%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP081^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:23 AM UTC 2026
% Result : Theorem 3.20s 1.72s
% Output : Refutation 3.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 139 ( 30 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 454 ( 19 ~; 10 |; 0 &; 419 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 305 ( 302 usr; 21 con; 0-7 aty)
% Number of variables : 38 ( 0 ^; 38 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_node: $tType ).
thf(type_def_7,type,
set_val: $tType ).
thf(type_def_8,type,
g: $tType ).
thf(type_def_9,type,
list_node: $tType ).
thf(type_def_10,type,
node: $tType ).
thf(type_def_11,type,
list_P561207620_edgeD: $tType ).
thf(type_def_12,type,
list_list_node: $tType ).
thf(type_def_13,type,
list_val: $tType ).
thf(type_def_14,type,
val: $tType ).
thf(type_def_15,type,
set_list_node: $tType ).
thf(type_def_16,type,
produc1432036078de_val: $tType ).
thf(type_def_17,type,
option_list_val: $tType ).
thf(func_def_0,type,
list_P561207620_edgeD: $tType ).
thf(func_def_1,type,
option_list_val: $tType ).
thf(func_def_2,type,
produc1432036078de_val: $tType ).
thf(func_def_3,type,
list_list_node: $tType ).
thf(func_def_4,type,
set_list_node: $tType ).
thf(func_def_5,type,
list_node: $tType ).
thf(func_def_6,type,
list_val: $tType ).
thf(func_def_7,type,
set_node: $tType ).
thf(func_def_8,type,
set_val: $tType ).
thf(func_def_9,type,
node: $tType ).
thf(func_def_10,type,
val: $tType ).
thf(func_def_11,type,
g: $tType ).
thf(func_def_12,type,
finite_finite_node: set_node > $o ).
thf(func_def_13,type,
finite_finite_val: set_val > $o ).
thf(func_def_14,type,
graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
thf(func_def_15,type,
graph_435229452_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > list_node > $o ).
thf(func_def_16,type,
graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
thf(func_def_17,type,
append_list_node: list_list_node > list_list_node > list_list_node ).
thf(func_def_18,type,
append_node: list_node > list_node > list_node ).
thf(func_def_19,type,
append_val: list_val > list_val > list_val ).
thf(func_def_20,type,
butlast_list_node: list_list_node > list_list_node ).
thf(func_def_21,type,
butlast_node: list_node > list_node ).
thf(func_def_22,type,
butlast_val: list_val > list_val ).
thf(func_def_23,type,
cons_list_node: list_node > list_list_node > list_list_node ).
thf(func_def_24,type,
cons_node: node > list_node > list_node ).
thf(func_def_25,type,
cons_val: val > list_val > list_val ).
thf(func_def_26,type,
nil_list_node: list_list_node ).
thf(func_def_27,type,
nil_node: list_node ).
thf(func_def_28,type,
nil_val: list_val ).
thf(func_def_29,type,
hd_node: list_node > node ).
thf(func_def_30,type,
hd_val: list_val > val ).
thf(func_def_31,type,
set_list_node2: list_list_node > set_list_node ).
thf(func_def_32,type,
set_node2: list_node > set_node ).
thf(func_def_33,type,
set_val2: list_val > set_val ).
thf(func_def_34,type,
tl_list_node: list_list_node > list_list_node ).
thf(func_def_35,type,
tl_node: list_node > list_node ).
thf(func_def_36,type,
tl_val: list_val > list_val ).
thf(func_def_37,type,
ord_less_eq_set_node: set_node > set_node > $o ).
thf(func_def_38,type,
ord_less_eq_set_val: set_val > set_val > $o ).
thf(func_def_39,type,
sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(func_def_40,type,
sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
thf(func_def_41,type,
sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
thf(func_def_42,type,
collect_node: ( node > $o ) > set_node ).
thf(func_def_43,type,
collect_val: ( val > $o ) > set_val ).
thf(func_def_44,type,
prefix_node: list_node > list_node > $o ).
thf(func_def_45,type,
suffix_node: list_node > list_node > $o ).
thf(func_def_46,type,
member_list_node: list_node > set_list_node > $o ).
thf(func_def_47,type,
member_node: node > set_node > $o ).
thf(func_def_48,type,
member_val: val > set_val > $o ).
thf(func_def_49,type,
alpha_n: g > list_node ).
thf(func_def_50,type,
phi_r: val ).
thf(func_def_51,type,
defs: g > node > set_val ).
thf(func_def_52,type,
g2: g ).
thf(func_def_53,type,
i: node ).
thf(func_def_54,type,
inEdges: g > node > list_P561207620_edgeD ).
thf(func_def_55,type,
invar: g > $o ).
thf(func_def_56,type,
m: node ).
thf(func_def_57,type,
ms: list_node ).
thf(func_def_58,type,
ms2: list_node ).
thf(func_def_59,type,
n: node ).
thf(func_def_60,type,
ns: list_node ).
thf(func_def_61,type,
phis: g > produc1432036078de_val > option_list_val ).
thf(func_def_62,type,
pred_phi_r: node ).
thf(func_def_63,type,
r: val ).
thf(func_def_64,type,
ri: list_node ).
thf(func_def_65,type,
rs: list_node ).
thf(func_def_66,type,
rs2: list_node ).
thf(func_def_67,type,
s: val ).
thf(func_def_78,type,
sP0: ( list_node > list_node > $o ) > $o ).
thf(func_def_79,type,
sP1: list_node > list_node > $o ).
thf(func_def_80,type,
sP2: ( list_node > list_node > $o ) > ( node > node > $o ) > $o ).
thf(func_def_81,type,
sP3: list_node > list_node > node > node > list_node > list_node > $o ).
thf(func_def_82,type,
sK4: ( list_node > list_node > $o ) > node ).
thf(func_def_83,type,
sK5: ( list_node > list_node > $o ) > list_node ).
thf(func_def_84,type,
sK6: ( list_node > list_node > $o ) > node ).
thf(func_def_85,type,
sK7: ( list_node > list_node > $o ) > list_node ).
thf(func_def_86,type,
sK8: ( list_node > list_node > $o ) > list_node ).
thf(func_def_87,type,
sK9: ( list_node > list_node > $o ) > list_node ).
thf(func_def_88,type,
sK10: ( list_node > list_node > $o ) > node ).
thf(func_def_89,type,
sK11: ( list_node > list_node > $o ) > node ).
thf(func_def_90,type,
sK12: ( list_node > list_node > $o ) > list_node ).
thf(func_def_91,type,
sK13: ( list_node > list_node > $o ) > node ).
thf(func_def_92,type,
sK14: node > list_node > list_node ).
thf(func_def_93,type,
sK15: node > list_node > list_node ).
thf(func_def_94,type,
sK16: node > node > list_node > list_node ).
thf(func_def_95,type,
sK17: node > node > list_node > list_node ).
thf(func_def_96,type,
sK18: node > node > list_node > list_node ).
thf(func_def_97,type,
sK19: node > node > list_node > list_node ).
thf(func_def_98,type,
sK20: node > node > list_node > list_node ).
thf(func_def_99,type,
sK21: node > node > list_node > list_node ).
thf(func_def_100,type,
sK22: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(func_def_101,type,
sK23: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(func_def_102,type,
sK24: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_103,type,
sK25: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_104,type,
sK26: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(func_def_105,type,
sK27: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(func_def_106,type,
sK28: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_107,type,
sK29: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(func_def_108,type,
sK30: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_109,type,
sK31: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(func_def_110,type,
sK32: node > list_node > list_node ).
thf(func_def_111,type,
sK33: node > list_node > list_node ).
thf(func_def_112,type,
sK34: ( ( node > node > $o ) > list_node > $o ) > node > node > $o ).
thf(func_def_113,type,
sK35: ( ( node > node > $o ) > list_node > $o ) > node ).
thf(func_def_114,type,
sK36: ( ( node > node > $o ) > list_node > $o ) > node > node > $o ).
thf(func_def_115,type,
sK37: ( ( node > node > $o ) > list_node > $o ) > list_node ).
thf(func_def_116,type,
sK38: ( ( node > node > $o ) > list_node > $o ) > node > node > $o ).
thf(func_def_117,type,
sK39: ( ( node > node > $o ) > list_node > $o ) > node ).
thf(func_def_118,type,
sK40: ( ( node > node > $o ) > list_node > $o ) > node ).
thf(func_def_119,type,
sK41: list_node > list_node > list_node > list_node ).
thf(func_def_120,type,
sK42: ( list_node > list_node > $o ) > node ).
thf(func_def_121,type,
sK43: ( list_node > list_node > $o ) > node ).
thf(func_def_122,type,
sK44: ( list_node > list_node > $o ) > list_node ).
thf(func_def_123,type,
sK45: ( list_node > list_node > $o ) > list_node ).
thf(func_def_124,type,
sK46: ( list_node > list_node > $o ) > node ).
thf(func_def_125,type,
sK47: ( list_node > list_node > $o ) > list_node ).
thf(func_def_126,type,
sK48: ( list_node > list_node > $o ) > node ).
thf(func_def_127,type,
sK49: ( list_node > list_node > $o ) > list_node ).
thf(func_def_128,type,
sK50: ( list_node > list_node > $o ) > node ).
thf(func_def_129,type,
sK51: ( list_node > list_node > $o ) > node ).
thf(func_def_130,type,
sK52: ( list_node > list_node > $o ) > node ).
thf(func_def_131,type,
sK53: ( list_node > list_node > $o ) > node ).
thf(func_def_132,type,
sK54: ( list_node > $o ) > node ).
thf(func_def_133,type,
sK55: ( list_node > $o ) > list_node ).
thf(func_def_134,type,
sK56: ( list_node > $o ) > node ).
thf(func_def_135,type,
sK57: list_node > ( node > $o ) > node ).
thf(func_def_136,type,
sK58: list_node > ( node > $o ) > node ).
thf(func_def_137,type,
sK59: list_node > ( node > $o ) > list_node ).
thf(func_def_138,type,
sK60: list_node > ( node > $o ) > node ).
thf(func_def_139,type,
sK61: list_node > ( node > $o ) > list_node ).
thf(func_def_140,type,
sK62: ( list_node > list_node > $o ) > list_node ).
thf(func_def_141,type,
sK63: ( list_node > list_node > $o ) > node ).
thf(func_def_142,type,
sK64: ( list_node > list_node > $o ) > node ).
thf(func_def_143,type,
sK65: ( list_node > list_node > $o ) > list_node ).
thf(func_def_144,type,
sK66: ( list_node > list_node > $o ) > list_node ).
thf(func_def_145,type,
sK67: ( list_node > list_node > $o ) > node ).
thf(func_def_146,type,
sK68: ( list_node > list_node > $o ) > node ).
thf(func_def_147,type,
sK69: ( list_node > list_node > $o ) > list_node ).
thf(func_def_148,type,
sK70: ( list_node > list_node > $o ) > list_node ).
thf(func_def_149,type,
sK71: ( list_node > list_node > $o ) > node ).
thf(func_def_150,type,
sK72: ( list_node > list_node > $o ) > list_node ).
thf(func_def_151,type,
sK73: ( list_node > list_node > $o ) > list_node ).
thf(func_def_152,type,
sK74: ( list_node > list_node > $o ) > list_node ).
thf(func_def_153,type,
sK75: ( list_node > list_node > $o ) > node ).
thf(func_def_154,type,
sK76: ( list_node > list_node > $o ) > list_node ).
thf(func_def_155,type,
sK77: ( list_node > list_node > $o ) > node ).
thf(func_def_156,type,
sK78: ( list_node > list_node > $o ) > list_node ).
thf(func_def_157,type,
sK79: ( list_node > list_node > $o ) > list_node ).
thf(func_def_158,type,
sK80: list_node > ( node > $o ) > node ).
thf(func_def_159,type,
sK81: list_node > ( node > $o ) > list_node ).
thf(func_def_160,type,
sK82: list_node > ( node > $o ) > list_node ).
thf(func_def_161,type,
sK83: list_node > node > list_node ).
thf(func_def_162,type,
sK84: list_node > node > list_node ).
thf(func_def_163,type,
sK85: list_node > list_node > node > node ).
thf(func_def_164,type,
sK86: ( list_node > $o ) > node ).
thf(func_def_165,type,
sK87: ( list_node > $o ) > node ).
thf(func_def_166,type,
sK88: ( list_node > $o ) > node ).
thf(func_def_167,type,
sK89: ( list_node > $o ) > list_node ).
thf(func_def_168,type,
sK90: list_node > ( node > $o ) > node ).
thf(func_def_169,type,
sK91: list_node > ( node > $o ) > list_node ).
thf(func_def_170,type,
sK92: list_node > ( node > $o ) > list_node ).
thf(func_def_171,type,
sK93: ( list_node > $o ) > list_node ).
thf(func_def_172,type,
sK94: ( list_node > $o ) > node ).
thf(func_def_173,type,
sK95: node > node > g > list_node > node > list_node ).
thf(func_def_174,type,
sK96: node > node > g > list_node > node > list_node ).
thf(func_def_175,type,
sK97: ( list_node > $o ) > node ).
thf(func_def_176,type,
sK98: ( list_node > $o ) > node ).
thf(func_def_177,type,
sK99: ( list_node > $o ) > list_node ).
thf(func_def_178,type,
sK100: ( list_node > $o ) > list_node ).
thf(func_def_179,type,
sK101: ( list_node > $o ) > node ).
thf(func_def_180,type,
sK102: node > list_node > list_node > list_node > list_node ).
thf(func_def_181,type,
sK103: node > node > g > list_node > list_node ).
thf(func_def_182,type,
sK104: list_node > node ).
thf(func_def_183,type,
sK105: list_node > list_node ).
thf(func_def_184,type,
sK106: list_node > node ).
thf(func_def_185,type,
sK107: list_node ).
thf(func_def_186,type,
sK108: node ).
thf(func_def_187,type,
sK109: list_node > node ).
thf(func_def_188,type,
sK110: ( list_node > list_node > $o ) > list_node ).
thf(func_def_189,type,
sK111: ( list_node > list_node > $o ) > node ).
thf(func_def_190,type,
sK112: ( list_node > list_node > $o ) > list_node ).
thf(func_def_191,type,
sK113: ( list_node > list_node > $o ) > node ).
thf(func_def_192,type,
sK114: ( list_node > list_node > $o ) > list_node ).
thf(func_def_193,type,
sK115: ( list_node > list_node > $o ) > list_node ).
thf(func_def_194,type,
sK116: list_node > list_node > node ).
thf(func_def_195,type,
sK117: list_node > list_node > list_node ).
thf(func_def_196,type,
sK118: list_node > list_node > list_node ).
thf(func_def_197,type,
sK119: list_node > list_node > node ).
thf(func_def_198,type,
sK120: list_node > list_node > node ).
thf(func_def_199,type,
sK121: list_node > list_node > list_node ).
thf(func_def_200,type,
sK122: list_node > list_node > node ).
thf(func_def_201,type,
sK123: list_node > list_node > list_node ).
thf(func_def_202,type,
sK124: list_node > ( node > $o ) > list_node ).
thf(func_def_203,type,
sK125: list_node > ( node > $o ) > node ).
thf(func_def_204,type,
sK126: list_node > ( node > $o ) > list_node ).
thf(func_def_205,type,
sK127: list_node > ( node > $o ) > node ).
thf(func_def_206,type,
sK128: list_node > ( node > $o ) > node ).
thf(func_def_207,type,
sK129: list_node > ( node > $o ) > list_node ).
thf(func_def_208,type,
sK130: list_node > ( node > $o ) > list_node ).
thf(func_def_209,type,
sK131: list_node > ( node > $o ) > node ).
thf(func_def_210,type,
sK132: list_node > node ).
thf(func_def_211,type,
sK133: list_node > node ).
thf(func_def_212,type,
sK134: list_node > list_node ).
thf(func_def_213,type,
sK135: list_node > node ).
thf(func_def_214,type,
sK136: node > list_node > list_node > list_node > list_node ).
thf(func_def_215,type,
sK137: list_node > node > list_node ).
thf(func_def_216,type,
sK138: list_node > node > list_node ).
thf(func_def_217,type,
sK139: ( list_node > list_node > $o ) > list_node ).
thf(func_def_218,type,
sK140: ( list_node > list_node > $o ) > node ).
thf(func_def_219,type,
sK141: ( list_node > list_node > $o ) > node ).
thf(func_def_220,type,
sK142: ( list_node > list_node > $o ) > list_node ).
thf(func_def_221,type,
sK143: ( list_node > list_node > $o ) > list_node ).
thf(func_def_222,type,
sK144: ( list_node > list_node > $o ) > node ).
thf(func_def_223,type,
sK145: ( list_node > list_node > $o ) > list_node ).
thf(func_def_224,type,
sK146: ( list_node > list_node > $o ) > node ).
thf(func_def_225,type,
sK147: list_node > node ).
thf(func_def_226,type,
sK148: list_node > list_node ).
thf(func_def_227,type,
sK149: list_node > list_node ).
thf(func_def_228,type,
sK150: list_node > node ).
thf(func_def_229,type,
sK151: list_node > node > g > ( node > $o ) > list_node ).
thf(func_def_230,type,
sK152: list_node > node > g > ( node > $o ) > node ).
thf(func_def_231,type,
sK153: ( ( node > node ) > list_node > list_node > $o ) > node > node ).
thf(func_def_232,type,
sK154: ( ( node > node ) > list_node > list_node > $o ) > list_node ).
thf(func_def_233,type,
sK155: ( ( node > node ) > list_node > list_node > $o ) > list_node ).
thf(func_def_234,type,
sK156: ( ( node > node ) > list_node > list_node > $o ) > list_node ).
thf(func_def_235,type,
sK157: ( ( node > node ) > list_node > list_node > $o ) > node ).
thf(func_def_236,type,
sK158: ( ( node > node ) > list_node > list_node > $o ) > node > node ).
thf(func_def_237,type,
sK159: list_node > node > list_node > list_node > list_node ).
thf(func_def_238,type,
sK160: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(func_def_239,type,
sK161: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_240,type,
sK162: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(func_def_241,type,
sK163: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(func_def_242,type,
sK164: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_243,type,
sK165: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(func_def_244,type,
sK166: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_245,type,
sK167: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(func_def_246,type,
sK168: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(func_def_247,type,
sK169: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_248,type,
sK170: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(func_def_249,type,
sK171: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(func_def_250,type,
sK172: ( list_node > list_node > $o ) > ( node > node > $o ) > node ).
thf(func_def_251,type,
sK173: ( list_node > list_node > $o ) > ( node > node > $o ) > list_node ).
thf(func_def_252,type,
sK174: ( list_node > list_node > $o ) > ( node > node > $o ) > node ).
thf(func_def_253,type,
sK175: ( list_node > list_node > $o ) > ( node > node > $o ) > list_node ).
thf(func_def_254,type,
sK176: ( list_node > list_node > $o ) > list_node ).
thf(func_def_255,type,
sK177: ( node > node > $o ) > ( list_node > list_node > $o ) > list_node ).
thf(func_def_256,type,
sK178: ( node > node > $o ) > ( list_node > list_node > $o ) > node ).
thf(func_def_257,type,
sK179: ( node > node > $o ) > ( list_node > list_node > $o ) > list_node ).
thf(func_def_258,type,
sK180: ( node > node > $o ) > ( list_node > list_node > $o ) > node ).
thf(func_def_259,type,
sK181: ( list_node > list_node > $o ) > list_node ).
thf(func_def_260,type,
sK182: ( list_node > $o ) > node ).
thf(func_def_261,type,
sK183: ( list_node > $o ) > node ).
thf(func_def_262,type,
sK184: ( list_node > $o ) > node ).
thf(func_def_263,type,
sK185: ( list_node > $o ) > list_node ).
thf(func_def_264,type,
sK186: node > list_node > list_node ).
thf(func_def_265,type,
sK187: node > list_node > list_node ).
thf(func_def_266,type,
sK188: ( list_node > $o ) > node ).
thf(func_def_267,type,
sK189: ( list_node > $o ) > list_node ).
thf(func_def_268,type,
sK190: ( node > $o ) > list_node > list_node ).
thf(func_def_269,type,
sK191: ( node > $o ) > list_node > node ).
thf(func_def_270,type,
sK192: ( node > $o ) > list_node > list_node ).
thf(func_def_271,type,
sK193: list_node > list_node > list_node > node > node > list_node > list_node ).
thf(func_def_272,type,
sK194: list_node > list_node > list_node > node > node > list_node > list_node ).
thf(func_def_273,type,
sK195: list_node > node > list_node ).
thf(func_def_274,type,
sK196: list_node > node > list_node ).
thf(func_def_275,type,
sK197: list_node > g > ( node > $o ) > node > list_node ).
thf(func_def_276,type,
sK198: list_node > g > ( node > $o ) > node > node ).
thf(func_def_277,type,
sK199: node > list_node > list_node ).
thf(func_def_278,type,
sK200: node > list_node > list_node ).
thf(func_def_279,type,
sK201: list_node > list_node ).
thf(func_def_280,type,
sK202: list_node > node ).
thf(func_def_281,type,
sK203: list_node > list_node ).
thf(func_def_282,type,
sK204: list_node > node ).
thf(func_def_283,type,
sK205: list_node > list_node > list_node > list_node > list_node ).
thf(func_def_284,type,
sK206: list_node > ( node > $o ) > list_node ).
thf(func_def_285,type,
sK207: list_node > ( node > $o ) > node ).
thf(func_def_286,type,
sK208: list_node > ( node > $o ) > list_node ).
thf(func_def_287,type,
sK209: list_node > list_node > list_node > node > list_node ).
thf(func_def_288,type,
sK210: node > list_node > list_node ).
thf(func_def_289,type,
sK211: node > list_node > list_node ).
thf(func_def_290,type,
sK212: node > list_node > node ).
thf(func_def_291,type,
sK213: node > list_node > list_node ).
thf(func_def_292,type,
sK214: node > list_node > list_node ).
thf(func_def_293,type,
sK215: ( list_node > $o ) > list_node ).
thf(func_def_294,type,
sK216: ( list_node > $o ) > node ).
thf(func_def_295,type,
sK217: node > list_node > list_node > list_node ).
thf(func_def_296,type,
sK218: list_node > list_node ).
thf(func_def_297,type,
sK219: list_node > node ).
thf(func_def_298,type,
sK220: list_node > list_node > list_node ).
thf(func_def_299,type,
sK221: node > list_node > list_node > node ).
thf(func_def_300,type,
sK222: ( list_node > list_node > $o ) > node ).
thf(func_def_301,type,
sK223: ( list_node > list_node > $o ) > list_node ).
thf(func_def_302,type,
sK224: ( list_node > list_node > $o ) > list_node ).
thf(func_def_303,type,
sK225: ( list_node > list_node > $o ) > list_node ).
thf(func_def_304,type,
sK226: ( ( node > node > $o ) > list_node > $o ) > list_node ).
thf(func_def_305,type,
sK227: ( ( node > node > $o ) > list_node > $o ) > node ).
thf(func_def_306,type,
sK228: ( ( node > node > $o ) > list_node > $o ) > node > node > $o ).
thf(func_def_307,type,
sK229: ( ( node > node > $o ) > list_node > $o ) > node > node > $o ).
thf(func_def_308,type,
sK230: ( list_node > $o ) > node ).
thf(func_def_309,type,
sK231: ( list_node > $o ) > list_node ).
thf(func_def_310,type,
sK232: ( list_node > $o ) > node ).
thf(func_def_311,type,
sK233: ( list_node > $o ) > node ).
thf(func_def_312,type,
sK234: node > node > list_node > g > node > list_node ).
thf(func_def_313,type,
sK235: node > node > list_node > g > node > list_node ).
thf(func_def_314,type,
sK236: list_node > node ).
thf(func_def_315,type,
sK237: list_node > node ).
thf(func_def_316,type,
sK238: list_node > list_node ).
thf(func_def_317,type,
sK239: node > g > node > node > list_node > list_node ).
thf(func_def_318,type,
sK240: node > g > node > node > list_node > list_node ).
thf(func_def_319,type,
sK241: node > g > node > node > list_node > list_node ).
thf(func_def_320,type,
sK242: ( node > $o ) > list_node > list_node ).
thf(func_def_321,type,
sK243: ( node > $o ) > list_node > node ).
thf(func_def_322,type,
sK244: ( node > $o ) > list_node > list_node ).
thf(func_def_324,type,
ph246:
!>[X0: $tType] : X0 ).
thf(f1956,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1955,f1493]) ).
thf(f1493,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f479]) ).
thf(f479,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) )
= $true ),
inference(fool_elimination,[status(thm)],[f478]) ).
thf(f478,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ),
file('/export/starexec/sandbox/tmp/tmp.4SP2TQ63UH/DTF2THF_20632.p',fact_3_assms_I7_J) ).
thf(f1955,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1954]) ).
thf(f1954,plain,
( ( $true != $true )
| ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) )
!= $true ) ),
inference(superposition,[status(thm)],[f1953,f1839]) ).
thf(f1839,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f1621,f1591]) ).
thf(f1591,plain,
( i
= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
( i
= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
file('/export/starexec/sandbox/tmp/tmp.4SP2TQ63UH/DTF2THF_20632.p',fact_1_ri__is__valid) ).
thf(f1621,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i )
= $true ),
inference(cnf_transformation,[status(thm)],[f875]) ).
thf(f875,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i )
= $true ),
inference(fool_elimination,[status(thm)],[f874]) ).
thf(f874,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i,
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i,
file('/export/starexec/sandbox/tmp/tmp.4SP2TQ63UH/DTF2THF_20632.p',fact_4_ri__props_I1_J) ).
thf(f1953,plain,
! [X0: node] :
( ( $true
!= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ X0 @ ri @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) )
| ( $true
!= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1952]) ).
thf(f1952,plain,
! [X0: node] :
( ( $true != $true )
| ( $true
!= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ X0 @ ri @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) )
| ( $true
!= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ X0 ) ) ),
inference(superposition,[status(thm)],[f1656,f1650]) ).
thf(f1650,plain,
! [X2: node,X3: list_node,X0: node,X1: list_node,X4: g,X5: node] :
( ( $true
= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ ( append_node @ X3 @ ( tl_node @ X1 ) ) @ X5 ) )
| ( $true
!= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ X3 @ X0 ) )
| ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X0 @ X1 @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1067]) ).
thf(f1067,plain,
! [X0: node,X1: list_node,X2: node,X3: list_node,X4: g,X5: node] :
( ( $true
= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ ( append_node @ X3 @ ( tl_node @ X1 ) ) @ X5 ) )
| ( $true
!= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ X3 @ X0 ) )
| ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X0 @ X1 @ X5 )
!= $true ) ),
inference(flattening,[status(thm)],[f1066]) ).
thf(f1066,plain,
! [X0: node,X1: list_node,X2: node,X3: list_node,X4: g,X5: node] :
( ( $true
= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ ( append_node @ X3 @ ( tl_node @ X1 ) ) @ X5 ) )
| ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X0 @ X1 @ X5 )
!= $true )
| ( $true
!= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ X3 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f659]) ).
thf(f659,plain,
! [X0: node,X1: list_node,X2: node,X3: list_node,X4: g,X5: node] :
( ( $true
= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ X3 @ X0 ) )
=> ( ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X0 @ X1 @ X5 )
= $true )
=> ( $true
= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ ( append_node @ X3 @ ( tl_node @ X1 ) ) @ X5 ) ) ) ),
inference(fool_elimination,[status(thm)],[f658]) ).
thf(f658,plain,
! [X0: node,X1: list_node,X2: node,X3: list_node,X4: g,X5: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ X3 @ X0 )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X0 @ X1 @ X5 )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ ( append_node @ X3 @ ( tl_node @ X1 ) ) @ X5 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X3: node,X4: list_node,X1: node,X2: list_node,X0: g,X5: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ X2 @ X3 )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ X3 @ X4 @ X5 )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ ( append_node @ X2 @ ( tl_node @ X4 ) ) @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4SP2TQ63UH/DTF2THF_20632.p',fact_5_old_Opath2__app) ).
thf(f1656,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f904]) ).
thf(f904,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
!= $true ),
inference(flattening,[status(thm)],[f407]) ).
thf(f407,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f406]) ).
thf(f406,plain,
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
inference(rectify,[status(thm)],[f352]) ).
thf(f352,negated_conjecture,
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
inference(negated_conjecture,[status(cth)],[f351]) ).
thf(f351,conjecture,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ),
file('/export/starexec/sandbox/tmp/tmp.4SP2TQ63UH/DTF2THF_20632.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP081^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.35 % Computer : n031.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue Feb 24 08:26:33 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : ITP081^1 : TPTP v9.2.1. Released v7.5.0.
% 0.21/0.47 % Domain : Interactive Theorem Proving
% 0.21/0.47 % Problem : Sledgehammer Irreducible problem prob_472__6626992_1
% 0.21/0.47 % Version : Especial.
% 0.21/0.47 % English :
% 0.21/0.47
% 0.21/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.21/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.21/0.47 % Source : [Des21]
% 0.21/0.47 % Names : Irreducible/prob_472__6626992_1 [Des21]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.60 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0
% 0.21/0.47 % Syntax : Number of formulae : 419 ( 146 unt; 68 typ; 0 def)
% 0.21/0.47 % Number of atoms : 1059 ( 603 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 14 ( 3 avg)
% 0.21/0.47 % Number of connectives : 4056 ( 203 ~; 21 |; 116 &;3214 @)
% 0.21/0.47 % ( 0 <=>; 502 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 26 ( 8 avg)
% 0.21/0.47 % Number of types : 13 ( 12 usr)
% 0.21/0.47 % Number of type conns : 242 ( 242 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 57 ( 56 usr; 17 con; 0-7 aty)
% 0.21/0.47 % Number of variables : 1257 ( 23 ^;1157 !; 77 ?;1257 :)
% 0.21/0.47 % SPC : TH0_THM_EQU_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:40:45.367
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % Could-be-implicit typings (12)
% 0.21/0.47 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mtf__edgeD_J_J,type,
% 0.21/0.47 list_P561207620_edgeD: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Option__Ooption_It__List__Olist_Itf__val_J_J,type,
% 0.21/0.47 option_list_val: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Product____Type__Oprod_Itf__node_Mtf__val_J,type,
% 0.21/0.47 produc1432036078de_val: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__List__Olist_It__List__Olist_Itf__node_J_J,type,
% 0.21/0.47 list_list_node: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Set__Oset_It__List__Olist_Itf__node_J_J,type,
% 0.21/0.47 set_list_node: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__List__Olist_Itf__node_J,type,
% 0.21/0.47 list_node: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__List__Olist_Itf__val_J,type,
% 0.21/0.47 list_val: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Set__Oset_Itf__node_J,type,
% 0.21/0.47 set_node: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Set__Oset_Itf__val_J,type,
% 0.21/0.47 set_val: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_tf__node,type,
% 0.21/0.47 node: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_tf__val,type,
% 0.21/0.47 val: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_tf__g,type,
% 0.21/0.47 g: $tType ).
% 0.21/0.47
% 0.21/0.47 % Explicit typings (56)
% 0.21/0.47 thf(sy_c_Finite__Set_Ofinite_001tf__node,type,
% 0.21/0.47 finite_finite_node: set_node > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Finite__Set_Ofinite_001tf__val,type,
% 0.21/0.47 finite_finite_val: set_val > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Graph__path_Ograph__path__base_Opath2_001tf__g_001tf__node_001tf__edgeD,type,
% 0.21/0.47 graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Graph__path_Ograph__path__base_Opath_001tf__g_001tf__node_001tf__edgeD,type,
% 0.21/0.47 graph_435229452_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > list_node > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors_001tf__g_001tf__node_001tf__edgeD,type,
% 0.21/0.47 graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Oappend_001t__List__Olist_Itf__node_J,type,
% 0.21/0.47 append_list_node: list_list_node > list_list_node > list_list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Oappend_001tf__node,type,
% 0.21/0.47 append_node: list_node > list_node > list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Oappend_001tf__val,type,
% 0.21/0.47 append_val: list_val > list_val > list_val ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Obutlast_001t__List__Olist_Itf__node_J,type,
% 0.21/0.47 butlast_list_node: list_list_node > list_list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Obutlast_001tf__node,type,
% 0.21/0.47 butlast_node: list_node > list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Obutlast_001tf__val,type,
% 0.21/0.47 butlast_val: list_val > list_val ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_OCons_001t__List__Olist_Itf__node_J,type,
% 0.21/0.47 cons_list_node: list_node > list_list_node > list_list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_OCons_001tf__node,type,
% 0.21/0.47 cons_node: node > list_node > list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_OCons_001tf__val,type,
% 0.21/0.47 cons_val: val > list_val > list_val ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__node_J,type,
% 0.21/0.47 nil_list_node: list_list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_ONil_001tf__node,type,
% 0.21/0.47 nil_node: list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_ONil_001tf__val,type,
% 0.21/0.47 nil_val: list_val ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_Ohd_001tf__node,type,
% 0.21/0.47 hd_node: list_node > node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_Ohd_001tf__val,type,
% 0.21/0.47 hd_val: list_val > val ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_Oset_001t__List__Olist_Itf__node_J,type,
% 0.21/0.47 set_list_node2: list_list_node > set_list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_Oset_001tf__node,type,
% 0.21/0.47 set_node2: list_node > set_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_Oset_001tf__val,type,
% 0.21/0.47 set_val2: list_val > set_val ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_Otl_001t__List__Olist_Itf__node_J,type,
% 0.21/0.47 tl_list_node: list_list_node > list_list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_Otl_001tf__node,type,
% 0.21/0.47 tl_node: list_node > list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_Otl_001tf__val,type,
% 0.21/0.47 tl_val: list_val > list_val ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__node_J,type,
% 0.21/0.47 ord_less_eq_set_node: set_node > set_node > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__val_J,type,
% 0.21/0.47 ord_less_eq_set_val: set_val > set_val > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 0.21/0.47 sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode_001tf__g_001tf__node_001tf__val,type,
% 0.21/0.47 sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg_001tf__g_001tf__node_001tf__val,type,
% 0.21/0.47 sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_OCollect_001tf__node,type,
% 0.21/0.47 collect_node: ( node > $o ) > set_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_OCollect_001tf__val,type,
% 0.21/0.47 collect_val: ( val > $o ) > set_val ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Sublist_Oprefix_001tf__node,type,
% 0.21/0.47 prefix_node: list_node > list_node > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Sublist_Osuffix_001tf__node,type,
% 0.21/0.47 suffix_node: list_node > list_node > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_member_001t__List__Olist_Itf__node_J,type,
% 0.21/0.47 member_list_node: list_node > set_list_node > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_member_001tf__node,type,
% 0.21/0.47 member_node: node > set_node > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_member_001tf__val,type,
% 0.21/0.47 member_val: val > set_val > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v__092_060alpha_062n,type,
% 0.21/0.47 alpha_n: g > list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v__092_060phi_062_092_060_094sub_062r,type,
% 0.21/0.47 phi_r: val ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_defs,type,
% 0.21/0.47 defs: g > node > set_val ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_g,type,
% 0.21/0.47 g2: g ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_i____,type,
% 0.21/0.47 i: node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_inEdges_H,type,
% 0.21/0.47 inEdges: g > node > list_P561207620_edgeD ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_invar,type,
% 0.21/0.47 invar: g > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_m,type,
% 0.21/0.47 m: node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_ms,type,
% 0.21/0.47 ms: list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_ms_H____,type,
% 0.21/0.47 ms2: list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_n,type,
% 0.21/0.47 n: node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_ns,type,
% 0.21/0.47 ns: list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_phis,type,
% 0.21/0.47 phis: g > produc1432036078de_val > option_list_val ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____,type,
% 0.21/0.47 pred_phi_r: node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_r,type,
% 0.21/0.47 r: val ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_ri____,type,
% 0.21/0.47 ri: list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_rs_H____,type,
% 0.21/0.47 rs: list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_rs____,type,
% 0.21/0.47 rs2: list_node ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_s,type,
% 0.21/0.47 s: val ).
% 0.21/0.47
% 0.21/0.47 % Relevant facts (350)
% 0.21/0.47 thf(fact_0_False,axiom,
% 0.21/0.47 r != phi_r ).
% 0.21/0.47
% 0.21/0.47 % False
% 0.21/0.47 thf(fact_1_ri__is__valid,axiom,
% 0.21/0.47 ( i
% 0.21/0.47 = ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ).
% 0.21/0.47
% 0.21/0.47 % ri_is_valid
% 0.21/0.47 thf(fact_2_old_Oinvar,axiom,
% 0.21/0.47 ! [G: g] : ( invar @ G ) ).
% 0.21/0.47
% 0.21/0.47 % old.invar
% 0.21/0.47 thf(fact_3_assms_I7_J,axiom,
% 0.21/0.47 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ).
% 0.21/0.47
% 0.21/0.47 % assms(7)
% 0.21/0.47 thf(fact_4_ri__props_I1_J,axiom,
% 0.21/0.47 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i ).
% 0.21/0.47
% 0.21/0.47 % ri_props(1)
% 0.21/0.47 thf(fact_5_old_Opath2__app,axiom,
% 0.21/0.47 ! [G: g,N: node,Ns: list_node,M: node,Ms: list_node,L: node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.47 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M @ Ms @ L )
% 0.21/0.47 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( tl_node @ Ms ) ) @ L ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.path2_app
% 0.21/0.47 thf(fact_6__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062,axiom,
% 0.21/0.47 ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r )
% 0.21/0.47 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ) ).
% 0.21/0.47
% 0.21/0.47 % \<open>defNode g \<phi>\<^sub>r \<noteq> defNode g r\<close>
% 0.21/0.47 thf(fact_7_rs_H__props_I1_J,axiom,
% 0.21/0.47 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r ).
% 0.21/0.47
% 0.21/0.47 % rs'_props(1)
% 0.21/0.47 thf(fact_8_assms_I10_J,axiom,
% 0.21/0.47 sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r ).
% 0.21/0.47
% 0.21/0.47 % assms(10)
% 0.21/0.47 thf(fact_9_rs__props_I1_J,axiom,
% 0.21/0.47 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ).
% 0.21/0.47
% 0.21/0.47 % rs_props(1)
% 0.21/0.47 thf(fact_10_ms_H__props_I1_J,axiom,
% 0.21/0.47 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i ).
% 0.21/0.47
% 0.21/0.47 % ms'_props(1)
% 0.21/0.47 thf(fact_11__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062i_A_061_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_061_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_092_060noteq_062_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.21/0.47 ( ( i
% 0.21/0.47 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 0.21/0.47 => ( ( ( i
% 0.21/0.47 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 0.21/0.47 => ( m != i ) )
% 0.21/0.47 => ~ ( ( i
% 0.21/0.47 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 0.21/0.47 => ( m = i ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % \<open>\<And>thesis. \<lbrakk>i = defNode g \<phi>\<^sub>r \<Longrightarrow> thesis; \<lbrakk>i \<noteq> defNode g \<phi>\<^sub>r; m = i\<rbrakk> \<Longrightarrow> thesis; \<lbrakk>i \<noteq> defNode g \<phi>\<^sub>r; m \<noteq> i\<rbrakk> \<Longrightarrow> thesis\<rbrakk> \<Longrightarrow> thesis\<close>
% 0.21/0.47 thf(fact_12_old_Opath2__split_I2_J,axiom,
% 0.21/0.47 ! [G: g,N: node,Ns: list_node,N2: node,Ns2: list_node,M: node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ Ns2 ) ) @ M )
% 0.21/0.47 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N2 @ ( cons_node @ N2 @ Ns2 ) @ M ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.path2_split(2)
% 0.21/0.47 thf(fact_13_old_Opath2__not__Nil,axiom,
% 0.21/0.47 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.47 => ( Ns != nil_node ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.path2_not_Nil
% 0.21/0.47 thf(fact_14_old_Opath2__not__Nil2,axiom,
% 0.21/0.47 ! [G: g,N: node,M: node] :
% 0.21/0.47 ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ nil_node @ M ) ).
% 0.21/0.47
% 0.21/0.47 % old.path2_not_Nil2
% 0.21/0.47 thf(fact_15_rs_H__props_I3_J,axiom,
% 0.21/0.47 member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ) ).
% 0.21/0.47
% 0.21/0.47 % rs'_props(3)
% 0.21/0.47 thf(fact_16_old_Opath2__hd__in___092_060alpha_062n,axiom,
% 0.21/0.47 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.47 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.path2_hd_in_\<alpha>n
% 0.21/0.47 thf(fact_17_old_Opath2__hd__in__ns,axiom,
% 0.21/0.47 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.47 => ( member_node @ N @ ( set_node2 @ Ns ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.path2_hd_in_ns
% 0.21/0.47 thf(fact_18_old_Opath2__in___092_060alpha_062n,axiom,
% 0.21/0.47 ! [G: g,N: node,Ns: list_node,M: node,L: node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.47 => ( ( member_node @ L @ ( set_node2 @ Ns ) )
% 0.21/0.47 => ( member_node @ L @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.path2_in_\<alpha>n
% 0.21/0.47 thf(fact_19_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 0.21/0.47 ! [X: list_node,Xs: list_list_node,Ys: list_list_node,Y: list_node] :
% 0.21/0.47 ( ( member_list_node @ X @ ( set_list_node2 @ Xs ) )
% 0.21/0.47 => ( member_list_node @ X @ ( set_list_node2 @ ( tl_list_node @ ( append_list_node @ Ys @ ( cons_list_node @ Y @ Xs ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.elem_set_implies_elem_tl_app_cons
% 0.21/0.47 thf(fact_20_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 0.21/0.47 ! [X: val,Xs: list_val,Ys: list_val,Y: val] :
% 0.21/0.47 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.21/0.47 => ( member_val @ X @ ( set_val2 @ ( tl_val @ ( append_val @ Ys @ ( cons_val @ Y @ Xs ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.elem_set_implies_elem_tl_app_cons
% 0.21/0.47 thf(fact_21_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 0.21/0.47 ! [X: node,Xs: list_node,Ys: list_node,Y: node] :
% 0.21/0.47 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.21/0.47 => ( member_node @ X @ ( set_node2 @ ( tl_node @ ( append_node @ Ys @ ( cons_node @ Y @ Xs ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.elem_set_implies_elem_tl_app_cons
% 0.21/0.47 thf(fact_22_ri__props_I2_J,axiom,
% 0.21/0.47 member_node @ i @ ( set_node2 @ ms ) ).
% 0.21/0.47
% 0.21/0.47 % ri_props(2)
% 0.21/0.47 thf(fact_23_old_Opath2__tl__in___092_060alpha_062n,axiom,
% 0.21/0.47 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.47 => ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.path2_tl_in_\<alpha>n
% 0.21/0.47 thf(fact_24_old_Opath2__last__in__ns,axiom,
% 0.21/0.47 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.47 => ( member_node @ M @ ( set_node2 @ Ns ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.path2_last_in_ns
% 0.21/0.47 thf(fact_25_old_Opath2__split_I1_J,axiom,
% 0.21/0.47 ! [G: g,N: node,Ns: list_node,N2: node,Ns2: list_node,M: node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ Ns2 ) ) @ M )
% 0.21/0.47 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ nil_node ) ) @ N2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.path2_split(1)
% 0.21/0.47 thf(fact_26_rs__props_I3_J,axiom,
% 0.21/0.47 ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % rs_props(3)
% 0.21/0.47 thf(fact_27_rs_H__loopfree,axiom,
% 0.21/0.47 ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % rs'_loopfree
% 0.21/0.47 thf(fact_28_rs__def,axiom,
% 0.21/0.47 ( rs2
% 0.21/0.47 = ( append_node @ rs @ ( cons_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ nil_node ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % rs_def
% 0.21/0.47 thf(fact_29_ri__props_I4_J,axiom,
% 0.21/0.47 prefix_node @ ri @ rs2 ).
% 0.21/0.47
% 0.21/0.47 % ri_props(4)
% 0.21/0.47 thf(fact_30_old_Oempty__path2,axiom,
% 0.21/0.47 ! [N: node,G: g] :
% 0.21/0.47 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.21/0.47 => ( ( invar @ G )
% 0.21/0.47 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( cons_node @ N @ nil_node ) @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.empty_path2
% 0.21/0.47 thf(fact_31_ms_H__props_I3_J,axiom,
% 0.21/0.47 ~ ( member_node @ i @ ( set_node2 @ ( butlast_node @ ms2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ms'_props(3)
% 0.21/0.47 thf(fact_32_rs_H__props_I4_J,axiom,
% 0.21/0.47 member_node @ pred_phi_r @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % rs'_props(4)
% 0.21/0.47 thf(fact_33_assms_I8_J,axiom,
% 0.21/0.47 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ).
