_length__append__singleton,axiom,
% 0.31/0.47 ! [Xs: list_char,X: char] :
% 0.31/0.47 ( ( size_size_list_char @ ( append_char @ Xs @ ( cons_char @ X @ nil_char ) ) )
% 0.31/0.47 = ( suc @ ( size_size_list_char @ Xs ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % length_append_singleton
% 0.31/0.47 thf(fact_303_length__append__singleton,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,X: node_p1234578834tr_b_c] :
% 0.31/0.47 ( ( size_s2106487044tr_b_c @ ( append846395565tr_b_c @ Xs @ ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) ) )
% 0.31/0.47 = ( suc @ ( size_s2106487044tr_b_c @ Xs ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % length_append_singleton
% 0.31/0.47 thf(fact_304_append__Nil2,axiom,
% 0.31/0.47 ! [Xs: list_char] :
% 0.31/0.47 ( ( append_char @ Xs @ nil_char )
% 0.31/0.47 = Xs ) ).
% 0.31/0.47
% 0.31/0.47 % append_Nil2
% 0.31/0.47 thf(fact_305_append__Nil2,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( append846395565tr_b_c @ Xs @ nil_no279930520tr_b_c )
% 0.31/0.47 = Xs ) ).
% 0.31/0.47
% 0.31/0.47 % append_Nil2
% 0.31/0.47 thf(fact_306_append__self__conv,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_char] :
% 0.31/0.47 ( ( ( append_char @ Xs @ Ys )
% 0.31/0.47 = Xs )
% 0.31/0.47 = ( Ys = nil_char ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_self_conv
% 0.31/0.47 thf(fact_307_append__self__conv,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( append846395565tr_b_c @ Xs @ Ys )
% 0.31/0.47 = Xs )
% 0.31/0.47 = ( Ys = nil_no279930520tr_b_c ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_self_conv
% 0.31/0.47 thf(fact_308_self__append__conv,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_char] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append_char @ Xs @ Ys ) )
% 0.31/0.47 = ( Ys = nil_char ) ) ).
% 0.31/0.47
% 0.31/0.47 % self_append_conv
% 0.31/0.47 thf(fact_309_self__append__conv,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append846395565tr_b_c @ Xs @ Ys ) )
% 0.31/0.47 = ( Ys = nil_no279930520tr_b_c ) ) ).
% 0.31/0.47
% 0.31/0.47 % self_append_conv
% 0.31/0.47 thf(fact_310_append__self__conv2,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_char] :
% 0.31/0.47 ( ( ( append_char @ Xs @ Ys )
% 0.31/0.47 = Ys )
% 0.31/0.47 = ( Xs = nil_char ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_self_conv2
% 0.31/0.47 thf(fact_311_append__self__conv2,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( append846395565tr_b_c @ Xs @ Ys )
% 0.31/0.47 = Ys )
% 0.31/0.47 = ( Xs = nil_no279930520tr_b_c ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_self_conv2
% 0.31/0.47 thf(fact_312_self__append__conv2,axiom,
% 0.31/0.47 ! [Ys: list_char,Xs: list_char] :
% 0.31/0.47 ( ( Ys
% 0.31/0.47 = ( append_char @ Xs @ Ys ) )
% 0.31/0.47 = ( Xs = nil_char ) ) ).
% 0.31/0.47
% 0.31/0.47 % self_append_conv2
% 0.31/0.47 thf(fact_313_self__append__conv2,axiom,
% 0.31/0.47 ! [Ys: list_n282880152tr_b_c,Xs: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( Ys
% 0.31/0.47 = ( append846395565tr_b_c @ Xs @ Ys ) )
% 0.31/0.47 = ( Xs = nil_no279930520tr_b_c ) ) ).
% 0.31/0.47
% 0.31/0.47 % self_append_conv2
% 0.31/0.47 thf(fact_314_Nil__is__append__conv,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_char] :
% 0.31/0.47 ( ( nil_char
% 0.31/0.47 = ( append_char @ Xs @ Ys ) )
% 0.31/0.47 = ( ( Xs = nil_char )
% 0.31/0.47 & ( Ys = nil_char ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Nil_is_append_conv
% 0.31/0.47 thf(fact_315_Nil__is__append__conv,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( nil_no279930520tr_b_c
% 0.31/0.47 = ( append846395565tr_b_c @ Xs @ Ys ) )
% 0.31/0.47 = ( ( Xs = nil_no279930520tr_b_c )
% 0.31/0.47 & ( Ys = nil_no279930520tr_b_c ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Nil_is_append_conv
% 0.31/0.47 thf(fact_316_append__is__Nil__conv,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_char] :
% 0.31/0.47 ( ( ( append_char @ Xs @ Ys )
% 0.31/0.47 = nil_char )
% 0.31/0.47 = ( ( Xs = nil_char )
% 0.31/0.47 & ( Ys = nil_char ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_is_Nil_conv
% 0.31/0.47 thf(fact_317_append__is__Nil__conv,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( append846395565tr_b_c @ Xs @ Ys )
% 0.31/0.47 = nil_no279930520tr_b_c )
% 0.31/0.47 = ( ( Xs = nil_no279930520tr_b_c )
% 0.31/0.47 & ( Ys = nil_no279930520tr_b_c ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_is_Nil_conv
% 0.31/0.47 thf(fact_318_append_Oright__neutral,axiom,
% 0.31/0.47 ! [A: list_char] :
% 0.31/0.47 ( ( append_char @ A @ nil_char )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % append.right_neutral
% 0.31/0.47 thf(fact_319_append_Oright__neutral,axiom,
% 0.31/0.47 ! [A: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( append846395565tr_b_c @ A @ nil_no279930520tr_b_c )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % append.right_neutral
% 0.31/0.47 thf(fact_320_set__decode__inverse,axiom,
% 0.31/0.47 ! [N: nat] :
% 0.31/0.47 ( ( nat_set_encode @ ( nat_set_decode @ N ) )
% 0.31/0.47 = N ) ).
% 0.31/0.47
% 0.31/0.47 % set_decode_inverse
% 0.31/0.47 thf(fact_321_append1__eq__conv,axiom,
% 0.31/0.47 ! [Xs: list_char,X: char,Ys: list_char,Y: char] :
% 0.31/0.47 ( ( ( append_char @ Xs @ ( cons_char @ X @ nil_char ) )
% 0.31/0.47 = ( append_char @ Ys @ ( cons_char @ Y @ nil_char ) ) )
% 0.31/0.47 = ( ( Xs = Ys )
% 0.31/0.47 & ( X = Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % append1_eq_conv
% 0.31/0.47 thf(fact_322_append1__eq__conv,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,X: node_p1234578834tr_b_c,Ys: list_n282880152tr_b_c,Y: node_p1234578834tr_b_c] :
% 0.31/0.47 ( ( ( append846395565tr_b_c @ Xs @ ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) )
% 0.31/0.47 = ( append846395565tr_b_c @ Ys @ ( cons_n413985352tr_b_c @ Y @ nil_no279930520tr_b_c ) ) )
% 0.31/0.47 = ( ( Xs = Ys )
% 0.31/0.47 & ( X = Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % append1_eq_conv
% 0.31/0.47 thf(fact_323_rev__induct,axiom,
% 0.31/0.47 ! [P: list_char > $o,Xs: list_char] :
% 0.31/0.47 ( ( P @ nil_char )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char] :
% 0.31/0.47 ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( append_char @ Xs2 @ ( cons_char @ X3 @ nil_char ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_induct
% 0.31/0.47 thf(fact_324_rev__induct,axiom,
% 0.31/0.47 ! [P: list_n282880152tr_b_c > $o,Xs: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( P @ nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( append846395565tr_b_c @ Xs2 @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_induct
% 0.31/0.47 thf(fact_325_rev__exhaust,axiom,
% 0.31/0.47 ! [Xs: list_char] :
% 0.31/0.47 ( ( Xs != nil_char )
% 0.31/0.47 => ~ ! [Ys3: list_char,Y3: char] :
% 0.31/0.47 ( Xs
% 0.31/0.47 != ( append_char @ Ys3 @ ( cons_char @ Y3 @ nil_char ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_exhaust
% 0.31/0.47 thf(fact_326_rev__exhaust,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( Xs != nil_no279930520tr_b_c )
% 0.31/0.47 => ~ ! [Ys3: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c] :
% 0.31/0.47 ( Xs
% 0.31/0.47 != ( append846395565tr_b_c @ Ys3 @ ( cons_n413985352tr_b_c @ Y3 @ nil_no279930520tr_b_c ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_exhaust
% 0.31/0.47 thf(fact_327_Cons__eq__append__conv,axiom,
% 0.31/0.47 ! [X: char,Xs: list_char,Ys: list_char,Zs2: list_char] :
% 0.31/0.47 ( ( ( cons_char @ X @ Xs )
% 0.31/0.47 = ( append_char @ Ys @ Zs2 ) )
% 0.31/0.47 = ( ( ( Ys = nil_char )
% 0.31/0.47 & ( ( cons_char @ X @ Xs )
% 0.31/0.47 = Zs2 ) )
% 0.31/0.47 | ? [Ys4: list_char] :
% 0.31/0.47 ( ( ( cons_char @ X @ Ys4 )
% 0.31/0.47 = Ys )
% 0.31/0.47 & ( Xs
% 0.31/0.47 = ( append_char @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Cons_eq_append_conv
% 0.31/0.47 thf(fact_328_Cons__eq__append__conv,axiom,
% 0.31/0.47 ! [X: node_p1234578834tr_b_c,Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c,Zs2: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( cons_n413985352tr_b_c @ X @ Xs )
% 0.31/0.47 = ( append846395565tr_b_c @ Ys @ Zs2 ) )
% 0.31/0.47 = ( ( ( Ys = nil_no279930520tr_b_c )
% 0.31/0.47 & ( ( cons_n413985352tr_b_c @ X @ Xs )
% 0.31/0.47 = Zs2 ) )
% 0.31/0.47 | ? [Ys4: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( cons_n413985352tr_b_c @ X @ Ys4 )
% 0.31/0.47 = Ys )
% 0.31/0.47 & ( Xs
% 0.31/0.47 = ( append846395565tr_b_c @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Cons_eq_append_conv
% 0.31/0.47 thf(fact_329_append__eq__Cons__conv,axiom,
% 0.31/0.47 ! [Ys: list_char,Zs2: list_char,X: char,Xs: list_char] :
% 0.31/0.47 ( ( ( append_char @ Ys @ Zs2 )
% 0.31/0.47 = ( cons_char @ X @ Xs ) )
% 0.31/0.47 = ( ( ( Ys = nil_char )
% 0.31/0.47 & ( Zs2
% 0.31/0.47 = ( cons_char @ X @ Xs ) ) )
% 0.31/0.47 | ? [Ys4: list_char] :
% 0.31/0.47 ( ( Ys
% 0.31/0.47 = ( cons_char @ X @ Ys4 ) )
% 0.31/0.47 & ( ( append_char @ Ys4 @ Zs2 )
% 0.31/0.47 = Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_eq_Cons_conv
% 0.31/0.47 thf(fact_330_append__eq__Cons__conv,axiom,
% 0.31/0.47 ! [Ys: list_n282880152tr_b_c,Zs2: list_n282880152tr_b_c,X: node_p1234578834tr_b_c,Xs: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( ( append846395565tr_b_c @ Ys @ Zs2 )
% 0.31/0.47 = ( cons_n413985352tr_b_c @ X @ Xs ) )
% 0.31/0.47 = ( ( ( Ys = nil_no279930520tr_b_c )
% 0.31/0.47 & ( Zs2
% 0.31/0.47 = ( cons_n413985352tr_b_c @ X @ Xs ) ) )
% 0.31/0.47 | ? [Ys4: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( Ys
% 0.31/0.47 = ( cons_n413985352tr_b_c @ X @ Ys4 ) )
% 0.31/0.47 & ( ( append846395565tr_b_c @ Ys4 @ Zs2 )
% 0.31/0.47 = Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_eq_Cons_conv
% 0.31/0.47 thf(fact_331_rev__nonempty__induct,axiom,
% 0.31/0.47 ! [Xs: list_char,P: list_char > $o] :
% 0.31/0.47 ( ( Xs != nil_char )
% 0.31/0.47 => ( ! [X3: char] : ( P @ ( cons_char @ X3 @ nil_char ) )
% 0.31/0.47 => ( ! [X3: char,Xs2: list_char] :
% 0.31/0.47 ( ( Xs2 != nil_char )
% 0.31/0.47 => ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( append_char @ Xs2 @ ( cons_char @ X3 @ nil_char ) ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_nonempty_induct
% 0.31/0.47 thf(fact_332_rev__nonempty__induct,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,P: list_n282880152tr_b_c > $o] :
% 0.31/0.47 ( ( Xs != nil_no279930520tr_b_c )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
% 0.31/0.47 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( Xs2 != nil_no279930520tr_b_c )
% 0.31/0.47 => ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( append846395565tr_b_c @ Xs2 @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_nonempty_induct
% 0.31/0.47 thf(fact_333_eq__Nil__appendI,axiom,
% 0.31/0.47 ! [Xs: list_char,Ys: list_char] :
% 0.31/0.47 ( ( Xs = Ys )
% 0.31/0.47 => ( Xs
% 0.31/0.47 = ( append_char @ nil_char @ Ys ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_Nil_appendI
% 0.31/0.47 thf(fact_334_eq__Nil__appendI,axiom,
% 0.31/0.47 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( Xs = Ys )
% 0.31/0.47 => ( Xs
% 0.31/0.47 = ( append846395565tr_b_c @ nil_no279930520tr_b_c @ Ys ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_Nil_appendI
% 0.31/0.47 thf(fact_335_append__Nil,axiom,
% 0.31/0.47 ! [Ys: list_char] :
% 0.31/0.47 ( ( append_char @ nil_char @ Ys )
% 0.31/0.47 = Ys ) ).
% 0.31/0.47
% 0.31/0.47 % append_Nil
% 0.31/0.47 thf(fact_336_append__Nil,axiom,
% 0.31/0.47 ! [Ys: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( append846395565tr_b_c @ nil_no279930520tr_b_c @ Ys )
% 0.31/0.47 = Ys ) ).
% 0.31/0.47
% 0.31/0.47 % append_Nil
% 0.31/0.47 thf(fact_337_append_Oleft__neutral,axiom,
% 0.31/0.47 ! [A: list_char] :
% 0.31/0.47 ( ( append_char @ nil_char @ A )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % append.left_neutral
% 0.31/0.47 thf(fact_338_append_Oleft__neutral,axiom,
% 0.31/0.47 ! [A: list_n282880152tr_b_c] :
% 0.31/0.47 ( ( append846395565tr_b_c @ nil_no279930520tr_b_c @ A )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % append.left_neutral
% 0.31/0.47
% 0.31/0.47 % Conjectures (4)
% 0.31/0.47 thf(conj_0,hypothesis,
% 0.31/0.47 ( ( docume1070804385_j_k_l @ h )
% 0.31/0.47 = bot_bo1111241908tr_d_e ) ).
% 0.31/0.47
% 0.31/0.47 thf(conj_1,hypothesis,
% 0.31/0.47 ( h2
% 0.31/0.47 = ( put_O_834343516_j_k_l @ ( cast_d1608273229_b_c_f @ ( docume1511108976tr_d_e @ ( suc @ zero_zero_nat ) ) ) @ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ) @ h ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(conj_2,hypothesis,
% 0.31/0.47 type_w92696601_j_k_l @ h ).
% 0.31/0.47
% 0.31/0.47 thf(conj_3,conjecture,
% 0.31/0.47 is_doc1417632087_j_k_l @ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 2.97/1.52 ---- Embedded in THF ---
% 2.97/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.97/1.52 %%% Generated on Tue Feb 24 08:28:33 EST 2026
% 2.97/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 2.97/1.52 %%% Logic specification used:
% 2.97/1.52 %%% thf(spec, logic, $$dhol).
% 2.97/1.52
% 2.97/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YeJj9WbkkZ/DTF2DTF6811.p
% See solution above
% 2.97/1.52 ------------------------
% 2.97/1.55 ---- Cleaned THF ---
% 2.97/1.56 thf(ty_n_t__ObjectClass__Oheap_It__Sum____Type__Osum_It__NodePointer__Onode____ptr_It__Sum____Type__Osum_It__ElementPointer__Oelement____ptr_Itf__a_J_Mt__Sum____Type__Osum_It__CharacterDataPointer__Ocharacter____data____ptr_Itf__b_J_Mtf__c_J_J_J_Mt__Sum____Type__Osum_It__DocumentPointer__Odocument____ptr_It__Sum____Type__Osum_It__ShadowRootPointer__Oshadow____root____ptr_Itf__d_J_Mtf__e_J_J_Mtf__f_J_J_Mt__Sum____Type__Osum_It__NodeClass__ORNode__ORNode____ext_It__Sum____Type__Osum_It__ElementClass__ORElement__ORElement____ext_Itf__c_Mtf__a_Mtf__b_Mtf__d_Mt__Option__Ooption_Itf__g_J_J_Mt__Sum____Type__Osum_It__CharacterDataClass__ORCharacterData__ORCharacterData____ext_It__Option__Ooption_Itf__h_J_J_Mtf__i_J_J_J_Mt__Sum____Type__Osum_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_Mtf__l_J_J_J,type,
% 2.97/1.56 heap_S1465075775_j_k_l: $tType ).
% 2.97/1.56
% 2.97/1.56 thf(ty_n_t__Option__Ooption_It__ObjectClass__ORObject__ORObject____ext_It__Sum____Type__Osum_It__NodeClass__ORNode__ORNode____ext_It__Sum____Type__Osum_It__ElementClass__ORElement__ORElement____ext_Itf__c_Mtf__a_Mtf__b_Mtf__d_Mt__Option__Ooption_Itf__g_J_J_Mt__Sum____Type__Osum_It__CharacterDataClass__ORCharacterData__ORCharacterData____ext_It__Option__Ooption_Itf__h_J_J_Mtf__i_J_J_J_Mt__Sum____Type__Osum_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_Mtf__l_J_J_J_J,type,
% 2.97/1.56 option1749760295_j_k_l: $tType ).
% 2.97/1.56
% 2.97/1.56 thf(ty_n_t__ObjectClass__ORObject__ORObject____ext_It__Sum____Type__Osum_It__NodeClass__ORNode__ORNode____ext_It__Sum____Type__Osum_It__ElementClass__ORElement__ORElement____ext_Itf__c_Mtf__a_Mtf__b_Mtf__d_Mt__Option__Ooption_Itf__g_J_J_Mt__Sum____Type__Osum_It__CharacterDataClass__ORCharacterData__ORCharacterData____ext_It__Option__Ooption_Itf__h_J_J_Mtf__i_J_J_J_Mt__Sum____Type__Osum_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_Mtf__l_J_J_J,type,
% 2.97/1.56 rObjec1413572695_j_k_l: $tType ).
% 2.97/1.56
% 2.97/1.56 thf(ty_n_t__ObjectPointer__Oobject____ptr_It__Sum____Type__Osum_It__NodePointer__Onode____ptr_It__Sum____Type__Osum_It__ElementPointer__Oelement____ptr_Itf__a_J_Mt__Sum____Type__Osum_It__CharacterDataPointer__Ocharacter____data____ptr_Itf__b_J_Mtf__c_J_J_J_Mt__Sum____Type__Osum_It__DocumentPointer__Odocument____ptr_It__Sum____Type__Osum_It__ShadowRootPointer__Oshadow____root____ptr_Itf__d_J_Mtf__e_J_J_Mtf__f_J_J_J,type,
% 2.97/1.56 object945351580_d_e_f: $tType ).
% 2.97/1.56
% 2.97/1.56 thf(ty_n_t__Option__Ooption_It__ObjectClass__ORObject__ORObject____ext_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_J_J,type,
% 2.97/1.56 option841825948on_j_k: $tType ).
% 2.97/1.56
% 2.97/1.56 thf(ty_n_t__ObjectClass__ORObject__ORObject____ext_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_J,type,
% 2.97/1.56 rObjec1617416918on_j_k: $tType ).
% 2.97/1.56
% 2.97/1.56 thf(ty_n_t__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J,type,
% 2.97/1.56 rDocum326988203on_j_k: $tType ).
% 2.97/1.56
% 2.97/1.56 thf(ty_n_t__List__Olist_It__List__Olist_It__NodePointer__Onode____ptr_It__Sum____Type__Osum_It__ElementPointer__Oelement____ptr_Itf__a_J_Mt__Sum____Type__Osum_It__CharacterDataPointer__Ocharacter____data____ptr_Itf__b_J_Mtf__c_J_J_J_J_J,type,
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% 2.97/1.56 some_element_ptr_a: element_ptr_a > option_element_ptr_a ).
% 2.97/1.56
% 2.97/1.56 thf(sy_c_Option_Ooption_OSome_001t__ObjectClass__ORObject__ORObject____ext_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_J,type,
% 2.97/1.56 some_R67702331on_j_k: rObjec1617416918on_j_k > option841825948on_j_k ).
% 2.97/1.56
% 2.97/1.56 thf(sy_c_Option_Ooption_OSome_001t__ObjectClass__ORObject__ORObject____ext_It__Sum____Type__Osum_It__NodeClass__ORNode__ORNode____ext_It__Sum____Type__Osum_It__ElementClass__ORElement__ORElement____ext_Itf__c_Mtf__a_Mtf__b_Mtf__d_Mt__Option__Ooption_Itf__g_J_J_Mt__Sum____Type__Osum_It__CharacterDataClass__ORCharacterData__ORCharacterData____ext_It__Option__Ooption_Itf__h_J_J_Mtf__i_J_J_J_Mt__Sum____Type__Osum_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_Mtf__l_J_J_J,type,
% 2.97/1.56 some_R1598191922_j_k_l: rObjec1413572695_j_k_l > option1749760295_j_k_l ).
% 2.97/1.56
% 2.97/1.56 thf(sy_c_Option_Ooption_OSome_001t__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J,type,
% 2.97/1.56 some_S1960742641on_j_k: sum_su1221287958on_j_k > option2026120038on_j_k ).
% 2.97/1.56
% 2.97/1.56 thf(sy_c_Option_Ooption_Osize__option_001t__DocumentPointer__Odocument____ptr_It__Sum____Type__Osum_It__ShadowRootPointer__Oshadow____root____ptr_Itf__d_J_Mtf__e_J_J,type,
% 2.97/1.56 size_o1635055885tr_d_e: ( docume1935157360tr_d_e > nat ) > option1330818496tr_d_e > nat ).
% 2.97/1.56
% 2.97/1.56 thf(sy_c_Option_Ooption_Osize__option_001t__ElementPointer__Oelement____ptr_Itf__a_J,type,
% 2.97/1.56 size_o1591053974_ptr_a: ( element_ptr_a > nat ) > option_element_ptr_a > nat ).
% 2.97/1.56
% 2.97/1.56 thf(sy_c_Option_Ooption_Osize__option_001t__ObjectClass__ORObject__ORObject____ext_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_J,type,
% 2.97/1.56 size_o26122489on_j_k: ( rObjec1617416918on_j_k > nat ) > option841825948on_j_k > nat ).
% 2.97/1.56
% 2.97/1.56 thf(sy_c_Option_Ooption_Osize__option_001t__ObjectClass__ORObject__ORObject____ext_It__Sum____Type__Osum_It__NodeClass__ORNode__ORNode____ext_It__Sum____Type__Osum_It__ElementClass__ORElement__ORElement____ext_Itf__c_Mtf__a_Mtf__b_Mtf__d_Mt__Option__Ooption_Itf__g_J_J_Mt__Sum____Type__Osum_It__CharacterDataClass__ORCharacterData__ORCharacterData____ext_It__Option__Ooption_Itf__h_J_J_Mtf__i_J_J_J_Mt__Sum____Type__Osum_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_Mtf__l_J_J_J,type,
% 2.97/1.56 size_o310046708_j_k_l: ( rObjec1413572695_j_k_l > nat ) > option1749760295_j_k_l > nat ).
% 2.97/1.56
% 2.97/1.56 thf(sy_c_Option_Ooption_Osize__option_001t__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J,type,
% 2.97/1.56 size_o1777465779on_j_k: ( sum_su1221287958on_j_k > nat ) > option2026120038on_j_k > nat ).
% 2.97/1.56
% 2.97/1.56 thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__DocumentPointer__Odocument____ptr_It__Sum____Type__Osum_It__ShadowRootPointer__Oshadow____root____ptr_Itf__d_J_Mtf__e_J_J_J,type,
% 2.97/1.56 bot_bo1111241908tr_d_e: fset_d1663890464tr_d_e ).
% 2.97/1.56
% 2.97/1.56 thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 2.97/1.56 bot_bot_nat: nat ).
% 2.97/1.56
% 2.97/1.56 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.97/1.56 bot_bot_set_nat: set_nat ).
% 2.97/1.56
% 2.97/1.56 thf(sy_c_Product__Type_OUnity,type,
% 2.97/1.56 product_Unity: product_unit ).
% 2.97/1.56
% 2.97/1.56 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 2.97/1.56 collect_nat: ( nat > $o ) > set_nat ).
% 2.97/1.56
% 2.97/1.56 thf(sy_c_ShadowRootClass_Otype__wf_001tf__a_001tf__b_001tf__c_001tf__d_001tf__e_001tf__f_001tf__g_001tf__h_001tf__i_001tf__j_001tf__k_001tf__l,type,
% 2.97/1.56 type_w92696601_j_k_l: heap_S1465075775_j_k_l > $o ).
% 2.97/1.56
% 2.97/1.56 thf(sy_c_member_001t__Nat__Onat,type,
% 2.97/1.56 member_nat: nat > set_nat > $o ).
