%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU676^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:32:57 AM UTC 2026
% Result : Theorem 80.87s 11.61s
% Output : Refutation 80.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 10
% Syntax : Number of formulae : 128 ( 64 unt; 0 typ; 1 def)
% Number of atoms : 1544 ( 318 equ; 0 cnn)
% Maximal formula atoms : 9 ( 12 avg)
% Number of connectives : 3258 ( 44 ~; 141 |; 111 &;2721 @)
% ( 1 <=>; 106 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 924 ( 919 usr; 12 con; 0-5 aty)
% ( 84 !!; 50 ??; 0 @@+; 0 @@-)
% Number of variables : 730 ( 45 sgn 192 !; 10 ?; 730 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
powerset: $i > $i ).
thf(func_def_4,type,
setunion: $i > $i ).
thf(func_def_5,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_6,type,
subset: $i > $i > $o ).
thf(func_def_7,type,
kpair: $i > $i > $i ).
thf(func_def_8,type,
cartprod: $i > $i > $i ).
thf(func_def_9,type,
singleton: $i > $o ).
thf(func_def_11,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_12,type,
breln: $i > $i > $i > $o ).
thf(func_def_13,type,
func: $i > $i > $i > $o ).
thf(func_def_14,type,
funcSet: $i > $i > $i ).
thf(func_def_15,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_16,type,
app: $o ).
thf(func_def_17,type,
infuncsetfunc: $o ).
thf(func_def_18,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_19,type,
vAND: $o > $o > $o ).
thf(func_def_20,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_23,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_24,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vIMP: $o > $o > $o ).
thf(func_def_27,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vNOT: $o > $o ).
thf(func_def_35,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
sK4: $i > $i > $i > $i ).
thf(func_def_37,type,
sK5: $i > $i > $i > $i ).
thf(func_def_39,type,
sK7: $i > $i ).
thf(func_def_40,type,
sK8: $i > $i ).
thf(func_def_41,type,
sK9: $i > $i ).
thf(func_def_42,type,
sK10: $i > $i ).
thf(func_def_43,type,
sK11: $i > $i > $i > $i > $i ).
thf(func_def_44,type,
sK12: $i > $i ).
thf(func_def_45,type,
sK13: $i > $i ).
thf(func_def_46,type,
sK14: $i > $i ).
thf(func_def_47,type,
sK15: $i > $i ).
thf(func_def_48,type,
sK16: $i > $i ).
thf(func_def_49,type,
sK17: $i > $i ).
thf(func_def_50,type,
sK18: $i > $i ).
thf(func_def_51,type,
sK19: $i > $i ).
thf(func_def_52,type,
sK20: $i > $i ).
thf(func_def_53,type,
sK21: $i > $i ).
thf(func_def_54,type,
sK22: $i > $i ).
thf(func_def_55,type,
sK23: $i > $i ).
thf(func_def_56,type,
sK24: $i > $i ).
thf(func_def_57,type,
sK25: $i > $i ).
thf(func_def_58,type,
sK26: $i > $i ).
thf(func_def_59,type,
sK27: $i > $i ).
thf(func_def_60,type,
sK28: $i > $i ).
thf(func_def_61,type,
sK29: $i > $i ).
thf(func_def_62,type,
sK30: $i > $i ).
thf(func_def_63,type,
sK31: $i > $i ).
thf(func_def_64,type,
sK32: $i > $i ).
thf(func_def_65,type,
sK33: $i > $i ).
thf(func_def_66,type,
sK34: $i > $i ).
thf(func_def_67,type,
sK35: $i > $i ).
thf(func_def_68,type,
sK36: $i > $i > $i > $i ).
thf(func_def_69,type,
sK37: $i > $i > $i > $i ).
thf(func_def_70,type,
sK38: $i > $i > $i > $i > $i ).
thf(func_def_71,type,
sK39: $i > $i > $i > $i > $i ).
thf(func_def_72,type,
sK40: $i > $i > $i > $i > $i ).
thf(func_def_73,type,
sK41: $i > $i > $i > $i > $i ).
thf(func_def_74,type,
sK42: $i > $i ).
thf(func_def_75,type,
sK43: $i > $i ).
thf(func_def_76,type,
sK44: $i > $i > $i > $i > $i ).
thf(func_def_77,type,
sK45: $i > $i ).
thf(func_def_78,type,
sK46: $i > $i > $i > $i > $i ).
thf(func_def_79,type,
sK47: $i > $i > $i > $i ).
thf(func_def_80,type,
sK48: $i > $i > $i > $i ).
thf(func_def_81,type,
sK49: $i > $i > $i > $i ).
thf(func_def_82,type,
sK50: $i > $i ).
thf(func_def_83,type,
sK51: $i > $i ).
thf(func_def_84,type,
sK52: $i > $i ).
thf(func_def_85,type,
sK53: $i > $i ).
thf(func_def_86,type,
sK54: $i > $i > $i > $i ).
thf(func_def_87,type,
sK55: $i > $i ).
thf(func_def_88,type,
sK56: $i > $i > $i > $i > $i ).
thf(func_def_89,type,
sK57: $i > $i > $i > $i ).
thf(func_def_90,type,
sK58: $i > $i ).
thf(func_def_91,type,
sK59: $i > $i ).
thf(func_def_92,type,
sK60: $i > $i > $i > $i ).
thf(func_def_93,type,
sK61: $i > $i > $i > $i ).
thf(func_def_94,type,
sK62: $i > $i > $i > $i ).
thf(func_def_95,type,
sK63: $i > $i > $i > $i ).
thf(func_def_96,type,
sK64: $i > $i > $i > $i ).
thf(func_def_97,type,
sK65: $i > $i > $i > $i ).
thf(func_def_98,type,
sK66: $i > $i > $i > $i ).
thf(func_def_99,type,
sK67: $i > $i > $i > $i ).
thf(func_def_100,type,
sK68: $i > $i ).
thf(func_def_101,type,
sK69: $i > $i ).
thf(func_def_102,type,
sK70: $i > $i > $i > $i ).
thf(func_def_103,type,
sK71: $i > $i > $i > $i ).
thf(func_def_104,type,
sK72: $i > $i ).
thf(func_def_105,type,
sK73: $i > $i > $i > $i ).
thf(func_def_106,type,
sK74: $i > $i > $i > $i ).
thf(func_def_107,type,
sK75: $i > $i > $i > $i ).
thf(func_def_108,type,
sK76: $i > $i > $i > $i ).
thf(func_def_109,type,
sK77: $i > $i > $i > $i ).
thf(func_def_110,type,
sK78: $i > $i ).
thf(func_def_111,type,
sK79: $i > $i ).
thf(func_def_112,type,
sK80: $i > $i > $i > $i ).
thf(func_def_113,type,
sK81: $i > $i > $i > $i ).
thf(func_def_114,type,
sK82: $i > $i > $i > $i ).
thf(func_def_115,type,
sK83: $i > $i > $i > $i ).
thf(func_def_116,type,
sK84: $i > $i > $i > $i ).
thf(func_def_117,type,
sK85: $i > $i ).
thf(func_def_118,type,
sK86: $i > $i > $i > $i ).
thf(func_def_119,type,
sK87: $i > $i > $i > $i ).
thf(func_def_120,type,
sK88: $i > $i > $i > $i ).
thf(func_def_121,type,
sK89: $i > $i > $i > $i ).
thf(func_def_122,type,
sK90: $i > $i > $i > $i ).
thf(func_def_123,type,
sK91: $i > $i > $i > $i ).
thf(func_def_124,type,
sK92: $i > $i ).
thf(func_def_125,type,
sK93: $i > $i ).
thf(func_def_126,type,
sK94: $i > $i > $i > $i ).
thf(func_def_127,type,
sK95: $i > $i > $i > $i ).
thf(func_def_128,type,
sK96: $i > $i > $i > $i ).
thf(func_def_129,type,
sK97: $i > $i > $i > $i ).
thf(func_def_130,type,
sK98: $i > $i > $i > $i ).
thf(func_def_131,type,
sK99: $i > $i > $i > $i ).
thf(func_def_132,type,
sK100: $i > $i ).
thf(func_def_133,type,
sK101: $i > $i ).
thf(func_def_134,type,
sK102: $i > $i ).
thf(func_def_135,type,
sK103: $i > $i > $i > $i ).
thf(func_def_136,type,
sK104: $i > $i > $i > $i ).
thf(func_def_137,type,
sK105: $i > $i > $i > $i ).
thf(func_def_138,type,
sK106: $i > $i > $i > $i ).
thf(func_def_139,type,
sK107: $i > $i ).
thf(func_def_140,type,
sK108: $i > $i > $i > $i ).
thf(func_def_141,type,
sK109: $i > $i > $i > $i ).
thf(func_def_142,type,
sK110: $i > $i > $i > $i ).
thf(func_def_143,type,
sK111: $i > $i ).
thf(func_def_144,type,
sK112: $i > $i > $i > $i ).
thf(func_def_145,type,
sK113: $i > $i > $i > $i ).
thf(func_def_146,type,
sK114: $i > $i > $i > $i ).
thf(func_def_147,type,
sK115: $i > $i > $i > $i ).
thf(func_def_148,type,
sK116: $i > $i > $i > $i ).
thf(func_def_149,type,
sK117: $i > $i > $i > $i ).
thf(func_def_150,type,
sK118: $i > $i ).
thf(func_def_151,type,
sK119: $i > $i ).
thf(func_def_152,type,
sK120: $i > $i > $i > $i ).
thf(func_def_153,type,
sK121: $i > $i > $i > $i ).
thf(func_def_154,type,
sK122: $i > $i > $i > $i ).
thf(func_def_155,type,
sK123: $i > $i > $i > $i ).
thf(func_def_156,type,
sK124: $i > $i > $i > $i ).
thf(func_def_157,type,
sK125: $i > $i > $i > $i ).
thf(func_def_158,type,
sK126: $i > $i > $i > $i ).
thf(func_def_159,type,
sK127: $i > $i > $i > $i ).
thf(func_def_160,type,
sK128: $i > $i ).
thf(func_def_161,type,
sK129: $i > $i ).
thf(func_def_162,type,
sK130: $i > $i ).
thf(func_def_163,type,
sK131: $i > $i > $i > $i ).
thf(func_def_164,type,
sK132: $i > $i > $i > $i ).
thf(func_def_165,type,
sK133: $i > $i > $i > $i ).
thf(func_def_166,type,
sK134: $i > $i > $i > $i ).
thf(func_def_167,type,
sK135: $i > $i ).
thf(func_def_168,type,
sK136: $i > $i > $i > $i ).
thf(func_def_169,type,
sK137: $i > $i > $i > $i ).
thf(func_def_170,type,
sK138: $i > $i > $i > $i ).
thf(func_def_171,type,
sK139: $i > $i ).
thf(func_def_172,type,
sK140: $i > $i ).
thf(func_def_173,type,
sK141: $i > $i > $i > $i ).
thf(func_def_174,type,
sK142: $i > $i > $i > $i ).
thf(func_def_175,type,
sK143: $i > $i > $i > $i ).
thf(func_def_176,type,
sK144: $i > $i > $i > $i ).
thf(func_def_177,type,
sK145: $i > $i > $i > $i ).
thf(func_def_178,type,
sK146: $i > $i > $i > $i ).
thf(func_def_179,type,
sK147: $i > $i ).
thf(func_def_180,type,
sK148: $i > $i ).
thf(func_def_181,type,
sK149: $i > $i ).
thf(func_def_182,type,
sK150: $i > $i ).
thf(func_def_183,type,
sK151: $i > $i > $i > $i ).
thf(func_def_184,type,
sK152: $i > $i > $i > $i ).
thf(func_def_185,type,
sK153: $i > $i > $i > $i ).
thf(func_def_186,type,
sK154: $i > $i > $i > $i ).
thf(func_def_187,type,
sK155: $i > $i > $i > $i ).
thf(func_def_188,type,
sK156: $i > $i > $i > $i ).
thf(func_def_189,type,
sK157: $i > $i > $i > $i ).
thf(func_def_190,type,
sK158: $i > $i > $i > $i ).
thf(func_def_191,type,
sK159: $i > $i > $i > $i ).
thf(func_def_192,type,
sK160: $i > $i > $i > $i ).
thf(func_def_193,type,
sK161: $i > $i > $i > $i ).
thf(func_def_194,type,
sK162: $i > $i > $i > $i ).
thf(func_def_195,type,
sK163: $i > $i > $i > $i ).
thf(func_def_196,type,
sK164: $i > $i > $i > $i ).
thf(func_def_197,type,
sK165: $i > $i > $i > $i ).
thf(func_def_198,type,
sK166: $i > $i ).
thf(func_def_199,type,
sK167: $i > $i ).
thf(func_def_200,type,
sK168: $i > $i ).
