%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:58:56 PM UTC 2026
% Result : Theorem 2.12s 1.98s
% Output : Refutation 2.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 2312 ( 422 equ; 0 cnn)
% Maximal formula atoms : 33 ( 60 avg)
% Number of connectives : 12509 (1820 ~;1798 |; 301 &;7043 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 8 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 1577 (1577 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1094 (1091 usr; 5 con; 0-3 aty)
% (1542 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 2483 (1926 ^; 550 !; 7 ?;2483 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
d_unsorted: $tType ).
thf(func_def_0,type,
unsorted: $tType ).
thf(func_def_1,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_2,type,
inv: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_3,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_4,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_5,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_6,type,
refl: ( $i > $i > $o ) > $o ).
thf(func_def_7,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(func_def_8,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_9,type,
symm: ( $i > $i > $o ) > $o ).
thf(func_def_10,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(func_def_11,type,
asymm: ( $i > $i > $o ) > $o ).
thf(func_def_12,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_13,type,
trans: ( $i > $i > $o ) > $o ).
thf(func_def_14,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_15,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_16,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_17,type,
po: ( $i > $i > $o ) > $o ).
thf(func_def_18,type,
so: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
total: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
term: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
ind: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
innf: ( $i > $i > $o ) > $i > $o ).
thf(func_def_23,type,
nfof: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_24,type,
norm: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
lconfl: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
sconfl: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
confl: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
cr: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
d_unsorted: $tType ).
thf(func_def_31,type,
d2unsorted: d_unsorted > $i ).
thf(func_def_32,type,
d_unsorted_0: d_unsorted ).
thf(func_def_52,type,
sK0: $i > d_unsorted ).
thf(func_def_54,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
sK3: $i > $i > $o ).
thf(func_def_58,type,
sK6: $i > $i > $o ).
thf(func_def_59,type,
sK7: $i > $i > $o ).
thf(func_def_60,type,
sK8: $i > $i > $o ).
thf(func_def_61,type,
sK9: $i > $i > $o ).
thf(func_def_62,type,
sK10: $i > $i > $o ).
thf(func_def_63,type,
sK11: $i > $i > $o ).
thf(func_def_64,type,
sK12: $i > $i > $o ).
thf(func_def_65,type,
sK13: $i > $i > $o ).
thf(func_def_66,type,
sK14: $i > $i > $o ).
thf(func_def_67,type,
sK15: $i > $i > $o ).
thf(func_def_68,type,
sK16: $i > $i > $o ).
thf(func_def_69,type,
sK17: $i > $i > $o ).
thf(func_def_70,type,
sK18: $i > $i > $o ).
thf(func_def_71,type,
sK19: $i > $i > $o ).
thf(func_def_72,type,
sK20: $i > $i > $o ).
thf(func_def_73,type,
sK21: $i > $i > $o ).
thf(func_def_74,type,
sK22: ( $i > $i > $o ) > $i ).
thf(func_def_75,type,
sK23: ( $i > $i > $o ) > $i ).
thf(func_def_76,type,
sK24: ( $i > $i > $o ) > $i ).
thf(func_def_77,type,
sK25: ( $i > $i > $o ) > $i ).
thf(func_def_78,type,
sK26: ( $i > $i > $o ) > $i ).
thf(func_def_79,type,
sK27: ( $i > $i > $o ) > $i ).
thf(func_def_80,type,
sK28: ( $i > $i > $o ) > $i ).
thf(func_def_81,type,
sK29: ( $i > $i > $o ) > $i ).
thf(func_def_82,type,
sK30: ( $i > $i > $o ) > $i ).
thf(func_def_83,type,
sK31: ( $i > $i > $o ) > $i ).
thf(func_def_84,type,
sK32: ( $i > $i > $o ) > $i ).
thf(func_def_85,type,
sK33: ( $i > $i > $o ) > $i ).
thf(func_def_86,type,
sK34: ( $i > $i > $o ) > $i ).
thf(func_def_87,type,
sK35: ( $i > $i > $o ) > $i ).
thf(func_def_88,type,
sK36: ( $i > $i > $o ) > $i ).
thf(func_def_89,type,
sK37: ( $i > $i > $o ) > $i ).
thf(func_def_90,type,
sK38: ( $i > $i > $o ) > $i ).
thf(func_def_91,type,
sK39: ( $i > $i > $o ) > $i ).
thf(func_def_92,type,
sK40: ( $i > $i > $o ) > $i ).
thf(func_def_93,type,
sK41: ( $i > $i > $o ) > $i ).
thf(func_def_94,type,
sK42: ( $i > $i > $o ) > $i ).
thf(func_def_95,type,
sK43: ( $i > $i > $o ) > $i ).
thf(func_def_96,type,
sK44: ( $i > $i > $o ) > $i ).
thf(func_def_97,type,
sK45: ( $i > $i > $o ) > $i ).
thf(func_def_98,type,
sK46: ( $i > $i > $o ) > $i ).
thf(func_def_99,type,
sK47: ( $i > $i > $o ) > $i ).
thf(func_def_100,type,
sK48: ( $i > $i > $o ) > $i ).
thf(func_def_101,type,
sK49: ( $i > $i > $o ) > $i ).
thf(func_def_102,type,
sK50: ( $i > $i > $o ) > $i ).
thf(func_def_103,type,
sK51: ( $i > $i > $o ) > $i ).
thf(func_def_104,type,
sK52: ( $i > $i > $o ) > $i ).
thf(func_def_105,type,
sK53: ( $i > $i > $o ) > $i ).
thf(func_def_106,type,
sK54: ( $i > $i > $o ) > $i ).
thf(func_def_107,type,
sK55: ( $i > $i > $o ) > $i ).
thf(func_def_108,type,
sK56: ( $i > $i > $o ) > $i ).
thf(func_def_109,type,
sK57: ( $i > $i > $o ) > $i ).
thf(func_def_110,type,
sK58: ( $i > $i > $o ) > $i ).
thf(func_def_111,type,
sK59: ( $i > $i > $o ) > $i ).
thf(func_def_112,type,
sK60: ( $i > $i > $o ) > $i ).
thf(func_def_113,type,
sK61: ( $i > $i > $o ) > $i ).
thf(func_def_114,type,
sK62: ( $i > $i > $o ) > $i ).
thf(func_def_115,type,
sK63: ( $i > $i > $o ) > $i ).
thf(func_def_116,type,
sK64: ( $i > $i > $o ) > $i ).
thf(func_def_117,type,
sK65: ( $i > $i > $o ) > $i ).
thf(func_def_118,type,
sK66: ( $i > $i > $o ) > $i ).
thf(func_def_119,type,
sK67: ( $i > $i > $o ) > $i ).
thf(func_def_120,type,
sK68: ( $i > $i > $o ) > $i ).
thf(func_def_121,type,
sK69: ( $i > $i > $o ) > $i ).
thf(func_def_122,type,
sK70: ( $i > $i > $o ) > $i ).
thf(func_def_123,type,
sK71: ( $i > $i > $o ) > $i ).
thf(func_def_124,type,
sK72: ( $i > $i > $o ) > $i ).
thf(func_def_125,type,
sK73: ( $i > $i > $o ) > $i ).
thf(func_def_126,type,
sK74: ( $i > $i > $o ) > $i ).
thf(func_def_127,type,
sK75: ( $i > $i > $o ) > $i ).
thf(func_def_128,type,
sK76: ( $i > $i > $o ) > $i ).
thf(func_def_129,type,
sK77: ( $i > $i > $o ) > $i ).
thf(func_def_130,type,
sK78: ( $i > $i > $o ) > $i ).
thf(func_def_131,type,
sK79: ( $i > $i > $o ) > $i ).
thf(func_def_132,type,
sK80: ( $i > $i > $o ) > $i ).
thf(func_def_133,type,
sK81: ( $i > $i > $o ) > $i ).
thf(func_def_134,type,
sK82: ( $i > $i > $o ) > $i ).
thf(func_def_135,type,
sK83: ( $i > $i > $o ) > $i ).
thf(func_def_136,type,
sK84: ( $i > $i > $o ) > $i ).
thf(func_def_137,type,
sK85: ( $i > $i > $o ) > $i ).
thf(func_def_138,type,
sK86: ( $i > $i > $o ) > $i ).
thf(func_def_139,type,
sK87: ( $i > $i > $o ) > $i ).
thf(func_def_140,type,
sK88: ( $i > $i > $o ) > $i ).
thf(func_def_141,type,
sK89: ( $i > $i > $o ) > $i ).
thf(func_def_142,type,
sK90: ( $i > $i > $o ) > $i ).
thf(func_def_143,type,
sK91: ( $i > $i > $o ) > $i ).
thf(func_def_144,type,
sK92: ( $i > $i > $o ) > $i ).
thf(func_def_145,type,
sK93: ( $i > $i > $o ) > $i ).
thf(func_def_146,type,
sK94: ( $i > $i > $o ) > $i ).
thf(func_def_147,type,
sK95: ( $i > $i > $o ) > $i ).
thf(func_def_148,type,
sK96: ( $i > $i > $o ) > $i ).
thf(func_def_149,type,
sK97: ( $i > $i > $o ) > $i ).
thf(func_def_150,type,
sK98: ( $i > $i > $o ) > $i ).
thf(func_def_151,type,
sK99: ( $i > $i > $o ) > $i ).
thf(func_def_152,type,
sK100: ( $i > $i > $o ) > $i ).
thf(func_def_153,type,
sK101: ( $i > $i > $o ) > $i ).
thf(func_def_154,type,
sK102: ( $i > $i > $o ) > $i ).
thf(func_def_155,type,
sK103: ( $i > $i > $o ) > $i ).
thf(func_def_156,type,
sK104: ( $i > $i > $o ) > $i ).
thf(func_def_157,type,
sK105: ( $i > $i > $o ) > $i ).
thf(func_def_158,type,
sK106: ( $i > $i > $o ) > $i ).
thf(func_def_159,type,
sK107: ( $i > $i > $o ) > $i ).
thf(func_def_160,type,
sK108: ( $i > $i > $o ) > $i ).
thf(func_def_161,type,
sK109: ( $i > $i > $o ) > $i ).
thf(func_def_162,type,
sK110: ( $i > $i > $o ) > $i ).
thf(func_def_163,type,
sK111: ( $i > $i > $o ) > $i ).
thf(func_def_164,type,
sK112: ( $i > $i > $o ) > $i ).
thf(func_def_165,type,
sK113: ( $i > $i > $o ) > $i ).
thf(func_def_166,type,
sK114: ( $i > $i > $o ) > $i ).
thf(func_def_167,type,
sK115: ( $i > $i > $o ) > $i ).
thf(func_def_168,type,
sK116: ( $i > $i > $o ) > $i ).
thf(func_def_169,type,
sK117: ( $i > $i > $o ) > $i ).
thf(func_def_170,type,
sK118: ( $i > $i > $o ) > $i ).
thf(func_def_171,type,
sK119: ( $i > $i > $o ) > $i ).
thf(func_def_172,type,
sK120: ( $i > $i > $o ) > $i ).
thf(func_def_173,type,
sK121: ( $i > $i > $o ) > $i ).
thf(func_def_174,type,
sK122: ( $i > $i > $o ) > $i ).
thf(func_def_175,type,
sK123: ( $i > $i > $o ) > $i ).
thf(func_def_176,type,
sK124: ( $i > $i > $o ) > $i ).
thf(func_def_177,type,
sK125: ( $i > $i > $o ) > $i ).
thf(func_def_178,type,
sK126: ( $i > $i > $o ) > $i ).
thf(func_def_179,type,
sK127: ( $i > $i > $o ) > $i ).
thf(func_def_180,type,
sK128: ( $i > $i > $o ) > $i ).
thf(func_def_181,type,
sK129: ( $i > $i > $o ) > $i ).
thf(func_def_182,type,
sK130: ( $i > $i > $o ) > $i ).
thf(func_def_183,type,
sK131: ( $i > $i > $o ) > $i ).
thf(func_def_184,type,
sK132: ( $i > $i > $o ) > $i ).
thf(func_def_185,type,
sK133: ( $i > $i > $o ) > $i ).
thf(func_def_186,type,
sK134: ( $i > $i > $o ) > $i ).
thf(func_def_187,type,
sK135: ( $i > $i > $o ) > $i ).
thf(func_def_188,type,
sK136: ( $i > $i > $o ) > $i ).
thf(func_def_189,type,
sK137: ( $i > $i > $o ) > $i ).
thf(func_def_190,type,
sK138: ( $i > $i > $o ) > $i ).
thf(func_def_191,type,
sK139: ( $i > $i > $o ) > $i ).
thf(func_def_192,type,
sK140: ( $i > $i > $o ) > $i ).
thf(func_def_193,type,
sK141: ( $i > $i > $o ) > $i ).
thf(func_def_194,type,
sK142: ( $i > $i > $o ) > $i ).
thf(func_def_195,type,
sK143: ( $i > $i > $o ) > $i ).
thf(func_def_196,type,
sK144: ( $i > $i > $o ) > $i ).
thf(func_def_197,type,
sK145: ( $i > $i > $o ) > $i ).
thf(func_def_198,type,
sK146: ( $i > $i > $o ) > $i ).
thf(func_def_199,type,
sK147: ( $i > $i > $o ) > $i ).
thf(func_def_200,type,
sK148: ( $i > $i > $o ) > $i ).
thf(func_def_201,type,
sK149: ( $i > $i > $o ) > $i ).
thf(func_def_202,type,
sK150: ( $i > $i > $o ) > $i ).
thf(func_def_203,type,
sK151: ( $i > $i > $o ) > $i ).
thf(func_def_204,type,
sK152: ( $i > $i > $o ) > $i ).
thf(func_def_205,type,
sK153: ( $i > $i > $o ) > $i ).
thf(func_def_206,type,
sK154: ( $i > $i > $o ) > $i ).
thf(func_def_207,type,
sK155: ( $i > $i > $o ) > $i ).
thf(func_def_208,type,
sK156: ( $i > $i > $o ) > $i ).
thf(func_def_209,type,
sK157: ( $i > $i > $o ) > $i ).
thf(func_def_210,type,
sK158: ( $i > $i > $o ) > $i ).
thf(func_def_211,type,
sK159: ( $i > $i > $o ) > $i ).
thf(func_def_212,type,
sK160: ( $i > $i > $o ) > $i ).
thf(func_def_213,type,
sK161: ( $i > $i > $o ) > $i ).
thf(func_def_214,type,
sK162: ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
sK163: ( $i > $i > $o ) > $i ).
thf(func_def_216,type,
sK164: ( $i > $i > $o ) > $i ).
thf(func_def_217,type,
sK165: ( $i > $i > $o ) > $i ).
thf(func_def_218,type,
sK166: ( $i > $i > $o ) > $i ).
thf(func_def_219,type,
sK167: ( $i > $i > $o ) > $i ).
thf(func_def_220,type,
sK168: ( $i > $i > $o ) > $i ).
thf(func_def_221,type,
sK169: ( $i > $i > $o ) > $i ).
thf(func_def_222,type,
sK170: ( $i > $i > $o ) > $i ).
thf(func_def_223,type,
sK171: ( $i > $i > $o ) > $i ).
thf(func_def_224,type,
sK172: ( $i > $i > $o ) > $i ).
thf(func_def_225,type,
sK173: ( $i > $i > $o ) > $i ).
thf(func_def_226,type,
sK174: ( $i > $i > $o ) > $i ).
thf(func_def_227,type,
sK175: ( $i > $i > $o ) > $i ).
thf(func_def_228,type,
sK176: ( $i > $i > $o ) > $i ).
thf(func_def_229,type,
sK177: ( $i > $i > $o ) > $i ).
thf(func_def_230,type,
sK178: ( $i > $i > $o ) > $i ).
thf(func_def_231,type,
sK179: ( $i > $i > $o ) > $i ).
thf(func_def_232,type,
sK180: ( $i > $i > $o ) > $i ).
thf(func_def_233,type,
sK181: ( $i > $i > $o ) > $i ).
thf(func_def_234,type,
sK182: ( $i > $i > $o ) > $i ).
thf(func_def_235,type,
sK183: ( $i > $i > $o ) > $i ).
thf(func_def_236,type,
sK184: ( $i > $i > $o ) > $i ).
thf(func_def_237,type,
sK185: ( $i > $i > $o ) > $i ).
thf(func_def_238,type,
sK186: ( $i > $i > $o ) > $i ).
thf(func_def_239,type,
sK187: ( $i > $i > $o ) > $i ).
thf(func_def_240,type,
sK188: ( $i > $i > $o ) > $i ).
thf(func_def_241,type,
sK189: ( $i > $i > $o ) > $i ).
thf(func_def_242,type,
sK190: ( $i > $i > $o ) > $i ).
thf(func_def_243,type,
sK191: ( $i > $i > $o ) > $i ).
thf(func_def_244,type,
sK192: ( $i > $i > $o ) > $i ).
thf(func_def_245,type,
sK193: ( $i > $i > $o ) > $i ).
thf(func_def_246,type,
sK194: ( $i > $i > $o ) > $i ).
thf(func_def_247,type,
sK195: ( $i > $i > $o ) > $i ).
thf(func_def_248,type,
sK196: ( $i > $i > $o ) > $i ).
thf(func_def_249,type,
sK197: ( $i > $i > $o ) > $i ).
thf(func_def_250,type,
sK198: ( $i > $i > $o ) > $i ).
thf(func_def_251,type,
sK199: ( $i > $i > $o ) > $i ).
thf(func_def_252,type,
sK200: ( $i > $i > $o ) > $i ).
thf(func_def_253,type,
sK201: ( $i > $i > $o ) > $i ).
thf(func_def_254,type,
sK202: ( $i > $i > $o ) > $i ).
thf(func_def_255,type,
sK203: ( $i > $i > $o ) > $i ).
thf(func_def_256,type,
sK204: ( $i > $i > $o ) > $i ).
thf(func_def_257,type,
sK205: ( $i > $i > $o ) > $i ).
thf(func_def_258,type,
sK206: ( $i > $i > $o ) > $i ).
thf(func_def_259,type,
sK207: ( $i > $i > $o ) > $i ).
thf(func_def_260,type,
sK208: ( $i > $i > $o ) > $i ).
thf(func_def_261,type,
sK209: ( $i > $i > $o ) > $i ).
thf(func_def_262,type,
sK210: ( $i > $i > $o ) > $i ).
thf(func_def_263,type,
sK211: ( $i > $i > $o ) > $i ).
thf(func_def_264,type,
sK212: ( $i > $i > $o ) > $i ).
thf(func_def_265,type,
sK213: ( $i > $i > $o ) > $i ).
thf(func_def_266,type,
sK214: ( $i > $i > $o ) > $i ).
thf(func_def_267,type,
sK215: ( $i > $i > $o ) > $i ).
thf(func_def_268,type,
sK216: ( $i > $i > $o ) > $i ).
thf(func_def_269,type,
sK217: ( $i > $i > $o ) > $i ).
thf(func_def_270,type,
sK218: ( $i > $i > $o ) > $i ).
thf(func_def_271,type,
sK219: ( $i > $i > $o ) > $i ).
thf(func_def_272,type,
sK220: ( $i > $i > $o ) > $i ).
thf(func_def_273,type,
sK221: ( $i > $i > $o ) > $i ).
thf(func_def_274,type,
sK222: ( $i > $i > $o ) > $i ).
thf(func_def_275,type,
sK223: ( $i > $i > $o ) > $i ).
thf(func_def_276,type,
sK224: ( $i > $i > $o ) > $i ).
thf(func_def_277,type,
sK225: ( $i > $i > $o ) > $i ).
thf(func_def_278,type,
sK226: ( $i > $i > $o ) > $i ).
thf(func_def_279,type,
sK227: ( $i > $i > $o ) > $i ).
thf(func_def_280,type,
sK228: ( $i > $i > $o ) > $i ).
thf(func_def_281,type,
sK229: ( $i > $i > $o ) > $i ).
thf(func_def_282,type,
sK230: ( $i > $i > $o ) > $i ).
thf(func_def_283,type,
sK231: ( $i > $i > $o ) > $i ).
thf(func_def_284,type,
sK232: ( $i > $i > $o ) > $i ).
thf(func_def_285,type,
sK233: ( $i > $i > $o ) > $i ).
thf(func_def_286,type,
sK234: ( $i > $i > $o ) > $i ).
thf(func_def_287,type,
sK235: ( $i > $i > $o ) > $i ).
thf(func_def_288,type,
sK236: ( $i > $i > $o ) > $i ).
thf(func_def_289,type,
sK237: ( $i > $i > $o ) > $i ).
thf(func_def_290,type,
sK238: ( $i > $i > $o ) > $i ).
thf(func_def_291,type,
sK239: ( $i > $i > $o ) > $i ).
thf(func_def_292,type,
sK240: ( $i > $i > $o ) > $i ).
thf(func_def_293,type,
sK241: ( $i > $i > $o ) > $i ).
thf(func_def_294,type,
sK242: ( $i > $i > $o ) > $i ).
thf(func_def_295,type,
sK243: ( $i > $i > $o ) > $i ).
thf(func_def_296,type,
sK244: ( $i > $i > $o ) > $i ).
thf(func_def_297,type,
sK245: ( $i > $i > $o ) > $i ).
thf(func_def_298,type,
sK246: ( $i > $i > $o ) > $i ).
thf(func_def_299,type,
sK247: ( $i > $i > $o ) > $i ).
thf(func_def_300,type,
sK248: ( $i > $i > $o ) > $i ).
thf(func_def_301,type,
sK249: ( $i > $i > $o ) > $i ).
thf(func_def_302,type,
sK250: ( $i > $i > $o ) > $i ).
thf(func_def_303,type,
sK251: ( $i > $i > $o ) > $i ).
thf(func_def_304,type,
sK252: ( $i > $i > $o ) > $i ).
thf(func_def_305,type,
sK253: ( $i > $i > $o ) > $i ).
thf(func_def_306,type,
sK254: ( $i > $i > $o ) > $i ).
thf(func_def_307,type,
sK255: ( $i > $i > $o ) > $i ).
thf(func_def_308,type,
sK256: ( $i > $i > $o ) > $i ).
thf(func_def_309,type,
sK257: ( $i > $i > $o ) > $i ).
thf(func_def_310,type,
sK258: ( $i > $i > $o ) > $i ).
thf(func_def_311,type,
sK259: ( $i > $i > $o ) > $i ).
thf(func_def_312,type,
sK260: ( $i > $i > $o ) > $i ).
thf(func_def_313,type,
sK261: ( $i > $i > $o ) > $i ).
thf(func_def_314,type,
sK262: ( $i > $i > $o ) > $i ).
thf(func_def_315,type,
sK263: ( $i > $i > $o ) > $i ).
thf(func_def_316,type,
sK264: ( $i > $i > $o ) > $i ).
thf(func_def_317,type,
sK265: ( $i > $i > $o ) > $i ).
thf(func_def_318,type,
sK266: ( $i > $i > $o ) > $i ).
thf(func_def_319,type,
sK267: ( $i > $i > $o ) > $i ).
thf(func_def_320,type,
sK268: ( $i > $i > $o ) > $i ).
thf(func_def_321,type,
sK269: ( $i > $i > $o ) > $i ).
thf(func_def_322,type,
sK270: ( $i > $i > $o ) > $i ).
thf(func_def_323,type,
sK271: ( $i > $i > $o ) > $i ).
thf(func_def_324,type,
sK272: ( $i > $i > $o ) > $i ).
thf(func_def_325,type,
sK273: ( $i > $i > $o ) > $i ).
thf(func_def_326,type,
sK274: ( $i > $i > $o ) > $i ).
thf(func_def_327,type,
sK275: ( $i > $i > $o ) > $i ).
thf(func_def_328,type,
sK276: ( $i > $i > $o ) > $i ).
thf(func_def_329,type,
sK277: ( $i > $i > $o ) > $i ).
thf(func_def_330,type,
sK278: ( $i > $i > $o ) > $i ).
thf(func_def_331,type,
sK279: ( $i > $i > $o ) > $i ).
thf(func_def_332,type,
sK280: ( $i > $i > $o ) > $i ).
thf(func_def_333,type,
sK281: ( $i > $i > $o ) > $i ).
thf(func_def_334,type,
sK282: ( $i > $i > $o ) > $i ).
thf(func_def_335,type,
sK283: ( $i > $i > $o ) > $i ).
thf(func_def_336,type,
sK284: ( $i > $i > $o ) > $i ).
thf(func_def_337,type,
sK285: ( $i > $i > $o ) > $i ).
thf(func_def_338,type,
sK286: ( $i > $i > $o ) > $i ).
thf(func_def_339,type,
sK287: ( $i > $i > $o ) > $i ).
thf(func_def_340,type,
sK288: ( $i > $i > $o ) > $i ).
thf(func_def_341,type,
sK289: ( $i > $i > $o ) > $i ).
thf(func_def_342,type,
sK290: ( $i > $i > $o ) > $i ).
thf(func_def_343,type,
sK291: ( $i > $i > $o ) > $i ).
thf(func_def_344,type,
sK292: ( $i > $i > $o ) > $i ).
thf(func_def_345,type,
sK293: ( $i > $i > $o ) > $i ).
thf(func_def_346,type,
sK294: ( $i > $i > $o ) > $i ).
thf(func_def_347,type,
sK295: ( $i > $i > $o ) > $i ).
thf(func_def_348,type,
sK296: ( $i > $i > $o ) > $i ).
thf(func_def_349,type,
sK297: ( $i > $i > $o ) > $i ).
thf(func_def_350,type,
sK298: ( $i > $i > $o ) > $i ).
thf(func_def_351,type,
sK299: ( $i > $i > $o ) > $i ).
thf(func_def_352,type,
sK300: ( $i > $i > $o ) > $i ).
thf(func_def_353,type,
sK301: ( $i > $i > $o ) > $i ).
thf(func_def_354,type,
sK302: ( $i > $i > $o ) > $i ).
thf(func_def_355,type,
sK303: ( $i > $i > $o ) > $i ).
thf(func_def_356,type,
sK304: ( $i > $i > $o ) > $i ).
thf(func_def_357,type,
sK305: ( $i > $i > $o ) > $i ).
thf(func_def_358,type,
sK306: ( $i > $i > $o ) > $i ).
thf(func_def_359,type,
sK307: ( $i > $i > $o ) > $i ).
thf(func_def_360,type,
sK308: ( $i > $i > $o ) > $i ).
thf(func_def_361,type,
sK309: ( $i > $i > $o ) > $i ).
thf(func_def_362,type,
sK310: ( $i > $i > $o ) > $i ).
thf(func_def_363,type,
sK311: ( $i > $i > $o ) > $i ).
thf(func_def_364,type,
sK312: ( $i > $i > $o ) > $i ).
thf(func_def_365,type,
sK313: ( $i > $i > $o ) > $i ).
thf(func_def_366,type,
sK314: ( $i > $i > $o ) > $i ).
thf(func_def_367,type,
sK315: ( $i > $i > $o ) > $i ).
thf(func_def_368,type,
sK316: ( $i > $i > $o ) > $i ).
thf(func_def_369,type,
sK317: ( $i > $i > $o ) > $i ).
thf(func_def_370,type,
sK318: ( $i > $i > $o ) > $i ).
thf(func_def_371,type,
sK319: ( $i > $i > $o ) > $i ).
thf(func_def_372,type,
sK320: ( $i > $i > $o ) > $i ).
thf(func_def_373,type,
sK321: ( $i > $i > $o ) > $i ).
thf(func_def_374,type,
sK322: ( $i > $i > $o ) > $i ).
thf(func_def_375,type,
sK323: ( $i > $i > $o ) > $i ).
thf(func_def_376,type,
sK324: ( $i > $i > $o ) > $i ).
thf(func_def_377,type,
sK325: ( $i > $i > $o ) > $i ).
thf(func_def_378,type,
sK326: ( $i > $i > $o ) > $i ).
thf(func_def_379,type,
sK327: ( $i > $i > $o ) > $i ).
thf(func_def_380,type,
sK328: ( $i > $i > $o ) > $i ).
thf(func_def_381,type,
sK329: ( $i > $i > $o ) > $i ).
thf(func_def_382,type,
sK330: ( $i > $i > $o ) > $i ).
thf(func_def_383,type,
sK331: ( $i > $i > $o ) > $i ).
thf(func_def_384,type,
sK332: ( $i > $i > $o ) > $i ).
thf(func_def_385,type,
sK333: ( $i > $i > $o ) > $i ).
thf(func_def_386,type,
sK334: ( $i > $i > $o ) > $i ).
thf(func_def_387,type,
sK335: ( $i > $i > $o ) > $i ).
thf(func_def_388,type,
sK336: ( $i > $i > $o ) > $i ).
thf(func_def_389,type,
sK337: ( $i > $i > $o ) > $i ).
thf(func_def_390,type,
sK338: ( $i > $i > $o ) > $i ).
thf(func_def_391,type,
sK339: ( $i > $i > $o ) > $i ).
thf(func_def_392,type,
sK340: ( $i > $i > $o ) > $i ).
thf(func_def_393,type,
sK341: ( $i > $i > $o ) > $i ).
thf(func_def_394,type,
sK342: ( $i > $i > $o ) > $i ).
thf(func_def_395,type,
sK343: ( $i > $i > $o ) > $i ).
thf(func_def_396,type,
sK344: ( $i > $i > $o ) > $i ).
thf(func_def_397,type,
sK345: ( $i > $i > $o ) > $i ).
thf(func_def_398,type,
sK346: ( $i > $i > $o ) > $i ).
thf(func_def_399,type,
sK347: ( $i > $i > $o ) > $i ).
thf(func_def_400,type,
sK348: ( $i > $i > $o ) > $i ).
thf(func_def_401,type,
sK349: ( $i > $i > $o ) > $i ).
thf(func_def_402,type,
sK350: ( $i > $i > $o ) > $i ).
thf(func_def_403,type,
sK351: ( $i > $i > $o ) > $i ).
thf(func_def_404,type,
sK352: ( $i > $i > $o ) > $i ).
thf(func_def_405,type,
sK353: ( $i > $i > $o ) > $i ).
thf(func_def_406,type,
sK354: ( $i > $i > $o ) > $i ).
thf(func_def_407,type,
sK355: ( $i > $i > $o ) > $i ).
thf(func_def_408,type,
sK356: ( $i > $i > $o ) > $i ).
thf(func_def_409,type,
sK357: ( $i > $i > $o ) > $i ).
thf(func_def_410,type,
sK358: ( $i > $i > $o ) > $i ).
thf(func_def_411,type,
sK359: ( $i > $i > $o ) > $i ).
thf(func_def_412,type,
sK360: ( $i > $i > $o ) > $i ).
thf(func_def_413,type,
sK361: ( $i > $i > $o ) > $i ).
thf(func_def_414,type,
sK362: ( $i > $i > $o ) > $i ).
thf(func_def_415,type,
sK363: ( $i > $i > $o ) > $i ).
thf(func_def_416,type,
sK364: ( $i > $i > $o ) > $i ).
thf(func_def_417,type,
sK365: ( $i > $i > $o ) > $i ).
thf(func_def_418,type,
sK366: ( $i > $i > $o ) > $i ).
thf(func_def_419,type,
sK367: ( $i > $i > $o ) > $i ).
thf(func_def_420,type,
sK368: ( $i > $i > $o ) > $i ).
thf(func_def_421,type,
sK369: ( $i > $i > $o ) > $i ).
thf(func_def_422,type,
sK370: ( $i > $i > $o ) > $i ).
thf(func_def_423,type,
sK371: ( $i > $i > $o ) > $i ).
thf(func_def_424,type,
sK372: ( $i > $i > $o ) > $i ).
thf(func_def_425,type,
sK373: ( $i > $i > $o ) > $i ).
thf(func_def_426,type,
sK374: ( $i > $i > $o ) > $i ).
thf(func_def_427,type,
sK375: ( $i > $i > $o ) > $i ).
thf(func_def_428,type,
sK376: ( $i > $i > $o ) > $i ).
thf(func_def_429,type,
sK377: ( $i > $i > $o ) > $i ).
thf(func_def_430,type,
sK378: ( $i > $i > $o ) > $i ).
thf(func_def_431,type,
sK379: ( $i > $i > $o ) > $i ).
thf(func_def_432,type,
sK380: ( $i > $i > $o ) > $i ).
thf(func_def_433,type,
sK381: ( $i > $i > $o ) > $i ).
thf(func_def_434,type,
sK382: ( $i > $i > $o ) > $i ).
thf(func_def_435,type,
sK383: ( $i > $i > $o ) > $i ).
thf(func_def_436,type,
sK384: ( $i > $i > $o ) > $i ).
thf(func_def_437,type,
sK385: ( $i > $i > $o ) > $i ).
thf(func_def_438,type,
sK386: ( $i > $i > $o ) > $i ).
thf(func_def_439,type,
sK387: ( $i > $i > $o ) > $i ).
thf(func_def_440,type,
sK388: ( $i > $i > $o ) > $i ).
thf(func_def_441,type,
sK389: ( $i > $i > $o ) > $i ).
thf(func_def_442,type,
sK390: ( $i > $i > $o ) > $i ).
thf(func_def_443,type,
sK391: ( $i > $i > $o ) > $i ).
thf(func_def_444,type,
sK392: ( $i > $i > $o ) > $i ).
thf(func_def_445,type,
sK393: ( $i > $i > $o ) > $i ).
thf(func_def_446,type,
sK394: ( $i > $i > $o ) > $i ).
thf(func_def_447,type,
sK395: ( $i > $i > $o ) > $i ).
thf(func_def_448,type,
sK396: ( $i > $i > $o ) > $i ).
thf(func_def_449,type,
sK397: ( $i > $i > $o ) > $i ).
thf(func_def_450,type,
sK398: ( $i > $i > $o ) > $i ).
thf(func_def_451,type,
sK399: ( $i > $i > $o ) > $i ).
thf(func_def_452,type,
sK400: ( $i > $i > $o ) > $i ).
thf(func_def_453,type,
sK401: ( $i > $i > $o ) > $i ).
thf(func_def_454,type,
sK402: ( $i > $i > $o ) > $i ).
thf(func_def_455,type,
sK403: ( $i > $i > $o ) > $i ).
thf(func_def_456,type,
sK404: ( $i > $i > $o ) > $i ).
thf(func_def_457,type,
sK405: ( $i > $i > $o ) > $i ).
thf(func_def_458,type,
sK406: ( $i > $i > $o ) > $i ).
thf(func_def_459,type,
sK407: ( $i > $i > $o ) > $i ).
thf(func_def_460,type,
sK408: ( $i > $i > $o ) > $i ).
thf(func_def_461,type,
sK409: ( $i > $i > $o ) > $i ).
thf(func_def_462,type,
sK410: ( $i > $i > $o ) > $i ).
thf(func_def_463,type,
sK411: ( $i > $i > $o ) > $i ).
thf(func_def_464,type,
sK412: ( $i > $i > $o ) > $i ).
thf(func_def_465,type,
sK413: ( $i > $i > $o ) > $i ).
thf(func_def_466,type,
sK414: ( $i > $i > $o ) > $i ).
thf(func_def_467,type,
sK415: ( $i > $i > $o ) > $i ).
thf(func_def_468,type,
sK416: ( $i > $i > $o ) > $i ).
thf(func_def_469,type,
sK417: ( $i > $i > $o ) > $i ).
thf(func_def_470,type,
sK418: ( $i > $i > $o ) > $i ).
thf(func_def_471,type,
sK419: ( $i > $i > $o ) > $i ).
thf(func_def_472,type,
sK420: ( $i > $i > $o ) > $i ).
thf(func_def_473,type,
sK421: ( $i > $i > $o ) > $i ).
thf(func_def_474,type,
sK422: ( $i > $i > $o ) > $i ).
thf(func_def_475,type,
sK423: ( $i > $i > $o ) > $i ).
thf(func_def_476,type,
sK424: ( $i > $i > $o ) > $i ).
thf(func_def_477,type,
sK425: ( $i > $i > $o ) > $i ).
thf(func_def_478,type,
sK426: ( $i > $i > $o ) > $i ).
thf(func_def_479,type,
sK427: ( $i > $i > $o ) > $i ).
thf(func_def_480,type,
sK428: ( $i > $i > $o ) > $i ).
thf(func_def_481,type,
sK429: ( $i > $i > $o ) > $i ).
thf(func_def_482,type,
sK430: ( $i > $i > $o ) > $i ).
thf(func_def_483,type,
sK431: ( $i > $i > $o ) > $i ).
thf(func_def_484,type,
sK432: ( $i > $i > $o ) > $i ).
thf(func_def_485,type,
sK433: ( $i > $i > $o ) > $i ).
thf(func_def_486,type,
sK434: ( $i > $i > $o ) > $i ).
thf(func_def_487,type,
sK435: ( $i > $i > $o ) > $i ).
thf(func_def_488,type,
sK436: ( $i > $i > $o ) > $i ).
thf(func_def_489,type,
sK437: ( $i > $i > $o ) > $i ).
thf(func_def_490,type,
sK438: ( $i > $i > $o ) > $i ).
thf(func_def_491,type,
sK439: ( $i > $i > $o ) > $i ).
thf(func_def_492,type,
sK440: ( $i > $i > $o ) > $i ).
thf(func_def_493,type,
sK441: ( $i > $i > $o ) > $i ).
thf(func_def_494,type,
sK442: ( $i > $i > $o ) > $i ).
thf(func_def_495,type,
sK443: ( $i > $i > $o ) > $i ).
thf(func_def_496,type,
sK444: ( $i > $i > $o ) > $i ).
thf(func_def_497,type,
sK445: ( $i > $i > $o ) > $i ).
thf(func_def_498,type,
sK446: ( $i > $i > $o ) > $i ).
thf(func_def_499,type,
sK447: ( $i > $i > $o ) > $i ).
thf(func_def_500,type,
sK448: ( $i > $i > $o ) > $i ).
thf(func_def_501,type,
sK449: ( $i > $i > $o ) > $i ).
thf(func_def_502,type,
sK450: ( $i > $i > $o ) > $i ).
thf(func_def_503,type,
sK451: ( $i > $i > $o ) > $i ).
thf(func_def_504,type,
sK452: ( $i > $i > $o ) > $i ).
thf(func_def_505,type,
sK453: ( $i > $i > $o ) > $i ).