% 0.21/0.47
% 0.21/0.47 % assms(8)
% 0.21/0.47 thf(fact_34_tl__append2,axiom,
% 0.21/0.47 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.21/0.47 ( ( Xs != nil_list_node )
% 0.21/0.47 => ( ( tl_list_node @ ( append_list_node @ Xs @ Ys ) )
% 0.21/0.47 = ( append_list_node @ ( tl_list_node @ Xs ) @ Ys ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tl_append2
% 0.21/0.47 thf(fact_35_tl__append2,axiom,
% 0.21/0.47 ! [Xs: list_val,Ys: list_val] :
% 0.21/0.47 ( ( Xs != nil_val )
% 0.21/0.47 => ( ( tl_val @ ( append_val @ Xs @ Ys ) )
% 0.21/0.47 = ( append_val @ ( tl_val @ Xs ) @ Ys ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tl_append2
% 0.21/0.47 thf(fact_36_tl__append2,axiom,
% 0.21/0.47 ! [Xs: list_node,Ys: list_node] :
% 0.21/0.47 ( ( Xs != nil_node )
% 0.21/0.47 => ( ( tl_node @ ( append_node @ Xs @ Ys ) )
% 0.21/0.47 = ( append_node @ ( tl_node @ Xs ) @ Ys ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tl_append2
% 0.21/0.47 thf(fact_37_list__e__eq__lel_I2_J,axiom,
% 0.21/0.47 ! [L1: list_val,E: val,L2: list_val,E2: val] :
% 0.21/0.47 ( ( ( append_val @ L1 @ ( cons_val @ E @ L2 ) )
% 0.21/0.47 = ( cons_val @ E2 @ nil_val ) )
% 0.21/0.47 = ( ( L1 = nil_val )
% 0.21/0.47 & ( E = E2 )
% 0.21/0.47 & ( L2 = nil_val ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_e_eq_lel(2)
% 0.21/0.47 thf(fact_38_list__e__eq__lel_I2_J,axiom,
% 0.21/0.47 ! [L1: list_list_node,E: list_node,L2: list_list_node,E2: list_node] :
% 0.21/0.47 ( ( ( append_list_node @ L1 @ ( cons_list_node @ E @ L2 ) )
% 0.21/0.47 = ( cons_list_node @ E2 @ nil_list_node ) )
% 0.21/0.47 = ( ( L1 = nil_list_node )
% 0.21/0.47 & ( E = E2 )
% 0.21/0.47 & ( L2 = nil_list_node ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_e_eq_lel(2)
% 0.21/0.47 thf(fact_39_list__e__eq__lel_I2_J,axiom,
% 0.21/0.47 ! [L1: list_node,E: node,L2: list_node,E2: node] :
% 0.21/0.47 ( ( ( append_node @ L1 @ ( cons_node @ E @ L2 ) )
% 0.21/0.47 = ( cons_node @ E2 @ nil_node ) )
% 0.21/0.47 = ( ( L1 = nil_node )
% 0.21/0.47 & ( E = E2 )
% 0.21/0.47 & ( L2 = nil_node ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_e_eq_lel(2)
% 0.21/0.47 thf(fact_40_list__e__eq__lel_I1_J,axiom,
% 0.21/0.47 ! [E2: val,L1: list_val,E: val,L2: list_val] :
% 0.21/0.47 ( ( ( cons_val @ E2 @ nil_val )
% 0.21/0.47 = ( append_val @ L1 @ ( cons_val @ E @ L2 ) ) )
% 0.21/0.47 = ( ( L1 = nil_val )
% 0.21/0.47 & ( E = E2 )
% 0.21/0.47 & ( L2 = nil_val ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_e_eq_lel(1)
% 0.21/0.47 thf(fact_41_list__e__eq__lel_I1_J,axiom,
% 0.21/0.47 ! [E2: list_node,L1: list_list_node,E: list_node,L2: list_list_node] :
% 0.21/0.47 ( ( ( cons_list_node @ E2 @ nil_list_node )
% 0.21/0.47 = ( append_list_node @ L1 @ ( cons_list_node @ E @ L2 ) ) )
% 0.21/0.47 = ( ( L1 = nil_list_node )
% 0.21/0.47 & ( E = E2 )
% 0.21/0.47 & ( L2 = nil_list_node ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_e_eq_lel(1)
% 0.21/0.47 thf(fact_42_list__e__eq__lel_I1_J,axiom,
% 0.21/0.47 ! [E2: node,L1: list_node,E: node,L2: list_node] :
% 0.21/0.47 ( ( ( cons_node @ E2 @ nil_node )
% 0.21/0.47 = ( append_node @ L1 @ ( cons_node @ E @ L2 ) ) )
% 0.21/0.47 = ( ( L1 = nil_node )
% 0.21/0.47 & ( E = E2 )
% 0.21/0.47 & ( L2 = nil_node ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_e_eq_lel(1)
% 0.21/0.47 thf(fact_43_list__se__match_I4_J,axiom,
% 0.21/0.47 ! [L2: list_val,A: val,L1: list_val] :
% 0.21/0.47 ( ( L2 != nil_val )
% 0.21/0.47 => ( ( ( cons_val @ A @ nil_val )
% 0.21/0.47 = ( append_val @ L1 @ L2 ) )
% 0.21/0.47 = ( ( L1 = nil_val )
% 0.21/0.47 & ( L2
% 0.21/0.47 = ( cons_val @ A @ nil_val ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_se_match(4)
% 0.21/0.47 thf(fact_44_list__se__match_I4_J,axiom,
% 0.21/0.47 ! [L2: list_list_node,A: list_node,L1: list_list_node] :
% 0.21/0.47 ( ( L2 != nil_list_node )
% 0.21/0.47 => ( ( ( cons_list_node @ A @ nil_list_node )
% 0.21/0.47 = ( append_list_node @ L1 @ L2 ) )
% 0.21/0.47 = ( ( L1 = nil_list_node )
% 0.21/0.47 & ( L2
% 0.21/0.47 = ( cons_list_node @ A @ nil_list_node ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_se_match(4)
% 0.21/0.47 thf(fact_45_list__se__match_I4_J,axiom,
% 0.21/0.47 ! [L2: list_node,A: node,L1: list_node] :
% 0.21/0.47 ( ( L2 != nil_node )
% 0.21/0.47 => ( ( ( cons_node @ A @ nil_node )
% 0.21/0.47 = ( append_node @ L1 @ L2 ) )
% 0.21/0.47 = ( ( L1 = nil_node )
% 0.21/0.47 & ( L2
% 0.21/0.47 = ( cons_node @ A @ nil_node ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_se_match(4)
% 0.21/0.47 thf(fact_46_list__se__match_I3_J,axiom,
% 0.21/0.47 ! [L1: list_val,A: val,L2: list_val] :
% 0.21/0.47 ( ( L1 != nil_val )
% 0.21/0.47 => ( ( ( cons_val @ A @ nil_val )
% 0.21/0.47 = ( append_val @ L1 @ L2 ) )
% 0.21/0.47 = ( ( L1
% 0.21/0.47 = ( cons_val @ A @ nil_val ) )
% 0.21/0.47 & ( L2 = nil_val ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_se_match(3)
% 0.21/0.47 thf(fact_47_list__se__match_I3_J,axiom,
% 0.21/0.47 ! [L1: list_list_node,A: list_node,L2: list_list_node] :
% 0.21/0.47 ( ( L1 != nil_list_node )
% 0.21/0.47 => ( ( ( cons_list_node @ A @ nil_list_node )
% 0.21/0.47 = ( append_list_node @ L1 @ L2 ) )
% 0.21/0.47 = ( ( L1
% 0.21/0.47 = ( cons_list_node @ A @ nil_list_node ) )
% 0.21/0.47 & ( L2 = nil_list_node ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_se_match(3)
% 0.21/0.47 thf(fact_48_list__se__match_I3_J,axiom,
% 0.21/0.47 ! [L1: list_node,A: node,L2: list_node] :
% 0.21/0.47 ( ( L1 != nil_node )
% 0.21/0.47 => ( ( ( cons_node @ A @ nil_node )
% 0.21/0.47 = ( append_node @ L1 @ L2 ) )
% 0.21/0.47 = ( ( L1
% 0.21/0.47 = ( cons_node @ A @ nil_node ) )
% 0.21/0.47 & ( L2 = nil_node ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_se_match(3)
% 0.21/0.47 thf(fact_49_list__se__match_I2_J,axiom,
% 0.21/0.47 ! [L2: list_val,L1: list_val,A: val] :
% 0.21/0.47 ( ( L2 != nil_val )
% 0.21/0.47 => ( ( ( append_val @ L1 @ L2 )
% 0.21/0.47 = ( cons_val @ A @ nil_val ) )
% 0.21/0.47 = ( ( L1 = nil_val )
% 0.21/0.47 & ( L2
% 0.21/0.47 = ( cons_val @ A @ nil_val ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_se_match(2)
% 0.21/0.47 thf(fact_50_list__se__match_I2_J,axiom,
% 0.21/0.47 ! [L2: list_list_node,L1: list_list_node,A: list_node] :
% 0.21/0.47 ( ( L2 != nil_list_node )
% 0.21/0.47 => ( ( ( append_list_node @ L1 @ L2 )
% 0.21/0.47 = ( cons_list_node @ A @ nil_list_node ) )
% 0.21/0.47 = ( ( L1 = nil_list_node )
% 0.21/0.47 & ( L2
% 0.21/0.47 = ( cons_list_node @ A @ nil_list_node ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_se_match(2)
% 0.21/0.47 thf(fact_51_list__se__match_I2_J,axiom,
% 0.21/0.47 ! [L2: list_node,L1: list_node,A: node] :
% 0.21/0.47 ( ( L2 != nil_node )
% 0.21/0.47 => ( ( ( append_node @ L1 @ L2 )
% 0.21/0.47 = ( cons_node @ A @ nil_node ) )
% 0.21/0.47 = ( ( L1 = nil_node )
% 0.21/0.47 & ( L2
% 0.21/0.47 = ( cons_node @ A @ nil_node ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_se_match(2)
% 0.21/0.47 thf(fact_52_list__se__match_I1_J,axiom,
% 0.21/0.47 ! [L1: list_val,L2: list_val,A: val] :
% 0.21/0.47 ( ( L1 != nil_val )
% 0.21/0.47 => ( ( ( append_val @ L1 @ L2 )
% 0.21/0.47 = ( cons_val @ A @ nil_val ) )
% 0.21/0.47 = ( ( L1
% 0.21/0.47 = ( cons_val @ A @ nil_val ) )
% 0.21/0.47 & ( L2 = nil_val ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_se_match(1)
% 0.21/0.47 thf(fact_53_list__se__match_I1_J,axiom,
% 0.21/0.47 ! [L1: list_list_node,L2: list_list_node,A: list_node] :
% 0.21/0.47 ( ( L1 != nil_list_node )
% 0.21/0.47 => ( ( ( append_list_node @ L1 @ L2 )
% 0.21/0.47 = ( cons_list_node @ A @ nil_list_node ) )
% 0.21/0.47 = ( ( L1
% 0.21/0.47 = ( cons_list_node @ A @ nil_list_node ) )
% 0.21/0.47 & ( L2 = nil_list_node ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_se_match(1)
% 0.21/0.47 thf(fact_54_list__se__match_I1_J,axiom,
% 0.21/0.47 ! [L1: list_node,L2: list_node,A: node] :
% 0.21/0.47 ( ( L1 != nil_node )
% 0.21/0.47 => ( ( ( append_node @ L1 @ L2 )
% 0.21/0.47 = ( cons_node @ A @ nil_node ) )
% 0.21/0.47 = ( ( L1
% 0.21/0.47 = ( cons_node @ A @ nil_node ) )
% 0.21/0.47 & ( L2 = nil_node ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_se_match(1)
% 0.21/0.47 thf(fact_55_list__ee__eq__leel_I2_J,axiom,
% 0.21/0.47 ! [L1: list_val,E1: val,E22: val,L2: list_val,E12: val,E23: val] :
% 0.21/0.47 ( ( ( append_val @ L1 @ ( cons_val @ E1 @ ( cons_val @ E22 @ L2 ) ) )
% 0.21/0.47 = ( cons_val @ E12 @ ( cons_val @ E23 @ nil_val ) ) )
% 0.21/0.47 = ( ( L1 = nil_val )
% 0.21/0.47 & ( E12 = E1 )
% 0.21/0.47 & ( E23 = E22 )
% 0.21/0.47 & ( L2 = nil_val ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_ee_eq_leel(2)
% 0.21/0.47 thf(fact_56_list__ee__eq__leel_I2_J,axiom,
% 0.21/0.47 ! [L1: list_list_node,E1: list_node,E22: list_node,L2: list_list_node,E12: list_node,E23: list_node] :
% 0.21/0.47 ( ( ( append_list_node @ L1 @ ( cons_list_node @ E1 @ ( cons_list_node @ E22 @ L2 ) ) )
% 0.21/0.47 = ( cons_list_node @ E12 @ ( cons_list_node @ E23 @ nil_list_node ) ) )
% 0.21/0.47 = ( ( L1 = nil_list_node )
% 0.21/0.47 & ( E12 = E1 )
% 0.21/0.47 & ( E23 = E22 )
% 0.21/0.47 & ( L2 = nil_list_node ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_ee_eq_leel(2)
% 0.21/0.47 thf(fact_57_list__ee__eq__leel_I2_J,axiom,
% 0.21/0.47 ! [L1: list_node,E1: node,E22: node,L2: list_node,E12: node,E23: node] :
% 0.21/0.47 ( ( ( append_node @ L1 @ ( cons_node @ E1 @ ( cons_node @ E22 @ L2 ) ) )
% 0.21/0.47 = ( cons_node @ E12 @ ( cons_node @ E23 @ nil_node ) ) )
% 0.21/0.47 = ( ( L1 = nil_node )
% 0.21/0.47 & ( E12 = E1 )
% 0.21/0.47 & ( E23 = E22 )
% 0.21/0.47 & ( L2 = nil_node ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_ee_eq_leel(2)
% 0.21/0.47 thf(fact_58_list__ee__eq__leel_I1_J,axiom,
% 0.21/0.47 ! [E12: val,E23: val,L1: list_val,E1: val,E22: val,L2: list_val] :
% 0.21/0.47 ( ( ( cons_val @ E12 @ ( cons_val @ E23 @ nil_val ) )
% 0.21/0.47 = ( append_val @ L1 @ ( cons_val @ E1 @ ( cons_val @ E22 @ L2 ) ) ) )
% 0.21/0.47 = ( ( L1 = nil_val )
% 0.21/0.47 & ( E12 = E1 )
% 0.21/0.47 & ( E23 = E22 )
% 0.21/0.47 & ( L2 = nil_val ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_ee_eq_leel(1)
% 0.21/0.47 thf(fact_59_list__ee__eq__leel_I1_J,axiom,
% 0.21/0.47 ! [E12: list_node,E23: list_node,L1: list_list_node,E1: list_node,E22: list_node,L2: list_list_node] :
% 0.21/0.47 ( ( ( cons_list_node @ E12 @ ( cons_list_node @ E23 @ nil_list_node ) )
% 0.21/0.47 = ( append_list_node @ L1 @ ( cons_list_node @ E1 @ ( cons_list_node @ E22 @ L2 ) ) ) )
% 0.21/0.47 = ( ( L1 = nil_list_node )
% 0.21/0.47 & ( E12 = E1 )
% 0.21/0.47 & ( E23 = E22 )
% 0.21/0.47 & ( L2 = nil_list_node ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_ee_eq_leel(1)
% 0.21/0.47 thf(fact_60_list__ee__eq__leel_I1_J,axiom,
% 0.21/0.47 ! [E12: node,E23: node,L1: list_node,E1: node,E22: node,L2: list_node] :
% 0.21/0.47 ( ( ( cons_node @ E12 @ ( cons_node @ E23 @ nil_node ) )
% 0.21/0.47 = ( append_node @ L1 @ ( cons_node @ E1 @ ( cons_node @ E22 @ L2 ) ) ) )
% 0.21/0.47 = ( ( L1 = nil_node )
% 0.21/0.47 & ( E12 = E1 )
% 0.21/0.47 & ( E23 = E22 )
% 0.21/0.47 & ( L2 = nil_node ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_ee_eq_leel(1)
% 0.21/0.47 thf(fact_61_ms_H__props_I2_J,axiom,
% 0.21/0.47 prefix_node @ ms2 @ ms ).
% 0.21/0.47
% 0.21/0.47 % ms'_props(2)
% 0.21/0.47 thf(fact_62_ri__props_I3_J,axiom,
% 0.21/0.47 ! [X2: node] :
% 0.21/0.47 ( ( member_node @ X2 @ ( set_node2 @ ( butlast_node @ ri ) ) )
% 0.21/0.47 => ~ ( member_node @ X2 @ ( set_node2 @ ms ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ri_props(3)
% 0.21/0.47 thf(fact_63_list_Oinject,axiom,
% 0.21/0.47 ! [X21: val,X22: list_val,Y21: val,Y22: list_val] :
% 0.21/0.47 ( ( ( cons_val @ X21 @ X22 )
% 0.21/0.47 = ( cons_val @ Y21 @ Y22 ) )
% 0.21/0.47 = ( ( X21 = Y21 )
% 0.21/0.47 & ( X22 = Y22 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list.inject
% 0.21/0.47 thf(fact_64_list_Oinject,axiom,
% 0.21/0.47 ! [X21: list_node,X22: list_list_node,Y21: list_node,Y22: list_list_node] :
% 0.21/0.47 ( ( ( cons_list_node @ X21 @ X22 )
% 0.21/0.47 = ( cons_list_node @ Y21 @ Y22 ) )
% 0.21/0.47 = ( ( X21 = Y21 )
% 0.21/0.47 & ( X22 = Y22 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list.inject
% 0.21/0.47 thf(fact_65_list_Oinject,axiom,
% 0.21/0.47 ! [X21: node,X22: list_node,Y21: node,Y22: list_node] :
% 0.21/0.47 ( ( ( cons_node @ X21 @ X22 )
% 0.21/0.47 = ( cons_node @ Y21 @ Y22 ) )
% 0.21/0.47 = ( ( X21 = Y21 )
% 0.21/0.47 & ( X22 = Y22 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list.inject
% 0.21/0.47 thf(fact_66_append_Oassoc,axiom,
% 0.21/0.47 ! [A: list_val,B: list_val,C: list_val] :
% 0.21/0.47 ( ( append_val @ ( append_val @ A @ B ) @ C )
% 0.21/0.47 = ( append_val @ A @ ( append_val @ B @ C ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append.assoc
% 0.21/0.47 thf(fact_67_append_Oassoc,axiom,
% 0.21/0.47 ! [A: list_node,B: list_node,C: list_node] :
% 0.21/0.47 ( ( append_node @ ( append_node @ A @ B ) @ C )
% 0.21/0.47 = ( append_node @ A @ ( append_node @ B @ C ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append.assoc
% 0.21/0.47 thf(fact_68_mem__Collect__eq,axiom,
% 0.21/0.47 ! [A: val,P: val > $o] :
% 0.21/0.47 ( ( member_val @ A @ ( collect_val @ P ) )
% 0.21/0.47 = ( P @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 % mem_Collect_eq
% 0.21/0.47 thf(fact_69_mem__Collect__eq,axiom,
% 0.21/0.47 ! [A: node,P: node > $o] :
% 0.21/0.47 ( ( member_node @ A @ ( collect_node @ P ) )
% 0.21/0.47 = ( P @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 % mem_Collect_eq
% 0.21/0.47 thf(fact_70_Collect__mem__eq,axiom,
% 0.21/0.47 ! [A2: set_val] :
% 0.21/0.47 ( ( collect_val
% 0.21/0.47 @ ^ [X3: val] : ( member_val @ X3 @ A2 ) )
% 0.21/0.47 = A2 ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mem_eq
% 0.21/0.47 thf(fact_71_Collect__mem__eq,axiom,
% 0.21/0.47 ! [A2: set_node] :
% 0.21/0.47 ( ( collect_node
% 0.21/0.47 @ ^ [X3: node] : ( member_node @ X3 @ A2 ) )
% 0.21/0.47 = A2 ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mem_eq
% 0.21/0.47 thf(fact_72_Collect__cong,axiom,
% 0.21/0.47 ! [P: node > $o,Q: node > $o] :
% 0.21/0.47 ( ! [X4: node] :
% 0.21/0.47 ( ( P @ X4 )
% 0.21/0.47 = ( Q @ X4 ) )
% 0.21/0.47 => ( ( collect_node @ P )
% 0.21/0.47 = ( collect_node @ Q ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_cong
% 0.21/0.47 thf(fact_73_Collect__cong,axiom,
% 0.21/0.47 ! [P: val > $o,Q: val > $o] :
% 0.21/0.47 ( ! [X4: val] :
% 0.21/0.47 ( ( P @ X4 )
% 0.21/0.47 = ( Q @ X4 ) )
% 0.21/0.47 => ( ( collect_val @ P )
% 0.21/0.47 = ( collect_val @ Q ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_cong
% 0.21/0.47 thf(fact_74_append__assoc,axiom,
% 0.21/0.47 ! [Xs: list_val,Ys: list_val,Zs: list_val] :
% 0.21/0.47 ( ( append_val @ ( append_val @ Xs @ Ys ) @ Zs )
% 0.21/0.47 = ( append_val @ Xs @ ( append_val @ Ys @ Zs ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_assoc
% 0.21/0.47 thf(fact_75_append__assoc,axiom,
% 0.21/0.47 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.21/0.47 ( ( append_node @ ( append_node @ Xs @ Ys ) @ Zs )
% 0.21/0.47 = ( append_node @ Xs @ ( append_node @ Ys @ Zs ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_assoc
% 0.21/0.47 thf(fact_76_append__same__eq,axiom,
% 0.21/0.47 ! [Ys: list_val,Xs: list_val,Zs: list_val] :
% 0.21/0.47 ( ( ( append_val @ Ys @ Xs )
% 0.21/0.47 = ( append_val @ Zs @ Xs ) )
% 0.21/0.47 = ( Ys = Zs ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_same_eq
% 0.21/0.47 thf(fact_77_append__same__eq,axiom,
% 0.21/0.47 ! [Ys: list_node,Xs: list_node,Zs: list_node] :
% 0.21/0.47 ( ( ( append_node @ Ys @ Xs )
% 0.21/0.47 = ( append_node @ Zs @ Xs ) )
% 0.21/0.47 = ( Ys = Zs ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_same_eq
% 0.21/0.47 thf(fact_78_same__append__eq,axiom,
% 0.21/0.47 ! [Xs: list_val,Ys: list_val,Zs: list_val] :
% 0.21/0.47 ( ( ( append_val @ Xs @ Ys )
% 0.21/0.47 = ( append_val @ Xs @ Zs ) )
% 0.21/0.47 = ( Ys = Zs ) ) ).
% 0.21/0.47
% 0.21/0.47 % same_append_eq
% 0.21/0.47 thf(fact_79_same__append__eq,axiom,
% 0.21/0.47 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.21/0.47 ( ( ( append_node @ Xs @ Ys )
% 0.21/0.47 = ( append_node @ Xs @ Zs ) )
% 0.21/0.47 = ( Ys = Zs ) ) ).
% 0.21/0.47
% 0.21/0.47 % same_append_eq
% 0.21/0.47 thf(fact_80_old_Opredecessor__is__node,axiom,
% 0.21/0.47 ! [N: node,G: g,N2: node] :
% 0.21/0.47 ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N2 ) ) )
% 0.21/0.47 => ( ( invar @ G )
% 0.21/0.47 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.predecessor_is_node
% 0.21/0.47 thf(fact_81_old_Osuccessor__is__node,axiom,
% 0.21/0.47 ! [N: node,G: g,N2: node] :
% 0.21/0.47 ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N2 ) ) )
% 0.21/0.47 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.21/0.47 => ( ( invar @ G )
% 0.21/0.47 => ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.successor_is_node
% 0.21/0.47 thf(fact_82_old_Osuccessor__in___092_060alpha_062n,axiom,
% 0.21/0.47 ! [G: g,N: node] :
% 0.21/0.47 ( ( ( graph_272749361_edgeD @ inEdges @ G @ N )
% 0.21/0.47 != nil_node )
% 0.21/0.47 => ( ( invar @ G )
% 0.21/0.47 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.successor_in_\<alpha>n
% 0.21/0.47 thf(fact_83_old_Opath2__app_H,axiom,
% 0.21/0.47 ! [G: g,N: node,Ns: list_node,M: node,Ms: list_node,L: node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.47 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M @ Ms @ L )
% 0.21/0.47 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ ( butlast_node @ Ns ) @ Ms ) @ L ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.path2_app'
% 0.21/0.47 thf(fact_84_append__Nil2,axiom,
% 0.21/0.47 ! [Xs: list_list_node] :
% 0.21/0.47 ( ( append_list_node @ Xs @ nil_list_node )
% 0.21/0.47 = Xs ) ).
% 0.21/0.47
% 0.21/0.47 % append_Nil2
% 0.21/0.47 thf(fact_85_append__Nil2,axiom,
% 0.21/0.47 ! [Xs: list_val] :
% 0.21/0.47 ( ( append_val @ Xs @ nil_val )
% 0.21/0.47 = Xs ) ).
% 0.21/0.47
% 0.21/0.47 % append_Nil2
% 0.21/0.47 thf(fact_86_append__Nil2,axiom,
% 0.21/0.47 ! [Xs: list_node] :
% 0.21/0.47 ( ( append_node @ Xs @ nil_node )
% 0.21/0.47 = Xs ) ).
% 0.21/0.47
% 0.21/0.47 % append_Nil2
% 0.21/0.47 thf(fact_87_append__self__conv,axiom,
% 0.21/0.47 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.21/0.47 ( ( ( append_list_node @ Xs @ Ys )
% 0.21/0.47 = Xs )
% 0.21/0.47 = ( Ys = nil_list_node ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_self_conv
% 0.21/0.47 thf(fact_88_append__self__conv,axiom,
% 0.21/0.47 ! [Xs: list_val,Ys: list_val] :
% 0.21/0.47 ( ( ( append_val @ Xs @ Ys )
% 0.21/0.47 = Xs )
% 0.21/0.47 = ( Ys = nil_val ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_self_conv
% 0.21/0.47 thf(fact_89_append__self__conv,axiom,
% 0.21/0.47 ! [Xs: list_node,Ys: list_node] :
% 0.21/0.47 ( ( ( append_node @ Xs @ Ys )
% 0.21/0.47 = Xs )
% 0.21/0.47 = ( Ys = nil_node ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_self_conv
% 0.21/0.47 thf(fact_90_self__append__conv,axiom,
% 0.21/0.47 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.21/0.47 ( ( Xs
% 0.21/0.47 = ( append_list_node @ Xs @ Ys ) )
% 0.21/0.47 = ( Ys = nil_list_node ) ) ).
% 0.21/0.47
% 0.21/0.47 % self_append_conv
% 0.21/0.47 thf(fact_91_self__append__conv,axiom,
% 0.21/0.47 ! [Xs: list_val,Ys: list_val] :
% 0.21/0.47 ( ( Xs
% 0.21/0.47 = ( append_val @ Xs @ Ys ) )
% 0.21/0.47 = ( Ys = nil_val ) ) ).
% 0.21/0.47
% 0.21/0.47 % self_append_conv
% 0.21/0.47 thf(fact_92_self__append__conv,axiom,
% 0.21/0.47 ! [Xs: list_node,Ys: list_node] :
% 0.21/0.47 ( ( Xs
% 0.21/0.47 = ( append_node @ Xs @ Ys ) )
% 0.21/0.47 = ( Ys = nil_node ) ) ).
% 0.21/0.47
% 0.21/0.47 % self_append_conv
% 0.21/0.47 thf(fact_93_append__self__conv2,axiom,
% 0.21/0.47 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.21/0.47 ( ( ( append_list_node @ Xs @ Ys )
% 0.21/0.47 = Ys )
% 0.21/0.47 = ( Xs = nil_list_node ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_self_conv2
% 0.21/0.47 thf(fact_94_append__self__conv2,axiom,
% 0.21/0.47 ! [Xs: list_val,Ys: list_val] :
% 0.21/0.47 ( ( ( append_val @ Xs @ Ys )
% 0.21/0.47 = Ys )
% 0.21/0.47 = ( Xs = nil_val ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_self_conv2
% 0.21/0.47 thf(fact_95_append__self__conv2,axiom,
% 0.21/0.47 ! [Xs: list_node,Ys: list_node] :
% 0.21/0.47 ( ( ( append_node @ Xs @ Ys )
% 0.21/0.47 = Ys )
% 0.21/0.47 = ( Xs = nil_node ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_self_conv2
% 0.21/0.47 thf(fact_96_self__append__conv2,axiom,
% 0.21/0.47 ! [Ys: list_list_node,Xs: list_list_node] :
% 0.21/0.47 ( ( Ys
% 0.21/0.47 = ( append_list_node @ Xs @ Ys ) )
% 0.21/0.47 = ( Xs = nil_list_node ) ) ).
% 0.21/0.47
% 0.21/0.47 % self_append_conv2
% 0.21/0.47 thf(fact_97_self__append__conv2,axiom,
% 0.21/0.47 ! [Ys: list_val,Xs: list_val] :
% 0.21/0.47 ( ( Ys
% 0.21/0.47 = ( append_val @ Xs @ Ys ) )
% 0.21/0.47 = ( Xs = nil_val ) ) ).
% 0.21/0.47
% 0.21/0.47 % self_append_conv2
% 0.21/0.47 thf(fact_98_self__append__conv2,axiom,
% 0.21/0.47 ! [Ys: list_node,Xs: list_node] :
% 0.21/0.47 ( ( Ys
% 0.21/0.47 = ( append_node @ Xs @ Ys ) )
% 0.21/0.47 = ( Xs = nil_node ) ) ).
% 0.21/0.47
% 0.21/0.47 % self_append_conv2
% 0.21/0.47 thf(fact_99_Nil__is__append__conv,axiom,
% 0.21/0.47 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.21/0.47 ( ( nil_list_node
% 0.21/0.47 = ( append_list_node @ Xs @ Ys ) )
% 0.21/0.47 = ( ( Xs = nil_list_node )
% 0.21/0.47 & ( Ys = nil_list_node ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Nil_is_append_conv
% 0.21/0.47 thf(fact_100_Nil__is__append__conv,axiom,
% 0.21/0.47 ! [Xs: list_val,Ys: list_val] :
% 0.21/0.47 ( ( nil_val
% 0.21/0.47 = ( append_val @ Xs @ Ys ) )
% 0.21/0.47 = ( ( Xs = nil_val )
% 0.21/0.47 & ( Ys = nil_val ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Nil_is_append_conv
% 0.21/0.47 thf(fact_101_Nil__is__append__conv,axiom,
% 0.21/0.47 ! [Xs: list_node,Ys: list_node] :
% 0.21/0.47 ( ( nil_node
% 0.21/0.47 = ( append_node @ Xs @ Ys ) )
% 0.21/0.47 = ( ( Xs = nil_node )
% 0.21/0.47 & ( Ys = nil_node ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Nil_is_append_conv
% 0.21/0.47 thf(fact_102_append__is__Nil__conv,axiom,
% 0.21/0.47 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.21/0.47 ( ( ( append_list_node @ Xs @ Ys )
% 0.21/0.47 = nil_list_node )
% 0.21/0.47 = ( ( Xs = nil_list_node )
% 0.21/0.47 & ( Ys = nil_list_node ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_is_Nil_conv
% 0.21/0.47 thf(fact_103_append__is__Nil__conv,axiom,
% 0.21/0.47 ! [Xs: list_val,Ys: list_val] :
% 0.21/0.47 ( ( ( append_val @ Xs @ Ys )
% 0.21/0.47 = nil_val )
% 0.21/0.47 = ( ( Xs = nil_val )
% 0.21/0.47 & ( Ys = nil_val ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_is_Nil_conv
% 0.21/0.47 thf(fact_104_append__is__Nil__conv,axiom,
% 0.21/0.47 ! [Xs: list_node,Ys: list_node] :
% 0.21/0.47 ( ( ( append_node @ Xs @ Ys )
% 0.21/0.47 = nil_node )
% 0.21/0.47 = ( ( Xs = nil_node )
% 0.21/0.47 & ( Ys = nil_node ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_is_Nil_conv
% 0.21/0.47 thf(fact_105_empty__append__eq__id,axiom,
% 0.21/0.47 ( ( append_list_node @ nil_list_node )
% 0.21/0.47 = ( ^ [X3: list_list_node] : X3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % empty_append_eq_id
% 0.21/0.47 thf(fact_106_empty__append__eq__id,axiom,
% 0.21/0.47 ( ( append_val @ nil_val )
% 0.21/0.47 = ( ^ [X3: list_val] : X3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % empty_append_eq_id
% 0.21/0.47 thf(fact_107_empty__append__eq__id,axiom,
% 0.21/0.47 ( ( append_node @ nil_node )
% 0.21/0.47 = ( ^ [X3: list_node] : X3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % empty_append_eq_id
% 0.21/0.47 thf(fact_108_append_Oright__neutral,axiom,
% 0.21/0.47 ! [A: list_list_node] :
% 0.21/0.47 ( ( append_list_node @ A @ nil_list_node )
% 0.21/0.47 = A ) ).
% 0.21/0.47
% 0.21/0.47 % append.right_neutral
% 0.21/0.47 thf(fact_109_append_Oright__neutral,axiom,
% 0.21/0.47 ! [A: list_val] :
% 0.21/0.47 ( ( append_val @ A @ nil_val )
% 0.21/0.47 = A ) ).
% 0.21/0.47
% 0.21/0.47 % append.right_neutral
% 0.21/0.47 thf(fact_110_append_Oright__neutral,axiom,
% 0.21/0.47 ! [A: list_node] :
% 0.21/0.47 ( ( append_node @ A @ nil_node )
% 0.21/0.47 = A ) ).
% 0.21/0.47
% 0.21/0.47 % append.right_neutral
% 0.21/0.47 thf(fact_111_old_Opath2__split__ex_H,axiom,
% 0.21/0.47 ! [G: g,N: node,Ns: list_node,M: node,X: node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.47 => ( ( member_node @ X @ ( set_node2 @ Ns ) )
% 0.21/0.47 => ~ ! [Ns_1: list_node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns_1 @ X )
% 0.21/0.47 => ! [Ns_2: list_node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ Ns_2 @ M )
% 0.21/0.47 => ( Ns
% 0.21/0.47 != ( append_node @ ( butlast_node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.path2_split_ex'
% 0.21/0.47 thf(fact_112_old_Opath2__prefix__ex,axiom,
% 0.21/0.47 ! [G: g,N: node,Ns: list_node,M: node,M2: node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.47 => ( ( member_node @ M2 @ ( set_node2 @ Ns ) )
% 0.21/0.47 => ~ ! [Ns3: list_node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns3 @ M2 )
% 0.21/0.47 => ( ( prefix_node @ Ns3 @ Ns )
% 0.21/0.47 => ( member_node @ M2 @ ( set_node2 @ ( butlast_node @ Ns3 ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.path2_prefix_ex
% 0.21/0.47 thf(fact_113_old_Opath2__split__first__prop,axiom,
% 0.21/0.47 ! [G: g,N: node,Ns: list_node,M: node,P: node > $o] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.47 => ( ? [X2: node] :
% 0.21/0.47 ( ( member_node @ X2 @ ( set_node2 @ Ns ) )
% 0.21/0.47 & ( P @ X2 ) )
% 0.21/0.47 => ~ ! [M3: node,Ns3: list_node] :
% 0.21/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns3 @ M3 )
% 0.21/0.47 => ( ( P @ M3 )
% 0.21/0.47 => ( ! [X2: node] :
% 0.21/0.47 ( ( member_node @ X2 @ ( set_node2 @ ( butlast_node @ Ns3 ) ) )
% 0.21/0.47 => ~ ( P @ X2 ) )
% 0.21/0.47 => ~ ( prefix_node @ Ns3 @ Ns ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.path2_split_first_prop
% 0.21/0.47 thf(fact_114_old_Opath2__induct,axiom,
% 0.21/0.47 ! [G: g,N: node,Ns: list_node,M: node,P: node > list_node > node > $o] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.48 => ( ( ( invar @ G )
% 0.21/0.48 => ( P @ M @ ( cons_node @ M @ nil_node ) @ M ) )
% 0.21/0.48 => ( ! [Ns4: list_node,N3: node,N4: node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N4 @ Ns4 @ M )
% 0.21/0.48 => ( ( P @ N4 @ Ns4 @ M )
% 0.21/0.48 => ( ( member_node @ N3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N4 ) ) )
% 0.21/0.48 => ( P @ N3 @ ( cons_node @ N3 @ Ns4 ) @ M ) ) ) )
% 0.21/0.48 => ( P @ N @ Ns @ M ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path2_induct
% 0.21/0.48 thf(fact_115_old_Opath2__split__ex,axiom,
% 0.21/0.48 ! [G: g,N: node,Ns: list_node,M: node,X: node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.48 => ( ( member_node @ X @ ( set_node2 @ Ns ) )
% 0.21/0.48 => ~ ! [Ns_1: list_node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns_1 @ X )
% 0.21/0.48 => ! [Ns_2: list_node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ Ns_2 @ M )
% 0.21/0.48 => ( ( Ns
% 0.21/0.48 = ( append_node @ Ns_1 @ ( tl_node @ Ns_2 ) ) )
% 0.21/0.48 => ( Ns
% 0.21/0.48 != ( append_node @ ( butlast_node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path2_split_ex
% 0.21/0.48 thf(fact_116_old_Opath2__prefix,axiom,
% 0.21/0.48 ! [G: g,N: node,Ns: list_node,M: node,Ns2: list_node,M2: node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.48 => ( ( prefix_node @ ( append_node @ Ns2 @ ( cons_node @ M2 @ nil_node ) ) @ Ns )
% 0.21/0.48 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns2 @ ( cons_node @ M2 @ nil_node ) ) @ M2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path2_prefix
% 0.21/0.48 thf(fact_117_old_Opath2__rev__induct,axiom,
% 0.21/0.48 ! [G: g,N: node,Ns: list_node,M: node,P: node > list_node > node > $o] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.48 => ( ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.21/0.48 => ( P @ N @ ( cons_node @ N @ nil_node ) @ N ) )
% 0.21/0.48 => ( ! [Ns4: list_node,M3: node,M4: node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns4 @ M3 )
% 0.21/0.48 => ( ( P @ N @ Ns4 @ M3 )
% 0.21/0.48 => ( ( member_node @ M3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M4 ) ) )
% 0.21/0.48 => ( P @ N @ ( append_node @ Ns4 @ ( cons_node @ M4 @ nil_node ) ) @ M4 ) ) ) )
% 0.21/0.48 => ( P @ N @ Ns @ M ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path2_rev_induct
% 0.21/0.48 thf(fact_118_old_Opath2__snoc,axiom,
% 0.21/0.48 ! [G: g,N: node,Ns: list_node,M: node,M2: node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.48 => ( ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M2 ) ) )
% 0.21/0.48 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ M2 @ nil_node ) ) @ M2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path2_snoc
% 0.21/0.48 thf(fact_119_append1__eq__conv,axiom,
% 0.21/0.48 ! [Xs: list_val,X: val,Ys: list_val,Y: val] :
% 0.21/0.48 ( ( ( append_val @ Xs @ ( cons_val @ X @ nil_val ) )
% 0.21/0.48 = ( append_val @ Ys @ ( cons_val @ Y @ nil_val ) ) )
% 0.21/0.48 = ( ( Xs = Ys )
% 0.21/0.48 & ( X = Y ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % append1_eq_conv
% 0.21/0.48 thf(fact_120_append1__eq__conv,axiom,
% 0.21/0.48 ! [Xs: list_list_node,X: list_node,Ys: list_list_node,Y: list_node] :
% 0.21/0.48 ( ( ( append_list_node @ Xs @ ( cons_list_node @ X @ nil_list_node ) )
% 0.21/0.48 = ( append_list_node @ Ys @ ( cons_list_node @ Y @ nil_list_node ) ) )
% 0.21/0.48 = ( ( Xs = Ys )
% 0.21/0.48 & ( X = Y ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % append1_eq_conv
% 0.21/0.48 thf(fact_121_append1__eq__conv,axiom,
% 0.21/0.48 ! [Xs: list_node,X: node,Ys: list_node,Y: node] :
% 0.21/0.48 ( ( ( append_node @ Xs @ ( cons_node @ X @ nil_node ) )
% 0.21/0.48 = ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 0.21/0.48 = ( ( Xs = Ys )
% 0.21/0.48 & ( X = Y ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % append1_eq_conv
% 0.21/0.48 thf(fact_122_butlast__snoc,axiom,
% 0.21/0.48 ! [Xs: list_val,X: val] :
% 0.21/0.48 ( ( butlast_val @ ( append_val @ Xs @ ( cons_val @ X @ nil_val ) ) )
% 0.21/0.48 = Xs ) ).
% 0.21/0.48
% 0.21/0.48 % butlast_snoc
% 0.21/0.48 thf(fact_123_butlast__snoc,axiom,
% 0.21/0.48 ! [Xs: list_list_node,X: list_node] :
% 0.21/0.48 ( ( butlast_list_node @ ( append_list_node @ Xs @ ( cons_list_node @ X @ nil_list_node ) ) )
% 0.21/0.48 = Xs ) ).
% 0.21/0.48
% 0.21/0.48 % butlast_snoc
% 0.21/0.48 thf(fact_124_butlast__snoc,axiom,
% 0.21/0.48 ! [Xs: list_node,X: node] :
% 0.21/0.48 ( ( butlast_node @ ( append_node @ Xs @ ( cons_node @ X @ nil_node ) ) )
% 0.21/0.48 = Xs ) ).
% 0.21/0.48
% 0.21/0.48 % butlast_snoc
% 0.21/0.48 thf(fact_125__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ms_H_O_A_092_060lbrakk_062g_A_092_060turnstile_062_Am_Nms_H_092_060rightarrow_062i_059_Aprefix_Ams_H_Ams_059_Ai_A_092_060notin_062_Aset_A_Ibutlast_Ams_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.21/0.48 ~ ! [Ms2: list_node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ Ms2 @ i )
% 0.21/0.48 => ( ( prefix_node @ Ms2 @ ms )
% 0.21/0.48 => ( member_node @ i @ ( set_node2 @ ( butlast_node @ Ms2 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % \<open>\<And>thesis. (\<And>ms'. \<lbrakk>g \<turnstile> m-ms'\<rightarrow>i; prefix ms' ms; i \<notin> set (butlast ms')\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.21/0.48 thf(fact_126__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062i_Ari_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nri_092_060rightarrow_062i_059_Ai_A_092_060in_062_Aset_Ams_059_A_092_060forall_062n_092_060in_062set_A_Ibutlast_Ari_J_O_An_A_092_060notin_062_Aset_Ams_059_Aprefix_Ari_Ars_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.21/0.48 ~ ! [I: node,Ri: list_node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ Ri @ I )
% 0.21/0.48 => ( ( member_node @ I @ ( set_node2 @ ms ) )
% 0.21/0.48 => ( ! [X2: node] :
% 0.21/0.48 ( ( member_node @ X2 @ ( set_node2 @ ( butlast_node @ Ri ) ) )
% 0.21/0.48 => ~ ( member_node @ X2 @ ( set_node2 @ ms ) ) )
% 0.21/0.48 => ~ ( prefix_node @ Ri @ rs2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % \<open>\<And>thesis. (\<And>i ri. \<lbrakk>g \<turnstile> defNode g r-ri\<rightarrow>i; i \<in> set ms; \<forall>n\<in>set (butlast ri). n \<notin> set ms; prefix ri rs\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.21/0.48 thf(fact_127_old_OCons__path2,axiom,
% 0.21/0.48 ! [G: g,N: node,Ns: list_node,M: node,N2: node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.48 => ( ( member_node @ N2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N ) ) )
% 0.21/0.48 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N2 @ ( cons_node @ N2 @ Ns ) @ M ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.Cons_path2
% 0.21/0.48 thf(fact_128_butlast_Osimps_I1_J,axiom,
% 0.21/0.48 ( ( butlast_list_node @ nil_list_node )
% 0.21/0.48 = nil_list_node ) ).
% 0.21/0.48
% 0.21/0.48 % butlast.simps(1)
% 0.21/0.48 thf(fact_129_butlast_Osimps_I1_J,axiom,
% 0.21/0.48 ( ( butlast_val @ nil_val )
% 0.21/0.48 = nil_val ) ).
% 0.21/0.48
% 0.21/0.48 % butlast.simps(1)
% 0.21/0.48 thf(fact_130_butlast_Osimps_I1_J,axiom,
% 0.21/0.48 ( ( butlast_node @ nil_node )
% 0.21/0.48 = nil_node ) ).
% 0.21/0.48
% 0.21/0.48 % butlast.simps(1)
% 0.21/0.48 thf(fact_131_in__set__butlastD,axiom,
% 0.21/0.48 ! [X: val,Xs: list_val] :
% 0.21/0.48 ( ( member_val @ X @ ( set_val2 @ ( butlast_val @ Xs ) ) )
% 0.21/0.48 => ( member_val @ X @ ( set_val2 @ Xs ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % in_set_butlastD
% 0.21/0.48 thf(fact_132_in__set__butlastD,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node] :
% 0.21/0.48 ( ( member_node @ X @ ( set_node2 @ ( butlast_node @ Xs ) ) )
% 0.21/0.48 => ( member_node @ X @ ( set_node2 @ Xs ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % in_set_butlastD
% 0.21/0.48 thf(fact_133_butlast__tl,axiom,
% 0.21/0.48 ! [Xs: list_val] :
% 0.21/0.48 ( ( butlast_val @ ( tl_val @ Xs ) )
% 0.21/0.48 = ( tl_val @ ( butlast_val @ Xs ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % butlast_tl
% 0.21/0.48 thf(fact_134_butlast__tl,axiom,
% 0.21/0.48 ! [Xs: list_node] :
% 0.21/0.48 ( ( butlast_node @ ( tl_node @ Xs ) )
% 0.21/0.48 = ( tl_node @ ( butlast_node @ Xs ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % butlast_tl
% 0.21/0.48 thf(fact_135_butlast_Osimps_I2_J,axiom,
% 0.21/0.48 ! [Xs: list_val,X: val] :
% 0.21/0.48 ( ( ( Xs = nil_val )
% 0.21/0.48 => ( ( butlast_val @ ( cons_val @ X @ Xs ) )
% 0.21/0.48 = nil_val ) )
% 0.21/0.48 & ( ( Xs != nil_val )
% 0.21/0.48 => ( ( butlast_val @ ( cons_val @ X @ Xs ) )
% 0.21/0.48 = ( cons_val @ X @ ( butlast_val @ Xs ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % butlast.simps(2)
% 0.21/0.48 thf(fact_136_butlast_Osimps_I2_J,axiom,
% 0.21/0.48 ! [Xs: list_list_node,X: list_node] :
% 0.21/0.48 ( ( ( Xs = nil_list_node )
% 0.21/0.48 => ( ( butlast_list_node @ ( cons_list_node @ X @ Xs ) )
% 0.21/0.48 = nil_list_node ) )
% 0.21/0.48 & ( ( Xs != nil_list_node )
% 0.21/0.48 => ( ( butlast_list_node @ ( cons_list_node @ X @ Xs ) )
% 0.21/0.48 = ( cons_list_node @ X @ ( butlast_list_node @ Xs ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % butlast.simps(2)
% 0.21/0.48 thf(fact_137_butlast_Osimps_I2_J,axiom,
% 0.21/0.48 ! [Xs: list_node,X: node] :
% 0.21/0.48 ( ( ( Xs = nil_node )
% 0.21/0.48 => ( ( butlast_node @ ( cons_node @ X @ Xs ) )
% 0.21/0.48 = nil_node ) )
% 0.21/0.48 & ( ( Xs != nil_node )
% 0.21/0.48 => ( ( butlast_node @ ( cons_node @ X @ Xs ) )
% 0.21/0.48 = ( cons_node @ X @ ( butlast_node @ Xs ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % butlast.simps(2)
% 0.21/0.48 thf(fact_138_butlast__append,axiom,
% 0.21/0.48 ! [Ys: list_list_node,Xs: list_list_node] :
% 0.21/0.48 ( ( ( Ys = nil_list_node )
% 0.21/0.48 => ( ( butlast_list_node @ ( append_list_node @ Xs @ Ys ) )
% 0.21/0.48 = ( butlast_list_node @ Xs ) ) )
% 0.21/0.48 & ( ( Ys != nil_list_node )
% 0.21/0.48 => ( ( butlast_list_node @ ( append_list_node @ Xs @ Ys ) )
% 0.21/0.48 = ( append_list_node @ Xs @ ( butlast_list_node @ Ys ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % butlast_append
% 0.21/0.48 thf(fact_139_butlast__append,axiom,
% 0.21/0.48 ! [Ys: list_val,Xs: list_val] :
% 0.21/0.48 ( ( ( Ys = nil_val )
% 0.21/0.48 => ( ( butlast_val @ ( append_val @ Xs @ Ys ) )
% 0.21/0.48 = ( butlast_val @ Xs ) ) )
% 0.21/0.48 & ( ( Ys != nil_val )
% 0.21/0.48 => ( ( butlast_val @ ( append_val @ Xs @ Ys ) )
% 0.21/0.48 = ( append_val @ Xs @ ( butlast_val @ Ys ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % butlast_append
% 0.21/0.48 thf(fact_140_butlast__append,axiom,
% 0.21/0.48 ! [Ys: list_node,Xs: list_node] :
% 0.21/0.48 ( ( ( Ys = nil_node )
% 0.21/0.48 => ( ( butlast_node @ ( append_node @ Xs @ Ys ) )
% 0.21/0.48 = ( butlast_node @ Xs ) ) )
% 0.21/0.48 & ( ( Ys != nil_node )
% 0.21/0.48 => ( ( butlast_node @ ( append_node @ Xs @ Ys ) )
% 0.21/0.48 = ( append_node @ Xs @ ( butlast_node @ Ys ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % butlast_append
% 0.21/0.48 thf(fact_141_in__set__butlast__appendI,axiom,
% 0.21/0.48 ! [X: val,Xs: list_val,Ys: list_val] :
% 0.21/0.48 ( ( ( member_val @ X @ ( set_val2 @ ( butlast_val @ Xs ) ) )
% 0.21/0.48 | ( member_val @ X @ ( set_val2 @ ( butlast_val @ Ys ) ) ) )
% 0.21/0.48 => ( member_val @ X @ ( set_val2 @ ( butlast_val @ ( append_val @ Xs @ Ys ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % in_set_butlast_appendI
% 0.21/0.48 thf(fact_142_in__set__butlast__appendI,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node,Ys: list_node] :
% 0.21/0.48 ( ( ( member_node @ X @ ( set_node2 @ ( butlast_node @ Xs ) ) )
% 0.21/0.48 | ( member_node @ X @ ( set_node2 @ ( butlast_node @ Ys ) ) ) )
% 0.21/0.48 => ( member_node @ X @ ( set_node2 @ ( butlast_node @ ( append_node @ Xs @ Ys ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % in_set_butlast_appendI
% 0.21/0.48 thf(fact_143_butlast__eq__cons__conv,axiom,
% 0.21/0.48 ! [L: list_val,X: val,Xs: list_val] :
% 0.21/0.48 ( ( ( butlast_val @ L )
% 0.21/0.48 = ( cons_val @ X @ Xs ) )
% 0.21/0.48 = ( ? [Xl: val] :
% 0.21/0.48 ( L
% 0.21/0.48 = ( cons_val @ X @ ( append_val @ Xs @ ( cons_val @ Xl @ nil_val ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % butlast_eq_cons_conv
% 0.21/0.48 thf(fact_144_butlast__eq__cons__conv,axiom,
% 0.21/0.48 ! [L: list_list_node,X: list_node,Xs: list_list_node] :
% 0.21/0.48 ( ( ( butlast_list_node @ L )
% 0.21/0.48 = ( cons_list_node @ X @ Xs ) )
% 0.21/0.48 = ( ? [Xl: list_node] :
% 0.21/0.48 ( L
% 0.21/0.48 = ( cons_list_node @ X @ ( append_list_node @ Xs @ ( cons_list_node @ Xl @ nil_list_node ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % butlast_eq_cons_conv
% 0.21/0.48 thf(fact_145_butlast__eq__cons__conv,axiom,
% 0.21/0.48 ! [L: list_node,X: node,Xs: list_node] :
% 0.21/0.48 ( ( ( butlast_node @ L )
% 0.21/0.48 = ( cons_node @ X @ Xs ) )
% 0.21/0.48 = ( ? [Xl: node] :
% 0.21/0.48 ( L
% 0.21/0.48 = ( cons_node @ X @ ( append_node @ Xs @ ( cons_node @ Xl @ nil_node ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % butlast_eq_cons_conv
% 0.21/0.48 thf(fact_146_butlast__eq__consE,axiom,
% 0.21/0.48 ! [L: list_val,X: val,Xs: list_val] :
% 0.21/0.48 ( ( ( butlast_val @ L )
% 0.21/0.48 = ( cons_val @ X @ Xs ) )
% 0.21/0.48 => ~ ! [Xl2: val] :
% 0.21/0.48 ( L
% 0.21/0.48 != ( cons_val @ X @ ( append_val @ Xs @ ( cons_val @ Xl2 @ nil_val ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % butlast_eq_consE
% 0.21/0.48 thf(fact_147_butlast__eq__consE,axiom,
% 0.21/0.48 ! [L: list_list_node,X: list_node,Xs: list_list_node] :
% 0.21/0.48 ( ( ( butlast_list_node @ L )
% 0.21/0.48 = ( cons_list_node @ X @ Xs ) )
% 0.21/0.48 => ~ ! [Xl2: list_node] :
% 0.21/0.48 ( L
% 0.21/0.48 != ( cons_list_node @ X @ ( append_list_node @ Xs @ ( cons_list_node @ Xl2 @ nil_list_node ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % butlast_eq_consE
% 0.21/0.48 thf(fact_148_butlast__eq__consE,axiom,
% 0.21/0.48 ! [L: list_node,X: node,Xs: list_node] :
% 0.21/0.48 ( ( ( butlast_node @ L )
% 0.21/0.48 = ( cons_node @ X @ Xs ) )
% 0.21/0.48 => ~ ! [Xl2: node] :
% 0.21/0.48 ( L
% 0.21/0.48 != ( cons_node @ X @ ( append_node @ Xs @ ( cons_node @ Xl2 @ nil_node ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % butlast_eq_consE
% 0.21/0.48 thf(fact_149_list__tail__coinc,axiom,
% 0.21/0.48 ! [N1: val,R1: list_val,N22: val,R2: list_val] :
% 0.21/0.48 ( ( ( cons_val @ N1 @ R1 )
% 0.21/0.48 = ( cons_val @ N22 @ R2 ) )
% 0.21/0.48 => ( ( N1 = N22 )
% 0.21/0.48 & ( R1 = R2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list_tail_coinc
% 0.21/0.48 thf(fact_150_list__tail__coinc,axiom,
% 0.21/0.48 ! [N1: list_node,R1: list_list_node,N22: list_node,R2: list_list_node] :
% 0.21/0.48 ( ( ( cons_list_node @ N1 @ R1 )
% 0.21/0.48 = ( cons_list_node @ N22 @ R2 ) )
% 0.21/0.48 => ( ( N1 = N22 )
% 0.21/0.48 & ( R1 = R2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list_tail_coinc
% 0.21/0.48 thf(fact_151_list__tail__coinc,axiom,
% 0.21/0.48 ! [N1: node,R1: list_node,N22: node,R2: list_node] :
% 0.21/0.48 ( ( ( cons_node @ N1 @ R1 )
% 0.21/0.48 = ( cons_node @ N22 @ R2 ) )
% 0.21/0.48 => ( ( N1 = N22 )
% 0.21/0.48 & ( R1 = R2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list_tail_coinc
% 0.21/0.48 thf(fact_152_not__Cons__self2,axiom,
% 0.21/0.48 ! [X: val,Xs: list_val] :
% 0.21/0.48 ( ( cons_val @ X @ Xs )
% 0.21/0.48 != Xs ) ).
