TSTP Solution File: SWW822_1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW822_1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 2 14:24:04 EDT 2023
% Result : Unsatisfiable 0.47s 0.71s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1436
% Syntax : Number of formulae : 3237 ( 999 unt; 424 typ; 0 def)
% Number of atoms : 7181 (4422 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 5932 (1564 ~;1225 |;2209 &)
% ( 560 <=>; 374 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 6443 (1359 atm;1387 fun;1435 num;2262 var)
% Number of types : 28 ( 26 usr; 2 ari)
% Number of type conns : 834 ( 339 >; 495 *; 0 +; 0 <<)
% Number of predicates : 489 ( 485 usr; 486 prp; 0-2 aty)
% Number of functors : 409 ( 398 usr; 66 con; 0-4 aty)
% Number of variables : 6098 (;4850 !;1248 ?;6098 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'S2': $tType ).
tff(type_def_6,type,
'S8': $tType ).
tff(type_def_7,type,
'S9': $tType ).
tff(type_def_8,type,
'S10': $tType ).
tff(type_def_9,type,
'S12': $tType ).
tff(type_def_10,type,
'S4': $tType ).
tff(type_def_11,type,
'S6': $tType ).
tff(type_def_12,type,
'S20': $tType ).
tff(type_def_13,type,
'S23': $tType ).
tff(type_def_14,type,
'S5': $tType ).
tff(type_def_15,type,
'S25': $tType ).
tff(type_def_16,type,
'S1': $tType ).
tff(type_def_17,type,
'S3': $tType ).
tff(type_def_18,type,
'S19': $tType ).
tff(type_def_19,type,
'S13': $tType ).
tff(type_def_20,type,
'S22': $tType ).
tff(type_def_21,type,
'S24': $tType ).
tff(type_def_22,type,
'S14': $tType ).
tff(type_def_23,type,
'S16': $tType ).
tff(type_def_24,type,
'S7': $tType ).
tff(type_def_25,type,
'S17': $tType ).
tff(type_def_26,type,
'S18': $tType ).
tff(type_def_27,type,
'S15': $tType ).
tff(type_def_28,type,
'S26': $tType ).
tff(type_def_29,type,
'S11': $tType ).
tff(type_def_30,type,
'S21': $tType ).
tff(func_def_0,type,
f56: ( 'S20' * $real ) > 'S1' ).
tff(func_def_1,type,
f34: ( 'S17' * 'S10' ) > 'S10' ).
tff(func_def_2,type,
f40: 'S18' ).
tff(func_def_3,type,
f21: 'S6' ).
tff(func_def_4,type,
f25: ( 'S15' * 'S10' ) > 'S2' ).
tff(func_def_5,type,
f65: 'S4' ).
tff(func_def_6,type,
f51: 'S10' ).
tff(func_def_7,type,
f36: 'S16' ).
tff(func_def_8,type,
f15: 'S2' ).
tff(func_def_9,type,
f60: 'S24' ).
tff(func_def_10,type,
f47: ( 'S2' * 'S22' ) > 'S1' ).
tff(func_def_11,type,
f19: ( 'S13' * 'S2' ) > $real ).
tff(func_def_12,type,
f35: 'S17' ).
tff(func_def_13,type,
f29: 'S15' ).
tff(func_def_14,type,
f7: 'S5' ).
tff(func_def_15,type,
f9: ( 'S7' * $int ) > 'S6' ).
tff(func_def_16,type,
f17: ( 'S12' * $real ) > 'S11' ).
tff(func_def_17,type,
f26: 'S15' ).
tff(func_def_18,type,
f57: ( 'S21' * 'S10' ) > 'S1' ).
tff(func_def_19,type,
f37: 'S17' > 'S1' ).
tff(func_def_20,type,
f58: ( 'S22' * 'S2' ) > 'S1' ).
tff(func_def_21,type,
f48: 'S22' ).
tff(func_def_22,type,
f66: ( 'S26' * 'S10' ) > 'S9' ).
tff(func_def_23,type,
f18: 'S12' ).
tff(func_def_24,type,
f20: 'S13' ).
tff(func_def_25,type,
f59: ( 'S24' * $real ) > 'S13' ).
tff(func_def_26,type,
f30: 'S14' ).
tff(func_def_27,type,
f10: 'S7' ).
tff(func_def_28,type,
f31: 'S16' ).
tff(func_def_29,type,
f5: 'S4' ).
tff(func_def_30,type,
f55: ( 'S19' * $int ) > 'S1' ).
tff(func_def_31,type,
f42: 'S19' ).
tff(func_def_32,type,
f39: ( 'S18' * 'S10' ) > 'S17' ).
tff(func_def_33,type,
f41: ( $int * 'S19' ) > 'S1' ).
tff(func_def_34,type,
f22: ( 'S14' * $real ) > $real ).
tff(func_def_35,type,
f43: ( $real * 'S20' ) > 'S1' ).
tff(func_def_36,type,
f63: ( 'S25' * $int ) > 'S8' ).
tff(func_def_37,type,
f3: ( 'S3' * 'S2' ) > 'S2' ).
tff(func_def_38,type,
f52: 'S18' ).
tff(func_def_39,type,
f14: 'S9' ).
tff(func_def_40,type,
f1: 'S1' ).
tff(func_def_41,type,
f62: 'S17' ).
tff(func_def_42,type,
f24: 'S3' ).
tff(func_def_43,type,
f27: ( 'S16' * 'S10' ) > $real ).
tff(func_def_44,type,
f23: 'S14' ).
tff(func_def_45,type,
f50: 'S23' ).
tff(func_def_46,type,
f38: 'S16' > 'S1' ).
tff(func_def_47,type,
f8: ( 'S6' * $int ) > $int ).
tff(func_def_48,type,
f64: 'S25' ).
tff(func_def_49,type,
f49: ( 'S23' * $real ) > 'S14' ).
tff(func_def_50,type,
f6: ( 'S5' * $int ) > 'S2' ).
tff(func_def_51,type,
f12: 'S8' ).
tff(func_def_52,type,
f33: 'S14' ).
tff(func_def_53,type,
f4: ( 'S4' * 'S2' ) > 'S3' ).
tff(func_def_54,type,
f16: ( 'S11' * $real ) > 'S10' ).
tff(func_def_55,type,
f13: ( 'S9' * 'S2' ) > 'S10' ).
tff(func_def_56,type,
f61: 'S18' ).
tff(func_def_57,type,
f2: 'S1' ).
tff(func_def_58,type,
f28: 'S16' ).
tff(func_def_59,type,
f46: 'S21' ).
tff(func_def_60,type,
f67: 'S26' ).
tff(func_def_61,type,
f44: 'S20' ).
tff(func_def_62,type,
f45: ( 'S10' * 'S21' ) > 'S1' ).
tff(func_def_63,type,
f53: 'S4' ).
tff(func_def_64,type,
f54: 'S4' ).
tff(func_def_65,type,
f32: 'S11' ).
tff(func_def_66,type,
f11: ( 'S8' * 'S2' ) > $int ).
tff(func_def_82,type,
sK0: 'S2' > 'S2' ).
tff(func_def_83,type,
sK1: 'S10' > 'S2' ).
tff(func_def_84,type,
sK2: $real > 'S2' ).
tff(func_def_85,type,
sK3: $int > 'S2' ).
tff(func_def_86,type,
sK4: 'S10' > $real ).
tff(func_def_87,type,
sK5: 'S10' > $real ).
tff(func_def_88,type,
sK6: 'S10' > $real ).
tff(func_def_89,type,
sK7: 'S10' > $real ).
tff(func_def_90,type,
sK8: $real > $real ).
tff(func_def_91,type,
sK9: $real > $real ).
tff(func_def_92,type,
sK10: 'S10' > $real ).
tff(func_def_93,type,
sK11: 'S10' > $real ).
tff(func_def_94,type,
sK12: $real > $real ).
tff(func_def_95,type,
sK13: $real > $real ).
tff(func_def_96,type,
sK14: $real > 'S2' ).
tff(func_def_97,type,
sK15: $int > 'S2' ).
tff(func_def_98,type,
sK16: 'S10' > 'S2' ).
tff(func_def_99,type,
sK17: 'S2' > 'S10' ).
tff(func_def_100,type,
sK18: $real > 'S10' ).
tff(func_def_101,type,
sK19: 'S2' > $real ).
tff(func_def_102,type,
sK20: 'S2' > $real ).
tff(func_def_103,type,
sK21: 'S2' > $real ).
tff(func_def_104,type,
sK22: 'S10' > $real ).
tff(func_def_105,type,
sK23: 'S10' > $real ).
tff(func_def_106,type,
sK24: 'S10' > $real ).
tff(func_def_107,type,
sK25: 'S10' > $real ).
tff(func_def_108,type,
sK26: $int > $int ).
tff(func_def_109,type,
sK27: 'S2' > $int ).
tff(func_def_110,type,
sK28: 'S2' > $int ).
tff(func_def_111,type,
sK29: 'S2' > $int ).
tff(func_def_112,type,
sK30: 'S2' > $int ).
tff(func_def_113,type,
sK31: 'S2' > $int ).
tff(func_def_114,type,
sK32: 'S2' > 'S6' ).
tff(func_def_115,type,
sK33: $real > $real ).
tff(func_def_116,type,
sK34: $real > $real ).
tff(func_def_117,type,
sK35: 'S2' > 'S2' ).
tff(func_def_118,type,
sK36: $int > 'S10' ).
tff(func_def_119,type,
sK37: $int > $real ).
tff(func_def_120,type,
sK38: $int > 'S2' ).
tff(func_def_121,type,
sK39: $int > $int ).
tff(func_def_122,type,
sK40: $real > $real ).
tff(func_def_123,type,
sK41: $int > $int ).
tff(func_def_124,type,
sK42: 'S10' > $real ).
tff(func_def_125,type,
sK43: 'S10' > $real ).
tff(func_def_126,type,
sK44: $real > $real ).
tff(func_def_127,type,
sK45: $real > $real ).
tff(func_def_128,type,
sK46: 'S10' > 'S10' ).
tff(func_def_129,type,
sK47: 'S10' > $real ).
tff(func_def_130,type,
sK48: 'S22' > 'S2' ).
tff(func_def_131,type,
sK49: 'S21' > 'S2' ).
tff(func_def_132,type,
sK50: 'S20' > 'S2' ).
tff(func_def_133,type,
sK51: 'S19' > 'S2' ).
tff(func_def_134,type,
sK52: ( $real * $real ) > $real ).
tff(func_def_135,type,
sK53: ( $real * $real ) > $real ).
tff(func_def_136,type,
sK54: ( 'S2' * 'S2' ) > $int ).
tff(func_def_137,type,
sK55: ( $real * $real ) > 'S2' ).
tff(func_def_138,type,
sK56: ( $real * $real ) > 'S2' ).
tff(func_def_139,type,
sK57: ( 'S2' * 'S2' ) > 'S2' ).
tff(func_def_140,type,
sK58: ( 'S2' * 'S2' ) > 'S2' ).
tff(func_def_141,type,
sK59: ( 'S2' * 'S2' ) > 'S2' ).
tff(func_def_142,type,
sK60: ( $int * 'S2' ) > 'S8' ).
tff(func_def_143,type,
sK61: ( $int * 'S2' ) > 'S8' ).
tff(func_def_144,type,
sK62: ( 'S10' * 'S2' ) > 'S9' ).
tff(func_def_145,type,
sK63: ( 'S10' * 'S2' ) > 'S9' ).
tff(func_def_146,type,
sK64: ( 'S10' * 'S2' ) > 'S9' ).
tff(func_def_147,type,
sK65: ( $int * 'S2' ) > 'S8' ).
tff(func_def_148,type,
sK66: ( 'S10' * 'S2' ) > 'S9' ).
tff(func_def_149,type,
sK67: ( $int * 'S2' ) > 'S8' ).
tff(func_def_150,type,
sK68: ( 'S10' * 'S2' ) > 'S9' ).
tff(func_def_151,type,
sK69: ( $int * 'S2' ) > 'S8' ).
tff(func_def_152,type,
sK70: ( 'S10' * 'S2' ) > 'S9' ).
tff(func_def_153,type,
sK71: ( 'S10' * 'S2' ) > 'S10' ).
tff(func_def_154,type,
sK72: ( 'S10' * 'S2' ) > 'S9' ).
tff(func_def_155,type,
sK73: ( 'S10' * 'S2' ) > 'S10' ).
tff(func_def_156,type,
sK74: ( $int * 'S2' ) > 'S8' ).
tff(func_def_157,type,
sK75: ( $int * 'S2' ) > $int ).
tff(func_def_158,type,
sK76: ( $int * 'S2' ) > 'S8' ).
tff(func_def_159,type,
sK77: ( $int * 'S2' ) > $int ).
tff(func_def_160,type,
sK78: ( $real * $real ) > 'S11' ).
tff(func_def_161,type,
sK79: ( $real * 'S2' ) > 'S13' ).
tff(func_def_162,type,
sK80: ( $real * 'S2' ) > 'S13' ).
tff(func_def_163,type,
sK81: ( $real * 'S2' ) > 'S13' ).
tff(func_def_164,type,
sK82: ( $real * 'S2' ) > 'S13' ).
tff(func_def_165,type,
sK83: ( $real * 'S2' ) > 'S13' ).
tff(func_def_166,type,
sK84: ( $real * 'S2' ) > 'S13' ).
tff(func_def_167,type,
sK85: ( $real * 'S2' ) > $real ).
tff(func_def_168,type,
sK86: ( $real * 'S2' ) > 'S13' ).
tff(func_def_169,type,
sK87: ( $real * 'S2' ) > $real ).
tff(func_def_170,type,
sK88: ( 'S2' * 'S2' ) > 'S3' ).
tff(func_def_171,type,
sK89: ( 'S2' * 'S2' ) > 'S3' ).
tff(func_def_172,type,
sK90: ( 'S2' * 'S2' ) > 'S3' ).
tff(func_def_173,type,
sK91: ( 'S2' * 'S2' ) > 'S3' ).
tff(func_def_174,type,
sK92: ( 'S2' * 'S2' ) > 'S3' ).
tff(func_def_175,type,
sK93: ( 'S2' * 'S2' ) > 'S3' ).
tff(func_def_176,type,
sK94: ( 'S2' * 'S2' ) > 'S3' ).
tff(func_def_177,type,
sK95: ( 'S2' * 'S2' ) > 'S2' ).
tff(func_def_178,type,
sK96: ( 'S2' * 'S2' ) > 'S3' ).
tff(func_def_179,type,
sK97: ( 'S2' * 'S2' ) > 'S2' ).
tff(func_def_180,type,
sK98: ( 'S2' * 'S2' ) > $int ).
tff(func_def_181,type,
sK99: ( 'S2' * 'S2' ) > 'S6' ).
tff(func_def_182,type,
sK100: ( 'S2' * 'S2' ) > $int ).
tff(func_def_183,type,
sK101: ( 'S2' * 'S2' ) > 'S2' ).
tff(func_def_184,type,
sK102: ( 'S2' * 'S2' ) > 'S2' ).
tff(func_def_185,type,
sK103: ( $int * $int ) > 'S2' ).
tff(func_def_186,type,
sK104: ( $real * $real ) > 'S2' ).
tff(func_def_187,type,
sK105: ( 'S10' * 'S10' ) > 'S2' ).
tff(func_def_188,type,
sK106: ( 'S10' * 'S10' ) > $real ).
tff(func_def_189,type,
sK107: ( $real * $real ) > $real ).
tff(func_def_190,type,
sK108: ( 'S2' * 'S2' ) > $int ).
tff(func_def_191,type,
sK109: ( 'S2' * 'S2' ) > $int ).
tff(func_def_192,type,
sK110: ( $real * $real ) > $real ).
tff(func_def_193,type,
sK111: ( $real * $real ) > 'S2' ).
tff(func_def_194,type,
sK112: ( 'S2' * $int ) > $int ).
tff(func_def_195,type,
sK113: ( 'S2' * $int ) > 'S8' ).
tff(func_def_196,type,
sK114: ( 'S2' * 'S10' ) > $int ).
tff(func_def_197,type,
sK115: ( 'S2' * 'S10' ) > 'S9' ).
tff(func_def_198,type,
sK116: ( 'S2' * $real ) > $int ).
tff(func_def_199,type,
sK117: ( 'S2' * $real ) > 'S13' ).
tff(func_def_200,type,
sK118: ( 'S2' * 'S2' ) > $int ).
tff(func_def_201,type,
sK119: ( 'S2' * 'S2' ) > 'S3' ).
tff(func_def_202,type,
sK120: ( 'S2' * 'S2' ) > $int ).
tff(func_def_203,type,
sK121: ( 'S2' * 'S2' ) > $int ).
tff(func_def_204,type,
sK122: ( 'S2' * 'S2' ) > $int ).
tff(func_def_205,type,
sK123: ( 'S2' * 'S2' ) > $int ).
tff(func_def_206,type,
sK124: ( 'S2' * 'S2' ) > $int ).
tff(func_def_207,type,
sK125: ( 'S2' * 'S2' ) > $int ).
tff(func_def_208,type,
sK126: ( 'S2' * 'S2' ) > $int ).
tff(func_def_209,type,
sK127: ( 'S2' * 'S2' ) > $int ).
tff(func_def_210,type,
sK128: ( 'S2' * 'S2' ) > $int ).
tff(func_def_211,type,
sK129: ( 'S2' * 'S2' ) > $int ).
tff(func_def_212,type,
sK130: ( 'S2' * 'S2' ) > $int ).
tff(func_def_213,type,
sK131: ( 'S2' * 'S2' ) > $int ).
tff(func_def_214,type,
sK132: ( 'S2' * 'S2' ) > $int ).
tff(func_def_215,type,
sK133: ( 'S2' * 'S2' ) > $int ).
tff(func_def_216,type,
sK134: ( 'S2' * 'S2' ) > $int ).
tff(func_def_217,type,
sK135: ( 'S2' * 'S2' ) > $int ).
tff(func_def_218,type,
sK136: ( 'S2' * 'S2' ) > $int ).
tff(func_def_219,type,
sK137: ( 'S2' * 'S2' ) > $int ).
tff(func_def_220,type,
sK138: ( 'S2' * 'S2' ) > $int ).
tff(func_def_221,type,
sK139: ( 'S2' * 'S2' ) > $int ).
tff(func_def_222,type,
sK140: ( 'S2' * 'S2' ) > $int ).
tff(func_def_223,type,
sK141: ( 'S2' * 'S2' ) > $int ).
tff(func_def_224,type,
sK142: ( 'S2' * 'S2' ) > 'S2' ).
tff(func_def_225,type,
sK143: ( 'S2' * 'S2' ) > $int ).
tff(func_def_226,type,
sK144: ( 'S2' * 'S2' ) > $int ).
tff(func_def_227,type,
sK145: ( 'S2' * 'S2' ) > $int ).
tff(func_def_228,type,
sK146: ( 'S2' * 'S2' ) > $int ).
tff(func_def_229,type,
sK147: ( 'S2' * 'S2' ) > $int ).
tff(func_def_230,type,
sK148: ( 'S10' * 'S10' ) > 'S14' ).
tff(func_def_231,type,
sK149: ( 'S10' * 'S10' ) > $real ).
tff(func_def_232,type,
sK150: ( 'S10' * 'S10' ) > 'S14' ).
tff(func_def_233,type,
sK151: ( 'S10' * 'S10' ) > $real ).
tff(func_def_234,type,
sK152: ( 'S10' * 'S2' * 'S2' ) > 'S9' ).
tff(func_def_235,type,
sK153: ( $int * 'S2' * 'S2' ) > 'S8' ).
tff(func_def_236,type,
sK154: ( $int * 'S2' * 'S2' ) > 'S8' ).
tff(func_def_237,type,
sK155: ( 'S10' * 'S2' * 'S2' ) > 'S9' ).
tff(func_def_238,type,
sK156: ( 'S10' * 'S2' * 'S2' ) > 'S9' ).
tff(func_def_239,type,
sK157: ( $int * 'S2' * 'S2' ) > 'S8' ).
tff(func_def_240,type,
sK158: ( $real * 'S2' * 'S2' ) > 'S13' ).
tff(func_def_241,type,
sK159: ( $real * 'S2' * 'S2' ) > 'S13' ).
tff(func_def_242,type,
sK160: ( $real * 'S2' * 'S2' ) > 'S13' ).
tff(func_def_243,type,
sK161: ( 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_244,type,
sK162: ( 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_245,type,
sK163: ( 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_246,type,
sK164: ( 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_247,type,
sK165: ( 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_248,type,
sK166: ( 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_249,type,
sK167: ( 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_250,type,
sK168: ( 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_251,type,
sK169: ( $int * $int * $int ) > 'S6' ).
tff(func_def_252,type,
sK170: ( $int * $int * $int ) > 'S6' ).
tff(func_def_253,type,
sK171: ( $int * $int * $int ) > 'S6' ).
tff(func_def_254,type,
sK172: ( $int * $int * $int ) > 'S6' ).
tff(func_def_255,type,
sK173: ( $real * $real * $real ) > 'S14' ).
tff(func_def_256,type,
sK174: ( $real * $real * $real ) > 'S14' ).
tff(func_def_257,type,
sK175: ( $real * $real * $real ) > 'S14' ).
tff(func_def_258,type,
sK176: ( $real * $real * $real ) > 'S14' ).
tff(func_def_259,type,
sK177: ( $real * $real * $real ) > 'S14' ).
tff(func_def_260,type,
sK178: ( $real * $real * $real ) > 'S14' ).
tff(func_def_261,type,
sK179: ( $real * $real * $real ) > 'S14' ).
tff(func_def_262,type,
sK180: ( $real * $real * $real ) > 'S14' ).
tff(func_def_263,type,
sK181: ( $real * $real * $real ) > 'S14' ).
tff(func_def_264,type,
sK182: ( $real * $real * $real ) > 'S14' ).
tff(func_def_265,type,
sK183: ( $real * $real * $real ) > 'S14' ).
tff(func_def_266,type,
sK184: ( $real * $real * $real ) > 'S14' ).
tff(func_def_267,type,
sK185: ( $real * $real * $real ) > 'S14' ).
tff(func_def_268,type,
sK186: ( 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_269,type,
sK187: ( 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_270,type,
sK188: ( 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_271,type,
sK189: ( 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_272,type,
sK190: ( 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_273,type,
sK191: ( 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_274,type,
sK192: ( 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_275,type,
sK193: ( 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_276,type,
sK194: ( 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_277,type,
sK195: ( 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_278,type,
sK196: ( 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_279,type,
sK197: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_280,type,
sK198: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_281,type,
sK199: ( 'S2' * 'S2' * 'S2' ) > 'S6' ).
tff(func_def_282,type,
sK200: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_283,type,
sK201: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_284,type,
sK202: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_285,type,
sK203: ( 'S2' * 'S2' * 'S2' ) > 'S6' ).
tff(func_def_286,type,
sK204: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_287,type,
sK205: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_288,type,
sK206: ( 'S2' * 'S2' * 'S2' ) > 'S6' ).
tff(func_def_289,type,
sK207: ( 'S2' * 'S2' * 'S2' ) > 'S6' ).
tff(func_def_290,type,
sK208: ( 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_291,type,
sK209: ( 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_292,type,
sK210: ( $int * $int * $int ) > 'S6' ).
tff(func_def_293,type,
sK211: ( $int * $int * $int ) > 'S6' ).
tff(func_def_294,type,
sK212: ( $real * $real * $real ) > 'S14' ).
tff(func_def_295,type,
sK213: ( $real * $real * $real ) > 'S14' ).
tff(func_def_296,type,
sK214: ( 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_297,type,
sK215: ( 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_298,type,
sK216: ( 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_299,type,
sK217: ( 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_300,type,
sK218: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_301,type,
sK219: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_302,type,
sK220: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_303,type,
sK221: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_304,type,
sK222: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_305,type,
sK223: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_306,type,
sK224: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_307,type,
sK225: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_308,type,
sK226: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_309,type,
sK227: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_310,type,
sK228: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_311,type,
sK229: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_312,type,
sK230: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_313,type,
sK231: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_314,type,
sK232: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_315,type,
sK233: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_316,type,
sK234: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_317,type,
sK235: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_318,type,
sK236: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_319,type,
sK237: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_320,type,
sK238: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_321,type,
sK239: ( 'S2' * 'S2' * 'S2' ) > 'S6' ).
tff(func_def_322,type,
sK240: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_323,type,
sK241: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_324,type,
sK242: ( 'S2' * 'S2' * 'S2' ) > 'S6' ).
tff(func_def_325,type,
sK243: ( 'S2' * 'S2' * 'S2' ) > 'S6' ).
tff(func_def_326,type,
sK244: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_327,type,
sK245: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_328,type,
sK246: ( 'S2' * 'S2' * 'S2' ) > 'S6' ).
tff(func_def_329,type,
sK247: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_330,type,
sK248: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_331,type,
sK249: ( 'S2' * 'S2' * 'S2' ) > 'S6' ).
tff(func_def_332,type,
sK250: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_333,type,
sK251: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_334,type,
sK252: ( 'S2' * 'S2' * 'S2' ) > 'S6' ).
tff(func_def_335,type,
sK253: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_336,type,
sK254: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_337,type,
sK255: ( 'S2' * 'S2' * 'S2' ) > 'S6' ).
tff(func_def_338,type,
sK256: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_339,type,
sK257: ( 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_340,type,
sK258: ( 'S2' * 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_341,type,
sK259: ( $int * $int * $int * $int ) > 'S6' ).
tff(func_def_342,type,
sK260: ( $int * $int * $int * $int ) > 'S6' ).
tff(func_def_343,type,
sK261: ( $real * $real * $real * $real ) > 'S14' ).
tff(func_def_344,type,
sK262: ( $real * $real * $real * $real ) > 'S14' ).
tff(func_def_345,type,
sK263: ( 'S10' * 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_346,type,
sK264: ( 'S10' * 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_347,type,
sK265: ( 'S10' * 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_348,type,
sK266: ( 'S2' * 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_349,type,
sK267: ( 'S2' * 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_350,type,
sK268: ( 'S2' * 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_351,type,
sK269: ( 'S2' * 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_352,type,
sK270: ( 'S2' * 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_353,type,
sK271: ( 'S2' * 'S2' * 'S2' * 'S2' ) > 'S2' ).
tff(func_def_354,type,
sK272: ( $int * $int * $int * $int ) > 'S6' ).
tff(func_def_355,type,
sK273: ( $int * $int * $int * $int ) > 'S6' ).
tff(func_def_356,type,
sK274: ( $int * $int * $int * $int ) > 'S6' ).
tff(func_def_357,type,
sK275: ( $int * $int * $int * $int ) > 'S6' ).
tff(func_def_358,type,
sK276: ( $int * $int * $int * $int ) > 'S6' ).
tff(func_def_359,type,
sK277: ( $int * $int * $int * $int ) > $int ).
tff(func_def_360,type,
sK278: ( $real * $real * $real * $real ) > 'S14' ).
tff(func_def_361,type,
sK279: ( $real * $real * $real * $real ) > 'S14' ).
tff(func_def_362,type,
sK280: ( $real * $real * $real * $real ) > 'S14' ).
tff(func_def_363,type,
sK281: ( $real * $real * $real * $real ) > 'S14' ).
tff(func_def_364,type,
sK282: ( $real * $real * $real * $real ) > 'S14' ).
tff(func_def_365,type,
sK283: ( $real * $real * $real * $real ) > 'S14' ).
tff(func_def_366,type,
sK284: ( $real * $real * $real * $real ) > 'S14' ).
tff(func_def_367,type,
sK285: ( $real * $real * $real * $real ) > $real ).
tff(func_def_368,type,
sK286: ( 'S10' * 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_369,type,
sK287: ( 'S10' * 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_370,type,
sK288: ( 'S10' * 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_371,type,
sK289: ( 'S10' * 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_372,type,
sK290: ( 'S10' * 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_373,type,
sK291: ( 'S10' * 'S10' * 'S10' * 'S10' ) > 'S10' ).
tff(func_def_374,type,
sK292: ( 'S2' * 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_375,type,
sK293: ( 'S2' * 'S2' * 'S2' * 'S2' ) > 'S3' ).
tff(func_def_376,type,
sK294: ( $int * $int * $int * $int ) > 'S6' ).
tff(func_def_377,type,
sK295: ( $int * $int * $int * $int ) > 'S6' ).
tff(func_def_378,type,
sK296: ( $real * $real * $real * $real ) > 'S14' ).
tff(func_def_379,type,
sK297: ( $real * $real * $real * $real ) > 'S14' ).
tff(func_def_380,type,
sK298: ( 'S10' * 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_381,type,
sK299: ( 'S10' * 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_382,type,
sK300: ( $real * $real * $real * $real ) > 'S14' ).
tff(func_def_383,type,
sK301: ( $real * $real * $real * $real ) > 'S14' ).
tff(func_def_384,type,
sK302: ( $real * $real * $real * $real ) > $real ).
tff(func_def_385,type,
sK303: ( 'S10' * 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_386,type,
sK304: ( 'S10' * 'S10' * 'S10' * 'S10' ) > 'S17' ).
tff(func_def_387,type,
sK305: ( 'S10' * 'S10' * 'S10' * 'S10' ) > 'S10' ).
tff(func_def_388,type,
sK306: ( 'S2' * 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_389,type,
sK307: ( 'S2' * 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_390,type,
sK308: ( 'S2' * 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_391,type,
sK309: ( 'S2' * 'S2' * 'S2' * 'S2' ) > $int ).
tff(func_def_392,type,
sK310: $real ).
tff(func_def_393,type,
sK311: $real ).
tff(func_def_394,type,
sK312: $real ).
tff(func_def_395,type,
sK313: $real ).
tff(func_def_396,type,
sK314: $real ).
tff(func_def_397,type,
sK315: $real ).
tff(func_def_398,type,
sK316: $real ).
tff(func_def_399,type,
sK317: $real ).
tff(func_def_400,type,
sK318: $real ).
tff(func_def_401,type,
sK319: $real ).
tff(func_def_402,type,
sK320: $real ).
tff(func_def_403,type,
sK321: $real ).
tff(func_def_404,type,
sK322: $real ).
tff(func_def_405,type,
sK323: $real ).
tff(func_def_406,type,
sK324: $real ).
tff(func_def_407,type,
sK325: $real ).
tff(func_def_408,type,
sK326: $real ).
tff(func_def_409,type,
sK327: $real ).
tff(func_def_410,type,
sK328: $real ).
tff(func_def_411,type,
sK329: $real ).
tff(func_def_412,type,
sK330: $real ).
tff(f6225,plain,
$false,
inference(avatar_sat_refutation,[],[f2932,f2936,f2941,f2946,f2951,f2956,f2961,f2966,f2971,f2976,f2981,f2986,f2991,f2996,f3001,f3006,f3011,f3016,f3021,f3026,f3030,f3034,f3038,f3042,f3046,f3050,f3054,f3058,f3062,f3066,f3070,f3074,f3078,f3082,f3086,f3090,f3095,f3100,f3104,f3109,f3113,f3118,f3122,f3126,f3130,f3134,f3138,f3142,f3146,f3150,f3154,f3158,f3162,f3166,f3170,f3174,f3178,f3182,f3186,f3190,f3194,f3198,f3202,f3206,f3210,f3214,f3218,f3222,f3226,f3230,f3234,f3238,f3242,f3246,f3250,f3254,f3258,f3262,f3266,f3270,f3274,f3278,f3282,f3286,f3290,f3294,f3298,f3302,f3306,f3310,f3314,f3318,f3322,f3326,f3330,f3334,f3338,f3342,f3346,f3350,f3354,f3358,f3362,f3366,f3384,f3390,f3394,f3398,f3402,f3406,f3411,f3415,f3419,f3423,f3428,f3432,f3437,f3441,f3446,f3450,f3455,f3459,f3465,f3470,f3476,f3481,f3487,f3492,f3496,f3500,f3504,f3508,f3514,f3519,f3523,f3527,f3531,f3536,f3540,f3545,f3549,f3554,f3558,f3562,f3566,f3570,f3574,f3578,f3582,f3586,f3590,f3594,f3598,f3602,f3606,f3610,f3614,f3618,f3622,f3626,f3630,f3634,f3638,f3642,f3646,f3650,f3654,f3658,f3662,f3666,f3670,f3674,f3678,f3682,f3686,f3690,f3694,f3698,f3702,f3706,f3710,f3722,f3726,f3730,f3734,f3738,f3742,f3746,f3750,f3754,f3758,f3770,f3774,f3778,f3782,f3786,f3790,f3794,f3798,f3802,f3806,f3810,f3814,f3818,f3822,f3826,f3830,f3834,f3838,f3842,f3846,f3850,f3854,f3858,f3862,f3866,f3870,f3874,f3878,f3882,f3886,f3890,f3894,f3898,f3902,f3906,f3910,f3914,f3918,f3922,f3926,f3930,f3934,f3938,f3956,f3980,f3984,f3990,f4424,f4428,f4438,f4442,f4446,f4454,f4459,f4477,f4481,f4485,f4489,f4493,f4497,f4501,f4506,f4510,f4514,f4518,f4522,f4526,f4530,f4534,f4538,f4542,f4546,f4551,f4555,f4559,f4563,f4567,f4571,f4575,f4579,f4583,f4587,f4591,f4596,f4600,f4604,f4608,f4612,f4616,f4620,f4624,f4628,f4632,f4636,f4641,f4645,f4649,f4653,f4657,f4661,f4665,f4669,f4673,f4677,f4681,f4686,f4690,f4694,f4698,f4702,f4706,f4710,f4714,f4718,f4722,f4726,f4731,f4735,f4739,f4743,f4747,f4751,f4755,f4759,f4763,f4774,f4860,f4876,f4880,f4884,f4888,f4893,f4900,f4909,f4914,f4919,f4926,f4933,f4942,f4947,f4957,f4962,f4972,f4976,f4980,f4984,f4989,f4994,f4999,f5003,f5007,f5011,f5015,f5019,f5023,f5027,f5031,f5035,f5039,f5043,f5047,f5051,f5057,f5061,f5065,f5070,f5074,f5078,f5082,f5086,f5090,f5094,f5098,f5102,f5106,f5110,f5114,f5118,f5122,f5126,f5130,f5134,f5138,f5142,f5146,f5150,f5154,f5158,f5162,f5166,f5170,f5174,f5178,f5182,f5186,f5190,f5194,f5201,f5205,f5209,f5213,f5218,f5224,f5228,f5232,f5237,f5243,f5248,f5252,f5257,f5261,f5266,f5270,f5274,f5279,f5283,f5287,f5291,f5359,f5445,f5473,f5490,f5494,f5498,f5502,f5506,f5510,f5516,f5527,f5532,f5555,f5561,f5584,f5590,f5594,f5600,f5605,f5612,f5617,f5633,f5638,f5645,f5649,f5655,f5661,f5665,f5669,f5673,f5677,f5681,f5685,f5689,f5693,f5697,f5701,f5705,f5709,f5713,f5717,f5721,f5725,f5730,f5734,f5738,f5742,f5746,f5750,f5754,f5758,f5762,f5766,f5770,f5776,f5780,f5784,f5788,f5792,f5796,f5800,f5804,f5808,f5812,f5817,f5821,f5825,f5910,f5961,f6127,f6195,f6199,f6203,f6207,f6212,f6221,f6224]) ).
tff(f6224,plain,
( ~ spl331_63
| spl331_485 ),
inference(avatar_contradiction_clause,[],[f6223]) ).
tff(f6223,plain,
( $false
| ~ spl331_63
| spl331_485 ),
inference(trivial_inequality_removal,[],[f6222]) ).
tff(f6222,plain,
( ( sK17(f15) != sK17(f15) )
| ~ spl331_63
| spl331_485 ),
inference(superposition,[],[f6220,f3201]) ).
tff(f3201,plain,
( ! [X0: 'S2'] : ( f13(f14,X0) = sK17(X0) )
| ~ spl331_63 ),
inference(avatar_component_clause,[],[f3200]) ).
tff(f3200,plain,
( spl331_63
<=> ! [X0: 'S2'] : ( f13(f14,X0) = sK17(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_63])]) ).
tff(f6220,plain,
( ( f13(f14,f15) != sK17(f15) )
| spl331_485 ),
inference(avatar_component_clause,[],[f6218]) ).
tff(f6218,plain,
( spl331_485
<=> ( f13(f14,f15) = sK17(f15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_485])]) ).
tff(f6221,plain,
( ~ spl331_485
| ~ spl331_65
| ~ spl331_324
| ~ spl331_326
| spl331_484 ),
inference(avatar_split_clause,[],[f6215,f6209,f4912,f4898,f3208,f6218]) ).
tff(f3208,plain,
( spl331_65
<=> ! [X0: 'S2'] : ( f19(f20,X0) = sK19(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_65])]) ).
tff(f4898,plain,
( spl331_324
<=> ! [X0: 'S2'] : ( sK17(X0) = sK18(sK19(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_324])]) ).
tff(f4912,plain,
( spl331_326
<=> ! [X0: $real] : ( f16(f17(f18,X0),0.0) = sK18(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_326])]) ).
tff(f6209,plain,
( spl331_484
<=> ( f13(f14,f15) = f16(f17(f18,f19(f20,f15)),0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_484])]) ).
tff(f6215,plain,
( ( f13(f14,f15) != sK17(f15) )
| ~ spl331_65
| ~ spl331_324
| ~ spl331_326
| spl331_484 ),
inference(forward_demodulation,[],[f6214,f4899]) ).
tff(f4899,plain,
( ! [X0: 'S2'] : ( sK17(X0) = sK18(sK19(X0)) )
| ~ spl331_324 ),
inference(avatar_component_clause,[],[f4898]) ).
tff(f6214,plain,
( ( f13(f14,f15) != sK18(sK19(f15)) )
| ~ spl331_65
| ~ spl331_326
| spl331_484 ),
inference(forward_demodulation,[],[f6213,f4913]) ).
tff(f4913,plain,
( ! [X0: $real] : ( f16(f17(f18,X0),0.0) = sK18(X0) )
| ~ spl331_326 ),
inference(avatar_component_clause,[],[f4912]) ).
tff(f6213,plain,
( ( f13(f14,f15) != f16(f17(f18,sK19(f15)),0.0) )
| ~ spl331_65
| spl331_484 ),
inference(forward_demodulation,[],[f6211,f3209]) ).
tff(f3209,plain,
( ! [X0: 'S2'] : ( f19(f20,X0) = sK19(X0) )
| ~ spl331_65 ),
inference(avatar_component_clause,[],[f3208]) ).
tff(f6211,plain,
( ( f13(f14,f15) != f16(f17(f18,f19(f20,f15)),0.0) )
| spl331_484 ),
inference(avatar_component_clause,[],[f6209]) ).
tff(f6212,plain,
~ spl331_484,
inference(avatar_split_clause,[],[f1467,f6209]) ).
tff(f1467,plain,
f13(f14,f15) != f16(f17(f18,f19(f20,f15)),0.0),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
f13(f14,f15) != f16(f17(f18,f19(f20,f15)),0.0),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_3) ).
tff(f6207,plain,
spl331_483,
inference(avatar_split_clause,[],[f598,f6205]) ).
tff(f6205,plain,
( spl331_483
<=> ! [X2: $real,X0: $real,X1: $real] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_483])]) ).
tff(f598,plain,
! [X2: $real,X0: $real,X1: $real] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(theory_axiom_139,[]) ).
tff(f6203,plain,
spl331_482,
inference(avatar_split_clause,[],[f587,f6201]) ).
tff(f6201,plain,
( spl331_482
<=> ! [X2: $real,X0: $real,X1: $real] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_482])]) ).
tff(f587,plain,
! [X2: $real,X0: $real,X1: $real] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_139,[]) ).
tff(f6199,plain,
spl331_481,
inference(avatar_split_clause,[],[f580,f6197]) ).
tff(f6197,plain,
( spl331_481
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_481])]) ).
tff(f580,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(theory_axiom_139,[]) ).
tff(f6195,plain,
spl331_480,
inference(avatar_split_clause,[],[f569,f6193]) ).
tff(f6193,plain,
( spl331_480
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_480])]) ).
tff(f569,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_139,[]) ).
tff(f6127,plain,
( spl331_479
| ~ spl331_326
| ~ spl331_462 ),
inference(avatar_split_clause,[],[f5970,f5764,f4912,f6125]) ).
tff(f6125,plain,
( spl331_479
<=> ! [X0: $real] : ( f51 != sK18(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_479])]) ).
tff(f5764,plain,
( spl331_462
<=> ! [X0: $real,X1: $real] :
( ( 1.0 = X1 )
| ( f16(f17(f18,X0),X1) != f51 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_462])]) ).
tff(f5970,plain,
( ! [X0: $real] : ( f51 != sK18(X0) )
| ~ spl331_326
| ~ spl331_462 ),
inference(evaluation,[],[f5968]) ).
tff(f5968,plain,
( ! [X0: $real] :
( ( f51 != sK18(X0) )
| ( 0.0 = 1.0 ) )
| ~ spl331_326
| ~ spl331_462 ),
inference(superposition,[],[f5765,f4913]) ).
tff(f5765,plain,
( ! [X0: $real,X1: $real] :
( ( f16(f17(f18,X0),X1) != f51 )
| ( 1.0 = X1 ) )
| ~ spl331_462 ),
inference(avatar_component_clause,[],[f5764]) ).
tff(f5961,plain,
( spl331_478
| spl331_12
| ~ spl331_423 ),
inference(avatar_split_clause,[],[f5574,f5559,f2983,f5958]) ).
tff(f5958,plain,
( spl331_478
<=> ( sK318 = sK24(sK18(sK318)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_478])]) ).
tff(f2983,plain,
( spl331_12
<=> $less(sK318,0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_12])]) ).
tff(f5559,plain,
( spl331_423
<=> ! [X0: $real] :
( ( sK24(sK18(X0)) = X0 )
| $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_423])]) ).
tff(f5574,plain,
( ( sK318 = sK24(sK18(sK318)) )
| spl331_12
| ~ spl331_423 ),
inference(resolution,[],[f5560,f2985]) ).
tff(f2985,plain,
( ~ $less(sK318,0.0)
| spl331_12 ),
inference(avatar_component_clause,[],[f2983]) ).
tff(f5560,plain,
( ! [X0: $real] :
( $less(X0,0.0)
| ( sK24(sK18(X0)) = X0 ) )
| ~ spl331_423 ),
inference(avatar_component_clause,[],[f5559]) ).
tff(f5910,plain,
( ~ spl331_477
| ~ spl331_131
| ~ spl331_436 ),
inference(avatar_split_clause,[],[f5886,f5659,f3502,f5907]) ).
tff(f5907,plain,
( spl331_477
<=> $less(sK40(2.0),1.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_477])]) ).
tff(f3502,plain,
( spl331_131
<=> ! [X0: 'S2'] : ~ $less(f19(f59(f60,2.0),X0),1.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_131])]) ).
tff(f5659,plain,
( spl331_436
<=> ! [X0: $real] : ( f19(f59(f60,X0),f6(f7,2)) = sK40(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_436])]) ).
tff(f5886,plain,
( ~ $less(sK40(2.0),1.0)
| ~ spl331_131
| ~ spl331_436 ),
inference(superposition,[],[f3503,f5660]) ).
tff(f5660,plain,
( ! [X0: $real] : ( f19(f59(f60,X0),f6(f7,2)) = sK40(X0) )
| ~ spl331_436 ),
inference(avatar_component_clause,[],[f5659]) ).
tff(f3503,plain,
( ! [X0: 'S2'] : ~ $less(f19(f59(f60,2.0),X0),1.0)
| ~ spl331_131 ),
inference(avatar_component_clause,[],[f3502]) ).
tff(f5825,plain,
spl331_476,
inference(avatar_split_clause,[],[f2915,f5823]) ).
tff(f5823,plain,
( spl331_476
<=> ! [X1: 'S10'] : ~ $less(f22(f49(f50,sK327),sK24(X1)),sK34(sK22(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_476])]) ).
tff(f2915,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK327),sK24(X1)),sK34(sK22(X1))),
inference(forward_demodulation,[],[f2914,f1573]) ).
tff(f1573,plain,
! [X0: 'S10'] : ( f27(f31,X0) = sK24(X0) ),
inference(cnf_transformation,[],[f947]) ).
tff(f947,plain,
! [X0: 'S10'] :
( ~ $less(sK24(X0),$uminus(sK24(X0)))
& ( f27(f31,X0) = sK24(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f623,f946]) ).
tff(f946,plain,
! [X0: 'S10'] :
( ? [X1: $real] :
( ~ $less(X1,$uminus(X1))
& ( f27(f31,X0) = X1 ) )
=> ( ~ $less(sK24(X0),$uminus(sK24(X0)))
& ( f27(f31,X0) = sK24(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f623,plain,
! [X0: 'S10'] :
? [X1: $real] :
( ~ $less(X1,$uminus(X1))
& ( f27(f31,X0) = X1 ) ),
inference(rectify,[],[f472]) ).
tff(f472,plain,
! [X0: 'S10'] :
? [X15: $real] :
( ~ $less(X15,$uminus(X15))
& ( f27(f31,X0) = X15 ) ),
inference(theory_normalization,[],[f64]) ).
tff(f64,axiom,
! [X0: 'S10'] :
? [X15: $real] :
( $lesseq($uminus(X15),X15)
& ( f27(f31,X0) = X15 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_64) ).
tff(f2914,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK327),f27(f31,X1)),sK34(sK22(X1))),
inference(forward_demodulation,[],[f2913,f1625]) ).
tff(f1625,plain,
! [X0: $real,X1: $real] : ( f22(f49(f50,X0),X1) = f22(f49(f50,X1),X0) ),
inference(cnf_transformation,[],[f417]) ).
tff(f417,axiom,
! [X0: $real,X1: $real] : ( f22(f49(f50,X0),X1) = f22(f49(f50,X1),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_417) ).
tff(f2913,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK327),sK34(sK22(X1))),
inference(forward_demodulation,[],[f2912,f1567]) ).
tff(f1567,plain,
! [X0: 'S10'] : ( f27(f36,X0) = sK22(X0) ),
inference(cnf_transformation,[],[f943]) ).
tff(f943,plain,
! [X0: 'S10'] :
( ( ~ $less(f27(f31,X0),sK22(X0))
| $less(sK22(X0),0.0) )
& ( ~ $less(f27(f31,X0),$uminus(sK22(X0)))
| ~ $less(sK22(X0),0.0) )
& ( f27(f36,X0) = sK22(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f817,f942]) ).
tff(f942,plain,
! [X0: 'S10'] :
( ? [X1: $real] :
( ( ~ $less(f27(f31,X0),X1)
| $less(X1,0.0) )
& ( ~ $less(f27(f31,X0),$uminus(X1))
| ~ $less(X1,0.0) )
& ( f27(f36,X0) = X1 ) )
=> ( ( ~ $less(f27(f31,X0),sK22(X0))
| $less(sK22(X0),0.0) )
& ( ~ $less(f27(f31,X0),$uminus(sK22(X0)))
| ~ $less(sK22(X0),0.0) )
& ( f27(f36,X0) = sK22(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f817,plain,
! [X0: 'S10'] :
? [X1: $real] :
( ( ~ $less(f27(f31,X0),X1)
| $less(X1,0.0) )
& ( ~ $less(f27(f31,X0),$uminus(X1))
| ~ $less(X1,0.0) )
& ( f27(f36,X0) = X1 ) ),
inference(ennf_transformation,[],[f621]) ).
tff(f621,plain,
! [X0: 'S10'] :
? [X1: $real] :
( ( ~ $less(X1,0.0)
=> ~ $less(f27(f31,X0),X1) )
& ( $less(X1,0.0)
=> ~ $less(f27(f31,X0),$uminus(X1)) )
& ( f27(f36,X0) = X1 ) ),
inference(rectify,[],[f470]) ).
tff(f470,plain,
! [X0: 'S10'] :
? [X14: $real] :
( ( ~ $less(X14,0.0)
=> ~ $less(f27(f31,X0),X14) )
& ( $less(X14,0.0)
=> ~ $less(f27(f31,X0),$uminus(X14)) )
& ( f27(f36,X0) = X14 ) ),
inference(theory_normalization,[],[f63]) ).
tff(f63,axiom,
! [X0: 'S10'] :
? [X14: $real] :
( ( ~ $less(X14,0.0)
=> $lesseq(X14,f27(f31,X0)) )
& ( $less(X14,0.0)
=> $lesseq($uminus(X14),f27(f31,X0)) )
& ( f27(f36,X0) = X14 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_63) ).
tff(f2912,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK327),sK34(f27(f36,X1))),
inference(forward_demodulation,[],[f2310,f1593]) ).
tff(f1593,plain,
! [X0: $real] : ( f22(f30,X0) = sK34(X0) ),
inference(cnf_transformation,[],[f966]) ).
tff(f966,plain,
! [X0: $real] :
( ( ( sK34(X0) = sK34(X0) )
| $less(sK34(X0),0.0) )
& ( ( sK34(X0) = $uminus(sK34(X0)) )
| ~ $less(sK34(X0),0.0) )
& ( f22(f30,X0) = sK34(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f820,f965]) ).
tff(f965,plain,
! [X0: $real] :
( ? [X1: $real] :
( ( ( X1 = X1 )
| $less(X1,0.0) )
& ( ( $uminus(X1) = X1 )
| ~ $less(X1,0.0) )
& ( f22(f30,X0) = X1 ) )
=> ( ( ( sK34(X0) = sK34(X0) )
| $less(sK34(X0),0.0) )
& ( ( sK34(X0) = $uminus(sK34(X0)) )
| ~ $less(sK34(X0),0.0) )
& ( f22(f30,X0) = sK34(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f820,plain,
! [X0: $real] :
? [X1: $real] :
( ( ( X1 = X1 )
| $less(X1,0.0) )
& ( ( $uminus(X1) = X1 )
| ~ $less(X1,0.0) )
& ( f22(f30,X0) = X1 ) ),
inference(ennf_transformation,[],[f632]) ).
tff(f632,plain,
! [X0: $real] :
? [X1: $real] :
( ( ~ $less(X1,0.0)
=> ( X1 = X1 ) )
& ( $less(X1,0.0)
=> ( $uminus(X1) = X1 ) )
& ( f22(f30,X0) = X1 ) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X0: $real] :
? [X10: $real] :
( ( ~ $less(X10,0.0)
=> ( X10 = X10 ) )
& ( $less(X10,0.0)
=> ( $uminus(X10) = X10 ) )
& ( f22(f30,X0) = X10 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_29) ).
tff(f2310,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK327),f22(f30,f27(f36,X1))),
inference(cnf_transformation,[],[f1452]) ).
tff(f1452,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK327),f22(f30,f27(f36,X1))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK327])],[f564,f1451]) ).
tff(f1451,plain,
( ? [X0: $real] :
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f22(f30,f27(f36,X1)))
=> ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK327),f22(f30,f27(f36,X1))) ),
introduced(choice_axiom,[]) ).
tff(f564,plain,
? [X0: $real] :
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f22(f30,f27(f36,X1))),
inference(theory_normalization,[],[f124]) ).
tff(f124,axiom,
? [X0: $real] :
! [X1: 'S10'] : $lesseq(f22(f30,f27(f36,X1)),f22(f49(f50,f27(f31,X1)),X0)),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_124) ).
tff(f5821,plain,
spl331_475,
inference(avatar_split_clause,[],[f2911,f5819]) ).
tff(f5819,plain,
( spl331_475
<=> ! [X1: 'S10'] : ~ $less(f22(f49(f50,sK326),sK24(X1)),sK34(sK23(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_475])]) ).
tff(f2911,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK326),sK24(X1)),sK34(sK23(X1))),
inference(forward_demodulation,[],[f2910,f1573]) ).
tff(f2910,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK326),f27(f31,X1)),sK34(sK23(X1))),
inference(forward_demodulation,[],[f2909,f1625]) ).
tff(f2909,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK326),sK34(sK23(X1))),
inference(forward_demodulation,[],[f2908,f1570]) ).
tff(f1570,plain,
! [X0: 'S10'] : ( f27(f28,X0) = sK23(X0) ),
inference(cnf_transformation,[],[f945]) ).
tff(f945,plain,
! [X0: 'S10'] :
( ( ~ $less(f27(f31,X0),sK23(X0))
| $less(sK23(X0),0.0) )
& ( ~ $less(f27(f31,X0),$uminus(sK23(X0)))
| ~ $less(sK23(X0),0.0) )
& ( f27(f28,X0) = sK23(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f818,f944]) ).
tff(f944,plain,
! [X0: 'S10'] :
( ? [X1: $real] :
( ( ~ $less(f27(f31,X0),X1)
| $less(X1,0.0) )
& ( ~ $less(f27(f31,X0),$uminus(X1))
| ~ $less(X1,0.0) )
& ( f27(f28,X0) = X1 ) )
=> ( ( ~ $less(f27(f31,X0),sK23(X0))
| $less(sK23(X0),0.0) )
& ( ~ $less(f27(f31,X0),$uminus(sK23(X0)))
| ~ $less(sK23(X0),0.0) )
& ( f27(f28,X0) = sK23(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f818,plain,
! [X0: 'S10'] :
? [X1: $real] :
( ( ~ $less(f27(f31,X0),X1)
| $less(X1,0.0) )
& ( ~ $less(f27(f31,X0),$uminus(X1))
| ~ $less(X1,0.0) )
& ( f27(f28,X0) = X1 ) ),
inference(ennf_transformation,[],[f622]) ).
tff(f622,plain,
! [X0: 'S10'] :
? [X1: $real] :
( ( ~ $less(X1,0.0)
=> ~ $less(f27(f31,X0),X1) )
& ( $less(X1,0.0)
=> ~ $less(f27(f31,X0),$uminus(X1)) )
& ( f27(f28,X0) = X1 ) ),
inference(rectify,[],[f471]) ).
tff(f471,plain,
! [X0: 'S10'] :
? [X12: $real] :
( ( ~ $less(X12,0.0)
=> ~ $less(f27(f31,X0),X12) )
& ( $less(X12,0.0)
=> ~ $less(f27(f31,X0),$uminus(X12)) )
& ( f27(f28,X0) = X12 ) ),
inference(theory_normalization,[],[f34]) ).
tff(f34,axiom,
! [X0: 'S10'] :
? [X12: $real] :
( ( ~ $less(X12,0.0)
=> $lesseq(X12,f27(f31,X0)) )
& ( $less(X12,0.0)
=> $lesseq($uminus(X12),f27(f31,X0)) )
& ( f27(f28,X0) = X12 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_34) ).
tff(f2908,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK326),sK34(f27(f28,X1))),
inference(forward_demodulation,[],[f2309,f1593]) ).
tff(f2309,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK326),f22(f30,f27(f28,X1))),
inference(cnf_transformation,[],[f1450]) ).
tff(f1450,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK326),f22(f30,f27(f28,X1))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK326])],[f563,f1449]) ).
tff(f1449,plain,
( ? [X0: $real] :
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f22(f30,f27(f28,X1)))
=> ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK326),f22(f30,f27(f28,X1))) ),
introduced(choice_axiom,[]) ).
tff(f563,plain,
? [X0: $real] :
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f22(f30,f27(f28,X1))),
inference(theory_normalization,[],[f129]) ).
tff(f129,axiom,
? [X0: $real] :
! [X1: 'S10'] : $lesseq(f22(f30,f27(f28,X1)),f22(f49(f50,f27(f31,X1)),X0)),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_129) ).
tff(f5817,plain,
( spl331_474
| spl331_11
| ~ spl331_423 ),
inference(avatar_split_clause,[],[f5573,f5559,f2978,f5814]) ).
tff(f5814,plain,
( spl331_474
<=> ( sK317 = sK24(sK18(sK317)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_474])]) ).
tff(f2978,plain,
( spl331_11
<=> $less(sK317,0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_11])]) ).
tff(f5573,plain,
( ( sK317 = sK24(sK18(sK317)) )
| spl331_11
| ~ spl331_423 ),
inference(resolution,[],[f5560,f2980]) ).
tff(f2980,plain,
( ~ $less(sK317,0.0)
| spl331_11 ),
inference(avatar_component_clause,[],[f2978]) ).
tff(f5812,plain,
spl331_473,
inference(avatar_split_clause,[],[f2904,f5810]) ).
tff(f5810,plain,
( spl331_473
<=> ! [X1: $real] : ~ $less(f22(f49(f50,sK324),sK34(X1)),sK24(sK18(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_473])]) ).
tff(f2904,plain,
! [X1: $real] : ~ $less(f22(f49(f50,sK324),sK34(X1)),sK24(sK18(X1))),
inference(forward_demodulation,[],[f2903,f1593]) ).
tff(f2903,plain,
! [X1: $real] : ~ $less(f22(f49(f50,sK324),f22(f30,X1)),sK24(sK18(X1))),
inference(forward_demodulation,[],[f2902,f1625]) ).
tff(f2902,plain,
! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK324),sK24(sK18(X1))),
inference(forward_demodulation,[],[f2901,f1559]) ).
tff(f1559,plain,
! [X0: $real] : ( f16(f32,X0) = sK18(X0) ),
inference(cnf_transformation,[],[f935]) ).
tff(f935,plain,
! [X0: $real] :
( ( sK18(X0) = f34(f35,sK18(X0)) )
& ( f16(f32,X0) = sK18(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f617,f934]) ).
tff(f934,plain,
! [X0: $real] :
( ? [X1: 'S10'] :
( ( f34(f35,X1) = X1 )
& ( f16(f32,X0) = X1 ) )
=> ( ( sK18(X0) = f34(f35,sK18(X0)) )
& ( f16(f32,X0) = sK18(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f617,plain,
! [X0: $real] :
? [X1: 'S10'] :
( ( f34(f35,X1) = X1 )
& ( f16(f32,X0) = X1 ) ),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X0: $real] :
? [X9: 'S10'] :
( ( f34(f35,X9) = X9 )
& ( f16(f32,X0) = X9 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_28) ).
tff(f2901,plain,
! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK324),sK24(f16(f32,X1))),
inference(forward_demodulation,[],[f2307,f1573]) ).
tff(f2307,plain,
! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK324),f27(f31,f16(f32,X1))),
inference(cnf_transformation,[],[f1446]) ).
tff(f1446,plain,
! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK324),f27(f31,f16(f32,X1))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK324])],[f561,f1445]) ).
tff(f1445,plain,
( ? [X0: $real] :
! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),X0),f27(f31,f16(f32,X1)))
=> ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK324),f27(f31,f16(f32,X1))) ),
introduced(choice_axiom,[]) ).
tff(f561,plain,
? [X0: $real] :
! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),X0),f27(f31,f16(f32,X1))),
inference(theory_normalization,[],[f51]) ).
tff(f51,axiom,
? [X0: $real] :
! [X1: $real] : $lesseq(f27(f31,f16(f32,X1)),f22(f49(f50,f22(f30,X1)),X0)),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_51) ).
tff(f5808,plain,
spl331_472,
inference(avatar_split_clause,[],[f2887,f5806]) ).
tff(f5806,plain,
( spl331_472
<=> ! [X1: 'S10'] : ~ $less(f22(f49(f50,sK320),sK24(X1)),sK34(sK22(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_472])]) ).
tff(f2887,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK320),sK24(X1)),sK34(sK22(X1))),
inference(forward_demodulation,[],[f2886,f1573]) ).
tff(f2886,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK320),f27(f31,X1)),sK34(sK22(X1))),
inference(forward_demodulation,[],[f2885,f1625]) ).
tff(f2885,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK320),sK34(sK22(X1))),
inference(forward_demodulation,[],[f2884,f1567]) ).
tff(f2884,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK320),sK34(f27(f36,X1))),
inference(forward_demodulation,[],[f2300,f1593]) ).
tff(f2300,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK320),f22(f30,f27(f36,X1))),
inference(cnf_transformation,[],[f1438]) ).
tff(f1438,plain,
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK320),f22(f30,f27(f36,X1)))
& ~ $less(sK320,0.0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK320])],[f557,f1437]) ).
tff(f1437,plain,
( ? [X0: $real] :
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f22(f30,f27(f36,X1)))
& ~ $less(X0,0.0) )
=> ( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK320),f22(f30,f27(f36,X1)))
& ~ $less(sK320,0.0) ) ),
introduced(choice_axiom,[]) ).
tff(f557,plain,
? [X0: $real] :
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f22(f30,f27(f36,X1)))
& ~ $less(X0,0.0) ),
inference(theory_normalization,[],[f126]) ).
tff(f126,axiom,
? [X0: $real] :
( ! [X1: 'S10'] : $lesseq(f22(f30,f27(f36,X1)),f22(f49(f50,f27(f31,X1)),X0))
& $lesseq(0.0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_126) ).
tff(f5804,plain,
spl331_471,
inference(avatar_split_clause,[],[f2883,f5802]) ).
tff(f5802,plain,
( spl331_471
<=> ! [X1: 'S10'] : ~ $less(f22(f49(f50,sK319),sK24(X1)),sK34(sK23(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_471])]) ).
tff(f2883,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK319),sK24(X1)),sK34(sK23(X1))),
inference(forward_demodulation,[],[f2882,f1573]) ).
tff(f2882,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK319),f27(f31,X1)),sK34(sK23(X1))),
inference(forward_demodulation,[],[f2881,f1625]) ).
tff(f2881,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK319),sK34(sK23(X1))),
inference(forward_demodulation,[],[f2880,f1570]) ).
tff(f2880,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK319),sK34(f27(f28,X1))),
inference(forward_demodulation,[],[f2298,f1593]) ).
tff(f2298,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK319),f22(f30,f27(f28,X1))),
inference(cnf_transformation,[],[f1436]) ).
tff(f1436,plain,
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK319),f22(f30,f27(f28,X1)))
& ~ $less(sK319,0.0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK319])],[f556,f1435]) ).
tff(f1435,plain,
( ? [X0: $real] :
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f22(f30,f27(f28,X1)))
& ~ $less(X0,0.0) )
=> ( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK319),f22(f30,f27(f28,X1)))
& ~ $less(sK319,0.0) ) ),
introduced(choice_axiom,[]) ).
tff(f556,plain,
? [X0: $real] :
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f22(f30,f27(f28,X1)))
& ~ $less(X0,0.0) ),
inference(theory_normalization,[],[f127]) ).
tff(f127,axiom,
? [X0: $real] :
( ! [X1: 'S10'] : $lesseq(f22(f30,f27(f28,X1)),f22(f49(f50,f27(f31,X1)),X0))
& $lesseq(0.0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_127) ).
tff(f5800,plain,
spl331_470,
inference(avatar_split_clause,[],[f2876,f5798]) ).
tff(f5798,plain,
( spl331_470
<=> ! [X1: $real] : ~ $less(f22(f49(f50,sK317),sK34(X1)),sK24(sK18(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_470])]) ).
tff(f2876,plain,
! [X1: $real] : ~ $less(f22(f49(f50,sK317),sK34(X1)),sK24(sK18(X1))),
inference(forward_demodulation,[],[f2875,f1593]) ).
tff(f2875,plain,
! [X1: $real] : ~ $less(f22(f49(f50,sK317),f22(f30,X1)),sK24(sK18(X1))),
inference(forward_demodulation,[],[f2874,f1625]) ).
tff(f2874,plain,
! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK317),sK24(sK18(X1))),
inference(forward_demodulation,[],[f2873,f1559]) ).
tff(f2873,plain,
! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK317),sK24(f16(f32,X1))),
inference(forward_demodulation,[],[f2294,f1573]) ).
tff(f2294,plain,
! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK317),f27(f31,f16(f32,X1))),
inference(cnf_transformation,[],[f1432]) ).