thf(func_def_506,type,
sK454: ( $i > $i > $o ) > $i ).
thf(func_def_507,type,
sK455: ( $i > $i > $o ) > $i ).
thf(func_def_508,type,
sK456: ( $i > $i > $o ) > $i ).
thf(func_def_509,type,
sK457: ( $i > $i > $o ) > $i ).
thf(func_def_510,type,
sK458: ( $i > $i > $o ) > $i ).
thf(func_def_511,type,
sK459: ( $i > $i > $o ) > $i ).
thf(func_def_512,type,
sK460: ( $i > $i > $o ) > $i ).
thf(func_def_513,type,
sK461: ( $i > $i > $o ) > $i ).
thf(func_def_514,type,
sK462: ( $i > $i > $o ) > $i ).
thf(func_def_515,type,
sK463: ( $i > $i > $o ) > $i ).
thf(func_def_516,type,
sK464: ( $i > $i > $o ) > $i ).
thf(func_def_517,type,
sK465: ( $i > $i > $o ) > $i ).
thf(func_def_518,type,
sK466: ( $i > $i > $o ) > $i ).
thf(func_def_519,type,
sK467: ( $i > $i > $o ) > $i ).
thf(func_def_520,type,
sK468: ( $i > $i > $o ) > $i ).
thf(func_def_521,type,
sK469: ( $i > $i > $o ) > $i ).
thf(func_def_522,type,
sK470: ( $i > $i > $o ) > $i ).
thf(func_def_523,type,
sK471: ( $i > $i > $o ) > $i ).
thf(func_def_524,type,
sK472: ( $i > $i > $o ) > $i ).
thf(func_def_525,type,
sK473: ( $i > $i > $o ) > $i ).
thf(func_def_526,type,
sK474: ( $i > $i > $o ) > $i ).
thf(func_def_527,type,
sK475: ( $i > $i > $o ) > $i ).
thf(func_def_528,type,
sK476: ( $i > $i > $o ) > $i ).
thf(func_def_529,type,
sK477: ( $i > $i > $o ) > $i ).
thf(func_def_530,type,
sK478: ( $i > $i > $o ) > $i ).
thf(func_def_531,type,
sK479: ( $i > $i > $o ) > $i ).
thf(func_def_532,type,
sK480: ( $i > $i > $o ) > $i ).
thf(func_def_533,type,
sK481: ( $i > $i > $o ) > $i ).
thf(func_def_534,type,
sK482: ( $i > $i > $o ) > $i ).
thf(func_def_535,type,
sK483: ( $i > $i > $o ) > $i ).
thf(func_def_536,type,
sK484: ( $i > $i > $o ) > $i ).
thf(func_def_537,type,
sK485: ( $i > $i > $o ) > $i ).
thf(func_def_538,type,
sK486: ( $i > $i > $o ) > $i ).
thf(func_def_539,type,
sK487: ( $i > $i > $o ) > $i ).
thf(func_def_540,type,
sK488: ( $i > $i > $o ) > $i ).
thf(func_def_541,type,
sK489: ( $i > $i > $o ) > $i ).
thf(func_def_542,type,
sK490: ( $i > $i > $o ) > $i ).
thf(func_def_543,type,
sK491: ( $i > $i > $o ) > $i ).
thf(func_def_544,type,
sK492: ( $i > $i > $o ) > $i ).
thf(func_def_545,type,
sK493: ( $i > $i > $o ) > $i ).
thf(func_def_546,type,
sK494: ( $i > $i > $o ) > $i ).
thf(func_def_547,type,
sK495: ( $i > $i > $o ) > $i ).
thf(func_def_548,type,
sK496: ( $i > $i > $o ) > $i ).
thf(func_def_549,type,
sK497: ( $i > $i > $o ) > $i ).
thf(func_def_550,type,
sK498: ( $i > $i > $o ) > $i ).
thf(func_def_551,type,
sK499: ( $i > $i > $o ) > $i ).
thf(func_def_552,type,
sK500: ( $i > $i > $o ) > $i ).
thf(func_def_553,type,
sK501: ( $i > $i > $o ) > $i ).
thf(func_def_554,type,
sK502: ( $i > $i > $o ) > $i ).
thf(func_def_555,type,
sK503: ( $i > $i > $o ) > $i ).
thf(func_def_556,type,
sK504: ( $i > $i > $o ) > $i ).
thf(func_def_557,type,
sK505: ( $i > $i > $o ) > $i ).
thf(func_def_558,type,
sK506: ( $i > $i > $o ) > $i ).
thf(func_def_559,type,
sK507: ( $i > $i > $o ) > $i ).
thf(func_def_560,type,
sK508: ( $i > $i > $o ) > $i ).
thf(func_def_561,type,
sK509: ( $i > $i > $o ) > $i ).
thf(func_def_562,type,
sK510: ( $i > $i > $o ) > $i ).
thf(func_def_563,type,
sK511: ( $i > $i > $o ) > $i ).
thf(func_def_564,type,
sK512: ( $i > $i > $o ) > $i ).
thf(func_def_565,type,
sK513: ( $i > $i > $o ) > $i ).
thf(func_def_566,type,
sK514: ( $i > $i > $o ) > $i ).
thf(func_def_567,type,
sK515: ( $i > $i > $o ) > $i ).
thf(func_def_568,type,
sK516: ( $i > $i > $o ) > $i ).
thf(func_def_569,type,
sK517: ( $i > $i > $o ) > $i ).
thf(func_def_570,type,
sK518: ( $i > $i > $o ) > $i ).
thf(func_def_571,type,
sK519: ( $i > $i > $o ) > $i ).
thf(func_def_572,type,
sK520: ( $i > $i > $o ) > $i ).
thf(func_def_573,type,
sK521: ( $i > $i > $o ) > $i ).
thf(func_def_574,type,
sK522: ( $i > $i > $o ) > $i ).
thf(func_def_575,type,
sK523: ( $i > $i > $o ) > $i ).
thf(func_def_576,type,
sK524: ( $i > $i > $o ) > $i ).
thf(func_def_577,type,
sK525: ( $i > $i > $o ) > $i ).
thf(func_def_578,type,
sK526: ( $i > $i > $o ) > $i ).
thf(func_def_579,type,
sK527: ( $i > $i > $o ) > $i ).
thf(func_def_580,type,
sK528: ( $i > $i > $o ) > $i ).
thf(func_def_581,type,
sK529: ( $i > $i > $o ) > $i ).
thf(func_def_582,type,
sK530: ( $i > $i > $o ) > $i ).
thf(func_def_583,type,
sK531: ( $i > $i > $o ) > $i ).
thf(func_def_584,type,
sK532: ( $i > $i > $o ) > $i ).
thf(func_def_585,type,
sK533: ( $i > $i > $o ) > $i ).
thf(func_def_586,type,
sK534: ( $i > $i > $o ) > $i ).
thf(func_def_587,type,
sK535: ( $i > $i > $o ) > $i ).
thf(func_def_588,type,
sK536: ( $i > $i > $o ) > $i ).
thf(func_def_589,type,
sK537: ( $i > $i > $o ) > $i ).
thf(func_def_590,type,
sK538: ( $i > $i > $o ) > $i ).
thf(func_def_591,type,
sK539: ( $i > $i > $o ) > $i ).
thf(func_def_592,type,
sK540: ( $i > $i > $o ) > $i ).
thf(func_def_593,type,
sK541: ( $i > $i > $o ) > $i ).
thf(func_def_594,type,
sK542: ( $i > $i > $o ) > $i ).
thf(func_def_595,type,
sK543: ( $i > $i > $o ) > $i ).
thf(func_def_596,type,
sK544: ( $i > $i > $o ) > $i ).
thf(func_def_597,type,
sK545: ( $i > $i > $o ) > $i ).
thf(func_def_598,type,
sK546: ( $i > $i > $o ) > $i ).
thf(func_def_599,type,
sK547: ( $i > $i > $o ) > $i ).
thf(func_def_600,type,
sK548: ( $i > $i > $o ) > $i ).
thf(func_def_601,type,
sK549: ( $i > $i > $o ) > $i ).
thf(func_def_602,type,
sK550: ( $i > $i > $o ) > $i ).
thf(func_def_603,type,
sK551: ( $i > $i > $o ) > $i ).
thf(func_def_604,type,
sK552: ( $i > $i > $o ) > $i ).
thf(func_def_605,type,
sK553: ( $i > $i > $o ) > $i ).
thf(func_def_606,type,
sK554: ( $i > $i > $o ) > $i ).
thf(func_def_607,type,
sK555: ( $i > $i > $o ) > $i ).
thf(func_def_608,type,
sK556: ( $i > $i > $o ) > $i ).
thf(func_def_609,type,
sK557: ( $i > $i > $o ) > $i ).
thf(func_def_610,type,
sK558: ( $i > $i > $o ) > $i ).
thf(func_def_611,type,
sK559: ( $i > $i > $o ) > $i ).
thf(func_def_612,type,
sK560: ( $i > $i > $o ) > $i ).
thf(func_def_613,type,
sK561: ( $i > $i > $o ) > $i ).
thf(func_def_614,type,
sK562: ( $i > $i > $o ) > $i ).
thf(func_def_615,type,
sK563: ( $i > $i > $o ) > $i ).
thf(func_def_616,type,
sK564: ( $i > $i > $o ) > $i ).
thf(func_def_617,type,
sK565: ( $i > $i > $o ) > $i ).
thf(func_def_618,type,
sK566: ( $i > $i > $o ) > $i ).
thf(func_def_619,type,
sK567: ( $i > $i > $o ) > $i ).
thf(func_def_620,type,
sK568: ( $i > $i > $o ) > $i ).
thf(func_def_621,type,
sK569: ( $i > $i > $o ) > $i ).
thf(func_def_622,type,
sK570: ( $i > $i > $o ) > $i ).
thf(func_def_623,type,
sK571: ( $i > $i > $o ) > $i ).
thf(func_def_624,type,
sK572: ( $i > $i > $o ) > $i ).
thf(func_def_625,type,
sK573: ( $i > $i > $o ) > $i ).
thf(func_def_626,type,
sK574: ( $i > $i > $o ) > $i ).
thf(func_def_627,type,
sK575: ( $i > $i > $o ) > $i ).
thf(func_def_628,type,
sK576: ( $i > $i > $o ) > $i ).
thf(func_def_629,type,
sK577: ( $i > $i > $o ) > $i ).
thf(func_def_630,type,
sK578: ( $i > $i > $o ) > $i ).
thf(func_def_631,type,
sK579: ( $i > $i > $o ) > $i ).
thf(func_def_632,type,
sK580: ( $i > $i > $o ) > $i ).
thf(func_def_633,type,
sK581: ( $i > $i > $o ) > $i ).
thf(func_def_634,type,
sK582: ( $i > $i > $o ) > $i ).
thf(func_def_635,type,
sK583: ( $i > $i > $o ) > $i ).
thf(func_def_636,type,
sK584: ( $i > $i > $o ) > $i ).
thf(func_def_637,type,
sK585: ( $i > $i > $o ) > $i ).
thf(func_def_638,type,
sK586: ( $i > $i > $o ) > $i ).
thf(func_def_639,type,
sK587: ( $i > $i > $o ) > $i ).
thf(func_def_640,type,
sK588: ( $i > $i > $o ) > $i ).
thf(func_def_641,type,
sK589: ( $i > $i > $o ) > $i ).
thf(func_def_642,type,
sK590: ( $i > $i > $o ) > $i ).
thf(func_def_643,type,
sK591: ( $i > $i > $o ) > $i ).
thf(func_def_644,type,
sK592: ( $i > $i > $o ) > $i ).
thf(func_def_645,type,
sK593: ( $i > $i > $o ) > $i ).
thf(func_def_646,type,
sK594: ( $i > $i > $o ) > $i ).
thf(func_def_647,type,
sK595: ( $i > $i > $o ) > $i ).
thf(func_def_648,type,
sK596: ( $i > $i > $o ) > $i ).
thf(func_def_649,type,
sK597: ( $i > $i > $o ) > $i ).
thf(func_def_650,type,
sK598: ( $i > $i > $o ) > $i ).
thf(func_def_651,type,
sK599: ( $i > $i > $o ) > $i ).
thf(func_def_652,type,
sK600: ( $i > $i > $o ) > $i ).
thf(func_def_653,type,
sK601: ( $i > $i > $o ) > $i ).
thf(func_def_654,type,
sK602: ( $i > $i > $o ) > $i ).
thf(func_def_655,type,
sK603: ( $i > $i > $o ) > $i ).
thf(func_def_656,type,
sK604: ( $i > $i > $o ) > $i ).
thf(func_def_657,type,
sK605: ( $i > $i > $o ) > $i ).
thf(func_def_658,type,
sK606: ( $i > $i > $o ) > $i ).
thf(func_def_659,type,
sK607: ( $i > $i > $o ) > $i ).
thf(func_def_660,type,
sK608: ( $i > $i > $o ) > $i ).
thf(func_def_661,type,
sK609: ( $i > $i > $o ) > $i ).
thf(func_def_662,type,
sK610: ( $i > $i > $o ) > $i ).
thf(func_def_663,type,
sK611: ( $i > $i > $o ) > $i ).
thf(func_def_664,type,
sK612: ( $i > $i > $o ) > $i ).
thf(func_def_665,type,
sK613: ( $i > $i > $o ) > $i ).
thf(func_def_666,type,
sK614: ( $i > $i > $o ) > $i ).
thf(func_def_667,type,
sK615: ( $i > $i > $o ) > $i ).
thf(func_def_668,type,
sK616: ( $i > $i > $o ) > $i ).
thf(func_def_669,type,
sK617: ( $i > $i > $o ) > $i ).
thf(func_def_670,type,
sK618: ( $i > $i > $o ) > $i ).
thf(func_def_671,type,
sK619: ( $i > $i > $o ) > $i ).
thf(func_def_672,type,
sK620: ( $i > $i > $o ) > $i ).
thf(func_def_673,type,
sK621: ( $i > $i > $o ) > $i ).
thf(func_def_674,type,
sK622: ( $i > $i > $o ) > $i ).
thf(func_def_675,type,
sK623: ( $i > $i > $o ) > $i ).
thf(func_def_676,type,
sK624: ( $i > $i > $o ) > $i ).
thf(func_def_677,type,
sK625: ( $i > $i > $o ) > $i ).
thf(func_def_678,type,
sK626: ( $i > $i > $o ) > $i ).
thf(func_def_679,type,
sK627: ( $i > $i > $o ) > $i ).
thf(func_def_680,type,
sK628: ( $i > $i > $o ) > $i ).
thf(func_def_681,type,
sK629: ( $i > $i > $o ) > $i ).
thf(func_def_682,type,
sK630: ( $i > $i > $o ) > $i ).
thf(func_def_683,type,
sK631: ( $i > $i > $o ) > $i ).
thf(func_def_684,type,
sK632: ( $i > $i > $o ) > $i ).
thf(func_def_685,type,
sK633: ( $i > $i > $o ) > $i ).
thf(func_def_686,type,
sK634: ( $i > $i > $o ) > $i ).
thf(func_def_687,type,
sK635: ( $i > $i > $o ) > $i ).
thf(func_def_688,type,
sK636: ( $i > $i > $o ) > $i ).
thf(func_def_689,type,
sK637: ( $i > $i > $o ) > $i ).
thf(func_def_690,type,
sK638: ( $i > $i > $o ) > $i ).
thf(func_def_691,type,
sK639: ( $i > $i > $o ) > $i ).
thf(func_def_692,type,
sK640: ( $i > $i > $o ) > $i ).
thf(func_def_693,type,
sK641: ( $i > $i > $o ) > $i ).
thf(func_def_694,type,
sK642: ( $i > $i > $o ) > $i ).
thf(func_def_695,type,
sK643: ( $i > $i > $o ) > $i ).
thf(func_def_696,type,
sK644: ( $i > $i > $o ) > $i ).
thf(func_def_697,type,
sK645: ( $i > $i > $o ) > $i ).
thf(func_def_698,type,
sK646: ( $i > $i > $o ) > $i ).
thf(func_def_699,type,
sK647: ( $i > $i > $o ) > $i ).
thf(func_def_700,type,
sK648: ( $i > $i > $o ) > $i ).
thf(func_def_701,type,
sK649: ( $i > $i > $o ) > $i ).
thf(func_def_702,type,
sK650: ( $i > $i > $o ) > $i ).
thf(func_def_703,type,
sK651: ( $i > $i > $o ) > $i ).
thf(func_def_704,type,
sK652: ( $i > $i > $o ) > $i ).
thf(func_def_705,type,
sK653: ( $i > $i > $o ) > $i ).
thf(func_def_706,type,
sK654: ( $i > $i > $o ) > $i ).
thf(func_def_707,type,
sK655: ( $i > $i > $o ) > $i ).
thf(func_def_708,type,
sK656: ( $i > $i > $o ) > $i ).
thf(func_def_709,type,
sK657: ( $i > $i > $o ) > $i ).
thf(func_def_710,type,
sK658: ( $i > $i > $o ) > $i ).
thf(func_def_711,type,
sK659: ( $i > $i > $o ) > $i ).
thf(func_def_712,type,
sK660: ( $i > $i > $o ) > $i ).
thf(func_def_713,type,
sK661: ( $i > $i > $o ) > $i ).
thf(func_def_714,type,
sK662: ( $i > $i > $o ) > $i ).
thf(func_def_715,type,
sK663: ( $i > $i > $o ) > $i ).
thf(func_def_716,type,
sK664: ( $i > $i > $o ) > $i ).
thf(func_def_717,type,
sK665: ( $i > $i > $o ) > $i ).
thf(func_def_718,type,
sK666: ( $i > $i > $o ) > $i ).
thf(func_def_719,type,
sK667: ( $i > $i > $o ) > $i ).
thf(func_def_720,type,
sK668: ( $i > $i > $o ) > $i ).
thf(func_def_721,type,
sK669: ( $i > $i > $o ) > $i ).
thf(func_def_722,type,
sK670: ( $i > $i > $o ) > $i ).
thf(func_def_723,type,
sK671: ( $i > $i > $o ) > $i ).
thf(func_def_724,type,
sK672: ( $i > $i > $o ) > $i ).
thf(func_def_725,type,
sK673: ( $i > $i > $o ) > $i ).
thf(func_def_726,type,
sK674: ( $i > $i > $o ) > $i ).
thf(func_def_727,type,
sK675: ( $i > $i > $o ) > $i ).
thf(func_def_728,type,
sK676: ( $i > $i > $o ) > $i ).
thf(func_def_729,type,
sK677: ( $i > $i > $o ) > $i ).
thf(func_def_730,type,
sK678: ( $i > $i > $o ) > $i ).
thf(func_def_731,type,
sK679: ( $i > $i > $o ) > $i ).
thf(func_def_732,type,
sK680: ( $i > $i > $o ) > $i ).
thf(func_def_733,type,
sK681: ( $i > $i > $o ) > $i ).
thf(func_def_734,type,
sK682: ( $i > $i > $o ) > $i ).
thf(func_def_735,type,
sK683: ( $i > $i > $o ) > $i ).
thf(func_def_736,type,
sK684: ( $i > $i > $o ) > $i ).
thf(func_def_737,type,
sK685: ( $i > $i > $o ) > $i ).
thf(func_def_738,type,
sK686: ( $i > $i > $o ) > $i ).
thf(func_def_739,type,
sK687: ( $i > $i > $o ) > $i ).
thf(func_def_740,type,
sK688: ( $i > $i > $o ) > $i ).
thf(func_def_741,type,
sK689: ( $i > $i > $o ) > $i ).
thf(func_def_742,type,
sK690: ( $i > $i > $o ) > $i ).
thf(func_def_743,type,
sK691: ( $i > $i > $o ) > $i ).
thf(func_def_744,type,
sK692: ( $i > $i > $o ) > $i ).
thf(func_def_745,type,
sK693: ( $i > $i > $o ) > $i ).
thf(func_def_746,type,
sK694: ( $i > $i > $o ) > $i ).
thf(func_def_747,type,
sK695: ( $i > $i > $o ) > $i ).
thf(func_def_748,type,
sK696: ( $i > $i > $o ) > $i ).
thf(func_def_749,type,
sK697: ( $i > $i > $o ) > $i ).
thf(func_def_750,type,
sK698: ( $i > $i > $o ) > $i ).
thf(func_def_751,type,
sK699: ( $i > $i > $o ) > $i ).
thf(func_def_752,type,
sK700: ( $i > $i > $o ) > $i ).
thf(func_def_753,type,
sK701: ( $i > $i > $o ) > $i ).
thf(func_def_754,type,
sK702: ( $i > $i > $o ) > $i ).
thf(func_def_755,type,
sK703: ( $i > $i > $o ) > $i ).
thf(func_def_756,type,
sK704: ( $i > $i > $o ) > $i ).
thf(func_def_757,type,
sK705: ( $i > $i > $o ) > $i ).
thf(func_def_758,type,
sK706: ( $i > $i > $o ) > $i ).
thf(func_def_759,type,
sK707: ( $i > $i > $o ) > $i ).
thf(func_def_760,type,
sK708: ( $i > $i > $o ) > $i ).
thf(func_def_761,type,
sK709: ( $i > $i > $o ) > $i ).
thf(func_def_762,type,
sK710: ( $i > $i > $o ) > $i ).
thf(func_def_763,type,
sK711: ( $i > $i > $o ) > $i ).
thf(func_def_764,type,
sK712: ( $i > $i > $o ) > $i ).
thf(func_def_765,type,
sK713: ( $i > $i > $o ) > $i ).
thf(func_def_766,type,
sK714: ( $i > $i > $o ) > $i ).
thf(func_def_767,type,
sK715: ( $i > $i > $o ) > $i ).
thf(func_def_768,type,
sK716: ( $i > $i > $o ) > $i ).
thf(func_def_769,type,
sK717: ( $i > $i > $o ) > $i ).
thf(func_def_770,type,
sK718: ( $i > $i > $o ) > $i ).
thf(func_def_771,type,
sK719: ( $i > $i > $o ) > $i ).
thf(func_def_772,type,
sK720: ( $i > $i > $o ) > $i ).
thf(func_def_773,type,
sK721: ( $i > $i > $o ) > $i ).
thf(func_def_774,type,
sK722: ( $i > $i > $o ) > $i ).
thf(func_def_775,type,
sK723: ( $i > $i > $o ) > $i ).
thf(func_def_776,type,
sK724: ( $i > $i > $o ) > $i ).
thf(func_def_777,type,
sK725: ( $i > $i > $o ) > $i ).
thf(func_def_778,type,
sK726: ( $i > $i > $o ) > $i ).
thf(func_def_779,type,
sK727: ( $i > $i > $o ) > $i ).
thf(func_def_780,type,
sK728: ( $i > $i > $o ) > $i ).
thf(func_def_781,type,
sK729: ( $i > $i > $o ) > $i ).
thf(func_def_782,type,
sK730: ( $i > $i > $o ) > $i ).
thf(func_def_783,type,
sK731: ( $i > $i > $o ) > $i ).
thf(func_def_784,type,
sK732: ( $i > $i > $o ) > $i ).
thf(func_def_785,type,
sK733: ( $i > $i > $o ) > $i ).
thf(func_def_786,type,
sK734: ( $i > $i > $o ) > $i ).
thf(func_def_787,type,
sK735: ( $i > $i > $o ) > $i ).
thf(func_def_788,type,
sK736: ( $i > $i > $o ) > $i ).
thf(func_def_789,type,
sK737: ( $i > $i > $o ) > $i ).
thf(func_def_790,type,
sK738: ( $i > $i > $o ) > $i ).
thf(func_def_791,type,
sK739: ( $i > $i > $o ) > $i ).
thf(func_def_792,type,
sK740: ( $i > $i > $o ) > $i ).
thf(func_def_793,type,
sK741: ( $i > $i > $o ) > $i ).
thf(func_def_794,type,
sK742: ( $i > $i > $o ) > $i ).
thf(func_def_795,type,
sK743: ( $i > $i > $o ) > $i ).
thf(func_def_796,type,
sK744: ( $i > $i > $o ) > $i ).
thf(func_def_797,type,
sK745: ( $i > $i > $o ) > $i ).
thf(func_def_798,type,
sK746: ( $i > $i > $o ) > $i ).
thf(func_def_799,type,
sK747: ( $i > $i > $o ) > $i ).
thf(func_def_800,type,
sK748: ( $i > $i > $o ) > $i ).
thf(func_def_801,type,
sK749: ( $i > $i > $o ) > $i ).
thf(func_def_802,type,
sK750: ( $i > $i > $o ) > $i ).
thf(func_def_803,type,
sK751: ( $i > $i > $o ) > $i ).
thf(func_def_804,type,
sK752: ( $i > $i > $o ) > $i ).
thf(func_def_805,type,
sK753: ( $i > $i > $o ) > $i ).
thf(func_def_806,type,
sK754: ( $i > $i > $o ) > $i ).
thf(func_def_807,type,
sK755: ( $i > $i > $o ) > $i ).
thf(func_def_808,type,
sK756: ( $i > $i > $o ) > $i ).
thf(func_def_809,type,
sK757: ( $i > $i > $o ) > $i ).
thf(func_def_810,type,
sK758: ( $i > $i > $o ) > $i ).
thf(func_def_811,type,
sK759: ( $i > $i > $o ) > $i ).
thf(func_def_812,type,
sK760: ( $i > $i > $o ) > $i ).
thf(func_def_813,type,
sK761: ( $i > $i > $o ) > $i ).
thf(func_def_814,type,
sK762: ( $i > $i > $o ) > $i ).
thf(func_def_815,type,
sK763: ( $i > $i > $o ) > $i ).
thf(func_def_816,type,
sK764: ( $i > $i > $o ) > $i ).
thf(func_def_817,type,
sK765: ( $i > $i > $o ) > $i ).
thf(func_def_818,type,
sK766: ( $i > $i > $o ) > $i ).
thf(func_def_819,type,
sK767: ( $i > $i > $o ) > $i ).
thf(func_def_820,type,
sK768: ( $i > $i > $o ) > $i ).
thf(func_def_821,type,
sK769: ( $i > $i > $o ) > $i ).
thf(func_def_822,type,
sK770: ( $i > $i > $o ) > $i ).
thf(func_def_823,type,
sK771: ( $i > $i > $o ) > $i ).
thf(func_def_824,type,
sK772: ( $i > $i > $o ) > $i ).
thf(func_def_825,type,
sK773: ( $i > $i > $o ) > $i ).
thf(func_def_826,type,
sK774: ( $i > $i > $o ) > $i ).
thf(func_def_827,type,
sK775: ( $i > $i > $o ) > $i ).
thf(func_def_828,type,
sK776: ( $i > $i > $o ) > $i ).
thf(func_def_829,type,
sK777: ( $i > $i > $o ) > $i ).
thf(func_def_830,type,
sK778: ( $i > $i > $o ) > $i ).
thf(func_def_831,type,
sK779: ( $i > $i > $o ) > $i ).
thf(func_def_832,type,
sK780: ( $i > $i > $o ) > $i ).
thf(func_def_833,type,
sK781: ( $i > $i > $o ) > $i ).
thf(func_def_834,type,
sK782: ( $i > $i > $o ) > $i ).
thf(func_def_835,type,
sK783: ( $i > $i > $o ) > $i ).
thf(func_def_836,type,
sK784: ( $i > $i > $o ) > $i ).
thf(func_def_837,type,
sK785: ( $i > $i > $o ) > $i ).
thf(func_def_838,type,
sK786: ( $i > $i > $o ) > $i ).
thf(func_def_839,type,
sK787: ( $i > $i > $o ) > $i ).
thf(func_def_840,type,
sK788: ( $i > $i > $o ) > $i ).
thf(func_def_841,type,
sK789: ( $i > $i > $o ) > $i ).
thf(func_def_842,type,
sK790: ( $i > $i > $o ) > $i ).
thf(func_def_843,type,
sK791: ( $i > $i > $o ) > $i ).
thf(func_def_844,type,
sK792: ( $i > $i > $o ) > $i ).
thf(func_def_845,type,
sK793: ( $i > $i > $o ) > $i ).
thf(func_def_846,type,
sK794: ( $i > $i > $o ) > $i ).
thf(func_def_847,type,
sK795: ( $i > $i > $o ) > $i ).
thf(func_def_848,type,
sK796: ( $i > $i > $o ) > $i ).
thf(func_def_849,type,
sK797: ( $i > $i > $o ) > $i ).
thf(func_def_850,type,
sK798: ( $i > $i > $o ) > $i ).
thf(func_def_851,type,
sK799: ( $i > $i > $o ) > $i ).
thf(func_def_852,type,
sK800: ( $i > $i > $o ) > $i ).
thf(func_def_853,type,
sK801: ( $i > $i > $o ) > $i ).
thf(func_def_854,type,
sK802: ( $i > $i > $o ) > $i ).
thf(func_def_855,type,
sK803: ( $i > $i > $o ) > $i ).
thf(func_def_856,type,
sK804: ( $i > $i > $o ) > $i ).
thf(func_def_857,type,
sK805: ( $i > $i > $o ) > $i ).
thf(func_def_858,type,
sK806: ( $i > $i > $o ) > $i ).
thf(func_def_859,type,
sK807: ( $i > $i > $o ) > $i ).
thf(func_def_860,type,
sK808: ( $i > $i > $o ) > $i ).
thf(func_def_861,type,
sK809: ( $i > $i > $o ) > $i ).
thf(func_def_862,type,
sK810: ( $i > $i > $o ) > $i ).
thf(func_def_863,type,
sK811: ( $i > $i > $o ) > $i ).
thf(func_def_864,type,
sK812: ( $i > $i > $o ) > $i ).
thf(func_def_865,type,
sK813: ( $i > $i > $o ) > $i ).
thf(func_def_866,type,
sK814: ( $i > $i > $o ) > $i ).
thf(func_def_867,type,
sK815: ( $i > $i > $o ) > $i ).
thf(func_def_868,type,
sK816: ( $i > $i > $o ) > $i ).
thf(func_def_869,type,
sK817: ( $i > $i > $o ) > $i ).
thf(func_def_870,type,
sK818: ( $i > $i > $o ) > $i ).
thf(func_def_871,type,
sK819: ( $i > $i > $o ) > $i ).
thf(func_def_872,type,
sK820: ( $i > $i > $o ) > $i ).
thf(func_def_873,type,
sK821: ( $i > $i > $o ) > $i ).
thf(func_def_874,type,
sK822: ( $i > $i > $o ) > $i ).
thf(func_def_875,type,
sK823: ( $i > $i > $o ) > $i ).
thf(func_def_876,type,
sK824: ( $i > $i > $o ) > $i ).
thf(func_def_877,type,
sK825: ( $i > $i > $o ) > $i ).
thf(func_def_878,type,
sK826: ( $i > $i > $o ) > $i ).
thf(func_def_879,type,
sK827: ( $i > $i > $o ) > $i ).
thf(func_def_880,type,
sK828: ( $i > $i > $o ) > $i ).
thf(func_def_881,type,
sK829: ( $i > $i > $o ) > $i ).
thf(func_def_882,type,
sK830: ( $i > $i > $o ) > $i ).
thf(func_def_883,type,
sK831: ( $i > $i > $o ) > $i ).
thf(func_def_884,type,
sK832: ( $i > $i > $o ) > $i ).
thf(func_def_885,type,
sK833: ( $i > $i > $o ) > $i ).
thf(func_def_886,type,
sK834: ( $i > $i > $o ) > $i ).
thf(func_def_887,type,
sK835: ( $i > $i > $o ) > $i ).
thf(func_def_888,type,
sK836: ( $i > $i > $o ) > $i ).
thf(func_def_889,type,
sK837: ( $i > $i > $o ) > $i ).
thf(func_def_890,type,
sK838: ( $i > $i > $o ) > $i ).
thf(func_def_891,type,
sK839: ( $i > $i > $o ) > $i ).
thf(func_def_892,type,
sK840: ( $i > $i > $o ) > $i ).
thf(func_def_893,type,
sK841: ( $i > $i > $o ) > $i ).
thf(func_def_894,type,
sK842: ( $i > $i > $o ) > $i ).
thf(func_def_895,type,
sK843: ( $i > $i > $o ) > $i ).
thf(func_def_896,type,
sK844: ( $i > $i > $o ) > $i ).
thf(func_def_897,type,
sK845: ( $i > $i > $o ) > $i ).
thf(func_def_898,type,
sK846: ( $i > $i > $o ) > $i ).
thf(func_def_899,type,
sK847: ( $i > $i > $o ) > $i ).
thf(func_def_900,type,
sK848: ( $i > $i > $o ) > $i ).
thf(func_def_901,type,
sK849: ( $i > $i > $o ) > $i ).
thf(func_def_902,type,
sK850: ( $i > $i > $o ) > $i ).
thf(func_def_903,type,
sK851: ( $i > $i > $o ) > $i ).
thf(func_def_904,type,
sK852: ( $i > $i > $o ) > $i ).
thf(func_def_905,type,
sK853: ( $i > $i > $o ) > $i ).
thf(func_def_906,type,
sK854: ( $i > $i > $o ) > $i ).
thf(func_def_907,type,
sK855: ( $i > $i > $o ) > $i ).
thf(func_def_908,type,
sK856: ( $i > $i > $o ) > $i ).
thf(func_def_909,type,
sK857: ( $i > $i > $o ) > $i ).
thf(func_def_910,type,
sK858: ( $i > $i > $o ) > $i ).
thf(func_def_911,type,
sK859: ( $i > $i > $o ) > $i ).
thf(func_def_912,type,
sK860: ( $i > $i > $o ) > $i ).
thf(func_def_913,type,
sK861: ( $i > $i > $o ) > $i ).
thf(func_def_914,type,
sK862: ( $i > $i > $o ) > $i ).
thf(func_def_915,type,
sK863: ( $i > $i > $o ) > $i ).
thf(func_def_916,type,
sK864: ( $i > $i > $o ) > $i ).
thf(func_def_917,type,
sK865: ( $i > $i > $o ) > $i ).
thf(func_def_918,type,
sK866: ( $i > $i > $o ) > $i ).
thf(func_def_919,type,
sK867: ( $i > $i > $o ) > $i ).
thf(func_def_920,type,
sK868: ( $i > $i > $o ) > $i ).
thf(func_def_921,type,
sK869: ( $i > $i > $o ) > $i ).
thf(func_def_922,type,
sK870: ( $i > $i > $o ) > $i ).
thf(func_def_923,type,
sK871: ( $i > $i > $o ) > $i ).
thf(func_def_924,type,
sK872: ( $i > $i > $o ) > $i ).
thf(func_def_925,type,
sK873: ( $i > $i > $o ) > $i ).
thf(func_def_926,type,
sK874: ( $i > $i > $o ) > $i ).
thf(func_def_927,type,
sK875: ( $i > $i > $o ) > $i ).
thf(func_def_928,type,
sK876: ( $i > $i > $o ) > $i ).
thf(func_def_929,type,
sK877: ( $i > $i > $o ) > $i ).
thf(func_def_930,type,
sK878: ( $i > $i > $o ) > $i ).
thf(func_def_931,type,
sK879: ( $i > $i > $o ) > $i ).
thf(func_def_932,type,
sK880: ( $i > $i > $o ) > $i ).
thf(func_def_933,type,
sK881: ( $i > $i > $o ) > $i ).
thf(func_def_934,type,
sK882: ( $i > $i > $o ) > $i ).
thf(func_def_935,type,
sK883: ( $i > $i > $o ) > $i ).
thf(func_def_936,type,
sK884: ( $i > $i > $o ) > $i ).
thf(func_def_937,type,
sK885: ( $i > $i > $o ) > $i ).
thf(func_def_938,type,
sK886: ( $i > $i > $o ) > $i ).
thf(func_def_939,type,
sK887: ( $i > $i > $o ) > $i ).
thf(func_def_940,type,
sK888: ( $i > $i > $o ) > $i ).
thf(func_def_941,type,
sK889: ( $i > $i > $o ) > $i ).
thf(func_def_942,type,
sK890: ( $i > $i > $o ) > $i ).
thf(func_def_943,type,
sK891: ( $i > $i > $o ) > $i ).
thf(func_def_944,type,
sK892: ( $i > $i > $o ) > $i ).
thf(func_def_945,type,
sK893: ( $i > $i > $o ) > $i ).
thf(func_def_946,type,
sK894: ( $i > $i > $o ) > $i ).
thf(func_def_947,type,
sK895: ( $i > $i > $o ) > $i ).
thf(func_def_948,type,
sK896: ( $i > $i > $o ) > $i ).
thf(func_def_949,type,
sK897: ( $i > $i > $o ) > $i ).
thf(func_def_950,type,
sK898: ( $i > $i > $o ) > $i ).
thf(func_def_951,type,
sK899: ( $i > $i > $o ) > $i ).
thf(func_def_952,type,
sK900: ( $i > $i > $o ) > $i ).
thf(func_def_953,type,
sK901: ( $i > $i > $o ) > $i ).
thf(func_def_954,type,
sK902: ( $i > $i > $o ) > $i ).
thf(func_def_955,type,
sK903: ( $i > $i > $o ) > $i ).
thf(func_def_956,type,
sK904: ( $i > $i > $o ) > $i ).
thf(func_def_957,type,
sK905: ( $i > $i > $o ) > $i ).
thf(func_def_958,type,
sK906: ( $i > $i > $o ) > $i ).
thf(func_def_959,type,
sK907: ( $i > $i > $o ) > $i ).
thf(func_def_960,type,
sK908: ( $i > $i > $o ) > $i ).
thf(func_def_961,type,
sK909: ( $i > $i > $o ) > $i ).
thf(func_def_962,type,
sK910: ( $i > $i > $o ) > $i ).
thf(func_def_963,type,
sK911: ( $i > $i > $o ) > $i ).
thf(func_def_964,type,
sK912: ( $i > $i > $o ) > $i ).
thf(func_def_965,type,
sK913: ( $i > $i > $o ) > $i ).
thf(func_def_966,type,
sK914: ( $i > $i > $o ) > $i ).
thf(func_def_967,type,
sK915: ( $i > $i > $o ) > $i ).
thf(func_def_968,type,
sK916: ( $i > $i > $o ) > $i ).
thf(func_def_969,type,
sK917: ( $i > $i > $o ) > $i ).