% 0.21/0.48
% 0.21/0.48 % not_Cons_self2
% 0.21/0.48 thf(fact_153_not__Cons__self2,axiom,
% 0.21/0.48 ! [X: list_node,Xs: list_list_node] :
% 0.21/0.48 ( ( cons_list_node @ X @ Xs )
% 0.21/0.48 != Xs ) ).
% 0.21/0.48
% 0.21/0.48 % not_Cons_self2
% 0.21/0.48 thf(fact_154_not__Cons__self2,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node] :
% 0.21/0.48 ( ( cons_node @ X @ Xs )
% 0.21/0.48 != Xs ) ).
% 0.21/0.48
% 0.21/0.48 % not_Cons_self2
% 0.21/0.48 thf(fact_155_append__eq__appendI,axiom,
% 0.21/0.48 ! [Xs: list_val,Xs1: list_val,Zs: list_val,Ys: list_val,Us: list_val] :
% 0.21/0.48 ( ( ( append_val @ Xs @ Xs1 )
% 0.21/0.48 = Zs )
% 0.21/0.48 => ( ( Ys
% 0.21/0.48 = ( append_val @ Xs1 @ Us ) )
% 0.21/0.48 => ( ( append_val @ Xs @ Ys )
% 0.21/0.48 = ( append_val @ Zs @ Us ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % append_eq_appendI
% 0.21/0.48 thf(fact_156_append__eq__appendI,axiom,
% 0.21/0.48 ! [Xs: list_node,Xs1: list_node,Zs: list_node,Ys: list_node,Us: list_node] :
% 0.21/0.48 ( ( ( append_node @ Xs @ Xs1 )
% 0.21/0.48 = Zs )
% 0.21/0.48 => ( ( Ys
% 0.21/0.48 = ( append_node @ Xs1 @ Us ) )
% 0.21/0.48 => ( ( append_node @ Xs @ Ys )
% 0.21/0.48 = ( append_node @ Zs @ Us ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % append_eq_appendI
% 0.21/0.48 thf(fact_157_append__eq__append__conv2,axiom,
% 0.21/0.48 ! [Xs: list_val,Ys: list_val,Zs: list_val,Ts: list_val] :
% 0.21/0.48 ( ( ( append_val @ Xs @ Ys )
% 0.21/0.48 = ( append_val @ Zs @ Ts ) )
% 0.21/0.48 = ( ? [Us2: list_val] :
% 0.21/0.48 ( ( ( Xs
% 0.21/0.48 = ( append_val @ Zs @ Us2 ) )
% 0.21/0.48 & ( ( append_val @ Us2 @ Ys )
% 0.21/0.48 = Ts ) )
% 0.21/0.48 | ( ( ( append_val @ Xs @ Us2 )
% 0.21/0.48 = Zs )
% 0.21/0.48 & ( Ys
% 0.21/0.48 = ( append_val @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % append_eq_append_conv2
% 0.21/0.48 thf(fact_158_append__eq__append__conv2,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node,Zs: list_node,Ts: list_node] :
% 0.21/0.48 ( ( ( append_node @ Xs @ Ys )
% 0.21/0.48 = ( append_node @ Zs @ Ts ) )
% 0.21/0.48 = ( ? [Us2: list_node] :
% 0.21/0.48 ( ( ( Xs
% 0.21/0.48 = ( append_node @ Zs @ Us2 ) )
% 0.21/0.48 & ( ( append_node @ Us2 @ Ys )
% 0.21/0.48 = Ts ) )
% 0.21/0.48 | ( ( ( append_node @ Xs @ Us2 )
% 0.21/0.48 = Zs )
% 0.21/0.48 & ( Ys
% 0.21/0.48 = ( append_node @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % append_eq_append_conv2
% 0.21/0.48 thf(fact_159_strict__sorted_Oinduct,axiom,
% 0.21/0.48 ! [P: list_val > $o,A0: list_val] :
% 0.21/0.48 ( ( P @ nil_val )
% 0.21/0.48 => ( ! [X4: val,Ys2: list_val] :
% 0.21/0.48 ( ( P @ Ys2 )
% 0.21/0.48 => ( P @ ( cons_val @ X4 @ Ys2 ) ) )
% 0.21/0.48 => ( P @ A0 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % strict_sorted.induct
% 0.21/0.48 thf(fact_160_strict__sorted_Oinduct,axiom,
% 0.21/0.48 ! [P: list_node > $o,A0: list_node] :
% 0.21/0.48 ( ( P @ nil_node )
% 0.21/0.48 => ( ! [X4: node,Ys2: list_node] :
% 0.21/0.48 ( ( P @ Ys2 )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ Ys2 ) ) )
% 0.21/0.48 => ( P @ A0 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % strict_sorted.induct
% 0.21/0.48 thf(fact_161_mergesort__by__rel__merge__induct,axiom,
% 0.21/0.48 ! [P: list_node > list_val > $o,R: node > val > $o,Xs: list_node,Ys: list_val] :
% 0.21/0.48 ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_val )
% 0.21/0.48 => ( ! [X_1: list_val] : ( P @ nil_node @ X_1 )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node,Y2: val,Ys2: list_val] :
% 0.21/0.48 ( ( R @ X4 @ Y2 )
% 0.21/0.48 => ( ( P @ Xs2 @ ( cons_val @ Y2 @ Ys2 ) )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node,Y2: val,Ys2: list_val] :
% 0.21/0.48 ( ~ ( R @ X4 @ Y2 )
% 0.21/0.48 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys2 )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mergesort_by_rel_merge_induct
% 0.21/0.48 thf(fact_162_mergesort__by__rel__merge__induct,axiom,
% 0.21/0.48 ! [P: list_val > list_val > $o,R: val > val > $o,Xs: list_val,Ys: list_val] :
% 0.21/0.48 ( ! [Xs2: list_val] : ( P @ Xs2 @ nil_val )
% 0.21/0.48 => ( ! [X_1: list_val] : ( P @ nil_val @ X_1 )
% 0.21/0.48 => ( ! [X4: val,Xs2: list_val,Y2: val,Ys2: list_val] :
% 0.21/0.48 ( ( R @ X4 @ Y2 )
% 0.21/0.48 => ( ( P @ Xs2 @ ( cons_val @ Y2 @ Ys2 ) )
% 0.21/0.48 => ( P @ ( cons_val @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( ! [X4: val,Xs2: list_val,Y2: val,Ys2: list_val] :
% 0.21/0.48 ( ~ ( R @ X4 @ Y2 )
% 0.21/0.48 => ( ( P @ ( cons_val @ X4 @ Xs2 ) @ Ys2 )
% 0.21/0.48 => ( P @ ( cons_val @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mergesort_by_rel_merge_induct
% 0.21/0.48 thf(fact_163_mergesort__by__rel__merge__induct,axiom,
% 0.21/0.48 ! [P: list_list_node > list_val > $o,R: list_node > val > $o,Xs: list_list_node,Ys: list_val] :
% 0.21/0.48 ( ! [Xs2: list_list_node] : ( P @ Xs2 @ nil_val )
% 0.21/0.48 => ( ! [X_1: list_val] : ( P @ nil_list_node @ X_1 )
% 0.21/0.48 => ( ! [X4: list_node,Xs2: list_list_node,Y2: val,Ys2: list_val] :
% 0.21/0.48 ( ( R @ X4 @ Y2 )
% 0.21/0.48 => ( ( P @ Xs2 @ ( cons_val @ Y2 @ Ys2 ) )
% 0.21/0.48 => ( P @ ( cons_list_node @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( ! [X4: list_node,Xs2: list_list_node,Y2: val,Ys2: list_val] :
% 0.21/0.48 ( ~ ( R @ X4 @ Y2 )
% 0.21/0.48 => ( ( P @ ( cons_list_node @ X4 @ Xs2 ) @ Ys2 )
% 0.21/0.48 => ( P @ ( cons_list_node @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mergesort_by_rel_merge_induct
% 0.21/0.48 thf(fact_164_mergesort__by__rel__merge__induct,axiom,
% 0.21/0.48 ! [P: list_node > list_list_node > $o,R: node > list_node > $o,Xs: list_node,Ys: list_list_node] :
% 0.21/0.48 ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_list_node )
% 0.21/0.48 => ( ! [X_1: list_list_node] : ( P @ nil_node @ X_1 )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node,Y2: list_node,Ys2: list_list_node] :
% 0.21/0.48 ( ( R @ X4 @ Y2 )
% 0.21/0.48 => ( ( P @ Xs2 @ ( cons_list_node @ Y2 @ Ys2 ) )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node,Y2: list_node,Ys2: list_list_node] :
% 0.21/0.48 ( ~ ( R @ X4 @ Y2 )
% 0.21/0.48 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys2 )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mergesort_by_rel_merge_induct
% 0.21/0.48 thf(fact_165_mergesort__by__rel__merge__induct,axiom,
% 0.21/0.48 ! [P: list_val > list_list_node > $o,R: val > list_node > $o,Xs: list_val,Ys: list_list_node] :
% 0.21/0.48 ( ! [Xs2: list_val] : ( P @ Xs2 @ nil_list_node )
% 0.21/0.48 => ( ! [X_1: list_list_node] : ( P @ nil_val @ X_1 )
% 0.21/0.48 => ( ! [X4: val,Xs2: list_val,Y2: list_node,Ys2: list_list_node] :
% 0.21/0.48 ( ( R @ X4 @ Y2 )
% 0.21/0.48 => ( ( P @ Xs2 @ ( cons_list_node @ Y2 @ Ys2 ) )
% 0.21/0.48 => ( P @ ( cons_val @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( ! [X4: val,Xs2: list_val,Y2: list_node,Ys2: list_list_node] :
% 0.21/0.48 ( ~ ( R @ X4 @ Y2 )
% 0.21/0.48 => ( ( P @ ( cons_val @ X4 @ Xs2 ) @ Ys2 )
% 0.21/0.48 => ( P @ ( cons_val @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mergesort_by_rel_merge_induct
% 0.21/0.48 thf(fact_166_mergesort__by__rel__merge__induct,axiom,
% 0.21/0.48 ! [P: list_list_node > list_list_node > $o,R: list_node > list_node > $o,Xs: list_list_node,Ys: list_list_node] :
% 0.21/0.48 ( ! [Xs2: list_list_node] : ( P @ Xs2 @ nil_list_node )
% 0.21/0.48 => ( ! [X_1: list_list_node] : ( P @ nil_list_node @ X_1 )
% 0.21/0.48 => ( ! [X4: list_node,Xs2: list_list_node,Y2: list_node,Ys2: list_list_node] :
% 0.21/0.48 ( ( R @ X4 @ Y2 )
% 0.21/0.48 => ( ( P @ Xs2 @ ( cons_list_node @ Y2 @ Ys2 ) )
% 0.21/0.48 => ( P @ ( cons_list_node @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( ! [X4: list_node,Xs2: list_list_node,Y2: list_node,Ys2: list_list_node] :
% 0.21/0.48 ( ~ ( R @ X4 @ Y2 )
% 0.21/0.48 => ( ( P @ ( cons_list_node @ X4 @ Xs2 ) @ Ys2 )
% 0.21/0.48 => ( P @ ( cons_list_node @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mergesort_by_rel_merge_induct
% 0.21/0.48 thf(fact_167_mergesort__by__rel__merge__induct,axiom,
% 0.21/0.48 ! [P: list_node > list_node > $o,R: node > node > $o,Xs: list_node,Ys: list_node] :
% 0.21/0.48 ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_node )
% 0.21/0.48 => ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.21/0.48 ( ( R @ X4 @ Y2 )
% 0.21/0.48 => ( ( P @ Xs2 @ ( cons_node @ Y2 @ Ys2 ) )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.21/0.48 ( ~ ( R @ X4 @ Y2 )
% 0.21/0.48 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys2 )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mergesort_by_rel_merge_induct
% 0.21/0.48 thf(fact_168_mergesort__by__rel__merge_Oinduct,axiom,
% 0.21/0.48 ! [P: ( node > node > $o ) > list_node > list_node > $o,A0: node > node > $o,A1: list_node,A22: list_node] :
% 0.21/0.48 ( ! [R3: node > node > $o,X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.21/0.48 ( ( ( R3 @ X4 @ Y2 )
% 0.21/0.48 => ( P @ R3 @ Xs2 @ ( cons_node @ Y2 @ Ys2 ) ) )
% 0.21/0.48 => ( ( ~ ( R3 @ X4 @ Y2 )
% 0.21/0.48 => ( P @ R3 @ ( cons_node @ X4 @ Xs2 ) @ Ys2 ) )
% 0.21/0.48 => ( P @ R3 @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( ! [R3: node > node > $o,Xs2: list_node] : ( P @ R3 @ Xs2 @ nil_node )
% 0.21/0.48 => ( ! [R3: node > node > $o,V: node,Va: list_node] : ( P @ R3 @ nil_node @ ( cons_node @ V @ Va ) )
% 0.21/0.48 => ( P @ A0 @ A1 @ A22 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mergesort_by_rel_merge.induct
% 0.21/0.48 thf(fact_169_map__tailrec__rev_Oinduct,axiom,
% 0.21/0.48 ! [P: ( node > node ) > list_node > list_node > $o,A0: node > node,A1: list_node,A22: list_node] :
% 0.21/0.48 ( ! [F: node > node,X_1: list_node] : ( P @ F @ nil_node @ X_1 )
% 0.21/0.48 => ( ! [F: node > node,A3: node,As: list_node,Bs: list_node] :
% 0.21/0.48 ( ( P @ F @ As @ ( cons_node @ ( F @ A3 ) @ Bs ) )
% 0.21/0.48 => ( P @ F @ ( cons_node @ A3 @ As ) @ Bs ) )
% 0.21/0.48 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % map_tailrec_rev.induct
% 0.21/0.48 thf(fact_170_list__nonempty__induct,axiom,
% 0.21/0.48 ! [Xs: list_node,P: list_node > $o] :
% 0.21/0.48 ( ( Xs != nil_node )
% 0.21/0.48 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node] :
% 0.21/0.48 ( ( Xs2 != nil_node )
% 0.21/0.48 => ( ( P @ Xs2 )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ Xs2 ) ) ) )
% 0.21/0.48 => ( P @ Xs ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list_nonempty_induct
% 0.21/0.48 thf(fact_171_list__all__zip_Oinduct,axiom,
% 0.21/0.48 ! [P: ( node > node > $o ) > list_node > list_node > $o,A0: node > node > $o,A1: list_node,A22: list_node] :
% 0.21/0.48 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node @ nil_node )
% 0.21/0.48 => ( ! [P2: node > node > $o,A3: node,As: list_node,B2: node,Bs: list_node] :
% 0.21/0.48 ( ( P @ P2 @ As @ Bs )
% 0.21/0.48 => ( P @ P2 @ ( cons_node @ A3 @ As ) @ ( cons_node @ B2 @ Bs ) ) )
% 0.21/0.48 => ( ! [P2: node > node > $o,V: node,Va: list_node] : ( P @ P2 @ ( cons_node @ V @ Va ) @ nil_node )
% 0.21/0.48 => ( ! [P2: node > node > $o,V: node,Va: list_node] : ( P @ P2 @ nil_node @ ( cons_node @ V @ Va ) )
% 0.21/0.48 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list_all_zip.induct
% 0.21/0.48 thf(fact_172_successively_Oinduct,axiom,
% 0.21/0.48 ! [P: ( node > node > $o ) > list_node > $o,A0: node > node > $o,A1: list_node] :
% 0.21/0.48 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node )
% 0.21/0.48 => ( ! [P2: node > node > $o,X4: node] : ( P @ P2 @ ( cons_node @ X4 @ nil_node ) )
% 0.21/0.48 => ( ! [P2: node > node > $o,X4: node,Y2: node,Xs2: list_node] :
% 0.21/0.48 ( ( P @ P2 @ ( cons_node @ Y2 @ Xs2 ) )
% 0.21/0.48 => ( P @ P2 @ ( cons_node @ X4 @ ( cons_node @ Y2 @ Xs2 ) ) ) )
% 0.21/0.48 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % successively.induct
% 0.21/0.48 thf(fact_173_list__induct__first2,axiom,
% 0.21/0.48 ! [P: list_node > $o,Xs: list_node] :
% 0.21/0.48 ( ( P @ nil_node )
% 0.21/0.48 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 0.21/0.48 => ( ! [X1: node,X23: node,Xs2: list_node] :
% 0.21/0.48 ( ( P @ Xs2 )
% 0.21/0.48 => ( P @ ( cons_node @ X1 @ ( cons_node @ X23 @ Xs2 ) ) ) )
% 0.21/0.48 => ( P @ Xs ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list_induct_first2
% 0.21/0.48 thf(fact_174_remdups__adj_Oinduct,axiom,
% 0.21/0.48 ! [P: list_node > $o,A0: list_node] :
% 0.21/0.48 ( ( P @ nil_node )
% 0.21/0.48 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 0.21/0.48 => ( ! [X4: node,Y2: node,Xs2: list_node] :
% 0.21/0.48 ( ( ( X4 = Y2 )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ Xs2 ) ) )
% 0.21/0.48 => ( ( ( X4 != Y2 )
% 0.21/0.48 => ( P @ ( cons_node @ Y2 @ Xs2 ) ) )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ ( cons_node @ Y2 @ Xs2 ) ) ) ) )
% 0.21/0.48 => ( P @ A0 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % remdups_adj.induct
% 0.21/0.48 thf(fact_175_sorted__wrt_Oinduct,axiom,
% 0.21/0.48 ! [P: ( node > node > $o ) > list_node > $o,A0: node > node > $o,A1: list_node] :
% 0.21/0.48 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node )
% 0.21/0.48 => ( ! [P2: node > node > $o,X4: node,Ys2: list_node] :
% 0.21/0.48 ( ( P @ P2 @ Ys2 )
% 0.21/0.48 => ( P @ P2 @ ( cons_node @ X4 @ Ys2 ) ) )
% 0.21/0.48 => ( P @ A0 @ A1 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % sorted_wrt.induct
% 0.21/0.48 thf(fact_176_remdups__adj_Ocases,axiom,
% 0.21/0.48 ! [X: list_node] :
% 0.21/0.48 ( ( X != nil_node )
% 0.21/0.48 => ( ! [X4: node] :
% 0.21/0.48 ( X
% 0.21/0.48 != ( cons_node @ X4 @ nil_node ) )
% 0.21/0.48 => ~ ! [X4: node,Y2: node,Xs2: list_node] :
% 0.21/0.48 ( X
% 0.21/0.48 != ( cons_node @ X4 @ ( cons_node @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % remdups_adj.cases
% 0.21/0.48 thf(fact_177_list__2pre__induct,axiom,
% 0.21/0.48 ! [P: list_node > list_node > $o,W1: list_node,W2: list_node] :
% 0.21/0.48 ( ( P @ nil_node @ nil_node )
% 0.21/0.48 => ( ! [E3: node,W12: list_node,W22: list_node] :
% 0.21/0.48 ( ( P @ W12 @ W22 )
% 0.21/0.48 => ( P @ ( cons_node @ E3 @ W12 ) @ W22 ) )
% 0.21/0.48 => ( ! [E3: node,W13: list_node,W23: list_node] :
% 0.21/0.48 ( ( P @ W13 @ W23 )
% 0.21/0.48 => ( P @ W13 @ ( cons_node @ E3 @ W23 ) ) )
% 0.21/0.48 => ( P @ W1 @ W2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list_2pre_induct
% 0.21/0.48 thf(fact_178_transpose_Ocases,axiom,
% 0.21/0.48 ! [X: list_list_node] :
% 0.21/0.48 ( ( X != nil_list_node )
% 0.21/0.48 => ( ! [Xss: list_list_node] :
% 0.21/0.48 ( X
% 0.21/0.48 != ( cons_list_node @ nil_node @ Xss ) )
% 0.21/0.48 => ~ ! [X4: node,Xs2: list_node,Xss: list_list_node] :
% 0.21/0.48 ( X
% 0.21/0.48 != ( cons_list_node @ ( cons_node @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % transpose.cases
% 0.21/0.48 thf(fact_179_shuffles_Oinduct,axiom,
% 0.21/0.48 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 0.21/0.48 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.21/0.48 => ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_node )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.21/0.48 ( ( P @ Xs2 @ ( cons_node @ Y2 @ Ys2 ) )
% 0.21/0.48 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys2 )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y2 @ Ys2 ) ) ) )
% 0.21/0.48 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % shuffles.induct
% 0.21/0.48 thf(fact_180_min__list_Oinduct,axiom,
% 0.21/0.48 ! [P: list_node > $o,A0: list_node] :
% 0.21/0.48 ( ! [X4: node,Xs2: list_node] :
% 0.21/0.48 ( ! [X212: node,X222: list_node] :
% 0.21/0.48 ( ( Xs2
% 0.21/0.48 = ( cons_node @ X212 @ X222 ) )
% 0.21/0.48 => ( P @ Xs2 ) )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ Xs2 ) ) )
% 0.21/0.48 => ( ( P @ nil_node )
% 0.21/0.48 => ( P @ A0 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % min_list.induct
% 0.21/0.48 thf(fact_181_min__list_Ocases,axiom,
% 0.21/0.48 ! [X: list_node] :
% 0.21/0.48 ( ! [X4: node,Xs2: list_node] :
% 0.21/0.48 ( X
% 0.21/0.48 != ( cons_node @ X4 @ Xs2 ) )
% 0.21/0.48 => ( X = nil_node ) ) ).
% 0.21/0.48
% 0.21/0.48 % min_list.cases
% 0.21/0.48 thf(fact_182_induct__list012,axiom,
% 0.21/0.48 ! [P: list_node > $o,Xs: list_node] :
% 0.21/0.48 ( ( P @ nil_node )
% 0.21/0.48 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 0.21/0.48 => ( ! [X4: node,Y2: node,Zs2: list_node] :
% 0.21/0.48 ( ( P @ Zs2 )
% 0.21/0.48 => ( ( P @ ( cons_node @ Y2 @ Zs2 ) )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ ( cons_node @ Y2 @ Zs2 ) ) ) ) )
% 0.21/0.48 => ( P @ Xs ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % induct_list012
% 0.21/0.48 thf(fact_183_splice_Oinduct,axiom,
% 0.21/0.48 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 0.21/0.48 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node,Ys2: list_node] :
% 0.21/0.48 ( ( P @ Ys2 @ Xs2 )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys2 ) )
% 0.21/0.48 => ( P @ A0 @ A1 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % splice.induct
% 0.21/0.48 thf(fact_184_list__induct2_H,axiom,
% 0.21/0.48 ! [P: list_node > list_node > $o,Xs: list_node,Ys: list_node] :
% 0.21/0.48 ( ( P @ nil_node @ nil_node )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node] : ( P @ ( cons_node @ X4 @ Xs2 ) @ nil_node )
% 0.21/0.48 => ( ! [Y2: node,Ys2: list_node] : ( P @ nil_node @ ( cons_node @ Y2 @ Ys2 ) )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.21/0.48 ( ( P @ Xs2 @ Ys2 )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y2 @ Ys2 ) ) )
% 0.21/0.48 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list_induct2'
% 0.21/0.48 thf(fact_185_neq__Nil__conv,axiom,
% 0.21/0.48 ! [Xs: list_node] :
% 0.21/0.48 ( ( Xs != nil_node )
% 0.21/0.48 = ( ? [Y3: node,Ys3: list_node] :
% 0.21/0.48 ( Xs
% 0.21/0.48 = ( cons_node @ Y3 @ Ys3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % neq_Nil_conv
% 0.21/0.48 thf(fact_186_list_Oinducts,axiom,
% 0.21/0.48 ! [P: list_node > $o,List: list_node] :
% 0.21/0.48 ( ( P @ nil_node )
% 0.21/0.48 => ( ! [X1: node,X23: list_node] :
% 0.21/0.48 ( ( P @ X23 )
% 0.21/0.48 => ( P @ ( cons_node @ X1 @ X23 ) ) )
% 0.21/0.48 => ( P @ List ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.inducts
% 0.21/0.48 thf(fact_187_list_Oexhaust,axiom,
% 0.21/0.48 ! [Y: list_node] :
% 0.21/0.48 ( ( Y != nil_node )
% 0.21/0.48 => ~ ! [X213: node,X223: list_node] :
% 0.21/0.48 ( Y
% 0.21/0.48 != ( cons_node @ X213 @ X223 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.exhaust
% 0.21/0.48 thf(fact_188_revg_Oinduct,axiom,
% 0.21/0.48 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 0.21/0.48 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.21/0.48 => ( ! [A3: node,As: list_node,B2: list_node] :
% 0.21/0.48 ( ( P @ As @ ( cons_node @ A3 @ B2 ) )
% 0.21/0.48 => ( P @ ( cons_node @ A3 @ As ) @ B2 ) )
% 0.21/0.48 => ( P @ A0 @ A1 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % revg.induct
% 0.21/0.48 thf(fact_189_list_OdiscI,axiom,
% 0.21/0.48 ! [List: list_node,X21: node,X22: list_node] :
% 0.21/0.48 ( ( List
% 0.21/0.48 = ( cons_node @ X21 @ X22 ) )
% 0.21/0.48 => ( List != nil_node ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.discI
% 0.21/0.48 thf(fact_190_neq__NilE,axiom,
% 0.21/0.48 ! [L: list_node] :
% 0.21/0.48 ( ( L != nil_node )
% 0.21/0.48 => ~ ! [X4: node,Xs2: list_node] :
% 0.21/0.48 ( L
% 0.21/0.48 != ( cons_node @ X4 @ Xs2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % neq_NilE
% 0.21/0.48 thf(fact_191_list_Odistinct_I1_J,axiom,
% 0.21/0.48 ! [X21: node,X22: list_node] :
% 0.21/0.48 ( nil_node
% 0.21/0.48 != ( cons_node @ X21 @ X22 ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.distinct(1)
% 0.21/0.48 thf(fact_192_list_Oset__cases,axiom,
% 0.21/0.48 ! [E2: val,A: list_val] :
% 0.21/0.48 ( ( member_val @ E2 @ ( set_val2 @ A ) )
% 0.21/0.48 => ( ! [Z2: list_val] :
% 0.21/0.48 ( A
% 0.21/0.48 != ( cons_val @ E2 @ Z2 ) )
% 0.21/0.48 => ~ ! [Z1: val,Z2: list_val] :
% 0.21/0.48 ( ( A
% 0.21/0.48 = ( cons_val @ Z1 @ Z2 ) )
% 0.21/0.48 => ~ ( member_val @ E2 @ ( set_val2 @ Z2 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.set_cases
% 0.21/0.48 thf(fact_193_list_Oset__cases,axiom,
% 0.21/0.48 ! [E2: node,A: list_node] :
% 0.21/0.48 ( ( member_node @ E2 @ ( set_node2 @ A ) )
% 0.21/0.48 => ( ! [Z2: list_node] :
% 0.21/0.48 ( A
% 0.21/0.48 != ( cons_node @ E2 @ Z2 ) )
% 0.21/0.48 => ~ ! [Z1: node,Z2: list_node] :
% 0.21/0.48 ( ( A
% 0.21/0.48 = ( cons_node @ Z1 @ Z2 ) )
% 0.21/0.48 => ~ ( member_node @ E2 @ ( set_node2 @ Z2 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.set_cases
% 0.21/0.48 thf(fact_194_set__ConsD,axiom,
% 0.21/0.48 ! [Y: val,X: val,Xs: list_val] :
% 0.21/0.48 ( ( member_val @ Y @ ( set_val2 @ ( cons_val @ X @ Xs ) ) )
% 0.21/0.48 => ( ( Y = X )
% 0.21/0.48 | ( member_val @ Y @ ( set_val2 @ Xs ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % set_ConsD
% 0.21/0.48 thf(fact_195_set__ConsD,axiom,
% 0.21/0.48 ! [Y: node,X: node,Xs: list_node] :
% 0.21/0.48 ( ( member_node @ Y @ ( set_node2 @ ( cons_node @ X @ Xs ) ) )
% 0.21/0.48 => ( ( Y = X )
% 0.21/0.48 | ( member_node @ Y @ ( set_node2 @ Xs ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % set_ConsD
% 0.21/0.48 thf(fact_196_list_Oset__intros_I1_J,axiom,
% 0.21/0.48 ! [X21: val,X22: list_val] : ( member_val @ X21 @ ( set_val2 @ ( cons_val @ X21 @ X22 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.set_intros(1)
% 0.21/0.48 thf(fact_197_list_Oset__intros_I1_J,axiom,
% 0.21/0.48 ! [X21: node,X22: list_node] : ( member_node @ X21 @ ( set_node2 @ ( cons_node @ X21 @ X22 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.set_intros(1)
% 0.21/0.48 thf(fact_198_list_Oset__intros_I2_J,axiom,
% 0.21/0.48 ! [Y: val,X22: list_val,X21: val] :
% 0.21/0.48 ( ( member_val @ Y @ ( set_val2 @ X22 ) )
% 0.21/0.48 => ( member_val @ Y @ ( set_val2 @ ( cons_val @ X21 @ X22 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.set_intros(2)
% 0.21/0.48 thf(fact_199_list_Oset__intros_I2_J,axiom,
% 0.21/0.48 ! [Y: node,X22: list_node,X21: node] :
% 0.21/0.48 ( ( member_node @ Y @ ( set_node2 @ X22 ) )
% 0.21/0.48 => ( member_node @ Y @ ( set_node2 @ ( cons_node @ X21 @ X22 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.set_intros(2)
% 0.21/0.48 thf(fact_200_Cons__eq__appendI,axiom,
% 0.21/0.48 ! [X: node,Xs1: list_node,Ys: list_node,Xs: list_node,Zs: list_node] :
% 0.21/0.48 ( ( ( cons_node @ X @ Xs1 )
% 0.21/0.48 = Ys )
% 0.21/0.48 => ( ( Xs
% 0.21/0.48 = ( append_node @ Xs1 @ Zs ) )
% 0.21/0.48 => ( ( cons_node @ X @ Xs )
% 0.21/0.48 = ( append_node @ Ys @ Zs ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % Cons_eq_appendI
% 0.21/0.48 thf(fact_201_append__Cons,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node,Ys: list_node] :
% 0.21/0.48 ( ( append_node @ ( cons_node @ X @ Xs ) @ Ys )
% 0.21/0.48 = ( cons_node @ X @ ( append_node @ Xs @ Ys ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % append_Cons
% 0.21/0.48 thf(fact_202_list__match__lel__lel,axiom,
% 0.21/0.48 ! [C1: list_node,Qs: node,C2: list_node,C12: list_node,Qs2: node,C22: list_node] :
% 0.21/0.48 ( ( ( append_node @ C1 @ ( cons_node @ Qs @ C2 ) )
% 0.21/0.48 = ( append_node @ C12 @ ( cons_node @ Qs2 @ C22 ) ) )
% 0.21/0.48 => ( ! [C21: list_node] :
% 0.21/0.48 ( ( C1
% 0.21/0.48 = ( append_node @ C12 @ ( cons_node @ Qs2 @ C21 ) ) )
% 0.21/0.48 => ( C22
% 0.21/0.48 != ( append_node @ C21 @ ( cons_node @ Qs @ C2 ) ) ) )
% 0.21/0.48 => ( ( ( C12 = C1 )
% 0.21/0.48 => ( ( Qs2 = Qs )
% 0.21/0.48 => ( C22 != C2 ) ) )
% 0.21/0.48 => ~ ! [C212: list_node] :
% 0.21/0.48 ( ( C12
% 0.21/0.48 = ( append_node @ C1 @ ( cons_node @ Qs @ C212 ) ) )
% 0.21/0.48 => ( C2
% 0.21/0.48 != ( append_node @ C212 @ ( cons_node @ Qs2 @ C22 ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list_match_lel_lel
% 0.21/0.48 thf(fact_203_eq__Nil__appendI,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node] :
% 0.21/0.48 ( ( Xs = Ys )
% 0.21/0.48 => ( Xs
% 0.21/0.48 = ( append_node @ nil_node @ Ys ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % eq_Nil_appendI
% 0.21/0.48 thf(fact_204_append__Nil,axiom,
% 0.21/0.48 ! [Ys: list_node] :
% 0.21/0.48 ( ( append_node @ nil_node @ Ys )
% 0.21/0.48 = Ys ) ).
% 0.21/0.48
% 0.21/0.48 % append_Nil
% 0.21/0.48 thf(fact_205_append_Oleft__neutral,axiom,
% 0.21/0.48 ! [A: list_node] :
% 0.21/0.48 ( ( append_node @ nil_node @ A )
% 0.21/0.48 = A ) ).
% 0.21/0.48
% 0.21/0.48 % append.left_neutral
% 0.21/0.48 thf(fact_206_list_Osel_I3_J,axiom,
% 0.21/0.48 ! [X21: node,X22: list_node] :
% 0.21/0.48 ( ( tl_node @ ( cons_node @ X21 @ X22 ) )
% 0.21/0.48 = X22 ) ).
% 0.21/0.48
% 0.21/0.48 % list.sel(3)
% 0.21/0.48 thf(fact_207_list_Osel_I2_J,axiom,
% 0.21/0.48 ( ( tl_node @ nil_node )
% 0.21/0.48 = nil_node ) ).