thf(func_def_201,type,
sK169: $i > $i > $i > $i ).
thf(func_def_202,type,
sK170: $i > $i > $i > $i ).
thf(func_def_203,type,
sK171: $i > $i > $i > $i ).
thf(func_def_204,type,
sK172: $i > $i > $i > $i ).
thf(func_def_205,type,
sK173: $i > $i > $i > $i ).
thf(func_def_206,type,
sK174: $i > $i > $i > $i ).
thf(func_def_207,type,
sK175: $i > $i > $i > $i ).
thf(func_def_208,type,
sK176: $i > $i > $i > $i ).
thf(func_def_209,type,
sK177: $i > $i ).
thf(func_def_210,type,
sK178: $i > $i ).
thf(func_def_211,type,
sK179: $i > $i > $i > $i ).
thf(func_def_212,type,
sK180: $i > $i > $i > $i ).
thf(func_def_213,type,
sK181: $i > $i > $i > $i ).
thf(func_def_214,type,
sK182: $i > $i ).
thf(func_def_215,type,
sK183: $i > $i > $i > $i ).
thf(func_def_216,type,
sK184: $i > $i > $i > $i ).
thf(func_def_217,type,
sK185: $i > $i > $i > $i ).
thf(func_def_218,type,
sK186: $i > $i > $i > $i ).
thf(func_def_219,type,
sK187: $i > $i > $i > $i ).
thf(func_def_220,type,
sK188: $i > $i ).
thf(func_def_221,type,
sK189: $i > $i ).
thf(func_def_222,type,
sK190: $i > $i > $i > $i ).
thf(func_def_223,type,
sK191: $i > $i > $i > $i ).
thf(func_def_224,type,
sK192: $i > $i > $i > $i ).
thf(func_def_225,type,
sK193: $i > $i > $i > $i ).
thf(func_def_226,type,
sK194: $i > $i > $i > $i ).
thf(func_def_227,type,
sK195: $i > $i > $i > $i ).
thf(func_def_228,type,
sK196: $i > $i ).
thf(func_def_229,type,
sK197: $i > $i > $i > $i ).
thf(func_def_230,type,
sK198: $i > $i ).
thf(func_def_231,type,
sK199: $i > $i ).
thf(func_def_232,type,
sK200: $i > $i > $i > $i ).
thf(func_def_233,type,
sK201: $i > $i > $i > $i ).
thf(func_def_234,type,
sK202: $i > $i > $i > $i ).
thf(func_def_235,type,
sK203: $i > $i > $i > $i ).
thf(func_def_236,type,
sK204: $i > $i > $i > $i ).
thf(func_def_237,type,
sK205: $i > $i > $i > $i ).
thf(func_def_238,type,
sK206: $i > $i > $i > $i ).
thf(func_def_239,type,
sK207: $i > $i > $i > $i ).
thf(func_def_240,type,
sK208: $i > $i > $i > $i ).
thf(func_def_241,type,
sK209: $i > $i > $i > $i ).
thf(func_def_242,type,
sK210: $i > $i > $i > $i ).
thf(func_def_243,type,
sK211: $i > $i > $i > $i ).
thf(func_def_244,type,
sK212: $i > $i > $i > $i ).
thf(func_def_245,type,
sK213: $i > $i > $i > $i ).
thf(func_def_246,type,
sK214: $i > $i > $i > $i ).
thf(func_def_247,type,
sK215: $i > $i ).
thf(func_def_248,type,
sK216: $i > $i ).
thf(func_def_249,type,
sK217: $i > $i ).
thf(func_def_250,type,
sK218: $i > $i > $i > $i ).
thf(func_def_251,type,
sK219: $i > $i > $i > $i ).
thf(func_def_252,type,
sK220: $i > $i > $i > $i ).
thf(func_def_253,type,
sK221: $i > $i > $i > $i ).
thf(func_def_254,type,
sK222: $i > $i > $i > $i ).
thf(func_def_255,type,
sK223: $i > $i > $i > $i ).
thf(func_def_256,type,
sK224: $i > $i ).
thf(func_def_257,type,
sK225: $i > $i ).
thf(func_def_258,type,
sK226: $i > $i ).
thf(func_def_259,type,
sK227: $i > $i > $i > $i ).
thf(func_def_260,type,
sK228: $i > $i ).
thf(func_def_261,type,
sK229: $i > $i > $i > $i ).
thf(func_def_262,type,
sK230: $i > $i > $i > $i ).
thf(func_def_263,type,
sK231: $i > $i > $i > $i ).
thf(func_def_264,type,
sK232: $i > $i > $i > $i ).
thf(func_def_265,type,
sK233: $i > $i ).
thf(func_def_266,type,
sK234: $i > $i > $i > $i ).
thf(func_def_267,type,
sK235: $i > $i > $i > $i ).
thf(func_def_268,type,
sK236: $i > $i > $i > $i ).
thf(func_def_269,type,
sK237: $i > $i ).
thf(func_def_270,type,
sK238: $i > $i > $i > $i ).
thf(func_def_271,type,
sK239: $i > $i > $i > $i ).
thf(func_def_272,type,
sK240: $i > $i > $i > $i ).
thf(func_def_273,type,
sK241: $i > $i > $i > $i ).
thf(func_def_274,type,
sK242: $i > $i ).
thf(func_def_275,type,
sK243: $i > $i ).
thf(func_def_276,type,
sK244: $i > $i ).
thf(func_def_277,type,
sK245: $i > $i > $i > $i ).
thf(func_def_278,type,
sK246: $i > $i > $i > $i ).
thf(func_def_279,type,
sK247: $i > $i > $i > $i ).
thf(func_def_280,type,
sK248: $i > $i > $i > $i ).
thf(func_def_281,type,
sK249: $i > $i ).
thf(func_def_282,type,
sK250: $i > $i ).
thf(func_def_283,type,
sK251: $i > $i ).
thf(func_def_284,type,
sK252: $i > $i > $i > $i ).
thf(func_def_285,type,
sK253: $i > $i > $i ).
thf(func_def_286,type,
sK254: $i > $i > $i ).
thf(func_def_287,type,
sK255: $i > $i ).
thf(func_def_288,type,
sK256: $i > $i ).
thf(func_def_289,type,
sK257: $i > $i > $i > $i ).
thf(func_def_290,type,
sK258: $i > $i ).
thf(func_def_291,type,
sK259: $i > $i > $i > $i ).
thf(func_def_292,type,
sK260: $i > $i > $i > $i ).
thf(func_def_293,type,
sK261: $i > $i > $i ).
thf(func_def_294,type,
sK262: $i > $i > $i ).
thf(func_def_295,type,
sK263: $i > $i > $i ).
thf(func_def_296,type,
sK264: $i > $i > $i > $i ).
thf(func_def_297,type,
sK265: $i > $i > $i ).
thf(func_def_298,type,
sK266: $i > $i > $i > $i ).
thf(func_def_299,type,
sK267: $i > $i > $i > $i ).
thf(func_def_300,type,
sK268: $i > $i ).
thf(func_def_301,type,
sK269: $i > $i > $i > $i ).
thf(func_def_302,type,
sK270: $i > $i > $i > $i ).
thf(func_def_303,type,
sK271: $i > $i > $i ).
thf(func_def_304,type,
sK272: $i > $i > $i ).
thf(func_def_305,type,
sK273: $i > $i > $i ).
thf(func_def_306,type,
sK274: $i > $i > $i > $i ).
thf(func_def_307,type,
sK275: $i > $i > $i ).
thf(func_def_308,type,
sK276: $i > $i > $i > $i ).
thf(func_def_309,type,
sK277: $i > $i > $i > $i ).
thf(func_def_310,type,
sK278: $i > $i ).
thf(func_def_311,type,
sK279: $i > $i > $i > $i ).
thf(func_def_312,type,
sK280: $i > $i > $i > $i ).
thf(func_def_313,type,
sK281: $i > $i > $i ).
thf(func_def_314,type,
sK282: $i > $i > $i ).
thf(func_def_315,type,
sK283: $i > $i > $i ).
thf(func_def_316,type,
sK284: $i > $i > $i > $i ).
thf(func_def_317,type,
sK285: $i > $i > $i ).
thf(func_def_318,type,
sK286: $i > $i > $i > $i ).
thf(func_def_319,type,
sK287: $i > $i > $i > $i ).
thf(func_def_320,type,
sK288: $i > $i ).
thf(func_def_321,type,
sK289: $i > $i > $i > $i ).
thf(func_def_322,type,
sK290: $i > $i > $i > $i ).
thf(func_def_323,type,
sK291: $i > $i ).
thf(func_def_324,type,
sK292: $i > $i > $i > $i ).
thf(func_def_325,type,
sK293: $i > $i ).
thf(func_def_326,type,
sK294: $i > $i > $i > $i ).
thf(func_def_327,type,
sK295: $i > $i > $i > $i ).
thf(func_def_328,type,
sK296: $i > $i > $i > $i ).
thf(func_def_329,type,
sK297: $i > $i > $i > $i ).
thf(func_def_330,type,
sK298: $i > $i > $i > $i ).
thf(func_def_331,type,
sK299: $i > $i > $i > $i ).
thf(func_def_332,type,
sK300: $i > $i > $i > $i ).
thf(func_def_333,type,
sK301: $i > $i > $i > $i ).
thf(func_def_334,type,
sK302: $i > $i > $i > $i ).
thf(func_def_335,type,
sK303: $i > $i > $i > $i ).
thf(func_def_336,type,
sK304: $i > $i > $i > $i ).
thf(func_def_337,type,
sK305: $i > $i > $i > $i ).
thf(func_def_338,type,
sK306: $i > $i > $i > $i ).
thf(func_def_339,type,
sK307: $i > $i > $i > $i ).
thf(func_def_340,type,
sK308: $i > $i > $i > $i ).
thf(func_def_341,type,
sK309: $i > $i > $i > $i ).
thf(func_def_342,type,
sK310: $i > $i > $i > $i ).
thf(func_def_343,type,
sK311: $i > $i > $i > $i ).
thf(func_def_344,type,
sK312: $i > $i > $i > $i ).
thf(func_def_345,type,
sK313: $i > $i ).
thf(func_def_346,type,
sK314: $i > $i ).
thf(func_def_347,type,
sK315: $i > $i ).
thf(func_def_348,type,
sK316: $i > $i > $i > $i > $i ).
thf(func_def_349,type,
sK317: $i > $i > $i > $i > $i ).
thf(func_def_350,type,
sK318: $i > $i ).
thf(func_def_351,type,
sK319: $i > $i ).
thf(func_def_352,type,
sK320: $i > $i ).
thf(func_def_353,type,
sK321: $i > $i > $i > $i > $i ).
thf(func_def_354,type,
sK322: $i > $i > $i > $i > $i ).
thf(func_def_355,type,
sK323: $i > $i > $i > $i > $i ).
thf(func_def_356,type,
sK324: $i > $i > $i > $i > $i ).
thf(func_def_357,type,
sK325: $i > $i > $i > $i > $i ).
thf(func_def_358,type,
sK326: $i > $i > $i ).
thf(func_def_359,type,
sK327: $i > $i > $i ).
thf(func_def_360,type,
sK328: $i > $i > $i ).
thf(func_def_361,type,
sK329: $i > $i ).
thf(func_def_362,type,
sK330: $i > $i > $i > $i ).
thf(func_def_363,type,
sK331: $i > $i > $i > $i ).
thf(func_def_364,type,
sK332: $i > $i > $i > $i ).
thf(func_def_365,type,
sK333: $i > $i > $i > $i ).
thf(func_def_366,type,
sK334: $i > $i > $i > $i ).
thf(func_def_367,type,
sK335: $i > $i > $i > $i ).
thf(func_def_368,type,
sK336: $i > $i > $i > $i ).
thf(func_def_369,type,
sK337: $i > $i > $i > $i ).
thf(func_def_370,type,
sK338: $i > $i > $i > $i ).
thf(func_def_371,type,
sK339: $i > $i > $i > $i ).
thf(func_def_372,type,
sK340: $i > $i > $i > $i ).
thf(func_def_373,type,
sK341: $i > $i > $i > $i ).
thf(func_def_374,type,
sK342: $i > $i > $i > $i > $i ).
thf(func_def_375,type,
sK343: $i > $i > $i > $i > $i ).
thf(func_def_376,type,
sK344: $i > $i > $i > $i > $i ).
thf(func_def_377,type,
sK345: $i > $i > $i > $i > $i ).
thf(func_def_378,type,
sK346: $i > $i > $i > $i > $i ).
thf(func_def_379,type,
sK347: $i > $i > $i > $i ).
thf(func_def_380,type,
sK348: $i > $i > $i > $i ).
thf(func_def_381,type,
sK349: $i > $i > $i > $i ).
thf(func_def_382,type,
sK350: $i > $i > $i > $i > $i ).