tff(f1432,plain,
( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK317),f27(f31,f16(f32,X1)))
& ~ $less(sK317,0.0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK317])],[f554,f1431]) ).
tff(f1431,plain,
( ? [X0: $real] :
( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),X0),f27(f31,f16(f32,X1)))
& ~ $less(X0,0.0) )
=> ( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK317),f27(f31,f16(f32,X1)))
& ~ $less(sK317,0.0) ) ),
introduced(choice_axiom,[]) ).
tff(f554,plain,
? [X0: $real] :
( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),X0),f27(f31,f16(f32,X1)))
& ~ $less(X0,0.0) ),
inference(theory_normalization,[],[f55]) ).
tff(f55,axiom,
? [X0: $real] :
( ! [X1: $real] : $lesseq(f27(f31,f16(f32,X1)),f22(f49(f50,f22(f30,X1)),X0))
& $lesseq(0.0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_55) ).
tff(f5796,plain,
spl331_469,
inference(avatar_split_clause,[],[f2859,f5794]) ).
tff(f5794,plain,
( spl331_469
<=> ! [X1: 'S10'] : ~ $less(f22(f49(f50,sK313),sK24(X1)),sK34(sK23(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_469])]) ).
tff(f2859,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK313),sK24(X1)),sK34(sK23(X1))),
inference(forward_demodulation,[],[f2858,f1573]) ).
tff(f2858,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK313),f27(f31,X1)),sK34(sK23(X1))),
inference(forward_demodulation,[],[f2857,f1625]) ).
tff(f2857,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK313),sK34(sK23(X1))),
inference(forward_demodulation,[],[f2856,f1570]) ).
tff(f2856,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK313),sK34(f27(f28,X1))),
inference(forward_demodulation,[],[f2286,f1593]) ).
tff(f2286,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK313),f22(f30,f27(f28,X1))),
inference(cnf_transformation,[],[f1424]) ).
tff(f1424,plain,
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK313),f22(f30,f27(f28,X1)))
& $less(0.0,sK313) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK313])],[f550,f1423]) ).
tff(f1423,plain,
( ? [X0: $real] :
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f22(f30,f27(f28,X1)))
& $less(0.0,X0) )
=> ( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK313),f22(f30,f27(f28,X1)))
& $less(0.0,sK313) ) ),
introduced(choice_axiom,[]) ).
tff(f550,plain,
? [X0: $real] :
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f22(f30,f27(f28,X1)))
& $less(0.0,X0) ),
inference(theory_normalization,[],[f128]) ).
tff(f128,axiom,
? [X0: $real] :
( ! [X1: 'S10'] : $lesseq(f22(f30,f27(f28,X1)),f22(f49(f50,f27(f31,X1)),X0))
& $less(0.0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_128) ).
tff(f5792,plain,
spl331_468,
inference(avatar_split_clause,[],[f2855,f5790]) ).
tff(f5790,plain,
( spl331_468
<=> ! [X1: 'S10'] : ~ $less(f22(f49(f50,sK312),sK24(X1)),sK34(sK22(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_468])]) ).
tff(f2855,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK312),sK24(X1)),sK34(sK22(X1))),
inference(forward_demodulation,[],[f2854,f1573]) ).
tff(f2854,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK312),f27(f31,X1)),sK34(sK22(X1))),
inference(forward_demodulation,[],[f2853,f1625]) ).
tff(f2853,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK312),sK34(sK22(X1))),
inference(forward_demodulation,[],[f2852,f1567]) ).
tff(f2852,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK312),sK34(f27(f36,X1))),
inference(forward_demodulation,[],[f2284,f1593]) ).
tff(f2284,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK312),f22(f30,f27(f36,X1))),
inference(cnf_transformation,[],[f1422]) ).
tff(f1422,plain,
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK312),f22(f30,f27(f36,X1)))
& $less(0.0,sK312) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK312])],[f549,f1421]) ).
tff(f1421,plain,
( ? [X0: $real] :
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f22(f30,f27(f36,X1)))
& $less(0.0,X0) )
=> ( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK312),f22(f30,f27(f36,X1)))
& $less(0.0,sK312) ) ),
introduced(choice_axiom,[]) ).
tff(f549,plain,
? [X0: $real] :
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f22(f30,f27(f36,X1)))
& $less(0.0,X0) ),
inference(theory_normalization,[],[f125]) ).
tff(f125,axiom,
? [X0: $real] :
( ! [X1: 'S10'] : $lesseq(f22(f30,f27(f36,X1)),f22(f49(f50,f27(f31,X1)),X0))
& $less(0.0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_125) ).
tff(f5788,plain,
spl331_467,
inference(avatar_split_clause,[],[f2848,f5786]) ).
tff(f5786,plain,
( spl331_467
<=> ! [X1: $real] : ~ $less(f22(f49(f50,sK310),sK34(X1)),sK24(sK18(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_467])]) ).
tff(f2848,plain,
! [X1: $real] : ~ $less(f22(f49(f50,sK310),sK34(X1)),sK24(sK18(X1))),
inference(forward_demodulation,[],[f2847,f1593]) ).
tff(f2847,plain,
! [X1: $real] : ~ $less(f22(f49(f50,sK310),f22(f30,X1)),sK24(sK18(X1))),
inference(forward_demodulation,[],[f2846,f1625]) ).
tff(f2846,plain,
! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK310),sK24(sK18(X1))),
inference(forward_demodulation,[],[f2845,f1559]) ).
tff(f2845,plain,
! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK310),sK24(f16(f32,X1))),
inference(forward_demodulation,[],[f2280,f1573]) ).
tff(f2280,plain,
! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK310),f27(f31,f16(f32,X1))),
inference(cnf_transformation,[],[f1418]) ).
tff(f1418,plain,
( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK310),f27(f31,f16(f32,X1)))
& $less(0.0,sK310) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK310])],[f547,f1417]) ).
tff(f1417,plain,
( ? [X0: $real] :
( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),X0),f27(f31,f16(f32,X1)))
& $less(0.0,X0) )
=> ( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK310),f27(f31,f16(f32,X1)))
& $less(0.0,sK310) ) ),
introduced(choice_axiom,[]) ).
tff(f547,plain,
? [X0: $real] :
( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),X0),f27(f31,f16(f32,X1)))
& $less(0.0,X0) ),
inference(theory_normalization,[],[f53]) ).
tff(f53,axiom,
? [X0: $real] :
( ! [X1: $real] : $lesseq(f27(f31,f16(f32,X1)),f22(f49(f50,f22(f30,X1)),X0))
& $less(0.0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_53) ).
tff(f5784,plain,
spl331_466,
inference(avatar_split_clause,[],[f2617,f5782]) ).
tff(f5782,plain,
( spl331_466
<=> ! [X0: $real,X1: $real] : ( sK107(X0,X1) = $sum(sK34(X0),$uminus(sK34(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_466])]) ).
tff(f2617,plain,
! [X0: $real,X1: $real] : ( sK107(X0,X1) = $sum(sK34(X0),$uminus(sK34(X1))) ),
inference(forward_demodulation,[],[f2616,f1593]) ).
tff(f2616,plain,
! [X0: $real,X1: $real] : ( sK107(X0,X1) = $sum(f22(f30,X0),$uminus(sK34(X1))) ),
inference(forward_demodulation,[],[f1845,f1593]) ).
tff(f1845,plain,
! [X0: $real,X1: $real] : ( $sum(f22(f30,X0),$uminus(f22(f30,X1))) = sK107(X0,X1) ),
inference(cnf_transformation,[],[f1127]) ).
tff(f1127,plain,
! [X0: $real,X1: $real] :
( ( ~ $less(f22(f30,$sum(X0,$uminus(X1))),sK107(X0,X1))
| $less(sK107(X0,X1),0.0) )
& ( ~ $less(f22(f30,$sum(X0,$uminus(X1))),$uminus(sK107(X0,X1)))
| ~ $less(sK107(X0,X1),0.0) )
& ( $sum(f22(f30,X0),$uminus(f22(f30,X1))) = sK107(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK107])],[f858,f1126]) ).
tff(f1126,plain,
! [X0: $real,X1: $real] :
( ? [X2: $real] :
( ( ~ $less(f22(f30,$sum(X0,$uminus(X1))),X2)
| $less(X2,0.0) )
& ( ~ $less(f22(f30,$sum(X0,$uminus(X1))),$uminus(X2))
| ~ $less(X2,0.0) )
& ( $sum(f22(f30,X0),$uminus(f22(f30,X1))) = X2 ) )
=> ( ( ~ $less(f22(f30,$sum(X0,$uminus(X1))),sK107(X0,X1))
| $less(sK107(X0,X1),0.0) )
& ( ~ $less(f22(f30,$sum(X0,$uminus(X1))),$uminus(sK107(X0,X1)))
| ~ $less(sK107(X0,X1),0.0) )
& ( $sum(f22(f30,X0),$uminus(f22(f30,X1))) = sK107(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f858,plain,
! [X0: $real,X1: $real] :
? [X2: $real] :
( ( ~ $less(f22(f30,$sum(X0,$uminus(X1))),X2)
| $less(X2,0.0) )
& ( ~ $less(f22(f30,$sum(X0,$uminus(X1))),$uminus(X2))
| ~ $less(X2,0.0) )
& ( $sum(f22(f30,X0),$uminus(f22(f30,X1))) = X2 ) ),
inference(ennf_transformation,[],[f685]) ).
tff(f685,plain,
! [X0: $real,X1: $real] :
? [X2: $real] :
( ( ~ $less(X2,0.0)
=> ~ $less(f22(f30,$sum(X0,$uminus(X1))),X2) )
& ( $less(X2,0.0)
=> ~ $less(f22(f30,$sum(X0,$uminus(X1))),$uminus(X2)) )
& ( $sum(f22(f30,X0),$uminus(f22(f30,X1))) = X2 ) ),
inference(rectify,[],[f511]) ).
tff(f511,plain,
! [X0: $real,X1: $real] :
? [X219: $real] :
( ( ~ $less(X219,0.0)
=> ~ $less(f22(f30,$sum(X0,$uminus(X1))),X219) )
& ( $less(X219,0.0)
=> ~ $less(f22(f30,$sum(X0,$uminus(X1))),$uminus(X219)) )
& ( $sum(f22(f30,X0),$uminus(f22(f30,X1))) = X219 ) ),
inference(theory_normalization,[],[f369]) ).
tff(f369,axiom,
! [X0: $real,X1: $real] :
? [X219: $real] :
( ( ~ $less(X219,0.0)
=> $lesseq(X219,f22(f30,$difference(X0,X1))) )
& ( $less(X219,0.0)
=> $lesseq($uminus(X219),f22(f30,$difference(X0,X1))) )
& ( $difference(f22(f30,X0),f22(f30,X1)) = X219 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_369) ).
tff(f5780,plain,
spl331_465,
inference(avatar_split_clause,[],[f2613,f5778]) ).
tff(f5778,plain,
( spl331_465
<=> ! [X0: 'S10',X1: 'S10'] : ( sK106(X0,X1) = $sum(sK24(X0),$uminus(sK24(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_465])]) ).
tff(f2613,plain,
! [X0: 'S10',X1: 'S10'] : ( sK106(X0,X1) = $sum(sK24(X0),$uminus(sK24(X1))) ),
inference(forward_demodulation,[],[f2612,f1573]) ).
tff(f2612,plain,
! [X0: 'S10',X1: 'S10'] : ( sK106(X0,X1) = $sum(f27(f31,X0),$uminus(sK24(X1))) ),
inference(forward_demodulation,[],[f1842,f1573]) ).
tff(f1842,plain,
! [X0: 'S10',X1: 'S10'] : ( $sum(f27(f31,X0),$uminus(f27(f31,X1))) = sK106(X0,X1) ),
inference(cnf_transformation,[],[f1125]) ).
tff(f1125,plain,
! [X0: 'S10',X1: 'S10'] :
( ( ~ $less(f27(f31,f34(f39(f61,X0),X1)),sK106(X0,X1))
| $less(sK106(X0,X1),0.0) )
& ( ~ $less(f27(f31,f34(f39(f61,X0),X1)),$uminus(sK106(X0,X1)))
| ~ $less(sK106(X0,X1),0.0) )
& ( $sum(f27(f31,X0),$uminus(f27(f31,X1))) = sK106(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK106])],[f857,f1124]) ).
tff(f1124,plain,
! [X0: 'S10',X1: 'S10'] :
( ? [X2: $real] :
( ( ~ $less(f27(f31,f34(f39(f61,X0),X1)),X2)
| $less(X2,0.0) )
& ( ~ $less(f27(f31,f34(f39(f61,X0),X1)),$uminus(X2))
| ~ $less(X2,0.0) )
& ( $sum(f27(f31,X0),$uminus(f27(f31,X1))) = X2 ) )
=> ( ( ~ $less(f27(f31,f34(f39(f61,X0),X1)),sK106(X0,X1))
| $less(sK106(X0,X1),0.0) )
& ( ~ $less(f27(f31,f34(f39(f61,X0),X1)),$uminus(sK106(X0,X1)))
| ~ $less(sK106(X0,X1),0.0) )
& ( $sum(f27(f31,X0),$uminus(f27(f31,X1))) = sK106(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f857,plain,
! [X0: 'S10',X1: 'S10'] :
? [X2: $real] :
( ( ~ $less(f27(f31,f34(f39(f61,X0),X1)),X2)
| $less(X2,0.0) )
& ( ~ $less(f27(f31,f34(f39(f61,X0),X1)),$uminus(X2))
| ~ $less(X2,0.0) )
& ( $sum(f27(f31,X0),$uminus(f27(f31,X1))) = X2 ) ),
inference(ennf_transformation,[],[f684]) ).
tff(f684,plain,
! [X0: 'S10',X1: 'S10'] :
? [X2: $real] :
( ( ~ $less(X2,0.0)
=> ~ $less(f27(f31,f34(f39(f61,X0),X1)),X2) )
& ( $less(X2,0.0)
=> ~ $less(f27(f31,f34(f39(f61,X0),X1)),$uminus(X2)) )
& ( $sum(f27(f31,X0),$uminus(f27(f31,X1))) = X2 ) ),
inference(rectify,[],[f510]) ).
tff(f510,plain,
! [X0: 'S10',X1: 'S10'] :
? [X220: $real] :
( ( ~ $less(X220,0.0)
=> ~ $less(f27(f31,f34(f39(f61,X0),X1)),X220) )
& ( $less(X220,0.0)
=> ~ $less(f27(f31,f34(f39(f61,X0),X1)),$uminus(X220)) )
& ( $sum(f27(f31,X0),$uminus(f27(f31,X1))) = X220 ) ),
inference(theory_normalization,[],[f370]) ).
tff(f370,axiom,
! [X0: 'S10',X1: 'S10'] :
? [X220: $real] :
( ( ~ $less(X220,0.0)
=> $lesseq(X220,f27(f31,f34(f39(f61,X0),X1))) )
& ( $less(X220,0.0)
=> $lesseq($uminus(X220),f27(f31,f34(f39(f61,X0),X1))) )
& ( $difference(f27(f31,X0),f27(f31,X1)) = X220 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_370) ).
tff(f5776,plain,
spl331_464,
inference(avatar_split_clause,[],[f2361,f5774]) ).
tff(f5774,plain,
( spl331_464
<=> ! [X0: $real,X1: $real] : ~ $less($sum(sK34(X0),sK34(X1)),sK34($sum(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_464])]) ).
tff(f2361,plain,
! [X0: $real,X1: $real] : ~ $less($sum(sK34(X0),sK34(X1)),sK34($sum(X0,X1))),
inference(forward_demodulation,[],[f2360,f1593]) ).
tff(f2360,plain,
! [X0: $real,X1: $real] : ~ $less($sum(f22(f30,X0),sK34(X1)),sK34($sum(X0,X1))),
inference(forward_demodulation,[],[f2359,f1593]) ).
tff(f2359,plain,
! [X0: $real,X1: $real] : ~ $less($sum(f22(f30,X0),f22(f30,X1)),sK34($sum(X0,X1))),
inference(forward_demodulation,[],[f1634,f1593]) ).
tff(f1634,plain,
! [X0: $real,X1: $real] : ~ $less($sum(f22(f30,X0),f22(f30,X1)),f22(f30,$sum(X0,X1))),
inference(cnf_transformation,[],[f488]) ).
tff(f488,plain,
! [X0: $real,X1: $real] : ~ $less($sum(f22(f30,X0),f22(f30,X1)),f22(f30,$sum(X0,X1))),
inference(theory_normalization,[],[f105]) ).
tff(f105,axiom,
! [X0: $real,X1: $real] : $lesseq(f22(f30,$sum(X0,X1)),$sum(f22(f30,X0),f22(f30,X1))),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_105) ).
tff(f5770,plain,
spl331_463,
inference(avatar_split_clause,[],[f2256,f5768]) ).
tff(f5768,plain,
( spl331_463
<=> ! [X0: $real,X3: $real,X2: $real,X1: $real] : ( $sum(X1,$uminus(X3)) = sK302(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_463])]) ).
tff(f2256,plain,
! [X2: $real,X3: $real,X0: $real,X1: $real] : ( $sum(X1,$uminus(X3)) = sK302(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1406]) ).
tff(f1406,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ( $sum($sum(f22(sK301(X0,X1,X2,X3),sK302(X0,X1,X2,X3)),f22(sK301(X0,X1,X2,X3),X3)),f22(sK300(X0,X1,X2,X3),sK302(X0,X1,X2,X3))) = $sum(f22(f49(f50,X0),X1),$uminus(f22(sK300(X0,X1,X2,X3),X3))) )
& ( $sum(X1,$uminus(X3)) = sK302(X0,X1,X2,X3) )
& ( f49(f50,$sum(X0,$uminus(X2))) = sK301(X0,X1,X2,X3) )
& ( f49(f50,X2) = sK300(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK300,sK301,sK302])],[f798,f1405]) ).
tff(f1405,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ? [X4: 'S14',X5: 'S14',X6: $real] :
( ( $sum($sum(f22(X5,X6),f22(X5,X3)),f22(X4,X6)) = $sum(f22(f49(f50,X0),X1),$uminus(f22(X4,X3))) )
& ( $sum(X1,$uminus(X3)) = X6 )
& ( f49(f50,$sum(X0,$uminus(X2))) = X5 )
& ( f49(f50,X2) = X4 ) )
=> ( ( $sum($sum(f22(sK301(X0,X1,X2,X3),sK302(X0,X1,X2,X3)),f22(sK301(X0,X1,X2,X3),X3)),f22(sK300(X0,X1,X2,X3),sK302(X0,X1,X2,X3))) = $sum(f22(f49(f50,X0),X1),$uminus(f22(sK300(X0,X1,X2,X3),X3))) )
& ( $sum(X1,$uminus(X3)) = sK302(X0,X1,X2,X3) )
& ( f49(f50,$sum(X0,$uminus(X2))) = sK301(X0,X1,X2,X3) )
& ( f49(f50,X2) = sK300(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f798,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X4: 'S14',X5: 'S14',X6: $real] :
( ( $sum($sum(f22(X5,X6),f22(X5,X3)),f22(X4,X6)) = $sum(f22(f49(f50,X0),X1),$uminus(f22(X4,X3))) )
& ( $sum(X1,$uminus(X3)) = X6 )
& ( f49(f50,$sum(X0,$uminus(X2))) = X5 )
& ( f49(f50,X2) = X4 ) ),
inference(rectify,[],[f541]) ).
tff(f541,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X235: 'S14',X236: 'S14',X237: $real] :
( ( $sum($sum(f22(X236,X237),f22(X236,X3)),f22(X235,X237)) = $sum(f22(f49(f50,X0),X1),$uminus(f22(X235,X3))) )
& ( $sum(X1,$uminus(X3)) = X237 )
& ( f49(f50,$sum(X0,$uminus(X2))) = X236 )
& ( f49(f50,X2) = X235 ) ),
inference(theory_normalization,[],[f385]) ).
tff(f385,axiom,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X235: 'S14',X236: 'S14',X237: $real] :
( ( $difference(f22(f49(f50,X0),X1),f22(X235,X3)) = $sum($sum(f22(X236,X237),f22(X236,X3)),f22(X235,X237)) )
& ( $difference(X1,X3) = X237 )
& ( f49(f50,$difference(X0,X2)) = X236 )
& ( f49(f50,X2) = X235 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_385) ).
tff(f5766,plain,
spl331_462,
inference(avatar_split_clause,[],[f1726,f5764]) ).
tff(f1726,plain,
! [X0: $real,X1: $real] :
( ( 1.0 = X1 )
| ( f16(f17(f18,X0),X1) != f51 ) ),
inference(cnf_transformation,[],[f1012]) ).
tff(f1012,plain,
! [X0: $real,X1: $real] :
( ( ( f16(f17(f18,X0),X1) = f51 )
| ( 1.0 != X1 )
| ( 0.0 != X0 ) )
& ( ( ( 1.0 = X1 )
& ( 0.0 = X0 ) )
| ( f16(f17(f18,X0),X1) != f51 ) ) ),
inference(flattening,[],[f1011]) ).
tff(f1011,plain,
! [X0: $real,X1: $real] :
( ( ( f16(f17(f18,X0),X1) = f51 )
| ( 1.0 != X1 )
| ( 0.0 != X0 ) )
& ( ( ( 1.0 = X1 )
& ( 0.0 = X0 ) )
| ( f16(f17(f18,X0),X1) != f51 ) ) ),
inference(nnf_transformation,[],[f123]) ).
tff(f123,axiom,
! [X0: $real,X1: $real] :
( ( f16(f17(f18,X0),X1) = f51 )
<=> ( ( 1.0 = X1 )
& ( 0.0 = X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_123) ).
tff(f5762,plain,
spl331_461,
inference(avatar_split_clause,[],[f1725,f5760]) ).
tff(f5760,plain,
( spl331_461
<=> ! [X0: $real,X1: $real] :
( ( 0.0 = X0 )
| ( f16(f17(f18,X0),X1) != f51 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_461])]) ).
tff(f1725,plain,
! [X0: $real,X1: $real] :
( ( 0.0 = X0 )
| ( f16(f17(f18,X0),X1) != f51 ) ),
inference(cnf_transformation,[],[f1012]) ).
tff(f5758,plain,
spl331_460,
inference(avatar_split_clause,[],[f1724,f5756]) ).
tff(f5756,plain,
( spl331_460
<=> ! [X0: $real,X1: $real] :
( ( f22(f33,X0) = f22(f33,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_460])]) ).
tff(f1724,plain,
! [X0: $real,X1: $real] :
( ( f22(f33,X0) = f22(f33,X1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1010]) ).
tff(f1010,plain,
! [X0: $real,X1: $real] :
( ( ( f22(f33,X0) = f22(f33,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( f22(f33,X0) != f22(f33,X1) ) ) ),
inference(nnf_transformation,[],[f37]) ).
tff(f37,axiom,
! [X0: $real,X1: $real] :
( ( f22(f33,X0) = f22(f33,X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_37) ).
tff(f5754,plain,
spl331_459,
inference(avatar_split_clause,[],[f1723,f5752]) ).
tff(f5752,plain,
( spl331_459
<=> ! [X0: $real,X1: $real] :
( ( X0 = X1 )
| ( f22(f33,X0) != f22(f33,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_459])]) ).
tff(f1723,plain,
! [X0: $real,X1: $real] :
( ( X0 = X1 )
| ( f22(f33,X0) != f22(f33,X1) ) ),
inference(cnf_transformation,[],[f1010]) ).
tff(f5750,plain,
spl331_458,
inference(avatar_split_clause,[],[f1722,f5748]) ).
tff(f5748,plain,
( spl331_458
<=> ! [X0: 'S10',X1: 'S10'] :
( ( f34(f35,X0) = f34(f35,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_458])]) ).
tff(f1722,plain,
! [X0: 'S10',X1: 'S10'] :
( ( f34(f35,X0) = f34(f35,X1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1009]) ).
tff(f1009,plain,
! [X0: 'S10',X1: 'S10'] :
( ( ( f34(f35,X0) = f34(f35,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( f34(f35,X0) != f34(f35,X1) ) ) ),
inference(nnf_transformation,[],[f35]) ).
tff(f35,axiom,
! [X0: 'S10',X1: 'S10'] :
( ( f34(f35,X0) = f34(f35,X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_35) ).
tff(f5746,plain,
spl331_457,
inference(avatar_split_clause,[],[f1721,f5744]) ).
tff(f5744,plain,
( spl331_457
<=> ! [X0: 'S10',X1: 'S10'] :
( ( X0 = X1 )
| ( f34(f35,X0) != f34(f35,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_457])]) ).
tff(f1721,plain,
! [X0: 'S10',X1: 'S10'] :
( ( X0 = X1 )
| ( f34(f35,X0) != f34(f35,X1) ) ),
inference(cnf_transformation,[],[f1009]) ).
tff(f5742,plain,
spl331_456,
inference(avatar_split_clause,[],[f1720,f5740]) ).
tff(f5740,plain,
( spl331_456
<=> ! [X0: 'S2',X1: 'S2'] :
( ( f11(f12,X0) = f11(f12,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_456])]) ).
tff(f1720,plain,
! [X0: 'S2',X1: 'S2'] :
( ( f11(f12,X0) = f11(f12,X1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1008]) ).
tff(f1008,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ( f11(f12,X0) = f11(f12,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( f11(f12,X0) != f11(f12,X1) ) ) ),
inference(nnf_transformation,[],[f7]) ).
tff(f7,axiom,
! [X0: 'S2',X1: 'S2'] :
( ( f11(f12,X0) = f11(f12,X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_7) ).
tff(f5738,plain,
spl331_455,
inference(avatar_split_clause,[],[f1719,f5736]) ).
tff(f5736,plain,
( spl331_455
<=> ! [X0: 'S2',X1: 'S2'] :
( ( X0 = X1 )
| ( f11(f12,X0) != f11(f12,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_455])]) ).
tff(f1719,plain,
! [X0: 'S2',X1: 'S2'] :
( ( X0 = X1 )
| ( f11(f12,X0) != f11(f12,X1) ) ),
inference(cnf_transformation,[],[f1008]) ).
tff(f5734,plain,
spl331_454,
inference(avatar_split_clause,[],[f1718,f5732]) ).
tff(f5732,plain,
( spl331_454
<=> ! [X0: 'S2',X1: 'S2'] :
( ( f3(f24,X0) = f3(f24,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_454])]) ).
tff(f1718,plain,
! [X0: 'S2',X1: 'S2'] :
( ( f3(f24,X0) = f3(f24,X1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1007]) ).
tff(f1007,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ( f3(f24,X0) = f3(f24,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( f3(f24,X0) != f3(f24,X1) ) ) ),
inference(nnf_transformation,[],[f10]) ).
tff(f10,axiom,
! [X0: 'S2',X1: 'S2'] :
( ( f3(f24,X0) = f3(f24,X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_10) ).
tff(f5730,plain,
( ~ spl331_453
| ~ spl331_105
| ~ spl331_430 ),
inference(avatar_split_clause,[],[f5627,f5615,f3381,f5727]) ).
tff(f5727,plain,
( spl331_453
<=> $less(sK24(f51),1.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_453])]) ).
tff(f3381,plain,
( spl331_105
<=> ( 1.0 = sK22(f51) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_105])]) ).
tff(f5615,plain,
( spl331_430
<=> ! [X0: 'S10'] :
( ~ $less(sK24(X0),sK22(X0))
| $less(sK22(X0),0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_430])]) ).
tff(f5627,plain,
( ~ $less(sK24(f51),1.0)
| ~ spl331_105
| ~ spl331_430 ),
inference(evaluation,[],[f5622]) ).
tff(f5622,plain,
( ~ $less(sK24(f51),1.0)
| $less(1.0,0.0)
| ~ spl331_105
| ~ spl331_430 ),
inference(superposition,[],[f5616,f3383]) ).
tff(f3383,plain,
( ( 1.0 = sK22(f51) )
| ~ spl331_105 ),
inference(avatar_component_clause,[],[f3381]) ).
tff(f5616,plain,
( ! [X0: 'S10'] :
( ~ $less(sK24(X0),sK22(X0))
| $less(sK22(X0),0.0) )
| ~ spl331_430 ),
inference(avatar_component_clause,[],[f5615]) ).
tff(f5725,plain,
spl331_452,
inference(avatar_split_clause,[],[f1717,f5723]) ).
tff(f5723,plain,
( spl331_452
<=> ! [X0: 'S2',X1: 'S2'] :
( ( X0 = X1 )
| ( f3(f24,X0) != f3(f24,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_452])]) ).
tff(f1717,plain,
! [X0: 'S2',X1: 'S2'] :
( ( X0 = X1 )
| ( f3(f24,X0) != f3(f24,X1) ) ),
inference(cnf_transformation,[],[f1007]) ).
tff(f5721,plain,
spl331_451,
inference(avatar_split_clause,[],[f1716,f5719]) ).
tff(f5719,plain,
( spl331_451
<=> ! [X0: 'S2',X1: 'S2'] :
( ( f19(f20,X0) = f19(f20,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_451])]) ).
tff(f1716,plain,
! [X0: 'S2',X1: 'S2'] :
( ( f19(f20,X0) = f19(f20,X1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1006]) ).
tff(f1006,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ( f19(f20,X0) = f19(f20,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( f19(f20,X0) != f19(f20,X1) ) ) ),
inference(nnf_transformation,[],[f8]) ).
tff(f8,axiom,
! [X0: 'S2',X1: 'S2'] :
( ( f19(f20,X0) = f19(f20,X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_8) ).
tff(f5717,plain,
spl331_450,
inference(avatar_split_clause,[],[f1715,f5715]) ).
tff(f5715,plain,
( spl331_450
<=> ! [X0: 'S2',X1: 'S2'] :
( ( X0 = X1 )
| ( f19(f20,X0) != f19(f20,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_450])]) ).
tff(f1715,plain,
! [X0: 'S2',X1: 'S2'] :
( ( X0 = X1 )
| ( f19(f20,X0) != f19(f20,X1) ) ),
inference(cnf_transformation,[],[f1006]) ).
tff(f5713,plain,
spl331_449,
inference(avatar_split_clause,[],[f1714,f5711]) ).
tff(f5711,plain,
( spl331_449
<=> ! [X0: $real,X1: $real] :
( ( f16(f32,X0) = f16(f32,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_449])]) ).
tff(f1714,plain,
! [X0: $real,X1: $real] :
( ( f16(f32,X0) = f16(f32,X1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1005]) ).
tff(f1005,plain,
! [X0: $real,X1: $real] :
( ( ( f16(f32,X0) = f16(f32,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( f16(f32,X0) != f16(f32,X1) ) ) ),
inference(nnf_transformation,[],[f36]) ).
tff(f36,axiom,
! [X0: $real,X1: $real] :
( ( f16(f32,X0) = f16(f32,X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_36) ).
tff(f5709,plain,
spl331_448,
inference(avatar_split_clause,[],[f1713,f5707]) ).
tff(f5707,plain,
( spl331_448
<=> ! [X0: $real,X1: $real] :
( ( X0 = X1 )
| ( f16(f32,X0) != f16(f32,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_448])]) ).
tff(f1713,plain,
! [X0: $real,X1: $real] :
( ( X0 = X1 )
| ( f16(f32,X0) != f16(f32,X1) ) ),
inference(cnf_transformation,[],[f1005]) ).
tff(f5705,plain,
spl331_447,
inference(avatar_split_clause,[],[f1712,f5703]) ).
tff(f5703,plain,
( spl331_447
<=> ! [X0: 'S2',X1: 'S2'] :
( ( f13(f14,X0) = f13(f14,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_447])]) ).
tff(f1712,plain,
! [X0: 'S2',X1: 'S2'] :
( ( f13(f14,X0) = f13(f14,X1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1004]) ).
tff(f1004,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ( f13(f14,X0) = f13(f14,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( f13(f14,X0) != f13(f14,X1) ) ) ),
inference(nnf_transformation,[],[f9]) ).
tff(f9,axiom,
! [X0: 'S2',X1: 'S2'] :
( ( f13(f14,X0) = f13(f14,X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_9) ).
tff(f5701,plain,
spl331_446,
inference(avatar_split_clause,[],[f1711,f5699]) ).
tff(f5699,plain,
( spl331_446
<=> ! [X0: 'S2',X1: 'S2'] :
( ( X0 = X1 )
| ( f13(f14,X0) != f13(f14,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_446])]) ).
tff(f1711,plain,
! [X0: 'S2',X1: 'S2'] :
( ( X0 = X1 )
| ( f13(f14,X0) != f13(f14,X1) ) ),
inference(cnf_transformation,[],[f1004]) ).
tff(f5697,plain,
spl331_445,
inference(avatar_split_clause,[],[f1710,f5695]) ).
tff(f5695,plain,
( spl331_445
<=> ! [X0: 'S10',X1: 'S21'] :
( ( f1 = f45(X0,X1) )
| ( f1 != f57(X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_445])]) ).
tff(f1710,plain,
! [X0: 'S10',X1: 'S21'] :
( ( f1 = f45(X0,X1) )
| ( f1 != f57(X1,X0) ) ),
inference(cnf_transformation,[],[f1003]) ).
tff(f1003,plain,
! [X0: 'S10',X1: 'S21'] :
( ( ( f1 = f45(X0,X1) )
| ( f1 != f57(X1,X0) ) )
& ( ( f1 = f57(X1,X0) )
| ( f1 != f45(X0,X1) ) ) ),
inference(nnf_transformation,[],[f121]) ).
tff(f121,axiom,
! [X0: 'S10',X1: 'S21'] :
( ( f1 = f45(X0,X1) )
<=> ( f1 = f57(X1,X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_121) ).
tff(f5693,plain,
spl331_444,
inference(avatar_split_clause,[],[f1709,f5691]) ).
tff(f5691,plain,
( spl331_444
<=> ! [X0: 'S10',X1: 'S21'] :
( ( f1 = f57(X1,X0) )
| ( f1 != f45(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_444])]) ).
tff(f1709,plain,
! [X0: 'S10',X1: 'S21'] :
( ( f1 = f57(X1,X0) )
| ( f1 != f45(X0,X1) ) ),
inference(cnf_transformation,[],[f1003]) ).
tff(f5689,plain,
spl331_443,
inference(avatar_split_clause,[],[f1708,f5687]) ).
tff(f5687,plain,
( spl331_443
<=> ! [X0: $real,X1: 'S20'] :
( ( f1 = f43(X0,X1) )
| ( f1 != f56(X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_443])]) ).
tff(f1708,plain,
! [X0: $real,X1: 'S20'] :
( ( f1 = f43(X0,X1) )
| ( f1 != f56(X1,X0) ) ),
inference(cnf_transformation,[],[f1002]) ).
tff(f1002,plain,
! [X0: $real,X1: 'S20'] :
( ( ( f1 = f43(X0,X1) )
| ( f1 != f56(X1,X0) ) )
& ( ( f1 = f56(X1,X0) )
| ( f1 != f43(X0,X1) ) ) ),
inference(nnf_transformation,[],[f120]) ).
tff(f120,axiom,
! [X0: $real,X1: 'S20'] :
( ( f1 = f43(X0,X1) )
<=> ( f1 = f56(X1,X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_120) ).
tff(f5685,plain,
spl331_442,
inference(avatar_split_clause,[],[f1707,f5683]) ).
tff(f5683,plain,
( spl331_442
<=> ! [X0: $real,X1: 'S20'] :
( ( f1 = f56(X1,X0) )
| ( f1 != f43(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_442])]) ).
tff(f1707,plain,
! [X0: $real,X1: 'S20'] :
( ( f1 = f56(X1,X0) )
| ( f1 != f43(X0,X1) ) ),
inference(cnf_transformation,[],[f1002]) ).
tff(f5681,plain,
spl331_441,
inference(avatar_split_clause,[],[f1706,f5679]) ).
tff(f5679,plain,
( spl331_441
<=> ! [X0: $int,X1: 'S19'] :
( ( f1 = f41(X0,X1) )
| ( f1 != f55(X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_441])]) ).
tff(f1706,plain,
! [X0: $int,X1: 'S19'] :
( ( f1 = f41(X0,X1) )
| ( f1 != f55(X1,X0) ) ),
inference(cnf_transformation,[],[f1001]) ).
tff(f1001,plain,
! [X0: $int,X1: 'S19'] :
( ( ( f1 = f41(X0,X1) )
| ( f1 != f55(X1,X0) ) )
& ( ( f1 = f55(X1,X0) )
| ( f1 != f41(X0,X1) ) ) ),
inference(nnf_transformation,[],[f119]) ).
tff(f119,axiom,
! [X0: $int,X1: 'S19'] :
( ( f1 = f41(X0,X1) )
<=> ( f1 = f55(X1,X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_119) ).
tff(f5677,plain,
spl331_440,
inference(avatar_split_clause,[],[f1705,f5675]) ).
tff(f5675,plain,
( spl331_440
<=> ! [X0: $int,X1: 'S19'] :
( ( f1 = f55(X1,X0) )
| ( f1 != f41(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_440])]) ).
tff(f1705,plain,
! [X0: $int,X1: 'S19'] :
( ( f1 = f55(X1,X0) )
| ( f1 != f41(X0,X1) ) ),
inference(cnf_transformation,[],[f1001]) ).
tff(f5673,plain,
spl331_439,
inference(avatar_split_clause,[],[f1703,f5671]) ).
tff(f5671,plain,
( spl331_439
<=> ! [X0: 'S10',X1: 'S10'] :
( ( f27(f36,X0) = f27(f36,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_439])]) ).
tff(f1703,plain,
! [X0: 'S10',X1: 'S10'] :
( ( f27(f36,X0) = f27(f36,X1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1000]) ).
tff(f1000,plain,
! [X0: 'S10',X1: 'S10'] :
( ( ( X0 = X1 )
| ( f27(f36,X0) != f27(f36,X1) )
| ( f27(f28,X0) != f27(f28,X1) ) )
& ( ( ( f27(f36,X0) = f27(f36,X1) )
& ( f27(f28,X0) = f27(f28,X1) ) )
| ( X0 != X1 ) ) ),
inference(flattening,[],[f999]) ).
tff(f999,plain,
! [X0: 'S10',X1: 'S10'] :
( ( ( X0 = X1 )
| ( f27(f36,X0) != f27(f36,X1) )
| ( f27(f28,X0) != f27(f28,X1) ) )
& ( ( ( f27(f36,X0) = f27(f36,X1) )
& ( f27(f28,X0) = f27(f28,X1) ) )
| ( X0 != X1 ) ) ),
inference(nnf_transformation,[],[f107]) ).
tff(f107,axiom,
! [X0: 'S10',X1: 'S10'] :
( ( X0 = X1 )
<=> ( ( f27(f36,X0) = f27(f36,X1) )
& ( f27(f28,X0) = f27(f28,X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_107) ).
tff(f5669,plain,
spl331_438,
inference(avatar_split_clause,[],[f1702,f5667]) ).
tff(f5667,plain,
( spl331_438
<=> ! [X0: 'S10',X1: 'S10'] :
( ( f27(f28,X0) = f27(f28,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_438])]) ).
tff(f1702,plain,
! [X0: 'S10',X1: 'S10'] :
( ( f27(f28,X0) = f27(f28,X1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1000]) ).
tff(f5665,plain,
spl331_437,
inference(avatar_split_clause,[],[f1608,f5663]) ).
tff(f5663,plain,
( spl331_437
<=> ! [X0: $int] : ( f11(f63(f64,X0),f6(f7,2)) = sK41(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_437])]) ).
tff(f1608,plain,
! [X0: $int] : ( f11(f63(f64,X0),f6(f7,2)) = sK41(X0) ),
inference(cnf_transformation,[],[f980]) ).
tff(f980,plain,
! [X0: $int] :
( ( sK41(X0) = f8(f21,sK41(X0)) )
& ( f11(f63(f64,X0),f6(f7,2)) = sK41(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f639,f979]) ).
tff(f979,plain,
! [X0: $int] :
( ? [X1: $int] :
( ( f8(f21,X1) = X1 )
& ( f11(f63(f64,X0),f6(f7,2)) = X1 ) )
=> ( ( sK41(X0) = f8(f21,sK41(X0)) )
& ( f11(f63(f64,X0),f6(f7,2)) = sK41(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f639,plain,
! [X0: $int] :
? [X1: $int] :
( ( f8(f21,X1) = X1 )
& ( f11(f63(f64,X0),f6(f7,2)) = X1 ) ),
inference(rectify,[],[f342]) ).
tff(f342,axiom,
! [X0: $int] :
? [X214: $int] :
( ( f8(f21,X214) = X214 )
& ( f11(f63(f64,X0),f6(f7,2)) = X214 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_342) ).
tff(f5661,plain,
spl331_436,
inference(avatar_split_clause,[],[f1606,f5659]) ).
tff(f1606,plain,
! [X0: $real] : ( f19(f59(f60,X0),f6(f7,2)) = sK40(X0) ),
inference(cnf_transformation,[],[f978]) ).
tff(f978,plain,
! [X0: $real] :
( ( sK40(X0) = f22(f23,sK40(X0)) )
& ( f19(f59(f60,X0),f6(f7,2)) = sK40(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f638,f977]) ).
tff(f977,plain,
! [X0: $real] :
( ? [X1: $real] :
( ( f22(f23,X1) = X1 )
& ( f19(f59(f60,X0),f6(f7,2)) = X1 ) )
=> ( ( sK40(X0) = f22(f23,sK40(X0)) )
& ( f19(f59(f60,X0),f6(f7,2)) = sK40(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f638,plain,
! [X0: $real] :
? [X1: $real] :
( ( f22(f23,X1) = X1 )
& ( f19(f59(f60,X0),f6(f7,2)) = X1 ) ),
inference(rectify,[],[f343]) ).
tff(f343,axiom,
! [X0: $real] :
? [X215: $real] :
( ( f22(f23,X215) = X215 )
& ( f19(f59(f60,X0),f6(f7,2)) = X215 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_343) ).
tff(f5655,plain,
( spl331_435
| ~ spl331_54
| ~ spl331_434 ),
inference(avatar_split_clause,[],[f5651,f5647,f3164,f5653]) ).
tff(f5653,plain,
( spl331_435
<=> ! [X0: 'S2'] : ~ $less(sK109(X0,X0),sK27(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_435])]) ).
tff(f3164,plain,
( spl331_54
<=> ! [X0: 'S2'] : ( sK27(X0) = sK28(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_54])]) ).
tff(f5647,plain,
( spl331_434
<=> ! [X0: 'S2'] : ~ $less(f8(f9(f10,sK28(X0)),sK28(X0)),sK28(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_434])]) ).
tff(f5651,plain,
( ! [X0: 'S2'] : ~ $less(sK109(X0,X0),sK27(X0))
| ~ spl331_54
| ~ spl331_434 ),
inference(forward_demodulation,[],[f5650,f2621]) ).
tff(f2621,plain,
! [X0: 'S2',X1: 'S2'] : ( sK109(X0,X1) = f8(f9(f10,sK27(X0)),sK27(X1)) ),
inference(forward_demodulation,[],[f2620,f1580]) ).
tff(f1580,plain,
! [X0: 'S2'] : ( f11(f12,X0) = sK27(X0) ),
inference(cnf_transformation,[],[f953]) ).
tff(f953,plain,
! [X0: 'S2'] :
( ( sK27(X0) = f8(f21,sK27(X0)) )
& ( f11(f12,X0) = sK27(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f626,f952]) ).
tff(f952,plain,
! [X0: 'S2'] :
( ? [X1: $int] :
( ( f8(f21,X1) = X1 )
& ( f11(f12,X0) = X1 ) )
=> ( ( sK27(X0) = f8(f21,sK27(X0)) )
& ( f11(f12,X0) = sK27(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f626,plain,
! [X0: 'S2'] :
? [X1: $int] :
( ( f8(f21,X1) = X1 )
& ( f11(f12,X0) = X1 ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X0: 'S2'] :
? [X4: $int] :
( ( f8(f21,X4) = X4 )
& ( f11(f12,X0) = X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_5) ).
tff(f2620,plain,
! [X0: 'S2',X1: 'S2'] : ( sK109(X0,X1) = f8(f9(f10,f11(f12,X0)),sK27(X1)) ),
inference(forward_demodulation,[],[f1850,f1580]) ).
tff(f1850,plain,
! [X0: 'S2',X1: 'S2'] : ( f8(f9(f10,f11(f12,X0)),f11(f12,X1)) = sK109(X0,X1) ),
inference(cnf_transformation,[],[f1131]) ).
tff(f1131,plain,
! [X0: 'S2',X1: 'S2'] :
( ( sK109(X0,X1) = f11(f12,f6(f7,sK109(X0,X1))) )
& ( f8(f9(f10,f11(f12,X0)),f11(f12,X1)) = sK109(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK109])],[f687,f1130]) ).
tff(f1130,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: $int] :
( ( f11(f12,f6(f7,X2)) = X2 )
& ( f8(f9(f10,f11(f12,X0)),f11(f12,X1)) = X2 ) )
=> ( ( sK109(X0,X1) = f11(f12,f6(f7,sK109(X0,X1))) )
& ( f8(f9(f10,f11(f12,X0)),f11(f12,X1)) = sK109(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f687,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int] :
( ( f11(f12,f6(f7,X2)) = X2 )
& ( f8(f9(f10,f11(f12,X0)),f11(f12,X1)) = X2 ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X20: $int] :
( ( f11(f12,f6(f7,X20)) = X20 )
& ( f8(f9(f10,f11(f12,X0)),f11(f12,X1)) = X20 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_85) ).
tff(f5650,plain,
( ! [X0: 'S2'] : ~ $less(f8(f9(f10,sK27(X0)),sK27(X0)),sK27(X0))
| ~ spl331_54
| ~ spl331_434 ),
inference(forward_demodulation,[],[f5648,f3165]) ).
tff(f3165,plain,
( ! [X0: 'S2'] : ( sK27(X0) = sK28(X0) )
| ~ spl331_54 ),
inference(avatar_component_clause,[],[f3164]) ).
tff(f5648,plain,
( ! [X0: 'S2'] : ~ $less(f8(f9(f10,sK28(X0)),sK28(X0)),sK28(X0))
| ~ spl331_434 ),
inference(avatar_component_clause,[],[f5647]) ).
tff(f5649,plain,
spl331_434,
inference(avatar_split_clause,[],[f1583,f5647]) ).
tff(f1583,plain,
! [X0: 'S2'] : ~ $less(f8(f9(f10,sK28(X0)),sK28(X0)),sK28(X0)),
inference(cnf_transformation,[],[f955]) ).
tff(f955,plain,
! [X0: 'S2'] :
( ~ $less(f8(f9(f10,sK28(X0)),sK28(X0)),sK28(X0))
& ( f11(f12,X0) = sK28(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f627,f954]) ).
tff(f954,plain,
! [X0: 'S2'] :
( ? [X1: $int] :
( ~ $less(f8(f9(f10,X1),X1),X1)
& ( f11(f12,X0) = X1 ) )
=> ( ~ $less(f8(f9(f10,sK28(X0)),sK28(X0)),sK28(X0))
& ( f11(f12,X0) = sK28(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f627,plain,
! [X0: 'S2'] :
? [X1: $int] :
( ~ $less(f8(f9(f10,X1),X1),X1)
& ( f11(f12,X0) = X1 ) ),
inference(rectify,[],[f473]) ).
tff(f473,plain,
! [X0: 'S2'] :
? [X22: $int] :
( ~ $less(f8(f9(f10,X22),X22),X22)
& ( f11(f12,X0) = X22 ) ),
inference(theory_normalization,[],[f132]) ).
tff(f132,axiom,
! [X0: 'S2'] :
? [X22: $int] :
( $lesseq(X22,f8(f9(f10,X22),X22))
& ( f11(f12,X0) = X22 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_132) ).
tff(f5645,plain,
( spl331_433
| ~ spl331_1
| ~ spl331_426 ),
inference(avatar_split_clause,[],[f5595,f5592,f2930,f5642]) ).
tff(f5642,plain,
( spl331_433
<=> ( 0 = sK39(0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_433])]) ).
tff(f2930,plain,
( spl331_1
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_1])]) ).
tff(f5592,plain,
( spl331_426
<=> ! [X0: $int] :
( ( sK39(X0) = X0 )
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_426])]) ).
tff(f5595,plain,
( ( 0 = sK39(0) )
| ~ spl331_1
| ~ spl331_426 ),
inference(resolution,[],[f5593,f2931]) ).
tff(f2931,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl331_1 ),
inference(avatar_component_clause,[],[f2930]) ).
tff(f5593,plain,
( ! [X0: $int] :
( $less(X0,0)
| ( sK39(X0) = X0 ) )
| ~ spl331_426 ),
inference(avatar_component_clause,[],[f5592]) ).
tff(f5638,plain,
spl331_432,
inference(avatar_split_clause,[],[f1576,f5636]) ).
tff(f5636,plain,
( spl331_432
<=> ! [X0: 'S10'] :
( ( sK25(X0) = $uminus(sK25(X0)) )
| ~ $less(sK25(X0),0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_432])]) ).
tff(f1576,plain,
! [X0: 'S10'] :
( ( sK25(X0) = $uminus(sK25(X0)) )
| ~ $less(sK25(X0),0.0) ),
inference(cnf_transformation,[],[f949]) ).
tff(f949,plain,
! [X0: 'S10'] :
( ( ( sK25(X0) = sK25(X0) )
| $less(sK25(X0),0.0) )
& ( ( sK25(X0) = $uminus(sK25(X0)) )
| ~ $less(sK25(X0),0.0) )
& ( f27(f31,X0) = sK25(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f819,f948]) ).
tff(f948,plain,
! [X0: 'S10'] :
( ? [X1: $real] :
( ( ( X1 = X1 )
| $less(X1,0.0) )
& ( ( $uminus(X1) = X1 )
| ~ $less(X1,0.0) )
& ( f27(f31,X0) = X1 ) )
=> ( ( ( sK25(X0) = sK25(X0) )
| $less(sK25(X0),0.0) )
& ( ( sK25(X0) = $uminus(sK25(X0)) )
| ~ $less(sK25(X0),0.0) )
& ( f27(f31,X0) = sK25(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f819,plain,
! [X0: 'S10'] :
? [X1: $real] :
( ( ( X1 = X1 )
| $less(X1,0.0) )
& ( ( $uminus(X1) = X1 )
| ~ $less(X1,0.0) )
& ( f27(f31,X0) = X1 ) ),
inference(ennf_transformation,[],[f624]) ).
tff(f624,plain,
! [X0: 'S10'] :
? [X1: $real] :
( ( ~ $less(X1,0.0)
=> ( X1 = X1 ) )
& ( $less(X1,0.0)
=> ( $uminus(X1) = X1 ) )
& ( f27(f31,X0) = X1 ) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X0: 'S10'] :
? [X11: $real] :
( ( ~ $less(X11,0.0)
=> ( X11 = X11 ) )
& ( $less(X11,0.0)
=> ( $uminus(X11) = X11 ) )
& ( f27(f31,X0) = X11 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_30) ).
tff(f5633,plain,
spl331_431,
inference(avatar_split_clause,[],[f1572,f5631]) ).
tff(f5631,plain,
( spl331_431
<=> ! [X0: 'S10'] :
( ~ $less(f27(f31,X0),sK23(X0))
| $less(sK23(X0),0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_431])]) ).
tff(f1572,plain,
! [X0: 'S10'] :
( ~ $less(f27(f31,X0),sK23(X0))
| $less(sK23(X0),0.0) ),
inference(cnf_transformation,[],[f945]) ).
tff(f5617,plain,
( spl331_430
| ~ spl331_68
| ~ spl331_429 ),
inference(avatar_split_clause,[],[f5613,f5610,f3220,f5615]) ).
tff(f3220,plain,
( spl331_68
<=> ! [X0: 'S10'] : ( f27(f31,X0) = sK24(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_68])]) ).
tff(f5610,plain,
( spl331_429
<=> ! [X0: 'S10'] :
( ~ $less(f27(f31,X0),sK22(X0))
| $less(sK22(X0),0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_429])]) ).
tff(f5613,plain,
( ! [X0: 'S10'] :
( ~ $less(sK24(X0),sK22(X0))
| $less(sK22(X0),0.0) )
| ~ spl331_68
| ~ spl331_429 ),
inference(forward_demodulation,[],[f5611,f3221]) ).
tff(f3221,plain,
( ! [X0: 'S10'] : ( f27(f31,X0) = sK24(X0) )
| ~ spl331_68 ),
inference(avatar_component_clause,[],[f3220]) ).
tff(f5611,plain,
( ! [X0: 'S10'] :
( ~ $less(f27(f31,X0),sK22(X0))
| $less(sK22(X0),0.0) )
| ~ spl331_429 ),
inference(avatar_component_clause,[],[f5610]) ).
tff(f5612,plain,
spl331_429,
inference(avatar_split_clause,[],[f1569,f5610]) ).
tff(f1569,plain,
! [X0: 'S10'] :
( ~ $less(f27(f31,X0),sK22(X0))
| $less(sK22(X0),0.0) ),
inference(cnf_transformation,[],[f943]) ).
tff(f5605,plain,
( spl331_428
| ~ spl331_249
| ~ spl331_427 ),
inference(avatar_split_clause,[],[f5601,f5598,f4487,f5603]) ).
tff(f5603,plain,
( spl331_428
<=> ! [X0: $int] :
( ( 0 = sK39(X0) )
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_428])]) ).
tff(f4487,plain,
( spl331_249
<=> ! [X0: $int] : ( f11(f12,f6(f7,X0)) = sK39(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_249])]) ).
tff(f5598,plain,
( spl331_427
<=> ! [X0: $int] :
( ( 0 = f11(f12,f6(f7,X0)) )
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_427])]) ).
tff(f5601,plain,
( ! [X0: $int] :
( ( 0 = sK39(X0) )
| ~ $less(X0,0) )
| ~ spl331_249
| ~ spl331_427 ),
inference(forward_demodulation,[],[f5599,f4488]) ).
tff(f4488,plain,
( ! [X0: $int] : ( f11(f12,f6(f7,X0)) = sK39(X0) )
| ~ spl331_249 ),
inference(avatar_component_clause,[],[f4487]) ).
tff(f5599,plain,
( ! [X0: $int] :
( ( 0 = f11(f12,f6(f7,X0)) )
| ~ $less(X0,0) )
| ~ spl331_427 ),
inference(avatar_component_clause,[],[f5598]) ).
tff(f5600,plain,
spl331_427,
inference(avatar_split_clause,[],[f1529,f5598]) ).
tff(f1529,plain,
! [X0: $int] :
( ( 0 = f11(f12,f6(f7,X0)) )
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f811]) ).
tff(f811,plain,
! [X0: $int] :
( ( 0 = f11(f12,f6(f7,X0)) )
| ~ $less(X0,0) ),
inference(ennf_transformation,[],[f456]) ).
tff(f456,axiom,
! [X0: $int] :
( $less(X0,0)
=> ( 0 = f11(f12,f6(f7,X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_456) ).
tff(f5594,plain,
( spl331_426
| ~ spl331_249
| ~ spl331_424 ),
inference(avatar_split_clause,[],[f5585,f5582,f4487,f5592]) ).
tff(f5582,plain,
( spl331_424
<=> ! [X0: $int] :
( ( f11(f12,f6(f7,X0)) = X0 )
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_424])]) ).
tff(f5585,plain,
( ! [X0: $int] :
( ( sK39(X0) = X0 )
| $less(X0,0) )
| ~ spl331_249
| ~ spl331_424 ),
inference(forward_demodulation,[],[f5583,f4488]) ).
tff(f5583,plain,
( ! [X0: $int] :
( ( f11(f12,f6(f7,X0)) = X0 )
| $less(X0,0) )
| ~ spl331_424 ),
inference(avatar_component_clause,[],[f5582]) ).
tff(f5590,plain,
( spl331_425
| ~ spl331_2
| ~ spl331_423 ),
inference(avatar_split_clause,[],[f5563,f5559,f2934,f5587]) ).
tff(f5587,plain,
( spl331_425
<=> ( 0.0 = sK24(sK18(0.0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_425])]) ).
tff(f2934,plain,
( spl331_2
<=> ! [X0: $real] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_2])]) ).
tff(f5563,plain,
( ( 0.0 = sK24(sK18(0.0)) )
| ~ spl331_2
| ~ spl331_423 ),
inference(resolution,[],[f5560,f2935]) ).
tff(f2935,plain,
( ! [X0: $real] : ~ $less(X0,X0)
| ~ spl331_2 ),
inference(avatar_component_clause,[],[f2934]) ).
tff(f5584,plain,
spl331_424,
inference(avatar_split_clause,[],[f1528,f5582]) ).
tff(f1528,plain,
! [X0: $int] :
( ( f11(f12,f6(f7,X0)) = X0 )
| $less(X0,0) ),
inference(cnf_transformation,[],[f810]) ).
tff(f810,plain,
! [X0: $int] :
( ( f11(f12,f6(f7,X0)) = X0 )
| $less(X0,0) ),
inference(ennf_transformation,[],[f461]) ).
tff(f461,plain,
! [X0: $int] :
( ~ $less(X0,0)
=> ( f11(f12,f6(f7,X0)) = X0 ) ),
inference(theory_normalization,[],[f455]) ).
tff(f455,axiom,
! [X0: $int] :
( $lesseq(0,X0)
=> ( f11(f12,f6(f7,X0)) = X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_455) ).
tff(f5561,plain,
( spl331_423
| ~ spl331_64
| ~ spl331_68
| ~ spl331_422 ),
inference(avatar_split_clause,[],[f5557,f5553,f3220,f3204,f5559]) ).
tff(f3204,plain,
( spl331_64
<=> ! [X0: $real] : ( f16(f32,X0) = sK18(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_64])]) ).
tff(f5553,plain,
( spl331_422
<=> ! [X0: $real] :
( ( f27(f31,f16(f32,X0)) = X0 )
| $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_422])]) ).
tff(f5557,plain,
( ! [X0: $real] :
( ( sK24(sK18(X0)) = X0 )
| $less(X0,0.0) )
| ~ spl331_64
| ~ spl331_68
| ~ spl331_422 ),
inference(forward_demodulation,[],[f5556,f3205]) ).
tff(f3205,plain,
( ! [X0: $real] : ( f16(f32,X0) = sK18(X0) )
| ~ spl331_64 ),
inference(avatar_component_clause,[],[f3204]) ).
tff(f5556,plain,
( ! [X0: $real] :
( ( sK24(f16(f32,X0)) = X0 )
| $less(X0,0.0) )
| ~ spl331_68
| ~ spl331_422 ),
inference(forward_demodulation,[],[f5554,f3221]) ).
tff(f5554,plain,
( ! [X0: $real] :
( ( f27(f31,f16(f32,X0)) = X0 )
| $less(X0,0.0) )
| ~ spl331_422 ),
inference(avatar_component_clause,[],[f5553]) ).
tff(f5555,plain,
spl331_422,
inference(avatar_split_clause,[],[f1527,f5553]) ).
tff(f1527,plain,
! [X0: $real] :
( ( f27(f31,f16(f32,X0)) = X0 )
| $less(X0,0.0) ),
inference(cnf_transformation,[],[f809]) ).
tff(f809,plain,
! [X0: $real] :
( ( ( f27(f31,f16(f32,X0)) = X0 )
| $less(X0,0.0) )
& ( ( f27(f31,f16(f32,X0)) = $uminus(X0) )
| ~ $less(X0,0.0) ) ),
inference(ennf_transformation,[],[f32]) ).
tff(f32,axiom,
! [X0: $real] :
( ( ~ $less(X0,0.0)
=> ( f27(f31,f16(f32,X0)) = X0 ) )
& ( $less(X0,0.0)
=> ( f27(f31,f16(f32,X0)) = $uminus(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_32) ).
tff(f5532,plain,
( spl331_421
| ~ spl331_73
| ~ spl331_420 ),
inference(avatar_split_clause,[],[f5528,f5525,f3240,f5530]) ).
tff(f5530,plain,
( spl331_421
<=> ! [X0: $real] :
( ( sK34(f22(f33,X0)) = X0 )
| $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_421])]) ).
tff(f3240,plain,
( spl331_73
<=> ! [X0: $real] : ( f22(f30,X0) = sK34(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_73])]) ).
tff(f5525,plain,
( spl331_420
<=> ! [X0: $real] :
( ( f22(f30,f22(f33,X0)) = X0 )
| $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_420])]) ).
tff(f5528,plain,
( ! [X0: $real] :
( ( sK34(f22(f33,X0)) = X0 )
| $less(X0,0.0) )
| ~ spl331_73
| ~ spl331_420 ),
inference(forward_demodulation,[],[f5526,f3241]) ).
tff(f3241,plain,
( ! [X0: $real] : ( f22(f30,X0) = sK34(X0) )
| ~ spl331_73 ),
inference(avatar_component_clause,[],[f3240]) ).
tff(f5526,plain,
( ! [X0: $real] :
( ( f22(f30,f22(f33,X0)) = X0 )
| $less(X0,0.0) )
| ~ spl331_420 ),
inference(avatar_component_clause,[],[f5525]) ).
tff(f5527,plain,
spl331_420,
inference(avatar_split_clause,[],[f1525,f5525]) ).
tff(f1525,plain,
! [X0: $real] :
( ( f22(f30,f22(f33,X0)) = X0 )
| $less(X0,0.0) ),
inference(cnf_transformation,[],[f808]) ).
tff(f808,plain,
! [X0: $real] :
( ( ( f22(f30,f22(f33,X0)) = X0 )
| $less(X0,0.0) )
& ( ( $uminus(X0) = f22(f30,f22(f33,X0)) )
| ~ $less(X0,0.0) ) ),
inference(ennf_transformation,[],[f33]) ).
tff(f33,axiom,
! [X0: $real] :
( ( ~ $less(X0,0.0)
=> ( f22(f30,f22(f33,X0)) = X0 ) )
& ( $less(X0,0.0)
=> ( $uminus(X0) = f22(f30,f22(f33,X0)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_33) ).
tff(f5516,plain,
( spl331_419
| ~ spl331_66
| ~ spl331_418 ),
inference(avatar_split_clause,[],[f5512,f5508,f3212,f5514]) ).
tff(f5514,plain,
( spl331_419
<=> ! [X0: 'S10'] : ( $uminus(sK22(X0)) = sK22(f34(f35,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_419])]) ).
tff(f3212,plain,
( spl331_66
<=> ! [X0: 'S10'] : ( f27(f36,X0) = sK22(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_66])]) ).
tff(f5508,plain,
( spl331_418
<=> ! [X0: 'S10'] : ( $uminus(f27(f36,X0)) = f27(f36,f34(f35,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_418])]) ).
tff(f5512,plain,
( ! [X0: 'S10'] : ( $uminus(sK22(X0)) = sK22(f34(f35,X0)) )
| ~ spl331_66
| ~ spl331_418 ),
inference(forward_demodulation,[],[f5511,f3213]) ).
tff(f3213,plain,
( ! [X0: 'S10'] : ( f27(f36,X0) = sK22(X0) )
| ~ spl331_66 ),
inference(avatar_component_clause,[],[f3212]) ).
tff(f5511,plain,
( ! [X0: 'S10'] : ( $uminus(f27(f36,X0)) = sK22(f34(f35,X0)) )
| ~ spl331_66
| ~ spl331_418 ),
inference(forward_demodulation,[],[f5509,f3213]) ).
tff(f5509,plain,
( ! [X0: 'S10'] : ( $uminus(f27(f36,X0)) = f27(f36,f34(f35,X0)) )
| ~ spl331_418 ),
inference(avatar_component_clause,[],[f5508]) ).