thf(func_def_970,type,
sK918: ( $i > $i > $o ) > $i ).
thf(func_def_971,type,
sK919: ( $i > $i > $o ) > $i ).
thf(func_def_972,type,
sK920: ( $i > $i > $o ) > $i ).
thf(func_def_973,type,
sK921: ( $i > $i > $o ) > $i ).
thf(func_def_974,type,
sK922: ( $i > $i > $o ) > $i ).
thf(func_def_975,type,
sK923: ( $i > $i > $o ) > $i ).
thf(func_def_976,type,
sK924: ( $i > $i > $o ) > $i ).
thf(func_def_977,type,
sK925: ( $i > $i > $o ) > $i ).
thf(func_def_978,type,
sK926: ( $i > $i > $o ) > $i ).
thf(func_def_979,type,
sK927: ( $i > $i > $o ) > $i ).
thf(func_def_980,type,
sK928: ( $i > $i > $o ) > $i ).
thf(func_def_981,type,
sK929: ( $i > $i > $o ) > $i ).
thf(func_def_982,type,
sK930: ( $i > $i > $o ) > $i ).
thf(func_def_983,type,
sK931: ( $i > $i > $o ) > $i ).
thf(func_def_984,type,
sK932: ( $i > $i > $o ) > $i ).
thf(func_def_985,type,
sK933: ( $i > $i > $o ) > $i ).
thf(func_def_986,type,
sK934: ( $i > $i > $o ) > $i ).
thf(func_def_987,type,
sK935: ( $i > $i > $o ) > $i ).
thf(func_def_988,type,
sK936: ( $i > $i > $o ) > $i ).
thf(func_def_989,type,
sK937: ( $i > $i > $o ) > $i ).
thf(func_def_990,type,
sK938: ( $i > $i > $o ) > $i ).
thf(func_def_991,type,
sK939: ( $i > $i > $o ) > $i ).
thf(func_def_992,type,
sK940: ( $i > $i > $o ) > $i ).
thf(func_def_993,type,
sK941: ( $i > $i > $o ) > $i ).
thf(func_def_994,type,
sK942: ( $i > $i > $o ) > $i ).
thf(func_def_995,type,
sK943: ( $i > $i > $o ) > $i ).
thf(func_def_996,type,
sK944: ( $i > $i > $o ) > $i ).
thf(func_def_997,type,
sK945: ( $i > $i > $o ) > $i ).
thf(func_def_998,type,
sK946: ( $i > $i > $o ) > $i ).
thf(func_def_999,type,
sK947: ( $i > $i > $o ) > $i ).
thf(func_def_1000,type,
sK948: ( $i > $i > $o ) > $i ).
thf(func_def_1001,type,
sK949: ( $i > $i > $o ) > $i ).
thf(func_def_1002,type,
sK950: ( $i > $i > $o ) > $i ).
thf(func_def_1003,type,
sK951: ( $i > $i > $o ) > $i ).
thf(func_def_1004,type,
sK952: ( $i > $i > $o ) > $i ).
thf(func_def_1005,type,
sK953: ( $i > $i > $o ) > $i ).
thf(func_def_1006,type,
sK954: ( $i > $i > $o ) > $i ).
thf(func_def_1007,type,
sK955: ( $i > $i > $o ) > $i ).
thf(func_def_1008,type,
sK956: ( $i > $i > $o ) > $i ).
thf(func_def_1009,type,
sK957: ( $i > $i > $o ) > $i ).
thf(func_def_1010,type,
sK958: ( $i > $i > $o ) > $i ).
thf(func_def_1011,type,
sK959: ( $i > $i > $o ) > $i ).
thf(func_def_1012,type,
sK960: ( $i > $i > $o ) > $i ).
thf(func_def_1013,type,
sK961: ( $i > $i > $o ) > $i ).
thf(func_def_1014,type,
sK962: ( $i > $i > $o ) > $i ).
thf(func_def_1015,type,
sK963: ( $i > $i > $o ) > $i ).
thf(func_def_1016,type,
sK964: ( $i > $i > $o ) > $i ).
thf(func_def_1017,type,
sK965: ( $i > $i > $o ) > $i ).
thf(func_def_1018,type,
sK966: ( $i > $i > $o ) > $i ).
thf(func_def_1019,type,
sK967: ( $i > $i > $o ) > $i ).
thf(func_def_1020,type,
sK968: ( $i > $i > $o ) > $i ).
thf(func_def_1021,type,
sK969: ( $i > $i > $o ) > $i ).
thf(func_def_1022,type,
sK970: ( $i > $i > $o ) > $i ).
thf(func_def_1023,type,
sK971: ( $i > $i > $o ) > $i ).
thf(func_def_1024,type,
sK972: ( $i > $i > $o ) > $i ).
thf(func_def_1025,type,
sK973: ( $i > $i > $o ) > $i ).
thf(func_def_1026,type,
sK974: ( $i > $i > $o ) > $i ).
thf(func_def_1027,type,
sK975: ( $i > $i > $o ) > $i ).
thf(func_def_1028,type,
sK976: ( $i > $i > $o ) > $i ).
thf(func_def_1029,type,
sK977: ( $i > $i > $o ) > $i ).
thf(func_def_1030,type,
sK978: ( $i > $i > $o ) > $i ).
thf(func_def_1031,type,
sK979: ( $i > $i > $o ) > $i ).
thf(func_def_1032,type,
sK980: ( $i > $i > $o ) > $i ).
thf(func_def_1033,type,
sK981: ( $i > $i > $o ) > $i ).
thf(func_def_1034,type,
sK982: ( $i > $i > $o ) > $i ).
thf(func_def_1035,type,
sK983: ( $i > $i > $o ) > $i ).
thf(func_def_1036,type,
sK984: ( $i > $i > $o ) > $i ).
thf(func_def_1037,type,
sK985: ( $i > $i > $o ) > $i ).
thf(func_def_1038,type,
sK986: ( $i > $i > $o ) > $i ).
thf(func_def_1039,type,
sK987: ( $i > $i > $o ) > $i ).
thf(func_def_1040,type,
sK988: ( $i > $i > $o ) > $i ).
thf(func_def_1041,type,
sK989: ( $i > $i > $o ) > $i ).
thf(func_def_1042,type,
sK990: ( $i > $i > $o ) > $i ).
thf(func_def_1043,type,
sK991: ( $i > $i > $o ) > $i ).
thf(func_def_1044,type,
sK992: ( $i > $i > $o ) > $i ).
thf(func_def_1045,type,
sK993: ( $i > $i > $o ) > $i ).
thf(func_def_1046,type,
sK994: ( $i > $i > $o ) > $i ).
thf(func_def_1047,type,
sK995: ( $i > $i > $o ) > $i ).
thf(func_def_1048,type,
sK996: ( $i > $i > $o ) > $i ).
thf(func_def_1049,type,
sK997: ( $i > $i > $o ) > $i ).
thf(func_def_1050,type,
sK998: ( $i > $i > $o ) > $i ).
thf(func_def_1051,type,
sK999: ( $i > $i > $o ) > $i ).
thf(func_def_1052,type,
sK1000: ( $i > $i > $o ) > $i ).
thf(func_def_1053,type,
sK1001: ( $i > $i > $o ) > $i ).
thf(func_def_1054,type,
sK1002: ( $i > $i > $o ) > $i ).
thf(func_def_1055,type,
sK1003: ( $i > $i > $o ) > $i ).
thf(func_def_1056,type,
sK1004: ( $i > $i > $o ) > $i ).
thf(func_def_1057,type,
sK1005: ( $i > $i > $o ) > $i ).
thf(func_def_1058,type,
sK1006: ( $i > $i > $o ) > $i ).
thf(func_def_1059,type,
sK1007: ( $i > $i > $o ) > $i ).
thf(func_def_1060,type,
sK1008: ( $i > $i > $o ) > $i ).
thf(func_def_1061,type,
sK1009: ( $i > $i > $o ) > $i ).
thf(func_def_1062,type,
sK1010: ( $i > $i > $o ) > $i ).
thf(func_def_1063,type,
sK1011: ( $i > $i > $o ) > $i ).
thf(func_def_1064,type,
sK1012: ( $i > $i > $o ) > $i ).
thf(func_def_1065,type,
sK1013: ( $i > $i > $o ) > $i ).
thf(func_def_1066,type,
sK1014: ( $i > $i > $o ) > $i ).
thf(func_def_1067,type,
sK1015: ( $i > $i > $o ) > $i ).
thf(func_def_1068,type,
sK1016: ( $i > $i > $o ) > $i ).
thf(func_def_1069,type,
sK1017: ( $i > $i > $o ) > $i ).
thf(func_def_1070,type,
sK1018: ( $i > $i > $o ) > $i ).
thf(func_def_1071,type,
sK1019: ( $i > $i > $o ) > $i ).
thf(func_def_1072,type,
sK1020: ( $i > $i > $o ) > $i ).
thf(func_def_1073,type,
sK1021: ( $i > $i > $o ) > $i ).
thf(func_def_1074,type,
sK1022: ( $i > $i > $o ) > $i ).
thf(func_def_1075,type,
sK1023: ( $i > $i > $o ) > $i ).
thf(func_def_1076,type,
sK1024: ( $i > $i > $o ) > $i ).
thf(func_def_1077,type,
sK1025: ( $i > $i > $o ) > $i ).
thf(func_def_1078,type,
sK1026: ( $i > $i > $o ) > $i ).
thf(func_def_1079,type,
sK1027: ( $i > $i > $o ) > $i ).
thf(func_def_1080,type,
sK1028: ( $i > $i > $o ) > $i ).
thf(func_def_1081,type,
sK1029: ( $i > $i > $o ) > $i ).
thf(func_def_1082,type,
sK1030: ( $i > $i > $o ) > $i ).
thf(func_def_1083,type,
sK1031: ( $i > $i > $o ) > $i ).
thf(func_def_1084,type,
sK1032: ( $i > $i > $o ) > $i ).
thf(func_def_1085,type,
sK1033: ( $i > $i > $o ) > $i ).
thf(func_def_1086,type,
sK1034: ( $i > $i > $o ) > $i ).
thf(func_def_1087,type,
sK1035: ( $i > $i > $o ) > $i ).
thf(func_def_1088,type,
sK1036: ( $i > $i > $o ) > $i ).
thf(func_def_1089,type,
sK1037: ( $i > $i > $o ) > $i ).
thf(func_def_1090,type,
sK1038: ( $i > $i > $o ) > $i ).
thf(func_def_1091,type,
sK1039: ( $i > $i > $o ) > $i ).
thf(func_def_1092,type,
sK1040: ( $i > $i > $o ) > $i ).
thf(func_def_1093,type,
sK1041: ( $i > $i > $o ) > $i ).
thf(func_def_1094,type,
sK1042: ( $i > $i > $o ) > $i ).
thf(func_def_1095,type,
sK1043: ( $i > $i > $o ) > $i ).
thf(func_def_1096,type,
sK1044: ( $i > $i > $o ) > $i ).
thf(func_def_1097,type,
sK1045: ( $i > $i > $o ) > $i ).
thf(func_def_1098,type,
sK1046: ( $i > $i > $o ) > $i ).
thf(func_def_1099,type,
sK1047: ( $i > $i > $o ) > $i ).
thf(func_def_1100,type,
sK1048: ( $i > $i > $o ) > $i ).
thf(func_def_1101,type,
sK1049: ( $i > $i > $o ) > $i ).
thf(func_def_1102,type,
sK1050: ( $i > $i > $o ) > $i ).
thf(func_def_1103,type,
sK1051: ( $i > $i > $o ) > $i ).
thf(func_def_1104,type,
sK1052: ( $i > $i > $o ) > $i ).
thf(func_def_1105,type,
sK1053: ( $i > $i > $o ) > $i ).
thf(func_def_1106,type,
sK1054: ( $i > $i > $o ) > $i ).
thf(func_def_1107,type,
sK1055: ( $i > $i > $o ) > $i ).
thf(func_def_1108,type,
sK1056: ( $i > $i > $o ) > $i ).
thf(func_def_1109,type,
sK1057: ( $i > $i > $o ) > $i ).
thf(func_def_1110,type,
sK1058: ( $i > $i > $o ) > $i ).
thf(func_def_1111,type,
sK1059: ( $i > $i > $o ) > $i ).
thf(func_def_1112,type,
sK1060: ( $i > $i > $o ) > $i ).
thf(f7204,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f721,f57]) ).
thf(f57,plain,
! [X0: $i,X1: $i] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f53,f53]) ).
thf(f53,plain,
! [X2: $i] :
( ( d2unsorted @ d_unsorted_0 )
= X2 ),
inference(forward_demodulation,[status(thm)],[f40,f34]) ).
thf(f34,plain,
! [X4: d_unsorted] : ( d_unsorted_0 = X4 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
!= ( d2unsorted @ X0 ) )
| ( X0 = X1 ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y4 = Y2 )
| ~ ( Y0 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y6 @ Y8 )
| ( Y1 @ Y7 @ Y8 )
| ~ ( Y1 @ Y7 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) ) )
& ! [X2: $i] :
( ( d2unsorted @ ( sK0 @ X2 ) )
= X2 )
& ( trsc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ! [X4: d_unsorted] : ( d_unsorted_0 = X4 )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y8 ) ) ) ) )
| ( Y1 @ Y3 @ Y2 )
| ( Y3 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y7 @ Y8 )
| ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y4 @ Y7 @ Y6 ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( ( Y5 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y5 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y2 @ Y4 @ Y3 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ( Y4 = Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y8 @ Y6 )
| ~ ( Y2 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y7 )
| ~ ( Y1 @ Y7 @ Y5 ) ) ) ) )
| ( Y1 @ Y4 @ Y3 )
| ( Y4 = Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) )
| ( Y5 @ Y3 @ Y4 ) ) )
& ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y7 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( join
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y6 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ( Y1 != Y2 ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 @ Y4 )
| ( Y0 @ Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y2 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) )
| ( Y1 @ Y4 ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13]) ).
thf(f13,plain,
! [X2: $i] :
( ? [X3: d_unsorted] :
( ( d2unsorted @ X3 )
= X2 )
=> ( ( d2unsorted @ ( sK0 @ X2 ) )
= X2 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
!= ( d2unsorted @ X0 ) )
| ( X0 = X1 ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y4 = Y2 )
| ~ ( Y0 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y6 @ Y8 )
| ( Y1 @ Y7 @ Y8 )
| ~ ( Y1 @ Y7 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) ) )
& ! [X2: $i] :
? [X3: d_unsorted] :
( ( d2unsorted @ X3 )
= X2 )
& ( trsc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ! [X4: d_unsorted] : ( d_unsorted_0 = X4 )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y8 ) ) ) ) )
| ( Y1 @ Y3 @ Y2 )
| ( Y3 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y7 @ Y8 )
| ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y4 @ Y7 @ Y6 ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( ( Y5 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y5 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y2 @ Y4 @ Y3 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ( Y4 = Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y8 @ Y6 )
| ~ ( Y2 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y7 )
| ~ ( Y1 @ Y7 @ Y5 ) ) ) ) )
| ( Y1 @ Y4 @ Y3 )
| ( Y4 = Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) )
| ( Y5 @ Y3 @ Y4 ) ) )
& ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y7 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( join
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y6 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ( Y1 != Y2 ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 @ Y4 )
| ( Y0 @ Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y2 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) )
| ( Y1 @ Y4 ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
( ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( ( d2unsorted @ X3 )
!= ( d2unsorted @ X4 ) )
| ( X3 = X4 ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y4 = Y2 )
| ~ ( Y0 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y6 @ Y8 )
| ( Y1 @ Y7 @ Y8 )
| ~ ( Y1 @ Y7 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) ) )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ( trsc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ! [X2: d_unsorted] : ( d_unsorted_0 = X2 )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y8 ) ) ) ) )
| ( Y1 @ Y3 @ Y2 )
| ( Y3 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y7 @ Y8 )
| ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y4 @ Y7 @ Y6 ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( ( Y5 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y5 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y2 @ Y4 @ Y3 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ( Y4 = Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y8 @ Y6 )
| ~ ( Y2 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y7 )
| ~ ( Y1 @ Y7 @ Y5 ) ) ) ) )
| ( Y1 @ Y4 @ Y3 )
| ( Y4 = Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) )
| ( Y5 @ Y3 @ Y4 ) ) )
& ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y7 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( join
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y6 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ( Y1 != Y2 ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 @ Y4 )
| ( Y0 @ Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y2 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) )
| ( Y1 @ Y4 ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X2: d_unsorted] : ( d_unsorted_0 = X2 )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( ( d2unsorted @ X3 )
= ( d2unsorted @ X4 ) )
=> ( X3 = X4 ) )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y7 )
| ~ ( Y1 @ Y7 @ Y5 ) ) ) ) )
| ( Y1 @ Y4 @ Y3 )
| ( Y4 = Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) )
| ( Y5 @ Y3 @ Y4 ) ) )
& ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y7 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( join
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y6 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ( Y1 != Y2 ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y2 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) ) )
& ( trsc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) ) ) )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y2 @ Y4 @ Y3 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ( Y4 = Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y8 @ Y6 )
| ~ ( Y2 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
& ( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) )
| ( Y1 @ Y4 ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y4 = Y2 )
| ~ ( Y0 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y6 @ Y8 )
| ( Y1 @ Y7 @ Y8 )
| ~ ( Y1 @ Y7 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 @ Y4 )
| ( Y0 @ Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y8 ) ) ) ) )
| ( Y1 @ Y3 @ Y2 )
| ( Y3 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y7 @ Y8 )
| ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y4 @ Y7 @ Y6 ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( ( Y5 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y5 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y2 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) ) )
& ! [X5: $i] :
? [X6: d_unsorted] :
( ( d2unsorted @ X6 )
= X5 )
& ( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y2 @ Y4 @ Y3 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ( Y4 = Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y8 @ Y6 )
| ~ ( Y2 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
& ( trsc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) ) )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ! [X97: d_unsorted] : ( d_unsorted_0 = X97 )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 @ Y4 )
| ( Y0 @ Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y8 ) ) ) ) )
| ( Y1 @ Y3 @ Y2 )
| ( Y3 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y7 @ Y8 )
| ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y4 @ Y7 @ Y6 ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( ( Y5 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y5 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y4 = Y2 )
| ~ ( Y0 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y6 @ Y8 )
| ( Y1 @ Y7 @ Y8 )
| ~ ( Y1 @ Y7 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( join
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y6 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ( Y1 != Y2 ) ) ) )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) )
| ( Y1 @ Y4 ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ! [X264: d_unsorted,X265: d_unsorted] :
( ( ( d2unsorted @ X264 )
= ( d2unsorted @ X265 ) )
=> ( X264 = X265 ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y7 )
| ~ ( Y1 @ Y7 @ Y5 ) ) ) ) )
| ( Y1 @ Y4 @ Y3 )
| ( Y4 = Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) )
| ( Y5 @ Y3 @ Y4 ) ) )
& ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y7 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( ( term
= ( ^ [X0: $i > $i > $o] :
! [X1: $i > $o,X2: $i] :
( ~ ( X1 @ X2 )
| ~ ! [X3: $i] :
( ~ ! [X4: $i] :
( ~ ( X1 @ X4 )
| ~ ( X0 @ X3 @ X4 ) )
| ~ ( X1 @ X3 ) ) ) ) )
& ! [X5: $i] :
? [X6: d_unsorted] :
( ( d2unsorted @ X6 )
= X5 )
& ( tc
= ( ^ [X7: $i > $i > $o,X8: $i,X9: $i] :
! [X10: $i > $i > $o] :
( ~ ! [X11: $i,X12: $i] :
( ~ ( X7 @ X11 @ X12 )
| ( X10 @ X11 @ X12 ) )
| ~ ! [X13: $i,X14: $i,X15: $i] :
( ~ ( X10 @ X13 @ X14 )
| ~ ( X10 @ X14 @ X15 )
| ( X10 @ X13 @ X15 ) )
| ( X10 @ X8 @ X9 ) ) ) )
& ( total
= ( ^ [X16: $i > $i > $o] :
! [X17: $i,X18: $i] :
( ( X17 = X18 )
| ( X16 @ X17 @ X18 )
| ( X16 @ X18 @ X17 ) ) ) )
& ( ( ^ [X19: $i > $i > $o] :
! [X20: $i > $i > $o,X21: $i,X22: $i,X23: $i > $i > $o,X24: $i] :
( ~ ! [X25: $i,X26: $i] :
( ~ ( X19 @ X26 @ X25 )
| ( X23 @ X26 @ X25 ) )
| ~ ! [X27: $i,X28: $i] :
( ~ ( X19 @ X27 @ X28 )
| ( X20 @ X27 @ X28 ) )
| ~ ! [X29: $i,X30: $i,X31: $i] :
( ( X23 @ X30 @ X31 )
| ~ ( X23 @ X30 @ X29 )
| ~ ( X23 @ X29 @ X31 ) )
| ~ ( X19 @ X24 @ X22 )
| ~ ! [X32: $i,X33: $i,X34: $i] :
( ( X20 @ X32 @ X34 )
| ~ ( X20 @ X32 @ X33 )
| ~ ( X20 @ X33 @ X34 ) )
| ~ ! [X35: $i] :
( ~ ! [X36: $i > $i > $o] :
( ~ ! [X37: $i,X38: $i] :
( ( X36 @ X38 @ X37 )
| ~ ( X19 @ X38 @ X37 ) )
| ~ ! [X39: $i,X40: $i,X41: $i] :
( ( X36 @ X39 @ X41 )
| ~ ( X36 @ X40 @ X41 )
| ~ ( X36 @ X39 @ X40 ) )
| ( X36 @ X22 @ X35 ) )
| ~ ! [X42: $i > $i > $o] :
( ~ ! [X43: $i,X44: $i,X45: $i] :
( ~ ( X42 @ X43 @ X44 )
| ~ ( X42 @ X44 @ X45 )
| ( X42 @ X43 @ X45 ) )
| ( X42 @ X21 @ X35 )
| ~ ! [X46: $i,X47: $i] :
( ~ ( X19 @ X46 @ X47 )
| ( X42 @ X46 @ X47 ) ) ) )
| ( X21 = X22 )
| ( X20 @ X22 @ X21 )
| ( ~ ! [X48: $i > $i > $o] :
( ~ ! [X49: $i,X50: $i] :
( ~ ( X19 @ X50 @ X49 )
| ( X48 @ X50 @ X49 ) )
| ~ ! [X51: $i,X52: $i,X53: $i] :
( ( X48 @ X53 @ X52 )
| ~ ( X48 @ X53 @ X51 )
| ~ ( X48 @ X51 @ X52 ) )
| ( X48 @ X24 @ X21 ) )
& ( X21 != X24 ) )
| ( X23 @ X21 @ X22 ) ) )
= sconfl )
& ( ( ^ [X54: $i > $i > $o,X55: $i,X56: $i] :
( ( X55 = X56 )
| ! [X57: $i > $i > $o] :
( ( X57 @ X56 @ X55 )
| ~ ! [X58: $i,X59: $i] :
( ( X57 @ X58 @ X59 )
| ~ ( X54 @ X58 @ X59 ) )
| ~ ! [X60: $i,X61: $i,X62: $i] :
( ~ ( X57 @ X62 @ X60 )
| ( X57 @ X61 @ X60 )
| ~ ( X57 @ X61 @ X62 ) ) )
| ! [X63: $i > $i > $o] :
( ( X63 @ X55 @ X56 )
| ~ ! [X64: $i,X65: $i] :
( ( X63 @ X65 @ X64 )
| ~ ( X54 @ X65 @ X64 ) )
| ~ ! [X66: $i,X67: $i,X68: $i] :
( ~ ( X63 @ X66 @ X67 )
| ~ ( X63 @ X68 @ X66 )
| ( X63 @ X68 @ X67 ) ) ) ) )
= trsc )
& ( ( ^ [X69: $i > $i > $o] :
! [X70: $i,X71: $i,X72: $i] :
( ( X69 @ X70 @ X72 )
| ~ ( X69 @ X70 @ X71 )
| ~ ( X69 @ X71 @ X72 ) ) )
= trans )
& ( ( ^ [X73: $i > $i > $o] :
( ! [X74: $i,X75: $i] :
( ( X74 = X75 )
| ~ ( X73 @ X75 @ X74 )
| ~ ( X73 @ X74 @ X75 ) )
& ! [X76: $i,X77: $i,X78: $i] :
( ( X73 @ X78 @ X77 )
| ~ ( X73 @ X78 @ X76 )
| ~ ( X73 @ X76 @ X77 ) )
& ! [X79: $i] : ( X73 @ X79 @ X79 ) ) )
= po )
& ( ( ^ [X80: $i > $i > $o] :
! [X81: $i] : ( X80 @ X81 @ X81 ) )
= refl )
& ( ( ^ [X82: $i > $i > $o,X83: $i,X84: $i] :
( ! [X85: $i] :
~ ( X82 @ X83 @ X85 )
& ( ( X83 = X84 )
| ! [X86: $i > $i > $o] :
( ( X86 @ X84 @ X83 )
| ~ ! [X87: $i,X88: $i,X89: $i] :
( ~ ( X86 @ X88 @ X87 )
| ~ ( X86 @ X87 @ X89 )
| ( X86 @ X88 @ X89 ) )
| ~ ! [X90: $i,X91: $i] :
( ~ ( X82 @ X91 @ X90 )
| ( X86 @ X91 @ X90 ) ) ) ) ) )
= nfof )
& ( ( ^ [X92: ( $i > $i > $o ) > $i > $i > $o] :
! [X93: $i > $i > $o] :
( ( X92 @ X93 )
= ( X92 @ ( X92 @ X93 ) ) ) )
= idem )
& ( ( ^ [X94: $i > $i > $o,X95: $i,X96: $i] :
( ( X95 = X96 )
| ( X94 @ X95 @ X96 ) ) )
= rc )
& ! [X97: d_unsorted] : ( d_unsorted_0 = X97 )
& ( mono
= ( ^ [X98: ( $i > $i > $o ) > $i > $i > $o] :
! [X99: $i,X100: $i > $i > $o,X101: $i > $i > $o,X102: $i] :
( ( X98 @ X101 @ X102 @ X99 )
| ~ ( X98 @ X100 @ X102 @ X99 )
| ~ ! [X103: $i,X104: $i] :
( ~ ( X100 @ X104 @ X103 )
| ( X101 @ X104 @ X103 ) ) ) ) )
& ( norm
= ( ^ [X105: $i > $i > $o] :
! [X106: $i,X107: $i] :
( ~ ( X105 @ X107 @ X106 )
| ~ ! [X108: $i] :
( ~ ! [X109: $i > $i > $o] :
( ~ ! [X110: $i,X111: $i,X112: $i] :
( ~ ( X109 @ X111 @ X110 )
| ( X109 @ X112 @ X110 )
| ~ ( X109 @ X112 @ X111 ) )
| ~ ! [X113: $i,X114: $i] :
( ( X109 @ X113 @ X114 )
| ~ ( X105 @ X113 @ X114 ) )
| ( X109 @ X107 @ X108 ) )
| ~ ! [X115: $i] :
~ ( X105 @ X108 @ X115 ) ) ) ) )
& ( ( ^ [X116: $i > $i > $o] :
( ! [X117: $i,X118: $i] :
( ~ ( X116 @ X117 @ X118 )
| ~ ( X116 @ X118 @ X117 ) )
& ! [X119: $i,X120: $i,X121: $i] :
( ~ ( X116 @ X121 @ X119 )
| ~ ( X116 @ X120 @ X121 )
| ( X116 @ X120 @ X119 ) ) ) )
= so )
& ( ( ^ [X122: $i > $i > $o] :
! [X123: $i] :
~ ( X122 @ X123 @ X123 ) )
= irrefl )
& ( antisymm
= ( ^ [X124: $i > $i > $o] :
! [X125: $i,X126: $i] :
( ~ ( X124 @ X126 @ X125 )
| ( X125 = X126 )
| ~ ( X124 @ X125 @ X126 ) ) ) )
& ( ( ^ [X127: $i > $i > $o,X128: $i,X129: $i] : ( X127 @ X129 @ X128 ) )
= inv )
& ( ( ^ [X130: $i > $i > $o] :
! [X131: $i,X132: $i] :
( ~ ( X130 @ X131 @ X132 )
| ( X130 @ X132 @ X131 ) ) )
= symm )
& ( ( ^ [X133: $i > $i > $o,X134: $i,X135: $i] :
( ( X133 @ X135 @ X134 )
| ( X133 @ X134 @ X135 ) ) )
= sc )
& ( subrel
= ( ^ [X136: $i > $i > $o,X137: $i > $i > $o] :
! [X138: $i,X139: $i] :
( ( X137 @ X139 @ X138 )
| ~ ( X136 @ X139 @ X138 ) ) ) )
& ( asymm
= ( ^ [X140: $i > $i > $o] :
! [X141: $i,X142: $i] :
( ~ ( X140 @ X142 @ X141 )
| ~ ( X140 @ X141 @ X142 ) ) ) )
& ( confl
= ( ^ [X143: $i > $i > $o] :
! [X144: $i,X145: $i > $i > $o,X146: $i,X147: $i,X148: $i > $i > $o] :
( ( ~ ! [X149: $i > $i > $o] :
( ~ ! [X150: $i,X151: $i,X152: $i] :
( ~ ( X149 @ X151 @ X152 )
| ~ ( X149 @ X150 @ X151 )
| ( X149 @ X150 @ X152 ) )
| ~ ! [X153: $i,X154: $i] :
( ( X149 @ X153 @ X154 )
| ~ ( X143 @ X153 @ X154 ) )
| ( X149 @ X144 @ X147 ) )
& ( X144 != X147 ) )
| ~ ! [X155: $i,X156: $i] :
( ~ ( X143 @ X155 @ X156 )
| ( X148 @ X155 @ X156 ) )
| ( ( X144 != X146 )
& ~ ! [X157: $i > $i > $o] :
( ~ ! [X158: $i,X159: $i,X160: $i] :
( ~ ( X157 @ X160 @ X158 )
| ~ ( X157 @ X158 @ X159 )
| ( X157 @ X160 @ X159 ) )
| ( X157 @ X144 @ X146 )
| ~ ! [X161: $i,X162: $i] :
( ( X157 @ X162 @ X161 )
| ~ ( X143 @ X162 @ X161 ) ) ) )
| ~ ! [X163: $i,X164: $i] :
( ( X145 @ X163 @ X164 )
| ~ ( X143 @ X163 @ X164 ) )
| ~ ! [X165: $i] :
( ~ ! [X166: $i > $i > $o] :
( ~ ! [X167: $i,X168: $i,X169: $i] :
( ( X166 @ X169 @ X167 )
| ~ ( X166 @ X168 @ X167 )
| ~ ( X166 @ X169 @ X168 ) )
| ( X166 @ X146 @ X165 )
| ~ ! [X170: $i,X171: $i] :
( ~ ( X143 @ X171 @ X170 )
| ( X166 @ X171 @ X170 ) ) )
| ~ ! [X172: $i > $i > $o] :
( ~ ! [X173: $i,X174: $i] :
( ~ ( X143 @ X174 @ X173 )
| ( X172 @ X174 @ X173 ) )
| ~ ! [X175: $i,X176: $i,X177: $i] :
( ~ ( X172 @ X175 @ X177 )
| ( X172 @ X175 @ X176 )
| ~ ( X172 @ X177 @ X176 ) )
| ( X172 @ X147 @ X165 ) ) )
| ( X145 @ X147 @ X146 )
| ~ ! [X178: $i,X179: $i,X180: $i] :
( ~ ( X145 @ X180 @ X179 )
| ( X145 @ X180 @ X178 )
| ~ ( X145 @ X179 @ X178 ) )
| ( X146 = X147 )
| ( X148 @ X146 @ X147 )
| ~ ! [X181: $i,X182: $i,X183: $i] :
( ( X148 @ X183 @ X181 )
| ~ ( X148 @ X183 @ X182 )
| ~ ( X148 @ X182 @ X181 ) ) ) ) )
& ( innf
= ( ^ [X184: $i > $i > $o,X185: $i] :
! [X186: $i] :
~ ( X184 @ X185 @ X186 ) ) )
& ( lconfl
= ( ^ [X187: $i > $i > $o] :
! [X188: $i > $i > $o,X189: $i,X190: $i,X191: $i,X192: $i > $i > $o] :
( ( X188 @ X189 @ X191 )
| ~ ! [X193: $i] :
( ~ ! [X194: $i > $i > $o] :
( ~ ! [X195: $i,X196: $i] :
( ( X194 @ X196 @ X195 )
| ~ ( X187 @ X196 @ X195 ) )
| ( X194 @ X191 @ X193 )
| ~ ! [X197: $i,X198: $i,X199: $i] :
( ~ ( X194 @ X198 @ X199 )
| ( X194 @ X197 @ X199 )
| ~ ( X194 @ X197 @ X198 ) ) )
| ~ ! [X200: $i > $i > $o] :
( ~ ! [X201: $i,X202: $i,X203: $i] :
( ~ ( X200 @ X202 @ X201 )
| ~ ( X200 @ X203 @ X202 )
| ( X200 @ X203 @ X201 ) )
| ~ ! [X204: $i,X205: $i] :
( ( X200 @ X205 @ X204 )
| ~ ( X187 @ X205 @ X204 ) )
| ( X200 @ X189 @ X193 ) ) )
| ~ ! [X206: $i,X207: $i] :
( ( X188 @ X207 @ X206 )
| ~ ( X187 @ X207 @ X206 ) )
| ~ ! [X208: $i,X209: $i] :
( ( X192 @ X209 @ X208 )
| ~ ( X187 @ X209 @ X208 ) )
| ( X192 @ X191 @ X189 )
| ~ ( X187 @ X190 @ X191 )
| ~ ! [X210: $i,X211: $i,X212: $i] :
( ~ ( X188 @ X212 @ X210 )
| ( X188 @ X211 @ X210 )
| ~ ( X188 @ X211 @ X212 ) )
| ~ ! [X213: $i,X214: $i,X215: $i] :
( ~ ( X192 @ X214 @ X215 )
| ( X192 @ X214 @ X213 )
| ~ ( X192 @ X215 @ X213 ) )
| ~ ( X187 @ X190 @ X189 )
| ( X189 = X191 ) ) ) )
& ( ( ^ [X216: $i > $i > $o,X217: $i,X218: $i] :
~ ( ( X217 != X218 )
& ~ ! [X219: $i > $i > $o] :
( ( X219 @ X218 @ X217 )
| ~ ! [X220: $i,X221: $i] :
( ~ ( X216 @ X220 @ X221 )
| ( X219 @ X220 @ X221 ) )
| ~ ! [X222: $i,X223: $i,X224: $i] :
( ~ ( X219 @ X222 @ X223 )
| ( X219 @ X222 @ X224 )
| ~ ( X219 @ X223 @ X224 ) ) )
& ~ ! [X225: $i > $i > $o] :
( ~ ! [X226: $i,X227: $i,X228: $i] :
( ~ ( X225 @ X227 @ X226 )
| ~ ( X225 @ X228 @ X227 )
| ( X225 @ X228 @ X226 ) )
| ~ ! [X229: $i,X230: $i] :
( ~ ( X216 @ X230 @ X229 )
| ( X225 @ X230 @ X229 ) )
| ( X225 @ X217 @ X218 ) )
& ! [X231: $i] :
( ~ ! [X232: $i > $i > $o] :
( ~ ! [X233: $i,X234: $i,X235: $i] :
( ~ ( X232 @ X235 @ X234 )
| ( X232 @ X233 @ X234 )
| ~ ( X232 @ X233 @ X235 ) )
| ( X232 @ X217 @ X231 )
| ~ ! [X236: $i,X237: $i] :
( ( X232 @ X237 @ X236 )
| ~ ( X216 @ X237 @ X236 ) ) )
| ~ ! [X238: $i > $i > $o] :
( ~ ! [X239: $i,X240: $i] :
( ( X238 @ X240 @ X239 )
| ~ ( X216 @ X240 @ X239 ) )
| ~ ! [X241: $i,X242: $i,X243: $i] :
( ~ ( X238 @ X242 @ X241 )
| ( X238 @ X242 @ X243 )
| ~ ( X238 @ X241 @ X243 ) )
| ( X238 @ X218 @ X231 ) ) ) ) )
= join )
& ( ( ^ [X244: $i > $i > $o,X245: $i,X246: $i] :
( ( X245 = X246 )
| ! [X247: $i > $i > $o] :
( ~ ! [X248: $i,X249: $i,X250: $i] :
( ~ ( X247 @ X249 @ X250 )
| ( X247 @ X249 @ X248 )
| ~ ( X247 @ X250 @ X248 ) )
| ( X247 @ X245 @ X246 )
| ~ ! [X251: $i,X252: $i] :
( ( X247 @ X252 @ X251 )
| ~ ( X244 @ X252 @ X251 ) ) ) ) )
= trc )
& ( ind
= ( ^ [X253: $i > $i > $o] :
! [X254: $i,X255: $i > $o] :
( ~ ! [X256: $i] :
( ( X255 @ X256 )
| ~ ! [X257: $i] :
( ( X255 @ X257 )
| ~ ! [X258: $i > $i > $o] :
( ~ ! [X259: $i,X260: $i] :
( ~ ( X253 @ X260 @ X259 )
| ( X258 @ X260 @ X259 ) )
| ~ ! [X261: $i,X262: $i,X263: $i] :
( ( X258 @ X262 @ X261 )
| ~ ( X258 @ X262 @ X263 )
| ~ ( X258 @ X263 @ X261 ) )
| ( X258 @ X256 @ X257 ) ) ) )
| ( X255 @ X254 ) ) ) )
& ! [X264: d_unsorted,X265: d_unsorted] :
( ( ( d2unsorted @ X264 )
= ( d2unsorted @ X265 ) )
=> ( X264 = X265 ) )
& ( infl
= ( ^ [X266: ( $i > $i > $o ) > $i > $i > $o] :
! [X267: $i,X268: $i,X269: $i > $i > $o] :
( ( X266 @ X269 @ X268 @ X267 )
| ~ ( X269 @ X268 @ X267 ) ) ) )
& ( ( ^ [X270: $i > $i > $o] :
! [X271: $i,X272: $i,X273: $i > $i > $o,X274: $i > $i > $o] :
( ~ ! [X275: $i] :
( ~ ! [X276: $i > $i > $o] :
( ~ ! [X277: $i,X278: $i,X279: $i] :
( ( X276 @ X277 @ X279 )
| ~ ( X276 @ X277 @ X278 )
| ~ ( X276 @ X278 @ X279 ) )
| ~ ! [X280: $i,X281: $i] :
( ~ ( X270 @ X280 @ X281 )
| ( X276 @ X280 @ X281 ) )
| ( X276 @ X271 @ X275 ) )
| ~ ! [X282: $i > $i > $o] :
( ~ ! [X283: $i,X284: $i] :
( ~ ( X270 @ X283 @ X284 )
| ( X282 @ X283 @ X284 ) )
| ( X282 @ X272 @ X275 )
| ~ ! [X285: $i,X286: $i,X287: $i] :
( ( X282 @ X285 @ X287 )
| ~ ( X282 @ X286 @ X287 )
| ~ ( X282 @ X285 @ X286 ) ) ) )
| ~ ! [X288: $i,X289: $i] :
( ~ ( X270 @ X288 @ X289 )
| ( X273 @ X288 @ X289 ) )
| ~ ! [X290: $i,X291: $i,X292: $i] :
( ~ ( X273 @ X290 @ X292 )
| ~ ( X273 @ X291 @ X290 )
| ( X273 @ X291 @ X292 ) )
| ( X273 @ X272 @ X271 )
| ( ~ ! [X293: $i > $i > $o] :
( ( X293 @ X271 @ X272 )
| ~ ! [X294: $i,X295: $i] :
( ( X293 @ X294 @ X295 )
| ~ ( X270 @ X294 @ X295 ) )
| ~ ! [X296: $i,X297: $i,X298: $i] :
( ~ ( X293 @ X298 @ X297 )
| ( X293 @ X296 @ X297 )
| ~ ( X293 @ X296 @ X298 ) ) )
& ( X271 != X272 )
& ~ ! [X299: $i > $i > $o] :
( ( X299 @ X272 @ X271 )
| ~ ! [X300: $i,X301: $i,X302: $i] :
( ~ ( X299 @ X301 @ X302 )
| ( X299 @ X300 @ X302 )
| ~ ( X299 @ X300 @ X301 ) )
| ~ ! [X303: $i,X304: $i] :
( ( X299 @ X304 @ X303 )
| ~ ( X270 @ X304 @ X303 ) ) ) )
| ~ ! [X305: $i,X306: $i] :
( ( X274 @ X306 @ X305 )
| ~ ( X270 @ X306 @ X305 ) )
| ( X271 = X272 )
| ( X274 @ X271 @ X272 )
| ~ ! [X307: $i,X308: $i,X309: $i] :
( ~ ( X274 @ X307 @ X309 )
| ~ ( X274 @ X308 @ X307 )
| ( X274 @ X308 @ X309 ) ) ) )
= cr ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( term
= ( ^ [X4: $i > $i > $o] :
! [X18: $i > $o,X19: $i] :
( ~ ( X18 @ X19 )
| ~ ! [X6: $i] :
( ~ ! [X7: $i] :
( ~ ( X18 @ X7 )
| ~ ( X4 @ X6 @ X7 ) )
| ~ ( X18 @ X6 ) ) ) ) )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ( tc
= ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X12: $i,X13: $i,X11: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 ) )
| ( X5 @ X6 @ X7 ) ) ) )
& ( total
= ( ^ [X4: $i > $i > $o] :
! [X6: $i,X7: $i] :
( ( X6 = X7 )
| ( X4 @ X6 @ X7 )
| ( X4 @ X7 @ X6 ) ) ) )
& ( ( ^ [X4: $i > $i > $o] :
! [X31: $i > $i > $o,X7: $i,X11: $i,X30: $i > $i > $o,X6: $i] :
( ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X30 @ X14 @ X15 ) )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X31 @ X14 @ X15 ) )
| ~ ! [X13: $i,X12: $i,X25: $i] :
( ( X30 @ X12 @ X25 )
| ~ ( X30 @ X12 @ X13 )
| ~ ( X30 @ X13 @ X25 ) )
| ~ ( X4 @ X6 @ X11 )
| ~ ! [X12: $i,X13: $i,X26: $i] :
( ( X31 @ X12 @ X26 )
| ~ ( X31 @ X12 @ X13 )
| ~ ( X31 @ X13 @ X26 ) )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X12: $i,X13: $i,X26: $i] :
( ( X5 @ X12 @ X26 )
| ~ ( X5 @ X13 @ X26 )
| ~ ( X5 @ X12 @ X13 ) )
| ( X5 @ X11 @ X27 ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X12: $i,X13: $i,X25: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X25 )
| ( X5 @ X12 @ X25 ) )
| ( X5 @ X7 @ X27 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) ) )
| ( X7 = X11 )
| ( X31 @ X11 @ X7 )
| ( ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X13: $i,X32: $i,X12: $i] :
( ( X5 @ X12 @ X32 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X32 ) )
| ( X5 @ X6 @ X7 ) )
& ( X6 != X7 ) )
| ( X30 @ X7 @ X11 ) ) )
= sconfl )
& ( ( ^ [X4: $i > $i > $o,X16: $i,X17: $i] :
( ( X16 = X17 )
| ! [X5: $i > $i > $o] :
( ( X5 @ X17 @ X16 )
| ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X11: $i,X12: $i,X13: $i] :
( ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 ) ) )
| ! [X5: $i > $i > $o] :
( ( X5 @ X16 @ X17 )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X13: $i,X11: $i,X12: $i] :
( ~ ( X5 @ X13 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X11 ) ) ) ) )
= trsc )
& ( ( ^ [X4: $i > $i > $o] :
! [X6: $i,X7: $i,X11: $i] :
( ( X4 @ X6 @ X11 )
| ~ ( X4 @ X6 @ X7 )
| ~ ( X4 @ X7 @ X11 ) ) )
= trans )
& ( ( ^ [X4: $i > $i > $o] :
( ! [X6: $i,X7: $i] :
( ( X6 = X7 )
| ~ ( X4 @ X7 @ X6 )
| ~ ( X4 @ X6 @ X7 ) )
& ! [X7: $i,X11: $i,X6: $i] :
( ( X4 @ X6 @ X11 )
| ~ ( X4 @ X6 @ X7 )
| ~ ( X4 @ X7 @ X11 ) )
& ! [X6: $i] : ( X4 @ X6 @ X6 ) ) )
= po )
& ( ( ^ [X4: $i > $i > $o] :
! [X6: $i] : ( X4 @ X6 @ X6 ) )