thf(func_def_383,type,
sK351: $i > $i ).
thf(func_def_384,type,
sK352: $i > $i > $i > $i > $i ).
thf(func_def_385,type,
sK353: $i > $i > $i > $i > $i > $i ).
thf(func_def_386,type,
sK354: $i > $i > $i > $i > $i > $i ).
thf(func_def_387,type,
sK355: $i > $i > $i > $i ).
thf(func_def_388,type,
sK356: $i > $i > $i > $i ).
thf(func_def_389,type,
sK357: $i > $i > $i > $i ).
thf(func_def_390,type,
sK358: $i > $i > $i > $i > $i ).
thf(func_def_391,type,
sK359: $i > $i ).
thf(func_def_392,type,
sK360: $i > $i > $i > $i > $i ).
thf(func_def_393,type,
sK361: $i > $i > $i > $i ).
thf(func_def_394,type,
sK362: $i > $i > $i > $i ).
thf(func_def_395,type,
sK363: $i > $i > $i > $i ).
thf(func_def_396,type,
sK364: $i > $i > $i > $i > $i ).
thf(func_def_397,type,
sK365: $i > $i ).
thf(func_def_398,type,
sK366: $i > $i > $i > $i > $i ).
thf(func_def_399,type,
sK367: $i > $i > $i > $i > $i > $i ).
thf(func_def_400,type,
sK368: $i > $i > $i > $i > $i > $i ).
thf(func_def_401,type,
sK369: $i > $i > $i > $i ).
thf(func_def_402,type,
sK370: $i > $i > $i > $i ).
thf(func_def_403,type,
sK371: $i > $i > $i > $i ).
thf(func_def_404,type,
sK372: $i > $i ).
thf(func_def_405,type,
sK373: $i > $i ).
thf(func_def_406,type,
sK374: $i > $i > $i ).
thf(func_def_407,type,
sK375: $i > $i > $i ).
thf(func_def_408,type,
sK376: $i > $i ).
thf(func_def_409,type,
sK377: $i > $i > $i ).
thf(func_def_410,type,
sK378: $i > $i ).
thf(func_def_411,type,
sK379: $i > $i > $i ).
thf(func_def_412,type,
sK380: $i > $i > $i ).
thf(func_def_413,type,
sK381: $i > $i > $i ).
thf(func_def_414,type,
sK382: $i > $i ).
thf(func_def_415,type,
sK383: $i > $i > $i ).
thf(func_def_416,type,
sK384: $i > $i > $i ).
thf(func_def_417,type,
sK385: $i > $i > $i ).
thf(func_def_418,type,
sK386: $i > $i ).
thf(func_def_419,type,
sK387: $i > $i > $i ).
thf(func_def_420,type,
sK388: $i > $i > $i ).
thf(func_def_421,type,
sK389: $i > $i > $i ).
thf(func_def_422,type,
sK390: $i > $i ).
thf(func_def_423,type,
sK391: $i > $i > $i ).
thf(func_def_424,type,
sK392: $i > $i > $i ).
thf(func_def_425,type,
sK393: $i > $i > $i ).
thf(func_def_426,type,
sK394: $i > $i ).
thf(func_def_427,type,
sK395: $i > $i > $i ).
thf(func_def_428,type,
sK396: $i > $i > $i ).
thf(func_def_429,type,
sK397: $i > $i > $i ).
thf(func_def_430,type,
sK398: $i > $i > $i > $i ).
thf(func_def_431,type,
sK399: $i > $i > $i > $i ).
thf(func_def_432,type,
sK400: $i > $i ).
thf(func_def_433,type,
sK401: $i > $i ).
thf(func_def_434,type,
sK402: $i > $i > $i > $i ).
thf(func_def_435,type,
sK403: $i > $i ).
thf(func_def_436,type,
sK404: $i > $i > $i > $i ).
thf(func_def_437,type,
sK405: $i > $i > $i > $i ).
thf(func_def_438,type,
sK406: $i > $i > $i > $i ).
thf(func_def_439,type,
sK407: $i > $i > $i > $i ).
thf(func_def_440,type,
sK408: $i > $i > $i > $i ).
thf(func_def_441,type,
sK409: $i > $i > $i > $i ).
thf(func_def_442,type,
sK410: $i > $i ).
thf(func_def_443,type,
sK411: $i > $i > $i > $i ).
thf(func_def_444,type,
sK412: $i > $i > $i > $i ).
thf(func_def_445,type,
sK413: $i > $i > $i > $i ).
thf(func_def_446,type,
sK414: $i > $i > $i > $i ).
thf(func_def_447,type,
sK415: $i > $i > $i > $i ).
thf(func_def_448,type,
sK416: $i > $i > $i > $i ).
thf(func_def_449,type,
sK417: $i > $i > $i > $i ).
thf(func_def_450,type,
sK418: $i > $i > $i > $i ).
thf(func_def_451,type,
sK419: $i > $i > $i > $i ).
thf(func_def_452,type,
sK420: $i > $i > $i > $i ).
thf(func_def_453,type,
sK421: $i > $i > $i > $i ).
thf(func_def_454,type,
sK422: $i > $i > $i > $i ).
thf(func_def_455,type,
sK423: $i > $i ).
thf(func_def_456,type,
sK424: $i > $i > $i > $i ).
thf(func_def_457,type,
sK425: $i > $i > $i > $i ).
thf(func_def_458,type,
sK426: $i > $i > $i > $i ).
thf(func_def_459,type,
sK427: $i > $i > $i > $i ).
thf(func_def_460,type,
sK428: $i > $i > $i > $i ).
thf(func_def_461,type,
sK429: $i > $i > $i > $i ).
thf(func_def_462,type,
sK430: $i > $i > $i > $i ).
thf(func_def_463,type,
sK431: $i > $i > $i > $i ).
thf(func_def_464,type,
sK432: $i > $i > $i > $i ).
thf(func_def_465,type,
sK433: $i > $i > $i > $i ).
thf(func_def_466,type,
sK434: $i > $i > $i > $i ).
thf(func_def_467,type,
sK435: $i > $i > $i > $i ).
thf(func_def_468,type,
sK436: $i > $i > $i > $i ).
thf(func_def_469,type,
sK437: $i > $i > $i > $i ).
thf(func_def_470,type,
sK438: $i > $i > $i > $i ).
thf(func_def_471,type,
sK439: $i > $i > $i > $i ).
thf(func_def_472,type,
sK440: $i > $i > $i > $i ).
thf(func_def_473,type,
sK441: $i > $i > $i > $i ).
thf(func_def_474,type,
sK442: $i > $i > $i > $i ).
thf(func_def_475,type,
sK443: $i > $i ).
thf(func_def_476,type,
sK444: $i > $i > $i > $i > $i > $i ).
thf(func_def_477,type,
sK445: $i > $i > $i > $i > $i > $i ).
thf(func_def_478,type,
sK446: $i > $i > $i > $i > $i > $i ).
thf(func_def_479,type,
sK447: $i > $i ).
thf(func_def_480,type,
sK448: $i > $i > $i > $i > $i ).
thf(func_def_481,type,
sK449: $i > $i > $i > $i > $i ).
thf(func_def_482,type,
sK450: $i > $i > $i ).
thf(func_def_483,type,
sK451: $i > $i ).
thf(func_def_484,type,
sK452: $i > $i > $i ).
thf(func_def_485,type,
sK453: $i > $i ).
thf(func_def_486,type,
sK454: $i > $i > $i ).
thf(func_def_487,type,
sK455: $i > $i > $i ).
thf(func_def_488,type,
sK456: $i > $i > $i ).
thf(func_def_489,type,
sK457: $i > $i ).
thf(func_def_490,type,
sK458: $i > $i > $i ).
thf(func_def_491,type,
sK459: $i > $i > $i ).
thf(func_def_492,type,
sK460: $i > $i > $i ).
thf(func_def_493,type,
sK461: $i > $i ).
thf(func_def_494,type,
sK462: $i > $i > $i ).
thf(func_def_495,type,
sK463: $i > $i > $i ).
thf(func_def_496,type,
sK464: $i > $i > $i ).
thf(func_def_497,type,
sK465: $i > $i ).
thf(func_def_498,type,
sK466: $i > $i > $i ).
thf(func_def_499,type,
sK467: $i > $i > $i ).
thf(func_def_500,type,
sK468: $i > $i > $i ).
thf(func_def_501,type,
sK469: $i > $i ).
thf(func_def_502,type,
sK470: $i > $i > $i ).
thf(func_def_503,type,
sK471: $i > $i > $i ).
thf(func_def_504,type,
sK472: $i > $i > $i ).
thf(func_def_505,type,
sK473: $i > $i ).
thf(func_def_506,type,
sK474: $i > $i > $i > $i ).
thf(func_def_507,type,
sK475: $i > $i > $i > $i ).
thf(func_def_508,type,
sK476: $i > $i > $i > $i ).
thf(func_def_509,type,
sK477: $i > $i > $i ).
thf(func_def_510,type,
sK478: $i > $i > $i > $i ).
thf(func_def_511,type,
sK479: $i > $i > $i ).
thf(func_def_512,type,
sK480: $i > $i ).
thf(func_def_513,type,
sK481: $i > $i > $i ).
thf(func_def_514,type,
sK482: $i > $i > $i > $i ).
thf(func_def_515,type,
sK483: $i > $i > $i > $i ).
thf(func_def_516,type,
sK484: $i > $i > $i > $i ).
thf(func_def_517,type,
sK485: $i > $i > $i > $i ).
thf(func_def_518,type,
sK486: $i > $i > $i > $i ).
thf(func_def_519,type,
sK487: $i > $i > $i > $i ).
thf(func_def_520,type,
sK488: $i > $i > $i > $i ).
thf(func_def_521,type,
sK489: $i > $i > $i > $i ).
thf(func_def_522,type,
sK490: $i > $i ).
thf(func_def_523,type,
sK491: $i > $i ).
thf(func_def_524,type,
sK492: $i > $i > $i > $i ).
thf(func_def_525,type,
sK493: $i > $i > $i > $i ).
thf(func_def_526,type,
sK494: $i > $i ).
thf(func_def_527,type,
sK495: $i > $i ).
thf(func_def_528,type,
sK496: $i > $i > $i > $i ).
thf(func_def_529,type,
sK497: $i > $i ).
thf(func_def_530,type,
sK498: $i > $i > $i > $i ).
thf(func_def_531,type,
sK499: $i > $i > $i > $i ).
thf(func_def_532,type,
sK500: $i > $i > $i > $i ).
thf(func_def_533,type,
sK501: $i > $i > $i > $i ).
thf(func_def_534,type,
sK502: $i > $i > $i > $i ).
thf(func_def_535,type,
sK503: $i > $i > $i > $i ).
thf(func_def_536,type,
sK504: $i > $i ).
thf(func_def_537,type,
sK505: $i > $i > $i > $i ).
thf(func_def_538,type,
sK506: $i > $i > $i > $i ).
thf(func_def_539,type,
sK507: $i > $i > $i > $i ).
thf(func_def_540,type,
sK508: $i > $i > $i > $i ).
thf(func_def_541,type,
sK509: $i > $i > $i > $i ).
thf(func_def_542,type,
sK510: $i > $i > $i > $i ).
thf(func_def_543,type,
sK511: $i > $i > $i > $i ).
thf(func_def_544,type,
sK512: $i > $i > $i > $i ).
thf(func_def_545,type,
sK513: $i > $i > $i > $i ).
thf(func_def_546,type,
sK514: $i > $i > $i > $i ).
thf(func_def_547,type,
sK515: $i > $i > $i > $i ).
thf(func_def_548,type,
sK516: $i > $i > $i > $i ).
thf(func_def_549,type,
sK517: $i > $i ).
thf(func_def_550,type,
sK518: $i > $i > $i > $i ).
thf(func_def_551,type,
sK519: $i > $i > $i > $i ).
thf(func_def_552,type,
sK520: $i > $i > $i > $i ).
thf(func_def_553,type,
sK521: $i > $i > $i > $i ).
thf(func_def_554,type,
sK522: $i > $i > $i > $i ).
thf(func_def_555,type,
sK523: $i > $i > $i > $i ).
thf(func_def_556,type,
sK524: $i > $i > $i > $i ).
thf(func_def_557,type,
sK525: $i > $i > $i > $i ).
thf(func_def_558,type,
sK526: $i > $i > $i > $i ).
thf(func_def_559,type,
sK527: $i > $i > $i > $i ).
thf(func_def_560,type,
sK528: $i > $i > $i > $i ).
thf(func_def_561,type,
sK529: $i > $i > $i > $i ).
thf(func_def_562,type,
sK530: $i > $i > $i > $i ).
thf(func_def_563,type,
sK531: $i > $i > $i > $i ).
thf(func_def_564,type,
sK532: $i > $i > $i > $i ).