tff(f5510,plain,
spl331_418,
inference(avatar_split_clause,[],[f1499,f5508]) ).
tff(f1499,plain,
! [X0: 'S10'] : ( $uminus(f27(f36,X0)) = f27(f36,f34(f35,X0)) ),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
! [X0: 'S10'] : ( $uminus(f27(f36,X0)) = f27(f36,f34(f35,X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_109) ).
tff(f5506,plain,
( spl331_417
| ~ spl331_70
| ~ spl331_140 ),
inference(avatar_split_clause,[],[f3985,f3543,f3228,f5504]) ).
tff(f5504,plain,
( spl331_417
<=> ! [X1: 'S2'] : ( sK27(X1) = sK26(sK27(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_417])]) ).
tff(f3228,plain,
( spl331_70
<=> ! [X0: $int] : ( f8(f21,X0) = sK26(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_70])]) ).
tff(f3543,plain,
( spl331_140
<=> ! [X0: 'S2'] : ( sK27(X0) = f8(f21,sK27(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_140])]) ).
tff(f3985,plain,
( ! [X1: 'S2'] : ( sK27(X1) = sK26(sK27(X1)) )
| ~ spl331_70
| ~ spl331_140 ),
inference(superposition,[],[f3544,f3229]) ).
tff(f3229,plain,
( ! [X0: $int] : ( f8(f21,X0) = sK26(X0) )
| ~ spl331_70 ),
inference(avatar_component_clause,[],[f3228]) ).
tff(f3544,plain,
( ! [X0: 'S2'] : ( sK27(X0) = f8(f21,sK27(X0)) )
| ~ spl331_140 ),
inference(avatar_component_clause,[],[f3543]) ).
tff(f5502,plain,
spl331_416,
inference(avatar_split_clause,[],[f594,f5500]) ).
tff(f5500,plain,
( spl331_416
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_416])]) ).
tff(f594,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_148,[]) ).
tff(f5498,plain,
spl331_415,
inference(avatar_split_clause,[],[f589,f5496]) ).
tff(f5496,plain,
( spl331_415
<=> ! [X0: $real,X1: $real] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_415])]) ).
tff(f589,plain,
! [X0: $real,X1: $real] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_142,[]) ).
tff(f5494,plain,
spl331_414,
inference(avatar_split_clause,[],[f576,f5492]) ).
tff(f5492,plain,
( spl331_414
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_414])]) ).
tff(f576,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_148,[]) ).
tff(f5490,plain,
spl331_413,
inference(avatar_split_clause,[],[f571,f5488]) ).
tff(f5488,plain,
( spl331_413
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_413])]) ).
tff(f571,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_142,[]) ).
tff(f5473,plain,
( spl331_412
| ~ spl331_72
| ~ spl331_136 ),
inference(avatar_split_clause,[],[f3975,f3525,f3236,f5471]) ).
tff(f5471,plain,
( spl331_412
<=> ! [X1: 'S2'] : ( sK19(X1) = sK33(sK19(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_412])]) ).
tff(f3236,plain,
( spl331_72
<=> ! [X0: $real] : ( f22(f23,X0) = sK33(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_72])]) ).
tff(f3525,plain,
( spl331_136
<=> ! [X0: 'S2'] : ( sK19(X0) = f22(f23,sK19(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_136])]) ).
tff(f3975,plain,
( ! [X1: 'S2'] : ( sK19(X1) = sK33(sK19(X1)) )
| ~ spl331_72
| ~ spl331_136 ),
inference(superposition,[],[f3526,f3237]) ).
tff(f3237,plain,
( ! [X0: $real] : ( f22(f23,X0) = sK33(X0) )
| ~ spl331_72 ),
inference(avatar_component_clause,[],[f3236]) ).
tff(f3526,plain,
( ! [X0: 'S2'] : ( sK19(X0) = f22(f23,sK19(X0)) )
| ~ spl331_136 ),
inference(avatar_component_clause,[],[f3525]) ).
tff(f5445,plain,
( spl331_411
| ~ spl331_109
| ~ spl331_378 ),
inference(avatar_split_clause,[],[f5238,f5152,f3400,f5443]) ).
tff(f5443,plain,
( spl331_411
<=> ! [X0: $real] : $less(X0,$sum(1.0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_411])]) ).
tff(f3400,plain,
( spl331_109
<=> ! [X0: $real,X1: $real] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_109])]) ).
tff(f5152,plain,
( spl331_378
<=> ! [X0: $real] : $less(X0,$sum(X0,1.0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_378])]) ).
tff(f5238,plain,
( ! [X0: $real] : $less(X0,$sum(1.0,X0))
| ~ spl331_109
| ~ spl331_378 ),
inference(superposition,[],[f5153,f3401]) ).
tff(f3401,plain,
( ! [X0: $real,X1: $real] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl331_109 ),
inference(avatar_component_clause,[],[f3400]) ).
tff(f5153,plain,
( ! [X0: $real] : $less(X0,$sum(X0,1.0))
| ~ spl331_378 ),
inference(avatar_component_clause,[],[f5152]) ).
tff(f5359,plain,
( spl331_410
| ~ spl331_107
| ~ spl331_367 ),
inference(avatar_split_clause,[],[f5196,f5108,f3392,f5357]) ).
tff(f5357,plain,
( spl331_410
<=> ! [X0: $int] : $less(X0,$sum(1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_410])]) ).
tff(f3392,plain,
( spl331_107
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_107])]) ).
tff(f5108,plain,
( spl331_367
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_367])]) ).
tff(f5196,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl331_107
| ~ spl331_367 ),
inference(superposition,[],[f5109,f3393]) ).
tff(f3393,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl331_107 ),
inference(avatar_component_clause,[],[f3392]) ).
tff(f5109,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl331_367 ),
inference(avatar_component_clause,[],[f5108]) ).
tff(f5291,plain,
spl331_409,
inference(avatar_split_clause,[],[f2907,f5289]) ).
tff(f5289,plain,
( spl331_409
<=> ! [X1: 'S10'] : ~ $less(f22(f49(f50,sK325),sK24(X1)),sK24(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_409])]) ).
tff(f2907,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK325),sK24(X1)),sK24(X1)),
inference(forward_demodulation,[],[f2906,f1625]) ).
tff(f2906,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK24(X1)),sK325),sK24(X1)),
inference(forward_demodulation,[],[f2905,f1573]) ).
tff(f2905,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK325),f27(f31,X1)),
inference(forward_demodulation,[],[f2308,f1488]) ).
tff(f1488,plain,
! [X0: 'S10'] : ( f27(f31,X0) = f27(f31,f34(f35,X0)) ),
inference(cnf_transformation,[],[f31]) ).
tff(f31,axiom,
! [X0: 'S10'] : ( f27(f31,X0) = f27(f31,f34(f35,X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_31) ).
tff(f2308,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK325),f27(f31,f34(f35,X1))),
inference(cnf_transformation,[],[f1448]) ).
tff(f1448,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK325),f27(f31,f34(f35,X1))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK325])],[f562,f1447]) ).
tff(f1447,plain,
( ? [X0: $real] :
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f27(f31,f34(f35,X1)))
=> ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK325),f27(f31,f34(f35,X1))) ),
introduced(choice_axiom,[]) ).
tff(f562,plain,
? [X0: $real] :
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f27(f31,f34(f35,X1))),
inference(theory_normalization,[],[f183]) ).
tff(f183,axiom,
? [X0: $real] :
! [X1: 'S10'] : $lesseq(f27(f31,f34(f35,X1)),f22(f49(f50,f27(f31,X1)),X0)),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_183) ).
tff(f5287,plain,
spl331_408,
inference(avatar_split_clause,[],[f2879,f5285]) ).
tff(f5285,plain,
( spl331_408
<=> ! [X1: 'S10'] : ~ $less(f22(f49(f50,sK318),sK24(X1)),sK24(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_408])]) ).
tff(f2879,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK318),sK24(X1)),sK24(X1)),
inference(forward_demodulation,[],[f2878,f1625]) ).
tff(f2878,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK24(X1)),sK318),sK24(X1)),
inference(forward_demodulation,[],[f2877,f1573]) ).
tff(f2877,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK318),f27(f31,X1)),
inference(forward_demodulation,[],[f2296,f1488]) ).
tff(f2296,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK318),f27(f31,f34(f35,X1))),
inference(cnf_transformation,[],[f1434]) ).
tff(f1434,plain,
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK318),f27(f31,f34(f35,X1)))
& ~ $less(sK318,0.0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK318])],[f555,f1433]) ).
tff(f1433,plain,
( ? [X0: $real] :
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f27(f31,f34(f35,X1)))
& ~ $less(X0,0.0) )
=> ( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK318),f27(f31,f34(f35,X1)))
& ~ $less(sK318,0.0) ) ),
introduced(choice_axiom,[]) ).
tff(f555,plain,
? [X0: $real] :
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f27(f31,f34(f35,X1)))
& ~ $less(X0,0.0) ),
inference(theory_normalization,[],[f130]) ).
tff(f130,axiom,
? [X0: $real] :
( ! [X1: 'S10'] : $lesseq(f27(f31,f34(f35,X1)),f22(f49(f50,f27(f31,X1)),X0))
& $lesseq(0.0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_130) ).
tff(f5283,plain,
spl331_407,
inference(avatar_split_clause,[],[f2851,f5281]) ).
tff(f5281,plain,
( spl331_407
<=> ! [X1: 'S10'] : ~ $less(f22(f49(f50,sK311),sK24(X1)),sK24(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_407])]) ).
tff(f2851,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK311),sK24(X1)),sK24(X1)),
inference(forward_demodulation,[],[f2850,f1625]) ).
tff(f2850,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,sK24(X1)),sK311),sK24(X1)),
inference(forward_demodulation,[],[f2849,f1573]) ).
tff(f2849,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK311),f27(f31,X1)),
inference(forward_demodulation,[],[f2282,f1488]) ).
tff(f2282,plain,
! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK311),f27(f31,f34(f35,X1))),
inference(cnf_transformation,[],[f1420]) ).
tff(f1420,plain,
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK311),f27(f31,f34(f35,X1)))
& $less(0.0,sK311) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK311])],[f548,f1419]) ).
tff(f1419,plain,
( ? [X0: $real] :
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f27(f31,f34(f35,X1)))
& $less(0.0,X0) )
=> ( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),sK311),f27(f31,f34(f35,X1)))
& $less(0.0,sK311) ) ),
introduced(choice_axiom,[]) ).
tff(f548,plain,
? [X0: $real] :
( ! [X1: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X1)),X0),f27(f31,f34(f35,X1)))
& $less(0.0,X0) ),
inference(theory_normalization,[],[f131]) ).
tff(f131,axiom,
? [X0: $real] :
( ! [X1: 'S10'] : $lesseq(f27(f31,f34(f35,X1)),f22(f49(f50,f27(f31,X1)),X0))
& $less(0.0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_131) ).
tff(f5279,plain,
( spl331_406
| ~ spl331_238
| ~ spl331_405 ),
inference(avatar_split_clause,[],[f5275,f5272,f3988,f5277]) ).
tff(f5277,plain,
( spl331_406
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK32(X0) = sK249(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_406])]) ).
tff(f3988,plain,
( spl331_238
<=> ! [X0: 'S2'] : ( sK32(X0) = f9(f10,sK27(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_238])]) ).
tff(f5272,plain,
( spl331_405
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK249(X0,X1,X2) = f9(f10,sK27(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_405])]) ).
tff(f5275,plain,
( ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK32(X0) = sK249(X0,X1,X2) )
| ~ spl331_238
| ~ spl331_405 ),
inference(forward_demodulation,[],[f5273,f3989]) ).
tff(f3989,plain,
( ! [X0: 'S2'] : ( sK32(X0) = f9(f10,sK27(X0)) )
| ~ spl331_238 ),
inference(avatar_component_clause,[],[f3988]) ).
tff(f5273,plain,
( ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK249(X0,X1,X2) = f9(f10,sK27(X0)) )
| ~ spl331_405 ),
inference(avatar_component_clause,[],[f5272]) ).
tff(f5274,plain,
spl331_405,
inference(avatar_split_clause,[],[f2802,f5272]) ).
tff(f2802,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK249(X0,X1,X2) = f9(f10,sK27(X0)) ),
inference(forward_demodulation,[],[f2140,f1580]) ).
tff(f2140,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f9(f10,f11(f12,X0)) = sK249(X0,X1,X2) ),
inference(cnf_transformation,[],[f1328]) ).
tff(f1328,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( f6(f7,f8(sK249(X0,X1,X2),f11(f12,f6(f7,$sum(sK251(X0,X1,X2),$uminus(sK250(X0,X1,X2))))))) = f6(f7,$sum(f8(sK249(X0,X1,X2),sK251(X0,X1,X2)),$uminus(f8(sK249(X0,X1,X2),sK250(X0,X1,X2))))) )
& ( f11(f12,X1) = sK251(X0,X1,X2) )
& ( f11(f12,X2) = sK250(X0,X1,X2) )
& ( f9(f10,f11(f12,X0)) = sK249(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK249,sK250,sK251])],[f770,f1327]) ).
tff(f1327,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S6',X4: $int,X5: $int] :
( ( f6(f7,f8(X3,f11(f12,f6(f7,$sum(X5,$uminus(X4)))))) = f6(f7,$sum(f8(X3,X5),$uminus(f8(X3,X4)))) )
& ( f11(f12,X1) = X5 )
& ( f11(f12,X2) = X4 )
& ( f9(f10,f11(f12,X0)) = X3 ) )
=> ( ( f6(f7,f8(sK249(X0,X1,X2),f11(f12,f6(f7,$sum(sK251(X0,X1,X2),$uminus(sK250(X0,X1,X2))))))) = f6(f7,$sum(f8(sK249(X0,X1,X2),sK251(X0,X1,X2)),$uminus(f8(sK249(X0,X1,X2),sK250(X0,X1,X2))))) )
& ( f11(f12,X1) = sK251(X0,X1,X2) )
& ( f11(f12,X2) = sK250(X0,X1,X2) )
& ( f9(f10,f11(f12,X0)) = sK249(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f770,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S6',X4: $int,X5: $int] :
( ( f6(f7,f8(X3,f11(f12,f6(f7,$sum(X5,$uminus(X4)))))) = f6(f7,$sum(f8(X3,X5),$uminus(f8(X3,X4)))) )
& ( f11(f12,X1) = X5 )
& ( f11(f12,X2) = X4 )
& ( f9(f10,f11(f12,X0)) = X3 ) ),
inference(rectify,[],[f533]) ).
tff(f533,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X36: 'S6',X37: $int,X38: $int] :
( ( f6(f7,f8(X36,f11(f12,f6(f7,$sum(X38,$uminus(X37)))))) = f6(f7,$sum(f8(X36,X38),$uminus(f8(X36,X37)))) )
& ( f11(f12,X1) = X38 )
& ( f11(f12,X2) = X37 )
& ( f9(f10,f11(f12,X0)) = X36 ) ),
inference(theory_normalization,[],[f143]) ).
tff(f143,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X36: 'S6',X37: $int,X38: $int] :
( ( f6(f7,f8(X36,f11(f12,f6(f7,$difference(X38,X37))))) = f6(f7,$difference(f8(X36,X38),f8(X36,X37))) )
& ( f11(f12,X1) = X38 )
& ( f11(f12,X2) = X37 )
& ( f9(f10,f11(f12,X0)) = X36 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_143) ).
tff(f5270,plain,
( spl331_404
| ~ spl331_133
| ~ spl331_224 ),
inference(avatar_split_clause,[],[f4420,f3896,f3512,f5268]) ).
tff(f5268,plain,
( spl331_404
<=> ! [X0: $real] : ~ $less(sK24(sK18(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_404])]) ).
tff(f3512,plain,
( spl331_133
<=> ! [X0: 'S10'] : ~ $less(sK24(X0),sK23(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_133])]) ).
tff(f3896,plain,
( spl331_224
<=> ! [X1: $real] : ( sK23(sK18(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_224])]) ).
tff(f4420,plain,
( ! [X0: $real] : ~ $less(sK24(sK18(X0)),X0)
| ~ spl331_133
| ~ spl331_224 ),
inference(superposition,[],[f3513,f3897]) ).
tff(f3897,plain,
( ! [X1: $real] : ( sK23(sK18(X1)) = X1 )
| ~ spl331_224 ),
inference(avatar_component_clause,[],[f3896]) ).
tff(f3513,plain,
( ! [X0: 'S10'] : ~ $less(sK24(X0),sK23(X0))
| ~ spl331_133 ),
inference(avatar_component_clause,[],[f3512]) ).
tff(f5266,plain,
( spl331_403
| ~ spl331_238
| ~ spl331_402 ),
inference(avatar_split_clause,[],[f5262,f5259,f3988,f5264]) ).
tff(f5264,plain,
( spl331_403
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK32(X0) = sK246(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_403])]) ).
tff(f5259,plain,
( spl331_402
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK246(X0,X1,X2) = f9(f10,sK27(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_402])]) ).
tff(f5262,plain,
( ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK32(X0) = sK246(X0,X1,X2) )
| ~ spl331_238
| ~ spl331_402 ),
inference(forward_demodulation,[],[f5260,f3989]) ).
tff(f5260,plain,
( ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK246(X0,X1,X2) = f9(f10,sK27(X0)) )
| ~ spl331_402 ),
inference(avatar_component_clause,[],[f5259]) ).
tff(f5261,plain,
spl331_402,
inference(avatar_split_clause,[],[f2798,f5259]) ).
tff(f2798,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK246(X0,X1,X2) = f9(f10,sK27(X0)) ),
inference(forward_demodulation,[],[f2136,f1580]) ).
tff(f2136,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f9(f10,f11(f12,X0)) = sK246(X0,X1,X2) ),
inference(cnf_transformation,[],[f1326]) ).
tff(f1326,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( f6(f7,f8(f9(f10,f8(sK246(X0,X1,X2),sK247(X0,X1,X2))),sK248(X0,X1,X2))) = f6(f7,f8(sK246(X0,X1,X2),f8(f9(f10,sK247(X0,X1,X2)),sK248(X0,X1,X2)))) )
& ( f11(f12,X2) = sK248(X0,X1,X2) )
& ( f11(f12,X1) = sK247(X0,X1,X2) )
& ( f9(f10,f11(f12,X0)) = sK246(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK246,sK247,sK248])],[f769,f1325]) ).
tff(f1325,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S6',X4: $int,X5: $int] :
( ( f6(f7,f8(f9(f10,f8(X3,X4)),X5)) = f6(f7,f8(X3,f8(f9(f10,X4),X5))) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X1) = X4 )
& ( f9(f10,f11(f12,X0)) = X3 ) )
=> ( ( f6(f7,f8(f9(f10,f8(sK246(X0,X1,X2),sK247(X0,X1,X2))),sK248(X0,X1,X2))) = f6(f7,f8(sK246(X0,X1,X2),f8(f9(f10,sK247(X0,X1,X2)),sK248(X0,X1,X2)))) )
& ( f11(f12,X2) = sK248(X0,X1,X2) )
& ( f11(f12,X1) = sK247(X0,X1,X2) )
& ( f9(f10,f11(f12,X0)) = sK246(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f769,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S6',X4: $int,X5: $int] :
( ( f6(f7,f8(f9(f10,f8(X3,X4)),X5)) = f6(f7,f8(X3,f8(f9(f10,X4),X5))) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X1) = X4 )
& ( f9(f10,f11(f12,X0)) = X3 ) ),
inference(rectify,[],[f148]) ).
tff(f148,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X46: 'S6',X47: $int,X48: $int] :
( ( f6(f7,f8(f9(f10,f8(X46,X47)),X48)) = f6(f7,f8(X46,f8(f9(f10,X47),X48))) )
& ( f11(f12,X2) = X48 )
& ( f11(f12,X1) = X47 )
& ( f9(f10,f11(f12,X0)) = X46 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_148) ).
tff(f5257,plain,
( spl331_401
| ~ spl331_238
| ~ spl331_400 ),
inference(avatar_split_clause,[],[f5253,f5250,f3988,f5255]) ).
tff(f5255,plain,
( spl331_401
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK32(X0) = sK243(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_401])]) ).
tff(f5250,plain,
( spl331_400
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK243(X0,X1,X2) = f9(f10,sK27(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_400])]) ).
tff(f5253,plain,
( ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK32(X0) = sK243(X0,X1,X2) )
| ~ spl331_238
| ~ spl331_400 ),
inference(forward_demodulation,[],[f5251,f3989]) ).
tff(f5251,plain,
( ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK243(X0,X1,X2) = f9(f10,sK27(X0)) )
| ~ spl331_400 ),
inference(avatar_component_clause,[],[f5250]) ).
tff(f5252,plain,
spl331_400,
inference(avatar_split_clause,[],[f2794,f5250]) ).
tff(f2794,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK243(X0,X1,X2) = f9(f10,sK27(X0)) ),
inference(forward_demodulation,[],[f2132,f1580]) ).
tff(f2132,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f9(f10,f11(f12,X0)) = sK243(X0,X1,X2) ),
inference(cnf_transformation,[],[f1324]) ).
tff(f1324,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( f6(f7,f8(sK243(X0,X1,X2),$sum(sK244(X0,X1,X2),sK245(X0,X1,X2)))) = f6(f7,$sum(f8(sK243(X0,X1,X2),sK244(X0,X1,X2)),f8(sK243(X0,X1,X2),sK245(X0,X1,X2)))) )
& ( f11(f12,X2) = sK245(X0,X1,X2) )
& ( f11(f12,X1) = sK244(X0,X1,X2) )
& ( f9(f10,f11(f12,X0)) = sK243(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK243,sK244,sK245])],[f768,f1323]) ).
tff(f1323,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S6',X4: $int,X5: $int] :
( ( f6(f7,f8(X3,$sum(X4,X5))) = f6(f7,$sum(f8(X3,X4),f8(X3,X5))) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X1) = X4 )
& ( f9(f10,f11(f12,X0)) = X3 ) )
=> ( ( f6(f7,f8(sK243(X0,X1,X2),$sum(sK244(X0,X1,X2),sK245(X0,X1,X2)))) = f6(f7,$sum(f8(sK243(X0,X1,X2),sK244(X0,X1,X2)),f8(sK243(X0,X1,X2),sK245(X0,X1,X2)))) )
& ( f11(f12,X2) = sK245(X0,X1,X2) )
& ( f11(f12,X1) = sK244(X0,X1,X2) )
& ( f9(f10,f11(f12,X0)) = sK243(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f768,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S6',X4: $int,X5: $int] :
( ( f6(f7,f8(X3,$sum(X4,X5))) = f6(f7,$sum(f8(X3,X4),f8(X3,X5))) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X1) = X4 )
& ( f9(f10,f11(f12,X0)) = X3 ) ),
inference(rectify,[],[f142]) ).
tff(f142,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X33: 'S6',X34: $int,X35: $int] :
( ( f6(f7,f8(X33,$sum(X34,X35))) = f6(f7,$sum(f8(X33,X34),f8(X33,X35))) )
& ( f11(f12,X2) = X35 )
& ( f11(f12,X1) = X34 )
& ( f9(f10,f11(f12,X0)) = X33 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_142) ).
tff(f5248,plain,
( spl331_399
| ~ spl331_238
| ~ spl331_398 ),
inference(avatar_split_clause,[],[f5244,f5241,f3988,f5246]) ).
tff(f5246,plain,
( spl331_399
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK242(X0,X1,X2) = sK32(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_399])]) ).
tff(f5241,plain,
( spl331_398
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK242(X0,X1,X2) = f9(f10,sK27(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_398])]) ).
tff(f5244,plain,
( ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK242(X0,X1,X2) = sK32(X2) )
| ~ spl331_238
| ~ spl331_398 ),
inference(forward_demodulation,[],[f5242,f3989]) ).
tff(f5242,plain,
( ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK242(X0,X1,X2) = f9(f10,sK27(X2)) )
| ~ spl331_398 ),
inference(avatar_component_clause,[],[f5241]) ).
tff(f5243,plain,
spl331_398,
inference(avatar_split_clause,[],[f2789,f5241]) ).
tff(f2789,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK242(X0,X1,X2) = f9(f10,sK27(X2)) ),
inference(forward_demodulation,[],[f2130,f1580]) ).
tff(f2130,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f9(f10,f11(f12,X2)) = sK242(X0,X1,X2) ),
inference(cnf_transformation,[],[f1322]) ).
tff(f1322,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( ~ $less(f8(sK242(X0,X1,X2),sK240(X0,X1,X2)),f8(sK242(X0,X1,X2),sK241(X0,X1,X2)))
| $less(sK240(X0,X1,X2),sK241(X0,X1,X2)) )
& ( f9(f10,f11(f12,X2)) = sK242(X0,X1,X2) )
& ( f11(f12,X0) = sK241(X0,X1,X2) )
& ( f11(f12,X1) = sK240(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK240,sK241,sK242])],[f889,f1321]) ).
tff(f1321,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: $int,X4: $int,X5: 'S6'] :
( ( ~ $less(f8(X5,X3),f8(X5,X4))
| $less(X3,X4) )
& ( f9(f10,f11(f12,X2)) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) )
=> ( ( ~ $less(f8(sK242(X0,X1,X2),sK240(X0,X1,X2)),f8(sK242(X0,X1,X2),sK241(X0,X1,X2)))
| $less(sK240(X0,X1,X2),sK241(X0,X1,X2)) )
& ( f9(f10,f11(f12,X2)) = sK242(X0,X1,X2) )
& ( f11(f12,X0) = sK241(X0,X1,X2) )
& ( f11(f12,X1) = sK240(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f889,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: 'S6'] :
( ( ~ $less(f8(X5,X3),f8(X5,X4))
| $less(X3,X4) )
& ( f9(f10,f11(f12,X2)) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) ),
inference(ennf_transformation,[],[f767]) ).
tff(f767,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: 'S6'] :
( ( ~ $less(X3,X4)
=> ~ $less(f8(X5,X3),f8(X5,X4)) )
& ( f9(f10,f11(f12,X2)) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) ),
inference(rectify,[],[f532]) ).
tff(f532,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X82: $int,X83: $int,X84: 'S6'] :
( ( ~ $less(X82,X83)
=> ~ $less(f8(X84,X82),f8(X84,X83)) )
& ( f9(f10,f11(f12,X2)) = X84 )
& ( f11(f12,X0) = X83 )
& ( f11(f12,X1) = X82 ) ),
inference(theory_normalization,[],[f162]) ).
tff(f162,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X82: $int,X83: $int,X84: 'S6'] :
( ( $lesseq(X83,X82)
=> $lesseq(f8(X84,X83),f8(X84,X82)) )
& ( f9(f10,f11(f12,X2)) = X84 )
& ( f11(f12,X0) = X83 )
& ( f11(f12,X1) = X82 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_162) ).
tff(f5237,plain,
( spl331_397
| ~ spl331_238
| ~ spl331_396 ),
inference(avatar_split_clause,[],[f5233,f5230,f3988,f5235]) ).
tff(f5235,plain,
( spl331_397
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK32(X0) = sK206(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_397])]) ).
tff(f5230,plain,
( spl331_396
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK206(X0,X1,X2) = f9(f10,sK27(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_396])]) ).
tff(f5233,plain,
( ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK32(X0) = sK206(X0,X1,X2) )
| ~ spl331_238
| ~ spl331_396 ),
inference(forward_demodulation,[],[f5231,f3989]) ).
tff(f5231,plain,
( ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK206(X0,X1,X2) = f9(f10,sK27(X0)) )
| ~ spl331_396 ),
inference(avatar_component_clause,[],[f5230]) ).
tff(f5232,plain,
spl331_396,
inference(avatar_split_clause,[],[f2759,f5230]) ).
tff(f2759,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK206(X0,X1,X2) = f9(f10,sK27(X0)) ),
inference(forward_demodulation,[],[f2073,f1580]) ).
tff(f2073,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f9(f10,f11(f12,X0)) = sK206(X0,X1,X2) ),
inference(cnf_transformation,[],[f1287]) ).
tff(f1287,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( ( f6(f7,f8(sK206(X0,X1,X2),f11(f12,X1))) = f6(f7,f8(sK206(X0,X1,X2),f11(f12,X2))) )
| ( ( f6(f7,0) != X0 )
& ( X1 != X2 ) ) )
& ( ( f6(f7,0) = X0 )
| ( X1 = X2 )
| ( f6(f7,f8(sK206(X0,X1,X2),f11(f12,X1))) != f6(f7,f8(sK206(X0,X1,X2),f11(f12,X2))) ) )
& ( f9(f10,f11(f12,X0)) = sK206(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK206])],[f1285,f1286]) ).
tff(f1286,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S6'] :
( ( ( f6(f7,f8(X3,f11(f12,X1))) = f6(f7,f8(X3,f11(f12,X2))) )
| ( ( f6(f7,0) != X0 )
& ( X1 != X2 ) ) )
& ( ( f6(f7,0) = X0 )
| ( X1 = X2 )
| ( f6(f7,f8(X3,f11(f12,X1))) != f6(f7,f8(X3,f11(f12,X2))) ) )
& ( f9(f10,f11(f12,X0)) = X3 ) )
=> ( ( ( f6(f7,f8(sK206(X0,X1,X2),f11(f12,X1))) = f6(f7,f8(sK206(X0,X1,X2),f11(f12,X2))) )
| ( ( f6(f7,0) != X0 )
& ( X1 != X2 ) ) )
& ( ( f6(f7,0) = X0 )
| ( X1 = X2 )
| ( f6(f7,f8(sK206(X0,X1,X2),f11(f12,X1))) != f6(f7,f8(sK206(X0,X1,X2),f11(f12,X2))) ) )
& ( f9(f10,f11(f12,X0)) = sK206(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1285,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S6'] :
( ( ( f6(f7,f8(X3,f11(f12,X1))) = f6(f7,f8(X3,f11(f12,X2))) )
| ( ( f6(f7,0) != X0 )
& ( X1 != X2 ) ) )
& ( ( f6(f7,0) = X0 )
| ( X1 = X2 )
| ( f6(f7,f8(X3,f11(f12,X1))) != f6(f7,f8(X3,f11(f12,X2))) ) )
& ( f9(f10,f11(f12,X0)) = X3 ) ),
inference(flattening,[],[f1284]) ).
tff(f1284,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S6'] :
( ( ( f6(f7,f8(X3,f11(f12,X1))) = f6(f7,f8(X3,f11(f12,X2))) )
| ( ( f6(f7,0) != X0 )
& ( X1 != X2 ) ) )
& ( ( f6(f7,0) = X0 )
| ( X1 = X2 )
| ( f6(f7,f8(X3,f11(f12,X1))) != f6(f7,f8(X3,f11(f12,X2))) ) )
& ( f9(f10,f11(f12,X0)) = X3 ) ),
inference(nnf_transformation,[],[f753]) ).
tff(f753,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S6'] :
( ( ( f6(f7,f8(X3,f11(f12,X1))) = f6(f7,f8(X3,f11(f12,X2))) )
<=> ( ( f6(f7,0) = X0 )
| ( X1 = X2 ) ) )
& ( f9(f10,f11(f12,X0)) = X3 ) ),
inference(rectify,[],[f156]) ).
tff(f156,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X70: 'S6'] :
( ( ( f6(f7,f8(X70,f11(f12,X1))) = f6(f7,f8(X70,f11(f12,X2))) )
<=> ( ( f6(f7,0) = X0 )
| ( X1 = X2 ) ) )
& ( f9(f10,f11(f12,X0)) = X70 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_156) ).
tff(f5228,plain,
spl331_395,
inference(avatar_split_clause,[],[f2619,f5226]) ).
tff(f5226,plain,
( spl331_395
<=> ! [X0: 'S2',X1: 'S2'] : ( sK108(X0,X1) = $sum(sK27(X0),sK27(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_395])]) ).
tff(f2619,plain,
! [X0: 'S2',X1: 'S2'] : ( sK108(X0,X1) = $sum(sK27(X0),sK27(X1)) ),
inference(forward_demodulation,[],[f2618,f1580]) ).
tff(f2618,plain,
! [X0: 'S2',X1: 'S2'] : ( sK108(X0,X1) = $sum(f11(f12,X0),sK27(X1)) ),
inference(forward_demodulation,[],[f1848,f1580]) ).
tff(f1848,plain,
! [X0: 'S2',X1: 'S2'] : ( $sum(f11(f12,X0),f11(f12,X1)) = sK108(X0,X1) ),
inference(cnf_transformation,[],[f1129]) ).
tff(f1129,plain,
! [X0: 'S2',X1: 'S2'] :
( ( sK108(X0,X1) = f11(f12,f6(f7,sK108(X0,X1))) )
& ( $sum(f11(f12,X0),f11(f12,X1)) = sK108(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK108])],[f686,f1128]) ).
tff(f1128,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: $int] :
( ( f11(f12,f6(f7,X2)) = X2 )
& ( $sum(f11(f12,X0),f11(f12,X1)) = X2 ) )
=> ( ( sK108(X0,X1) = f11(f12,f6(f7,sK108(X0,X1))) )
& ( $sum(f11(f12,X0),f11(f12,X1)) = sK108(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f686,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int] :
( ( f11(f12,f6(f7,X2)) = X2 )
& ( $sum(f11(f12,X0),f11(f12,X1)) = X2 ) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X21: $int] :
( ( f11(f12,f6(f7,X21)) = X21 )
& ( $sum(f11(f12,X0),f11(f12,X1)) = X21 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_99) ).
tff(f5224,plain,
( spl331_394
| ~ spl331_64
| ~ spl331_393 ),
inference(avatar_split_clause,[],[f5219,f5215,f3204,f5221]) ).
tff(f5221,plain,
( spl331_394
<=> ( f34(f39(f52,f51),f51) = sK18(-1.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_394])]) ).
tff(f5215,plain,
( spl331_393
<=> ( f34(f39(f52,f51),f51) = f16(f32,-1.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_393])]) ).
tff(f5219,plain,
( ( f34(f39(f52,f51),f51) = sK18(-1.0) )
| ~ spl331_64
| ~ spl331_393 ),
inference(forward_demodulation,[],[f5217,f3205]) ).
tff(f5217,plain,
( ( f34(f39(f52,f51),f51) = f16(f32,-1.0) )
| ~ spl331_393 ),
inference(avatar_component_clause,[],[f5215]) ).
tff(f5218,plain,
spl331_393,
inference(avatar_split_clause,[],[f2333,f5215]) ).
tff(f2333,plain,
f34(f39(f52,f51),f51) = f16(f32,-1.0),
inference(evaluation,[],[f1466]) ).
tff(f1466,plain,
f34(f39(f52,f51),f51) = f16(f32,$uminus(1.0)),
inference(cnf_transformation,[],[f175]) ).
tff(f175,axiom,
f34(f39(f52,f51),f51) = f16(f32,$uminus(1.0)),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_175) ).
tff(f5213,plain,
spl331_392,
inference(avatar_split_clause,[],[f2258,f5211]) ).
tff(f5211,plain,
( spl331_392
<=> ! [X0: 'S10',X3: 'S10',X2: 'S10',X1: 'S10'] : ( f39(f52,X2) = sK303(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_392])]) ).
tff(f2258,plain,
! [X2: 'S10',X3: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X2) = sK303(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1408]) ).
tff(f1408,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ( f34(f39(f61,f34(f39(f52,X0),X1)),f34(sK303(X0,X1,X2,X3),X3)) = f34(f39(f40,f34(f39(f40,f34(sK304(X0,X1,X2,X3),sK305(X0,X1,X2,X3))),f34(sK304(X0,X1,X2,X3),X3))),f34(sK303(X0,X1,X2,X3),sK305(X0,X1,X2,X3))) )
& ( f34(f39(f61,X1),X3) = sK305(X0,X1,X2,X3) )
& ( f39(f52,f34(f39(f61,X0),X2)) = sK304(X0,X1,X2,X3) )
& ( f39(f52,X2) = sK303(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK303,sK304,sK305])],[f799,f1407]) ).
tff(f1407,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ? [X4: 'S17',X5: 'S17',X6: 'S10'] :
( ( f34(f39(f61,f34(f39(f52,X0),X1)),f34(X4,X3)) = f34(f39(f40,f34(f39(f40,f34(X5,X6)),f34(X5,X3))),f34(X4,X6)) )
& ( f34(f39(f61,X1),X3) = X6 )
& ( f39(f52,f34(f39(f61,X0),X2)) = X5 )
& ( f39(f52,X2) = X4 ) )
=> ( ( f34(f39(f61,f34(f39(f52,X0),X1)),f34(sK303(X0,X1,X2,X3),X3)) = f34(f39(f40,f34(f39(f40,f34(sK304(X0,X1,X2,X3),sK305(X0,X1,X2,X3))),f34(sK304(X0,X1,X2,X3),X3))),f34(sK303(X0,X1,X2,X3),sK305(X0,X1,X2,X3))) )
& ( f34(f39(f61,X1),X3) = sK305(X0,X1,X2,X3) )
& ( f39(f52,f34(f39(f61,X0),X2)) = sK304(X0,X1,X2,X3) )
& ( f39(f52,X2) = sK303(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f799,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X4: 'S17',X5: 'S17',X6: 'S10'] :
( ( f34(f39(f61,f34(f39(f52,X0),X1)),f34(X4,X3)) = f34(f39(f40,f34(f39(f40,f34(X5,X6)),f34(X5,X3))),f34(X4,X6)) )
& ( f34(f39(f61,X1),X3) = X6 )
& ( f39(f52,f34(f39(f61,X0),X2)) = X5 )
& ( f39(f52,X2) = X4 ) ),
inference(rectify,[],[f384]) ).
tff(f384,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X232: 'S17',X233: 'S17',X234: 'S10'] :
( ( f34(f39(f61,f34(f39(f52,X0),X1)),f34(X232,X3)) = f34(f39(f40,f34(f39(f40,f34(X233,X234)),f34(X233,X3))),f34(X232,X234)) )
& ( f34(f39(f61,X1),X3) = X234 )
& ( f39(f52,f34(f39(f61,X0),X2)) = X233 )
& ( f39(f52,X2) = X232 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_384) ).
tff(f5209,plain,
spl331_391,
inference(avatar_split_clause,[],[f2254,f5207]) ).
tff(f5207,plain,
( spl331_391
<=> ! [X0: $real,X3: $real,X2: $real,X1: $real] : ( f49(f50,X2) = sK300(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_391])]) ).
tff(f2254,plain,
! [X2: $real,X3: $real,X0: $real,X1: $real] : ( f49(f50,X2) = sK300(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1406]) ).
tff(f5205,plain,
spl331_390,
inference(avatar_split_clause,[],[f2252,f5203]) ).
tff(f5203,plain,
( spl331_390
<=> ! [X0: 'S10',X3: 'S10',X2: 'S10',X1: 'S10'] : ( f39(f52,X2) = sK299(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_390])]) ).
tff(f2252,plain,
! [X2: 'S10',X3: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X2) = sK299(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1404]) ).
tff(f1404,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ( f34(sK298(X0,X1,X2,X3),f34(sK299(X0,X1,X2,X3),X3)) = f34(sK299(X0,X1,X2,X3),f34(sK298(X0,X1,X2,X3),X3)) )
& ( f39(f52,X2) = sK299(X0,X1,X2,X3) )
& ( f39(f52,f34(f39(f52,X0),X1)) = sK298(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK298,sK299])],[f797,f1403]) ).
tff(f1403,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ? [X4: 'S17',X5: 'S17'] :
( ( f34(X4,f34(X5,X3)) = f34(X5,f34(X4,X3)) )
& ( f39(f52,X2) = X5 )
& ( f39(f52,f34(f39(f52,X0),X1)) = X4 ) )
=> ( ( f34(sK298(X0,X1,X2,X3),f34(sK299(X0,X1,X2,X3),X3)) = f34(sK299(X0,X1,X2,X3),f34(sK298(X0,X1,X2,X3),X3)) )
& ( f39(f52,X2) = sK299(X0,X1,X2,X3) )
& ( f39(f52,f34(f39(f52,X0),X1)) = sK298(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f797,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X4: 'S17',X5: 'S17'] :
( ( f34(X4,f34(X5,X3)) = f34(X5,f34(X4,X3)) )
& ( f39(f52,X2) = X5 )
& ( f39(f52,f34(f39(f52,X0),X1)) = X4 ) ),
inference(rectify,[],[f253]) ).
tff(f253,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X160: 'S17',X161: 'S17'] :
( ( f34(X160,f34(X161,X3)) = f34(X161,f34(X160,X3)) )
& ( f39(f52,X2) = X161 )
& ( f39(f52,f34(f39(f52,X0),X1)) = X160 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_253) ).
tff(f5201,plain,
spl331_389,
inference(avatar_split_clause,[],[f2249,f5199]) ).
tff(f5199,plain,
( spl331_389
<=> ! [X0: $real,X3: $real,X2: $real,X1: $real] : ( f49(f50,X2) = sK297(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_389])]) ).
tff(f2249,plain,
! [X2: $real,X3: $real,X0: $real,X1: $real] : ( f49(f50,X2) = sK297(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1402]) ).
tff(f1402,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ( f22(sK296(X0,X1,X2,X3),f22(sK297(X0,X1,X2,X3),X3)) = f22(sK297(X0,X1,X2,X3),f22(sK296(X0,X1,X2,X3),X3)) )
& ( f49(f50,X2) = sK297(X0,X1,X2,X3) )
& ( f49(f50,f22(f49(f50,X0),X1)) = sK296(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK296,sK297])],[f796,f1401]) ).
tff(f1401,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ? [X4: 'S14',X5: 'S14'] :
( ( f22(X4,f22(X5,X3)) = f22(X5,f22(X4,X3)) )
& ( f49(f50,X2) = X5 )
& ( f49(f50,f22(f49(f50,X0),X1)) = X4 ) )
=> ( ( f22(sK296(X0,X1,X2,X3),f22(sK297(X0,X1,X2,X3),X3)) = f22(sK297(X0,X1,X2,X3),f22(sK296(X0,X1,X2,X3),X3)) )
& ( f49(f50,X2) = sK297(X0,X1,X2,X3) )
& ( f49(f50,f22(f49(f50,X0),X1)) = sK296(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f796,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X4: 'S14',X5: 'S14'] :
( ( f22(X4,f22(X5,X3)) = f22(X5,f22(X4,X3)) )
& ( f49(f50,X2) = X5 )
& ( f49(f50,f22(f49(f50,X0),X1)) = X4 ) ),
inference(rectify,[],[f251]) ).
tff(f251,axiom,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X156: 'S14',X157: 'S14'] :
( ( f22(X156,f22(X157,X3)) = f22(X157,f22(X156,X3)) )
& ( f49(f50,X2) = X157 )
& ( f49(f50,f22(f49(f50,X0),X1)) = X156 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_251) ).
tff(f5194,plain,
spl331_388,
inference(avatar_split_clause,[],[f2246,f5192]) ).
tff(f5192,plain,
( spl331_388
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( f9(f10,X2) = sK295(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_388])]) ).
tff(f2246,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] : ( f9(f10,X2) = sK295(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1400]) ).
tff(f1400,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
( ( f8(sK294(X0,X1,X2,X3),f8(sK295(X0,X1,X2,X3),X3)) = f8(sK295(X0,X1,X2,X3),f8(sK294(X0,X1,X2,X3),X3)) )
& ( f9(f10,X2) = sK295(X0,X1,X2,X3) )
& ( f9(f10,f8(f9(f10,X0),X1)) = sK294(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK294,sK295])],[f795,f1399]) ).
tff(f1399,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
( ? [X4: 'S6',X5: 'S6'] :
( ( f8(X4,f8(X5,X3)) = f8(X5,f8(X4,X3)) )
& ( f9(f10,X2) = X5 )
& ( f9(f10,f8(f9(f10,X0),X1)) = X4 ) )
=> ( ( f8(sK294(X0,X1,X2,X3),f8(sK295(X0,X1,X2,X3),X3)) = f8(sK295(X0,X1,X2,X3),f8(sK294(X0,X1,X2,X3),X3)) )
& ( f9(f10,X2) = sK295(X0,X1,X2,X3) )
& ( f9(f10,f8(f9(f10,X0),X1)) = sK294(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f795,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X4: 'S6',X5: 'S6'] :
( ( f8(X4,f8(X5,X3)) = f8(X5,f8(X4,X3)) )
& ( f9(f10,X2) = X5 )
& ( f9(f10,f8(f9(f10,X0),X1)) = X4 ) ),
inference(rectify,[],[f252]) ).
tff(f252,axiom,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X158: 'S6',X159: 'S6'] :
( ( f8(X158,f8(X159,X3)) = f8(X159,f8(X158,X3)) )
& ( f9(f10,X2) = X159 )
& ( f9(f10,f8(f9(f10,X0),X1)) = X158 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_252) ).
tff(f5190,plain,
spl331_387,
inference(avatar_split_clause,[],[f2243,f5188]) ).
tff(f5188,plain,
( spl331_387
<=> ! [X0: 'S2',X3: 'S2',X2: 'S2',X1: 'S2'] : ( f4(f54,X2) = sK293(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_387])]) ).
tff(f2243,plain,
! [X2: 'S2',X3: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X2) = sK293(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1398]) ).
tff(f1398,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
( ( f3(sK292(X0,X1,X2,X3),f3(sK293(X0,X1,X2,X3),X3)) = f3(sK293(X0,X1,X2,X3),f3(sK292(X0,X1,X2,X3),X3)) )
& ( f4(f54,X2) = sK293(X0,X1,X2,X3) )
& ( f4(f54,f3(f4(f54,X0),X1)) = sK292(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK292,sK293])],[f794,f1397]) ).
tff(f1397,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
( ? [X4: 'S3',X5: 'S3'] :
( ( f3(X4,f3(X5,X3)) = f3(X5,f3(X4,X3)) )
& ( f4(f54,X2) = X5 )
& ( f4(f54,f3(f4(f54,X0),X1)) = X4 ) )
=> ( ( f3(sK292(X0,X1,X2,X3),f3(sK293(X0,X1,X2,X3),X3)) = f3(sK293(X0,X1,X2,X3),f3(sK292(X0,X1,X2,X3),X3)) )
& ( f4(f54,X2) = sK293(X0,X1,X2,X3) )
& ( f4(f54,f3(f4(f54,X0),X1)) = sK292(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f794,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X4: 'S3',X5: 'S3'] :
( ( f3(X4,f3(X5,X3)) = f3(X5,f3(X4,X3)) )
& ( f4(f54,X2) = X5 )
& ( f4(f54,f3(f4(f54,X0),X1)) = X4 ) ),
inference(rectify,[],[f250]) ).
tff(f250,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X154: 'S3',X155: 'S3'] :
( ( f3(X154,f3(X155,X3)) = f3(X155,f3(X154,X3)) )
& ( f4(f54,X2) = X155 )
& ( f4(f54,f3(f4(f54,X0),X1)) = X154 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_250) ).
tff(f5186,plain,
spl331_386,
inference(avatar_split_clause,[],[f2239,f5184]) ).
tff(f5184,plain,
( spl331_386
<=> ! [X0: 'S10',X3: 'S10',X2: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK290(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_386])]) ).
tff(f2239,plain,
! [X2: 'S10',X3: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK290(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1396]) ).
tff(f1396,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ( f34(f39(f52,f34(sK290(X0,X1,X2,X3),X1)),sK291(X0,X1,X2,X3)) = f34(sK290(X0,X1,X2,X3),f34(f39(f52,X1),sK291(X0,X1,X2,X3))) )
& ( f34(f39(f52,X2),X3) = sK291(X0,X1,X2,X3) )
& ( f39(f52,X0) = sK290(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK290,sK291])],[f793,f1395]) ).
tff(f1395,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ? [X4: 'S17',X5: 'S10'] :
( ( f34(f39(f52,f34(X4,X1)),X5) = f34(X4,f34(f39(f52,X1),X5)) )
& ( f34(f39(f52,X2),X3) = X5 )
& ( f39(f52,X0) = X4 ) )
=> ( ( f34(f39(f52,f34(sK290(X0,X1,X2,X3),X1)),sK291(X0,X1,X2,X3)) = f34(sK290(X0,X1,X2,X3),f34(f39(f52,X1),sK291(X0,X1,X2,X3))) )
& ( f34(f39(f52,X2),X3) = sK291(X0,X1,X2,X3) )
& ( f39(f52,X0) = sK290(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f793,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X4: 'S17',X5: 'S10'] :
( ( f34(f39(f52,f34(X4,X1)),X5) = f34(X4,f34(f39(f52,X1),X5)) )
& ( f34(f39(f52,X2),X3) = X5 )
& ( f39(f52,X0) = X4 ) ),
inference(rectify,[],[f249]) ).
tff(f249,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X152: 'S17',X153: 'S10'] :
( ( f34(f39(f52,f34(X152,X1)),X153) = f34(X152,f34(f39(f52,X1),X153)) )
& ( f34(f39(f52,X2),X3) = X153 )
& ( f39(f52,X0) = X152 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_249) ).
tff(f5182,plain,
spl331_385,
inference(avatar_split_clause,[],[f2235,f5180]) ).
tff(f5180,plain,
( spl331_385
<=> ! [X0: 'S10',X3: 'S10',X2: 'S10',X1: 'S10'] : ( f39(f52,X1) = sK289(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_385])]) ).
tff(f2235,plain,
! [X2: 'S10',X3: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X1) = sK289(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1394]) ).
tff(f1394,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( f34(f39(f40,f34(sK288(X0,X1,X2,X3),X2)),f34(sK289(X0,X1,X2,X3),X3)) = f34(f39(f40,f34(sK288(X0,X1,X2,X3),X3)),f34(sK289(X0,X1,X2,X3),X2)) ) )
& ( ( f34(f39(f40,f34(sK288(X0,X1,X2,X3),X2)),f34(sK289(X0,X1,X2,X3),X3)) != f34(f39(f40,f34(sK288(X0,X1,X2,X3),X3)),f34(sK289(X0,X1,X2,X3),X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f39(f52,X1) = sK289(X0,X1,X2,X3) )
& ( f39(f52,X0) = sK288(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK288,sK289])],[f1392,f1393]) ).
tff(f1393,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ? [X4: 'S17',X5: 'S17'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( f34(f39(f40,f34(X4,X2)),f34(X5,X3)) = f34(f39(f40,f34(X4,X3)),f34(X5,X2)) ) )
& ( ( f34(f39(f40,f34(X4,X2)),f34(X5,X3)) != f34(f39(f40,f34(X4,X3)),f34(X5,X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f39(f52,X1) = X5 )
& ( f39(f52,X0) = X4 ) )
=> ( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( f34(f39(f40,f34(sK288(X0,X1,X2,X3),X2)),f34(sK289(X0,X1,X2,X3),X3)) = f34(f39(f40,f34(sK288(X0,X1,X2,X3),X3)),f34(sK289(X0,X1,X2,X3),X2)) ) )
& ( ( f34(f39(f40,f34(sK288(X0,X1,X2,X3),X2)),f34(sK289(X0,X1,X2,X3),X3)) != f34(f39(f40,f34(sK288(X0,X1,X2,X3),X3)),f34(sK289(X0,X1,X2,X3),X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f39(f52,X1) = sK289(X0,X1,X2,X3) )
& ( f39(f52,X0) = sK288(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1392,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X4: 'S17',X5: 'S17'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( f34(f39(f40,f34(X4,X2)),f34(X5,X3)) = f34(f39(f40,f34(X4,X3)),f34(X5,X2)) ) )
& ( ( f34(f39(f40,f34(X4,X2)),f34(X5,X3)) != f34(f39(f40,f34(X4,X3)),f34(X5,X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f39(f52,X1) = X5 )
& ( f39(f52,X0) = X4 ) ),
inference(flattening,[],[f1391]) ).
tff(f1391,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X4: 'S17',X5: 'S17'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( f34(f39(f40,f34(X4,X2)),f34(X5,X3)) = f34(f39(f40,f34(X4,X3)),f34(X5,X2)) ) )
& ( ( f34(f39(f40,f34(X4,X2)),f34(X5,X3)) != f34(f39(f40,f34(X4,X3)),f34(X5,X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f39(f52,X1) = X5 )
& ( f39(f52,X0) = X4 ) ),
inference(nnf_transformation,[],[f792]) ).
tff(f792,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X4: 'S17',X5: 'S17'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
<=> ( f34(f39(f40,f34(X4,X2)),f34(X5,X3)) != f34(f39(f40,f34(X4,X3)),f34(X5,X2)) ) )
& ( f39(f52,X1) = X5 )
& ( f39(f52,X0) = X4 ) ),
inference(rectify,[],[f284]) ).
tff(f284,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X183: 'S17',X184: 'S17'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
<=> ( f34(f39(f40,f34(X183,X2)),f34(X184,X3)) != f34(f39(f40,f34(X183,X3)),f34(X184,X2)) ) )
& ( f39(f52,X1) = X184 )
& ( f39(f52,X0) = X183 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_284) ).
tff(f5178,plain,
spl331_384,
inference(avatar_split_clause,[],[f2234,f5176]) ).
tff(f5176,plain,
( spl331_384
<=> ! [X0: 'S10',X3: 'S10',X2: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK288(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_384])]) ).
tff(f2234,plain,
! [X2: 'S10',X3: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK288(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1394]) ).
tff(f5174,plain,
spl331_383,
inference(avatar_split_clause,[],[f2230,f5172]) ).
tff(f5172,plain,
( spl331_383
<=> ! [X0: 'S10',X3: 'S10',X2: 'S10',X1: 'S10'] : ( f39(f52,X2) = sK287(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_383])]) ).
tff(f2230,plain,
! [X2: 'S10',X3: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X2) = sK287(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1390]) ).
tff(f1390,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ( ( f34(f39(f40,f34(sK286(X0,X1,X2,X3),X1)),f34(sK287(X0,X1,X2,X3),X3)) = f34(f39(f40,f34(sK286(X0,X1,X2,X3),X3)),f34(sK287(X0,X1,X2,X3),X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( f34(f39(f40,f34(sK286(X0,X1,X2,X3),X1)),f34(sK287(X0,X1,X2,X3),X3)) != f34(f39(f40,f34(sK286(X0,X1,X2,X3),X3)),f34(sK287(X0,X1,X2,X3),X1)) ) )
& ( f39(f52,X2) = sK287(X0,X1,X2,X3) )
& ( f39(f52,X0) = sK286(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK286,sK287])],[f1388,f1389]) ).
tff(f1389,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ? [X4: 'S17',X5: 'S17'] :
( ( ( f34(f39(f40,f34(X4,X1)),f34(X5,X3)) = f34(f39(f40,f34(X4,X3)),f34(X5,X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( f34(f39(f40,f34(X4,X1)),f34(X5,X3)) != f34(f39(f40,f34(X4,X3)),f34(X5,X1)) ) )
& ( f39(f52,X2) = X5 )
& ( f39(f52,X0) = X4 ) )
=> ( ( ( f34(f39(f40,f34(sK286(X0,X1,X2,X3),X1)),f34(sK287(X0,X1,X2,X3),X3)) = f34(f39(f40,f34(sK286(X0,X1,X2,X3),X3)),f34(sK287(X0,X1,X2,X3),X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( f34(f39(f40,f34(sK286(X0,X1,X2,X3),X1)),f34(sK287(X0,X1,X2,X3),X3)) != f34(f39(f40,f34(sK286(X0,X1,X2,X3),X3)),f34(sK287(X0,X1,X2,X3),X1)) ) )
& ( f39(f52,X2) = sK287(X0,X1,X2,X3) )
& ( f39(f52,X0) = sK286(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1388,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X4: 'S17',X5: 'S17'] :
( ( ( f34(f39(f40,f34(X4,X1)),f34(X5,X3)) = f34(f39(f40,f34(X4,X3)),f34(X5,X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( f34(f39(f40,f34(X4,X1)),f34(X5,X3)) != f34(f39(f40,f34(X4,X3)),f34(X5,X1)) ) )
& ( f39(f52,X2) = X5 )
& ( f39(f52,X0) = X4 ) ),
inference(flattening,[],[f1387]) ).
tff(f1387,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X4: 'S17',X5: 'S17'] :
( ( ( f34(f39(f40,f34(X4,X1)),f34(X5,X3)) = f34(f39(f40,f34(X4,X3)),f34(X5,X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( f34(f39(f40,f34(X4,X1)),f34(X5,X3)) != f34(f39(f40,f34(X4,X3)),f34(X5,X1)) ) )
& ( f39(f52,X2) = X5 )
& ( f39(f52,X0) = X4 ) ),
inference(nnf_transformation,[],[f791]) ).
tff(f791,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X4: 'S17',X5: 'S17'] :
( ( ( f34(f39(f40,f34(X4,X1)),f34(X5,X3)) = f34(f39(f40,f34(X4,X3)),f34(X5,X1)) )
<=> ( ( X1 = X3 )
| ( X0 = X2 ) ) )
& ( f39(f52,X2) = X5 )
& ( f39(f52,X0) = X4 ) ),
inference(rectify,[],[f215]) ).
tff(f215,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X118: 'S17',X119: 'S17'] :
( ( ( f34(f39(f40,f34(X118,X1)),f34(X119,X3)) = f34(f39(f40,f34(X118,X3)),f34(X119,X1)) )
<=> ( ( X1 = X3 )
| ( X0 = X2 ) ) )
& ( f39(f52,X2) = X119 )
& ( f39(f52,X0) = X118 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_215) ).
tff(f5170,plain,
spl331_382,
inference(avatar_split_clause,[],[f2229,f5168]) ).
tff(f5168,plain,
( spl331_382
<=> ! [X0: 'S10',X3: 'S10',X2: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK286(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_382])]) ).
tff(f2229,plain,
! [X2: 'S10',X3: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK286(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1390]) ).
tff(f5166,plain,
spl331_381,
inference(avatar_split_clause,[],[f2226,f5164]) ).
tff(f5164,plain,
( spl331_381
<=> ! [X0: $real,X3: $real,X2: $real,X1: $real] : ( f49(f50,X0) = sK284(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_381])]) ).
tff(f2226,plain,
! [X2: $real,X3: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK284(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1386]) ).
tff(f1386,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ( f22(f49(f50,f22(sK284(X0,X1,X2,X3),X1)),sK285(X0,X1,X2,X3)) = f22(sK284(X0,X1,X2,X3),f22(f49(f50,X1),sK285(X0,X1,X2,X3))) )
& ( f22(f49(f50,X2),X3) = sK285(X0,X1,X2,X3) )
& ( f49(f50,X0) = sK284(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK284,sK285])],[f790,f1385]) ).
tff(f1385,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ? [X4: 'S14',X5: $real] :
( ( f22(f49(f50,f22(X4,X1)),X5) = f22(X4,f22(f49(f50,X1),X5)) )
& ( f22(f49(f50,X2),X3) = X5 )
& ( f49(f50,X0) = X4 ) )
=> ( ( f22(f49(f50,f22(sK284(X0,X1,X2,X3),X1)),sK285(X0,X1,X2,X3)) = f22(sK284(X0,X1,X2,X3),f22(f49(f50,X1),sK285(X0,X1,X2,X3))) )
& ( f22(f49(f50,X2),X3) = sK285(X0,X1,X2,X3) )
& ( f49(f50,X0) = sK284(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f790,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X4: 'S14',X5: $real] :
( ( f22(f49(f50,f22(X4,X1)),X5) = f22(X4,f22(f49(f50,X1),X5)) )
& ( f22(f49(f50,X2),X3) = X5 )
& ( f49(f50,X0) = X4 ) ),
inference(rectify,[],[f247]) ).
tff(f247,axiom,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X148: 'S14',X149: $real] :
( ( f22(f49(f50,f22(X148,X1)),X149) = f22(X148,f22(f49(f50,X1),X149)) )
& ( f22(f49(f50,X2),X3) = X149 )
& ( f49(f50,X0) = X148 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_247) ).
tff(f5162,plain,
spl331_380,
inference(avatar_split_clause,[],[f2222,f5160]) ).
tff(f5160,plain,
( spl331_380
<=> ! [X0: $real,X3: $real,X2: $real,X1: $real] : ( f49(f50,X1) = sK283(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_380])]) ).
tff(f2222,plain,
! [X2: $real,X3: $real,X0: $real,X1: $real] : ( f49(f50,X1) = sK283(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1384]) ).
tff(f1384,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( $sum(f22(sK282(X0,X1,X2,X3),X2),f22(sK283(X0,X1,X2,X3),X3)) = $sum(f22(sK282(X0,X1,X2,X3),X3),f22(sK283(X0,X1,X2,X3),X2)) ) )
& ( ( $sum(f22(sK282(X0,X1,X2,X3),X2),f22(sK283(X0,X1,X2,X3),X3)) != $sum(f22(sK282(X0,X1,X2,X3),X3),f22(sK283(X0,X1,X2,X3),X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f49(f50,X1) = sK283(X0,X1,X2,X3) )
& ( f49(f50,X0) = sK282(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK282,sK283])],[f1382,f1383]) ).
tff(f1383,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ? [X4: 'S14',X5: 'S14'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( $sum(f22(X4,X2),f22(X5,X3)) = $sum(f22(X4,X3),f22(X5,X2)) ) )
& ( ( $sum(f22(X4,X2),f22(X5,X3)) != $sum(f22(X4,X3),f22(X5,X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f49(f50,X1) = X5 )
& ( f49(f50,X0) = X4 ) )
=> ( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( $sum(f22(sK282(X0,X1,X2,X3),X2),f22(sK283(X0,X1,X2,X3),X3)) = $sum(f22(sK282(X0,X1,X2,X3),X3),f22(sK283(X0,X1,X2,X3),X2)) ) )
& ( ( $sum(f22(sK282(X0,X1,X2,X3),X2),f22(sK283(X0,X1,X2,X3),X3)) != $sum(f22(sK282(X0,X1,X2,X3),X3),f22(sK283(X0,X1,X2,X3),X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f49(f50,X1) = sK283(X0,X1,X2,X3) )
& ( f49(f50,X0) = sK282(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1382,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X4: 'S14',X5: 'S14'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( $sum(f22(X4,X2),f22(X5,X3)) = $sum(f22(X4,X3),f22(X5,X2)) ) )
& ( ( $sum(f22(X4,X2),f22(X5,X3)) != $sum(f22(X4,X3),f22(X5,X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f49(f50,X1) = X5 )
& ( f49(f50,X0) = X4 ) ),
inference(flattening,[],[f1381]) ).
tff(f1381,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X4: 'S14',X5: 'S14'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( $sum(f22(X4,X2),f22(X5,X3)) = $sum(f22(X4,X3),f22(X5,X2)) ) )
& ( ( $sum(f22(X4,X2),f22(X5,X3)) != $sum(f22(X4,X3),f22(X5,X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f49(f50,X1) = X5 )
& ( f49(f50,X0) = X4 ) ),
inference(nnf_transformation,[],[f789]) ).
tff(f789,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X4: 'S14',X5: 'S14'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
<=> ( $sum(f22(X4,X2),f22(X5,X3)) != $sum(f22(X4,X3),f22(X5,X2)) ) )
& ( f49(f50,X1) = X5 )
& ( f49(f50,X0) = X4 ) ),
inference(rectify,[],[f285]) ).
tff(f285,axiom,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X185: 'S14',X186: 'S14'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
<=> ( $sum(f22(X185,X2),f22(X186,X3)) != $sum(f22(X185,X3),f22(X186,X2)) ) )
& ( f49(f50,X1) = X186 )
& ( f49(f50,X0) = X185 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_285) ).
tff(f5158,plain,
spl331_379,
inference(avatar_split_clause,[],[f2221,f5156]) ).