= refl )
& ( ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
( ! [X22: $i] :
~ ( X4 @ X6 @ X22 )
& ( ( X6 = X7 )
| ! [X5: $i > $i > $o] :
( ( X5 @ X7 @ X6 )
| ~ ! [X13: $i,X12: $i,X11: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 ) )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) ) ) ) )
= nfof )
& ( ( ^ [X8: ( $i > $i > $o ) > $i > $i > $o] :
! [X4: $i > $i > $o] :
( ( X8 @ X4 )
= ( X8 @ ( X8 @ X4 ) ) ) )
= idem )
& ( ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
( ( X6 = X7 )
| ( X4 @ X6 @ X7 ) ) )
= rc )
& ! [X1: d_unsorted] : ( d_unsorted_0 = X1 )
& ( mono
= ( ^ [X8: ( $i > $i > $o ) > $i > $i > $o] :
! [X10: $i,X4: $i > $i > $o,X5: $i > $i > $o,X9: $i] :
( ( X8 @ X5 @ X9 @ X10 )
| ~ ( X8 @ X4 @ X9 @ X10 )
| ~ ! [X7: $i,X6: $i] :
( ~ ( X4 @ X6 @ X7 )
| ( X5 @ X6 @ X7 ) ) ) ) )
& ( norm
= ( ^ [X4: $i > $i > $o] :
! [X23: $i,X6: $i] :
( ~ ( X4 @ X6 @ X23 )
| ~ ! [X24: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X11: $i,X13: $i,X12: $i] :
( ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 ) )
| ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X6 @ X24 ) )
| ~ ! [X22: $i] :
~ ( X4 @ X24 @ X22 ) ) ) ) )
& ( ( ^ [X4: $i > $i > $o] :
( ! [X7: $i,X6: $i] :
( ~ ( X4 @ X7 @ X6 )
| ~ ( X4 @ X6 @ X7 ) )
& ! [X11: $i,X6: $i,X7: $i] :
( ~ ( X4 @ X7 @ X11 )
| ~ ( X4 @ X6 @ X7 )
| ( X4 @ X6 @ X11 ) ) ) )
= so )
& ( ( ^ [X4: $i > $i > $o] :
! [X6: $i] :
~ ( X4 @ X6 @ X6 ) )
= irrefl )
& ( antisymm
= ( ^ [X4: $i > $i > $o] :
! [X7: $i,X6: $i] :
( ~ ( X4 @ X6 @ X7 )
| ( X6 = X7 )
| ~ ( X4 @ X7 @ X6 ) ) ) )
& ( ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] : ( X4 @ X7 @ X6 ) )
= inv )
& ( ( ^ [X4: $i > $i > $o] :
! [X6: $i,X7: $i] :
( ~ ( X4 @ X6 @ X7 )
| ( X4 @ X7 @ X6 ) ) )
= symm )
& ( ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
( ( X4 @ X7 @ X6 )
| ( X4 @ X6 @ X7 ) ) )
= sc )
& ( subrel
= ( ^ [X4: $i > $i > $o,X5: $i > $i > $o] :
! [X7: $i,X6: $i] :
( ( X5 @ X6 @ X7 )
| ~ ( X4 @ X6 @ X7 ) ) ) )
& ( asymm
= ( ^ [X4: $i > $i > $o] :
! [X7: $i,X6: $i] :
( ~ ( X4 @ X6 @ X7 )
| ~ ( X4 @ X7 @ X6 ) ) ) )
& ( confl
= ( ^ [X4: $i > $i > $o] :
! [X6: $i,X34: $i > $i > $o,X7: $i,X11: $i,X33: $i > $i > $o] :
( ( ~ ! [X5: $i > $i > $o] :
( ~ ! [X12: $i,X13: $i,X26: $i] :
( ~ ( X5 @ X13 @ X26 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X26 ) )
| ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X6 @ X11 ) )
& ( X6 != X11 ) )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X33 @ X14 @ X15 ) )
| ( ( X6 != X7 )
& ~ ! [X5: $i > $i > $o] :
( ~ ! [X13: $i,X35: $i,X12: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X35 )
| ( X5 @ X12 @ X35 ) )
| ( X5 @ X6 @ X7 )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) ) ) )
| ~ ! [X14: $i,X15: $i] :
( ( X34 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X25: $i,X13: $i,X12: $i] :
( ( X5 @ X12 @ X25 )
| ~ ( X5 @ X13 @ X25 )
| ~ ( X5 @ X12 @ X13 ) )
| ( X5 @ X7 @ X27 )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X12: $i,X26: $i,X13: $i] :
( ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X26 )
| ~ ( X5 @ X13 @ X26 ) )
| ( X5 @ X11 @ X27 ) ) )
| ( X34 @ X11 @ X7 )
| ~ ! [X26: $i,X13: $i,X12: $i] :
( ~ ( X34 @ X12 @ X13 )
| ( X34 @ X12 @ X26 )
| ~ ( X34 @ X13 @ X26 ) )
| ( X7 = X11 )
| ( X33 @ X7 @ X11 )
| ~ ! [X25: $i,X13: $i,X12: $i] :
( ( X33 @ X12 @ X25 )
| ~ ( X33 @ X12 @ X13 )
| ~ ( X33 @ X13 @ X25 ) ) ) ) )
& ( innf
= ( ^ [X4: $i > $i > $o,X6: $i] :
! [X7: $i] :
~ ( X4 @ X6 @ X7 ) ) )
& ( lconfl
= ( ^ [X4: $i > $i > $o] :
! [X28: $i > $i > $o,X7: $i,X6: $i,X11: $i,X29: $i > $i > $o] :
( ( X28 @ X7 @ X11 )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X11 @ X27 )
| ~ ! [X12: $i,X13: $i,X26: $i] :
( ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 )
| ~ ( X5 @ X12 @ X13 ) ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X25: $i,X13: $i,X12: $i] :
( ~ ( X5 @ X13 @ X25 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X25 ) )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X7 @ X27 ) ) )
| ~ ! [X15: $i,X14: $i] :
( ( X28 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X15: $i,X14: $i] :
( ( X29 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X29 @ X11 @ X7 )
| ~ ( X4 @ X6 @ X11 )
| ~ ! [X25: $i,X12: $i,X13: $i] :
( ~ ( X28 @ X13 @ X25 )
| ( X28 @ X12 @ X25 )
| ~ ( X28 @ X12 @ X13 ) )
| ~ ! [X26: $i,X12: $i,X13: $i] :
( ~ ( X29 @ X12 @ X13 )
| ( X29 @ X12 @ X26 )
| ~ ( X29 @ X13 @ X26 ) )
| ~ ( X4 @ X6 @ X7 )
| ( X7 = X11 ) ) ) )
& ( ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
~ ( ( X6 != X7 )
& ~ ! [X5: $i > $i > $o] :
( ( X5 @ X7 @ X6 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X12: $i,X13: $i,X25: $i] :
( ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X25 )
| ~ ( X5 @ X13 @ X25 ) ) )
& ~ ! [X5: $i > $i > $o] :
( ~ ! [X26: $i,X13: $i,X12: $i] :
( ~ ( X5 @ X13 @ X26 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X26 ) )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ( X5 @ X6 @ X7 ) )
& ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X12: $i,X26: $i,X13: $i] :
( ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 )
| ~ ( X5 @ X12 @ X13 ) )
| ( X5 @ X6 @ X27 )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X13: $i,X12: $i,X25: $i] :
( ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X25 )
| ~ ( X5 @ X13 @ X25 ) )
| ( X5 @ X7 @ X27 ) ) ) ) )
= join )
& ( ( ^ [X4: $i > $i > $o,X16: $i,X17: $i] :
( ( X16 = X17 )
| ! [X5: $i > $i > $o] :
( ~ ! [X11: $i,X12: $i,X13: $i] :
( ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X11 )
| ~ ( X5 @ X13 @ X11 ) )
| ( X5 @ X16 @ X17 )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) ) ) ) )
= trc )
& ( ind
= ( ^ [X4: $i > $i > $o] :
! [X21: $i,X20: $i > $o] :
( ~ ! [X6: $i] :
( ( X20 @ X6 )
| ~ ! [X7: $i] :
( ( X20 @ X7 )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X11: $i,X12: $i,X13: $i] :
( ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 ) )
| ( X5 @ X6 @ X7 ) ) ) )
| ( X20 @ X21 ) ) ) )
& ! [X3: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) )
& ( infl
= ( ^ [X8: ( $i > $i > $o ) > $i > $i > $o] :
! [X7: $i,X6: $i,X4: $i > $i > $o] :
( ( X8 @ X4 @ X6 @ X7 )
| ~ ( X4 @ X6 @ X7 ) ) ) )
& ( ( ^ [X4: $i > $i > $o] :
! [X7: $i,X6: $i,X37: $i > $i > $o,X36: $i > $i > $o] :
( ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X12: $i,X13: $i,X25: $i] :
( ( X5 @ X12 @ X25 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X25 ) )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ( X5 @ X7 @ X27 ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ( X5 @ X6 @ X27 )
| ~ ! [X12: $i,X13: $i,X26: $i] :
( ( X5 @ X12 @ X26 )
| ~ ( X5 @ X13 @ X26 )
| ~ ( X5 @ X12 @ X13 ) ) ) )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X37 @ X14 @ X15 ) )
| ~ ! [X13: $i,X12: $i,X26: $i] :
( ~ ( X37 @ X13 @ X26 )
| ~ ( X37 @ X12 @ X13 )
| ( X37 @ X12 @ X26 ) )
| ( X37 @ X6 @ X7 )
| ( ~ ! [X5: $i > $i > $o] :
( ( X5 @ X7 @ X6 )
| ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X12: $i,X11: $i,X13: $i] :
( ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 ) ) )
& ( X6 != X7 )
& ~ ! [X5: $i > $i > $o] :
( ( X5 @ X6 @ X7 )
| ~ ! [X12: $i,X13: $i,X11: $i] :
( ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 ) )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) ) ) )
| ~ ! [X15: $i,X14: $i] :
( ( X36 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X6 = X7 )
| ( X36 @ X7 @ X6 )
| ~ ! [X13: $i,X12: $i,X25: $i] :
( ~ ( X36 @ X13 @ X25 )
| ~ ( X36 @ X12 @ X13 )
| ( X36 @ X12 @ X25 ) ) ) )
= cr ) ),
file('/export/starexec/sandbox/tmp/tmp.L1wr6hYwUS/DTF2THF_12102.p',sev441_1) ).
thf(f40,plain,
! [X2: $i] :
( ( d2unsorted @ ( sK0 @ X2 ) )
= X2 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f721,plain,
sK5 != sK4,
inference(duplicate_literal_removal,[status(thm)],[f720]) ).
thf(f720,plain,
( ( sK5 != sK4 )
| ( sK5 != sK4 ) ),
inference(equality_proxy_clausification,[status(thm)],[f694]) ).
thf(f694,plain,
( ( ( sK5 = sK4 )
= $false )
| ( sK5 != sK4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f693]) ).
thf(f693,plain,
( ( sK5 != sK4 )
| ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ sK5 @ sK4 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) )
| ( sK5 = sK4 ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f662]) ).
thf(f662,plain,
( ( $false
= ( sK4 = sK5 ) )
| ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ sK5 @ sK4 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) )
| ( sK5 = sK4 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( $false
= ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ sK4 @ sK5 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) )
| ( sK4 = sK5 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ sK5 @ sK4 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) )
| ( sK5 = sK4 ) ) )
| ( $false
= ( sK4 = sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK3 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
| ( Y0 @ sK4 @ sK5 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK3 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ sK5 @ sK4 ) ) )
| ( sK4 = sK5 ) )
= $false )
| ( $false
= ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ sK4 @ sK5 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) )
| ( sK4 = sK5 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ sK5 @ sK4 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) )
| ( sK5 = sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK3 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
| ( Y0 @ sK4 @ sK5 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK3 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ sK5 @ sK4 ) ) )
| ( sK4 = sK5 ) )
!= ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ sK4 @ sK5 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) )
| ( sK4 = sK5 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ sK5 @ sK4 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) )
| ( sK5 = sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y4 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK3 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ sK4 @ Y0 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y4 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK3 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ Y0 @ sK4 ) ) )
| ( sK4 = Y0 ) )
@ sK5 )
!= ( ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ sK4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y4 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) )
| ( sK4 = Y0 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ Y0 @ sK4 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y4 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) )
| ( Y0 = sK4 ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ sK4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y4 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) )
| ( sK4 = Y0 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ Y0 @ sK4 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y4 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) )
| ( Y0 = sK4 ) ) )
!= ( ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y4 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK3 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ sK4 @ Y0 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y4 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK3 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ Y0 @ sK4 ) ) )
| ( sK4 = Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ^ [Y0: $i,Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 @ Y3 )
| ~ ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) )
| ( Y0 = Y1 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 @ Y3 )
| ~ ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) )
| ( Y1 = Y0 ) )
@ sK4 )
!= ( ^ [Y0: $i,Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 )
| ~ ( Y2 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( sK3 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y4 @ Y5 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( sK3 @ Y4 @ Y3 )
| ( Y2 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y1 @ Y0 ) ) )
| ( Y0 = Y1 ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ^ [Y0: $i,Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 )
| ~ ( Y2 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( sK3 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y4 @ Y5 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( sK3 @ Y4 @ Y3 )
| ( Y2 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y1 @ Y0 ) ) )
| ( Y0 = Y1 ) ) )
!= ( ^ [Y0: $i,Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 @ Y3 )
| ~ ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) )
| ( Y0 = Y1 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 @ Y3 )
| ~ ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) )
| ( Y1 = Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y2 = Y1 ) )
@ sK3 )
!= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) )
@ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) ) )
!= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y2 = Y1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ^ [Y0: $i > $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ( Y1 @ Y3 @ Y2 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ( Y2 = Y3 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y5 )
| ~ ( Y4 @ Y7 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y5 ) ) ) ) ) )
@ Y0 ) ) ) )
!= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f47,f39,f31,f37,f42]) ).
thf(f42,plain,
( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f37,plain,
( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f31,plain,
( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f39,plain,
( trsc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f47,plain,
( trsc
!= ( ^ [Y0: $i > $i > $o] : ( sc @ ( rc @ ( tc @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( trsc
!= ( ^ [Y0: $i > $i > $o] : ( sc @ ( rc @ ( tc @ Y0 ) ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( trsc
!= ( ^ [Y0: $i > $i > $o] : ( sc @ ( rc @ ( tc @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X0 ) ) ) )
!= trsc ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( ( ^ [X4: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X4 ) ) ) )
!= trsc ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( ^ [X4: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X4 ) ) ) )
= trsc ),
file('/export/starexec/sandbox/tmp/tmp.L1wr6hYwUS/DTF2THF_12102.p',transitive_reflexive_symmetric_closure) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n001.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 09:30:18 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.46 ---- Original DTF file ---
% 0.32/0.46 thf(spec,logic,$$dhol).
% 0.32/0.46 %------------------------------------------------------------------------------
% 0.32/0.46 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.32/0.46 % Domain : Software Verification
% 0.32/0.46 % Problem : Benchmark: SEV441^1, Active target: transitive_reflexive_symmetric_closure
% 0.32/0.46 % Version : Especial.
% 0.32/0.46 % English :
% 0.32/0.46
% 0.32/0.46 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.32/0.46 % Source : [Kon26]
% 0.32/0.46 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.32/0.46
% 0.32/0.46 % Status : Theorem
% 0.32/0.46 % Rating : ? v9.3.0
% 0.32/0.46 % Syntax : Number of formulae : 35 ( 1 unt; 33 typ; 0 def)
% 0.32/0.46 % Number of atoms : 84 ( 51 equ; 0 cnn)
% 0.32/0.46 % Maximal formula atoms : 33 ( 42 avg)
% 0.32/0.46 % Number of connectives : 979 ( 227 ~; 218 |; 43 &; 490 @)
% 0.32/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.32/0.46 % Maximal formula depth : 32 ( 17 avg)
% 0.32/0.46 % Number of types : 4 ( 2 usr)
% 0.32/0.46 % Number of type conns : 262 ( 262 >; 0 *; 0 +; 0 <<)
% 0.32/0.46 % Number of symbols : 32 ( 31 usr; 1 con; 0-3 aty)
% 0.32/0.46 % Number of variables : 311 ( 48 ^; 262 !; 1 ?; 311 :)
% 0.32/0.46 % SPC : TH0_THM_EQU_NAR
% 0.32/0.46
% 0.32/0.46 % Comments :
% 0.32/0.46 %------------------------------------------------------------------------------
% 0.32/0.46 thf(unsorted_type,type,
% 0.32/0.46 unsorted: $tType ).
% 0.32/0.46
% 0.32/0.46 thf(subrel_decl,type,
% 0.32/0.46 subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(inv_decl,type,
% 0.32/0.46 inv: ( $i > $i > $o ) > $i > $i > $o ).
% 0.32/0.46
% 0.32/0.46 thf(idem_decl,type,
% 0.32/0.46 idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(infl_decl,type,
% 0.32/0.46 infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(mono_decl,type,
% 0.32/0.46 mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(refl_decl,type,
% 0.32/0.46 refl: ( $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(irrefl_decl,type,
% 0.32/0.46 irrefl: ( $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(rc_decl,type,
% 0.32/0.46 rc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.32/0.46
% 0.32/0.46 thf(symm_decl,type,
% 0.32/0.46 symm: ( $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(antisymm_decl,type,
% 0.32/0.46 antisymm: ( $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(asymm_decl,type,
% 0.32/0.46 asymm: ( $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(sc_decl,type,
% 0.32/0.46 sc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.32/0.46
% 0.32/0.46 thf(trans_decl,type,
% 0.32/0.46 trans: ( $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(tc_decl,type,
% 0.32/0.46 tc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.32/0.46
% 0.32/0.46 thf(trc_decl,type,
% 0.32/0.46 trc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.32/0.46
% 0.32/0.46 thf(trsc_decl,type,
% 0.32/0.46 trsc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.32/0.46
% 0.32/0.46 thf(po_decl,type,
% 0.32/0.46 po: ( $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(so_decl,type,
% 0.32/0.46 so: ( $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(total_decl,type,
% 0.32/0.46 total: ( $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(term_decl,type,
% 0.32/0.46 term: ( $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(ind_decl,type,
% 0.32/0.46 ind: ( $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(innf_decl,type,
% 0.32/0.46 innf: ( $i > $i > $o ) > $i > $o ).
% 0.32/0.46
% 0.32/0.46 thf(nfof_decl,type,
% 0.32/0.46 nfof: ( $i > $i > $o ) > $i > $i > $o ).
% 0.32/0.46
% 0.32/0.46 thf(norm_decl,type,
% 0.32/0.46 norm: ( $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(join_decl,type,
% 0.32/0.46 join: ( $i > $i > $o ) > $i > $i > $o ).
% 0.32/0.46
% 0.32/0.46 thf(lconfl_decl,type,
% 0.32/0.46 lconfl: ( $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(sconfl_decl,type,
% 0.32/0.46 sconfl: ( $i > $i > $o ) > $o ).
% 0.32/0.46
% 0.32/0.46 thf(confl_decl,type,
% 0.32/0.46 confl: ( $i > $i > $o ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(cr_decl,type,
% 0.32/0.47 cr: ( $i > $i > $o ) > $o ).
% 0.32/0.47
% 0.32/0.47 %----Types of the domains
% 0.32/0.47 thf(d_unsorted_type,type,
% 0.32/0.47 d_unsorted: $tType ).
% 0.32/0.47
% 0.32/0.47 %----Types of the promotion functions
% 0.32/0.47 thf(d2unsorted_decl,type,
% 0.32/0.47 d2unsorted: d_unsorted > $i ).
% 0.32/0.47
% 0.32/0.47 %----Types of the domain elements
% 0.32/0.47 thf(d_unsorted_0_decl,type,
% 0.32/0.47 d_unsorted_0: d_unsorted ).
% 0.32/0.47
% 0.32/0.47 thf(sev441_1,axiom,
% 0.32/0.47 ( ! [U: $i] :
% 0.32/0.47 ? [DU: d_unsorted] :
% 0.32/0.47 ( U
% 0.32/0.47 = ( d2unsorted @ DU ) )
% 0.32/0.47 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 0.32/0.47 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 0.32/0.47 ( ( ( d2unsorted @ DU1 )
% 0.32/0.47 = ( d2unsorted @ DU2 ) )
% 0.32/0.47 => ( DU1 = DU2 ) )
% 0.32/0.47 & ( subrel
% 0.32/0.47 = ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
% 0.32/0.47 ! [X: $i,Y: $i] :
% 0.32/0.47 ( ~ ( R @ X @ Y )
% 0.32/0.47 | ( S @ X @ Y ) ) ) )
% 0.32/0.47 & ( inv
% 0.32/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) )
% 0.32/0.47 & ( idem
% 0.32/0.47 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 0.32/0.47 ! [R: $i > $i > $o] :
% 0.32/0.47 ( ( F @ R )
% 0.32/0.47 = ( F @ ( F @ R ) ) ) ) )
% 0.32/0.47 & ( infl
% 0.32/0.47 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 0.32/0.47 ! [R: $i > $i > $o,X: $i,Y: $i] :
% 0.32/0.47 ( ~ ( R @ X @ Y )
% 0.32/0.47 | ( F @ R @ X @ Y ) ) ) )
% 0.32/0.47 & ( mono
% 0.32/0.47 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 0.32/0.47 ! [R: $i > $i > $o,S: $i > $i > $o,Bound_variable_510: $i,Bound_variable_512: $i] :
% 0.32/0.47 ( ~ ! [X: $i,Y: $i] :
% 0.32/0.47 ( ~ ( R @ X @ Y )
% 0.32/0.47 | ( S @ X @ Y ) )
% 0.32/0.47 | ~ ( F @ R @ Bound_variable_510 @ Bound_variable_512 )
% 0.32/0.47 | ( F @ S @ Bound_variable_510 @ Bound_variable_512 ) ) ) )
% 0.32/0.47 & ( refl
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ! [X: $i] : ( R @ X @ X ) ) )
% 0.32/0.47 & ( irrefl
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ! [X: $i] :
% 0.32/0.47 ~ ( R @ X @ X ) ) )
% 0.32/0.47 & ( rc
% 0.32/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.32/0.47 ( ( X = Y )
% 0.32/0.47 | ( R @ X @ Y ) ) ) )
% 0.32/0.47 & ( symm
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ! [X: $i,Y: $i] :
% 0.32/0.47 ( ~ ( R @ X @ Y )
% 0.32/0.47 | ( R @ Y @ X ) ) ) )
% 0.32/0.47 & ( antisymm
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ! [X: $i,Y: $i] :
% 0.32/0.47 ( ~ ( R @ X @ Y )
% 0.32/0.47 | ~ ( R @ Y @ X )
% 0.32/0.47 | ( X = Y ) ) ) )
% 0.32/0.47 & ( asymm
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ! [X: $i,Y: $i] :
% 0.32/0.47 ( ~ ( R @ X @ Y )
% 0.32/0.47 | ~ ( R @ Y @ X ) ) ) )
% 0.32/0.47 & ( sc
% 0.32/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.32/0.47 ( ( R @ Y @ X )
% 0.32/0.47 | ( R @ X @ Y ) ) ) )
% 0.32/0.47 & ( trans
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ! [X: $i,Y: $i,Z: $i] :
% 0.32/0.47 ( ~ ( R @ X @ Y )
% 0.32/0.47 | ~ ( R @ Y @ Z )
% 0.32/0.47 | ( R @ X @ Z ) ) ) )
% 0.32/0.47 & ( tc
% 0.32/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.32/0.47 ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ X @ Y ) ) ) )
% 0.32/0.47 & ( trc
% 0.32/0.47 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 0.32/0.47 ( ( Flatten_var_0 = Flatten_var_1 )
% 0.32/0.47 | ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 0.32/0.47 & ( trsc
% 0.32/0.47 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 0.32/0.47 ( ( Flatten_var_0 = Flatten_var_1 )
% 0.32/0.47 | ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ Flatten_var_1 @ Flatten_var_0 ) )
% 0.32/0.47 | ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 0.32/0.47 & ( po
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ( ! [X: $i] : ( R @ X @ X )
% 0.32/0.47 & ! [X: $i,Y: $i] :
% 0.32/0.47 ( ~ ( R @ X @ Y )
% 0.32/0.47 | ~ ( R @ Y @ X )
% 0.32/0.47 | ( X = Y ) )
% 0.32/0.47 & ! [X: $i,Y: $i,Z: $i] :
% 0.32/0.47 ( ~ ( R @ X @ Y )
% 0.32/0.47 | ~ ( R @ Y @ Z )
% 0.32/0.47 | ( R @ X @ Z ) ) ) ) )
% 0.32/0.47 & ( so
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ( ! [X: $i,Y: $i] :
% 0.32/0.47 ( ~ ( R @ X @ Y )
% 0.32/0.47 | ~ ( R @ Y @ X ) )
% 0.32/0.47 & ! [X: $i,Y: $i,Z: $i] :
% 0.32/0.47 ( ~ ( R @ X @ Y )
% 0.32/0.47 | ~ ( R @ Y @ Z )
% 0.32/0.47 | ( R @ X @ Z ) ) ) ) )
% 0.32/0.47 & ( total
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ! [X: $i,Y: $i] :
% 0.32/0.47 ( ( X = Y )
% 0.32/0.47 | ( R @ X @ Y )
% 0.32/0.47 | ( R @ Y @ X ) ) ) )
% 0.32/0.47 & ( term
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ! [A: $i > $o,Bound_variable_862: $i] :
% 0.32/0.47 ( ~ ( A @ Bound_variable_862 )
% 0.32/0.47 | ~ ! [X: $i] :
% 0.32/0.47 ( ~ ( A @ X )
% 0.32/0.47 | ~ ! [Y: $i] :
% 0.32/0.47 ( ~ ( A @ Y )
% 0.32/0.47 | ~ ( R @ X @ Y ) ) ) ) ) )
% 0.32/0.47 & ( ind
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ! [P: $i > $o,Bound_variable_917: $i] :
% 0.32/0.47 ( ~ ! [X: $i] :
% 0.32/0.47 ( ~ ! [Y: $i] :
% 0.32/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ X @ Y ) )
% 0.32/0.47 | ( P @ Y ) )
% 0.32/0.47 | ( P @ X ) )
% 0.32/0.47 | ( P @ Bound_variable_917 ) ) ) )
% 0.32/0.47 & ( innf
% 0.32/0.47 = ( ^ [R: $i > $i > $o,X: $i] :
% 0.32/0.47 ! [Y: $i] :
% 0.32/0.47 ~ ( R @ X @ Y ) ) )
% 0.32/0.47 & ( nfof
% 0.32/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.32/0.47 ( ( ( X = Y )
% 0.32/0.47 | ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ Y @ X ) ) )
% 0.32/0.47 & ! [Bound_variable_985: $i] :
% 0.32/0.47 ~ ( R @ X @ Bound_variable_985 ) ) ) )
% 0.32/0.47 & ( norm
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ! [X: $i,Bound_variable_1075: $i] :
% 0.32/0.47 ( ~ ( R @ X @ Bound_variable_1075 )
% 0.32/0.47 | ~ ! [Bound_variable_1049: $i] :
% 0.32/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ X @ Bound_variable_1049 ) )
% 0.32/0.47 | ~ ! [Bound_variable_985: $i] :
% 0.32/0.47 ~ ( R @ Bound_variable_1049 @ Bound_variable_985 ) ) ) ) )
% 0.32/0.47 & ( join
% 0.32/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.32/0.47 ~ ( ( X != Y )
% 0.32/0.47 & ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ Y @ X ) )
% 0.32/0.47 & ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ X @ Y ) )
% 0.32/0.47 & ! [Bound_variable_1218: $i] :
% 0.32/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ Y @ Bound_variable_1218 ) )
% 0.32/0.47 | ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ X @ Bound_variable_1218 ) ) ) ) ) )
% 0.32/0.47 & ( lconfl
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ! [X: $i,Y: $i,Z: $i,Bound_variable_1293: $i > $i > $o,Bound_variable_1309: $i > $i > $o] :
% 0.32/0.47 ( ~ ( R @ X @ Z )
% 0.32/0.47 | ~ ( R @ X @ Y )
% 0.32/0.47 | ( Y = Z )
% 0.32/0.47 | ~ ! [Bound_variable_1218: $i] :
% 0.32/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ Y @ Bound_variable_1218 ) )
% 0.32/0.47 | ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ Z @ Bound_variable_1218 ) ) )
% 0.32/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.32/0.47 ( ~ ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( Bound_variable_1293 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.32/0.47 | ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( Bound_variable_1293 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( Bound_variable_1293 @ Y @ Z )
% 0.32/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.32/0.47 ( ~ ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( Bound_variable_1309 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.32/0.47 | ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( Bound_variable_1309 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( Bound_variable_1309 @ Z @ Y ) ) ) )
% 0.32/0.47 & ( sconfl
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ! [X: $i,Y: $i,Z: $i,Bound_variable_1371: $i > $i > $o,Bound_variable_1387: $i > $i > $o] :
% 0.32/0.47 ( ~ ( R @ X @ Z )
% 0.32/0.47 | ( ( X != Y )
% 0.32/0.47 & ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1347: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1347 )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1347 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ X @ Y ) ) )
% 0.32/0.47 | ( Y = Z )
% 0.32/0.47 | ~ ! [Bound_variable_1218: $i] :
% 0.32/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ Y @ Bound_variable_1218 ) )
% 0.32/0.47 | ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ Z @ Bound_variable_1218 ) ) )
% 0.32/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.32/0.47 ( ~ ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( Bound_variable_1371 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.32/0.47 | ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( Bound_variable_1371 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( Bound_variable_1371 @ Y @ Z )
% 0.32/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.32/0.47 ( ~ ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( Bound_variable_1387 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.32/0.47 | ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( Bound_variable_1387 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( Bound_variable_1387 @ Z @ Y ) ) ) )
% 0.32/0.47 & ( confl
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ! [X: $i,Y: $i,Z: $i,Bound_variable_1444: $i > $i > $o,Bound_variable_1460: $i > $i > $o] :
% 0.32/0.47 ( ( ( X != Z )
% 0.32/0.47 & ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ X @ Z ) ) )
% 0.32/0.47 | ( ( X != Y )
% 0.32/0.47 & ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1422: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1422 )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1422 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ X @ Y ) ) )
% 0.32/0.47 | ( Y = Z )
% 0.32/0.47 | ~ ! [Bound_variable_1218: $i] :
% 0.32/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ Y @ Bound_variable_1218 ) )
% 0.32/0.47 | ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ Z @ Bound_variable_1218 ) ) )
% 0.32/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.32/0.47 ( ~ ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( Bound_variable_1444 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.32/0.47 | ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( Bound_variable_1444 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( Bound_variable_1444 @ Y @ Z )
% 0.32/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.32/0.47 ( ~ ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( Bound_variable_1460 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.32/0.47 | ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( Bound_variable_1460 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( Bound_variable_1460 @ Z @ Y ) ) ) )
% 0.32/0.47 & ( cr
% 0.32/0.47 = ( ^ [R: $i > $i > $o] :
% 0.32/0.47 ! [X: $i,Y: $i,Bound_variable_1522: $i > $i > $o,Bound_variable_1538: $i > $i > $o] :
% 0.32/0.47 ( ( ( X != Y )
% 0.32/0.47 & ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ Y @ X ) )
% 0.32/0.47 & ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ X @ Y ) ) )
% 0.32/0.47 | ( X = Y )
% 0.32/0.47 | ~ ! [Bound_variable_1218: $i] :
% 0.32/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ Y @ Bound_variable_1218 ) )
% 0.32/0.47 | ~ ! [S: $i > $i > $o] :
% 0.32/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.32/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.32/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( S @ X @ Bound_variable_1218 ) ) )
% 0.32/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.32/0.47 ( ~ ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( Bound_variable_1522 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.32/0.47 | ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( Bound_variable_1522 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( Bound_variable_1522 @ Y @ X )
% 0.32/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.32/0.47 ( ~ ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_674 )
% 0.32/0.47 | ~ ( Bound_variable_1538 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.32/0.47 | ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.32/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.32/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.32/0.47 | ( Bound_variable_1538 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.32/0.47 | ( Bound_variable_1538 @ X @ Y ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(transitive_reflexive_symmetric_closure,conjecture,
% 0.32/0.47 ( trsc
% 0.32/0.47 = ( ^ [R: $i > $i > $o] : ( sc @ ( rc @ ( tc @ R ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 ------------------------
% 1.93/1.37 ---- Embedded in THF ---
% 1.93/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.93/1.37 %%% Generated on Tue May 05 09:30:19 EDT 2026
% 1.93/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.93/1.37 %%% Logic specification used:
% 1.93/1.37 %%% thf(spec, logic, $$dhol).