thf(func_def_565,type,
sK533: $i > $i > $i > $i ).
thf(func_def_566,type,
sK534: $i > $i > $i > $i ).
thf(func_def_567,type,
sK535: $i > $i > $i > $i ).
thf(func_def_568,type,
sK536: $i > $i > $i > $i ).
thf(func_def_569,type,
sK537: $i > $i > $i > $i ).
thf(func_def_570,type,
sK538: $i > $i ).
thf(func_def_571,type,
sK539: $i > $i > $i > $i > $i ).
thf(func_def_572,type,
sK540: $i > $i > $i > $i ).
thf(func_def_573,type,
sK541: $i > $i > $i > $i ).
thf(func_def_574,type,
sK542: $i > $i > $i > $i ).
thf(func_def_575,type,
sK543: $i > $i > $i > $i ).
thf(func_def_576,type,
sK544: $i > $i > $i > $i ).
thf(func_def_577,type,
sK545: $i > $i ).
thf(func_def_578,type,
sK546: $i > $i > $i ).
thf(func_def_579,type,
sK547: $i > $i > $i ).
thf(func_def_580,type,
sK548: $i > $i > $i ).
thf(func_def_581,type,
sK549: $i > $i ).
thf(func_def_582,type,
sK550: $i > $i > $i ).
thf(func_def_583,type,
sK551: $i > $i > $i ).
thf(func_def_584,type,
sK552: $i > $i > $i ).
thf(func_def_585,type,
sK553: $i > $i > $i > $i ).
thf(func_def_586,type,
sK554: $i > $i > $i > $i ).
thf(func_def_587,type,
sK555: $i > $i > $i > $i ).
thf(func_def_588,type,
sK556: $i > $i ).
thf(func_def_589,type,
sK557: $i > $i ).
thf(func_def_590,type,
sK558: $i > $i > $i ).
thf(func_def_591,type,
sK559: $i > $i > $i ).
thf(func_def_592,type,
sK560: $i > $i > $i ).
thf(func_def_593,type,
sK561: $i > $i > $i > $i ).
thf(func_def_594,type,
sK562: $i > $i > $i ).
thf(func_def_595,type,
sK563: $i > $i > $i ).
thf(func_def_596,type,
sK564: $i > $i > $i ).
thf(func_def_597,type,
sK565: $i > $i > $i > $i ).
thf(func_def_598,type,
sK566: $i > $i > $i > $i ).
thf(func_def_599,type,
sK567: $i > $i > $i > $i ).
thf(func_def_600,type,
sK568: $i > $i > $i > $i ).
thf(func_def_601,type,
sK569: $i > $i > $i ).
thf(func_def_602,type,
sK570: $i > $i > $i ).
thf(func_def_603,type,
sK571: $i > $i > $i ).
thf(func_def_604,type,
sK572: $i > $i > $i ).
thf(func_def_605,type,
sK573: $i > $i > $i ).
thf(func_def_606,type,
sK574: $i > $i > $i ).
thf(func_def_607,type,
sK575: $i > $i > $i > $i ).
thf(func_def_608,type,
sK576: $i > $i > $i ).
thf(func_def_609,type,
sK577: $i > $i > $i > $i ).
thf(func_def_610,type,
sK578: $i > $i > $i ).
thf(func_def_611,type,
sK579: $i > $i > $i > $i ).
thf(func_def_612,type,
sK580: $i > $i > $i > $i ).
thf(func_def_613,type,
sK581: $i > $i > $i > $i ).
thf(func_def_614,type,
sK582: $i > $i > $i > $i ).
thf(func_def_615,type,
sK583: $i > $i > $i > $i ).
thf(func_def_616,type,
sK584: $i > $i > $i > $i ).
thf(func_def_617,type,
sK585: $i > $i ).
thf(func_def_618,type,
sK586: $i > $i > $i > $i > $i ).
thf(func_def_619,type,
sK587: $i > $i > $i > $i > $i ).
thf(func_def_620,type,
sK588: $i > $i > $i > $i > $i ).
thf(func_def_621,type,
sK589: $i > $i ).
thf(func_def_622,type,
sK590: $i > $i > $i > $i > $i > $i ).
thf(func_def_623,type,
sK591: $i > $i > $i > $i > $i ).
thf(func_def_624,type,
sK592: $i > $i > $i > $i > $i ).
thf(func_def_625,type,
sK593: $i > $i > $i > $i > $i ).
thf(func_def_626,type,
sK594: $i > $i ).
thf(func_def_627,type,
sK595: $i > $i > $i > $i ).
thf(func_def_628,type,
sK596: $i > $i ).
thf(func_def_629,type,
sK597: $i > $i > $i > $i > $i ).
thf(func_def_630,type,
sK598: $i > $i > $i ).
thf(func_def_631,type,
sK599: $i > $i > $i ).
thf(func_def_632,type,
sK600: $i > $i > $i ).
thf(func_def_633,type,
sK601: $i > $i > $i > $i ).
thf(func_def_634,type,
sK602: $i > $i > $i ).
thf(func_def_635,type,
sK603: $i > $i > $i ).
thf(func_def_636,type,
sK604: $i > $i > $i ).
thf(func_def_637,type,
sK605: $i > $i > $i > $i ).
thf(func_def_638,type,
sK606: $i > $i > $i ).
thf(func_def_639,type,
sK607: $i > $i > $i ).
thf(func_def_640,type,
sK608: $i > $i > $i ).
thf(func_def_641,type,
sK609: $i > $i > $i > $i ).
thf(func_def_642,type,
sK610: $i > $i > $i > $i ).
thf(func_def_643,type,
sK611: $i > $i > $i > $i ).
thf(func_def_644,type,
sK612: $i > $i > $i ).
thf(func_def_645,type,
sK613: $i > $i > $i ).
thf(func_def_646,type,
sK614: $i > $i > $i > $i ).
thf(func_def_647,type,
sK615: $i > $i > $i > $i ).
thf(func_def_648,type,
sK616: $i > $i > $i > $i ).
thf(func_def_649,type,
sK617: $i > $i > $i > $i ).
thf(func_def_650,type,
sK618: $i > $i ).
thf(func_def_651,type,
sK619: $i > $i > $i ).
thf(func_def_652,type,
sK620: $i > $i ).
thf(func_def_653,type,
sK621: $i > $i ).
thf(func_def_654,type,
sK622: $i > $i ).
thf(func_def_655,type,
sK623: $i > $i > $i > $i ).
thf(func_def_656,type,
sK624: $i > $i > $i ).
thf(func_def_657,type,
sK625: $i > $i > $i ).
thf(func_def_658,type,
sK626: $i > $i > $i > $i ).
thf(func_def_659,type,
sK627: $i > $i > $i ).
thf(func_def_660,type,
sK628: $i > $i > $i ).
thf(func_def_661,type,
sK629: $i > $i > $i ).
thf(func_def_662,type,
sK630: $i > $i > $i ).
thf(func_def_663,type,
sK631: $i > $i > $i > $i ).
thf(func_def_664,type,
sK632: $i > $i > $i ).
thf(func_def_665,type,
sK633: $i > $i > $i ).
thf(func_def_666,type,
sK634: $i > $i > $i ).
thf(func_def_667,type,
sK635: $i > $i > $i ).
thf(func_def_668,type,
sK636: $i > $i > $i ).
thf(func_def_669,type,
sK637: $i > $i > $i ).
thf(func_def_670,type,
sK638: $i > $i > $i ).
thf(func_def_671,type,
sK639: $i > $i > $i > $i ).
thf(func_def_672,type,
sK640: $i > $i > $i > $i ).
thf(func_def_673,type,
sK641: $i > $i > $i ).
thf(func_def_674,type,
sK642: $i > $i > $i ).
thf(func_def_675,type,
sK643: $i > $i > $i ).
thf(func_def_676,type,
sK644: $i > $i > $i ).
thf(func_def_677,type,
sK645: $i > $i > $i ).
thf(func_def_678,type,
sK646: $i > $i > $i ).
thf(func_def_679,type,
sK647: $i > $i > $i ).
thf(func_def_680,type,
sK648: $i > $i > $i ).
thf(func_def_681,type,
sK649: $i > $i > $i ).
thf(func_def_682,type,
sK650: $i > $i > $i > $i ).
thf(func_def_683,type,
sK651: $i > $i > $i > $i ).
thf(func_def_684,type,
sK652: $i > $i > $i ).
thf(func_def_685,type,
sK653: $i > $i > $i > $i ).
thf(func_def_686,type,
sK654: $i > $i > $i > $i ).
thf(func_def_687,type,
sK655: $i > $i > $i > $i ).
thf(func_def_688,type,
sK656: $i > $i > $i > $i ).
thf(func_def_689,type,
sK657: ( $i > $o ) > $i > $i > $i ).
thf(func_def_690,type,
sK658: ( $i > $o ) > $i > $i > $i ).
thf(func_def_691,type,
sK659: ( $i > $o ) > $i > $i > $i ).
thf(func_def_692,type,
sK660: $i > ( $i > $o ) > $i > $i ).
thf(func_def_693,type,
sK661: $i > ( $i > $o ) > $i > $i ).
thf(func_def_694,type,
sK662: $i > ( $i > $o ) > $i > $i ).
thf(func_def_695,type,
sK663: $i > $i > $i ).
thf(func_def_696,type,
sK664: $i > $i > $i ).
thf(func_def_697,type,
sK665: $i > ( $i > $o ) > $i > $i ).
thf(func_def_698,type,
sK666: $i > $i > $i > $i ).
thf(func_def_699,type,
sK667: $i > ( $i > $o ) > $i > $i ).
thf(func_def_700,type,
sK668: $i > $i > $i > $i ).
thf(func_def_701,type,
sK669: $i > $i > $i > $i > $i ).
thf(func_def_702,type,
sK670: $i > $i > $i > $i > $i ).
thf(func_def_703,type,
sK671: $i > $i > $i > $i > $i ).
thf(func_def_704,type,
sK672: $i > $i > $i > $i > $i ).
thf(func_def_705,type,
sK673: $i > $i > $i > $i ).
thf(func_def_706,type,
sK674: $i > $i > ( $i > $o ) > $i ).
thf(func_def_707,type,
sK675: $i > $i > $i ).
thf(func_def_708,type,
sK676: $i > $i > $i ).
thf(func_def_709,type,
sK677: $i > $i > $i ).
thf(func_def_710,type,
sK678: $i > $i > $i ).
thf(func_def_711,type,
sK679: $i > $i > $i ).
thf(func_def_712,type,
sK680: $i > $i > $i ).
thf(func_def_713,type,
sK681: $i > $i > $i ).
thf(func_def_714,type,
sK682: $i > $i > $i ).
thf(func_def_715,type,
sK683: $i > $i > $i ).
thf(func_def_716,type,
sK684: $i > $i > $i ).
thf(func_def_717,type,
sK685: $i > $i > $i > $i ).
thf(func_def_718,type,
sK686: $i > $i > $i > $i ).
thf(func_def_719,type,
sK687: $i > $i > $i > $i ).
thf(func_def_720,type,
sK688: $i > $i > $i ).
thf(func_def_721,type,
sK689: $i > $i > $i ).
thf(func_def_722,type,
sK690: $i > $i > $i > $i ).
thf(func_def_723,type,
sK691: $i > $i > $i > $i ).
thf(func_def_724,type,
sK692: $i > $i > $i ).
thf(func_def_725,type,
sK693: $i > $i ).
thf(func_def_726,type,
sK694: $i > $i ).
thf(func_def_727,type,
sK695: $i > $i ).
thf(func_def_728,type,
sK696: $i > $i ).
thf(func_def_729,type,
sK697: $i > $i ).
thf(func_def_730,type,
sK698: $i > $i ).
thf(func_def_731,type,
sK699: $i > $i > $i > $i ).
thf(func_def_732,type,
sK700: $i > $i > $i > $i ).
thf(func_def_733,type,
sK701: $i > $i > $i > $i ).
thf(func_def_734,type,
sK702: $i > $i ).
thf(func_def_735,type,
sK703: $i > $i > $i > $i ).
thf(func_def_736,type,
sK704: $i > $i > $i > $i ).
thf(func_def_737,type,
sK705: $i > $i > $i > $i ).
thf(func_def_738,type,
sK706: $i > $i > $i > $i ).
thf(func_def_739,type,
sK707: $i > $i ).
thf(func_def_740,type,
sK708: $i > $i ).
thf(func_def_741,type,
sK709: $i > $i > $i > $i > $i ).
thf(func_def_742,type,
sK710: $i > $i > $i > $i > $i ).
thf(func_def_743,type,
sK711: $i > $i > $i > $i > $i ).
thf(func_def_744,type,
sK712: $i > $i > $i > $i > $i ).
thf(func_def_745,type,
sK713: $i > $i > $i > $i > $i ).