% 0.21/0.48
% 0.21/0.48 % list.sel(2)
% 0.21/0.48 thf(fact_208_list__append__eq__Cons__cases,axiom,
% 0.21/0.48 ! [Ys: list_node,Zs: list_node,X: node,Xs: list_node] :
% 0.21/0.48 ( ( ( append_node @ Ys @ Zs )
% 0.21/0.48 = ( cons_node @ X @ Xs ) )
% 0.21/0.48 => ( ( ( Ys = nil_node )
% 0.21/0.48 => ( Zs
% 0.21/0.48 != ( cons_node @ X @ Xs ) ) )
% 0.21/0.48 => ~ ! [Ys4: list_node] :
% 0.21/0.48 ( ( Ys
% 0.21/0.48 = ( cons_node @ X @ Ys4 ) )
% 0.21/0.48 => ( ( append_node @ Ys4 @ Zs )
% 0.21/0.48 != Xs ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list_append_eq_Cons_cases
% 0.21/0.48 thf(fact_209_list__Cons__eq__append__cases,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.21/0.48 ( ( ( cons_node @ X @ Xs )
% 0.21/0.48 = ( append_node @ Ys @ Zs ) )
% 0.21/0.48 => ( ( ( Ys = nil_node )
% 0.21/0.48 => ( Zs
% 0.21/0.48 != ( cons_node @ X @ Xs ) ) )
% 0.21/0.48 => ~ ! [Ys4: list_node] :
% 0.21/0.48 ( ( Ys
% 0.21/0.48 = ( cons_node @ X @ Ys4 ) )
% 0.21/0.48 => ( ( append_node @ Ys4 @ Zs )
% 0.21/0.48 != Xs ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list_Cons_eq_append_cases
% 0.21/0.48 thf(fact_210_rev__nonempty__induct2_H,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node,P: list_node > list_node > $o] :
% 0.21/0.48 ( ( Xs != nil_node )
% 0.21/0.48 => ( ( Ys != nil_node )
% 0.21/0.48 => ( ! [X4: node,Y2: node] : ( P @ ( cons_node @ X4 @ nil_node ) @ ( cons_node @ Y2 @ nil_node ) )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node,Y2: node] :
% 0.21/0.48 ( ( Xs2 != nil_node )
% 0.21/0.48 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( cons_node @ Y2 @ nil_node ) ) )
% 0.21/0.48 => ( ! [X4: node,Y2: node,Ys2: list_node] :
% 0.21/0.48 ( ( Ys2 != nil_node )
% 0.21/0.48 => ( P @ ( cons_node @ X4 @ nil_node ) @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.21/0.48 ( ( P @ Xs2 @ Ys2 )
% 0.21/0.48 => ( ( Xs2 != nil_node )
% 0.21/0.48 => ( ( Ys2 != nil_node )
% 0.21/0.48 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) ) ) )
% 0.21/0.48 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % rev_nonempty_induct2'
% 0.21/0.48 thf(fact_211_rev__nonempty__induct,axiom,
% 0.21/0.48 ! [Xs: list_node,P: list_node > $o] :
% 0.21/0.48 ( ( Xs != nil_node )
% 0.21/0.48 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node] :
% 0.21/0.48 ( ( Xs2 != nil_node )
% 0.21/0.48 => ( ( P @ Xs2 )
% 0.21/0.48 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) ) ) )
% 0.21/0.48 => ( P @ Xs ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % rev_nonempty_induct
% 0.21/0.48 thf(fact_212_append__eq__Cons__conv,axiom,
% 0.21/0.48 ! [Ys: list_node,Zs: list_node,X: node,Xs: list_node] :
% 0.21/0.48 ( ( ( append_node @ Ys @ Zs )
% 0.21/0.48 = ( cons_node @ X @ Xs ) )
% 0.21/0.48 = ( ( ( Ys = nil_node )
% 0.21/0.48 & ( Zs
% 0.21/0.48 = ( cons_node @ X @ Xs ) ) )
% 0.21/0.48 | ? [Ys5: list_node] :
% 0.21/0.48 ( ( Ys
% 0.21/0.48 = ( cons_node @ X @ Ys5 ) )
% 0.21/0.48 & ( ( append_node @ Ys5 @ Zs )
% 0.21/0.48 = Xs ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % append_eq_Cons_conv
% 0.21/0.48 thf(fact_213_Cons__eq__append__conv,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.21/0.48 ( ( ( cons_node @ X @ Xs )
% 0.21/0.48 = ( append_node @ Ys @ Zs ) )
% 0.21/0.48 = ( ( ( Ys = nil_node )
% 0.21/0.48 & ( ( cons_node @ X @ Xs )
% 0.21/0.48 = Zs ) )
% 0.21/0.48 | ? [Ys5: list_node] :
% 0.21/0.48 ( ( ( cons_node @ X @ Ys5 )
% 0.21/0.48 = Ys )
% 0.21/0.48 & ( Xs
% 0.21/0.48 = ( append_node @ Ys5 @ Zs ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % Cons_eq_append_conv
% 0.21/0.48 thf(fact_214_neq__Nil__rev__conv,axiom,
% 0.21/0.48 ! [L: list_node] :
% 0.21/0.48 ( ( L != nil_node )
% 0.21/0.48 = ( ? [Xs3: list_node,X3: node] :
% 0.21/0.48 ( L
% 0.21/0.48 = ( append_node @ Xs3 @ ( cons_node @ X3 @ nil_node ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % neq_Nil_rev_conv
% 0.21/0.48 thf(fact_215_rev__induct2_H,axiom,
% 0.21/0.48 ! [P: list_node > list_node > $o,Xs: list_node,Ys: list_node] :
% 0.21/0.48 ( ( P @ nil_node @ nil_node )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ nil_node )
% 0.21/0.48 => ( ! [Y2: node,Ys2: list_node] : ( P @ nil_node @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.21/0.48 ( ( P @ Xs2 @ Ys2 )
% 0.21/0.48 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) )
% 0.21/0.48 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % rev_induct2'
% 0.21/0.48 thf(fact_216_neq__Nil__revE,axiom,
% 0.21/0.48 ! [L: list_node] :
% 0.21/0.48 ( ( L != nil_node )
% 0.21/0.48 => ~ ! [Ll: list_node,E3: node] :
% 0.21/0.48 ( L
% 0.21/0.48 != ( append_node @ Ll @ ( cons_node @ E3 @ nil_node ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % neq_Nil_revE
% 0.21/0.48 thf(fact_217_rev__exhaust,axiom,
% 0.21/0.48 ! [Xs: list_node] :
% 0.21/0.48 ( ( Xs != nil_node )
% 0.21/0.48 => ~ ! [Ys2: list_node,Y2: node] :
% 0.21/0.48 ( Xs
% 0.21/0.48 != ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % rev_exhaust
% 0.21/0.48 thf(fact_218_rev__induct,axiom,
% 0.21/0.48 ! [P: list_node > $o,Xs: list_node] :
% 0.21/0.48 ( ( P @ nil_node )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node] :
% 0.21/0.48 ( ( P @ Xs2 )
% 0.21/0.48 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) ) )
% 0.21/0.48 => ( P @ Xs ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % rev_induct
% 0.21/0.48 thf(fact_219_split__list__first__prop__iff,axiom,
% 0.21/0.48 ! [Xs: list_node,P: node > $o] :
% 0.21/0.48 ( ( ? [X3: node] :
% 0.21/0.48 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 0.21/0.48 & ( P @ X3 ) ) )
% 0.21/0.48 = ( ? [Ys3: list_node,X3: node] :
% 0.21/0.48 ( ? [Zs3: list_node] :
% 0.21/0.48 ( Xs
% 0.21/0.48 = ( append_node @ Ys3 @ ( cons_node @ X3 @ Zs3 ) ) )
% 0.21/0.48 & ( P @ X3 )
% 0.21/0.48 & ! [Y3: node] :
% 0.21/0.48 ( ( member_node @ Y3 @ ( set_node2 @ Ys3 ) )
% 0.21/0.48 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % split_list_first_prop_iff
% 0.21/0.48 thf(fact_220_split__list__last__prop__iff,axiom,
% 0.21/0.48 ! [Xs: list_node,P: node > $o] :
% 0.21/0.48 ( ( ? [X3: node] :
% 0.21/0.48 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 0.21/0.48 & ( P @ X3 ) ) )
% 0.21/0.48 = ( ? [Ys3: list_node,X3: node,Zs3: list_node] :
% 0.21/0.48 ( ( Xs
% 0.21/0.48 = ( append_node @ Ys3 @ ( cons_node @ X3 @ Zs3 ) ) )
% 0.21/0.48 & ( P @ X3 )
% 0.21/0.48 & ! [Y3: node] :
% 0.21/0.48 ( ( member_node @ Y3 @ ( set_node2 @ Zs3 ) )
% 0.21/0.48 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % split_list_last_prop_iff
% 0.21/0.48 thf(fact_221_in__set__conv__decomp__first,axiom,
% 0.21/0.48 ! [X: val,Xs: list_val] :
% 0.21/0.48 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.21/0.48 = ( ? [Ys3: list_val,Zs3: list_val] :
% 0.21/0.48 ( ( Xs
% 0.21/0.48 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs3 ) ) )
% 0.21/0.48 & ~ ( member_val @ X @ ( set_val2 @ Ys3 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % in_set_conv_decomp_first
% 0.21/0.48 thf(fact_222_in__set__conv__decomp__first,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node] :
% 0.21/0.48 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.21/0.48 = ( ? [Ys3: list_node,Zs3: list_node] :
% 0.21/0.48 ( ( Xs
% 0.21/0.48 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs3 ) ) )
% 0.21/0.48 & ~ ( member_node @ X @ ( set_node2 @ Ys3 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % in_set_conv_decomp_first
% 0.21/0.48 thf(fact_223_in__set__conv__decomp__last,axiom,
% 0.21/0.48 ! [X: val,Xs: list_val] :
% 0.21/0.48 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.21/0.48 = ( ? [Ys3: list_val,Zs3: list_val] :
% 0.21/0.48 ( ( Xs
% 0.21/0.48 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs3 ) ) )
% 0.21/0.48 & ~ ( member_val @ X @ ( set_val2 @ Zs3 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % in_set_conv_decomp_last
% 0.21/0.48 thf(fact_224_in__set__conv__decomp__last,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node] :
% 0.21/0.48 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.21/0.48 = ( ? [Ys3: list_node,Zs3: list_node] :
% 0.21/0.48 ( ( Xs
% 0.21/0.48 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs3 ) ) )
% 0.21/0.48 & ~ ( member_node @ X @ ( set_node2 @ Zs3 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % in_set_conv_decomp_last
% 0.21/0.48 thf(fact_225_split__list__first__propE,axiom,
% 0.21/0.48 ! [Xs: list_node,P: node > $o] :
% 0.21/0.48 ( ? [X2: node] :
% 0.21/0.48 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.21/0.48 & ( P @ X2 ) )
% 0.21/0.48 => ~ ! [Ys2: list_node,X4: node] :
% 0.21/0.48 ( ? [Zs2: list_node] :
% 0.21/0.48 ( Xs
% 0.21/0.48 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.21/0.48 => ( ( P @ X4 )
% 0.21/0.48 => ~ ! [Xa: node] :
% 0.21/0.48 ( ( member_node @ Xa @ ( set_node2 @ Ys2 ) )
% 0.21/0.48 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % split_list_first_propE
% 0.21/0.48 thf(fact_226_split__list__last__propE,axiom,
% 0.21/0.48 ! [Xs: list_node,P: node > $o] :
% 0.21/0.48 ( ? [X2: node] :
% 0.21/0.48 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.21/0.48 & ( P @ X2 ) )
% 0.21/0.48 => ~ ! [Ys2: list_node,X4: node,Zs2: list_node] :
% 0.21/0.48 ( ( Xs
% 0.21/0.48 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.21/0.48 => ( ( P @ X4 )
% 0.21/0.48 => ~ ! [Xa: node] :
% 0.21/0.48 ( ( member_node @ Xa @ ( set_node2 @ Zs2 ) )
% 0.21/0.48 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % split_list_last_propE
% 0.21/0.48 thf(fact_227_split__list__first__prop,axiom,
% 0.21/0.48 ! [Xs: list_node,P: node > $o] :
% 0.21/0.48 ( ? [X2: node] :
% 0.21/0.48 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.21/0.48 & ( P @ X2 ) )
% 0.21/0.48 => ? [Ys2: list_node,X4: node] :
% 0.21/0.48 ( ? [Zs2: list_node] :
% 0.21/0.48 ( Xs
% 0.21/0.48 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.21/0.48 & ( P @ X4 )
% 0.21/0.48 & ! [Xa: node] :
% 0.21/0.48 ( ( member_node @ Xa @ ( set_node2 @ Ys2 ) )
% 0.21/0.48 => ~ ( P @ Xa ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % split_list_first_prop
% 0.21/0.48 thf(fact_228_split__list__last__prop,axiom,
% 0.21/0.48 ! [Xs: list_node,P: node > $o] :
% 0.21/0.48 ( ? [X2: node] :
% 0.21/0.48 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.21/0.48 & ( P @ X2 ) )
% 0.21/0.48 => ? [Ys2: list_node,X4: node,Zs2: list_node] :
% 0.21/0.48 ( ( Xs
% 0.21/0.48 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.21/0.48 & ( P @ X4 )
% 0.21/0.48 & ! [Xa: node] :
% 0.21/0.48 ( ( member_node @ Xa @ ( set_node2 @ Zs2 ) )
% 0.21/0.48 => ~ ( P @ Xa ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % split_list_last_prop
% 0.21/0.48 thf(fact_229_in__set__list__format,axiom,
% 0.21/0.48 ! [E2: val,L: list_val] :
% 0.21/0.48 ( ( member_val @ E2 @ ( set_val2 @ L ) )
% 0.21/0.48 => ~ ! [L12: list_val,L22: list_val] :
% 0.21/0.48 ( L
% 0.21/0.48 != ( append_val @ L12 @ ( cons_val @ E2 @ L22 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % in_set_list_format
% 0.21/0.48 thf(fact_230_in__set__list__format,axiom,
% 0.21/0.48 ! [E2: node,L: list_node] :
% 0.21/0.48 ( ( member_node @ E2 @ ( set_node2 @ L ) )
% 0.21/0.48 => ~ ! [L12: list_node,L22: list_node] :
% 0.21/0.48 ( L
% 0.21/0.48 != ( append_node @ L12 @ ( cons_node @ E2 @ L22 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % in_set_list_format
% 0.21/0.48 thf(fact_231_in__set__conv__decomp,axiom,
% 0.21/0.48 ! [X: val,Xs: list_val] :
% 0.21/0.48 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.21/0.48 = ( ? [Ys3: list_val,Zs3: list_val] :
% 0.21/0.48 ( Xs
% 0.21/0.48 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs3 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % in_set_conv_decomp
% 0.21/0.48 thf(fact_232_in__set__conv__decomp,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node] :
% 0.21/0.48 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.21/0.48 = ( ? [Ys3: list_node,Zs3: list_node] :
% 0.21/0.48 ( Xs
% 0.21/0.48 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs3 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % in_set_conv_decomp
% 0.21/0.48 thf(fact_233_append__Cons__eq__iff,axiom,
% 0.21/0.48 ! [X: val,Xs: list_val,Ys: list_val,Xs4: list_val,Ys6: list_val] :
% 0.21/0.48 ( ~ ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.21/0.48 => ( ~ ( member_val @ X @ ( set_val2 @ Ys ) )
% 0.21/0.48 => ( ( ( append_val @ Xs @ ( cons_val @ X @ Ys ) )
% 0.21/0.48 = ( append_val @ Xs4 @ ( cons_val @ X @ Ys6 ) ) )
% 0.21/0.48 = ( ( Xs = Xs4 )
% 0.21/0.48 & ( Ys = Ys6 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % append_Cons_eq_iff
% 0.21/0.48 thf(fact_234_append__Cons__eq__iff,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node,Ys: list_node,Xs4: list_node,Ys6: list_node] :
% 0.21/0.48 ( ~ ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.21/0.48 => ( ~ ( member_node @ X @ ( set_node2 @ Ys ) )
% 0.21/0.48 => ( ( ( append_node @ Xs @ ( cons_node @ X @ Ys ) )
% 0.21/0.48 = ( append_node @ Xs4 @ ( cons_node @ X @ Ys6 ) ) )
% 0.21/0.48 = ( ( Xs = Xs4 )
% 0.21/0.48 & ( Ys = Ys6 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % append_Cons_eq_iff
% 0.21/0.48 thf(fact_235_split__list__propE,axiom,
% 0.21/0.48 ! [Xs: list_node,P: node > $o] :
% 0.21/0.48 ( ? [X2: node] :
% 0.21/0.48 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.21/0.48 & ( P @ X2 ) )
% 0.21/0.48 => ~ ! [Ys2: list_node,X4: node] :
% 0.21/0.48 ( ? [Zs2: list_node] :
% 0.21/0.48 ( Xs
% 0.21/0.48 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.21/0.48 => ~ ( P @ X4 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % split_list_propE
% 0.21/0.48 thf(fact_236_split__list__first,axiom,
% 0.21/0.48 ! [X: val,Xs: list_val] :
% 0.21/0.48 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.21/0.48 => ? [Ys2: list_val,Zs2: list_val] :
% 0.21/0.48 ( ( Xs
% 0.21/0.48 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs2 ) ) )
% 0.21/0.48 & ~ ( member_val @ X @ ( set_val2 @ Ys2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % split_list_first
% 0.21/0.48 thf(fact_237_split__list__first,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node] :
% 0.21/0.48 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.21/0.48 => ? [Ys2: list_node,Zs2: list_node] :
% 0.21/0.48 ( ( Xs
% 0.21/0.48 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs2 ) ) )
% 0.21/0.48 & ~ ( member_node @ X @ ( set_node2 @ Ys2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % split_list_first
% 0.21/0.48 thf(fact_238_xy__in__set__cases,axiom,
% 0.21/0.48 ! [X: val,L: list_val,Y: val] :
% 0.21/0.48 ( ( member_val @ X @ ( set_val2 @ L ) )
% 0.21/0.48 => ( ( member_val @ Y @ ( set_val2 @ L ) )
% 0.21/0.48 => ( ( ( X = Y )
% 0.21/0.48 => ! [L12: list_val,L22: list_val] :
% 0.21/0.48 ( L
% 0.21/0.48 != ( append_val @ L12 @ ( cons_val @ Y @ L22 ) ) ) )
% 0.21/0.48 => ( ( ( X != Y )
% 0.21/0.48 => ! [L12: list_val,L22: list_val,L3: list_val] :
% 0.21/0.48 ( L
% 0.21/0.48 != ( append_val @ L12 @ ( cons_val @ X @ ( append_val @ L22 @ ( cons_val @ Y @ L3 ) ) ) ) ) )
% 0.21/0.48 => ~ ( ( X != Y )
% 0.21/0.48 => ! [L12: list_val,L22: list_val,L3: list_val] :
% 0.21/0.48 ( L
% 0.21/0.48 != ( append_val @ L12 @ ( cons_val @ Y @ ( append_val @ L22 @ ( cons_val @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % xy_in_set_cases
% 0.21/0.48 thf(fact_239_xy__in__set__cases,axiom,
% 0.21/0.48 ! [X: node,L: list_node,Y: node] :
% 0.21/0.48 ( ( member_node @ X @ ( set_node2 @ L ) )
% 0.21/0.48 => ( ( member_node @ Y @ ( set_node2 @ L ) )
% 0.21/0.48 => ( ( ( X = Y )
% 0.21/0.48 => ! [L12: list_node,L22: list_node] :
% 0.21/0.48 ( L
% 0.21/0.48 != ( append_node @ L12 @ ( cons_node @ Y @ L22 ) ) ) )
% 0.21/0.48 => ( ( ( X != Y )
% 0.21/0.48 => ! [L12: list_node,L22: list_node,L3: list_node] :
% 0.21/0.48 ( L
% 0.21/0.48 != ( append_node @ L12 @ ( cons_node @ X @ ( append_node @ L22 @ ( cons_node @ Y @ L3 ) ) ) ) ) )
% 0.21/0.48 => ~ ( ( X != Y )
% 0.21/0.48 => ! [L12: list_node,L22: list_node,L3: list_node] :
% 0.21/0.48 ( L
% 0.21/0.48 != ( append_node @ L12 @ ( cons_node @ Y @ ( append_node @ L22 @ ( cons_node @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % xy_in_set_cases
% 0.21/0.48 thf(fact_240_split__list__prop,axiom,
% 0.21/0.48 ! [Xs: list_node,P: node > $o] :
% 0.21/0.48 ( ? [X2: node] :
% 0.21/0.48 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.21/0.48 & ( P @ X2 ) )
% 0.21/0.48 => ? [Ys2: list_node,X4: node] :
% 0.21/0.48 ( ? [Zs2: list_node] :
% 0.21/0.48 ( Xs
% 0.21/0.48 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.21/0.48 & ( P @ X4 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % split_list_prop
% 0.21/0.48 thf(fact_241_split__list__last,axiom,
% 0.21/0.48 ! [X: val,Xs: list_val] :
% 0.21/0.48 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.21/0.48 => ? [Ys2: list_val,Zs2: list_val] :
% 0.21/0.48 ( ( Xs
% 0.21/0.48 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs2 ) ) )
% 0.21/0.48 & ~ ( member_val @ X @ ( set_val2 @ Zs2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % split_list_last
% 0.21/0.48 thf(fact_242_split__list__last,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node] :
% 0.21/0.48 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.21/0.48 => ? [Ys2: list_node,Zs2: list_node] :
% 0.21/0.48 ( ( Xs
% 0.21/0.48 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs2 ) ) )
% 0.21/0.48 & ~ ( member_node @ X @ ( set_node2 @ Zs2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % split_list_last
% 0.21/0.48 thf(fact_243_split__list,axiom,
% 0.21/0.48 ! [X: val,Xs: list_val] :
% 0.21/0.48 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.21/0.48 => ? [Ys2: list_val,Zs2: list_val] :
% 0.21/0.48 ( Xs
% 0.21/0.48 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % split_list
% 0.21/0.48 thf(fact_244_split__list,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node] :
% 0.21/0.48 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.21/0.48 => ? [Ys2: list_node,Zs2: list_node] :
% 0.21/0.48 ( Xs
% 0.21/0.48 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % split_list
% 0.21/0.48 thf(fact_245_tl__obtain__elem,axiom,
% 0.21/0.48 ! [Xs: list_node] :
% 0.21/0.48 ( ( Xs != nil_node )
% 0.21/0.48 => ( ( ( tl_node @ Xs )
% 0.21/0.48 = nil_node )
% 0.21/0.48 => ~ ! [E3: node] :
% 0.21/0.48 ( Xs
% 0.21/0.48 != ( cons_node @ E3 @ nil_node ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % tl_obtain_elem
% 0.21/0.48 thf(fact_246_tl__Nil,axiom,
% 0.21/0.48 ! [Xs: list_node] :
% 0.21/0.48 ( ( ( tl_node @ Xs )
% 0.21/0.48 = nil_node )
% 0.21/0.48 = ( ( Xs = nil_node )
% 0.21/0.48 | ? [X3: node] :
% 0.21/0.48 ( Xs
% 0.21/0.48 = ( cons_node @ X3 @ nil_node ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % tl_Nil
% 0.21/0.48 thf(fact_247_Nil__tl,axiom,
% 0.21/0.48 ! [Xs: list_node] :
% 0.21/0.48 ( ( nil_node
% 0.21/0.48 = ( tl_node @ Xs ) )
% 0.21/0.48 = ( ( Xs = nil_node )
% 0.21/0.48 | ? [X3: node] :
% 0.21/0.48 ( Xs
% 0.21/0.48 = ( cons_node @ X3 @ nil_node ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % Nil_tl
% 0.21/0.48 thf(fact_248_list_Oset__sel_I2_J,axiom,
% 0.21/0.48 ! [A: list_val,X: val] :
% 0.21/0.48 ( ( A != nil_val )
% 0.21/0.48 => ( ( member_val @ X @ ( set_val2 @ ( tl_val @ A ) ) )
% 0.21/0.48 => ( member_val @ X @ ( set_val2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.set_sel(2)
% 0.21/0.48 thf(fact_249_list_Oset__sel_I2_J,axiom,
% 0.21/0.48 ! [A: list_node,X: node] :
% 0.21/0.48 ( ( A != nil_node )
% 0.21/0.48 => ( ( member_node @ X @ ( set_node2 @ ( tl_node @ A ) ) )
% 0.21/0.48 => ( member_node @ X @ ( set_node2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.set_sel(2)
% 0.21/0.48 thf(fact_250_prefix__snoc,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node,Y: node] :
% 0.21/0.48 ( ( prefix_node @ Xs @ ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 0.21/0.48 = ( ( Xs
% 0.21/0.48 = ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 0.21/0.48 | ( prefix_node @ Xs @ Ys ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % prefix_snoc
% 0.21/0.48 thf(fact_251_old_Opath2__split__first__last,axiom,
% 0.21/0.48 ! [G: g,N: node,Ns: list_node,M: node,X: node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.48 => ( ( member_node @ X @ ( set_node2 @ Ns ) )
% 0.21/0.48 => ~ ! [Ns_1: list_node,Ns_3: list_node,Ns_2: list_node] :
% 0.21/0.48 ( ( Ns
% 0.21/0.48 = ( append_node @ Ns_1 @ ( append_node @ Ns_3 @ Ns_2 ) ) )
% 0.21/0.48 => ( ( prefix_node @ ( append_node @ Ns_1 @ ( cons_node @ X @ nil_node ) ) @ Ns )
% 0.21/0.48 => ( ( suffix_node @ ( cons_node @ X @ Ns_2 ) @ Ns )
% 0.21/0.48 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns_1 @ ( cons_node @ X @ nil_node ) ) @ X )
% 0.21/0.48 => ( ~ ( member_node @ X @ ( set_node2 @ Ns_1 ) )
% 0.21/0.48 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ Ns_3 @ X )
% 0.21/0.48 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ ( cons_node @ X @ Ns_2 ) @ M )
% 0.21/0.48 => ( member_node @ X @ ( set_node2 @ Ns_2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path2_split_first_last
% 0.21/0.48 thf(fact_252_same__prefix__nil,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node] :
% 0.21/0.48 ( ( prefix_node @ ( append_node @ Xs @ Ys ) @ Xs )
% 0.21/0.48 = ( Ys = nil_node ) ) ).
% 0.21/0.48
% 0.21/0.48 % same_prefix_nil
% 0.21/0.48 thf(fact_253_old_Opath2__simple__loop,axiom,
% 0.21/0.48 ! [G: g,N: node,Ns: list_node,N2: node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ N )
% 0.21/0.48 => ( ( member_node @ N2 @ ( set_node2 @ Ns ) )
% 0.21/0.48 => ~ ! [Ns3: list_node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns3 @ N )
% 0.21/0.48 => ( ( member_node @ N2 @ ( set_node2 @ Ns3 ) )
% 0.21/0.48 => ( ~ ( member_node @ N @ ( set_node2 @ ( tl_node @ ( butlast_node @ Ns3 ) ) ) )
% 0.21/0.48 => ~ ( ord_less_eq_set_node @ ( set_node2 @ Ns3 ) @ ( set_node2 @ Ns ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path2_simple_loop
% 0.21/0.48 thf(fact_254_old_Opath2__cases,axiom,
% 0.21/0.48 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.48 => ( ( ( Ns
% 0.21/0.48 = ( cons_node @ N @ nil_node ) )
% 0.21/0.48 => ( M != N ) )
% 0.21/0.48 => ~ ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( hd_node @ ( tl_node @ Ns ) ) @ ( tl_node @ Ns ) @ M )
% 0.21/0.48 => ~ ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ ( tl_node @ Ns ) ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path2_cases
% 0.21/0.48 thf(fact_255_old_Opath__snoc,axiom,
% 0.21/0.48 ! [G: g,Ns: list_node,N: node,M: node] :
% 0.21/0.48 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ N @ nil_node ) ) )
% 0.21/0.48 => ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M ) ) )
% 0.21/0.48 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ N @ ( cons_node @ M @ nil_node ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path_snoc
% 0.21/0.48 thf(fact_256_phiUses__finite,axiom,
% 0.21/0.48 ! [N: node,G: g] :
% 0.21/0.48 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.21/0.48 => ( finite_finite_val @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % phiUses_finite
% 0.21/0.48 thf(fact_257_old_Opath2__split__last__prop,axiom,
% 0.21/0.48 ! [G: g,N: node,Ns: list_node,M: node,P: node > $o] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.48 => ( ? [X2: node] :
% 0.21/0.48 ( ( member_node @ X2 @ ( set_node2 @ Ns ) )
% 0.21/0.48 & ( P @ X2 ) )
% 0.21/0.48 => ~ ! [N3: node,Ns3: list_node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N3 @ Ns3 @ M )
% 0.21/0.48 => ( ( P @ N3 )
% 0.21/0.48 => ( ! [X2: node] :
% 0.21/0.48 ( ( member_node @ X2 @ ( set_node2 @ ( tl_node @ Ns3 ) ) )
% 0.21/0.48 => ~ ( P @ X2 ) )
% 0.21/0.48 => ~ ( suffix_node @ Ns3 @ Ns ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path2_split_last_prop
% 0.21/0.48 thf(fact_258_defs__finite,axiom,
% 0.21/0.48 ! [G: g,N: node] : ( finite_finite_val @ ( defs @ G @ N ) ) ).
% 0.21/0.48
% 0.21/0.48 % defs_finite
% 0.21/0.48 thf(fact_259_prefix__order_Oorder__refl,axiom,
% 0.21/0.48 ! [X: list_node] : ( prefix_node @ X @ X ) ).
% 0.21/0.48
% 0.21/0.48 % prefix_order.order_refl
% 0.21/0.48 thf(fact_260_prefix__order_Odual__order_Orefl,axiom,
% 0.21/0.48 ! [A: list_node] : ( prefix_node @ A @ A ) ).
% 0.21/0.48
% 0.21/0.48 % prefix_order.dual_order.refl
% 0.21/0.48 thf(fact_261_suffix__order_Oorder__refl,axiom,
% 0.21/0.48 ! [X: list_node] : ( suffix_node @ X @ X ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_order.order_refl
% 0.21/0.48 thf(fact_262_suffix__order_Odual__order_Orefl,axiom,
% 0.21/0.48 ! [A: list_node] : ( suffix_node @ A @ A ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_order.dual_order.refl
% 0.21/0.48 thf(fact_263_old_Opath__not__Nil,axiom,
% 0.21/0.48 ! [G: g,Ns: list_node] :
% 0.21/0.48 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 0.21/0.48 => ( Ns != nil_node ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path_not_Nil
% 0.21/0.48 thf(fact_264_old_Opath2__hd,axiom,
% 0.21/0.48 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.48 => ( N
% 0.21/0.48 = ( hd_node @ Ns ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path2_hd
% 0.21/0.48 thf(fact_265_old_Opath2__forget__hd,axiom,
% 0.21/0.48 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.21/0.48 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.21/0.48 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( hd_node @ Ns ) @ Ns @ M ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path2_forget_hd
% 0.21/0.48 thf(fact_266_old_Opath__hd,axiom,
% 0.21/0.48 ! [G: g,N: node,Ns: list_node] :
% 0.21/0.48 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ Ns ) )
% 0.21/0.48 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ nil_node ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path_hd
% 0.21/0.48 thf(fact_267_old_Opath__split_I2_J,axiom,
% 0.21/0.48 ! [G: g,Ns: list_node,M: node,Ns2: list_node] :
% 0.21/0.48 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ M @ Ns2 ) ) )
% 0.21/0.48 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ M @ Ns2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path_split(2)
% 0.21/0.48 thf(fact_268_List_Ofinite__set,axiom,
% 0.21/0.48 ! [Xs: list_node] : ( finite_finite_node @ ( set_node2 @ Xs ) ) ).
% 0.21/0.48
% 0.21/0.48 % List.finite_set
% 0.21/0.48 thf(fact_269_List_Ofinite__set,axiom,
% 0.21/0.48 ! [Xs: list_val] : ( finite_finite_val @ ( set_val2 @ Xs ) ) ).
% 0.21/0.48
% 0.21/0.48 % List.finite_set
% 0.21/0.48 thf(fact_270_Cons__prefix__Cons,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node,Y: node,Ys: list_node] :
% 0.21/0.48 ( ( prefix_node @ ( cons_node @ X @ Xs ) @ ( cons_node @ Y @ Ys ) )
% 0.21/0.48 = ( ( X = Y )
% 0.21/0.48 & ( prefix_node @ Xs @ Ys ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % Cons_prefix_Cons
% 0.21/0.48 thf(fact_271_prefix__code_I1_J,axiom,
% 0.21/0.48 ! [Xs: list_node] : ( prefix_node @ nil_node @ Xs ) ).
% 0.21/0.48
% 0.21/0.48 % prefix_code(1)
% 0.21/0.48 thf(fact_272_prefix__Nil,axiom,
% 0.21/0.48 ! [Xs: list_node] :
% 0.21/0.48 ( ( prefix_node @ Xs @ nil_node )
% 0.21/0.48 = ( Xs = nil_node ) ) ).
% 0.21/0.48
% 0.21/0.48 % prefix_Nil
% 0.21/0.48 thf(fact_273_prefix__bot_Obot_Oextremum__unique,axiom,
% 0.21/0.48 ! [A: list_node] :
% 0.21/0.48 ( ( prefix_node @ A @ nil_node )
% 0.21/0.48 = ( A = nil_node ) ) ).
% 0.21/0.48
% 0.21/0.48 % prefix_bot.bot.extremum_unique
% 0.21/0.48 thf(fact_274_suffix__bot_Obot_Oextremum__unique,axiom,
% 0.21/0.48 ! [A: list_node] :
% 0.21/0.48 ( ( suffix_node @ A @ nil_node )
% 0.21/0.48 = ( A = nil_node ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_bot.bot.extremum_unique
% 0.21/0.48 thf(fact_275_suffix__Nil,axiom,
% 0.21/0.48 ! [Xs: list_node] :
% 0.21/0.48 ( ( suffix_node @ Xs @ nil_node )
% 0.21/0.48 = ( Xs = nil_node ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_Nil
% 0.21/0.48 thf(fact_276_same__prefix__prefix,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.21/0.48 ( ( prefix_node @ ( append_node @ Xs @ Ys ) @ ( append_node @ Xs @ Zs ) )
% 0.21/0.48 = ( prefix_node @ Ys @ Zs ) ) ).
% 0.21/0.48
% 0.21/0.48 % same_prefix_prefix
% 0.21/0.48 thf(fact_277_same__suffix__suffix,axiom,
% 0.21/0.48 ! [Ys: list_node,Xs: list_node,Zs: list_node] :
% 0.21/0.48 ( ( suffix_node @ ( append_node @ Ys @ Xs ) @ ( append_node @ Zs @ Xs ) )
% 0.21/0.48 = ( suffix_node @ Ys @ Zs ) ) ).
% 0.21/0.48
% 0.21/0.48 % same_suffix_suffix
% 0.21/0.48 thf(fact_278_old_Oempty__path,axiom,
% 0.21/0.48 ! [N: node,G: g] :
% 0.21/0.48 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.21/0.48 => ( ( invar @ G )
% 0.21/0.48 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ nil_node ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.empty_path
% 0.21/0.48 thf(fact_279_old_Opath__split_I1_J,axiom,
% 0.21/0.48 ! [G: g,Ns: list_node,M: node,Ns2: list_node] :
% 0.21/0.48 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ M @ Ns2 ) ) )
% 0.21/0.48 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ M @ nil_node ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path_split(1)
% 0.21/0.48 thf(fact_280_old_OCons__path,axiom,
% 0.21/0.48 ! [G: g,Ns: list_node,N2: node] :
% 0.21/0.48 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 0.21/0.48 => ( ( member_node @ N2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns ) ) ) )
% 0.21/0.48 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N2 @ Ns ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.Cons_path
% 0.21/0.48 thf(fact_281_old_Opath_Osimps,axiom,
% 0.21/0.48 ! [G: g,A: list_node] :
% 0.21/0.48 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ A )
% 0.21/0.48 = ( ? [N5: node] :
% 0.21/0.48 ( ( A
% 0.21/0.48 = ( cons_node @ N5 @ nil_node ) )
% 0.21/0.48 & ( member_node @ N5 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.21/0.48 & ( invar @ G ) )
% 0.21/0.48 | ? [Ns5: list_node,N6: node] :
% 0.21/0.48 ( ( A
% 0.21/0.48 = ( cons_node @ N6 @ Ns5 ) )
% 0.21/0.48 & ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns5 )
% 0.21/0.48 & ( member_node @ N6 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns5 ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path.simps
% 0.21/0.48 thf(fact_282_old_Opath_Oinducts,axiom,
% 0.21/0.48 ! [G: g,X: list_node,P: list_node > $o] :
% 0.21/0.48 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ X )
% 0.21/0.48 => ( ! [N4: node] :
% 0.21/0.48 ( ( member_node @ N4 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.21/0.48 => ( ( invar @ G )
% 0.21/0.48 => ( P @ ( cons_node @ N4 @ nil_node ) ) ) )
% 0.21/0.48 => ( ! [Ns4: list_node,N3: node] :
% 0.21/0.48 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns4 )
% 0.21/0.48 => ( ( P @ Ns4 )
% 0.21/0.48 => ( ( member_node @ N3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns4 ) ) ) )
% 0.21/0.48 => ( P @ ( cons_node @ N3 @ Ns4 ) ) ) ) )
% 0.21/0.48 => ( P @ X ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path.inducts
% 0.21/0.48 thf(fact_283_old_Opath_Ocases,axiom,
% 0.21/0.48 ! [G: g,A: list_node] :
% 0.21/0.48 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ A )
% 0.21/0.48 => ( ! [N4: node] :
% 0.21/0.48 ( ( A
% 0.21/0.48 = ( cons_node @ N4 @ nil_node ) )
% 0.21/0.48 => ( ( member_node @ N4 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.21/0.48 => ~ ( invar @ G ) ) )
% 0.21/0.48 => ~ ! [Ns4: list_node,N3: node] :
% 0.21/0.48 ( ( A
% 0.21/0.48 = ( cons_node @ N3 @ Ns4 ) )
% 0.21/0.48 => ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns4 )
% 0.21/0.48 => ~ ( member_node @ N3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns4 ) ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path.cases
% 0.21/0.48 thf(fact_284_same__suffix__nil,axiom,
% 0.21/0.48 ! [Ys: list_node,Xs: list_node] :
% 0.21/0.48 ( ( suffix_node @ ( append_node @ Ys @ Xs ) @ Xs )
% 0.21/0.48 = ( Ys = nil_node ) ) ).
% 0.21/0.48
% 0.21/0.48 % same_suffix_nil
% 0.21/0.48 thf(fact_285_hd__append2,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node] :
% 0.21/0.48 ( ( Xs != nil_node )
% 0.21/0.48 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 0.21/0.48 = ( hd_node @ Xs ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % hd_append2
% 0.21/0.48 thf(fact_286_suffix__snoc,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node,Y: node] :
% 0.21/0.48 ( ( suffix_node @ Xs @ ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 0.21/0.48 = ( ( Xs = nil_node )
% 0.21/0.48 | ? [Zs3: list_node] :
% 0.21/0.48 ( ( Xs
% 0.21/0.48 = ( append_node @ Zs3 @ ( cons_node @ Y @ nil_node ) ) )
% 0.21/0.48 & ( suffix_node @ Zs3 @ Ys ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_snoc
% 0.21/0.48 thf(fact_287_snoc__suffix__snoc,axiom,
% 0.21/0.48 ! [Xs: list_node,X: node,Ys: list_node,Y: node] :
% 0.21/0.48 ( ( suffix_node @ ( append_node @ Xs @ ( cons_node @ X @ nil_node ) ) @ ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 0.21/0.48 = ( ( X = Y )
% 0.21/0.48 & ( suffix_node @ Xs @ Ys ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % snoc_suffix_snoc
% 0.21/0.48 thf(fact_288_hd__Cons__tl,axiom,
% 0.21/0.48 ! [Xs: list_node] :
% 0.21/0.48 ( ( Xs != nil_node )
% 0.21/0.48 => ( ( cons_node @ ( hd_node @ Xs ) @ ( tl_node @ Xs ) )
% 0.21/0.48 = Xs ) ) ).
% 0.21/0.48
% 0.21/0.48 % hd_Cons_tl
% 0.21/0.48 thf(fact_289_list_Ocollapse,axiom,
% 0.21/0.48 ! [List: list_node] :
% 0.21/0.48 ( ( List != nil_node )
% 0.21/0.48 => ( ( cons_node @ ( hd_node @ List ) @ ( tl_node @ List ) )
% 0.21/0.48 = List ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.collapse
% 0.21/0.48 thf(fact_290_in__hd__or__tl__conv,axiom,
% 0.21/0.48 ! [L: list_val,X: val] :
% 0.21/0.48 ( ( L != nil_val )
% 0.21/0.48 => ( ( ( X
% 0.21/0.48 = ( hd_val @ L ) )
% 0.21/0.48 | ( member_val @ X @ ( set_val2 @ ( tl_val @ L ) ) ) )
% 0.21/0.48 = ( member_val @ X @ ( set_val2 @ L ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % in_hd_or_tl_conv
% 0.21/0.48 thf(fact_291_in__hd__or__tl__conv,axiom,
% 0.21/0.48 ! [L: list_node,X: node] :
% 0.21/0.48 ( ( L != nil_node )
% 0.21/0.48 => ( ( ( X
% 0.21/0.48 = ( hd_node @ L ) )
% 0.21/0.48 | ( member_node @ X @ ( set_node2 @ ( tl_node @ L ) ) ) )
% 0.21/0.48 = ( member_node @ X @ ( set_node2 @ L ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % in_hd_or_tl_conv
% 0.21/0.48 thf(fact_292_old_Opath__invar,axiom,
% 0.21/0.48 ! [G: g,Ns: list_node] :
% 0.21/0.48 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 0.21/0.48 => ( invar @ G ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path_invar
% 0.21/0.48 thf(fact_293_old_Opath__in___092_060alpha_062n,axiom,
% 0.21/0.48 ! [G: g,Ns: list_node,N: node] :
% 0.21/0.48 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 0.21/0.48 => ( ( member_node @ N @ ( set_node2 @ Ns ) )
% 0.21/0.48 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path_in_\<alpha>n
% 0.21/0.48 thf(fact_294_old_Opath__by__tail,axiom,
% 0.21/0.48 ! [G: g,N: node,N2: node,Ns: list_node,Ms: list_node] :
% 0.21/0.48 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ ( cons_node @ N2 @ Ns ) ) )
% 0.21/0.48 => ( ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N2 @ Ns ) )
% 0.21/0.48 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N2 @ Ms ) ) )
% 0.21/0.48 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ ( cons_node @ N2 @ Ms ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.path_by_tail
% 0.21/0.48 thf(fact_295_set__mono__suffix,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node] :
% 0.21/0.48 ( ( suffix_node @ Xs @ Ys )
% 0.21/0.48 => ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ ( set_node2 @ Ys ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % set_mono_suffix
% 0.21/0.48 thf(fact_296_subset__Collect__conv,axiom,
% 0.21/0.48 ! [S: set_node,P: node > $o] :
% 0.21/0.48 ( ( ord_less_eq_set_node @ S @ ( collect_node @ P ) )
% 0.21/0.48 = ( ! [X3: node] :
% 0.21/0.48 ( ( member_node @ X3 @ S )
% 0.21/0.48 => ( P @ X3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % subset_Collect_conv
% 0.21/0.48 thf(fact_297_ord__eq__le__eq__trans,axiom,
% 0.21/0.48 ! [A: set_node,B: set_node,C: set_node,D: set_node] :
% 0.21/0.48 ( ( A = B )
% 0.21/0.48 => ( ( ord_less_eq_set_node @ B @ C )
% 0.21/0.48 => ( ( C = D )
% 0.21/0.48 => ( ord_less_eq_set_node @ A @ D ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % ord_eq_le_eq_trans
% 0.21/0.48 thf(fact_298_suffix__ConsD2,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node,Y: node,Ys: list_node] :
% 0.21/0.48 ( ( suffix_node @ ( cons_node @ X @ Xs ) @ ( cons_node @ Y @ Ys ) )
% 0.21/0.48 => ( suffix_node @ Xs @ Ys ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_ConsD2
% 0.21/0.48 thf(fact_299_suffix__ConsI,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node,Y: node] :
% 0.21/0.48 ( ( suffix_node @ Xs @ Ys )
% 0.21/0.48 => ( suffix_node @ Xs @ ( cons_node @ Y @ Ys ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_ConsI
% 0.21/0.48 thf(fact_300_suffix__ConsD,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node,Ys: list_node] :
% 0.21/0.48 ( ( suffix_node @ ( cons_node @ X @ Xs ) @ Ys )
% 0.21/0.48 => ( suffix_node @ Xs @ Ys ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_ConsD
% 0.21/0.48 thf(fact_301_suffix__Cons,axiom,
% 0.21/0.48 ! [Xs: list_node,Y: node,Ys: list_node] :
% 0.21/0.48 ( ( suffix_node @ Xs @ ( cons_node @ Y @ Ys ) )
% 0.21/0.48 = ( ( Xs
% 0.21/0.48 = ( cons_node @ Y @ Ys ) )
% 0.21/0.48 | ( suffix_node @ Xs @ Ys ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_Cons
% 0.21/0.48 thf(fact_302_suffix__bot_Obot_Oextremum__uniqueI,axiom,
% 0.21/0.48 ! [A: list_node] :
% 0.21/0.48 ( ( suffix_node @ A @ nil_node )
% 0.21/0.48 => ( A = nil_node ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_bot.bot.extremum_uniqueI
% 0.21/0.48 thf(fact_303_suffix__bot_Obot_Oextremum,axiom,
% 0.21/0.48 ! [A: list_node] : ( suffix_node @ nil_node @ A ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_bot.bot.extremum
% 0.21/0.48 thf(fact_304_Nil__suffix,axiom,
% 0.21/0.48 ! [Xs: list_node] : ( suffix_node @ nil_node @ Xs ) ).
% 0.21/0.48
% 0.21/0.48 % Nil_suffix
% 0.21/0.48 thf(fact_305_suffixE,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node] :
% 0.21/0.48 ( ( suffix_node @ Xs @ Ys )
% 0.21/0.48 => ~ ! [Zs2: list_node] :
% 0.21/0.48 ( Ys
% 0.21/0.48 != ( append_node @ Zs2 @ Xs ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffixE
% 0.21/0.48 thf(fact_306_suffixI,axiom,
% 0.21/0.48 ! [Ys: list_node,Zs: list_node,Xs: list_node] :
% 0.21/0.48 ( ( Ys
% 0.21/0.48 = ( append_node @ Zs @ Xs ) )
% 0.21/0.48 => ( suffix_node @ Xs @ Ys ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffixI
% 0.21/0.48 thf(fact_307_Sublist_Osuffix__def,axiom,
% 0.21/0.48 ( suffix_node
% 0.21/0.48 = ( ^ [Xs3: list_node,Ys3: list_node] :
% 0.21/0.48 ? [Zs3: list_node] :
% 0.21/0.48 ( Ys3
% 0.21/0.48 = ( append_node @ Zs3 @ Xs3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % Sublist.suffix_def
% 0.21/0.48 thf(fact_308_suffix__append,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.21/0.48 ( ( suffix_node @ Xs @ ( append_node @ Ys @ Zs ) )
% 0.21/0.48 = ( ( suffix_node @ Xs @ Zs )
% 0.21/0.48 | ? [Xs5: list_node] :
% 0.21/0.48 ( ( Xs
% 0.21/0.48 = ( append_node @ Xs5 @ Zs ) )
% 0.21/0.48 & ( suffix_node @ Xs5 @ Ys ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_append
% 0.21/0.48 thf(fact_309_suffix__appendD,axiom,
% 0.21/0.48 ! [Zs: list_node,Xs: list_node,Ys: list_node] :
% 0.21/0.48 ( ( suffix_node @ ( append_node @ Zs @ Xs ) @ Ys )
% 0.21/0.48 => ( suffix_node @ Xs @ Ys ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_appendD
% 0.21/0.48 thf(fact_310_suffix__appendI,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.21/0.48 ( ( suffix_node @ Xs @ Ys )
% 0.21/0.48 => ( suffix_node @ Xs @ ( append_node @ Zs @ Ys ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_appendI
% 0.21/0.48 thf(fact_311_suffix__tl,axiom,
% 0.21/0.48 ! [Xs: list_node] : ( suffix_node @ ( tl_node @ Xs ) @ Xs ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_tl
% 0.21/0.48 thf(fact_312_suffix__same__cases,axiom,
% 0.21/0.48 ! [Xs_1: list_node,Ys: list_node,Xs_2: list_node] :
% 0.21/0.48 ( ( suffix_node @ Xs_1 @ Ys )
% 0.21/0.48 => ( ( suffix_node @ Xs_2 @ Ys )
% 0.21/0.48 => ( ( suffix_node @ Xs_1 @ Xs_2 )
% 0.21/0.48 | ( suffix_node @ Xs_2 @ Xs_1 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_same_cases
% 0.21/0.48 thf(fact_313_suffix__order_Oeq__iff,axiom,
% 0.21/0.48 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 0.21/0.48 = ( ^ [X3: list_node,Y3: list_node] :
% 0.21/0.48 ( ( suffix_node @ X3 @ Y3 )
% 0.21/0.48 & ( suffix_node @ Y3 @ X3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_order.eq_iff
% 0.21/0.48 thf(fact_314_suffix__order_Oantisym,axiom,
% 0.21/0.48 ! [X: list_node,Y: list_node] :
% 0.21/0.48 ( ( suffix_node @ X @ Y )
% 0.21/0.48 => ( ( suffix_node @ Y @ X )
% 0.21/0.48 => ( X = Y ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_order.antisym
% 0.21/0.48 thf(fact_315_suffix__order_Oeq__refl,axiom,
% 0.21/0.48 ! [X: list_node,Y: list_node] :
% 0.21/0.48 ( ( X = Y )
% 0.21/0.48 => ( suffix_node @ X @ Y ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_order.eq_refl
% 0.21/0.48 thf(fact_316_suffix__order_Oorder_Otrans,axiom,
% 0.21/0.48 ! [A: list_node,B: list_node,C: list_node] :
% 0.21/0.48 ( ( suffix_node @ A @ B )
% 0.21/0.48 => ( ( suffix_node @ B @ C )
% 0.21/0.48 => ( suffix_node @ A @ C ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_order.order.trans
% 0.21/0.48 thf(fact_317_suffix__order_Oorder__trans,axiom,
% 0.21/0.48 ! [X: list_node,Y: list_node,Z3: list_node] :
% 0.21/0.48 ( ( suffix_node @ X @ Y )
% 0.21/0.48 => ( ( suffix_node @ Y @ Z3 )
% 0.21/0.48 => ( suffix_node @ X @ Z3 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_order.order_trans
% 0.21/0.48 thf(fact_318_suffix__order_Oantisym__conv,axiom,
% 0.21/0.48 ! [Y: list_node,X: list_node] :
% 0.21/0.48 ( ( suffix_node @ Y @ X )
% 0.21/0.48 => ( ( suffix_node @ X @ Y )
% 0.21/0.48 = ( X = Y ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_order.antisym_conv
% 0.21/0.48 thf(fact_319_suffix__order_Oorder_Oeq__iff,axiom,
% 0.21/0.48 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 0.21/0.48 = ( ^ [A4: list_node,B3: list_node] :
% 0.21/0.48 ( ( suffix_node @ A4 @ B3 )
% 0.21/0.48 & ( suffix_node @ B3 @ A4 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_order.order.eq_iff
% 0.21/0.48 thf(fact_320_suffix__order_Oorder_Oantisym,axiom,
% 0.21/0.48 ! [A: list_node,B: list_node] :
% 0.21/0.48 ( ( suffix_node @ A @ B )
% 0.21/0.48 => ( ( suffix_node @ B @ A )
% 0.21/0.48 => ( A = B ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_order.order.antisym
% 0.21/0.48 thf(fact_321_suffix__order_Oord__eq__le__trans,axiom,
% 0.21/0.48 ! [A: list_node,B: list_node,C: list_node] :
% 0.21/0.48 ( ( A = B )
% 0.21/0.48 => ( ( suffix_node @ B @ C )
% 0.21/0.48 => ( suffix_node @ A @ C ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_order.ord_eq_le_trans
% 0.21/0.48 thf(fact_322_suffix__order_Oord__le__eq__trans,axiom,
% 0.21/0.48 ! [A: list_node,B: list_node,C: list_node] :
% 0.21/0.48 ( ( suffix_node @ A @ B )
% 0.21/0.48 => ( ( B = C )
% 0.21/0.48 => ( suffix_node @ A @ C ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_order.ord_le_eq_trans
% 0.21/0.48 thf(fact_323_suffix__order_Odual__order_Otrans,axiom,
% 0.21/0.48 ! [B: list_node,A: list_node,C: list_node] :
% 0.21/0.48 ( ( suffix_node @ B @ A )
% 0.21/0.48 => ( ( suffix_node @ C @ B )
% 0.21/0.48 => ( suffix_node @ C @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_order.dual_order.trans
% 0.21/0.48 thf(fact_324_suffix__order_Odual__order_Oeq__iff,axiom,
% 0.21/0.48 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 0.21/0.48 = ( ^ [A4: list_node,B3: list_node] :
% 0.21/0.48 ( ( suffix_node @ B3 @ A4 )
% 0.21/0.48 & ( suffix_node @ A4 @ B3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_order.dual_order.eq_iff
% 0.21/0.48 thf(fact_325_suffix__order_Odual__order_Oantisym,axiom,
% 0.21/0.48 ! [B: list_node,A: list_node] :
% 0.21/0.48 ( ( suffix_node @ B @ A )
% 0.21/0.48 => ( ( suffix_node @ A @ B )
% 0.21/0.48 => ( A = B ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % suffix_order.dual_order.antisym
% 0.21/0.48 thf(fact_326_list_Osel_I1_J,axiom,
% 0.21/0.48 ! [X21: node,X22: list_node] :
% 0.21/0.48 ( ( hd_node @ ( cons_node @ X21 @ X22 ) )
% 0.21/0.48 = X21 ) ).
% 0.21/0.48
% 0.21/0.48 % list.sel(1)
% 0.21/0.48 thf(fact_327_finite__list,axiom,
% 0.21/0.48 ! [A2: set_node] :
% 0.21/0.48 ( ( finite_finite_node @ A2 )
% 0.21/0.48 => ? [Xs2: list_node] :
% 0.21/0.48 ( ( set_node2 @ Xs2 )
% 0.21/0.48 = A2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % finite_list
% 0.21/0.48 thf(fact_328_finite__list,axiom,
% 0.21/0.48 ! [A2: set_val] :
% 0.21/0.48 ( ( finite_finite_val @ A2 )
% 0.21/0.48 => ? [Xs2: list_val] :
% 0.21/0.48 ( ( set_val2 @ Xs2 )
% 0.21/0.48 = A2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % finite_list
% 0.21/0.48 thf(fact_329_subset__code_I1_J,axiom,
% 0.21/0.48 ! [Xs: list_val,B4: set_val] :
% 0.21/0.48 ( ( ord_less_eq_set_val @ ( set_val2 @ Xs ) @ B4 )
% 0.21/0.48 = ( ! [X3: val] :
% 0.21/0.48 ( ( member_val @ X3 @ ( set_val2 @ Xs ) )
% 0.21/0.48 => ( member_val @ X3 @ B4 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % subset_code(1)
% 0.21/0.48 thf(fact_330_subset__code_I1_J,axiom,
% 0.21/0.48 ! [Xs: list_node,B4: set_node] :
% 0.21/0.48 ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ B4 )
% 0.21/0.48 = ( ! [X3: node] :
% 0.21/0.48 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 0.21/0.48 => ( member_node @ X3 @ B4 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % subset_code(1)
% 0.21/0.48 thf(fact_331_set__mono__prefix,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node] :
% 0.21/0.48 ( ( prefix_node @ Xs @ Ys )
% 0.21/0.48 => ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ ( set_node2 @ Ys ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % set_mono_prefix
% 0.21/0.48 thf(fact_332_list_Oset__sel_I1_J,axiom,
% 0.21/0.48 ! [A: list_val] :
% 0.21/0.48 ( ( A != nil_val )
% 0.21/0.48 => ( member_val @ ( hd_val @ A ) @ ( set_val2 @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.set_sel(1)
% 0.21/0.48 thf(fact_333_list_Oset__sel_I1_J,axiom,
% 0.21/0.48 ! [A: list_node] :
% 0.21/0.48 ( ( A != nil_node )
% 0.21/0.48 => ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.set_sel(1)
% 0.21/0.48 thf(fact_334_hd__in__set,axiom,
% 0.21/0.48 ! [Xs: list_val] :
% 0.21/0.48 ( ( Xs != nil_val )
% 0.21/0.48 => ( member_val @ ( hd_val @ Xs ) @ ( set_val2 @ Xs ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % hd_in_set
% 0.21/0.48 thf(fact_335_hd__in__set,axiom,
% 0.21/0.48 ! [Xs: list_node] :
% 0.21/0.48 ( ( Xs != nil_node )
% 0.21/0.48 => ( member_node @ ( hd_node @ Xs ) @ ( set_node2 @ Xs ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % hd_in_set
% 0.21/0.48 thf(fact_336_hd__append,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node] :
% 0.21/0.48 ( ( ( Xs = nil_node )
% 0.21/0.48 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 0.21/0.48 = ( hd_node @ Ys ) ) )
% 0.21/0.48 & ( ( Xs != nil_node )
% 0.21/0.48 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 0.21/0.48 = ( hd_node @ Xs ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % hd_append
% 0.21/0.48 thf(fact_337_longest__common__prefix,axiom,
% 0.21/0.48 ! [Xs: list_node,Ys: list_node] :
% 0.21/0.48 ? [Ps: list_node,Xs6: list_node,Ys4: list_node] :
% 0.21/0.48 ( ( Xs
% 0.21/0.48 = ( append_node @ Ps @ Xs6 ) )
% 0.21/0.48 & ( Ys
% 0.21/0.48 = ( append_node @ Ps @ Ys4 ) )
% 0.21/0.48 & ( ( Xs6 = nil_node )
% 0.21/0.48 | ( Ys4 = nil_node )
% 0.21/0.48 | ( ( hd_node @ Xs6 )
% 0.21/0.48 != ( hd_node @ Ys4 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % longest_common_prefix
% 0.21/0.48 thf(fact_338_not__suffix__cases,axiom,
% 0.21/0.48 ! [Ps2: list_node,Ls: list_node] :
% 0.21/0.48 ( ~ ( suffix_node @ Ps2 @ Ls )
% 0.21/0.48 => ( ( ( Ps2 != nil_node )
% 0.21/0.48 => ( Ls != nil_node ) )
% 0.21/0.48 => ( ! [A3: node,As: list_node] :
% 0.21/0.48 ( ( Ps2
% 0.21/0.48 = ( append_node @ As @ ( cons_node @ A3 @ nil_node ) ) )
% 0.21/0.48 => ! [X4: node,Xs2: list_node] :
% 0.21/0.48 ( ( Ls
% 0.21/0.48 = ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) )
% 0.21/0.48 => ( ( X4 = A3 )
% 0.21/0.48 => ( suffix_node @ As @ Xs2 ) ) ) )
% 0.21/0.48 => ~ ! [A3: node] :
% 0.21/0.48 ( ? [As: list_node] :
% 0.21/0.48 ( Ps2
% 0.21/0.48 = ( append_node @ As @ ( cons_node @ A3 @ nil_node ) ) )
% 0.21/0.48 => ! [X4: node] :
% 0.21/0.48 ( ? [Xs2: list_node] :
% 0.21/0.48 ( Ls
% 0.21/0.48 = ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) )
% 0.21/0.48 => ( X4 = A3 ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % not_suffix_cases
% 0.21/0.48 thf(fact_339_not__suffix__induct,axiom,
% 0.21/0.48 ! [Ps2: list_node,Ls: list_node,P: list_node > list_node > $o] :
% 0.21/0.48 ( ~ ( suffix_node @ Ps2 @ Ls )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ nil_node )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.21/0.48 ( ( X4 != Y2 )
% 0.21/0.48 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) )
% 0.21/0.48 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.21/0.48 ( ( X4 = Y2 )
% 0.21/0.48 => ( ~ ( suffix_node @ Xs2 @ Ys2 )
% 0.21/0.48 => ( ( P @ Xs2 @ Ys2 )
% 0.21/0.48 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) ) ) )
% 0.21/0.48 => ( P @ Ps2 @ Ls ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % not_suffix_induct
% 0.21/0.48 thf(fact_340_list_Oexpand,axiom,
% 0.21/0.48 ! [List: list_node,List2: list_node] :
% 0.21/0.48 ( ( ( List = nil_node )
% 0.21/0.48 = ( List2 = nil_node ) )
% 0.21/0.48 => ( ( ( List != nil_node )
% 0.21/0.48 => ( ( List2 != nil_node )
% 0.21/0.48 => ( ( ( hd_node @ List )
% 0.21/0.48 = ( hd_node @ List2 ) )
% 0.21/0.48 & ( ( tl_node @ List )
% 0.21/0.48 = ( tl_node @ List2 ) ) ) ) )
% 0.21/0.48 => ( List = List2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.expand
% 0.21/0.48 thf(fact_341_not__hd__in__tl,axiom,
% 0.21/0.48 ! [X: val,Xs: list_val] :
% 0.21/0.48 ( ( X
% 0.21/0.48 != ( hd_val @ Xs ) )
% 0.21/0.48 => ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.21/0.48 => ( member_val @ X @ ( set_val2 @ ( tl_val @ Xs ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % not_hd_in_tl
% 0.21/0.48 thf(fact_342_not__hd__in__tl,axiom,
% 0.21/0.48 ! [X: node,Xs: list_node] :
% 0.21/0.48 ( ( X
% 0.21/0.48 != ( hd_node @ Xs ) )
% 0.21/0.48 => ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.21/0.48 => ( member_node @ X @ ( set_node2 @ ( tl_node @ Xs ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % not_hd_in_tl
% 0.21/0.48 thf(fact_343_set__subset__Cons,axiom,
% 0.21/0.48 ! [Xs: list_node,X: node] : ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ ( set_node2 @ ( cons_node @ X @ Xs ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % set_subset_Cons
% 0.21/0.48 thf(fact_344_list_Oexhaust__sel,axiom,
% 0.21/0.48 ! [List: list_node] :
% 0.21/0.48 ( ( List != nil_node )
% 0.21/0.48 => ( List
% 0.21/0.48 = ( cons_node @ ( hd_node @ List ) @ ( tl_node @ List ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % list.exhaust_sel
% 0.21/0.48 thf(fact_345_tl__subset,axiom,
% 0.21/0.48 ! [Xs: list_node,A2: set_node] :
% 0.21/0.48 ( ( Xs != nil_node )
% 0.21/0.48 => ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ A2 )
% 0.21/0.48 => ( ord_less_eq_set_node @ ( set_node2 @ ( tl_node @ Xs ) ) @ A2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % tl_subset
% 0.21/0.48 thf(fact_346_butlast__subset,axiom,
% 0.21/0.48 ! [Xs: list_node,A2: set_node] :
% 0.21/0.48 ( ( Xs != nil_node )
% 0.21/0.48 => ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ A2 )
% 0.21/0.48 => ( ord_less_eq_set_node @ ( set_node2 @ ( butlast_node @ Xs ) ) @ A2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % butlast_subset
% 0.21/0.48 thf(fact_347_prefix__same__cases,axiom,
% 0.21/0.48 ! [Xs_1: list_node,Ys: list_node,Xs_2: list_node] :
% 0.21/0.48 ( ( prefix_node @ Xs_1 @ Ys )
% 0.21/0.48 => ( ( prefix_node @ Xs_2 @ Ys )
% 0.21/0.48 => ( ( prefix_node @ Xs_1 @ Xs_2 )
% 0.21/0.48 | ( prefix_node @ Xs_2 @ Xs_1 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % prefix_same_cases
% 0.21/0.48 thf(fact_348_prefix__order_Oeq__iff,axiom,
% 0.21/0.48 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 0.21/0.48 = ( ^ [X3: list_node,Y3: list_node] :
% 0.21/0.48 ( ( prefix_node @ X3 @ Y3 )
% 0.21/0.48 & ( prefix_node @ Y3 @ X3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % prefix_order.eq_iff
% 0.21/0.48 thf(fact_349_prefix__order_Oantisym,axiom,
% 0.21/0.48 ! [X: list_node,Y: list_node] :
% 0.21/0.48 ( ( prefix_node @ X @ Y )
% 0.21/0.48 => ( ( prefix_node @ Y @ X )
% 0.21/0.48 => ( X = Y ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % prefix_order.antisym
% 0.21/0.48
% 0.21/0.48 % Conjectures (1)
% 0.21/0.48 thf(conj_0,conjecture,
% 0.21/0.48 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ).