% 1.93/1.37
% 1.93/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.L1wr6hYwUS/DTF2DTF12102.p
% See solution above
% 1.93/1.37 ------------------------
% 1.93/1.39 ---- Cleaned THF ---
% 1.93/1.39 thf(unsorted_type,type,
% 1.93/1.39 unsorted: $tType ).
% 1.93/1.39
% 1.93/1.39 thf(subrel_decl,type,
% 1.93/1.39 subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(inv_decl,type,
% 1.93/1.39 inv: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(idem_decl,type,
% 1.93/1.39 idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(infl_decl,type,
% 1.93/1.39 infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(mono_decl,type,
% 1.93/1.39 mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(refl_decl,type,
% 1.93/1.39 refl: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(irrefl_decl,type,
% 1.93/1.39 irrefl: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(rc_decl,type,
% 1.93/1.39 rc: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(symm_decl,type,
% 1.93/1.39 symm: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(antisymm_decl,type,
% 1.93/1.39 antisymm: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(asymm_decl,type,
% 1.93/1.39 asymm: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(sc_decl,type,
% 1.93/1.39 sc: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(trans_decl,type,
% 1.93/1.39 trans: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(tc_decl,type,
% 1.93/1.39 tc: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(trc_decl,type,
% 1.93/1.39 trc: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(trsc_decl,type,
% 1.93/1.39 trsc: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(po_decl,type,
% 1.93/1.39 po: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(so_decl,type,
% 1.93/1.39 so: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(total_decl,type,
% 1.93/1.39 total: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(term_decl,type,
% 1.93/1.39 term: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(ind_decl,type,
% 1.93/1.39 ind: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(innf_decl,type,
% 1.93/1.39 innf: ( $i > $i > $o ) > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(nfof_decl,type,
% 1.93/1.39 nfof: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(norm_decl,type,
% 1.93/1.39 norm: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(join_decl,type,
% 1.93/1.39 join: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(lconfl_decl,type,
% 1.93/1.39 lconfl: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(sconfl_decl,type,
% 1.93/1.39 sconfl: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(confl_decl,type,
% 1.93/1.39 confl: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(cr_decl,type,
% 1.93/1.39 cr: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(d_unsorted_type,type,
% 1.93/1.39 d_unsorted: $tType ).
% 1.93/1.39
% 1.93/1.39 thf(d2unsorted_decl,type,
% 1.93/1.39 d2unsorted: d_unsorted > $i ).
% 1.93/1.39
% 1.93/1.39 thf(d_unsorted_0_decl,type,
% 1.93/1.39 d_unsorted_0: d_unsorted ).
% 1.93/1.39
% 1.93/1.39 thf(sev441_1,axiom,
% 1.93/1.39 ( ! [U: $i] :
% 1.93/1.40 ? [DU: d_unsorted] :
% 1.93/1.40 ( U
% 1.93/1.40 = ( d2unsorted @ DU ) )
% 1.93/1.40 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 1.93/1.40 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 1.93/1.40 ( ( ( d2unsorted @ DU1 )
% 1.93/1.40 = ( d2unsorted @ DU2 ) )
% 1.93/1.40 => ( DU1 = DU2 ) )
% 1.93/1.40 & ( subrel
% 1.93/1.40 = ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
% 1.93/1.40 ! [X: $i,Y: $i] :
% 1.93/1.40 ( ~ ( R @ X @ Y )
% 1.93/1.40 | ( S @ X @ Y ) ) ) )
% 1.93/1.40 & ( inv
% 1.93/1.40 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) )
% 1.93/1.40 & ( idem
% 1.93/1.40 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 1.93/1.40 ! [R: $i > $i > $o] :
% 1.93/1.40 ( ( F @ R )
% 1.93/1.40 = ( F @ ( F @ R ) ) ) ) )
% 1.93/1.40 & ( infl
% 1.93/1.40 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 1.93/1.40 ! [R: $i > $i > $o,X: $i,Y: $i] :
% 1.93/1.40 ( ~ ( R @ X @ Y )
% 1.93/1.40 | ( F @ R @ X @ Y ) ) ) )
% 1.93/1.40 & ( mono
% 1.93/1.40 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 1.93/1.40 ! [R: $i > $i > $o,S: $i > $i > $o,Bound_variable_510: $i,Bound_variable_512: $i] :
% 1.93/1.40 ( ~ ! [X: $i,Y: $i] :
% 1.93/1.40 ( ~ ( R @ X @ Y )
% 1.93/1.40 | ( S @ X @ Y ) )
% 1.93/1.40 | ~ ( F @ R @ Bound_variable_510 @ Bound_variable_512 )
% 1.93/1.40 | ( F @ S @ Bound_variable_510 @ Bound_variable_512 ) ) ) )
% 1.93/1.40 & ( refl
% 1.93/1.40 = ( ^ [R: $i > $i > $o] :
% 1.93/1.40 ! [X: $i] : ( R @ X @ X ) ) )
% 1.93/1.40 & ( irrefl
% 1.93/1.40 = ( ^ [R: $i > $i > $o] :
% 1.93/1.40 ! [X: $i] :
% 1.93/1.40 ~ ( R @ X @ X ) ) )
% 1.93/1.40 & ( rc
% 1.93/1.40 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 1.93/1.40 ( ( X = Y )
% 1.93/1.40 | ( R @ X @ Y ) ) ) )
% 1.93/1.40 & ( symm
% 1.93/1.40 = ( ^ [R: $i > $i > $o] :
% 1.93/1.40 ! [X: $i,Y: $i] :
% 1.93/1.40 ( ~ ( R @ X @ Y )
% 1.93/1.40 | ( R @ Y @ X ) ) ) )
% 1.93/1.40 & ( antisymm
% 1.93/1.40 = ( ^ [R: $i > $i > $o] :
% 1.93/1.40 ! [X: $i,Y: $i] :
% 1.93/1.40 ( ~ ( R @ X @ Y )
% 1.93/1.40 | ~ ( R @ Y @ X )
% 1.93/1.40 | ( X = Y ) ) ) )
% 1.93/1.40 & ( asymm
% 1.93/1.40 = ( ^ [R: $i > $i > $o] :
% 1.93/1.40 ! [X: $i,Y: $i] :
% 1.93/1.40 ( ~ ( R @ X @ Y )
% 1.93/1.40 | ~ ( R @ Y @ X ) ) ) )
% 1.93/1.40 & ( sc
% 1.93/1.40 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 1.93/1.40 ( ( R @ Y @ X )
% 1.93/1.40 | ( R @ X @ Y ) ) ) )
% 1.93/1.40 & ( trans
% 1.93/1.40 = ( ^ [R: $i > $i > $o] :
% 1.93/1.40 ! [X: $i,Y: $i,Z: $i] :
% 1.93/1.40 ( ~ ( R @ X @ Y )
% 1.93/1.40 | ~ ( R @ Y @ Z )
% 1.93/1.40 | ( R @ X @ Z ) ) ) )
% 1.93/1.40 & ( tc
% 1.93/1.40 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 1.93/1.40 ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ X @ Y ) ) ) )
% 1.93/1.40 & ( trc
% 1.93/1.40 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 1.93/1.40 ( ( Flatten_var_0 = Flatten_var_1 )
% 1.93/1.40 | ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 1.93/1.40 & ( trsc
% 1.93/1.40 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 1.93/1.40 ( ( Flatten_var_0 = Flatten_var_1 )
% 1.93/1.40 | ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ Flatten_var_1 @ Flatten_var_0 ) )
% 1.93/1.40 | ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 1.93/1.40 & ( po
% 1.93/1.40 = ( ^ [R: $i > $i > $o] :
% 1.93/1.40 ( ! [X: $i] : ( R @ X @ X )
% 1.93/1.40 & ! [X: $i,Y: $i] :
% 1.93/1.40 ( ~ ( R @ X @ Y )
% 1.93/1.40 | ~ ( R @ Y @ X )
% 1.93/1.40 | ( X = Y ) )
% 1.93/1.40 & ! [X: $i,Y: $i,Z: $i] :
% 1.93/1.40 ( ~ ( R @ X @ Y )
% 1.93/1.40 | ~ ( R @ Y @ Z )
% 1.93/1.40 | ( R @ X @ Z ) ) ) ) )
% 1.93/1.40 & ( so
% 1.93/1.40 = ( ^ [R: $i > $i > $o] :
% 1.93/1.40 ( ! [X: $i,Y: $i] :
% 1.93/1.40 ( ~ ( R @ X @ Y )
% 1.93/1.40 | ~ ( R @ Y @ X ) )
% 1.93/1.40 & ! [X: $i,Y: $i,Z: $i] :
% 1.93/1.40 ( ~ ( R @ X @ Y )
% 1.93/1.40 | ~ ( R @ Y @ Z )
% 1.93/1.40 | ( R @ X @ Z ) ) ) ) )
% 1.93/1.40 & ( total
% 1.93/1.40 = ( ^ [R: $i > $i > $o] :
% 1.93/1.40 ! [X: $i,Y: $i] :
% 1.93/1.40 ( ( X = Y )
% 1.93/1.40 | ( R @ X @ Y )
% 1.93/1.40 | ( R @ Y @ X ) ) ) )
% 1.93/1.40 & ( term
% 1.93/1.40 = ( ^ [R: $i > $i > $o] :
% 1.93/1.40 ! [A: $i > $o,Bound_variable_862: $i] :
% 1.93/1.40 ( ~ ( A @ Bound_variable_862 )
% 1.93/1.40 | ~ ! [X: $i] :
% 1.93/1.40 ( ~ ( A @ X )
% 1.93/1.40 | ~ ! [Y: $i] :
% 1.93/1.40 ( ~ ( A @ Y )
% 1.93/1.40 | ~ ( R @ X @ Y ) ) ) ) ) )
% 1.93/1.40 & ( ind
% 1.93/1.40 = ( ^ [R: $i > $i > $o] :
% 1.93/1.40 ! [P: $i > $o,Bound_variable_917: $i] :
% 1.93/1.40 ( ~ ! [X: $i] :
% 1.93/1.40 ( ~ ! [Y: $i] :
% 1.93/1.40 ( ~ ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ X @ Y ) )
% 1.93/1.40 | ( P @ Y ) )
% 1.93/1.40 | ( P @ X ) )
% 1.93/1.40 | ( P @ Bound_variable_917 ) ) ) )
% 1.93/1.40 & ( innf
% 1.93/1.40 = ( ^ [R: $i > $i > $o,X: $i] :
% 1.93/1.40 ! [Y: $i] :
% 1.93/1.40 ~ ( R @ X @ Y ) ) )
% 1.93/1.40 & ( nfof
% 1.93/1.40 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 1.93/1.40 ( ( ( X = Y )
% 1.93/1.40 | ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ Y @ X ) ) )
% 1.93/1.40 & ! [Bound_variable_985: $i] :
% 1.93/1.40 ~ ( R @ X @ Bound_variable_985 ) ) ) )
% 1.93/1.40 & ( norm
% 1.93/1.40 = ( ^ [R: $i > $i > $o] :
% 1.93/1.40 ! [X: $i,Bound_variable_1075: $i] :
% 1.93/1.40 ( ~ ( R @ X @ Bound_variable_1075 )
% 1.93/1.40 | ~ ! [Bound_variable_1049: $i] :
% 1.93/1.40 ( ~ ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ X @ Bound_variable_1049 ) )
% 1.93/1.40 | ~ ! [Bound_variable_985: $i] :
% 1.93/1.40 ~ ( R @ Bound_variable_1049 @ Bound_variable_985 ) ) ) ) )
% 1.93/1.40 & ( join
% 1.93/1.40 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 1.93/1.40 ~ ( ( X != Y )
% 1.93/1.40 & ~ ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ Y @ X ) )
% 1.93/1.40 & ~ ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ X @ Y ) )
% 1.93/1.40 & ! [Bound_variable_1218: $i] :
% 1.93/1.40 ( ~ ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ Y @ Bound_variable_1218 ) )
% 1.93/1.40 | ~ ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ X @ Bound_variable_1218 ) ) ) ) ) )
% 1.93/1.40 & ( lconfl
% 1.93/1.40 = ( ^ [R: $i > $i > $o] :
% 1.93/1.40 ! [X: $i,Y: $i,Z: $i,Bound_variable_1293: $i > $i > $o,Bound_variable_1309: $i > $i > $o] :
% 1.93/1.40 ( ~ ( R @ X @ Z )
% 1.93/1.40 | ~ ( R @ X @ Y )
% 1.93/1.40 | ( Y = Z )
% 1.93/1.40 | ~ ! [Bound_variable_1218: $i] :
% 1.93/1.40 ( ~ ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ Y @ Bound_variable_1218 ) )
% 1.93/1.40 | ~ ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ Z @ Bound_variable_1218 ) ) )
% 1.93/1.40 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.40 ( ~ ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( Bound_variable_1293 @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.40 | ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( Bound_variable_1293 @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( Bound_variable_1293 @ Y @ Z )
% 1.93/1.40 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.40 ( ~ ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( Bound_variable_1309 @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.40 | ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( Bound_variable_1309 @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( Bound_variable_1309 @ Z @ Y ) ) ) )
% 1.93/1.40 & ( sconfl
% 1.93/1.40 = ( ^ [R: $i > $i > $o] :
% 1.93/1.40 ! [X: $i,Y: $i,Z: $i,Bound_variable_1371: $i > $i > $o,Bound_variable_1387: $i > $i > $o] :
% 1.93/1.40 ( ~ ( R @ X @ Z )
% 1.93/1.40 | ( ( X != Y )
% 1.93/1.40 & ~ ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1347: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Bound_variable_1347 )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Bound_variable_1347 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ X @ Y ) ) )
% 1.93/1.40 | ( Y = Z )
% 1.93/1.40 | ~ ! [Bound_variable_1218: $i] :
% 1.93/1.40 ( ~ ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ Y @ Bound_variable_1218 ) )
% 1.93/1.40 | ~ ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ Z @ Bound_variable_1218 ) ) )
% 1.93/1.40 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.40 ( ~ ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( Bound_variable_1371 @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.40 | ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( Bound_variable_1371 @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( Bound_variable_1371 @ Y @ Z )
% 1.93/1.40 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.40 ( ~ ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( Bound_variable_1387 @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.40 | ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( Bound_variable_1387 @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( Bound_variable_1387 @ Z @ Y ) ) ) )
% 1.93/1.40 & ( confl
% 1.93/1.40 = ( ^ [R: $i > $i > $o] :
% 1.93/1.40 ! [X: $i,Y: $i,Z: $i,Bound_variable_1444: $i > $i > $o,Bound_variable_1460: $i > $i > $o] :
% 1.93/1.40 ( ( ( X != Z )
% 1.93/1.40 & ~ ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ X @ Z ) ) )
% 1.93/1.40 | ( ( X != Y )
% 1.93/1.40 & ~ ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1422: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Bound_variable_1422 )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Bound_variable_1422 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ X @ Y ) ) )
% 1.93/1.40 | ( Y = Z )
% 1.93/1.40 | ~ ! [Bound_variable_1218: $i] :
% 1.93/1.40 ( ~ ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.40 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.40 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.40 | ( S @ Y @ Bound_variable_1218 ) )
% 1.93/1.40 | ~ ! [S: $i > $i > $o] :
% 1.93/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.12/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.12/1.40 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.12/1.40 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.12/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.12/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.12/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.12/1.40 | ( S @ Z @ Bound_variable_1218 ) ) )
% 2.12/1.40 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.12/1.40 ( ~ ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_674 )
% 2.12/1.40 | ~ ( Bound_variable_1444 @ Bound_variable_674 @ Bound_variable_1125 )
% 2.12/1.40 | ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.12/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.12/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.12/1.40 | ( Bound_variable_1444 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.12/1.40 | ( Bound_variable_1444 @ Y @ Z )
% 2.12/1.40 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.12/1.40 ( ~ ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_674 )
% 2.12/1.40 | ~ ( Bound_variable_1460 @ Bound_variable_674 @ Bound_variable_1106 )
% 2.12/1.40 | ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.12/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.12/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.12/1.40 | ( Bound_variable_1460 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.12/1.40 | ( Bound_variable_1460 @ Z @ Y ) ) ) )
% 2.12/1.40 & ( cr
% 2.12/1.40 = ( ^ [R: $i > $i > $o] :
% 2.12/1.40 ! [X: $i,Y: $i,Bound_variable_1522: $i > $i > $o,Bound_variable_1538: $i > $i > $o] :
% 2.12/1.40 ( ( ( X != Y )
% 2.12/1.40 & ~ ! [S: $i > $i > $o] :
% 2.12/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.12/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.12/1.40 | ~ ( S @ Bound_variable_674 @ Z )
% 2.12/1.40 | ( S @ Bound_variable_672 @ Z ) )
% 2.12/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.12/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.12/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.12/1.40 | ( S @ Y @ X ) )
% 2.12/1.40 & ~ ! [S: $i > $i > $o] :
% 2.12/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.12/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.12/1.40 | ~ ( S @ Bound_variable_674 @ Z )
% 2.12/1.40 | ( S @ Bound_variable_672 @ Z ) )
% 2.12/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.12/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.12/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.12/1.40 | ( S @ X @ Y ) ) )
% 2.12/1.40 | ( X = Y )
% 2.12/1.40 | ~ ! [Bound_variable_1218: $i] :
% 2.12/1.40 ( ~ ! [S: $i > $i > $o] :
% 2.12/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.12/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.12/1.40 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 2.12/1.40 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.12/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.12/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.12/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.12/1.40 | ( S @ Y @ Bound_variable_1218 ) )
% 2.12/1.40 | ~ ! [S: $i > $i > $o] :
% 2.12/1.40 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.12/1.40 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.12/1.40 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.12/1.40 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.12/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.12/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.12/1.40 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.12/1.40 | ( S @ X @ Bound_variable_1218 ) ) )
% 2.12/1.40 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.12/1.40 ( ~ ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_674 )
% 2.12/1.40 | ~ ( Bound_variable_1522 @ Bound_variable_674 @ Bound_variable_1125 )
% 2.12/1.40 | ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.12/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.12/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.12/1.40 | ( Bound_variable_1522 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.12/1.40 | ( Bound_variable_1522 @ Y @ X )
% 2.12/1.40 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.12/1.40 ( ~ ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_674 )
% 2.12/1.40 | ~ ( Bound_variable_1538 @ Bound_variable_674 @ Bound_variable_1106 )
% 2.12/1.40 | ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.12/1.40 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.12/1.40 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.12/1.40 | ( Bound_variable_1538 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.12/1.40 | ( Bound_variable_1538 @ X @ Y ) ) ) ) ) ).
% 2.12/1.40
% 2.12/1.40 thf(transitive_reflexive_symmetric_closure,conjecture,
% 2.12/1.40 ( trsc
% 2.12/1.40 = ( ^ [R: $i > $i > $o] : ( sc @ ( rc @ ( tc @ R ) ) ) ) ) ).
% 2.12/1.40 ------------------------
% 2.12/1.41 % (12208)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/18Mi)
% 2.12/1.41 % (12204)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_12102 for (2999ds/27Mi)
% 2.12/1.41 % (12208)Instruction limit reached!
% 2.12/1.41 % (12208)------------------------------
% 2.12/1.41 % (12208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.41 % (12208)Termination reason: Unknown
% 2.12/1.41 % (12208)Termination phase: Property scanning
% 2.12/1.41
% 2.12/1.41 % (12208)Memory used [KB]: 1535
% 2.12/1.41 % (12208)Time elapsed: 0.006 s
% 2.12/1.41 % (12208)Instructions burned: 18 (million)
% 2.12/1.41 % (12208)------------------------------
% 2.12/1.41 % (12208)------------------------------
% 2.12/1.42 % (12203)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_12102 for (2999ds/4Mi)
% 2.12/1.42 % (12205)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/2Mi)
% 2.12/1.42 % (12206)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_12102 for (2999ds/2Mi)
% 2.12/1.42 % (12207)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_12102 for (2999ds/275Mi)
% 2.12/1.42 % (12202)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/183Mi)
% 2.12/1.42 % (12204)Instruction limit reached!
% 2.12/1.42 % (12204)------------------------------
% 2.12/1.42 % (12204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.42 % (12204)Termination reason: Unknown
% 2.12/1.42 % (12204)Termination phase: Preprocessing 3
% 2.12/1.42
% 2.12/1.42 % (12204)Memory used [KB]: 1535
% 2.12/1.42 % (12204)Time elapsed: 0.009 s
% 2.12/1.42 % (12204)Instructions burned: 28 (million)
% 2.12/1.42 % (12204)------------------------------
% 2.12/1.42 % (12204)------------------------------
% 2.12/1.42 % (12205)Instruction limit reached!
% 2.12/1.42 % (12205)------------------------------
% 2.12/1.42 % (12205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.42 % (12205)Termination reason: Unknown
% 2.12/1.42 % (12206)Instruction limit reached!
% 2.12/1.42 % (12206)------------------------------
% 2.12/1.42 % (12206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.42 % (12205)Termination phase: shuffling
% 2.12/1.42
% 2.12/1.42 % (12205)Memory used [KB]: 1023
% 2.12/1.42 % (12205)Time elapsed: 0.003 s
% 2.12/1.42 % (12205)Instructions burned: 2 (million)
% 2.12/1.42 % (12205)------------------------------
% 2.12/1.42 % (12205)------------------------------
% 2.12/1.42 % (12206)Termination reason: Unknown
% 2.12/1.42 % (12206)Termination phase: shuffling
% 2.12/1.42
% 2.12/1.42 % (12206)Memory used [KB]: 1023
% 2.12/1.42 % (12206)Time elapsed: 0.003 s
% 2.12/1.42 % (12206)Instructions burned: 2 (million)
% 2.12/1.42 % (12206)------------------------------
% 2.12/1.42 % (12206)------------------------------
% 2.12/1.42 % (12203)Instruction limit reached!
% 2.12/1.42 % (12203)------------------------------
% 2.12/1.42 % (12203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.42 % (12203)Termination reason: Unknown
% 2.12/1.42 % (12203)Termination phase: shuffling
% 2.12/1.42
% 2.12/1.42 % (12203)Memory used [KB]: 1151
% 2.12/1.42 % (12203)Time elapsed: 0.004 s
% 2.12/1.42 % (12203)Instructions burned: 4 (million)
% 2.12/1.42 % (12203)------------------------------
% 2.12/1.42 % (12203)------------------------------
% 2.12/1.42 % (12209)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/3Mi)
% 2.12/1.42 % (12209)Instruction limit reached!
% 2.12/1.42 % (12209)------------------------------
% 2.12/1.42 % (12209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.42 % (12209)Termination reason: Unknown
% 2.12/1.42 % (12209)Termination phase: shuffling
% 2.12/1.42
% 2.12/1.42 % (12209)Memory used [KB]: 1151
% 2.12/1.42 % (12209)Time elapsed: 0.002 s
% 2.12/1.42 % (12209)Instructions burned: 4 (million)
% 2.12/1.42 % (12209)------------------------------
% 2.12/1.42 % (12209)------------------------------
% 2.12/1.43 % (12210)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_12102 for (2999ds/37Mi)
% 2.12/1.43 % (12207)Refutation not found, incomplete strategy
% 2.12/1.43 % (12207)------------------------------
% 2.12/1.43 % (12207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.43 % (12207)Termination reason: Refutation not found, incomplete strategy
% 2.12/1.43
% 2.12/1.43
% 2.12/1.43 % (12207)Memory used [KB]: 6012
% 2.12/1.43 % (12207)Time elapsed: 0.016 s
% 2.12/1.43 % (12207)Instructions burned: 28 (million)
% 2.12/1.43 % (12207)------------------------------
% 2.12/1.43 % (12207)------------------------------
% 2.12/1.43 % (12214)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/7Mi)
% 2.12/1.43 % (12213)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_12102 for (2999ds/1041Mi)
% 2.12/1.44 % (12211)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_12102 for (2999ds/15Mi)
% 2.12/1.44 % (12212)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_12102 for (2999ds/3Mi)
% 2.12/1.44 % (12214)Instruction limit reached!
% 2.12/1.44 % (12214)------------------------------
% 2.12/1.44 % (12214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.44 % (12214)Termination reason: Unknown
% 2.12/1.44 % (12214)Termination phase: shuffling
% 2.12/1.44
% 2.12/1.44 % (12214)Memory used [KB]: 1279
% 2.12/1.44 % (12214)Time elapsed: 0.003 s
% 2.12/1.44 % (12214)Instructions burned: 8 (million)
% 2.12/1.44 % (12214)------------------------------
% 2.12/1.44 % (12214)------------------------------
% 2.12/1.44 % (12212)Instruction limit reached!
% 2.12/1.44 % (12212)------------------------------
% 2.12/1.44 % (12212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.44 % (12212)Termination reason: Unknown
% 2.12/1.44 % (12212)Termination phase: shuffling
% 2.12/1.44
% 2.12/1.44 % (12212)Memory used [KB]: 1151
% 2.12/1.44 % (12212)Time elapsed: 0.004 s
% 2.12/1.44 % (12212)Instructions burned: 4 (million)
% 2.12/1.44 % (12212)------------------------------
% 2.12/1.44 % (12212)------------------------------
% 2.12/1.44 % (12210)Instruction limit reached!
% 2.12/1.44 % (12210)------------------------------
% 2.12/1.44 % (12210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.44 % (12210)Termination reason: Unknown
% 2.12/1.44 % (12210)Termination phase: Saturation
% 2.12/1.44
% 2.12/1.44 % (12210)Memory used [KB]: 6012
% 2.12/1.44 % (12210)Time elapsed: 0.012 s
% 2.12/1.44 % (12210)Instructions burned: 38 (million)
% 2.12/1.44 % (12210)------------------------------
% 2.12/1.44 % (12210)------------------------------
% 2.12/1.44 % (12211)Instruction limit reached!
% 2.12/1.44 % (12211)------------------------------
% 2.12/1.44 % (12211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.44 % (12211)Termination reason: Unknown
% 2.12/1.44 % (12211)Termination phase: Property scanning
% 2.12/1.44
% 2.12/1.44 % (12211)Memory used [KB]: 1407
% 2.12/1.44 % (12211)Time elapsed: 0.010 s
% 2.12/1.44 % (12211)Instructions burned: 16 (million)
% 2.12/1.44 % (12211)------------------------------
% 2.12/1.44 % (12211)------------------------------
% 2.12/1.45 % (12216)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_12102 for (2999ds/3Mi)
% 2.12/1.45 % (12215)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/16Mi)
% 2.12/1.45 % (12216)Instruction limit reached!
% 2.12/1.45 % (12216)------------------------------
% 2.12/1.45 % (12216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.45 % (12216)Termination reason: Unknown
% 2.12/1.45 % (12216)Termination phase: shuffling
% 2.12/1.45
% 2.12/1.45 % (12216)Memory used [KB]: 1151
% 2.12/1.45 % (12216)Time elapsed: 0.002 s
% 2.12/1.45 % (12216)Instructions burned: 4 (million)
% 2.12/1.45 % (12216)------------------------------
% 2.12/1.45 % (12216)------------------------------
% 2.12/1.45 % (12218)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/7Mi)
% 2.12/1.45 % (12215)Instruction limit reached!
% 2.12/1.45 % (12215)------------------------------
% 2.12/1.45 % (12215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.45 % (12215)Termination reason: Unknown
% 2.12/1.45 % (12215)Termination phase: Property scanning
% 2.12/1.45
% 2.12/1.45 % (12215)Memory used [KB]: 1407
% 2.12/1.45 % (12215)Time elapsed: 0.006 s
% 2.12/1.45 % (12215)Instructions burned: 17 (million)
% 2.12/1.45 % (12215)------------------------------
% 2.12/1.45 % (12215)------------------------------
% 2.12/1.45 % (12218)Instruction limit reached!
% 2.12/1.45 % (12218)------------------------------
% 2.12/1.45 % (12218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.45 % (12218)Termination reason: Unknown
% 2.12/1.45 % (12218)Termination phase: shuffling
% 2.12/1.45
% 2.12/1.45 % (12218)Memory used [KB]: 1279
% 2.12/1.45 % (12218)Time elapsed: 0.004 s
% 2.12/1.45 % (12218)Instructions burned: 8 (million)
% 2.12/1.45 % (12218)------------------------------
% 2.12/1.45 % (12218)------------------------------
% 2.12/1.46 % (12217)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_12102 for (2999ds/3Mi)
% 2.12/1.46 % (12221)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/4Mi)
% 2.12/1.46 % (12221)Instruction limit reached!
% 2.12/1.46 % (12221)------------------------------
% 2.12/1.46 % (12221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.46 % (12221)Termination reason: Unknown
% 2.12/1.46 % (12221)Termination phase: shuffling
% 2.12/1.46
% 2.12/1.46 % (12221)Memory used [KB]: 1151
% 2.12/1.46 % (12221)Time elapsed: 0.002 s
% 2.12/1.46 % (12221)Instructions burned: 4 (million)
% 2.12/1.46 % (12221)------------------------------
% 2.12/1.46 % (12221)------------------------------
% 2.12/1.46 % (12217)Instruction limit reached!
% 2.12/1.46 % (12217)------------------------------
% 2.12/1.46 % (12217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.46 % (12217)Termination reason: Unknown
% 2.12/1.46 % (12217)Termination phase: shuffling
% 2.12/1.46
% 2.12/1.46 % (12217)Memory used [KB]: 1151
% 2.12/1.46 % (12217)Time elapsed: 0.004 s
% 2.12/1.46 % (12217)Instructions burned: 4 (million)
% 2.12/1.46 % (12217)------------------------------
% 2.12/1.46 % (12217)------------------------------
% 2.12/1.46 % (12222)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/18Mi)
% 2.12/1.46 % (12219)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/3Mi)
% 2.12/1.46 % (12223)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/710Mi)
% 2.12/1.46 % (12219)Instruction limit reached!
% 2.12/1.46 % (12219)------------------------------
% 2.12/1.46 % (12219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.46 % (12219)Termination reason: Unknown
% 2.12/1.46 % (12219)Termination phase: shuffling
% 2.12/1.46
% 2.12/1.46 % (12219)Memory used [KB]: 1151
% 2.12/1.46 % (12219)Time elapsed: 0.004 s
% 2.12/1.46 % (12219)Instructions burned: 4 (million)
% 2.12/1.46 % (12219)------------------------------
% 2.12/1.46 % (12219)------------------------------
% 2.12/1.47 % (12222)Instruction limit reached!
% 2.12/1.47 % (12222)------------------------------
% 2.12/1.47 % (12222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.47 % (12222)Termination reason: Unknown
% 2.12/1.47 % (12222)Termination phase: Property scanning
% 2.12/1.47
% 2.12/1.47 % (12222)Memory used [KB]: 1407
% 2.12/1.47 % (12222)Time elapsed: 0.007 s
% 2.12/1.47 % (12222)Instructions burned: 19 (million)
% 2.12/1.47 % (12222)------------------------------
% 2.12/1.47 % (12222)------------------------------
% 2.12/1.47 % (12224)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/6Mi)
% 2.12/1.47 % (12224)Instruction limit reached!
% 2.12/1.47 % (12224)------------------------------
% 2.12/1.47 % (12224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.47 % (12224)Termination reason: Unknown
% 2.12/1.47 % (12224)Termination phase: shuffling
% 2.12/1.47
% 2.12/1.47 % (12224)Memory used [KB]: 1279
% 2.12/1.47 % (12224)Time elapsed: 0.003 s
% 2.12/1.47 % (12224)Instructions burned: 8 (million)
% 2.12/1.47 % (12224)------------------------------
% 2.12/1.47 % (12224)------------------------------
% 2.12/1.47 % (12225)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_12102 for (2999ds/902Mi)
% 2.12/1.47 % (12226)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_12102 for (2999ds/21Mi)
% 2.12/1.48 % (12227)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/5Mi)
% 2.12/1.48 % (12228)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/6Mi)
% 2.12/1.48 % (12227)Instruction limit reached!
% 2.12/1.48 % (12227)------------------------------
% 2.12/1.48 % (12227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.48 % (12227)Termination reason: Unknown
% 2.12/1.48 % (12227)Termination phase: shuffling
% 2.12/1.48
% 2.12/1.48 % (12227)Memory used [KB]: 1279
% 2.12/1.48 % (12227)Time elapsed: 0.004 s
% 2.12/1.48 % (12227)Instructions burned: 8 (million)
% 2.12/1.48 % (12227)------------------------------
% 2.12/1.48 % (12227)------------------------------
% 2.12/1.48 % (12228)Instruction limit reached!
% 2.12/1.48 % (12228)------------------------------
% 2.12/1.48 % (12228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.48 % (12228)Termination reason: Unknown
% 2.12/1.48 % (12228)Termination phase: shuffling
% 2.12/1.48
% 2.12/1.48 % (12228)Memory used [KB]: 1279
% 2.12/1.48 % (12228)Time elapsed: 0.003 s
% 2.12/1.48 % (12228)Instructions burned: 8 (million)
% 2.12/1.48 % (12228)------------------------------
% 2.12/1.48 % (12228)------------------------------
% 2.12/1.48 % (12226)Instruction limit reached!
% 2.12/1.48 % (12226)------------------------------
% 2.12/1.48 % (12226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.48 % (12226)Termination reason: Unknown
% 2.12/1.48 % (12226)Termination phase: Property scanning
% 2.12/1.48
% 2.12/1.48 % (12226)Memory used [KB]: 1407
% 2.12/1.48 % (12226)Time elapsed: 0.008 s
% 2.12/1.48 % (12226)Instructions burned: 22 (million)
% 2.12/1.48 % (12226)------------------------------
% 2.12/1.48 % (12226)------------------------------
% 2.12/1.49 % (12229)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/377Mi)
% 2.12/1.49 % (12230)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/779Mi)
% 2.12/1.49 % (12225)Refutation not found, incomplete strategy
% 2.12/1.49 % (12225)------------------------------
% 2.12/1.49 % (12225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.49 % (12225)Termination reason: Refutation not found, incomplete strategy
% 2.12/1.49
% 2.12/1.49
% 2.12/1.49 % (12225)Memory used [KB]: 6012
% 2.12/1.49 % (12225)Time elapsed: 0.017 s
% 2.12/1.49 % (12225)Instructions burned: 48 (million)
% 2.12/1.49 % (12225)------------------------------
% 2.12/1.49 % (12225)------------------------------
% 2.12/1.49 % (12231)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/19Mi)
% 2.12/1.50 % (12231)Instruction limit reached!
% 2.12/1.50 % (12231)------------------------------
% 2.12/1.50 % (12231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.50 % (12231)Termination reason: Unknown
% 2.12/1.50 % (12231)Termination phase: Property scanning
% 2.12/1.50
% 2.12/1.50 % (12231)Memory used [KB]: 1407
% 2.12/1.50 % (12231)Time elapsed: 0.007 s
% 2.12/1.50 % (12231)Instructions burned: 19 (million)
% 2.12/1.50 % (12231)------------------------------
% 2.12/1.50 % (12231)------------------------------
% 2.12/1.50 % (12232)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/879Mi)
% 2.12/1.51 % (12233)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_12102 for (2999ds/17Mi)
% 2.12/1.51 % (12202)Instruction limit reached!
% 2.12/1.51 % (12202)------------------------------
% 2.12/1.51 % (12202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.51 % (12202)Termination reason: Unknown
% 2.12/1.51 % (12202)Termination phase: Saturation
% 2.12/1.51
% 2.12/1.51 % (12202)Memory used [KB]: 6652
% 2.12/1.51 % (12202)Time elapsed: 0.092 s
% 2.12/1.51 % (12202)Instructions burned: 183 (million)
% 2.12/1.51 % (12202)------------------------------
% 2.12/1.51 % (12202)------------------------------
% 2.12/1.51 % (12233)Instruction limit reached!
% 2.12/1.51 % (12233)------------------------------
% 2.12/1.51 % (12233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.51 % (12233)Termination reason: Unknown
% 2.12/1.51 % (12233)Termination phase: Property scanning
% 2.12/1.51
% 2.12/1.51 % (12233)Memory used [KB]: 1535
% 2.12/1.51 % (12233)Time elapsed: 0.007 s
% 2.12/1.51 % (12233)Instructions burned: 18 (million)
% 2.12/1.51 % (12233)------------------------------
% 2.12/1.51 % (12233)------------------------------
% 2.12/1.52 % (12234)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_12102 for (2998ds/3Mi)
% 2.12/1.52 % (12234)Instruction limit reached!
% 2.12/1.52 % (12234)------------------------------
% 2.12/1.52 % (12234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.52 % (12234)Termination reason: Unknown
% 2.12/1.52 % (12234)Termination phase: shuffling
% 2.12/1.52
% 2.12/1.52 % (12234)Memory used [KB]: 1151
% 2.12/1.52 % (12234)Time elapsed: 0.002 s
% 2.12/1.52 % (12234)Instructions burned: 3 (million)
% 2.12/1.52 % (12234)------------------------------
% 2.12/1.52 % (12234)------------------------------
% 2.12/1.52 % (12235)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_12102 for (2998ds/30Mi)
% 2.12/1.53 % (12236)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_12102 for (2998ds/127Mi)
% 2.12/1.53 % (12235)Instruction limit reached!
% 2.12/1.53 % (12235)------------------------------
% 2.12/1.53 % (12235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.53 % (12235)Termination reason: Unknown
% 2.12/1.53 % (12235)Termination phase: Property scanning
% 2.12/1.53
% 2.12/1.53 % (12235)Memory used [KB]: 1535
% 2.12/1.53 % (12235)Time elapsed: 0.010 s
% 2.12/1.53 % (12235)Instructions burned: 30 (million)
% 2.12/1.53 % (12235)------------------------------
% 2.12/1.53 % (12235)------------------------------
% 2.12/1.54 % (12237)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_12102 for (2998ds/100Mi)
% 2.12/1.57 % (12236)Instruction limit reached!