thf(func_def_746,type,
sK714: $i > $i > $i > $i > $i ).
thf(func_def_747,type,
sK715: $i > $i > $i > $i > $i ).
thf(func_def_748,type,
sK716: $i > $i > $i ).
thf(func_def_749,type,
sK717: $i > $i > $i > $i ).
thf(func_def_750,type,
sK718: $i > $i > $i > $i ).
thf(func_def_751,type,
sK719: $i > $i > $i > $i > $i ).
thf(func_def_752,type,
sK720: $i > $i > $i > $i ).
thf(func_def_753,type,
sK721: $i > $i > $i > $i ).
thf(func_def_754,type,
sK722: $i > $i > $i > $i > $i ).
thf(func_def_755,type,
sK723: $i > $i ).
thf(func_def_756,type,
sK724: $i > $i ).
thf(func_def_757,type,
sK725: $i > $i ).
thf(func_def_758,type,
sK726: $i > $i > $i ).
thf(func_def_759,type,
sK727: $i > $i ).
thf(func_def_760,type,
sK728: $i > $i > $i ).
thf(func_def_761,type,
sK729: $i > $i > $i ).
thf(func_def_762,type,
sK730: $i > $i > $i ).
thf(func_def_763,type,
sK731: $i > $i ).
thf(func_def_764,type,
sK732: $i > $i > $i ).
thf(func_def_765,type,
sK733: $i > $i > $i ).
thf(func_def_766,type,
sK734: $i > $i ).
thf(func_def_767,type,
sK735: $i > $i ).
thf(func_def_768,type,
sK736: $i > $i ).
thf(func_def_769,type,
sK737: $i > $i ).
thf(func_def_770,type,
sK738: $i > $i ).
thf(func_def_771,type,
sK739: $i > $i > $i ).
thf(func_def_772,type,
sK740: $i > $i > $i ).
thf(func_def_773,type,
sK741: $i > $i > $i ).
thf(func_def_774,type,
sK742: $i > $i ).
thf(func_def_775,type,
sK743: $i > $i > $i ).
thf(func_def_776,type,
sK744: $i > $i > $i ).
thf(func_def_777,type,
sK745: $i > $i > $i > $i ).
thf(func_def_778,type,
sK746: $i > $i > $i > $i ).
thf(func_def_779,type,
sK747: $i > $i > $i > $i ).
thf(func_def_780,type,
sK748: $i > $i > $i > $i ).
thf(func_def_781,type,
sK749: $i > $i > $i ).
thf(func_def_782,type,
sK750: $i > $i ).
thf(func_def_783,type,
sK751: $i > $i > $i ).
thf(func_def_784,type,
sK752: $i > $i > $i ).
thf(func_def_785,type,
sK753: $i > $i ).
thf(func_def_786,type,
sK754: $i > $i ).
thf(func_def_787,type,
sK755: $i > $i > $i ).
thf(func_def_788,type,
sK756: $i > $i ).
thf(func_def_789,type,
sK757: $i > $i > $i ).
thf(func_def_790,type,
sK758: $i > $i > $i ).
thf(func_def_791,type,
sK759: $i > $i ).
thf(func_def_792,type,
sK760: $i > $i ).
thf(func_def_793,type,
sK761: $i > $i ).
thf(func_def_794,type,
sK762: $i > $i ).
thf(func_def_795,type,
sK763: $i > $i ).
thf(func_def_796,type,
sK764: $i > $i > $i ).
thf(func_def_797,type,
sK765: $i > $i > $i > $i ).
thf(func_def_798,type,
sK766: $i > $i > $i > $i ).
thf(func_def_799,type,
sK767: $i > $i > $i > $i ).
thf(func_def_800,type,
sK768: $i > $i > $i > $i ).
thf(func_def_801,type,
sK769: $i > $i > $i ).
thf(func_def_802,type,
sK770: $i > $i > $i ).
thf(func_def_803,type,
sK771: $i > $i > $i ).
thf(func_def_804,type,
sK772: $i > $i ).
thf(func_def_805,type,
sK773: $i > $i ).
thf(func_def_806,type,
sK774: $i > $i ).
thf(func_def_807,type,
sK775: $i > $i ).
thf(func_def_808,type,
sK776: $i > $i ).
thf(func_def_809,type,
sK777: $i > $i ).
thf(func_def_810,type,
sK778: $i > $i ).
thf(func_def_811,type,
sK779: $i > $i ).
thf(func_def_812,type,
sK780: $i > $i ).
thf(func_def_813,type,
sK781: $i > $i ).
thf(func_def_814,type,
sK782: $i > $i > $i > $i ).
thf(func_def_815,type,
sK783: $i > $i > $i > $i ).
thf(func_def_816,type,
sK784: $i > $i > $i > $i > $i ).
thf(func_def_817,type,
sK785: $i > $i > $i > $i ).
thf(func_def_818,type,
sK786: $i > $i > $i > $i > $i ).
thf(func_def_819,type,
sK787: $i > $i > $i ).
thf(func_def_820,type,
sK788: $i > $i ).
thf(func_def_821,type,
sK789: $i > $i > $i ).
thf(func_def_822,type,
sK790: $i > $i > $i ).
thf(func_def_823,type,
sK791: $i > $i > $i ).
thf(func_def_824,type,
sK792: $i > $i > $i ).
thf(func_def_825,type,
sK793: $i > $i > $i ).
thf(func_def_826,type,
sK794: $i > $i ).
thf(func_def_827,type,
sK795: $i > $i > $i ).
thf(func_def_828,type,
sK796: $i > $i > $i > $i ).
thf(func_def_829,type,
sK797: $i > $i ).
thf(func_def_830,type,
sK798: $i > $i ).
thf(func_def_831,type,
sK799: $i > $i > $i ).
thf(func_def_832,type,
sK800: $i > $i > $i > $i ).
thf(func_def_833,type,
sK801: $i > $i > $i ).
thf(func_def_834,type,
sK802: $i > $i ).
thf(func_def_835,type,
sK803: $i > $i > $i ).
thf(func_def_836,type,
sK804: $i > $i > $i > $i ).
thf(func_def_837,type,
sK805: $i > $i > $i > $i ).
thf(func_def_838,type,
sK806: $i > $i > $i ).
thf(func_def_839,type,
sK807: $i > $i > $i > $i ).
thf(func_def_840,type,
sK808: $i > $i ).
thf(func_def_841,type,
sK809: $i > $i ).
thf(func_def_842,type,
sK810: $i > $i ).
thf(func_def_843,type,
sK811: $i > $i ).
thf(func_def_844,type,
sK812: $i > $i > $i ).
thf(func_def_845,type,
sK813: $i > $i > $i ).
thf(func_def_846,type,
sK814: $i > $i ).
thf(func_def_847,type,
sK815: $i > $i > $i ).
thf(func_def_848,type,
sK816: $i > $i > $i ).
thf(func_def_849,type,
sK817: $i > $i ).
thf(func_def_850,type,
sK818: $i > $i ).
thf(func_def_851,type,
sK819: $i > $i ).
thf(func_def_852,type,
sK820: $i > $i ).
thf(func_def_853,type,
sK821: $i > $i > $i ).
thf(func_def_854,type,
sK822: $i > $i > $i ).
thf(func_def_855,type,
sK823: $i > $i > $i ).
thf(func_def_856,type,
sK824: $i > $i ).
thf(func_def_857,type,
sK825: $i > $i ).
thf(func_def_858,type,
sK826: $i > $i ).
thf(func_def_859,type,
sK827: $i > $i > $i ).
thf(func_def_860,type,
sK828: $i > $i ).
thf(func_def_861,type,
sK829: $i > $i > $i ).
thf(func_def_862,type,
sK830: $i > $i > $i ).
thf(func_def_863,type,
sK831: $i > $i > $i ).
thf(func_def_864,type,
sK832: $i > $i > $i ).
thf(func_def_865,type,
sK833: $i > $i ).
thf(func_def_866,type,
sK834: $i > $i ).
thf(func_def_867,type,
sK835: $i > $i > $i > $i ).
thf(func_def_868,type,
sK836: $i > $i > $i ).
thf(func_def_869,type,
sK837: $i > $i > $i ).
thf(func_def_870,type,
sK838: $i > $i > $i ).
thf(func_def_871,type,
sK839: $i > $i > $i > $i ).
thf(func_def_872,type,
sK840: $i > $i > $i > $i ).
thf(func_def_873,type,
sK841: $i > $i > $i ).
thf(func_def_874,type,
sK842: $i > $i > $i ).
thf(func_def_875,type,
sK843: $i > $i ).
thf(func_def_876,type,
sK844: $i > $i ).
thf(func_def_877,type,
sK845: $i > $i > $i ).
thf(func_def_878,type,
sK846: $i > $i > $i > $i ).
thf(func_def_879,type,
sK847: $i > $i > $i ).
thf(func_def_880,type,
sK848: $i > $i > $i ).
thf(func_def_881,type,
sK849: $i > $i > $i > $i ).
thf(func_def_882,type,
sK850: $i > $i > $i ).
thf(func_def_883,type,
sK851: $i > $i > $i > $i ).
thf(func_def_884,type,
sK852: $i > $i > $i > $i ).
thf(func_def_885,type,
sK853: $i > $i > $i ).
thf(func_def_886,type,
sK854: $i > $i > $i ).
thf(func_def_887,type,
sK855: $i > $i > $i ).
thf(func_def_888,type,
sK856: $i > $i ).
thf(func_def_889,type,
sK857: $i > $i > $i > $i ).
thf(func_def_890,type,
sK858: $i > $i > $i > $i ).
thf(func_def_891,type,
sK859: $i > $i > $i > $i ).
thf(func_def_892,type,
sK860: $i > $i ).
thf(func_def_893,type,
sK861: $i > $i ).
thf(func_def_894,type,
sK862: $i > $i > $i > $i ).
thf(func_def_895,type,
sK863: $i > $i > $i > $i ).
thf(func_def_896,type,
sK864: $i > $i > $i ).
thf(func_def_897,type,
sK865: $i > $i > $i > $i ).
thf(func_def_898,type,
sK866: $i > $i > $i ).
thf(func_def_899,type,
sK867: $i > $i > $i > $i ).
thf(func_def_900,type,
sK868: $i > $i ).
thf(func_def_901,type,
sK869: $i > $i > $i ).
thf(func_def_902,type,
sK870: $i > $i > $i ).
thf(func_def_903,type,
sK871: $i > $i > $i ).
thf(func_def_904,type,
sK872: $i > $i > $i > $i ).
thf(func_def_905,type,
sK873: $i > $i > $i > $i ).
thf(func_def_906,type,
sK874: $i > $i > $i > $i ).
thf(func_def_907,type,
sK875: $i > $i > $i > $i ).
thf(func_def_908,type,
sK876: $i > $i > $i ).
thf(func_def_909,type,
sK877: $i > $i > $i ).
thf(func_def_910,type,
sK878: $i > $i > $i > $i ).
thf(func_def_911,type,
sK879: $i > $i > $i ).
thf(func_def_912,type,
sK880: $i > $i > $i > $i ).
thf(func_def_913,type,
sK881: $i > $i > $i > $i ).
thf(func_def_914,type,
sK882: $i > $i > $i > $i ).
thf(func_def_915,type,
sK883: $i > $i > $i > $i ).
thf(func_def_916,type,
sK884: $i > $i ).
thf(func_def_917,type,
sK885: $i > $i ).
thf(func_def_918,type,
sK886: $i > $i ).
thf(func_def_919,type,
sK887: $i > $i ).
thf(func_def_920,type,
sK888: $i > $i ).
thf(f1,axiom,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(f2,axiom,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(f3,axiom,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(f4,axiom,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
& ( breln @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',func) ).
thf(f5,axiom,
( funcSet
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X1 ) )
@ ^ [X2: $i] : ( func @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcSet) ).
thf(f6,axiom,
( ap
= ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] :
( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap) ).
thf(f7,axiom,
( app
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app) ).
thf(f8,axiom,
( infuncsetfunc
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(f9,conjecture,
( app
=> ( infuncsetfunc
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2p) ).
thf(f10,negated_conjecture,
~ ( app
=> ( infuncsetfunc
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f11,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f12,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f14,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f16,plain,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
& ( breln @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f17,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( funcSet
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X1 ) )
@ ^ [X2: $i] : ( func @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f19,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] : ( func @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ap
= ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] :
( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f21,plain,
( ap
= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( app
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f23,plain,
( app
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( ap @ Y2 @ Y1 @ Y0 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f24,plain,
( infuncsetfunc
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f25,plain,
( infuncsetfunc
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( func @ Y2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
~ ( app
=> ( infuncsetfunc
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ) ),
inference(rectify,[],[f10]) ).