% 2.97/1.56
% 2.97/1.56 thf(sy_v_h,type,
% 2.97/1.56 h: heap_S1465075775_j_k_l ).
% 2.97/1.56
% 2.97/1.56 thf(sy_v_h_H,type,
% 2.97/1.56 h2: heap_S1465075775_j_k_l ).
% 2.97/1.56
% 2.97/1.56 thf(fact_0_cast_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t__inject,axiom,
% 2.97/1.56 ! [X: rObjec1617416918on_j_k,Y: rObjec1617416918on_j_k] :
% 2.97/1.56 ( ( ( cast_D1252964113_h_i_l @ X )
% 2.97/1.56 = ( cast_D1252964113_h_i_l @ Y ) )
% 2.97/1.56 = ( X = Y ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_1_cast_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r_092_060_094sub_0622_092_060_094sub_062o_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r__inject,axiom,
% 2.97/1.56 ! [X: docume1935157360tr_d_e,Y: docume1935157360tr_d_e] :
% 2.97/1.56 ( ( ( cast_d1608273229_b_c_f @ X )
% 2.97/1.56 = ( cast_d1608273229_b_c_f @ Y ) )
% 2.97/1.56 = ( X = Y ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_2_document__ptr_Oinject_I1_J,axiom,
% 2.97/1.56 ! [X1: nat,Y1: nat] :
% 2.97/1.56 ( ( ( docume1511108976tr_d_e @ X1 )
% 2.97/1.56 = ( docume1511108976tr_d_e @ Y1 ) )
% 2.97/1.56 = ( X1 = Y1 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_3_RDocument_Oext__inject,axiom,
% 2.97/1.56 ! [Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k,Nothinga2: product_unit,Doctype2: list_char,Document_element2: option_element_ptr_a,Disconnected_nodes2: list_n282880152tr_b_c,More2: option2026120038on_j_k] :
% 2.97/1.56 ( ( ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More )
% 2.97/1.56 = ( rDocum427676485on_j_k @ Nothinga2 @ Doctype2 @ Document_element2 @ Disconnected_nodes2 @ More2 ) )
% 2.97/1.56 = ( ( Nothinga = Nothinga2 )
% 2.97/1.56 & ( Doctype = Doctype2 )
% 2.97/1.56 & ( Document_element = Document_element2 )
% 2.97/1.56 & ( Disconnected_nodes = Disconnected_nodes2 )
% 2.97/1.56 & ( More = More2 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_4_RObject_Oext__inject,axiom,
% 2.97/1.56 ! [Nothing: product_unit,More: rDocum326988203on_j_k,Nothing2: product_unit,More2: rDocum326988203on_j_k] :
% 2.97/1.56 ( ( ( rObjec1303043984on_j_k @ Nothing @ More )
% 2.97/1.56 = ( rObjec1303043984on_j_k @ Nothing2 @ More2 ) )
% 2.97/1.56 = ( ( Nothing = Nothing2 )
% 2.97/1.56 & ( More = More2 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_5_RObject_Oext__inject,axiom,
% 2.97/1.56 ! [Nothing: product_unit,More: product_unit,Nothing2: product_unit,More2: product_unit] :
% 2.97/1.56 ( ( ( rObjec730108904t_unit @ Nothing @ More )
% 2.97/1.56 = ( rObjec730108904t_unit @ Nothing2 @ More2 ) )
% 2.97/1.56 = ( ( Nothing = Nothing2 )
% 2.97/1.56 & ( More = More2 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_6_nat_Oinject,axiom,
% 2.97/1.56 ! [X2: nat,Y2: nat] :
% 2.97/1.56 ( ( ( suc @ X2 )
% 2.97/1.56 = ( suc @ Y2 ) )
% 2.97/1.56 = ( X2 = Y2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_7_old_Onat_Oinject,axiom,
% 2.97/1.56 ! [Nat: nat,Nat2: nat] :
% 2.97/1.56 ( ( ( suc @ Nat )
% 2.97/1.56 = ( suc @ Nat2 ) )
% 2.97/1.56 = ( Nat = Nat2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_8_RDocument_Ocases__scheme,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k] :
% 2.97/1.56 ~ ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list_char,Document_element3: option_element_ptr_a,Disconnected_nodes3: list_n282880152tr_b_c,More3: option2026120038on_j_k] :
% 2.97/1.56 ( R
% 2.97/1.56 != ( rObjec1303043984on_j_k @ Nothing3 @ ( rDocum427676485on_j_k @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_9_RDocument_Oinduct__scheme,axiom,
% 2.97/1.56 ! [P: rObjec1617416918on_j_k > $o,R: rObjec1617416918on_j_k] :
% 2.97/1.56 ( ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list_char,Document_element3: option_element_ptr_a,Disconnected_nodes3: list_n282880152tr_b_c,More3: option2026120038on_j_k] : ( P @ ( rObjec1303043984on_j_k @ Nothing3 @ ( rDocum427676485on_j_k @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) ) )
% 2.97/1.56 => ( P @ R ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_10_bot__nat__def,axiom,
% 2.97/1.56 bot_bot_nat = zero_zero_nat ).
% 2.97/1.56
% 2.97/1.56 thf(fact_11_RObject_Oinduct,axiom,
% 2.97/1.56 ! [P: rObjec103300152t_unit > $o,R: rObjec103300152t_unit] :
% 2.97/1.56 ( ! [Nothing3: product_unit] : ( P @ ( rObjec730108904t_unit @ Nothing3 @ product_Unity ) )
% 2.97/1.56 => ( P @ R ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_12_RObject_Ocases,axiom,
% 2.97/1.56 ! [R: rObjec103300152t_unit] :
% 2.97/1.56 ~ ! [Nothing3: product_unit] :
% 2.97/1.56 ( R
% 2.97/1.56 != ( rObjec730108904t_unit @ Nothing3 @ product_Unity ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_13_zero__reorient,axiom,
% 2.97/1.56 ! [X: nat] :
% 2.97/1.56 ( ( zero_zero_nat = X )
% 2.97/1.56 = ( X = zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_14_n__not__Suc__n,axiom,
% 2.97/1.56 ! [N: nat] :
% 2.97/1.56 ( N
% 2.97/1.56 != ( suc @ N ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_15_Suc__inject,axiom,
% 2.97/1.56 ! [X: nat,Y: nat] :
% 2.97/1.56 ( ( ( suc @ X )
% 2.97/1.56 = ( suc @ Y ) )
% 2.97/1.56 => ( X = Y ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_16_RObject_Oinduct__scheme,axiom,
% 2.97/1.56 ! [P: rObjec1617416918on_j_k > $o,R: rObjec1617416918on_j_k] :
% 2.97/1.56 ( ! [Nothing3: product_unit,More3: rDocum326988203on_j_k] : ( P @ ( rObjec1303043984on_j_k @ Nothing3 @ More3 ) )
% 2.97/1.56 => ( P @ R ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_17_RObject_Oinduct__scheme,axiom,
% 2.97/1.56 ! [P: rObjec103300152t_unit > $o,R: rObjec103300152t_unit] :
% 2.97/1.56 ( ! [Nothing3: product_unit,More3: product_unit] : ( P @ ( rObjec730108904t_unit @ Nothing3 @ More3 ) )
% 2.97/1.56 => ( P @ R ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_18_RObject_Ocases__scheme,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k] :
% 2.97/1.56 ~ ! [Nothing3: product_unit,More3: rDocum326988203on_j_k] :
% 2.97/1.56 ( R
% 2.97/1.56 != ( rObjec1303043984on_j_k @ Nothing3 @ More3 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_19_RObject_Ocases__scheme,axiom,
% 2.97/1.56 ! [R: rObjec103300152t_unit] :
% 2.97/1.56 ~ ! [Nothing3: product_unit,More3: product_unit] :
% 2.97/1.56 ( R
% 2.97/1.56 != ( rObjec730108904t_unit @ Nothing3 @ More3 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_20_RDocument_Oext__induct,axiom,
% 2.97/1.56 ! [P: rDocum326988203on_j_k > $o,R: rDocum326988203on_j_k] :
% 2.97/1.56 ( ! [Nothinga3: product_unit,Doctype3: list_char,Document_element3: option_element_ptr_a,Disconnected_nodes3: list_n282880152tr_b_c,More3: option2026120038on_j_k] : ( P @ ( rDocum427676485on_j_k @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) )
% 2.97/1.56 => ( P @ R ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_21_not0__implies__Suc,axiom,
% 2.97/1.56 ! [N: nat] :
% 2.97/1.56 ( ( N != zero_zero_nat )
% 2.97/1.56 => ? [M: nat] :
% 2.97/1.56 ( N
% 2.97/1.56 = ( suc @ M ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_22_old_Onat_Oinducts,axiom,
% 2.97/1.56 ! [P: nat > $o,Nat: nat] :
% 2.97/1.56 ( ( P @ zero_zero_nat )
% 2.97/1.56 => ( ! [Nat3: nat] :
% 2.97/1.56 ( ( P @ Nat3 )
% 2.97/1.56 => ( P @ ( suc @ Nat3 ) ) )
% 2.97/1.56 => ( P @ Nat ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_23_old_Onat_Oexhaust,axiom,
% 2.97/1.56 ! [Y: nat] :
% 2.97/1.56 ( ( Y != zero_zero_nat )
% 2.97/1.56 => ~ ! [Nat3: nat] :
% 2.97/1.56 ( Y
% 2.97/1.56 != ( suc @ Nat3 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_24_Zero__not__Suc,axiom,
% 2.97/1.56 ! [M2: nat] :
% 2.97/1.56 ( zero_zero_nat
% 2.97/1.56 != ( suc @ M2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_25_Zero__neq__Suc,axiom,
% 2.97/1.56 ! [M2: nat] :
% 2.97/1.56 ( zero_zero_nat
% 2.97/1.56 != ( suc @ M2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_26_Suc__neq__Zero,axiom,
% 2.97/1.56 ! [M2: nat] :
% 2.97/1.56 ( ( suc @ M2 )
% 2.97/1.56 != zero_zero_nat ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_27_zero__induct,axiom,
% 2.97/1.56 ! [P: nat > $o,K: nat] :
% 2.97/1.56 ( ( P @ K )
% 2.97/1.56 => ( ! [N2: nat] :
% 2.97/1.56 ( ( P @ ( suc @ N2 ) )
% 2.97/1.56 => ( P @ N2 ) )
% 2.97/1.56 => ( P @ zero_zero_nat ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_28_diff__induct,axiom,
% 2.97/1.56 ! [P: nat > nat > $o,M2: nat,N: nat] :
% 2.97/1.56 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 2.97/1.56 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 2.97/1.56 => ( ! [X3: nat,Y3: nat] :
% 2.97/1.56 ( ( P @ X3 @ Y3 )
% 2.97/1.56 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 2.97/1.56 => ( P @ M2 @ N ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_29_nat__induct,axiom,
% 2.97/1.56 ! [P: nat > $o,N: nat] :
% 2.97/1.56 ( ( P @ zero_zero_nat )
% 2.97/1.56 => ( ! [N2: nat] :
% 2.97/1.56 ( ( P @ N2 )
% 2.97/1.56 => ( P @ ( suc @ N2 ) ) )
% 2.97/1.56 => ( P @ N ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_30_nat_OdiscI,axiom,
% 2.97/1.56 ! [Nat: nat,X2: nat] :
% 2.97/1.56 ( ( Nat
% 2.97/1.56 = ( suc @ X2 ) )
% 2.97/1.56 => ( Nat != zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_31_old_Onat_Odistinct_I1_J,axiom,
% 2.97/1.56 ! [Nat2: nat] :
% 2.97/1.56 ( zero_zero_nat
% 2.97/1.56 != ( suc @ Nat2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_32_old_Onat_Odistinct_I2_J,axiom,
% 2.97/1.56 ! [Nat2: nat] :
% 2.97/1.56 ( ( suc @ Nat2 )
% 2.97/1.56 != zero_zero_nat ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_33_nat_Odistinct_I1_J,axiom,
% 2.97/1.56 ! [X2: nat] :
% 2.97/1.56 ( zero_zero_nat
% 2.97/1.56 != ( suc @ X2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_34_document__ptr_Osize__gen_I1_J,axiom,
% 2.97/1.56 ! [X: sum_su1576157353tr_d_e > nat,X1: nat] :
% 2.97/1.56 ( ( docume1799427087tr_d_e @ X @ ( docume1511108976tr_d_e @ X1 ) )
% 2.97/1.56 = ( suc @ zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_35_document__ptr_Osize_I3_J,axiom,
% 2.97/1.56 ! [X1: nat] :
% 2.97/1.56 ( ( size_s724035844tr_d_e @ ( docume1511108976tr_d_e @ X1 ) )
% 2.97/1.56 = ( suc @ zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_36_put_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__def,axiom,
% 2.97/1.56 ( put_D_2126422573_h_i_l
% 2.97/1.56 = ( ^ [Document_ptr: docume1935157360tr_d_e,Document: rObjec1617416918on_j_k] : ( put_O_834343516_j_k_l @ ( cast_d1608273229_b_c_f @ Document_ptr ) @ ( cast_D1252964113_h_i_l @ Document ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_37_exists__least__lemma,axiom,
% 2.97/1.56 ! [P: nat > $o] :
% 2.97/1.56 ( ~ ( P @ zero_zero_nat )
% 2.97/1.56 => ( ? [X_1: nat] : ( P @ X_1 )
% 2.97/1.56 => ? [N2: nat] :
% 2.97/1.56 ( ~ ( P @ N2 )
% 2.97/1.56 & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_38_list__decode_Ocases,axiom,
% 2.97/1.56 ! [X: nat] :
% 2.97/1.56 ( ( X != zero_zero_nat )
% 2.97/1.56 => ~ ! [N2: nat] :
% 2.97/1.56 ( X
% 2.97/1.56 != ( suc @ N2 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_39_object__empty,axiom,
% 2.97/1.56 ! [X: rObjec1617416918on_j_k] :
% 2.97/1.56 ( ( rObjec1303043984on_j_k @ product_Unity @ ( more_R1625109589on_j_k @ X ) )
% 2.97/1.56 = X ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_40_object__empty,axiom,
% 2.97/1.56 ! [X: rObjec103300152t_unit] :
% 2.97/1.56 ( ( rObjec730108904t_unit @ product_Unity @ ( more_Product_unit @ X ) )
% 2.97/1.56 = X ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_41_mem__Collect__eq,axiom,
% 2.97/1.56 ! [A: nat,P: nat > $o] :
% 2.97/1.56 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 2.97/1.56 = ( P @ A ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_42_Collect__mem__eq,axiom,
% 2.97/1.56 ! [A2: set_nat] :
% 2.97/1.56 ( ( collect_nat
% 2.97/1.56 @ ^ [X4: nat] : ( member_nat @ X4 @ A2 ) )
% 2.97/1.56 = A2 ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_43_RDocument_Oupdate__convs_I1_J,axiom,
% 2.97/1.56 ! [Nothing2: product_unit > product_unit,Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 2.97/1.56 ( ( nothin1105341917on_j_k @ Nothing2 @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 2.97/1.56 = ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ ( Nothing2 @ Nothinga ) @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_44_RDocument_Oupdate__convs_I2_J,axiom,
% 2.97/1.56 ! [Doctype2: list_char > list_char,Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 2.97/1.56 ( ( doctyp68000440on_j_k @ Doctype2 @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 2.97/1.56 = ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ ( Doctype2 @ Doctype ) @ Document_element @ Disconnected_nodes @ More ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_45_RDocument_Oupdate__convs_I3_J,axiom,
% 2.97/1.56 ! [Document_element2: option_element_ptr_a > option_element_ptr_a,Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 2.97/1.56 ( ( docume244715269on_j_k @ Document_element2 @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 2.97/1.56 = ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ ( Document_element2 @ Document_element ) @ Disconnected_nodes @ More ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_46_RDocument_Oupdate__convs_I4_J,axiom,
% 2.97/1.56 ! [Disconnected_nodes2: list_n282880152tr_b_c > list_n282880152tr_b_c,Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 2.97/1.56 ( ( discon442323090on_j_k @ Disconnected_nodes2 @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 2.97/1.56 = ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ ( Disconnected_nodes2 @ Disconnected_nodes ) @ More ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_47_size__neq__size__imp__neq,axiom,
% 2.97/1.56 ! [X: docume1935157360tr_d_e,Y: docume1935157360tr_d_e] :
% 2.97/1.56 ( ( ( size_s724035844tr_d_e @ X )
% 2.97/1.56 != ( size_s724035844tr_d_e @ Y ) )
% 2.97/1.56 => ( X != Y ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_48_size__neq__size__imp__neq,axiom,
% 2.97/1.56 ! [X: list_n282880152tr_b_c,Y: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ X )
% 2.97/1.56 != ( size_s2106487044tr_b_c @ Y ) )
% 2.97/1.56 => ( X != Y ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_49_size__neq__size__imp__neq,axiom,
% 2.97/1.56 ! [X: list_char,Y: list_char] :
% 2.97/1.56 ( ( ( size_size_list_char @ X )
% 2.97/1.56 != ( size_size_list_char @ Y ) )
% 2.97/1.56 => ( X != Y ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_50_size__neq__size__imp__neq,axiom,
% 2.97/1.56 ! [X: option2026120038on_j_k,Y: option2026120038on_j_k] :
% 2.97/1.56 ( ( ( size_s1129069050on_j_k @ X )
% 2.97/1.56 != ( size_s1129069050on_j_k @ Y ) )
% 2.97/1.56 => ( X != Y ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_51_size__neq__size__imp__neq,axiom,
% 2.97/1.56 ! [X: option_element_ptr_a,Y: option_element_ptr_a] :
% 2.97/1.56 ( ( ( size_s1129684517_ptr_a @ X )
% 2.97/1.56 != ( size_s1129684517_ptr_a @ Y ) )
% 2.97/1.56 => ( X != Y ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_52_RObject_Oselect__convs_I2_J,axiom,
% 2.97/1.56 ! [Nothing: product_unit,More: rDocum326988203on_j_k] :
% 2.97/1.56 ( ( more_R1625109589on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ More ) )
% 2.97/1.56 = More ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_53_RObject_Oselect__convs_I2_J,axiom,
% 2.97/1.56 ! [Nothing: product_unit,More: product_unit] :
% 2.97/1.56 ( ( more_Product_unit @ ( rObjec730108904t_unit @ Nothing @ More ) )
% 2.97/1.56 = More ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_54_document__ptr_Osize__neq,axiom,
% 2.97/1.56 ! [X: docume1935157360tr_d_e] :
% 2.97/1.56 ( ( size_s724035844tr_d_e @ X )
% 2.97/1.56 != zero_zero_nat ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_55_object__more__extend__id,axiom,
% 2.97/1.56 ! [X: rObjec103300152t_unit,Y: product_unit] :
% 2.97/1.56 ( ( more_Product_unit @ ( extend_Product_unit @ X @ Y ) )
% 2.97/1.56 = Y ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_56_object__more__extend__id,axiom,
% 2.97/1.56 ! [X: rObjec103300152t_unit,Y: rDocum326988203on_j_k] :
% 2.97/1.56 ( ( more_R1625109589on_j_k @ ( extend1066431834on_j_k @ X @ Y ) )
% 2.97/1.56 = Y ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_57_RDocument_Oupdate__convs_I5_J,axiom,
% 2.97/1.56 ! [More2: option2026120038on_j_k > option2026120038on_j_k,Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 2.97/1.56 ( ( more_u1044474223_c_a_b @ More2 @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 2.97/1.56 = ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ ( More2 @ More ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_58_is__document__ptr__ref,axiom,
% 2.97/1.56 ! [N: nat] : ( is_doc2037328342tr_d_e @ ( docume1511108976tr_d_e @ N ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_59_RDocument_Oselect__convs_I5_J,axiom,
% 2.97/1.56 ! [Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 2.97/1.56 ( ( more_c1453068134on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 2.97/1.56 = More ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_60_RDocument_Oselect__convs_I4_J,axiom,
% 2.97/1.56 ! [Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 2.97/1.56 ( ( discon866287741on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 2.97/1.56 = Disconnected_nodes ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_61_RDocument_Oselect__convs_I3_J,axiom,
% 2.97/1.56 ! [Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 2.97/1.56 ( ( docume1175131570on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 2.97/1.56 = Document_element ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_62_RDocument_Oselect__convs_I2_J,axiom,
% 2.97/1.56 ! [Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 2.97/1.56 ( ( doctyp814403297on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 2.97/1.56 = Doctype ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_63_RDocument_Oselect__convs_I1_J,axiom,
% 2.97/1.56 ! [Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
% 2.97/1.56 ( ( nothin757132294on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 2.97/1.56 = Nothinga ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_64_RDocument_Ounfold__congs_I6_J,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: option2026120038on_j_k,F: option2026120038on_j_k > option2026120038on_j_k,F2: option2026120038on_j_k > option2026120038on_j_k] :
% 2.97/1.56 ( ( R = R2 )
% 2.97/1.56 => ( ( ( more_c1453068134on_j_k @ R2 )
% 2.97/1.56 = V )
% 2.97/1.56 => ( ! [V2: option2026120038on_j_k] :
% 2.97/1.56 ( ( V2 = V )
% 2.97/1.56 => ( ( F @ V2 )
% 2.97/1.56 = ( F2 @ V2 ) ) )
% 2.97/1.56 => ( ( more_u1044474223_c_a_b @ F @ R )
% 2.97/1.56 = ( more_u1044474223_c_a_b @ F2 @ R2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_65_RDocument_Ofold__congs_I6_J,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: option2026120038on_j_k,F: option2026120038on_j_k > option2026120038on_j_k,F2: option2026120038on_j_k > option2026120038on_j_k] :
% 2.97/1.56 ( ( R = R2 )
% 2.97/1.56 => ( ( ( more_c1453068134on_j_k @ R2 )
% 2.97/1.56 = V )
% 2.97/1.56 => ( ! [V2: option2026120038on_j_k] :
% 2.97/1.56 ( ( V = V2 )
% 2.97/1.56 => ( ( F @ V2 )
% 2.97/1.56 = ( F2 @ V2 ) ) )
% 2.97/1.56 => ( ( more_u1044474223_c_a_b @ F @ R )
% 2.97/1.56 = ( more_u1044474223_c_a_b @ F2 @ R2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_66_RDocument_Ounfold__congs_I3_J,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: list_char,F: list_char > list_char,F2: list_char > list_char] :
% 2.97/1.56 ( ( R = R2 )
% 2.97/1.56 => ( ( ( doctyp814403297on_j_k @ R2 )
% 2.97/1.56 = V )
% 2.97/1.56 => ( ! [V2: list_char] :
% 2.97/1.56 ( ( V2 = V )
% 2.97/1.56 => ( ( F @ V2 )
% 2.97/1.56 = ( F2 @ V2 ) ) )
% 2.97/1.56 => ( ( doctyp68000440on_j_k @ F @ R )
% 2.97/1.56 = ( doctyp68000440on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_67_RDocument_Ounfold__congs_I4_J,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: option_element_ptr_a,F: option_element_ptr_a > option_element_ptr_a,F2: option_element_ptr_a > option_element_ptr_a] :
% 2.97/1.56 ( ( R = R2 )
% 2.97/1.56 => ( ( ( docume1175131570on_j_k @ R2 )
% 2.97/1.56 = V )
% 2.97/1.56 => ( ! [V2: option_element_ptr_a] :
% 2.97/1.56 ( ( V2 = V )
% 2.97/1.56 => ( ( F @ V2 )
% 2.97/1.56 = ( F2 @ V2 ) ) )
% 2.97/1.56 => ( ( docume244715269on_j_k @ F @ R )
% 2.97/1.56 = ( docume244715269on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_68_RDocument_Ounfold__congs_I5_J,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: list_n282880152tr_b_c,F: list_n282880152tr_b_c > list_n282880152tr_b_c,F2: list_n282880152tr_b_c > list_n282880152tr_b_c] :
% 2.97/1.56 ( ( R = R2 )
% 2.97/1.56 => ( ( ( discon866287741on_j_k @ R2 )
% 2.97/1.56 = V )
% 2.97/1.56 => ( ! [V2: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( V2 = V )
% 2.97/1.56 => ( ( F @ V2 )
% 2.97/1.56 = ( F2 @ V2 ) ) )
% 2.97/1.56 => ( ( discon442323090on_j_k @ F @ R )
% 2.97/1.56 = ( discon442323090on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_69_RDocument_Ofold__congs_I3_J,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: list_char,F: list_char > list_char,F2: list_char > list_char] :
% 2.97/1.56 ( ( R = R2 )
% 2.97/1.56 => ( ( ( doctyp814403297on_j_k @ R2 )
% 2.97/1.56 = V )
% 2.97/1.56 => ( ! [V2: list_char] :
% 2.97/1.56 ( ( V = V2 )
% 2.97/1.56 => ( ( F @ V2 )
% 2.97/1.56 = ( F2 @ V2 ) ) )
% 2.97/1.56 => ( ( doctyp68000440on_j_k @ F @ R )
% 2.97/1.56 = ( doctyp68000440on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_70_RDocument_Ofold__congs_I4_J,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: option_element_ptr_a,F: option_element_ptr_a > option_element_ptr_a,F2: option_element_ptr_a > option_element_ptr_a] :
% 2.97/1.56 ( ( R = R2 )
% 2.97/1.56 => ( ( ( docume1175131570on_j_k @ R2 )
% 2.97/1.56 = V )
% 2.97/1.56 => ( ! [V2: option_element_ptr_a] :
% 2.97/1.56 ( ( V = V2 )
% 2.97/1.56 => ( ( F @ V2 )
% 2.97/1.56 = ( F2 @ V2 ) ) )
% 2.97/1.56 => ( ( docume244715269on_j_k @ F @ R )
% 2.97/1.56 = ( docume244715269on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_71_RDocument_Ofold__congs_I5_J,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: list_n282880152tr_b_c,F: list_n282880152tr_b_c > list_n282880152tr_b_c,F2: list_n282880152tr_b_c > list_n282880152tr_b_c] :
% 2.97/1.56 ( ( R = R2 )
% 2.97/1.56 => ( ( ( discon866287741on_j_k @ R2 )
% 2.97/1.56 = V )
% 2.97/1.56 => ( ! [V2: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( V = V2 )
% 2.97/1.56 => ( ( F @ V2 )
% 2.97/1.56 = ( F2 @ V2 ) ) )
% 2.97/1.56 => ( ( discon442323090on_j_k @ F @ R )
% 2.97/1.56 = ( discon442323090on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_72_RDocument_Ounfold__congs_I2_J,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: product_unit,F: product_unit > product_unit,F2: product_unit > product_unit] :