% 2.12/1.57 % (12236)------------------------------
% 2.12/1.57 % (12236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.57 % (12236)Termination reason: Unknown
% 2.12/1.57 % (12236)Termination phase: Saturation
% 2.12/1.57
% 2.12/1.57 % (12236)Memory used [KB]: 6396
% 2.12/1.57 % (12236)Time elapsed: 0.038 s
% 2.12/1.57 % (12236)Instructions burned: 128 (million)
% 2.12/1.57 % (12236)------------------------------
% 2.12/1.57 % (12236)------------------------------
% 2.12/1.57 % (12237)Instruction limit reached!
% 2.12/1.57 % (12237)------------------------------
% 2.12/1.57 % (12237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.57 % (12237)Termination reason: Unknown
% 2.12/1.57 % (12237)Termination phase: Saturation
% 2.12/1.57
% 2.12/1.57 % (12237)Memory used [KB]: 6012
% 2.12/1.57 % (12237)Time elapsed: 0.028 s
% 2.12/1.57 % (12237)Instructions burned: 100 (million)
% 2.12/1.57 % (12237)------------------------------
% 2.12/1.57 % (12237)------------------------------
% 2.12/1.58 % (12238)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_12102 for (2998ds/3Mi)
% 2.12/1.58 % (12239)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_12102 for (2998ds/20Mi)
% 2.12/1.58 % (12238)Instruction limit reached!
% 2.12/1.58 % (12238)------------------------------
% 2.12/1.58 % (12238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.58 % (12238)Termination reason: Unknown
% 2.12/1.58 % (12238)Termination phase: shuffling
% 2.12/1.58
% 2.12/1.58 % (12238)Memory used [KB]: 1151
% 2.12/1.58 % (12238)Time elapsed: 0.003 s
% 2.12/1.58 % (12238)Instructions burned: 4 (million)
% 2.12/1.58 % (12238)------------------------------
% 2.12/1.58 % (12238)------------------------------
% 2.12/1.58 % (12239)Instruction limit reached!
% 2.12/1.58 % (12239)------------------------------
% 2.12/1.58 % (12239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.58 % (12239)Termination reason: Unknown
% 2.12/1.58 % (12239)Termination phase: Property scanning
% 2.12/1.58
% 2.12/1.58 % (12239)Memory used [KB]: 1535
% 2.12/1.58 % (12239)Time elapsed: 0.008 s
% 2.12/1.58 % (12239)Instructions burned: 22 (million)
% 2.12/1.58 % (12239)------------------------------
% 2.12/1.58 % (12239)------------------------------
% 2.12/1.59 % (12240)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_12102 for (2998ds/86Mi)
% 2.12/1.59 % (12241)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_12102 for (2998ds/107Mi)
% 2.12/1.60 % (12229)Instruction limit reached!
% 2.12/1.60 % (12229)------------------------------
% 2.12/1.60 % (12229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.60 % (12229)Termination reason: Unknown
% 2.12/1.60 % (12229)Termination phase: Saturation
% 2.12/1.60
% 2.12/1.60 % (12229)Memory used [KB]: 7419
% 2.12/1.60 % (12229)Time elapsed: 0.113 s
% 2.12/1.60 % (12229)Instructions burned: 377 (million)
% 2.12/1.60 % (12229)------------------------------
% 2.12/1.60 % (12229)------------------------------
% 2.12/1.61 % (12242)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_12102 for (2998ds/39Mi)
% 2.12/1.61 % (12240)Instruction limit reached!
% 2.12/1.61 % (12240)------------------------------
% 2.12/1.61 % (12240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.61 % (12240)Termination reason: Unknown
% 2.12/1.61 % (12240)Termination phase: Saturation
% 2.12/1.61
% 2.12/1.61 % (12240)Memory used [KB]: 6140
% 2.12/1.61 % (12240)Time elapsed: 0.026 s
% 2.12/1.61 % (12240)Instructions burned: 86 (million)
% 2.12/1.61 % (12240)------------------------------
% 2.12/1.61 % (12240)------------------------------
% 2.12/1.62 % (12242)Instruction limit reached!
% 2.12/1.62 % (12242)------------------------------
% 2.12/1.62 % (12242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.62 % (12242)Termination reason: Unknown
% 2.12/1.62 % (12242)Termination phase: Saturation
% 2.12/1.62
% 2.12/1.62 % (12242)Memory used [KB]: 6012
% 2.12/1.62 % (12242)Time elapsed: 0.012 s
% 2.12/1.62 % (12242)Instructions burned: 41 (million)
% 2.12/1.62 % (12242)------------------------------
% 2.12/1.62 % (12242)------------------------------
% 2.12/1.62 % (12243)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_12102 for (2997ds/448Mi)
% 2.12/1.62 % (12241)Instruction limit reached!
% 2.12/1.62 % (12241)------------------------------
% 2.12/1.62 % (12241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.62 % (12241)Termination reason: Unknown
% 2.12/1.62 % (12241)Termination phase: Saturation
% 2.12/1.62
% 2.12/1.62 % (12241)Memory used [KB]: 6396
% 2.12/1.62 % (12241)Time elapsed: 0.032 s
% 2.12/1.62 % (12241)Instructions burned: 108 (million)
% 2.12/1.62 % (12241)------------------------------
% 2.12/1.62 % (12241)------------------------------
% 2.12/1.63 % (12244)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_12102 for (2997ds/46Mi)
% 2.12/1.63 % (12243)Refutation not found, incomplete strategy
% 2.12/1.63 % (12243)------------------------------
% 2.12/1.63 % (12243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.63 % (12243)Termination reason: Refutation not found, incomplete strategy
% 2.12/1.63
% 2.12/1.63
% 2.12/1.63 % (12243)Memory used [KB]: 6012
% 2.12/1.63 % (12243)Time elapsed: 0.011 s
% 2.12/1.63 % (12243)Instructions burned: 34 (million)
% 2.12/1.63 % (12243)------------------------------
% 2.12/1.63 % (12243)------------------------------
% 2.12/1.63 % (12245)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_12102 for (2997ds/98Mi)
% 2.12/1.64 % (12246)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_12102 for (2997ds/507Mi)
% 2.12/1.64 % (12244)Instruction limit reached!
% 2.12/1.64 % (12244)------------------------------
% 2.12/1.64 % (12244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.64 % (12244)Termination reason: Unknown
% 2.12/1.64 % (12244)Termination phase: Saturation
% 2.12/1.64
% 2.12/1.64 % (12244)Memory used [KB]: 6012
% 2.12/1.64 % (12244)Time elapsed: 0.014 s
% 2.12/1.64 % (12244)Instructions burned: 46 (million)
% 2.12/1.64 % (12244)------------------------------
% 2.12/1.64 % (12244)------------------------------
% 2.12/1.65 % (12247)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_12102 for (2997ds/149Mi)
% 2.12/1.66 % (12223)Instruction limit reached!
% 2.12/1.66 % (12223)------------------------------
% 2.12/1.66 % (12223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.66 % (12223)Termination reason: Unknown
% 2.12/1.66 % (12223)Termination phase: Saturation
% 2.12/1.66
% 2.12/1.66 % (12223)Memory used [KB]: 8827
% 2.12/1.66 % (12223)Time elapsed: 0.197 s
% 2.12/1.66 % (12223)Instructions burned: 710 (million)
% 2.12/1.66 % (12223)------------------------------
% 2.12/1.66 % (12223)------------------------------
% 2.12/1.66 % (12245)Instruction limit reached!
% 2.12/1.66 % (12245)------------------------------
% 2.12/1.66 % (12245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.66 % (12245)Termination reason: Unknown
% 2.12/1.66 % (12245)Termination phase: Saturation
% 2.12/1.66
% 2.12/1.66 % (12245)Memory used [KB]: 1535
% 2.12/1.66 % (12245)Time elapsed: 0.027 s
% 2.12/1.66 % (12245)Instructions burned: 98 (million)
% 2.12/1.66 % (12245)------------------------------
% 2.12/1.66 % (12245)------------------------------
% 2.12/1.67 % (12248)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_12102 for (2997ds/39Mi)
% 2.12/1.67 % (12249)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_12102 for (2997ds/6Mi)
% 2.12/1.67 % (12249)Instruction limit reached!
% 2.12/1.67 % (12249)------------------------------
% 2.12/1.67 % (12249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.67 % (12249)Termination reason: Unknown
% 2.12/1.67 % (12249)Termination phase: shuffling
% 2.12/1.67
% 2.12/1.67 % (12249)Memory used [KB]: 1279
% 2.12/1.67 % (12249)Time elapsed: 0.004 s
% 2.12/1.67 % (12249)Instructions burned: 7 (million)
% 2.12/1.67 % (12249)------------------------------
% 2.12/1.67 % (12249)------------------------------
% 2.12/1.68 % (12248)Instruction limit reached!
% 2.12/1.68 % (12248)------------------------------
% 2.12/1.68 % (12248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.68 % (12248)Termination reason: Unknown
% 2.12/1.68 % (12248)Termination phase: Property scanning
% 2.12/1.68
% 2.12/1.68 % (12248)Memory used [KB]: 1535
% 2.12/1.68 % (12248)Time elapsed: 0.011 s
% 2.12/1.68 % (12248)Instructions burned: 41 (million)
% 2.12/1.68 % (12248)------------------------------
% 2.12/1.68 % (12248)------------------------------
% 2.12/1.68 % (12250)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_12102 for (2997ds/1087Mi)
% 2.12/1.69 % (12251)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_12102 for (2997ds/47Mi)
% 2.12/1.70 % (12251)Instruction limit reached!
% 2.12/1.70 % (12251)------------------------------
% 2.12/1.70 % (12251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.70 % (12251)Termination reason: Unknown
% 2.12/1.70 % (12251)Termination phase: Saturation
% 2.12/1.70
% 2.12/1.70 % (12251)Memory used [KB]: 6012
% 2.12/1.70 % (12251)Time elapsed: 0.014 s
% 2.12/1.70 % (12251)Instructions burned: 50 (million)
% 2.12/1.70 % (12251)------------------------------
% 2.12/1.70 % (12251)------------------------------
% 2.12/1.70 % (12247)Instruction limit reached!
% 2.12/1.70 % (12247)------------------------------
% 2.12/1.70 % (12247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.70 % (12230)Instruction limit reached!
% 2.12/1.70 % (12230)------------------------------
% 2.12/1.70 % (12230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.70 % (12247)Termination reason: Unknown
% 2.12/1.70 % (12247)Termination phase: Saturation
% 2.12/1.70
% 2.12/1.70 % (12247)Memory used [KB]: 6396
% 2.12/1.70 % (12247)Time elapsed: 0.048 s
% 2.12/1.70 % (12247)Instructions burned: 149 (million)
% 2.12/1.70 % (12247)------------------------------
% 2.12/1.70 % (12247)------------------------------
% 2.12/1.70 % (12230)Termination reason: Unknown
% 2.12/1.70 % (12230)Termination phase: Saturation
% 2.12/1.70
% 2.12/1.70 % (12230)Memory used [KB]: 7036
% 2.12/1.70 % (12230)Time elapsed: 0.212 s
% 2.12/1.70 % (12230)Instructions burned: 782 (million)
% 2.12/1.70 % (12230)------------------------------
% 2.12/1.70 % (12230)------------------------------
% 2.12/1.71 % (12252)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_12102 for (2997ds/44Mi)
% 2.12/1.71 % (12254)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_12102 for (2997ds/62Mi)
% 2.12/1.71 % (12253)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_12102 for (2997ds/432Mi)
% 2.12/1.71 % (12213)Instruction limit reached!
% 2.12/1.71 % (12213)------------------------------
% 2.12/1.71 % (12213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.71 % (12213)Termination reason: Unknown
% 2.12/1.71 % (12213)Termination phase: Saturation
% 2.12/1.71
% 2.12/1.71 % (12213)Memory used [KB]: 6908
% 2.12/1.71 % (12213)Time elapsed: 0.302 s
% 2.12/1.71 % (12213)Instructions burned: 1041 (million)
% 2.12/1.71 % (12213)------------------------------
% 2.12/1.71 % (12213)------------------------------
% 2.12/1.72 % (12252)Refutation not found, incomplete strategy
% 2.12/1.72 % (12252)------------------------------
% 2.12/1.72 % (12252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.72 % (12252)Termination reason: Refutation not found, incomplete strategy
% 2.12/1.72
% 2.12/1.72
% 2.12/1.72 % (12252)Memory used [KB]: 1535
% 2.12/1.72 % (12252)Time elapsed: 0.009 s
% 2.12/1.72 % (12252)Instructions burned: 32 (million)
% 2.12/1.72 % (12252)------------------------------
% 2.12/1.72 % (12252)------------------------------
% 2.12/1.72 % (12255)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_12102 for (2996ds/31Mi)
% 2.12/1.73 % (12254)Instruction limit reached!
% 2.12/1.73 % (12254)------------------------------
% 2.12/1.73 % (12254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.73 % (12254)Termination reason: Unknown
% 2.12/1.73 % (12254)Termination phase: Saturation
% 2.12/1.73 % (12256)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_12102 for (2996ds/96Mi)
% 2.12/1.73
% 2.12/1.73 % (12254)Memory used [KB]: 6396
% 2.12/1.73 % (12254)Time elapsed: 0.017 s
% 2.12/1.73 % (12254)Instructions burned: 65 (million)
% 2.12/1.73 % (12254)------------------------------
% 2.12/1.73 % (12254)------------------------------
% 2.12/1.73 % (12255)Instruction limit reached!
% 2.12/1.73 % (12255)------------------------------
% 2.12/1.73 % (12255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.73 % (12255)Termination reason: Unknown
% 2.12/1.73 % (12255)Termination phase: Property scanning
% 2.12/1.73
% 2.12/1.73 % (12255)Memory used [KB]: 1535
% 2.12/1.73 % (12255)Time elapsed: 0.011 s
% 2.12/1.73 % (12255)Instructions burned: 34 (million)
% 2.12/1.73 % (12255)------------------------------
% 2.12/1.73 % (12255)------------------------------
% 2.12/1.73 % (12257)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_12102 for (2996ds/453Mi)
% 2.12/1.74 % (12258)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_12102 for (2996ds/71Mi)
% 2.12/1.75 % (12256)Instruction limit reached!
% 2.12/1.75 % (12256)------------------------------
% 2.12/1.75 % (12256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.75 % (12256)Termination reason: Unknown
% 2.12/1.75 % (12256)Termination phase: Saturation
% 2.12/1.75
% 2.12/1.75 % (12256)Memory used [KB]: 6396
% 2.12/1.75 % (12256)Time elapsed: 0.026 s
% 2.12/1.75 % (12256)Instructions burned: 98 (million)
% 2.12/1.75 % (12256)------------------------------
% 2.12/1.75 % (12256)------------------------------
% 2.12/1.76 % (12259)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_12102 for (2996ds/83Mi)
% 2.12/1.77 % (12258)Instruction limit reached!
% 2.12/1.77 % (12258)------------------------------
% 2.12/1.77 % (12258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.77 % (12258)Termination reason: Unknown
% 2.12/1.77 % (12258)Termination phase: Saturation
% 2.12/1.77
% 2.12/1.77 % (12258)Memory used [KB]: 6140
% 2.12/1.77 % (12258)Time elapsed: 0.024 s
% 2.12/1.77 % (12258)Instructions burned: 73 (million)
% 2.12/1.77 % (12258)------------------------------
% 2.12/1.77 % (12258)------------------------------
% 2.12/1.77 % (12259)Refutation not found, incomplete strategy
% 2.12/1.77 % (12259)------------------------------
% 2.12/1.77 % (12259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.77 % (12259)Termination reason: Refutation not found, incomplete strategy
% 2.12/1.77
% 2.12/1.77
% 2.12/1.77 % (12259)Memory used [KB]: 6012
% 2.12/1.77 % (12259)Time elapsed: 0.009 s
% 2.12/1.77 % (12259)Instructions burned: 31 (million)
% 2.12/1.77 % (12259)------------------------------
% 2.12/1.77 % (12259)------------------------------
% 2.12/1.77 % (12232)Instruction limit reached!
% 2.12/1.77 % (12232)------------------------------
% 2.12/1.77 % (12232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.77 % (12232)Termination reason: Unknown
% 2.12/1.77 % (12232)Termination phase: Saturation
% 2.12/1.77
% 2.12/1.77 % (12232)Memory used [KB]: 8827
% 2.12/1.77 % (12232)Time elapsed: 0.269 s
% 2.12/1.77 % (12232)Instructions burned: 881 (million)
% 2.12/1.77 % (12232)------------------------------
% 2.12/1.77 % (12232)------------------------------
% 2.12/1.78 % (12260)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_12102 for (2996ds/11Mi)
% 2.12/1.78 % (12261)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_12102 for (2996ds/41Mi)
% 2.12/1.78 % (12262)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12102 for (2996ds/6Mi)
% 2.12/1.78 % (12260)Instruction limit reached!
% 2.12/1.78 % (12260)------------------------------
% 2.12/1.78 % (12260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.78 % (12260)Termination reason: Unknown
% 2.12/1.78 % (12260)Termination phase: shuffling
% 2.12/1.78
% 2.12/1.78 % (12260)Memory used [KB]: 1279
% 2.12/1.78 % (12260)Time elapsed: 0.005 s
% 2.12/1.78 % (12260)Instructions burned: 12 (million)
% 2.12/1.78 % (12260)------------------------------
% 2.12/1.78 % (12260)------------------------------
% 2.12/1.78 % (12262)Instruction limit reached!
% 2.12/1.78 % (12262)------------------------------
% 2.12/1.78 % (12262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.78 % (12262)Termination reason: Unknown
% 2.12/1.78 % (12262)Termination phase: shuffling
% 2.12/1.78
% 2.12/1.78 % (12262)Memory used [KB]: 1279
% 2.12/1.78 % (12262)Time elapsed: 0.003 s
% 2.12/1.78 % (12262)Instructions burned: 7 (million)
% 2.12/1.78 % (12262)------------------------------
% 2.12/1.78 % (12262)------------------------------
% 2.12/1.79 % (12261)Instruction limit reached!
% 2.12/1.79 % (12261)------------------------------
% 2.12/1.79 % (12261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.79 % (12261)Termination reason: Unknown
% 2.12/1.79 % (12261)Termination phase: Saturation
% 2.12/1.79
% 2.12/1.79 % (12261)Memory used [KB]: 6012
% 2.12/1.79 % (12261)Time elapsed: 0.011 s
% 2.12/1.79 % (12261)Instructions burned: 41 (million)
% 2.12/1.79 % (12261)------------------------------
% 2.12/1.79 % (12261)------------------------------
% 2.12/1.79 % (12263)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_12102 for (2996ds/150Mi)
% 2.12/1.79 % (12264)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_12102 for (2996ds/343Mi)
% 2.12/1.80 % (12266)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_12102 for (2996ds/109Mi)
% 2.12/1.80 % (12246)Instruction limit reached!
% 2.12/1.80 % (12246)------------------------------
% 2.12/1.80 % (12246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.80 % (12246)Termination reason: Unknown
% 2.12/1.80 % (12246)Termination phase: Saturation
% 2.12/1.80
% 2.12/1.80 % (12246)Memory used [KB]: 6652
% 2.12/1.80 % (12246)Time elapsed: 0.158 s
% 2.12/1.80 % (12246)Instructions burned: 507 (million)
% 2.12/1.80 % (12246)------------------------------
% 2.12/1.80 % (12246)------------------------------
% 2.12/1.80 % (12264)Refutation not found, incomplete strategy
% 2.12/1.80 % (12264)------------------------------
% 2.12/1.80 % (12264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.80 % (12264)Termination reason: Refutation not found, incomplete strategy
% 2.12/1.80
% 2.12/1.80
% 2.12/1.80 % (12264)Memory used [KB]: 6012
% 2.12/1.80 % (12264)Time elapsed: 0.011 s
% 2.12/1.80 % (12264)Instructions burned: 33 (million)
% 2.12/1.80 % (12264)------------------------------
% 2.12/1.80 % (12264)------------------------------
% 2.12/1.81 % (12267)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_12102 for (2995ds/253Mi)
% 2.12/1.81 % (12263)Refutation not found, incomplete strategy
% 2.12/1.81 % (12263)------------------------------
% 2.12/1.81 % (12263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.81 % (12263)Termination reason: Refutation not found, incomplete strategy
% 2.12/1.81
% 2.12/1.81
% 2.12/1.81 % (12263)Memory used [KB]: 6140
% 2.12/1.81 % (12263)Time elapsed: 0.022 s
% 2.12/1.81 % (12263)Instructions burned: 79 (million)
% 2.12/1.81 % (12263)------------------------------
% 2.12/1.81 % (12263)------------------------------
% 2.12/1.81 % (12268)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_12102 for (2995ds/140Mi)
% 2.12/1.82 % (12267)Refutation not found, incomplete strategy
% 2.12/1.82 % (12267)------------------------------
% 2.12/1.82 % (12267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.82 % (12267)Termination reason: Refutation not found, incomplete strategy
% 2.12/1.82
% 2.12/1.82
% 2.12/1.82 % (12267)Memory used [KB]: 6012
% 2.12/1.82 % (12267)Time elapsed: 0.010 s
% 2.12/1.82 % (12267)Instructions burned: 28 (million)
% 2.12/1.82 % (12267)------------------------------
% 2.12/1.82 % (12267)------------------------------
% 2.12/1.82 % (12269)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_12102 for (2995ds/614Mi)
% 2.12/1.82 % (12253)Instruction limit reached!
% 2.12/1.82 % (12253)------------------------------
% 2.12/1.82 % (12253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.82 % (12253)Termination reason: Unknown
% 2.12/1.82 % (12253)Termination phase: Saturation
% 2.12/1.82
% 2.12/1.82 % (12253)Memory used [KB]: 2046
% 2.12/1.82 % (12253)Time elapsed: 0.137 s
% 2.12/1.82 % (12253)Instructions burned: 432 (million)
% 2.12/1.82 % (12253)------------------------------
% 2.12/1.82 % (12253)------------------------------
% 2.12/1.83 % (12266)Instruction limit reached!
% 2.12/1.83 % (12266)------------------------------
% 2.12/1.83 % (12266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.83 % (12266)Termination reason: Unknown
% 2.12/1.83 % (12266)Termination phase: Saturation
% 2.12/1.83
% 2.12/1.83 % (12266)Memory used [KB]: 6396
% 2.12/1.83 % (12266)Time elapsed: 0.029 s
% 2.12/1.83 % (12266)Instructions burned: 110 (million)
% 2.12/1.83 % (12266)------------------------------
% 2.12/1.83 % (12266)------------------------------
% 2.12/1.83 % (12270)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_12102 for (2995ds/202Mi)
% 2.12/1.83 % (12268)Refutation not found, incomplete strategy
% 2.12/1.83 % (12268)------------------------------
% 2.12/1.83 % (12268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.83 % (12268)Termination reason: Refutation not found, incomplete strategy
% 2.12/1.83
% 2.12/1.83
% 2.12/1.83 % (12268)Memory used [KB]: 6140
% 2.12/1.83 % (12268)Time elapsed: 0.020 s
% 2.12/1.83 % (12268)Instructions burned: 65 (million)
% 2.12/1.83 % (12268)------------------------------
% 2.12/1.83 % (12268)------------------------------
% 2.12/1.83 % (12271)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_12102 for (2995ds/339Mi)
% 2.12/1.83 % (12272)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_12102 for (2995ds/283Mi)
% 2.12/1.84 % (12273)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_12102 for (2995ds/134Mi)
% 2.12/1.84 % (12270)Refutation not found, incomplete strategy
% 2.12/1.84 % (12270)------------------------------
% 2.12/1.84 % (12270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.84 % (12270)Termination reason: Refutation not found, incomplete strategy
% 2.12/1.84
% 2.12/1.84
% 2.12/1.84 % (12270)Memory used [KB]: 6012
% 2.12/1.84 % (12270)Time elapsed: 0.014 s
% 2.12/1.84 % (12270)Instructions burned: 45 (million)
% 2.12/1.84 % (12270)------------------------------
% 2.12/1.84 % (12270)------------------------------
% 2.12/1.85 % (12271)Refutation not found, incomplete strategy
% 2.12/1.85 % (12271)------------------------------
% 2.12/1.85 % (12271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.85 % (12271)Termination reason: Refutation not found, incomplete strategy
% 2.12/1.85
% 2.12/1.85
% 2.12/1.85 % (12271)Memory used [KB]: 6012
% 2.12/1.85 % (12271)Time elapsed: 0.013 s
% 2.12/1.85 % (12271)Instructions burned: 49 (million)
% 2.12/1.85 % (12271)------------------------------
% 2.12/1.85 % (12271)------------------------------
% 2.12/1.85 % (12274)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_12102 for (2995ds/298Mi)
% 2.12/1.85 % (12257)Instruction limit reached!
% 2.12/1.85 % (12257)------------------------------
% 2.12/1.85 % (12257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.85 % (12257)Termination reason: Unknown
% 2.12/1.85 % (12257)Termination phase: Saturation
% 2.12/1.85
% 2.12/1.85 % (12257)Memory used [KB]: 6524
% 2.12/1.85 % (12257)Time elapsed: 0.143 s
% 2.12/1.85 % (12257)Instructions burned: 455 (million)
% 2.12/1.85 % (12257)------------------------------
% 2.12/1.85 % (12257)------------------------------
% 2.12/1.86 % (12275)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_12102 for (2995ds/192Mi)
% 2.12/1.86 % (12276)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_12102 for (2995ds/258Mi)
% 2.12/1.88 % (12273)Instruction limit reached!
% 2.12/1.88 % (12273)------------------------------
% 2.12/1.88 % (12273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.88 % (12273)Termination reason: Unknown
% 2.12/1.88 % (12273)Termination phase: Saturation
% 2.12/1.88
% 2.12/1.88 % (12273)Memory used [KB]: 6396
% 2.12/1.88 % (12273)Time elapsed: 0.040 s
% 2.12/1.88 % (12273)Instructions burned: 134 (million)
% 2.12/1.88 % (12273)------------------------------
% 2.12/1.88 % (12273)------------------------------
% 2.12/1.89 % (12277)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_12102 for (2995ds/90Mi)
% 2.12/1.90 % (12272)Instruction limit reached!
% 2.12/1.90 % (12272)------------------------------
% 2.12/1.90 % (12272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.90 % (12272)Termination reason: Unknown
% 2.12/1.90 % (12272)Termination phase: Saturation
% 2.12/1.90
% 2.12/1.90 % (12272)Memory used [KB]: 6652
% 2.12/1.90 % (12272)Time elapsed: 0.070 s
% 2.12/1.90 % (12272)Instructions burned: 284 (million)
% 2.12/1.90 % (12272)------------------------------
% 2.12/1.90 % (12272)------------------------------
% 2.12/1.91 % (12275)Instruction limit reached!
% 2.12/1.91 % (12275)------------------------------
% 2.12/1.91 % (12275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.91 % (12275)Termination reason: Unknown
% 2.12/1.91 % (12275)Termination phase: Saturation
% 2.12/1.91
% 2.12/1.91 % (12275)Memory used [KB]: 6652
% 2.12/1.91 % (12275)Time elapsed: 0.052 s
% 2.12/1.91 % (12275)Instructions burned: 194 (million)
% 2.12/1.91 % (12275)------------------------------
% 2.12/1.91 % (12275)------------------------------
% 2.12/1.91 % (12278)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_12102 for (2995ds/231Mi)
% 2.12/1.91 % (12277)Instruction limit reached!
% 2.12/1.91 % (12277)------------------------------
% 2.12/1.91 % (12277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.91 % (12277)Termination reason: Unknown
% 2.12/1.91 % (12277)Termination phase: Saturation
% 2.12/1.91
% 2.12/1.91 % (12277)Memory used [KB]: 6268
% 2.12/1.91 % (12277)Time elapsed: 0.027 s
% 2.12/1.91 % (12277)Instructions burned: 90 (million)
% 2.12/1.91 % (12277)------------------------------
% 2.12/1.91 % (12277)------------------------------
% 2.12/1.92 % (12279)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_12102 for (2994ds/458Mi)
% 2.12/1.92 % (12280)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_12102 for (2994ds/31Mi)
% 2.12/1.93 % (12274)Instruction limit reached!
% 2.12/1.93 % (12274)------------------------------
% 2.12/1.93 % (12274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.93 % (12280)Instruction limit reached!
% 2.12/1.93 % (12280)------------------------------
% 2.12/1.93 % (12280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.93 % (12280)Termination reason: Unknown
% 2.12/1.93 % (12280)Termination phase: Property scanning
% 2.12/1.93
% 2.12/1.93 % (12280)Memory used [KB]: 1535
% 2.12/1.93 % (12280)Time elapsed: 0.009 s
% 2.12/1.93 % (12280)Instructions burned: 31 (million)
% 2.12/1.93 % (12280)------------------------------
% 2.12/1.93 % (12280)------------------------------
% 2.12/1.93 % (12274)Termination reason: Unknown
% 2.12/1.93 % (12274)Termination phase: Saturation
% 2.12/1.93
% 2.12/1.93 % (12274)Memory used [KB]: 6396
% 2.12/1.93 % (12274)Time elapsed: 0.081 s
% 2.12/1.93 % (12274)Instructions burned: 300 (million)
% 2.12/1.93 % (12274)------------------------------
% 2.12/1.93 % (12274)------------------------------
% 2.12/1.93 % (12276)Instruction limit reached!
% 2.12/1.93 % (12276)------------------------------
% 2.12/1.93 % (12276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.93 % (12276)Termination reason: Unknown
% 2.12/1.93 % (12276)Termination phase: Saturation
% 2.12/1.93
% 2.12/1.93 % (12276)Memory used [KB]: 6908
% 2.12/1.93 % (12276)Time elapsed: 0.070 s
% 2.12/1.93 % (12276)Instructions burned: 259 (million)
% 2.12/1.93 % (12276)------------------------------
% 2.12/1.93 % (12276)------------------------------
% 2.12/1.94 % (12281)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_12102 for (2994ds/297Mi)
% 2.12/1.94 % (12282)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_12102 for (2994ds/987Mi)
% 2.12/1.94 % (12283)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_12102 for (2994ds/182Mi)
% 2.12/1.95 % (12281)Refutation not found, incomplete strategy
% 2.12/1.95 % (12281)------------------------------
% 2.12/1.95 % (12281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.95 % (12281)Termination reason: Refutation not found, incomplete strategy
% 2.12/1.95
% 2.12/1.95
% 2.12/1.95 % (12281)Memory used [KB]: 6012
% 2.12/1.95 % (12281)Time elapsed: 0.010 s
% 2.12/1.95 % (12281)Instructions burned: 35 (million)
% 2.12/1.95 % (12281)------------------------------
% 2.12/1.95 % (12281)------------------------------
% 2.12/1.96 % (12284)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_12102 for (2994ds/182Mi)
% 2.12/1.96 % (12250)First to succeed.
% 2.12/1.97 % (12278)Instruction limit reached!
% 2.12/1.97 % (12278)------------------------------
% 2.12/1.97 % (12278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.97 % (12278)Termination reason: Unknown
% 2.12/1.97 % (12278)Termination phase: Saturation
% 2.12/1.97
% 2.12/1.97 % (12278)Memory used [KB]: 6396
% 2.12/1.97 % (12278)Time elapsed: 0.055 s
% 2.12/1.97 % (12278)Instructions burned: 234 (million)
% 2.12/1.97 % (12278)------------------------------
% 2.12/1.97 % (12278)------------------------------
% 2.12/1.97 % (12269)Instruction limit reached!
% 2.12/1.97 % (12269)------------------------------
% 2.12/1.97 % (12269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.97 % (12269)Termination reason: Unknown
% 2.12/1.97 % (12269)Termination phase: Saturation
% 2.12/1.97
% 2.12/1.97 % (12269)Memory used [KB]: 8059
% 2.12/1.97 % (12269)Time elapsed: 0.156 s
% 2.12/1.97 % (12269)Instructions burned: 614 (million)
% 2.12/1.97 % (12269)------------------------------
% 2.12/1.97 % (12269)------------------------------
% 2.12/1.98 % (12250)Refutation found. Thanks to Tanya!
% 2.12/1.98 % SZS status Theorem for DTF2THF_12102
% 2.12/1.98 % SZS output start Proof for DTF2THF_12102
% 2.12/1.98 thf(type_def_6, type, d_unsorted: $tType).
% 2.12/1.98 thf(func_def_0, type, unsorted: $tType).
% 2.12/1.98 thf(func_def_1, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o).
% 2.12/1.98 thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_6, type, refl: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_7, type, irrefl: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o).
% 2.12/1.98 thf(func_def_9, type, symm: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_10, type, antisymm: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_11, type, asymm: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o).
% 2.12/1.98 thf(func_def_13, type, trans: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o).
% 2.12/1.98 thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o).
% 2.12/1.98 thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o).
% 2.12/1.98 thf(func_def_17, type, po: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_18, type, so: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_19, type, total: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_20, type, term: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_21, type, ind: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o).
% 2.12/1.98 thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o).
% 2.12/1.98 thf(func_def_24, type, norm: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o).
% 2.12/1.98 thf(func_def_26, type, lconfl: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_27, type, sconfl: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_28, type, confl: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_29, type, cr: ($i > $i > $o) > $o).
% 2.12/1.98 thf(func_def_30, type, d_unsorted: $tType).
% 2.12/1.98 thf(func_def_31, type, d2unsorted: d_unsorted > $i).
% 2.12/1.98 thf(func_def_32, type, d_unsorted_0: d_unsorted).
% 2.12/1.98 thf(func_def_52, type, sK0: $i > d_unsorted).
% 2.12/1.98 thf(func_def_54, type, ph2: !>[X0: $tType]:(X0)).
% 2.12/1.98 thf(func_def_55, type, sK3: $i > $i > $o).
% 2.12/1.98 thf(func_def_58, type, sK6: $i > $i > $o).
% 2.12/1.98 thf(func_def_59, type, sK7: $i > $i > $o).
% 2.12/1.98 thf(func_def_60, type, sK8: $i > $i > $o).
% 2.12/1.98 thf(func_def_61, type, sK9: $i > $i > $o).
% 2.12/1.98 thf(func_def_62, type, sK10: $i > $i > $o).
% 2.12/1.98 thf(func_def_63, type, sK11: $i > $i > $o).
% 2.12/1.98 thf(func_def_64, type, sK12: $i > $i > $o).
% 2.12/1.98 thf(func_def_65, type, sK13: $i > $i > $o).
% 2.12/1.98 thf(func_def_66, type, sK14: $i > $i > $o).
% 2.12/1.98 thf(func_def_67, type, sK15: $i > $i > $o).
% 2.12/1.98 thf(func_def_68, type, sK16: $i > $i > $o).
% 2.12/1.98 thf(func_def_69, type, sK17: $i > $i > $o).
% 2.12/1.98 thf(func_def_70, type, sK18: $i > $i > $o).
% 2.12/1.98 thf(func_def_71, type, sK19: $i > $i > $o).
% 2.12/1.98 thf(func_def_72, type, sK20: $i > $i > $o).
% 2.12/1.98 thf(func_def_73, type, sK21: $i > $i > $o).