% 0.21/0.48
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 ------------------------
% 2.98/1.57 ---- Embedded in THF ---
% 2.98/1.57 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.98/1.57 %%% Generated on Tue Feb 24 08:26:34 EST 2026
% 2.98/1.57 %%% using '$$dhol' embedding, version 1.3.0.
% 2.98/1.57 %%% Logic specification used:
% 2.98/1.57 %%% thf(spec, logic, $$dhol).
% 2.98/1.57
% 2.98/1.57 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4SP2TQ63UH/DTF2DTF20632.p
% See solution above
% 2.98/1.57 ------------------------
% 3.16/1.61 ---- Cleaned THF ---
% 3.16/1.62 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mtf__edgeD_J_J,type,
% 3.16/1.62 list_P561207620_edgeD: $tType ).
% 3.16/1.62
% 3.16/1.62 thf(ty_n_t__Option__Ooption_It__List__Olist_Itf__val_J_J,type,
% 3.16/1.62 option_list_val: $tType ).
% 3.16/1.62
% 3.16/1.62 thf(ty_n_t__Product____Type__Oprod_Itf__node_Mtf__val_J,type,
% 3.16/1.62 produc1432036078de_val: $tType ).
% 3.16/1.62
% 3.16/1.62 thf(ty_n_t__List__Olist_It__List__Olist_Itf__node_J_J,type,
% 3.16/1.62 list_list_node: $tType ).
% 3.16/1.62
% 3.16/1.62 thf(ty_n_t__Set__Oset_It__List__Olist_Itf__node_J_J,type,
% 3.16/1.62 set_list_node: $tType ).
% 3.16/1.62
% 3.16/1.62 thf(ty_n_t__List__Olist_Itf__node_J,type,
% 3.16/1.62 list_node: $tType ).
% 3.16/1.62
% 3.16/1.62 thf(ty_n_t__List__Olist_Itf__val_J,type,
% 3.16/1.62 list_val: $tType ).
% 3.16/1.62
% 3.16/1.62 thf(ty_n_t__Set__Oset_Itf__node_J,type,
% 3.16/1.62 set_node: $tType ).
% 3.16/1.62
% 3.16/1.62 thf(ty_n_t__Set__Oset_Itf__val_J,type,
% 3.16/1.62 set_val: $tType ).
% 3.16/1.62
% 3.16/1.62 thf(ty_n_tf__node,type,
% 3.16/1.62 node: $tType ).
% 3.16/1.62
% 3.16/1.62 thf(ty_n_tf__val,type,
% 3.16/1.62 val: $tType ).
% 3.16/1.62
% 3.16/1.62 thf(ty_n_tf__g,type,
% 3.16/1.62 g: $tType ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_Finite__Set_Ofinite_001tf__node,type,
% 3.16/1.62 finite_finite_node: set_node > $o ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_Finite__Set_Ofinite_001tf__val,type,
% 3.16/1.62 finite_finite_val: set_val > $o ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_Graph__path_Ograph__path__base_Opath2_001tf__g_001tf__node_001tf__edgeD,type,
% 3.16/1.62 graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_Graph__path_Ograph__path__base_Opath_001tf__g_001tf__node_001tf__edgeD,type,
% 3.16/1.62 graph_435229452_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > list_node > $o ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors_001tf__g_001tf__node_001tf__edgeD,type,
% 3.16/1.62 graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Oappend_001t__List__Olist_Itf__node_J,type,
% 3.16/1.62 append_list_node: list_list_node > list_list_node > list_list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Oappend_001tf__node,type,
% 3.16/1.62 append_node: list_node > list_node > list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Oappend_001tf__val,type,
% 3.16/1.62 append_val: list_val > list_val > list_val ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Obutlast_001t__List__Olist_Itf__node_J,type,
% 3.16/1.62 butlast_list_node: list_list_node > list_list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Obutlast_001tf__node,type,
% 3.16/1.62 butlast_node: list_node > list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Obutlast_001tf__val,type,
% 3.16/1.62 butlast_val: list_val > list_val ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Olist_OCons_001t__List__Olist_Itf__node_J,type,
% 3.16/1.62 cons_list_node: list_node > list_list_node > list_list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Olist_OCons_001tf__node,type,
% 3.16/1.62 cons_node: node > list_node > list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Olist_OCons_001tf__val,type,
% 3.16/1.62 cons_val: val > list_val > list_val ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__node_J,type,
% 3.16/1.62 nil_list_node: list_list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Olist_ONil_001tf__node,type,
% 3.16/1.62 nil_node: list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Olist_ONil_001tf__val,type,
% 3.16/1.62 nil_val: list_val ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Olist_Ohd_001tf__node,type,
% 3.16/1.62 hd_node: list_node > node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Olist_Ohd_001tf__val,type,
% 3.16/1.62 hd_val: list_val > val ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Olist_Oset_001t__List__Olist_Itf__node_J,type,
% 3.16/1.62 set_list_node2: list_list_node > set_list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Olist_Oset_001tf__node,type,
% 3.16/1.62 set_node2: list_node > set_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Olist_Oset_001tf__val,type,
% 3.16/1.62 set_val2: list_val > set_val ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Olist_Otl_001t__List__Olist_Itf__node_J,type,
% 3.16/1.62 tl_list_node: list_list_node > list_list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Olist_Otl_001tf__node,type,
% 3.16/1.62 tl_node: list_node > list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_List_Olist_Otl_001tf__val,type,
% 3.16/1.62 tl_val: list_val > list_val ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__node_J,type,
% 3.16/1.62 ord_less_eq_set_node: set_node > set_node > $o ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__val_J,type,
% 3.16/1.62 ord_less_eq_set_val: set_val > set_val > $o ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 3.16/1.62 sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode_001tf__g_001tf__node_001tf__val,type,
% 3.16/1.62 sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg_001tf__g_001tf__node_001tf__val,type,
% 3.16/1.62 sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_Set_OCollect_001tf__node,type,
% 3.16/1.62 collect_node: ( node > $o ) > set_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_Set_OCollect_001tf__val,type,
% 3.16/1.62 collect_val: ( val > $o ) > set_val ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_Sublist_Oprefix_001tf__node,type,
% 3.16/1.62 prefix_node: list_node > list_node > $o ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_Sublist_Osuffix_001tf__node,type,
% 3.16/1.62 suffix_node: list_node > list_node > $o ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_member_001t__List__Olist_Itf__node_J,type,
% 3.16/1.62 member_list_node: list_node > set_list_node > $o ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_member_001tf__node,type,
% 3.16/1.62 member_node: node > set_node > $o ).
% 3.16/1.62
% 3.16/1.62 thf(sy_c_member_001tf__val,type,
% 3.16/1.62 member_val: val > set_val > $o ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v__092_060alpha_062n,type,
% 3.16/1.62 alpha_n: g > list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v__092_060phi_062_092_060_094sub_062r,type,
% 3.16/1.62 phi_r: val ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_defs,type,
% 3.16/1.62 defs: g > node > set_val ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_g,type,
% 3.16/1.62 g2: g ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_i____,type,
% 3.16/1.62 i: node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_inEdges_H,type,
% 3.16/1.62 inEdges: g > node > list_P561207620_edgeD ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_invar,type,
% 3.16/1.62 invar: g > $o ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_m,type,
% 3.16/1.62 m: node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_ms,type,
% 3.16/1.62 ms: list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_ms_H____,type,
% 3.16/1.62 ms2: list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_n,type,
% 3.16/1.62 n: node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_ns,type,
% 3.16/1.62 ns: list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_phis,type,
% 3.16/1.62 phis: g > produc1432036078de_val > option_list_val ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____,type,
% 3.16/1.62 pred_phi_r: node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_r,type,
% 3.16/1.62 r: val ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_ri____,type,
% 3.16/1.62 ri: list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_rs_H____,type,
% 3.16/1.62 rs: list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_rs____,type,
% 3.16/1.62 rs2: list_node ).
% 3.16/1.62
% 3.16/1.62 thf(sy_v_s,type,
% 3.16/1.62 s: val ).
% 3.16/1.62
% 3.16/1.62 thf(fact_0_False,axiom,
% 3.16/1.62 r != phi_r ).
% 3.16/1.62
% 3.16/1.62 thf(fact_1_ri__is__valid,axiom,
% 3.16/1.62 ( i
% 3.16/1.62 = ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_2_old_Oinvar,axiom,
% 3.16/1.62 ! [G: g] : ( invar @ G ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_3_assms_I7_J,axiom,
% 3.16/1.62 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_4_ri__props_I1_J,axiom,
% 3.16/1.62 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i ).
% 3.16/1.62
% 3.16/1.62 thf(fact_5_old_Opath2__app,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node,Ms: list_node,L: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M @ Ms @ L )
% 3.16/1.62 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( tl_node @ Ms ) ) @ L ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_6__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062,axiom,
% 3.16/1.62 ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r )
% 3.16/1.62 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_7_rs_H__props_I1_J,axiom,
% 3.16/1.62 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r ).
% 3.16/1.62
% 3.16/1.62 thf(fact_8_assms_I10_J,axiom,
% 3.16/1.62 sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r ).
% 3.16/1.62
% 3.16/1.62 thf(fact_9_rs__props_I1_J,axiom,
% 3.16/1.62 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_10_ms_H__props_I1_J,axiom,
% 3.16/1.62 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i ).
% 3.16/1.62
% 3.16/1.62 thf(fact_11__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062i_A_061_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_061_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_092_060noteq_062_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 3.16/1.62 ( ( i
% 3.16/1.62 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 3.16/1.62 => ( ( ( i
% 3.16/1.62 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 3.16/1.62 => ( m != i ) )
% 3.16/1.62 => ~ ( ( i
% 3.16/1.62 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 3.16/1.62 => ( m = i ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_12_old_Opath2__split_I2_J,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,N2: node,Ns2: list_node,M: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ Ns2 ) ) @ M )
% 3.16/1.62 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N2 @ ( cons_node @ N2 @ Ns2 ) @ M ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_13_old_Opath2__not__Nil,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( Ns != nil_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_14_old_Opath2__not__Nil2,axiom,
% 3.16/1.62 ! [G: g,N: node,M: node] :
% 3.16/1.62 ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ nil_node @ M ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_15_rs_H__props_I3_J,axiom,
% 3.16/1.62 member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_16_old_Opath2__hd__in___092_060alpha_062n,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_17_old_Opath2__hd__in__ns,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( member_node @ N @ ( set_node2 @ Ns ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_18_old_Opath2__in___092_060alpha_062n,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node,L: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( ( member_node @ L @ ( set_node2 @ Ns ) )
% 3.16/1.62 => ( member_node @ L @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_19_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 3.16/1.62 ! [X: list_node,Xs: list_list_node,Ys: list_list_node,Y: list_node] :
% 3.16/1.62 ( ( member_list_node @ X @ ( set_list_node2 @ Xs ) )
% 3.16/1.62 => ( member_list_node @ X @ ( set_list_node2 @ ( tl_list_node @ ( append_list_node @ Ys @ ( cons_list_node @ Y @ Xs ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_20_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 3.16/1.62 ! [X: val,Xs: list_val,Ys: list_val,Y: val] :
% 3.16/1.62 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 3.16/1.62 => ( member_val @ X @ ( set_val2 @ ( tl_val @ ( append_val @ Ys @ ( cons_val @ Y @ Xs ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_21_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node,Ys: list_node,Y: node] :
% 3.16/1.62 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 3.16/1.62 => ( member_node @ X @ ( set_node2 @ ( tl_node @ ( append_node @ Ys @ ( cons_node @ Y @ Xs ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_22_ri__props_I2_J,axiom,
% 3.16/1.62 member_node @ i @ ( set_node2 @ ms ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_23_old_Opath2__tl__in___092_060alpha_062n,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_24_old_Opath2__last__in__ns,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( member_node @ M @ ( set_node2 @ Ns ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_25_old_Opath2__split_I1_J,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,N2: node,Ns2: list_node,M: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ Ns2 ) ) @ M )
% 3.16/1.62 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ nil_node ) ) @ N2 ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_26_rs__props_I3_J,axiom,
% 3.16/1.62 ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs2 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_27_rs_H__loopfree,axiom,
% 3.16/1.62 ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_28_rs__def,axiom,
% 3.16/1.62 ( rs2
% 3.16/1.62 = ( append_node @ rs @ ( cons_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ nil_node ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_29_ri__props_I4_J,axiom,
% 3.16/1.62 prefix_node @ ri @ rs2 ).
% 3.16/1.62
% 3.16/1.62 thf(fact_30_old_Oempty__path2,axiom,
% 3.16/1.62 ! [N: node,G: g] :
% 3.16/1.62 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 3.16/1.62 => ( ( invar @ G )
% 3.16/1.62 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( cons_node @ N @ nil_node ) @ N ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_31_ms_H__props_I3_J,axiom,
% 3.16/1.62 ~ ( member_node @ i @ ( set_node2 @ ( butlast_node @ ms2 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_32_rs_H__props_I4_J,axiom,
% 3.16/1.62 member_node @ pred_phi_r @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_33_assms_I8_J,axiom,
% 3.16/1.62 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_34_tl__append2,axiom,
% 3.16/1.62 ! [Xs: list_list_node,Ys: list_list_node] :
% 3.16/1.62 ( ( Xs != nil_list_node )
% 3.16/1.62 => ( ( tl_list_node @ ( append_list_node @ Xs @ Ys ) )
% 3.16/1.62 = ( append_list_node @ ( tl_list_node @ Xs ) @ Ys ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_35_tl__append2,axiom,
% 3.16/1.62 ! [Xs: list_val,Ys: list_val] :
% 3.16/1.62 ( ( Xs != nil_val )
% 3.16/1.62 => ( ( tl_val @ ( append_val @ Xs @ Ys ) )
% 3.16/1.62 = ( append_val @ ( tl_val @ Xs ) @ Ys ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_36_tl__append2,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( Xs != nil_node )
% 3.16/1.62 => ( ( tl_node @ ( append_node @ Xs @ Ys ) )
% 3.16/1.62 = ( append_node @ ( tl_node @ Xs ) @ Ys ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_37_list__e__eq__lel_I2_J,axiom,
% 3.16/1.62 ! [L1: list_val,E: val,L2: list_val,E2: val] :
% 3.16/1.62 ( ( ( append_val @ L1 @ ( cons_val @ E @ L2 ) )
% 3.16/1.62 = ( cons_val @ E2 @ nil_val ) )
% 3.16/1.62 = ( ( L1 = nil_val )
% 3.16/1.62 & ( E = E2 )
% 3.16/1.62 & ( L2 = nil_val ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_38_list__e__eq__lel_I2_J,axiom,
% 3.16/1.62 ! [L1: list_list_node,E: list_node,L2: list_list_node,E2: list_node] :
% 3.16/1.62 ( ( ( append_list_node @ L1 @ ( cons_list_node @ E @ L2 ) )
% 3.16/1.62 = ( cons_list_node @ E2 @ nil_list_node ) )
% 3.16/1.62 = ( ( L1 = nil_list_node )
% 3.16/1.62 & ( E = E2 )
% 3.16/1.62 & ( L2 = nil_list_node ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_39_list__e__eq__lel_I2_J,axiom,
% 3.16/1.62 ! [L1: list_node,E: node,L2: list_node,E2: node] :
% 3.16/1.62 ( ( ( append_node @ L1 @ ( cons_node @ E @ L2 ) )
% 3.16/1.62 = ( cons_node @ E2 @ nil_node ) )
% 3.16/1.62 = ( ( L1 = nil_node )
% 3.16/1.62 & ( E = E2 )
% 3.16/1.62 & ( L2 = nil_node ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_40_list__e__eq__lel_I1_J,axiom,
% 3.16/1.62 ! [E2: val,L1: list_val,E: val,L2: list_val] :
% 3.16/1.62 ( ( ( cons_val @ E2 @ nil_val )
% 3.16/1.62 = ( append_val @ L1 @ ( cons_val @ E @ L2 ) ) )
% 3.16/1.62 = ( ( L1 = nil_val )
% 3.16/1.62 & ( E = E2 )
% 3.16/1.62 & ( L2 = nil_val ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_41_list__e__eq__lel_I1_J,axiom,
% 3.16/1.62 ! [E2: list_node,L1: list_list_node,E: list_node,L2: list_list_node] :
% 3.16/1.62 ( ( ( cons_list_node @ E2 @ nil_list_node )
% 3.16/1.62 = ( append_list_node @ L1 @ ( cons_list_node @ E @ L2 ) ) )
% 3.16/1.62 = ( ( L1 = nil_list_node )
% 3.16/1.62 & ( E = E2 )
% 3.16/1.62 & ( L2 = nil_list_node ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_42_list__e__eq__lel_I1_J,axiom,
% 3.16/1.62 ! [E2: node,L1: list_node,E: node,L2: list_node] :
% 3.16/1.62 ( ( ( cons_node @ E2 @ nil_node )
% 3.16/1.62 = ( append_node @ L1 @ ( cons_node @ E @ L2 ) ) )
% 3.16/1.62 = ( ( L1 = nil_node )
% 3.16/1.62 & ( E = E2 )
% 3.16/1.62 & ( L2 = nil_node ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_43_list__se__match_I4_J,axiom,
% 3.16/1.62 ! [L2: list_val,A: val,L1: list_val] :
% 3.16/1.62 ( ( L2 != nil_val )
% 3.16/1.62 => ( ( ( cons_val @ A @ nil_val )
% 3.16/1.62 = ( append_val @ L1 @ L2 ) )
% 3.16/1.62 = ( ( L1 = nil_val )
% 3.16/1.62 & ( L2
% 3.16/1.62 = ( cons_val @ A @ nil_val ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_44_list__se__match_I4_J,axiom,
% 3.16/1.62 ! [L2: list_list_node,A: list_node,L1: list_list_node] :
% 3.16/1.62 ( ( L2 != nil_list_node )
% 3.16/1.62 => ( ( ( cons_list_node @ A @ nil_list_node )
% 3.16/1.62 = ( append_list_node @ L1 @ L2 ) )
% 3.16/1.62 = ( ( L1 = nil_list_node )
% 3.16/1.62 & ( L2
% 3.16/1.62 = ( cons_list_node @ A @ nil_list_node ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_45_list__se__match_I4_J,axiom,
% 3.16/1.62 ! [L2: list_node,A: node,L1: list_node] :
% 3.16/1.62 ( ( L2 != nil_node )
% 3.16/1.62 => ( ( ( cons_node @ A @ nil_node )
% 3.16/1.62 = ( append_node @ L1 @ L2 ) )
% 3.16/1.62 = ( ( L1 = nil_node )
% 3.16/1.62 & ( L2
% 3.16/1.62 = ( cons_node @ A @ nil_node ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_46_list__se__match_I3_J,axiom,
% 3.16/1.62 ! [L1: list_val,A: val,L2: list_val] :
% 3.16/1.62 ( ( L1 != nil_val )
% 3.16/1.62 => ( ( ( cons_val @ A @ nil_val )
% 3.16/1.62 = ( append_val @ L1 @ L2 ) )
% 3.16/1.62 = ( ( L1
% 3.16/1.62 = ( cons_val @ A @ nil_val ) )
% 3.16/1.62 & ( L2 = nil_val ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_47_list__se__match_I3_J,axiom,
% 3.16/1.62 ! [L1: list_list_node,A: list_node,L2: list_list_node] :
% 3.16/1.62 ( ( L1 != nil_list_node )
% 3.16/1.62 => ( ( ( cons_list_node @ A @ nil_list_node )
% 3.16/1.62 = ( append_list_node @ L1 @ L2 ) )
% 3.16/1.62 = ( ( L1
% 3.16/1.62 = ( cons_list_node @ A @ nil_list_node ) )
% 3.16/1.62 & ( L2 = nil_list_node ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_48_list__se__match_I3_J,axiom,
% 3.16/1.62 ! [L1: list_node,A: node,L2: list_node] :
% 3.16/1.62 ( ( L1 != nil_node )
% 3.16/1.62 => ( ( ( cons_node @ A @ nil_node )
% 3.16/1.62 = ( append_node @ L1 @ L2 ) )
% 3.16/1.62 = ( ( L1
% 3.16/1.62 = ( cons_node @ A @ nil_node ) )
% 3.16/1.62 & ( L2 = nil_node ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_49_list__se__match_I2_J,axiom,
% 3.16/1.62 ! [L2: list_val,L1: list_val,A: val] :
% 3.16/1.62 ( ( L2 != nil_val )
% 3.16/1.62 => ( ( ( append_val @ L1 @ L2 )
% 3.16/1.62 = ( cons_val @ A @ nil_val ) )
% 3.16/1.62 = ( ( L1 = nil_val )
% 3.16/1.62 & ( L2
% 3.16/1.62 = ( cons_val @ A @ nil_val ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_50_list__se__match_I2_J,axiom,
% 3.16/1.62 ! [L2: list_list_node,L1: list_list_node,A: list_node] :
% 3.16/1.62 ( ( L2 != nil_list_node )
% 3.16/1.62 => ( ( ( append_list_node @ L1 @ L2 )
% 3.16/1.62 = ( cons_list_node @ A @ nil_list_node ) )
% 3.16/1.62 = ( ( L1 = nil_list_node )
% 3.16/1.62 & ( L2
% 3.16/1.62 = ( cons_list_node @ A @ nil_list_node ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_51_list__se__match_I2_J,axiom,
% 3.16/1.62 ! [L2: list_node,L1: list_node,A: node] :
% 3.16/1.62 ( ( L2 != nil_node )
% 3.16/1.62 => ( ( ( append_node @ L1 @ L2 )
% 3.16/1.62 = ( cons_node @ A @ nil_node ) )
% 3.16/1.62 = ( ( L1 = nil_node )
% 3.16/1.62 & ( L2
% 3.16/1.62 = ( cons_node @ A @ nil_node ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_52_list__se__match_I1_J,axiom,
% 3.16/1.62 ! [L1: list_val,L2: list_val,A: val] :
% 3.16/1.62 ( ( L1 != nil_val )
% 3.16/1.62 => ( ( ( append_val @ L1 @ L2 )
% 3.16/1.62 = ( cons_val @ A @ nil_val ) )
% 3.16/1.62 = ( ( L1
% 3.16/1.62 = ( cons_val @ A @ nil_val ) )
% 3.16/1.62 & ( L2 = nil_val ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_53_list__se__match_I1_J,axiom,
% 3.16/1.62 ! [L1: list_list_node,L2: list_list_node,A: list_node] :
% 3.16/1.62 ( ( L1 != nil_list_node )
% 3.16/1.62 => ( ( ( append_list_node @ L1 @ L2 )
% 3.16/1.62 = ( cons_list_node @ A @ nil_list_node ) )
% 3.16/1.62 = ( ( L1
% 3.16/1.62 = ( cons_list_node @ A @ nil_list_node ) )
% 3.16/1.62 & ( L2 = nil_list_node ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_54_list__se__match_I1_J,axiom,
% 3.16/1.62 ! [L1: list_node,L2: list_node,A: node] :
% 3.16/1.62 ( ( L1 != nil_node )
% 3.16/1.62 => ( ( ( append_node @ L1 @ L2 )
% 3.16/1.62 = ( cons_node @ A @ nil_node ) )
% 3.16/1.62 = ( ( L1
% 3.16/1.62 = ( cons_node @ A @ nil_node ) )
% 3.16/1.62 & ( L2 = nil_node ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_55_list__ee__eq__leel_I2_J,axiom,
% 3.16/1.62 ! [L1: list_val,E1: val,E22: val,L2: list_val,E12: val,E23: val] :
% 3.16/1.62 ( ( ( append_val @ L1 @ ( cons_val @ E1 @ ( cons_val @ E22 @ L2 ) ) )
% 3.16/1.62 = ( cons_val @ E12 @ ( cons_val @ E23 @ nil_val ) ) )
% 3.16/1.62 = ( ( L1 = nil_val )
% 3.16/1.62 & ( E12 = E1 )
% 3.16/1.62 & ( E23 = E22 )
% 3.16/1.62 & ( L2 = nil_val ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_56_list__ee__eq__leel_I2_J,axiom,
% 3.16/1.62 ! [L1: list_list_node,E1: list_node,E22: list_node,L2: list_list_node,E12: list_node,E23: list_node] :
% 3.16/1.62 ( ( ( append_list_node @ L1 @ ( cons_list_node @ E1 @ ( cons_list_node @ E22 @ L2 ) ) )
% 3.16/1.62 = ( cons_list_node @ E12 @ ( cons_list_node @ E23 @ nil_list_node ) ) )
% 3.16/1.62 = ( ( L1 = nil_list_node )
% 3.16/1.62 & ( E12 = E1 )
% 3.16/1.62 & ( E23 = E22 )
% 3.16/1.62 & ( L2 = nil_list_node ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_57_list__ee__eq__leel_I2_J,axiom,
% 3.16/1.62 ! [L1: list_node,E1: node,E22: node,L2: list_node,E12: node,E23: node] :
% 3.16/1.62 ( ( ( append_node @ L1 @ ( cons_node @ E1 @ ( cons_node @ E22 @ L2 ) ) )
% 3.16/1.62 = ( cons_node @ E12 @ ( cons_node @ E23 @ nil_node ) ) )
% 3.16/1.62 = ( ( L1 = nil_node )
% 3.16/1.62 & ( E12 = E1 )
% 3.16/1.62 & ( E23 = E22 )
% 3.16/1.62 & ( L2 = nil_node ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_58_list__ee__eq__leel_I1_J,axiom,
% 3.16/1.62 ! [E12: val,E23: val,L1: list_val,E1: val,E22: val,L2: list_val] :
% 3.16/1.62 ( ( ( cons_val @ E12 @ ( cons_val @ E23 @ nil_val ) )
% 3.16/1.62 = ( append_val @ L1 @ ( cons_val @ E1 @ ( cons_val @ E22 @ L2 ) ) ) )
% 3.16/1.62 = ( ( L1 = nil_val )
% 3.16/1.62 & ( E12 = E1 )
% 3.16/1.62 & ( E23 = E22 )
% 3.16/1.62 & ( L2 = nil_val ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_59_list__ee__eq__leel_I1_J,axiom,
% 3.16/1.62 ! [E12: list_node,E23: list_node,L1: list_list_node,E1: list_node,E22: list_node,L2: list_list_node] :
% 3.16/1.62 ( ( ( cons_list_node @ E12 @ ( cons_list_node @ E23 @ nil_list_node ) )
% 3.16/1.62 = ( append_list_node @ L1 @ ( cons_list_node @ E1 @ ( cons_list_node @ E22 @ L2 ) ) ) )
% 3.16/1.62 = ( ( L1 = nil_list_node )
% 3.16/1.62 & ( E12 = E1 )
% 3.16/1.62 & ( E23 = E22 )
% 3.16/1.62 & ( L2 = nil_list_node ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_60_list__ee__eq__leel_I1_J,axiom,
% 3.16/1.62 ! [E12: node,E23: node,L1: list_node,E1: node,E22: node,L2: list_node] :
% 3.16/1.62 ( ( ( cons_node @ E12 @ ( cons_node @ E23 @ nil_node ) )
% 3.16/1.62 = ( append_node @ L1 @ ( cons_node @ E1 @ ( cons_node @ E22 @ L2 ) ) ) )
% 3.16/1.62 = ( ( L1 = nil_node )
% 3.16/1.62 & ( E12 = E1 )
% 3.16/1.62 & ( E23 = E22 )
% 3.16/1.62 & ( L2 = nil_node ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_61_ms_H__props_I2_J,axiom,
% 3.16/1.62 prefix_node @ ms2 @ ms ).
% 3.16/1.62
% 3.16/1.62 thf(fact_62_ri__props_I3_J,axiom,
% 3.16/1.62 ! [X2: node] :
% 3.16/1.62 ( ( member_node @ X2 @ ( set_node2 @ ( butlast_node @ ri ) ) )
% 3.16/1.62 => ~ ( member_node @ X2 @ ( set_node2 @ ms ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_63_list_Oinject,axiom,
% 3.16/1.62 ! [X21: val,X22: list_val,Y21: val,Y22: list_val] :
% 3.16/1.62 ( ( ( cons_val @ X21 @ X22 )
% 3.16/1.62 = ( cons_val @ Y21 @ Y22 ) )
% 3.16/1.62 = ( ( X21 = Y21 )
% 3.16/1.62 & ( X22 = Y22 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_64_list_Oinject,axiom,
% 3.16/1.62 ! [X21: list_node,X22: list_list_node,Y21: list_node,Y22: list_list_node] :
% 3.16/1.62 ( ( ( cons_list_node @ X21 @ X22 )
% 3.16/1.62 = ( cons_list_node @ Y21 @ Y22 ) )
% 3.16/1.62 = ( ( X21 = Y21 )
% 3.16/1.62 & ( X22 = Y22 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_65_list_Oinject,axiom,
% 3.16/1.62 ! [X21: node,X22: list_node,Y21: node,Y22: list_node] :
% 3.16/1.62 ( ( ( cons_node @ X21 @ X22 )
% 3.16/1.62 = ( cons_node @ Y21 @ Y22 ) )
% 3.16/1.62 = ( ( X21 = Y21 )
% 3.16/1.62 & ( X22 = Y22 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_66_append_Oassoc,axiom,
% 3.16/1.62 ! [A: list_val,B: list_val,C: list_val] :
% 3.16/1.62 ( ( append_val @ ( append_val @ A @ B ) @ C )
% 3.16/1.62 = ( append_val @ A @ ( append_val @ B @ C ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_67_append_Oassoc,axiom,
% 3.16/1.62 ! [A: list_node,B: list_node,C: list_node] :
% 3.16/1.62 ( ( append_node @ ( append_node @ A @ B ) @ C )
% 3.16/1.62 = ( append_node @ A @ ( append_node @ B @ C ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_68_mem__Collect__eq,axiom,
% 3.16/1.62 ! [A: val,P: val > $o] :
% 3.16/1.62 ( ( member_val @ A @ ( collect_val @ P ) )
% 3.16/1.62 = ( P @ A ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_69_mem__Collect__eq,axiom,
% 3.16/1.62 ! [A: node,P: node > $o] :
% 3.16/1.62 ( ( member_node @ A @ ( collect_node @ P ) )
% 3.16/1.62 = ( P @ A ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_70_Collect__mem__eq,axiom,
% 3.16/1.62 ! [A2: set_val] :
% 3.16/1.62 ( ( collect_val
% 3.16/1.62 @ ^ [X3: val] : ( member_val @ X3 @ A2 ) )
% 3.16/1.62 = A2 ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_71_Collect__mem__eq,axiom,
% 3.16/1.62 ! [A2: set_node] :
% 3.16/1.62 ( ( collect_node
% 3.16/1.62 @ ^ [X3: node] : ( member_node @ X3 @ A2 ) )
% 3.16/1.62 = A2 ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_72_Collect__cong,axiom,
% 3.16/1.62 ! [P: node > $o,Q: node > $o] :
% 3.16/1.62 ( ! [X4: node] :
% 3.16/1.62 ( ( P @ X4 )
% 3.16/1.62 = ( Q @ X4 ) )
% 3.16/1.62 => ( ( collect_node @ P )
% 3.16/1.62 = ( collect_node @ Q ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_73_Collect__cong,axiom,
% 3.16/1.62 ! [P: val > $o,Q: val > $o] :
% 3.16/1.62 ( ! [X4: val] :
% 3.16/1.62 ( ( P @ X4 )
% 3.16/1.62 = ( Q @ X4 ) )
% 3.16/1.62 => ( ( collect_val @ P )
% 3.16/1.62 = ( collect_val @ Q ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_74_append__assoc,axiom,
% 3.16/1.62 ! [Xs: list_val,Ys: list_val,Zs: list_val] :
% 3.16/1.62 ( ( append_val @ ( append_val @ Xs @ Ys ) @ Zs )
% 3.16/1.62 = ( append_val @ Xs @ ( append_val @ Ys @ Zs ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_75_append__assoc,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 3.16/1.62 ( ( append_node @ ( append_node @ Xs @ Ys ) @ Zs )
% 3.16/1.62 = ( append_node @ Xs @ ( append_node @ Ys @ Zs ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_76_append__same__eq,axiom,
% 3.16/1.62 ! [Ys: list_val,Xs: list_val,Zs: list_val] :
% 3.16/1.62 ( ( ( append_val @ Ys @ Xs )
% 3.16/1.62 = ( append_val @ Zs @ Xs ) )
% 3.16/1.62 = ( Ys = Zs ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_77_append__same__eq,axiom,
% 3.16/1.62 ! [Ys: list_node,Xs: list_node,Zs: list_node] :
% 3.16/1.62 ( ( ( append_node @ Ys @ Xs )
% 3.16/1.62 = ( append_node @ Zs @ Xs ) )
% 3.16/1.62 = ( Ys = Zs ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_78_same__append__eq,axiom,
% 3.16/1.62 ! [Xs: list_val,Ys: list_val,Zs: list_val] :
% 3.16/1.62 ( ( ( append_val @ Xs @ Ys )
% 3.16/1.62 = ( append_val @ Xs @ Zs ) )
% 3.16/1.62 = ( Ys = Zs ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_79_same__append__eq,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 3.16/1.62 ( ( ( append_node @ Xs @ Ys )
% 3.16/1.62 = ( append_node @ Xs @ Zs ) )
% 3.16/1.62 = ( Ys = Zs ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_80_old_Opredecessor__is__node,axiom,
% 3.16/1.62 ! [N: node,G: g,N2: node] :
% 3.16/1.62 ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N2 ) ) )
% 3.16/1.62 => ( ( invar @ G )
% 3.16/1.62 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_81_old_Osuccessor__is__node,axiom,
% 3.16/1.62 ! [N: node,G: g,N2: node] :
% 3.16/1.62 ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N2 ) ) )
% 3.16/1.62 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 3.16/1.62 => ( ( invar @ G )
% 3.16/1.62 => ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_82_old_Osuccessor__in___092_060alpha_062n,axiom,
% 3.16/1.62 ! [G: g,N: node] :
% 3.16/1.62 ( ( ( graph_272749361_edgeD @ inEdges @ G @ N )
% 3.16/1.62 != nil_node )
% 3.16/1.62 => ( ( invar @ G )
% 3.16/1.62 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_83_old_Opath2__app_H,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node,Ms: list_node,L: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M @ Ms @ L )
% 3.16/1.62 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ ( butlast_node @ Ns ) @ Ms ) @ L ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_84_append__Nil2,axiom,
% 3.16/1.62 ! [Xs: list_list_node] :
% 3.16/1.62 ( ( append_list_node @ Xs @ nil_list_node )
% 3.16/1.62 = Xs ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_85_append__Nil2,axiom,
% 3.16/1.62 ! [Xs: list_val] :
% 3.16/1.62 ( ( append_val @ Xs @ nil_val )
% 3.16/1.62 = Xs ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_86_append__Nil2,axiom,
% 3.16/1.62 ! [Xs: list_node] :
% 3.16/1.62 ( ( append_node @ Xs @ nil_node )
% 3.16/1.62 = Xs ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_87_append__self__conv,axiom,
% 3.16/1.62 ! [Xs: list_list_node,Ys: list_list_node] :
% 3.16/1.62 ( ( ( append_list_node @ Xs @ Ys )
% 3.16/1.62 = Xs )
% 3.16/1.62 = ( Ys = nil_list_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_88_append__self__conv,axiom,
% 3.16/1.62 ! [Xs: list_val,Ys: list_val] :
% 3.16/1.62 ( ( ( append_val @ Xs @ Ys )
% 3.16/1.62 = Xs )
% 3.16/1.62 = ( Ys = nil_val ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_89_append__self__conv,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( ( append_node @ Xs @ Ys )
% 3.16/1.62 = Xs )
% 3.16/1.62 = ( Ys = nil_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_90_self__append__conv,axiom,
% 3.16/1.62 ! [Xs: list_list_node,Ys: list_list_node] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_list_node @ Xs @ Ys ) )
% 3.16/1.62 = ( Ys = nil_list_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_91_self__append__conv,axiom,
% 3.16/1.62 ! [Xs: list_val,Ys: list_val] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_val @ Xs @ Ys ) )
% 3.16/1.62 = ( Ys = nil_val ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_92_self__append__conv,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_node @ Xs @ Ys ) )
% 3.16/1.62 = ( Ys = nil_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_93_append__self__conv2,axiom,
% 3.16/1.62 ! [Xs: list_list_node,Ys: list_list_node] :
% 3.16/1.62 ( ( ( append_list_node @ Xs @ Ys )
% 3.16/1.62 = Ys )
% 3.16/1.62 = ( Xs = nil_list_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_94_append__self__conv2,axiom,
% 3.16/1.62 ! [Xs: list_val,Ys: list_val] :
% 3.16/1.62 ( ( ( append_val @ Xs @ Ys )
% 3.16/1.62 = Ys )
% 3.16/1.62 = ( Xs = nil_val ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_95_append__self__conv2,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( ( append_node @ Xs @ Ys )
% 3.16/1.62 = Ys )
% 3.16/1.62 = ( Xs = nil_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_96_self__append__conv2,axiom,
% 3.16/1.62 ! [Ys: list_list_node,Xs: list_list_node] :
% 3.16/1.62 ( ( Ys
% 3.16/1.62 = ( append_list_node @ Xs @ Ys ) )
% 3.16/1.62 = ( Xs = nil_list_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_97_self__append__conv2,axiom,
% 3.16/1.62 ! [Ys: list_val,Xs: list_val] :
% 3.16/1.62 ( ( Ys
% 3.16/1.62 = ( append_val @ Xs @ Ys ) )
% 3.16/1.62 = ( Xs = nil_val ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_98_self__append__conv2,axiom,
% 3.16/1.62 ! [Ys: list_node,Xs: list_node] :
% 3.16/1.62 ( ( Ys
% 3.16/1.62 = ( append_node @ Xs @ Ys ) )
% 3.16/1.62 = ( Xs = nil_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_99_Nil__is__append__conv,axiom,
% 3.16/1.62 ! [Xs: list_list_node,Ys: list_list_node] :
% 3.16/1.62 ( ( nil_list_node
% 3.16/1.62 = ( append_list_node @ Xs @ Ys ) )
% 3.16/1.62 = ( ( Xs = nil_list_node )
% 3.16/1.62 & ( Ys = nil_list_node ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_100_Nil__is__append__conv,axiom,
% 3.16/1.62 ! [Xs: list_val,Ys: list_val] :
% 3.16/1.62 ( ( nil_val
% 3.16/1.62 = ( append_val @ Xs @ Ys ) )
% 3.16/1.62 = ( ( Xs = nil_val )
% 3.16/1.62 & ( Ys = nil_val ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_101_Nil__is__append__conv,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( nil_node
% 3.16/1.62 = ( append_node @ Xs @ Ys ) )
% 3.16/1.62 = ( ( Xs = nil_node )
% 3.16/1.62 & ( Ys = nil_node ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_102_append__is__Nil__conv,axiom,
% 3.16/1.62 ! [Xs: list_list_node,Ys: list_list_node] :
% 3.16/1.62 ( ( ( append_list_node @ Xs @ Ys )
% 3.16/1.62 = nil_list_node )
% 3.16/1.62 = ( ( Xs = nil_list_node )
% 3.16/1.62 & ( Ys = nil_list_node ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_103_append__is__Nil__conv,axiom,
% 3.16/1.62 ! [Xs: list_val,Ys: list_val] :
% 3.16/1.62 ( ( ( append_val @ Xs @ Ys )
% 3.16/1.62 = nil_val )
% 3.16/1.62 = ( ( Xs = nil_val )
% 3.16/1.62 & ( Ys = nil_val ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_104_append__is__Nil__conv,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( ( append_node @ Xs @ Ys )
% 3.16/1.62 = nil_node )
% 3.16/1.62 = ( ( Xs = nil_node )
% 3.16/1.62 & ( Ys = nil_node ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_105_empty__append__eq__id,axiom,
% 3.16/1.62 ( ( append_list_node @ nil_list_node )
% 3.16/1.62 = ( ^ [X3: list_list_node] : X3 ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_106_empty__append__eq__id,axiom,
% 3.16/1.62 ( ( append_val @ nil_val )
% 3.16/1.62 = ( ^ [X3: list_val] : X3 ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_107_empty__append__eq__id,axiom,
% 3.16/1.62 ( ( append_node @ nil_node )
% 3.16/1.62 = ( ^ [X3: list_node] : X3 ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_108_append_Oright__neutral,axiom,
% 3.16/1.62 ! [A: list_list_node] :
% 3.16/1.62 ( ( append_list_node @ A @ nil_list_node )
% 3.16/1.62 = A ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_109_append_Oright__neutral,axiom,
% 3.16/1.62 ! [A: list_val] :
% 3.16/1.62 ( ( append_val @ A @ nil_val )
% 3.16/1.62 = A ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_110_append_Oright__neutral,axiom,
% 3.16/1.62 ! [A: list_node] :
% 3.16/1.62 ( ( append_node @ A @ nil_node )
% 3.16/1.62 = A ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_111_old_Opath2__split__ex_H,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node,X: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( ( member_node @ X @ ( set_node2 @ Ns ) )
% 3.16/1.62 => ~ ! [Ns_1: list_node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns_1 @ X )
% 3.16/1.62 => ! [Ns_2: list_node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ Ns_2 @ M )
% 3.16/1.62 => ( Ns
% 3.16/1.62 != ( append_node @ ( butlast_node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_112_old_Opath2__prefix__ex,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node,M2: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( ( member_node @ M2 @ ( set_node2 @ Ns ) )
% 3.16/1.62 => ~ ! [Ns3: list_node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns3 @ M2 )
% 3.16/1.62 => ( ( prefix_node @ Ns3 @ Ns )
% 3.16/1.62 => ( member_node @ M2 @ ( set_node2 @ ( butlast_node @ Ns3 ) ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_113_old_Opath2__split__first__prop,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node,P: node > $o] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( ? [X2: node] :
% 3.16/1.62 ( ( member_node @ X2 @ ( set_node2 @ Ns ) )
% 3.16/1.62 & ( P @ X2 ) )
% 3.16/1.62 => ~ ! [M3: node,Ns3: list_node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns3 @ M3 )
% 3.16/1.62 => ( ( P @ M3 )
% 3.16/1.62 => ( ! [X2: node] :
% 3.16/1.62 ( ( member_node @ X2 @ ( set_node2 @ ( butlast_node @ Ns3 ) ) )
% 3.16/1.62 => ~ ( P @ X2 ) )
% 3.16/1.62 => ~ ( prefix_node @ Ns3 @ Ns ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_114_old_Opath2__induct,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node,P: node > list_node > node > $o] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( ( ( invar @ G )
% 3.16/1.62 => ( P @ M @ ( cons_node @ M @ nil_node ) @ M ) )
% 3.16/1.62 => ( ! [Ns4: list_node,N3: node,N4: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N4 @ Ns4 @ M )
% 3.16/1.62 => ( ( P @ N4 @ Ns4 @ M )
% 3.16/1.62 => ( ( member_node @ N3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N4 ) ) )
% 3.16/1.62 => ( P @ N3 @ ( cons_node @ N3 @ Ns4 ) @ M ) ) ) )
% 3.16/1.62 => ( P @ N @ Ns @ M ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_115_old_Opath2__split__ex,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node,X: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( ( member_node @ X @ ( set_node2 @ Ns ) )
% 3.16/1.62 => ~ ! [Ns_1: list_node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns_1 @ X )
% 3.16/1.62 => ! [Ns_2: list_node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ Ns_2 @ M )
% 3.16/1.62 => ( ( Ns
% 3.16/1.62 = ( append_node @ Ns_1 @ ( tl_node @ Ns_2 ) ) )
% 3.16/1.62 => ( Ns
% 3.16/1.62 != ( append_node @ ( butlast_node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_116_old_Opath2__prefix,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node,Ns2: list_node,M2: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( ( prefix_node @ ( append_node @ Ns2 @ ( cons_node @ M2 @ nil_node ) ) @ Ns )
% 3.16/1.62 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns2 @ ( cons_node @ M2 @ nil_node ) ) @ M2 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_117_old_Opath2__rev__induct,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node,P: node > list_node > node > $o] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 3.16/1.62 => ( P @ N @ ( cons_node @ N @ nil_node ) @ N ) )
% 3.16/1.62 => ( ! [Ns4: list_node,M3: node,M4: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns4 @ M3 )
% 3.16/1.62 => ( ( P @ N @ Ns4 @ M3 )
% 3.16/1.62 => ( ( member_node @ M3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M4 ) ) )
% 3.16/1.62 => ( P @ N @ ( append_node @ Ns4 @ ( cons_node @ M4 @ nil_node ) ) @ M4 ) ) ) )
% 3.16/1.62 => ( P @ N @ Ns @ M ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_118_old_Opath2__snoc,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node,M2: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M2 ) ) )
% 3.16/1.62 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ M2 @ nil_node ) ) @ M2 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_119_append1__eq__conv,axiom,
% 3.16/1.62 ! [Xs: list_val,X: val,Ys: list_val,Y: val] :