% 2.97/1.56 ( ( R = R2 )
% 2.97/1.56 => ( ( ( nothin757132294on_j_k @ R2 )
% 2.97/1.56 = V )
% 2.97/1.56 => ( ! [V2: product_unit] :
% 2.97/1.56 ( ( V2 = V )
% 2.97/1.56 => ( ( F @ V2 )
% 2.97/1.56 = ( F2 @ V2 ) ) )
% 2.97/1.56 => ( ( nothin1105341917on_j_k @ F @ R )
% 2.97/1.56 = ( nothin1105341917on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_73_RDocument_Ofold__congs_I2_J,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: product_unit,F: product_unit > product_unit,F2: product_unit > product_unit] :
% 2.97/1.56 ( ( R = R2 )
% 2.97/1.56 => ( ( ( nothin757132294on_j_k @ R2 )
% 2.97/1.56 = V )
% 2.97/1.56 => ( ! [V2: product_unit] :
% 2.97/1.56 ( ( V = V2 )
% 2.97/1.56 => ( ( F @ V2 )
% 2.97/1.56 = ( F2 @ V2 ) ) )
% 2.97/1.56 => ( ( nothin1105341917on_j_k @ F @ R )
% 2.97/1.56 = ( nothin1105341917on_j_k @ F2 @ R2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_74_length__0__conv,axiom,
% 2.97/1.56 ! [Xs: list_l118626078tr_b_c] :
% 2.97/1.56 ( ( ( size_s9369994tr_b_c @ Xs )
% 2.97/1.56 = zero_zero_nat )
% 2.97/1.56 = ( Xs = nil_li198338206tr_b_c ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_75_length__0__conv,axiom,
% 2.97/1.56 ! [Xs: list_list_char] :
% 2.97/1.56 ( ( ( size_s2008079621t_char @ Xs )
% 2.97/1.56 = zero_zero_nat )
% 2.97/1.56 = ( Xs = nil_list_char ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_76_length__0__conv,axiom,
% 2.97/1.56 ! [Xs: list_char] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs )
% 2.97/1.56 = zero_zero_nat )
% 2.97/1.56 = ( Xs = nil_char ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_77_length__0__conv,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs )
% 2.97/1.56 = zero_zero_nat )
% 2.97/1.56 = ( Xs = nil_no279930520tr_b_c ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_78_RDocument_Osurjective,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k] :
% 2.97/1.56 ( R
% 2.97/1.56 = ( rObjec1303043984on_j_k @ ( nothin1567949605on_j_k @ R ) @ ( rDocum427676485on_j_k @ ( nothin757132294on_j_k @ R ) @ ( doctyp814403297on_j_k @ R ) @ ( docume1175131570on_j_k @ R ) @ ( discon866287741on_j_k @ R ) @ ( more_c1453068134on_j_k @ R ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_79_RDocument_Oequality,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k] :
% 2.97/1.56 ( ( ( nothin1567949605on_j_k @ R )
% 2.97/1.56 = ( nothin1567949605on_j_k @ R2 ) )
% 2.97/1.56 => ( ( ( nothin757132294on_j_k @ R )
% 2.97/1.56 = ( nothin757132294on_j_k @ R2 ) )
% 2.97/1.56 => ( ( ( doctyp814403297on_j_k @ R )
% 2.97/1.56 = ( doctyp814403297on_j_k @ R2 ) )
% 2.97/1.56 => ( ( ( docume1175131570on_j_k @ R )
% 2.97/1.56 = ( docume1175131570on_j_k @ R2 ) )
% 2.97/1.56 => ( ( ( discon866287741on_j_k @ R )
% 2.97/1.56 = ( discon866287741on_j_k @ R2 ) )
% 2.97/1.56 => ( ( ( more_c1453068134on_j_k @ R )
% 2.97/1.56 = ( more_c1453068134on_j_k @ R2 ) )
% 2.97/1.56 => ( R = R2 ) ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_80_option_Osize_I3_J,axiom,
% 2.97/1.56 ( ( size_s7667464on_j_k @ none_R1587534007on_j_k )
% 2.97/1.56 = ( suc @ zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_81_option_Osize_I3_J,axiom,
% 2.97/1.56 ( ( size_s1129684517_ptr_a @ none_element_ptr_a )
% 2.97/1.56 = ( suc @ zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_82_option_Osize_I3_J,axiom,
% 2.97/1.56 ( ( size_s1129069050on_j_k @ none_S1393028981on_j_k )
% 2.97/1.56 = ( suc @ zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_83_list_Osize_I3_J,axiom,
% 2.97/1.56 ( ( size_s9369994tr_b_c @ nil_li198338206tr_b_c )
% 2.97/1.56 = zero_zero_nat ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_84_list_Osize_I3_J,axiom,
% 2.97/1.56 ( ( size_s2008079621t_char @ nil_list_char )
% 2.97/1.56 = zero_zero_nat ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_85_list_Osize_I3_J,axiom,
% 2.97/1.56 ( ( size_size_list_char @ nil_char )
% 2.97/1.56 = zero_zero_nat ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_86_list_Osize_I3_J,axiom,
% 2.97/1.56 ( ( size_s2106487044tr_b_c @ nil_no279930520tr_b_c )
% 2.97/1.56 = zero_zero_nat ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_87_document__ptr_Osize_I4_J,axiom,
% 2.97/1.56 ! [X2: sum_su1576157353tr_d_e] :
% 2.97/1.56 ( ( size_s724035844tr_d_e @ ( docume1825929374tr_d_e @ X2 ) )
% 2.97/1.56 = ( suc @ zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_88_RObject_Osurjective,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k] :
% 2.97/1.56 ( R
% 2.97/1.56 = ( rObjec1303043984on_j_k @ ( nothin1567949605on_j_k @ R ) @ ( more_R1625109589on_j_k @ R ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_89_RObject_Osurjective,axiom,
% 2.97/1.56 ! [R: rObjec103300152t_unit] :
% 2.97/1.56 ( R
% 2.97/1.56 = ( rObjec730108904t_unit @ ( nothing_Product_unit @ R ) @ ( more_Product_unit @ R ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_90_document__ptr_Oinject_I2_J,axiom,
% 2.97/1.56 ! [X2: sum_su1576157353tr_d_e,Y2: sum_su1576157353tr_d_e] :
% 2.97/1.56 ( ( ( docume1825929374tr_d_e @ X2 )
% 2.97/1.56 = ( docume1825929374tr_d_e @ Y2 ) )
% 2.97/1.56 = ( X2 = Y2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_91_neq__if__length__neq,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs )
% 2.97/1.56 != ( size_s2106487044tr_b_c @ Ys ) )
% 2.97/1.56 => ( Xs != Ys ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_92_neq__if__length__neq,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_char] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs )
% 2.97/1.56 != ( size_size_list_char @ Ys ) )
% 2.97/1.56 => ( Xs != Ys ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_93_Ex__list__of__length,axiom,
% 2.97/1.56 ! [N: nat] :
% 2.97/1.56 ? [Xs2: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( size_s2106487044tr_b_c @ Xs2 )
% 2.97/1.56 = N ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_94_Ex__list__of__length,axiom,
% 2.97/1.56 ! [N: nat] :
% 2.97/1.56 ? [Xs2: list_char] :
% 2.97/1.56 ( ( size_size_list_char @ Xs2 )
% 2.97/1.56 = N ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_95_document__ptr_Odistinct_I1_J,axiom,
% 2.97/1.56 ! [X1: nat,X2: sum_su1576157353tr_d_e] :
% 2.97/1.56 ( ( docume1511108976tr_d_e @ X1 )
% 2.97/1.56 != ( docume1825929374tr_d_e @ X2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_96_document__ptr_Oinduct,axiom,
% 2.97/1.56 ! [P: docume1935157360tr_d_e > $o,Document_ptr2: docume1935157360tr_d_e] :
% 2.97/1.56 ( ! [X3: nat] : ( P @ ( docume1511108976tr_d_e @ X3 ) )
% 2.97/1.56 => ( ! [X3: sum_su1576157353tr_d_e] : ( P @ ( docume1825929374tr_d_e @ X3 ) )
% 2.97/1.56 => ( P @ Document_ptr2 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_97_document__ptr_Oexhaust,axiom,
% 2.97/1.56 ! [Y: docume1935157360tr_d_e] :
% 2.97/1.56 ( ! [X12: nat] :
% 2.97/1.56 ( Y
% 2.97/1.56 != ( docume1511108976tr_d_e @ X12 ) )
% 2.97/1.56 => ~ ! [X22: sum_su1576157353tr_d_e] :
% 2.97/1.56 ( Y
% 2.97/1.56 != ( docume1825929374tr_d_e @ X22 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_98_RObject_Oselect__convs_I1_J,axiom,
% 2.97/1.56 ! [Nothing: product_unit,More: rDocum326988203on_j_k] :
% 2.97/1.56 ( ( nothin1567949605on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ More ) )
% 2.97/1.56 = Nothing ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_99_RObject_Oselect__convs_I1_J,axiom,
% 2.97/1.56 ! [Nothing: product_unit,More: product_unit] :
% 2.97/1.56 ( ( nothing_Product_unit @ ( rObjec730108904t_unit @ Nothing @ More ) )
% 2.97/1.56 = Nothing ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_100_RObject_Oequality,axiom,
% 2.97/1.56 ! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k] :
% 2.97/1.56 ( ( ( nothin1567949605on_j_k @ R )
% 2.97/1.56 = ( nothin1567949605on_j_k @ R2 ) )
% 2.97/1.56 => ( ( ( more_R1625109589on_j_k @ R )
% 2.97/1.56 = ( more_R1625109589on_j_k @ R2 ) )
% 2.97/1.56 => ( R = R2 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_101_RObject_Oequality,axiom,
% 2.97/1.56 ! [R: rObjec103300152t_unit,R2: rObjec103300152t_unit] :
% 2.97/1.56 ( ( ( nothing_Product_unit @ R )
% 2.97/1.56 = ( nothing_Product_unit @ R2 ) )
% 2.97/1.56 => ( ( ( more_Product_unit @ R )
% 2.97/1.56 = ( more_Product_unit @ R2 ) )
% 2.97/1.56 => ( R = R2 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_102_option_Osize__neq,axiom,
% 2.97/1.56 ! [X: option2026120038on_j_k] :
% 2.97/1.56 ( ( size_s1129069050on_j_k @ X )
% 2.97/1.56 != zero_zero_nat ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_103_option_Osize__neq,axiom,
% 2.97/1.56 ! [X: option_element_ptr_a] :
% 2.97/1.56 ( ( size_s1129684517_ptr_a @ X )
% 2.97/1.56 != zero_zero_nat ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_104_option_Osize__gen_I1_J,axiom,
% 2.97/1.56 ! [X: rObjec1617416918on_j_k > nat] :
% 2.97/1.56 ( ( size_o26122489on_j_k @ X @ none_R1587534007on_j_k )
% 2.97/1.56 = ( suc @ zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_105_option_Osize__gen_I1_J,axiom,
% 2.97/1.56 ! [X: element_ptr_a > nat] :
% 2.97/1.56 ( ( size_o1591053974_ptr_a @ X @ none_element_ptr_a )
% 2.97/1.56 = ( suc @ zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_106_option_Osize__gen_I1_J,axiom,
% 2.97/1.56 ! [X: sum_su1221287958on_j_k > nat] :
% 2.97/1.56 ( ( size_o1777465779on_j_k @ X @ none_S1393028981on_j_k )
% 2.97/1.56 = ( suc @ zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_107_length__code,axiom,
% 2.97/1.56 ( size_s2106487044tr_b_c
% 2.97/1.56 = ( gen_le955068453tr_b_c @ zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_108_length__code,axiom,
% 2.97/1.56 ( size_size_list_char
% 2.97/1.56 = ( gen_length_char @ zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_109_document__ptr_Osize__gen_I2_J,axiom,
% 2.97/1.56 ! [X: sum_su1576157353tr_d_e > nat,X2: sum_su1576157353tr_d_e] :
% 2.97/1.56 ( ( docume1799427087tr_d_e @ X @ ( docume1825929374tr_d_e @ X2 ) )
% 2.97/1.56 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_110_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__none,axiom,
% 2.97/1.56 ! [Obj: rObjec1413572695_j_k_l] :
% 2.97/1.56 ( ( ( cast_O1034441233_j_k_l @ Obj )
% 2.97/1.56 = none_R1587534007on_j_k )
% 2.97/1.56 = ( ~ ? [Document: rObjec1617416918on_j_k] :
% 2.97/1.56 ( ( cast_D1252964113_h_i_l @ Document )
% 2.97/1.56 = Obj ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_111_list__ex1__simps_I1_J,axiom,
% 2.97/1.56 ! [P: list_n282880152tr_b_c > $o] :
% 2.97/1.56 ~ ( list_e529904353tr_b_c @ P @ nil_li198338206tr_b_c ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_112_list__ex1__simps_I1_J,axiom,
% 2.97/1.56 ! [P: list_char > $o] :
% 2.97/1.56 ~ ( list_ex1_list_char @ P @ nil_list_char ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_113_list__ex1__simps_I1_J,axiom,
% 2.97/1.56 ! [P: char > $o] :
% 2.97/1.56 ~ ( list_ex1_char @ P @ nil_char ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_114_list__ex1__simps_I1_J,axiom,
% 2.97/1.56 ! [P: node_p1234578834tr_b_c > $o] :
% 2.97/1.56 ~ ( list_e469495899tr_b_c @ P @ nil_no279930520tr_b_c ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_115_is__document__kind__def,axiom,
% 2.97/1.56 ( is_doc1417632087_j_k_l
% 2.97/1.56 = ( ^ [Ptr: rObjec1413572695_j_k_l] :
% 2.97/1.56 ( ( cast_O1034441233_j_k_l @ Ptr )
% 2.97/1.56 != none_R1587534007on_j_k ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_116_add__right__cancel,axiom,
% 2.97/1.56 ! [B: nat,A: nat,C: nat] :
% 2.97/1.56 ( ( ( plus_plus_nat @ B @ A )
% 2.97/1.56 = ( plus_plus_nat @ C @ A ) )
% 2.97/1.56 = ( B = C ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_117_add__left__cancel,axiom,
% 2.97/1.56 ! [A: nat,B: nat,C: nat] :
% 2.97/1.56 ( ( ( plus_plus_nat @ A @ B )
% 2.97/1.56 = ( plus_plus_nat @ A @ C ) )
% 2.97/1.56 = ( B = C ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_118_zero__eq__add__iff__both__eq__0,axiom,
% 2.97/1.56 ! [X: nat,Y: nat] :
% 2.97/1.56 ( ( zero_zero_nat
% 2.97/1.56 = ( plus_plus_nat @ X @ Y ) )
% 2.97/1.56 = ( ( X = zero_zero_nat )
% 2.97/1.56 & ( Y = zero_zero_nat ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_119_add__eq__0__iff__both__eq__0,axiom,
% 2.97/1.56 ! [X: nat,Y: nat] :
% 2.97/1.56 ( ( ( plus_plus_nat @ X @ Y )
% 2.97/1.56 = zero_zero_nat )
% 2.97/1.56 = ( ( X = zero_zero_nat )
% 2.97/1.56 & ( Y = zero_zero_nat ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_120_add__cancel__right__right,axiom,
% 2.97/1.56 ! [A: nat,B: nat] :
% 2.97/1.56 ( ( A
% 2.97/1.56 = ( plus_plus_nat @ A @ B ) )
% 2.97/1.56 = ( B = zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_121_add__cancel__right__left,axiom,
% 2.97/1.56 ! [A: nat,B: nat] :
% 2.97/1.56 ( ( A
% 2.97/1.56 = ( plus_plus_nat @ B @ A ) )
% 2.97/1.56 = ( B = zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_122_add__cancel__left__right,axiom,
% 2.97/1.56 ! [A: nat,B: nat] :
% 2.97/1.56 ( ( ( plus_plus_nat @ A @ B )
% 2.97/1.56 = A )
% 2.97/1.56 = ( B = zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_123_add__cancel__left__left,axiom,
% 2.97/1.56 ! [B: nat,A: nat] :
% 2.97/1.56 ( ( ( plus_plus_nat @ B @ A )
% 2.97/1.56 = A )
% 2.97/1.56 = ( B = zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_124_add_Oright__neutral,axiom,
% 2.97/1.56 ! [A: nat] :
% 2.97/1.56 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 2.97/1.56 = A ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_125_add_Oleft__neutral,axiom,
% 2.97/1.56 ! [A: nat] :
% 2.97/1.56 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 2.97/1.56 = A ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_126_add__Suc__right,axiom,
% 2.97/1.56 ! [M2: nat,N: nat] :
% 2.97/1.56 ( ( plus_plus_nat @ M2 @ ( suc @ N ) )
% 2.97/1.56 = ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_127_Nat_Oadd__0__right,axiom,
% 2.97/1.56 ! [M2: nat] :
% 2.97/1.56 ( ( plus_plus_nat @ M2 @ zero_zero_nat )
% 2.97/1.56 = M2 ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_128_add__is__0,axiom,
% 2.97/1.56 ! [M2: nat,N: nat] :
% 2.97/1.56 ( ( ( plus_plus_nat @ M2 @ N )
% 2.97/1.56 = zero_zero_nat )
% 2.97/1.56 = ( ( M2 = zero_zero_nat )
% 2.97/1.56 & ( N = zero_zero_nat ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_129_gen__length__def,axiom,
% 2.97/1.56 ( gen_le955068453tr_b_c
% 2.97/1.56 = ( ^ [N3: nat,Xs3: list_n282880152tr_b_c] : ( plus_plus_nat @ N3 @ ( size_s2106487044tr_b_c @ Xs3 ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_130_gen__length__def,axiom,
% 2.97/1.56 ( gen_length_char
% 2.97/1.56 = ( ^ [N3: nat,Xs3: list_char] : ( plus_plus_nat @ N3 @ ( size_size_list_char @ Xs3 ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_131_add__right__imp__eq,axiom,
% 2.97/1.56 ! [B: nat,A: nat,C: nat] :
% 2.97/1.56 ( ( ( plus_plus_nat @ B @ A )
% 2.97/1.56 = ( plus_plus_nat @ C @ A ) )
% 2.97/1.56 => ( B = C ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_132_add__left__imp__eq,axiom,
% 2.97/1.56 ! [A: nat,B: nat,C: nat] :
% 2.97/1.56 ( ( ( plus_plus_nat @ A @ B )
% 2.97/1.56 = ( plus_plus_nat @ A @ C ) )
% 2.97/1.56 => ( B = C ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_133_add_Oleft__commute,axiom,
% 2.97/1.56 ! [B: nat,A: nat,C: nat] :
% 2.97/1.56 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 2.97/1.56 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_134_add_Ocommute,axiom,
% 2.97/1.56 ( plus_plus_nat
% 2.97/1.56 = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_135_add_Oassoc,axiom,
% 2.97/1.56 ! [A: nat,B: nat,C: nat] :
% 2.97/1.56 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.97/1.56 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_136_group__cancel_Oadd2,axiom,
% 2.97/1.56 ! [B3: nat,K: nat,B: nat,A: nat] :
% 2.97/1.56 ( ( B3
% 2.97/1.56 = ( plus_plus_nat @ K @ B ) )
% 2.97/1.56 => ( ( plus_plus_nat @ A @ B3 )
% 2.97/1.56 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_137_group__cancel_Oadd1,axiom,
% 2.97/1.56 ! [A2: nat,K: nat,A: nat,B: nat] :
% 2.97/1.56 ( ( A2
% 2.97/1.56 = ( plus_plus_nat @ K @ A ) )
% 2.97/1.56 => ( ( plus_plus_nat @ A2 @ B )
% 2.97/1.56 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_138_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.97/1.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.97/1.56 ( ( ( I = J )
% 2.97/1.56 & ( K = L ) )
% 2.97/1.56 => ( ( plus_plus_nat @ I @ K )
% 2.97/1.56 = ( plus_plus_nat @ J @ L ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_139_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.97/1.56 ! [A: nat,B: nat,C: nat] :
% 2.97/1.56 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.97/1.56 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_140_add_Ocomm__neutral,axiom,
% 2.97/1.56 ! [A: nat] :
% 2.97/1.56 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 2.97/1.56 = A ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_141_comm__monoid__add__class_Oadd__0,axiom,
% 2.97/1.56 ! [A: nat] :
% 2.97/1.56 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 2.97/1.56 = A ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_142_add__Suc,axiom,
% 2.97/1.56 ! [M2: nat,N: nat] :
% 2.97/1.56 ( ( plus_plus_nat @ ( suc @ M2 ) @ N )
% 2.97/1.56 = ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_143_nat__arith_Osuc1,axiom,
% 2.97/1.56 ! [A2: nat,K: nat,A: nat] :
% 2.97/1.56 ( ( A2
% 2.97/1.56 = ( plus_plus_nat @ K @ A ) )
% 2.97/1.56 => ( ( suc @ A2 )
% 2.97/1.56 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_144_add__Suc__shift,axiom,
% 2.97/1.56 ! [M2: nat,N: nat] :
% 2.97/1.56 ( ( plus_plus_nat @ ( suc @ M2 ) @ N )
% 2.97/1.56 = ( plus_plus_nat @ M2 @ ( suc @ N ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_145_add__eq__self__zero,axiom,
% 2.97/1.56 ! [M2: nat,N: nat] :
% 2.97/1.56 ( ( ( plus_plus_nat @ M2 @ N )
% 2.97/1.56 = M2 )
% 2.97/1.56 => ( N = zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_146_plus__nat_Oadd__0,axiom,
% 2.97/1.56 ! [N: nat] :
% 2.97/1.56 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 2.97/1.56 = N ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_147_one__is__add,axiom,
% 2.97/1.56 ! [M2: nat,N: nat] :
% 2.97/1.56 ( ( ( suc @ zero_zero_nat )
% 2.97/1.56 = ( plus_plus_nat @ M2 @ N ) )
% 2.97/1.56 = ( ( ( M2
% 2.97/1.56 = ( suc @ zero_zero_nat ) )
% 2.97/1.56 & ( N = zero_zero_nat ) )
% 2.97/1.56 | ( ( M2 = zero_zero_nat )
% 2.97/1.56 & ( N
% 2.97/1.56 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_148_add__is__1,axiom,
% 2.97/1.56 ! [M2: nat,N: nat] :
% 2.97/1.56 ( ( ( plus_plus_nat @ M2 @ N )
% 2.97/1.56 = ( suc @ zero_zero_nat ) )
% 2.97/1.56 = ( ( ( M2
% 2.97/1.56 = ( suc @ zero_zero_nat ) )
% 2.97/1.56 & ( N = zero_zero_nat ) )
% 2.97/1.56 | ( ( M2 = zero_zero_nat )
% 2.97/1.56 & ( N
% 2.97/1.56 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_149_gen__length__code_I1_J,axiom,
% 2.97/1.56 ! [N: nat] :
% 2.97/1.56 ( ( gen_le170886571tr_b_c @ N @ nil_li198338206tr_b_c )
% 2.97/1.56 = N ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_150_gen__length__code_I1_J,axiom,
% 2.97/1.56 ! [N: nat] :
% 2.97/1.56 ( ( gen_length_list_char @ N @ nil_list_char )
% 2.97/1.56 = N ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_151_gen__length__code_I1_J,axiom,
% 2.97/1.56 ! [N: nat] :
% 2.97/1.56 ( ( gen_length_char @ N @ nil_char )
% 2.97/1.56 = N ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_152_gen__length__code_I1_J,axiom,
% 2.97/1.56 ! [N: nat] :
% 2.97/1.56 ( ( gen_le955068453tr_b_c @ N @ nil_no279930520tr_b_c )
% 2.97/1.56 = N ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_153_Euclid__induct,axiom,
% 2.97/1.56 ! [P: nat > nat > $o,A: nat,B: nat] :
% 2.97/1.56 ( ! [A4: nat,B4: nat] :
% 2.97/1.56 ( ( P @ A4 @ B4 )
% 2.97/1.56 = ( P @ B4 @ A4 ) )
% 2.97/1.56 => ( ! [A4: nat] : ( P @ A4 @ zero_zero_nat )
% 2.97/1.56 => ( ! [A4: nat,B4: nat] :
% 2.97/1.56 ( ( P @ A4 @ B4 )
% 2.97/1.56 => ( P @ A4 @ ( plus_plus_nat @ A4 @ B4 ) ) )
% 2.97/1.56 => ( P @ A @ B ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_154_triangle__Suc,axiom,
% 2.97/1.56 ! [N: nat] :
% 2.97/1.56 ( ( nat_triangle @ ( suc @ N ) )
% 2.97/1.56 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_155_verit__sum__simplify,axiom,
% 2.97/1.56 ! [A: nat] :
% 2.97/1.56 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 2.97/1.56 = A ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_156_add__0__iff,axiom,
% 2.97/1.56 ! [B: nat,A: nat] :
% 2.97/1.56 ( ( B
% 2.97/1.56 = ( plus_plus_nat @ B @ A ) )
% 2.97/1.56 = ( A = zero_zero_nat ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_157_option_Osize__gen_I2_J,axiom,
% 2.97/1.56 ! [X: rObjec1617416918on_j_k > nat,X2: rObjec1617416918on_j_k] :
% 2.97/1.56 ( ( size_o26122489on_j_k @ X @ ( some_R67702331on_j_k @ X2 ) )
% 2.97/1.56 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_158_option_Osize__gen_I2_J,axiom,
% 2.97/1.56 ! [X: docume1935157360tr_d_e > nat,X2: docume1935157360tr_d_e] :
% 2.97/1.56 ( ( size_o1635055885tr_d_e @ X @ ( some_d1631029323tr_d_e @ X2 ) )
% 2.97/1.56 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_159_option_Osize__gen_I2_J,axiom,
% 2.97/1.56 ! [X: rObjec1413572695_j_k_l > nat,X2: rObjec1413572695_j_k_l] :
% 2.97/1.56 ( ( size_o310046708_j_k_l @ X @ ( some_R1598191922_j_k_l @ X2 ) )
% 2.97/1.56 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_160_option_Osize__gen_I2_J,axiom,
% 2.97/1.56 ! [X: sum_su1221287958on_j_k > nat,X2: sum_su1221287958on_j_k] :
% 2.97/1.56 ( ( size_o1777465779on_j_k @ X @ ( some_S1960742641on_j_k @ X2 ) )
% 2.97/1.56 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_161_option_Osize__gen_I2_J,axiom,
% 2.97/1.56 ! [X: element_ptr_a > nat,X2: element_ptr_a] :
% 2.97/1.56 ( ( size_o1591053974_ptr_a @ X @ ( some_element_ptr_a @ X2 ) )
% 2.97/1.56 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_162_option_Oinject,axiom,
% 2.97/1.56 ! [X2: sum_su1221287958on_j_k,Y2: sum_su1221287958on_j_k] :
% 2.97/1.56 ( ( ( some_S1960742641on_j_k @ X2 )
% 2.97/1.56 = ( some_S1960742641on_j_k @ Y2 ) )
% 2.97/1.56 = ( X2 = Y2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_163_option_Oinject,axiom,
% 2.97/1.56 ! [X2: element_ptr_a,Y2: element_ptr_a] :
% 2.97/1.56 ( ( ( some_element_ptr_a @ X2 )
% 2.97/1.56 = ( some_element_ptr_a @ Y2 ) )
% 2.97/1.56 = ( X2 = Y2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_164_option_Oinject,axiom,
% 2.97/1.56 ! [X2: rObjec1617416918on_j_k,Y2: rObjec1617416918on_j_k] :
% 2.97/1.56 ( ( ( some_R67702331on_j_k @ X2 )
% 2.97/1.56 = ( some_R67702331on_j_k @ Y2 ) )
% 2.97/1.56 = ( X2 = Y2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_165_option_Oinject,axiom,