% 2.12/1.98 thf(func_def_74, type, sK22: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_75, type, sK23: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_76, type, sK24: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_77, type, sK25: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_78, type, sK26: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_79, type, sK27: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_80, type, sK28: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_81, type, sK29: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_82, type, sK30: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_83, type, sK31: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_84, type, sK32: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_85, type, sK33: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_86, type, sK34: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_87, type, sK35: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_88, type, sK36: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_89, type, sK37: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_90, type, sK38: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_91, type, sK39: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_92, type, sK40: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_93, type, sK41: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_94, type, sK42: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_95, type, sK43: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_96, type, sK44: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_97, type, sK45: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_98, type, sK46: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_99, type, sK47: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_100, type, sK48: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_101, type, sK49: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_102, type, sK50: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_103, type, sK51: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_104, type, sK52: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_105, type, sK53: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_106, type, sK54: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_107, type, sK55: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_108, type, sK56: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_109, type, sK57: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_110, type, sK58: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_111, type, sK59: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_112, type, sK60: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_113, type, sK61: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_114, type, sK62: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_115, type, sK63: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_116, type, sK64: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_117, type, sK65: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_118, type, sK66: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_119, type, sK67: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_120, type, sK68: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_121, type, sK69: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_122, type, sK70: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_123, type, sK71: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_124, type, sK72: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_125, type, sK73: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_126, type, sK74: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_127, type, sK75: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_128, type, sK76: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_129, type, sK77: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_130, type, sK78: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_131, type, sK79: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_132, type, sK80: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_133, type, sK81: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_134, type, sK82: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_135, type, sK83: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_136, type, sK84: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_137, type, sK85: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_138, type, sK86: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_139, type, sK87: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_140, type, sK88: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_141, type, sK89: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_142, type, sK90: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_143, type, sK91: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_144, type, sK92: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_145, type, sK93: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_146, type, sK94: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_147, type, sK95: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_148, type, sK96: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_149, type, sK97: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_150, type, sK98: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_151, type, sK99: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_152, type, sK100: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_153, type, sK101: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_154, type, sK102: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_155, type, sK103: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_156, type, sK104: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_157, type, sK105: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_158, type, sK106: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_159, type, sK107: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_160, type, sK108: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_161, type, sK109: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_162, type, sK110: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_163, type, sK111: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_164, type, sK112: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_165, type, sK113: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_166, type, sK114: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_167, type, sK115: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_168, type, sK116: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_169, type, sK117: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_170, type, sK118: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_171, type, sK119: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_172, type, sK120: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_173, type, sK121: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_174, type, sK122: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_175, type, sK123: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_176, type, sK124: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_177, type, sK125: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_178, type, sK126: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_179, type, sK127: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_180, type, sK128: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_181, type, sK129: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_182, type, sK130: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_183, type, sK131: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_184, type, sK132: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_185, type, sK133: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_186, type, sK134: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_187, type, sK135: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_188, type, sK136: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_189, type, sK137: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_190, type, sK138: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_191, type, sK139: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_192, type, sK140: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_193, type, sK141: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_194, type, sK142: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_195, type, sK143: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_196, type, sK144: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_197, type, sK145: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_198, type, sK146: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_199, type, sK147: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_200, type, sK148: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_201, type, sK149: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_202, type, sK150: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_203, type, sK151: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_204, type, sK152: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_205, type, sK153: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_206, type, sK154: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_207, type, sK155: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_208, type, sK156: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_209, type, sK157: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_210, type, sK158: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_211, type, sK159: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_212, type, sK160: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_213, type, sK161: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_214, type, sK162: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_215, type, sK163: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_216, type, sK164: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_217, type, sK165: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_218, type, sK166: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_219, type, sK167: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_220, type, sK168: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_221, type, sK169: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_222, type, sK170: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_223, type, sK171: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_224, type, sK172: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_225, type, sK173: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_226, type, sK174: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_227, type, sK175: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_228, type, sK176: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_229, type, sK177: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_230, type, sK178: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_231, type, sK179: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_232, type, sK180: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_233, type, sK181: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_234, type, sK182: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_235, type, sK183: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_236, type, sK184: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_237, type, sK185: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_238, type, sK186: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_239, type, sK187: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_240, type, sK188: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_241, type, sK189: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_242, type, sK190: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_243, type, sK191: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_244, type, sK192: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_245, type, sK193: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_246, type, sK194: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_247, type, sK195: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_248, type, sK196: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_249, type, sK197: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_250, type, sK198: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_251, type, sK199: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_252, type, sK200: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_253, type, sK201: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_254, type, sK202: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_255, type, sK203: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_256, type, sK204: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_257, type, sK205: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_258, type, sK206: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_259, type, sK207: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_260, type, sK208: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_261, type, sK209: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_262, type, sK210: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_263, type, sK211: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_264, type, sK212: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_265, type, sK213: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_266, type, sK214: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_267, type, sK215: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_268, type, sK216: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_269, type, sK217: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_270, type, sK218: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_271, type, sK219: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_272, type, sK220: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_273, type, sK221: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_274, type, sK222: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_275, type, sK223: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_276, type, sK224: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_277, type, sK225: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_278, type, sK226: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_279, type, sK227: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_280, type, sK228: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_281, type, sK229: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_282, type, sK230: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_283, type, sK231: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_284, type, sK232: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_285, type, sK233: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_286, type, sK234: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_287, type, sK235: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_288, type, sK236: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_289, type, sK237: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_290, type, sK238: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_291, type, sK239: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_292, type, sK240: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_293, type, sK241: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_294, type, sK242: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_295, type, sK243: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_296, type, sK244: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_297, type, sK245: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_298, type, sK246: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_299, type, sK247: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_300, type, sK248: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_301, type, sK249: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_302, type, sK250: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_303, type, sK251: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_304, type, sK252: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_305, type, sK253: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_306, type, sK254: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_307, type, sK255: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_308, type, sK256: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_309, type, sK257: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_310, type, sK258: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_311, type, sK259: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_312, type, sK260: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_313, type, sK261: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_314, type, sK262: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_315, type, sK263: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_316, type, sK264: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_317, type, sK265: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_318, type, sK266: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_319, type, sK267: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_320, type, sK268: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_321, type, sK269: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_322, type, sK270: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_323, type, sK271: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_324, type, sK272: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_325, type, sK273: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_326, type, sK274: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_327, type, sK275: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_328, type, sK276: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_329, type, sK277: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_330, type, sK278: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_331, type, sK279: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_332, type, sK280: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_333, type, sK281: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_334, type, sK282: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_335, type, sK283: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_336, type, sK284: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_337, type, sK285: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_338, type, sK286: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_339, type, sK287: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_340, type, sK288: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_341, type, sK289: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_342, type, sK290: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_343, type, sK291: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_344, type, sK292: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_345, type, sK293: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_346, type, sK294: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_347, type, sK295: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_348, type, sK296: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_349, type, sK297: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_350, type, sK298: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_351, type, sK299: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_352, type, sK300: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_353, type, sK301: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_354, type, sK302: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_355, type, sK303: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_356, type, sK304: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_357, type, sK305: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_358, type, sK306: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_359, type, sK307: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_360, type, sK308: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_361, type, sK309: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_362, type, sK310: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_363, type, sK311: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_364, type, sK312: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_365, type, sK313: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_366, type, sK314: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_367, type, sK315: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_368, type, sK316: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_369, type, sK317: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_370, type, sK318: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_371, type, sK319: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_372, type, sK320: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_373, type, sK321: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_374, type, sK322: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_375, type, sK323: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_376, type, sK324: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_377, type, sK325: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_378, type, sK326: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_379, type, sK327: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_380, type, sK328: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_381, type, sK329: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_382, type, sK330: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_383, type, sK331: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_384, type, sK332: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_385, type, sK333: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_386, type, sK334: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_387, type, sK335: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_388, type, sK336: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_389, type, sK337: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_390, type, sK338: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_391, type, sK339: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_392, type, sK340: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_393, type, sK341: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_394, type, sK342: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_395, type, sK343: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_396, type, sK344: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_397, type, sK345: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_398, type, sK346: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_399, type, sK347: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_400, type, sK348: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_401, type, sK349: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_402, type, sK350: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_403, type, sK351: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_404, type, sK352: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_405, type, sK353: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_406, type, sK354: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_407, type, sK355: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_408, type, sK356: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_409, type, sK357: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_410, type, sK358: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_411, type, sK359: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_412, type, sK360: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_413, type, sK361: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_414, type, sK362: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_415, type, sK363: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_416, type, sK364: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_417, type, sK365: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_418, type, sK366: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_419, type, sK367: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_420, type, sK368: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_421, type, sK369: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_422, type, sK370: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_423, type, sK371: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_424, type, sK372: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_425, type, sK373: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_426, type, sK374: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_427, type, sK375: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_428, type, sK376: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_429, type, sK377: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_430, type, sK378: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_431, type, sK379: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_432, type, sK380: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_433, type, sK381: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_434, type, sK382: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_435, type, sK383: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_436, type, sK384: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_437, type, sK385: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_438, type, sK386: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_439, type, sK387: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_440, type, sK388: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_441, type, sK389: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_442, type, sK390: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_443, type, sK391: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_444, type, sK392: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_445, type, sK393: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_446, type, sK394: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_447, type, sK395: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_448, type, sK396: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_449, type, sK397: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_450, type, sK398: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_451, type, sK399: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_452, type, sK400: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_453, type, sK401: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_454, type, sK402: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_455, type, sK403: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_456, type, sK404: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_457, type, sK405: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_458, type, sK406: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_459, type, sK407: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_460, type, sK408: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_461, type, sK409: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_462, type, sK410: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_463, type, sK411: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_464, type, sK412: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_465, type, sK413: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_466, type, sK414: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_467, type, sK415: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_468, type, sK416: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_469, type, sK417: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_470, type, sK418: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_471, type, sK419: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_472, type, sK420: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_473, type, sK421: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_474, type, sK422: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_475, type, sK423: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_476, type, sK424: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_477, type, sK425: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_478, type, sK426: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_479, type, sK427: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_480, type, sK428: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_481, type, sK429: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_482, type, sK430: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_483, type, sK431: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_484, type, sK432: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_485, type, sK433: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_486, type, sK434: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_487, type, sK435: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_488, type, sK436: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_489, type, sK437: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_490, type, sK438: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_491, type, sK439: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_492, type, sK440: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_493, type, sK441: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_494, type, sK442: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_495, type, sK443: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_496, type, sK444: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_497, type, sK445: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_498, type, sK446: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_499, type, sK447: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_500, type, sK448: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_501, type, sK449: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_502, type, sK450: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_503, type, sK451: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_504, type, sK452: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_505, type, sK453: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_506, type, sK454: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_507, type, sK455: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_508, type, sK456: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_509, type, sK457: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_510, type, sK458: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_511, type, sK459: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_512, type, sK460: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_513, type, sK461: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_514, type, sK462: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_515, type, sK463: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_516, type, sK464: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_517, type, sK465: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_518, type, sK466: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_519, type, sK467: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_520, type, sK468: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_521, type, sK469: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_522, type, sK470: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_523, type, sK471: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_524, type, sK472: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_525, type, sK473: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_526, type, sK474: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_527, type, sK475: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_528, type, sK476: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_529, type, sK477: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_530, type, sK478: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_531, type, sK479: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_532, type, sK480: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_533, type, sK481: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_534, type, sK482: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_535, type, sK483: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_536, type, sK484: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_537, type, sK485: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_538, type, sK486: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_539, type, sK487: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_540, type, sK488: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_541, type, sK489: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_542, type, sK490: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_543, type, sK491: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_544, type, sK492: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_545, type, sK493: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_546, type, sK494: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_547, type, sK495: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_548, type, sK496: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_549, type, sK497: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_550, type, sK498: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_551, type, sK499: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_552, type, sK500: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_553, type, sK501: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_554, type, sK502: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_555, type, sK503: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_556, type, sK504: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_557, type, sK505: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_558, type, sK506: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_559, type, sK507: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_560, type, sK508: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_561, type, sK509: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_562, type, sK510: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_563, type, sK511: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_564, type, sK512: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_565, type, sK513: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_566, type, sK514: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_567, type, sK515: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_568, type, sK516: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_569, type, sK517: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_570, type, sK518: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_571, type, sK519: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_572, type, sK520: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_573, type, sK521: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_574, type, sK522: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_575, type, sK523: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_576, type, sK524: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_577, type, sK525: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_578, type, sK526: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_579, type, sK527: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_580, type, sK528: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_581, type, sK529: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_582, type, sK530: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_583, type, sK531: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_584, type, sK532: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_585, type, sK533: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_586, type, sK534: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_587, type, sK535: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_588, type, sK536: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_589, type, sK537: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_590, type, sK538: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_591, type, sK539: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_592, type, sK540: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_593, type, sK541: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_594, type, sK542: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_595, type, sK543: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_596, type, sK544: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_597, type, sK545: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_598, type, sK546: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_599, type, sK547: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_600, type, sK548: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_601, type, sK549: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_602, type, sK550: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_603, type, sK551: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_604, type, sK552: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_605, type, sK553: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_606, type, sK554: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_607, type, sK555: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_608, type, sK556: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_609, type, sK557: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_610, type, sK558: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_611, type, sK559: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_612, type, sK560: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_613, type, sK561: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_614, type, sK562: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_615, type, sK563: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_616, type, sK564: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_617, type, sK565: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_618, type, sK566: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_619, type, sK567: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_620, type, sK568: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_621, type, sK569: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_622, type, sK570: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_623, type, sK571: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_624, type, sK572: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_625, type, sK573: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_626, type, sK574: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_627, type, sK575: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_628, type, sK576: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_629, type, sK577: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_630, type, sK578: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_631, type, sK579: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_632, type, sK580: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_633, type, sK581: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_634, type, sK582: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_635, type, sK583: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_636, type, sK584: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_637, type, sK585: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_638, type, sK586: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_639, type, sK587: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_640, type, sK588: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_641, type, sK589: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_642, type, sK590: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_643, type, sK591: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_644, type, sK592: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_645, type, sK593: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_646, type, sK594: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_647, type, sK595: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_648, type, sK596: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_649, type, sK597: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_650, type, sK598: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_651, type, sK599: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_652, type, sK600: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_653, type, sK601: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_654, type, sK602: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_655, type, sK603: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_656, type, sK604: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_657, type, sK605: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_658, type, sK606: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_659, type, sK607: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_660, type, sK608: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_661, type, sK609: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_662, type, sK610: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_663, type, sK611: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_664, type, sK612: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_665, type, sK613: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_666, type, sK614: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_667, type, sK615: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_668, type, sK616: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_669, type, sK617: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_670, type, sK618: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_671, type, sK619: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_672, type, sK620: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_673, type, sK621: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_674, type, sK622: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_675, type, sK623: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_676, type, sK624: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_677, type, sK625: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_678, type, sK626: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_679, type, sK627: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_680, type, sK628: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_681, type, sK629: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_682, type, sK630: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_683, type, sK631: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_684, type, sK632: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_685, type, sK633: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_686, type, sK634: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_687, type, sK635: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_688, type, sK636: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_689, type, sK637: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_690, type, sK638: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_691, type, sK639: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_692, type, sK640: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_693, type, sK641: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_694, type, sK642: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_695, type, sK643: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_696, type, sK644: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_697, type, sK645: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_698, type, sK646: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_699, type, sK647: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_700, type, sK648: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_701, type, sK649: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_702, type, sK650: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_703, type, sK651: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_704, type, sK652: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_705, type, sK653: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_706, type, sK654: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_707, type, sK655: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_708, type, sK656: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_709, type, sK657: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_710, type, sK658: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_711, type, sK659: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_712, type, sK660: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_713, type, sK661: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_714, type, sK662: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_715, type, sK663: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_716, type, sK664: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_717, type, sK665: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_718, type, sK666: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_719, type, sK667: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_720, type, sK668: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_721, type, sK669: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_722, type, sK670: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_723, type, sK671: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_724, type, sK672: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_725, type, sK673: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_726, type, sK674: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_727, type, sK675: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_728, type, sK676: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_729, type, sK677: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_730, type, sK678: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_731, type, sK679: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_732, type, sK680: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_733, type, sK681: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_734, type, sK682: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_735, type, sK683: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_736, type, sK684: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_737, type, sK685: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_738, type, sK686: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_739, type, sK687: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_740, type, sK688: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_741, type, sK689: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_742, type, sK690: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_743, type, sK691: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_744, type, sK692: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_745, type, sK693: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_746, type, sK694: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_747, type, sK695: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_748, type, sK696: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_749, type, sK697: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_750, type, sK698: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_751, type, sK699: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_752, type, sK700: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_753, type, sK701: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_754, type, sK702: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_755, type, sK703: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_756, type, sK704: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_757, type, sK705: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_758, type, sK706: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_759, type, sK707: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_760, type, sK708: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_761, type, sK709: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_762, type, sK710: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_763, type, sK711: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_764, type, sK712: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_765, type, sK713: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_766, type, sK714: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_767, type, sK715: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_768, type, sK716: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_769, type, sK717: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_770, type, sK718: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_771, type, sK719: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_772, type, sK720: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_773, type, sK721: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_774, type, sK722: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_775, type, sK723: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_776, type, sK724: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_777, type, sK725: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_778, type, sK726: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_779, type, sK727: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_780, type, sK728: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_781, type, sK729: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_782, type, sK730: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_783, type, sK731: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_784, type, sK732: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_785, type, sK733: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_786, type, sK734: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_787, type, sK735: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_788, type, sK736: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_789, type, sK737: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_790, type, sK738: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_791, type, sK739: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_792, type, sK740: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_793, type, sK741: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_794, type, sK742: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_795, type, sK743: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_796, type, sK744: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_797, type, sK745: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_798, type, sK746: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_799, type, sK747: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_800, type, sK748: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_801, type, sK749: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_802, type, sK750: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_803, type, sK751: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_804, type, sK752: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_805, type, sK753: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_806, type, sK754: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_807, type, sK755: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_808, type, sK756: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_809, type, sK757: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_810, type, sK758: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_811, type, sK759: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_812, type, sK760: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_813, type, sK761: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_814, type, sK762: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_815, type, sK763: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_816, type, sK764: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_817, type, sK765: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_818, type, sK766: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_819, type, sK767: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_820, type, sK768: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_821, type, sK769: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_822, type, sK770: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_823, type, sK771: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_824, type, sK772: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_825, type, sK773: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_826, type, sK774: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_827, type, sK775: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_828, type, sK776: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_829, type, sK777: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_830, type, sK778: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_831, type, sK779: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_832, type, sK780: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_833, type, sK781: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_834, type, sK782: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_835, type, sK783: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_836, type, sK784: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_837, type, sK785: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_838, type, sK786: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_839, type, sK787: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_840, type, sK788: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_841, type, sK789: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_842, type, sK790: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_843, type, sK791: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_844, type, sK792: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_845, type, sK793: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_846, type, sK794: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_847, type, sK795: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_848, type, sK796: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_849, type, sK797: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_850, type, sK798: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_851, type, sK799: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_852, type, sK800: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_853, type, sK801: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_854, type, sK802: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_855, type, sK803: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_856, type, sK804: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_857, type, sK805: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_858, type, sK806: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_859, type, sK807: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_860, type, sK808: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_861, type, sK809: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_862, type, sK810: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_863, type, sK811: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_864, type, sK812: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_865, type, sK813: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_866, type, sK814: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_867, type, sK815: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_868, type, sK816: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_869, type, sK817: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_870, type, sK818: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_871, type, sK819: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_872, type, sK820: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_873, type, sK821: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_874, type, sK822: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_875, type, sK823: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_876, type, sK824: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_877, type, sK825: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_878, type, sK826: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_879, type, sK827: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_880, type, sK828: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_881, type, sK829: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_882, type, sK830: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_883, type, sK831: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_884, type, sK832: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_885, type, sK833: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_886, type, sK834: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_887, type, sK835: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_888, type, sK836: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_889, type, sK837: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_890, type, sK838: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_891, type, sK839: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_892, type, sK840: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_893, type, sK841: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_894, type, sK842: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_895, type, sK843: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_896, type, sK844: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_897, type, sK845: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_898, type, sK846: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_899, type, sK847: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_900, type, sK848: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_901, type, sK849: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_902, type, sK850: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_903, type, sK851: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_904, type, sK852: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_905, type, sK853: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_906, type, sK854: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_907, type, sK855: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_908, type, sK856: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_909, type, sK857: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_910, type, sK858: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_911, type, sK859: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_912, type, sK860: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_913, type, sK861: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_914, type, sK862: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_915, type, sK863: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_916, type, sK864: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_917, type, sK865: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_918, type, sK866: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_919, type, sK867: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_920, type, sK868: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_921, type, sK869: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_922, type, sK870: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_923, type, sK871: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_924, type, sK872: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_925, type, sK873: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_926, type, sK874: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_927, type, sK875: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_928, type, sK876: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_929, type, sK877: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_930, type, sK878: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_931, type, sK879: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_932, type, sK880: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_933, type, sK881: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_934, type, sK882: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_935, type, sK883: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_936, type, sK884: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_937, type, sK885: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_938, type, sK886: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_939, type, sK887: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_940, type, sK888: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_941, type, sK889: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_942, type, sK890: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_943, type, sK891: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_944, type, sK892: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_945, type, sK893: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_946, type, sK894: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_947, type, sK895: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_948, type, sK896: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_949, type, sK897: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_950, type, sK898: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_951, type, sK899: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_952, type, sK900: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_953, type, sK901: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_954, type, sK902: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_955, type, sK903: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_956, type, sK904: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_957, type, sK905: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_958, type, sK906: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_959, type, sK907: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_960, type, sK908: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_961, type, sK909: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_962, type, sK910: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_963, type, sK911: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_964, type, sK912: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_965, type, sK913: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_966, type, sK914: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_967, type, sK915: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_968, type, sK916: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_969, type, sK917: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_970, type, sK918: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_971, type, sK919: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_972, type, sK920: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_973, type, sK921: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_974, type, sK922: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_975, type, sK923: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_976, type, sK924: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_977, type, sK925: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_978, type, sK926: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_979, type, sK927: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_980, type, sK928: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_981, type, sK929: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_982, type, sK930: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_983, type, sK931: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_984, type, sK932: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_985, type, sK933: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_986, type, sK934: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_987, type, sK935: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_988, type, sK936: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_989, type, sK937: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_990, type, sK938: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_991, type, sK939: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_992, type, sK940: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_993, type, sK941: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_994, type, sK942: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_995, type, sK943: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_996, type, sK944: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_997, type, sK945: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_998, type, sK946: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_999, type, sK947: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1000, type, sK948: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1001, type, sK949: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1002, type, sK950: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1003, type, sK951: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1004, type, sK952: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1005, type, sK953: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1006, type, sK954: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1007, type, sK955: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1008, type, sK956: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1009, type, sK957: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1010, type, sK958: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1011, type, sK959: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1012, type, sK960: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1013, type, sK961: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1014, type, sK962: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1015, type, sK963: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1016, type, sK964: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1017, type, sK965: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1018, type, sK966: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1019, type, sK967: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1020, type, sK968: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1021, type, sK969: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1022, type, sK970: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1023, type, sK971: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1024, type, sK972: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1025, type, sK973: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1026, type, sK974: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1027, type, sK975: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1028, type, sK976: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1029, type, sK977: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1030, type, sK978: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1031, type, sK979: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1032, type, sK980: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1033, type, sK981: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1034, type, sK982: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1035, type, sK983: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1036, type, sK984: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1037, type, sK985: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1038, type, sK986: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1039, type, sK987: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1040, type, sK988: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1041, type, sK989: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1042, type, sK990: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1043, type, sK991: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1044, type, sK992: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1045, type, sK993: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1046, type, sK994: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1047, type, sK995: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1048, type, sK996: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1049, type, sK997: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1050, type, sK998: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1051, type, sK999: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1052, type, sK1000: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1053, type, sK1001: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1054, type, sK1002: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1055, type, sK1003: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1056, type, sK1004: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1057, type, sK1005: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1058, type, sK1006: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1059, type, sK1007: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1060, type, sK1008: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1061, type, sK1009: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1062, type, sK1010: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1063, type, sK1011: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1064, type, sK1012: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1065, type, sK1013: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1066, type, sK1014: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1067, type, sK1015: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1068, type, sK1016: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1069, type, sK1017: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1070, type, sK1018: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1071, type, sK1019: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1072, type, sK1020: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1073, type, sK1021: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1074, type, sK1022: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1075, type, sK1023: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1076, type, sK1024: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1077, type, sK1025: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1078, type, sK1026: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1079, type, sK1027: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1080, type, sK1028: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1081, type, sK1029: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1082, type, sK1030: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1083, type, sK1031: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1084, type, sK1032: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1085, type, sK1033: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1086, type, sK1034: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1087, type, sK1035: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1088, type, sK1036: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1089, type, sK1037: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1090, type, sK1038: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1091, type, sK1039: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1092, type, sK1040: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1093, type, sK1041: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1094, type, sK1042: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1095, type, sK1043: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1096, type, sK1044: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1097, type, sK1045: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1098, type, sK1046: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1099, type, sK1047: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1100, type, sK1048: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1101, type, sK1049: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1102, type, sK1050: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1103, type, sK1051: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1104, type, sK1052: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1105, type, sK1053: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1106, type, sK1054: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1107, type, sK1055: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1108, type, sK1056: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1109, type, sK1057: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1110, type, sK1058: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1111, type, sK1059: ($i > $i > $o) > $i).
% 2.12/1.98 thf(func_def_1112, type, sK1060: ($i > $i > $o) > $i).
% 2.12/1.98 thf(f7204,plain,(
% 2.12/1.98 $false),
% 2.12/1.98 inference(subsumption_resolution,[status(thm)],[f721,f57])).
% 2.12/1.98 thf(f57,plain,(
% 2.12/1.98 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 2.12/1.98 inference(superposition,[status(thm)],[f53,f53])).
% 2.12/1.98 thf(f53,plain,(
% 2.12/1.98 ( ! [X2 : $i] : (((d2unsorted @ d_unsorted_0) = X2)) )),
% 2.12/1.98 inference(forward_demodulation,[status(thm)],[f40,f34])).
% 2.12/1.98 thf(f34,plain,(
% 2.12/1.98 ( ! [X4 : d_unsorted] : ((d_unsorted_0 = X4)) )),
% 2.12/1.98 inference(cnf_transformation,[status(thm)],[f14])).
% 2.12/1.98 thf(f14,plain,(
% 2.12/1.98 (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y3))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1)))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) != (d2unsorted @ X0)) | (X0 = X1)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((Y4 = Y2) | (~ (Y0 @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y8)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y7 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (Y0 @ Y3 @ Y2))) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y1 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))) | (Y5 @ Y4 @ Y2)))))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y1 @ Y3))) | (Y0 @ Y1 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & ! [X2 : $i] : ((d2unsorted @ (sK0 @ X2)) = X2) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y2 @ Y3)) | (Y0 @ Y1 @ Y2 @ Y3)))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y7))) | (Y1 @ Y6 @ Y8))))))))) | (Y1 @ Y3 @ Y2)) | (Y3 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y7 @ Y8)) | (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y6 @ Y7))))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y2 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y10 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y8 @ Y10)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y4 @ Y7 @ Y6)))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))) | (Y6 @ Y5 @ Y3)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | ((~ (Y5 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y5 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y8 @ Y7)))))))))))))))))))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y6 @ Y7)))))))))))))))))) | (~ (Y0 @ Y1 @ Y2))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))) | (Y1 = Y2)))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)) | (Y2 = Y1)))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((Y2 @ Y4 @ Y3) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y9))) | (Y6 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))))))))) | (Y5 @ Y3 @ Y4)) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y10 @ Y8) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y10 @ Y9)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (Y0 @ Y1 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y6)) | (~ (Y2 @ Y7 @ Y8))) | (Y2 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))))))))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y2))) | (Y0 @ Y3 @ Y1)))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y7))) | (~ (Y1 @ Y7 @ Y5)))))))))) | (Y1 @ Y4 @ Y3)) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y1 @ Y5 @ Y6)))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y6))))))))))) | (Y5 @ Y3 @ Y4))))) & (~ (Y4 = Y3))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y3))))))) | (Y2 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y2 @ Y6 @ Y5) | (~ (Y2 @ Y6 @ Y7))) | (~ (Y2 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y9 @ Y7)))))))))))))))))))))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))) | (Y1 = Y2)) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y6))))))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6))))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (Y1 = Y2)))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y6)))))))) | (~ (Y0 @ Y3 @ Y1 @ Y4))) | (Y0 @ Y2 @ Y1 @ Y4)))))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y2 @ Y4)))))))))) | (~ (Y2 @ Y1))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))) | (Y1 @ Y4))))) | (Y1 @ Y3))))))))))))),
% 2.12/1.98 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13])).
% 2.12/1.98 thf(f13,plain,(
% 2.12/1.98 ! [X2 : $i] : (? [X3 : d_unsorted] : ((d2unsorted @ X3) = X2) => ((d2unsorted @ (sK0 @ X2)) = X2))),
% 2.12/1.98 introduced(definition,[],[choice_axiom])).
% 2.12/1.98 thf(f12,plain,(
% 2.12/1.98 (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y3))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1)))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) != (d2unsorted @ X0)) | (X0 = X1)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((Y4 = Y2) | (~ (Y0 @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y8)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y7 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (Y0 @ Y3 @ Y2))) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y1 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))) | (Y5 @ Y4 @ Y2)))))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y1 @ Y3))) | (Y0 @ Y1 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & ! [X2 : $i] : ? [X3 : d_unsorted] : ((d2unsorted @ X3) = X2) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y2 @ Y3)) | (Y0 @ Y1 @ Y2 @ Y3)))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y7))) | (Y1 @ Y6 @ Y8))))))))) | (Y1 @ Y3 @ Y2)) | (Y3 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y7 @ Y8)) | (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y6 @ Y7))))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y2 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y10 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y8 @ Y10)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y4 @ Y7 @ Y6)))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))) | (Y6 @ Y5 @ Y3)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | ((~ (Y5 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y5 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y8 @ Y7)))))))))))))))))))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y6 @ Y7)))))))))))))))))) | (~ (Y0 @ Y1 @ Y2))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))) | (Y1 = Y2)))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)) | (Y2 = Y1)))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((Y2 @ Y4 @ Y3) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y9))) | (Y6 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))))))))) | (Y5 @ Y3 @ Y4)) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y10 @ Y8) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y10 @ Y9)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (Y0 @ Y1 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y6)) | (~ (Y2 @ Y7 @ Y8))) | (Y2 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))))))))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y2))) | (Y0 @ Y3 @ Y1)))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y7))) | (~ (Y1 @ Y7 @ Y5)))))))))) | (Y1 @ Y4 @ Y3)) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y1 @ Y5 @ Y6)))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y6))))))))))) | (Y5 @ Y3 @ Y4))))) & (~ (Y4 = Y3))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y3))))))) | (Y2 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y2 @ Y6 @ Y5) | (~ (Y2 @ Y6 @ Y7))) | (~ (Y2 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y9 @ Y7)))))))))))))))))))))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))) | (Y1 = Y2)) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y6))))))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6))))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (Y1 = Y2)))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y6)))))))) | (~ (Y0 @ Y3 @ Y1 @ Y4))) | (Y0 @ Y2 @ Y1 @ Y4)))))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y2 @ Y4)))))))))) | (~ (Y2 @ Y1))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))) | (Y1 @ Y4))))) | (Y1 @ Y3))))))))))))),
% 2.12/1.98 inference(rectify,[status(thm)],[f11])).
% 2.12/1.98 thf(f11,plain,(
% 2.12/1.98 (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y3))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1)))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : (((d2unsorted @ X3) != (d2unsorted @ X4)) | (X3 = X4)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((Y4 = Y2) | (~ (Y0 @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y8)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y7 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (Y0 @ Y3 @ Y2))) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y1 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))) | (Y5 @ Y4 @ Y2)))))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y1 @ Y3))) | (Y0 @ Y1 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y2 @ Y3)) | (Y0 @ Y1 @ Y2 @ Y3)))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y7))) | (Y1 @ Y6 @ Y8))))))))) | (Y1 @ Y3 @ Y2)) | (Y3 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y7 @ Y8)) | (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y6 @ Y7))))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y2 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y10 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y8 @ Y10)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y4 @ Y7 @ Y6)))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))) | (Y6 @ Y5 @ Y3)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | ((~ (Y5 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y5 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y8 @ Y7)))))))))))))))))))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y6 @ Y7)))))))))))))))))) | (~ (Y0 @ Y1 @ Y2))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))) | (Y1 = Y2)))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)) | (Y2 = Y1)))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((Y2 @ Y4 @ Y3) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y9))) | (Y6 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))))))))) | (Y5 @ Y3 @ Y4)) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y10 @ Y8) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y10 @ Y9)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (Y0 @ Y1 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y6)) | (~ (Y2 @ Y7 @ Y8))) | (Y2 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))))))))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y2))) | (Y0 @ Y3 @ Y1)))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y7))) | (~ (Y1 @ Y7 @ Y5)))))))))) | (Y1 @ Y4 @ Y3)) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y1 @ Y5 @ Y6)))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y6))))))))))) | (Y5 @ Y3 @ Y4))))) & (~ (Y4 = Y3))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y3))))))) | (Y2 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y2 @ Y6 @ Y5) | (~ (Y2 @ Y6 @ Y7))) | (~ (Y2 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y9 @ Y7)))))))))))))))))))))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))) | (Y1 = Y2)) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y6))))))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6))))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (Y1 = Y2)))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y6)))))))) | (~ (Y0 @ Y3 @ Y1 @ Y4))) | (Y0 @ Y2 @ Y1 @ Y4)))))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y2 @ Y4)))))))))) | (~ (Y2 @ Y1))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))) | (Y1 @ Y4))))) | (Y1 @ Y3))))))))))))),
% 2.12/1.98 inference(ennf_transformation,[status(thm)],[f10])).
% 2.12/1.98 thf(f10,plain,(
% 2.12/1.98 ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : (((d2unsorted @ X3) = (d2unsorted @ X4)) => (X3 = X4)) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y3))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1)))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y7))) | (~ (Y1 @ Y7 @ Y5)))))))))) | (Y1 @ Y4 @ Y3)) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y1 @ Y5 @ Y6)))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y6))))))))))) | (Y5 @ Y3 @ Y4))))) & (~ (Y4 = Y3))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y3))))))) | (Y2 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y2 @ Y6 @ Y5) | (~ (Y2 @ Y6 @ Y7))) | (~ (Y2 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y9 @ Y7)))))))))))))))))))))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y6))))))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6))))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (Y1 = Y2)))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y2))) | (Y0 @ Y3 @ Y1)))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))) | (Y1 = Y2)))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y6 @ Y7)))))))))))))))))) | (~ (Y0 @ Y1 @ Y2))))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y2 @ Y4)))))))))) | (~ (Y2 @ Y1))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((Y2 @ Y4 @ Y3) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y9))) | (Y6 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))))))))) | (Y5 @ Y3 @ Y4)) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y10 @ Y8) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y10 @ Y9)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (Y0 @ Y1 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y6)) | (~ (Y2 @ Y7 @ Y8))) | (Y2 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))))))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))) | (Y1 @ Y4))))) | (Y1 @ Y3)))))))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((Y4 = Y2) | (~ (Y0 @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y8)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y7 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (Y0 @ Y3 @ Y2))) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y1 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))) | (Y5 @ Y4 @ Y2)))))))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y6)))))))) | (~ (Y0 @ Y3 @ Y1 @ Y4))) | (Y0 @ Y2 @ Y1 @ Y4)))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y1 @ Y3))) | (Y0 @ Y1 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))) | (Y1 = Y2)) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y7))) | (Y1 @ Y6 @ Y8))))))))) | (Y1 @ Y3 @ Y2)) | (Y3 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y7 @ Y8)) | (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y6 @ Y7))))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y2 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y10 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y8 @ Y10)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y4 @ Y7 @ Y6)))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))) | (Y6 @ Y5 @ Y3)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | ((~ (Y5 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y5 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y8 @ Y7)))))))))))))))))))))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y2 @ Y3)) | (Y0 @ Y1 @ Y2 @ Y3)))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)) | (Y2 = Y1)))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))),
% 2.12/1.98 inference(rectify,[status(thm)],[f6])).
% 2.12/1.98 thf(f6,plain,(
% 2.12/1.98 (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y2 @ Y4)))))))))) | (~ (Y2 @ Y1))))))))) & ! [X5 : $i] : ? [X6 : d_unsorted] : ((d2unsorted @ X6) = X5) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)) | (Y2 = Y1)))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((Y2 @ Y4 @ Y3) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y9))) | (Y6 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))))))))) | (Y5 @ Y3 @ Y4)) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y10 @ Y8) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y10 @ Y9)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (Y0 @ Y1 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y6)) | (~ (Y2 @ Y7 @ Y8))) | (Y2 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))))))))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y2))) | (Y0 @ Y3 @ Y1)))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y1 @ Y3))) | (Y0 @ Y1 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))) | (Y1 = Y2)) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))) & ! [X97 : d_unsorted] : (d_unsorted_0 = X97) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y6)))))))) | (~ (Y0 @ Y3 @ Y1 @ Y4))) | (Y0 @ Y2 @ Y1 @ Y4)))))))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y6 @ Y7)))))))))))))))))) | (~ (Y0 @ Y1 @ Y2))))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y3))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1)))))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! 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@ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y8 @ Y10)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y4 @ Y7 @ Y6)))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))) | (Y6 @ Y5 @ Y3)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | ((~ (Y5 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y5 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y8 @ Y7)))))))))))))))))))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((Y4 = Y2) | (~ (Y0 @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y8)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y7 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (Y0 @ Y3 @ Y2))) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y1 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))) | (Y5 @ Y4 @ Y2)))))))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y6))))))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6))))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (Y1 = Y2)))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))) | (Y1 = Y2)))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))) | (Y1 @ Y4))))) | (Y1 @ Y3)))))))))))) & ! [X264 : d_unsorted,X265 : d_unsorted] : (((d2unsorted @ X264) = (d2unsorted @ X265)) => (X264 = X265)) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y2 @ Y3)) | (Y0 @ Y1 @ Y2 @ Y3)))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y7))) | (~ (Y1 @ Y7 @ Y5)))))))))) | (Y1 @ Y4 @ Y3)) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y1 @ Y5 @ Y6)))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y6))))))))))) | (Y5 @ Y3 @ Y4))))) & (~ (Y4 = Y3))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y3))))))) | (Y2 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y2 @ Y6 @ Y5) | (~ (Y2 @ Y6 @ Y7))) | (~ (Y2 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y9 @ Y7))))))))))))))))))))))))))))),
% 2.12/1.98 inference(fool_elimination,[status(thm)],[f5])).