% 3.16/1.62 ( ( ( append_val @ Xs @ ( cons_val @ X @ nil_val ) )
% 3.16/1.62 = ( append_val @ Ys @ ( cons_val @ Y @ nil_val ) ) )
% 3.16/1.62 = ( ( Xs = Ys )
% 3.16/1.62 & ( X = Y ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_120_append1__eq__conv,axiom,
% 3.16/1.62 ! [Xs: list_list_node,X: list_node,Ys: list_list_node,Y: list_node] :
% 3.16/1.62 ( ( ( append_list_node @ Xs @ ( cons_list_node @ X @ nil_list_node ) )
% 3.16/1.62 = ( append_list_node @ Ys @ ( cons_list_node @ Y @ nil_list_node ) ) )
% 3.16/1.62 = ( ( Xs = Ys )
% 3.16/1.62 & ( X = Y ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_121_append1__eq__conv,axiom,
% 3.16/1.62 ! [Xs: list_node,X: node,Ys: list_node,Y: node] :
% 3.16/1.62 ( ( ( append_node @ Xs @ ( cons_node @ X @ nil_node ) )
% 3.16/1.62 = ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 3.16/1.62 = ( ( Xs = Ys )
% 3.16/1.62 & ( X = Y ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_122_butlast__snoc,axiom,
% 3.16/1.62 ! [Xs: list_val,X: val] :
% 3.16/1.62 ( ( butlast_val @ ( append_val @ Xs @ ( cons_val @ X @ nil_val ) ) )
% 3.16/1.62 = Xs ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_123_butlast__snoc,axiom,
% 3.16/1.62 ! [Xs: list_list_node,X: list_node] :
% 3.16/1.62 ( ( butlast_list_node @ ( append_list_node @ Xs @ ( cons_list_node @ X @ nil_list_node ) ) )
% 3.16/1.62 = Xs ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_124_butlast__snoc,axiom,
% 3.16/1.62 ! [Xs: list_node,X: node] :
% 3.16/1.62 ( ( butlast_node @ ( append_node @ Xs @ ( cons_node @ X @ nil_node ) ) )
% 3.16/1.62 = Xs ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_125__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ms_H_O_A_092_060lbrakk_062g_A_092_060turnstile_062_Am_Nms_H_092_060rightarrow_062i_059_Aprefix_Ams_H_Ams_059_Ai_A_092_060notin_062_Aset_A_Ibutlast_Ams_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 3.16/1.62 ~ ! [Ms2: list_node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ Ms2 @ i )
% 3.16/1.62 => ( ( prefix_node @ Ms2 @ ms )
% 3.16/1.62 => ( member_node @ i @ ( set_node2 @ ( butlast_node @ Ms2 ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_126__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062i_Ari_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nri_092_060rightarrow_062i_059_Ai_A_092_060in_062_Aset_Ams_059_A_092_060forall_062n_092_060in_062set_A_Ibutlast_Ari_J_O_An_A_092_060notin_062_Aset_Ams_059_Aprefix_Ari_Ars_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 3.16/1.62 ~ ! [I: node,Ri: list_node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ Ri @ I )
% 3.16/1.62 => ( ( member_node @ I @ ( set_node2 @ ms ) )
% 3.16/1.62 => ( ! [X2: node] :
% 3.16/1.62 ( ( member_node @ X2 @ ( set_node2 @ ( butlast_node @ Ri ) ) )
% 3.16/1.62 => ~ ( member_node @ X2 @ ( set_node2 @ ms ) ) )
% 3.16/1.62 => ~ ( prefix_node @ Ri @ rs2 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_127_old_OCons__path2,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node,N2: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( ( member_node @ N2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N ) ) )
% 3.16/1.62 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N2 @ ( cons_node @ N2 @ Ns ) @ M ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_128_butlast_Osimps_I1_J,axiom,
% 3.16/1.62 ( ( butlast_list_node @ nil_list_node )
% 3.16/1.62 = nil_list_node ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_129_butlast_Osimps_I1_J,axiom,
% 3.16/1.62 ( ( butlast_val @ nil_val )
% 3.16/1.62 = nil_val ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_130_butlast_Osimps_I1_J,axiom,
% 3.16/1.62 ( ( butlast_node @ nil_node )
% 3.16/1.62 = nil_node ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_131_in__set__butlastD,axiom,
% 3.16/1.62 ! [X: val,Xs: list_val] :
% 3.16/1.62 ( ( member_val @ X @ ( set_val2 @ ( butlast_val @ Xs ) ) )
% 3.16/1.62 => ( member_val @ X @ ( set_val2 @ Xs ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_132_in__set__butlastD,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node] :
% 3.16/1.62 ( ( member_node @ X @ ( set_node2 @ ( butlast_node @ Xs ) ) )
% 3.16/1.62 => ( member_node @ X @ ( set_node2 @ Xs ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_133_butlast__tl,axiom,
% 3.16/1.62 ! [Xs: list_val] :
% 3.16/1.62 ( ( butlast_val @ ( tl_val @ Xs ) )
% 3.16/1.62 = ( tl_val @ ( butlast_val @ Xs ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_134_butlast__tl,axiom,
% 3.16/1.62 ! [Xs: list_node] :
% 3.16/1.62 ( ( butlast_node @ ( tl_node @ Xs ) )
% 3.16/1.62 = ( tl_node @ ( butlast_node @ Xs ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_135_butlast_Osimps_I2_J,axiom,
% 3.16/1.62 ! [Xs: list_val,X: val] :
% 3.16/1.62 ( ( ( Xs = nil_val )
% 3.16/1.62 => ( ( butlast_val @ ( cons_val @ X @ Xs ) )
% 3.16/1.62 = nil_val ) )
% 3.16/1.62 & ( ( Xs != nil_val )
% 3.16/1.62 => ( ( butlast_val @ ( cons_val @ X @ Xs ) )
% 3.16/1.62 = ( cons_val @ X @ ( butlast_val @ Xs ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_136_butlast_Osimps_I2_J,axiom,
% 3.16/1.62 ! [Xs: list_list_node,X: list_node] :
% 3.16/1.62 ( ( ( Xs = nil_list_node )
% 3.16/1.62 => ( ( butlast_list_node @ ( cons_list_node @ X @ Xs ) )
% 3.16/1.62 = nil_list_node ) )
% 3.16/1.62 & ( ( Xs != nil_list_node )
% 3.16/1.62 => ( ( butlast_list_node @ ( cons_list_node @ X @ Xs ) )
% 3.16/1.62 = ( cons_list_node @ X @ ( butlast_list_node @ Xs ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_137_butlast_Osimps_I2_J,axiom,
% 3.16/1.62 ! [Xs: list_node,X: node] :
% 3.16/1.62 ( ( ( Xs = nil_node )
% 3.16/1.62 => ( ( butlast_node @ ( cons_node @ X @ Xs ) )
% 3.16/1.62 = nil_node ) )
% 3.16/1.62 & ( ( Xs != nil_node )
% 3.16/1.62 => ( ( butlast_node @ ( cons_node @ X @ Xs ) )
% 3.16/1.62 = ( cons_node @ X @ ( butlast_node @ Xs ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_138_butlast__append,axiom,
% 3.16/1.62 ! [Ys: list_list_node,Xs: list_list_node] :
% 3.16/1.62 ( ( ( Ys = nil_list_node )
% 3.16/1.62 => ( ( butlast_list_node @ ( append_list_node @ Xs @ Ys ) )
% 3.16/1.62 = ( butlast_list_node @ Xs ) ) )
% 3.16/1.62 & ( ( Ys != nil_list_node )
% 3.16/1.62 => ( ( butlast_list_node @ ( append_list_node @ Xs @ Ys ) )
% 3.16/1.62 = ( append_list_node @ Xs @ ( butlast_list_node @ Ys ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_139_butlast__append,axiom,
% 3.16/1.62 ! [Ys: list_val,Xs: list_val] :
% 3.16/1.62 ( ( ( Ys = nil_val )
% 3.16/1.62 => ( ( butlast_val @ ( append_val @ Xs @ Ys ) )
% 3.16/1.62 = ( butlast_val @ Xs ) ) )
% 3.16/1.62 & ( ( Ys != nil_val )
% 3.16/1.62 => ( ( butlast_val @ ( append_val @ Xs @ Ys ) )
% 3.16/1.62 = ( append_val @ Xs @ ( butlast_val @ Ys ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_140_butlast__append,axiom,
% 3.16/1.62 ! [Ys: list_node,Xs: list_node] :
% 3.16/1.62 ( ( ( Ys = nil_node )
% 3.16/1.62 => ( ( butlast_node @ ( append_node @ Xs @ Ys ) )
% 3.16/1.62 = ( butlast_node @ Xs ) ) )
% 3.16/1.62 & ( ( Ys != nil_node )
% 3.16/1.62 => ( ( butlast_node @ ( append_node @ Xs @ Ys ) )
% 3.16/1.62 = ( append_node @ Xs @ ( butlast_node @ Ys ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_141_in__set__butlast__appendI,axiom,
% 3.16/1.62 ! [X: val,Xs: list_val,Ys: list_val] :
% 3.16/1.62 ( ( ( member_val @ X @ ( set_val2 @ ( butlast_val @ Xs ) ) )
% 3.16/1.62 | ( member_val @ X @ ( set_val2 @ ( butlast_val @ Ys ) ) ) )
% 3.16/1.62 => ( member_val @ X @ ( set_val2 @ ( butlast_val @ ( append_val @ Xs @ Ys ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_142_in__set__butlast__appendI,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( ( member_node @ X @ ( set_node2 @ ( butlast_node @ Xs ) ) )
% 3.16/1.62 | ( member_node @ X @ ( set_node2 @ ( butlast_node @ Ys ) ) ) )
% 3.16/1.62 => ( member_node @ X @ ( set_node2 @ ( butlast_node @ ( append_node @ Xs @ Ys ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_143_butlast__eq__cons__conv,axiom,
% 3.16/1.62 ! [L: list_val,X: val,Xs: list_val] :
% 3.16/1.62 ( ( ( butlast_val @ L )
% 3.16/1.62 = ( cons_val @ X @ Xs ) )
% 3.16/1.62 = ( ? [Xl: val] :
% 3.16/1.62 ( L
% 3.16/1.62 = ( cons_val @ X @ ( append_val @ Xs @ ( cons_val @ Xl @ nil_val ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_144_butlast__eq__cons__conv,axiom,
% 3.16/1.62 ! [L: list_list_node,X: list_node,Xs: list_list_node] :
% 3.16/1.62 ( ( ( butlast_list_node @ L )
% 3.16/1.62 = ( cons_list_node @ X @ Xs ) )
% 3.16/1.62 = ( ? [Xl: list_node] :
% 3.16/1.62 ( L
% 3.16/1.62 = ( cons_list_node @ X @ ( append_list_node @ Xs @ ( cons_list_node @ Xl @ nil_list_node ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_145_butlast__eq__cons__conv,axiom,
% 3.16/1.62 ! [L: list_node,X: node,Xs: list_node] :
% 3.16/1.62 ( ( ( butlast_node @ L )
% 3.16/1.62 = ( cons_node @ X @ Xs ) )
% 3.16/1.62 = ( ? [Xl: node] :
% 3.16/1.62 ( L
% 3.16/1.62 = ( cons_node @ X @ ( append_node @ Xs @ ( cons_node @ Xl @ nil_node ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_146_butlast__eq__consE,axiom,
% 3.16/1.62 ! [L: list_val,X: val,Xs: list_val] :
% 3.16/1.62 ( ( ( butlast_val @ L )
% 3.16/1.62 = ( cons_val @ X @ Xs ) )
% 3.16/1.62 => ~ ! [Xl2: val] :
% 3.16/1.62 ( L
% 3.16/1.62 != ( cons_val @ X @ ( append_val @ Xs @ ( cons_val @ Xl2 @ nil_val ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_147_butlast__eq__consE,axiom,
% 3.16/1.62 ! [L: list_list_node,X: list_node,Xs: list_list_node] :
% 3.16/1.62 ( ( ( butlast_list_node @ L )
% 3.16/1.62 = ( cons_list_node @ X @ Xs ) )
% 3.16/1.62 => ~ ! [Xl2: list_node] :
% 3.16/1.62 ( L
% 3.16/1.62 != ( cons_list_node @ X @ ( append_list_node @ Xs @ ( cons_list_node @ Xl2 @ nil_list_node ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_148_butlast__eq__consE,axiom,
% 3.16/1.62 ! [L: list_node,X: node,Xs: list_node] :
% 3.16/1.62 ( ( ( butlast_node @ L )
% 3.16/1.62 = ( cons_node @ X @ Xs ) )
% 3.16/1.62 => ~ ! [Xl2: node] :
% 3.16/1.62 ( L
% 3.16/1.62 != ( cons_node @ X @ ( append_node @ Xs @ ( cons_node @ Xl2 @ nil_node ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_149_list__tail__coinc,axiom,
% 3.16/1.62 ! [N1: val,R1: list_val,N22: val,R2: list_val] :
% 3.16/1.62 ( ( ( cons_val @ N1 @ R1 )
% 3.16/1.62 = ( cons_val @ N22 @ R2 ) )
% 3.16/1.62 => ( ( N1 = N22 )
% 3.16/1.62 & ( R1 = R2 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_150_list__tail__coinc,axiom,
% 3.16/1.62 ! [N1: list_node,R1: list_list_node,N22: list_node,R2: list_list_node] :
% 3.16/1.62 ( ( ( cons_list_node @ N1 @ R1 )
% 3.16/1.62 = ( cons_list_node @ N22 @ R2 ) )
% 3.16/1.62 => ( ( N1 = N22 )
% 3.16/1.62 & ( R1 = R2 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_151_list__tail__coinc,axiom,
% 3.16/1.62 ! [N1: node,R1: list_node,N22: node,R2: list_node] :
% 3.16/1.62 ( ( ( cons_node @ N1 @ R1 )
% 3.16/1.62 = ( cons_node @ N22 @ R2 ) )
% 3.16/1.62 => ( ( N1 = N22 )
% 3.16/1.62 & ( R1 = R2 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_152_not__Cons__self2,axiom,
% 3.16/1.62 ! [X: val,Xs: list_val] :
% 3.16/1.62 ( ( cons_val @ X @ Xs )
% 3.16/1.62 != Xs ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_153_not__Cons__self2,axiom,
% 3.16/1.62 ! [X: list_node,Xs: list_list_node] :
% 3.16/1.62 ( ( cons_list_node @ X @ Xs )
% 3.16/1.62 != Xs ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_154_not__Cons__self2,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node] :
% 3.16/1.62 ( ( cons_node @ X @ Xs )
% 3.16/1.62 != Xs ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_155_append__eq__appendI,axiom,
% 3.16/1.62 ! [Xs: list_val,Xs1: list_val,Zs: list_val,Ys: list_val,Us: list_val] :
% 3.16/1.62 ( ( ( append_val @ Xs @ Xs1 )
% 3.16/1.62 = Zs )
% 3.16/1.62 => ( ( Ys
% 3.16/1.62 = ( append_val @ Xs1 @ Us ) )
% 3.16/1.62 => ( ( append_val @ Xs @ Ys )
% 3.16/1.62 = ( append_val @ Zs @ Us ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_156_append__eq__appendI,axiom,
% 3.16/1.62 ! [Xs: list_node,Xs1: list_node,Zs: list_node,Ys: list_node,Us: list_node] :
% 3.16/1.62 ( ( ( append_node @ Xs @ Xs1 )
% 3.16/1.62 = Zs )
% 3.16/1.62 => ( ( Ys
% 3.16/1.62 = ( append_node @ Xs1 @ Us ) )
% 3.16/1.62 => ( ( append_node @ Xs @ Ys )
% 3.16/1.62 = ( append_node @ Zs @ Us ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_157_append__eq__append__conv2,axiom,
% 3.16/1.62 ! [Xs: list_val,Ys: list_val,Zs: list_val,Ts: list_val] :
% 3.16/1.62 ( ( ( append_val @ Xs @ Ys )
% 3.16/1.62 = ( append_val @ Zs @ Ts ) )
% 3.16/1.62 = ( ? [Us2: list_val] :
% 3.16/1.62 ( ( ( Xs
% 3.16/1.62 = ( append_val @ Zs @ Us2 ) )
% 3.16/1.62 & ( ( append_val @ Us2 @ Ys )
% 3.16/1.62 = Ts ) )
% 3.16/1.62 | ( ( ( append_val @ Xs @ Us2 )
% 3.16/1.62 = Zs )
% 3.16/1.62 & ( Ys
% 3.16/1.62 = ( append_val @ Us2 @ Ts ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_158_append__eq__append__conv2,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node,Zs: list_node,Ts: list_node] :
% 3.16/1.62 ( ( ( append_node @ Xs @ Ys )
% 3.16/1.62 = ( append_node @ Zs @ Ts ) )
% 3.16/1.62 = ( ? [Us2: list_node] :
% 3.16/1.62 ( ( ( Xs
% 3.16/1.62 = ( append_node @ Zs @ Us2 ) )
% 3.16/1.62 & ( ( append_node @ Us2 @ Ys )
% 3.16/1.62 = Ts ) )
% 3.16/1.62 | ( ( ( append_node @ Xs @ Us2 )
% 3.16/1.62 = Zs )
% 3.16/1.62 & ( Ys
% 3.16/1.62 = ( append_node @ Us2 @ Ts ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_159_strict__sorted_Oinduct,axiom,
% 3.16/1.62 ! [P: list_val > $o,A0: list_val] :
% 3.16/1.62 ( ( P @ nil_val )
% 3.16/1.62 => ( ! [X4: val,Ys2: list_val] :
% 3.16/1.62 ( ( P @ Ys2 )
% 3.16/1.62 => ( P @ ( cons_val @ X4 @ Ys2 ) ) )
% 3.16/1.62 => ( P @ A0 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_160_strict__sorted_Oinduct,axiom,
% 3.16/1.62 ! [P: list_node > $o,A0: list_node] :
% 3.16/1.62 ( ( P @ nil_node )
% 3.16/1.62 => ( ! [X4: node,Ys2: list_node] :
% 3.16/1.62 ( ( P @ Ys2 )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ Ys2 ) ) )
% 3.16/1.62 => ( P @ A0 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_161_mergesort__by__rel__merge__induct,axiom,
% 3.16/1.62 ! [P: list_node > list_val > $o,R: node > val > $o,Xs: list_node,Ys: list_val] :
% 3.16/1.62 ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_val )
% 3.16/1.62 => ( ! [X_1: list_val] : ( P @ nil_node @ X_1 )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node,Y2: val,Ys2: list_val] :
% 3.16/1.62 ( ( R @ X4 @ Y2 )
% 3.16/1.62 => ( ( P @ Xs2 @ ( cons_val @ Y2 @ Ys2 ) )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node,Y2: val,Ys2: list_val] :
% 3.16/1.62 ( ~ ( R @ X4 @ Y2 )
% 3.16/1.62 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys2 )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_162_mergesort__by__rel__merge__induct,axiom,
% 3.16/1.62 ! [P: list_val > list_val > $o,R: val > val > $o,Xs: list_val,Ys: list_val] :
% 3.16/1.62 ( ! [Xs2: list_val] : ( P @ Xs2 @ nil_val )
% 3.16/1.62 => ( ! [X_1: list_val] : ( P @ nil_val @ X_1 )
% 3.16/1.62 => ( ! [X4: val,Xs2: list_val,Y2: val,Ys2: list_val] :
% 3.16/1.62 ( ( R @ X4 @ Y2 )
% 3.16/1.62 => ( ( P @ Xs2 @ ( cons_val @ Y2 @ Ys2 ) )
% 3.16/1.62 => ( P @ ( cons_val @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( ! [X4: val,Xs2: list_val,Y2: val,Ys2: list_val] :
% 3.16/1.62 ( ~ ( R @ X4 @ Y2 )
% 3.16/1.62 => ( ( P @ ( cons_val @ X4 @ Xs2 ) @ Ys2 )
% 3.16/1.62 => ( P @ ( cons_val @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_163_mergesort__by__rel__merge__induct,axiom,
% 3.16/1.62 ! [P: list_list_node > list_val > $o,R: list_node > val > $o,Xs: list_list_node,Ys: list_val] :
% 3.16/1.62 ( ! [Xs2: list_list_node] : ( P @ Xs2 @ nil_val )
% 3.16/1.62 => ( ! [X_1: list_val] : ( P @ nil_list_node @ X_1 )
% 3.16/1.62 => ( ! [X4: list_node,Xs2: list_list_node,Y2: val,Ys2: list_val] :
% 3.16/1.62 ( ( R @ X4 @ Y2 )
% 3.16/1.62 => ( ( P @ Xs2 @ ( cons_val @ Y2 @ Ys2 ) )
% 3.16/1.62 => ( P @ ( cons_list_node @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( ! [X4: list_node,Xs2: list_list_node,Y2: val,Ys2: list_val] :
% 3.16/1.62 ( ~ ( R @ X4 @ Y2 )
% 3.16/1.62 => ( ( P @ ( cons_list_node @ X4 @ Xs2 ) @ Ys2 )
% 3.16/1.62 => ( P @ ( cons_list_node @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_164_mergesort__by__rel__merge__induct,axiom,
% 3.16/1.62 ! [P: list_node > list_list_node > $o,R: node > list_node > $o,Xs: list_node,Ys: list_list_node] :
% 3.16/1.62 ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_list_node )
% 3.16/1.62 => ( ! [X_1: list_list_node] : ( P @ nil_node @ X_1 )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node,Y2: list_node,Ys2: list_list_node] :
% 3.16/1.62 ( ( R @ X4 @ Y2 )
% 3.16/1.62 => ( ( P @ Xs2 @ ( cons_list_node @ Y2 @ Ys2 ) )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node,Y2: list_node,Ys2: list_list_node] :
% 3.16/1.62 ( ~ ( R @ X4 @ Y2 )
% 3.16/1.62 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys2 )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_165_mergesort__by__rel__merge__induct,axiom,
% 3.16/1.62 ! [P: list_val > list_list_node > $o,R: val > list_node > $o,Xs: list_val,Ys: list_list_node] :
% 3.16/1.62 ( ! [Xs2: list_val] : ( P @ Xs2 @ nil_list_node )
% 3.16/1.62 => ( ! [X_1: list_list_node] : ( P @ nil_val @ X_1 )
% 3.16/1.62 => ( ! [X4: val,Xs2: list_val,Y2: list_node,Ys2: list_list_node] :
% 3.16/1.62 ( ( R @ X4 @ Y2 )
% 3.16/1.62 => ( ( P @ Xs2 @ ( cons_list_node @ Y2 @ Ys2 ) )
% 3.16/1.62 => ( P @ ( cons_val @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( ! [X4: val,Xs2: list_val,Y2: list_node,Ys2: list_list_node] :
% 3.16/1.62 ( ~ ( R @ X4 @ Y2 )
% 3.16/1.62 => ( ( P @ ( cons_val @ X4 @ Xs2 ) @ Ys2 )
% 3.16/1.62 => ( P @ ( cons_val @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_166_mergesort__by__rel__merge__induct,axiom,
% 3.16/1.62 ! [P: list_list_node > list_list_node > $o,R: list_node > list_node > $o,Xs: list_list_node,Ys: list_list_node] :
% 3.16/1.62 ( ! [Xs2: list_list_node] : ( P @ Xs2 @ nil_list_node )
% 3.16/1.62 => ( ! [X_1: list_list_node] : ( P @ nil_list_node @ X_1 )
% 3.16/1.62 => ( ! [X4: list_node,Xs2: list_list_node,Y2: list_node,Ys2: list_list_node] :
% 3.16/1.62 ( ( R @ X4 @ Y2 )
% 3.16/1.62 => ( ( P @ Xs2 @ ( cons_list_node @ Y2 @ Ys2 ) )
% 3.16/1.62 => ( P @ ( cons_list_node @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( ! [X4: list_node,Xs2: list_list_node,Y2: list_node,Ys2: list_list_node] :
% 3.16/1.62 ( ~ ( R @ X4 @ Y2 )
% 3.16/1.62 => ( ( P @ ( cons_list_node @ X4 @ Xs2 ) @ Ys2 )
% 3.16/1.62 => ( P @ ( cons_list_node @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_167_mergesort__by__rel__merge__induct,axiom,
% 3.16/1.62 ! [P: list_node > list_node > $o,R: node > node > $o,Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_node )
% 3.16/1.62 => ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 3.16/1.62 ( ( R @ X4 @ Y2 )
% 3.16/1.62 => ( ( P @ Xs2 @ ( cons_node @ Y2 @ Ys2 ) )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 3.16/1.62 ( ~ ( R @ X4 @ Y2 )
% 3.16/1.62 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys2 )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_168_mergesort__by__rel__merge_Oinduct,axiom,
% 3.16/1.62 ! [P: ( node > node > $o ) > list_node > list_node > $o,A0: node > node > $o,A1: list_node,A22: list_node] :
% 3.16/1.62 ( ! [R3: node > node > $o,X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 3.16/1.62 ( ( ( R3 @ X4 @ Y2 )
% 3.16/1.62 => ( P @ R3 @ Xs2 @ ( cons_node @ Y2 @ Ys2 ) ) )
% 3.16/1.62 => ( ( ~ ( R3 @ X4 @ Y2 )
% 3.16/1.62 => ( P @ R3 @ ( cons_node @ X4 @ Xs2 ) @ Ys2 ) )
% 3.16/1.62 => ( P @ R3 @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( ! [R3: node > node > $o,Xs2: list_node] : ( P @ R3 @ Xs2 @ nil_node )
% 3.16/1.62 => ( ! [R3: node > node > $o,V: node,Va: list_node] : ( P @ R3 @ nil_node @ ( cons_node @ V @ Va ) )
% 3.16/1.62 => ( P @ A0 @ A1 @ A22 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_169_map__tailrec__rev_Oinduct,axiom,
% 3.16/1.62 ! [P: ( node > node ) > list_node > list_node > $o,A0: node > node,A1: list_node,A22: list_node] :
% 3.16/1.62 ( ! [F: node > node,X_1: list_node] : ( P @ F @ nil_node @ X_1 )
% 3.16/1.62 => ( ! [F: node > node,A3: node,As: list_node,Bs: list_node] :
% 3.16/1.62 ( ( P @ F @ As @ ( cons_node @ ( F @ A3 ) @ Bs ) )
% 3.16/1.62 => ( P @ F @ ( cons_node @ A3 @ As ) @ Bs ) )
% 3.16/1.62 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_170_list__nonempty__induct,axiom,
% 3.16/1.62 ! [Xs: list_node,P: list_node > $o] :
% 3.16/1.62 ( ( Xs != nil_node )
% 3.16/1.62 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node] :
% 3.16/1.62 ( ( Xs2 != nil_node )
% 3.16/1.62 => ( ( P @ Xs2 )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ Xs2 ) ) ) )
% 3.16/1.62 => ( P @ Xs ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_171_list__all__zip_Oinduct,axiom,
% 3.16/1.62 ! [P: ( node > node > $o ) > list_node > list_node > $o,A0: node > node > $o,A1: list_node,A22: list_node] :
% 3.16/1.62 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node @ nil_node )
% 3.16/1.62 => ( ! [P2: node > node > $o,A3: node,As: list_node,B2: node,Bs: list_node] :
% 3.16/1.62 ( ( P @ P2 @ As @ Bs )
% 3.16/1.62 => ( P @ P2 @ ( cons_node @ A3 @ As ) @ ( cons_node @ B2 @ Bs ) ) )
% 3.16/1.62 => ( ! [P2: node > node > $o,V: node,Va: list_node] : ( P @ P2 @ ( cons_node @ V @ Va ) @ nil_node )
% 3.16/1.62 => ( ! [P2: node > node > $o,V: node,Va: list_node] : ( P @ P2 @ nil_node @ ( cons_node @ V @ Va ) )
% 3.16/1.62 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_172_successively_Oinduct,axiom,
% 3.16/1.62 ! [P: ( node > node > $o ) > list_node > $o,A0: node > node > $o,A1: list_node] :
% 3.16/1.62 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node )
% 3.16/1.62 => ( ! [P2: node > node > $o,X4: node] : ( P @ P2 @ ( cons_node @ X4 @ nil_node ) )
% 3.16/1.62 => ( ! [P2: node > node > $o,X4: node,Y2: node,Xs2: list_node] :
% 3.16/1.62 ( ( P @ P2 @ ( cons_node @ Y2 @ Xs2 ) )
% 3.16/1.62 => ( P @ P2 @ ( cons_node @ X4 @ ( cons_node @ Y2 @ Xs2 ) ) ) )
% 3.16/1.62 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_173_list__induct__first2,axiom,
% 3.16/1.62 ! [P: list_node > $o,Xs: list_node] :
% 3.16/1.62 ( ( P @ nil_node )
% 3.16/1.62 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 3.16/1.62 => ( ! [X1: node,X23: node,Xs2: list_node] :
% 3.16/1.62 ( ( P @ Xs2 )
% 3.16/1.62 => ( P @ ( cons_node @ X1 @ ( cons_node @ X23 @ Xs2 ) ) ) )
% 3.16/1.62 => ( P @ Xs ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_174_remdups__adj_Oinduct,axiom,
% 3.16/1.62 ! [P: list_node > $o,A0: list_node] :
% 3.16/1.62 ( ( P @ nil_node )
% 3.16/1.62 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 3.16/1.62 => ( ! [X4: node,Y2: node,Xs2: list_node] :
% 3.16/1.62 ( ( ( X4 = Y2 )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ Xs2 ) ) )
% 3.16/1.62 => ( ( ( X4 != Y2 )
% 3.16/1.62 => ( P @ ( cons_node @ Y2 @ Xs2 ) ) )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ ( cons_node @ Y2 @ Xs2 ) ) ) ) )
% 3.16/1.62 => ( P @ A0 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_175_sorted__wrt_Oinduct,axiom,
% 3.16/1.62 ! [P: ( node > node > $o ) > list_node > $o,A0: node > node > $o,A1: list_node] :
% 3.16/1.62 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node )
% 3.16/1.62 => ( ! [P2: node > node > $o,X4: node,Ys2: list_node] :
% 3.16/1.62 ( ( P @ P2 @ Ys2 )
% 3.16/1.62 => ( P @ P2 @ ( cons_node @ X4 @ Ys2 ) ) )
% 3.16/1.62 => ( P @ A0 @ A1 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_176_remdups__adj_Ocases,axiom,
% 3.16/1.62 ! [X: list_node] :
% 3.16/1.62 ( ( X != nil_node )
% 3.16/1.62 => ( ! [X4: node] :
% 3.16/1.62 ( X
% 3.16/1.62 != ( cons_node @ X4 @ nil_node ) )
% 3.16/1.62 => ~ ! [X4: node,Y2: node,Xs2: list_node] :
% 3.16/1.62 ( X
% 3.16/1.62 != ( cons_node @ X4 @ ( cons_node @ Y2 @ Xs2 ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_177_list__2pre__induct,axiom,
% 3.16/1.62 ! [P: list_node > list_node > $o,W1: list_node,W2: list_node] :
% 3.16/1.62 ( ( P @ nil_node @ nil_node )
% 3.16/1.62 => ( ! [E3: node,W12: list_node,W22: list_node] :
% 3.16/1.62 ( ( P @ W12 @ W22 )
% 3.16/1.62 => ( P @ ( cons_node @ E3 @ W12 ) @ W22 ) )
% 3.16/1.62 => ( ! [E3: node,W13: list_node,W23: list_node] :
% 3.16/1.62 ( ( P @ W13 @ W23 )
% 3.16/1.62 => ( P @ W13 @ ( cons_node @ E3 @ W23 ) ) )
% 3.16/1.62 => ( P @ W1 @ W2 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_178_transpose_Ocases,axiom,
% 3.16/1.62 ! [X: list_list_node] :
% 3.16/1.62 ( ( X != nil_list_node )
% 3.16/1.62 => ( ! [Xss: list_list_node] :
% 3.16/1.62 ( X
% 3.16/1.62 != ( cons_list_node @ nil_node @ Xss ) )
% 3.16/1.62 => ~ ! [X4: node,Xs2: list_node,Xss: list_list_node] :
% 3.16/1.62 ( X
% 3.16/1.62 != ( cons_list_node @ ( cons_node @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_179_shuffles_Oinduct,axiom,
% 3.16/1.62 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 3.16/1.62 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 3.16/1.62 => ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_node )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 3.16/1.62 ( ( P @ Xs2 @ ( cons_node @ Y2 @ Ys2 ) )
% 3.16/1.62 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys2 )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y2 @ Ys2 ) ) ) )
% 3.16/1.62 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_180_min__list_Oinduct,axiom,
% 3.16/1.62 ! [P: list_node > $o,A0: list_node] :
% 3.16/1.62 ( ! [X4: node,Xs2: list_node] :
% 3.16/1.62 ( ! [X212: node,X222: list_node] :
% 3.16/1.62 ( ( Xs2
% 3.16/1.62 = ( cons_node @ X212 @ X222 ) )
% 3.16/1.62 => ( P @ Xs2 ) )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ Xs2 ) ) )
% 3.16/1.62 => ( ( P @ nil_node )
% 3.16/1.62 => ( P @ A0 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_181_min__list_Ocases,axiom,
% 3.16/1.62 ! [X: list_node] :
% 3.16/1.62 ( ! [X4: node,Xs2: list_node] :
% 3.16/1.62 ( X
% 3.16/1.62 != ( cons_node @ X4 @ Xs2 ) )
% 3.16/1.62 => ( X = nil_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_182_induct__list012,axiom,
% 3.16/1.62 ! [P: list_node > $o,Xs: list_node] :
% 3.16/1.62 ( ( P @ nil_node )
% 3.16/1.62 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 3.16/1.62 => ( ! [X4: node,Y2: node,Zs2: list_node] :
% 3.16/1.62 ( ( P @ Zs2 )
% 3.16/1.62 => ( ( P @ ( cons_node @ Y2 @ Zs2 ) )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ ( cons_node @ Y2 @ Zs2 ) ) ) ) )
% 3.16/1.62 => ( P @ Xs ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_183_splice_Oinduct,axiom,
% 3.16/1.62 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 3.16/1.62 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node,Ys2: list_node] :
% 3.16/1.62 ( ( P @ Ys2 @ Xs2 )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys2 ) )
% 3.16/1.62 => ( P @ A0 @ A1 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_184_list__induct2_H,axiom,
% 3.16/1.62 ! [P: list_node > list_node > $o,Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( P @ nil_node @ nil_node )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node] : ( P @ ( cons_node @ X4 @ Xs2 ) @ nil_node )
% 3.16/1.62 => ( ! [Y2: node,Ys2: list_node] : ( P @ nil_node @ ( cons_node @ Y2 @ Ys2 ) )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 3.16/1.62 ( ( P @ Xs2 @ Ys2 )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y2 @ Ys2 ) ) )
% 3.16/1.62 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_185_neq__Nil__conv,axiom,
% 3.16/1.62 ! [Xs: list_node] :
% 3.16/1.62 ( ( Xs != nil_node )
% 3.16/1.62 = ( ? [Y3: node,Ys3: list_node] :
% 3.16/1.62 ( Xs
% 3.16/1.62 = ( cons_node @ Y3 @ Ys3 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_186_list_Oinducts,axiom,
% 3.16/1.62 ! [P: list_node > $o,List: list_node] :
% 3.16/1.62 ( ( P @ nil_node )
% 3.16/1.62 => ( ! [X1: node,X23: list_node] :
% 3.16/1.62 ( ( P @ X23 )
% 3.16/1.62 => ( P @ ( cons_node @ X1 @ X23 ) ) )
% 3.16/1.62 => ( P @ List ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_187_list_Oexhaust,axiom,
% 3.16/1.62 ! [Y: list_node] :
% 3.16/1.62 ( ( Y != nil_node )
% 3.16/1.62 => ~ ! [X213: node,X223: list_node] :
% 3.16/1.62 ( Y
% 3.16/1.62 != ( cons_node @ X213 @ X223 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_188_revg_Oinduct,axiom,
% 3.16/1.62 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 3.16/1.62 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 3.16/1.62 => ( ! [A3: node,As: list_node,B2: list_node] :
% 3.16/1.62 ( ( P @ As @ ( cons_node @ A3 @ B2 ) )
% 3.16/1.62 => ( P @ ( cons_node @ A3 @ As ) @ B2 ) )
% 3.16/1.62 => ( P @ A0 @ A1 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_189_list_OdiscI,axiom,
% 3.16/1.62 ! [List: list_node,X21: node,X22: list_node] :
% 3.16/1.62 ( ( List
% 3.16/1.62 = ( cons_node @ X21 @ X22 ) )
% 3.16/1.62 => ( List != nil_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_190_neq__NilE,axiom,
% 3.16/1.62 ! [L: list_node] :
% 3.16/1.62 ( ( L != nil_node )
% 3.16/1.62 => ~ ! [X4: node,Xs2: list_node] :
% 3.16/1.62 ( L
% 3.16/1.62 != ( cons_node @ X4 @ Xs2 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_191_list_Odistinct_I1_J,axiom,
% 3.16/1.62 ! [X21: node,X22: list_node] :
% 3.16/1.62 ( nil_node
% 3.16/1.62 != ( cons_node @ X21 @ X22 ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_192_list_Oset__cases,axiom,
% 3.16/1.62 ! [E2: val,A: list_val] :
% 3.16/1.62 ( ( member_val @ E2 @ ( set_val2 @ A ) )
% 3.16/1.62 => ( ! [Z2: list_val] :
% 3.16/1.62 ( A
% 3.16/1.62 != ( cons_val @ E2 @ Z2 ) )
% 3.16/1.62 => ~ ! [Z1: val,Z2: list_val] :
% 3.16/1.62 ( ( A
% 3.16/1.62 = ( cons_val @ Z1 @ Z2 ) )
% 3.16/1.62 => ~ ( member_val @ E2 @ ( set_val2 @ Z2 ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_193_list_Oset__cases,axiom,
% 3.16/1.62 ! [E2: node,A: list_node] :
% 3.16/1.62 ( ( member_node @ E2 @ ( set_node2 @ A ) )
% 3.16/1.62 => ( ! [Z2: list_node] :
% 3.16/1.62 ( A
% 3.16/1.62 != ( cons_node @ E2 @ Z2 ) )
% 3.16/1.62 => ~ ! [Z1: node,Z2: list_node] :
% 3.16/1.62 ( ( A
% 3.16/1.62 = ( cons_node @ Z1 @ Z2 ) )
% 3.16/1.62 => ~ ( member_node @ E2 @ ( set_node2 @ Z2 ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_194_set__ConsD,axiom,
% 3.16/1.62 ! [Y: val,X: val,Xs: list_val] :
% 3.16/1.62 ( ( member_val @ Y @ ( set_val2 @ ( cons_val @ X @ Xs ) ) )
% 3.16/1.62 => ( ( Y = X )
% 3.16/1.62 | ( member_val @ Y @ ( set_val2 @ Xs ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_195_set__ConsD,axiom,
% 3.16/1.62 ! [Y: node,X: node,Xs: list_node] :
% 3.16/1.62 ( ( member_node @ Y @ ( set_node2 @ ( cons_node @ X @ Xs ) ) )
% 3.16/1.62 => ( ( Y = X )
% 3.16/1.62 | ( member_node @ Y @ ( set_node2 @ Xs ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_196_list_Oset__intros_I1_J,axiom,
% 3.16/1.62 ! [X21: val,X22: list_val] : ( member_val @ X21 @ ( set_val2 @ ( cons_val @ X21 @ X22 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_197_list_Oset__intros_I1_J,axiom,
% 3.16/1.62 ! [X21: node,X22: list_node] : ( member_node @ X21 @ ( set_node2 @ ( cons_node @ X21 @ X22 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_198_list_Oset__intros_I2_J,axiom,
% 3.16/1.62 ! [Y: val,X22: list_val,X21: val] :
% 3.16/1.62 ( ( member_val @ Y @ ( set_val2 @ X22 ) )
% 3.16/1.62 => ( member_val @ Y @ ( set_val2 @ ( cons_val @ X21 @ X22 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_199_list_Oset__intros_I2_J,axiom,
% 3.16/1.62 ! [Y: node,X22: list_node,X21: node] :
% 3.16/1.62 ( ( member_node @ Y @ ( set_node2 @ X22 ) )
% 3.16/1.62 => ( member_node @ Y @ ( set_node2 @ ( cons_node @ X21 @ X22 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_200_Cons__eq__appendI,axiom,
% 3.16/1.62 ! [X: node,Xs1: list_node,Ys: list_node,Xs: list_node,Zs: list_node] :
% 3.16/1.62 ( ( ( cons_node @ X @ Xs1 )
% 3.16/1.62 = Ys )
% 3.16/1.62 => ( ( Xs
% 3.16/1.62 = ( append_node @ Xs1 @ Zs ) )
% 3.16/1.62 => ( ( cons_node @ X @ Xs )
% 3.16/1.62 = ( append_node @ Ys @ Zs ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_201_append__Cons,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( append_node @ ( cons_node @ X @ Xs ) @ Ys )
% 3.16/1.62 = ( cons_node @ X @ ( append_node @ Xs @ Ys ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_202_list__match__lel__lel,axiom,
% 3.16/1.62 ! [C1: list_node,Qs: node,C2: list_node,C12: list_node,Qs2: node,C22: list_node] :
% 3.16/1.62 ( ( ( append_node @ C1 @ ( cons_node @ Qs @ C2 ) )
% 3.16/1.62 = ( append_node @ C12 @ ( cons_node @ Qs2 @ C22 ) ) )
% 3.16/1.62 => ( ! [C21: list_node] :
% 3.16/1.62 ( ( C1
% 3.16/1.62 = ( append_node @ C12 @ ( cons_node @ Qs2 @ C21 ) ) )
% 3.16/1.62 => ( C22
% 3.16/1.62 != ( append_node @ C21 @ ( cons_node @ Qs @ C2 ) ) ) )
% 3.16/1.62 => ( ( ( C12 = C1 )
% 3.16/1.62 => ( ( Qs2 = Qs )
% 3.16/1.62 => ( C22 != C2 ) ) )
% 3.16/1.62 => ~ ! [C212: list_node] :
% 3.16/1.62 ( ( C12
% 3.16/1.62 = ( append_node @ C1 @ ( cons_node @ Qs @ C212 ) ) )
% 3.16/1.62 => ( C2
% 3.16/1.62 != ( append_node @ C212 @ ( cons_node @ Qs2 @ C22 ) ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_203_eq__Nil__appendI,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( Xs = Ys )
% 3.16/1.62 => ( Xs
% 3.16/1.62 = ( append_node @ nil_node @ Ys ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_204_append__Nil,axiom,
% 3.16/1.62 ! [Ys: list_node] :
% 3.16/1.62 ( ( append_node @ nil_node @ Ys )
% 3.16/1.62 = Ys ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_205_append_Oleft__neutral,axiom,
% 3.16/1.62 ! [A: list_node] :
% 3.16/1.62 ( ( append_node @ nil_node @ A )
% 3.16/1.62 = A ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_206_list_Osel_I3_J,axiom,
% 3.16/1.62 ! [X21: node,X22: list_node] :
% 3.16/1.62 ( ( tl_node @ ( cons_node @ X21 @ X22 ) )
% 3.16/1.62 = X22 ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_207_list_Osel_I2_J,axiom,
% 3.16/1.62 ( ( tl_node @ nil_node )
% 3.16/1.62 = nil_node ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_208_list__append__eq__Cons__cases,axiom,
% 3.16/1.62 ! [Ys: list_node,Zs: list_node,X: node,Xs: list_node] :
% 3.16/1.62 ( ( ( append_node @ Ys @ Zs )
% 3.16/1.62 = ( cons_node @ X @ Xs ) )
% 3.16/1.62 => ( ( ( Ys = nil_node )
% 3.16/1.62 => ( Zs
% 3.16/1.62 != ( cons_node @ X @ Xs ) ) )
% 3.16/1.62 => ~ ! [Ys4: list_node] :
% 3.16/1.62 ( ( Ys
% 3.16/1.62 = ( cons_node @ X @ Ys4 ) )
% 3.16/1.62 => ( ( append_node @ Ys4 @ Zs )
% 3.16/1.62 != Xs ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_209_list__Cons__eq__append__cases,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node,Ys: list_node,Zs: list_node] :
% 3.16/1.62 ( ( ( cons_node @ X @ Xs )
% 3.16/1.62 = ( append_node @ Ys @ Zs ) )
% 3.16/1.62 => ( ( ( Ys = nil_node )
% 3.16/1.62 => ( Zs
% 3.16/1.62 != ( cons_node @ X @ Xs ) ) )
% 3.16/1.62 => ~ ! [Ys4: list_node] :
% 3.16/1.62 ( ( Ys
% 3.16/1.62 = ( cons_node @ X @ Ys4 ) )
% 3.16/1.62 => ( ( append_node @ Ys4 @ Zs )
% 3.16/1.62 != Xs ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_210_rev__nonempty__induct2_H,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node,P: list_node > list_node > $o] :
% 3.16/1.62 ( ( Xs != nil_node )
% 3.16/1.62 => ( ( Ys != nil_node )
% 3.16/1.62 => ( ! [X4: node,Y2: node] : ( P @ ( cons_node @ X4 @ nil_node ) @ ( cons_node @ Y2 @ nil_node ) )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node,Y2: node] :
% 3.16/1.62 ( ( Xs2 != nil_node )
% 3.16/1.62 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( cons_node @ Y2 @ nil_node ) ) )
% 3.16/1.62 => ( ! [X4: node,Y2: node,Ys2: list_node] :
% 3.16/1.62 ( ( Ys2 != nil_node )
% 3.16/1.62 => ( P @ ( cons_node @ X4 @ nil_node ) @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 3.16/1.62 ( ( P @ Xs2 @ Ys2 )
% 3.16/1.62 => ( ( Xs2 != nil_node )
% 3.16/1.62 => ( ( Ys2 != nil_node )
% 3.16/1.62 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) ) ) )
% 3.16/1.62 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_211_rev__nonempty__induct,axiom,
% 3.16/1.62 ! [Xs: list_node,P: list_node > $o] :
% 3.16/1.62 ( ( Xs != nil_node )
% 3.16/1.62 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node] :
% 3.16/1.62 ( ( Xs2 != nil_node )
% 3.16/1.62 => ( ( P @ Xs2 )
% 3.16/1.62 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) ) ) )
% 3.16/1.62 => ( P @ Xs ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_212_append__eq__Cons__conv,axiom,
% 3.16/1.62 ! [Ys: list_node,Zs: list_node,X: node,Xs: list_node] :
% 3.16/1.62 ( ( ( append_node @ Ys @ Zs )
% 3.16/1.62 = ( cons_node @ X @ Xs ) )
% 3.16/1.62 = ( ( ( Ys = nil_node )
% 3.16/1.62 & ( Zs
% 3.16/1.62 = ( cons_node @ X @ Xs ) ) )
% 3.16/1.62 | ? [Ys5: list_node] :
% 3.16/1.62 ( ( Ys
% 3.16/1.62 = ( cons_node @ X @ Ys5 ) )
% 3.16/1.62 & ( ( append_node @ Ys5 @ Zs )
% 3.16/1.62 = Xs ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_213_Cons__eq__append__conv,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node,Ys: list_node,Zs: list_node] :
% 3.16/1.62 ( ( ( cons_node @ X @ Xs )
% 3.16/1.62 = ( append_node @ Ys @ Zs ) )
% 3.16/1.62 = ( ( ( Ys = nil_node )
% 3.16/1.62 & ( ( cons_node @ X @ Xs )
% 3.16/1.62 = Zs ) )
% 3.16/1.62 | ? [Ys5: list_node] :
% 3.16/1.62 ( ( ( cons_node @ X @ Ys5 )
% 3.16/1.62 = Ys )
% 3.16/1.62 & ( Xs
% 3.16/1.62 = ( append_node @ Ys5 @ Zs ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_214_neq__Nil__rev__conv,axiom,
% 3.16/1.62 ! [L: list_node] :
% 3.16/1.62 ( ( L != nil_node )
% 3.16/1.62 = ( ? [Xs3: list_node,X3: node] :
% 3.16/1.62 ( L
% 3.16/1.62 = ( append_node @ Xs3 @ ( cons_node @ X3 @ nil_node ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_215_rev__induct2_H,axiom,
% 3.16/1.62 ! [P: list_node > list_node > $o,Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( P @ nil_node @ nil_node )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ nil_node )
% 3.16/1.62 => ( ! [Y2: node,Ys2: list_node] : ( P @ nil_node @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 3.16/1.62 ( ( P @ Xs2 @ Ys2 )
% 3.16/1.62 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) )
% 3.16/1.62 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_216_neq__Nil__revE,axiom,
% 3.16/1.62 ! [L: list_node] :
% 3.16/1.62 ( ( L != nil_node )
% 3.16/1.62 => ~ ! [Ll: list_node,E3: node] :
% 3.16/1.62 ( L
% 3.16/1.62 != ( append_node @ Ll @ ( cons_node @ E3 @ nil_node ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_217_rev__exhaust,axiom,
% 3.16/1.62 ! [Xs: list_node] :
% 3.16/1.62 ( ( Xs != nil_node )
% 3.16/1.62 => ~ ! [Ys2: list_node,Y2: node] :
% 3.16/1.62 ( Xs
% 3.16/1.62 != ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_218_rev__induct,axiom,
% 3.16/1.62 ! [P: list_node > $o,Xs: list_node] :
% 3.16/1.62 ( ( P @ nil_node )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node] :
% 3.16/1.62 ( ( P @ Xs2 )
% 3.16/1.62 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) ) )
% 3.16/1.62 => ( P @ Xs ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_219_split__list__first__prop__iff,axiom,
% 3.16/1.62 ! [Xs: list_node,P: node > $o] :
% 3.16/1.62 ( ( ? [X3: node] :
% 3.16/1.62 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 3.16/1.62 & ( P @ X3 ) ) )
% 3.16/1.62 = ( ? [Ys3: list_node,X3: node] :
% 3.16/1.62 ( ? [Zs3: list_node] :
% 3.16/1.62 ( Xs
% 3.16/1.62 = ( append_node @ Ys3 @ ( cons_node @ X3 @ Zs3 ) ) )
% 3.16/1.62 & ( P @ X3 )
% 3.16/1.62 & ! [Y3: node] :
% 3.16/1.62 ( ( member_node @ Y3 @ ( set_node2 @ Ys3 ) )
% 3.16/1.62 => ~ ( P @ Y3 ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_220_split__list__last__prop__iff,axiom,
% 3.16/1.62 ! [Xs: list_node,P: node > $o] :
% 3.16/1.62 ( ( ? [X3: node] :
% 3.16/1.62 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 3.16/1.62 & ( P @ X3 ) ) )
% 3.16/1.62 = ( ? [Ys3: list_node,X3: node,Zs3: list_node] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_node @ Ys3 @ ( cons_node @ X3 @ Zs3 ) ) )
% 3.16/1.62 & ( P @ X3 )
% 3.16/1.62 & ! [Y3: node] :
% 3.16/1.62 ( ( member_node @ Y3 @ ( set_node2 @ Zs3 ) )
% 3.16/1.62 => ~ ( P @ Y3 ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_221_in__set__conv__decomp__first,axiom,
% 3.16/1.62 ! [X: val,Xs: list_val] :
% 3.16/1.62 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 3.16/1.62 = ( ? [Ys3: list_val,Zs3: list_val] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs3 ) ) )
% 3.16/1.62 & ~ ( member_val @ X @ ( set_val2 @ Ys3 ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_222_in__set__conv__decomp__first,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node] :
% 3.16/1.62 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 3.16/1.62 = ( ? [Ys3: list_node,Zs3: list_node] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs3 ) ) )
% 3.16/1.62 & ~ ( member_node @ X @ ( set_node2 @ Ys3 ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_223_in__set__conv__decomp__last,axiom,