% 2.97/1.56 ! [X2: docume1935157360tr_d_e,Y2: docume1935157360tr_d_e] :
% 2.97/1.56 ( ( ( some_d1631029323tr_d_e @ X2 )
% 2.97/1.56 = ( some_d1631029323tr_d_e @ Y2 ) )
% 2.97/1.56 = ( X2 = Y2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_166_option_Oinject,axiom,
% 2.97/1.56 ! [X2: rObjec1413572695_j_k_l,Y2: rObjec1413572695_j_k_l] :
% 2.97/1.56 ( ( ( some_R1598191922_j_k_l @ X2 )
% 2.97/1.56 = ( some_R1598191922_j_k_l @ Y2 ) )
% 2.97/1.56 = ( X2 = Y2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_167_not__Some__eq,axiom,
% 2.97/1.56 ! [X: option841825948on_j_k] :
% 2.97/1.56 ( ( ! [Y4: rObjec1617416918on_j_k] :
% 2.97/1.56 ( X
% 2.97/1.56 != ( some_R67702331on_j_k @ Y4 ) ) )
% 2.97/1.56 = ( X = none_R1587534007on_j_k ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_168_not__Some__eq,axiom,
% 2.97/1.56 ! [X: option1330818496tr_d_e] :
% 2.97/1.56 ( ( ! [Y4: docume1935157360tr_d_e] :
% 2.97/1.56 ( X
% 2.97/1.56 != ( some_d1631029323tr_d_e @ Y4 ) ) )
% 2.97/1.56 = ( X = none_d1458959567tr_d_e ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_169_not__Some__eq,axiom,
% 2.97/1.56 ! [X: option1749760295_j_k_l] :
% 2.97/1.56 ( ( ! [Y4: rObjec1413572695_j_k_l] :
% 2.97/1.56 ( X
% 2.97/1.56 != ( some_R1598191922_j_k_l @ Y4 ) ) )
% 2.97/1.56 = ( X = none_R1773662646_j_k_l ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_170_not__Some__eq,axiom,
% 2.97/1.56 ! [X: option_element_ptr_a] :
% 2.97/1.56 ( ( ! [Y4: element_ptr_a] :
% 2.97/1.56 ( X
% 2.97/1.56 != ( some_element_ptr_a @ Y4 ) ) )
% 2.97/1.56 = ( X = none_element_ptr_a ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_171_not__Some__eq,axiom,
% 2.97/1.56 ! [X: option2026120038on_j_k] :
% 2.97/1.56 ( ( ! [Y4: sum_su1221287958on_j_k] :
% 2.97/1.56 ( X
% 2.97/1.56 != ( some_S1960742641on_j_k @ Y4 ) ) )
% 2.97/1.56 = ( X = none_S1393028981on_j_k ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_172_not__None__eq,axiom,
% 2.97/1.56 ! [X: option841825948on_j_k] :
% 2.97/1.56 ( ( X != none_R1587534007on_j_k )
% 2.97/1.56 = ( ? [Y4: rObjec1617416918on_j_k] :
% 2.97/1.56 ( X
% 2.97/1.56 = ( some_R67702331on_j_k @ Y4 ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_173_not__None__eq,axiom,
% 2.97/1.56 ! [X: option1330818496tr_d_e] :
% 2.97/1.56 ( ( X != none_d1458959567tr_d_e )
% 2.97/1.56 = ( ? [Y4: docume1935157360tr_d_e] :
% 2.97/1.56 ( X
% 2.97/1.56 = ( some_d1631029323tr_d_e @ Y4 ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_174_not__None__eq,axiom,
% 2.97/1.56 ! [X: option1749760295_j_k_l] :
% 2.97/1.56 ( ( X != none_R1773662646_j_k_l )
% 2.97/1.56 = ( ? [Y4: rObjec1413572695_j_k_l] :
% 2.97/1.56 ( X
% 2.97/1.56 = ( some_R1598191922_j_k_l @ Y4 ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_175_not__None__eq,axiom,
% 2.97/1.56 ! [X: option_element_ptr_a] :
% 2.97/1.56 ( ( X != none_element_ptr_a )
% 2.97/1.56 = ( ? [Y4: element_ptr_a] :
% 2.97/1.56 ( X
% 2.97/1.56 = ( some_element_ptr_a @ Y4 ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_176_not__None__eq,axiom,
% 2.97/1.56 ! [X: option2026120038on_j_k] :
% 2.97/1.56 ( ( X != none_S1393028981on_j_k )
% 2.97/1.56 = ( ? [Y4: sum_su1221287958on_j_k] :
% 2.97/1.56 ( X
% 2.97/1.56 = ( some_S1960742641on_j_k @ Y4 ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_177_triangle__0,axiom,
% 2.97/1.56 ( ( nat_triangle @ zero_zero_nat )
% 2.97/1.56 = zero_zero_nat ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_178_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__inv,axiom,
% 2.97/1.56 ! [Document2: rObjec1617416918on_j_k] :
% 2.97/1.56 ( ( cast_O1034441233_j_k_l @ ( cast_D1252964113_h_i_l @ Document2 ) )
% 2.97/1.56 = ( some_R67702331on_j_k @ Document2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_179_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__some,axiom,
% 2.97/1.56 ! [Obj: rObjec1413572695_j_k_l,Document2: rObjec1617416918on_j_k] :
% 2.97/1.56 ( ( ( cast_O1034441233_j_k_l @ Obj )
% 2.97/1.56 = ( some_R67702331on_j_k @ Document2 ) )
% 2.97/1.56 = ( ( cast_D1252964113_h_i_l @ Document2 )
% 2.97/1.56 = Obj ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_180_option_Odistinct_I1_J,axiom,
% 2.97/1.56 ! [X2: rObjec1617416918on_j_k] :
% 2.97/1.56 ( none_R1587534007on_j_k
% 2.97/1.56 != ( some_R67702331on_j_k @ X2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_181_option_Odistinct_I1_J,axiom,
% 2.97/1.56 ! [X2: docume1935157360tr_d_e] :
% 2.97/1.56 ( none_d1458959567tr_d_e
% 2.97/1.56 != ( some_d1631029323tr_d_e @ X2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_182_option_Odistinct_I1_J,axiom,
% 2.97/1.56 ! [X2: rObjec1413572695_j_k_l] :
% 2.97/1.56 ( none_R1773662646_j_k_l
% 2.97/1.56 != ( some_R1598191922_j_k_l @ X2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_183_option_Odistinct_I1_J,axiom,
% 2.97/1.56 ! [X2: element_ptr_a] :
% 2.97/1.56 ( none_element_ptr_a
% 2.97/1.56 != ( some_element_ptr_a @ X2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_184_option_Odistinct_I1_J,axiom,
% 2.97/1.56 ! [X2: sum_su1221287958on_j_k] :
% 2.97/1.56 ( none_S1393028981on_j_k
% 2.97/1.56 != ( some_S1960742641on_j_k @ X2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_185_option_OdiscI,axiom,
% 2.97/1.56 ! [Option: option841825948on_j_k,X2: rObjec1617416918on_j_k] :
% 2.97/1.56 ( ( Option
% 2.97/1.56 = ( some_R67702331on_j_k @ X2 ) )
% 2.97/1.56 => ( Option != none_R1587534007on_j_k ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_186_option_OdiscI,axiom,
% 2.97/1.56 ! [Option: option1330818496tr_d_e,X2: docume1935157360tr_d_e] :
% 2.97/1.56 ( ( Option
% 2.97/1.56 = ( some_d1631029323tr_d_e @ X2 ) )
% 2.97/1.56 => ( Option != none_d1458959567tr_d_e ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_187_option_OdiscI,axiom,
% 2.97/1.56 ! [Option: option1749760295_j_k_l,X2: rObjec1413572695_j_k_l] :
% 2.97/1.56 ( ( Option
% 2.97/1.56 = ( some_R1598191922_j_k_l @ X2 ) )
% 2.97/1.56 => ( Option != none_R1773662646_j_k_l ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_188_option_OdiscI,axiom,
% 2.97/1.56 ! [Option: option_element_ptr_a,X2: element_ptr_a] :
% 2.97/1.56 ( ( Option
% 2.97/1.56 = ( some_element_ptr_a @ X2 ) )
% 2.97/1.56 => ( Option != none_element_ptr_a ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_189_option_OdiscI,axiom,
% 2.97/1.56 ! [Option: option2026120038on_j_k,X2: sum_su1221287958on_j_k] :
% 2.97/1.56 ( ( Option
% 2.97/1.56 = ( some_S1960742641on_j_k @ X2 ) )
% 2.97/1.56 => ( Option != none_S1393028981on_j_k ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_190_option_Oexhaust,axiom,
% 2.97/1.56 ! [Y: option_element_ptr_a] :
% 2.97/1.56 ( ( Y != none_element_ptr_a )
% 2.97/1.56 => ~ ! [X22: element_ptr_a] :
% 2.97/1.56 ( Y
% 2.97/1.56 != ( some_element_ptr_a @ X22 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_191_option_Oexhaust,axiom,
% 2.97/1.56 ! [Y: option2026120038on_j_k] :
% 2.97/1.56 ( ( Y != none_S1393028981on_j_k )
% 2.97/1.56 => ~ ! [X22: sum_su1221287958on_j_k] :
% 2.97/1.56 ( Y
% 2.97/1.56 != ( some_S1960742641on_j_k @ X22 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_192_option_Oinducts,axiom,
% 2.97/1.56 ! [P: option_element_ptr_a > $o,Option: option_element_ptr_a] :
% 2.97/1.56 ( ( P @ none_element_ptr_a )
% 2.97/1.56 => ( ! [X3: element_ptr_a] : ( P @ ( some_element_ptr_a @ X3 ) )
% 2.97/1.56 => ( P @ Option ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_193_option_Oinducts,axiom,
% 2.97/1.56 ! [P: option2026120038on_j_k > $o,Option: option2026120038on_j_k] :
% 2.97/1.56 ( ( P @ none_S1393028981on_j_k )
% 2.97/1.56 => ( ! [X3: sum_su1221287958on_j_k] : ( P @ ( some_S1960742641on_j_k @ X3 ) )
% 2.97/1.56 => ( P @ Option ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_194_split__option__ex,axiom,
% 2.97/1.56 ( ( ^ [P2: option_element_ptr_a > $o] :
% 2.97/1.56 ? [X5: option_element_ptr_a] : ( P2 @ X5 ) )
% 2.97/1.56 = ( ^ [P3: option_element_ptr_a > $o] :
% 2.97/1.56 ( ( P3 @ none_element_ptr_a )
% 2.97/1.56 | ? [X4: element_ptr_a] : ( P3 @ ( some_element_ptr_a @ X4 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_195_split__option__ex,axiom,
% 2.97/1.56 ( ( ^ [P2: option2026120038on_j_k > $o] :
% 2.97/1.56 ? [X5: option2026120038on_j_k] : ( P2 @ X5 ) )
% 2.97/1.56 = ( ^ [P3: option2026120038on_j_k > $o] :
% 2.97/1.56 ( ( P3 @ none_S1393028981on_j_k )
% 2.97/1.56 | ? [X4: sum_su1221287958on_j_k] : ( P3 @ ( some_S1960742641on_j_k @ X4 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_196_split__option__all,axiom,
% 2.97/1.56 ( ( ^ [P2: option_element_ptr_a > $o] :
% 2.97/1.56 ! [X5: option_element_ptr_a] : ( P2 @ X5 ) )
% 2.97/1.56 = ( ^ [P3: option_element_ptr_a > $o] :
% 2.97/1.56 ( ( P3 @ none_element_ptr_a )
% 2.97/1.56 & ! [X4: element_ptr_a] : ( P3 @ ( some_element_ptr_a @ X4 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_197_split__option__all,axiom,
% 2.97/1.56 ( ( ^ [P2: option2026120038on_j_k > $o] :
% 2.97/1.56 ! [X5: option2026120038on_j_k] : ( P2 @ X5 ) )
% 2.97/1.56 = ( ^ [P3: option2026120038on_j_k > $o] :
% 2.97/1.56 ( ( P3 @ none_S1393028981on_j_k )
% 2.97/1.56 & ! [X4: sum_su1221287958on_j_k] : ( P3 @ ( some_S1960742641on_j_k @ X4 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_198_combine__options__cases,axiom,
% 2.97/1.56 ! [X: option_element_ptr_a,P: option_element_ptr_a > option_element_ptr_a > $o,Y: option_element_ptr_a] :
% 2.97/1.56 ( ( ( X = none_element_ptr_a )
% 2.97/1.56 => ( P @ X @ Y ) )
% 2.97/1.56 => ( ( ( Y = none_element_ptr_a )
% 2.97/1.56 => ( P @ X @ Y ) )
% 2.97/1.56 => ( ! [A4: element_ptr_a,B4: element_ptr_a] :
% 2.97/1.56 ( ( X
% 2.97/1.56 = ( some_element_ptr_a @ A4 ) )
% 2.97/1.56 => ( ( Y
% 2.97/1.56 = ( some_element_ptr_a @ B4 ) )
% 2.97/1.56 => ( P @ X @ Y ) ) )
% 2.97/1.56 => ( P @ X @ Y ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_199_combine__options__cases,axiom,
% 2.97/1.56 ! [X: option_element_ptr_a,P: option_element_ptr_a > option2026120038on_j_k > $o,Y: option2026120038on_j_k] :
% 2.97/1.56 ( ( ( X = none_element_ptr_a )
% 2.97/1.56 => ( P @ X @ Y ) )
% 2.97/1.56 => ( ( ( Y = none_S1393028981on_j_k )
% 2.97/1.56 => ( P @ X @ Y ) )
% 2.97/1.56 => ( ! [A4: element_ptr_a,B4: sum_su1221287958on_j_k] :
% 2.97/1.56 ( ( X
% 2.97/1.56 = ( some_element_ptr_a @ A4 ) )
% 2.97/1.56 => ( ( Y
% 2.97/1.56 = ( some_S1960742641on_j_k @ B4 ) )
% 2.97/1.56 => ( P @ X @ Y ) ) )
% 2.97/1.56 => ( P @ X @ Y ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_200_combine__options__cases,axiom,
% 2.97/1.56 ! [X: option2026120038on_j_k,P: option2026120038on_j_k > option_element_ptr_a > $o,Y: option_element_ptr_a] :
% 2.97/1.56 ( ( ( X = none_S1393028981on_j_k )
% 2.97/1.56 => ( P @ X @ Y ) )
% 2.97/1.56 => ( ( ( Y = none_element_ptr_a )
% 2.97/1.56 => ( P @ X @ Y ) )
% 2.97/1.56 => ( ! [A4: sum_su1221287958on_j_k,B4: element_ptr_a] :
% 2.97/1.56 ( ( X
% 2.97/1.56 = ( some_S1960742641on_j_k @ A4 ) )
% 2.97/1.56 => ( ( Y
% 2.97/1.56 = ( some_element_ptr_a @ B4 ) )
% 2.97/1.56 => ( P @ X @ Y ) ) )
% 2.97/1.56 => ( P @ X @ Y ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_201_combine__options__cases,axiom,
% 2.97/1.56 ! [X: option2026120038on_j_k,P: option2026120038on_j_k > option2026120038on_j_k > $o,Y: option2026120038on_j_k] :
% 2.97/1.56 ( ( ( X = none_S1393028981on_j_k )
% 2.97/1.56 => ( P @ X @ Y ) )
% 2.97/1.56 => ( ( ( Y = none_S1393028981on_j_k )
% 2.97/1.56 => ( P @ X @ Y ) )
% 2.97/1.56 => ( ! [A4: sum_su1221287958on_j_k,B4: sum_su1221287958on_j_k] :
% 2.97/1.56 ( ( X
% 2.97/1.56 = ( some_S1960742641on_j_k @ A4 ) )
% 2.97/1.56 => ( ( Y
% 2.97/1.56 = ( some_S1960742641on_j_k @ B4 ) )
% 2.97/1.56 => ( P @ X @ Y ) ) )
% 2.97/1.56 => ( P @ X @ Y ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_202_document__ptr__casts__commute2,axiom,
% 2.97/1.56 ! [Document_ptr2: docume1935157360tr_d_e] :
% 2.97/1.56 ( ( cast_o761049241_d_e_f @ ( cast_d1608273229_b_c_f @ Document_ptr2 ) )
% 2.97/1.56 = ( some_d1631029323tr_d_e @ Document_ptr2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_203_document__ptr__casts__commute,axiom,
% 2.97/1.56 ! [Ptr2: object945351580_d_e_f,Document_ptr2: docume1935157360tr_d_e] :
% 2.97/1.56 ( ( ( cast_o761049241_d_e_f @ Ptr2 )
% 2.97/1.56 = ( some_d1631029323tr_d_e @ Document_ptr2 ) )
% 2.97/1.56 = ( ( cast_d1608273229_b_c_f @ Document_ptr2 )
% 2.97/1.56 = Ptr2 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_204_get__document__ptr__simp,axiom,
% 2.97/1.56 ! [Ptr2: object945351580_d_e_f,Document_ptr2: docume1935157360tr_d_e,Obj: rObjec1413572695_j_k_l,H: heap_S1465075775_j_k_l] :
% 2.97/1.56 ( ( ( Ptr2
% 2.97/1.56 = ( cast_d1608273229_b_c_f @ Document_ptr2 ) )
% 2.97/1.56 => ( ( get_D_1192261494_j_k_l @ Document_ptr2 @ ( put_O_834343516_j_k_l @ Ptr2 @ Obj @ H ) )
% 2.97/1.56 = ( cast_O1034441233_j_k_l @ Obj ) ) )
% 2.97/1.56 & ( ( Ptr2
% 2.97/1.56 != ( cast_d1608273229_b_c_f @ Document_ptr2 ) )
% 2.97/1.56 => ( ( get_D_1192261494_j_k_l @ Document_ptr2 @ ( put_O_834343516_j_k_l @ Ptr2 @ Obj @ H ) )
% 2.97/1.56 = ( get_D_1192261494_j_k_l @ Document_ptr2 @ H ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_205_split__Nil__iff,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_char] :
% 2.97/1.56 ( ( ( splice_char @ Xs @ Ys )
% 2.97/1.56 = nil_char )
% 2.97/1.56 = ( ( Xs = nil_char )
% 2.97/1.56 & ( Ys = nil_char ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_206_split__Nil__iff,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( splice1294941035tr_b_c @ Xs @ Ys )
% 2.97/1.56 = nil_no279930520tr_b_c )
% 2.97/1.56 = ( ( Xs = nil_no279930520tr_b_c )
% 2.97/1.56 & ( Ys = nil_no279930520tr_b_c ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_207_splice__Nil2,axiom,
% 2.97/1.56 ! [Xs: list_char] :
% 2.97/1.56 ( ( splice_char @ Xs @ nil_char )
% 2.97/1.56 = Xs ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_208_splice__Nil2,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( splice1294941035tr_b_c @ Xs @ nil_no279930520tr_b_c )
% 2.97/1.56 = Xs ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_209_splice_Osimps_I1_J,axiom,
% 2.97/1.56 ! [Ys: list_char] :
% 2.97/1.56 ( ( splice_char @ nil_char @ Ys )
% 2.97/1.56 = Ys ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_210_splice_Osimps_I1_J,axiom,
% 2.97/1.56 ! [Ys: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( splice1294941035tr_b_c @ nil_no279930520tr_b_c @ Ys )
% 2.97/1.56 = Ys ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_211_get__object__ptr__simp1,axiom,
% 2.97/1.56 ! [Object_ptr: object945351580_d_e_f,Object: rObjec1413572695_j_k_l,H: heap_S1465075775_j_k_l] :
% 2.97/1.56 ( ( get_O_623850005_j_k_l @ Object_ptr @ ( put_O_834343516_j_k_l @ Object_ptr @ Object @ H ) )
% 2.97/1.56 = ( some_R1598191922_j_k_l @ Object ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_212_count__list_Osimps_I1_J,axiom,
% 2.97/1.56 ! [Y: char] :
% 2.97/1.56 ( ( count_list_char @ nil_char @ Y )
% 2.97/1.56 = zero_zero_nat ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_213_count__list_Osimps_I1_J,axiom,
% 2.97/1.56 ! [Y: node_p1234578834tr_b_c] :
% 2.97/1.56 ( ( count_2128515342tr_b_c @ nil_no279930520tr_b_c @ Y )
% 2.97/1.56 = zero_zero_nat ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_214_get__object__ptr__simp2,axiom,
% 2.97/1.56 ! [Object_ptr: object945351580_d_e_f,Object_ptr2: object945351580_d_e_f,Object: rObjec1413572695_j_k_l,H: heap_S1465075775_j_k_l] :
% 2.97/1.56 ( ( Object_ptr != Object_ptr2 )
% 2.97/1.56 => ( ( get_O_623850005_j_k_l @ Object_ptr @ ( put_O_834343516_j_k_l @ Object_ptr2 @ Object @ H ) )
% 2.97/1.56 = ( get_O_623850005_j_k_l @ Object_ptr @ H ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_215_transpose_Ocases,axiom,
% 2.97/1.56 ! [X: list_list_char] :
% 2.97/1.56 ( ( X != nil_list_char )
% 2.97/1.56 => ( ! [Xss: list_list_char] :
% 2.97/1.56 ( X
% 2.97/1.56 != ( cons_list_char @ nil_char @ Xss ) )
% 2.97/1.56 => ~ ! [X3: char,Xs2: list_char,Xss: list_list_char] :
% 2.97/1.56 ( X
% 2.97/1.56 != ( cons_list_char @ ( cons_char @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_216_transpose_Ocases,axiom,
% 2.97/1.56 ! [X: list_l118626078tr_b_c] :
% 2.97/1.56 ( ( X != nil_li198338206tr_b_c )
% 2.97/1.56 => ( ! [Xss: list_l118626078tr_b_c] :
% 2.97/1.56 ( X
% 2.97/1.56 != ( cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ Xss ) )
% 2.97/1.56 => ~ ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Xss: list_l118626078tr_b_c] :
% 2.97/1.56 ( X
% 2.97/1.56 != ( cons_l1809994318tr_b_c @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_217_list_Odistinct_I1_J,axiom,
% 2.97/1.56 ! [X21: char,X222: list_char] :
% 2.97/1.56 ( nil_char
% 2.97/1.56 != ( cons_char @ X21 @ X222 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_218_list_Odistinct_I1_J,axiom,
% 2.97/1.56 ! [X21: node_p1234578834tr_b_c,X222: list_n282880152tr_b_c] :
% 2.97/1.56 ( nil_no279930520tr_b_c
% 2.97/1.56 != ( cons_n413985352tr_b_c @ X21 @ X222 ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_219_list_OdiscI,axiom,
% 2.97/1.56 ! [List: list_char,X21: char,X222: list_char] :
% 2.97/1.56 ( ( List
% 2.97/1.56 = ( cons_char @ X21 @ X222 ) )
% 2.97/1.56 => ( List != nil_char ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_220_list_OdiscI,axiom,
% 2.97/1.56 ! [List: list_n282880152tr_b_c,X21: node_p1234578834tr_b_c,X222: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( List
% 2.97/1.56 = ( cons_n413985352tr_b_c @ X21 @ X222 ) )
% 2.97/1.56 => ( List != nil_no279930520tr_b_c ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_221_list_Oexhaust,axiom,
% 2.97/1.56 ! [Y: list_char] :
% 2.97/1.56 ( ( Y != nil_char )
% 2.97/1.56 => ~ ! [X212: char,X223: list_char] :
% 2.97/1.56 ( Y
% 2.97/1.56 != ( cons_char @ X212 @ X223 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_222_list_Oexhaust,axiom,
% 2.97/1.56 ! [Y: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( Y != nil_no279930520tr_b_c )
% 2.97/1.56 => ~ ! [X212: node_p1234578834tr_b_c,X223: list_n282880152tr_b_c] :
% 2.97/1.56 ( Y
% 2.97/1.56 != ( cons_n413985352tr_b_c @ X212 @ X223 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_223_list_Oinducts,axiom,
% 2.97/1.56 ! [P: list_char > $o,List: list_char] :
% 2.97/1.56 ( ( P @ nil_char )
% 2.97/1.56 => ( ! [X12: char,X22: list_char] :
% 2.97/1.56 ( ( P @ X22 )
% 2.97/1.56 => ( P @ ( cons_char @ X12 @ X22 ) ) )
% 2.97/1.56 => ( P @ List ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_224_list_Oinducts,axiom,
% 2.97/1.56 ! [P: list_n282880152tr_b_c > $o,List: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( P @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X12: node_p1234578834tr_b_c,X22: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( P @ X22 )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X12 @ X22 ) ) )
% 2.97/1.56 => ( P @ List ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_225_neq__Nil__conv,axiom,
% 2.97/1.56 ! [Xs: list_char] :
% 2.97/1.56 ( ( Xs != nil_char )
% 2.97/1.56 = ( ? [Y4: char,Ys2: list_char] :
% 2.97/1.56 ( Xs
% 2.97/1.56 = ( cons_char @ Y4 @ Ys2 ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_226_neq__Nil__conv,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( Xs != nil_no279930520tr_b_c )
% 2.97/1.56 = ( ? [Y4: node_p1234578834tr_b_c,Ys2: list_n282880152tr_b_c] :
% 2.97/1.56 ( Xs
% 2.97/1.56 = ( cons_n413985352tr_b_c @ Y4 @ Ys2 ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_227_list__induct2_H,axiom,
% 2.97/1.56 ! [P: list_char > list_char > $o,Xs: list_char,Ys: list_char] :
% 2.97/1.56 ( ( P @ nil_char @ nil_char )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char] : ( P @ ( cons_char @ X3 @ Xs2 ) @ nil_char )
% 2.97/1.56 => ( ! [Y3: char,Ys3: list_char] : ( P @ nil_char @ ( cons_char @ Y3 @ Ys3 ) )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char] :
% 2.97/1.56 ( ( P @ Xs2 @ Ys3 )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_228_list__induct2_H,axiom,
% 2.97/1.56 ! [P: list_char > list_n282880152tr_b_c > $o,Xs: list_char,Ys: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( P @ nil_char @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char] : ( P @ ( cons_char @ X3 @ Xs2 ) @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] : ( P @ nil_char @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( P @ Xs2 @ Ys3 )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_229_list__induct2_H,axiom,
% 2.97/1.56 ! [P: list_n282880152tr_b_c > list_char > $o,Xs: list_n282880152tr_b_c,Ys: list_char] :
% 2.97/1.56 ( ( P @ nil_no279930520tr_b_c @ nil_char )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ nil_char )
% 2.97/1.56 => ( ! [Y3: char,Ys3: list_char] : ( P @ nil_no279930520tr_b_c @ ( cons_char @ Y3 @ Ys3 ) )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char] :
% 2.97/1.56 ( ( P @ Xs2 @ Ys3 )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_230_list__induct2_H,axiom,
% 2.97/1.56 ! [P: list_n282880152tr_b_c > list_n282880152tr_b_c > $o,Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( P @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] : ( P @ nil_no279930520tr_b_c @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( P @ Xs2 @ Ys3 )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_231_splice_Oinduct,axiom,
% 2.97/1.56 ! [P: list_char > list_char > $o,A0: list_char,A1: list_char] :
% 2.97/1.56 ( ! [X_12: list_char] : ( P @ nil_char @ X_12 )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Ys3: list_char] :
% 2.97/1.56 ( ( P @ Ys3 @ Xs2 )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ Ys3 ) )
% 2.97/1.56 => ( P @ A0 @ A1 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_232_splice_Oinduct,axiom,
% 2.97/1.56 ! [P: list_n282880152tr_b_c > list_n282880152tr_b_c > $o,A0: list_n282880152tr_b_c,A1: list_n282880152tr_b_c] :
% 2.97/1.56 ( ! [X_12: list_n282880152tr_b_c] : ( P @ nil_no279930520tr_b_c @ X_12 )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Ys3: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( P @ Ys3 @ Xs2 )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ Ys3 ) )
% 2.97/1.56 => ( P @ A0 @ A1 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_233_induct__list012,axiom,
% 2.97/1.56 ! [P: list_char > $o,Xs: list_char] :
% 2.97/1.56 ( ( P @ nil_char )
% 2.97/1.56 => ( ! [X3: char] : ( P @ ( cons_char @ X3 @ nil_char ) )
% 2.97/1.56 => ( ! [X3: char,Y3: char,Zs: list_char] :
% 2.97/1.56 ( ( P @ Zs )
% 2.97/1.56 => ( ( P @ ( cons_char @ Y3 @ Zs ) )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ ( cons_char @ Y3 @ Zs ) ) ) ) )
% 2.97/1.56 => ( P @ Xs ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_234_induct__list012,axiom,