tff(f5156,plain,
( spl331_379
<=> ! [X0: $real,X3: $real,X2: $real,X1: $real] : ( f49(f50,X0) = sK282(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_379])]) ).
tff(f2221,plain,
! [X2: $real,X3: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK282(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1384]) ).
tff(f5154,plain,
( spl331_378
| ~ spl331_2
| ~ spl331_243 ),
inference(avatar_split_clause,[],[f4775,f4444,f2934,f5152]) ).
tff(f4444,plain,
( spl331_243
<=> ! [X0: $real,X1: $real] :
( $less(X0,X1)
| $less(X1,$sum(X0,1.0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_243])]) ).
tff(f4775,plain,
( ! [X0: $real] : $less(X0,$sum(X0,1.0))
| ~ spl331_2
| ~ spl331_243 ),
inference(resolution,[],[f4445,f2935]) ).
tff(f4445,plain,
( ! [X0: $real,X1: $real] :
( $less(X1,$sum(X0,1.0))
| $less(X0,X1) )
| ~ spl331_243 ),
inference(avatar_component_clause,[],[f4444]) ).
tff(f5150,plain,
spl331_377,
inference(avatar_split_clause,[],[f2217,f5148]) ).
tff(f5148,plain,
( spl331_377
<=> ! [X0: $real,X3: $real,X2: $real,X1: $real] : ( f49(f50,X2) = sK281(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_377])]) ).
tff(f2217,plain,
! [X2: $real,X3: $real,X0: $real,X1: $real] : ( f49(f50,X2) = sK281(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1380]) ).
tff(f1380,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ( ( $sum(f22(sK280(X0,X1,X2,X3),X1),f22(sK281(X0,X1,X2,X3),X3)) = $sum(f22(sK280(X0,X1,X2,X3),X3),f22(sK281(X0,X1,X2,X3),X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( $sum(f22(sK280(X0,X1,X2,X3),X1),f22(sK281(X0,X1,X2,X3),X3)) != $sum(f22(sK280(X0,X1,X2,X3),X3),f22(sK281(X0,X1,X2,X3),X1)) ) )
& ( f49(f50,X2) = sK281(X0,X1,X2,X3) )
& ( f49(f50,X0) = sK280(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK280,sK281])],[f1378,f1379]) ).
tff(f1379,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ? [X4: 'S14',X5: 'S14'] :
( ( ( $sum(f22(X4,X1),f22(X5,X3)) = $sum(f22(X4,X3),f22(X5,X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( $sum(f22(X4,X1),f22(X5,X3)) != $sum(f22(X4,X3),f22(X5,X1)) ) )
& ( f49(f50,X2) = X5 )
& ( f49(f50,X0) = X4 ) )
=> ( ( ( $sum(f22(sK280(X0,X1,X2,X3),X1),f22(sK281(X0,X1,X2,X3),X3)) = $sum(f22(sK280(X0,X1,X2,X3),X3),f22(sK281(X0,X1,X2,X3),X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( $sum(f22(sK280(X0,X1,X2,X3),X1),f22(sK281(X0,X1,X2,X3),X3)) != $sum(f22(sK280(X0,X1,X2,X3),X3),f22(sK281(X0,X1,X2,X3),X1)) ) )
& ( f49(f50,X2) = sK281(X0,X1,X2,X3) )
& ( f49(f50,X0) = sK280(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1378,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X4: 'S14',X5: 'S14'] :
( ( ( $sum(f22(X4,X1),f22(X5,X3)) = $sum(f22(X4,X3),f22(X5,X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( $sum(f22(X4,X1),f22(X5,X3)) != $sum(f22(X4,X3),f22(X5,X1)) ) )
& ( f49(f50,X2) = X5 )
& ( f49(f50,X0) = X4 ) ),
inference(flattening,[],[f1377]) ).
tff(f1377,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X4: 'S14',X5: 'S14'] :
( ( ( $sum(f22(X4,X1),f22(X5,X3)) = $sum(f22(X4,X3),f22(X5,X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( $sum(f22(X4,X1),f22(X5,X3)) != $sum(f22(X4,X3),f22(X5,X1)) ) )
& ( f49(f50,X2) = X5 )
& ( f49(f50,X0) = X4 ) ),
inference(nnf_transformation,[],[f788]) ).
tff(f788,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X4: 'S14',X5: 'S14'] :
( ( ( $sum(f22(X4,X1),f22(X5,X3)) = $sum(f22(X4,X3),f22(X5,X1)) )
<=> ( ( X1 = X3 )
| ( X0 = X2 ) ) )
& ( f49(f50,X2) = X5 )
& ( f49(f50,X0) = X4 ) ),
inference(rectify,[],[f216]) ).
tff(f216,axiom,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X120: 'S14',X121: 'S14'] :
( ( ( $sum(f22(X120,X1),f22(X121,X3)) = $sum(f22(X120,X3),f22(X121,X1)) )
<=> ( ( X1 = X3 )
| ( X0 = X2 ) ) )
& ( f49(f50,X2) = X121 )
& ( f49(f50,X0) = X120 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_216) ).
tff(f5146,plain,
spl331_376,
inference(avatar_split_clause,[],[f2216,f5144]) ).
tff(f5144,plain,
( spl331_376
<=> ! [X0: $real,X3: $real,X2: $real,X1: $real] : ( f49(f50,X0) = sK280(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_376])]) ).
tff(f2216,plain,
! [X2: $real,X3: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK280(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1380]) ).
tff(f5142,plain,
spl331_375,
inference(avatar_split_clause,[],[f2214,f5140]) ).
tff(f5140,plain,
( spl331_375
<=> ! [X0: $real,X3: $real,X2: $real,X1: $real] : ( f49(f50,X0) = sK279(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_375])]) ).
tff(f2214,plain,
! [X2: $real,X3: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK279(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1376]) ).
tff(f1376,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ( f34(f39(f52,f16(f17(f18,X0),X1)),f16(f17(f18,X2),X3)) = f16(f17(f18,$sum(f22(sK279(X0,X1,X2,X3),X2),$uminus(f22(sK278(X0,X1,X2,X3),X3)))),$sum(f22(sK279(X0,X1,X2,X3),X3),f22(sK278(X0,X1,X2,X3),X2))) )
& ( f49(f50,X0) = sK279(X0,X1,X2,X3) )
& ( f49(f50,X1) = sK278(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK278,sK279])],[f787,f1375]) ).
tff(f1375,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ? [X4: 'S14',X5: 'S14'] :
( ( f34(f39(f52,f16(f17(f18,X0),X1)),f16(f17(f18,X2),X3)) = f16(f17(f18,$sum(f22(X5,X2),$uminus(f22(X4,X3)))),$sum(f22(X5,X3),f22(X4,X2))) )
& ( f49(f50,X0) = X5 )
& ( f49(f50,X1) = X4 ) )
=> ( ( f34(f39(f52,f16(f17(f18,X0),X1)),f16(f17(f18,X2),X3)) = f16(f17(f18,$sum(f22(sK279(X0,X1,X2,X3),X2),$uminus(f22(sK278(X0,X1,X2,X3),X3)))),$sum(f22(sK279(X0,X1,X2,X3),X3),f22(sK278(X0,X1,X2,X3),X2))) )
& ( f49(f50,X0) = sK279(X0,X1,X2,X3) )
& ( f49(f50,X1) = sK278(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f787,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X4: 'S14',X5: 'S14'] :
( ( f34(f39(f52,f16(f17(f18,X0),X1)),f16(f17(f18,X2),X3)) = f16(f17(f18,$sum(f22(X5,X2),$uminus(f22(X4,X3)))),$sum(f22(X5,X3),f22(X4,X2))) )
& ( f49(f50,X0) = X5 )
& ( f49(f50,X1) = X4 ) ),
inference(rectify,[],[f540]) ).
tff(f540,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X105: 'S14',X106: 'S14'] :
( ( f34(f39(f52,f16(f17(f18,X0),X1)),f16(f17(f18,X2),X3)) = f16(f17(f18,$sum(f22(X106,X2),$uminus(f22(X105,X3)))),$sum(f22(X106,X3),f22(X105,X2))) )
& ( f49(f50,X0) = X106 )
& ( f49(f50,X1) = X105 ) ),
inference(theory_normalization,[],[f171]) ).
tff(f171,axiom,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X105: 'S14',X106: 'S14'] :
( ( f34(f39(f52,f16(f17(f18,X0),X1)),f16(f17(f18,X2),X3)) = f16(f17(f18,$difference(f22(X106,X2),f22(X105,X3))),$sum(f22(X106,X3),f22(X105,X2))) )
& ( f49(f50,X0) = X106 )
& ( f49(f50,X1) = X105 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_171) ).
tff(f5138,plain,
spl331_374,
inference(avatar_split_clause,[],[f2213,f5136]) ).
tff(f5136,plain,
( spl331_374
<=> ! [X0: $real,X3: $real,X2: $real,X1: $real] : ( f49(f50,X1) = sK278(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_374])]) ).
tff(f2213,plain,
! [X2: $real,X3: $real,X0: $real,X1: $real] : ( f49(f50,X1) = sK278(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1376]) ).
tff(f5134,plain,
spl331_373,
inference(avatar_split_clause,[],[f2210,f5132]) ).
tff(f5132,plain,
( spl331_373
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( f9(f10,X0) = sK276(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_373])]) ).
tff(f2210,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] : ( f9(f10,X0) = sK276(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1374]) ).
tff(f1374,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
( ( f8(f9(f10,f8(sK276(X0,X1,X2,X3),X1)),sK277(X0,X1,X2,X3)) = f8(sK276(X0,X1,X2,X3),f8(f9(f10,X1),sK277(X0,X1,X2,X3))) )
& ( f8(f9(f10,X2),X3) = sK277(X0,X1,X2,X3) )
& ( f9(f10,X0) = sK276(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK276,sK277])],[f786,f1373]) ).
tff(f1373,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
( ? [X4: 'S6',X5: $int] :
( ( f8(f9(f10,f8(X4,X1)),X5) = f8(X4,f8(f9(f10,X1),X5)) )
& ( f8(f9(f10,X2),X3) = X5 )
& ( f9(f10,X0) = X4 ) )
=> ( ( f8(f9(f10,f8(sK276(X0,X1,X2,X3),X1)),sK277(X0,X1,X2,X3)) = f8(sK276(X0,X1,X2,X3),f8(f9(f10,X1),sK277(X0,X1,X2,X3))) )
& ( f8(f9(f10,X2),X3) = sK277(X0,X1,X2,X3) )
& ( f9(f10,X0) = sK276(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f786,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X4: 'S6',X5: $int] :
( ( f8(f9(f10,f8(X4,X1)),X5) = f8(X4,f8(f9(f10,X1),X5)) )
& ( f8(f9(f10,X2),X3) = X5 )
& ( f9(f10,X0) = X4 ) ),
inference(rectify,[],[f248]) ).
tff(f248,axiom,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X150: 'S6',X151: $int] :
( ( f8(f9(f10,f8(X150,X1)),X151) = f8(X150,f8(f9(f10,X1),X151)) )
& ( f8(f9(f10,X2),X3) = X151 )
& ( f9(f10,X0) = X150 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_248) ).
tff(f5130,plain,
spl331_372,
inference(avatar_split_clause,[],[f2206,f5128]) ).
tff(f5128,plain,
( spl331_372
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( f9(f10,X1) = sK275(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_372])]) ).
tff(f2206,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] : ( f9(f10,X1) = sK275(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1372]) ).
tff(f1372,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( $sum(f8(sK274(X0,X1,X2,X3),X2),f8(sK275(X0,X1,X2,X3),X3)) = $sum(f8(sK274(X0,X1,X2,X3),X3),f8(sK275(X0,X1,X2,X3),X2)) ) )
& ( ( $sum(f8(sK274(X0,X1,X2,X3),X2),f8(sK275(X0,X1,X2,X3),X3)) != $sum(f8(sK274(X0,X1,X2,X3),X3),f8(sK275(X0,X1,X2,X3),X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f9(f10,X1) = sK275(X0,X1,X2,X3) )
& ( f9(f10,X0) = sK274(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK274,sK275])],[f1370,f1371]) ).
tff(f1371,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
( ? [X4: 'S6',X5: 'S6'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( $sum(f8(X4,X2),f8(X5,X3)) = $sum(f8(X4,X3),f8(X5,X2)) ) )
& ( ( $sum(f8(X4,X2),f8(X5,X3)) != $sum(f8(X4,X3),f8(X5,X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f9(f10,X1) = X5 )
& ( f9(f10,X0) = X4 ) )
=> ( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( $sum(f8(sK274(X0,X1,X2,X3),X2),f8(sK275(X0,X1,X2,X3),X3)) = $sum(f8(sK274(X0,X1,X2,X3),X3),f8(sK275(X0,X1,X2,X3),X2)) ) )
& ( ( $sum(f8(sK274(X0,X1,X2,X3),X2),f8(sK275(X0,X1,X2,X3),X3)) != $sum(f8(sK274(X0,X1,X2,X3),X3),f8(sK275(X0,X1,X2,X3),X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f9(f10,X1) = sK275(X0,X1,X2,X3) )
& ( f9(f10,X0) = sK274(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1370,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X4: 'S6',X5: 'S6'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( $sum(f8(X4,X2),f8(X5,X3)) = $sum(f8(X4,X3),f8(X5,X2)) ) )
& ( ( $sum(f8(X4,X2),f8(X5,X3)) != $sum(f8(X4,X3),f8(X5,X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f9(f10,X1) = X5 )
& ( f9(f10,X0) = X4 ) ),
inference(flattening,[],[f1369]) ).
tff(f1369,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X4: 'S6',X5: 'S6'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( $sum(f8(X4,X2),f8(X5,X3)) = $sum(f8(X4,X3),f8(X5,X2)) ) )
& ( ( $sum(f8(X4,X2),f8(X5,X3)) != $sum(f8(X4,X3),f8(X5,X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f9(f10,X1) = X5 )
& ( f9(f10,X0) = X4 ) ),
inference(nnf_transformation,[],[f785]) ).
tff(f785,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X4: 'S6',X5: 'S6'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
<=> ( $sum(f8(X4,X2),f8(X5,X3)) != $sum(f8(X4,X3),f8(X5,X2)) ) )
& ( f9(f10,X1) = X5 )
& ( f9(f10,X0) = X4 ) ),
inference(rectify,[],[f286]) ).
tff(f286,axiom,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X187: 'S6',X188: 'S6'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
<=> ( $sum(f8(X187,X2),f8(X188,X3)) != $sum(f8(X187,X3),f8(X188,X2)) ) )
& ( f9(f10,X1) = X188 )
& ( f9(f10,X0) = X187 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_286) ).
tff(f5126,plain,
spl331_371,
inference(avatar_split_clause,[],[f2205,f5124]) ).
tff(f5124,plain,
( spl331_371
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( f9(f10,X0) = sK274(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_371])]) ).
tff(f2205,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] : ( f9(f10,X0) = sK274(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1372]) ).
tff(f5122,plain,
spl331_370,
inference(avatar_split_clause,[],[f2201,f5120]) ).
tff(f5120,plain,
( spl331_370
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( f9(f10,X2) = sK273(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_370])]) ).
tff(f2201,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] : ( f9(f10,X2) = sK273(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1368]) ).
tff(f1368,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
( ( ( $sum(f8(sK272(X0,X1,X2,X3),X1),f8(sK273(X0,X1,X2,X3),X3)) = $sum(f8(sK272(X0,X1,X2,X3),X3),f8(sK273(X0,X1,X2,X3),X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( $sum(f8(sK272(X0,X1,X2,X3),X1),f8(sK273(X0,X1,X2,X3),X3)) != $sum(f8(sK272(X0,X1,X2,X3),X3),f8(sK273(X0,X1,X2,X3),X1)) ) )
& ( f9(f10,X2) = sK273(X0,X1,X2,X3) )
& ( f9(f10,X0) = sK272(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK272,sK273])],[f1366,f1367]) ).
tff(f1367,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
( ? [X4: 'S6',X5: 'S6'] :
( ( ( $sum(f8(X4,X1),f8(X5,X3)) = $sum(f8(X4,X3),f8(X5,X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( $sum(f8(X4,X1),f8(X5,X3)) != $sum(f8(X4,X3),f8(X5,X1)) ) )
& ( f9(f10,X2) = X5 )
& ( f9(f10,X0) = X4 ) )
=> ( ( ( $sum(f8(sK272(X0,X1,X2,X3),X1),f8(sK273(X0,X1,X2,X3),X3)) = $sum(f8(sK272(X0,X1,X2,X3),X3),f8(sK273(X0,X1,X2,X3),X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( $sum(f8(sK272(X0,X1,X2,X3),X1),f8(sK273(X0,X1,X2,X3),X3)) != $sum(f8(sK272(X0,X1,X2,X3),X3),f8(sK273(X0,X1,X2,X3),X1)) ) )
& ( f9(f10,X2) = sK273(X0,X1,X2,X3) )
& ( f9(f10,X0) = sK272(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1366,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X4: 'S6',X5: 'S6'] :
( ( ( $sum(f8(X4,X1),f8(X5,X3)) = $sum(f8(X4,X3),f8(X5,X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( $sum(f8(X4,X1),f8(X5,X3)) != $sum(f8(X4,X3),f8(X5,X1)) ) )
& ( f9(f10,X2) = X5 )
& ( f9(f10,X0) = X4 ) ),
inference(flattening,[],[f1365]) ).
tff(f1365,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X4: 'S6',X5: 'S6'] :
( ( ( $sum(f8(X4,X1),f8(X5,X3)) = $sum(f8(X4,X3),f8(X5,X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( $sum(f8(X4,X1),f8(X5,X3)) != $sum(f8(X4,X3),f8(X5,X1)) ) )
& ( f9(f10,X2) = X5 )
& ( f9(f10,X0) = X4 ) ),
inference(nnf_transformation,[],[f784]) ).
tff(f784,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X4: 'S6',X5: 'S6'] :
( ( ( $sum(f8(X4,X1),f8(X5,X3)) = $sum(f8(X4,X3),f8(X5,X1)) )
<=> ( ( X1 = X3 )
| ( X0 = X2 ) ) )
& ( f9(f10,X2) = X5 )
& ( f9(f10,X0) = X4 ) ),
inference(rectify,[],[f217]) ).
tff(f217,axiom,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X122: 'S6',X123: 'S6'] :
( ( ( $sum(f8(X122,X1),f8(X123,X3)) = $sum(f8(X122,X3),f8(X123,X1)) )
<=> ( ( X1 = X3 )
| ( X0 = X2 ) ) )
& ( f9(f10,X2) = X123 )
& ( f9(f10,X0) = X122 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_217) ).
tff(f5118,plain,
spl331_369,
inference(avatar_split_clause,[],[f2200,f5116]) ).
tff(f5116,plain,
( spl331_369
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( f9(f10,X0) = sK272(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_369])]) ).
tff(f2200,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] : ( f9(f10,X0) = sK272(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1368]) ).
tff(f5114,plain,
spl331_368,
inference(avatar_split_clause,[],[f2197,f5112]) ).
tff(f5112,plain,
( spl331_368
<=> ! [X0: 'S2',X3: 'S2',X2: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK270(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_368])]) ).
tff(f2197,plain,
! [X2: 'S2',X3: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK270(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1364]) ).
tff(f1364,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
( ( f3(f4(f54,f3(sK270(X0,X1,X2,X3),X1)),sK271(X0,X1,X2,X3)) = f3(sK270(X0,X1,X2,X3),f3(f4(f54,X1),sK271(X0,X1,X2,X3))) )
& ( f3(f4(f54,X2),X3) = sK271(X0,X1,X2,X3) )
& ( f4(f54,X0) = sK270(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK270,sK271])],[f783,f1363]) ).
tff(f1363,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
( ? [X4: 'S3',X5: 'S2'] :
( ( f3(f4(f54,f3(X4,X1)),X5) = f3(X4,f3(f4(f54,X1),X5)) )
& ( f3(f4(f54,X2),X3) = X5 )
& ( f4(f54,X0) = X4 ) )
=> ( ( f3(f4(f54,f3(sK270(X0,X1,X2,X3),X1)),sK271(X0,X1,X2,X3)) = f3(sK270(X0,X1,X2,X3),f3(f4(f54,X1),sK271(X0,X1,X2,X3))) )
& ( f3(f4(f54,X2),X3) = sK271(X0,X1,X2,X3) )
& ( f4(f54,X0) = sK270(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f783,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X4: 'S3',X5: 'S2'] :
( ( f3(f4(f54,f3(X4,X1)),X5) = f3(X4,f3(f4(f54,X1),X5)) )
& ( f3(f4(f54,X2),X3) = X5 )
& ( f4(f54,X0) = X4 ) ),
inference(rectify,[],[f246]) ).
tff(f246,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X146: 'S3',X147: 'S2'] :
( ( f3(f4(f54,f3(X146,X1)),X147) = f3(X146,f3(f4(f54,X1),X147)) )
& ( f3(f4(f54,X2),X3) = X147 )
& ( f4(f54,X0) = X146 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_246) ).
tff(f5110,plain,
( spl331_367
| ~ spl331_1
| ~ spl331_241 ),
inference(avatar_split_clause,[],[f4764,f4436,f2930,f5108]) ).
tff(f4436,plain,
( spl331_241
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_241])]) ).
tff(f4764,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl331_1
| ~ spl331_241 ),
inference(resolution,[],[f4437,f2931]) ).
tff(f4437,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl331_241 ),
inference(avatar_component_clause,[],[f4436]) ).
tff(f5106,plain,
spl331_366,
inference(avatar_split_clause,[],[f2193,f5104]) ).
tff(f5104,plain,
( spl331_366
<=> ! [X0: 'S2',X3: 'S2',X2: 'S2',X1: 'S2'] : ( f4(f54,X1) = sK269(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_366])]) ).
tff(f2193,plain,
! [X2: 'S2',X3: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X1) = sK269(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1362]) ).
tff(f1362,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( f3(f4(f53,f3(sK268(X0,X1,X2,X3),X2)),f3(sK269(X0,X1,X2,X3),X3)) = f3(f4(f53,f3(sK268(X0,X1,X2,X3),X3)),f3(sK269(X0,X1,X2,X3),X2)) ) )
& ( ( f3(f4(f53,f3(sK268(X0,X1,X2,X3),X2)),f3(sK269(X0,X1,X2,X3),X3)) != f3(f4(f53,f3(sK268(X0,X1,X2,X3),X3)),f3(sK269(X0,X1,X2,X3),X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f4(f54,X1) = sK269(X0,X1,X2,X3) )
& ( f4(f54,X0) = sK268(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK268,sK269])],[f1360,f1361]) ).
tff(f1361,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
( ? [X4: 'S3',X5: 'S3'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( f3(f4(f53,f3(X4,X2)),f3(X5,X3)) = f3(f4(f53,f3(X4,X3)),f3(X5,X2)) ) )
& ( ( f3(f4(f53,f3(X4,X2)),f3(X5,X3)) != f3(f4(f53,f3(X4,X3)),f3(X5,X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f4(f54,X1) = X5 )
& ( f4(f54,X0) = X4 ) )
=> ( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( f3(f4(f53,f3(sK268(X0,X1,X2,X3),X2)),f3(sK269(X0,X1,X2,X3),X3)) = f3(f4(f53,f3(sK268(X0,X1,X2,X3),X3)),f3(sK269(X0,X1,X2,X3),X2)) ) )
& ( ( f3(f4(f53,f3(sK268(X0,X1,X2,X3),X2)),f3(sK269(X0,X1,X2,X3),X3)) != f3(f4(f53,f3(sK268(X0,X1,X2,X3),X3)),f3(sK269(X0,X1,X2,X3),X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f4(f54,X1) = sK269(X0,X1,X2,X3) )
& ( f4(f54,X0) = sK268(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1360,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X4: 'S3',X5: 'S3'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( f3(f4(f53,f3(X4,X2)),f3(X5,X3)) = f3(f4(f53,f3(X4,X3)),f3(X5,X2)) ) )
& ( ( f3(f4(f53,f3(X4,X2)),f3(X5,X3)) != f3(f4(f53,f3(X4,X3)),f3(X5,X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f4(f54,X1) = X5 )
& ( f4(f54,X0) = X4 ) ),
inference(flattening,[],[f1359]) ).
tff(f1359,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X4: 'S3',X5: 'S3'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
| ( f3(f4(f53,f3(X4,X2)),f3(X5,X3)) = f3(f4(f53,f3(X4,X3)),f3(X5,X2)) ) )
& ( ( f3(f4(f53,f3(X4,X2)),f3(X5,X3)) != f3(f4(f53,f3(X4,X3)),f3(X5,X2)) )
| ( X2 = X3 )
| ( X0 = X1 ) )
& ( f4(f54,X1) = X5 )
& ( f4(f54,X0) = X4 ) ),
inference(nnf_transformation,[],[f782]) ).
tff(f782,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X4: 'S3',X5: 'S3'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
<=> ( f3(f4(f53,f3(X4,X2)),f3(X5,X3)) != f3(f4(f53,f3(X4,X3)),f3(X5,X2)) ) )
& ( f4(f54,X1) = X5 )
& ( f4(f54,X0) = X4 ) ),
inference(rectify,[],[f283]) ).
tff(f283,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X181: 'S3',X182: 'S3'] :
( ( ( ( X2 != X3 )
& ( X0 != X1 ) )
<=> ( f3(f4(f53,f3(X181,X2)),f3(X182,X3)) != f3(f4(f53,f3(X181,X3)),f3(X182,X2)) ) )
& ( f4(f54,X1) = X182 )
& ( f4(f54,X0) = X181 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_283) ).
tff(f5102,plain,
spl331_365,
inference(avatar_split_clause,[],[f2192,f5100]) ).
tff(f5100,plain,
( spl331_365
<=> ! [X0: 'S2',X3: 'S2',X2: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK268(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_365])]) ).
tff(f2192,plain,
! [X2: 'S2',X3: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK268(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1362]) ).
tff(f5098,plain,
spl331_364,
inference(avatar_split_clause,[],[f2188,f5096]) ).
tff(f5096,plain,
( spl331_364
<=> ! [X0: 'S2',X3: 'S2',X2: 'S2',X1: 'S2'] : ( f4(f54,X2) = sK267(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_364])]) ).
tff(f2188,plain,
! [X2: 'S2',X3: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X2) = sK267(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1358]) ).
tff(f1358,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
( ( ( f3(f4(f53,f3(sK266(X0,X1,X2,X3),X1)),f3(sK267(X0,X1,X2,X3),X3)) = f3(f4(f53,f3(sK266(X0,X1,X2,X3),X3)),f3(sK267(X0,X1,X2,X3),X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( f3(f4(f53,f3(sK266(X0,X1,X2,X3),X1)),f3(sK267(X0,X1,X2,X3),X3)) != f3(f4(f53,f3(sK266(X0,X1,X2,X3),X3)),f3(sK267(X0,X1,X2,X3),X1)) ) )
& ( f4(f54,X2) = sK267(X0,X1,X2,X3) )
& ( f4(f54,X0) = sK266(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK266,sK267])],[f1356,f1357]) ).
tff(f1357,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
( ? [X4: 'S3',X5: 'S3'] :
( ( ( f3(f4(f53,f3(X4,X1)),f3(X5,X3)) = f3(f4(f53,f3(X4,X3)),f3(X5,X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( f3(f4(f53,f3(X4,X1)),f3(X5,X3)) != f3(f4(f53,f3(X4,X3)),f3(X5,X1)) ) )
& ( f4(f54,X2) = X5 )
& ( f4(f54,X0) = X4 ) )
=> ( ( ( f3(f4(f53,f3(sK266(X0,X1,X2,X3),X1)),f3(sK267(X0,X1,X2,X3),X3)) = f3(f4(f53,f3(sK266(X0,X1,X2,X3),X3)),f3(sK267(X0,X1,X2,X3),X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( f3(f4(f53,f3(sK266(X0,X1,X2,X3),X1)),f3(sK267(X0,X1,X2,X3),X3)) != f3(f4(f53,f3(sK266(X0,X1,X2,X3),X3)),f3(sK267(X0,X1,X2,X3),X1)) ) )
& ( f4(f54,X2) = sK267(X0,X1,X2,X3) )
& ( f4(f54,X0) = sK266(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1356,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X4: 'S3',X5: 'S3'] :
( ( ( f3(f4(f53,f3(X4,X1)),f3(X5,X3)) = f3(f4(f53,f3(X4,X3)),f3(X5,X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( f3(f4(f53,f3(X4,X1)),f3(X5,X3)) != f3(f4(f53,f3(X4,X3)),f3(X5,X1)) ) )
& ( f4(f54,X2) = X5 )
& ( f4(f54,X0) = X4 ) ),
inference(flattening,[],[f1355]) ).
tff(f1355,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X4: 'S3',X5: 'S3'] :
( ( ( f3(f4(f53,f3(X4,X1)),f3(X5,X3)) = f3(f4(f53,f3(X4,X3)),f3(X5,X1)) )
| ( ( X1 != X3 )
& ( X0 != X2 ) ) )
& ( ( X1 = X3 )
| ( X0 = X2 )
| ( f3(f4(f53,f3(X4,X1)),f3(X5,X3)) != f3(f4(f53,f3(X4,X3)),f3(X5,X1)) ) )
& ( f4(f54,X2) = X5 )
& ( f4(f54,X0) = X4 ) ),
inference(nnf_transformation,[],[f781]) ).
tff(f781,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X4: 'S3',X5: 'S3'] :
( ( ( f3(f4(f53,f3(X4,X1)),f3(X5,X3)) = f3(f4(f53,f3(X4,X3)),f3(X5,X1)) )
<=> ( ( X1 = X3 )
| ( X0 = X2 ) ) )
& ( f4(f54,X2) = X5 )
& ( f4(f54,X0) = X4 ) ),
inference(rectify,[],[f214]) ).
tff(f214,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X116: 'S3',X117: 'S3'] :
( ( ( f3(f4(f53,f3(X116,X1)),f3(X117,X3)) = f3(f4(f53,f3(X116,X3)),f3(X117,X1)) )
<=> ( ( X1 = X3 )
| ( X0 = X2 ) ) )
& ( f4(f54,X2) = X117 )
& ( f4(f54,X0) = X116 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_214) ).
tff(f5094,plain,
spl331_363,
inference(avatar_split_clause,[],[f2187,f5092]) ).
tff(f5092,plain,
( spl331_363
<=> ! [X0: 'S2',X3: 'S2',X2: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK266(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_363])]) ).
tff(f2187,plain,
! [X2: 'S2',X3: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK266(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1358]) ).
tff(f5090,plain,
spl331_362,
inference(avatar_split_clause,[],[f2185,f5088]) ).
tff(f5088,plain,
( spl331_362
<=> ! [X0: 'S10',X3: 'S10',X2: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK265(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_362])]) ).
tff(f2185,plain,
! [X2: 'S10',X3: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK265(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1354]) ).
tff(f1354,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ( f34(f39(f61,f34(sK265(X0,X1,X2,X3),X1)),f34(f39(f52,X2),X3)) = f34(f39(f40,f34(sK265(X0,X1,X2,X3),f34(f39(f61,X1),X3))),f34(f39(f52,f34(f39(f61,X0),X2)),X3)) )
& ( f39(f52,X0) = sK265(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK265])],[f780,f1353]) ).
tff(f1353,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ? [X4: 'S17'] :
( ( f34(f39(f61,f34(X4,X1)),f34(f39(f52,X2),X3)) = f34(f39(f40,f34(X4,f34(f39(f61,X1),X3))),f34(f39(f52,f34(f39(f61,X0),X2)),X3)) )
& ( f39(f52,X0) = X4 ) )
=> ( ( f34(f39(f61,f34(sK265(X0,X1,X2,X3),X1)),f34(f39(f52,X2),X3)) = f34(f39(f40,f34(sK265(X0,X1,X2,X3),f34(f39(f61,X1),X3))),f34(f39(f52,f34(f39(f61,X0),X2)),X3)) )
& ( f39(f52,X0) = sK265(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f780,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X4: 'S17'] :
( ( f34(f39(f61,f34(X4,X1)),f34(f39(f52,X2),X3)) = f34(f39(f40,f34(X4,f34(f39(f61,X1),X3))),f34(f39(f52,f34(f39(f61,X0),X2)),X3)) )
& ( f39(f52,X0) = X4 ) ),
inference(rectify,[],[f410]) ).
tff(f410,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X262: 'S17'] :
( ( f34(f39(f61,f34(X262,X1)),f34(f39(f52,X2),X3)) = f34(f39(f40,f34(X262,f34(f39(f61,X1),X3))),f34(f39(f52,f34(f39(f61,X0),X2)),X3)) )
& ( f39(f52,X0) = X262 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_410) ).
tff(f5086,plain,
spl331_361,
inference(avatar_split_clause,[],[f2183,f5084]) ).
tff(f5084,plain,
( spl331_361
<=> ! [X0: 'S10',X3: 'S10',X2: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK264(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_361])]) ).
tff(f2183,plain,
! [X2: 'S10',X3: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK264(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1352]) ).
tff(f1352,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ( f34(f39(f52,f34(sK264(X0,X1,X2,X3),X1)),f34(f39(f52,X2),X3)) = f34(f39(f52,f34(sK264(X0,X1,X2,X3),X2)),f34(f39(f52,X1),X3)) )
& ( f39(f52,X0) = sK264(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK264])],[f779,f1351]) ).
tff(f1351,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ? [X4: 'S17'] :
( ( f34(f39(f52,f34(X4,X1)),f34(f39(f52,X2),X3)) = f34(f39(f52,f34(X4,X2)),f34(f39(f52,X1),X3)) )
& ( f39(f52,X0) = X4 ) )
=> ( ( f34(f39(f52,f34(sK264(X0,X1,X2,X3),X1)),f34(f39(f52,X2),X3)) = f34(f39(f52,f34(sK264(X0,X1,X2,X3),X2)),f34(f39(f52,X1),X3)) )
& ( f39(f52,X0) = sK264(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f779,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X4: 'S17'] :
( ( f34(f39(f52,f34(X4,X1)),f34(f39(f52,X2),X3)) = f34(f39(f52,f34(X4,X2)),f34(f39(f52,X1),X3)) )
& ( f39(f52,X0) = X4 ) ),
inference(rectify,[],[f257]) ).
tff(f257,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X165: 'S17'] :
( ( f34(f39(f52,f34(X165,X1)),f34(f39(f52,X2),X3)) = f34(f39(f52,f34(X165,X2)),f34(f39(f52,X1),X3)) )
& ( f39(f52,X0) = X165 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_257) ).
tff(f5082,plain,
spl331_360,
inference(avatar_split_clause,[],[f2181,f5080]) ).
tff(f5080,plain,
( spl331_360
<=> ! [X0: 'S10',X3: 'S10',X2: 'S10',X1: 'S10'] : ( f39(f40,X0) = sK263(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_360])]) ).
tff(f2181,plain,
! [X2: 'S10',X3: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f40,X0) = sK263(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1350]) ).
tff(f1350,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ( f34(f39(f40,f34(sK263(X0,X1,X2,X3),X1)),f34(f39(f40,X2),X3)) = f34(f39(f40,f34(sK263(X0,X1,X2,X3),X2)),f34(f39(f40,X1),X3)) )
& ( f39(f40,X0) = sK263(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK263])],[f778,f1349]) ).
tff(f1349,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
( ? [X4: 'S17'] :
( ( f34(f39(f40,f34(X4,X1)),f34(f39(f40,X2),X3)) = f34(f39(f40,f34(X4,X2)),f34(f39(f40,X1),X3)) )
& ( f39(f40,X0) = X4 ) )
=> ( ( f34(f39(f40,f34(sK263(X0,X1,X2,X3),X1)),f34(f39(f40,X2),X3)) = f34(f39(f40,f34(sK263(X0,X1,X2,X3),X2)),f34(f39(f40,X1),X3)) )
& ( f39(f40,X0) = sK263(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f778,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X4: 'S17'] :
( ( f34(f39(f40,f34(X4,X1)),f34(f39(f40,X2),X3)) = f34(f39(f40,f34(X4,X2)),f34(f39(f40,X1),X3)) )
& ( f39(f40,X0) = X4 ) ),
inference(rectify,[],[f273]) ).
tff(f273,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10',X3: 'S10'] :
? [X171: 'S17'] :
( ( f34(f39(f40,f34(X171,X1)),f34(f39(f40,X2),X3)) = f34(f39(f40,f34(X171,X2)),f34(f39(f40,X1),X3)) )
& ( f39(f40,X0) = X171 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_273) ).
tff(f5078,plain,
spl331_359,
inference(avatar_split_clause,[],[f2179,f5076]) ).
tff(f5076,plain,
( spl331_359
<=> ! [X0: $real,X3: $real,X2: $real,X1: $real] : ( f49(f50,X0) = sK262(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_359])]) ).
tff(f2179,plain,
! [X2: $real,X3: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK262(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1348]) ).
tff(f1348,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ( f22(f49(f50,f22(sK262(X0,X1,X2,X3),X1)),f22(f49(f50,X2),X3)) = f22(f49(f50,f22(sK262(X0,X1,X2,X3),X2)),f22(f49(f50,X1),X3)) )
& ( f49(f50,X0) = sK262(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK262])],[f777,f1347]) ).
tff(f1347,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ? [X4: 'S14'] :
( ( f22(f49(f50,f22(X4,X1)),f22(f49(f50,X2),X3)) = f22(f49(f50,f22(X4,X2)),f22(f49(f50,X1),X3)) )
& ( f49(f50,X0) = X4 ) )
=> ( ( f22(f49(f50,f22(sK262(X0,X1,X2,X3),X1)),f22(f49(f50,X2),X3)) = f22(f49(f50,f22(sK262(X0,X1,X2,X3),X2)),f22(f49(f50,X1),X3)) )
& ( f49(f50,X0) = sK262(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f777,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X4: 'S14'] :
( ( f22(f49(f50,f22(X4,X1)),f22(f49(f50,X2),X3)) = f22(f49(f50,f22(X4,X2)),f22(f49(f50,X1),X3)) )
& ( f49(f50,X0) = X4 ) ),
inference(rectify,[],[f255]) ).
tff(f255,axiom,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X163: 'S14'] :
( ( f22(f49(f50,f22(X163,X1)),f22(f49(f50,X2),X3)) = f22(f49(f50,f22(X163,X2)),f22(f49(f50,X1),X3)) )
& ( f49(f50,X0) = X163 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_255) ).
tff(f5074,plain,
spl331_358,
inference(avatar_split_clause,[],[f2177,f5072]) ).
tff(f5072,plain,
( spl331_358
<=> ! [X0: $real,X3: $real,X2: $real,X1: $real] : ( f49(f50,X0) = sK261(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_358])]) ).
tff(f2177,plain,
! [X2: $real,X3: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK261(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1346]) ).
tff(f1346,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ( $sum(f22(sK261(X0,X1,X2,X3),X1),$uminus(f22(f49(f50,X2),X3))) = $sum(f22(sK261(X0,X1,X2,X3),$sum(X1,$uminus(X3))),f22(f49(f50,$sum(X0,$uminus(X2))),X3)) )
& ( f49(f50,X0) = sK261(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK261])],[f776,f1345]) ).
tff(f1345,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
( ? [X4: 'S14'] :
( ( $sum(f22(X4,X1),$uminus(f22(f49(f50,X2),X3))) = $sum(f22(X4,$sum(X1,$uminus(X3))),f22(f49(f50,$sum(X0,$uminus(X2))),X3)) )
& ( f49(f50,X0) = X4 ) )
=> ( ( $sum(f22(sK261(X0,X1,X2,X3),X1),$uminus(f22(f49(f50,X2),X3))) = $sum(f22(sK261(X0,X1,X2,X3),$sum(X1,$uminus(X3))),f22(f49(f50,$sum(X0,$uminus(X2))),X3)) )
& ( f49(f50,X0) = sK261(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f776,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X4: 'S14'] :
( ( $sum(f22(X4,X1),$uminus(f22(f49(f50,X2),X3))) = $sum(f22(X4,$sum(X1,$uminus(X3))),f22(f49(f50,$sum(X0,$uminus(X2))),X3)) )
& ( f49(f50,X0) = X4 ) ),
inference(rectify,[],[f539]) ).
tff(f539,plain,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X263: 'S14'] :
( ( $sum(f22(X263,X1),$uminus(f22(f49(f50,X2),X3))) = $sum(f22(X263,$sum(X1,$uminus(X3))),f22(f49(f50,$sum(X0,$uminus(X2))),X3)) )
& ( f49(f50,X0) = X263 ) ),
inference(theory_normalization,[],[f411]) ).
tff(f411,axiom,
! [X0: $real,X1: $real,X2: $real,X3: $real] :
? [X263: 'S14'] :
( ( $difference(f22(X263,X1),f22(f49(f50,X2),X3)) = $sum(f22(X263,$difference(X1,X3)),f22(f49(f50,$difference(X0,X2)),X3)) )
& ( f49(f50,X0) = X263 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_411) ).
tff(f5070,plain,
spl331_357,
inference(avatar_split_clause,[],[f2175,f5068]) ).
tff(f5068,plain,
( spl331_357
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( f9(f10,X0) = sK260(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_357])]) ).
tff(f2175,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] : ( f9(f10,X0) = sK260(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1344]) ).
tff(f1344,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
( ( f8(f9(f10,f8(sK260(X0,X1,X2,X3),X1)),f8(f9(f10,X2),X3)) = f8(f9(f10,f8(sK260(X0,X1,X2,X3),X2)),f8(f9(f10,X1),X3)) )
& ( f9(f10,X0) = sK260(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK260])],[f775,f1343]) ).
tff(f1343,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
( ? [X4: 'S6'] :
( ( f8(f9(f10,f8(X4,X1)),f8(f9(f10,X2),X3)) = f8(f9(f10,f8(X4,X2)),f8(f9(f10,X1),X3)) )
& ( f9(f10,X0) = X4 ) )
=> ( ( f8(f9(f10,f8(sK260(X0,X1,X2,X3),X1)),f8(f9(f10,X2),X3)) = f8(f9(f10,f8(sK260(X0,X1,X2,X3),X2)),f8(f9(f10,X1),X3)) )
& ( f9(f10,X0) = sK260(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f775,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X4: 'S6'] :
( ( f8(f9(f10,f8(X4,X1)),f8(f9(f10,X2),X3)) = f8(f9(f10,f8(X4,X2)),f8(f9(f10,X1),X3)) )
& ( f9(f10,X0) = X4 ) ),
inference(rectify,[],[f256]) ).
tff(f256,axiom,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X164: 'S6'] :
( ( f8(f9(f10,f8(X164,X1)),f8(f9(f10,X2),X3)) = f8(f9(f10,f8(X164,X2)),f8(f9(f10,X1),X3)) )
& ( f9(f10,X0) = X164 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_256) ).
tff(f5065,plain,
spl331_356,
inference(avatar_split_clause,[],[f2173,f5063]) ).
tff(f5063,plain,
( spl331_356
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( f9(f10,X0) = sK259(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_356])]) ).
tff(f2173,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] : ( f9(f10,X0) = sK259(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1342]) ).
tff(f1342,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
( ( $sum(f8(sK259(X0,X1,X2,X3),X1),$uminus(f8(f9(f10,X2),X3))) = $sum(f8(sK259(X0,X1,X2,X3),$sum(X1,$uminus(X3))),f8(f9(f10,$sum(X0,$uminus(X2))),X3)) )
& ( f9(f10,X0) = sK259(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK259])],[f774,f1341]) ).
tff(f1341,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
( ? [X4: 'S6'] :
( ( $sum(f8(X4,X1),$uminus(f8(f9(f10,X2),X3))) = $sum(f8(X4,$sum(X1,$uminus(X3))),f8(f9(f10,$sum(X0,$uminus(X2))),X3)) )
& ( f9(f10,X0) = X4 ) )
=> ( ( $sum(f8(sK259(X0,X1,X2,X3),X1),$uminus(f8(f9(f10,X2),X3))) = $sum(f8(sK259(X0,X1,X2,X3),$sum(X1,$uminus(X3))),f8(f9(f10,$sum(X0,$uminus(X2))),X3)) )
& ( f9(f10,X0) = sK259(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f774,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X4: 'S6'] :
( ( $sum(f8(X4,X1),$uminus(f8(f9(f10,X2),X3))) = $sum(f8(X4,$sum(X1,$uminus(X3))),f8(f9(f10,$sum(X0,$uminus(X2))),X3)) )
& ( f9(f10,X0) = X4 ) ),
inference(rectify,[],[f538]) ).
tff(f538,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X264: 'S6'] :
( ( $sum(f8(X264,X1),$uminus(f8(f9(f10,X2),X3))) = $sum(f8(X264,$sum(X1,$uminus(X3))),f8(f9(f10,$sum(X0,$uminus(X2))),X3)) )
& ( f9(f10,X0) = X264 ) ),
inference(theory_normalization,[],[f412]) ).
tff(f412,axiom,
! [X0: $int,X1: $int,X2: $int,X3: $int] :
? [X264: 'S6'] :
( ( $difference(f8(X264,X1),f8(f9(f10,X2),X3)) = $sum(f8(X264,$difference(X1,X3)),f8(f9(f10,$difference(X0,X2)),X3)) )
& ( f9(f10,X0) = X264 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_412) ).
tff(f5061,plain,
spl331_355,
inference(avatar_split_clause,[],[f2171,f5059]) ).
tff(f5059,plain,
( spl331_355
<=> ! [X0: 'S2',X3: 'S2',X2: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK258(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_355])]) ).
tff(f2171,plain,
! [X2: 'S2',X3: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK258(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1340]) ).
tff(f1340,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
( ( f3(f4(f54,f3(sK258(X0,X1,X2,X3),X1)),f3(f4(f54,X2),X3)) = f3(f4(f54,f3(sK258(X0,X1,X2,X3),X2)),f3(f4(f54,X1),X3)) )
& ( f4(f54,X0) = sK258(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK258])],[f773,f1339]) ).
tff(f1339,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
( ? [X4: 'S3'] :
( ( f3(f4(f54,f3(X4,X1)),f3(f4(f54,X2),X3)) = f3(f4(f54,f3(X4,X2)),f3(f4(f54,X1),X3)) )
& ( f4(f54,X0) = X4 ) )
=> ( ( f3(f4(f54,f3(sK258(X0,X1,X2,X3),X1)),f3(f4(f54,X2),X3)) = f3(f4(f54,f3(sK258(X0,X1,X2,X3),X2)),f3(f4(f54,X1),X3)) )
& ( f4(f54,X0) = sK258(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f773,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X4: 'S3'] :
( ( f3(f4(f54,f3(X4,X1)),f3(f4(f54,X2),X3)) = f3(f4(f54,f3(X4,X2)),f3(f4(f54,X1),X3)) )
& ( f4(f54,X0) = X4 ) ),
inference(rectify,[],[f254]) ).
tff(f254,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X162: 'S3'] :
( ( f3(f4(f54,f3(X162,X1)),f3(f4(f54,X2),X3)) = f3(f4(f54,f3(X162,X2)),f3(f4(f54,X1),X3)) )
& ( f4(f54,X0) = X162 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_254) ).
tff(f5057,plain,
( spl331_354
| ~ spl331_76
| ~ spl331_238
| ~ spl331_353 ),
inference(avatar_split_clause,[],[f5053,f5049,f3988,f3252,f5055]) ).
tff(f5055,plain,
( spl331_354
<=> ! [X0: 'S2',X1: 'S2'] : ( sK32(X0) = sK99(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_354])]) ).
tff(f3252,plain,
( spl331_76
<=> ! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK98(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_76])]) ).
tff(f5049,plain,
( spl331_353
<=> ! [X0: 'S2',X1: 'S2'] : ( f9(f10,sK98(X0,X1)) = sK99(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_353])]) ).
tff(f5053,plain,
( ! [X0: 'S2',X1: 'S2'] : ( sK32(X0) = sK99(X0,X1) )
| ~ spl331_76
| ~ spl331_238
| ~ spl331_353 ),
inference(forward_demodulation,[],[f5052,f3989]) ).
tff(f5052,plain,
( ! [X0: 'S2',X1: 'S2'] : ( sK99(X0,X1) = f9(f10,sK27(X0)) )
| ~ spl331_76
| ~ spl331_353 ),
inference(forward_demodulation,[],[f5050,f3253]) ).
tff(f3253,plain,
( ! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK98(X0,X1) )
| ~ spl331_76 ),
inference(avatar_component_clause,[],[f3252]) ).
tff(f5050,plain,
( ! [X0: 'S2',X1: 'S2'] : ( f9(f10,sK98(X0,X1)) = sK99(X0,X1) )
| ~ spl331_353 ),
inference(avatar_component_clause,[],[f5049]) ).
tff(f5051,plain,
spl331_353,
inference(avatar_split_clause,[],[f1825,f5049]) ).
tff(f1825,plain,
! [X0: 'S2',X1: 'S2'] : ( f9(f10,sK98(X0,X1)) = sK99(X0,X1) ),
inference(cnf_transformation,[],[f1109]) ).
tff(f1109,plain,
! [X0: 'S2',X1: 'S2'] :
( ( f6(f7,f8(sK99(X0,X1),$sum(sK100(X0,X1),1))) = f6(f7,$sum(sK98(X0,X1),f8(sK99(X0,X1),sK100(X0,X1)))) )
& ( f11(f12,X1) = sK100(X0,X1) )
& ( f9(f10,sK98(X0,X1)) = sK99(X0,X1) )
& ( f11(f12,X0) = sK98(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK98,sK99,sK100])],[f678,f1108,f1107]) ).
tff(f1107,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: $int] :
( ? [X3: 'S6',X4: $int] :
( ( f6(f7,f8(X3,$sum(X4,1))) = f6(f7,$sum(X2,f8(X3,X4))) )
& ( f11(f12,X1) = X4 )
& ( f9(f10,X2) = X3 ) )
& ( f11(f12,X0) = X2 ) )
=> ( ? [X4: $int,X3: 'S6'] :
( ( f6(f7,f8(X3,$sum(X4,1))) = f6(f7,$sum(sK98(X0,X1),f8(X3,X4))) )
& ( f11(f12,X1) = X4 )
& ( f9(f10,sK98(X0,X1)) = X3 ) )
& ( f11(f12,X0) = sK98(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1108,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X4: $int,X3: 'S6'] :
( ( f6(f7,f8(X3,$sum(X4,1))) = f6(f7,$sum(sK98(X0,X1),f8(X3,X4))) )
& ( f11(f12,X1) = X4 )
& ( f9(f10,sK98(X0,X1)) = X3 ) )
=> ( ( f6(f7,f8(sK99(X0,X1),$sum(sK100(X0,X1),1))) = f6(f7,$sum(sK98(X0,X1),f8(sK99(X0,X1),sK100(X0,X1)))) )
& ( f11(f12,X1) = sK100(X0,X1) )
& ( f9(f10,sK98(X0,X1)) = sK99(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f678,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int] :
( ? [X3: 'S6',X4: $int] :
( ( f6(f7,f8(X3,$sum(X4,1))) = f6(f7,$sum(X2,f8(X3,X4))) )
& ( f11(f12,X1) = X4 )
& ( f9(f10,X2) = X3 ) )
& ( f11(f12,X0) = X2 ) ),
inference(rectify,[],[f141]) ).
tff(f141,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X30: $int] :
( ? [X31: 'S6',X32: $int] :
( ( f6(f7,f8(X31,$sum(X32,1))) = f6(f7,$sum(X30,f8(X31,X32))) )
& ( f11(f12,X1) = X32 )
& ( f9(f10,X30) = X31 ) )
& ( f11(f12,X0) = X30 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_141) ).
tff(f5047,plain,
spl331_352,
inference(avatar_split_clause,[],[f1822,f5045]) ).
tff(f5045,plain,
( spl331_352
<=> ! [X0: 'S2',X1: 'S2'] : ( f3(sK96(X0,X1),X1) = sK97(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_352])]) ).
tff(f1822,plain,
! [X0: 'S2',X1: 'S2'] : ( f3(sK96(X0,X1),X1) = sK97(X0,X1) ),
inference(cnf_transformation,[],[f1106]) ).
tff(f1106,plain,
! [X0: 'S2',X1: 'S2'] :
( ( f3(sK96(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f3(f4(f54,X0),f3(f4(f54,sK97(X0,X1)),sK97(X0,X1))) )
& ( f3(sK96(X0,X1),X1) = sK97(X0,X1) )
& ( f4(f65,X0) = sK96(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK96,sK97])],[f677,f1105,f1104]) ).
tff(f1104,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: 'S3'] :
( ? [X3: 'S2'] :
( ( f3(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f3(f4(f54,X0),f3(f4(f54,X3),X3)) )
& ( f3(X2,X1) = X3 ) )
& ( f4(f65,X0) = X2 ) )
=> ( ? [X3: 'S2'] :
( ( f3(f4(f54,X0),f3(f4(f54,X3),X3)) = f3(sK96(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) )
& ( f3(sK96(X0,X1),X1) = X3 ) )
& ( f4(f65,X0) = sK96(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1105,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X3: 'S2'] :
( ( f3(f4(f54,X0),f3(f4(f54,X3),X3)) = f3(sK96(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) )
& ( f3(sK96(X0,X1),X1) = X3 ) )
=> ( ( f3(sK96(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f3(f4(f54,X0),f3(f4(f54,sK97(X0,X1)),sK97(X0,X1))) )
& ( f3(sK96(X0,X1),X1) = sK97(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f677,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S3'] :
( ? [X3: 'S2'] :
( ( f3(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f3(f4(f54,X0),f3(f4(f54,X3),X3)) )
& ( f3(X2,X1) = X3 ) )
& ( f4(f65,X0) = X2 ) ),
inference(rectify,[],[f400]) ).
tff(f400,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X251: 'S3'] :
( ? [X252: 'S2'] :
( ( f3(X251,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f3(f4(f54,X0),f3(f4(f54,X252),X252)) )
& ( f3(X251,X1) = X252 ) )
& ( f4(f65,X0) = X251 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_400) ).
tff(f5043,plain,
spl331_351,
inference(avatar_split_clause,[],[f1819,f5041]) ).
tff(f5041,plain,
( spl331_351
<=> ! [X0: 'S2',X1: 'S2'] : ( f3(sK94(X0,X1),X1) = sK95(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_351])]) ).
tff(f1819,plain,
! [X0: 'S2',X1: 'S2'] : ( f3(sK94(X0,X1),X1) = sK95(X0,X1) ),
inference(cnf_transformation,[],[f1103]) ).
tff(f1103,plain,
! [X0: 'S2',X1: 'S2'] :
( ( f3(sK94(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f3(f4(f54,sK95(X0,X1)),sK95(X0,X1)) )
& ( f3(sK94(X0,X1),X1) = sK95(X0,X1) )
& ( f4(f65,X0) = sK94(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK94,sK95])],[f676,f1102,f1101]) ).
tff(f1101,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: 'S3'] :
( ? [X3: 'S2'] :
( ( f3(X2,f6(f7,$product(2,f11(f12,X1)))) = f3(f4(f54,X3),X3) )
& ( f3(X2,X1) = X3 ) )
& ( f4(f65,X0) = X2 ) )
=> ( ? [X3: 'S2'] :
( ( f3(f4(f54,X3),X3) = f3(sK94(X0,X1),f6(f7,$product(2,f11(f12,X1)))) )
& ( f3(sK94(X0,X1),X1) = X3 ) )
& ( f4(f65,X0) = sK94(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1102,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X3: 'S2'] :
( ( f3(f4(f54,X3),X3) = f3(sK94(X0,X1),f6(f7,$product(2,f11(f12,X1)))) )
& ( f3(sK94(X0,X1),X1) = X3 ) )
=> ( ( f3(sK94(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f3(f4(f54,sK95(X0,X1)),sK95(X0,X1)) )
& ( f3(sK94(X0,X1),X1) = sK95(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f676,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S3'] :
( ? [X3: 'S2'] :
( ( f3(X2,f6(f7,$product(2,f11(f12,X1)))) = f3(f4(f54,X3),X3) )
& ( f3(X2,X1) = X3 ) )
& ( f4(f65,X0) = X2 ) ),
inference(rectify,[],[f396]) ).
tff(f396,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X243: 'S3'] :
( ? [X244: 'S2'] :
( ( f3(X243,f6(f7,$product(2,f11(f12,X1)))) = f3(f4(f54,X244),X244) )
& ( f3(X243,X1) = X244 ) )
& ( f4(f65,X0) = X243 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_396) ).
tff(f5039,plain,
spl331_350,
inference(avatar_split_clause,[],[f1803,f5037]) ).
tff(f5037,plain,
( spl331_350
<=> ! [X0: $real,X1: 'S2'] : ( f19(sK86(X0,X1),X1) = sK87(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_350])]) ).
tff(f1803,plain,
! [X0: $real,X1: 'S2'] : ( f19(sK86(X0,X1),X1) = sK87(X0,X1) ),
inference(cnf_transformation,[],[f1088]) ).
tff(f1088,plain,
! [X0: $real,X1: 'S2'] :
( ( f19(sK86(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f22(f49(f50,X0),f22(f49(f50,sK87(X0,X1)),sK87(X0,X1))) )
& ( f19(sK86(X0,X1),X1) = sK87(X0,X1) )
& ( f59(f60,X0) = sK86(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK86,sK87])],[f669,f1087,f1086]) ).
tff(f1086,plain,
! [X0: $real,X1: 'S2'] :
( ? [X2: 'S13'] :
( ? [X3: $real] :
( ( f19(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f22(f49(f50,X0),f22(f49(f50,X3),X3)) )
& ( f19(X2,X1) = X3 ) )
& ( f59(f60,X0) = X2 ) )
=> ( ? [X3: $real] :
( ( f22(f49(f50,X0),f22(f49(f50,X3),X3)) = f19(sK86(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) )
& ( f19(sK86(X0,X1),X1) = X3 ) )
& ( f59(f60,X0) = sK86(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1087,plain,
! [X0: $real,X1: 'S2'] :
( ? [X3: $real] :
( ( f22(f49(f50,X0),f22(f49(f50,X3),X3)) = f19(sK86(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) )
& ( f19(sK86(X0,X1),X1) = X3 ) )
=> ( ( f19(sK86(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f22(f49(f50,X0),f22(f49(f50,sK87(X0,X1)),sK87(X0,X1))) )
& ( f19(sK86(X0,X1),X1) = sK87(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f669,plain,
! [X0: $real,X1: 'S2'] :
? [X2: 'S13'] :
( ? [X3: $real] :
( ( f19(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f22(f49(f50,X0),f22(f49(f50,X3),X3)) )
& ( f19(X2,X1) = X3 ) )
& ( f59(f60,X0) = X2 ) ),
inference(rectify,[],[f399]) ).
tff(f399,axiom,
! [X0: $real,X1: 'S2'] :
? [X249: 'S13'] :
( ? [X250: $real] :
( ( f19(X249,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f22(f49(f50,X0),f22(f49(f50,X250),X250)) )
& ( f19(X249,X1) = X250 ) )
& ( f59(f60,X0) = X249 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_399) ).
tff(f5035,plain,
spl331_349,
inference(avatar_split_clause,[],[f1800,f5033]) ).
tff(f5033,plain,
( spl331_349
<=> ! [X0: $real,X1: 'S2'] : ( f19(sK84(X0,X1),X1) = sK85(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_349])]) ).
tff(f1800,plain,
! [X0: $real,X1: 'S2'] : ( f19(sK84(X0,X1),X1) = sK85(X0,X1) ),
inference(cnf_transformation,[],[f1085]) ).
tff(f1085,plain,
! [X0: $real,X1: 'S2'] :
( ( f19(sK84(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f22(f49(f50,sK85(X0,X1)),sK85(X0,X1)) )
& ( f19(sK84(X0,X1),X1) = sK85(X0,X1) )
& ( f59(f60,X0) = sK84(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK84,sK85])],[f668,f1084,f1083]) ).
tff(f1083,plain,
! [X0: $real,X1: 'S2'] :
( ? [X2: 'S13'] :
( ? [X3: $real] :
( ( f19(X2,f6(f7,$product(2,f11(f12,X1)))) = f22(f49(f50,X3),X3) )
& ( f19(X2,X1) = X3 ) )
& ( f59(f60,X0) = X2 ) )
=> ( ? [X3: $real] :
( ( f22(f49(f50,X3),X3) = f19(sK84(X0,X1),f6(f7,$product(2,f11(f12,X1)))) )
& ( f19(sK84(X0,X1),X1) = X3 ) )
& ( f59(f60,X0) = sK84(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1084,plain,
! [X0: $real,X1: 'S2'] :
( ? [X3: $real] :
( ( f22(f49(f50,X3),X3) = f19(sK84(X0,X1),f6(f7,$product(2,f11(f12,X1)))) )
& ( f19(sK84(X0,X1),X1) = X3 ) )
=> ( ( f19(sK84(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f22(f49(f50,sK85(X0,X1)),sK85(X0,X1)) )
& ( f19(sK84(X0,X1),X1) = sK85(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f668,plain,
! [X0: $real,X1: 'S2'] :
? [X2: 'S13'] :
( ? [X3: $real] :
( ( f19(X2,f6(f7,$product(2,f11(f12,X1)))) = f22(f49(f50,X3),X3) )
& ( f19(X2,X1) = X3 ) )
& ( f59(f60,X0) = X2 ) ),
inference(rectify,[],[f395]) ).
tff(f395,axiom,
! [X0: $real,X1: 'S2'] :
? [X241: 'S13'] :
( ? [X242: $real] :
( ( f19(X241,f6(f7,$product(2,f11(f12,X1)))) = f22(f49(f50,X242),X242) )
& ( f19(X241,X1) = X242 ) )
& ( f59(f60,X0) = X241 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_395) ).
tff(f5031,plain,
spl331_348,
inference(avatar_split_clause,[],[f1785,f5029]) ).
tff(f5029,plain,
( spl331_348
<=> ! [X0: $int,X1: 'S2'] : ( f11(sK76(X0,X1),X1) = sK77(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_348])]) ).
tff(f1785,plain,
! [X0: $int,X1: 'S2'] : ( f11(sK76(X0,X1),X1) = sK77(X0,X1) ),
inference(cnf_transformation,[],[f1070]) ).
tff(f1070,plain,
! [X0: $int,X1: 'S2'] :
( ( f11(sK76(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f8(f9(f10,X0),f8(f9(f10,sK77(X0,X1)),sK77(X0,X1))) )
& ( f11(sK76(X0,X1),X1) = sK77(X0,X1) )
& ( f63(f64,X0) = sK76(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK76,sK77])],[f661,f1069,f1068]) ).
tff(f1068,plain,
! [X0: $int,X1: 'S2'] :
( ? [X2: 'S8'] :
( ? [X3: $int] :
( ( f11(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f8(f9(f10,X0),f8(f9(f10,X3),X3)) )
& ( f11(X2,X1) = X3 ) )
& ( f63(f64,X0) = X2 ) )
=> ( ? [X3: $int] :
( ( f8(f9(f10,X0),f8(f9(f10,X3),X3)) = f11(sK76(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) )
& ( f11(sK76(X0,X1),X1) = X3 ) )
& ( f63(f64,X0) = sK76(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1069,plain,
! [X0: $int,X1: 'S2'] :
( ? [X3: $int] :
( ( f8(f9(f10,X0),f8(f9(f10,X3),X3)) = f11(sK76(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) )
& ( f11(sK76(X0,X1),X1) = X3 ) )
=> ( ( f11(sK76(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f8(f9(f10,X0),f8(f9(f10,sK77(X0,X1)),sK77(X0,X1))) )
& ( f11(sK76(X0,X1),X1) = sK77(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f661,plain,
! [X0: $int,X1: 'S2'] :
? [X2: 'S8'] :
( ? [X3: $int] :
( ( f11(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f8(f9(f10,X0),f8(f9(f10,X3),X3)) )
& ( f11(X2,X1) = X3 ) )
& ( f63(f64,X0) = X2 ) ),
inference(rectify,[],[f398]) ).