% 3.16/1.62 ! [X: val,Xs: list_val] :
% 3.16/1.62 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 3.16/1.62 = ( ? [Ys3: list_val,Zs3: list_val] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs3 ) ) )
% 3.16/1.62 & ~ ( member_val @ X @ ( set_val2 @ Zs3 ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_224_in__set__conv__decomp__last,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node] :
% 3.16/1.62 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 3.16/1.62 = ( ? [Ys3: list_node,Zs3: list_node] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs3 ) ) )
% 3.16/1.62 & ~ ( member_node @ X @ ( set_node2 @ Zs3 ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_225_split__list__first__propE,axiom,
% 3.16/1.62 ! [Xs: list_node,P: node > $o] :
% 3.16/1.62 ( ? [X2: node] :
% 3.16/1.62 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 3.16/1.62 & ( P @ X2 ) )
% 3.16/1.62 => ~ ! [Ys2: list_node,X4: node] :
% 3.16/1.62 ( ? [Zs2: list_node] :
% 3.16/1.62 ( Xs
% 3.16/1.62 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 3.16/1.62 => ( ( P @ X4 )
% 3.16/1.62 => ~ ! [Xa: node] :
% 3.16/1.62 ( ( member_node @ Xa @ ( set_node2 @ Ys2 ) )
% 3.16/1.62 => ~ ( P @ Xa ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_226_split__list__last__propE,axiom,
% 3.16/1.62 ! [Xs: list_node,P: node > $o] :
% 3.16/1.62 ( ? [X2: node] :
% 3.16/1.62 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 3.16/1.62 & ( P @ X2 ) )
% 3.16/1.62 => ~ ! [Ys2: list_node,X4: node,Zs2: list_node] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 3.16/1.62 => ( ( P @ X4 )
% 3.16/1.62 => ~ ! [Xa: node] :
% 3.16/1.62 ( ( member_node @ Xa @ ( set_node2 @ Zs2 ) )
% 3.16/1.62 => ~ ( P @ Xa ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_227_split__list__first__prop,axiom,
% 3.16/1.62 ! [Xs: list_node,P: node > $o] :
% 3.16/1.62 ( ? [X2: node] :
% 3.16/1.62 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 3.16/1.62 & ( P @ X2 ) )
% 3.16/1.62 => ? [Ys2: list_node,X4: node] :
% 3.16/1.62 ( ? [Zs2: list_node] :
% 3.16/1.62 ( Xs
% 3.16/1.62 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 3.16/1.62 & ( P @ X4 )
% 3.16/1.62 & ! [Xa: node] :
% 3.16/1.62 ( ( member_node @ Xa @ ( set_node2 @ Ys2 ) )
% 3.16/1.62 => ~ ( P @ Xa ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_228_split__list__last__prop,axiom,
% 3.16/1.62 ! [Xs: list_node,P: node > $o] :
% 3.16/1.62 ( ? [X2: node] :
% 3.16/1.62 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 3.16/1.62 & ( P @ X2 ) )
% 3.16/1.62 => ? [Ys2: list_node,X4: node,Zs2: list_node] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 3.16/1.62 & ( P @ X4 )
% 3.16/1.62 & ! [Xa: node] :
% 3.16/1.62 ( ( member_node @ Xa @ ( set_node2 @ Zs2 ) )
% 3.16/1.62 => ~ ( P @ Xa ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_229_in__set__list__format,axiom,
% 3.16/1.62 ! [E2: val,L: list_val] :
% 3.16/1.62 ( ( member_val @ E2 @ ( set_val2 @ L ) )
% 3.16/1.62 => ~ ! [L12: list_val,L22: list_val] :
% 3.16/1.62 ( L
% 3.16/1.62 != ( append_val @ L12 @ ( cons_val @ E2 @ L22 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_230_in__set__list__format,axiom,
% 3.16/1.62 ! [E2: node,L: list_node] :
% 3.16/1.62 ( ( member_node @ E2 @ ( set_node2 @ L ) )
% 3.16/1.62 => ~ ! [L12: list_node,L22: list_node] :
% 3.16/1.62 ( L
% 3.16/1.62 != ( append_node @ L12 @ ( cons_node @ E2 @ L22 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_231_in__set__conv__decomp,axiom,
% 3.16/1.62 ! [X: val,Xs: list_val] :
% 3.16/1.62 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 3.16/1.62 = ( ? [Ys3: list_val,Zs3: list_val] :
% 3.16/1.62 ( Xs
% 3.16/1.62 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs3 ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_232_in__set__conv__decomp,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node] :
% 3.16/1.62 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 3.16/1.62 = ( ? [Ys3: list_node,Zs3: list_node] :
% 3.16/1.62 ( Xs
% 3.16/1.62 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs3 ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_233_append__Cons__eq__iff,axiom,
% 3.16/1.62 ! [X: val,Xs: list_val,Ys: list_val,Xs4: list_val,Ys6: list_val] :
% 3.16/1.62 ( ~ ( member_val @ X @ ( set_val2 @ Xs ) )
% 3.16/1.62 => ( ~ ( member_val @ X @ ( set_val2 @ Ys ) )
% 3.16/1.62 => ( ( ( append_val @ Xs @ ( cons_val @ X @ Ys ) )
% 3.16/1.62 = ( append_val @ Xs4 @ ( cons_val @ X @ Ys6 ) ) )
% 3.16/1.62 = ( ( Xs = Xs4 )
% 3.16/1.62 & ( Ys = Ys6 ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_234_append__Cons__eq__iff,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node,Ys: list_node,Xs4: list_node,Ys6: list_node] :
% 3.16/1.62 ( ~ ( member_node @ X @ ( set_node2 @ Xs ) )
% 3.16/1.62 => ( ~ ( member_node @ X @ ( set_node2 @ Ys ) )
% 3.16/1.62 => ( ( ( append_node @ Xs @ ( cons_node @ X @ Ys ) )
% 3.16/1.62 = ( append_node @ Xs4 @ ( cons_node @ X @ Ys6 ) ) )
% 3.16/1.62 = ( ( Xs = Xs4 )
% 3.16/1.62 & ( Ys = Ys6 ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_235_split__list__propE,axiom,
% 3.16/1.62 ! [Xs: list_node,P: node > $o] :
% 3.16/1.62 ( ? [X2: node] :
% 3.16/1.62 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 3.16/1.62 & ( P @ X2 ) )
% 3.16/1.62 => ~ ! [Ys2: list_node,X4: node] :
% 3.16/1.62 ( ? [Zs2: list_node] :
% 3.16/1.62 ( Xs
% 3.16/1.62 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 3.16/1.62 => ~ ( P @ X4 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_236_split__list__first,axiom,
% 3.16/1.62 ! [X: val,Xs: list_val] :
% 3.16/1.62 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 3.16/1.62 => ? [Ys2: list_val,Zs2: list_val] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs2 ) ) )
% 3.16/1.62 & ~ ( member_val @ X @ ( set_val2 @ Ys2 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_237_split__list__first,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node] :
% 3.16/1.62 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 3.16/1.62 => ? [Ys2: list_node,Zs2: list_node] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs2 ) ) )
% 3.16/1.62 & ~ ( member_node @ X @ ( set_node2 @ Ys2 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_238_xy__in__set__cases,axiom,
% 3.16/1.62 ! [X: val,L: list_val,Y: val] :
% 3.16/1.62 ( ( member_val @ X @ ( set_val2 @ L ) )
% 3.16/1.62 => ( ( member_val @ Y @ ( set_val2 @ L ) )
% 3.16/1.62 => ( ( ( X = Y )
% 3.16/1.62 => ! [L12: list_val,L22: list_val] :
% 3.16/1.62 ( L
% 3.16/1.62 != ( append_val @ L12 @ ( cons_val @ Y @ L22 ) ) ) )
% 3.16/1.62 => ( ( ( X != Y )
% 3.16/1.62 => ! [L12: list_val,L22: list_val,L3: list_val] :
% 3.16/1.62 ( L
% 3.16/1.62 != ( append_val @ L12 @ ( cons_val @ X @ ( append_val @ L22 @ ( cons_val @ Y @ L3 ) ) ) ) ) )
% 3.16/1.62 => ~ ( ( X != Y )
% 3.16/1.62 => ! [L12: list_val,L22: list_val,L3: list_val] :
% 3.16/1.62 ( L
% 3.16/1.62 != ( append_val @ L12 @ ( cons_val @ Y @ ( append_val @ L22 @ ( cons_val @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_239_xy__in__set__cases,axiom,
% 3.16/1.62 ! [X: node,L: list_node,Y: node] :
% 3.16/1.62 ( ( member_node @ X @ ( set_node2 @ L ) )
% 3.16/1.62 => ( ( member_node @ Y @ ( set_node2 @ L ) )
% 3.16/1.62 => ( ( ( X = Y )
% 3.16/1.62 => ! [L12: list_node,L22: list_node] :
% 3.16/1.62 ( L
% 3.16/1.62 != ( append_node @ L12 @ ( cons_node @ Y @ L22 ) ) ) )
% 3.16/1.62 => ( ( ( X != Y )
% 3.16/1.62 => ! [L12: list_node,L22: list_node,L3: list_node] :
% 3.16/1.62 ( L
% 3.16/1.62 != ( append_node @ L12 @ ( cons_node @ X @ ( append_node @ L22 @ ( cons_node @ Y @ L3 ) ) ) ) ) )
% 3.16/1.62 => ~ ( ( X != Y )
% 3.16/1.62 => ! [L12: list_node,L22: list_node,L3: list_node] :
% 3.16/1.62 ( L
% 3.16/1.62 != ( append_node @ L12 @ ( cons_node @ Y @ ( append_node @ L22 @ ( cons_node @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_240_split__list__prop,axiom,
% 3.16/1.62 ! [Xs: list_node,P: node > $o] :
% 3.16/1.62 ( ? [X2: node] :
% 3.16/1.62 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 3.16/1.62 & ( P @ X2 ) )
% 3.16/1.62 => ? [Ys2: list_node,X4: node] :
% 3.16/1.62 ( ? [Zs2: list_node] :
% 3.16/1.62 ( Xs
% 3.16/1.62 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 3.16/1.62 & ( P @ X4 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_241_split__list__last,axiom,
% 3.16/1.62 ! [X: val,Xs: list_val] :
% 3.16/1.62 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 3.16/1.62 => ? [Ys2: list_val,Zs2: list_val] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs2 ) ) )
% 3.16/1.62 & ~ ( member_val @ X @ ( set_val2 @ Zs2 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_242_split__list__last,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node] :
% 3.16/1.62 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 3.16/1.62 => ? [Ys2: list_node,Zs2: list_node] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs2 ) ) )
% 3.16/1.62 & ~ ( member_node @ X @ ( set_node2 @ Zs2 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_243_split__list,axiom,
% 3.16/1.62 ! [X: val,Xs: list_val] :
% 3.16/1.62 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 3.16/1.62 => ? [Ys2: list_val,Zs2: list_val] :
% 3.16/1.62 ( Xs
% 3.16/1.62 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs2 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_244_split__list,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node] :
% 3.16/1.62 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 3.16/1.62 => ? [Ys2: list_node,Zs2: list_node] :
% 3.16/1.62 ( Xs
% 3.16/1.62 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs2 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_245_tl__obtain__elem,axiom,
% 3.16/1.62 ! [Xs: list_node] :
% 3.16/1.62 ( ( Xs != nil_node )
% 3.16/1.62 => ( ( ( tl_node @ Xs )
% 3.16/1.62 = nil_node )
% 3.16/1.62 => ~ ! [E3: node] :
% 3.16/1.62 ( Xs
% 3.16/1.62 != ( cons_node @ E3 @ nil_node ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_246_tl__Nil,axiom,
% 3.16/1.62 ! [Xs: list_node] :
% 3.16/1.62 ( ( ( tl_node @ Xs )
% 3.16/1.62 = nil_node )
% 3.16/1.62 = ( ( Xs = nil_node )
% 3.16/1.62 | ? [X3: node] :
% 3.16/1.62 ( Xs
% 3.16/1.62 = ( cons_node @ X3 @ nil_node ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_247_Nil__tl,axiom,
% 3.16/1.62 ! [Xs: list_node] :
% 3.16/1.62 ( ( nil_node
% 3.16/1.62 = ( tl_node @ Xs ) )
% 3.16/1.62 = ( ( Xs = nil_node )
% 3.16/1.62 | ? [X3: node] :
% 3.16/1.62 ( Xs
% 3.16/1.62 = ( cons_node @ X3 @ nil_node ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_248_list_Oset__sel_I2_J,axiom,
% 3.16/1.62 ! [A: list_val,X: val] :
% 3.16/1.62 ( ( A != nil_val )
% 3.16/1.62 => ( ( member_val @ X @ ( set_val2 @ ( tl_val @ A ) ) )
% 3.16/1.62 => ( member_val @ X @ ( set_val2 @ A ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_249_list_Oset__sel_I2_J,axiom,
% 3.16/1.62 ! [A: list_node,X: node] :
% 3.16/1.62 ( ( A != nil_node )
% 3.16/1.62 => ( ( member_node @ X @ ( set_node2 @ ( tl_node @ A ) ) )
% 3.16/1.62 => ( member_node @ X @ ( set_node2 @ A ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_250_prefix__snoc,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node,Y: node] :
% 3.16/1.62 ( ( prefix_node @ Xs @ ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 3.16/1.62 = ( ( Xs
% 3.16/1.62 = ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 3.16/1.62 | ( prefix_node @ Xs @ Ys ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_251_old_Opath2__split__first__last,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node,X: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( ( member_node @ X @ ( set_node2 @ Ns ) )
% 3.16/1.62 => ~ ! [Ns_1: list_node,Ns_3: list_node,Ns_2: list_node] :
% 3.16/1.62 ( ( Ns
% 3.16/1.62 = ( append_node @ Ns_1 @ ( append_node @ Ns_3 @ Ns_2 ) ) )
% 3.16/1.62 => ( ( prefix_node @ ( append_node @ Ns_1 @ ( cons_node @ X @ nil_node ) ) @ Ns )
% 3.16/1.62 => ( ( suffix_node @ ( cons_node @ X @ Ns_2 ) @ Ns )
% 3.16/1.62 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns_1 @ ( cons_node @ X @ nil_node ) ) @ X )
% 3.16/1.62 => ( ~ ( member_node @ X @ ( set_node2 @ Ns_1 ) )
% 3.16/1.62 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ Ns_3 @ X )
% 3.16/1.62 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ ( cons_node @ X @ Ns_2 ) @ M )
% 3.16/1.62 => ( member_node @ X @ ( set_node2 @ Ns_2 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_252_same__prefix__nil,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( prefix_node @ ( append_node @ Xs @ Ys ) @ Xs )
% 3.16/1.62 = ( Ys = nil_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_253_old_Opath2__simple__loop,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,N2: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ N )
% 3.16/1.62 => ( ( member_node @ N2 @ ( set_node2 @ Ns ) )
% 3.16/1.62 => ~ ! [Ns3: list_node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns3 @ N )
% 3.16/1.62 => ( ( member_node @ N2 @ ( set_node2 @ Ns3 ) )
% 3.16/1.62 => ( ~ ( member_node @ N @ ( set_node2 @ ( tl_node @ ( butlast_node @ Ns3 ) ) ) )
% 3.16/1.62 => ~ ( ord_less_eq_set_node @ ( set_node2 @ Ns3 ) @ ( set_node2 @ Ns ) ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_254_old_Opath2__cases,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( ( ( Ns
% 3.16/1.62 = ( cons_node @ N @ nil_node ) )
% 3.16/1.62 => ( M != N ) )
% 3.16/1.62 => ~ ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( hd_node @ ( tl_node @ Ns ) ) @ ( tl_node @ Ns ) @ M )
% 3.16/1.62 => ~ ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ ( tl_node @ Ns ) ) ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_255_old_Opath__snoc,axiom,
% 3.16/1.62 ! [G: g,Ns: list_node,N: node,M: node] :
% 3.16/1.62 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ N @ nil_node ) ) )
% 3.16/1.62 => ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M ) ) )
% 3.16/1.62 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ N @ ( cons_node @ M @ nil_node ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_256_phiUses__finite,axiom,
% 3.16/1.62 ! [N: node,G: g] :
% 3.16/1.62 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 3.16/1.62 => ( finite_finite_val @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_257_old_Opath2__split__last__prop,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node,P: node > $o] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( ? [X2: node] :
% 3.16/1.62 ( ( member_node @ X2 @ ( set_node2 @ Ns ) )
% 3.16/1.62 & ( P @ X2 ) )
% 3.16/1.62 => ~ ! [N3: node,Ns3: list_node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N3 @ Ns3 @ M )
% 3.16/1.62 => ( ( P @ N3 )
% 3.16/1.62 => ( ! [X2: node] :
% 3.16/1.62 ( ( member_node @ X2 @ ( set_node2 @ ( tl_node @ Ns3 ) ) )
% 3.16/1.62 => ~ ( P @ X2 ) )
% 3.16/1.62 => ~ ( suffix_node @ Ns3 @ Ns ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_258_defs__finite,axiom,
% 3.16/1.62 ! [G: g,N: node] : ( finite_finite_val @ ( defs @ G @ N ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_259_prefix__order_Oorder__refl,axiom,
% 3.16/1.62 ! [X: list_node] : ( prefix_node @ X @ X ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_260_prefix__order_Odual__order_Orefl,axiom,
% 3.16/1.62 ! [A: list_node] : ( prefix_node @ A @ A ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_261_suffix__order_Oorder__refl,axiom,
% 3.16/1.62 ! [X: list_node] : ( suffix_node @ X @ X ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_262_suffix__order_Odual__order_Orefl,axiom,
% 3.16/1.62 ! [A: list_node] : ( suffix_node @ A @ A ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_263_old_Opath__not__Nil,axiom,
% 3.16/1.62 ! [G: g,Ns: list_node] :
% 3.16/1.62 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 3.16/1.62 => ( Ns != nil_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_264_old_Opath2__hd,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( N
% 3.16/1.62 = ( hd_node @ Ns ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_265_old_Opath2__forget__hd,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node,M: node] :
% 3.16/1.62 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 3.16/1.62 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( hd_node @ Ns ) @ Ns @ M ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_266_old_Opath__hd,axiom,
% 3.16/1.62 ! [G: g,N: node,Ns: list_node] :
% 3.16/1.62 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ Ns ) )
% 3.16/1.62 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ nil_node ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_267_old_Opath__split_I2_J,axiom,
% 3.16/1.62 ! [G: g,Ns: list_node,M: node,Ns2: list_node] :
% 3.16/1.62 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ M @ Ns2 ) ) )
% 3.16/1.62 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ M @ Ns2 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_268_List_Ofinite__set,axiom,
% 3.16/1.62 ! [Xs: list_node] : ( finite_finite_node @ ( set_node2 @ Xs ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_269_List_Ofinite__set,axiom,
% 3.16/1.62 ! [Xs: list_val] : ( finite_finite_val @ ( set_val2 @ Xs ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_270_Cons__prefix__Cons,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node,Y: node,Ys: list_node] :
% 3.16/1.62 ( ( prefix_node @ ( cons_node @ X @ Xs ) @ ( cons_node @ Y @ Ys ) )
% 3.16/1.62 = ( ( X = Y )
% 3.16/1.62 & ( prefix_node @ Xs @ Ys ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_271_prefix__code_I1_J,axiom,
% 3.16/1.62 ! [Xs: list_node] : ( prefix_node @ nil_node @ Xs ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_272_prefix__Nil,axiom,
% 3.16/1.62 ! [Xs: list_node] :
% 3.16/1.62 ( ( prefix_node @ Xs @ nil_node )
% 3.16/1.62 = ( Xs = nil_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_273_prefix__bot_Obot_Oextremum__unique,axiom,
% 3.16/1.62 ! [A: list_node] :
% 3.16/1.62 ( ( prefix_node @ A @ nil_node )
% 3.16/1.62 = ( A = nil_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_274_suffix__bot_Obot_Oextremum__unique,axiom,
% 3.16/1.62 ! [A: list_node] :
% 3.16/1.62 ( ( suffix_node @ A @ nil_node )
% 3.16/1.62 = ( A = nil_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_275_suffix__Nil,axiom,
% 3.16/1.62 ! [Xs: list_node] :
% 3.16/1.62 ( ( suffix_node @ Xs @ nil_node )
% 3.16/1.62 = ( Xs = nil_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_276_same__prefix__prefix,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 3.16/1.62 ( ( prefix_node @ ( append_node @ Xs @ Ys ) @ ( append_node @ Xs @ Zs ) )
% 3.16/1.62 = ( prefix_node @ Ys @ Zs ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_277_same__suffix__suffix,axiom,
% 3.16/1.62 ! [Ys: list_node,Xs: list_node,Zs: list_node] :
% 3.16/1.62 ( ( suffix_node @ ( append_node @ Ys @ Xs ) @ ( append_node @ Zs @ Xs ) )
% 3.16/1.62 = ( suffix_node @ Ys @ Zs ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_278_old_Oempty__path,axiom,
% 3.16/1.62 ! [N: node,G: g] :
% 3.16/1.62 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 3.16/1.62 => ( ( invar @ G )
% 3.16/1.62 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ nil_node ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_279_old_Opath__split_I1_J,axiom,
% 3.16/1.62 ! [G: g,Ns: list_node,M: node,Ns2: list_node] :
% 3.16/1.62 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ M @ Ns2 ) ) )
% 3.16/1.62 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ M @ nil_node ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_280_old_OCons__path,axiom,
% 3.16/1.62 ! [G: g,Ns: list_node,N2: node] :
% 3.16/1.62 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 3.16/1.62 => ( ( member_node @ N2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns ) ) ) )
% 3.16/1.62 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N2 @ Ns ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_281_old_Opath_Osimps,axiom,
% 3.16/1.62 ! [G: g,A: list_node] :
% 3.16/1.62 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ A )
% 3.16/1.62 = ( ? [N5: node] :
% 3.16/1.62 ( ( A
% 3.16/1.62 = ( cons_node @ N5 @ nil_node ) )
% 3.16/1.62 & ( member_node @ N5 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 3.16/1.62 & ( invar @ G ) )
% 3.16/1.62 | ? [Ns5: list_node,N6: node] :
% 3.16/1.62 ( ( A
% 3.16/1.62 = ( cons_node @ N6 @ Ns5 ) )
% 3.16/1.62 & ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns5 )
% 3.16/1.62 & ( member_node @ N6 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns5 ) ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_282_old_Opath_Oinducts,axiom,
% 3.16/1.62 ! [G: g,X: list_node,P: list_node > $o] :
% 3.16/1.62 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ X )
% 3.16/1.62 => ( ! [N4: node] :
% 3.16/1.62 ( ( member_node @ N4 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 3.16/1.62 => ( ( invar @ G )
% 3.16/1.62 => ( P @ ( cons_node @ N4 @ nil_node ) ) ) )
% 3.16/1.62 => ( ! [Ns4: list_node,N3: node] :
% 3.16/1.62 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns4 )
% 3.16/1.62 => ( ( P @ Ns4 )
% 3.16/1.62 => ( ( member_node @ N3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns4 ) ) ) )
% 3.16/1.62 => ( P @ ( cons_node @ N3 @ Ns4 ) ) ) ) )
% 3.16/1.62 => ( P @ X ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_283_old_Opath_Ocases,axiom,
% 3.16/1.62 ! [G: g,A: list_node] :
% 3.16/1.62 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ A )
% 3.16/1.62 => ( ! [N4: node] :
% 3.16/1.62 ( ( A
% 3.16/1.62 = ( cons_node @ N4 @ nil_node ) )
% 3.16/1.62 => ( ( member_node @ N4 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 3.16/1.62 => ~ ( invar @ G ) ) )
% 3.16/1.62 => ~ ! [Ns4: list_node,N3: node] :
% 3.16/1.62 ( ( A
% 3.16/1.62 = ( cons_node @ N3 @ Ns4 ) )
% 3.16/1.62 => ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns4 )
% 3.16/1.62 => ~ ( member_node @ N3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns4 ) ) ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_284_same__suffix__nil,axiom,
% 3.16/1.62 ! [Ys: list_node,Xs: list_node] :
% 3.16/1.62 ( ( suffix_node @ ( append_node @ Ys @ Xs ) @ Xs )
% 3.16/1.62 = ( Ys = nil_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_285_hd__append2,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( Xs != nil_node )
% 3.16/1.62 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 3.16/1.62 = ( hd_node @ Xs ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_286_suffix__snoc,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node,Y: node] :
% 3.16/1.62 ( ( suffix_node @ Xs @ ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 3.16/1.62 = ( ( Xs = nil_node )
% 3.16/1.62 | ? [Zs3: list_node] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_node @ Zs3 @ ( cons_node @ Y @ nil_node ) ) )
% 3.16/1.62 & ( suffix_node @ Zs3 @ Ys ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_287_snoc__suffix__snoc,axiom,
% 3.16/1.62 ! [Xs: list_node,X: node,Ys: list_node,Y: node] :
% 3.16/1.62 ( ( suffix_node @ ( append_node @ Xs @ ( cons_node @ X @ nil_node ) ) @ ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 3.16/1.62 = ( ( X = Y )
% 3.16/1.62 & ( suffix_node @ Xs @ Ys ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_288_hd__Cons__tl,axiom,
% 3.16/1.62 ! [Xs: list_node] :
% 3.16/1.62 ( ( Xs != nil_node )
% 3.16/1.62 => ( ( cons_node @ ( hd_node @ Xs ) @ ( tl_node @ Xs ) )
% 3.16/1.62 = Xs ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_289_list_Ocollapse,axiom,
% 3.16/1.62 ! [List: list_node] :
% 3.16/1.62 ( ( List != nil_node )
% 3.16/1.62 => ( ( cons_node @ ( hd_node @ List ) @ ( tl_node @ List ) )
% 3.16/1.62 = List ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_290_in__hd__or__tl__conv,axiom,
% 3.16/1.62 ! [L: list_val,X: val] :
% 3.16/1.62 ( ( L != nil_val )
% 3.16/1.62 => ( ( ( X
% 3.16/1.62 = ( hd_val @ L ) )
% 3.16/1.62 | ( member_val @ X @ ( set_val2 @ ( tl_val @ L ) ) ) )
% 3.16/1.62 = ( member_val @ X @ ( set_val2 @ L ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_291_in__hd__or__tl__conv,axiom,
% 3.16/1.62 ! [L: list_node,X: node] :
% 3.16/1.62 ( ( L != nil_node )
% 3.16/1.62 => ( ( ( X
% 3.16/1.62 = ( hd_node @ L ) )
% 3.16/1.62 | ( member_node @ X @ ( set_node2 @ ( tl_node @ L ) ) ) )
% 3.16/1.62 = ( member_node @ X @ ( set_node2 @ L ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_292_old_Opath__invar,axiom,
% 3.16/1.62 ! [G: g,Ns: list_node] :
% 3.16/1.62 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 3.16/1.62 => ( invar @ G ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_293_old_Opath__in___092_060alpha_062n,axiom,
% 3.16/1.62 ! [G: g,Ns: list_node,N: node] :
% 3.16/1.62 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 3.16/1.62 => ( ( member_node @ N @ ( set_node2 @ Ns ) )
% 3.16/1.62 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_294_old_Opath__by__tail,axiom,
% 3.16/1.62 ! [G: g,N: node,N2: node,Ns: list_node,Ms: list_node] :
% 3.16/1.62 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ ( cons_node @ N2 @ Ns ) ) )
% 3.16/1.62 => ( ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N2 @ Ns ) )
% 3.16/1.62 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N2 @ Ms ) ) )
% 3.16/1.62 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ ( cons_node @ N2 @ Ms ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_295_set__mono__suffix,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( suffix_node @ Xs @ Ys )
% 3.16/1.62 => ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ ( set_node2 @ Ys ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_296_subset__Collect__conv,axiom,
% 3.16/1.62 ! [S: set_node,P: node > $o] :
% 3.16/1.62 ( ( ord_less_eq_set_node @ S @ ( collect_node @ P ) )
% 3.16/1.62 = ( ! [X3: node] :
% 3.16/1.62 ( ( member_node @ X3 @ S )
% 3.16/1.62 => ( P @ X3 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_297_ord__eq__le__eq__trans,axiom,
% 3.16/1.62 ! [A: set_node,B: set_node,C: set_node,D: set_node] :
% 3.16/1.62 ( ( A = B )
% 3.16/1.62 => ( ( ord_less_eq_set_node @ B @ C )
% 3.16/1.62 => ( ( C = D )
% 3.16/1.62 => ( ord_less_eq_set_node @ A @ D ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_298_suffix__ConsD2,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node,Y: node,Ys: list_node] :
% 3.16/1.62 ( ( suffix_node @ ( cons_node @ X @ Xs ) @ ( cons_node @ Y @ Ys ) )
% 3.16/1.62 => ( suffix_node @ Xs @ Ys ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_299_suffix__ConsI,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node,Y: node] :
% 3.16/1.62 ( ( suffix_node @ Xs @ Ys )
% 3.16/1.62 => ( suffix_node @ Xs @ ( cons_node @ Y @ Ys ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_300_suffix__ConsD,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( suffix_node @ ( cons_node @ X @ Xs ) @ Ys )
% 3.16/1.62 => ( suffix_node @ Xs @ Ys ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_301_suffix__Cons,axiom,
% 3.16/1.62 ! [Xs: list_node,Y: node,Ys: list_node] :
% 3.16/1.62 ( ( suffix_node @ Xs @ ( cons_node @ Y @ Ys ) )
% 3.16/1.62 = ( ( Xs
% 3.16/1.62 = ( cons_node @ Y @ Ys ) )
% 3.16/1.62 | ( suffix_node @ Xs @ Ys ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_302_suffix__bot_Obot_Oextremum__uniqueI,axiom,
% 3.16/1.62 ! [A: list_node] :
% 3.16/1.62 ( ( suffix_node @ A @ nil_node )
% 3.16/1.62 => ( A = nil_node ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_303_suffix__bot_Obot_Oextremum,axiom,
% 3.16/1.62 ! [A: list_node] : ( suffix_node @ nil_node @ A ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_304_Nil__suffix,axiom,
% 3.16/1.62 ! [Xs: list_node] : ( suffix_node @ nil_node @ Xs ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_305_suffixE,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( suffix_node @ Xs @ Ys )
% 3.16/1.62 => ~ ! [Zs2: list_node] :
% 3.16/1.62 ( Ys
% 3.16/1.62 != ( append_node @ Zs2 @ Xs ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_306_suffixI,axiom,
% 3.16/1.62 ! [Ys: list_node,Zs: list_node,Xs: list_node] :
% 3.16/1.62 ( ( Ys
% 3.16/1.62 = ( append_node @ Zs @ Xs ) )
% 3.16/1.62 => ( suffix_node @ Xs @ Ys ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_307_Sublist_Osuffix__def,axiom,
% 3.16/1.62 ( suffix_node
% 3.16/1.62 = ( ^ [Xs3: list_node,Ys3: list_node] :
% 3.16/1.62 ? [Zs3: list_node] :
% 3.16/1.62 ( Ys3
% 3.16/1.62 = ( append_node @ Zs3 @ Xs3 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_308_suffix__append,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 3.16/1.62 ( ( suffix_node @ Xs @ ( append_node @ Ys @ Zs ) )
% 3.16/1.62 = ( ( suffix_node @ Xs @ Zs )
% 3.16/1.62 | ? [Xs5: list_node] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_node @ Xs5 @ Zs ) )
% 3.16/1.62 & ( suffix_node @ Xs5 @ Ys ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_309_suffix__appendD,axiom,
% 3.16/1.62 ! [Zs: list_node,Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( suffix_node @ ( append_node @ Zs @ Xs ) @ Ys )
% 3.16/1.62 => ( suffix_node @ Xs @ Ys ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_310_suffix__appendI,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 3.16/1.62 ( ( suffix_node @ Xs @ Ys )
% 3.16/1.62 => ( suffix_node @ Xs @ ( append_node @ Zs @ Ys ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_311_suffix__tl,axiom,
% 3.16/1.62 ! [Xs: list_node] : ( suffix_node @ ( tl_node @ Xs ) @ Xs ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_312_suffix__same__cases,axiom,
% 3.16/1.62 ! [Xs_1: list_node,Ys: list_node,Xs_2: list_node] :
% 3.16/1.62 ( ( suffix_node @ Xs_1 @ Ys )
% 3.16/1.62 => ( ( suffix_node @ Xs_2 @ Ys )
% 3.16/1.62 => ( ( suffix_node @ Xs_1 @ Xs_2 )
% 3.16/1.62 | ( suffix_node @ Xs_2 @ Xs_1 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_313_suffix__order_Oeq__iff,axiom,
% 3.16/1.62 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 3.16/1.62 = ( ^ [X3: list_node,Y3: list_node] :
% 3.16/1.62 ( ( suffix_node @ X3 @ Y3 )
% 3.16/1.62 & ( suffix_node @ Y3 @ X3 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_314_suffix__order_Oantisym,axiom,
% 3.16/1.62 ! [X: list_node,Y: list_node] :
% 3.16/1.62 ( ( suffix_node @ X @ Y )
% 3.16/1.62 => ( ( suffix_node @ Y @ X )
% 3.16/1.62 => ( X = Y ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_315_suffix__order_Oeq__refl,axiom,
% 3.16/1.62 ! [X: list_node,Y: list_node] :
% 3.16/1.62 ( ( X = Y )
% 3.16/1.62 => ( suffix_node @ X @ Y ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_316_suffix__order_Oorder_Otrans,axiom,
% 3.16/1.62 ! [A: list_node,B: list_node,C: list_node] :
% 3.16/1.62 ( ( suffix_node @ A @ B )
% 3.16/1.62 => ( ( suffix_node @ B @ C )
% 3.16/1.62 => ( suffix_node @ A @ C ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_317_suffix__order_Oorder__trans,axiom,
% 3.16/1.62 ! [X: list_node,Y: list_node,Z3: list_node] :
% 3.16/1.62 ( ( suffix_node @ X @ Y )
% 3.16/1.62 => ( ( suffix_node @ Y @ Z3 )
% 3.16/1.62 => ( suffix_node @ X @ Z3 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_318_suffix__order_Oantisym__conv,axiom,
% 3.16/1.62 ! [Y: list_node,X: list_node] :
% 3.16/1.62 ( ( suffix_node @ Y @ X )
% 3.16/1.62 => ( ( suffix_node @ X @ Y )
% 3.16/1.62 = ( X = Y ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_319_suffix__order_Oorder_Oeq__iff,axiom,
% 3.16/1.62 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 3.16/1.62 = ( ^ [A4: list_node,B3: list_node] :
% 3.16/1.62 ( ( suffix_node @ A4 @ B3 )
% 3.16/1.62 & ( suffix_node @ B3 @ A4 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_320_suffix__order_Oorder_Oantisym,axiom,
% 3.16/1.62 ! [A: list_node,B: list_node] :
% 3.16/1.62 ( ( suffix_node @ A @ B )
% 3.16/1.62 => ( ( suffix_node @ B @ A )
% 3.16/1.62 => ( A = B ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_321_suffix__order_Oord__eq__le__trans,axiom,
% 3.16/1.62 ! [A: list_node,B: list_node,C: list_node] :
% 3.16/1.62 ( ( A = B )
% 3.16/1.62 => ( ( suffix_node @ B @ C )
% 3.16/1.62 => ( suffix_node @ A @ C ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_322_suffix__order_Oord__le__eq__trans,axiom,
% 3.16/1.62 ! [A: list_node,B: list_node,C: list_node] :
% 3.16/1.62 ( ( suffix_node @ A @ B )
% 3.16/1.62 => ( ( B = C )
% 3.16/1.62 => ( suffix_node @ A @ C ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_323_suffix__order_Odual__order_Otrans,axiom,
% 3.16/1.62 ! [B: list_node,A: list_node,C: list_node] :
% 3.16/1.62 ( ( suffix_node @ B @ A )
% 3.16/1.62 => ( ( suffix_node @ C @ B )
% 3.16/1.62 => ( suffix_node @ C @ A ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_324_suffix__order_Odual__order_Oeq__iff,axiom,
% 3.16/1.62 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 3.16/1.62 = ( ^ [A4: list_node,B3: list_node] :
% 3.16/1.62 ( ( suffix_node @ B3 @ A4 )
% 3.16/1.62 & ( suffix_node @ A4 @ B3 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_325_suffix__order_Odual__order_Oantisym,axiom,
% 3.16/1.62 ! [B: list_node,A: list_node] :
% 3.16/1.62 ( ( suffix_node @ B @ A )
% 3.16/1.62 => ( ( suffix_node @ A @ B )
% 3.16/1.62 => ( A = B ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_326_list_Osel_I1_J,axiom,
% 3.16/1.62 ! [X21: node,X22: list_node] :
% 3.16/1.62 ( ( hd_node @ ( cons_node @ X21 @ X22 ) )
% 3.16/1.62 = X21 ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_327_finite__list,axiom,
% 3.16/1.62 ! [A2: set_node] :
% 3.16/1.62 ( ( finite_finite_node @ A2 )
% 3.16/1.62 => ? [Xs2: list_node] :
% 3.16/1.62 ( ( set_node2 @ Xs2 )
% 3.16/1.62 = A2 ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_328_finite__list,axiom,
% 3.16/1.62 ! [A2: set_val] :
% 3.16/1.62 ( ( finite_finite_val @ A2 )
% 3.16/1.62 => ? [Xs2: list_val] :
% 3.16/1.62 ( ( set_val2 @ Xs2 )
% 3.16/1.62 = A2 ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_329_subset__code_I1_J,axiom,
% 3.16/1.62 ! [Xs: list_val,B4: set_val] :
% 3.16/1.62 ( ( ord_less_eq_set_val @ ( set_val2 @ Xs ) @ B4 )
% 3.16/1.62 = ( ! [X3: val] :
% 3.16/1.62 ( ( member_val @ X3 @ ( set_val2 @ Xs ) )
% 3.16/1.62 => ( member_val @ X3 @ B4 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_330_subset__code_I1_J,axiom,
% 3.16/1.62 ! [Xs: list_node,B4: set_node] :
% 3.16/1.62 ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ B4 )
% 3.16/1.62 = ( ! [X3: node] :
% 3.16/1.62 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 3.16/1.62 => ( member_node @ X3 @ B4 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_331_set__mono__prefix,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( prefix_node @ Xs @ Ys )
% 3.16/1.62 => ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ ( set_node2 @ Ys ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_332_list_Oset__sel_I1_J,axiom,
% 3.16/1.62 ! [A: list_val] :
% 3.16/1.62 ( ( A != nil_val )
% 3.16/1.62 => ( member_val @ ( hd_val @ A ) @ ( set_val2 @ A ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_333_list_Oset__sel_I1_J,axiom,
% 3.16/1.62 ! [A: list_node] :
% 3.16/1.62 ( ( A != nil_node )
% 3.16/1.62 => ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_334_hd__in__set,axiom,
% 3.16/1.62 ! [Xs: list_val] :
% 3.16/1.62 ( ( Xs != nil_val )
% 3.16/1.62 => ( member_val @ ( hd_val @ Xs ) @ ( set_val2 @ Xs ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_335_hd__in__set,axiom,
% 3.16/1.62 ! [Xs: list_node] :
% 3.16/1.62 ( ( Xs != nil_node )
% 3.16/1.62 => ( member_node @ ( hd_node @ Xs ) @ ( set_node2 @ Xs ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_336_hd__append,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node] :
% 3.16/1.62 ( ( ( Xs = nil_node )
% 3.16/1.62 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 3.16/1.62 = ( hd_node @ Ys ) ) )
% 3.16/1.62 & ( ( Xs != nil_node )
% 3.16/1.62 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 3.16/1.62 = ( hd_node @ Xs ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_337_longest__common__prefix,axiom,
% 3.16/1.62 ! [Xs: list_node,Ys: list_node] :
% 3.16/1.62 ? [Ps: list_node,Xs6: list_node,Ys4: list_node] :
% 3.16/1.62 ( ( Xs
% 3.16/1.62 = ( append_node @ Ps @ Xs6 ) )
% 3.16/1.62 & ( Ys
% 3.16/1.62 = ( append_node @ Ps @ Ys4 ) )
% 3.16/1.62 & ( ( Xs6 = nil_node )
% 3.16/1.62 | ( Ys4 = nil_node )
% 3.16/1.62 | ( ( hd_node @ Xs6 )
% 3.16/1.62 != ( hd_node @ Ys4 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_338_not__suffix__cases,axiom,
% 3.16/1.62 ! [Ps2: list_node,Ls: list_node] :
% 3.16/1.62 ( ~ ( suffix_node @ Ps2 @ Ls )
% 3.16/1.62 => ( ( ( Ps2 != nil_node )
% 3.16/1.62 => ( Ls != nil_node ) )
% 3.16/1.62 => ( ! [A3: node,As: list_node] :
% 3.16/1.62 ( ( Ps2
% 3.16/1.62 = ( append_node @ As @ ( cons_node @ A3 @ nil_node ) ) )
% 3.16/1.62 => ! [X4: node,Xs2: list_node] :
% 3.16/1.62 ( ( Ls
% 3.16/1.62 = ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) )
% 3.16/1.62 => ( ( X4 = A3 )
% 3.16/1.62 => ( suffix_node @ As @ Xs2 ) ) ) )
% 3.16/1.62 => ~ ! [A3: node] :
% 3.16/1.62 ( ? [As: list_node] :
% 3.16/1.62 ( Ps2
% 3.16/1.62 = ( append_node @ As @ ( cons_node @ A3 @ nil_node ) ) )
% 3.16/1.62 => ! [X4: node] :
% 3.16/1.62 ( ? [Xs2: list_node] :
% 3.16/1.62 ( Ls
% 3.16/1.62 = ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) )
% 3.16/1.62 => ( X4 = A3 ) ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_339_not__suffix__induct,axiom,
% 3.16/1.62 ! [Ps2: list_node,Ls: list_node,P: list_node > list_node > $o] :
% 3.16/1.62 ( ~ ( suffix_node @ Ps2 @ Ls )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ nil_node )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 3.16/1.62 ( ( X4 != Y2 )
% 3.16/1.62 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) )
% 3.16/1.62 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 3.16/1.62 ( ( X4 = Y2 )
% 3.16/1.62 => ( ~ ( suffix_node @ Xs2 @ Ys2 )
% 3.16/1.62 => ( ( P @ Xs2 @ Ys2 )
% 3.16/1.62 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) ) ) )
% 3.16/1.62 => ( P @ Ps2 @ Ls ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_340_list_Oexpand,axiom,
% 3.16/1.62 ! [List: list_node,List2: list_node] :
% 3.16/1.62 ( ( ( List = nil_node )
% 3.16/1.62 = ( List2 = nil_node ) )
% 3.16/1.62 => ( ( ( List != nil_node )
% 3.16/1.62 => ( ( List2 != nil_node )
% 3.16/1.62 => ( ( ( hd_node @ List )
% 3.16/1.62 = ( hd_node @ List2 ) )
% 3.16/1.62 & ( ( tl_node @ List )
% 3.16/1.62 = ( tl_node @ List2 ) ) ) ) )
% 3.16/1.62 => ( List = List2 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_341_not__hd__in__tl,axiom,
% 3.16/1.62 ! [X: val,Xs: list_val] :
% 3.16/1.62 ( ( X
% 3.16/1.62 != ( hd_val @ Xs ) )
% 3.16/1.62 => ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 3.16/1.62 => ( member_val @ X @ ( set_val2 @ ( tl_val @ Xs ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_342_not__hd__in__tl,axiom,
% 3.16/1.62 ! [X: node,Xs: list_node] :
% 3.16/1.62 ( ( X
% 3.16/1.62 != ( hd_node @ Xs ) )
% 3.16/1.62 => ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 3.16/1.62 => ( member_node @ X @ ( set_node2 @ ( tl_node @ Xs ) ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_343_set__subset__Cons,axiom,
% 3.16/1.62 ! [Xs: list_node,X: node] : ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ ( set_node2 @ ( cons_node @ X @ Xs ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_344_list_Oexhaust__sel,axiom,
% 3.16/1.62 ! [List: list_node] :
% 3.16/1.62 ( ( List != nil_node )
% 3.16/1.62 => ( List
% 3.16/1.62 = ( cons_node @ ( hd_node @ List ) @ ( tl_node @ List ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_345_tl__subset,axiom,
% 3.16/1.62 ! [Xs: list_node,A2: set_node] :
% 3.16/1.62 ( ( Xs != nil_node )
% 3.16/1.62 => ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ A2 )
% 3.16/1.62 => ( ord_less_eq_set_node @ ( set_node2 @ ( tl_node @ Xs ) ) @ A2 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_346_butlast__subset,axiom,
% 3.16/1.62 ! [Xs: list_node,A2: set_node] :
% 3.16/1.62 ( ( Xs != nil_node )
% 3.16/1.62 => ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ A2 )
% 3.16/1.62 => ( ord_less_eq_set_node @ ( set_node2 @ ( butlast_node @ Xs ) ) @ A2 ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_347_prefix__same__cases,axiom,
% 3.16/1.62 ! [Xs_1: list_node,Ys: list_node,Xs_2: list_node] :
% 3.16/1.62 ( ( prefix_node @ Xs_1 @ Ys )
% 3.16/1.62 => ( ( prefix_node @ Xs_2 @ Ys )
% 3.16/1.62 => ( ( prefix_node @ Xs_1 @ Xs_2 )
% 3.16/1.62 | ( prefix_node @ Xs_2 @ Xs_1 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_348_prefix__order_Oeq__iff,axiom,
% 3.16/1.62 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 3.16/1.62 = ( ^ [X3: list_node,Y3: list_node] :
% 3.16/1.62 ( ( prefix_node @ X3 @ Y3 )
% 3.16/1.62 & ( prefix_node @ Y3 @ X3 ) ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(fact_349_prefix__order_Oantisym,axiom,
% 3.16/1.62 ! [X: list_node,Y: list_node] :
% 3.16/1.62 ( ( prefix_node @ X @ Y )
% 3.16/1.62 => ( ( prefix_node @ Y @ X )
% 3.16/1.62 => ( X = Y ) ) ) ).