% 2.97/1.56 ! [P: list_n282880152tr_b_c > $o,Xs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( P @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Y3: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( P @ Zs )
% 2.97/1.56 => ( ( P @ ( cons_n413985352tr_b_c @ Y3 @ Zs ) )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ ( cons_n413985352tr_b_c @ Y3 @ Zs ) ) ) ) )
% 2.97/1.56 => ( P @ Xs ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_235_shuffles_Oinduct,axiom,
% 2.97/1.56 ! [P: list_char > list_char > $o,A0: list_char,A1: list_char] :
% 2.97/1.56 ( ! [X_12: list_char] : ( P @ nil_char @ X_12 )
% 2.97/1.56 => ( ! [Xs2: list_char] : ( P @ Xs2 @ nil_char )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char] :
% 2.97/1.56 ( ( P @ Xs2 @ ( cons_char @ Y3 @ Ys3 ) )
% 2.97/1.56 => ( ( P @ ( cons_char @ X3 @ Xs2 ) @ Ys3 )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) ) ) )
% 2.97/1.56 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_236_shuffles_Oinduct,axiom,
% 2.97/1.56 ! [P: list_n282880152tr_b_c > list_n282880152tr_b_c > $o,A0: list_n282880152tr_b_c,A1: list_n282880152tr_b_c] :
% 2.97/1.56 ( ! [X_12: list_n282880152tr_b_c] : ( P @ nil_no279930520tr_b_c @ X_12 )
% 2.97/1.56 => ( ! [Xs2: list_n282880152tr_b_c] : ( P @ Xs2 @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( P @ Xs2 @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) )
% 2.97/1.56 => ( ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ Ys3 )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) ) ) )
% 2.97/1.56 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_237_remdups__adj_Ocases,axiom,
% 2.97/1.56 ! [X: list_char] :
% 2.97/1.56 ( ( X != nil_char )
% 2.97/1.56 => ( ! [X3: char] :
% 2.97/1.56 ( X
% 2.97/1.56 != ( cons_char @ X3 @ nil_char ) )
% 2.97/1.56 => ~ ! [X3: char,Y3: char,Xs2: list_char] :
% 2.97/1.56 ( X
% 2.97/1.56 != ( cons_char @ X3 @ ( cons_char @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_238_remdups__adj_Ocases,axiom,
% 2.97/1.56 ! [X: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( X != nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c] :
% 2.97/1.56 ( X
% 2.97/1.56 != ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
% 2.97/1.56 => ~ ! [X3: node_p1234578834tr_b_c,Y3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
% 2.97/1.56 ( X
% 2.97/1.56 != ( cons_n413985352tr_b_c @ X3 @ ( cons_n413985352tr_b_c @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_239_sorted__wrt_Oinduct,axiom,
% 2.97/1.56 ! [P: ( char > char > $o ) > list_char > $o,A0: char > char > $o,A1: list_char] :
% 2.97/1.56 ( ! [P4: char > char > $o] : ( P @ P4 @ nil_char )
% 2.97/1.56 => ( ! [P4: char > char > $o,X3: char,Ys3: list_char] :
% 2.97/1.56 ( ( P @ P4 @ Ys3 )
% 2.97/1.56 => ( P @ P4 @ ( cons_char @ X3 @ Ys3 ) ) )
% 2.97/1.56 => ( P @ A0 @ A1 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_240_sorted__wrt_Oinduct,axiom,
% 2.97/1.56 ! [P: ( node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o ) > list_n282880152tr_b_c > $o,A0: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o,A1: list_n282880152tr_b_c] :
% 2.97/1.56 ( ! [P4: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o] : ( P @ P4 @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [P4: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o,X3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( P @ P4 @ Ys3 )
% 2.97/1.56 => ( P @ P4 @ ( cons_n413985352tr_b_c @ X3 @ Ys3 ) ) )
% 2.97/1.56 => ( P @ A0 @ A1 ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_241_remdups__adj_Oinduct,axiom,
% 2.97/1.56 ! [P: list_char > $o,A0: list_char] :
% 2.97/1.56 ( ( P @ nil_char )
% 2.97/1.56 => ( ! [X3: char] : ( P @ ( cons_char @ X3 @ nil_char ) )
% 2.97/1.56 => ( ! [X3: char,Y3: char,Xs2: list_char] :
% 2.97/1.56 ( ( ( X3 = Y3 )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) ) )
% 2.97/1.56 => ( ( ( X3 != Y3 )
% 2.97/1.56 => ( P @ ( cons_char @ Y3 @ Xs2 ) ) )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ ( cons_char @ Y3 @ Xs2 ) ) ) ) )
% 2.97/1.56 => ( P @ A0 ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_242_remdups__adj_Oinduct,axiom,
% 2.97/1.56 ! [P: list_n282880152tr_b_c > $o,A0: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( P @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Y3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( X3 = Y3 )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) ) )
% 2.97/1.56 => ( ( ( X3 != Y3 )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ Y3 @ Xs2 ) ) )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ ( cons_n413985352tr_b_c @ Y3 @ Xs2 ) ) ) ) )
% 2.97/1.56 => ( P @ A0 ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_243_successively_Oinduct,axiom,
% 2.97/1.56 ! [P: ( char > char > $o ) > list_char > $o,A0: char > char > $o,A1: list_char] :
% 2.97/1.56 ( ! [P4: char > char > $o] : ( P @ P4 @ nil_char )
% 2.97/1.56 => ( ! [P4: char > char > $o,X3: char] : ( P @ P4 @ ( cons_char @ X3 @ nil_char ) )
% 2.97/1.56 => ( ! [P4: char > char > $o,X3: char,Y3: char,Xs2: list_char] :
% 2.97/1.56 ( ( P @ P4 @ ( cons_char @ Y3 @ Xs2 ) )
% 2.97/1.56 => ( P @ P4 @ ( cons_char @ X3 @ ( cons_char @ Y3 @ Xs2 ) ) ) )
% 2.97/1.56 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_244_successively_Oinduct,axiom,
% 2.97/1.56 ! [P: ( node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o ) > list_n282880152tr_b_c > $o,A0: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o,A1: list_n282880152tr_b_c] :
% 2.97/1.56 ( ! [P4: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o] : ( P @ P4 @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [P4: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o,X3: node_p1234578834tr_b_c] : ( P @ P4 @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
% 2.97/1.56 => ( ! [P4: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o,X3: node_p1234578834tr_b_c,Y3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( P @ P4 @ ( cons_n413985352tr_b_c @ Y3 @ Xs2 ) )
% 2.97/1.56 => ( P @ P4 @ ( cons_n413985352tr_b_c @ X3 @ ( cons_n413985352tr_b_c @ Y3 @ Xs2 ) ) ) )
% 2.97/1.56 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_245_list__nonempty__induct,axiom,
% 2.97/1.56 ! [Xs: list_char,P: list_char > $o] :
% 2.97/1.56 ( ( Xs != nil_char )
% 2.97/1.56 => ( ! [X3: char] : ( P @ ( cons_char @ X3 @ nil_char ) )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char] :
% 2.97/1.56 ( ( Xs2 != nil_char )
% 2.97/1.56 => ( ( P @ Xs2 )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) ) ) )
% 2.97/1.56 => ( P @ Xs ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_246_list__nonempty__induct,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,P: list_n282880152tr_b_c > $o] :
% 2.97/1.56 ( ( Xs != nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( Xs2 != nil_no279930520tr_b_c )
% 2.97/1.56 => ( ( P @ Xs2 )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) ) ) )
% 2.97/1.56 => ( P @ Xs ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_247_list__induct4,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_char,Zs2: list_char,Ws: list_char,P: list_char > list_char > list_char > list_char > $o] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs )
% 2.97/1.56 = ( size_size_list_char @ Ys ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys )
% 2.97/1.56 = ( size_size_list_char @ Zs2 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Zs2 )
% 2.97/1.56 = ( size_size_list_char @ Ws ) )
% 2.97/1.56 => ( ( P @ nil_char @ nil_char @ nil_char @ nil_char )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: char,Zs: list_char,W: char,Ws2: list_char] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs2 )
% 2.97/1.56 = ( size_size_list_char @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys3 )
% 2.97/1.56 = ( size_size_list_char @ Zs ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Zs )
% 2.97/1.56 = ( size_size_list_char @ Ws2 ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_248_list__induct4,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_char,Zs2: list_char,Ws: list_n282880152tr_b_c,P: list_char > list_char > list_char > list_n282880152tr_b_c > $o] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs )
% 2.97/1.56 = ( size_size_list_char @ Ys ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys )
% 2.97/1.56 = ( size_size_list_char @ Zs2 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Zs2 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ws ) )
% 2.97/1.56 => ( ( P @ nil_char @ nil_char @ nil_char @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: char,Zs: list_char,W: node_p1234578834tr_b_c,Ws2: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs2 )
% 2.97/1.56 = ( size_size_list_char @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys3 )
% 2.97/1.56 = ( size_size_list_char @ Zs ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Zs )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ws2 ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_n413985352tr_b_c @ W @ Ws2 ) ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_249_list__induct4,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_char,Zs2: list_n282880152tr_b_c,Ws: list_char,P: list_char > list_char > list_n282880152tr_b_c > list_char > $o] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs )
% 2.97/1.56 = ( size_size_list_char @ Ys ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Zs2 )
% 2.97/1.56 = ( size_size_list_char @ Ws ) )
% 2.97/1.56 => ( ( P @ nil_char @ nil_char @ nil_no279930520tr_b_c @ nil_char )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c,W: char,Ws2: list_char] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs2 )
% 2.97/1.56 = ( size_size_list_char @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys3 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Zs )
% 2.97/1.56 = ( size_size_list_char @ Ws2 ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_250_list__induct4,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_n282880152tr_b_c,Zs2: list_char,Ws: list_char,P: list_char > list_n282880152tr_b_c > list_char > list_char > $o] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Ys )
% 2.97/1.56 = ( size_size_list_char @ Zs2 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Zs2 )
% 2.97/1.56 = ( size_size_list_char @ Ws ) )
% 2.97/1.56 => ( ( P @ nil_char @ nil_no279930520tr_b_c @ nil_char @ nil_char )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: char,Zs: list_char,W: char,Ws2: list_char] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs2 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Ys3 )
% 2.97/1.56 = ( size_size_list_char @ Zs ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Zs )
% 2.97/1.56 = ( size_size_list_char @ Ws2 ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_251_list__induct4,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_char,Zs2: list_char,Ws: list_char,P: list_n282880152tr_b_c > list_char > list_char > list_char > $o] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs )
% 2.97/1.56 = ( size_size_list_char @ Ys ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys )
% 2.97/1.56 = ( size_size_list_char @ Zs2 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Zs2 )
% 2.97/1.56 = ( size_size_list_char @ Ws ) )
% 2.97/1.56 => ( ( P @ nil_no279930520tr_b_c @ nil_char @ nil_char @ nil_char )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char,Z: char,Zs: list_char,W: char,Ws2: list_char] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 2.97/1.56 = ( size_size_list_char @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys3 )
% 2.97/1.56 = ( size_size_list_char @ Zs ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Zs )
% 2.97/1.56 = ( size_size_list_char @ Ws2 ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_252_list__induct4,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_char,Zs2: list_n282880152tr_b_c,Ws: list_n282880152tr_b_c,P: list_char > list_char > list_n282880152tr_b_c > list_n282880152tr_b_c > $o] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs )
% 2.97/1.56 = ( size_size_list_char @ Ys ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Zs2 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ws ) )
% 2.97/1.56 => ( ( P @ nil_char @ nil_char @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c,W: node_p1234578834tr_b_c,Ws2: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs2 )
% 2.97/1.56 = ( size_size_list_char @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys3 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Zs )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ws2 ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) @ ( cons_n413985352tr_b_c @ W @ Ws2 ) ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_253_list__induct4,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_n282880152tr_b_c,Zs2: list_char,Ws: list_n282880152tr_b_c,P: list_char > list_n282880152tr_b_c > list_char > list_n282880152tr_b_c > $o] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Ys )
% 2.97/1.56 = ( size_size_list_char @ Zs2 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Zs2 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ws ) )
% 2.97/1.56 => ( ( P @ nil_char @ nil_no279930520tr_b_c @ nil_char @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: char,Zs: list_char,W: node_p1234578834tr_b_c,Ws2: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs2 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Ys3 )
% 2.97/1.56 = ( size_size_list_char @ Zs ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Zs )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ws2 ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_n413985352tr_b_c @ W @ Ws2 ) ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_254_list__induct4,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_n282880152tr_b_c,Zs2: list_n282880152tr_b_c,Ws: list_char,P: list_char > list_n282880152tr_b_c > list_n282880152tr_b_c > list_char > $o] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Ys )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Zs2 )
% 2.97/1.56 = ( size_size_list_char @ Ws ) )
% 2.97/1.56 => ( ( P @ nil_char @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c @ nil_char )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c,W: char,Ws2: list_char] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs2 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Ys3 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Zs )
% 2.97/1.56 = ( size_size_list_char @ Ws2 ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_255_list__induct4,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_char,Zs2: list_char,Ws: list_n282880152tr_b_c,P: list_n282880152tr_b_c > list_char > list_char > list_n282880152tr_b_c > $o] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs )
% 2.97/1.56 = ( size_size_list_char @ Ys ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys )
% 2.97/1.56 = ( size_size_list_char @ Zs2 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Zs2 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ws ) )
% 2.97/1.56 => ( ( P @ nil_no279930520tr_b_c @ nil_char @ nil_char @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char,Z: char,Zs: list_char,W: node_p1234578834tr_b_c,Ws2: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 2.97/1.56 = ( size_size_list_char @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys3 )
% 2.97/1.56 = ( size_size_list_char @ Zs ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Zs )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ws2 ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_n413985352tr_b_c @ W @ Ws2 ) ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_256_list__induct4,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_char,Zs2: list_n282880152tr_b_c,Ws: list_char,P: list_n282880152tr_b_c > list_char > list_n282880152tr_b_c > list_char > $o] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs )
% 2.97/1.56 = ( size_size_list_char @ Ys ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Zs2 )
% 2.97/1.56 = ( size_size_list_char @ Ws ) )
% 2.97/1.56 => ( ( P @ nil_no279930520tr_b_c @ nil_char @ nil_no279930520tr_b_c @ nil_char )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c,W: char,Ws2: list_char] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 2.97/1.56 = ( size_size_list_char @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys3 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Zs )
% 2.97/1.56 = ( size_size_list_char @ Ws2 ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_257_list__induct3,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_char,Zs2: list_char,P: list_char > list_char > list_char > $o] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs )
% 2.97/1.56 = ( size_size_list_char @ Ys ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys )
% 2.97/1.56 = ( size_size_list_char @ Zs2 ) )
% 2.97/1.56 => ( ( P @ nil_char @ nil_char @ nil_char )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: char,Zs: list_char] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs2 )
% 2.97/1.56 = ( size_size_list_char @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys3 )
% 2.97/1.56 = ( size_size_list_char @ Zs ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_258_list__induct3,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_char,Zs2: list_n282880152tr_b_c,P: list_char > list_char > list_n282880152tr_b_c > $o] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs )
% 2.97/1.56 = ( size_size_list_char @ Ys ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 2.97/1.56 => ( ( P @ nil_char @ nil_char @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs2 )
% 2.97/1.56 = ( size_size_list_char @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys3 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_259_list__induct3,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_n282880152tr_b_c,Zs2: list_char,P: list_char > list_n282880152tr_b_c > list_char > $o] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Ys )
% 2.97/1.56 = ( size_size_list_char @ Zs2 ) )
% 2.97/1.56 => ( ( P @ nil_char @ nil_no279930520tr_b_c @ nil_char )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: char,Zs: list_char] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs2 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Ys3 )
% 2.97/1.56 = ( size_size_list_char @ Zs ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_260_list__induct3,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_n282880152tr_b_c,Zs2: list_n282880152tr_b_c,P: list_char > list_n282880152tr_b_c > list_n282880152tr_b_c > $o] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Ys )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 2.97/1.56 => ( ( P @ nil_char @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs2 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Ys3 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_261_list__induct3,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_char,Zs2: list_char,P: list_n282880152tr_b_c > list_char > list_char > $o] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs )
% 2.97/1.56 = ( size_size_list_char @ Ys ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys )
% 2.97/1.56 = ( size_size_list_char @ Zs2 ) )
% 2.97/1.56 => ( ( P @ nil_no279930520tr_b_c @ nil_char @ nil_char )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char,Z: char,Zs: list_char] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 2.97/1.56 = ( size_size_list_char @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys3 )
% 2.97/1.56 = ( size_size_list_char @ Zs ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_262_list__induct3,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_char,Zs2: list_n282880152tr_b_c,P: list_n282880152tr_b_c > list_char > list_n282880152tr_b_c > $o] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs )
% 2.97/1.56 = ( size_size_list_char @ Ys ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 2.97/1.56 => ( ( P @ nil_no279930520tr_b_c @ nil_char @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 2.97/1.56 = ( size_size_list_char @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_size_list_char @ Ys3 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_263_list__induct3,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c,Zs2: list_char,P: list_n282880152tr_b_c > list_n282880152tr_b_c > list_char > $o] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Ys )
% 2.97/1.56 = ( size_size_list_char @ Zs2 ) )
% 2.97/1.56 => ( ( P @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c @ nil_char )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: char,Zs: list_char] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Ys3 )
% 2.97/1.56 = ( size_size_list_char @ Zs ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_264_list__induct3,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c,Zs2: list_n282880152tr_b_c,P: list_n282880152tr_b_c > list_n282880152tr_b_c > list_n282880152tr_b_c > $o] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Ys )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs2 ) )
% 2.97/1.56 => ( ( P @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 2.97/1.56 => ( ( ( size_s2106487044tr_b_c @ Ys3 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Zs ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_265_list__induct2,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_char,P: list_char > list_char > $o] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs )
% 2.97/1.56 = ( size_size_list_char @ Ys ) )
% 2.97/1.56 => ( ( P @ nil_char @ nil_char )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs2 )
% 2.97/1.56 = ( size_size_list_char @ Ys3 ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_266_list__induct2,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_n282880152tr_b_c,P: list_char > list_n282880152tr_b_c > $o] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys ) )
% 2.97/1.56 => ( ( P @ nil_char @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( size_size_list_char @ Xs2 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 )
% 2.97/1.56 => ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_267_list__induct2,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_char,P: list_n282880152tr_b_c > list_char > $o] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs )
% 2.97/1.56 = ( size_size_list_char @ Ys ) )