tff(f398,axiom,
! [X0: $int,X1: 'S2'] :
? [X247: 'S8'] :
( ? [X248: $int] :
( ( f11(X247,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f8(f9(f10,X0),f8(f9(f10,X248),X248)) )
& ( f11(X247,X1) = X248 ) )
& ( f63(f64,X0) = X247 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_398) ).
tff(f5027,plain,
( spl331_347
| ~ spl331_40
| ~ spl331_329 ),
inference(avatar_split_clause,[],[f4936,f4931,f3107,f5025]) ).
tff(f5025,plain,
( spl331_347
<=> ! [X2: 'S2'] : ~ $less(sK19(X2),0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_347])]) ).
tff(f3107,plain,
( spl331_40
<=> ! [X0: 'S10'] : ~ $less(sK24(X0),0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_40])]) ).
tff(f4931,plain,
( spl331_329
<=> ! [X0: 'S2'] : ( sK19(X0) = sK24(sK17(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_329])]) ).
tff(f4936,plain,
( ! [X2: 'S2'] : ~ $less(sK19(X2),0.0)
| ~ spl331_40
| ~ spl331_329 ),
inference(superposition,[],[f3108,f4932]) ).
tff(f4932,plain,
( ! [X0: 'S2'] : ( sK19(X0) = sK24(sK17(X0)) )
| ~ spl331_329 ),
inference(avatar_component_clause,[],[f4931]) ).
tff(f3108,plain,
( ! [X0: 'S10'] : ~ $less(sK24(X0),0.0)
| ~ spl331_40 ),
inference(avatar_component_clause,[],[f3107]) ).
tff(f5023,plain,
spl331_346,
inference(avatar_split_clause,[],[f1782,f5021]) ).
tff(f5021,plain,
( spl331_346
<=> ! [X0: $int,X1: 'S2'] : ( f11(sK74(X0,X1),X1) = sK75(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_346])]) ).
tff(f1782,plain,
! [X0: $int,X1: 'S2'] : ( f11(sK74(X0,X1),X1) = sK75(X0,X1) ),
inference(cnf_transformation,[],[f1067]) ).
tff(f1067,plain,
! [X0: $int,X1: 'S2'] :
( ( f11(sK74(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f8(f9(f10,sK75(X0,X1)),sK75(X0,X1)) )
& ( f11(sK74(X0,X1),X1) = sK75(X0,X1) )
& ( f63(f64,X0) = sK74(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK74,sK75])],[f660,f1066,f1065]) ).
tff(f1065,plain,
! [X0: $int,X1: 'S2'] :
( ? [X2: 'S8'] :
( ? [X3: $int] :
( ( f11(X2,f6(f7,$product(2,f11(f12,X1)))) = f8(f9(f10,X3),X3) )
& ( f11(X2,X1) = X3 ) )
& ( f63(f64,X0) = X2 ) )
=> ( ? [X3: $int] :
( ( f8(f9(f10,X3),X3) = f11(sK74(X0,X1),f6(f7,$product(2,f11(f12,X1)))) )
& ( f11(sK74(X0,X1),X1) = X3 ) )
& ( f63(f64,X0) = sK74(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1066,plain,
! [X0: $int,X1: 'S2'] :
( ? [X3: $int] :
( ( f8(f9(f10,X3),X3) = f11(sK74(X0,X1),f6(f7,$product(2,f11(f12,X1)))) )
& ( f11(sK74(X0,X1),X1) = X3 ) )
=> ( ( f11(sK74(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f8(f9(f10,sK75(X0,X1)),sK75(X0,X1)) )
& ( f11(sK74(X0,X1),X1) = sK75(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f660,plain,
! [X0: $int,X1: 'S2'] :
? [X2: 'S8'] :
( ? [X3: $int] :
( ( f11(X2,f6(f7,$product(2,f11(f12,X1)))) = f8(f9(f10,X3),X3) )
& ( f11(X2,X1) = X3 ) )
& ( f63(f64,X0) = X2 ) ),
inference(rectify,[],[f394]) ).
tff(f394,axiom,
! [X0: $int,X1: 'S2'] :
? [X239: 'S8'] :
( ? [X240: $int] :
( ( f11(X239,f6(f7,$product(2,f11(f12,X1)))) = f8(f9(f10,X240),X240) )
& ( f11(X239,X1) = X240 ) )
& ( f63(f64,X0) = X239 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_394) ).
tff(f5019,plain,
spl331_345,
inference(avatar_split_clause,[],[f1779,f5017]) ).
tff(f5017,plain,
( spl331_345
<=> ! [X0: 'S10',X1: 'S2'] : ( f13(sK72(X0,X1),X1) = sK73(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_345])]) ).
tff(f1779,plain,
! [X0: 'S10',X1: 'S2'] : ( f13(sK72(X0,X1),X1) = sK73(X0,X1) ),
inference(cnf_transformation,[],[f1064]) ).
tff(f1064,plain,
! [X0: 'S10',X1: 'S2'] :
( ( f13(sK72(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f34(f39(f52,X0),f34(f39(f52,sK73(X0,X1)),sK73(X0,X1))) )
& ( f13(sK72(X0,X1),X1) = sK73(X0,X1) )
& ( f66(f67,X0) = sK72(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72,sK73])],[f659,f1063,f1062]) ).
tff(f1062,plain,
! [X0: 'S10',X1: 'S2'] :
( ? [X2: 'S9'] :
( ? [X3: 'S10'] :
( ( f13(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f34(f39(f52,X0),f34(f39(f52,X3),X3)) )
& ( f13(X2,X1) = X3 ) )
& ( f66(f67,X0) = X2 ) )
=> ( ? [X3: 'S10'] :
( ( f34(f39(f52,X0),f34(f39(f52,X3),X3)) = f13(sK72(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) )
& ( f13(sK72(X0,X1),X1) = X3 ) )
& ( f66(f67,X0) = sK72(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1063,plain,
! [X0: 'S10',X1: 'S2'] :
( ? [X3: 'S10'] :
( ( f34(f39(f52,X0),f34(f39(f52,X3),X3)) = f13(sK72(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) )
& ( f13(sK72(X0,X1),X1) = X3 ) )
=> ( ( f13(sK72(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f34(f39(f52,X0),f34(f39(f52,sK73(X0,X1)),sK73(X0,X1))) )
& ( f13(sK72(X0,X1),X1) = sK73(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f659,plain,
! [X0: 'S10',X1: 'S2'] :
? [X2: 'S9'] :
( ? [X3: 'S10'] :
( ( f13(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f34(f39(f52,X0),f34(f39(f52,X3),X3)) )
& ( f13(X2,X1) = X3 ) )
& ( f66(f67,X0) = X2 ) ),
inference(rectify,[],[f401]) ).
tff(f401,axiom,
! [X0: 'S10',X1: 'S2'] :
? [X253: 'S9'] :
( ? [X254: 'S10'] :
( ( f13(X253,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f34(f39(f52,X0),f34(f39(f52,X254),X254)) )
& ( f13(X253,X1) = X254 ) )
& ( f66(f67,X0) = X253 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_401) ).
tff(f5015,plain,
spl331_344,
inference(avatar_split_clause,[],[f1776,f5013]) ).
tff(f5013,plain,
( spl331_344
<=> ! [X0: 'S10',X1: 'S2'] : ( f13(sK70(X0,X1),X1) = sK71(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_344])]) ).
tff(f1776,plain,
! [X0: 'S10',X1: 'S2'] : ( f13(sK70(X0,X1),X1) = sK71(X0,X1) ),
inference(cnf_transformation,[],[f1061]) ).
tff(f1061,plain,
! [X0: 'S10',X1: 'S2'] :
( ( f13(sK70(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f34(f39(f52,sK71(X0,X1)),sK71(X0,X1)) )
& ( f13(sK70(X0,X1),X1) = sK71(X0,X1) )
& ( f66(f67,X0) = sK70(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK70,sK71])],[f658,f1060,f1059]) ).
tff(f1059,plain,
! [X0: 'S10',X1: 'S2'] :
( ? [X2: 'S9'] :
( ? [X3: 'S10'] :
( ( f13(X2,f6(f7,$product(2,f11(f12,X1)))) = f34(f39(f52,X3),X3) )
& ( f13(X2,X1) = X3 ) )
& ( f66(f67,X0) = X2 ) )
=> ( ? [X3: 'S10'] :
( ( f34(f39(f52,X3),X3) = f13(sK70(X0,X1),f6(f7,$product(2,f11(f12,X1)))) )
& ( f13(sK70(X0,X1),X1) = X3 ) )
& ( f66(f67,X0) = sK70(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1060,plain,
! [X0: 'S10',X1: 'S2'] :
( ? [X3: 'S10'] :
( ( f34(f39(f52,X3),X3) = f13(sK70(X0,X1),f6(f7,$product(2,f11(f12,X1)))) )
& ( f13(sK70(X0,X1),X1) = X3 ) )
=> ( ( f13(sK70(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f34(f39(f52,sK71(X0,X1)),sK71(X0,X1)) )
& ( f13(sK70(X0,X1),X1) = sK71(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f658,plain,
! [X0: 'S10',X1: 'S2'] :
? [X2: 'S9'] :
( ? [X3: 'S10'] :
( ( f13(X2,f6(f7,$product(2,f11(f12,X1)))) = f34(f39(f52,X3),X3) )
& ( f13(X2,X1) = X3 ) )
& ( f66(f67,X0) = X2 ) ),
inference(rectify,[],[f397]) ).
tff(f397,axiom,
! [X0: 'S10',X1: 'S2'] :
? [X245: 'S9'] :
( ? [X246: 'S10'] :
( ( f13(X245,f6(f7,$product(2,f11(f12,X1)))) = f34(f39(f52,X246),X246) )
& ( f13(X245,X1) = X246 ) )
& ( f66(f67,X0) = X245 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_397) ).
tff(f5011,plain,
spl331_343,
inference(avatar_split_clause,[],[f1618,f5009]) ).
tff(f5009,plain,
( spl331_343
<=> ! [X0: $real,X1: $real] : ( f27(f36,f16(f17(f18,X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_343])]) ).
tff(f1618,plain,
! [X0: $real,X1: $real] : ( f27(f36,f16(f17(f18,X0),X1)) = X1 ),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
! [X0: $real,X1: $real] : ( f27(f36,f16(f17(f18,X0),X1)) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_108) ).
tff(f5007,plain,
spl331_342,
inference(avatar_split_clause,[],[f1617,f5005]) ).
tff(f5005,plain,
( spl331_342
<=> ! [X0: $real,X1: $real] : ( f27(f28,f16(f17(f18,X0),X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_342])]) ).
tff(f1617,plain,
! [X0: $real,X1: $real] : ( f27(f28,f16(f17(f18,X0),X1)) = X0 ),
inference(cnf_transformation,[],[f40]) ).
tff(f40,axiom,
! [X0: $real,X1: $real] : ( f27(f28,f16(f17(f18,X0),X1)) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_40) ).
tff(f5003,plain,
spl331_341,
inference(avatar_split_clause,[],[f1597,f5001]) ).
tff(f5001,plain,
( spl331_341
<=> ! [X0: 'S2'] : ( sK35(X0) = f3(f4(f65,sK35(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_341])]) ).
tff(f1597,plain,
! [X0: 'S2'] : ( sK35(X0) = f3(f4(f65,sK35(X0)),X0) ),
inference(cnf_transformation,[],[f968]) ).
tff(f968,plain,
! [X0: 'S2'] :
( ( sK35(X0) = f3(f4(f65,sK35(X0)),X0) )
& ( f6(f7,$sum(0,1)) = sK35(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f633,f967]) ).
tff(f967,plain,
! [X0: 'S2'] :
( ? [X1: 'S2'] :
( ( f3(f4(f65,X1),X0) = X1 )
& ( f6(f7,$sum(0,1)) = X1 ) )
=> ( ( sK35(X0) = f3(f4(f65,sK35(X0)),X0) )
& ( f6(f7,$sum(0,1)) = sK35(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f633,plain,
! [X0: 'S2'] :
? [X1: 'S2'] :
( ( f3(f4(f65,X1),X0) = X1 )
& ( f6(f7,$sum(0,1)) = X1 ) ),
inference(rectify,[],[f446]) ).
tff(f446,axiom,
! [X0: 'S2'] :
? [X290: 'S2'] :
( ( f3(f4(f65,X290),X0) = X290 )
& ( f6(f7,$sum(0,1)) = X290 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_446) ).
tff(f4999,plain,
spl331_340,
inference(avatar_split_clause,[],[f1534,f4997]) ).
tff(f4997,plain,
( spl331_340
<=> ! [X0: 'S10'] : ( f16(f17(f18,sK4(X0)),sK5(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_340])]) ).
tff(f1534,plain,
! [X0: 'S10'] : ( f16(f17(f18,sK4(X0)),sK5(X0)) = X0 ),
inference(cnf_transformation,[],[f909]) ).
tff(f909,plain,
! [X0: 'S10'] : ( f16(f17(f18,sK4(X0)),sK5(X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f816,f908]) ).
tff(f908,plain,
! [X0: 'S10'] :
( ? [X1: $real,X2: $real] : ( f16(f17(f18,X1),X2) = X0 )
=> ( f16(f17(f18,sK4(X0)),sK5(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f816,plain,
! [X0: 'S10'] :
? [X1: $real,X2: $real] : ( f16(f17(f18,X1),X2) = X0 ),
inference(ennf_transformation,[],[f612]) ).
tff(f612,plain,
! [X0: 'S10'] :
~ ! [X1: $real,X2: $real] : ( f16(f17(f18,X1),X2) != X0 ),
inference(flattening,[],[f611]) ).
tff(f611,plain,
! [X0: 'S10'] :
~ ! [X1: $real,X2: $real] :
( ~ f16(f17(f18,X1),X2) = X0 ),
inference(true_and_false_elimination,[],[f14]) ).
tff(f14,axiom,
! [X0: 'S10'] :
( ! [X1: $real,X2: $real] :
( ( f16(f17(f18,X1),X2) = X0 )
=> $false )
=> $false ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_14) ).
tff(f4994,plain,
( spl331_339
| ~ spl331_73
| ~ spl331_338 ),
inference(avatar_split_clause,[],[f4990,f4987,f3240,f4992]) ).
tff(f4992,plain,
( spl331_339
<=> ! [X0: $real] :
( ( $uminus(X0) = sK34(X0) )
| ~ $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_339])]) ).
tff(f4987,plain,
( spl331_338
<=> ! [X0: $real] :
( ( f22(f30,X0) = $uminus(X0) )
| ~ $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_338])]) ).
tff(f4990,plain,
( ! [X0: $real] :
( ( $uminus(X0) = sK34(X0) )
| ~ $less(X0,0.0) )
| ~ spl331_73
| ~ spl331_338 ),
inference(forward_demodulation,[],[f4988,f3241]) ).
tff(f4988,plain,
( ! [X0: $real] :
( ( f22(f30,X0) = $uminus(X0) )
| ~ $less(X0,0.0) )
| ~ spl331_338 ),
inference(avatar_component_clause,[],[f4987]) ).
tff(f4989,plain,
spl331_338,
inference(avatar_split_clause,[],[f1522,f4987]) ).
tff(f1522,plain,
! [X0: $real] :
( ( f22(f30,X0) = $uminus(X0) )
| ~ $less(X0,0.0) ),
inference(cnf_transformation,[],[f807]) ).
tff(f807,plain,
! [X0: $real] :
( ( ( f22(f30,X0) = X0 )
| $less(X0,0.0) )
& ( ( f22(f30,X0) = $uminus(X0) )
| ~ $less(X0,0.0) ) ),
inference(ennf_transformation,[],[f61]) ).
tff(f61,axiom,
! [X0: $real] :
( ( ~ $less(X0,0.0)
=> ( f22(f30,X0) = X0 ) )
& ( $less(X0,0.0)
=> ( f22(f30,X0) = $uminus(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_61) ).
tff(f4984,plain,
spl331_337,
inference(avatar_split_clause,[],[f1497,f4982]) ).
tff(f4982,plain,
( spl331_337
<=> ! [X0: $int] : ( f11(f63(f64,X0),f6(f7,1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_337])]) ).
tff(f1497,plain,
! [X0: $int] : ( f11(f63(f64,X0),f6(f7,1)) = X0 ),
inference(cnf_transformation,[],[f344]) ).
tff(f344,axiom,
! [X0: $int] : ( f11(f63(f64,X0),f6(f7,1)) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_344) ).
tff(f4980,plain,
spl331_336,
inference(avatar_split_clause,[],[f1493,f4978]) ).
tff(f4978,plain,
( spl331_336
<=> ! [X0: 'S2'] : ( f3(f4(f65,X0),f6(f7,1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_336])]) ).
tff(f1493,plain,
! [X0: 'S2'] : ( f3(f4(f65,X0),f6(f7,1)) = X0 ),
inference(cnf_transformation,[],[f450]) ).
tff(f450,axiom,
! [X0: 'S2'] : ( f3(f4(f65,X0),f6(f7,1)) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_450) ).
tff(f4976,plain,
spl331_335,
inference(avatar_split_clause,[],[f1491,f4974]) ).
tff(f4974,plain,
( spl331_335
<=> ! [X0: $real] : ( f19(f59(f60,X0),f6(f7,1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_335])]) ).
tff(f1491,plain,
! [X0: $real] : ( f19(f59(f60,X0),f6(f7,1)) = X0 ),
inference(cnf_transformation,[],[f345]) ).
tff(f345,axiom,
! [X0: $real] : ( f19(f59(f60,X0),f6(f7,1)) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_345) ).
tff(f4972,plain,
spl331_334,
inference(avatar_split_clause,[],[f1489,f4970]) ).
tff(f4970,plain,
( spl331_334
<=> ! [X0: 'S10'] : ( f13(f66(f67,X0),f6(f7,1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_334])]) ).
tff(f1489,plain,
! [X0: 'S10'] : ( f13(f66(f67,X0),f6(f7,1)) = X0 ),
inference(cnf_transformation,[],[f347]) ).
tff(f347,axiom,
! [X0: 'S10'] : ( f13(f66(f67,X0),f6(f7,1)) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_347) ).
tff(f4962,plain,
( spl331_333
| ~ spl331_68
| ~ spl331_332 ),
inference(avatar_split_clause,[],[f4958,f4955,f3220,f4960]) ).
tff(f4960,plain,
( spl331_333
<=> ! [X0: 'S10'] : ( f27(f31,f34(f35,X0)) = sK24(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_333])]) ).
tff(f4955,plain,
( spl331_332
<=> ! [X0: 'S10'] : ( f27(f31,X0) = f27(f31,f34(f35,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_332])]) ).
tff(f4958,plain,
( ! [X0: 'S10'] : ( f27(f31,f34(f35,X0)) = sK24(X0) )
| ~ spl331_68
| ~ spl331_332 ),
inference(forward_demodulation,[],[f4956,f3221]) ).
tff(f4956,plain,
( ! [X0: 'S10'] : ( f27(f31,X0) = f27(f31,f34(f35,X0)) )
| ~ spl331_332 ),
inference(avatar_component_clause,[],[f4955]) ).
tff(f4957,plain,
spl331_332,
inference(avatar_split_clause,[],[f1488,f4955]) ).
tff(f4947,plain,
( spl331_331
| ~ spl331_67
| ~ spl331_330 ),
inference(avatar_split_clause,[],[f4943,f4940,f3216,f4945]) ).
tff(f4945,plain,
( spl331_331
<=> ! [X0: 'S10'] : ( f27(f28,f34(f35,X0)) = sK23(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_331])]) ).
tff(f3216,plain,
( spl331_67
<=> ! [X0: 'S10'] : ( f27(f28,X0) = sK23(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_67])]) ).
tff(f4940,plain,
( spl331_330
<=> ! [X0: 'S10'] : ( f27(f28,X0) = f27(f28,f34(f35,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_330])]) ).
tff(f4943,plain,
( ! [X0: 'S10'] : ( f27(f28,f34(f35,X0)) = sK23(X0) )
| ~ spl331_67
| ~ spl331_330 ),
inference(forward_demodulation,[],[f4941,f3217]) ).
tff(f3217,plain,
( ! [X0: 'S10'] : ( f27(f28,X0) = sK23(X0) )
| ~ spl331_67 ),
inference(avatar_component_clause,[],[f3216]) ).
tff(f4941,plain,
( ! [X0: 'S10'] : ( f27(f28,X0) = f27(f28,f34(f35,X0)) )
| ~ spl331_330 ),
inference(avatar_component_clause,[],[f4940]) ).
tff(f4942,plain,
spl331_330,
inference(avatar_split_clause,[],[f1487,f4940]) ).
tff(f1487,plain,
! [X0: 'S10'] : ( f27(f28,X0) = f27(f28,f34(f35,X0)) ),
inference(cnf_transformation,[],[f27]) ).
tff(f27,axiom,
! [X0: 'S10'] : ( f27(f28,X0) = f27(f28,f34(f35,X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_27) ).
tff(f4933,plain,
( spl331_329
| ~ spl331_63
| ~ spl331_65
| ~ spl331_68
| ~ spl331_328 ),
inference(avatar_split_clause,[],[f4929,f4924,f3220,f3208,f3200,f4931]) ).
tff(f4924,plain,
( spl331_328
<=> ! [X0: 'S2'] : ( f19(f20,X0) = f27(f31,f13(f14,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_328])]) ).
tff(f4929,plain,
( ! [X0: 'S2'] : ( sK19(X0) = sK24(sK17(X0)) )
| ~ spl331_63
| ~ spl331_65
| ~ spl331_68
| ~ spl331_328 ),
inference(forward_demodulation,[],[f4928,f3209]) ).
tff(f4928,plain,
( ! [X0: 'S2'] : ( f19(f20,X0) = sK24(sK17(X0)) )
| ~ spl331_63
| ~ spl331_68
| ~ spl331_328 ),
inference(forward_demodulation,[],[f4927,f3221]) ).
tff(f4927,plain,
( ! [X0: 'S2'] : ( f19(f20,X0) = f27(f31,sK17(X0)) )
| ~ spl331_63
| ~ spl331_328 ),
inference(forward_demodulation,[],[f4925,f3201]) ).
tff(f4925,plain,
( ! [X0: 'S2'] : ( f19(f20,X0) = f27(f31,f13(f14,X0)) )
| ~ spl331_328 ),
inference(avatar_component_clause,[],[f4924]) ).
tff(f4926,plain,
spl331_328,
inference(avatar_split_clause,[],[f1486,f4924]) ).
tff(f1486,plain,
! [X0: 'S2'] : ( f19(f20,X0) = f27(f31,f13(f14,X0)) ),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
! [X0: 'S2'] : ( f19(f20,X0) = f27(f31,f13(f14,X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_16) ).
tff(f4919,plain,
spl331_327,
inference(avatar_split_clause,[],[f1485,f4917]) ).
tff(f4917,plain,
( spl331_327
<=> ! [X0: 'S2'] : ( f19(f20,X0) = f27(f28,f13(f14,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_327])]) ).
tff(f1485,plain,
! [X0: 'S2'] : ( f19(f20,X0) = f27(f28,f13(f14,X0)) ),
inference(cnf_transformation,[],[f12]) ).
tff(f12,axiom,
! [X0: 'S2'] : ( f19(f20,X0) = f27(f28,f13(f14,X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_12) ).
tff(f4914,plain,
( spl331_326
| ~ spl331_64
| ~ spl331_325 ),
inference(avatar_split_clause,[],[f4910,f4907,f3204,f4912]) ).
tff(f4907,plain,
( spl331_325
<=> ! [X0: $real] : ( f16(f32,X0) = f16(f17(f18,X0),0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_325])]) ).
tff(f4910,plain,
( ! [X0: $real] : ( f16(f17(f18,X0),0.0) = sK18(X0) )
| ~ spl331_64
| ~ spl331_325 ),
inference(forward_demodulation,[],[f4908,f3205]) ).
tff(f4908,plain,
( ! [X0: $real] : ( f16(f32,X0) = f16(f17(f18,X0),0.0) )
| ~ spl331_325 ),
inference(avatar_component_clause,[],[f4907]) ).
tff(f4909,plain,
spl331_325,
inference(avatar_split_clause,[],[f1484,f4907]) ).
tff(f1484,plain,
! [X0: $real] : ( f16(f32,X0) = f16(f17(f18,X0),0.0) ),
inference(cnf_transformation,[],[f39]) ).
tff(f39,axiom,
! [X0: $real] : ( f16(f32,X0) = f16(f17(f18,X0),0.0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_39) ).
tff(f4900,plain,
( spl331_324
| ~ spl331_63
| ~ spl331_64
| ~ spl331_65
| ~ spl331_323 ),
inference(avatar_split_clause,[],[f4896,f4891,f3208,f3204,f3200,f4898]) ).
tff(f4891,plain,
( spl331_323
<=> ! [X0: 'S2'] : ( f13(f14,X0) = f16(f32,f19(f20,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_323])]) ).
tff(f4896,plain,
( ! [X0: 'S2'] : ( sK17(X0) = sK18(sK19(X0)) )
| ~ spl331_63
| ~ spl331_64
| ~ spl331_65
| ~ spl331_323 ),
inference(forward_demodulation,[],[f4895,f3201]) ).
tff(f4895,plain,
( ! [X0: 'S2'] : ( f13(f14,X0) = sK18(sK19(X0)) )
| ~ spl331_64
| ~ spl331_65
| ~ spl331_323 ),
inference(forward_demodulation,[],[f4894,f3205]) ).
tff(f4894,plain,
( ! [X0: 'S2'] : ( f13(f14,X0) = f16(f32,sK19(X0)) )
| ~ spl331_65
| ~ spl331_323 ),
inference(forward_demodulation,[],[f4892,f3209]) ).
tff(f4892,plain,
( ! [X0: 'S2'] : ( f13(f14,X0) = f16(f32,f19(f20,X0)) )
| ~ spl331_323 ),
inference(avatar_component_clause,[],[f4891]) ).
tff(f4893,plain,
spl331_323,
inference(avatar_split_clause,[],[f1483,f4891]) ).
tff(f1483,plain,
! [X0: 'S2'] : ( f13(f14,X0) = f16(f32,f19(f20,X0)) ),
inference(cnf_transformation,[],[f17]) ).
tff(f17,axiom,
! [X0: 'S2'] : ( f13(f14,X0) = f16(f32,f19(f20,X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_17) ).
tff(f4888,plain,
spl331_322,
inference(avatar_split_clause,[],[f593,f4886]) ).
tff(f4886,plain,
( spl331_322
<=> ! [X0: $real,X1: $real] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_322])]) ).
tff(f593,plain,
! [X0: $real,X1: $real] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_147,[]) ).
tff(f4884,plain,
spl331_321,
inference(avatar_split_clause,[],[f592,f4882]) ).
tff(f4882,plain,
( spl331_321
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_321])]) ).
tff(f592,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_146,[]) ).
tff(f4880,plain,
spl331_320,
inference(avatar_split_clause,[],[f575,f4878]) ).
tff(f4878,plain,
( spl331_320
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_320])]) ).
tff(f575,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_147,[]) ).
tff(f4876,plain,
spl331_319,
inference(avatar_split_clause,[],[f574,f4874]) ).
tff(f4874,plain,
( spl331_319
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_319])]) ).
tff(f574,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_146,[]) ).
tff(f4860,plain,
( spl331_318
| spl331_17
| ~ spl331_245 ),
inference(avatar_split_clause,[],[f4473,f4457,f3008,f4857]) ).
tff(f4857,plain,
( spl331_318
<=> ( sK323 = sK34(sK323) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_318])]) ).
tff(f3008,plain,
( spl331_17
<=> $less(sK323,0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_17])]) ).
tff(f4457,plain,
( spl331_245
<=> ! [X0: $real] :
( ( sK34(X0) = X0 )
| $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_245])]) ).
tff(f4473,plain,
( ( sK323 = sK34(sK323) )
| spl331_17
| ~ spl331_245 ),
inference(resolution,[],[f4458,f3010]) ).
tff(f3010,plain,
( ~ $less(sK323,0.0)
| spl331_17 ),
inference(avatar_component_clause,[],[f3008]) ).
tff(f4458,plain,
( ! [X0: $real] :
( $less(X0,0.0)
| ( sK34(X0) = X0 ) )
| ~ spl331_245 ),
inference(avatar_component_clause,[],[f4457]) ).
tff(f4774,plain,
( spl331_317
| spl331_16
| ~ spl331_245 ),
inference(avatar_split_clause,[],[f4472,f4457,f3003,f4771]) ).
tff(f4771,plain,
( spl331_317
<=> ( sK322 = sK34(sK322) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_317])]) ).
tff(f3003,plain,
( spl331_16
<=> $less(sK322,0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_16])]) ).
tff(f4472,plain,
( ( sK322 = sK34(sK322) )
| spl331_16
| ~ spl331_245 ),
inference(resolution,[],[f4458,f3005]) ).
tff(f3005,plain,
( ~ $less(sK322,0.0)
| spl331_16 ),
inference(avatar_component_clause,[],[f3003]) ).
tff(f4763,plain,
spl331_316,
inference(avatar_split_clause,[],[f2844,f4761]) ).
tff(f4761,plain,
( spl331_316
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2',X3: 'S2'] : ( sK306(X0,X1,X2,X3) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_316])]) ).
tff(f2844,plain,
! [X2: 'S2',X3: 'S2',X0: 'S2',X1: 'S2'] : ( sK306(X0,X1,X2,X3) = sK27(X1) ),
inference(forward_demodulation,[],[f2262,f1580]) ).
tff(f2262,plain,
! [X2: 'S2',X3: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK306(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1410]) ).
tff(f1410,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
( ( ~ $less(f8(f9(f10,sK306(X0,X1,X2,X3)),sK308(X0,X1,X2,X3)),f8(f9(f10,sK307(X0,X1,X2,X3)),sK309(X0,X1,X2,X3)))
| $less(sK308(X0,X1,X2,X3),sK309(X0,X1,X2,X3))
| $less(sK306(X0,X1,X2,X3),sK307(X0,X1,X2,X3)) )
& ( f11(f12,X2) = sK309(X0,X1,X2,X3) )
& ( f11(f12,X3) = sK308(X0,X1,X2,X3) )
& ( f11(f12,X0) = sK307(X0,X1,X2,X3) )
& ( f11(f12,X1) = sK306(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK306,sK307,sK308,sK309])],[f899,f1409]) ).
tff(f1409,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
( ? [X4: $int,X5: $int,X6: $int,X7: $int] :
( ( ~ $less(f8(f9(f10,X4),X6),f8(f9(f10,X5),X7))
| $less(X6,X7)
| $less(X4,X5) )
& ( f11(f12,X2) = X7 )
& ( f11(f12,X3) = X6 )
& ( f11(f12,X0) = X5 )
& ( f11(f12,X1) = X4 ) )
=> ( ( ~ $less(f8(f9(f10,sK306(X0,X1,X2,X3)),sK308(X0,X1,X2,X3)),f8(f9(f10,sK307(X0,X1,X2,X3)),sK309(X0,X1,X2,X3)))
| $less(sK308(X0,X1,X2,X3),sK309(X0,X1,X2,X3))
| $less(sK306(X0,X1,X2,X3),sK307(X0,X1,X2,X3)) )
& ( f11(f12,X2) = sK309(X0,X1,X2,X3) )
& ( f11(f12,X3) = sK308(X0,X1,X2,X3) )
& ( f11(f12,X0) = sK307(X0,X1,X2,X3) )
& ( f11(f12,X1) = sK306(X0,X1,X2,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f899,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X4: $int,X5: $int,X6: $int,X7: $int] :
( ( ~ $less(f8(f9(f10,X4),X6),f8(f9(f10,X5),X7))
| $less(X6,X7)
| $less(X4,X5) )
& ( f11(f12,X2) = X7 )
& ( f11(f12,X3) = X6 )
& ( f11(f12,X0) = X5 )
& ( f11(f12,X1) = X4 ) ),
inference(flattening,[],[f898]) ).
tff(f898,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X4: $int,X5: $int,X6: $int,X7: $int] :
( ( ~ $less(f8(f9(f10,X4),X6),f8(f9(f10,X5),X7))
| $less(X6,X7)
| $less(X4,X5) )
& ( f11(f12,X2) = X7 )
& ( f11(f12,X3) = X6 )
& ( f11(f12,X0) = X5 )
& ( f11(f12,X1) = X4 ) ),
inference(ennf_transformation,[],[f800]) ).
tff(f800,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X4: $int,X5: $int,X6: $int,X7: $int] :
( ( ~ $less(X4,X5)
=> ( ~ $less(X6,X7)
=> ~ $less(f8(f9(f10,X4),X6),f8(f9(f10,X5),X7)) ) )
& ( f11(f12,X2) = X7 )
& ( f11(f12,X3) = X6 )
& ( f11(f12,X0) = X5 )
& ( f11(f12,X1) = X4 ) ),
inference(rectify,[],[f542]) ).
tff(f542,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X92: $int,X93: $int,X94: $int,X95: $int] :
( ( ~ $less(X92,X93)
=> ( ~ $less(X94,X95)
=> ~ $less(f8(f9(f10,X92),X94),f8(f9(f10,X93),X95)) ) )
& ( f11(f12,X2) = X95 )
& ( f11(f12,X3) = X94 )
& ( f11(f12,X0) = X93 )
& ( f11(f12,X1) = X92 ) ),
inference(theory_normalization,[],[f165]) ).
tff(f165,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2',X3: 'S2'] :
? [X92: $int,X93: $int,X94: $int,X95: $int] :
( ( $lesseq(X93,X92)
=> ( $lesseq(X95,X94)
=> $lesseq(f8(f9(f10,X93),X95),f8(f9(f10,X92),X94)) ) )
& ( f11(f12,X2) = X95 )
& ( f11(f12,X3) = X94 )
& ( f11(f12,X0) = X93 )
& ( f11(f12,X1) = X92 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_165) ).
tff(f4759,plain,
spl331_315,
inference(avatar_split_clause,[],[f2843,f4757]) ).
tff(f4757,plain,
( spl331_315
<=> ! [X0: 'S2',X3: 'S2',X2: 'S2',X1: 'S2'] : ( sK27(X0) = sK307(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_315])]) ).
tff(f2843,plain,
! [X2: 'S2',X3: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK307(X0,X1,X2,X3) ),
inference(forward_demodulation,[],[f2263,f1580]) ).
tff(f2263,plain,
! [X2: 'S2',X3: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK307(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1410]) ).
tff(f4755,plain,
spl331_314,
inference(avatar_split_clause,[],[f2842,f4753]) ).
tff(f4753,plain,
( spl331_314
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2',X3: 'S2'] : ( sK308(X0,X1,X2,X3) = sK27(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_314])]) ).
tff(f2842,plain,
! [X2: 'S2',X3: 'S2',X0: 'S2',X1: 'S2'] : ( sK308(X0,X1,X2,X3) = sK27(X3) ),
inference(forward_demodulation,[],[f2264,f1580]) ).
tff(f2264,plain,
! [X2: 'S2',X3: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X3) = sK308(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1410]) ).
tff(f4751,plain,
spl331_313,
inference(avatar_split_clause,[],[f2841,f4749]) ).
tff(f4749,plain,
( spl331_313
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2',X3: 'S2'] : ( sK309(X0,X1,X2,X3) = sK27(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_313])]) ).
tff(f2841,plain,
! [X2: 'S2',X3: 'S2',X0: 'S2',X1: 'S2'] : ( sK309(X0,X1,X2,X3) = sK27(X2) ),
inference(forward_demodulation,[],[f2265,f1580]) ).
tff(f2265,plain,
! [X2: 'S2',X3: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X2) = sK309(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1410]) ).
tff(f4747,plain,
spl331_312,
inference(avatar_split_clause,[],[f2676,f4745]) ).
tff(f4745,plain,
( spl331_312
<=> ! [X0: 'S10',X1: 'S10'] : ( sK148(X0,X1) = f49(f50,sK22(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_312])]) ).
tff(f2676,plain,
! [X0: 'S10',X1: 'S10'] : ( sK148(X0,X1) = f49(f50,sK22(X0)) ),
inference(forward_demodulation,[],[f1913,f1567]) ).
tff(f1913,plain,
! [X0: 'S10',X1: 'S10'] : ( f49(f50,f27(f36,X0)) = sK148(X0,X1) ),
inference(cnf_transformation,[],[f1172]) ).
tff(f1172,plain,
! [X0: 'S10',X1: 'S10'] :
( ( f34(f39(f52,X0),X1) = f16(f17(f18,$sum(f22(sK150(X0,X1),sK151(X0,X1)),$uminus(f22(sK148(X0,X1),sK149(X0,X1))))),$sum(f22(sK150(X0,X1),sK149(X0,X1)),f22(sK148(X0,X1),sK151(X0,X1)))) )
& ( f27(f28,X1) = sK151(X0,X1) )
& ( f49(f50,f27(f28,X0)) = sK150(X0,X1) )
& ( f27(f36,X1) = sK149(X0,X1) )
& ( f49(f50,f27(f36,X0)) = sK148(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK148,sK149,sK150,sK151])],[f704,f1171]) ).
tff(f1171,plain,
! [X0: 'S10',X1: 'S10'] :
( ? [X2: 'S14',X3: $real,X4: 'S14',X5: $real] :
( ( f34(f39(f52,X0),X1) = f16(f17(f18,$sum(f22(X4,X5),$uminus(f22(X2,X3)))),$sum(f22(X4,X3),f22(X2,X5))) )
& ( f27(f28,X1) = X5 )
& ( f49(f50,f27(f28,X0)) = X4 )
& ( f27(f36,X1) = X3 )
& ( f49(f50,f27(f36,X0)) = X2 ) )
=> ( ( f34(f39(f52,X0),X1) = f16(f17(f18,$sum(f22(sK150(X0,X1),sK151(X0,X1)),$uminus(f22(sK148(X0,X1),sK149(X0,X1))))),$sum(f22(sK150(X0,X1),sK149(X0,X1)),f22(sK148(X0,X1),sK151(X0,X1)))) )
& ( f27(f28,X1) = sK151(X0,X1) )
& ( f49(f50,f27(f28,X0)) = sK150(X0,X1) )
& ( f27(f36,X1) = sK149(X0,X1) )
& ( f49(f50,f27(f36,X0)) = sK148(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f704,plain,
! [X0: 'S10',X1: 'S10'] :
? [X2: 'S14',X3: $real,X4: 'S14',X5: $real] :
( ( f34(f39(f52,X0),X1) = f16(f17(f18,$sum(f22(X4,X5),$uminus(f22(X2,X3)))),$sum(f22(X4,X3),f22(X2,X5))) )
& ( f27(f28,X1) = X5 )
& ( f49(f50,f27(f28,X0)) = X4 )
& ( f27(f36,X1) = X3 )
& ( f49(f50,f27(f36,X0)) = X2 ) ),
inference(rectify,[],[f521]) ).
tff(f521,plain,
! [X0: 'S10',X1: 'S10'] :
? [X108: 'S14',X109: $real,X110: 'S14',X111: $real] :
( ( f34(f39(f52,X0),X1) = f16(f17(f18,$sum(f22(X110,X111),$uminus(f22(X108,X109)))),$sum(f22(X110,X109),f22(X108,X111))) )
& ( f27(f28,X1) = X111 )
& ( f49(f50,f27(f28,X0)) = X110 )
& ( f27(f36,X1) = X109 )
& ( f49(f50,f27(f36,X0)) = X108 ) ),
inference(theory_normalization,[],[f182]) ).
tff(f182,axiom,
! [X0: 'S10',X1: 'S10'] :
? [X108: 'S14',X109: $real,X110: 'S14',X111: $real] :
( ( f34(f39(f52,X0),X1) = f16(f17(f18,$difference(f22(X110,X111),f22(X108,X109))),$sum(f22(X110,X109),f22(X108,X111))) )
& ( f27(f28,X1) = X111 )
& ( f49(f50,f27(f28,X0)) = X110 )
& ( f27(f36,X1) = X109 )
& ( f49(f50,f27(f36,X0)) = X108 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_182) ).
tff(f4743,plain,
spl331_311,
inference(avatar_split_clause,[],[f2674,f4741]) ).
tff(f4741,plain,
( spl331_311
<=> ! [X0: 'S10',X1: 'S10'] : ( sK150(X0,X1) = f49(f50,sK23(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_311])]) ).
tff(f2674,plain,
! [X0: 'S10',X1: 'S10'] : ( sK150(X0,X1) = f49(f50,sK23(X0)) ),
inference(forward_demodulation,[],[f1915,f1570]) ).
tff(f1915,plain,
! [X0: 'S10',X1: 'S10'] : ( f49(f50,f27(f28,X0)) = sK150(X0,X1) ),
inference(cnf_transformation,[],[f1172]) ).
tff(f4739,plain,
spl331_310,
inference(avatar_split_clause,[],[f2093,f4737]) ).
tff(f4737,plain,
( spl331_310
<=> ! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X1) = sK217(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_310])]) ).
tff(f2093,plain,
! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X1) = sK217(X0,X1,X2) ),
inference(cnf_transformation,[],[f1301]) ).
tff(f1301,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ( f34(sK216(X0,X1,X2),f34(sK217(X0,X1,X2),X2)) = f34(sK217(X0,X1,X2),f34(sK216(X0,X1,X2),X2)) )
& ( f39(f52,X1) = sK217(X0,X1,X2) )
& ( f39(f52,X0) = sK216(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK216,sK217])],[f759,f1300]) ).
tff(f1300,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ? [X3: 'S17',X4: 'S17'] :
( ( f34(X3,f34(X4,X2)) = f34(X4,f34(X3,X2)) )
& ( f39(f52,X1) = X4 )
& ( f39(f52,X0) = X3 ) )
=> ( ( f34(sK216(X0,X1,X2),f34(sK217(X0,X1,X2),X2)) = f34(sK217(X0,X1,X2),f34(sK216(X0,X1,X2),X2)) )
& ( f39(f52,X1) = sK217(X0,X1,X2) )
& ( f39(f52,X0) = sK216(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f759,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X3: 'S17',X4: 'S17'] :
( ( f34(X3,f34(X4,X2)) = f34(X4,f34(X3,X2)) )
& ( f39(f52,X1) = X4 )
& ( f39(f52,X0) = X3 ) ),
inference(rectify,[],[f231]) ).
tff(f231,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X130: 'S17',X131: 'S17'] :
( ( f34(X130,f34(X131,X2)) = f34(X131,f34(X130,X2)) )
& ( f39(f52,X1) = X131 )
& ( f39(f52,X0) = X130 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_231) ).
tff(f4735,plain,
spl331_309,
inference(avatar_split_clause,[],[f2092,f4733]) ).
tff(f4733,plain,
( spl331_309
<=> ! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK216(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_309])]) ).
tff(f2092,plain,
! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK216(X0,X1,X2) ),
inference(cnf_transformation,[],[f1301]) ).
tff(f4731,plain,
( spl331_308
| spl331_15
| ~ spl331_245 ),
inference(avatar_split_clause,[],[f4471,f4457,f2998,f4728]) ).
tff(f4728,plain,
( spl331_308
<=> ( sK321 = sK34(sK321) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_308])]) ).
tff(f2998,plain,
( spl331_15
<=> $less(sK321,0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_15])]) ).
tff(f4471,plain,
( ( sK321 = sK34(sK321) )
| spl331_15
| ~ spl331_245 ),
inference(resolution,[],[f4458,f3000]) ).
tff(f3000,plain,
( ~ $less(sK321,0.0)
| spl331_15 ),
inference(avatar_component_clause,[],[f2998]) ).
tff(f4726,plain,
spl331_307,
inference(avatar_split_clause,[],[f2090,f4724]) ).
tff(f4724,plain,
( spl331_307
<=> ! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f40,X1) = sK215(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_307])]) ).
tff(f2090,plain,
! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f40,X1) = sK215(X0,X1,X2) ),
inference(cnf_transformation,[],[f1299]) ).
tff(f1299,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ( f34(sK214(X0,X1,X2),f34(sK215(X0,X1,X2),X2)) = f34(sK215(X0,X1,X2),f34(sK214(X0,X1,X2),X2)) )
& ( f39(f40,X1) = sK215(X0,X1,X2) )
& ( f39(f40,X0) = sK214(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK214,sK215])],[f758,f1298]) ).
tff(f1298,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ? [X3: 'S17',X4: 'S17'] :
( ( f34(X3,f34(X4,X2)) = f34(X4,f34(X3,X2)) )
& ( f39(f40,X1) = X4 )
& ( f39(f40,X0) = X3 ) )
=> ( ( f34(sK214(X0,X1,X2),f34(sK215(X0,X1,X2),X2)) = f34(sK215(X0,X1,X2),f34(sK214(X0,X1,X2),X2)) )
& ( f39(f40,X1) = sK215(X0,X1,X2) )
& ( f39(f40,X0) = sK214(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f758,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X3: 'S17',X4: 'S17'] :
( ( f34(X3,f34(X4,X2)) = f34(X4,f34(X3,X2)) )
& ( f39(f40,X1) = X4 )
& ( f39(f40,X0) = X3 ) ),
inference(rectify,[],[f261]) ).
tff(f261,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X166: 'S17',X167: 'S17'] :
( ( f34(X166,f34(X167,X2)) = f34(X167,f34(X166,X2)) )
& ( f39(f40,X1) = X167 )
& ( f39(f40,X0) = X166 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_261) ).
tff(f4722,plain,
spl331_306,
inference(avatar_split_clause,[],[f2089,f4720]) ).
tff(f4720,plain,
( spl331_306
<=> ! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f40,X0) = sK214(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_306])]) ).
tff(f2089,plain,
! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f40,X0) = sK214(X0,X1,X2) ),
inference(cnf_transformation,[],[f1299]) ).
tff(f4718,plain,
spl331_305,
inference(avatar_split_clause,[],[f2087,f4716]) ).
tff(f4716,plain,
( spl331_305
<=> ! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X1) = sK213(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_305])]) ).
tff(f2087,plain,
! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X1) = sK213(X0,X1,X2) ),
inference(cnf_transformation,[],[f1297]) ).
tff(f1297,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( f22(sK212(X0,X1,X2),f22(sK213(X0,X1,X2),X2)) = f22(sK213(X0,X1,X2),f22(sK212(X0,X1,X2),X2)) )
& ( f49(f50,X1) = sK213(X0,X1,X2) )
& ( f49(f50,X0) = sK212(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK212,sK213])],[f757,f1296]) ).
tff(f1296,plain,
! [X0: $real,X1: $real,X2: $real] :
( ? [X3: 'S14',X4: 'S14'] :
( ( f22(X3,f22(X4,X2)) = f22(X4,f22(X3,X2)) )
& ( f49(f50,X1) = X4 )
& ( f49(f50,X0) = X3 ) )
=> ( ( f22(sK212(X0,X1,X2),f22(sK213(X0,X1,X2),X2)) = f22(sK213(X0,X1,X2),f22(sK212(X0,X1,X2),X2)) )
& ( f49(f50,X1) = sK213(X0,X1,X2) )
& ( f49(f50,X0) = sK212(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f757,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14',X4: 'S14'] :
( ( f22(X3,f22(X4,X2)) = f22(X4,f22(X3,X2)) )
& ( f49(f50,X1) = X4 )
& ( f49(f50,X0) = X3 ) ),
inference(rectify,[],[f229]) ).
tff(f229,axiom,
! [X0: $real,X1: $real,X2: $real] :
? [X126: 'S14',X127: 'S14'] :
( ( f22(X126,f22(X127,X2)) = f22(X127,f22(X126,X2)) )
& ( f49(f50,X1) = X127 )
& ( f49(f50,X0) = X126 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_229) ).
tff(f4714,plain,
spl331_304,
inference(avatar_split_clause,[],[f2086,f4712]) ).
tff(f4712,plain,
( spl331_304
<=> ! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK212(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_304])]) ).
tff(f2086,plain,
! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK212(X0,X1,X2) ),
inference(cnf_transformation,[],[f1297]) ).
tff(f4710,plain,
spl331_303,
inference(avatar_split_clause,[],[f2084,f4708]) ).
tff(f4708,plain,
( spl331_303
<=> ! [X2: $int,X0: $int,X1: $int] : ( f9(f10,X1) = sK211(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_303])]) ).
tff(f2084,plain,
! [X2: $int,X0: $int,X1: $int] : ( f9(f10,X1) = sK211(X0,X1,X2) ),
inference(cnf_transformation,[],[f1295]) ).
tff(f1295,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( f8(sK210(X0,X1,X2),f8(sK211(X0,X1,X2),X2)) = f8(sK211(X0,X1,X2),f8(sK210(X0,X1,X2),X2)) )
& ( f9(f10,X1) = sK211(X0,X1,X2) )
& ( f9(f10,X0) = sK210(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK210,sK211])],[f756,f1294]) ).
tff(f1294,plain,
! [X0: $int,X1: $int,X2: $int] :
( ? [X3: 'S6',X4: 'S6'] :
( ( f8(X3,f8(X4,X2)) = f8(X4,f8(X3,X2)) )
& ( f9(f10,X1) = X4 )
& ( f9(f10,X0) = X3 ) )
=> ( ( f8(sK210(X0,X1,X2),f8(sK211(X0,X1,X2),X2)) = f8(sK211(X0,X1,X2),f8(sK210(X0,X1,X2),X2)) )
& ( f9(f10,X1) = sK211(X0,X1,X2) )
& ( f9(f10,X0) = sK210(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f756,plain,
! [X0: $int,X1: $int,X2: $int] :
? [X3: 'S6',X4: 'S6'] :
( ( f8(X3,f8(X4,X2)) = f8(X4,f8(X3,X2)) )
& ( f9(f10,X1) = X4 )
& ( f9(f10,X0) = X3 ) ),
inference(rectify,[],[f230]) ).
tff(f230,axiom,
! [X0: $int,X1: $int,X2: $int] :
? [X128: 'S6',X129: 'S6'] :
( ( f8(X128,f8(X129,X2)) = f8(X129,f8(X128,X2)) )
& ( f9(f10,X1) = X129 )
& ( f9(f10,X0) = X128 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_230) ).
tff(f4706,plain,
spl331_302,
inference(avatar_split_clause,[],[f2083,f4704]) ).
tff(f4704,plain,
( spl331_302
<=> ! [X2: $int,X0: $int,X1: $int] : ( f9(f10,X0) = sK210(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_302])]) ).
tff(f2083,plain,
! [X2: $int,X0: $int,X1: $int] : ( f9(f10,X0) = sK210(X0,X1,X2) ),
inference(cnf_transformation,[],[f1295]) ).
tff(f4702,plain,
spl331_301,
inference(avatar_split_clause,[],[f2081,f4700]) ).
tff(f4700,plain,
( spl331_301
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X1) = sK209(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_301])]) ).
tff(f2081,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X1) = sK209(X0,X1,X2) ),
inference(cnf_transformation,[],[f1293]) ).
tff(f1293,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( f3(sK208(X0,X1,X2),f3(sK209(X0,X1,X2),X2)) = f3(sK209(X0,X1,X2),f3(sK208(X0,X1,X2),X2)) )
& ( f4(f54,X1) = sK209(X0,X1,X2) )
& ( f4(f54,X0) = sK208(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK208,sK209])],[f755,f1292]) ).
tff(f1292,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S3',X4: 'S3'] :
( ( f3(X3,f3(X4,X2)) = f3(X4,f3(X3,X2)) )
& ( f4(f54,X1) = X4 )
& ( f4(f54,X0) = X3 ) )
=> ( ( f3(sK208(X0,X1,X2),f3(sK209(X0,X1,X2),X2)) = f3(sK209(X0,X1,X2),f3(sK208(X0,X1,X2),X2)) )
& ( f4(f54,X1) = sK209(X0,X1,X2) )
& ( f4(f54,X0) = sK208(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f755,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S3',X4: 'S3'] :
( ( f3(X3,f3(X4,X2)) = f3(X4,f3(X3,X2)) )
& ( f4(f54,X1) = X4 )
& ( f4(f54,X0) = X3 ) ),
inference(rectify,[],[f228]) ).
tff(f228,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X124: 'S3',X125: 'S3'] :
( ( f3(X124,f3(X125,X2)) = f3(X125,f3(X124,X2)) )
& ( f4(f54,X1) = X125 )
& ( f4(f54,X0) = X124 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_228) ).
tff(f4698,plain,
spl331_300,
inference(avatar_split_clause,[],[f2080,f4696]) ).
tff(f4696,plain,
( spl331_300
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK208(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_300])]) ).
tff(f2080,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK208(X0,X1,X2) ),
inference(cnf_transformation,[],[f1293]) ).
tff(f4694,plain,
spl331_299,
inference(avatar_split_clause,[],[f2053,f4692]) ).
tff(f4692,plain,
( spl331_299
<=> ! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK196(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_299])]) ).
tff(f2053,plain,
! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK196(X0,X1,X2) ),
inference(cnf_transformation,[],[f1269]) ).
tff(f1269,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ( f34(sK196(X0,X1,X2),f34(f39(f40,X1),X2)) = f34(f39(f40,f34(sK196(X0,X1,X2),X1)),f34(sK196(X0,X1,X2),X2)) )
& ( f39(f52,X0) = sK196(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK196])],[f749,f1268]) ).
tff(f1268,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ? [X3: 'S17'] :
( ( f34(X3,f34(f39(f40,X1),X2)) = f34(f39(f40,f34(X3,X1)),f34(X3,X2)) )
& ( f39(f52,X0) = X3 ) )
=> ( ( f34(sK196(X0,X1,X2),f34(f39(f40,X1),X2)) = f34(f39(f40,f34(sK196(X0,X1,X2),X1)),f34(sK196(X0,X1,X2),X2)) )
& ( f39(f52,X0) = sK196(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f749,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X3: 'S17'] :
( ( f34(X3,f34(f39(f40,X1),X2)) = f34(f39(f40,f34(X3,X1)),f34(X3,X2)) )
& ( f39(f52,X0) = X3 ) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X17: 'S17'] :
( ( f34(X17,f34(f39(f40,X1),X2)) = f34(f39(f40,f34(X17,X1)),f34(X17,X2)) )
& ( f39(f52,X0) = X17 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_67) ).
tff(f4690,plain,
spl331_298,
inference(avatar_split_clause,[],[f2051,f4688]) ).
tff(f4688,plain,
( spl331_298
<=> ! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK195(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_298])]) ).
tff(f2051,plain,
! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK195(X0,X1,X2) ),
inference(cnf_transformation,[],[f1267]) ).
tff(f1267,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ( f34(sK195(X0,X1,X2),f34(f39(f40,X1),X2)) = f34(f39(f40,f34(sK195(X0,X1,X2),X1)),f34(sK195(X0,X1,X2),X2)) )
& ( f39(f52,X0) = sK195(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK195])],[f748,f1266]) ).
tff(f1266,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ? [X3: 'S17'] :
( ( f34(X3,f34(f39(f40,X1),X2)) = f34(f39(f40,f34(X3,X1)),f34(X3,X2)) )
& ( f39(f52,X0) = X3 ) )
=> ( ( f34(sK195(X0,X1,X2),f34(f39(f40,X1),X2)) = f34(f39(f40,f34(sK195(X0,X1,X2),X1)),f34(sK195(X0,X1,X2),X2)) )
& ( f39(f52,X0) = sK195(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f748,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X3: 'S17'] :
( ( f34(X3,f34(f39(f40,X1),X2)) = f34(f39(f40,f34(X3,X1)),f34(X3,X2)) )
& ( f39(f52,X0) = X3 ) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X19: 'S17'] :
( ( f34(X19,f34(f39(f40,X1),X2)) = f34(f39(f40,f34(X19,X1)),f34(X19,X2)) )
& ( f39(f52,X0) = X19 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_69) ).
tff(f4686,plain,
( spl331_297
| spl331_14
| ~ spl331_245 ),
inference(avatar_split_clause,[],[f4470,f4457,f2993,f4683]) ).
tff(f4683,plain,
( spl331_297
<=> ( sK320 = sK34(sK320) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_297])]) ).
tff(f2993,plain,
( spl331_14
<=> $less(sK320,0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_14])]) ).
tff(f4470,plain,
( ( sK320 = sK34(sK320) )
| spl331_14
| ~ spl331_245 ),
inference(resolution,[],[f4458,f2995]) ).
tff(f2995,plain,
( ~ $less(sK320,0.0)
| spl331_14 ),
inference(avatar_component_clause,[],[f2993]) ).
tff(f4681,plain,
spl331_296,
inference(avatar_split_clause,[],[f2049,f4679]) ).
tff(f4679,plain,
( spl331_296
<=> ! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK194(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_296])]) ).
tff(f2049,plain,
! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK194(X0,X1,X2) ),
inference(cnf_transformation,[],[f1265]) ).
tff(f1265,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ( f34(sK194(X0,X1,X2),f34(f39(f40,X1),X2)) = f34(f39(f40,f34(sK194(X0,X1,X2),X1)),f34(sK194(X0,X1,X2),X2)) )
& ( f39(f52,X0) = sK194(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK194])],[f747,f1264]) ).
tff(f1264,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ? [X3: 'S17'] :
( ( f34(X3,f34(f39(f40,X1),X2)) = f34(f39(f40,f34(X3,X1)),f34(X3,X2)) )
& ( f39(f52,X0) = X3 ) )
=> ( ( f34(sK194(X0,X1,X2),f34(f39(f40,X1),X2)) = f34(f39(f40,f34(sK194(X0,X1,X2),X1)),f34(sK194(X0,X1,X2),X2)) )
& ( f39(f52,X0) = sK194(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f747,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X3: 'S17'] :
( ( f34(X3,f34(f39(f40,X1),X2)) = f34(f39(f40,f34(X3,X1)),f34(X3,X2)) )
& ( f39(f52,X0) = X3 ) ),
inference(rectify,[],[f280]) ).
tff(f280,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X178: 'S17'] :
( ( f34(X178,f34(f39(f40,X1),X2)) = f34(f39(f40,f34(X178,X1)),f34(X178,X2)) )
& ( f39(f52,X0) = X178 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_280) ).
tff(f4677,plain,
spl331_295,
inference(avatar_split_clause,[],[f2047,f4675]) ).
tff(f4675,plain,
( spl331_295
<=> ! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK193(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_295])]) ).
tff(f2047,plain,
! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK193(X0,X1,X2) ),
inference(cnf_transformation,[],[f1263]) ).
tff(f1263,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ( f34(sK193(X0,X1,X2),f34(f39(f61,X1),X2)) = f34(f39(f61,f34(sK193(X0,X1,X2),X1)),f34(sK193(X0,X1,X2),X2)) )
& ( f39(f52,X0) = sK193(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK193])],[f746,f1262]) ).
tff(f1262,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ? [X3: 'S17'] :
( ( f34(X3,f34(f39(f61,X1),X2)) = f34(f39(f61,f34(X3,X1)),f34(X3,X2)) )
& ( f39(f52,X0) = X3 ) )
=> ( ( f34(sK193(X0,X1,X2),f34(f39(f61,X1),X2)) = f34(f39(f61,f34(sK193(X0,X1,X2),X1)),f34(sK193(X0,X1,X2),X2)) )
& ( f39(f52,X0) = sK193(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f746,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X3: 'S17'] :
( ( f34(X3,f34(f39(f61,X1),X2)) = f34(f39(f61,f34(X3,X1)),f34(X3,X2)) )
& ( f39(f52,X0) = X3 ) ),
inference(rectify,[],[f381]) ).
tff(f381,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X229: 'S17'] :
( ( f34(X229,f34(f39(f61,X1),X2)) = f34(f39(f61,f34(X229,X1)),f34(X229,X2)) )
& ( f39(f52,X0) = X229 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_381) ).
tff(f4673,plain,
spl331_294,
inference(avatar_split_clause,[],[f2045,f4671]) ).
tff(f4671,plain,
( spl331_294
<=> ! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK192(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_294])]) ).
tff(f2045,plain,
! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK192(X0,X1,X2) ),
inference(cnf_transformation,[],[f1261]) ).
tff(f1261,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ( f34(sK192(X0,X1,X2),f34(f39(f61,X1),X2)) = f34(f39(f61,f34(sK192(X0,X1,X2),X1)),f34(sK192(X0,X1,X2),X2)) )
& ( f39(f52,X0) = sK192(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK192])],[f745,f1260]) ).
tff(f1260,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ? [X3: 'S17'] :
( ( f34(X3,f34(f39(f61,X1),X2)) = f34(f39(f61,f34(X3,X1)),f34(X3,X2)) )
& ( f39(f52,X0) = X3 ) )
=> ( ( f34(sK192(X0,X1,X2),f34(f39(f61,X1),X2)) = f34(f39(f61,f34(sK192(X0,X1,X2),X1)),f34(sK192(X0,X1,X2),X2)) )
& ( f39(f52,X0) = sK192(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f745,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X3: 'S17'] :
( ( f34(X3,f34(f39(f61,X1),X2)) = f34(f39(f61,f34(X3,X1)),f34(X3,X2)) )
& ( f39(f52,X0) = X3 ) ),
inference(rectify,[],[f383]) ).
tff(f383,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X231: 'S17'] :
( ( f34(X231,f34(f39(f61,X1),X2)) = f34(f39(f61,f34(X231,X1)),f34(X231,X2)) )
& ( f39(f52,X0) = X231 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_383) ).
tff(f4669,plain,
spl331_293,
inference(avatar_split_clause,[],[f2043,f4667]) ).
tff(f4667,plain,
( spl331_293
<=> ! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK191(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_293])]) ).
tff(f2043,plain,
! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK191(X0,X1,X2) ),
inference(cnf_transformation,[],[f1259]) ).
tff(f1259,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ( f34(f39(f52,f34(sK191(X0,X1,X2),X1)),X2) = f34(f39(f52,f34(sK191(X0,X1,X2),X2)),X1) )
& ( f39(f52,X0) = sK191(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK191])],[f744,f1258]) ).
tff(f1258,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ? [X3: 'S17'] :
( ( f34(f39(f52,f34(X3,X1)),X2) = f34(f39(f52,f34(X3,X2)),X1) )
& ( f39(f52,X0) = X3 ) )
=> ( ( f34(f39(f52,f34(sK191(X0,X1,X2),X1)),X2) = f34(f39(f52,f34(sK191(X0,X1,X2),X2)),X1) )
& ( f39(f52,X0) = sK191(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f744,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X3: 'S17'] :
( ( f34(f39(f52,f34(X3,X1)),X2) = f34(f39(f52,f34(X3,X2)),X1) )
& ( f39(f52,X0) = X3 ) ),
inference(rectify,[],[f245]) ).
tff(f245,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X145: 'S17'] :
( ( f34(f39(f52,f34(X145,X1)),X2) = f34(f39(f52,f34(X145,X2)),X1) )
& ( f39(f52,X0) = X145 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_245) ).
tff(f4665,plain,
spl331_292,
inference(avatar_split_clause,[],[f2041,f4663]) ).
tff(f4663,plain,
( spl331_292
<=> ! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK190(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_292])]) ).
tff(f2041,plain,
! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK190(X0,X1,X2) ),
inference(cnf_transformation,[],[f1257]) ).
tff(f1257,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ( f34(sK190(X0,X1,X2),f34(f39(f52,X1),X2)) = f34(f39(f52,f34(sK190(X0,X1,X2),X1)),X2) )
& ( f39(f52,X0) = sK190(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK190])],[f743,f1256]) ).