thf(f27,plain,
~ ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 )
= $true ) ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f28,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true ) )
& ( infuncsetfunc = $true )
& ( app = $true ) ),
inference(ennf_transformation,[],[f27]) ).
thf(f29,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true ) )
& ( infuncsetfunc = $true )
& ( app = $true ) ),
inference(flattening,[],[f28]) ).
thf(f30,plain,
( ( $true
!= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( funcSet @ sK0 @ sK1 ) ) )
& ( infuncsetfunc = $true )
& ( app = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f29]) ).
thf(f31,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f32,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f33,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f34,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f35,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] : ( func @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f36,plain,
( ap
= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f37,plain,
( app
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( ap @ Y2 @ Y1 @ Y0 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f38,plain,
( infuncsetfunc
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( func @ Y2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f39,plain,
app = $true,
inference(cnf_transformation,[],[f30]) ).
thf(f40,plain,
infuncsetfunc = $true,
inference(cnf_transformation,[],[f30]) ).
thf(f41,plain,
( $true
= ( in @ sK2 @ ( funcSet @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f42,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f43,plain,
( $true
!= ( in @ ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) @ sK1 ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f46,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( setadjoin @ Y3 @ emptyset )
= Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f32,f31]) ).
thf(f47,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( in @ Y7 @ Y6 )
& ( ( setadjoin @ Y7 @ emptyset )
= Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f34,f33,f46]) ).
thf(f48,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( in @ Y10 @ Y9 )
& ( ( setadjoin @ Y10 @ emptyset )
= Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y0
@ Y1
@ Y2 ) ) ) ),
inference(definition_unfolding,[],[f35,f47]) ).
thf(f49,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( in @ Y10 @ Y9 )
& ( ( setadjoin @ Y10 @ emptyset )
= Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y2
@ Y1
@ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in
@ ( ^ [Y4: $i,Y5: $i,Y6: $i,Y7: $i] :
( setunion
@ ( dsetconstr @ Y5
@ ^ [Y8: $i] : ( in @ ( kpair @ Y7 @ Y8 ) @ Y6 ) ) )
@ Y2
@ Y1
@ Y0
@ Y3 )
@ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f37,f39,f47,f36]) ).
thf(f50,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y3 @ Y4 ) )
@ ^ [Y5: $i] :
( ^ [Y6: $i,Y7: $i,Y8: $i] :
( ( ^ [Y9: $i,Y10: $i,Y11: $i] : ( subset @ Y11 @ ( cartprod @ Y9 @ Y10 ) )
@ Y6
@ Y7
@ Y8 )
& ( !! @ $i
@ ^ [Y9: $i] :
( ( in @ Y9 @ Y6 )
=> ( ^ [Y10: $i,Y11: $i > $o] :
( ^ [Y12: $i] :
( ?? @ $i
@ ^ [Y13: $i] :
( ( in @ Y13 @ Y12 )
& ( ( setadjoin @ Y13 @ emptyset )
= Y12 ) ) )
@ ( dsetconstr @ Y10
@ ^ [Y12: $i] : ( Y11 @ Y12 ) ) )
@ Y7
@ ^ [Y10: $i] : ( in @ ( kpair @ Y9 @ Y10 ) @ Y8 ) ) ) ) )
@ Y3
@ Y4
@ Y5 ) )
@ Y2
@ Y1 ) )
=> ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( in @ Y10 @ Y9 )
& ( ( setadjoin @ Y10 @ emptyset )
= Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y2
@ Y1
@ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f38,f40,f48,f47]) ).
thf(f51,plain,
( $true
!= ( in
@ ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) )
@ sK0
@ sK1
@ sK2
@ sK3 )
@ sK1 ) ),
inference(definition_unfolding,[],[f43,f36]) ).
thf(f52,plain,
( $true
= ( in @ sK2
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( in @ Y10 @ Y9 )
& ( ( setadjoin @ Y10 @ emptyset )
= Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y0
@ Y1
@ Y2 ) )
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[],[f41,f48]) ).
thf(f53,plain,
( $true
= ( in @ sK2
@ ( dsetconstr @ ( powerset @ ( cartprod @ sK0 @ sK1 ) )
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ sK0 @ sK1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ sK1
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ sK1
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK2 ) ) )
@ sK1 ) ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f55,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y3 @ Y4 ) )
@ ^ [Y5: $i] :
( ^ [Y6: $i,Y7: $i,Y8: $i] :
( ( ^ [Y9: $i,Y10: $i,Y11: $i] : ( subset @ Y11 @ ( cartprod @ Y9 @ Y10 ) )
@ Y6
@ Y7
@ Y8 )
& ( !! @ $i
@ ^ [Y9: $i] :
( ( in @ Y9 @ Y6 )
=> ( ^ [Y10: $i,Y11: $i > $o] :
( ^ [Y12: $i] :
( ?? @ $i
@ ^ [Y13: $i] :
( ( in @ Y13 @ Y12 )
& ( ( setadjoin @ Y13 @ emptyset )
= Y12 ) ) )
@ ( dsetconstr @ Y10
@ ^ [Y12: $i] : ( Y11 @ Y12 ) ) )
@ Y7
@ ^ [Y10: $i] : ( in @ ( kpair @ Y9 @ Y10 ) @ Y8 ) ) ) ) )
@ Y3
@ Y4
@ Y5 ) )
@ Y2
@ Y1 ) )
=> ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( in @ Y10 @ Y9 )
& ( ( setadjoin @ Y10 @ emptyset )
= Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y2
@ Y1
@ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f50]) ).
thf(f56,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ Y1 @ Y0 ) )
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( subset @ X1 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ Y1 @ Y0 ) )
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( subset @ X1 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ X2 ) )
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ Y0 @ X2 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ X2
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( subset @ X1 @ ( cartprod @ Y0 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ X2 ) )
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ Y0 @ X2 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ X2
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( subset @ X1 @ ( cartprod @ Y0 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ X3 @ X2 ) )
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( subset @ X1 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ X3 @ X2 ) )
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ( subset @ X1 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ X3 @ X2 ) )
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ X3 @ X2 ) )
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f61]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ X3 @ X2 ) )
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f62]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ X3 @ X2 ) )
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ X3 @ X2 ) )
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ X3 @ X2 ) )
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X1 ) ) ) )
@ ( sK4 @ X4 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ X3 @ X2 ) )
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true
= ( ( in @ ( sK4 @ X4 @ X1 @ X2 )
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
& ( ( setadjoin @ ( sK4 @ X4 @ X1 @ X2 ) @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ X3 @ X2 ) )
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true
= ( ( setadjoin @ ( sK4 @ X4 @ X1 @ X2 ) @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ X3 @ X2 ) )
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true
= ( in @ ( sK4 @ X4 @ X1 @ X2 )
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f68]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ X3 @ X2 ) )
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) )
= ( setadjoin @ ( sK4 @ X4 @ X1 @ X2 ) @ emptyset ) ) ),
inference(equality_proxy_clausification,[],[f69]) ).
thf(f72,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( in @ Y10 @ Y9 )
& ( ( setadjoin @ Y10 @ emptyset )
= Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y2
@ Y1
@ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in
@ ( ^ [Y4: $i,Y5: $i,Y6: $i,Y7: $i] :
( setunion
@ ( dsetconstr @ Y5
@ ^ [Y8: $i] : ( in @ ( kpair @ Y7 @ Y8 ) @ Y6 ) ) )
@ Y2
@ Y1
@ Y0
@ Y3 )
@ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f49]) ).
thf(f73,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ X1 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y2 @ Y3 ) @ X1 ) ) )
@ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ X1 @ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) )
& ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ X1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y2 @ Y3 ) @ X1 ) ) )
@ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( subset @ X1 @ ( cartprod @ Y0 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y1 @ Y2 ) @ X1 ) ) )
@ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( subset @ X1 @ ( cartprod @ Y0 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y1 @ Y2 ) @ X1 ) ) )
@ X2 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( subset @ X1 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) )
@ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( subset @ X1 @ ( cartprod @ X3 @ X2 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) )
@ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) )
@ X2 ) ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) )
@ ( sK5 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) )
@ X2 ) ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X1 ) ) ) ) ) )
@ ( sK5 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ X1 ) ) )
@ X2 ) )
@ X4 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X3 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) ) ) ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) ) ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) )
| ( $true
= ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) )
@ X5 ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f83]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X1 ) ) ) )
@ X5 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) )
& ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ( setadjoin @ X5 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) )
| ( $false
= ( in @ X5
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) )
!= ( setadjoin @ X5 @ emptyset ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( subset @ X1 @ ( cartprod @ X3 @ X2 ) ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X1 ) ) )
@ X2 ) )
| ( $false
= ( in @ X5
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f89]) ).
thf(f128,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( in @ ( sK5 @ X0 @ sK2 @ sK1 ) @ X0 ) )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f54,f85]) ).
thf(f130,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK5 @ X0 @ sK2 @ sK1 ) @ X0 ) )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f128]) ).
thf(f276,plain,
( ( $true = $false )
| ( $true
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f53,f63]) ).
thf(f277,plain,
( $true
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f276]) ).
thf(f314,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $true
= ( in @ ( sK4 @ X0 @ sK2 @ sK1 )
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK2 ) ) ) ) ),
inference(constrained_superposition,[],[f53,f70]) ).
thf(f315,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK4 @ X0 @ sK2 @ sK1 )
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK2 ) ) ) )
| ( $false
= ( in @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f314]) ).
thf(f335,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK2 ) )
= ( setadjoin @ ( sK4 @ X0 @ sK2 @ sK1 ) @ emptyset ) ) ),
inference(constrained_superposition,[],[f53,f71]) ).
thf(f347,plain,
! [X0: $i] :
( ( ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK2 ) )
= ( setadjoin @ ( sK4 @ X0 @ sK2 @ sK1 ) @ emptyset ) )
| ( $false
= ( in @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f335]) ).
thf(f630,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( setadjoin @ X4 @ emptyset )
!= ( setadjoin @ ( sK4 @ ( sK5 @ X0 @ X1 @ X2 ) @ sK2 @ sK1 ) @ emptyset ) )
| ( $false
= ( in @ X5 @ X3 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X3 @ sK1 ) ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X5 @ Y0 ) @ sK2 ) ) )
@ sK1 ) )
| ( $false
= ( in @ X4 @ ( setadjoin @ ( sK4 @ ( sK5 @ X0 @ X1 @ X2 ) @ sK2 @ sK1 ) @ emptyset ) ) )
| ( $false
= ( in @ ( sK5 @ X0 @ X1 @ X2 ) @ sK0 ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : sK2 ) )
| ( ( ^ [Y0: $i] : X2 )
!= ( ^ [Y0: $i] : sK1 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X3 ) ) ),
inference(constrained_superposition,[],[f90,f347]) ).
thf(f1745,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X1 @ sK2 @ sK1 ) @ ( setadjoin @ ( sK4 @ X0 @ sK2 @ sK1 ) @ emptyset ) ) )
| ( $false
= ( in @ X1 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X0 ) ) ),
inference(constrained_superposition,[],[f315,f347]) ).
thf(f1965,definition,
( spl6_42
<=> ( $true
= ( in @ ( sK5 @ sK0 @ sK2 @ sK1 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_42])],[avatar_definition]) ).
thf(f1966,plain,
( ( $true
!= ( in @ ( sK5 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| spl6_42 ),
inference(avatar_component_clause,[],[f1965]) ).
thf(f1967,plain,
( ( $true
= ( in @ ( sK5 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ~ spl6_42 ),
inference(avatar_component_clause,[],[f1965]) ).
thf(f2434,plain,
( ( $true != $true )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| spl6_42 ),
inference(constrained_superposition,[],[f1966,f130]) ).
thf(f2435,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| spl6_42 ),
inference(trivial_inequality_removal,[],[f2434]) ).
thf(f2437,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| spl6_42 ),
inference(forward_demodulation,[],[f2435,f42]) ).
thf(f2438,plain,
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| spl6_42 ),
inference(trivial_inequality_removal,[],[f2437]) ).
thf(f2440,plain,
( ( $true = $false )
| spl6_42 ),
inference(constrained_superposition,[],[f2438,f277]) ).
thf(f2444,plain,
( $false
| spl6_42 ),
inference(trivial_inequality_removal,[],[f2440]) ).
thf(f2445,plain,
spl6_42,
inference(avatar_contradiction_clause,[],[f2444]) ).
thf(f8767,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] : sK2 )
!= ( ^ [Y0: $i] : X3 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ sK1 ) ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK2 ) ) )
@ sK1 ) )
| ( $false
= ( in @ ( sK4 @ ( sK5 @ X2 @ X3 @ X4 ) @ sK2 @ sK1 ) @ ( setadjoin @ ( sK4 @ ( sK5 @ X2 @ X3 @ X4 ) @ sK2 @ sK1 ) @ emptyset ) ) )
| ( $false
= ( in @ ( sK5 @ X2 @ X3 @ X4 ) @ sK0 ) )
| ( $false
= ( in @ X0 @ X1 ) )
| ( ( ^ [Y0: $i] : X4 )
!= ( ^ [Y0: $i] : sK1 ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X2 ) ) ),
inference(equality_resolution,[],[f630]) ).