% 2.97/1.56 => ( ( P @ nil_no279930520tr_b_c @ nil_char )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 2.97/1.56 = ( size_size_list_char @ Ys3 ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_268_list__induct2,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c,P: list_n282880152tr_b_c > list_n282880152tr_b_c > $o] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys ) )
% 2.97/1.56 => ( ( P @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( size_s2106487044tr_b_c @ Xs2 )
% 2.97/1.56 = ( size_s2106487044tr_b_c @ Ys3 ) )
% 2.97/1.56 => ( ( P @ Xs2 @ Ys3 )
% 2.97/1.56 => ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) ) ) )
% 2.97/1.56 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_269_splice_Oelims,axiom,
% 2.97/1.56 ! [X: list_char,Xa: list_char,Y: list_char] :
% 2.97/1.56 ( ( ( splice_char @ X @ Xa )
% 2.97/1.56 = Y )
% 2.97/1.56 => ( ( ( X = nil_char )
% 2.97/1.56 => ( Y != Xa ) )
% 2.97/1.56 => ~ ! [X3: char,Xs2: list_char] :
% 2.97/1.56 ( ( X
% 2.97/1.56 = ( cons_char @ X3 @ Xs2 ) )
% 2.97/1.56 => ( Y
% 2.97/1.56 != ( cons_char @ X3 @ ( splice_char @ Xa @ Xs2 ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_270_splice_Oelims,axiom,
% 2.97/1.56 ! [X: list_n282880152tr_b_c,Xa: list_n282880152tr_b_c,Y: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( splice1294941035tr_b_c @ X @ Xa )
% 2.97/1.56 = Y )
% 2.97/1.56 => ( ( ( X = nil_no279930520tr_b_c )
% 2.97/1.56 => ( Y != Xa ) )
% 2.97/1.56 => ~ ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( X
% 2.97/1.56 = ( cons_n413985352tr_b_c @ X3 @ Xs2 ) )
% 2.97/1.56 => ( Y
% 2.97/1.56 != ( cons_n413985352tr_b_c @ X3 @ ( splice1294941035tr_b_c @ Xa @ Xs2 ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_271_get__object__ptr__simp,axiom,
% 2.97/1.56 ! [Ptr2: object945351580_d_e_f,Object_ptr: object945351580_d_e_f,Obj: rObjec1413572695_j_k_l,H: heap_S1465075775_j_k_l] :
% 2.97/1.56 ( ( ( Ptr2 = Object_ptr )
% 2.97/1.56 => ( ( get_O_623850005_j_k_l @ Object_ptr @ ( put_O_834343516_j_k_l @ Ptr2 @ Obj @ H ) )
% 2.97/1.56 = ( some_R1598191922_j_k_l @ Obj ) ) )
% 2.97/1.56 & ( ( Ptr2 != Object_ptr )
% 2.97/1.56 => ( ( get_O_623850005_j_k_l @ Object_ptr @ ( put_O_834343516_j_k_l @ Ptr2 @ Obj @ H ) )
% 2.97/1.56 = ( get_O_623850005_j_k_l @ Object_ptr @ H ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_272_n__lists__Nil,axiom,
% 2.97/1.56 ! [N: nat] :
% 2.97/1.56 ( ( ( N = zero_zero_nat )
% 2.97/1.56 => ( ( n_lists_char @ N @ nil_char )
% 2.97/1.56 = ( cons_list_char @ nil_char @ nil_list_char ) ) )
% 2.97/1.56 & ( ( N != zero_zero_nat )
% 2.97/1.56 => ( ( n_lists_char @ N @ nil_char )
% 2.97/1.56 = nil_list_char ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_273_n__lists__Nil,axiom,
% 2.97/1.56 ! [N: nat] :
% 2.97/1.56 ( ( ( N = zero_zero_nat )
% 2.97/1.56 => ( ( n_list1807568544tr_b_c @ N @ nil_no279930520tr_b_c )
% 2.97/1.56 = ( cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c ) ) )
% 2.97/1.56 & ( ( N != zero_zero_nat )
% 2.97/1.56 => ( ( n_list1807568544tr_b_c @ N @ nil_no279930520tr_b_c )
% 2.97/1.56 = nil_li198338206tr_b_c ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_274_n__lists_Osimps_I1_J,axiom,
% 2.97/1.56 ! [Xs: list_char] :
% 2.97/1.56 ( ( n_lists_char @ zero_zero_nat @ Xs )
% 2.97/1.56 = ( cons_list_char @ nil_char @ nil_list_char ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_275_n__lists_Osimps_I1_J,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( n_list1807568544tr_b_c @ zero_zero_nat @ Xs )
% 2.97/1.56 = ( cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_276_product__lists_Osimps_I1_J,axiom,
% 2.97/1.56 ( ( product_lists_char @ nil_list_char )
% 2.97/1.56 = ( cons_list_char @ nil_char @ nil_list_char ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_277_product__lists_Osimps_I1_J,axiom,
% 2.97/1.56 ( ( produc1509350401tr_b_c @ nil_li198338206tr_b_c )
% 2.97/1.56 = ( cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_278_subseqs_Osimps_I1_J,axiom,
% 2.97/1.56 ( ( subseqs_char @ nil_char )
% 2.97/1.56 = ( cons_list_char @ nil_char @ nil_list_char ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_279_subseqs_Osimps_I1_J,axiom,
% 2.97/1.56 ( ( subseq1828679783tr_b_c @ nil_no279930520tr_b_c )
% 2.97/1.56 = ( cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_280_insert__Nil,axiom,
% 2.97/1.56 ! [X: char] :
% 2.97/1.56 ( ( insert_char @ X @ nil_char )
% 2.97/1.56 = ( cons_char @ X @ nil_char ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_281_insert__Nil,axiom,
% 2.97/1.56 ! [X: node_p1234578834tr_b_c] :
% 2.97/1.56 ( ( insert678865070tr_b_c @ X @ nil_no279930520tr_b_c )
% 2.97/1.56 = ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_282_nths__singleton,axiom,
% 2.97/1.56 ! [A2: set_nat,X: char] :
% 2.97/1.56 ( ( ( member_nat @ zero_zero_nat @ A2 )
% 2.97/1.56 => ( ( nths_char @ ( cons_char @ X @ nil_char ) @ A2 )
% 2.97/1.56 = ( cons_char @ X @ nil_char ) ) )
% 2.97/1.56 & ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 2.97/1.56 => ( ( nths_char @ ( cons_char @ X @ nil_char ) @ A2 )
% 2.97/1.56 = nil_char ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_283_nths__singleton,axiom,
% 2.97/1.56 ! [A2: set_nat,X: node_p1234578834tr_b_c] :
% 2.97/1.56 ( ( ( member_nat @ zero_zero_nat @ A2 )
% 2.97/1.56 => ( ( nths_n1256675478tr_b_c @ ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) @ A2 )
% 2.97/1.56 = ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) ) )
% 2.97/1.56 & ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 2.97/1.56 => ( ( nths_n1256675478tr_b_c @ ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) @ A2 )
% 2.97/1.56 = nil_no279930520tr_b_c ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_284_nths__nil,axiom,
% 2.97/1.56 ! [A2: set_nat] :
% 2.97/1.56 ( ( nths_char @ nil_char @ A2 )
% 2.97/1.56 = nil_char ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_285_nths__nil,axiom,
% 2.97/1.56 ! [A2: set_nat] :
% 2.97/1.56 ( ( nths_n1256675478tr_b_c @ nil_no279930520tr_b_c @ A2 )
% 2.97/1.56 = nil_no279930520tr_b_c ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_286_nths__empty,axiom,
% 2.97/1.56 ! [Xs: list_char] :
% 2.97/1.56 ( ( nths_char @ Xs @ bot_bot_set_nat )
% 2.97/1.56 = nil_char ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_287_nths__empty,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( nths_n1256675478tr_b_c @ Xs @ bot_bot_set_nat )
% 2.97/1.56 = nil_no279930520tr_b_c ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_288_bind__split__asm,axiom,
% 2.97/1.56 ! [P: option_element_ptr_a > $o,M2: option_element_ptr_a,F: element_ptr_a > option_element_ptr_a] :
% 2.97/1.56 ( ( P @ ( bind_e22036734_ptr_a @ M2 @ F ) )
% 2.97/1.56 = ( ~ ( ( ( M2 = none_element_ptr_a )
% 2.97/1.56 & ~ ( P @ none_element_ptr_a ) )
% 2.97/1.56 | ? [X4: element_ptr_a] :
% 2.97/1.56 ( ( M2
% 2.97/1.56 = ( some_element_ptr_a @ X4 ) )
% 2.97/1.56 & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_289_bind__split__asm,axiom,
% 2.97/1.56 ! [P: option2026120038on_j_k > $o,M2: option_element_ptr_a,F: element_ptr_a > option2026120038on_j_k] :
% 2.97/1.56 ( ( P @ ( bind_e1012152651on_j_k @ M2 @ F ) )
% 2.97/1.56 = ( ~ ( ( ( M2 = none_element_ptr_a )
% 2.97/1.56 & ~ ( P @ none_S1393028981on_j_k ) )
% 2.97/1.56 | ? [X4: element_ptr_a] :
% 2.97/1.56 ( ( M2
% 2.97/1.56 = ( some_element_ptr_a @ X4 ) )
% 2.97/1.56 & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_290_bind__split__asm,axiom,
% 2.97/1.56 ! [P: option_element_ptr_a > $o,M2: option2026120038on_j_k,F: sum_su1221287958on_j_k > option_element_ptr_a] :
% 2.97/1.56 ( ( P @ ( bind_S287509021_ptr_a @ M2 @ F ) )
% 2.97/1.56 = ( ~ ( ( ( M2 = none_S1393028981on_j_k )
% 2.97/1.56 & ~ ( P @ none_element_ptr_a ) )
% 2.97/1.56 | ? [X4: sum_su1221287958on_j_k] :
% 2.97/1.56 ( ( M2
% 2.97/1.56 = ( some_S1960742641on_j_k @ X4 ) )
% 2.97/1.56 & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_291_bind__split__asm,axiom,
% 2.97/1.56 ! [P: option2026120038on_j_k > $o,M2: option2026120038on_j_k,F: sum_su1221287958on_j_k > option2026120038on_j_k] :
% 2.97/1.56 ( ( P @ ( bind_S607117548on_j_k @ M2 @ F ) )
% 2.97/1.56 = ( ~ ( ( ( M2 = none_S1393028981on_j_k )
% 2.97/1.56 & ~ ( P @ none_S1393028981on_j_k ) )
% 2.97/1.56 | ? [X4: sum_su1221287958on_j_k] :
% 2.97/1.56 ( ( M2
% 2.97/1.56 = ( some_S1960742641on_j_k @ X4 ) )
% 2.97/1.56 & ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_292_bind__split,axiom,
% 2.97/1.56 ! [P: option_element_ptr_a > $o,M2: option_element_ptr_a,F: element_ptr_a > option_element_ptr_a] :
% 2.97/1.56 ( ( P @ ( bind_e22036734_ptr_a @ M2 @ F ) )
% 2.97/1.56 = ( ( ( M2 = none_element_ptr_a )
% 2.97/1.56 => ( P @ none_element_ptr_a ) )
% 2.97/1.56 & ! [V3: element_ptr_a] :
% 2.97/1.56 ( ( M2
% 2.97/1.56 = ( some_element_ptr_a @ V3 ) )
% 2.97/1.56 => ( P @ ( F @ V3 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_293_bind__split,axiom,
% 2.97/1.56 ! [P: option2026120038on_j_k > $o,M2: option_element_ptr_a,F: element_ptr_a > option2026120038on_j_k] :
% 2.97/1.56 ( ( P @ ( bind_e1012152651on_j_k @ M2 @ F ) )
% 2.97/1.56 = ( ( ( M2 = none_element_ptr_a )
% 2.97/1.56 => ( P @ none_S1393028981on_j_k ) )
% 2.97/1.56 & ! [V3: element_ptr_a] :
% 2.97/1.56 ( ( M2
% 2.97/1.56 = ( some_element_ptr_a @ V3 ) )
% 2.97/1.56 => ( P @ ( F @ V3 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_294_bind__split,axiom,
% 2.97/1.56 ! [P: option_element_ptr_a > $o,M2: option2026120038on_j_k,F: sum_su1221287958on_j_k > option_element_ptr_a] :
% 2.97/1.56 ( ( P @ ( bind_S287509021_ptr_a @ M2 @ F ) )
% 2.97/1.56 = ( ( ( M2 = none_S1393028981on_j_k )
% 2.97/1.56 => ( P @ none_element_ptr_a ) )
% 2.97/1.56 & ! [V3: sum_su1221287958on_j_k] :
% 2.97/1.56 ( ( M2
% 2.97/1.56 = ( some_S1960742641on_j_k @ V3 ) )
% 2.97/1.56 => ( P @ ( F @ V3 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_295_bind__split,axiom,
% 2.97/1.56 ! [P: option2026120038on_j_k > $o,M2: option2026120038on_j_k,F: sum_su1221287958on_j_k > option2026120038on_j_k] :
% 2.97/1.56 ( ( P @ ( bind_S607117548on_j_k @ M2 @ F ) )
% 2.97/1.56 = ( ( ( M2 = none_S1393028981on_j_k )
% 2.97/1.56 => ( P @ none_S1393028981on_j_k ) )
% 2.97/1.56 & ! [V3: sum_su1221287958on_j_k] :
% 2.97/1.56 ( ( M2
% 2.97/1.56 = ( some_S1960742641on_j_k @ V3 ) )
% 2.97/1.56 => ( P @ ( F @ V3 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_296_bind_Obind__lzero,axiom,
% 2.97/1.56 ! [F: element_ptr_a > option_element_ptr_a] :
% 2.97/1.56 ( ( bind_e22036734_ptr_a @ none_element_ptr_a @ F )
% 2.97/1.56 = none_element_ptr_a ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_297_bind_Obind__lzero,axiom,
% 2.97/1.56 ! [F: element_ptr_a > option2026120038on_j_k] :
% 2.97/1.56 ( ( bind_e1012152651on_j_k @ none_element_ptr_a @ F )
% 2.97/1.56 = none_S1393028981on_j_k ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_298_bind_Obind__lzero,axiom,
% 2.97/1.56 ! [F: sum_su1221287958on_j_k > option_element_ptr_a] :
% 2.97/1.56 ( ( bind_S287509021_ptr_a @ none_S1393028981on_j_k @ F )
% 2.97/1.56 = none_element_ptr_a ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_299_bind_Obind__lzero,axiom,
% 2.97/1.56 ! [F: sum_su1221287958on_j_k > option2026120038on_j_k] :
% 2.97/1.56 ( ( bind_S607117548on_j_k @ none_S1393028981on_j_k @ F )
% 2.97/1.56 = none_S1393028981on_j_k ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_300_set__encode__empty,axiom,
% 2.97/1.56 ( ( nat_set_encode @ bot_bot_set_nat )
% 2.97/1.56 = zero_zero_nat ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_301_set__decode__zero,axiom,
% 2.97/1.56 ( ( nat_set_decode @ zero_zero_nat )
% 2.97/1.56 = bot_bot_set_nat ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_302_length__append__singleton,axiom,
% 2.97/1.56 ! [Xs: list_char,X: char] :
% 2.97/1.56 ( ( size_size_list_char @ ( append_char @ Xs @ ( cons_char @ X @ nil_char ) ) )
% 2.97/1.56 = ( suc @ ( size_size_list_char @ Xs ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_303_length__append__singleton,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,X: node_p1234578834tr_b_c] :
% 2.97/1.56 ( ( size_s2106487044tr_b_c @ ( append846395565tr_b_c @ Xs @ ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) ) )
% 2.97/1.56 = ( suc @ ( size_s2106487044tr_b_c @ Xs ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_304_append__Nil2,axiom,
% 2.97/1.56 ! [Xs: list_char] :
% 2.97/1.56 ( ( append_char @ Xs @ nil_char )
% 2.97/1.56 = Xs ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_305_append__Nil2,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( append846395565tr_b_c @ Xs @ nil_no279930520tr_b_c )
% 2.97/1.56 = Xs ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_306_append__self__conv,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_char] :
% 2.97/1.56 ( ( ( append_char @ Xs @ Ys )
% 2.97/1.56 = Xs )
% 2.97/1.56 = ( Ys = nil_char ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_307_append__self__conv,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( append846395565tr_b_c @ Xs @ Ys )
% 2.97/1.56 = Xs )
% 2.97/1.56 = ( Ys = nil_no279930520tr_b_c ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_308_self__append__conv,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_char] :
% 2.97/1.56 ( ( Xs
% 2.97/1.56 = ( append_char @ Xs @ Ys ) )
% 2.97/1.56 = ( Ys = nil_char ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_309_self__append__conv,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( Xs
% 2.97/1.56 = ( append846395565tr_b_c @ Xs @ Ys ) )
% 2.97/1.56 = ( Ys = nil_no279930520tr_b_c ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_310_append__self__conv2,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_char] :
% 2.97/1.56 ( ( ( append_char @ Xs @ Ys )
% 2.97/1.56 = Ys )
% 2.97/1.56 = ( Xs = nil_char ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_311_append__self__conv2,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( append846395565tr_b_c @ Xs @ Ys )
% 2.97/1.56 = Ys )
% 2.97/1.56 = ( Xs = nil_no279930520tr_b_c ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_312_self__append__conv2,axiom,
% 2.97/1.56 ! [Ys: list_char,Xs: list_char] :
% 2.97/1.56 ( ( Ys
% 2.97/1.56 = ( append_char @ Xs @ Ys ) )
% 2.97/1.56 = ( Xs = nil_char ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_313_self__append__conv2,axiom,
% 2.97/1.56 ! [Ys: list_n282880152tr_b_c,Xs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( Ys
% 2.97/1.56 = ( append846395565tr_b_c @ Xs @ Ys ) )
% 2.97/1.56 = ( Xs = nil_no279930520tr_b_c ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_314_Nil__is__append__conv,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_char] :
% 2.97/1.56 ( ( nil_char
% 2.97/1.56 = ( append_char @ Xs @ Ys ) )
% 2.97/1.56 = ( ( Xs = nil_char )
% 2.97/1.56 & ( Ys = nil_char ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_315_Nil__is__append__conv,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( nil_no279930520tr_b_c
% 2.97/1.56 = ( append846395565tr_b_c @ Xs @ Ys ) )
% 2.97/1.56 = ( ( Xs = nil_no279930520tr_b_c )
% 2.97/1.56 & ( Ys = nil_no279930520tr_b_c ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_316_append__is__Nil__conv,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_char] :
% 2.97/1.56 ( ( ( append_char @ Xs @ Ys )
% 2.97/1.56 = nil_char )
% 2.97/1.56 = ( ( Xs = nil_char )
% 2.97/1.56 & ( Ys = nil_char ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_317_append__is__Nil__conv,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( append846395565tr_b_c @ Xs @ Ys )
% 2.97/1.56 = nil_no279930520tr_b_c )
% 2.97/1.56 = ( ( Xs = nil_no279930520tr_b_c )
% 2.97/1.56 & ( Ys = nil_no279930520tr_b_c ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_318_append_Oright__neutral,axiom,
% 2.97/1.56 ! [A: list_char] :
% 2.97/1.56 ( ( append_char @ A @ nil_char )
% 2.97/1.56 = A ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_319_append_Oright__neutral,axiom,
% 2.97/1.56 ! [A: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( append846395565tr_b_c @ A @ nil_no279930520tr_b_c )
% 2.97/1.56 = A ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_320_set__decode__inverse,axiom,
% 2.97/1.56 ! [N: nat] :
% 2.97/1.56 ( ( nat_set_encode @ ( nat_set_decode @ N ) )
% 2.97/1.56 = N ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_321_append1__eq__conv,axiom,
% 2.97/1.56 ! [Xs: list_char,X: char,Ys: list_char,Y: char] :
% 2.97/1.56 ( ( ( append_char @ Xs @ ( cons_char @ X @ nil_char ) )
% 2.97/1.56 = ( append_char @ Ys @ ( cons_char @ Y @ nil_char ) ) )
% 2.97/1.56 = ( ( Xs = Ys )
% 2.97/1.56 & ( X = Y ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_322_append1__eq__conv,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,X: node_p1234578834tr_b_c,Ys: list_n282880152tr_b_c,Y: node_p1234578834tr_b_c] :
% 2.97/1.56 ( ( ( append846395565tr_b_c @ Xs @ ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) )
% 2.97/1.56 = ( append846395565tr_b_c @ Ys @ ( cons_n413985352tr_b_c @ Y @ nil_no279930520tr_b_c ) ) )
% 2.97/1.56 = ( ( Xs = Ys )
% 2.97/1.56 & ( X = Y ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_323_rev__induct,axiom,
% 2.97/1.56 ! [P: list_char > $o,Xs: list_char] :
% 2.97/1.56 ( ( P @ nil_char )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char] :
% 2.97/1.56 ( ( P @ Xs2 )
% 2.97/1.56 => ( P @ ( append_char @ Xs2 @ ( cons_char @ X3 @ nil_char ) ) ) )
% 2.97/1.56 => ( P @ Xs ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_324_rev__induct,axiom,
% 2.97/1.56 ! [P: list_n282880152tr_b_c > $o,Xs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( P @ nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( P @ Xs2 )
% 2.97/1.56 => ( P @ ( append846395565tr_b_c @ Xs2 @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) ) ) )
% 2.97/1.56 => ( P @ Xs ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_325_rev__exhaust,axiom,
% 2.97/1.56 ! [Xs: list_char] :
% 2.97/1.56 ( ( Xs != nil_char )
% 2.97/1.56 => ~ ! [Ys3: list_char,Y3: char] :
% 2.97/1.56 ( Xs
% 2.97/1.56 != ( append_char @ Ys3 @ ( cons_char @ Y3 @ nil_char ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_326_rev__exhaust,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( Xs != nil_no279930520tr_b_c )
% 2.97/1.56 => ~ ! [Ys3: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c] :
% 2.97/1.56 ( Xs
% 2.97/1.56 != ( append846395565tr_b_c @ Ys3 @ ( cons_n413985352tr_b_c @ Y3 @ nil_no279930520tr_b_c ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_327_Cons__eq__append__conv,axiom,
% 2.97/1.56 ! [X: char,Xs: list_char,Ys: list_char,Zs2: list_char] :
% 2.97/1.56 ( ( ( cons_char @ X @ Xs )
% 2.97/1.56 = ( append_char @ Ys @ Zs2 ) )
% 2.97/1.56 = ( ( ( Ys = nil_char )
% 2.97/1.56 & ( ( cons_char @ X @ Xs )
% 2.97/1.56 = Zs2 ) )
% 2.97/1.56 | ? [Ys4: list_char] :
% 2.97/1.56 ( ( ( cons_char @ X @ Ys4 )
% 2.97/1.56 = Ys )
% 2.97/1.56 & ( Xs
% 2.97/1.56 = ( append_char @ Ys4 @ Zs2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_328_Cons__eq__append__conv,axiom,
% 2.97/1.56 ! [X: node_p1234578834tr_b_c,Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c,Zs2: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( cons_n413985352tr_b_c @ X @ Xs )
% 2.97/1.56 = ( append846395565tr_b_c @ Ys @ Zs2 ) )
% 2.97/1.56 = ( ( ( Ys = nil_no279930520tr_b_c )
% 2.97/1.56 & ( ( cons_n413985352tr_b_c @ X @ Xs )
% 2.97/1.56 = Zs2 ) )
% 2.97/1.56 | ? [Ys4: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( cons_n413985352tr_b_c @ X @ Ys4 )
% 2.97/1.56 = Ys )
% 2.97/1.56 & ( Xs
% 2.97/1.56 = ( append846395565tr_b_c @ Ys4 @ Zs2 ) ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_329_append__eq__Cons__conv,axiom,
% 2.97/1.56 ! [Ys: list_char,Zs2: list_char,X: char,Xs: list_char] :
% 2.97/1.56 ( ( ( append_char @ Ys @ Zs2 )
% 2.97/1.56 = ( cons_char @ X @ Xs ) )
% 2.97/1.56 = ( ( ( Ys = nil_char )
% 2.97/1.56 & ( Zs2
% 2.97/1.56 = ( cons_char @ X @ Xs ) ) )
% 2.97/1.56 | ? [Ys4: list_char] :
% 2.97/1.56 ( ( Ys
% 2.97/1.56 = ( cons_char @ X @ Ys4 ) )
% 2.97/1.56 & ( ( append_char @ Ys4 @ Zs2 )
% 2.97/1.56 = Xs ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_330_append__eq__Cons__conv,axiom,
% 2.97/1.56 ! [Ys: list_n282880152tr_b_c,Zs2: list_n282880152tr_b_c,X: node_p1234578834tr_b_c,Xs: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( ( append846395565tr_b_c @ Ys @ Zs2 )
% 2.97/1.56 = ( cons_n413985352tr_b_c @ X @ Xs ) )
% 2.97/1.56 = ( ( ( Ys = nil_no279930520tr_b_c )
% 2.97/1.56 & ( Zs2
% 2.97/1.56 = ( cons_n413985352tr_b_c @ X @ Xs ) ) )
% 2.97/1.56 | ? [Ys4: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( Ys
% 2.97/1.56 = ( cons_n413985352tr_b_c @ X @ Ys4 ) )
% 2.97/1.56 & ( ( append846395565tr_b_c @ Ys4 @ Zs2 )
% 2.97/1.56 = Xs ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_331_rev__nonempty__induct,axiom,
% 2.97/1.56 ! [Xs: list_char,P: list_char > $o] :
% 2.97/1.56 ( ( Xs != nil_char )
% 2.97/1.56 => ( ! [X3: char] : ( P @ ( cons_char @ X3 @ nil_char ) )
% 2.97/1.56 => ( ! [X3: char,Xs2: list_char] :
% 2.97/1.56 ( ( Xs2 != nil_char )
% 2.97/1.56 => ( ( P @ Xs2 )
% 2.97/1.56 => ( P @ ( append_char @ Xs2 @ ( cons_char @ X3 @ nil_char ) ) ) ) )
% 2.97/1.56 => ( P @ Xs ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_332_rev__nonempty__induct,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,P: list_n282880152tr_b_c > $o] :
% 2.97/1.56 ( ( Xs != nil_no279930520tr_b_c )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
% 2.97/1.56 => ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( Xs2 != nil_no279930520tr_b_c )
% 2.97/1.56 => ( ( P @ Xs2 )
% 2.97/1.56 => ( P @ ( append846395565tr_b_c @ Xs2 @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) ) ) ) )
% 2.97/1.56 => ( P @ Xs ) ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_333_eq__Nil__appendI,axiom,
% 2.97/1.56 ! [Xs: list_char,Ys: list_char] :
% 2.97/1.56 ( ( Xs = Ys )
% 2.97/1.56 => ( Xs
% 2.97/1.56 = ( append_char @ nil_char @ Ys ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_334_eq__Nil__appendI,axiom,
% 2.97/1.56 ! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( Xs = Ys )
% 2.97/1.56 => ( Xs
% 2.97/1.56 = ( append846395565tr_b_c @ nil_no279930520tr_b_c @ Ys ) ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_335_append__Nil,axiom,
% 2.97/1.56 ! [Ys: list_char] :
% 2.97/1.56 ( ( append_char @ nil_char @ Ys )
% 2.97/1.56 = Ys ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_336_append__Nil,axiom,
% 2.97/1.56 ! [Ys: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( append846395565tr_b_c @ nil_no279930520tr_b_c @ Ys )
% 2.97/1.56 = Ys ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_337_append_Oleft__neutral,axiom,
% 2.97/1.56 ! [A: list_char] :
% 2.97/1.56 ( ( append_char @ nil_char @ A )
% 2.97/1.56 = A ) ).