tff(f1256,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ? [X3: 'S17'] :
( ( f34(X3,f34(f39(f52,X1),X2)) = f34(f39(f52,f34(X3,X1)),X2) )
& ( f39(f52,X0) = X3 ) )
=> ( ( f34(sK190(X0,X1,X2),f34(f39(f52,X1),X2)) = f34(f39(f52,f34(sK190(X0,X1,X2),X1)),X2) )
& ( f39(f52,X0) = sK190(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f743,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X3: 'S17'] :
( ( f34(X3,f34(f39(f52,X1),X2)) = f34(f39(f52,f34(X3,X1)),X2) )
& ( f39(f52,X0) = X3 ) ),
inference(rectify,[],[f241]) ).
tff(f241,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X141: 'S17'] :
( ( f34(f39(f52,f34(X141,X1)),X2) = f34(X141,f34(f39(f52,X1),X2)) )
& ( f39(f52,X0) = X141 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_241) ).
tff(f4661,plain,
spl331_291,
inference(avatar_split_clause,[],[f2039,f4659]) ).
tff(f4659,plain,
( spl331_291
<=> ! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK189(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_291])]) ).
tff(f2039,plain,
! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f52,X0) = sK189(X0,X1,X2) ),
inference(cnf_transformation,[],[f1255]) ).
tff(f1255,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ( f34(sK189(X0,X1,X2),f34(f39(f52,X1),X2)) = f34(f39(f52,f34(sK189(X0,X1,X2),X1)),X2) )
& ( f39(f52,X0) = sK189(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK189])],[f742,f1254]) ).
tff(f1254,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ? [X3: 'S17'] :
( ( f34(X3,f34(f39(f52,X1),X2)) = f34(f39(f52,f34(X3,X1)),X2) )
& ( f39(f52,X0) = X3 ) )
=> ( ( f34(sK189(X0,X1,X2),f34(f39(f52,X1),X2)) = f34(f39(f52,f34(sK189(X0,X1,X2),X1)),X2) )
& ( f39(f52,X0) = sK189(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f742,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X3: 'S17'] :
( ( f34(X3,f34(f39(f52,X1),X2)) = f34(f39(f52,f34(X3,X1)),X2) )
& ( f39(f52,X0) = X3 ) ),
inference(rectify,[],[f235]) ).
tff(f235,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X135: 'S17'] :
( ( f34(X135,f34(f39(f52,X1),X2)) = f34(f39(f52,f34(X135,X1)),X2) )
& ( f39(f52,X0) = X135 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_235) ).
tff(f4657,plain,
spl331_290,
inference(avatar_split_clause,[],[f2037,f4655]) ).
tff(f4655,plain,
( spl331_290
<=> ! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f40,X0) = sK188(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_290])]) ).
tff(f2037,plain,
! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f40,X0) = sK188(X0,X1,X2) ),
inference(cnf_transformation,[],[f1253]) ).
tff(f1253,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ( f34(f39(f40,f34(sK188(X0,X1,X2),X1)),X2) = f34(f39(f40,f34(sK188(X0,X1,X2),X2)),X1) )
& ( f39(f40,X0) = sK188(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK188])],[f741,f1252]) ).
tff(f1252,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ? [X3: 'S17'] :
( ( f34(f39(f40,f34(X3,X1)),X2) = f34(f39(f40,f34(X3,X2)),X1) )
& ( f39(f40,X0) = X3 ) )
=> ( ( f34(f39(f40,f34(sK188(X0,X1,X2),X1)),X2) = f34(f39(f40,f34(sK188(X0,X1,X2),X2)),X1) )
& ( f39(f40,X0) = sK188(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f741,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X3: 'S17'] :
( ( f34(f39(f40,f34(X3,X1)),X2) = f34(f39(f40,f34(X3,X2)),X1) )
& ( f39(f40,X0) = X3 ) ),
inference(rectify,[],[f270]) ).
tff(f270,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X170: 'S17'] :
( ( f34(f39(f40,f34(X170,X1)),X2) = f34(f39(f40,f34(X170,X2)),X1) )
& ( f39(f40,X0) = X170 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_270) ).
tff(f4653,plain,
spl331_289,
inference(avatar_split_clause,[],[f2035,f4651]) ).
tff(f4651,plain,
( spl331_289
<=> ! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f40,X0) = sK187(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_289])]) ).
tff(f2035,plain,
! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f40,X0) = sK187(X0,X1,X2) ),
inference(cnf_transformation,[],[f1251]) ).
tff(f1251,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ( f34(sK187(X0,X1,X2),f34(f39(f40,X1),X2)) = f34(f39(f40,f34(sK187(X0,X1,X2),X1)),X2) )
& ( f39(f40,X0) = sK187(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK187])],[f740,f1250]) ).
tff(f1250,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ? [X3: 'S17'] :
( ( f34(X3,f34(f39(f40,X1),X2)) = f34(f39(f40,f34(X3,X1)),X2) )
& ( f39(f40,X0) = X3 ) )
=> ( ( f34(sK187(X0,X1,X2),f34(f39(f40,X1),X2)) = f34(f39(f40,f34(sK187(X0,X1,X2),X1)),X2) )
& ( f39(f40,X0) = sK187(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f740,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X3: 'S17'] :
( ( f34(X3,f34(f39(f40,X1),X2)) = f34(f39(f40,f34(X3,X1)),X2) )
& ( f39(f40,X0) = X3 ) ),
inference(rectify,[],[f267]) ).
tff(f267,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X169: 'S17'] :
( ( f34(f39(f40,f34(X169,X1)),X2) = f34(X169,f34(f39(f40,X1),X2)) )
& ( f39(f40,X0) = X169 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_267) ).
tff(f4649,plain,
spl331_288,
inference(avatar_split_clause,[],[f2033,f4647]) ).
tff(f4647,plain,
( spl331_288
<=> ! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f40,X0) = sK186(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_288])]) ).
tff(f2033,plain,
! [X2: 'S10',X0: 'S10',X1: 'S10'] : ( f39(f40,X0) = sK186(X0,X1,X2) ),
inference(cnf_transformation,[],[f1249]) ).
tff(f1249,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ( f34(sK186(X0,X1,X2),f34(f39(f40,X1),X2)) = f34(f39(f40,f34(sK186(X0,X1,X2),X1)),X2) )
& ( f39(f40,X0) = sK186(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK186])],[f739,f1248]) ).
tff(f1248,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
( ? [X3: 'S17'] :
( ( f34(X3,f34(f39(f40,X1),X2)) = f34(f39(f40,f34(X3,X1)),X2) )
& ( f39(f40,X0) = X3 ) )
=> ( ( f34(sK186(X0,X1,X2),f34(f39(f40,X1),X2)) = f34(f39(f40,f34(sK186(X0,X1,X2),X1)),X2) )
& ( f39(f40,X0) = sK186(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f739,plain,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X3: 'S17'] :
( ( f34(X3,f34(f39(f40,X1),X2)) = f34(f39(f40,f34(X3,X1)),X2) )
& ( f39(f40,X0) = X3 ) ),
inference(rectify,[],[f264]) ).
tff(f264,axiom,
! [X0: 'S10',X1: 'S10',X2: 'S10'] :
? [X168: 'S17'] :
( ( f34(X168,f34(f39(f40,X1),X2)) = f34(f39(f40,f34(X168,X1)),X2) )
& ( f39(f40,X0) = X168 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_264) ).
tff(f4645,plain,
spl331_287,
inference(avatar_split_clause,[],[f2030,f4643]) ).
tff(f4643,plain,
( spl331_287
<=> ! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK185(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_287])]) ).
tff(f2030,plain,
! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK185(X0,X1,X2) ),
inference(cnf_transformation,[],[f1247]) ).
tff(f1247,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( ( ( ~ $less(f22(sK185(X0,X1,X2),X2),f22(sK185(X0,X1,X2),X1))
| $less(X2,X1) )
& ( ~ $less(X2,X1)
| $less(f22(sK185(X0,X1,X2),X2),f22(sK185(X0,X1,X2),X1)) ) )
| ~ $less(0.0,X0) )
& ( f49(f50,X0) = sK185(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK185])],[f1245,f1246]) ).
tff(f1246,plain,
! [X0: $real,X1: $real,X2: $real] :
( ? [X3: 'S14'] :
( ( ( ( ~ $less(f22(X3,X2),f22(X3,X1))
| $less(X2,X1) )
& ( ~ $less(X2,X1)
| $less(f22(X3,X2),f22(X3,X1)) ) )
| ~ $less(0.0,X0) )
& ( f49(f50,X0) = X3 ) )
=> ( ( ( ( ~ $less(f22(sK185(X0,X1,X2),X2),f22(sK185(X0,X1,X2),X1))
| $less(X2,X1) )
& ( ~ $less(X2,X1)
| $less(f22(sK185(X0,X1,X2),X2),f22(sK185(X0,X1,X2),X1)) ) )
| ~ $less(0.0,X0) )
& ( f49(f50,X0) = sK185(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1245,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( ( ( ~ $less(f22(X3,X2),f22(X3,X1))
| $less(X2,X1) )
& ( ~ $less(X2,X1)
| $less(f22(X3,X2),f22(X3,X1)) ) )
| ~ $less(0.0,X0) )
& ( f49(f50,X0) = X3 ) ),
inference(nnf_transformation,[],[f881]) ).
tff(f881,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( ( ~ $less(f22(X3,X2),f22(X3,X1))
<=> ~ $less(X2,X1) )
| ~ $less(0.0,X0) )
& ( f49(f50,X0) = X3 ) ),
inference(ennf_transformation,[],[f738]) ).
tff(f738,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( $less(0.0,X0)
=> ( ~ $less(f22(X3,X2),f22(X3,X1))
<=> ~ $less(X2,X1) ) )
& ( f49(f50,X0) = X3 ) ),
inference(rectify,[],[f527]) ).
tff(f527,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X269: 'S14'] :
( ( $less(0.0,X0)
=> ( ~ $less(f22(X269,X2),f22(X269,X1))
<=> ~ $less(X2,X1) ) )
& ( f49(f50,X0) = X269 ) ),
inference(theory_normalization,[],[f425]) ).
tff(f425,axiom,
! [X0: $real,X1: $real,X2: $real] :
? [X269: 'S14'] :
( ( $less(0.0,X0)
=> ( $lesseq(f22(X269,X1),f22(X269,X2))
<=> $lesseq(X1,X2) ) )
& ( f49(f50,X0) = X269 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_425) ).
tff(f4641,plain,
( spl331_286
| spl331_13
| ~ spl331_245 ),
inference(avatar_split_clause,[],[f4469,f4457,f2988,f4638]) ).
tff(f4638,plain,
( spl331_286
<=> ( sK319 = sK34(sK319) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_286])]) ).
tff(f2988,plain,
( spl331_13
<=> $less(sK319,0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_13])]) ).
tff(f4469,plain,
( ( sK319 = sK34(sK319) )
| spl331_13
| ~ spl331_245 ),
inference(resolution,[],[f4458,f2990]) ).
tff(f2990,plain,
( ~ $less(sK319,0.0)
| spl331_13 ),
inference(avatar_component_clause,[],[f2988]) ).
tff(f4636,plain,
spl331_285,
inference(avatar_split_clause,[],[f2028,f4634]) ).
tff(f4634,plain,
( spl331_285
<=> ! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK184(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_285])]) ).
tff(f2028,plain,
! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK184(X0,X1,X2) ),
inference(cnf_transformation,[],[f1244]) ).
tff(f1244,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( $less(f22(sK184(X0,X1,X2),X1),f22(sK184(X0,X1,X2),X2))
| ~ $less(X1,X2)
| ~ $less(0.0,X0) )
& ( f49(f50,X0) = sK184(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK184])],[f880,f1243]) ).
tff(f1243,plain,
! [X0: $real,X1: $real,X2: $real] :
( ? [X3: 'S14'] :
( ( $less(f22(X3,X1),f22(X3,X2))
| ~ $less(X1,X2)
| ~ $less(0.0,X0) )
& ( f49(f50,X0) = X3 ) )
=> ( ( $less(f22(sK184(X0,X1,X2),X1),f22(sK184(X0,X1,X2),X2))
| ~ $less(X1,X2)
| ~ $less(0.0,X0) )
& ( f49(f50,X0) = sK184(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f880,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( $less(f22(X3,X1),f22(X3,X2))
| ~ $less(X1,X2)
| ~ $less(0.0,X0) )
& ( f49(f50,X0) = X3 ) ),
inference(flattening,[],[f879]) ).
tff(f879,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( $less(f22(X3,X1),f22(X3,X2))
| ~ $less(X1,X2)
| ~ $less(0.0,X0) )
& ( f49(f50,X0) = X3 ) ),
inference(ennf_transformation,[],[f737]) ).
tff(f737,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( $less(0.0,X0)
=> ( $less(X1,X2)
=> $less(f22(X3,X1),f22(X3,X2)) ) )
& ( f49(f50,X0) = X3 ) ),
inference(rectify,[],[f427]) ).
tff(f427,axiom,
! [X0: $real,X1: $real,X2: $real] :
? [X271: 'S14'] :
( ( $less(0.0,X0)
=> ( $less(X1,X2)
=> $less(f22(X271,X1),f22(X271,X2)) ) )
& ( f49(f50,X0) = X271 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_427) ).
tff(f4632,plain,
spl331_284,
inference(avatar_split_clause,[],[f2025,f4630]) ).
tff(f4630,plain,
( spl331_284
<=> ! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK183(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_284])]) ).
tff(f2025,plain,
! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK183(X0,X1,X2) ),
inference(cnf_transformation,[],[f1242]) ).
tff(f1242,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( ( ( ( f22(sK183(X0,X1,X2),X1) = f22(sK183(X0,X1,X2),X2) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( f22(sK183(X0,X1,X2),X1) != f22(sK183(X0,X1,X2),X2) ) ) )
| ( 0.0 = X0 ) )
& ( f49(f50,X0) = sK183(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK183])],[f1240,f1241]) ).
tff(f1241,plain,
! [X0: $real,X1: $real,X2: $real] :
( ? [X3: 'S14'] :
( ( ( ( ( f22(X3,X1) = f22(X3,X2) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( f22(X3,X1) != f22(X3,X2) ) ) )
| ( 0.0 = X0 ) )
& ( f49(f50,X0) = X3 ) )
=> ( ( ( ( ( f22(sK183(X0,X1,X2),X1) = f22(sK183(X0,X1,X2),X2) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( f22(sK183(X0,X1,X2),X1) != f22(sK183(X0,X1,X2),X2) ) ) )
| ( 0.0 = X0 ) )
& ( f49(f50,X0) = sK183(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1240,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( ( ( ( f22(X3,X1) = f22(X3,X2) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( f22(X3,X1) != f22(X3,X2) ) ) )
| ( 0.0 = X0 ) )
& ( f49(f50,X0) = X3 ) ),
inference(nnf_transformation,[],[f878]) ).
tff(f878,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( ( ( f22(X3,X1) = f22(X3,X2) )
<=> ( X1 = X2 ) )
| ( 0.0 = X0 ) )
& ( f49(f50,X0) = X3 ) ),
inference(ennf_transformation,[],[f736]) ).
tff(f736,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( ( 0.0 != X0 )
=> ( ( f22(X3,X1) = f22(X3,X2) )
<=> ( X1 = X2 ) ) )
& ( f49(f50,X0) = X3 ) ),
inference(rectify,[],[f422]) ).
tff(f422,axiom,
! [X0: $real,X1: $real,X2: $real] :
? [X268: 'S14'] :
( ( ( 0.0 != X0 )
=> ( ( f22(X268,X1) = f22(X268,X2) )
<=> ( X1 = X2 ) ) )
& ( f49(f50,X0) = X268 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_422) ).
tff(f4628,plain,
spl331_283,
inference(avatar_split_clause,[],[f2023,f4626]) ).
tff(f4626,plain,
( spl331_283
<=> ! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK182(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_283])]) ).
tff(f2023,plain,
! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK182(X0,X1,X2) ),
inference(cnf_transformation,[],[f1239]) ).
tff(f1239,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( f34(f39(f52,f16(f32,X0)),f16(f17(f18,X1),X2)) = f16(f17(f18,f22(sK182(X0,X1,X2),X1)),f22(sK182(X0,X1,X2),X2)) )
& ( f49(f50,X0) = sK182(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK182])],[f735,f1238]) ).
tff(f1238,plain,
! [X0: $real,X1: $real,X2: $real] :
( ? [X3: 'S14'] :
( ( f34(f39(f52,f16(f32,X0)),f16(f17(f18,X1),X2)) = f16(f17(f18,f22(X3,X1)),f22(X3,X2)) )
& ( f49(f50,X0) = X3 ) )
=> ( ( f34(f39(f52,f16(f32,X0)),f16(f17(f18,X1),X2)) = f16(f17(f18,f22(sK182(X0,X1,X2),X1)),f22(sK182(X0,X1,X2),X2)) )
& ( f49(f50,X0) = sK182(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f735,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( f34(f39(f52,f16(f32,X0)),f16(f17(f18,X1),X2)) = f16(f17(f18,f22(X3,X1)),f22(X3,X2)) )
& ( f49(f50,X0) = X3 ) ),
inference(rectify,[],[f178]) ).
tff(f178,axiom,
! [X0: $real,X1: $real,X2: $real] :
? [X107: 'S14'] :
( ( f34(f39(f52,f16(f32,X0)),f16(f17(f18,X1),X2)) = f16(f17(f18,f22(X107,X1)),f22(X107,X2)) )
& ( f49(f50,X0) = X107 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_178) ).
tff(f4624,plain,
spl331_282,
inference(avatar_split_clause,[],[f2021,f4622]) ).
tff(f4622,plain,
( spl331_282
<=> ! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK181(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_282])]) ).
tff(f2021,plain,
! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK181(X0,X1,X2) ),
inference(cnf_transformation,[],[f1237]) ).
tff(f1237,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( f22(f49(f50,f22(sK181(X0,X1,X2),X1)),X2) = f22(f49(f50,f22(sK181(X0,X1,X2),X2)),X1) )
& ( f49(f50,X0) = sK181(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK181])],[f734,f1236]) ).
tff(f1236,plain,
! [X0: $real,X1: $real,X2: $real] :
( ? [X3: 'S14'] :
( ( f22(f49(f50,f22(X3,X1)),X2) = f22(f49(f50,f22(X3,X2)),X1) )
& ( f49(f50,X0) = X3 ) )
=> ( ( f22(f49(f50,f22(sK181(X0,X1,X2),X1)),X2) = f22(f49(f50,f22(sK181(X0,X1,X2),X2)),X1) )
& ( f49(f50,X0) = sK181(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f734,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( f22(f49(f50,f22(X3,X1)),X2) = f22(f49(f50,f22(X3,X2)),X1) )
& ( f49(f50,X0) = X3 ) ),
inference(rectify,[],[f243]) ).
tff(f243,axiom,
! [X0: $real,X1: $real,X2: $real] :
? [X143: 'S14'] :
( ( f22(f49(f50,f22(X143,X1)),X2) = f22(f49(f50,f22(X143,X2)),X1) )
& ( f49(f50,X0) = X143 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_243) ).
tff(f4620,plain,
spl331_281,
inference(avatar_split_clause,[],[f2019,f4618]) ).
tff(f4618,plain,
( spl331_281
<=> ! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK180(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_281])]) ).
tff(f2019,plain,
! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK180(X0,X1,X2) ),
inference(cnf_transformation,[],[f1235]) ).
tff(f1235,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( f22(sK180(X0,X1,X2),f22(f49(f50,X1),X2)) = f22(f49(f50,f22(sK180(X0,X1,X2),X1)),X2) )
& ( f49(f50,X0) = sK180(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK180])],[f733,f1234]) ).
tff(f1234,plain,
! [X0: $real,X1: $real,X2: $real] :
( ? [X3: 'S14'] :
( ( f22(X3,f22(f49(f50,X1),X2)) = f22(f49(f50,f22(X3,X1)),X2) )
& ( f49(f50,X0) = X3 ) )
=> ( ( f22(sK180(X0,X1,X2),f22(f49(f50,X1),X2)) = f22(f49(f50,f22(sK180(X0,X1,X2),X1)),X2) )
& ( f49(f50,X0) = sK180(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f733,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( f22(X3,f22(f49(f50,X1),X2)) = f22(f49(f50,f22(X3,X1)),X2) )
& ( f49(f50,X0) = X3 ) ),
inference(rectify,[],[f239]) ).
tff(f239,axiom,
! [X0: $real,X1: $real,X2: $real] :
? [X139: 'S14'] :
( ( f22(f49(f50,f22(X139,X1)),X2) = f22(X139,f22(f49(f50,X1),X2)) )
& ( f49(f50,X0) = X139 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_239) ).
tff(f4616,plain,
spl331_280,
inference(avatar_split_clause,[],[f2017,f4614]) ).
tff(f4614,plain,
( spl331_280
<=> ! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK179(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_280])]) ).
tff(f2017,plain,
! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK179(X0,X1,X2) ),
inference(cnf_transformation,[],[f1233]) ).
tff(f1233,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( f22(sK179(X0,X1,X2),f22(f49(f50,X1),X2)) = f22(f49(f50,f22(sK179(X0,X1,X2),X1)),X2) )
& ( f49(f50,X0) = sK179(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK179])],[f732,f1232]) ).
tff(f1232,plain,
! [X0: $real,X1: $real,X2: $real] :
( ? [X3: 'S14'] :
( ( f22(X3,f22(f49(f50,X1),X2)) = f22(f49(f50,f22(X3,X1)),X2) )
& ( f49(f50,X0) = X3 ) )
=> ( ( f22(sK179(X0,X1,X2),f22(f49(f50,X1),X2)) = f22(f49(f50,f22(sK179(X0,X1,X2),X1)),X2) )
& ( f49(f50,X0) = sK179(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f732,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( f22(X3,f22(f49(f50,X1),X2)) = f22(f49(f50,f22(X3,X1)),X2) )
& ( f49(f50,X0) = X3 ) ),
inference(rectify,[],[f418]) ).
tff(f418,axiom,
! [X0: $real,X1: $real,X2: $real] :
? [X266: 'S14'] :
( ( f22(f49(f50,f22(X266,X1)),X2) = f22(X266,f22(f49(f50,X1),X2)) )
& ( f49(f50,X0) = X266 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_418) ).
tff(f4612,plain,
spl331_279,
inference(avatar_split_clause,[],[f2015,f4610]) ).
tff(f4610,plain,
( spl331_279
<=> ! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK178(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_279])]) ).
tff(f2015,plain,
! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK178(X0,X1,X2) ),
inference(cnf_transformation,[],[f1231]) ).
tff(f1231,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( f22(sK178(X0,X1,X2),f22(f49(f50,X1),X2)) = f22(f49(f50,f22(sK178(X0,X1,X2),X1)),X2) )
& ( f49(f50,X0) = sK178(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK178])],[f731,f1230]) ).
tff(f1230,plain,
! [X0: $real,X1: $real,X2: $real] :
( ? [X3: 'S14'] :
( ( f22(X3,f22(f49(f50,X1),X2)) = f22(f49(f50,f22(X3,X1)),X2) )
& ( f49(f50,X0) = X3 ) )
=> ( ( f22(sK178(X0,X1,X2),f22(f49(f50,X1),X2)) = f22(f49(f50,f22(sK178(X0,X1,X2),X1)),X2) )
& ( f49(f50,X0) = sK178(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f731,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( f22(X3,f22(f49(f50,X1),X2)) = f22(f49(f50,f22(X3,X1)),X2) )
& ( f49(f50,X0) = X3 ) ),
inference(rectify,[],[f233]) ).
tff(f233,axiom,
! [X0: $real,X1: $real,X2: $real] :
? [X133: 'S14'] :
( ( f22(X133,f22(f49(f50,X1),X2)) = f22(f49(f50,f22(X133,X1)),X2) )
& ( f49(f50,X0) = X133 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_233) ).
tff(f4608,plain,
spl331_278,
inference(avatar_split_clause,[],[f2013,f4606]) ).
tff(f4606,plain,
( spl331_278
<=> ! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK177(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_278])]) ).
tff(f2013,plain,
! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK177(X0,X1,X2) ),
inference(cnf_transformation,[],[f1229]) ).
tff(f1229,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( f22(sK177(X0,X1,X2),$sum(X1,X2)) = $sum(f22(sK177(X0,X1,X2),X1),f22(sK177(X0,X1,X2),X2)) )
& ( f49(f50,X0) = sK177(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK177])],[f730,f1228]) ).
tff(f1228,plain,
! [X0: $real,X1: $real,X2: $real] :
( ? [X3: 'S14'] :
( ( f22(X3,$sum(X1,X2)) = $sum(f22(X3,X1),f22(X3,X2)) )
& ( f49(f50,X0) = X3 ) )
=> ( ( f22(sK177(X0,X1,X2),$sum(X1,X2)) = $sum(f22(sK177(X0,X1,X2),X1),f22(sK177(X0,X1,X2),X2)) )
& ( f49(f50,X0) = sK177(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f730,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( f22(X3,$sum(X1,X2)) = $sum(f22(X3,X1),f22(X3,X2)) )
& ( f49(f50,X0) = X3 ) ),
inference(rectify,[],[f281]) ).
tff(f281,axiom,
! [X0: $real,X1: $real,X2: $real] :
? [X179: 'S14'] :
( ( f22(X179,$sum(X1,X2)) = $sum(f22(X179,X1),f22(X179,X2)) )
& ( f49(f50,X0) = X179 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_281) ).
tff(f4604,plain,
spl331_277,
inference(avatar_split_clause,[],[f2011,f4602]) ).
tff(f4602,plain,
( spl331_277
<=> ! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK176(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_277])]) ).
tff(f2011,plain,
! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK176(X0,X1,X2) ),
inference(cnf_transformation,[],[f1227]) ).
tff(f1227,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( f22(sK176(X0,X1,X2),$sum(X1,X2)) = $sum(f22(sK176(X0,X1,X2),X1),f22(sK176(X0,X1,X2),X2)) )
& ( f49(f50,X0) = sK176(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK176])],[f729,f1226]) ).
tff(f1226,plain,
! [X0: $real,X1: $real,X2: $real] :
( ? [X3: 'S14'] :
( ( f22(X3,$sum(X1,X2)) = $sum(f22(X3,X1),f22(X3,X2)) )
& ( f49(f50,X0) = X3 ) )
=> ( ( f22(sK176(X0,X1,X2),$sum(X1,X2)) = $sum(f22(sK176(X0,X1,X2),X1),f22(sK176(X0,X1,X2),X2)) )
& ( f49(f50,X0) = sK176(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f729,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( f22(X3,$sum(X1,X2)) = $sum(f22(X3,X1),f22(X3,X2)) )
& ( f49(f50,X0) = X3 ) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X0: $real,X1: $real,X2: $real] :
? [X16: 'S14'] :
( ( f22(X16,$sum(X1,X2)) = $sum(f22(X16,X1),f22(X16,X2)) )
& ( f49(f50,X0) = X16 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_66) ).
tff(f4600,plain,
spl331_276,
inference(avatar_split_clause,[],[f2009,f4598]) ).
tff(f4598,plain,
( spl331_276
<=> ! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK175(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_276])]) ).
tff(f2009,plain,
! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK175(X0,X1,X2) ),
inference(cnf_transformation,[],[f1225]) ).
tff(f1225,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( f22(sK175(X0,X1,X2),$sum(X1,X2)) = $sum(f22(sK175(X0,X1,X2),X1),f22(sK175(X0,X1,X2),X2)) )
& ( f49(f50,X0) = sK175(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK175])],[f728,f1224]) ).
tff(f1224,plain,
! [X0: $real,X1: $real,X2: $real] :
( ? [X3: 'S14'] :
( ( f22(X3,$sum(X1,X2)) = $sum(f22(X3,X1),f22(X3,X2)) )
& ( f49(f50,X0) = X3 ) )
=> ( ( f22(sK175(X0,X1,X2),$sum(X1,X2)) = $sum(f22(sK175(X0,X1,X2),X1),f22(sK175(X0,X1,X2),X2)) )
& ( f49(f50,X0) = sK175(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f728,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( f22(X3,$sum(X1,X2)) = $sum(f22(X3,X1),f22(X3,X2)) )
& ( f49(f50,X0) = X3 ) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X0: $real,X1: $real,X2: $real] :
? [X18: 'S14'] :
( ( f22(X18,$sum(X1,X2)) = $sum(f22(X18,X1),f22(X18,X2)) )
& ( f49(f50,X0) = X18 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_68) ).
tff(f4596,plain,
( spl331_275
| spl331_12
| ~ spl331_245 ),
inference(avatar_split_clause,[],[f4468,f4457,f2983,f4593]) ).
tff(f4593,plain,
( spl331_275
<=> ( sK318 = sK34(sK318) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_275])]) ).
tff(f4468,plain,
( ( sK318 = sK34(sK318) )
| spl331_12
| ~ spl331_245 ),
inference(resolution,[],[f4458,f2985]) ).
tff(f4591,plain,
spl331_274,
inference(avatar_split_clause,[],[f2007,f4589]) ).
tff(f4589,plain,
( spl331_274
<=> ! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK174(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_274])]) ).
tff(f2007,plain,
! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK174(X0,X1,X2) ),
inference(cnf_transformation,[],[f1223]) ).
tff(f1223,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( f22(sK174(X0,X1,X2),$sum(X1,$uminus(X2))) = $sum(f22(sK174(X0,X1,X2),X1),$uminus(f22(sK174(X0,X1,X2),X2))) )
& ( f49(f50,X0) = sK174(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK174])],[f727,f1222]) ).
tff(f1222,plain,
! [X0: $real,X1: $real,X2: $real] :
( ? [X3: 'S14'] :
( ( f22(X3,$sum(X1,$uminus(X2))) = $sum(f22(X3,X1),$uminus(f22(X3,X2))) )
& ( f49(f50,X0) = X3 ) )
=> ( ( f22(sK174(X0,X1,X2),$sum(X1,$uminus(X2))) = $sum(f22(sK174(X0,X1,X2),X1),$uminus(f22(sK174(X0,X1,X2),X2))) )
& ( f49(f50,X0) = sK174(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f727,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( f22(X3,$sum(X1,$uminus(X2))) = $sum(f22(X3,X1),$uminus(f22(X3,X2))) )
& ( f49(f50,X0) = X3 ) ),
inference(rectify,[],[f526]) ).
tff(f526,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X228: 'S14'] :
( ( f22(X228,$sum(X1,$uminus(X2))) = $sum(f22(X228,X1),$uminus(f22(X228,X2))) )
& ( f49(f50,X0) = X228 ) ),
inference(theory_normalization,[],[f380]) ).
tff(f380,axiom,
! [X0: $real,X1: $real,X2: $real] :
? [X228: 'S14'] :
( ( f22(X228,$difference(X1,X2)) = $difference(f22(X228,X1),f22(X228,X2)) )
& ( f49(f50,X0) = X228 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_380) ).
tff(f4587,plain,
spl331_273,
inference(avatar_split_clause,[],[f2005,f4585]) ).
tff(f4585,plain,
( spl331_273
<=> ! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK173(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_273])]) ).
tff(f2005,plain,
! [X2: $real,X0: $real,X1: $real] : ( f49(f50,X0) = sK173(X0,X1,X2) ),
inference(cnf_transformation,[],[f1221]) ).
tff(f1221,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( f22(sK173(X0,X1,X2),$sum(X1,$uminus(X2))) = $sum(f22(sK173(X0,X1,X2),X1),$uminus(f22(sK173(X0,X1,X2),X2))) )
& ( f49(f50,X0) = sK173(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK173])],[f726,f1220]) ).
tff(f1220,plain,
! [X0: $real,X1: $real,X2: $real] :
( ? [X3: 'S14'] :
( ( f22(X3,$sum(X1,$uminus(X2))) = $sum(f22(X3,X1),$uminus(f22(X3,X2))) )
& ( f49(f50,X0) = X3 ) )
=> ( ( f22(sK173(X0,X1,X2),$sum(X1,$uminus(X2))) = $sum(f22(sK173(X0,X1,X2),X1),$uminus(f22(sK173(X0,X1,X2),X2))) )
& ( f49(f50,X0) = sK173(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f726,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X3: 'S14'] :
( ( f22(X3,$sum(X1,$uminus(X2))) = $sum(f22(X3,X1),$uminus(f22(X3,X2))) )
& ( f49(f50,X0) = X3 ) ),
inference(rectify,[],[f525]) ).
tff(f525,plain,
! [X0: $real,X1: $real,X2: $real] :
? [X230: 'S14'] :
( ( f22(X230,$sum(X1,$uminus(X2))) = $sum(f22(X230,X1),$uminus(f22(X230,X2))) )
& ( f49(f50,X0) = X230 ) ),
inference(theory_normalization,[],[f382]) ).
tff(f382,axiom,
! [X0: $real,X1: $real,X2: $real] :
? [X230: 'S14'] :
( ( f22(X230,$difference(X1,X2)) = $difference(f22(X230,X1),f22(X230,X2)) )
& ( f49(f50,X0) = X230 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_382) ).
tff(f4583,plain,
spl331_272,
inference(avatar_split_clause,[],[f2003,f4581]) ).
tff(f4581,plain,
( spl331_272
<=> ! [X2: $int,X0: $int,X1: $int] : ( f9(f10,X0) = sK172(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_272])]) ).
tff(f2003,plain,
! [X2: $int,X0: $int,X1: $int] : ( f9(f10,X0) = sK172(X0,X1,X2) ),
inference(cnf_transformation,[],[f1219]) ).
tff(f1219,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( f8(f9(f10,f8(sK172(X0,X1,X2),X1)),X2) = f8(f9(f10,f8(sK172(X0,X1,X2),X2)),X1) )
& ( f9(f10,X0) = sK172(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK172])],[f725,f1218]) ).
tff(f1218,plain,
! [X0: $int,X1: $int,X2: $int] :
( ? [X3: 'S6'] :
( ( f8(f9(f10,f8(X3,X1)),X2) = f8(f9(f10,f8(X3,X2)),X1) )
& ( f9(f10,X0) = X3 ) )
=> ( ( f8(f9(f10,f8(sK172(X0,X1,X2),X1)),X2) = f8(f9(f10,f8(sK172(X0,X1,X2),X2)),X1) )
& ( f9(f10,X0) = sK172(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f725,plain,
! [X0: $int,X1: $int,X2: $int] :
? [X3: 'S6'] :
( ( f8(f9(f10,f8(X3,X1)),X2) = f8(f9(f10,f8(X3,X2)),X1) )
& ( f9(f10,X0) = X3 ) ),
inference(rectify,[],[f244]) ).
tff(f244,axiom,
! [X0: $int,X1: $int,X2: $int] :
? [X144: 'S6'] :
( ( f8(f9(f10,f8(X144,X1)),X2) = f8(f9(f10,f8(X144,X2)),X1) )
& ( f9(f10,X0) = X144 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_244) ).
tff(f4579,plain,
spl331_271,
inference(avatar_split_clause,[],[f2001,f4577]) ).
tff(f4577,plain,
( spl331_271
<=> ! [X2: $int,X0: $int,X1: $int] : ( f9(f10,X0) = sK171(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_271])]) ).
tff(f2001,plain,
! [X2: $int,X0: $int,X1: $int] : ( f9(f10,X0) = sK171(X0,X1,X2) ),
inference(cnf_transformation,[],[f1217]) ).
tff(f1217,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( f8(sK171(X0,X1,X2),f8(f9(f10,X1),X2)) = f8(f9(f10,f8(sK171(X0,X1,X2),X1)),X2) )
& ( f9(f10,X0) = sK171(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK171])],[f724,f1216]) ).
tff(f1216,plain,
! [X0: $int,X1: $int,X2: $int] :
( ? [X3: 'S6'] :
( ( f8(X3,f8(f9(f10,X1),X2)) = f8(f9(f10,f8(X3,X1)),X2) )
& ( f9(f10,X0) = X3 ) )
=> ( ( f8(sK171(X0,X1,X2),f8(f9(f10,X1),X2)) = f8(f9(f10,f8(sK171(X0,X1,X2),X1)),X2) )
& ( f9(f10,X0) = sK171(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f724,plain,
! [X0: $int,X1: $int,X2: $int] :
? [X3: 'S6'] :
( ( f8(X3,f8(f9(f10,X1),X2)) = f8(f9(f10,f8(X3,X1)),X2) )
& ( f9(f10,X0) = X3 ) ),
inference(rectify,[],[f240]) ).
tff(f240,axiom,
! [X0: $int,X1: $int,X2: $int] :
? [X140: 'S6'] :
( ( f8(f9(f10,f8(X140,X1)),X2) = f8(X140,f8(f9(f10,X1),X2)) )
& ( f9(f10,X0) = X140 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_240) ).
tff(f4575,plain,
spl331_270,
inference(avatar_split_clause,[],[f1999,f4573]) ).
tff(f4573,plain,
( spl331_270
<=> ! [X2: $int,X0: $int,X1: $int] : ( f9(f10,X0) = sK170(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_270])]) ).
tff(f1999,plain,
! [X2: $int,X0: $int,X1: $int] : ( f9(f10,X0) = sK170(X0,X1,X2) ),
inference(cnf_transformation,[],[f1215]) ).
tff(f1215,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( f8(sK170(X0,X1,X2),f8(f9(f10,X1),X2)) = f8(f9(f10,f8(sK170(X0,X1,X2),X1)),X2) )
& ( f9(f10,X0) = sK170(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK170])],[f723,f1214]) ).
tff(f1214,plain,
! [X0: $int,X1: $int,X2: $int] :
( ? [X3: 'S6'] :
( ( f8(X3,f8(f9(f10,X1),X2)) = f8(f9(f10,f8(X3,X1)),X2) )
& ( f9(f10,X0) = X3 ) )
=> ( ( f8(sK170(X0,X1,X2),f8(f9(f10,X1),X2)) = f8(f9(f10,f8(sK170(X0,X1,X2),X1)),X2) )
& ( f9(f10,X0) = sK170(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f723,plain,
! [X0: $int,X1: $int,X2: $int] :
? [X3: 'S6'] :
( ( f8(X3,f8(f9(f10,X1),X2)) = f8(f9(f10,f8(X3,X1)),X2) )
& ( f9(f10,X0) = X3 ) ),
inference(rectify,[],[f234]) ).
tff(f234,axiom,
! [X0: $int,X1: $int,X2: $int] :
? [X134: 'S6'] :
( ( f8(X134,f8(f9(f10,X1),X2)) = f8(f9(f10,f8(X134,X1)),X2) )
& ( f9(f10,X0) = X134 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_234) ).
tff(f4571,plain,
spl331_269,
inference(avatar_split_clause,[],[f1997,f4569]) ).
tff(f4569,plain,
( spl331_269
<=> ! [X2: $int,X0: $int,X1: $int] : ( f9(f10,X0) = sK169(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_269])]) ).
tff(f1997,plain,
! [X2: $int,X0: $int,X1: $int] : ( f9(f10,X0) = sK169(X0,X1,X2) ),
inference(cnf_transformation,[],[f1213]) ).
tff(f1213,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( f8(sK169(X0,X1,X2),$sum(X1,X2)) = $sum(f8(sK169(X0,X1,X2),X1),f8(sK169(X0,X1,X2),X2)) )
& ( f9(f10,X0) = sK169(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK169])],[f722,f1212]) ).
tff(f1212,plain,
! [X0: $int,X1: $int,X2: $int] :
( ? [X3: 'S6'] :
( ( f8(X3,$sum(X1,X2)) = $sum(f8(X3,X1),f8(X3,X2)) )
& ( f9(f10,X0) = X3 ) )
=> ( ( f8(sK169(X0,X1,X2),$sum(X1,X2)) = $sum(f8(sK169(X0,X1,X2),X1),f8(sK169(X0,X1,X2),X2)) )
& ( f9(f10,X0) = sK169(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f722,plain,
! [X0: $int,X1: $int,X2: $int] :
? [X3: 'S6'] :
( ( f8(X3,$sum(X1,X2)) = $sum(f8(X3,X1),f8(X3,X2)) )
& ( f9(f10,X0) = X3 ) ),
inference(rectify,[],[f282]) ).
tff(f282,axiom,
! [X0: $int,X1: $int,X2: $int] :
? [X180: 'S6'] :
( ( f8(X180,$sum(X1,X2)) = $sum(f8(X180,X1),f8(X180,X2)) )
& ( f9(f10,X0) = X180 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_282) ).
tff(f4567,plain,
spl331_268,
inference(avatar_split_clause,[],[f1995,f4565]) ).
tff(f4565,plain,
( spl331_268
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK168(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_268])]) ).
tff(f1995,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK168(X0,X1,X2) ),
inference(cnf_transformation,[],[f1211]) ).
tff(f1211,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( f3(sK168(X0,X1,X2),f3(f4(f53,X1),X2)) = f3(f4(f53,f3(sK168(X0,X1,X2),X1)),f3(sK168(X0,X1,X2),X2)) )
& ( f4(f54,X0) = sK168(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK168])],[f721,f1210]) ).
tff(f1210,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S3'] :
( ( f3(X3,f3(f4(f53,X1),X2)) = f3(f4(f53,f3(X3,X1)),f3(X3,X2)) )
& ( f4(f54,X0) = X3 ) )
=> ( ( f3(sK168(X0,X1,X2),f3(f4(f53,X1),X2)) = f3(f4(f53,f3(sK168(X0,X1,X2),X1)),f3(sK168(X0,X1,X2),X2)) )
& ( f4(f54,X0) = sK168(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f721,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S3'] :
( ( f3(X3,f3(f4(f53,X1),X2)) = f3(f4(f53,f3(X3,X1)),f3(X3,X2)) )
& ( f4(f54,X0) = X3 ) ),
inference(rectify,[],[f279]) ).
tff(f279,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X177: 'S3'] :
( ( f3(X177,f3(f4(f53,X1),X2)) = f3(f4(f53,f3(X177,X1)),f3(X177,X2)) )
& ( f4(f54,X0) = X177 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_279) ).
tff(f4563,plain,
spl331_267,
inference(avatar_split_clause,[],[f1993,f4561]) ).
tff(f4561,plain,
( spl331_267
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK167(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_267])]) ).
tff(f1993,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK167(X0,X1,X2) ),
inference(cnf_transformation,[],[f1209]) ).
tff(f1209,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( f3(f4(f54,f3(sK167(X0,X1,X2),X1)),X2) = f3(f4(f54,f3(sK167(X0,X1,X2),X2)),X1) )
& ( f4(f54,X0) = sK167(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK167])],[f720,f1208]) ).
tff(f1208,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S3'] :
( ( f3(f4(f54,f3(X3,X1)),X2) = f3(f4(f54,f3(X3,X2)),X1) )
& ( f4(f54,X0) = X3 ) )
=> ( ( f3(f4(f54,f3(sK167(X0,X1,X2),X1)),X2) = f3(f4(f54,f3(sK167(X0,X1,X2),X2)),X1) )
& ( f4(f54,X0) = sK167(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f720,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S3'] :
( ( f3(f4(f54,f3(X3,X1)),X2) = f3(f4(f54,f3(X3,X2)),X1) )
& ( f4(f54,X0) = X3 ) ),
inference(rectify,[],[f242]) ).
tff(f242,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X142: 'S3'] :
( ( f3(f4(f54,f3(X142,X1)),X2) = f3(f4(f54,f3(X142,X2)),X1) )
& ( f4(f54,X0) = X142 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_242) ).
tff(f4559,plain,
spl331_266,
inference(avatar_split_clause,[],[f1991,f4557]) ).
tff(f4557,plain,
( spl331_266
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK166(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_266])]) ).
tff(f1991,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK166(X0,X1,X2) ),
inference(cnf_transformation,[],[f1207]) ).
tff(f1207,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( f3(sK166(X0,X1,X2),f3(f4(f54,X1),X2)) = f3(f4(f54,f3(sK166(X0,X1,X2),X1)),X2) )
& ( f4(f54,X0) = sK166(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK166])],[f719,f1206]) ).
tff(f1206,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S3'] :
( ( f3(X3,f3(f4(f54,X1),X2)) = f3(f4(f54,f3(X3,X1)),X2) )
& ( f4(f54,X0) = X3 ) )
=> ( ( f3(sK166(X0,X1,X2),f3(f4(f54,X1),X2)) = f3(f4(f54,f3(sK166(X0,X1,X2),X1)),X2) )
& ( f4(f54,X0) = sK166(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f719,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S3'] :
( ( f3(X3,f3(f4(f54,X1),X2)) = f3(f4(f54,f3(X3,X1)),X2) )
& ( f4(f54,X0) = X3 ) ),
inference(rectify,[],[f238]) ).
tff(f238,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X138: 'S3'] :
( ( f3(f4(f54,f3(X138,X1)),X2) = f3(X138,f3(f4(f54,X1),X2)) )
& ( f4(f54,X0) = X138 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_238) ).
tff(f4555,plain,
spl331_265,
inference(avatar_split_clause,[],[f1989,f4553]) ).
tff(f4553,plain,
( spl331_265
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK165(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_265])]) ).
tff(f1989,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f54,X0) = sK165(X0,X1,X2) ),
inference(cnf_transformation,[],[f1205]) ).
tff(f1205,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( f3(sK165(X0,X1,X2),f3(f4(f54,X1),X2)) = f3(f4(f54,f3(sK165(X0,X1,X2),X1)),X2) )
& ( f4(f54,X0) = sK165(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK165])],[f718,f1204]) ).
tff(f1204,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S3'] :
( ( f3(X3,f3(f4(f54,X1),X2)) = f3(f4(f54,f3(X3,X1)),X2) )
& ( f4(f54,X0) = X3 ) )
=> ( ( f3(sK165(X0,X1,X2),f3(f4(f54,X1),X2)) = f3(f4(f54,f3(sK165(X0,X1,X2),X1)),X2) )
& ( f4(f54,X0) = sK165(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f718,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S3'] :
( ( f3(X3,f3(f4(f54,X1),X2)) = f3(f4(f54,f3(X3,X1)),X2) )
& ( f4(f54,X0) = X3 ) ),
inference(rectify,[],[f232]) ).
tff(f232,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X132: 'S3'] :
( ( f3(X132,f3(f4(f54,X1),X2)) = f3(f4(f54,f3(X132,X1)),X2) )
& ( f4(f54,X0) = X132 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_232) ).
tff(f4551,plain,
( spl331_264
| spl331_11
| ~ spl331_245 ),
inference(avatar_split_clause,[],[f4467,f4457,f2978,f4548]) ).
tff(f4548,plain,
( spl331_264
<=> ( sK317 = sK34(sK317) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_264])]) ).
tff(f4467,plain,
( ( sK317 = sK34(sK317) )
| spl331_11
| ~ spl331_245 ),
inference(resolution,[],[f4458,f2980]) ).
tff(f4546,plain,
spl331_263,
inference(avatar_split_clause,[],[f1987,f4544]) ).
tff(f4544,plain,
( spl331_263
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK164(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_263])]) ).
tff(f1987,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK164(X0,X1,X2) ),
inference(cnf_transformation,[],[f1203]) ).
tff(f1203,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( $less(f11(f12,X1),f11(f12,X2))
| ~ $less(f11(f12,f3(sK164(X0,X1,X2),X1)),f11(f12,f3(sK164(X0,X1,X2),X2)))
| ~ $less(0,f11(f12,X0)) )
& ( f4(f65,X0) = sK164(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK164])],[f877,f1202]) ).
tff(f1202,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S3'] :
( ( $less(f11(f12,X1),f11(f12,X2))
| ~ $less(f11(f12,f3(X3,X1)),f11(f12,f3(X3,X2)))
| ~ $less(0,f11(f12,X0)) )
& ( f4(f65,X0) = X3 ) )
=> ( ( $less(f11(f12,X1),f11(f12,X2))
| ~ $less(f11(f12,f3(sK164(X0,X1,X2),X1)),f11(f12,f3(sK164(X0,X1,X2),X2)))
| ~ $less(0,f11(f12,X0)) )
& ( f4(f65,X0) = sK164(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f877,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S3'] :
( ( $less(f11(f12,X1),f11(f12,X2))
| ~ $less(f11(f12,f3(X3,X1)),f11(f12,f3(X3,X2)))
| ~ $less(0,f11(f12,X0)) )
& ( f4(f65,X0) = X3 ) ),
inference(flattening,[],[f876]) ).
tff(f876,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S3'] :
( ( $less(f11(f12,X1),f11(f12,X2))
| ~ $less(f11(f12,f3(X3,X1)),f11(f12,f3(X3,X2)))
| ~ $less(0,f11(f12,X0)) )
& ( f4(f65,X0) = X3 ) ),
inference(ennf_transformation,[],[f717]) ).
tff(f717,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S3'] :
( ( $less(0,f11(f12,X0))
=> ( $less(f11(f12,f3(X3,X1)),f11(f12,f3(X3,X2)))
=> $less(f11(f12,X1),f11(f12,X2)) ) )
& ( f4(f65,X0) = X3 ) ),
inference(rectify,[],[f444]) ).
tff(f444,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X288: 'S3'] :
( ( $less(0,f11(f12,X0))
=> ( $less(f11(f12,f3(X288,X1)),f11(f12,f3(X288,X2)))
=> $less(f11(f12,X1),f11(f12,X2)) ) )
& ( f4(f65,X0) = X288 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_444) ).
tff(f4542,plain,
spl331_262,
inference(avatar_split_clause,[],[f1985,f4540]) ).
tff(f4540,plain,
( spl331_262
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK163(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_262])]) ).
tff(f1985,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK163(X0,X1,X2) ),
inference(cnf_transformation,[],[f1201]) ).
tff(f1201,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( f3(f4(f65,f3(sK163(X0,X1,X2),X1)),X2) = f3(sK163(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f4(f65,X0) = sK163(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK163])],[f716,f1200]) ).
tff(f1200,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S3'] :
( ( f3(f4(f65,f3(X3,X1)),X2) = f3(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f4(f65,X0) = X3 ) )
=> ( ( f3(f4(f65,f3(sK163(X0,X1,X2),X1)),X2) = f3(sK163(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f4(f65,X0) = sK163(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f716,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S3'] :
( ( f3(f4(f65,f3(X3,X1)),X2) = f3(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f4(f65,X0) = X3 ) ),
inference(rectify,[],[f437]) ).
tff(f437,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X285: 'S3'] :
( ( f3(X285,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) = f3(f4(f65,f3(X285,X1)),X2) )
& ( f4(f65,X0) = X285 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_437) ).
tff(f4538,plain,
spl331_261,
inference(avatar_split_clause,[],[f1983,f4536]) ).
tff(f4536,plain,
( spl331_261
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK162(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_261])]) ).
tff(f1983,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK162(X0,X1,X2) ),
inference(cnf_transformation,[],[f1199]) ).
tff(f1199,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( f3(f4(f54,f3(sK162(X0,X1,X2),X1)),f3(sK162(X0,X1,X2),X2)) = f3(sK162(X0,X1,X2),f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f4(f65,X0) = sK162(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK162])],[f715,f1198]) ).
tff(f1198,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S3'] :
( ( f3(f4(f54,f3(X3,X1)),f3(X3,X2)) = f3(X3,f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f4(f65,X0) = X3 ) )
=> ( ( f3(f4(f54,f3(sK162(X0,X1,X2),X1)),f3(sK162(X0,X1,X2),X2)) = f3(sK162(X0,X1,X2),f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f4(f65,X0) = sK162(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f715,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S3'] :
( ( f3(f4(f54,f3(X3,X1)),f3(X3,X2)) = f3(X3,f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f4(f65,X0) = X3 ) ),
inference(rectify,[],[f304]) ).
tff(f304,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X192: 'S3'] :
( ( f3(f4(f54,f3(X192,X1)),f3(X192,X2)) = f3(X192,f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f4(f65,X0) = X192 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_304) ).
tff(f4534,plain,
spl331_260,
inference(avatar_split_clause,[],[f1981,f4532]) ).
tff(f4532,plain,
( spl331_260
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK161(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_260])]) ).
tff(f1981,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK161(X0,X1,X2) ),
inference(cnf_transformation,[],[f1197]) ).
tff(f1197,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( f3(f4(f65,f3(sK161(X0,X1,X2),X1)),X2) = f3(sK161(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f4(f65,X0) = sK161(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK161])],[f714,f1196]) ).
tff(f1196,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S3'] :
( ( f3(f4(f65,f3(X3,X1)),X2) = f3(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f4(f65,X0) = X3 ) )
=> ( ( f3(f4(f65,f3(sK161(X0,X1,X2),X1)),X2) = f3(sK161(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f4(f65,X0) = sK161(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f714,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S3'] :
( ( f3(f4(f65,f3(X3,X1)),X2) = f3(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f4(f65,X0) = X3 ) ),
inference(rectify,[],[f312]) ).
tff(f312,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X196: 'S3'] :
( ( f3(f4(f65,f3(X196,X1)),X2) = f3(X196,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f4(f65,X0) = X196 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_312) ).
tff(f4530,plain,
spl331_259,
inference(avatar_split_clause,[],[f1979,f4528]) ).
tff(f4528,plain,
( spl331_259
<=> ! [X2: 'S2',X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK160(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_259])]) ).
tff(f1979,plain,
! [X2: 'S2',X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK160(X0,X1,X2) ),
inference(cnf_transformation,[],[f1195]) ).
tff(f1195,plain,
! [X0: $real,X1: 'S2',X2: 'S2'] :
( ( f19(f59(f60,f19(sK160(X0,X1,X2),X1)),X2) = f19(sK160(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f59(f60,X0) = sK160(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK160])],[f713,f1194]) ).
tff(f1194,plain,
! [X0: $real,X1: 'S2',X2: 'S2'] :
( ? [X3: 'S13'] :
( ( f19(f59(f60,f19(X3,X1)),X2) = f19(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f59(f60,X0) = X3 ) )
=> ( ( f19(f59(f60,f19(sK160(X0,X1,X2),X1)),X2) = f19(sK160(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f59(f60,X0) = sK160(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f713,plain,
! [X0: $real,X1: 'S2',X2: 'S2'] :
? [X3: 'S13'] :
( ( f19(f59(f60,f19(X3,X1)),X2) = f19(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f59(f60,X0) = X3 ) ),
inference(rectify,[],[f436]) ).
tff(f436,axiom,
! [X0: $real,X1: 'S2',X2: 'S2'] :
? [X284: 'S13'] :
( ( f19(X284,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) = f19(f59(f60,f19(X284,X1)),X2) )
& ( f59(f60,X0) = X284 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_436) ).
tff(f4526,plain,
spl331_258,
inference(avatar_split_clause,[],[f1977,f4524]) ).
tff(f4524,plain,
( spl331_258
<=> ! [X2: 'S2',X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK159(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_258])]) ).
tff(f1977,plain,
! [X2: 'S2',X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK159(X0,X1,X2) ),
inference(cnf_transformation,[],[f1193]) ).
tff(f1193,plain,
! [X0: $real,X1: 'S2',X2: 'S2'] :
( ( f22(f49(f50,f19(sK159(X0,X1,X2),X1)),f19(sK159(X0,X1,X2),X2)) = f19(sK159(X0,X1,X2),f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f59(f60,X0) = sK159(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK159])],[f712,f1192]) ).
tff(f1192,plain,
! [X0: $real,X1: 'S2',X2: 'S2'] :
( ? [X3: 'S13'] :
( ( f22(f49(f50,f19(X3,X1)),f19(X3,X2)) = f19(X3,f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f59(f60,X0) = X3 ) )
=> ( ( f22(f49(f50,f19(sK159(X0,X1,X2),X1)),f19(sK159(X0,X1,X2),X2)) = f19(sK159(X0,X1,X2),f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f59(f60,X0) = sK159(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f712,plain,
! [X0: $real,X1: 'S2',X2: 'S2'] :
? [X3: 'S13'] :
( ( f22(f49(f50,f19(X3,X1)),f19(X3,X2)) = f19(X3,f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f59(f60,X0) = X3 ) ),
inference(rectify,[],[f303]) ).
tff(f303,axiom,
! [X0: $real,X1: 'S2',X2: 'S2'] :
? [X191: 'S13'] :
( ( f22(f49(f50,f19(X191,X1)),f19(X191,X2)) = f19(X191,f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f59(f60,X0) = X191 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_303) ).
tff(f4522,plain,
spl331_257,
inference(avatar_split_clause,[],[f1975,f4520]) ).
tff(f4520,plain,
( spl331_257
<=> ! [X2: 'S2',X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK158(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_257])]) ).
tff(f1975,plain,
! [X2: 'S2',X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK158(X0,X1,X2) ),
inference(cnf_transformation,[],[f1191]) ).
tff(f1191,plain,
! [X0: $real,X1: 'S2',X2: 'S2'] :
( ( f19(f59(f60,f19(sK158(X0,X1,X2),X1)),X2) = f19(sK158(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f59(f60,X0) = sK158(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK158])],[f711,f1190]) ).
tff(f1190,plain,
! [X0: $real,X1: 'S2',X2: 'S2'] :
( ? [X3: 'S13'] :
( ( f19(f59(f60,f19(X3,X1)),X2) = f19(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f59(f60,X0) = X3 ) )
=> ( ( f19(f59(f60,f19(sK158(X0,X1,X2),X1)),X2) = f19(sK158(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f59(f60,X0) = sK158(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f711,plain,
! [X0: $real,X1: 'S2',X2: 'S2'] :
? [X3: 'S13'] :
( ( f19(f59(f60,f19(X3,X1)),X2) = f19(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f59(f60,X0) = X3 ) ),
inference(rectify,[],[f311]) ).
tff(f311,axiom,
! [X0: $real,X1: 'S2',X2: 'S2'] :
? [X195: 'S13'] :
( ( f19(f59(f60,f19(X195,X1)),X2) = f19(X195,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f59(f60,X0) = X195 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_311) ).
tff(f4518,plain,
spl331_256,
inference(avatar_split_clause,[],[f1973,f4516]) ).
tff(f4516,plain,
( spl331_256
<=> ! [X2: 'S2',X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK157(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_256])]) ).
tff(f1973,plain,
! [X2: 'S2',X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK157(X0,X1,X2) ),
inference(cnf_transformation,[],[f1189]) ).
tff(f1189,plain,
! [X0: $int,X1: 'S2',X2: 'S2'] :
( ( f11(f63(f64,f11(sK157(X0,X1,X2),X1)),X2) = f11(sK157(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f63(f64,X0) = sK157(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK157])],[f710,f1188]) ).
tff(f1188,plain,
! [X0: $int,X1: 'S2',X2: 'S2'] :
( ? [X3: 'S8'] :
( ( f11(f63(f64,f11(X3,X1)),X2) = f11(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f63(f64,X0) = X3 ) )
=> ( ( f11(f63(f64,f11(sK157(X0,X1,X2),X1)),X2) = f11(sK157(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f63(f64,X0) = sK157(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f710,plain,
! [X0: $int,X1: 'S2',X2: 'S2'] :
? [X3: 'S8'] :
( ( f11(f63(f64,f11(X3,X1)),X2) = f11(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f63(f64,X0) = X3 ) ),
inference(rectify,[],[f435]) ).
tff(f435,axiom,
! [X0: $int,X1: 'S2',X2: 'S2'] :
? [X283: 'S8'] :
( ( f11(X283,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) = f11(f63(f64,f11(X283,X1)),X2) )
& ( f63(f64,X0) = X283 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_435) ).
tff(f4514,plain,
spl331_255,
inference(avatar_split_clause,[],[f1971,f4512]) ).
tff(f4512,plain,
( spl331_255
<=> ! [X2: 'S2',X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK156(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_255])]) ).
tff(f1971,plain,
! [X2: 'S2',X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK156(X0,X1,X2) ),
inference(cnf_transformation,[],[f1187]) ).
tff(f1187,plain,
! [X0: 'S10',X1: 'S2',X2: 'S2'] :
( ( f13(f66(f67,f13(sK156(X0,X1,X2),X1)),X2) = f13(sK156(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f66(f67,X0) = sK156(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK156])],[f709,f1186]) ).
tff(f1186,plain,
! [X0: 'S10',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S9'] :
( ( f13(f66(f67,f13(X3,X1)),X2) = f13(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f66(f67,X0) = X3 ) )
=> ( ( f13(f66(f67,f13(sK156(X0,X1,X2),X1)),X2) = f13(sK156(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f66(f67,X0) = sK156(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f709,plain,
! [X0: 'S10',X1: 'S2',X2: 'S2'] :
? [X3: 'S9'] :
( ( f13(f66(f67,f13(X3,X1)),X2) = f13(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f66(f67,X0) = X3 ) ),
inference(rectify,[],[f438]) ).
tff(f438,axiom,
! [X0: 'S10',X1: 'S2',X2: 'S2'] :
? [X286: 'S9'] :
( ( f13(X286,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) = f13(f66(f67,f13(X286,X1)),X2) )
& ( f66(f67,X0) = X286 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_438) ).
tff(f4510,plain,
spl331_254,
inference(avatar_split_clause,[],[f1969,f4508]) ).
tff(f4508,plain,
( spl331_254
<=> ! [X2: 'S2',X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK155(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_254])]) ).
tff(f1969,plain,
! [X2: 'S2',X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK155(X0,X1,X2) ),
inference(cnf_transformation,[],[f1185]) ).
tff(f1185,plain,
! [X0: 'S10',X1: 'S2',X2: 'S2'] :
( ( f34(f39(f52,f13(sK155(X0,X1,X2),X1)),f13(sK155(X0,X1,X2),X2)) = f13(sK155(X0,X1,X2),f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f66(f67,X0) = sK155(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK155])],[f708,f1184]) ).
tff(f1184,plain,
! [X0: 'S10',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S9'] :
( ( f34(f39(f52,f13(X3,X1)),f13(X3,X2)) = f13(X3,f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f66(f67,X0) = X3 ) )
=> ( ( f34(f39(f52,f13(sK155(X0,X1,X2),X1)),f13(sK155(X0,X1,X2),X2)) = f13(sK155(X0,X1,X2),f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f66(f67,X0) = sK155(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f708,plain,
! [X0: 'S10',X1: 'S2',X2: 'S2'] :
? [X3: 'S9'] :
( ( f34(f39(f52,f13(X3,X1)),f13(X3,X2)) = f13(X3,f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f66(f67,X0) = X3 ) ),
inference(rectify,[],[f305]) ).
tff(f305,axiom,
! [X0: 'S10',X1: 'S2',X2: 'S2'] :
? [X193: 'S9'] :
( ( f34(f39(f52,f13(X193,X1)),f13(X193,X2)) = f13(X193,f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f66(f67,X0) = X193 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_305) ).
tff(f4506,plain,
( spl331_253
| ~ spl331_2
| ~ spl331_245 ),
inference(avatar_split_clause,[],[f4460,f4457,f2934,f4503]) ).
tff(f4503,plain,
( spl331_253
<=> ( 0.0 = sK34(0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_253])]) ).
tff(f4460,plain,
( ( 0.0 = sK34(0.0) )
| ~ spl331_2
| ~ spl331_245 ),
inference(resolution,[],[f4458,f2935]) ).
tff(f4501,plain,
spl331_252,
inference(avatar_split_clause,[],[f1967,f4499]) ).
tff(f4499,plain,
( spl331_252
<=> ! [X2: 'S2',X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK154(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_252])]) ).
tff(f1967,plain,
! [X2: 'S2',X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK154(X0,X1,X2) ),
inference(cnf_transformation,[],[f1183]) ).
tff(f1183,plain,
! [X0: $int,X1: 'S2',X2: 'S2'] :
( ( f8(f9(f10,f11(sK154(X0,X1,X2),X1)),f11(sK154(X0,X1,X2),X2)) = f11(sK154(X0,X1,X2),f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f63(f64,X0) = sK154(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK154])],[f707,f1182]) ).