thf(f34932,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : X3 )
!= ( ^ [Y0: $i] : sK1 ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) )
@ sK1 ) )
| ( $false
= ( in @ ( sK4 @ ( sK5 @ X2 @ sK2 @ X3 ) @ sK2 @ sK1 ) @ ( setadjoin @ ( sK4 @ ( sK5 @ X2 @ sK2 @ X3 ) @ sK2 @ sK1 ) @ emptyset ) ) )
| ( $false
= ( in @ ( sK5 @ X2 @ sK2 @ X3 ) @ sK0 ) )
| ( ( in @ X1 @ X0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) ) ),
inference(equality_resolution,[],[f8767]) ).
thf(f35048,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ ( sK5 @ X1 @ sK2 @ sK1 ) @ sK2 @ sK1 ) @ ( setadjoin @ ( sK4 @ ( sK5 @ X1 @ sK2 @ sK1 ) @ sK2 @ sK1 ) @ emptyset ) ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK2 ) ) )
@ sK1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X2 @ sK1 ) ) )
| ( $false
= ( in @ X0 @ X2 ) )
| ( $false
= ( in @ ( sK5 @ X1 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X2 ) ) ),
inference(equality_resolution,[],[f34932]) ).
thf(f43825,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK5 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ ( sK5 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( ^ [Y0: $i] : ( sK5 @ X0 @ sK2 @ sK1 ) )
!= ( ^ [Y0: $i] : ( sK5 @ X0 @ sK2 @ sK1 ) ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) )
@ sK1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X2 @ sK1 ) ) )
| ( $false
= ( in @ X1 @ X2 ) )
| ( $false
= ( in @ ( sK5 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) ) ),
inference(constrained_superposition,[],[f1745,f35048]) ).
thf(f43976,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK5 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( ( ^ [Y0: $i] : ( sK5 @ X0 @ sK2 @ sK1 ) )
!= ( ^ [Y0: $i] : ( sK5 @ X0 @ sK2 @ sK1 ) ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) )
@ sK1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X2 @ sK1 ) ) )
| ( $false
= ( in @ X1 @ X2 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) ) ),
inference(duplicate_literal_removal,[],[f43825]) ).
thf(f43977,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK5 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK2 ) ) )
@ sK1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X2 @ sK1 ) ) )
| ( $false
= ( in @ X1 @ X2 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X2 ) ) ),
inference(trivial_inequality_removal,[],[f43976]) ).
thf(f44957,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $false
= ( in @ ( sK5 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ sK1 ) ) )
| ( $false
= ( in @ sK3 @ X1 ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X0 ) ) ),
inference(constrained_superposition,[],[f54,f43977]) ).
thf(f45059,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK5 @ X0 @ sK2 @ sK1 ) @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ sK1 ) ) )
| ( $false
= ( in @ sK3 @ X1 ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X0 ) ) ),
inference(trivial_inequality_removal,[],[f44957]) ).
thf(f45123,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK0 ) ) )
| ~ spl6_42 ),
inference(constrained_superposition,[],[f1967,f45059]) ).
thf(f45124,plain,
( ! [X0: $i] :
( ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK0 ) )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK1 ) ) ) )
| ~ spl6_42 ),
inference(trivial_inequality_removal,[],[f45123]) ).
thf(f45141,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ~ spl6_42 ),
inference(equality_resolution,[],[f45124]) ).
thf(f45143,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ~ spl6_42 ),
inference(forward_demodulation,[],[f45141,f42]) ).
thf(f45144,plain,
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK0 @ sK1 ) ) )
| ~ spl6_42 ),
inference(trivial_inequality_removal,[],[f45143]) ).
thf(f45146,plain,
( ( $true = $false )
| ~ spl6_42 ),
inference(constrained_superposition,[],[f45144,f277]) ).
thf(f45150,plain,
( $false
| ~ spl6_42 ),
inference(trivial_inequality_removal,[],[f45146]) ).
thf(f45151,plain,
~ spl6_42,
inference(avatar_contradiction_clause,[],[f45150]) ).
cnf(s1178,plain,
spl6_42,
inference(sat_conversion,[],[f2445]) ).
cnf(s16781,plain,
~ spl6_42,
inference(sat_conversion,[],[f45151]) ).
cnf(s16782,plain,
$false,
inference(rat,[],[s1178,s16781]) ).
thf(f45153,plain,
$false,
inference(avatar_sat_refutation,[],[s16782]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU676^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n006.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 14:07:09 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.90/1.22 % (773699)Will run a generic schedule for satisfiability detection.
% 6.90/1.22 % (773707)dis+10_1_sil=32000:sp=arity:random_seed=2476164163:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.90/1.22 % (773705)% WARNING: option uhcvi not known.
% 6.90/1.22 % (773705)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3283850388:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.90/1.22 % (773708)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=699885078:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.90/1.22 % (773705)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.90/1.22 % (773704)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1217874028_2999 on theBenchmark for (2999ds/0Mi)
% 6.90/1.22 % (773708)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.90/1.22 % (773705)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.90/1.22 % (773706)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4118419565:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.90/1.22 % Exception at run slice level
% 6.90/1.22 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.22 % (773709)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2209443828:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.90/1.22 % (773710)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4086365869:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.90/1.22 % (773716)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2159221868:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.90/1.22 % Exception at run slice level
% 6.90/1.22 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.22 % (773707)Instruction limit reached!
% 6.90/1.22 % (773707)------------------------------
% 6.90/1.22 % (773707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.22 % (773707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.22 % (773707)CaDiCaL version: 2.1.3
% 6.90/1.22 % (773707)Termination reason: Instruction limit
% 6.90/1.22 % (773707)Termination phase: Saturation
% 6.90/1.22 % (773707)Time elapsed: 0.038 s
% 6.90/1.22 % (773707)Peak memory usage: 12 MB
% 6.90/1.22 % (773707)Instructions burned: 104 (million)
% 6.90/1.22 % (773720)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=86353124:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.90/1.22 % (773721)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=896147334:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 6.90/1.22 % (773721)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.90/1.22 % (773721)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.90/1.22 % (773708)Instruction limit reached!
% 6.90/1.22 % (773708)------------------------------
% 6.90/1.22 % (773708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.22 % (773708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.22 % (773708)CaDiCaL version: 2.1.3
% 6.90/1.22 % (773708)Termination reason: Instruction limit
% 6.90/1.22 % (773708)Termination phase: Saturation
% 6.90/1.22 % (773708)Time elapsed: 0.054 s
% 6.90/1.22 % (773708)Peak memory usage: 12 MB
% 6.90/1.22 % (773708)Instructions burned: 117 (million)
% 6.90/1.22 % (773720)Instruction limit reached!
% 6.90/1.22 % (773720)------------------------------
% 6.90/1.22 % (773720)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.22 % (773720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.22 % (773720)CaDiCaL version: 2.1.3
% 6.90/1.22 % (773720)Termination reason: Instruction limit
% 6.90/1.22 % (773720)Termination phase: Saturation
% 6.90/1.22 % (773720)Time elapsed: 0.034 s
% 6.90/1.22 % (773720)Peak memory usage: 13 MB
% 6.90/1.22 % (773720)Instructions burned: 134 (million)
% 6.90/1.22 % (773709)Instruction limit reached!
% 6.90/1.22 % (773709)------------------------------
% 6.90/1.22 % (773709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.22 % (773709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.62/3.14 % (773709)CaDiCaL version: 2.1.3
% 20.62/3.14 % (773709)Termination reason: Instruction limit
% 20.62/3.14 % (773709)Termination phase: Saturation
% 20.62/3.14 % (773709)Time elapsed: 0.062 s
% 20.62/3.14 % (773709)Peak memory usage: 12 MB
% 20.62/3.14 % (773709)Instructions burned: 131 (million)
% 20.62/3.14 % (773724)ott-21_1_sil=16000:fs=off:random_seed=3826002485:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 20.62/3.14 % (773725)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1791682620:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 20.62/3.14 % (773726)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2905654286:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 20.62/3.14 % Exception at run slice level
% 20.62/3.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.62/3.14 % (773730)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1833475601:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 20.62/3.14 % (773710)Instruction limit reached!
% 20.62/3.14 % (773710)------------------------------
% 20.62/3.14 % (773710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.62/3.14 % (773710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.62/3.14 % (773710)CaDiCaL version: 2.1.3
% 20.62/3.14 % (773710)Termination reason: Instruction limit
% 20.62/3.14 % (773710)Termination phase: Saturation
% 20.62/3.14 % (773710)Time elapsed: 0.126 s
% 20.62/3.14 % (773710)Peak memory usage: 12 MB
% 20.62/3.14 % (773710)Instructions burned: 159 (million)
% 20.62/3.14 % (773724)Instruction limit reached!
% 20.62/3.14 % (773724)------------------------------
% 20.62/3.14 % (773724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.62/3.14 % (773724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.62/3.14 % (773724)CaDiCaL version: 2.1.3
% 20.62/3.14 % (773724)Termination reason: Instruction limit
% 20.62/3.14 % (773724)Termination phase: Saturation
% 20.62/3.14 % (773724)Time elapsed: 0.081 s
% 20.62/3.14 % (773724)Peak memory usage: 12 MB
% 20.62/3.14 % (773724)Instructions burned: 182 (million)
% 20.62/3.14 % (773732)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3607116105:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 20.62/3.14 % Exception at run slice level
% 20.62/3.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.62/3.14 % (773733)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1945684276:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 20.62/3.14 % (773733)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 20.62/3.14 % (773735)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2777582619:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 20.62/3.14 % (773735)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 20.62/3.14 % (773725)Instruction limit reached!
% 20.62/3.14 % (773725)------------------------------
% 20.62/3.14 % (773725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.62/3.14 % (773725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.62/3.14 % (773725)CaDiCaL version: 2.1.3
% 20.62/3.14 % (773725)Termination reason: Instruction limit
% 20.62/3.14 % (773725)Termination phase: Saturation
% 20.62/3.14 % (773725)Time elapsed: 0.130 s
% 20.62/3.14 % (773725)Peak memory usage: 13 MB
% 20.62/3.14 % (773725)Instructions burned: 478 (million)
% 20.62/3.14 % (773738)fmb+10_1_sil=64000:random_seed=1001758237:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 20.62/3.14 % (773738)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 20.62/3.14 % Exception at run slice level
% 20.62/3.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.62/3.14 % (773740)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1682707403:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 20.62/3.14 % Exception at run slice level
% 20.62/3.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.62/3.14 % (773742)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=127094420:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 46.02/6.75 % Exception at run slice level
% 46.02/6.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 46.02/6.75 % (773744)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3454129510:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 46.02/6.75 % (773744)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 46.02/6.75 % (773721)Instruction limit reached!
% 46.02/6.75 % (773721)------------------------------
% 46.02/6.75 % (773721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.02/6.75 % (773721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.02/6.75 % (773721)CaDiCaL version: 2.1.3
% 46.02/6.75 % (773721)Termination reason: Instruction limit
% 46.02/6.75 % (773721)Termination phase: Saturation
% 46.02/6.75 % (773721)Time elapsed: 0.307 s
% 46.02/6.75 % (773721)Peak memory usage: 14 MB
% 46.02/6.75 % (773721)Instructions burned: 684 (million)
% 46.02/6.75 % (773746)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=4254408436:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 46.02/6.75 % (773746)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 46.02/6.75 % (773746)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 46.02/6.75 % (773733)Instruction limit reached!
% 46.02/6.75 % (773733)------------------------------
% 46.02/6.75 % (773733)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.02/6.75 % (773733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.02/6.75 % (773733)CaDiCaL version: 2.1.3
% 46.02/6.75 % (773733)Termination reason: Instruction limit
% 46.02/6.75 % (773733)Termination phase: Saturation
% 46.02/6.75 % (773733)Time elapsed: 0.305 s
% 46.02/6.75 % (773733)Peak memory usage: 15 MB
% 46.02/6.75 % (773733)Instructions burned: 694 (million)
% 46.02/6.75 % (773748)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2173300056:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 46.02/6.75 % Exception at run slice level
% 46.02/6.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 46.02/6.75 % (773750)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2645545313:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 46.02/6.75 % Exception at run slice level
% 46.02/6.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 46.02/6.75 % (773752)ott-2_1_sil=16000:newcnf=on:random_seed=3633520780:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 46.02/6.75 % (773752)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 46.02/6.75 % (773730)Instruction limit reached!