% 2.97/1.56
% 2.97/1.56 thf(fact_338_append_Oleft__neutral,axiom,
% 2.97/1.56 ! [A: list_n282880152tr_b_c] :
% 2.97/1.56 ( ( append846395565tr_b_c @ nil_no279930520tr_b_c @ A )
% 2.97/1.56 = A ) ).
% 2.97/1.56
% 2.97/1.56 thf(conj_0,hypothesis,
% 2.97/1.56 ( ( docume1070804385_j_k_l @ h )
% 2.97/1.56 = bot_bo1111241908tr_d_e ) ).
% 2.97/1.56
% 2.97/1.56 thf(conj_1,hypothesis,
% 2.97/1.56 ( h2
% 2.97/1.56 = ( put_O_834343516_j_k_l @ ( cast_d1608273229_b_c_f @ ( docume1511108976tr_d_e @ ( suc @ zero_zero_nat ) ) ) @ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ) @ h ) ) ).
% 2.97/1.56
% 2.97/1.56 thf(conj_2,hypothesis,
% 2.97/1.56 type_w92696601_j_k_l @ h ).
% 2.97/1.56
% 2.97/1.56 thf(conj_3,conjecture,
% 2.97/1.56 is_doc1417632087_j_k_l @ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ) ).
% 2.97/1.56 ------------------------
% 3.03/1.60 % (7082)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6811 for (2999ds/183Mi)
% 3.03/1.60 % (7083)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_6811 for (2999ds/4Mi)
% 3.03/1.60 % (7087)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_6811 for (2999ds/275Mi)
% 3.03/1.60 % (7083)Instruction limit reached!
% 3.03/1.60 % (7083)------------------------------
% 3.03/1.60 % (7083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.60 % (7083)Termination reason: Unknown
% 3.03/1.60 % (7083)Termination phase: shuffling
% 3.03/1.60
% 3.03/1.60 % (7083)Memory used [KB]: 1663
% 3.03/1.60 % (7083)Time elapsed: 0.004 s
% 3.03/1.60 % (7083)Instructions burned: 7 (million)
% 3.03/1.60 % (7083)------------------------------
% 3.03/1.60 % (7083)------------------------------
% 3.03/1.61 % (7084)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_6811 for (2999ds/27Mi)
% 3.03/1.61 % (7085)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6811 for (2999ds/2Mi)
% 3.03/1.61 % (7086)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_6811 for (2999ds/2Mi)
% 3.03/1.61 % (7088)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6811 for (2999ds/18Mi)
% 3.03/1.61 % (7085)Instruction limit reached!
% 3.03/1.61 % (7085)------------------------------
% 3.03/1.61 % (7085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.61 % (7085)Termination reason: Unknown
% 3.03/1.61 % (7085)Termination phase: shuffling
% 3.03/1.61
% 3.03/1.61 % (7085)Memory used [KB]: 1535
% 3.03/1.61 % (7085)Time elapsed: 0.004 s
% 3.03/1.61 % (7085)Instructions burned: 2 (million)
% 3.03/1.61 % (7085)------------------------------
% 3.03/1.61 % (7085)------------------------------
% 3.03/1.61 % (7086)Instruction limit reached!
% 3.03/1.61 % (7086)------------------------------
% 3.03/1.61 % (7086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.61 % (7086)Termination reason: Unknown
% 3.03/1.61 % (7086)Termination phase: shuffling
% 3.03/1.61
% 3.03/1.61 % (7086)Memory used [KB]: 1535
% 3.03/1.61 % (7086)Time elapsed: 0.004 s
% 3.03/1.61 % (7086)Instructions burned: 2 (million)
% 3.03/1.61 % (7086)------------------------------
% 3.03/1.61 % (7086)------------------------------
% 3.03/1.61 % (7089)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6811 for (2999ds/3Mi)
% 3.03/1.61 % (7089)Instruction limit reached!
% 3.03/1.61 % (7089)------------------------------
% 3.03/1.61 % (7089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.61 % (7089)Termination reason: Unknown
% 3.03/1.61 % (7089)Termination phase: shuffling
% 3.03/1.61
% 3.03/1.61 % (7089)Memory used [KB]: 1535
% 3.03/1.61 % (7089)Time elapsed: 0.003 s
% 3.03/1.61 % (7089)Instructions burned: 6 (million)
% 3.03/1.61 % (7089)------------------------------
% 3.03/1.61 % (7089)------------------------------
% 3.03/1.62 % (7087)Refutation not found, incomplete strategy
% 3.03/1.62 % (7087)------------------------------
% 3.03/1.62 % (7087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.62 % (7087)Termination reason: Refutation not found, incomplete strategy
% 3.03/1.62
% 3.03/1.62
% 3.03/1.62 % (7087)Memory used [KB]: 6524
% 3.03/1.62 % (7087)Time elapsed: 0.017 s
% 3.03/1.62 % (7087)Instructions burned: 47 (million)
% 3.03/1.62 % (7087)------------------------------
% 3.03/1.62 % (7087)------------------------------
% 3.03/1.62 % (7088)Instruction limit reached!
% 3.03/1.62 % (7088)------------------------------
% 3.03/1.62 % (7088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.62 % (7088)Termination reason: Unknown
% 3.03/1.62 % (7088)Termination phase: shuffling
% 3.03/1.62
% 3.03/1.62 % (7088)Memory used [KB]: 1918
% 3.03/1.62 % (7088)Time elapsed: 0.013 s
% 3.03/1.62 % (7088)Instructions burned: 18 (million)
% 3.03/1.62 % (7088)------------------------------
% 3.03/1.62 % (7088)------------------------------
% 3.03/1.62 % (7092)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_6811 for (2999ds/3Mi)
% 3.03/1.62 % (7092)Instruction limit reached!
% 3.03/1.62 % (7092)------------------------------
% 3.03/1.62 % (7092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.62 % (7092)Termination reason: Unknown
% 3.03/1.62 % (7092)Termination phase: shuffling
% 3.03/1.62
% 3.03/1.62 % (7092)Memory used [KB]: 1535
% 3.03/1.62 % (7092)Time elapsed: 0.002 s
% 3.03/1.62 % (7092)Instructions burned: 3 (million)
% 3.03/1.62 % (7092)------------------------------
% 3.03/1.62 % (7092)------------------------------
% 3.03/1.62 % (7084)Instruction limit reached!
% 3.03/1.62 % (7084)------------------------------
% 3.03/1.62 % (7084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.62 % (7084)Termination reason: Unknown
% 3.03/1.62 % (7084)Termination phase: Property scanning
% 3.03/1.62
% 3.03/1.62 % (7084)Memory used [KB]: 1918
% 3.03/1.62 % (7084)Time elapsed: 0.019 s
% 3.03/1.62 % (7084)Instructions burned: 29 (million)
% 3.03/1.62 % (7084)------------------------------
% 3.03/1.62 % (7084)------------------------------
% 3.03/1.63 % (7090)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_6811 for (2999ds/37Mi)
% 3.03/1.63 % (7091)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_6811 for (2999ds/15Mi)
% 3.03/1.63 % (7093)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_6811 for (2999ds/1041Mi)
% 3.03/1.63 % (7095)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6811 for (2999ds/16Mi)
% 3.03/1.64 % (7094)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6811 for (2999ds/7Mi)
% 3.03/1.64 % (7091)Instruction limit reached!
% 3.03/1.64 % (7091)------------------------------
% 3.03/1.64 % (7091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.64 % (7091)Termination reason: Unknown
% 3.03/1.64 % (7091)Termination phase: shuffling
% 3.03/1.64
% 3.03/1.64 % (7091)Memory used [KB]: 1918
% 3.03/1.64 % (7091)Time elapsed: 0.012 s
% 3.03/1.64 % (7091)Instructions burned: 16 (million)
% 3.03/1.64 % (7091)------------------------------
% 3.03/1.64 % (7091)------------------------------
% 3.03/1.64 % (7095)Instruction limit reached!
% 3.03/1.64 % (7095)------------------------------
% 3.03/1.64 % (7095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.64 % (7095)Termination reason: Unknown
% 3.03/1.64 % (7095)Termination phase: shuffling
% 3.03/1.64
% 3.03/1.64 % (7095)Memory used [KB]: 1791
% 3.03/1.64 % (7095)Time elapsed: 0.007 s
% 3.03/1.64 % (7095)Instructions burned: 19 (million)
% 3.03/1.64 % (7095)------------------------------
% 3.03/1.64 % (7095)------------------------------
% 3.03/1.64 % (7094)Instruction limit reached!
% 3.03/1.64 % (7094)------------------------------
% 3.03/1.64 % (7094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.64 % (7094)Termination reason: Unknown
% 3.03/1.64 % (7094)Termination phase: shuffling
% 3.03/1.64
% 3.03/1.64 % (7094)Memory used [KB]: 1535
% 3.03/1.64 % (7094)Time elapsed: 0.005 s
% 3.03/1.64 % (7094)Instructions burned: 7 (million)
% 3.03/1.64 % (7094)------------------------------
% 3.03/1.64 % (7094)------------------------------
% 3.03/1.64 % (7096)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_6811 for (2999ds/3Mi)
% 3.03/1.64 % (7096)Instruction limit reached!
% 3.03/1.64 % (7096)------------------------------
% 3.03/1.64 % (7096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.64 % (7096)Termination reason: Unknown
% 3.03/1.64 % (7096)Termination phase: shuffling
% 3.03/1.64
% 3.03/1.64 % (7096)Memory used [KB]: 1535
% 3.03/1.64 % (7096)Time elapsed: 0.004 s
% 3.03/1.64 % (7096)Instructions burned: 4 (million)
% 3.03/1.64 % (7096)------------------------------
% 3.03/1.64 % (7096)------------------------------
% 3.03/1.64 % (7090)Instruction limit reached!
% 3.03/1.64 % (7090)------------------------------
% 3.03/1.64 % (7090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.64 % (7090)Termination reason: Unknown
% 3.03/1.64 % (7090)Termination phase: shuffling
% 3.03/1.64
% 3.03/1.64 % (7090)Memory used [KB]: 2302
% 3.03/1.64 % (7090)Time elapsed: 0.021 s
% 3.03/1.64 % (7090)Instructions burned: 37 (million)
% 3.03/1.64 % (7090)------------------------------
% 3.03/1.64 % (7090)------------------------------
% 3.03/1.65 % (7098)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_6811 for (2999ds/7Mi)
% 3.03/1.65 % (7099)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_6811 for (2999ds/3Mi)
% 3.03/1.65 % (7098)Instruction limit reached!
% 3.03/1.65 % (7098)------------------------------
% 3.03/1.65 % (7098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.65 % (7098)Termination reason: Unknown
% 3.03/1.65 % (7098)Termination phase: shuffling
% 3.03/1.65
% 3.03/1.65 % (7098)Memory used [KB]: 1663
% 3.03/1.65 % (7098)Time elapsed: 0.004 s
% 3.03/1.65 % (7098)Instructions burned: 9 (million)
% 3.03/1.65 % (7098)------------------------------
% 3.03/1.65 % (7098)------------------------------
% 3.03/1.65 % (7082)Instruction limit reached!
% 3.03/1.65 % (7082)------------------------------
% 3.03/1.65 % (7082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.65 % (7082)Termination reason: Unknown
% 3.03/1.65 % (7082)Termination phase: Saturation
% 3.03/1.65
% 3.03/1.65 % (7082)Memory used [KB]: 7675
% 3.03/1.65 % (7082)Time elapsed: 0.054 s
% 3.03/1.65 % (7082)Instructions burned: 183 (million)
% 3.03/1.65 % (7082)------------------------------
% 3.03/1.65 % (7082)------------------------------
% 3.03/1.65 % (7099)Instruction limit reached!
% 3.03/1.65 % (7099)------------------------------
% 3.03/1.65 % (7099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.65 % (7099)Termination reason: Unknown
% 3.03/1.65 % (7099)Termination phase: shuffling
% 3.03/1.65
% 3.03/1.65 % (7099)Memory used [KB]: 1663
% 3.03/1.65 % (7099)Time elapsed: 0.003 s
% 3.03/1.65 % (7099)Instructions burned: 5 (million)
% 3.03/1.65 % (7099)------------------------------
% 3.03/1.65 % (7099)------------------------------
% 3.03/1.65 % (7097)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_6811 for (2999ds/3Mi)
% 3.03/1.66 % (7097)Instruction limit reached!
% 3.03/1.66 % (7097)------------------------------
% 3.03/1.66 % (7097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.66 % (7097)Termination reason: Unknown
% 3.03/1.66 % (7097)Termination phase: shuffling
% 3.03/1.66
% 3.03/1.66 % (7097)Memory used [KB]: 1535
% 3.03/1.66 % (7097)Time elapsed: 0.004 s
% 3.03/1.66 % (7097)Instructions burned: 3 (million)
% 3.03/1.66 % (7097)------------------------------
% 3.03/1.66 % (7097)------------------------------
% 3.03/1.66 % (7100)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_6811 for (2999ds/4Mi)
% 3.03/1.66 % (7102)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_6811 for (2999ds/710Mi)
% 3.03/1.66 % (7100)Instruction limit reached!
% 3.03/1.66 % (7100)------------------------------
% 3.03/1.66 % (7100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.66 % (7100)Termination reason: Unknown
% 3.03/1.66 % (7100)Termination phase: shuffling
% 3.03/1.66
% 3.03/1.66 % (7100)Memory used [KB]: 1535
% 3.03/1.66 % (7100)Time elapsed: 0.004 s
% 3.03/1.66 % (7100)Instructions burned: 6 (million)
% 3.03/1.66 % (7100)------------------------------
% 3.03/1.66 % (7100)------------------------------
% 3.03/1.66 % (7103)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6811 for (2999ds/6Mi)
% 3.03/1.66 % (7101)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_6811 for (2999ds/18Mi)
% 3.03/1.66 % (7104)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_6811 for (2999ds/902Mi)
% 3.03/1.66 % (7103)Instruction limit reached!
% 3.03/1.66 % (7103)------------------------------
% 3.03/1.66 % (7103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.66 % (7103)Termination reason: Unknown
% 3.03/1.66 % (7103)Termination phase: shuffling
% 3.03/1.66
% 3.03/1.66 % (7103)Memory used [KB]: 1535
% 3.03/1.66 % (7103)Time elapsed: 0.003 s
% 3.03/1.66 % (7103)Instructions burned: 6 (million)
% 3.03/1.66 % (7103)------------------------------
% 3.03/1.66 % (7103)------------------------------
% 3.03/1.67 % (7101)Instruction limit reached!
% 3.03/1.67 % (7101)------------------------------
% 3.03/1.67 % (7101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.67 % (7101)Termination reason: Unknown
% 3.03/1.67 % (7101)Termination phase: shuffling
% 3.03/1.67
% 3.03/1.67 % (7101)Memory used [KB]: 1791
% 3.03/1.67 % (7101)Time elapsed: 0.009 s
% 3.03/1.67 % (7101)Instructions burned: 18 (million)
% 3.03/1.67 % (7101)------------------------------
% 3.03/1.67 % (7101)------------------------------
% 3.03/1.67 % (7106)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_6811 for (2999ds/5Mi)
% 3.03/1.67 % (7107)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_6811 for (2999ds/6Mi)
% 3.03/1.67 % (7106)Instruction limit reached!
% 3.03/1.67 % (7106)------------------------------
% 3.03/1.67 % (7106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.67 % (7106)Termination reason: Unknown
% 3.03/1.67 % (7106)Termination phase: shuffling
% 3.03/1.67
% 3.03/1.67 % (7106)Memory used [KB]: 1663
% 3.03/1.67 % (7106)Time elapsed: 0.004 s
% 3.03/1.67 % (7106)Instructions burned: 7 (million)
% 3.03/1.67 % (7106)------------------------------
% 3.03/1.67 % (7106)------------------------------
% 3.03/1.67 % (7105)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_6811 for (2999ds/21Mi)
% 3.03/1.67 % (7107)Instruction limit reached!
% 3.03/1.67 % (7107)------------------------------
% 3.03/1.67 % (7107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.67 % (7107)Termination reason: Unknown
% 3.03/1.67 % (7107)Termination phase: shuffling
% 3.03/1.67
% 3.03/1.67 % (7107)Memory used [KB]: 1663
% 3.03/1.67 % (7107)Time elapsed: 0.003 s
% 3.03/1.67 % (7107)Instructions burned: 7 (million)
% 3.03/1.67 % (7107)------------------------------
% 3.03/1.67 % (7107)------------------------------
% 3.03/1.68 % (7102)First to succeed.
% 3.03/1.68 % (7102)Refutation found. Thanks to Tanya!
% 3.03/1.68 % SZS status Theorem for DTF2THF_6811
% 3.03/1.68 % SZS output start Proof for DTF2THF_6811
% 3.03/1.68 thf(type_def_5, type, product_unit: $tType).
% 3.03/1.68 thf(type_def_6, type, list_char: $tType).
% 3.03/1.68 thf(type_def_7, type, option_element_ptr_a: $tType).
% 3.03/1.68 thf(type_def_8, type, list_n282880152tr_b_c: $tType).
% 3.03/1.68 thf(type_def_9, type, option2026120038on_j_k: $tType).
% 3.03/1.68 thf(type_def_10, type, rDocum326988203on_j_k: $tType).
% 3.03/1.68 thf(type_def_12, type, rObjec1617416918on_j_k: $tType).
% 3.03/1.68 thf(type_def_13, type, rObjec1413572695_j_k_l: $tType).
% 3.03/1.68 thf(type_def_14, type, option841825948on_j_k: $tType).
% 3.03/1.68 thf(type_def_15, type, heap_S1465075775_j_k_l: $tType).
% 3.03/1.68 thf(type_def_16, type, fset_d1663890464tr_d_e: $tType).
% 3.03/1.68 thf(type_def_17, type, docume1935157360tr_d_e: $tType).
% 3.03/1.68 thf(type_def_18, type, object945351580_d_e_f: $tType).
% 3.03/1.68 thf(type_def_19, type, option1330818496tr_d_e: $tType).
% 3.03/1.68 thf(type_def_20, type, sum_su1576157353tr_d_e: $tType).
% 3.03/1.68 thf(type_def_21, type, nat: $tType).
% 3.03/1.68 thf(type_def_22, type, node_p1234578834tr_b_c: $tType).
% 3.03/1.68 thf(type_def_23, type, char: $tType).
% 3.03/1.68 thf(type_def_24, type, list_l118626078tr_b_c: $tType).
% 3.03/1.68 thf(type_def_25, type, list_list_char: $tType).
% 3.03/1.68 thf(type_def_26, type, set_nat: $tType).
% 3.03/1.68 thf(type_def_27, type, rObjec103300152t_unit: $tType).
% 3.03/1.68 thf(type_def_28, type, option1749760295_j_k_l: $tType).
% 3.03/1.68 thf(type_def_29, type, element_ptr_a: $tType).
% 3.03/1.68 thf(type_def_30, type, sum_su1221287958on_j_k: $tType).
% 3.03/1.68 thf(func_def_0, type, heap_S1465075775_j_k_l: $tType).
% 3.03/1.68 thf(func_def_1, type, option1749760295_j_k_l: $tType).
% 3.03/1.68 thf(func_def_2, type, rObjec1413572695_j_k_l: $tType).
% 3.03/1.68 thf(func_def_3, type, object945351580_d_e_f: $tType).
% 3.03/1.68 thf(func_def_4, type, option841825948on_j_k: $tType).
% 3.03/1.68 thf(func_def_5, type, rObjec1617416918on_j_k: $tType).
% 3.03/1.68 thf(func_def_6, type, rDocum326988203on_j_k: $tType).
% 3.03/1.68 thf(func_def_7, type, list_l118626078tr_b_c: $tType).
% 3.03/1.68 thf(func_def_8, type, list_n282880152tr_b_c: $tType).
% 3.03/1.68 thf(func_def_9, type, node_p1234578834tr_b_c: $tType).
% 3.03/1.68 thf(func_def_10, type, option2026120038on_j_k: $tType).
% 3.03/1.68 thf(func_def_11, type, option1330818496tr_d_e: $tType).
% 3.03/1.68 thf(func_def_12, type, fset_d1663890464tr_d_e: $tType).
% 3.03/1.68 thf(func_def_13, type, sum_su1221287958on_j_k: $tType).
% 3.03/1.68 thf(func_def_14, type, docume1935157360tr_d_e: $tType).
% 3.03/1.68 thf(func_def_15, type, sum_su1576157353tr_d_e: $tType).
% 3.03/1.68 thf(func_def_16, type, rObjec103300152t_unit: $tType).
% 3.03/1.68 thf(func_def_17, type, option_element_ptr_a: $tType).
% 3.03/1.68 thf(func_def_18, type, list_list_char: $tType).
% 3.03/1.68 thf(func_def_19, type, element_ptr_a: $tType).
% 3.03/1.68 thf(func_def_20, type, list_char: $tType).
% 3.03/1.68 thf(func_def_21, type, set_nat: $tType).
% 3.03/1.68 thf(func_def_22, type, product_unit: $tType).
% 3.03/1.68 thf(func_def_23, type, char: $tType).
% 3.03/1.68 thf(func_def_24, type, nat: $tType).
% 3.03/1.68 thf(func_def_25, type, rDocum427676485on_j_k: product_unit > list_char > option_element_ptr_a > list_n282880152tr_b_c > option2026120038on_j_k > rDocum326988203on_j_k).
% 3.03/1.68 thf(func_def_26, type, discon866287741on_j_k: rObjec1617416918on_j_k > list_n282880152tr_b_c).
% 3.03/1.68 thf(func_def_27, type, discon442323090on_j_k: (list_n282880152tr_b_c > list_n282880152tr_b_c) > rObjec1617416918on_j_k > rObjec1617416918on_j_k).
% 3.03/1.68 thf(func_def_28, type, doctyp814403297on_j_k: rObjec1617416918on_j_k > list_char).
% 3.03/1.68 thf(func_def_29, type, doctyp68000440on_j_k: (list_char > list_char) > rObjec1617416918on_j_k > rObjec1617416918on_j_k).
% 3.03/1.68 thf(func_def_30, type, docume1175131570on_j_k: rObjec1617416918on_j_k > option_element_ptr_a).
% 3.03/1.68 thf(func_def_31, type, docume244715269on_j_k: (option_element_ptr_a > option_element_ptr_a) > rObjec1617416918on_j_k > rObjec1617416918on_j_k).
% 3.03/1.68 thf(func_def_32, type, more_c1453068134on_j_k: rObjec1617416918on_j_k > option2026120038on_j_k).
% 3.03/1.68 thf(func_def_33, type, more_u1044474223_c_a_b: (option2026120038on_j_k > option2026120038on_j_k) > rObjec1617416918on_j_k > rObjec1617416918on_j_k).
% 3.03/1.68 thf(func_def_34, type, nothin757132294on_j_k: rObjec1617416918on_j_k > product_unit).
% 3.03/1.68 thf(func_def_35, type, nothin1105341917on_j_k: (product_unit > product_unit) > rObjec1617416918on_j_k > rObjec1617416918on_j_k).
% 3.03/1.68 thf(func_def_36, type, cast_D1252964113_h_i_l: rObjec1617416918on_j_k > rObjec1413572695_j_k_l).
% 3.03/1.68 thf(func_def_37, type, cast_O1034441233_j_k_l: rObjec1413572695_j_k_l > option841825948on_j_k).
% 3.03/1.68 thf(func_def_38, type, docume1070804385_j_k_l: heap_S1465075775_j_k_l > fset_d1663890464tr_d_e).
% 3.03/1.68 thf(func_def_39, type, get_D_1192261494_j_k_l: docume1935157360tr_d_e > heap_S1465075775_j_k_l > option841825948on_j_k).
% 3.03/1.68 thf(func_def_40, type, is_doc1417632087_j_k_l: rObjec1413572695_j_k_l > $o).
% 3.03/1.68 thf(func_def_41, type, put_D_2126422573_h_i_l: docume1935157360tr_d_e > rObjec1617416918on_j_k > heap_S1465075775_j_k_l > heap_S1465075775_j_k_l).
% 3.03/1.68 thf(func_def_42, type, cast_d1608273229_b_c_f: docume1935157360tr_d_e > object945351580_d_e_f).
% 3.03/1.68 thf(func_def_43, type, cast_o761049241_d_e_f: object945351580_d_e_f > option1330818496tr_d_e).
% 3.03/1.68 thf(func_def_44, type, docume1825929374tr_d_e: sum_su1576157353tr_d_e > docume1935157360tr_d_e).
% 3.03/1.68 thf(func_def_45, type, docume1511108976tr_d_e: nat > docume1935157360tr_d_e).
% 3.03/1.68 thf(func_def_46, type, docume1799427087tr_d_e: (sum_su1576157353tr_d_e > nat) > docume1935157360tr_d_e > nat).
% 3.03/1.68 thf(func_def_47, type, is_doc2037328342tr_d_e: docume1935157360tr_d_e > $o).
% 3.03/1.68 thf(func_def_48, type, plus_plus_nat: nat > nat > nat).
% 3.03/1.68 thf(func_def_49, type, zero_zero_nat: nat).