tff(f1182,plain,
! [X0: $int,X1: 'S2',X2: 'S2'] :
( ? [X3: 'S8'] :
( ( f8(f9(f10,f11(X3,X1)),f11(X3,X2)) = f11(X3,f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f63(f64,X0) = X3 ) )
=> ( ( f8(f9(f10,f11(sK154(X0,X1,X2),X1)),f11(sK154(X0,X1,X2),X2)) = f11(sK154(X0,X1,X2),f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f63(f64,X0) = sK154(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f707,plain,
! [X0: $int,X1: 'S2',X2: 'S2'] :
? [X3: 'S8'] :
( ( f8(f9(f10,f11(X3,X1)),f11(X3,X2)) = f11(X3,f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f63(f64,X0) = X3 ) ),
inference(rectify,[],[f302]) ).
tff(f302,axiom,
! [X0: $int,X1: 'S2',X2: 'S2'] :
? [X190: 'S8'] :
( ( f8(f9(f10,f11(X190,X1)),f11(X190,X2)) = f11(X190,f6(f7,$sum(f11(f12,X1),f11(f12,X2)))) )
& ( f63(f64,X0) = X190 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_302) ).
tff(f4497,plain,
spl331_251,
inference(avatar_split_clause,[],[f1965,f4495]) ).
tff(f4495,plain,
( spl331_251
<=> ! [X2: 'S2',X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK153(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_251])]) ).
tff(f1965,plain,
! [X2: 'S2',X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK153(X0,X1,X2) ),
inference(cnf_transformation,[],[f1181]) ).
tff(f1181,plain,
! [X0: $int,X1: 'S2',X2: 'S2'] :
( ( f11(f63(f64,f11(sK153(X0,X1,X2),X1)),X2) = f11(sK153(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f63(f64,X0) = sK153(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK153])],[f706,f1180]) ).
tff(f1180,plain,
! [X0: $int,X1: 'S2',X2: 'S2'] :
( ? [X3: 'S8'] :
( ( f11(f63(f64,f11(X3,X1)),X2) = f11(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f63(f64,X0) = X3 ) )
=> ( ( f11(f63(f64,f11(sK153(X0,X1,X2),X1)),X2) = f11(sK153(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f63(f64,X0) = sK153(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f706,plain,
! [X0: $int,X1: 'S2',X2: 'S2'] :
? [X3: 'S8'] :
( ( f11(f63(f64,f11(X3,X1)),X2) = f11(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f63(f64,X0) = X3 ) ),
inference(rectify,[],[f310]) ).
tff(f310,axiom,
! [X0: $int,X1: 'S2',X2: 'S2'] :
? [X194: 'S8'] :
( ( f11(f63(f64,f11(X194,X1)),X2) = f11(X194,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f63(f64,X0) = X194 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_310) ).
tff(f4493,plain,
spl331_250,
inference(avatar_split_clause,[],[f1963,f4491]) ).
tff(f4491,plain,
( spl331_250
<=> ! [X2: 'S2',X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK152(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_250])]) ).
tff(f1963,plain,
! [X2: 'S2',X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK152(X0,X1,X2) ),
inference(cnf_transformation,[],[f1179]) ).
tff(f1179,plain,
! [X0: 'S10',X1: 'S2',X2: 'S2'] :
( ( f13(f66(f67,f13(sK152(X0,X1,X2),X1)),X2) = f13(sK152(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f66(f67,X0) = sK152(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK152])],[f705,f1178]) ).
tff(f1178,plain,
! [X0: 'S10',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S9'] :
( ( f13(f66(f67,f13(X3,X1)),X2) = f13(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f66(f67,X0) = X3 ) )
=> ( ( f13(f66(f67,f13(sK152(X0,X1,X2),X1)),X2) = f13(sK152(X0,X1,X2),f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f66(f67,X0) = sK152(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f705,plain,
! [X0: 'S10',X1: 'S2',X2: 'S2'] :
? [X3: 'S9'] :
( ( f13(f66(f67,f13(X3,X1)),X2) = f13(X3,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f66(f67,X0) = X3 ) ),
inference(rectify,[],[f313]) ).
tff(f313,axiom,
! [X0: 'S10',X1: 'S2',X2: 'S2'] :
? [X197: 'S9'] :
( ( f13(f66(f67,f13(X197,X1)),X2) = f13(X197,f6(f7,f8(f9(f10,f11(f12,X1)),f11(f12,X2)))) )
& ( f66(f67,X0) = X197 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_313) ).
tff(f4489,plain,
spl331_249,
inference(avatar_split_clause,[],[f1604,f4487]) ).
tff(f1604,plain,
! [X0: $int] : ( f11(f12,f6(f7,X0)) = sK39(X0) ),
inference(cnf_transformation,[],[f976]) ).
tff(f976,plain,
! [X0: $int] :
( ( ( f11(f12,f6(f7,$product(2,X0))) = $sum(sK39(X0),sK39(X0)) )
| $less(X0,0) )
& ( f11(f12,f6(f7,X0)) = sK39(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39])],[f824,f975]) ).
tff(f975,plain,
! [X0: $int] :
( ? [X1: $int] :
( ( ( f11(f12,f6(f7,$product(2,X0))) = $sum(X1,X1) )
| $less(X0,0) )
& ( f11(f12,f6(f7,X0)) = X1 ) )
=> ( ( ( f11(f12,f6(f7,$product(2,X0))) = $sum(sK39(X0),sK39(X0)) )
| $less(X0,0) )
& ( f11(f12,f6(f7,X0)) = sK39(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f824,plain,
! [X0: $int] :
? [X1: $int] :
( ( ( f11(f12,f6(f7,$product(2,X0))) = $sum(X1,X1) )
| $less(X0,0) )
& ( f11(f12,f6(f7,X0)) = X1 ) ),
inference(ennf_transformation,[],[f637]) ).
tff(f637,plain,
! [X0: $int] :
? [X1: $int] :
( ( ~ $less(X0,0)
=> ( f11(f12,f6(f7,$product(2,X0))) = $sum(X1,X1) ) )
& ( f11(f12,f6(f7,X0)) = X1 ) ),
inference(rectify,[],[f478]) ).
tff(f478,plain,
! [X0: $int] :
? [X115: $int] :
( ( ~ $less(X0,0)
=> ( f11(f12,f6(f7,$product(2,X0))) = $sum(X115,X115) ) )
& ( f11(f12,f6(f7,X0)) = X115 ) ),
inference(theory_normalization,[],[f213]) ).
tff(f213,axiom,
! [X0: $int] :
? [X115: $int] :
( ( $lesseq(0,X0)
=> ( f11(f12,f6(f7,$product(2,X0))) = $sum(X115,X115) ) )
& ( f11(f12,f6(f7,X0)) = X115 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_213) ).
tff(f4485,plain,
spl331_248,
inference(avatar_split_clause,[],[f1602,f4483]) ).
tff(f4483,plain,
( spl331_248
<=> ! [X0: $int] : ( f3(f24,f6(f7,X0)) = sK38(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_248])]) ).
tff(f1602,plain,
! [X0: $int] : ( f3(f24,f6(f7,X0)) = sK38(X0) ),
inference(cnf_transformation,[],[f974]) ).
tff(f974,plain,
! [X0: $int] :
( ( ( f3(f24,f6(f7,$product(2,X0))) = f3(f4(f53,sK38(X0)),sK38(X0)) )
| $less(X0,0) )
& ( f3(f24,f6(f7,X0)) = sK38(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38])],[f823,f973]) ).
tff(f973,plain,
! [X0: $int] :
( ? [X1: 'S2'] :
( ( ( f3(f24,f6(f7,$product(2,X0))) = f3(f4(f53,X1),X1) )
| $less(X0,0) )
& ( f3(f24,f6(f7,X0)) = X1 ) )
=> ( ( ( f3(f24,f6(f7,$product(2,X0))) = f3(f4(f53,sK38(X0)),sK38(X0)) )
| $less(X0,0) )
& ( f3(f24,f6(f7,X0)) = sK38(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f823,plain,
! [X0: $int] :
? [X1: 'S2'] :
( ( ( f3(f24,f6(f7,$product(2,X0))) = f3(f4(f53,X1),X1) )
| $less(X0,0) )
& ( f3(f24,f6(f7,X0)) = X1 ) ),
inference(ennf_transformation,[],[f636]) ).
tff(f636,plain,
! [X0: $int] :
? [X1: 'S2'] :
( ( ~ $less(X0,0)
=> ( f3(f24,f6(f7,$product(2,X0))) = f3(f4(f53,X1),X1) ) )
& ( f3(f24,f6(f7,X0)) = X1 ) ),
inference(rectify,[],[f477]) ).
tff(f477,plain,
! [X0: $int] :
? [X112: 'S2'] :
( ( ~ $less(X0,0)
=> ( f3(f24,f6(f7,$product(2,X0))) = f3(f4(f53,X112),X112) ) )
& ( f3(f24,f6(f7,X0)) = X112 ) ),
inference(theory_normalization,[],[f210]) ).
tff(f210,axiom,
! [X0: $int] :
? [X112: 'S2'] :
( ( $lesseq(0,X0)
=> ( f3(f24,f6(f7,$product(2,X0))) = f3(f4(f53,X112),X112) ) )
& ( f3(f24,f6(f7,X0)) = X112 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_210) ).
tff(f4481,plain,
spl331_247,
inference(avatar_split_clause,[],[f1600,f4479]) ).
tff(f4479,plain,
( spl331_247
<=> ! [X0: $int] : ( f19(f20,f6(f7,X0)) = sK37(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_247])]) ).
tff(f1600,plain,
! [X0: $int] : ( f19(f20,f6(f7,X0)) = sK37(X0) ),
inference(cnf_transformation,[],[f972]) ).
tff(f972,plain,
! [X0: $int] :
( ( ( f19(f20,f6(f7,$product(2,X0))) = $sum(sK37(X0),sK37(X0)) )
| $less(X0,0) )
& ( f19(f20,f6(f7,X0)) = sK37(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f822,f971]) ).
tff(f971,plain,
! [X0: $int] :
( ? [X1: $real] :
( ( ( f19(f20,f6(f7,$product(2,X0))) = $sum(X1,X1) )
| $less(X0,0) )
& ( f19(f20,f6(f7,X0)) = X1 ) )
=> ( ( ( f19(f20,f6(f7,$product(2,X0))) = $sum(sK37(X0),sK37(X0)) )
| $less(X0,0) )
& ( f19(f20,f6(f7,X0)) = sK37(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f822,plain,
! [X0: $int] :
? [X1: $real] :
( ( ( f19(f20,f6(f7,$product(2,X0))) = $sum(X1,X1) )
| $less(X0,0) )
& ( f19(f20,f6(f7,X0)) = X1 ) ),
inference(ennf_transformation,[],[f635]) ).
tff(f635,plain,
! [X0: $int] :
? [X1: $real] :
( ( ~ $less(X0,0)
=> ( f19(f20,f6(f7,$product(2,X0))) = $sum(X1,X1) ) )
& ( f19(f20,f6(f7,X0)) = X1 ) ),
inference(rectify,[],[f476]) ).
tff(f476,plain,
! [X0: $int] :
? [X114: $real] :
( ( ~ $less(X0,0)
=> ( f19(f20,f6(f7,$product(2,X0))) = $sum(X114,X114) ) )
& ( f19(f20,f6(f7,X0)) = X114 ) ),
inference(theory_normalization,[],[f212]) ).
tff(f212,axiom,
! [X0: $int] :
? [X114: $real] :
( ( $lesseq(0,X0)
=> ( f19(f20,f6(f7,$product(2,X0))) = $sum(X114,X114) ) )
& ( f19(f20,f6(f7,X0)) = X114 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_212) ).
tff(f4477,plain,
spl331_246,
inference(avatar_split_clause,[],[f1598,f4475]) ).
tff(f4475,plain,
( spl331_246
<=> ! [X0: $int] : ( f13(f14,f6(f7,X0)) = sK36(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_246])]) ).
tff(f1598,plain,
! [X0: $int] : ( f13(f14,f6(f7,X0)) = sK36(X0) ),
inference(cnf_transformation,[],[f970]) ).
tff(f970,plain,
! [X0: $int] :
( ( ( f13(f14,f6(f7,$product(2,X0))) = f34(f39(f40,sK36(X0)),sK36(X0)) )
| $less(X0,0) )
& ( f13(f14,f6(f7,X0)) = sK36(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36])],[f821,f969]) ).
tff(f969,plain,
! [X0: $int] :
( ? [X1: 'S10'] :
( ( ( f13(f14,f6(f7,$product(2,X0))) = f34(f39(f40,X1),X1) )
| $less(X0,0) )
& ( f13(f14,f6(f7,X0)) = X1 ) )
=> ( ( ( f13(f14,f6(f7,$product(2,X0))) = f34(f39(f40,sK36(X0)),sK36(X0)) )
| $less(X0,0) )
& ( f13(f14,f6(f7,X0)) = sK36(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f821,plain,
! [X0: $int] :
? [X1: 'S10'] :
( ( ( f13(f14,f6(f7,$product(2,X0))) = f34(f39(f40,X1),X1) )
| $less(X0,0) )
& ( f13(f14,f6(f7,X0)) = X1 ) ),
inference(ennf_transformation,[],[f634]) ).
tff(f634,plain,
! [X0: $int] :
? [X1: 'S10'] :
( ( ~ $less(X0,0)
=> ( f13(f14,f6(f7,$product(2,X0))) = f34(f39(f40,X1),X1) ) )
& ( f13(f14,f6(f7,X0)) = X1 ) ),
inference(rectify,[],[f475]) ).
tff(f475,plain,
! [X0: $int] :
? [X113: 'S10'] :
( ( ~ $less(X0,0)
=> ( f13(f14,f6(f7,$product(2,X0))) = f34(f39(f40,X113),X113) ) )
& ( f13(f14,f6(f7,X0)) = X113 ) ),
inference(theory_normalization,[],[f211]) ).
tff(f211,axiom,
! [X0: $int] :
? [X113: 'S10'] :
( ( $lesseq(0,X0)
=> ( f13(f14,f6(f7,$product(2,X0))) = f34(f39(f40,X113),X113) ) )
& ( f13(f14,f6(f7,X0)) = X113 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_211) ).
tff(f4459,plain,
( spl331_245
| ~ spl331_73
| ~ spl331_244 ),
inference(avatar_split_clause,[],[f4455,f4452,f3240,f4457]) ).
tff(f4452,plain,
( spl331_244
<=> ! [X0: $real] :
( ( f22(f30,X0) = X0 )
| $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_244])]) ).
tff(f4455,plain,
( ! [X0: $real] :
( ( sK34(X0) = X0 )
| $less(X0,0.0) )
| ~ spl331_73
| ~ spl331_244 ),
inference(forward_demodulation,[],[f4453,f3241]) ).
tff(f4453,plain,
( ! [X0: $real] :
( ( f22(f30,X0) = X0 )
| $less(X0,0.0) )
| ~ spl331_244 ),
inference(avatar_component_clause,[],[f4452]) ).
tff(f4454,plain,
spl331_244,
inference(avatar_split_clause,[],[f1523,f4452]) ).
tff(f1523,plain,
! [X0: $real] :
( ( f22(f30,X0) = X0 )
| $less(X0,0.0) ),
inference(cnf_transformation,[],[f807]) ).
tff(f4446,plain,
spl331_243,
inference(avatar_split_clause,[],[f595,f4444]) ).
tff(f595,plain,
! [X0: $real,X1: $real] :
( $less(X0,X1)
| $less(X1,$sum(X0,1.0)) ),
introduced(theory_axiom_150,[]) ).
tff(f4442,plain,
spl331_242,
inference(avatar_split_clause,[],[f585,f4440]) ).
tff(f4440,plain,
( spl331_242
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_242])]) ).
tff(f585,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_164,[]) ).
tff(f4438,plain,
spl331_241,
inference(avatar_split_clause,[],[f577,f4436]) ).
tff(f577,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_150,[]) ).
tff(f4428,plain,
( spl331_240
| ~ spl331_36
| ~ spl331_110 ),
inference(avatar_split_clause,[],[f3961,f3404,f3088,f4426]) ).
tff(f4426,plain,
( spl331_240
<=> ! [X0: $real] : ( 0.0 = $product(0.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_240])]) ).
tff(f3088,plain,
( spl331_36
<=> ! [X0: $real] : ( 0.0 = $product(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_36])]) ).
tff(f3404,plain,
( spl331_110
<=> ! [X0: $real,X1: $real] : ( $product(X0,X1) = $product(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_110])]) ).
tff(f3961,plain,
( ! [X0: $real] : ( 0.0 = $product(0.0,X0) )
| ~ spl331_36
| ~ spl331_110 ),
inference(superposition,[],[f3405,f3089]) ).
tff(f3089,plain,
( ! [X0: $real] : ( 0.0 = $product(X0,0.0) )
| ~ spl331_36 ),
inference(avatar_component_clause,[],[f3088]) ).
tff(f3405,plain,
( ! [X0: $real,X1: $real] : ( $product(X0,X1) = $product(X1,X0) )
| ~ spl331_110 ),
inference(avatar_component_clause,[],[f3404]) ).
tff(f4424,plain,
( spl331_239
| ~ spl331_32
| ~ spl331_108 ),
inference(avatar_split_clause,[],[f3957,f3396,f3072,f4422]) ).
tff(f4422,plain,
( spl331_239
<=> ! [X0: $int] : ( 0 = $product(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_239])]) ).
tff(f3072,plain,
( spl331_32
<=> ! [X0: $int] : ( 0 = $product(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_32])]) ).
tff(f3396,plain,
( spl331_108
<=> ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_108])]) ).
tff(f3957,plain,
( ! [X0: $int] : ( 0 = $product(0,X0) )
| ~ spl331_32
| ~ spl331_108 ),
inference(superposition,[],[f3397,f3073]) ).
tff(f3073,plain,
( ! [X0: $int] : ( 0 = $product(X0,0) )
| ~ spl331_32 ),
inference(avatar_component_clause,[],[f3072]) ).
tff(f3397,plain,
( ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) )
| ~ spl331_108 ),
inference(avatar_component_clause,[],[f3396]) ).
tff(f3990,plain,
( spl331_238
| ~ spl331_57
| ~ spl331_141 ),
inference(avatar_split_clause,[],[f3550,f3547,f3176,f3988]) ).
tff(f3176,plain,
( spl331_57
<=> ! [X0: 'S2'] : ( sK27(X0) = sK31(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_57])]) ).
tff(f3547,plain,
( spl331_141
<=> ! [X0: 'S2'] : ( f9(f10,sK31(X0)) = sK32(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_141])]) ).
tff(f3550,plain,
( ! [X0: 'S2'] : ( sK32(X0) = f9(f10,sK27(X0)) )
| ~ spl331_57
| ~ spl331_141 ),
inference(forward_demodulation,[],[f3548,f3177]) ).
tff(f3177,plain,
( ! [X0: 'S2'] : ( sK27(X0) = sK31(X0) )
| ~ spl331_57 ),
inference(avatar_component_clause,[],[f3176]) ).
tff(f3548,plain,
( ! [X0: 'S2'] : ( f9(f10,sK31(X0)) = sK32(X0) )
| ~ spl331_141 ),
inference(avatar_component_clause,[],[f3547]) ).
tff(f3984,plain,
( spl331_237
| ~ spl331_52
| ~ spl331_139 ),
inference(avatar_split_clause,[],[f3541,f3538,f3156,f3982]) ).
tff(f3982,plain,
( spl331_237
<=> ! [X0: 'S2'] : ( sK19(X0) = f22(f30,sK19(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_237])]) ).
tff(f3156,plain,
( spl331_52
<=> ! [X0: 'S2'] : ( sK19(X0) = sK21(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_52])]) ).
tff(f3538,plain,
( spl331_139
<=> ! [X0: 'S2'] : ( sK21(X0) = f22(f30,sK21(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_139])]) ).
tff(f3541,plain,
( ! [X0: 'S2'] : ( sK19(X0) = f22(f30,sK19(X0)) )
| ~ spl331_52
| ~ spl331_139 ),
inference(forward_demodulation,[],[f3539,f3157]) ).
tff(f3157,plain,
( ! [X0: 'S2'] : ( sK19(X0) = sK21(X0) )
| ~ spl331_52 ),
inference(avatar_component_clause,[],[f3156]) ).
tff(f3539,plain,
( ! [X0: 'S2'] : ( sK21(X0) = f22(f30,sK21(X0)) )
| ~ spl331_139 ),
inference(avatar_component_clause,[],[f3538]) ).
tff(f3980,plain,
( spl331_236
| ~ spl331_51
| ~ spl331_137 ),
inference(avatar_split_clause,[],[f3532,f3529,f3152,f3978]) ).
tff(f3978,plain,
( spl331_236
<=> ! [X0: 'S2'] : ( sK19(X0) = f22(f33,sK19(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_236])]) ).
tff(f3152,plain,
( spl331_51
<=> ! [X0: 'S2'] : ( sK19(X0) = sK20(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_51])]) ).
tff(f3529,plain,
( spl331_137
<=> ! [X0: 'S2'] : ( sK20(X0) = f22(f33,sK20(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_137])]) ).
tff(f3532,plain,
( ! [X0: 'S2'] : ( sK19(X0) = f22(f33,sK19(X0)) )
| ~ spl331_51
| ~ spl331_137 ),
inference(forward_demodulation,[],[f3530,f3153]) ).
tff(f3153,plain,
( ! [X0: 'S2'] : ( sK19(X0) = sK20(X0) )
| ~ spl331_51 ),
inference(avatar_component_clause,[],[f3152]) ).
tff(f3530,plain,
( ! [X0: 'S2'] : ( sK20(X0) = f22(f33,sK20(X0)) )
| ~ spl331_137 ),
inference(avatar_component_clause,[],[f3529]) ).
tff(f3956,plain,
spl331_235,
inference(avatar_split_clause,[],[f2808,f3954]) ).
tff(f3954,plain,
( spl331_235
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK256(X0,X1,X2) = sK27(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_235])]) ).
tff(f2808,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK256(X0,X1,X2) = sK27(X2) ),
inference(forward_demodulation,[],[f2150,f1580]) ).
tff(f2150,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X2) = sK256(X0,X1,X2) ),
inference(cnf_transformation,[],[f1336]) ).
tff(f1336,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( $less(f8(sK255(X0,X1,X2),sK257(X0,X1,X2)),f8(sK255(X0,X1,X2),sK256(X0,X1,X2)))
| ~ $less(sK257(X0,X1,X2),sK256(X0,X1,X2)) )
& ( $less(sK257(X0,X1,X2),sK256(X0,X1,X2))
| ~ $less(f8(sK255(X0,X1,X2),sK257(X0,X1,X2)),f8(sK255(X0,X1,X2),sK256(X0,X1,X2))) )
& ( f11(f12,X1) = sK257(X0,X1,X2) )
& ( f11(f12,X2) = sK256(X0,X1,X2) )
& ( f9(f10,$sum(f11(f12,X0),1)) = sK255(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK255,sK256,sK257])],[f1334,f1335]) ).
tff(f1335,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S6',X4: $int,X5: $int] :
( ( $less(f8(X3,X5),f8(X3,X4))
| ~ $less(X5,X4) )
& ( $less(X5,X4)
| ~ $less(f8(X3,X5),f8(X3,X4)) )
& ( f11(f12,X1) = X5 )
& ( f11(f12,X2) = X4 )
& ( f9(f10,$sum(f11(f12,X0),1)) = X3 ) )
=> ( ( $less(f8(sK255(X0,X1,X2),sK257(X0,X1,X2)),f8(sK255(X0,X1,X2),sK256(X0,X1,X2)))
| ~ $less(sK257(X0,X1,X2),sK256(X0,X1,X2)) )
& ( $less(sK257(X0,X1,X2),sK256(X0,X1,X2))
| ~ $less(f8(sK255(X0,X1,X2),sK257(X0,X1,X2)),f8(sK255(X0,X1,X2),sK256(X0,X1,X2))) )
& ( f11(f12,X1) = sK257(X0,X1,X2) )
& ( f11(f12,X2) = sK256(X0,X1,X2) )
& ( f9(f10,$sum(f11(f12,X0),1)) = sK255(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1334,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S6',X4: $int,X5: $int] :
( ( $less(f8(X3,X5),f8(X3,X4))
| ~ $less(X5,X4) )
& ( $less(X5,X4)
| ~ $less(f8(X3,X5),f8(X3,X4)) )
& ( f11(f12,X1) = X5 )
& ( f11(f12,X2) = X4 )
& ( f9(f10,$sum(f11(f12,X0),1)) = X3 ) ),
inference(flattening,[],[f1333]) ).
tff(f1333,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S6',X4: $int,X5: $int] :
( ( $less(f8(X3,X5),f8(X3,X4))
| ~ $less(X5,X4) )
& ( $less(X5,X4)
| ~ $less(f8(X3,X5),f8(X3,X4)) )
& ( f11(f12,X1) = X5 )
& ( f11(f12,X2) = X4 )
& ( f9(f10,$sum(f11(f12,X0),1)) = X3 ) ),
inference(nnf_transformation,[],[f772]) ).
tff(f772,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S6',X4: $int,X5: $int] :
( ( $less(f8(X3,X5),f8(X3,X4))
<=> $less(X5,X4) )
& ( f11(f12,X1) = X5 )
& ( f11(f12,X2) = X4 )
& ( f9(f10,$sum(f11(f12,X0),1)) = X3 ) ),
inference(rectify,[],[f159]) ).
tff(f159,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X73: 'S6',X74: $int,X75: $int] :
( ( $less(f8(X73,X75),f8(X73,X74))
<=> $less(X75,X74) )
& ( f11(f12,X1) = X75 )
& ( f11(f12,X2) = X74 )
& ( f9(f10,$sum(f11(f12,X0),1)) = X73 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_159) ).
tff(f3938,plain,
spl331_234,
inference(avatar_split_clause,[],[f2807,f3936]) ).
tff(f3936,plain,
( spl331_234
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK257(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_234])]) ).
tff(f2807,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK257(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2151,f1580]) ).
tff(f2151,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK257(X0,X1,X2) ),
inference(cnf_transformation,[],[f1336]) ).
tff(f3934,plain,
spl331_233,
inference(avatar_split_clause,[],[f2804,f3932]) ).
tff(f3932,plain,
( spl331_233
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK253(X0,X1,X2) = sK27(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_233])]) ).
tff(f2804,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK253(X0,X1,X2) = sK27(X2) ),
inference(forward_demodulation,[],[f2145,f1580]) ).
tff(f2145,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X2) = sK253(X0,X1,X2) ),
inference(cnf_transformation,[],[f1332]) ).
tff(f1332,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( ~ $less(f8(sK252(X0,X1,X2),sK253(X0,X1,X2)),f8(sK252(X0,X1,X2),sK254(X0,X1,X2)))
| $less(sK253(X0,X1,X2),sK254(X0,X1,X2)) )
& ( ~ $less(sK253(X0,X1,X2),sK254(X0,X1,X2))
| $less(f8(sK252(X0,X1,X2),sK253(X0,X1,X2)),f8(sK252(X0,X1,X2),sK254(X0,X1,X2))) )
& ( f11(f12,X1) = sK254(X0,X1,X2) )
& ( f11(f12,X2) = sK253(X0,X1,X2) )
& ( f9(f10,$sum(f11(f12,X0),1)) = sK252(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK252,sK253,sK254])],[f1330,f1331]) ).
tff(f1331,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: 'S6',X4: $int,X5: $int] :
( ( ~ $less(f8(X3,X4),f8(X3,X5))
| $less(X4,X5) )
& ( ~ $less(X4,X5)
| $less(f8(X3,X4),f8(X3,X5)) )
& ( f11(f12,X1) = X5 )
& ( f11(f12,X2) = X4 )
& ( f9(f10,$sum(f11(f12,X0),1)) = X3 ) )
=> ( ( ~ $less(f8(sK252(X0,X1,X2),sK253(X0,X1,X2)),f8(sK252(X0,X1,X2),sK254(X0,X1,X2)))
| $less(sK253(X0,X1,X2),sK254(X0,X1,X2)) )
& ( ~ $less(sK253(X0,X1,X2),sK254(X0,X1,X2))
| $less(f8(sK252(X0,X1,X2),sK253(X0,X1,X2)),f8(sK252(X0,X1,X2),sK254(X0,X1,X2))) )
& ( f11(f12,X1) = sK254(X0,X1,X2) )
& ( f11(f12,X2) = sK253(X0,X1,X2) )
& ( f9(f10,$sum(f11(f12,X0),1)) = sK252(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1330,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S6',X4: $int,X5: $int] :
( ( ~ $less(f8(X3,X4),f8(X3,X5))
| $less(X4,X5) )
& ( ~ $less(X4,X5)
| $less(f8(X3,X4),f8(X3,X5)) )
& ( f11(f12,X1) = X5 )
& ( f11(f12,X2) = X4 )
& ( f9(f10,$sum(f11(f12,X0),1)) = X3 ) ),
inference(flattening,[],[f1329]) ).
tff(f1329,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S6',X4: $int,X5: $int] :
( ( ~ $less(f8(X3,X4),f8(X3,X5))
| $less(X4,X5) )
& ( ~ $less(X4,X5)
| $less(f8(X3,X4),f8(X3,X5)) )
& ( f11(f12,X1) = X5 )
& ( f11(f12,X2) = X4 )
& ( f9(f10,$sum(f11(f12,X0),1)) = X3 ) ),
inference(nnf_transformation,[],[f771]) ).
tff(f771,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: 'S6',X4: $int,X5: $int] :
( ( ~ $less(f8(X3,X4),f8(X3,X5))
<=> ~ $less(X4,X5) )
& ( f11(f12,X1) = X5 )
& ( f11(f12,X2) = X4 )
& ( f9(f10,$sum(f11(f12,X0),1)) = X3 ) ),
inference(rectify,[],[f534]) ).
tff(f534,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X76: 'S6',X77: $int,X78: $int] :
( ( ~ $less(f8(X76,X77),f8(X76,X78))
<=> ~ $less(X77,X78) )
& ( f11(f12,X1) = X78 )
& ( f11(f12,X2) = X77 )
& ( f9(f10,$sum(f11(f12,X0),1)) = X76 ) ),
inference(theory_normalization,[],[f160]) ).
tff(f160,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X76: 'S6',X77: $int,X78: $int] :
( ( $lesseq(f8(X76,X78),f8(X76,X77))
<=> $lesseq(X78,X77) )
& ( f11(f12,X1) = X78 )
& ( f11(f12,X2) = X77 )
& ( f9(f10,$sum(f11(f12,X0),1)) = X76 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_160) ).
tff(f3930,plain,
spl331_232,
inference(avatar_split_clause,[],[f2803,f3928]) ).
tff(f3928,plain,
( spl331_232
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK254(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_232])]) ).
tff(f2803,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK254(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2146,f1580]) ).
tff(f2146,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK254(X0,X1,X2) ),
inference(cnf_transformation,[],[f1332]) ).
tff(f3926,plain,
spl331_231,
inference(avatar_split_clause,[],[f2801,f3924]) ).
tff(f3924,plain,
( spl331_231
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK250(X0,X1,X2) = sK27(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_231])]) ).
tff(f2801,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK250(X0,X1,X2) = sK27(X2) ),
inference(forward_demodulation,[],[f2141,f1580]) ).
tff(f2141,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X2) = sK250(X0,X1,X2) ),
inference(cnf_transformation,[],[f1328]) ).
tff(f3922,plain,
spl331_230,
inference(avatar_split_clause,[],[f2800,f3920]) ).
tff(f3920,plain,
( spl331_230
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK251(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_230])]) ).
tff(f2800,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK251(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2142,f1580]) ).
tff(f2142,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK251(X0,X1,X2) ),
inference(cnf_transformation,[],[f1328]) ).
tff(f3918,plain,
spl331_229,
inference(avatar_split_clause,[],[f2797,f3916]) ).
tff(f3916,plain,
( spl331_229
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK247(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_229])]) ).
tff(f2797,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK247(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2137,f1580]) ).
tff(f2137,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK247(X0,X1,X2) ),
inference(cnf_transformation,[],[f1326]) ).
tff(f3914,plain,
spl331_228,
inference(avatar_split_clause,[],[f2796,f3912]) ).
tff(f3912,plain,
( spl331_228
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK248(X0,X1,X2) = sK27(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_228])]) ).
tff(f2796,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK248(X0,X1,X2) = sK27(X2) ),
inference(forward_demodulation,[],[f2138,f1580]) ).
tff(f2138,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X2) = sK248(X0,X1,X2) ),
inference(cnf_transformation,[],[f1326]) ).
tff(f3910,plain,
spl331_227,
inference(avatar_split_clause,[],[f2793,f3908]) ).
tff(f3908,plain,
( spl331_227
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK244(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_227])]) ).
tff(f2793,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK244(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2133,f1580]) ).
tff(f2133,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK244(X0,X1,X2) ),
inference(cnf_transformation,[],[f1324]) ).
tff(f3906,plain,
spl331_226,
inference(avatar_split_clause,[],[f2792,f3904]) ).
tff(f3904,plain,
( spl331_226
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK245(X0,X1,X2) = sK27(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_226])]) ).
tff(f2792,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK245(X0,X1,X2) = sK27(X2) ),
inference(forward_demodulation,[],[f2134,f1580]) ).
tff(f2134,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X2) = sK245(X0,X1,X2) ),
inference(cnf_transformation,[],[f1324]) ).
tff(f3902,plain,
spl331_225,
inference(avatar_split_clause,[],[f2791,f3900]) ).
tff(f3900,plain,
( spl331_225
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK240(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_225])]) ).
tff(f2791,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK240(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2128,f1580]) ).
tff(f2128,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK240(X0,X1,X2) ),
inference(cnf_transformation,[],[f1322]) ).
tff(f3898,plain,
( spl331_224
| ~ spl331_67
| ~ spl331_126 ),
inference(avatar_split_clause,[],[f3482,f3479,f3216,f3896]) ).
tff(f3479,plain,
( spl331_126
<=> ! [X0: $real] : ( f27(f28,sK18(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_126])]) ).
tff(f3482,plain,
( ! [X1: $real] : ( sK23(sK18(X1)) = X1 )
| ~ spl331_67
| ~ spl331_126 ),
inference(superposition,[],[f3480,f3217]) ).
tff(f3480,plain,
( ! [X0: $real] : ( f27(f28,sK18(X0)) = X0 )
| ~ spl331_126 ),
inference(avatar_component_clause,[],[f3479]) ).
tff(f3894,plain,
spl331_223,
inference(avatar_split_clause,[],[f2790,f3892]) ).
tff(f3892,plain,
( spl331_223
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK241(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_223])]) ).
tff(f2790,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK241(X0,X1,X2) ),
inference(forward_demodulation,[],[f2129,f1580]) ).
tff(f2129,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK241(X0,X1,X2) ),
inference(cnf_transformation,[],[f1322]) ).
tff(f3890,plain,
spl331_222,
inference(avatar_split_clause,[],[f2788,f3888]) ).
tff(f3888,plain,
( spl331_222
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK236(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_222])]) ).
tff(f2788,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK236(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2123,f1580]) ).
tff(f2123,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK236(X0,X1,X2) ),
inference(cnf_transformation,[],[f1320]) ).
tff(f1320,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( $less(f8(sK239(X0,X1,X2),sK237(X0,X1,X2)),f8(sK239(X0,X1,X2),sK236(X0,X1,X2)))
| ~ $less(0,sK238(X0,X1,X2))
| ~ $less(sK237(X0,X1,X2),sK236(X0,X1,X2)) )
& ( f9(f10,sK238(X0,X1,X2)) = sK239(X0,X1,X2) )
& ( f11(f12,X2) = sK238(X0,X1,X2) )
& ( f11(f12,X0) = sK237(X0,X1,X2) )
& ( f11(f12,X1) = sK236(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK236,sK237,sK238,sK239])],[f888,f1319,f1318]) ).
tff(f1318,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: $int,X4: $int,X5: $int] :
( ? [X6: 'S6'] :
( ( $less(f8(X6,X4),f8(X6,X3))
| ~ $less(0,X5)
| ~ $less(X4,X3) )
& ( f9(f10,X5) = X6 ) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) )
=> ( ? [X6: 'S6'] :
( ( $less(f8(X6,sK237(X0,X1,X2)),f8(X6,sK236(X0,X1,X2)))
| ~ $less(0,sK238(X0,X1,X2))
| ~ $less(sK237(X0,X1,X2),sK236(X0,X1,X2)) )
& ( f9(f10,sK238(X0,X1,X2)) = X6 ) )
& ( f11(f12,X2) = sK238(X0,X1,X2) )
& ( f11(f12,X0) = sK237(X0,X1,X2) )
& ( f11(f12,X1) = sK236(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1319,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X6: 'S6'] :
( ( $less(f8(X6,sK237(X0,X1,X2)),f8(X6,sK236(X0,X1,X2)))
| ~ $less(0,sK238(X0,X1,X2))
| ~ $less(sK237(X0,X1,X2),sK236(X0,X1,X2)) )
& ( f9(f10,sK238(X0,X1,X2)) = X6 ) )
=> ( ( $less(f8(sK239(X0,X1,X2),sK237(X0,X1,X2)),f8(sK239(X0,X1,X2),sK236(X0,X1,X2)))
| ~ $less(0,sK238(X0,X1,X2))
| ~ $less(sK237(X0,X1,X2),sK236(X0,X1,X2)) )
& ( f9(f10,sK238(X0,X1,X2)) = sK239(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f888,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ? [X6: 'S6'] :
( ( $less(f8(X6,X4),f8(X6,X3))
| ~ $less(0,X5)
| ~ $less(X4,X3) )
& ( f9(f10,X5) = X6 ) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) ),
inference(flattening,[],[f887]) ).
tff(f887,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ? [X6: 'S6'] :
( ( $less(f8(X6,X4),f8(X6,X3))
| ~ $less(0,X5)
| ~ $less(X4,X3) )
& ( f9(f10,X5) = X6 ) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) ),
inference(ennf_transformation,[],[f766]) ).
tff(f766,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ? [X6: 'S6'] :
( ( $less(X4,X3)
=> ( $less(0,X5)
=> $less(f8(X6,X4),f8(X6,X3)) ) )
& ( f9(f10,X5) = X6 ) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) ),
inference(rectify,[],[f164]) ).
tff(f164,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X88: $int,X89: $int,X90: $int] :
( ? [X91: 'S6'] :
( ( $less(X89,X88)
=> ( $less(0,X90)
=> $less(f8(X91,X89),f8(X91,X88)) ) )
& ( f9(f10,X90) = X91 ) )
& ( f11(f12,X2) = X90 )
& ( f11(f12,X0) = X89 )
& ( f11(f12,X1) = X88 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_164) ).
tff(f3886,plain,
spl331_221,
inference(avatar_split_clause,[],[f2787,f3884]) ).
tff(f3884,plain,
( spl331_221
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK237(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_221])]) ).
tff(f2787,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK237(X0,X1,X2) ),
inference(forward_demodulation,[],[f2124,f1580]) ).
tff(f2124,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK237(X0,X1,X2) ),
inference(cnf_transformation,[],[f1320]) ).
tff(f3882,plain,
spl331_220,
inference(avatar_split_clause,[],[f2786,f3880]) ).
tff(f3880,plain,
( spl331_220
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK238(X0,X1,X2) = sK27(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_220])]) ).
tff(f2786,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK238(X0,X1,X2) = sK27(X2) ),
inference(forward_demodulation,[],[f2125,f1580]) ).
tff(f2125,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X2) = sK238(X0,X1,X2) ),
inference(cnf_transformation,[],[f1320]) ).
tff(f3878,plain,
spl331_219,
inference(avatar_split_clause,[],[f2785,f3876]) ).
tff(f3876,plain,
( spl331_219
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK233(X0,X1,X2) = sK27(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_219])]) ).
tff(f2785,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK233(X0,X1,X2) = sK27(X2) ),
inference(forward_demodulation,[],[f2117,f1580]) ).
tff(f2117,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X2) = sK233(X0,X1,X2) ),
inference(cnf_transformation,[],[f1317]) ).
tff(f1317,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( $less(f8(f9(f10,sK235(X0,X1,X2)),sK234(X0,X1,X2)),f8(f9(f10,sK233(X0,X1,X2)),sK234(X0,X1,X2)))
| ~ $less(sK235(X0,X1,X2),sK233(X0,X1,X2))
| ~ $less(0,sK234(X0,X1,X2)) )
& ( ( $less(sK235(X0,X1,X2),sK233(X0,X1,X2))
& $less(0,sK234(X0,X1,X2)) )
| ~ $less(f8(f9(f10,sK235(X0,X1,X2)),sK234(X0,X1,X2)),f8(f9(f10,sK233(X0,X1,X2)),sK234(X0,X1,X2))) )
& ( f11(f12,X0) = sK235(X0,X1,X2) )
& ( f11(f12,X1) = sK234(X0,X1,X2) )
& ( f11(f12,X2) = sK233(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK233,sK234,sK235])],[f1315,f1316]) ).
tff(f1316,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: $int,X4: $int,X5: $int] :
( ( $less(f8(f9(f10,X5),X4),f8(f9(f10,X3),X4))
| ~ $less(X5,X3)
| ~ $less(0,X4) )
& ( ( $less(X5,X3)
& $less(0,X4) )
| ~ $less(f8(f9(f10,X5),X4),f8(f9(f10,X3),X4)) )
& ( f11(f12,X0) = X5 )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X2) = X3 ) )
=> ( ( $less(f8(f9(f10,sK235(X0,X1,X2)),sK234(X0,X1,X2)),f8(f9(f10,sK233(X0,X1,X2)),sK234(X0,X1,X2)))
| ~ $less(sK235(X0,X1,X2),sK233(X0,X1,X2))
| ~ $less(0,sK234(X0,X1,X2)) )
& ( ( $less(sK235(X0,X1,X2),sK233(X0,X1,X2))
& $less(0,sK234(X0,X1,X2)) )
| ~ $less(f8(f9(f10,sK235(X0,X1,X2)),sK234(X0,X1,X2)),f8(f9(f10,sK233(X0,X1,X2)),sK234(X0,X1,X2))) )
& ( f11(f12,X0) = sK235(X0,X1,X2) )
& ( f11(f12,X1) = sK234(X0,X1,X2) )
& ( f11(f12,X2) = sK233(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1315,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ( $less(f8(f9(f10,X5),X4),f8(f9(f10,X3),X4))
| ~ $less(X5,X3)
| ~ $less(0,X4) )
& ( ( $less(X5,X3)
& $less(0,X4) )
| ~ $less(f8(f9(f10,X5),X4),f8(f9(f10,X3),X4)) )
& ( f11(f12,X0) = X5 )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X2) = X3 ) ),
inference(flattening,[],[f1314]) ).
tff(f1314,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ( $less(f8(f9(f10,X5),X4),f8(f9(f10,X3),X4))
| ~ $less(X5,X3)
| ~ $less(0,X4) )
& ( ( $less(X5,X3)
& $less(0,X4) )
| ~ $less(f8(f9(f10,X5),X4),f8(f9(f10,X3),X4)) )
& ( f11(f12,X0) = X5 )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X2) = X3 ) ),
inference(nnf_transformation,[],[f765]) ).
tff(f765,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ( $less(f8(f9(f10,X5),X4),f8(f9(f10,X3),X4))
<=> ( $less(X5,X3)
& $less(0,X4) ) )
& ( f11(f12,X0) = X5 )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X2) = X3 ) ),
inference(rectify,[],[f153]) ).
tff(f153,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X60: $int,X61: $int,X62: $int] :
( ( $less(f8(f9(f10,X62),X61),f8(f9(f10,X60),X61))
<=> ( $less(X62,X60)
& $less(0,X61) ) )
& ( f11(f12,X0) = X62 )
& ( f11(f12,X1) = X61 )
& ( f11(f12,X2) = X60 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_153) ).
tff(f3874,plain,
spl331_218,
inference(avatar_split_clause,[],[f2784,f3872]) ).
tff(f3872,plain,
( spl331_218
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK234(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_218])]) ).
tff(f2784,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK234(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2118,f1580]) ).
tff(f2118,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK234(X0,X1,X2) ),
inference(cnf_transformation,[],[f1317]) ).
tff(f3870,plain,
spl331_217,
inference(avatar_split_clause,[],[f2783,f3868]) ).
tff(f3868,plain,
( spl331_217
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK235(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_217])]) ).
tff(f2783,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK235(X0,X1,X2) ),
inference(forward_demodulation,[],[f2119,f1580]) ).
tff(f2119,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK235(X0,X1,X2) ),
inference(cnf_transformation,[],[f1317]) ).
tff(f3866,plain,
spl331_216,
inference(avatar_split_clause,[],[f2782,f3864]) ).
tff(f3864,plain,
( spl331_216
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK230(X0,X1,X2) = sK27(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_216])]) ).
tff(f2782,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK230(X0,X1,X2) = sK27(X2) ),
inference(forward_demodulation,[],[f2111,f1580]) ).
tff(f2111,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X2) = sK230(X0,X1,X2) ),
inference(cnf_transformation,[],[f1313]) ).
tff(f1313,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( ~ $less(f8(f9(f10,sK230(X0,X1,X2)),sK231(X0,X1,X2)),f8(f9(f10,sK232(X0,X1,X2)),sK231(X0,X1,X2)))
| ( $less(sK230(X0,X1,X2),sK232(X0,X1,X2))
& $less(0,sK231(X0,X1,X2)) ) )
& ( ~ $less(sK230(X0,X1,X2),sK232(X0,X1,X2))
| ~ $less(0,sK231(X0,X1,X2))
| $less(f8(f9(f10,sK230(X0,X1,X2)),sK231(X0,X1,X2)),f8(f9(f10,sK232(X0,X1,X2)),sK231(X0,X1,X2))) )
& ( f11(f12,X0) = sK232(X0,X1,X2) )
& ( f11(f12,X1) = sK231(X0,X1,X2) )
& ( f11(f12,X2) = sK230(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK230,sK231,sK232])],[f1311,f1312]) ).
tff(f1312,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: $int,X4: $int,X5: $int] :
( ( ~ $less(f8(f9(f10,X3),X4),f8(f9(f10,X5),X4))
| ( $less(X3,X5)
& $less(0,X4) ) )
& ( ~ $less(X3,X5)
| ~ $less(0,X4)
| $less(f8(f9(f10,X3),X4),f8(f9(f10,X5),X4)) )
& ( f11(f12,X0) = X5 )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X2) = X3 ) )
=> ( ( ~ $less(f8(f9(f10,sK230(X0,X1,X2)),sK231(X0,X1,X2)),f8(f9(f10,sK232(X0,X1,X2)),sK231(X0,X1,X2)))
| ( $less(sK230(X0,X1,X2),sK232(X0,X1,X2))
& $less(0,sK231(X0,X1,X2)) ) )
& ( ~ $less(sK230(X0,X1,X2),sK232(X0,X1,X2))
| ~ $less(0,sK231(X0,X1,X2))
| $less(f8(f9(f10,sK230(X0,X1,X2)),sK231(X0,X1,X2)),f8(f9(f10,sK232(X0,X1,X2)),sK231(X0,X1,X2))) )
& ( f11(f12,X0) = sK232(X0,X1,X2) )
& ( f11(f12,X1) = sK231(X0,X1,X2) )
& ( f11(f12,X2) = sK230(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1311,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ( ~ $less(f8(f9(f10,X3),X4),f8(f9(f10,X5),X4))
| ( $less(X3,X5)
& $less(0,X4) ) )
& ( ~ $less(X3,X5)
| ~ $less(0,X4)
| $less(f8(f9(f10,X3),X4),f8(f9(f10,X5),X4)) )
& ( f11(f12,X0) = X5 )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X2) = X3 ) ),
inference(flattening,[],[f1310]) ).
tff(f1310,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ( ~ $less(f8(f9(f10,X3),X4),f8(f9(f10,X5),X4))
| ( $less(X3,X5)
& $less(0,X4) ) )
& ( ~ $less(X3,X5)
| ~ $less(0,X4)
| $less(f8(f9(f10,X3),X4),f8(f9(f10,X5),X4)) )
& ( f11(f12,X0) = X5 )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X2) = X3 ) ),
inference(nnf_transformation,[],[f886]) ).
tff(f886,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ( ~ $less(f8(f9(f10,X3),X4),f8(f9(f10,X5),X4))
<=> ( ~ $less(X3,X5)
| ~ $less(0,X4) ) )
& ( f11(f12,X0) = X5 )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X2) = X3 ) ),
inference(ennf_transformation,[],[f764]) ).
tff(f764,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ( ~ $less(f8(f9(f10,X3),X4),f8(f9(f10,X5),X4))
<=> ( $less(0,X4)
=> ~ $less(X3,X5) ) )
& ( f11(f12,X0) = X5 )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X2) = X3 ) ),
inference(rectify,[],[f531]) ).
tff(f531,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X67: $int,X68: $int,X69: $int] :
( ( ~ $less(f8(f9(f10,X67),X68),f8(f9(f10,X69),X68))
<=> ( $less(0,X68)
=> ~ $less(X67,X69) ) )
& ( f11(f12,X0) = X69 )
& ( f11(f12,X1) = X68 )
& ( f11(f12,X2) = X67 ) ),
inference(theory_normalization,[],[f155]) ).
tff(f155,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X67: $int,X68: $int,X69: $int] :
( ( $lesseq(f8(f9(f10,X69),X68),f8(f9(f10,X67),X68))
<=> ( $less(0,X68)
=> $lesseq(X69,X67) ) )
& ( f11(f12,X0) = X69 )
& ( f11(f12,X1) = X68 )
& ( f11(f12,X2) = X67 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_155) ).
tff(f3862,plain,
spl331_215,
inference(avatar_split_clause,[],[f2781,f3860]) ).
tff(f3860,plain,
( spl331_215
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK231(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_215])]) ).
tff(f2781,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK231(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2112,f1580]) ).
tff(f2112,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK231(X0,X1,X2) ),
inference(cnf_transformation,[],[f1313]) ).
tff(f3858,plain,
spl331_214,
inference(avatar_split_clause,[],[f2780,f3856]) ).
tff(f3856,plain,
( spl331_214
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK232(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_214])]) ).
tff(f2780,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK232(X0,X1,X2) ),
inference(forward_demodulation,[],[f2113,f1580]) ).
tff(f2113,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK232(X0,X1,X2) ),
inference(cnf_transformation,[],[f1313]) ).
tff(f3854,plain,
( spl331_213
| ~ spl331_66
| ~ spl331_124 ),
inference(avatar_split_clause,[],[f3471,f3468,f3212,f3852]) ).
tff(f3852,plain,
( spl331_213
<=> ! [X1: $real] : ( 0.0 = sK22(sK18(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_213])]) ).
tff(f3468,plain,
( spl331_124
<=> ! [X0: $real] : ( 0.0 = f27(f36,sK18(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_124])]) ).
tff(f3471,plain,
( ! [X1: $real] : ( 0.0 = sK22(sK18(X1)) )
| ~ spl331_66
| ~ spl331_124 ),
inference(superposition,[],[f3469,f3213]) ).
tff(f3469,plain,
( ! [X0: $real] : ( 0.0 = f27(f36,sK18(X0)) )
| ~ spl331_124 ),
inference(avatar_component_clause,[],[f3468]) ).
tff(f3850,plain,
spl331_212,
inference(avatar_split_clause,[],[f2779,f3848]) ).
tff(f3848,plain,
( spl331_212
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK227(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_212])]) ).
tff(f2779,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK227(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2107,f1580]) ).
tff(f2107,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK227(X0,X1,X2) ),
inference(cnf_transformation,[],[f1309]) ).
tff(f1309,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( $less(f8(f9(f10,sK228(X0,X1,X2)),sK229(X0,X1,X2)),f8(f9(f10,sK227(X0,X1,X2)),sK229(X0,X1,X2)))
| ~ $less(0,sK229(X0,X1,X2))
| ~ $less(sK228(X0,X1,X2),sK227(X0,X1,X2)) )
& ( f11(f12,X2) = sK229(X0,X1,X2) )
& ( f11(f12,X0) = sK228(X0,X1,X2) )
& ( f11(f12,X1) = sK227(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK227,sK228,sK229])],[f885,f1308]) ).
tff(f1308,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: $int,X4: $int,X5: $int] :
( ( $less(f8(f9(f10,X4),X5),f8(f9(f10,X3),X5))
| ~ $less(0,X5)
| ~ $less(X4,X3) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) )
=> ( ( $less(f8(f9(f10,sK228(X0,X1,X2)),sK229(X0,X1,X2)),f8(f9(f10,sK227(X0,X1,X2)),sK229(X0,X1,X2)))
| ~ $less(0,sK229(X0,X1,X2))
| ~ $less(sK228(X0,X1,X2),sK227(X0,X1,X2)) )
& ( f11(f12,X2) = sK229(X0,X1,X2) )
& ( f11(f12,X0) = sK228(X0,X1,X2) )
& ( f11(f12,X1) = sK227(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f885,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ( $less(f8(f9(f10,X4),X5),f8(f9(f10,X3),X5))
| ~ $less(0,X5)
| ~ $less(X4,X3) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) ),
inference(flattening,[],[f884]) ).
tff(f884,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ( $less(f8(f9(f10,X4),X5),f8(f9(f10,X3),X5))
| ~ $less(0,X5)
| ~ $less(X4,X3) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) ),
inference(ennf_transformation,[],[f763]) ).
tff(f763,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ( $less(X4,X3)
=> ( $less(0,X5)
=> $less(f8(f9(f10,X4),X5),f8(f9(f10,X3),X5)) ) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) ),
inference(rectify,[],[f163]) ).
tff(f163,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X85: $int,X86: $int,X87: $int] :
( ( $less(X86,X85)
=> ( $less(0,X87)
=> $less(f8(f9(f10,X86),X87),f8(f9(f10,X85),X87)) ) )
& ( f11(f12,X2) = X87 )
& ( f11(f12,X0) = X86 )
& ( f11(f12,X1) = X85 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_163) ).
tff(f3846,plain,
spl331_211,
inference(avatar_split_clause,[],[f2778,f3844]) ).
tff(f3844,plain,
( spl331_211
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK228(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_211])]) ).
tff(f2778,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK228(X0,X1,X2) ),
inference(forward_demodulation,[],[f2108,f1580]) ).
tff(f2108,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK228(X0,X1,X2) ),
inference(cnf_transformation,[],[f1309]) ).
tff(f3842,plain,
spl331_210,
inference(avatar_split_clause,[],[f2777,f3840]) ).
tff(f3840,plain,
( spl331_210
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK229(X0,X1,X2) = sK27(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_210])]) ).
tff(f2777,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK229(X0,X1,X2) = sK27(X2) ),
inference(forward_demodulation,[],[f2109,f1580]) ).
tff(f2109,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X2) = sK229(X0,X1,X2) ),
inference(cnf_transformation,[],[f1309]) ).
tff(f3838,plain,
spl331_209,
inference(avatar_split_clause,[],[f2776,f3836]) ).
tff(f3836,plain,
( spl331_209
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK224(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_209])]) ).
tff(f2776,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK224(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2103,f1580]) ).
tff(f2103,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK224(X0,X1,X2) ),
inference(cnf_transformation,[],[f1307]) ).
tff(f1307,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( ~ $less(f8(f9(f10,sK224(X0,X1,X2)),sK226(X0,X1,X2)),f8(f9(f10,sK225(X0,X1,X2)),sK226(X0,X1,X2)))
| $less(sK224(X0,X1,X2),sK225(X0,X1,X2)) )
& ( f11(f12,X2) = sK226(X0,X1,X2) )
& ( f11(f12,X0) = sK225(X0,X1,X2) )
& ( f11(f12,X1) = sK224(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK224,sK225,sK226])],[f883,f1306]) ).
tff(f1306,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: $int,X4: $int,X5: $int] :
( ( ~ $less(f8(f9(f10,X3),X5),f8(f9(f10,X4),X5))
| $less(X3,X4) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) )
=> ( ( ~ $less(f8(f9(f10,sK224(X0,X1,X2)),sK226(X0,X1,X2)),f8(f9(f10,sK225(X0,X1,X2)),sK226(X0,X1,X2)))
| $less(sK224(X0,X1,X2),sK225(X0,X1,X2)) )
& ( f11(f12,X2) = sK226(X0,X1,X2) )
& ( f11(f12,X0) = sK225(X0,X1,X2) )
& ( f11(f12,X1) = sK224(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f883,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ( ~ $less(f8(f9(f10,X3),X5),f8(f9(f10,X4),X5))
| $less(X3,X4) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) ),
inference(ennf_transformation,[],[f762]) ).
tff(f762,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ( ~ $less(X3,X4)
=> ~ $less(f8(f9(f10,X3),X5),f8(f9(f10,X4),X5)) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) ),
inference(rectify,[],[f530]) ).
tff(f530,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X79: $int,X80: $int,X81: $int] :
( ( ~ $less(X79,X80)
=> ~ $less(f8(f9(f10,X79),X81),f8(f9(f10,X80),X81)) )
& ( f11(f12,X2) = X81 )
& ( f11(f12,X0) = X80 )
& ( f11(f12,X1) = X79 ) ),
inference(theory_normalization,[],[f161]) ).
tff(f161,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X79: $int,X80: $int,X81: $int] :
( ( $lesseq(X80,X79)
=> $lesseq(f8(f9(f10,X80),X81),f8(f9(f10,X79),X81)) )
& ( f11(f12,X2) = X81 )
& ( f11(f12,X0) = X80 )
& ( f11(f12,X1) = X79 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_161) ).
tff(f3834,plain,
spl331_208,
inference(avatar_split_clause,[],[f2775,f3832]) ).
tff(f3832,plain,
( spl331_208
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK225(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_208])]) ).
tff(f2775,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK225(X0,X1,X2) ),
inference(forward_demodulation,[],[f2104,f1580]) ).
tff(f2104,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK225(X0,X1,X2) ),
inference(cnf_transformation,[],[f1307]) ).
tff(f3830,plain,
spl331_207,
inference(avatar_split_clause,[],[f2774,f3828]) ).
tff(f3828,plain,
( spl331_207
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK226(X0,X1,X2) = sK27(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_207])]) ).
tff(f2774,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK226(X0,X1,X2) = sK27(X2) ),
inference(forward_demodulation,[],[f2105,f1580]) ).
tff(f2105,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X2) = sK226(X0,X1,X2) ),
inference(cnf_transformation,[],[f1307]) ).
tff(f3826,plain,
spl331_206,
inference(avatar_split_clause,[],[f2773,f3824]) ).
tff(f3824,plain,
( spl331_206
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK221(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_206])]) ).
tff(f2773,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK221(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2099,f1580]) ).
tff(f2099,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK221(X0,X1,X2) ),
inference(cnf_transformation,[],[f1305]) ).
tff(f1305,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( f6(f7,f8(f9(f10,f11(f12,f6(f7,$sum(sK222(X0,X1,X2),$uminus(sK221(X0,X1,X2)))))),sK223(X0,X1,X2))) = f6(f7,$sum(f8(f9(f10,sK222(X0,X1,X2)),sK223(X0,X1,X2)),$uminus(f8(f9(f10,sK221(X0,X1,X2)),sK223(X0,X1,X2))))) )
& ( f11(f12,X2) = sK223(X0,X1,X2) )
& ( f11(f12,X0) = sK222(X0,X1,X2) )
& ( f11(f12,X1) = sK221(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK221,sK222,sK223])],[f761,f1304]) ).
tff(f1304,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: $int,X4: $int,X5: $int] :
( ( f6(f7,f8(f9(f10,f11(f12,f6(f7,$sum(X4,$uminus(X3))))),X5)) = f6(f7,$sum(f8(f9(f10,X4),X5),$uminus(f8(f9(f10,X3),X5)))) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) )
=> ( ( f6(f7,f8(f9(f10,f11(f12,f6(f7,$sum(sK222(X0,X1,X2),$uminus(sK221(X0,X1,X2)))))),sK223(X0,X1,X2))) = f6(f7,$sum(f8(f9(f10,sK222(X0,X1,X2)),sK223(X0,X1,X2)),$uminus(f8(f9(f10,sK221(X0,X1,X2)),sK223(X0,X1,X2))))) )
& ( f11(f12,X2) = sK223(X0,X1,X2) )
& ( f11(f12,X0) = sK222(X0,X1,X2) )
& ( f11(f12,X1) = sK221(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f761,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ( f6(f7,f8(f9(f10,f11(f12,f6(f7,$sum(X4,$uminus(X3))))),X5)) = f6(f7,$sum(f8(f9(f10,X4),X5),$uminus(f8(f9(f10,X3),X5)))) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X0) = X4 )
& ( f11(f12,X1) = X3 ) ),
inference(rectify,[],[f529]) ).
tff(f529,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X52: $int,X53: $int,X54: $int] :
( ( f6(f7,f8(f9(f10,f11(f12,f6(f7,$sum(X53,$uminus(X52))))),X54)) = f6(f7,$sum(f8(f9(f10,X53),X54),$uminus(f8(f9(f10,X52),X54)))) )
& ( f11(f12,X2) = X54 )
& ( f11(f12,X0) = X53 )
& ( f11(f12,X1) = X52 ) ),
inference(theory_normalization,[],[f150]) ).
tff(f150,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X52: $int,X53: $int,X54: $int] :
( ( f6(f7,f8(f9(f10,f11(f12,f6(f7,$difference(X53,X52)))),X54)) = f6(f7,$difference(f8(f9(f10,X53),X54),f8(f9(f10,X52),X54))) )
& ( f11(f12,X2) = X54 )
& ( f11(f12,X0) = X53 )
& ( f11(f12,X1) = X52 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_150) ).
tff(f3822,plain,
spl331_205,
inference(avatar_split_clause,[],[f2772,f3820]) ).
tff(f3820,plain,
( spl331_205
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK222(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_205])]) ).
tff(f2772,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK222(X0,X1,X2) ),
inference(forward_demodulation,[],[f2100,f1580]) ).
tff(f2100,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK222(X0,X1,X2) ),
inference(cnf_transformation,[],[f1305]) ).
tff(f3818,plain,
spl331_204,
inference(avatar_split_clause,[],[f2771,f3816]) ).
tff(f3816,plain,
( spl331_204
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK223(X0,X1,X2) = sK27(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_204])]) ).
tff(f2771,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK223(X0,X1,X2) = sK27(X2) ),
inference(forward_demodulation,[],[f2101,f1580]) ).
tff(f2101,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X2) = sK223(X0,X1,X2) ),
inference(cnf_transformation,[],[f1305]) ).
tff(f3814,plain,
spl331_203,
inference(avatar_split_clause,[],[f2768,f3812]) ).
tff(f3812,plain,
( spl331_203
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK218(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_203])]) ).
tff(f2768,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK218(X0,X1,X2) ),
inference(forward_demodulation,[],[f2095,f1580]) ).
tff(f2095,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK218(X0,X1,X2) ),
inference(cnf_transformation,[],[f1303]) ).
tff(f1303,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( f6(f7,f8(f9(f10,$sum(sK218(X0,X1,X2),sK219(X0,X1,X2))),sK220(X0,X1,X2))) = f6(f7,$sum(f8(f9(f10,sK218(X0,X1,X2)),sK220(X0,X1,X2)),f8(f9(f10,sK219(X0,X1,X2)),sK220(X0,X1,X2)))) )
& ( f11(f12,X2) = sK220(X0,X1,X2) )
& ( f11(f12,X1) = sK219(X0,X1,X2) )
& ( f11(f12,X0) = sK218(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK218,sK219,sK220])],[f760,f1302]) ).