% 3.16/1.62
% 3.16/1.62 thf(conj_0,conjecture,
% 3.16/1.62 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ).
% 3.16/1.62 ------------------------
% 3.16/1.65 % (20841)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20632 for (2999ds/183Mi)
% 3.16/1.65 % (20843)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_20632 for (2999ds/27Mi)
% 3.16/1.65 % (20845)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_20632 for (2999ds/2Mi)
% 3.16/1.65 % (20847)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20632 for (2999ds/18Mi)
% 3.16/1.65 % (20844)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20632 for (2999ds/2Mi)
% 3.16/1.65 % (20845)Instruction limit reached!
% 3.16/1.65 % (20845)------------------------------
% 3.16/1.65 % (20845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.65 % (20845)Termination reason: Unknown
% 3.16/1.65 % (20845)Termination phase: shuffling
% 3.16/1.65
% 3.16/1.65 % (20845)Memory used [KB]: 1535
% 3.16/1.65 % (20845)Time elapsed: 0.004 s
% 3.16/1.65 % (20845)Instructions burned: 4 (million)
% 3.16/1.65 % (20845)------------------------------
% 3.16/1.65 % (20845)------------------------------
% 3.16/1.65 % (20846)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_20632 for (2999ds/275Mi)
% 3.16/1.65 % (20844)Instruction limit reached!
% 3.16/1.65 % (20844)------------------------------
% 3.16/1.65 % (20844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.65 % (20844)Termination reason: Unknown
% 3.16/1.65 % (20844)Termination phase: shuffling
% 3.16/1.65
% 3.16/1.65 % (20844)Memory used [KB]: 1535
% 3.16/1.65 % (20844)Time elapsed: 0.003 s
% 3.16/1.65 % (20844)Instructions burned: 3 (million)
% 3.16/1.65 % (20844)------------------------------
% 3.16/1.65 % (20844)------------------------------
% 3.16/1.66 % (20843)Instruction limit reached!
% 3.16/1.66 % (20843)------------------------------
% 3.16/1.66 % (20843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.66 % (20843)Termination reason: Unknown
% 3.16/1.66 % (20843)Termination phase: shuffling
% 3.16/1.66
% 3.16/1.66 % (20843)Memory used [KB]: 1918
% 3.16/1.66 % (20843)Time elapsed: 0.012 s
% 3.16/1.66 % (20843)Instructions burned: 29 (million)
% 3.16/1.66 % (20843)------------------------------
% 3.16/1.66 % (20843)------------------------------
% 3.16/1.66 % (20847)Instruction limit reached!
% 3.16/1.66 % (20847)------------------------------
% 3.16/1.66 % (20847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.66 % (20847)Termination reason: Unknown
% 3.16/1.66 % (20847)Termination phase: shuffling
% 3.16/1.66
% 3.16/1.66 % (20847)Memory used [KB]: 1791
% 3.16/1.66 % (20847)Time elapsed: 0.009 s
% 3.16/1.66 % (20847)Instructions burned: 19 (million)
% 3.16/1.66 % (20847)------------------------------
% 3.16/1.66 % (20847)------------------------------
% 3.16/1.66 % (20842)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_20632 for (2999ds/4Mi)
% 3.16/1.66 % (20849)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_20632 for (2999ds/37Mi)
% 3.16/1.67 % (20842)Instruction limit reached!
% 3.16/1.67 % (20842)------------------------------
% 3.16/1.67 % (20842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.67 % (20842)Termination reason: Unknown
% 3.16/1.67 % (20842)Termination phase: shuffling
% 3.16/1.67
% 3.16/1.67 % (20842)Memory used [KB]: 1663
% 3.16/1.67 % (20842)Time elapsed: 0.004 s
% 3.16/1.67 % (20842)Instructions burned: 5 (million)
% 3.16/1.67 % (20842)------------------------------
% 3.16/1.67 % (20842)------------------------------
% 3.16/1.67 % (20848)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20632 for (2999ds/3Mi)
% 3.16/1.67 % (20848)Instruction limit reached!
% 3.16/1.67 % (20848)------------------------------
% 3.16/1.67 % (20848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.67 % (20848)Termination reason: Unknown
% 3.16/1.67 % (20848)Termination phase: shuffling
% 3.16/1.67
% 3.16/1.67 % (20848)Memory used [KB]: 1535
% 3.16/1.67 % (20848)Time elapsed: 0.004 s
% 3.16/1.67 % (20848)Instructions burned: 6 (million)
% 3.16/1.67 % (20848)------------------------------
% 3.16/1.67 % (20848)------------------------------
% 3.16/1.67 % (20851)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_20632 for (2999ds/3Mi)
% 3.16/1.67 % (20851)Instruction limit reached!
% 3.16/1.67 % (20851)------------------------------
% 3.16/1.67 % (20851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.67 % (20851)Termination reason: Unknown
% 3.16/1.67 % (20851)Termination phase: shuffling
% 3.16/1.67
% 3.16/1.67 % (20851)Memory used [KB]: 1535
% 3.16/1.67 % (20851)Time elapsed: 0.003 s
% 3.16/1.67 % (20851)Instructions burned: 6 (million)
% 3.16/1.67 % (20851)------------------------------
% 3.16/1.67 % (20851)------------------------------
% 3.16/1.68 % (20850)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_20632 for (2999ds/15Mi)
% 3.16/1.68 % (20852)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_20632 for (2999ds/1041Mi)
% 3.16/1.68 % (20849)Instruction limit reached!
% 3.16/1.68 % (20849)------------------------------
% 3.16/1.68 % (20849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.68 % (20849)Termination reason: Unknown
% 3.16/1.68 % (20849)Termination phase: shuffling
% 3.16/1.68
% 3.16/1.68 % (20849)Memory used [KB]: 2302
% 3.16/1.68 % (20849)Time elapsed: 0.014 s
% 3.16/1.68 % (20849)Instructions burned: 40 (million)
% 3.16/1.68 % (20849)------------------------------
% 3.16/1.68 % (20849)------------------------------
% 3.16/1.68 % (20853)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20632 for (2999ds/7Mi)
% 3.16/1.68 % (20853)Instruction limit reached!
% 3.16/1.68 % (20853)------------------------------
% 3.16/1.68 % (20853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.68 % (20853)Termination reason: Unknown
% 3.16/1.68 % (20853)Termination phase: shuffling
% 3.16/1.68
% 3.16/1.68 % (20853)Memory used [KB]: 1663
% 3.16/1.68 % (20853)Time elapsed: 0.004 s
% 3.16/1.68 % (20853)Instructions burned: 9 (million)
% 3.16/1.68 % (20853)------------------------------
% 3.16/1.68 % (20853)------------------------------
% 3.16/1.68 % (20854)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20632 for (2999ds/16Mi)
% 3.16/1.68 % (20850)Instruction limit reached!
% 3.16/1.68 % (20850)------------------------------
% 3.16/1.68 % (20850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.68 % (20850)Termination reason: Unknown
% 3.16/1.68 % (20850)Termination phase: shuffling
% 3.16/1.68
% 3.16/1.68 % (20850)Memory used [KB]: 1791
% 3.16/1.68 % (20850)Time elapsed: 0.010 s
% 3.16/1.68 % (20850)Instructions burned: 15 (million)
% 3.16/1.68 % (20850)------------------------------
% 3.16/1.68 % (20850)------------------------------
% 3.16/1.69 % (20855)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_20632 for (2999ds/3Mi)
% 3.16/1.69 % (20855)Instruction limit reached!
% 3.16/1.69 % (20855)------------------------------
% 3.16/1.69 % (20855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.69 % (20855)Termination reason: Unknown
% 3.16/1.69 % (20855)Termination phase: shuffling
% 3.16/1.69
% 3.16/1.69 % (20855)Memory used [KB]: 1535
% 3.16/1.69 % (20855)Time elapsed: 0.002 s
% 3.16/1.69 % (20855)Instructions burned: 3 (million)
% 3.16/1.69 % (20855)------------------------------
% 3.16/1.69 % (20855)------------------------------
% 3.16/1.69 % (20854)Instruction limit reached!
% 3.16/1.69 % (20854)------------------------------
% 3.16/1.69 % (20854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.69 % (20854)Termination reason: Unknown
% 3.16/1.69 % (20854)Termination phase: shuffling
% 3.16/1.69
% 3.16/1.69 % (20854)Memory used [KB]: 1791
% 3.16/1.69 % (20854)Time elapsed: 0.009 s
% 3.16/1.69 % (20854)Instructions burned: 16 (million)
% 3.16/1.69 % (20854)------------------------------
% 3.16/1.69 % (20854)------------------------------
% 3.16/1.69 % (20857)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_20632 for (2999ds/3Mi)
% 3.16/1.69 % (20857)Instruction limit reached!
% 3.16/1.69 % (20857)------------------------------
% 3.16/1.69 % (20857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.69 % (20857)Termination reason: Unknown
% 3.16/1.69 % (20857)Termination phase: shuffling
% 3.16/1.69
% 3.16/1.69 % (20857)Memory used [KB]: 1535
% 3.16/1.69 % (20857)Time elapsed: 0.002 s
% 3.16/1.69 % (20857)Instructions burned: 3 (million)
% 3.16/1.69 % (20857)------------------------------
% 3.16/1.69 % (20857)------------------------------
% 3.20/1.70 % (20859)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20632 for (2999ds/3Mi)
% 3.20/1.70 % (20858)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20632 for (2999ds/7Mi)
% 3.20/1.70 % (20859)Instruction limit reached!
% 3.20/1.70 % (20859)------------------------------
% 3.20/1.70 % (20859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.70 % (20859)Termination reason: Unknown
% 3.20/1.70 % (20859)Termination phase: shuffling
% 3.20/1.70
% 3.20/1.70 % (20859)Memory used [KB]: 1663
% 3.20/1.70 % (20859)Time elapsed: 0.003 s
% 3.20/1.70 % (20859)Instructions burned: 5 (million)
% 3.20/1.70 % (20859)------------------------------
% 3.20/1.70 % (20859)------------------------------
% 3.20/1.70 % (20858)Instruction limit reached!
% 3.20/1.70 % (20858)------------------------------
% 3.20/1.70 % (20858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.70 % (20858)Termination reason: Unknown
% 3.20/1.70 % (20858)Termination phase: shuffling
% 3.20/1.70
% 3.20/1.70 % (20858)Memory used [KB]: 1535
% 3.20/1.70 % (20858)Time elapsed: 0.004 s
% 3.20/1.70 % (20858)Instructions burned: 7 (million)
% 3.20/1.70 % (20858)------------------------------
% 3.20/1.70 % (20858)------------------------------
% 3.20/1.70 % (20861)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20632 for (2999ds/18Mi)
% 3.20/1.70 % (20860)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20632 for (2999ds/4Mi)
% 3.20/1.70 % (20841)Instruction limit reached!
% 3.20/1.70 % (20841)------------------------------
% 3.20/1.70 % (20841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.70 % (20841)Termination reason: Unknown
% 3.20/1.70 % (20841)Termination phase: Saturation
% 3.20/1.70
% 3.20/1.70 % (20841)Memory used [KB]: 7547
% 3.20/1.70 % (20841)Time elapsed: 0.057 s
% 3.20/1.70 % (20841)Instructions burned: 185 (million)
% 3.20/1.70 % (20841)------------------------------
% 3.20/1.70 % (20841)------------------------------
% 3.20/1.70 % (20860)Instruction limit reached!
% 3.20/1.70 % (20860)------------------------------
% 3.20/1.70 % (20860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.70 % (20860)Termination reason: Unknown
% 3.20/1.70 % (20860)Termination phase: shuffling
% 3.20/1.70
% 3.20/1.70 % (20860)Memory used [KB]: 1535
% 3.20/1.70 % (20860)Time elapsed: 0.003 s
% 3.20/1.70 % (20860)Instructions burned: 5 (million)
% 3.20/1.70 % (20860)------------------------------
% 3.20/1.70 % (20860)------------------------------
% 3.20/1.71 % (20861)Instruction limit reached!
% 3.20/1.71 % (20861)------------------------------
% 3.20/1.71 % (20861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.71 % (20861)Termination reason: Unknown
% 3.20/1.71 % (20861)Termination phase: shuffling
% 3.20/1.71
% 3.20/1.71 % (20861)Memory used [KB]: 1791
% 3.20/1.71 % (20861)Time elapsed: 0.007 s
% 3.20/1.71 % (20861)Instructions burned: 18 (million)
% 3.20/1.71 % (20861)------------------------------
% 3.20/1.71 % (20861)------------------------------
% 3.20/1.71 % (20862)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20632 for (2999ds/710Mi)
% 3.20/1.71 % (20863)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20632 for (2999ds/6Mi)
% 3.20/1.71 % (20863)Instruction limit reached!
% 3.20/1.71 % (20863)------------------------------
% 3.20/1.71 % (20863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.71 % (20863)Termination reason: Unknown
% 3.20/1.71 % (20863)Termination phase: shuffling
% 3.20/1.71
% 3.20/1.71 % (20863)Memory used [KB]: 1535
% 3.20/1.71 % (20863)Time elapsed: 0.003 s
% 3.20/1.71 % (20863)Instructions burned: 6 (million)
% 3.20/1.71 % (20863)------------------------------
% 3.20/1.71 % (20863)------------------------------
% 3.20/1.71 % (20865)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_20632 for (2999ds/21Mi)
% 3.20/1.71 % (20864)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_20632 for (2999ds/902Mi)
% 3.20/1.71 % (20846)First to succeed.
% 3.20/1.72 % (20866)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20632 for (2999ds/5Mi)
% 3.20/1.72 % (20846)Refutation found. Thanks to Tanya!
% 3.20/1.72 % SZS status Theorem for DTF2THF_20632
% 3.20/1.72 % SZS output start Proof for DTF2THF_20632
% 3.20/1.72 thf(type_def_5, type, set_node: $tType).
% 3.20/1.72 thf(type_def_7, type, set_val: $tType).
% 3.20/1.72 thf(type_def_8, type, g: $tType).
% 3.20/1.72 thf(type_def_9, type, list_node: $tType).
% 3.20/1.72 thf(type_def_10, type, node: $tType).
% 3.20/1.72 thf(type_def_11, type, list_P561207620_edgeD: $tType).
% 3.20/1.72 thf(type_def_12, type, list_list_node: $tType).
% 3.20/1.72 thf(type_def_13, type, list_val: $tType).
% 3.20/1.72 thf(type_def_14, type, val: $tType).
% 3.20/1.72 thf(type_def_15, type, set_list_node: $tType).
% 3.20/1.72 thf(type_def_16, type, produc1432036078de_val: $tType).
% 3.20/1.72 thf(type_def_17, type, option_list_val: $tType).
% 3.20/1.72 thf(func_def_0, type, list_P561207620_edgeD: $tType).
% 3.20/1.72 thf(func_def_1, type, option_list_val: $tType).
% 3.20/1.72 thf(func_def_2, type, produc1432036078de_val: $tType).
% 3.20/1.72 thf(func_def_3, type, list_list_node: $tType).
% 3.20/1.72 thf(func_def_4, type, set_list_node: $tType).
% 3.20/1.72 thf(func_def_5, type, list_node: $tType).
% 3.20/1.72 thf(func_def_6, type, list_val: $tType).
% 3.20/1.72 thf(func_def_7, type, set_node: $tType).
% 3.20/1.72 thf(func_def_8, type, set_val: $tType).
% 3.20/1.72 thf(func_def_9, type, node: $tType).
% 3.20/1.72 thf(func_def_10, type, val: $tType).
% 3.20/1.72 thf(func_def_11, type, g: $tType).
% 3.20/1.72 thf(func_def_12, type, finite_finite_node: set_node > $o).
% 3.20/1.72 thf(func_def_13, type, finite_finite_val: set_val > $o).
% 3.20/1.72 thf(func_def_14, type, graph_1012773594_edgeD: (g > list_node) > (g > $o) > (g > node > list_P561207620_edgeD) > g > node > list_node > node > $o).
% 3.20/1.72 thf(func_def_15, type, graph_435229452_edgeD: (g > list_node) > (g > $o) > (g > node > list_P561207620_edgeD) > g > list_node > $o).
% 3.20/1.72 thf(func_def_16, type, graph_272749361_edgeD: (g > node > list_P561207620_edgeD) > g > node > list_node).
% 3.20/1.72 thf(func_def_17, type, append_list_node: list_list_node > list_list_node > list_list_node).
% 3.20/1.72 thf(func_def_18, type, append_node: list_node > list_node > list_node).
% 3.20/1.72 thf(func_def_19, type, append_val: list_val > list_val > list_val).
% 3.20/1.72 thf(func_def_20, type, butlast_list_node: list_list_node > list_list_node).
% 3.20/1.72 thf(func_def_21, type, butlast_node: list_node > list_node).
% 3.20/1.72 thf(func_def_22, type, butlast_val: list_val > list_val).
% 3.20/1.72 thf(func_def_23, type, cons_list_node: list_node > list_list_node > list_list_node).
% 3.20/1.72 thf(func_def_24, type, cons_node: node > list_node > list_node).
% 3.20/1.72 thf(func_def_25, type, cons_val: val > list_val > list_val).
% 3.20/1.72 thf(func_def_26, type, nil_list_node: list_list_node).
% 3.20/1.72 thf(func_def_27, type, nil_node: list_node).
% 3.20/1.72 thf(func_def_28, type, nil_val: list_val).
% 3.20/1.72 thf(func_def_29, type, hd_node: list_node > node).
% 3.20/1.72 thf(func_def_30, type, hd_val: list_val > val).
% 3.20/1.72 thf(func_def_31, type, set_list_node2: list_list_node > set_list_node).
% 3.20/1.72 thf(func_def_32, type, set_node2: list_node > set_node).
% 3.20/1.72 thf(func_def_33, type, set_val2: list_val > set_val).
% 3.20/1.72 thf(func_def_34, type, tl_list_node: list_list_node > list_list_node).
% 3.20/1.72 thf(func_def_35, type, tl_node: list_node > list_node).
% 3.20/1.72 thf(func_def_36, type, tl_val: list_val > list_val).
% 3.20/1.72 thf(func_def_37, type, ord_less_eq_set_node: set_node > set_node > $o).
% 3.20/1.72 thf(func_def_38, type, ord_less_eq_set_val: set_val > set_val > $o).
% 3.20/1.72 thf(func_def_39, type, sSA_CF848637139eD_val: (g > list_node) > (g > node > list_P561207620_edgeD) > (g > produc1432036078de_val > option_list_val) > g > node > set_val).
% 3.20/1.72 thf(func_def_40, type, sSA_CF551432799de_val: (g > list_node) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > val > node).
% 3.20/1.72 thf(func_def_41, type, sSA_CF1252180629de_val: (g > list_node) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > val > val > $o).
% 3.20/1.72 thf(func_def_42, type, collect_node: (node > $o) > set_node).
% 3.20/1.72 thf(func_def_43, type, collect_val: (val > $o) > set_val).
% 3.20/1.72 thf(func_def_44, type, prefix_node: list_node > list_node > $o).
% 3.20/1.72 thf(func_def_45, type, suffix_node: list_node > list_node > $o).
% 3.20/1.72 thf(func_def_46, type, member_list_node: list_node > set_list_node > $o).
% 3.20/1.72 thf(func_def_47, type, member_node: node > set_node > $o).
% 3.20/1.72 thf(func_def_48, type, member_val: val > set_val > $o).
% 3.20/1.72 thf(func_def_49, type, alpha_n: g > list_node).
% 3.20/1.72 thf(func_def_50, type, phi_r: val).
% 3.20/1.72 thf(func_def_51, type, defs: g > node > set_val).
% 3.20/1.72 thf(func_def_52, type, g2: g).
% 3.20/1.72 thf(func_def_53, type, i: node).
% 3.20/1.72 thf(func_def_54, type, inEdges: g > node > list_P561207620_edgeD).
% 3.20/1.72 thf(func_def_55, type, invar: g > $o).
% 3.20/1.72 thf(func_def_56, type, m: node).
% 3.20/1.72 thf(func_def_57, type, ms: list_node).
% 3.20/1.72 thf(func_def_58, type, ms2: list_node).
% 3.20/1.72 thf(func_def_59, type, n: node).
% 3.20/1.72 thf(func_def_60, type, ns: list_node).
% 3.20/1.72 thf(func_def_61, type, phis: g > produc1432036078de_val > option_list_val).
% 3.20/1.72 thf(func_def_62, type, pred_phi_r: node).
% 3.20/1.72 thf(func_def_63, type, r: val).
% 3.20/1.72 thf(func_def_64, type, ri: list_node).
% 3.20/1.72 thf(func_def_65, type, rs: list_node).
% 3.20/1.72 thf(func_def_66, type, rs2: list_node).
% 3.20/1.72 thf(func_def_67, type, s: val).
% 3.20/1.72 thf(func_def_78, type, sP0: (list_node > list_node > $o) > $o).
% 3.20/1.72 thf(func_def_79, type, sP1: list_node > list_node > $o).
% 3.20/1.72 thf(func_def_80, type, sP2: (list_node > list_node > $o) > (node > node > $o) > $o).
% 3.20/1.72 thf(func_def_81, type, sP3: list_node > list_node > node > node > list_node > list_node > $o).
% 3.20/1.72 thf(func_def_82, type, sK4: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_83, type, sK5: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_84, type, sK6: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_85, type, sK7: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_86, type, sK8: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_87, type, sK9: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_88, type, sK10: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_89, type, sK11: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_90, type, sK12: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_91, type, sK13: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_92, type, sK14: node > list_node > list_node).
% 3.20/1.72 thf(func_def_93, type, sK15: node > list_node > list_node).
% 3.20/1.72 thf(func_def_94, type, sK16: node > node > list_node > list_node).
% 3.20/1.72 thf(func_def_95, type, sK17: node > node > list_node > list_node).
% 3.20/1.72 thf(func_def_96, type, sK18: node > node > list_node > list_node).
% 3.20/1.72 thf(func_def_97, type, sK19: node > node > list_node > list_node).
% 3.20/1.72 thf(func_def_98, type, sK20: node > node > list_node > list_node).
% 3.20/1.72 thf(func_def_99, type, sK21: node > node > list_node > list_node).
% 3.20/1.72 thf(func_def_100, type, sK22: ((node > node > $o) > list_node > list_node > $o) > node > node > $o).
% 3.20/1.72 thf(func_def_101, type, sK23: ((node > node > $o) > list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_102, type, sK24: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_103, type, sK25: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_104, type, sK26: ((node > node > $o) > list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_105, type, sK27: ((node > node > $o) > list_node > list_node > $o) > node > node > $o).
% 3.20/1.72 thf(func_def_106, type, sK28: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_107, type, sK29: ((node > node > $o) > list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_108, type, sK30: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_109, type, sK31: ((node > node > $o) > list_node > list_node > $o) > node > node > $o).
% 3.20/1.72 thf(func_def_110, type, sK32: node > list_node > list_node).
% 3.20/1.72 thf(func_def_111, type, sK33: node > list_node > list_node).
% 3.20/1.72 thf(func_def_112, type, sK34: ((node > node > $o) > list_node > $o) > node > node > $o).
% 3.20/1.72 thf(func_def_113, type, sK35: ((node > node > $o) > list_node > $o) > node).
% 3.20/1.72 thf(func_def_114, type, sK36: ((node > node > $o) > list_node > $o) > node > node > $o).
% 3.20/1.72 thf(func_def_115, type, sK37: ((node > node > $o) > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_116, type, sK38: ((node > node > $o) > list_node > $o) > node > node > $o).
% 3.20/1.72 thf(func_def_117, type, sK39: ((node > node > $o) > list_node > $o) > node).
% 3.20/1.72 thf(func_def_118, type, sK40: ((node > node > $o) > list_node > $o) > node).
% 3.20/1.72 thf(func_def_119, type, sK41: list_node > list_node > list_node > list_node).
% 3.20/1.72 thf(func_def_120, type, sK42: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_121, type, sK43: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_122, type, sK44: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_123, type, sK45: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_124, type, sK46: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_125, type, sK47: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_126, type, sK48: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_127, type, sK49: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_128, type, sK50: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_129, type, sK51: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_130, type, sK52: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_131, type, sK53: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_132, type, sK54: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_133, type, sK55: (list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_134, type, sK56: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_135, type, sK57: list_node > (node > $o) > node).
% 3.20/1.72 thf(func_def_136, type, sK58: list_node > (node > $o) > node).
% 3.20/1.72 thf(func_def_137, type, sK59: list_node > (node > $o) > list_node).
% 3.20/1.72 thf(func_def_138, type, sK60: list_node > (node > $o) > node).
% 3.20/1.72 thf(func_def_139, type, sK61: list_node > (node > $o) > list_node).
% 3.20/1.72 thf(func_def_140, type, sK62: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_141, type, sK63: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_142, type, sK64: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_143, type, sK65: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_144, type, sK66: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_145, type, sK67: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_146, type, sK68: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_147, type, sK69: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_148, type, sK70: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_149, type, sK71: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_150, type, sK72: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_151, type, sK73: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_152, type, sK74: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_153, type, sK75: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_154, type, sK76: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_155, type, sK77: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_156, type, sK78: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_157, type, sK79: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_158, type, sK80: list_node > (node > $o) > node).
% 3.20/1.72 thf(func_def_159, type, sK81: list_node > (node > $o) > list_node).
% 3.20/1.72 thf(func_def_160, type, sK82: list_node > (node > $o) > list_node).
% 3.20/1.72 thf(func_def_161, type, sK83: list_node > node > list_node).
% 3.20/1.72 thf(func_def_162, type, sK84: list_node > node > list_node).
% 3.20/1.72 thf(func_def_163, type, sK85: list_node > list_node > node > node).
% 3.20/1.72 thf(func_def_164, type, sK86: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_165, type, sK87: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_166, type, sK88: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_167, type, sK89: (list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_168, type, sK90: list_node > (node > $o) > node).
% 3.20/1.72 thf(func_def_169, type, sK91: list_node > (node > $o) > list_node).
% 3.20/1.72 thf(func_def_170, type, sK92: list_node > (node > $o) > list_node).
% 3.20/1.72 thf(func_def_171, type, sK93: (list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_172, type, sK94: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_173, type, sK95: node > node > g > list_node > node > list_node).
% 3.20/1.72 thf(func_def_174, type, sK96: node > node > g > list_node > node > list_node).
% 3.20/1.72 thf(func_def_175, type, sK97: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_176, type, sK98: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_177, type, sK99: (list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_178, type, sK100: (list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_179, type, sK101: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_180, type, sK102: node > list_node > list_node > list_node > list_node).
% 3.20/1.72 thf(func_def_181, type, sK103: node > node > g > list_node > list_node).
% 3.20/1.72 thf(func_def_182, type, sK104: list_node > node).
% 3.20/1.72 thf(func_def_183, type, sK105: list_node > list_node).
% 3.20/1.72 thf(func_def_184, type, sK106: list_node > node).
% 3.20/1.72 thf(func_def_185, type, sK107: list_node).
% 3.20/1.72 thf(func_def_186, type, sK108: node).
% 3.20/1.72 thf(func_def_187, type, sK109: list_node > node).
% 3.20/1.72 thf(func_def_188, type, sK110: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_189, type, sK111: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_190, type, sK112: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_191, type, sK113: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_192, type, sK114: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_193, type, sK115: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_194, type, sK116: list_node > list_node > node).
% 3.20/1.72 thf(func_def_195, type, sK117: list_node > list_node > list_node).
% 3.20/1.72 thf(func_def_196, type, sK118: list_node > list_node > list_node).
% 3.20/1.72 thf(func_def_197, type, sK119: list_node > list_node > node).
% 3.20/1.72 thf(func_def_198, type, sK120: list_node > list_node > node).
% 3.20/1.72 thf(func_def_199, type, sK121: list_node > list_node > list_node).
% 3.20/1.72 thf(func_def_200, type, sK122: list_node > list_node > node).
% 3.20/1.72 thf(func_def_201, type, sK123: list_node > list_node > list_node).
% 3.20/1.72 thf(func_def_202, type, sK124: list_node > (node > $o) > list_node).
% 3.20/1.72 thf(func_def_203, type, sK125: list_node > (node > $o) > node).
% 3.20/1.72 thf(func_def_204, type, sK126: list_node > (node > $o) > list_node).
% 3.20/1.72 thf(func_def_205, type, sK127: list_node > (node > $o) > node).
% 3.20/1.72 thf(func_def_206, type, sK128: list_node > (node > $o) > node).
% 3.20/1.72 thf(func_def_207, type, sK129: list_node > (node > $o) > list_node).
% 3.20/1.72 thf(func_def_208, type, sK130: list_node > (node > $o) > list_node).
% 3.20/1.72 thf(func_def_209, type, sK131: list_node > (node > $o) > node).
% 3.20/1.72 thf(func_def_210, type, sK132: list_node > node).
% 3.20/1.72 thf(func_def_211, type, sK133: list_node > node).
% 3.20/1.72 thf(func_def_212, type, sK134: list_node > list_node).
% 3.20/1.72 thf(func_def_213, type, sK135: list_node > node).
% 3.20/1.72 thf(func_def_214, type, sK136: node > list_node > list_node > list_node > list_node).
% 3.20/1.72 thf(func_def_215, type, sK137: list_node > node > list_node).
% 3.20/1.72 thf(func_def_216, type, sK138: list_node > node > list_node).
% 3.20/1.72 thf(func_def_217, type, sK139: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_218, type, sK140: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_219, type, sK141: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_220, type, sK142: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_221, type, sK143: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_222, type, sK144: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_223, type, sK145: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_224, type, sK146: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_225, type, sK147: list_node > node).
% 3.20/1.72 thf(func_def_226, type, sK148: list_node > list_node).
% 3.20/1.72 thf(func_def_227, type, sK149: list_node > list_node).
% 3.20/1.72 thf(func_def_228, type, sK150: list_node > node).
% 3.20/1.72 thf(func_def_229, type, sK151: list_node > node > g > (node > $o) > list_node).
% 3.20/1.72 thf(func_def_230, type, sK152: list_node > node > g > (node > $o) > node).
% 3.20/1.72 thf(func_def_231, type, sK153: ((node > node) > list_node > list_node > $o) > node > node).
% 3.20/1.72 thf(func_def_232, type, sK154: ((node > node) > list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_233, type, sK155: ((node > node) > list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_234, type, sK156: ((node > node) > list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_235, type, sK157: ((node > node) > list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_236, type, sK158: ((node > node) > list_node > list_node > $o) > node > node).
% 3.20/1.72 thf(func_def_237, type, sK159: list_node > node > list_node > list_node > list_node).
% 3.20/1.72 thf(func_def_238, type, sK160: ((node > node > $o) > list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_239, type, sK161: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_240, type, sK162: ((node > node > $o) > list_node > list_node > $o) > node > node > $o).
% 3.20/1.72 thf(func_def_241, type, sK163: ((node > node > $o) > list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_242, type, sK164: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_243, type, sK165: ((node > node > $o) > list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_244, type, sK166: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_245, type, sK167: ((node > node > $o) > list_node > list_node > $o) > node > node > $o).
% 3.20/1.72 thf(func_def_246, type, sK168: ((node > node > $o) > list_node > list_node > $o) > node > node > $o).
% 3.20/1.72 thf(func_def_247, type, sK169: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_248, type, sK170: ((node > node > $o) > list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_249, type, sK171: ((node > node > $o) > list_node > list_node > $o) > node > node > $o).
% 3.20/1.72 thf(func_def_250, type, sK172: (list_node > list_node > $o) > (node > node > $o) > node).
% 3.20/1.72 thf(func_def_251, type, sK173: (list_node > list_node > $o) > (node > node > $o) > list_node).
% 3.20/1.72 thf(func_def_252, type, sK174: (list_node > list_node > $o) > (node > node > $o) > node).
% 3.20/1.72 thf(func_def_253, type, sK175: (list_node > list_node > $o) > (node > node > $o) > list_node).
% 3.20/1.72 thf(func_def_254, type, sK176: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_255, type, sK177: (node > node > $o) > (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_256, type, sK178: (node > node > $o) > (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_257, type, sK179: (node > node > $o) > (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_258, type, sK180: (node > node > $o) > (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_259, type, sK181: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_260, type, sK182: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_261, type, sK183: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_262, type, sK184: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_263, type, sK185: (list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_264, type, sK186: node > list_node > list_node).
% 3.20/1.72 thf(func_def_265, type, sK187: node > list_node > list_node).
% 3.20/1.72 thf(func_def_266, type, sK188: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_267, type, sK189: (list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_268, type, sK190: (node > $o) > list_node > list_node).
% 3.20/1.72 thf(func_def_269, type, sK191: (node > $o) > list_node > node).
% 3.20/1.72 thf(func_def_270, type, sK192: (node > $o) > list_node > list_node).
% 3.20/1.72 thf(func_def_271, type, sK193: list_node > list_node > list_node > node > node > list_node > list_node).
% 3.20/1.72 thf(func_def_272, type, sK194: list_node > list_node > list_node > node > node > list_node > list_node).
% 3.20/1.72 thf(func_def_273, type, sK195: list_node > node > list_node).
% 3.20/1.72 thf(func_def_274, type, sK196: list_node > node > list_node).
% 3.20/1.72 thf(func_def_275, type, sK197: list_node > g > (node > $o) > node > list_node).
% 3.20/1.72 thf(func_def_276, type, sK198: list_node > g > (node > $o) > node > node).
% 3.20/1.72 thf(func_def_277, type, sK199: node > list_node > list_node).
% 3.20/1.72 thf(func_def_278, type, sK200: node > list_node > list_node).
% 3.20/1.72 thf(func_def_279, type, sK201: list_node > list_node).
% 3.20/1.72 thf(func_def_280, type, sK202: list_node > node).
% 3.20/1.72 thf(func_def_281, type, sK203: list_node > list_node).
% 3.20/1.72 thf(func_def_282, type, sK204: list_node > node).
% 3.20/1.72 thf(func_def_283, type, sK205: list_node > list_node > list_node > list_node > list_node).
% 3.20/1.72 thf(func_def_284, type, sK206: list_node > (node > $o) > list_node).
% 3.20/1.72 thf(func_def_285, type, sK207: list_node > (node > $o) > node).
% 3.20/1.72 thf(func_def_286, type, sK208: list_node > (node > $o) > list_node).
% 3.20/1.72 thf(func_def_287, type, sK209: list_node > list_node > list_node > node > list_node).
% 3.20/1.72 thf(func_def_288, type, sK210: node > list_node > list_node).
% 3.20/1.72 thf(func_def_289, type, sK211: node > list_node > list_node).
% 3.20/1.72 thf(func_def_290, type, sK212: node > list_node > node).
% 3.20/1.72 thf(func_def_291, type, sK213: node > list_node > list_node).
% 3.20/1.72 thf(func_def_292, type, sK214: node > list_node > list_node).
% 3.20/1.72 thf(func_def_293, type, sK215: (list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_294, type, sK216: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_295, type, sK217: node > list_node > list_node > list_node).
% 3.20/1.72 thf(func_def_296, type, sK218: list_node > list_node).
% 3.20/1.72 thf(func_def_297, type, sK219: list_node > node).
% 3.20/1.72 thf(func_def_298, type, sK220: list_node > list_node > list_node).
% 3.20/1.72 thf(func_def_299, type, sK221: node > list_node > list_node > node).
% 3.20/1.72 thf(func_def_300, type, sK222: (list_node > list_node > $o) > node).
% 3.20/1.72 thf(func_def_301, type, sK223: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_302, type, sK224: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_303, type, sK225: (list_node > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_304, type, sK226: ((node > node > $o) > list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_305, type, sK227: ((node > node > $o) > list_node > $o) > node).
% 3.20/1.72 thf(func_def_306, type, sK228: ((node > node > $o) > list_node > $o) > node > node > $o).
% 3.20/1.72 thf(func_def_307, type, sK229: ((node > node > $o) > list_node > $o) > node > node > $o).
% 3.20/1.72 thf(func_def_308, type, sK230: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_309, type, sK231: (list_node > $o) > list_node).
% 3.20/1.72 thf(func_def_310, type, sK232: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_311, type, sK233: (list_node > $o) > node).
% 3.20/1.72 thf(func_def_312, type, sK234: node > node > list_node > g > node > list_node).
% 3.20/1.72 thf(func_def_313, type, sK235: node > node > list_node > g > node > list_node).
% 3.20/1.72 thf(func_def_314, type, sK236: list_node > node).
% 3.20/1.72 thf(func_def_315, type, sK237: list_node > node).
% 3.20/1.72 thf(func_def_316, type, sK238: list_node > list_node).
% 3.20/1.72 thf(func_def_317, type, sK239: node > g > node > node > list_node > list_node).
% 3.20/1.72 thf(func_def_318, type, sK240: node > g > node > node > list_node > list_node).
% 3.20/1.72 thf(func_def_319, type, sK241: node > g > node > node > list_node > list_node).
% 3.20/1.72 thf(func_def_320, type, sK242: (node > $o) > list_node > list_node).
% 3.20/1.72 thf(func_def_321, type, sK243: (node > $o) > list_node > node).
% 3.20/1.72 thf(func_def_322, type, sK244: (node > $o) > list_node > list_node).
% 3.20/1.72 thf(func_def_324, type, ph246: !>[X0: $tType]:(X0)).
% 3.20/1.72 thf(f1956,plain,(
% 3.20/1.72 $false),
% 3.20/1.72 inference(subsumption_resolution,[status(thm)],[f1955,f1493])).
% 3.20/1.72 thf(f1493,plain,(
% 3.20/1.72 ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r)) = $true)),
% 3.20/1.72 inference(cnf_transformation,[status(thm)],[f479])).
% 3.20/1.72 thf(f479,plain,(
% 3.20/1.72 ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r)) = $true)),
% 3.20/1.72 inference(fool_elimination,[status(thm)],[f478])).
% 3.20/1.72 thf(f478,plain,(
% 3.20/1.72 (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r))),
% 3.20/1.72 inference(rectify,[status(thm)],[f4])).
% 3.20/1.72 thf(f4,axiom,(
% 3.20/1.72 (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r))),
% 3.20/1.72 file('/export/starexec/sandbox/tmp/tmp.4SP2TQ63UH/DTF2THF_20632.p',fact_3_assms_I7_J)).
% 3.20/1.72 thf(f1955,plain,(
% 3.20/1.72 ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r)) != $true)),
% 3.20/1.72 inference(trivial_inequality_removal,[status(thm)],[f1954])).
% 3.20/1.72 thf(f1954,plain,(
% 3.20/1.72 ($true != $true) | ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r)) != $true)),
% 3.20/1.72 inference(superposition,[status(thm)],[f1953,f1839])).
% 3.20/1.72 thf(f1839,plain,(
% 3.20/1.72 ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ ri @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r)) = $true)),
% 3.20/1.72 inference(definition_unfolding,[status(thm)],[f1621,f1591])).
% 3.20/1.72 thf(f1591,plain,(
% 3.20/1.72 (i = (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r))),
% 3.20/1.72 inference(cnf_transformation,[status(thm)],[f2])).
% 3.20/1.72 thf(f2,axiom,(
% 3.20/1.72 (i = (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r))),
% 3.20/1.72 file('/export/starexec/sandbox/tmp/tmp.4SP2TQ63UH/DTF2THF_20632.p',fact_1_ri__is__valid)).
% 3.20/1.72 thf(f1621,plain,(
% 3.20/1.72 ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ ri @ i) = $true)),
% 3.20/1.72 inference(cnf_transformation,[status(thm)],[f875])).
% 3.20/1.72 thf(f875,plain,(
% 3.20/1.72 ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ ri @ i) = $true)),
% 3.20/1.72 inference(fool_elimination,[status(thm)],[f874])).
% 3.20/1.72 thf(f874,plain,(
% 3.20/1.72 (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ ri @ i)),
% 3.20/1.72 inference(rectify,[status(thm)],[f5])).
% 3.20/1.72 thf(f5,axiom,(
% 3.20/1.72 (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ ri @ i)),
% 3.20/1.72 file('/export/starexec/sandbox/tmp/tmp.4SP2TQ63UH/DTF2THF_20632.p',fact_4_ri__props_I1_J)).
% 3.20/1.72 thf(f1953,plain,(
% 3.20/1.72 ( ! [X0 : node] : (($true != (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ X0 @ ri @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r))) | ($true != (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ X0))) )),
% 3.20/1.72 inference(trivial_inequality_removal,[status(thm)],[f1952])).
% 3.20/1.72 thf(f1952,plain,(
% 3.20/1.72 ( ! [X0 : node] : (($true != $true) | ($true != (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ X0 @ ri @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r))) | ($true != (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ X0))) )),
% 3.20/1.72 inference(superposition,[status(thm)],[f1656,f1650])).
% 3.20/1.72 thf(f1650,plain,(
% 3.20/1.72 ( ! [X2 : node,X3 : list_node,X0 : node,X1 : list_node,X4 : g,X5 : node] : (($true = (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ (append_node @ X3 @ (tl_node @ X1)) @ X5)) | ($true != (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ X3 @ X0)) | ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X0 @ X1 @ X5) != $true)) )),
% 3.20/1.72 inference(cnf_transformation,[status(thm)],[f1067])).
% 3.20/1.72 thf(f1067,plain,(
% 3.20/1.72 ! [X0 : node,X1 : list_node,X2 : node,X3 : list_node,X4 : g,X5 : node] : (($true = (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ (append_node @ X3 @ (tl_node @ X1)) @ X5)) | ($true != (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ X3 @ X0)) | ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X0 @ X1 @ X5) != $true))),
% 3.20/1.72 inference(flattening,[status(thm)],[f1066])).
% 3.20/1.72 thf(f1066,plain,(
% 3.20/1.72 ! [X0 : node,X1 : list_node,X2 : node,X3 : list_node,X4 : g,X5 : node] : ((($true = (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ (append_node @ X3 @ (tl_node @ X1)) @ X5)) | ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X0 @ X1 @ X5) != $true)) | ($true != (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ X3 @ X0)))),
% 3.20/1.72 inference(ennf_transformation,[status(thm)],[f659])).
% 3.20/1.72 thf(f659,plain,(
% 3.20/1.72 ! [X0 : node,X1 : list_node,X2 : node,X3 : list_node,X4 : g,X5 : node] : (($true = (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ X3 @ X0)) => (((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X0 @ X1 @ X5) = $true) => ($true = (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ (append_node @ X3 @ (tl_node @ X1)) @ X5))))),
% 3.20/1.72 inference(fool_elimination,[status(thm)],[f658])).
% 3.20/1.72 thf(f658,plain,(
% 3.20/1.72 ! [X0 : node,X1 : list_node,X2 : node,X3 : list_node,X4 : g,X5 : node] : ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ X3 @ X0) => ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X0 @ X1 @ X5) => (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X4 @ X2 @ (append_node @ X3 @ (tl_node @ X1)) @ X5)))),
% 3.20/1.72 inference(rectify,[status(thm)],[f6])).
% 3.20/1.72 thf(f6,axiom,(
% 3.20/1.72 ! [X3 : node,X4 : list_node,X1 : node,X2 : list_node,X0 : g,X5 : node] : ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ X2 @ X3) => ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ X3 @ X4 @ X5) => (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ (append_node @ X2 @ (tl_node @ X4)) @ X5)))),
% 3.20/1.72 file('/export/starexec/sandbox/tmp/tmp.4SP2TQ63UH/DTF2THF_20632.p',fact_5_old_Opath2__app)).
% 3.20/1.72 thf(f1656,plain,(
% 3.20/1.72 ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ (append_node @ ns @ (tl_node @ ri)) @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r)) != $true)),
% 3.20/1.72 inference(cnf_transformation,[status(thm)],[f904])).
% 3.20/1.72 thf(f904,plain,(
% 3.20/1.72 ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ (append_node @ ns @ (tl_node @ ri)) @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r)) != $true)),
% 3.20/1.72 inference(flattening,[status(thm)],[f407])).
% 3.20/1.72 thf(f407,plain,(
% 3.20/1.72 ~((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ (append_node @ ns @ (tl_node @ ri)) @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r)) = $true)),
% 3.20/1.72 inference(fool_elimination,[status(thm)],[f406])).
% 3.20/1.72 thf(f406,plain,(
% 3.20/1.72 ~(graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ (append_node @ ns @ (tl_node @ ri)) @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r))),
% 3.20/1.72 inference(rectify,[status(thm)],[f352])).
% 3.20/1.72 thf(f352,negated_conjecture,(
% 3.20/1.72 ~(graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ (append_node @ ns @ (tl_node @ ri)) @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r))),
% 3.20/1.72 inference(negated_conjecture,[status(cth)],[f351])).
% 3.20/1.72 thf(f351,conjecture,(
% 3.20/1.72 (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ (append_node @ ns @ (tl_node @ ri)) @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r))),
% 3.20/1.72 file('/export/starexec/sandbox/tmp/tmp.4SP2TQ63UH/DTF2THF_20632.p',conj_0)).
% 3.20/1.72 % SZS output end Proof for DTF2THF_20632
% 3.20/1.72 % (20846)------------------------------
% 3.20/1.72 % (20846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.72 % (20846)Termination reason: Refutation
% 3.20/1.72
% 3.20/1.72 % (20846)Memory used [KB]: 7931
% 3.20/1.72 % (20846)Time elapsed: 0.064 s
% 3.20/1.72 % (20846)Instructions burned: 189 (million)
% 3.20/1.72 % (20846)------------------------------
% 3.20/1.72 % (20846)------------------------------
% 3.20/1.72 % (20840)Success in time 0.085 s
%------------------------------------------------------------------------------