% 3.03/1.68 thf(func_def_50, type, append846395565tr_b_c: list_n282880152tr_b_c > list_n282880152tr_b_c > list_n282880152tr_b_c).
% 3.03/1.68 thf(func_def_51, type, append_char: list_char > list_char > list_char).
% 3.03/1.68 thf(func_def_52, type, count_2128515342tr_b_c: list_n282880152tr_b_c > node_p1234578834tr_b_c > nat).
% 3.03/1.68 thf(func_def_53, type, count_list_char: list_char > char > nat).
% 3.03/1.68 thf(func_def_54, type, gen_le170886571tr_b_c: nat > list_l118626078tr_b_c > nat).
% 3.03/1.68 thf(func_def_55, type, gen_length_list_char: nat > list_list_char > nat).
% 3.03/1.68 thf(func_def_56, type, gen_le955068453tr_b_c: nat > list_n282880152tr_b_c > nat).
% 3.03/1.68 thf(func_def_57, type, gen_length_char: nat > list_char > nat).
% 3.03/1.68 thf(func_def_58, type, insert678865070tr_b_c: node_p1234578834tr_b_c > list_n282880152tr_b_c > list_n282880152tr_b_c).
% 3.03/1.68 thf(func_def_59, type, insert_char: char > list_char > list_char).
% 3.03/1.68 thf(func_def_60, type, cons_l1809994318tr_b_c: list_n282880152tr_b_c > list_l118626078tr_b_c > list_l118626078tr_b_c).
% 3.03/1.68 thf(func_def_61, type, cons_list_char: list_char > list_list_char > list_list_char).
% 3.03/1.68 thf(func_def_62, type, cons_n413985352tr_b_c: node_p1234578834tr_b_c > list_n282880152tr_b_c > list_n282880152tr_b_c).
% 3.03/1.68 thf(func_def_63, type, cons_char: char > list_char > list_char).
% 3.03/1.68 thf(func_def_64, type, nil_li198338206tr_b_c: list_l118626078tr_b_c).
% 3.03/1.68 thf(func_def_65, type, nil_list_char: list_list_char).
% 3.03/1.68 thf(func_def_66, type, nil_no279930520tr_b_c: list_n282880152tr_b_c).
% 3.03/1.68 thf(func_def_67, type, nil_char: list_char).
% 3.03/1.68 thf(func_def_68, type, list_e529904353tr_b_c: (list_n282880152tr_b_c > $o) > list_l118626078tr_b_c > $o).
% 3.03/1.68 thf(func_def_69, type, list_ex1_list_char: (list_char > $o) > list_list_char > $o).
% 3.03/1.68 thf(func_def_70, type, list_e469495899tr_b_c: (node_p1234578834tr_b_c > $o) > list_n282880152tr_b_c > $o).
% 3.03/1.68 thf(func_def_71, type, list_ex1_char: (char > $o) > list_char > $o).
% 3.03/1.68 thf(func_def_72, type, n_list1807568544tr_b_c: nat > list_n282880152tr_b_c > list_l118626078tr_b_c).
% 3.03/1.68 thf(func_def_73, type, n_lists_char: nat > list_char > list_list_char).
% 3.03/1.68 thf(func_def_74, type, nths_n1256675478tr_b_c: list_n282880152tr_b_c > set_nat > list_n282880152tr_b_c).
% 3.03/1.68 thf(func_def_75, type, nths_char: list_char > set_nat > list_char).
% 3.03/1.68 thf(func_def_76, type, produc1509350401tr_b_c: list_l118626078tr_b_c > list_l118626078tr_b_c).
% 3.03/1.68 thf(func_def_77, type, product_lists_char: list_list_char > list_list_char).
% 3.03/1.68 thf(func_def_78, type, splice1294941035tr_b_c: list_n282880152tr_b_c > list_n282880152tr_b_c > list_n282880152tr_b_c).
% 3.03/1.68 thf(func_def_79, type, splice_char: list_char > list_char > list_char).
% 3.03/1.68 thf(func_def_80, type, subseq1828679783tr_b_c: list_n282880152tr_b_c > list_l118626078tr_b_c).
% 3.03/1.68 thf(func_def_81, type, subseqs_char: list_char > list_list_char).
% 3.03/1.68 thf(func_def_82, type, suc: nat > nat).
% 3.03/1.68 thf(func_def_83, type, size_s724035844tr_d_e: docume1935157360tr_d_e > nat).
% 3.03/1.68 thf(func_def_84, type, size_s9369994tr_b_c: list_l118626078tr_b_c > nat).
% 3.03/1.68 thf(func_def_85, type, size_s2008079621t_char: list_list_char > nat).
% 3.03/1.68 thf(func_def_86, type, size_s2106487044tr_b_c: list_n282880152tr_b_c > nat).
% 3.03/1.68 thf(func_def_87, type, size_size_list_char: list_char > nat).
% 3.03/1.68 thf(func_def_88, type, size_s1129684517_ptr_a: option_element_ptr_a > nat).
% 3.03/1.68 thf(func_def_89, type, size_s7667464on_j_k: option841825948on_j_k > nat).
% 3.03/1.68 thf(func_def_90, type, size_s1129069050on_j_k: option2026120038on_j_k > nat).
% 3.03/1.68 thf(func_def_91, type, nat_set_decode: nat > set_nat).
% 3.03/1.68 thf(func_def_92, type, nat_set_encode: set_nat > nat).
% 3.03/1.68 thf(func_def_93, type, nat_triangle: nat > nat).
% 3.03/1.68 thf(func_def_94, type, rObjec1303043984on_j_k: product_unit > rDocum326988203on_j_k > rObjec1617416918on_j_k).
% 3.03/1.68 thf(func_def_95, type, rObjec730108904t_unit: product_unit > product_unit > rObjec103300152t_unit).
% 3.03/1.68 thf(func_def_96, type, extend1066431834on_j_k: rObjec103300152t_unit > rDocum326988203on_j_k > rObjec1617416918on_j_k).
% 3.03/1.68 thf(func_def_97, type, extend_Product_unit: rObjec103300152t_unit > product_unit > rObjec103300152t_unit).
% 3.03/1.68 thf(func_def_98, type, more_R1625109589on_j_k: rObjec1617416918on_j_k > rDocum326988203on_j_k).
% 3.03/1.68 thf(func_def_99, type, more_Product_unit: rObjec103300152t_unit > product_unit).
% 3.03/1.68 thf(func_def_100, type, nothin1567949605on_j_k: rObjec1617416918on_j_k > product_unit).
% 3.03/1.68 thf(func_def_101, type, nothing_Product_unit: rObjec103300152t_unit > product_unit).
% 3.03/1.68 thf(func_def_102, type, get_O_623850005_j_k_l: object945351580_d_e_f > heap_S1465075775_j_k_l > option1749760295_j_k_l).
% 3.03/1.68 thf(func_def_103, type, put_O_834343516_j_k_l: object945351580_d_e_f > rObjec1413572695_j_k_l > heap_S1465075775_j_k_l > heap_S1465075775_j_k_l).
% 3.03/1.68 thf(func_def_104, type, bind_e22036734_ptr_a: option_element_ptr_a > (element_ptr_a > option_element_ptr_a) > option_element_ptr_a).
% 3.03/1.68 thf(func_def_105, type, bind_e1012152651on_j_k: option_element_ptr_a > (element_ptr_a > option2026120038on_j_k) > option2026120038on_j_k).
% 3.03/1.68 thf(func_def_106, type, bind_S287509021_ptr_a: option2026120038on_j_k > (sum_su1221287958on_j_k > option_element_ptr_a) > option_element_ptr_a).
% 3.03/1.68 thf(func_def_107, type, bind_S607117548on_j_k: option2026120038on_j_k > (sum_su1221287958on_j_k > option2026120038on_j_k) > option2026120038on_j_k).
% 3.03/1.68 thf(func_def_108, type, none_d1458959567tr_d_e: option1330818496tr_d_e).
% 3.03/1.68 thf(func_def_109, type, none_element_ptr_a: option_element_ptr_a).
% 3.03/1.68 thf(func_def_110, type, none_R1587534007on_j_k: option841825948on_j_k).
% 3.03/1.68 thf(func_def_111, type, none_R1773662646_j_k_l: option1749760295_j_k_l).
% 3.03/1.68 thf(func_def_112, type, none_S1393028981on_j_k: option2026120038on_j_k).
% 3.03/1.68 thf(func_def_113, type, some_d1631029323tr_d_e: docume1935157360tr_d_e > option1330818496tr_d_e).
% 3.03/1.68 thf(func_def_114, type, some_element_ptr_a: element_ptr_a > option_element_ptr_a).
% 3.03/1.68 thf(func_def_115, type, some_R67702331on_j_k: rObjec1617416918on_j_k > option841825948on_j_k).
% 3.03/1.68 thf(func_def_116, type, some_R1598191922_j_k_l: rObjec1413572695_j_k_l > option1749760295_j_k_l).
% 3.03/1.68 thf(func_def_117, type, some_S1960742641on_j_k: sum_su1221287958on_j_k > option2026120038on_j_k).
% 3.03/1.68 thf(func_def_118, type, size_o1635055885tr_d_e: (docume1935157360tr_d_e > nat) > option1330818496tr_d_e > nat).
% 3.03/1.68 thf(func_def_119, type, size_o1591053974_ptr_a: (element_ptr_a > nat) > option_element_ptr_a > nat).
% 3.03/1.68 thf(func_def_120, type, size_o26122489on_j_k: (rObjec1617416918on_j_k > nat) > option841825948on_j_k > nat).
% 3.03/1.68 thf(func_def_121, type, size_o310046708_j_k_l: (rObjec1413572695_j_k_l > nat) > option1749760295_j_k_l > nat).
% 3.03/1.68 thf(func_def_122, type, size_o1777465779on_j_k: (sum_su1221287958on_j_k > nat) > option2026120038on_j_k > nat).
% 3.03/1.68 thf(func_def_123, type, bot_bo1111241908tr_d_e: fset_d1663890464tr_d_e).
% 3.03/1.68 thf(func_def_124, type, bot_bot_nat: nat).
% 3.03/1.68 thf(func_def_125, type, bot_bot_set_nat: set_nat).
% 3.03/1.68 thf(func_def_126, type, product_Unity: product_unit).
% 3.03/1.68 thf(func_def_127, type, collect_nat: (nat > $o) > set_nat).
% 3.03/1.68 thf(func_def_128, type, type_w92696601_j_k_l: heap_S1465075775_j_k_l > $o).
% 3.03/1.68 thf(func_def_129, type, member_nat: nat > set_nat > $o).
% 3.03/1.68 thf(func_def_130, type, h: heap_S1465075775_j_k_l).
% 3.03/1.68 thf(func_def_131, type, h2: heap_S1465075775_j_k_l).
% 3.03/1.68 thf(func_def_144, type, sK0: nat > nat).
% 3.03/1.68 thf(func_def_145, type, sK1: rObjec1413572695_j_k_l > rObjec1617416918on_j_k).
% 3.03/1.68 thf(func_def_146, type, sK2: nat > nat).
% 3.03/1.68 thf(func_def_147, type, sK3: (rObjec103300152t_unit > $o) > product_unit).
% 3.03/1.68 thf(func_def_148, type, sK4: (nat > $o) > nat).
% 3.03/1.68 thf(func_def_149, type, sK5: (nat > $o) > nat).
% 3.03/1.68 thf(func_def_150, type, sK6: (rObjec1617416918on_j_k > $o) > product_unit).
% 3.03/1.68 thf(func_def_151, type, sK7: (rObjec1617416918on_j_k > $o) > list_char).
% 3.03/1.68 thf(func_def_152, type, sK8: (rObjec1617416918on_j_k > $o) > list_n282880152tr_b_c).
% 3.03/1.68 thf(func_def_153, type, sK9: (rObjec1617416918on_j_k > $o) > option2026120038on_j_k).
% 3.03/1.68 thf(func_def_154, type, sK10: (rObjec1617416918on_j_k > $o) > option_element_ptr_a).
% 3.03/1.68 thf(func_def_155, type, sK11: (rObjec1617416918on_j_k > $o) > product_unit).
% 3.03/1.68 thf(func_def_156, type, sK12: rObjec103300152t_unit > product_unit).
% 3.03/1.68 thf(func_def_157, type, sK13: docume1935157360tr_d_e > sum_su1576157353tr_d_e).
% 3.03/1.68 thf(func_def_158, type, sK14: docume1935157360tr_d_e > nat).
% 3.03/1.68 thf(func_def_159, type, sK15: rObjec1617416918on_j_k > product_unit).
% 3.03/1.68 thf(func_def_160, type, sK16: rObjec1617416918on_j_k > rDocum326988203on_j_k).
% 3.03/1.68 thf(func_def_161, type, sK17: (nat > $o) > nat).
% 3.03/1.68 thf(func_def_162, type, sK18: (rDocum326988203on_j_k > $o) > list_char).
% 3.03/1.68 thf(func_def_163, type, sK19: (rDocum326988203on_j_k > $o) > list_n282880152tr_b_c).
% 3.03/1.68 thf(func_def_164, type, sK20: (rDocum326988203on_j_k > $o) > option_element_ptr_a).
% 3.03/1.68 thf(func_def_165, type, sK21: (rDocum326988203on_j_k > $o) > option2026120038on_j_k).
% 3.03/1.68 thf(func_def_166, type, sK22: (rDocum326988203on_j_k > $o) > product_unit).
% 3.03/1.68 thf(func_def_167, type, sK23: (nat > $o) > nat).
% 3.03/1.68 thf(func_def_168, type, sK24: (docume1935157360tr_d_e > $o) > nat).
% 3.03/1.68 thf(func_def_169, type, sK25: (docume1935157360tr_d_e > $o) > sum_su1576157353tr_d_e).
% 3.03/1.68 thf(func_def_170, type, sK26: (rObjec1617416918on_j_k > $o) > product_unit).
% 3.03/1.68 thf(func_def_171, type, sK27: (rObjec1617416918on_j_k > $o) > rDocum326988203on_j_k).
% 3.03/1.68 thf(func_def_172, type, sK28: rObjec1617416918on_j_k > option2026120038on_j_k).
% 3.03/1.68 thf(func_def_173, type, sK29: rObjec1617416918on_j_k > product_unit).
% 3.03/1.68 thf(func_def_174, type, sK30: rObjec1617416918on_j_k > list_char).
% 3.03/1.68 thf(func_def_175, type, sK31: rObjec1617416918on_j_k > list_n282880152tr_b_c).
% 3.03/1.68 thf(func_def_176, type, sK32: rObjec1617416918on_j_k > product_unit).
% 3.03/1.68 thf(func_def_177, type, sK33: rObjec1617416918on_j_k > option_element_ptr_a).
% 3.03/1.68 thf(func_def_178, type, sK34: nat > nat).
% 3.03/1.68 thf(func_def_179, type, sK35: (nat > nat > $o) > nat).
% 3.03/1.68 thf(func_def_180, type, sK36: (nat > nat > $o) > nat).
% 3.03/1.68 thf(func_def_181, type, sK37: (nat > nat > $o) > nat).
% 3.03/1.68 thf(func_def_182, type, sK38: (nat > nat > $o) > nat).
% 3.03/1.68 thf(f870,plain,(
% 3.03/1.68 $false),
% 3.03/1.68 inference(subsumption_resolution,[status(thm)],[f869,f847])).
% 3.03/1.68 thf(f847,plain,(
% 3.03/1.68 ( ! [X1 : rObjec1617416918on_j_k] : ((none_R1587534007on_j_k != (cast_O1034441233_j_k_l @ (cast_D1252964113_h_i_l @ X1)))) )),
% 3.03/1.68 inference(equality_resolution,[status(thm)],[f775])).
% 3.03/1.68 thf(f775,plain,(
% 3.03/1.68 ( ! [X0 : rObjec1413572695_j_k_l,X1 : rObjec1617416918on_j_k] : (((cast_D1252964113_h_i_l @ X1) != X0) | (none_R1587534007on_j_k != (cast_O1034441233_j_k_l @ X0))) )),
% 3.03/1.68 inference(cnf_transformation,[status(thm)],[f717])).
% 3.03/1.68 thf(f717,plain,(
% 3.03/1.68 ! [X0 : rObjec1413572695_j_k_l] : ((! [X1 : rObjec1617416918on_j_k] : ((cast_D1252964113_h_i_l @ X1) != X0) | (none_R1587534007on_j_k != (cast_O1034441233_j_k_l @ X0))) & ((none_R1587534007on_j_k = (cast_O1034441233_j_k_l @ X0)) | ((cast_D1252964113_h_i_l @ (sK1 @ X0)) = X0)))),
% 3.03/1.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f715,f716])).
% 3.03/1.68 thf(f716,plain,(
% 3.03/1.68 ! [X0 : rObjec1413572695_j_k_l] : (? [X2 : rObjec1617416918on_j_k] : ((cast_D1252964113_h_i_l @ X2) = X0) => ((cast_D1252964113_h_i_l @ (sK1 @ X0)) = X0))),
% 3.03/1.68 introduced(definition,[],[choice_axiom])).
% 3.03/1.68 thf(f715,plain,(
% 3.03/1.68 ! [X0 : rObjec1413572695_j_k_l] : ((! [X1 : rObjec1617416918on_j_k] : ((cast_D1252964113_h_i_l @ X1) != X0) | (none_R1587534007on_j_k != (cast_O1034441233_j_k_l @ X0))) & ((none_R1587534007on_j_k = (cast_O1034441233_j_k_l @ X0)) | ? [X2 : rObjec1617416918on_j_k] : ((cast_D1252964113_h_i_l @ X2) = X0)))),
% 3.03/1.68 inference(rectify,[status(thm)],[f714])).
% 3.03/1.68 thf(f714,plain,(
% 3.03/1.68 ! [X0 : rObjec1413572695_j_k_l] : ((! [X1 : rObjec1617416918on_j_k] : ((cast_D1252964113_h_i_l @ X1) != X0) | (none_R1587534007on_j_k != (cast_O1034441233_j_k_l @ X0))) & ((none_R1587534007on_j_k = (cast_O1034441233_j_k_l @ X0)) | ? [X1 : rObjec1617416918on_j_k] : ((cast_D1252964113_h_i_l @ X1) = X0)))),
% 3.03/1.68 inference(nnf_transformation,[status(thm)],[f702])).
% 3.03/1.68 thf(f702,plain,(
% 3.03/1.68 ! [X0 : rObjec1413572695_j_k_l] : (! [X1 : rObjec1617416918on_j_k] : ((cast_D1252964113_h_i_l @ X1) != X0) <=> (none_R1587534007on_j_k = (cast_O1034441233_j_k_l @ X0)))),
% 3.03/1.68 inference(ennf_transformation,[status(thm)],[f651])).
% 3.03/1.68 thf(f651,plain,(
% 3.03/1.68 ! [X0 : rObjec1413572695_j_k_l] : ((none_R1587534007on_j_k = (cast_O1034441233_j_k_l @ X0)) <=> ~? [X1 : rObjec1617416918on_j_k] : ((cast_D1252964113_h_i_l @ X1) = X0))),
% 3.03/1.68 inference(fool_elimination,[status(thm)],[f650])).
% 3.03/1.68 thf(f650,plain,(
% 3.03/1.68 ! [X0 : rObjec1413572695_j_k_l] : (~? [X1 : rObjec1617416918on_j_k] : ((cast_D1252964113_h_i_l @ X1) = X0) = (none_R1587534007on_j_k = (cast_O1034441233_j_k_l @ X0)))),
% 3.03/1.68 inference(rectify,[status(thm)],[f111])).
% 3.03/1.68 thf(f111,axiom,(
% 3.03/1.68 ! [X53 : rObjec1413572695_j_k_l] : (~? [X37 : rObjec1617416918on_j_k] : ((cast_D1252964113_h_i_l @ X37) = X53) = (none_R1587534007on_j_k = (cast_O1034441233_j_k_l @ X53)))),
% 3.03/1.68 file('/export/starexec/sandbox2/tmp/tmp.YeJj9WbkkZ/DTF2THF_6811.p',fact_110_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__none)).
% 3.03/1.68 thf(f869,plain,(
% 3.03/1.68 (none_R1587534007on_j_k = (cast_O1034441233_j_k_l @ (cast_D1252964113_h_i_l @ (rObjec1303043984on_j_k @ product_Unity @ (rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k)))))),
% 3.03/1.68 inference(equality_proxy_clausification,[status(thm)],[f868])).
% 3.03/1.68 thf(f868,plain,(
% 3.03/1.68 ((none_R1587534007on_j_k = (cast_O1034441233_j_k_l @ (cast_D1252964113_h_i_l @ (rObjec1303043984on_j_k @ product_Unity @ (rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k))))) = $true)),
% 3.03/1.68 inference(not_proxy_clausification,[status(thm)],[f867])).
% 3.03/1.68 thf(f867,plain,(
% 3.03/1.68 ((~ (none_R1587534007on_j_k = (cast_O1034441233_j_k_l @ (cast_D1252964113_h_i_l @ (rObjec1303043984on_j_k @ product_Unity @ (rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k)))))) != $true)),
% 3.03/1.68 inference(beta_eta_normalization,[status(thm)],[f846])).
% 3.03/1.68 thf(f846,plain,(
% 3.03/1.68 ($true != ((^[Y0 : rObjec1413572695_j_k_l]: (~ (none_R1587534007on_j_k = (cast_O1034441233_j_k_l @ Y0)))) @ (cast_D1252964113_h_i_l @ (rObjec1303043984on_j_k @ product_Unity @ (rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k)))))),
% 3.03/1.68 inference(definition_unfolding,[status(thm)],[f808,f805])).
% 3.03/1.68 thf(f805,plain,(
% 3.03/1.68 (is_doc1417632087_j_k_l = (^[Y0 : rObjec1413572695_j_k_l]: (~ (none_R1587534007on_j_k = (cast_O1034441233_j_k_l @ Y0)))))),
% 3.03/1.68 inference(cnf_transformation,[status(thm)],[f503])).
% 3.03/1.68 thf(f503,plain,(
% 3.03/1.68 (is_doc1417632087_j_k_l = (^[Y0 : rObjec1413572695_j_k_l]: (~ (none_R1587534007on_j_k = (cast_O1034441233_j_k_l @ Y0)))))),
% 3.03/1.68 inference(fool_elimination,[status(thm)],[f502])).
% 3.03/1.68 thf(f502,plain,(
% 3.03/1.68 ((^[X0 : rObjec1413572695_j_k_l] : ((none_R1587534007on_j_k != (cast_O1034441233_j_k_l @ X0)))) = is_doc1417632087_j_k_l)),
% 3.03/1.68 inference(rectify,[status(thm)],[f116])).
% 3.03/1.68 thf(f116,axiom,(
% 3.03/1.68 ((^[X54 : rObjec1413572695_j_k_l] : ((none_R1587534007on_j_k != (cast_O1034441233_j_k_l @ X54)))) = is_doc1417632087_j_k_l)),
% 3.03/1.68 file('/export/starexec/sandbox2/tmp/tmp.YeJj9WbkkZ/DTF2THF_6811.p',fact_115_is__document__kind__def)).
% 3.03/1.68 thf(f808,plain,(
% 3.03/1.68 ((is_doc1417632087_j_k_l @ (cast_D1252964113_h_i_l @ (rObjec1303043984on_j_k @ product_Unity @ (rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k)))) != $true)),
% 3.03/1.68 inference(cnf_transformation,[status(thm)],[f656])).
% 3.03/1.68 thf(f656,plain,(
% 3.03/1.68 ((is_doc1417632087_j_k_l @ (cast_D1252964113_h_i_l @ (rObjec1303043984on_j_k @ product_Unity @ (rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k)))) != $true)),
% 3.03/1.68 inference(flattening,[status(thm)],[f371])).
% 3.03/1.68 thf(f371,plain,(
% 3.03/1.68 ~((is_doc1417632087_j_k_l @ (cast_D1252964113_h_i_l @ (rObjec1303043984on_j_k @ product_Unity @ (rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k)))) = $true)),
% 3.03/1.68 inference(fool_elimination,[status(thm)],[f370])).
% 3.03/1.68 thf(f370,plain,(
% 3.03/1.68 ~(is_doc1417632087_j_k_l @ (cast_D1252964113_h_i_l @ (rObjec1303043984on_j_k @ product_Unity @ (rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k))))),
% 3.03/1.68 inference(rectify,[status(thm)],[f344])).
% 3.03/1.68 thf(f344,negated_conjecture,(
% 3.03/1.68 ~(is_doc1417632087_j_k_l @ (cast_D1252964113_h_i_l @ (rObjec1303043984on_j_k @ product_Unity @ (rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k))))),
% 3.03/1.68 inference(negated_conjecture,[status(cth)],[f343])).
% 3.03/1.68 thf(f343,conjecture,(
% 3.03/1.68 (is_doc1417632087_j_k_l @ (cast_D1252964113_h_i_l @ (rObjec1303043984on_j_k @ product_Unity @ (rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k))))),
% 3.03/1.68 file('/export/starexec/sandbox2/tmp/tmp.YeJj9WbkkZ/DTF2THF_6811.p',conj_3)).
% 3.03/1.68 % SZS output end Proof for DTF2THF_6811
% 3.03/1.68 % (7102)------------------------------
% 3.03/1.68 % (7102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.68 % (7102)Termination reason: Refutation
% 3.03/1.68
% 3.03/1.68 % (7102)Memory used [KB]: 6652
% 3.03/1.68 % (7102)Time elapsed: 0.018 s
% 3.03/1.68 % (7102)Instructions burned: 55 (million)
% 3.03/1.68 % (7102)------------------------------
% 3.03/1.68 % (7102)------------------------------
% 3.03/1.68 % (7081)Success in time 0.104 s
%------------------------------------------------------------------------------