% 2.12/1.98 thf(f5,plain,(
% 2.12/1.98 (term = (^[X0 : $i > $i > $o] : (! [X1 : $i > $o,X2 : $i] : (~(X1 @ X2) | ~! [X3 : $i] : (~! [X4 : $i] : (~(X1 @ X4) | ~(X0 @ X3 @ X4)) | ~(X1 @ X3)))))) & ! [X5 : $i] : ? [X6 : d_unsorted] : ((d2unsorted @ X6) = X5) & (tc = (^[X7 : $i > $i > $o, X8 : $i, X9 : $i] : (! [X10 : $i > $i > $o] : (~! [X11 : $i,X12 : $i] : (~(X7 @ X11 @ X12) | (X10 @ X11 @ X12)) | ~! [X13 : $i,X14 : $i,X15 : $i] : (~(X10 @ X13 @ X14) | ~(X10 @ X14 @ X15) | (X10 @ X13 @ X15)) | (X10 @ X8 @ X9))))) & (total = (^[X16 : $i > $i > $o] : (! [X17 : $i,X18 : $i] : ((X17 = X18) | (X16 @ X17 @ X18) | (X16 @ X18 @ X17))))) & ((^[X19 : $i > $i > $o] : (! [X20 : $i > $i > $o,X21 : $i,X22 : $i,X23 : $i > $i > $o,X24 : $i] : (~! [X25 : $i,X26 : $i] : (~(X19 @ X26 @ X25) | (X23 @ X26 @ X25)) | ~! [X27 : $i,X28 : $i] : (~(X19 @ X27 @ X28) | (X20 @ X27 @ X28)) | ~! [X29 : $i,X30 : $i,X31 : $i] : ((X23 @ X30 @ X31) | ~(X23 @ X30 @ X29) | ~(X23 @ X29 @ X31)) | ~(X19 @ X24 @ X22) | ~! [X32 : $i,X33 : $i,X34 : $i] : ((X20 @ X32 @ X34) | ~(X20 @ X32 @ X33) | ~(X20 @ X33 @ X34)) | ~! [X35 : $i] : (~! [X36 : $i > $i > $o] : (~! [X37 : $i,X38 : $i] : ((X36 @ X38 @ X37) | ~(X19 @ X38 @ X37)) | ~! [X39 : $i,X40 : $i,X41 : $i] : ((X36 @ X39 @ X41) | ~(X36 @ X40 @ X41) | ~(X36 @ X39 @ X40)) | (X36 @ X22 @ X35)) | ~! [X42 : $i > $i > $o] : (~! [X43 : $i,X44 : $i,X45 : $i] : (~(X42 @ X43 @ X44) | ~(X42 @ X44 @ X45) | (X42 @ X43 @ X45)) | (X42 @ X21 @ X35) | ~! [X46 : $i,X47 : $i] : (~(X19 @ X46 @ X47) | (X42 @ X46 @ X47)))) | (X21 = X22) | (X20 @ X22 @ X21) | (~! [X48 : $i > $i > $o] : (~! [X49 : $i,X50 : $i] : (~(X19 @ X50 @ X49) | (X48 @ X50 @ X49)) | ~! [X51 : $i,X52 : $i,X53 : $i] : ((X48 @ X53 @ X52) | ~(X48 @ X53 @ X51) | ~(X48 @ X51 @ X52)) | (X48 @ X24 @ X21)) & (X21 != X24)) | (X23 @ X21 @ X22)))) = sconfl) & ((^[X54 : $i > $i > $o, X55 : $i, X56 : $i] : ((X55 = X56) | ! [X57 : $i > $i > $o] : ((X57 @ X56 @ X55) | ~! [X58 : $i,X59 : $i] : ((X57 @ X58 @ X59) | ~(X54 @ X58 @ X59)) | ~! [X60 : $i,X61 : $i,X62 : $i] : (~(X57 @ X62 @ X60) | (X57 @ X61 @ X60) | ~(X57 @ X61 @ X62))) | ! [X63 : $i > $i > $o] : ((X63 @ X55 @ X56) | ~! [X64 : $i,X65 : $i] : ((X63 @ X65 @ X64) | ~(X54 @ X65 @ X64)) | ~! [X66 : $i,X67 : $i,X68 : $i] : (~(X63 @ X66 @ X67) | ~(X63 @ X68 @ X66) | (X63 @ X68 @ X67))))) = trsc) & ((^[X69 : $i > $i > $o] : (! [X70 : $i,X71 : $i,X72 : $i] : ((X69 @ X70 @ X72) | ~(X69 @ X70 @ X71) | ~(X69 @ X71 @ X72)))) = trans) & ((^[X73 : $i > $i > $o] : (! [X74 : $i,X75 : $i] : ((X74 = X75) | ~(X73 @ X75 @ X74) | ~(X73 @ X74 @ X75)) & ! [X76 : $i,X77 : $i,X78 : $i] : ((X73 @ X78 @ X77) | ~(X73 @ X78 @ X76) | ~(X73 @ X76 @ X77)) & ! [X79 : $i] : (X73 @ X79 @ X79))) = po) & ((^[X80 : $i > $i > $o] : (! [X81 : $i] : (X80 @ X81 @ X81))) = refl) & ((^[X82 : $i > $i > $o, X83 : $i, X84 : $i] : (! [X85 : $i] : ~(X82 @ X83 @ X85) & ((X83 = X84) | ! [X86 : $i > $i > $o] : ((X86 @ X84 @ X83) | ~! [X87 : $i,X88 : $i,X89 : $i] : (~(X86 @ X88 @ X87) | ~(X86 @ X87 @ X89) | (X86 @ X88 @ X89)) | ~! [X90 : $i,X91 : $i] : (~(X82 @ X91 @ X90) | (X86 @ X91 @ X90)))))) = nfof) & ((^[X92 : ($i > $i > $o) > $i > $i > $o] : (! [X93 : $i > $i > $o] : ((X92 @ X93) = (X92 @ (X92 @ X93))))) = idem) & ((^[X94 : $i > $i > $o, X95 : $i, X96 : $i] : ((X95 = X96) | (X94 @ X95 @ X96))) = rc) & ! [X97 : d_unsorted] : (d_unsorted_0 = X97) & (mono = (^[X98 : ($i > $i > $o) > $i > $i > $o] : (! [X99 : $i,X100 : $i > $i > $o,X101 : $i > $i > $o,X102 : $i] : ((X98 @ X101 @ X102 @ X99) | ~(X98 @ X100 @ X102 @ X99) | ~! [X103 : $i,X104 : $i] : (~(X100 @ X104 @ X103) | (X101 @ X104 @ X103)))))) & (norm = (^[X105 : $i > $i > $o] : (! [X106 : $i,X107 : $i] : (~(X105 @ X107 @ X106) | ~! [X108 : $i] : (~! [X109 : $i > $i > $o] : (~! [X110 : $i,X111 : $i,X112 : $i] : (~(X109 @ X111 @ X110) | (X109 @ X112 @ X110) | ~(X109 @ X112 @ X111)) | ~! [X113 : $i,X114 : $i] : ((X109 @ X113 @ X114) | ~(X105 @ X113 @ X114)) | (X109 @ X107 @ X108)) | ~! [X115 : $i] : ~(X105 @ X108 @ X115)))))) & ((^[X116 : $i > $i > $o] : (! [X117 : $i,X118 : $i] : (~(X116 @ X117 @ X118) | ~(X116 @ X118 @ X117)) & ! [X119 : $i,X120 : $i,X121 : $i] : (~(X116 @ X121 @ X119) | ~(X116 @ X120 @ X121) | (X116 @ X120 @ X119)))) = so) & ((^[X122 : $i > $i > $o] : (! [X123 : $i] : ~(X122 @ X123 @ X123))) = irrefl) & (antisymm = (^[X124 : $i > $i > $o] : (! [X125 : $i,X126 : $i] : (~(X124 @ X126 @ X125) | (X125 = X126) | ~(X124 @ X125 @ X126))))) & ((^[X127 : $i > $i > $o, X128 : $i, X129 : $i] : (X127 @ X129 @ X128)) = inv) & ((^[X130 : $i > $i > $o] : (! [X131 : $i,X132 : $i] : (~(X130 @ X131 @ X132) | (X130 @ X132 @ X131)))) = symm) & ((^[X133 : $i > $i > $o, X134 : $i, X135 : $i] : ((X133 @ X135 @ X134) | (X133 @ X134 @ X135))) = sc) & (subrel = (^[X136 : $i > $i > $o, X137 : $i > $i > $o] : (! [X138 : $i,X139 : $i] : ((X137 @ X139 @ X138) | ~(X136 @ X139 @ X138))))) & (asymm = (^[X140 : $i > $i > $o] : (! [X141 : $i,X142 : $i] : (~(X140 @ X142 @ X141) | ~(X140 @ X141 @ X142))))) & (confl = (^[X143 : $i > $i > $o] : (! [X144 : $i,X145 : $i > $i > $o,X146 : $i,X147 : $i,X148 : $i > $i > $o] : ((~! [X149 : $i > $i > $o] : (~! [X150 : $i,X151 : $i,X152 : $i] : (~(X149 @ X151 @ X152) | ~(X149 @ X150 @ X151) | (X149 @ X150 @ X152)) | ~! [X153 : $i,X154 : $i] : ((X149 @ X153 @ X154) | ~(X143 @ X153 @ X154)) | (X149 @ X144 @ X147)) & (X144 != X147)) | ~! [X155 : $i,X156 : $i] : (~(X143 @ X155 @ X156) | (X148 @ X155 @ X156)) | ((X144 != X146) & ~! [X157 : $i > $i > $o] : (~! [X158 : $i,X159 : $i,X160 : $i] : (~(X157 @ X160 @ X158) | ~(X157 @ X158 @ X159) | (X157 @ X160 @ X159)) | (X157 @ X144 @ X146) | ~! [X161 : $i,X162 : $i] : ((X157 @ X162 @ X161) | ~(X143 @ X162 @ X161)))) | ~! [X163 : $i,X164 : $i] : ((X145 @ X163 @ X164) | ~(X143 @ X163 @ X164)) | ~! [X165 : $i] : (~! [X166 : $i > $i > $o] : (~! [X167 : $i,X168 : $i,X169 : $i] : ((X166 @ X169 @ X167) | ~(X166 @ X168 @ X167) | ~(X166 @ X169 @ X168)) | (X166 @ X146 @ X165) | ~! [X170 : $i,X171 : $i] : (~(X143 @ X171 @ X170) | (X166 @ X171 @ X170))) | ~! [X172 : $i > $i > $o] : (~! [X173 : $i,X174 : $i] : (~(X143 @ X174 @ X173) | (X172 @ X174 @ X173)) | ~! [X175 : $i,X176 : $i,X177 : $i] : (~(X172 @ X175 @ X177) | (X172 @ X175 @ X176) | ~(X172 @ X177 @ X176)) | (X172 @ X147 @ X165))) | (X145 @ X147 @ X146) | ~! [X178 : $i,X179 : $i,X180 : $i] : (~(X145 @ X180 @ X179) | (X145 @ X180 @ X178) | ~(X145 @ X179 @ X178)) | (X146 = X147) | (X148 @ X146 @ X147) | ~! [X181 : $i,X182 : $i,X183 : $i] : ((X148 @ X183 @ X181) | ~(X148 @ X183 @ X182) | ~(X148 @ X182 @ X181)))))) & (innf = (^[X184 : $i > $i > $o, X185 : $i] : (! [X186 : $i] : ~(X184 @ X185 @ X186)))) & (lconfl = (^[X187 : $i > $i > $o] : (! [X188 : $i > $i > $o,X189 : $i,X190 : $i,X191 : $i,X192 : $i > $i > $o] : ((X188 @ X189 @ X191) | ~! [X193 : $i] : (~! [X194 : $i > $i > $o] : (~! [X195 : $i,X196 : $i] : ((X194 @ X196 @ X195) | ~(X187 @ X196 @ X195)) | (X194 @ X191 @ X193) | ~! [X197 : $i,X198 : $i,X199 : $i] : (~(X194 @ X198 @ X199) | (X194 @ X197 @ X199) | ~(X194 @ X197 @ X198))) | ~! [X200 : $i > $i > $o] : (~! [X201 : $i,X202 : $i,X203 : $i] : (~(X200 @ X202 @ X201) | ~(X200 @ X203 @ X202) | (X200 @ X203 @ X201)) | ~! [X204 : $i,X205 : $i] : ((X200 @ X205 @ X204) | ~(X187 @ X205 @ X204)) | (X200 @ X189 @ X193))) | ~! [X206 : $i,X207 : $i] : ((X188 @ X207 @ X206) | ~(X187 @ X207 @ X206)) | ~! [X208 : $i,X209 : $i] : ((X192 @ X209 @ X208) | ~(X187 @ X209 @ X208)) | (X192 @ X191 @ X189) | ~(X187 @ X190 @ X191) | ~! [X210 : $i,X211 : $i,X212 : $i] : (~(X188 @ X212 @ X210) | (X188 @ X211 @ X210) | ~(X188 @ X211 @ X212)) | ~! [X213 : $i,X214 : $i,X215 : $i] : (~(X192 @ X214 @ X215) | (X192 @ X214 @ X213) | ~(X192 @ X215 @ X213)) | ~(X187 @ X190 @ X189) | (X189 = X191))))) & ((^[X216 : $i > $i > $o, X217 : $i, X218 : $i] : (~((X217 != X218) & ~! [X219 : $i > $i > $o] : ((X219 @ X218 @ X217) | ~! [X220 : $i,X221 : $i] : (~(X216 @ X220 @ X221) | (X219 @ X220 @ X221)) | ~! [X222 : $i,X223 : $i,X224 : $i] : (~(X219 @ X222 @ X223) | (X219 @ X222 @ X224) | ~(X219 @ X223 @ X224))) & ~! [X225 : $i > $i > $o] : (~! [X226 : $i,X227 : $i,X228 : $i] : (~(X225 @ X227 @ X226) | ~(X225 @ X228 @ X227) | (X225 @ X228 @ X226)) | ~! [X229 : $i,X230 : $i] : (~(X216 @ X230 @ X229) | (X225 @ X230 @ X229)) | (X225 @ X217 @ X218)) & ! [X231 : $i] : (~! [X232 : $i > $i > $o] : (~! [X233 : $i,X234 : $i,X235 : $i] : (~(X232 @ X235 @ X234) | (X232 @ X233 @ X234) | ~(X232 @ X233 @ X235)) | (X232 @ X217 @ X231) | ~! [X236 : $i,X237 : $i] : ((X232 @ X237 @ X236) | ~(X216 @ X237 @ X236))) | ~! [X238 : $i > $i > $o] : (~! [X239 : $i,X240 : $i] : ((X238 @ X240 @ X239) | ~(X216 @ X240 @ X239)) | ~! [X241 : $i,X242 : $i,X243 : $i] : (~(X238 @ X242 @ X241) | (X238 @ X242 @ X243) | ~(X238 @ X241 @ X243)) | (X238 @ X218 @ X231)))))) = join) & ((^[X244 : $i > $i > $o, X245 : $i, X246 : $i] : ((X245 = X246) | ! [X247 : $i > $i > $o] : (~! [X248 : $i,X249 : $i,X250 : $i] : (~(X247 @ X249 @ X250) | (X247 @ X249 @ X248) | ~(X247 @ X250 @ X248)) | (X247 @ X245 @ X246) | ~! [X251 : $i,X252 : $i] : ((X247 @ X252 @ X251) | ~(X244 @ X252 @ X251))))) = trc) & (ind = (^[X253 : $i > $i > $o] : (! [X254 : $i,X255 : $i > $o] : (~! [X256 : $i] : ((X255 @ X256) | ~! [X257 : $i] : ((X255 @ X257) | ~! [X258 : $i > $i > $o] : (~! [X259 : $i,X260 : $i] : (~(X253 @ X260 @ X259) | (X258 @ X260 @ X259)) | ~! [X261 : $i,X262 : $i,X263 : $i] : ((X258 @ X262 @ X261) | ~(X258 @ X262 @ X263) | ~(X258 @ X263 @ X261)) | (X258 @ X256 @ X257)))) | (X255 @ X254))))) & ! [X264 : d_unsorted,X265 : d_unsorted] : (((d2unsorted @ X264) = (d2unsorted @ X265)) => (X264 = X265)) & (infl = (^[X266 : ($i > $i > $o) > $i > $i > $o] : (! [X267 : $i,X268 : $i,X269 : $i > $i > $o] : ((X266 @ X269 @ X268 @ X267) | ~(X269 @ X268 @ X267))))) & ((^[X270 : $i > $i > $o] : (! [X271 : $i,X272 : $i,X273 : $i > $i > $o,X274 : $i > $i > $o] : (~! [X275 : $i] : (~! [X276 : $i > $i > $o] : (~! [X277 : $i,X278 : $i,X279 : $i] : ((X276 @ X277 @ X279) | ~(X276 @ X277 @ X278) | ~(X276 @ X278 @ X279)) | ~! [X280 : $i,X281 : $i] : (~(X270 @ X280 @ X281) | (X276 @ X280 @ X281)) | (X276 @ X271 @ X275)) | ~! [X282 : $i > $i > $o] : (~! [X283 : $i,X284 : $i] : (~(X270 @ X283 @ X284) | (X282 @ X283 @ X284)) | (X282 @ X272 @ X275) | ~! [X285 : $i,X286 : $i,X287 : $i] : ((X282 @ X285 @ X287) | ~(X282 @ X286 @ X287) | ~(X282 @ X285 @ X286)))) | ~! [X288 : $i,X289 : $i] : (~(X270 @ X288 @ X289) | (X273 @ X288 @ X289)) | ~! [X290 : $i,X291 : $i,X292 : $i] : (~(X273 @ X290 @ X292) | ~(X273 @ X291 @ X290) | (X273 @ X291 @ X292)) | (X273 @ X272 @ X271) | (~! [X293 : $i > $i > $o] : ((X293 @ X271 @ X272) | ~! [X294 : $i,X295 : $i] : ((X293 @ X294 @ X295) | ~(X270 @ X294 @ X295)) | ~! [X296 : $i,X297 : $i,X298 : $i] : (~(X293 @ X298 @ X297) | (X293 @ X296 @ X297) | ~(X293 @ X296 @ X298))) & (X271 != X272) & ~! [X299 : $i > $i > $o] : ((X299 @ X272 @ X271) | ~! [X300 : $i,X301 : $i,X302 : $i] : (~(X299 @ X301 @ X302) | (X299 @ X300 @ X302) | ~(X299 @ X300 @ X301)) | ~! [X303 : $i,X304 : $i] : ((X299 @ X304 @ X303) | ~(X270 @ X304 @ X303)))) | ~! [X305 : $i,X306 : $i] : ((X274 @ X306 @ X305) | ~(X270 @ X306 @ X305)) | (X271 = X272) | (X274 @ X271 @ X272) | ~! [X307 : $i,X308 : $i,X309 : $i] : (~(X274 @ X307 @ X309) | ~(X274 @ X308 @ X307) | (X274 @ X308 @ X309))))) = cr)),
% 2.12/1.98 inference(rectify,[status(thm)],[f1])).
% 2.12/1.98 thf(f1,axiom,(
% 2.12/1.98 (term = (^[X4 : $i > $i > $o] : (! [X18 : $i > $o,X19 : $i] : (~(X18 @ X19) | ~! [X6 : $i] : (~! [X7 : $i] : (~(X18 @ X7) | ~(X4 @ X6 @ X7)) | ~(X18 @ X6)))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & (tc = (^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : (! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X12 : $i,X13 : $i,X11 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X11) | (X5 @ X12 @ X11)) | (X5 @ X6 @ X7))))) & (total = (^[X4 : $i > $i > $o] : (! [X6 : $i,X7 : $i] : ((X6 = X7) | (X4 @ X6 @ X7) | (X4 @ X7 @ X6))))) & ((^[X4 : $i > $i > $o] : (! [X31 : $i > $i > $o,X7 : $i,X11 : $i,X30 : $i > $i > $o,X6 : $i] : (~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X30 @ X14 @ X15)) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X31 @ X14 @ X15)) | ~! [X13 : $i,X12 : $i,X25 : $i] : ((X30 @ X12 @ X25) | ~(X30 @ X12 @ X13) | ~(X30 @ X13 @ X25)) | ~(X4 @ X6 @ X11) | ~! [X12 : $i,X13 : $i,X26 : $i] : ((X31 @ X12 @ X26) | ~(X31 @ X12 @ X13) | ~(X31 @ X13 @ X26)) | ~! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X12 : $i,X13 : $i,X26 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13)) | (X5 @ X11 @ X27)) | ~! [X5 : $i > $i > $o] : (~! [X12 : $i,X13 : $i,X25 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X25) | (X5 @ X12 @ X25)) | (X5 @ X7 @ X27) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)))) | (X7 = X11) | (X31 @ X11 @ X7) | (~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X13 : $i,X32 : $i,X12 : $i] : ((X5 @ X12 @ X32) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X32)) | (X5 @ X6 @ X7)) & (X6 != X7)) | (X30 @ X7 @ X11)))) = sconfl) & ((^[X4 : $i > $i > $o, X16 : $i, X17 : $i] : ((X16 = X17) | ! [X5 : $i > $i > $o] : ((X5 @ X17 @ X16) | ~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X11 : $i,X12 : $i,X13 : $i] : (~(X5 @ X13 @ X11) | (X5 @ X12 @ X11) | ~(X5 @ X12 @ X13))) | ! [X5 : $i > $i > $o] : ((X5 @ X16 @ X17) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X13 : $i,X11 : $i,X12 : $i] : (~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X11))))) = trsc) & ((^[X4 : $i > $i > $o] : (! [X6 : $i,X7 : $i,X11 : $i] : ((X4 @ X6 @ X11) | ~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X11)))) = trans) & ((^[X4 : $i > $i > $o] : (! [X6 : $i,X7 : $i] : ((X6 = X7) | ~(X4 @ X7 @ X6) | ~(X4 @ X6 @ X7)) & ! [X7 : $i,X11 : $i,X6 : $i] : ((X4 @ X6 @ X11) | ~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X11)) & ! [X6 : $i] : (X4 @ X6 @ X6))) = po) & ((^[X4 : $i > $i > $o] : (! [X6 : $i] : (X4 @ X6 @ X6))) = refl) & ((^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : (! [X22 : $i] : ~(X4 @ X6 @ X22) & ((X6 = X7) | ! [X5 : $i > $i > $o] : ((X5 @ X7 @ X6) | ~! [X13 : $i,X12 : $i,X11 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X11) | (X5 @ X12 @ X11)) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)))))) = nfof) & ((^[X8 : ($i > $i > $o) > $i > $i > $o] : (! [X4 : $i > $i > $o] : ((X8 @ X4) = (X8 @ (X8 @ X4))))) = idem) & ((^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : ((X6 = X7) | (X4 @ X6 @ X7))) = rc) & ! [X1 : d_unsorted] : (d_unsorted_0 = X1) & (mono = (^[X8 : ($i > $i > $o) > $i > $i > $o] : (! [X10 : $i,X4 : $i > $i > $o,X5 : $i > $i > $o,X9 : $i] : ((X8 @ X5 @ X9 @ X10) | ~(X8 @ X4 @ X9 @ X10) | ~! [X7 : $i,X6 : $i] : (~(X4 @ X6 @ X7) | (X5 @ X6 @ X7)))))) & (norm = (^[X4 : $i > $i > $o] : (! [X23 : $i,X6 : $i] : (~(X4 @ X6 @ X23) | ~! [X24 : $i] : (~! [X5 : $i > $i > $o] : (~! [X11 : $i,X13 : $i,X12 : $i] : (~(X5 @ X13 @ X11) | (X5 @ X12 @ X11) | ~(X5 @ X12 @ X13)) | ~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X6 @ X24)) | ~! [X22 : $i] : ~(X4 @ X24 @ X22)))))) & ((^[X4 : $i > $i > $o] : (! [X7 : $i,X6 : $i] : (~(X4 @ X7 @ X6) | ~(X4 @ X6 @ X7)) & ! [X11 : $i,X6 : $i,X7 : $i] : (~(X4 @ X7 @ X11) | ~(X4 @ X6 @ X7) | (X4 @ X6 @ X11)))) = so) & ((^[X4 : $i > $i > $o] : (! [X6 : $i] : ~(X4 @ X6 @ X6))) = irrefl) & (antisymm = (^[X4 : $i > $i > $o] : (! [X7 : $i,X6 : $i] : (~(X4 @ X6 @ X7) | (X6 = X7) | ~(X4 @ X7 @ X6))))) & ((^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : (X4 @ X7 @ X6)) = inv) & ((^[X4 : $i > $i > $o] : (! [X6 : $i,X7 : $i] : (~(X4 @ X6 @ X7) | (X4 @ X7 @ X6)))) = symm) & ((^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : ((X4 @ X7 @ X6) | (X4 @ X6 @ X7))) = sc) & (subrel = (^[X4 : $i > $i > $o, X5 : $i > $i > $o] : (! [X7 : $i,X6 : $i] : ((X5 @ X6 @ X7) | ~(X4 @ X6 @ X7))))) & (asymm = (^[X4 : $i > $i > $o] : (! [X7 : $i,X6 : $i] : (~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X6))))) & (confl = (^[X4 : $i > $i > $o] : (! [X6 : $i,X34 : $i > $i > $o,X7 : $i,X11 : $i,X33 : $i > $i > $o] : ((~! [X5 : $i > $i > $o] : (~! [X12 : $i,X13 : $i,X26 : $i] : (~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X26)) | ~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X6 @ X11)) & (X6 != X11)) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X33 @ X14 @ X15)) | ((X6 != X7) & ~! [X5 : $i > $i > $o] : (~! [X13 : $i,X35 : $i,X12 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X35) | (X5 @ X12 @ X35)) | (X5 @ X6 @ X7) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)))) | ~! [X14 : $i,X15 : $i] : ((X34 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X25 : $i,X13 : $i,X12 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13)) | (X5 @ X7 @ X27) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15))) | ~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X12 : $i,X26 : $i,X13 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X26) | ~(X5 @ X13 @ X26)) | (X5 @ X11 @ X27))) | (X34 @ X11 @ X7) | ~! [X26 : $i,X13 : $i,X12 : $i] : (~(X34 @ X12 @ X13) | (X34 @ X12 @ X26) | ~(X34 @ X13 @ X26)) | (X7 = X11) | (X33 @ X7 @ X11) | ~! [X25 : $i,X13 : $i,X12 : $i] : ((X33 @ X12 @ X25) | ~(X33 @ X12 @ X13) | ~(X33 @ X13 @ X25)))))) & (innf = (^[X4 : $i > $i > $o, X6 : $i] : (! [X7 : $i] : ~(X4 @ X6 @ X7)))) & (lconfl = (^[X4 : $i > $i > $o] : (! [X28 : $i > $i > $o,X7 : $i,X6 : $i,X11 : $i,X29 : $i > $i > $o] : ((X28 @ X7 @ X11) | ~! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X11 @ X27) | ~! [X12 : $i,X13 : $i,X26 : $i] : (~(X5 @ X13 @ X26) | (X5 @ X12 @ X26) | ~(X5 @ X12 @ X13))) | ~! [X5 : $i > $i > $o] : (~! [X25 : $i,X13 : $i,X12 : $i] : (~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X25)) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X7 @ X27))) | ~! [X15 : $i,X14 : $i] : ((X28 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X15 : $i,X14 : $i] : ((X29 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X29 @ X11 @ X7) | ~(X4 @ X6 @ X11) | ~! [X25 : $i,X12 : $i,X13 : $i] : (~(X28 @ X13 @ X25) | (X28 @ X12 @ X25) | ~(X28 @ X12 @ X13)) | ~! [X26 : $i,X12 : $i,X13 : $i] : (~(X29 @ X12 @ X13) | (X29 @ X12 @ X26) | ~(X29 @ X13 @ X26)) | ~(X4 @ X6 @ X7) | (X7 = X11))))) & ((^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : (~((X6 != X7) & ~! [X5 : $i > $i > $o] : ((X5 @ X7 @ X6) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X12 : $i,X13 : $i,X25 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X25) | ~(X5 @ X13 @ X25))) & ~! [X5 : $i > $i > $o] : (~! [X26 : $i,X13 : $i,X12 : $i] : (~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X26)) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | (X5 @ X6 @ X7)) & ! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X12 : $i,X26 : $i,X13 : $i] : (~(X5 @ X13 @ X26) | (X5 @ X12 @ X26) | ~(X5 @ X12 @ X13)) | (X5 @ X6 @ X27) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15))) | ~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X13 : $i,X12 : $i,X25 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X25) | ~(X5 @ X13 @ X25)) | (X5 @ X7 @ X27)))))) = join) & ((^[X4 : $i > $i > $o, X16 : $i, X17 : $i] : ((X16 = X17) | ! [X5 : $i > $i > $o] : (~! [X11 : $i,X12 : $i,X13 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X11) | ~(X5 @ X13 @ X11)) | (X5 @ X16 @ X17) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15))))) = trc) & (ind = (^[X4 : $i > $i > $o] : (! [X21 : $i,X20 : $i > $o] : (~! [X6 : $i] : ((X20 @ X6) | ~! [X7 : $i] : ((X20 @ X7) | ~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X11 : $i,X12 : $i,X13 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X11)) | (X5 @ X6 @ X7)))) | (X20 @ X21))))) & ! [X3 : d_unsorted,X2 : d_unsorted] : (((d2unsorted @ X2) = (d2unsorted @ X3)) => (X2 = X3)) & (infl = (^[X8 : ($i > $i > $o) > $i > $i > $o] : (! [X7 : $i,X6 : $i,X4 : $i > $i > $o] : ((X8 @ X4 @ X6 @ X7) | ~(X4 @ X6 @ X7))))) & ((^[X4 : $i > $i > $o] : (! [X7 : $i,X6 : $i,X37 : $i > $i > $o,X36 : $i > $i > $o] : (~! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X12 : $i,X13 : $i,X25 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X25)) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | (X5 @ X7 @ X27)) | ~! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | (X5 @ X6 @ X27) | ~! [X12 : $i,X13 : $i,X26 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13)))) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X37 @ X14 @ X15)) | ~! [X13 : $i,X12 : $i,X26 : $i] : (~(X37 @ X13 @ X26) | ~(X37 @ X12 @ X13) | (X37 @ X12 @ X26)) | (X37 @ X6 @ X7) | (~! [X5 : $i > $i > $o] : ((X5 @ X7 @ X6) | ~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X12 : $i,X11 : $i,X13 : $i] : (~(X5 @ X13 @ X11) | (X5 @ X12 @ X11) | ~(X5 @ X12 @ X13))) & (X6 != X7) & ~! [X5 : $i > $i > $o] : ((X5 @ X6 @ X7) | ~! [X12 : $i,X13 : $i,X11 : $i] : (~(X5 @ X13 @ X11) | (X5 @ X12 @ X11) | ~(X5 @ X12 @ X13)) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)))) | ~! [X15 : $i,X14 : $i] : ((X36 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X6 = X7) | (X36 @ X7 @ X6) | ~! [X13 : $i,X12 : $i,X25 : $i] : (~(X36 @ X13 @ X25) | ~(X36 @ X12 @ X13) | (X36 @ X12 @ X25))))) = cr)),
% 2.12/1.98 file('/export/starexec/sandbox/tmp/tmp.L1wr6hYwUS/DTF2THF_12102.p',sev441_1)).
% 2.12/1.98 thf(f40,plain,(
% 2.12/1.98 ( ! [X2 : $i] : (((d2unsorted @ (sK0 @ X2)) = X2)) )),
% 2.12/1.98 inference(cnf_transformation,[status(thm)],[f14])).
% 2.12/1.98 thf(f721,plain,(
% 2.12/1.98 (sK5 != sK4)),
% 2.12/1.98 inference(duplicate_literal_removal,[status(thm)],[f720])).
% 2.12/1.98 thf(f720,plain,(
% 2.12/1.98 (sK5 != sK4) | (sK5 != sK4)),
% 2.12/1.98 inference(equality_proxy_clausification,[status(thm)],[f694])).
% 2.12/1.98 thf(f694,plain,(
% 2.12/1.98 ((sK5 = sK4) = $false) | (sK5 != sK4)),
% 2.12/1.98 inference(binary_proxy_clausification,[status(thm)],[f693])).
% 2.12/1.98 thf(f693,plain,(
% 2.12/1.98 (sK5 != sK4) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ sK5 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))) | (sK5 = sK4)) = $false)),
% 2.12/1.98 inference(equality_proxy_clausification,[status(thm)],[f662])).
% 2.12/1.98 thf(f662,plain,(
% 2.12/1.98 ($false = (sK4 = sK5)) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ sK5 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))) | (sK5 = sK4)) = $false)),
% 2.12/1.98 inference(binary_proxy_clausification,[status(thm)],[f68])).
% 2.12/1.98 thf(f68,plain,(
% 2.12/1.98 ($false = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ sK4 @ sK5) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))) | (sK4 = sK5)) | ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ sK5 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))) | (sK5 = sK4)))) | ($false = (sK4 = sK5))),
% 2.12/1.98 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 2.12/1.98 thf(f67,plain,(
% 2.12/1.98 ((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK3 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ sK4 @ sK5)))) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK3 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ sK5 @ sK4))))) | (sK4 = sK5)) = $false) | ($false = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ sK4 @ sK5) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))) | (sK4 = sK5)) | ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ sK5 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))) | (sK5 = sK4))))),
% 2.12/1.98 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 2.12/1.98 thf(f65,plain,(
% 2.12/1.98 ((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK3 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ sK4 @ sK5)))) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK3 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ sK5 @ sK4))))) | (sK4 = sK5)) != (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ sK4 @ sK5) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))) | (sK4 = sK5)) | ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ sK5 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))) | (sK5 = sK4))))),
% 2.12/1.98 inference(beta_eta_normalization,[status(thm)],[f64])).
% 2.12/1.98 thf(f64,plain,(
% 2.12/1.98 (((^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y3) | (~ (Y1 @ Y2 @ Y4))) | (~ (Y1 @ Y4 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK3 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ sK4 @ Y0)))) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y4)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK3 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ Y0 @ sK4))))) | (sK4 = Y0))) @ sK5) != ((^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ sK4 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) | (~ (Y1 @ Y3 @ Y2))) | (~ (Y1 @ Y4 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))) | (sK4 = Y0)) | ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ Y0 @ sK4) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) | (~ (Y1 @ Y3 @ Y2))) | (~ (Y1 @ Y4 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))) | (Y0 = sK4)))) @ sK5))),
% 2.12/1.98 inference(negative_extensionality,[status(thm)],[f63])).
% 2.12/1.98 thf(f63,plain,(
% 2.12/1.98 ((^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ sK4 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) | (~ (Y1 @ Y3 @ Y2))) | (~ (Y1 @ Y4 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))) | (sK4 = Y0)) | ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ Y0 @ sK4) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) | (~ (Y1 @ Y3 @ Y2))) | (~ (Y1 @ Y4 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))) | (Y0 = sK4)))) != (^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y3) | (~ (Y1 @ Y2 @ Y4))) | (~ (Y1 @ Y4 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK3 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ sK4 @ Y0)))) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y4)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK3 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ Y0 @ sK4))))) | (sK4 = Y0))))),
% 2.12/1.98 inference(beta_eta_normalization,[status(thm)],[f62])).
% 2.12/1.98 thf(f62,plain,(
% 2.12/1.98 (((^[Y0 : $i]: ((^[Y1 : $i]: (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) | (~ (Y2 @ Y4 @ Y3))) | (~ (Y2 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))))) | (Y0 = Y1)) | ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y1 @ Y0) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) | (~ (Y2 @ Y4 @ Y3))) | (~ (Y2 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))))) | (Y1 = Y0)))))) @ sK4) != ((^[Y0 : $i]: ((^[Y1 : $i]: (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y4) | (~ (Y2 @ Y3 @ Y5))) | (~ (Y2 @ Y5 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK3 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))) | (Y2 @ Y0 @ Y1)))) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y5)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK3 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y1 @ Y0))))) | (Y0 = Y1))))) @ sK4))),
% 2.12/1.98 inference(negative_extensionality,[status(thm)],[f61])).
% 2.12/1.98 thf(f61,plain,(
% 2.12/1.98 ((^[Y0 : $i]: ((^[Y1 : $i]: (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y4) | (~ (Y2 @ Y3 @ Y5))) | (~ (Y2 @ Y5 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK3 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))) | (Y2 @ Y0 @ Y1)))) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y5)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK3 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y1 @ Y0))))) | (Y0 = Y1))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) | (~ (Y2 @ Y4 @ Y3))) | (~ (Y2 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))))) | (Y0 = Y1)) | ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y1 @ Y0) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) | (~ (Y2 @ Y4 @ Y3))) | (~ (Y2 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))))) | (Y1 = Y0)))))))),
% 2.12/1.98 inference(beta_eta_normalization,[status(thm)],[f60])).
% 2.12/1.98 thf(f60,plain,(
% 2.12/1.98 (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))) | (Y1 = Y2)) | ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))) | (Y2 = Y1)))))))) @ sK3) != ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2))))))) @ sK3))),
% 2.12/1.98 inference(negative_extensionality,[status(thm)],[f49])).
% 2.12/1.98 thf(f49,plain,(
% 2.12/1.98 ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2))))))) != (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))) | (Y1 = Y2)) | ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))) | (Y2 = Y1)))))))))),
% 2.12/1.98 inference(beta_eta_normalization,[status(thm)],[f48])).
% 2.12/1.98 thf(f48,plain,(
% 2.12/1.98 ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (Y1 @ Y3 @ Y2))))))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (Y2 = Y3))))))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) | (~ (Y4 @ Y6 @ Y5))) | (~ (Y4 @ Y7 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y5)))))))))))))))) @ Y0)))) != (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2))))))))),
% 2.12/1.98 inference(definition_unfolding,[status(thm)],[f47,f39,f31,f37,f42])).
% 2.12/1.98 thf(f42,plain,(
% 2.12/1.98 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))))))))))))),
% 2.12/1.98 inference(cnf_transformation,[status(thm)],[f14])).
% 2.12/1.98 thf(f37,plain,(
% 2.12/1.98 (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))),
% 2.12/1.98 inference(cnf_transformation,[status(thm)],[f14])).
% 2.12/1.98 thf(f31,plain,(
% 2.12/1.98 (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))),
% 2.12/1.98 inference(cnf_transformation,[status(thm)],[f14])).
% 2.12/1.98 thf(f39,plain,(
% 2.12/1.98 (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2))))))))),
% 2.12/1.98 inference(cnf_transformation,[status(thm)],[f14])).
% 2.12/1.98 thf(f47,plain,(
% 2.12/1.98 (trsc != (^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))))),
% 2.12/1.98 inference(cnf_transformation,[status(thm)],[f9])).
% 2.12/1.98 thf(f9,plain,(
% 2.12/1.98 (trsc != (^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))))),
% 2.12/1.98 inference(flattening,[status(thm)],[f8])).
% 2.12/1.98 thf(f8,plain,(
% 2.12/1.98 ~(trsc = (^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))))),
% 2.12/1.98 inference(fool_elimination,[status(thm)],[f7])).
% 2.12/1.98 thf(f7,plain,(
% 2.12/1.98 ~((^[X0 : $i > $i > $o] : (sc @ (rc @ (tc @ X0)))) = trsc)),
% 2.12/1.98 inference(rectify,[status(thm)],[f3])).
% 2.12/1.98 thf(f3,negated_conjecture,(
% 2.12/1.98 ~((^[X4 : $i > $i > $o] : (sc @ (rc @ (tc @ X4)))) = trsc)),
% 2.12/1.98 inference(negated_conjecture,[status(cth)],[f2])).
% 2.12/1.98 thf(f2,conjecture,(
% 2.12/1.98 ((^[X4 : $i > $i > $o] : (sc @ (rc @ (tc @ X4)))) = trsc)),
% 2.12/1.98 file('/export/starexec/sandbox/tmp/tmp.L1wr6hYwUS/DTF2THF_12102.p',transitive_reflexive_symmetric_closure)).
% 2.12/1.98 % SZS output end Proof for DTF2THF_12102
% 2.12/1.98 % (12250)------------------------------
% 2.12/1.98 % (12250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.98 % (12250)Termination reason: Refutation
% 2.12/1.98
% 2.12/1.98 % (12250)Memory used [KB]: 11001
% 2.12/1.98 % (12250)Time elapsed: 0.295 s
% 2.12/1.98 % (12250)Instructions burned: 967 (million)
% 2.12/1.98 % (12250)------------------------------
% 2.12/1.98 % (12250)------------------------------
% 2.12/1.98 % (12201)Success in time 0.57 s
%------------------------------------------------------------------------------