% 46.02/6.75 % (773730)------------------------------
% 46.02/6.75 % (773730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.02/6.75 % (773730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.02/6.75 % (773730)CaDiCaL version: 2.1.3
% 46.02/6.75 % (773730)Termination reason: Instruction limit
% 46.02/6.75 % (773730)Termination phase: Saturation
% 46.02/6.75 % (773730)Time elapsed: 0.565 s
% 46.02/6.75 % (773730)Peak memory usage: 16 MB
% 46.02/6.75 % (773730)Instructions burned: 1182 (million)
% 46.02/6.75 % (773756)ott+10_1_sil=32000:tgt=ground:random_seed=2001082091:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 46.02/6.75 % (773735)Instruction limit reached!
% 46.02/6.75 % (773735)------------------------------
% 46.02/6.75 % (773735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.02/6.75 % (773735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.02/6.75 % (773735)CaDiCaL version: 2.1.3
% 46.02/6.75 % (773735)Termination reason: Instruction limit
% 46.02/6.75 % (773735)Termination phase: Saturation
% 46.02/6.75 % (773735)Time elapsed: 0.711 s
% 46.02/6.75 % (773735)Peak memory usage: 14 MB
% 46.02/6.75 % (773735)Instructions burned: 880 (million)
% 46.02/6.75 % (773758)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3390552302:i=54282_2990 on theBenchmark for (2990ds/54282Mi)
% 46.02/6.75 % Exception at run slice level
% 46.02/6.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 46.02/6.75 % (773760)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=4037639941:i=3512:aac=none_2990 on theBenchmark for (2990ds/3512Mi)
% 80.87/11.61 % (773760)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 80.87/11.61 % (773752)Instruction limit reached!
% 80.87/11.61 % (773752)------------------------------
% 80.87/11.61 % (773752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.87/11.61 % (773752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.87/11.61 % (773752)CaDiCaL version: 2.1.3
% 80.87/11.61 % (773752)Termination reason: Instruction limit
% 80.87/11.61 % (773752)Termination phase: Saturation
% 80.87/11.61 % (773752)Time elapsed: 0.553 s
% 80.87/11.61 % (773752)Peak memory usage: 16 MB
% 80.87/11.61 % (773752)Instructions burned: 869 (million)
% 80.87/11.61 % (773762)dis+21_1_sil=32000:sas=cadical:random_seed=2712465406:i=3773:amm=off_2988 on theBenchmark for (2988ds/3773Mi)
% 80.87/11.61 % (773746)Instruction limit reached!
% 80.87/11.61 % (773746)------------------------------
% 80.87/11.61 % (773746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.87/11.61 % (773746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.87/11.61 % (773746)CaDiCaL version: 2.1.3
% 80.87/11.61 % (773746)Termination reason: Instruction limit
% 80.87/11.61 % (773746)Termination phase: Saturation
% 80.87/11.61 % (773746)Time elapsed: 0.819 s
% 80.87/11.61 % (773746)Peak memory usage: 33 MB
% 80.87/11.61 % (773746)Instructions burned: 1474 (million)
% 80.87/11.61 % (773764)ott+11_1_sil=16000:gs=on:random_seed=2553518786:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2987 on theBenchmark for (2987ds/2251Mi)
% 80.87/11.61 % (773764)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 80.87/11.61 % (773744)Instruction limit reached!
% 80.87/11.61 % (773744)------------------------------
% 80.87/11.61 % (773744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.87/11.61 % (773744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.87/11.61 % (773744)CaDiCaL version: 2.1.3
% 80.87/11.61 % (773744)Termination reason: Instruction limit
% 80.87/11.61 % (773744)Termination phase: Saturation
% 80.87/11.61 % (773744)Time elapsed: 1.396 s
% 80.87/11.61 % (773744)Peak memory usage: 18 MB
% 80.87/11.61 % (773744)Instructions burned: 5134 (million)
% 80.87/11.61 % (773767)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=956962590:fmbsr=1.6:i=67534_2983 on theBenchmark for (2983ds/67534Mi)
% 80.87/11.61 % Exception at run slice level
% 80.87/11.61 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 80.87/11.61 % (773769)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=1763531856:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2982 on theBenchmark for (2982ds/4591Mi)
% 80.87/11.61 % (773764)Instruction limit reached!
% 80.87/11.61 % (773764)------------------------------
% 80.87/11.61 % (773764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.87/11.61 % (773764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.87/11.61 % (773764)CaDiCaL version: 2.1.3
% 80.87/11.61 % (773764)Termination reason: Instruction limit
% 80.87/11.61 % (773764)Termination phase: Saturation
% 80.87/11.61 % (773764)Time elapsed: 0.890 s
% 80.87/11.61 % (773764)Peak memory usage: 16 MB
% 80.87/11.61 % (773764)Instructions burned: 2251 (million)
% 80.87/11.61 % (773772)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=1054067232:i=29340_2978 on theBenchmark for (2978ds/29340Mi)
% 80.87/11.61 % (773760)Instruction limit reached!
% 80.87/11.61 % (773760)------------------------------
% 80.87/11.61 % (773760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.87/11.61 % (773760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.87/11.61 % (773760)CaDiCaL version: 2.1.3
% 80.87/11.61 % (773760)Termination reason: Instruction limit
% 80.87/11.61 % (773760)Termination phase: Saturation
% 80.87/11.61 % (773760)Time elapsed: 1.918 s
% 80.87/11.61 % (773760)Peak memory usage: 16 MB
% 80.87/11.61 % (773760)Instructions burned: 3514 (million)
% 80.87/11.61 % (773769)Instruction limit reached!
% 80.87/11.61 % (773769)------------------------------
% 80.87/11.61 % (773769)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.87/11.61 % (773769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.87/11.61 % (773769)CaDiCaL version: 2.1.3
% 80.87/11.61 % (773769)Termination reason: Instruction limit
% 80.87/11.61 % (773769)Termination phase: Saturation
% 80.87/11.61 % (773769)Time elapsed: 1.205 s
% 80.87/11.61 % (773769)Peak memory usage: 18 MB
% 80.87/11.61 % (773769)Instructions burned: 4594 (million)
% 80.87/11.61 % (773783)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=941212543:i=5497:nm=2_2970 on theBenchmark for (2970ds/5497Mi)
% 80.87/11.61 % Exception at run slice level
% 80.87/11.61 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 80.87/11.61 % (773782)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=1984745372:i=5211_2970 on theBenchmark for (2970ds/5211Mi)
% 80.87/11.61 % (773785)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=2525541985:fmbsr=2:i=46332_2970 on theBenchmark for (2970ds/46332Mi)
% 80.87/11.61 % Exception at run slice level
% 80.87/11.61 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 80.87/11.61 % (773788)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=1938654636:i=14071_2970 on theBenchmark for (2970ds/14071Mi)
% 80.87/11.61 % Exception at run slice level
% 80.87/11.61 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 80.87/11.61 % (773790)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4196630205:i=22565:add=on:rawr=on_2970 on theBenchmark for (2970ds/22565Mi)
% 80.87/11.61 % (773756)Instruction limit reached!
% 80.87/11.61 % (773756)------------------------------
% 80.87/11.61 % (773756)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.87/11.61 % (773756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.87/11.61 % (773756)CaDiCaL version: 2.1.3
% 80.87/11.61 % (773756)Termination reason: Instruction limit
% 80.87/11.61 % (773756)Termination phase: Saturation
% 80.87/11.61 % (773756)Time elapsed: 2.378 s
% 80.87/11.61 % (773756)Peak memory usage: 26 MB
% 80.87/11.61 % (773756)Instructions burned: 5116 (million)
% 80.87/11.61 % (773792)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=4165173735:i=8173:av=off_2968 on theBenchmark for (2968ds/8173Mi)
% 80.87/11.61 % (773762)Instruction limit reached!
% 80.87/11.61 % (773762)------------------------------
% 80.87/11.61 % (773762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.87/11.61 % (773762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.87/11.61 % (773762)CaDiCaL version: 2.1.3
% 80.87/11.61 % (773762)Termination reason: Instruction limit
% 80.87/11.61 % (773762)Termination phase: Saturation
% 80.87/11.61 % (773762)Time elapsed: 2.128 s
% 80.87/11.61 % (773762)Peak memory usage: 17 MB
% 80.87/11.61 % (773762)Instructions burned: 3774 (million)
% 80.87/11.61 % (773794)dis+10_16:1_sil=16000:random_seed=4843150:i=9155:fsr=off_2966 on theBenchmark for (2966ds/9155Mi)
% 80.87/11.61 % (773782)Instruction limit reached!
% 80.87/11.61 % (773782)------------------------------
% 80.87/11.61 % (773782)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.87/11.61 % (773782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.87/11.61 % (773782)CaDiCaL version: 2.1.3
% 80.87/11.61 % (773782)Termination reason: Instruction limit
% 80.87/11.61 % (773782)Termination phase: Saturation
% 80.87/11.61 % (773782)Time elapsed: 2.204 s
% 80.87/11.61 % (773782)Peak memory usage: 19 MB
% 80.87/11.61 % (773782)Instructions burned: 5213 (million)
% 80.87/11.61 % (773800)ott-3_8_sil=64000:random_seed=1697875373:i=20139:bs=on_2948 on theBenchmark for (2948ds/20139Mi)
% 80.87/11.61 % (773792)Instruction limit reached!
% 80.87/11.61 % (773792)------------------------------
% 80.87/11.61 % (773792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.87/11.61 % (773792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.87/11.61 % (773792)CaDiCaL version: 2.1.3
% 80.87/11.61 % (773792)Termination reason: Instruction limit
% 80.87/11.61 % (773792)Termination phase: Saturation
% 80.87/11.61 % (773792)Time elapsed: 3.357 s
% 80.87/11.61 % (773792)Peak memory usage: 34 MB
% 80.87/11.61 % (773792)Instructions burned: 8175 (million)
% 80.87/11.61 % (773802)fmb+10_1_sil=64000:tgt=ground:sas=cadical:bce=on:fmbss=9:random_seed=2355392302:fmbsr=2:i=32576_2935 on theBenchmark for (2935ds/32576Mi)
% 80.87/11.61 % Exception at run slice level
% 80.87/11.61 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 80.87/11.61 % (773805)ott+10_8:1_sil=16000:sp=arity:gs=on:random_seed=3123459916:i=11404_2934 on theBenchmark for (2934ds/11404Mi)
% 80.87/11.61 % (773794)Instruction limit reached!
% 80.87/11.61 % (773794)------------------------------
% 80.87/11.61 % (773794)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.87/11.61 % (773794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.87/11.61 % (773794)CaDiCaL version: 2.1.3
% 80.87/11.61 % (773794)Termination reason: Instruction limit
% 80.87/11.61 % (773794)Termination phase: Saturation
% 80.87/11.61 % (773794)Time elapsed: 4.039 s
% 80.87/11.61 % (773794)Peak memory usage: 19 MB
% 80.87/11.61 % (773794)Instructions burned: 9155 (million)
% 80.87/11.61 % (773808)ott-11_1_sil=16000:alpa=false:sac=on:random_seed=2205898849:i=14134_2926 on theBenchmark for (2926ds/14134Mi)
% 80.87/11.61 % (773808)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 80.87/11.61 % (773790)Instruction limit reached!
% 80.87/11.61 % (773790)------------------------------
% 80.87/11.61 % (773790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.87/11.61 % (773790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.87/11.61 % (773790)CaDiCaL version: 2.1.3
% 80.87/11.61 % (773790)Termination reason: Instruction limit
% 80.87/11.61 % (773790)Termination phase: Saturation
% 80.87/11.61 % (773790)Time elapsed: 5.570 s
% 80.87/11.61 % (773790)Peak memory usage: 33 MB
% 80.87/11.61 % (773790)Instructions burned: 22565 (million)
% 80.87/11.61 % (773812)dis+33_16_sil=32000:sac=on:random_seed=2602807533:i=15851:nm=0_2914 on theBenchmark for (2914ds/15851Mi)
% 80.87/11.61 % (773706) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-773699-773706"...
% 80.87/11.61 % (773706)...printing done.
% 80.87/11.61 % (773706)Refutation found. Thanks to Tanya!
% 80.87/11.61 % SZS status Theorem for theBenchmark
% 80.87/11.61 % SZS output start Proof for theBenchmark
% See solution above
% 80.87/11.62 % (773706)------------------------------
% 80.87/11.62 % (773706)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.87/11.62 % (773706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.87/11.62 % (773706)CaDiCaL version: 2.1.3
% 80.87/11.62 % (773706)Termination reason: Refutation
% 80.87/11.62 % (773706)Time elapsed: 11.346 s
% 80.87/11.62 % (773706)Peak memory usage: 34 MB
% 80.87/11.62 % (773706)Instructions burned: 25598 (million)
% 80.87/11.62 % (773699)Success in time 11.396 s
% 80.87/11.62 % Vampire exiting
%------------------------------------------------------------------------------