tff(f1302,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: $int,X4: $int,X5: $int] :
( ( f6(f7,f8(f9(f10,$sum(X3,X4)),X5)) = f6(f7,$sum(f8(f9(f10,X3),X5),f8(f9(f10,X4),X5))) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 ) )
=> ( ( f6(f7,f8(f9(f10,$sum(sK218(X0,X1,X2),sK219(X0,X1,X2))),sK220(X0,X1,X2))) = f6(f7,$sum(f8(f9(f10,sK218(X0,X1,X2)),sK220(X0,X1,X2)),f8(f9(f10,sK219(X0,X1,X2)),sK220(X0,X1,X2)))) )
& ( f11(f12,X2) = sK220(X0,X1,X2) )
& ( f11(f12,X1) = sK219(X0,X1,X2) )
& ( f11(f12,X0) = sK218(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f760,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int,X4: $int,X5: $int] :
( ( f6(f7,f8(f9(f10,$sum(X3,X4)),X5)) = f6(f7,$sum(f8(f9(f10,X3),X5),f8(f9(f10,X4),X5))) )
& ( f11(f12,X2) = X5 )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 ) ),
inference(rectify,[],[f149]) ).
tff(f149,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X49: $int,X50: $int,X51: $int] :
( ( f6(f7,f8(f9(f10,$sum(X49,X50)),X51)) = f6(f7,$sum(f8(f9(f10,X49),X51),f8(f9(f10,X50),X51))) )
& ( f11(f12,X2) = X51 )
& ( f11(f12,X1) = X50 )
& ( f11(f12,X0) = X49 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_149) ).
tff(f3810,plain,
( spl331_202
| ~ spl331_66
| ~ spl331_122 ),
inference(avatar_split_clause,[],[f3460,f3457,f3212,f3808]) ).
tff(f3808,plain,
( spl331_202
<=> ! [X1: 'S2'] : ( 0.0 = sK22(sK17(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_202])]) ).
tff(f3457,plain,
( spl331_122
<=> ! [X0: 'S2'] : ( 0.0 = f27(f36,sK17(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_122])]) ).
tff(f3460,plain,
( ! [X1: 'S2'] : ( 0.0 = sK22(sK17(X1)) )
| ~ spl331_66
| ~ spl331_122 ),
inference(superposition,[],[f3458,f3213]) ).
tff(f3458,plain,
( ! [X0: 'S2'] : ( 0.0 = f27(f36,sK17(X0)) )
| ~ spl331_122 ),
inference(avatar_component_clause,[],[f3457]) ).
tff(f3806,plain,
spl331_201,
inference(avatar_split_clause,[],[f2767,f3804]) ).
tff(f3804,plain,
( spl331_201
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK219(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_201])]) ).
tff(f2767,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK219(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2096,f1580]) ).
tff(f2096,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK219(X0,X1,X2) ),
inference(cnf_transformation,[],[f1303]) ).
tff(f3802,plain,
spl331_200,
inference(avatar_split_clause,[],[f2766,f3800]) ).
tff(f3800,plain,
( spl331_200
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK220(X0,X1,X2) = sK27(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_200])]) ).
tff(f2766,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK220(X0,X1,X2) = sK27(X2) ),
inference(forward_demodulation,[],[f2097,f1580]) ).
tff(f2097,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X2) = sK220(X0,X1,X2) ),
inference(cnf_transformation,[],[f1303]) ).
tff(f3798,plain,
spl331_199,
inference(avatar_split_clause,[],[f2752,f3796]) ).
tff(f3796,plain,
( spl331_199
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK202(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_199])]) ).
tff(f2752,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK202(X0,X1,X2) ),
inference(forward_demodulation,[],[f2066,f1580]) ).
tff(f2066,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK202(X0,X1,X2) ),
inference(cnf_transformation,[],[f1283]) ).
tff(f1283,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( $less(f8(sK203(X0,X1,X2),sK205(X0,X1,X2)),f8(sK203(X0,X1,X2),sK204(X0,X1,X2)))
| ~ $less(sK205(X0,X1,X2),sK204(X0,X1,X2))
| ~ $less(0,sK202(X0,X1,X2)) )
& ( ( $less(sK205(X0,X1,X2),sK204(X0,X1,X2))
& $less(0,sK202(X0,X1,X2)) )
| ~ $less(f8(sK203(X0,X1,X2),sK205(X0,X1,X2)),f8(sK203(X0,X1,X2),sK204(X0,X1,X2))) )
& ( f11(f12,X1) = sK205(X0,X1,X2) )
& ( f11(f12,X2) = sK204(X0,X1,X2) )
& ( f9(f10,sK202(X0,X1,X2)) = sK203(X0,X1,X2) )
& ( f11(f12,X0) = sK202(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK202,sK203,sK204,sK205])],[f1280,f1282,f1281]) ).
tff(f1281,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: $int] :
( ? [X4: 'S6',X5: $int,X6: $int] :
( ( $less(f8(X4,X6),f8(X4,X5))
| ~ $less(X6,X5)
| ~ $less(0,X3) )
& ( ( $less(X6,X5)
& $less(0,X3) )
| ~ $less(f8(X4,X6),f8(X4,X5)) )
& ( f11(f12,X1) = X6 )
& ( f11(f12,X2) = X5 )
& ( f9(f10,X3) = X4 ) )
& ( f11(f12,X0) = X3 ) )
=> ( ? [X6: $int,X5: $int,X4: 'S6'] :
( ( $less(f8(X4,X6),f8(X4,X5))
| ~ $less(X6,X5)
| ~ $less(0,sK202(X0,X1,X2)) )
& ( ( $less(X6,X5)
& $less(0,sK202(X0,X1,X2)) )
| ~ $less(f8(X4,X6),f8(X4,X5)) )
& ( f11(f12,X1) = X6 )
& ( f11(f12,X2) = X5 )
& ( f9(f10,sK202(X0,X1,X2)) = X4 ) )
& ( f11(f12,X0) = sK202(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1282,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X6: $int,X5: $int,X4: 'S6'] :
( ( $less(f8(X4,X6),f8(X4,X5))
| ~ $less(X6,X5)
| ~ $less(0,sK202(X0,X1,X2)) )
& ( ( $less(X6,X5)
& $less(0,sK202(X0,X1,X2)) )
| ~ $less(f8(X4,X6),f8(X4,X5)) )
& ( f11(f12,X1) = X6 )
& ( f11(f12,X2) = X5 )
& ( f9(f10,sK202(X0,X1,X2)) = X4 ) )
=> ( ( $less(f8(sK203(X0,X1,X2),sK205(X0,X1,X2)),f8(sK203(X0,X1,X2),sK204(X0,X1,X2)))
| ~ $less(sK205(X0,X1,X2),sK204(X0,X1,X2))
| ~ $less(0,sK202(X0,X1,X2)) )
& ( ( $less(sK205(X0,X1,X2),sK204(X0,X1,X2))
& $less(0,sK202(X0,X1,X2)) )
| ~ $less(f8(sK203(X0,X1,X2),sK205(X0,X1,X2)),f8(sK203(X0,X1,X2),sK204(X0,X1,X2))) )
& ( f11(f12,X1) = sK205(X0,X1,X2) )
& ( f11(f12,X2) = sK204(X0,X1,X2) )
& ( f9(f10,sK202(X0,X1,X2)) = sK203(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1280,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int] :
( ? [X4: 'S6',X5: $int,X6: $int] :
( ( $less(f8(X4,X6),f8(X4,X5))
| ~ $less(X6,X5)
| ~ $less(0,X3) )
& ( ( $less(X6,X5)
& $less(0,X3) )
| ~ $less(f8(X4,X6),f8(X4,X5)) )
& ( f11(f12,X1) = X6 )
& ( f11(f12,X2) = X5 )
& ( f9(f10,X3) = X4 ) )
& ( f11(f12,X0) = X3 ) ),
inference(flattening,[],[f1279]) ).
tff(f1279,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int] :
( ? [X4: 'S6',X5: $int,X6: $int] :
( ( $less(f8(X4,X6),f8(X4,X5))
| ~ $less(X6,X5)
| ~ $less(0,X3) )
& ( ( $less(X6,X5)
& $less(0,X3) )
| ~ $less(f8(X4,X6),f8(X4,X5)) )
& ( f11(f12,X1) = X6 )
& ( f11(f12,X2) = X5 )
& ( f9(f10,X3) = X4 ) )
& ( f11(f12,X0) = X3 ) ),
inference(nnf_transformation,[],[f752]) ).
tff(f752,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int] :
( ? [X4: 'S6',X5: $int,X6: $int] :
( ( $less(f8(X4,X6),f8(X4,X5))
<=> ( $less(X6,X5)
& $less(0,X3) ) )
& ( f11(f12,X1) = X6 )
& ( f11(f12,X2) = X5 )
& ( f9(f10,X3) = X4 ) )
& ( f11(f12,X0) = X3 ) ),
inference(rectify,[],[f152]) ).
tff(f152,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X56: $int] :
( ? [X57: 'S6',X58: $int,X59: $int] :
( ( $less(f8(X57,X59),f8(X57,X58))
<=> ( $less(X59,X58)
& $less(0,X56) ) )
& ( f11(f12,X1) = X59 )
& ( f11(f12,X2) = X58 )
& ( f9(f10,X56) = X57 ) )
& ( f11(f12,X0) = X56 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_152) ).
tff(f3794,plain,
spl331_198,
inference(avatar_split_clause,[],[f2751,f3792]) ).
tff(f3792,plain,
( spl331_198
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK204(X0,X1,X2) = sK27(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_198])]) ).
tff(f2751,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK204(X0,X1,X2) = sK27(X2) ),
inference(forward_demodulation,[],[f2068,f1580]) ).
tff(f2068,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X2) = sK204(X0,X1,X2) ),
inference(cnf_transformation,[],[f1283]) ).
tff(f3790,plain,
spl331_197,
inference(avatar_split_clause,[],[f2750,f3788]) ).
tff(f3788,plain,
( spl331_197
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK205(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_197])]) ).
tff(f2750,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK205(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2069,f1580]) ).
tff(f2069,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK205(X0,X1,X2) ),
inference(cnf_transformation,[],[f1283]) ).
tff(f3786,plain,
spl331_196,
inference(avatar_split_clause,[],[f2749,f3784]) ).
tff(f3784,plain,
( spl331_196
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK198(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_196])]) ).
tff(f2749,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK198(X0,X1,X2) ),
inference(forward_demodulation,[],[f2059,f1580]) ).
tff(f2059,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK198(X0,X1,X2) ),
inference(cnf_transformation,[],[f1278]) ).
tff(f1278,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( ~ $less(f8(sK199(X0,X1,X2),sK200(X0,X1,X2)),f8(sK199(X0,X1,X2),sK201(X0,X1,X2)))
| ( $less(sK200(X0,X1,X2),sK201(X0,X1,X2))
& $less(0,sK198(X0,X1,X2)) ) )
& ( ~ $less(sK200(X0,X1,X2),sK201(X0,X1,X2))
| ~ $less(0,sK198(X0,X1,X2))
| $less(f8(sK199(X0,X1,X2),sK200(X0,X1,X2)),f8(sK199(X0,X1,X2),sK201(X0,X1,X2))) )
& ( f11(f12,X1) = sK201(X0,X1,X2) )
& ( f11(f12,X2) = sK200(X0,X1,X2) )
& ( f9(f10,sK198(X0,X1,X2)) = sK199(X0,X1,X2) )
& ( f11(f12,X0) = sK198(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK198,sK199,sK200,sK201])],[f1275,f1277,f1276]) ).
tff(f1276,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: $int] :
( ? [X4: 'S6',X5: $int,X6: $int] :
( ( ~ $less(f8(X4,X5),f8(X4,X6))
| ( $less(X5,X6)
& $less(0,X3) ) )
& ( ~ $less(X5,X6)
| ~ $less(0,X3)
| $less(f8(X4,X5),f8(X4,X6)) )
& ( f11(f12,X1) = X6 )
& ( f11(f12,X2) = X5 )
& ( f9(f10,X3) = X4 ) )
& ( f11(f12,X0) = X3 ) )
=> ( ? [X6: $int,X5: $int,X4: 'S6'] :
( ( ~ $less(f8(X4,X5),f8(X4,X6))
| ( $less(X5,X6)
& $less(0,sK198(X0,X1,X2)) ) )
& ( ~ $less(X5,X6)
| ~ $less(0,sK198(X0,X1,X2))
| $less(f8(X4,X5),f8(X4,X6)) )
& ( f11(f12,X1) = X6 )
& ( f11(f12,X2) = X5 )
& ( f9(f10,sK198(X0,X1,X2)) = X4 ) )
& ( f11(f12,X0) = sK198(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1277,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X6: $int,X5: $int,X4: 'S6'] :
( ( ~ $less(f8(X4,X5),f8(X4,X6))
| ( $less(X5,X6)
& $less(0,sK198(X0,X1,X2)) ) )
& ( ~ $less(X5,X6)
| ~ $less(0,sK198(X0,X1,X2))
| $less(f8(X4,X5),f8(X4,X6)) )
& ( f11(f12,X1) = X6 )
& ( f11(f12,X2) = X5 )
& ( f9(f10,sK198(X0,X1,X2)) = X4 ) )
=> ( ( ~ $less(f8(sK199(X0,X1,X2),sK200(X0,X1,X2)),f8(sK199(X0,X1,X2),sK201(X0,X1,X2)))
| ( $less(sK200(X0,X1,X2),sK201(X0,X1,X2))
& $less(0,sK198(X0,X1,X2)) ) )
& ( ~ $less(sK200(X0,X1,X2),sK201(X0,X1,X2))
| ~ $less(0,sK198(X0,X1,X2))
| $less(f8(sK199(X0,X1,X2),sK200(X0,X1,X2)),f8(sK199(X0,X1,X2),sK201(X0,X1,X2))) )
& ( f11(f12,X1) = sK201(X0,X1,X2) )
& ( f11(f12,X2) = sK200(X0,X1,X2) )
& ( f9(f10,sK198(X0,X1,X2)) = sK199(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1275,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int] :
( ? [X4: 'S6',X5: $int,X6: $int] :
( ( ~ $less(f8(X4,X5),f8(X4,X6))
| ( $less(X5,X6)
& $less(0,X3) ) )
& ( ~ $less(X5,X6)
| ~ $less(0,X3)
| $less(f8(X4,X5),f8(X4,X6)) )
& ( f11(f12,X1) = X6 )
& ( f11(f12,X2) = X5 )
& ( f9(f10,X3) = X4 ) )
& ( f11(f12,X0) = X3 ) ),
inference(flattening,[],[f1274]) ).
tff(f1274,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int] :
( ? [X4: 'S6',X5: $int,X6: $int] :
( ( ~ $less(f8(X4,X5),f8(X4,X6))
| ( $less(X5,X6)
& $less(0,X3) ) )
& ( ~ $less(X5,X6)
| ~ $less(0,X3)
| $less(f8(X4,X5),f8(X4,X6)) )
& ( f11(f12,X1) = X6 )
& ( f11(f12,X2) = X5 )
& ( f9(f10,X3) = X4 ) )
& ( f11(f12,X0) = X3 ) ),
inference(nnf_transformation,[],[f882]) ).
tff(f882,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int] :
( ? [X4: 'S6',X5: $int,X6: $int] :
( ( ~ $less(f8(X4,X5),f8(X4,X6))
<=> ( ~ $less(X5,X6)
| ~ $less(0,X3) ) )
& ( f11(f12,X1) = X6 )
& ( f11(f12,X2) = X5 )
& ( f9(f10,X3) = X4 ) )
& ( f11(f12,X0) = X3 ) ),
inference(ennf_transformation,[],[f751]) ).
tff(f751,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int] :
( ? [X4: 'S6',X5: $int,X6: $int] :
( ( ~ $less(f8(X4,X5),f8(X4,X6))
<=> ( $less(0,X3)
=> ~ $less(X5,X6) ) )
& ( f11(f12,X1) = X6 )
& ( f11(f12,X2) = X5 )
& ( f9(f10,X3) = X4 ) )
& ( f11(f12,X0) = X3 ) ),
inference(rectify,[],[f528]) ).
tff(f528,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X63: $int] :
( ? [X64: 'S6',X65: $int,X66: $int] :
( ( ~ $less(f8(X64,X65),f8(X64,X66))
<=> ( $less(0,X63)
=> ~ $less(X65,X66) ) )
& ( f11(f12,X1) = X66 )
& ( f11(f12,X2) = X65 )
& ( f9(f10,X63) = X64 ) )
& ( f11(f12,X0) = X63 ) ),
inference(theory_normalization,[],[f154]) ).
tff(f154,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X63: $int] :
( ? [X64: 'S6',X65: $int,X66: $int] :
( ( $lesseq(f8(X64,X66),f8(X64,X65))
<=> ( $less(0,X63)
=> $lesseq(X66,X65) ) )
& ( f11(f12,X1) = X66 )
& ( f11(f12,X2) = X65 )
& ( f9(f10,X63) = X64 ) )
& ( f11(f12,X0) = X63 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_154) ).
tff(f3782,plain,
spl331_195,
inference(avatar_split_clause,[],[f2748,f3780]) ).
tff(f3780,plain,
( spl331_195
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK200(X0,X1,X2) = sK27(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_195])]) ).
tff(f2748,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK200(X0,X1,X2) = sK27(X2) ),
inference(forward_demodulation,[],[f2061,f1580]) ).
tff(f2061,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X2) = sK200(X0,X1,X2) ),
inference(cnf_transformation,[],[f1278]) ).
tff(f3778,plain,
spl331_194,
inference(avatar_split_clause,[],[f2747,f3776]) ).
tff(f3776,plain,
( spl331_194
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK201(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_194])]) ).
tff(f2747,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK201(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2062,f1580]) ).
tff(f2062,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK201(X0,X1,X2) ),
inference(cnf_transformation,[],[f1278]) ).
tff(f3774,plain,
spl331_193,
inference(avatar_split_clause,[],[f2746,f3772]) ).
tff(f3772,plain,
( spl331_193
<=> ! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK197(X0,X1,X2) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_193])]) ).
tff(f2746,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( sK197(X0,X1,X2) = sK27(X1) ),
inference(forward_demodulation,[],[f2055,f1580]) ).
tff(f2055,plain,
! [X2: 'S2',X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK197(X0,X1,X2) ),
inference(cnf_transformation,[],[f1273]) ).
tff(f1273,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),sK197(X0,X1,X2))) = f6(f7,f8(f9(f10,f11(f12,X2)),sK197(X0,X1,X2))) )
| ( ( f6(f7,0) != X1 )
& ( X0 != X2 ) ) )
& ( ( f6(f7,0) = X1 )
| ( X0 = X2 )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),sK197(X0,X1,X2))) != f6(f7,f8(f9(f10,f11(f12,X2)),sK197(X0,X1,X2))) ) )
& ( f11(f12,X1) = sK197(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK197])],[f1271,f1272]) ).
tff(f1272,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
( ? [X3: $int] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),X3)) = f6(f7,f8(f9(f10,f11(f12,X2)),X3)) )
| ( ( f6(f7,0) != X1 )
& ( X0 != X2 ) ) )
& ( ( f6(f7,0) = X1 )
| ( X0 = X2 )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),X3)) != f6(f7,f8(f9(f10,f11(f12,X2)),X3)) ) )
& ( f11(f12,X1) = X3 ) )
=> ( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),sK197(X0,X1,X2))) = f6(f7,f8(f9(f10,f11(f12,X2)),sK197(X0,X1,X2))) )
| ( ( f6(f7,0) != X1 )
& ( X0 != X2 ) ) )
& ( ( f6(f7,0) = X1 )
| ( X0 = X2 )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),sK197(X0,X1,X2))) != f6(f7,f8(f9(f10,f11(f12,X2)),sK197(X0,X1,X2))) ) )
& ( f11(f12,X1) = sK197(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1271,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),X3)) = f6(f7,f8(f9(f10,f11(f12,X2)),X3)) )
| ( ( f6(f7,0) != X1 )
& ( X0 != X2 ) ) )
& ( ( f6(f7,0) = X1 )
| ( X0 = X2 )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),X3)) != f6(f7,f8(f9(f10,f11(f12,X2)),X3)) ) )
& ( f11(f12,X1) = X3 ) ),
inference(flattening,[],[f1270]) ).
tff(f1270,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),X3)) = f6(f7,f8(f9(f10,f11(f12,X2)),X3)) )
| ( ( f6(f7,0) != X1 )
& ( X0 != X2 ) ) )
& ( ( f6(f7,0) = X1 )
| ( X0 = X2 )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),X3)) != f6(f7,f8(f9(f10,f11(f12,X2)),X3)) ) )
& ( f11(f12,X1) = X3 ) ),
inference(nnf_transformation,[],[f750]) ).
tff(f750,plain,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X3: $int] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),X3)) = f6(f7,f8(f9(f10,f11(f12,X2)),X3)) )
<=> ( ( f6(f7,0) = X1 )
| ( X0 = X2 ) ) )
& ( f11(f12,X1) = X3 ) ),
inference(rectify,[],[f157]) ).
tff(f157,axiom,
! [X0: 'S2',X1: 'S2',X2: 'S2'] :
? [X71: $int] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),X71)) = f6(f7,f8(f9(f10,f11(f12,X2)),X71)) )
<=> ( ( f6(f7,0) = X1 )
| ( X0 = X2 ) ) )
& ( f11(f12,X1) = X71 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_157) ).
tff(f3770,plain,
spl331_192,
inference(avatar_split_clause,[],[f2327,f3768]) ).
tff(f3768,plain,
( spl331_192
<=> ! [X0: 'S2',X1: 'S2'] : ( f6(f7,1) = sK101(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_192])]) ).
tff(f2327,plain,
! [X0: 'S2',X1: 'S2'] : ( f6(f7,1) = sK101(X0,X1) ),
inference(evaluation,[],[f1828]) ).
tff(f1828,plain,
! [X0: 'S2',X1: 'S2'] : ( f6(f7,$sum(0,1)) = sK101(X0,X1) ),
inference(cnf_transformation,[],[f1113]) ).
tff(f1113,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ( f3(f4(f65,X0),X1) = sK101(X0,X1) )
| ( ( sK101(X0,X1) != X0 )
& ( f6(f7,0) != X1 ) ) )
& ( ( sK101(X0,X1) = X0 )
| ( f6(f7,0) = X1 )
| ( f3(f4(f65,X0),X1) != sK101(X0,X1) ) )
& ( f6(f7,$sum(0,1)) = sK101(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK101])],[f1111,f1112]) ).
tff(f1112,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: 'S2'] :
( ( ( f3(f4(f65,X0),X1) = X2 )
| ( ( X0 != X2 )
& ( f6(f7,0) != X1 ) ) )
& ( ( X0 = X2 )
| ( f6(f7,0) = X1 )
| ( f3(f4(f65,X0),X1) != X2 ) )
& ( f6(f7,$sum(0,1)) = X2 ) )
=> ( ( ( f3(f4(f65,X0),X1) = sK101(X0,X1) )
| ( ( sK101(X0,X1) != X0 )
& ( f6(f7,0) != X1 ) ) )
& ( ( sK101(X0,X1) = X0 )
| ( f6(f7,0) = X1 )
| ( f3(f4(f65,X0),X1) != sK101(X0,X1) ) )
& ( f6(f7,$sum(0,1)) = sK101(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1111,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2'] :
( ( ( f3(f4(f65,X0),X1) = X2 )
| ( ( X0 != X2 )
& ( f6(f7,0) != X1 ) ) )
& ( ( X0 = X2 )
| ( f6(f7,0) = X1 )
| ( f3(f4(f65,X0),X1) != X2 ) )
& ( f6(f7,$sum(0,1)) = X2 ) ),
inference(flattening,[],[f1110]) ).
tff(f1110,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2'] :
( ( ( f3(f4(f65,X0),X1) = X2 )
| ( ( X0 != X2 )
& ( f6(f7,0) != X1 ) ) )
& ( ( X0 = X2 )
| ( f6(f7,0) = X1 )
| ( f3(f4(f65,X0),X1) != X2 ) )
& ( f6(f7,$sum(0,1)) = X2 ) ),
inference(nnf_transformation,[],[f679]) ).
tff(f679,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2'] :
( ( ( f3(f4(f65,X0),X1) = X2 )
<=> ( ( X0 = X2 )
| ( f6(f7,0) = X1 ) ) )
& ( f6(f7,$sum(0,1)) = X2 ) ),
inference(rectify,[],[f445]) ).
tff(f445,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X289: 'S2'] :
( ( ( f3(f4(f65,X0),X1) = X289 )
<=> ( ( X0 = X289 )
| ( f6(f7,0) = X1 ) ) )
& ( f6(f7,$sum(0,1)) = X289 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_445) ).
tff(f3758,plain,
spl331_191,
inference(avatar_split_clause,[],[f2326,f3756]) ).
tff(f3756,plain,
( spl331_191
<=> ! [X0: 'S2',X1: 'S2'] : ( f6(f7,1) = sK102(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_191])]) ).
tff(f2326,plain,
! [X0: 'S2',X1: 'S2'] : ( f6(f7,1) = sK102(X0,X1) ),
inference(evaluation,[],[f1832]) ).
tff(f1832,plain,
! [X0: 'S2',X1: 'S2'] : ( f6(f7,$sum(0,1)) = sK102(X0,X1) ),
inference(cnf_transformation,[],[f1117]) ).
tff(f1117,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = sK102(X0,X1) )
| ( sK102(X0,X1) != X1 )
| ( sK102(X0,X1) != X0 ) )
& ( ( ( sK102(X0,X1) = X1 )
& ( sK102(X0,X1) = X0 ) )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != sK102(X0,X1) ) )
& ( f6(f7,$sum(0,1)) = sK102(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK102])],[f1115,f1116]) ).
tff(f1116,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
| ( X1 != X2 )
| ( X0 != X2 ) )
& ( ( ( X1 = X2 )
& ( X0 = X2 ) )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != X2 ) )
& ( f6(f7,$sum(0,1)) = X2 ) )
=> ( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = sK102(X0,X1) )
| ( sK102(X0,X1) != X1 )
| ( sK102(X0,X1) != X0 ) )
& ( ( ( sK102(X0,X1) = X1 )
& ( sK102(X0,X1) = X0 ) )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != sK102(X0,X1) ) )
& ( f6(f7,$sum(0,1)) = sK102(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1115,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
| ( X1 != X2 )
| ( X0 != X2 ) )
& ( ( ( X1 = X2 )
& ( X0 = X2 ) )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != X2 ) )
& ( f6(f7,$sum(0,1)) = X2 ) ),
inference(flattening,[],[f1114]) ).
tff(f1114,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
| ( X1 != X2 )
| ( X0 != X2 ) )
& ( ( ( X1 = X2 )
& ( X0 = X2 ) )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != X2 ) )
& ( f6(f7,$sum(0,1)) = X2 ) ),
inference(nnf_transformation,[],[f680]) ).
tff(f680,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
<=> ( ( X1 = X2 )
& ( X0 = X2 ) ) )
& ( f6(f7,$sum(0,1)) = X2 ) ),
inference(rectify,[],[f151]) ).
tff(f151,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X55: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X55 )
<=> ( ( X1 = X55 )
& ( X0 = X55 ) ) )
& ( f6(f7,$sum(0,1)) = X55 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_151) ).
tff(f3754,plain,
spl331_190,
inference(avatar_split_clause,[],[f2325,f3752]) ).
tff(f3752,plain,
( spl331_190
<=> ! [X0: $int,X1: $int] : ( f6(f7,2) = sK103(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_190])]) ).
tff(f2325,plain,
! [X0: $int,X1: $int] : ( f6(f7,2) = sK103(X0,X1) ),
inference(evaluation,[],[f1836]) ).
tff(f1836,plain,
! [X0: $int,X1: $int] : ( f6(f7,$sum($sum(0,1),1)) = sK103(X0,X1) ),
inference(cnf_transformation,[],[f1119]) ).
tff(f1119,plain,
! [X0: $int,X1: $int] :
( ( f8(f9(f10,$sum(X0,$uminus(X1))),$sum(X0,X1)) = $sum(f11(f63(f64,X0),sK103(X0,X1)),$uminus(f11(f63(f64,X1),sK103(X0,X1)))) )
& ( f6(f7,$sum($sum(0,1),1)) = sK103(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK103])],[f681,f1118]) ).
tff(f1118,plain,
! [X0: $int,X1: $int] :
( ? [X2: 'S2'] :
( ( f8(f9(f10,$sum(X0,$uminus(X1))),$sum(X0,X1)) = $sum(f11(f63(f64,X0),X2),$uminus(f11(f63(f64,X1),X2))) )
& ( f6(f7,$sum($sum(0,1),1)) = X2 ) )
=> ( ( f8(f9(f10,$sum(X0,$uminus(X1))),$sum(X0,X1)) = $sum(f11(f63(f64,X0),sK103(X0,X1)),$uminus(f11(f63(f64,X1),sK103(X0,X1)))) )
& ( f6(f7,$sum($sum(0,1),1)) = sK103(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f681,plain,
! [X0: $int,X1: $int] :
? [X2: 'S2'] :
( ( f8(f9(f10,$sum(X0,$uminus(X1))),$sum(X0,X1)) = $sum(f11(f63(f64,X0),X2),$uminus(f11(f63(f64,X1),X2))) )
& ( f6(f7,$sum($sum(0,1),1)) = X2 ) ),
inference(rectify,[],[f508]) ).
tff(f508,plain,
! [X0: $int,X1: $int] :
? [X261: 'S2'] :
( ( $sum(f11(f63(f64,X0),X261),$uminus(f11(f63(f64,X1),X261))) = f8(f9(f10,$sum(X0,$uminus(X1))),$sum(X0,X1)) )
& ( f6(f7,$sum($sum(0,1),1)) = X261 ) ),
inference(theory_normalization,[],[f409]) ).
tff(f409,axiom,
! [X0: $int,X1: $int] :
? [X261: 'S2'] :
( ( $difference(f11(f63(f64,X0),X261),f11(f63(f64,X1),X261)) = f8(f9(f10,$difference(X0,X1)),$sum(X0,X1)) )
& ( f6(f7,$sum($sum(0,1),1)) = X261 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_409) ).
tff(f3750,plain,
spl331_189,
inference(avatar_split_clause,[],[f2324,f3748]) ).
tff(f3748,plain,
( spl331_189
<=> ! [X0: $real,X1: $real] : ( f6(f7,2) = sK104(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_189])]) ).
tff(f2324,plain,
! [X0: $real,X1: $real] : ( f6(f7,2) = sK104(X0,X1) ),
inference(evaluation,[],[f1838]) ).
tff(f1838,plain,
! [X0: $real,X1: $real] : ( f6(f7,$sum($sum(0,1),1)) = sK104(X0,X1) ),
inference(cnf_transformation,[],[f1121]) ).
tff(f1121,plain,
! [X0: $real,X1: $real] :
( ( f22(f49(f50,$sum(X0,$uminus(X1))),$sum(X0,X1)) = $sum(f19(f59(f60,X0),sK104(X0,X1)),$uminus(f19(f59(f60,X1),sK104(X0,X1)))) )
& ( f6(f7,$sum($sum(0,1),1)) = sK104(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK104])],[f682,f1120]) ).
tff(f1120,plain,
! [X0: $real,X1: $real] :
( ? [X2: 'S2'] :
( ( f22(f49(f50,$sum(X0,$uminus(X1))),$sum(X0,X1)) = $sum(f19(f59(f60,X0),X2),$uminus(f19(f59(f60,X1),X2))) )
& ( f6(f7,$sum($sum(0,1),1)) = X2 ) )
=> ( ( f22(f49(f50,$sum(X0,$uminus(X1))),$sum(X0,X1)) = $sum(f19(f59(f60,X0),sK104(X0,X1)),$uminus(f19(f59(f60,X1),sK104(X0,X1)))) )
& ( f6(f7,$sum($sum(0,1),1)) = sK104(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f682,plain,
! [X0: $real,X1: $real] :
? [X2: 'S2'] :
( ( f22(f49(f50,$sum(X0,$uminus(X1))),$sum(X0,X1)) = $sum(f19(f59(f60,X0),X2),$uminus(f19(f59(f60,X1),X2))) )
& ( f6(f7,$sum($sum(0,1),1)) = X2 ) ),
inference(rectify,[],[f509]) ).
tff(f509,plain,
! [X0: $real,X1: $real] :
? [X260: 'S2'] :
( ( $sum(f19(f59(f60,X0),X260),$uminus(f19(f59(f60,X1),X260))) = f22(f49(f50,$sum(X0,$uminus(X1))),$sum(X0,X1)) )
& ( f6(f7,$sum($sum(0,1),1)) = X260 ) ),
inference(theory_normalization,[],[f408]) ).
tff(f408,axiom,
! [X0: $real,X1: $real] :
? [X260: 'S2'] :
( ( $difference(f19(f59(f60,X0),X260),f19(f59(f60,X1),X260)) = f22(f49(f50,$difference(X0,X1)),$sum(X0,X1)) )
& ( f6(f7,$sum($sum(0,1),1)) = X260 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_408) ).
tff(f3746,plain,
spl331_188,
inference(avatar_split_clause,[],[f2323,f3744]) ).
tff(f3744,plain,
( spl331_188
<=> ! [X0: 'S10',X1: 'S10'] : ( f6(f7,2) = sK105(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_188])]) ).
tff(f2323,plain,
! [X0: 'S10',X1: 'S10'] : ( f6(f7,2) = sK105(X0,X1) ),
inference(evaluation,[],[f1840]) ).
tff(f1840,plain,
! [X0: 'S10',X1: 'S10'] : ( f6(f7,$sum($sum(0,1),1)) = sK105(X0,X1) ),
inference(cnf_transformation,[],[f1123]) ).
tff(f1123,plain,
! [X0: 'S10',X1: 'S10'] :
( ( f34(f39(f52,f34(f39(f61,X0),X1)),f34(f39(f40,X0),X1)) = f34(f39(f61,f13(f66(f67,X0),sK105(X0,X1))),f13(f66(f67,X1),sK105(X0,X1))) )
& ( f6(f7,$sum($sum(0,1),1)) = sK105(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK105])],[f683,f1122]) ).
tff(f1122,plain,
! [X0: 'S10',X1: 'S10'] :
( ? [X2: 'S2'] :
( ( f34(f39(f52,f34(f39(f61,X0),X1)),f34(f39(f40,X0),X1)) = f34(f39(f61,f13(f66(f67,X0),X2)),f13(f66(f67,X1),X2)) )
& ( f6(f7,$sum($sum(0,1),1)) = X2 ) )
=> ( ( f34(f39(f52,f34(f39(f61,X0),X1)),f34(f39(f40,X0),X1)) = f34(f39(f61,f13(f66(f67,X0),sK105(X0,X1))),f13(f66(f67,X1),sK105(X0,X1))) )
& ( f6(f7,$sum($sum(0,1),1)) = sK105(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f683,plain,
! [X0: 'S10',X1: 'S10'] :
? [X2: 'S2'] :
( ( f34(f39(f52,f34(f39(f61,X0),X1)),f34(f39(f40,X0),X1)) = f34(f39(f61,f13(f66(f67,X0),X2)),f13(f66(f67,X1),X2)) )
& ( f6(f7,$sum($sum(0,1),1)) = X2 ) ),
inference(rectify,[],[f407]) ).
tff(f407,axiom,
! [X0: 'S10',X1: 'S10'] :
? [X259: 'S2'] :
( ( f34(f39(f61,f13(f66(f67,X0),X259)),f13(f66(f67,X1),X259)) = f34(f39(f52,f34(f39(f61,X0),X1)),f34(f39(f40,X0),X1)) )
& ( f6(f7,$sum($sum(0,1),1)) = X259 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_407) ).
tff(f3742,plain,
spl331_187,
inference(avatar_split_clause,[],[f1902,f3740]) ).
tff(f3740,plain,
( spl331_187
<=> ! [X0: 'S2',X1: 'S2'] : ( f6(f7,0) = sK142(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_187])]) ).
tff(f1902,plain,
! [X0: 'S2',X1: 'S2'] : ( f6(f7,0) = sK142(X0,X1) ),
inference(cnf_transformation,[],[f1166]) ).
tff(f1166,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ( f6(f7,f8(f9(f10,sK143(X0,X1)),sK144(X0,X1))) = f6(f7,$sum(sK144(X0,X1),f8(f9(f10,f11(f12,f6(f7,$sum(sK143(X0,X1),$uminus(1))))),sK144(X0,X1)))) )
| ( sK142(X0,X1) = X0 ) )
& ( ( sK142(X0,X1) = f6(f7,f8(f9(f10,sK143(X0,X1)),sK144(X0,X1))) )
| ( sK142(X0,X1) != X0 ) )
& ( f11(f12,X1) = sK144(X0,X1) )
& ( f11(f12,X0) = sK143(X0,X1) )
& ( f6(f7,0) = sK142(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK142,sK143,sK144])],[f872,f1165]) ).
tff(f1165,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: 'S2',X3: $int,X4: $int] :
( ( ( f6(f7,f8(f9(f10,X3),X4)) = f6(f7,$sum(X4,f8(f9(f10,f11(f12,f6(f7,$sum(X3,$uminus(1))))),X4))) )
| ( X0 = X2 ) )
& ( ( f6(f7,f8(f9(f10,X3),X4)) = X2 )
| ( X0 != X2 ) )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 )
& ( f6(f7,0) = X2 ) )
=> ( ( ( f6(f7,f8(f9(f10,sK143(X0,X1)),sK144(X0,X1))) = f6(f7,$sum(sK144(X0,X1),f8(f9(f10,f11(f12,f6(f7,$sum(sK143(X0,X1),$uminus(1))))),sK144(X0,X1)))) )
| ( sK142(X0,X1) = X0 ) )
& ( ( sK142(X0,X1) = f6(f7,f8(f9(f10,sK143(X0,X1)),sK144(X0,X1))) )
| ( sK142(X0,X1) != X0 ) )
& ( f11(f12,X1) = sK144(X0,X1) )
& ( f11(f12,X0) = sK143(X0,X1) )
& ( f6(f7,0) = sK142(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f872,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2',X3: $int,X4: $int] :
( ( ( f6(f7,f8(f9(f10,X3),X4)) = f6(f7,$sum(X4,f8(f9(f10,f11(f12,f6(f7,$sum(X3,$uminus(1))))),X4))) )
| ( X0 = X2 ) )
& ( ( f6(f7,f8(f9(f10,X3),X4)) = X2 )
| ( X0 != X2 ) )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 )
& ( f6(f7,0) = X2 ) ),
inference(ennf_transformation,[],[f702]) ).
tff(f702,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2',X3: $int,X4: $int] :
( ( ( X0 != X2 )
=> ( f6(f7,f8(f9(f10,X3),X4)) = f6(f7,$sum(X4,f8(f9(f10,f11(f12,f6(f7,$sum(X3,$uminus(1))))),X4))) ) )
& ( ( X0 = X2 )
=> ( f6(f7,f8(f9(f10,X3),X4)) = X2 ) )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 )
& ( f6(f7,0) = X2 ) ),
inference(rectify,[],[f519]) ).
tff(f519,plain,
! [X0: 'S2',X1: 'S2'] :
? [X174: 'S2',X175: $int,X176: $int] :
( ( ( X0 != X174 )
=> ( f6(f7,f8(f9(f10,X175),X176)) = f6(f7,$sum(X176,f8(f9(f10,f11(f12,f6(f7,$sum(X175,$uminus(1))))),X176))) ) )
& ( ( X0 = X174 )
=> ( f6(f7,f8(f9(f10,X175),X176)) = X174 ) )
& ( f11(f12,X1) = X176 )
& ( f11(f12,X0) = X175 )
& ( f6(f7,0) = X174 ) ),
inference(theory_normalization,[],[f278]) ).
tff(f278,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X174: 'S2',X175: $int,X176: $int] :
( ( ( X0 != X174 )
=> ( f6(f7,f8(f9(f10,X175),X176)) = f6(f7,$sum(X176,f8(f9(f10,f11(f12,f6(f7,$difference(X175,1)))),X176))) ) )
& ( ( X0 = X174 )
=> ( f6(f7,f8(f9(f10,X175),X176)) = X174 ) )
& ( f11(f12,X1) = X176 )
& ( f11(f12,X0) = X175 )
& ( f6(f7,0) = X174 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_278) ).
tff(f3738,plain,
spl331_186,
inference(avatar_split_clause,[],[f1867,f3736]) ).
tff(f3736,plain,
( spl331_186
<=> ! [X0: 'S2',X1: 'S2'] : ( f4(f65,X1) = sK119(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_186])]) ).
tff(f1867,plain,
! [X0: 'S2',X1: 'S2'] : ( f4(f65,X1) = sK119(X0,X1) ),
inference(cnf_transformation,[],[f1143]) ).
tff(f1143,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ( f3(sK119(X0,X1),X0) = f3(f4(f54,f3(sK119(X0,X1),f6(f7,$sum(sK118(X0,X1),$uminus(1))))),X1) )
| ~ $less(0,sK118(X0,X1)) )
& ( f4(f65,X1) = sK119(X0,X1) )
& ( f11(f12,X0) = sK118(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK118,sK119])],[f862,f1142]) ).
tff(f1142,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: $int,X3: 'S3'] :
( ( ( f3(X3,X0) = f3(f4(f54,f3(X3,f6(f7,$sum(X2,$uminus(1))))),X1) )
| ~ $less(0,X2) )
& ( f4(f65,X1) = X3 )
& ( f11(f12,X0) = X2 ) )
=> ( ( ( f3(sK119(X0,X1),X0) = f3(f4(f54,f3(sK119(X0,X1),f6(f7,$sum(sK118(X0,X1),$uminus(1))))),X1) )
| ~ $less(0,sK118(X0,X1)) )
& ( f4(f65,X1) = sK119(X0,X1) )
& ( f11(f12,X0) = sK118(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f862,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: 'S3'] :
( ( ( f3(X3,X0) = f3(f4(f54,f3(X3,f6(f7,$sum(X2,$uminus(1))))),X1) )
| ~ $less(0,X2) )
& ( f4(f65,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(ennf_transformation,[],[f692]) ).
tff(f692,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: 'S3'] :
( ( $less(0,X2)
=> ( f3(X3,X0) = f3(f4(f54,f3(X3,f6(f7,$sum(X2,$uminus(1))))),X1) ) )
& ( f4(f65,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(rectify,[],[f515]) ).
tff(f515,plain,
! [X0: 'S2',X1: 'S2'] :
? [X279: $int,X280: 'S3'] :
( ( $less(0,X279)
=> ( f3(X280,X0) = f3(f4(f54,f3(X280,f6(f7,$sum(X279,$uminus(1))))),X1) ) )
& ( f4(f65,X1) = X280 )
& ( f11(f12,X0) = X279 ) ),
inference(theory_normalization,[],[f433]) ).
tff(f433,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X279: $int,X280: 'S3'] :
( ( $less(0,X279)
=> ( f3(f4(f54,f3(X280,f6(f7,$difference(X279,1)))),X1) = f3(X280,X0) ) )
& ( f4(f65,X1) = X280 )
& ( f11(f12,X0) = X279 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_433) ).
tff(f3734,plain,
spl331_185,
inference(avatar_split_clause,[],[f1864,f3732]) ).
tff(f3732,plain,
( spl331_185
<=> ! [X0: 'S2',X1: $real] : ( f59(f60,X1) = sK117(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_185])]) ).
tff(f1864,plain,
! [X0: 'S2',X1: $real] : ( f59(f60,X1) = sK117(X0,X1) ),
inference(cnf_transformation,[],[f1141]) ).
tff(f1141,plain,
! [X0: 'S2',X1: $real] :
( ( ( f19(sK117(X0,X1),X0) = f22(f49(f50,f19(sK117(X0,X1),f6(f7,$sum(sK116(X0,X1),$uminus(1))))),X1) )
| ~ $less(0,sK116(X0,X1)) )
& ( f59(f60,X1) = sK117(X0,X1) )
& ( f11(f12,X0) = sK116(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK116,sK117])],[f861,f1140]) ).
tff(f1140,plain,
! [X0: 'S2',X1: $real] :
( ? [X2: $int,X3: 'S13'] :
( ( ( f19(X3,X0) = f22(f49(f50,f19(X3,f6(f7,$sum(X2,$uminus(1))))),X1) )
| ~ $less(0,X2) )
& ( f59(f60,X1) = X3 )
& ( f11(f12,X0) = X2 ) )
=> ( ( ( f19(sK117(X0,X1),X0) = f22(f49(f50,f19(sK117(X0,X1),f6(f7,$sum(sK116(X0,X1),$uminus(1))))),X1) )
| ~ $less(0,sK116(X0,X1)) )
& ( f59(f60,X1) = sK117(X0,X1) )
& ( f11(f12,X0) = sK116(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f861,plain,
! [X0: 'S2',X1: $real] :
? [X2: $int,X3: 'S13'] :
( ( ( f19(X3,X0) = f22(f49(f50,f19(X3,f6(f7,$sum(X2,$uminus(1))))),X1) )
| ~ $less(0,X2) )
& ( f59(f60,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(ennf_transformation,[],[f691]) ).
tff(f691,plain,
! [X0: 'S2',X1: $real] :
? [X2: $int,X3: 'S13'] :
( ( $less(0,X2)
=> ( f19(X3,X0) = f22(f49(f50,f19(X3,f6(f7,$sum(X2,$uminus(1))))),X1) ) )
& ( f59(f60,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(rectify,[],[f514]) ).
tff(f514,plain,
! [X0: 'S2',X1: $real] :
? [X277: $int,X278: 'S13'] :
( ( $less(0,X277)
=> ( f19(X278,X0) = f22(f49(f50,f19(X278,f6(f7,$sum(X277,$uminus(1))))),X1) ) )
& ( f59(f60,X1) = X278 )
& ( f11(f12,X0) = X277 ) ),
inference(theory_normalization,[],[f432]) ).
tff(f432,axiom,
! [X0: 'S2',X1: $real] :
? [X277: $int,X278: 'S13'] :
( ( $less(0,X277)
=> ( f22(f49(f50,f19(X278,f6(f7,$difference(X277,1)))),X1) = f19(X278,X0) ) )
& ( f59(f60,X1) = X278 )
& ( f11(f12,X0) = X277 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_432) ).
tff(f3730,plain,
spl331_184,
inference(avatar_split_clause,[],[f1861,f3728]) ).
tff(f3728,plain,
( spl331_184
<=> ! [X0: 'S2',X1: 'S10'] : ( f66(f67,X1) = sK115(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_184])]) ).
tff(f1861,plain,
! [X0: 'S2',X1: 'S10'] : ( f66(f67,X1) = sK115(X0,X1) ),
inference(cnf_transformation,[],[f1139]) ).
tff(f1139,plain,
! [X0: 'S2',X1: 'S10'] :
( ( ( f13(sK115(X0,X1),X0) = f34(f39(f52,f13(sK115(X0,X1),f6(f7,$sum(sK114(X0,X1),$uminus(1))))),X1) )
| ~ $less(0,sK114(X0,X1)) )
& ( f66(f67,X1) = sK115(X0,X1) )
& ( f11(f12,X0) = sK114(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK114,sK115])],[f860,f1138]) ).
tff(f1138,plain,
! [X0: 'S2',X1: 'S10'] :
( ? [X2: $int,X3: 'S9'] :
( ( ( f13(X3,X0) = f34(f39(f52,f13(X3,f6(f7,$sum(X2,$uminus(1))))),X1) )
| ~ $less(0,X2) )
& ( f66(f67,X1) = X3 )
& ( f11(f12,X0) = X2 ) )
=> ( ( ( f13(sK115(X0,X1),X0) = f34(f39(f52,f13(sK115(X0,X1),f6(f7,$sum(sK114(X0,X1),$uminus(1))))),X1) )
| ~ $less(0,sK114(X0,X1)) )
& ( f66(f67,X1) = sK115(X0,X1) )
& ( f11(f12,X0) = sK114(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f860,plain,
! [X0: 'S2',X1: 'S10'] :
? [X2: $int,X3: 'S9'] :
( ( ( f13(X3,X0) = f34(f39(f52,f13(X3,f6(f7,$sum(X2,$uminus(1))))),X1) )
| ~ $less(0,X2) )
& ( f66(f67,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(ennf_transformation,[],[f690]) ).
tff(f690,plain,
! [X0: 'S2',X1: 'S10'] :
? [X2: $int,X3: 'S9'] :
( ( $less(0,X2)
=> ( f13(X3,X0) = f34(f39(f52,f13(X3,f6(f7,$sum(X2,$uminus(1))))),X1) ) )
& ( f66(f67,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(rectify,[],[f513]) ).
tff(f513,plain,
! [X0: 'S2',X1: 'S10'] :
? [X281: $int,X282: 'S9'] :
( ( $less(0,X281)
=> ( f13(X282,X0) = f34(f39(f52,f13(X282,f6(f7,$sum(X281,$uminus(1))))),X1) ) )
& ( f66(f67,X1) = X282 )
& ( f11(f12,X0) = X281 ) ),
inference(theory_normalization,[],[f434]) ).
tff(f434,axiom,
! [X0: 'S2',X1: 'S10'] :
? [X281: $int,X282: 'S9'] :
( ( $less(0,X281)
=> ( f34(f39(f52,f13(X282,f6(f7,$difference(X281,1)))),X1) = f13(X282,X0) ) )
& ( f66(f67,X1) = X282 )
& ( f11(f12,X0) = X281 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_434) ).
tff(f3726,plain,
spl331_183,
inference(avatar_split_clause,[],[f1858,f3724]) ).
tff(f3724,plain,
( spl331_183
<=> ! [X0: 'S2',X1: $int] : ( f63(f64,X1) = sK113(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_183])]) ).
tff(f1858,plain,
! [X0: 'S2',X1: $int] : ( f63(f64,X1) = sK113(X0,X1) ),
inference(cnf_transformation,[],[f1137]) ).
tff(f1137,plain,
! [X0: 'S2',X1: $int] :
( ( ( f11(sK113(X0,X1),X0) = f8(f9(f10,f11(sK113(X0,X1),f6(f7,$sum(sK112(X0,X1),$uminus(1))))),X1) )
| ~ $less(0,sK112(X0,X1)) )
& ( f63(f64,X1) = sK113(X0,X1) )
& ( f11(f12,X0) = sK112(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK112,sK113])],[f859,f1136]) ).
tff(f1136,plain,
! [X0: 'S2',X1: $int] :
( ? [X2: $int,X3: 'S8'] :
( ( ( f11(X3,X0) = f8(f9(f10,f11(X3,f6(f7,$sum(X2,$uminus(1))))),X1) )
| ~ $less(0,X2) )
& ( f63(f64,X1) = X3 )
& ( f11(f12,X0) = X2 ) )
=> ( ( ( f11(sK113(X0,X1),X0) = f8(f9(f10,f11(sK113(X0,X1),f6(f7,$sum(sK112(X0,X1),$uminus(1))))),X1) )
| ~ $less(0,sK112(X0,X1)) )
& ( f63(f64,X1) = sK113(X0,X1) )
& ( f11(f12,X0) = sK112(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f859,plain,
! [X0: 'S2',X1: $int] :
? [X2: $int,X3: 'S8'] :
( ( ( f11(X3,X0) = f8(f9(f10,f11(X3,f6(f7,$sum(X2,$uminus(1))))),X1) )
| ~ $less(0,X2) )
& ( f63(f64,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(ennf_transformation,[],[f689]) ).
tff(f689,plain,
! [X0: 'S2',X1: $int] :
? [X2: $int,X3: 'S8'] :
( ( $less(0,X2)
=> ( f11(X3,X0) = f8(f9(f10,f11(X3,f6(f7,$sum(X2,$uminus(1))))),X1) ) )
& ( f63(f64,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(rectify,[],[f512]) ).
tff(f512,plain,
! [X0: 'S2',X1: $int] :
? [X275: $int,X276: 'S8'] :
( ( $less(0,X275)
=> ( f11(X276,X0) = f8(f9(f10,f11(X276,f6(f7,$sum(X275,$uminus(1))))),X1) ) )
& ( f63(f64,X1) = X276 )
& ( f11(f12,X0) = X275 ) ),
inference(theory_normalization,[],[f431]) ).
tff(f431,axiom,
! [X0: 'S2',X1: $int] :
? [X275: $int,X276: 'S8'] :
( ( $less(0,X275)
=> ( f8(f9(f10,f11(X276,f6(f7,$difference(X275,1)))),X1) = f11(X276,X0) ) )
& ( f63(f64,X1) = X276 )
& ( f11(f12,X0) = X275 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_431) ).
tff(f3722,plain,
spl331_182,
inference(avatar_split_clause,[],[f1853,f3720]) ).
tff(f3720,plain,
( spl331_182
<=> ! [X0: $real,X1: $real] : ( f6(f7,2) = sK111(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_182])]) ).
tff(f1853,plain,
! [X0: $real,X1: $real] : ( f6(f7,2) = sK111(X0,X1) ),
inference(cnf_transformation,[],[f1135]) ).
tff(f1135,plain,
! [X0: $real,X1: $real] :
( ( ( sK110(X0,X1) = $sum(f19(f59(f60,X0),sK111(X0,X1)),f19(f59(f60,X1),sK111(X0,X1))) )
| ( sK110(X0,X1) != X1 )
| ( sK110(X0,X1) != X0 ) )
& ( ( ( sK110(X0,X1) = X1 )
& ( sK110(X0,X1) = X0 ) )
| ( sK110(X0,X1) != $sum(f19(f59(f60,X0),sK111(X0,X1)),f19(f59(f60,X1),sK111(X0,X1))) ) )
& ( f6(f7,2) = sK111(X0,X1) )
& ( 0.0 = sK110(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK110,sK111])],[f1133,f1134]) ).
tff(f1134,plain,
! [X0: $real,X1: $real] :
( ? [X2: $real,X3: 'S2'] :
( ( ( $sum(f19(f59(f60,X0),X3),f19(f59(f60,X1),X3)) = X2 )
| ( X1 != X2 )
| ( X0 != X2 ) )
& ( ( ( X1 = X2 )
& ( X0 = X2 ) )
| ( $sum(f19(f59(f60,X0),X3),f19(f59(f60,X1),X3)) != X2 ) )
& ( f6(f7,2) = X3 )
& ( 0.0 = X2 ) )
=> ( ( ( sK110(X0,X1) = $sum(f19(f59(f60,X0),sK111(X0,X1)),f19(f59(f60,X1),sK111(X0,X1))) )
| ( sK110(X0,X1) != X1 )
| ( sK110(X0,X1) != X0 ) )
& ( ( ( sK110(X0,X1) = X1 )
& ( sK110(X0,X1) = X0 ) )
| ( sK110(X0,X1) != $sum(f19(f59(f60,X0),sK111(X0,X1)),f19(f59(f60,X1),sK111(X0,X1))) ) )
& ( f6(f7,2) = sK111(X0,X1) )
& ( 0.0 = sK110(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1133,plain,
! [X0: $real,X1: $real] :
? [X2: $real,X3: 'S2'] :
( ( ( $sum(f19(f59(f60,X0),X3),f19(f59(f60,X1),X3)) = X2 )
| ( X1 != X2 )
| ( X0 != X2 ) )
& ( ( ( X1 = X2 )
& ( X0 = X2 ) )
| ( $sum(f19(f59(f60,X0),X3),f19(f59(f60,X1),X3)) != X2 ) )
& ( f6(f7,2) = X3 )
& ( 0.0 = X2 ) ),
inference(flattening,[],[f1132]) ).
tff(f1132,plain,
! [X0: $real,X1: $real] :
? [X2: $real,X3: 'S2'] :
( ( ( $sum(f19(f59(f60,X0),X3),f19(f59(f60,X1),X3)) = X2 )
| ( X1 != X2 )
| ( X0 != X2 ) )
& ( ( ( X1 = X2 )
& ( X0 = X2 ) )
| ( $sum(f19(f59(f60,X0),X3),f19(f59(f60,X1),X3)) != X2 ) )
& ( f6(f7,2) = X3 )
& ( 0.0 = X2 ) ),
inference(nnf_transformation,[],[f688]) ).
tff(f688,plain,
! [X0: $real,X1: $real] :
? [X2: $real,X3: 'S2'] :
( ( ( $sum(f19(f59(f60,X0),X3),f19(f59(f60,X1),X3)) = X2 )
<=> ( ( X1 = X2 )
& ( X0 = X2 ) ) )
& ( f6(f7,2) = X3 )
& ( 0.0 = X2 ) ),
inference(rectify,[],[f430]) ).
tff(f430,axiom,
! [X0: $real,X1: $real] :
? [X273: $real,X274: 'S2'] :
( ( ( $sum(f19(f59(f60,X0),X274),f19(f59(f60,X1),X274)) = X273 )
<=> ( ( X1 = X273 )
& ( X0 = X273 ) ) )
& ( f6(f7,2) = X274 )
& ( 0.0 = X273 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_430) ).
tff(f3710,plain,
spl331_181,
inference(avatar_split_clause,[],[f1821,f3708]) ).
tff(f3708,plain,
( spl331_181
<=> ! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK96(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_181])]) ).
tff(f1821,plain,
! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK96(X0,X1) ),
inference(cnf_transformation,[],[f1106]) ).
tff(f3706,plain,
spl331_180,
inference(avatar_split_clause,[],[f1818,f3704]) ).
tff(f3704,plain,
( spl331_180
<=> ! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK94(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_180])]) ).
tff(f1818,plain,
! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK94(X0,X1) ),
inference(cnf_transformation,[],[f1103]) ).
tff(f3702,plain,
spl331_179,
inference(avatar_split_clause,[],[f1815,f3700]) ).
tff(f3700,plain,
( spl331_179
<=> ! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK93(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_179])]) ).
tff(f1815,plain,
! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK93(X0,X1) ),
inference(cnf_transformation,[],[f1100]) ).
tff(f1100,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ( f3(sK93(X0,X1),X1) = f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,f3(sK93(X0,X1),f6(f7,$sum(f11(f12,X1),$uminus(1))))))) )
| ( f6(f7,0) = X1 ) )
& ( ( f6(f7,1) = f3(sK93(X0,X1),X1) )
| ( f6(f7,0) != X1 ) )
& ( f4(f65,X0) = sK93(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK93])],[f856,f1099]) ).
tff(f1099,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: 'S3'] :
( ( ( f3(X2,X1) = f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,f3(X2,f6(f7,$sum(f11(f12,X1),$uminus(1))))))) )
| ( f6(f7,0) = X1 ) )
& ( ( f6(f7,1) = f3(X2,X1) )
| ( f6(f7,0) != X1 ) )
& ( f4(f65,X0) = X2 ) )
=> ( ( ( f3(sK93(X0,X1),X1) = f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,f3(sK93(X0,X1),f6(f7,$sum(f11(f12,X1),$uminus(1))))))) )
| ( f6(f7,0) = X1 ) )
& ( ( f6(f7,1) = f3(sK93(X0,X1),X1) )
| ( f6(f7,0) != X1 ) )
& ( f4(f65,X0) = sK93(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f856,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S3'] :
( ( ( f3(X2,X1) = f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,f3(X2,f6(f7,$sum(f11(f12,X1),$uminus(1))))))) )
| ( f6(f7,0) = X1 ) )
& ( ( f6(f7,1) = f3(X2,X1) )
| ( f6(f7,0) != X1 ) )
& ( f4(f65,X0) = X2 ) ),
inference(ennf_transformation,[],[f675]) ).
tff(f675,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S3'] :
( ( ( f6(f7,0) != X1 )
=> ( f3(X2,X1) = f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,f3(X2,f6(f7,$sum(f11(f12,X1),$uminus(1))))))) ) )
& ( ( f6(f7,0) = X1 )
=> ( f6(f7,1) = f3(X2,X1) ) )
& ( f4(f65,X0) = X2 ) ),
inference(rectify,[],[f507]) ).
tff(f507,plain,
! [X0: 'S2',X1: 'S2'] :
? [X265: 'S3'] :
( ( ( f6(f7,0) != X1 )
=> ( f3(X265,X1) = f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,f3(X265,f6(f7,$sum(f11(f12,X1),$uminus(1))))))) ) )
& ( ( f6(f7,0) = X1 )
=> ( f6(f7,1) = f3(X265,X1) ) )
& ( f4(f65,X0) = X265 ) ),
inference(theory_normalization,[],[f414]) ).
tff(f414,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X265: 'S3'] :
( ( ( f6(f7,0) != X1 )
=> ( f3(X265,X1) = f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,f3(X265,f6(f7,$difference(f11(f12,X1),1)))))) ) )
& ( ( f6(f7,0) = X1 )
=> ( f6(f7,1) = f3(X265,X1) ) )
& ( f4(f65,X0) = X265 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_414) ).
tff(f3698,plain,
spl331_178,
inference(avatar_split_clause,[],[f1813,f3696]) ).
tff(f3696,plain,
( spl331_178
<=> ! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK92(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_178])]) ).
tff(f1813,plain,
! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK92(X0,X1) ),
inference(cnf_transformation,[],[f1098]) ).
tff(f1098,plain,
! [X0: 'S2',X1: 'S2'] :
( ( f3(sK92(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f3(f4(f54,X0),f3(f4(f65,f3(sK92(X0,X1),X1)),f6(f7,2))) )
& ( f4(f65,X0) = sK92(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK92])],[f674,f1097]) ).
tff(f1097,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: 'S3'] :
( ( f3(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f3(f4(f54,X0),f3(f4(f65,f3(X2,X1)),f6(f7,2))) )
& ( f4(f65,X0) = X2 ) )
=> ( ( f3(sK92(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f3(f4(f54,X0),f3(f4(f65,f3(sK92(X0,X1),X1)),f6(f7,2))) )
& ( f4(f65,X0) = sK92(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f674,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S3'] :
( ( f3(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f3(f4(f54,X0),f3(f4(f65,f3(X2,X1)),f6(f7,2))) )
& ( f4(f65,X0) = X2 ) ),
inference(rectify,[],[f404]) ).
tff(f404,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X257: 'S3'] :
( ( f3(X257,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f3(f4(f54,X0),f3(f4(f65,f3(X257,X1)),f6(f7,2))) )
& ( f4(f65,X0) = X257 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_404) ).
tff(f3694,plain,
spl331_177,
inference(avatar_split_clause,[],[f1811,f3692]) ).
tff(f3692,plain,
( spl331_177
<=> ! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK91(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_177])]) ).
tff(f1811,plain,
! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK91(X0,X1) ),
inference(cnf_transformation,[],[f1096]) ).
tff(f1096,plain,
! [X0: 'S2',X1: 'S2'] :
( ( f3(sK91(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f3(f4(f65,f3(sK91(X0,X1),X1)),f6(f7,2)) )
& ( f4(f65,X0) = sK91(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK91])],[f673,f1095]) ).
tff(f1095,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: 'S3'] :
( ( f3(X2,f6(f7,$product(2,f11(f12,X1)))) = f3(f4(f65,f3(X2,X1)),f6(f7,2)) )
& ( f4(f65,X0) = X2 ) )
=> ( ( f3(sK91(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f3(f4(f65,f3(sK91(X0,X1),X1)),f6(f7,2)) )
& ( f4(f65,X0) = sK91(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f673,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S3'] :
( ( f3(X2,f6(f7,$product(2,f11(f12,X1)))) = f3(f4(f65,f3(X2,X1)),f6(f7,2)) )
& ( f4(f65,X0) = X2 ) ),
inference(rectify,[],[f320]) ).
tff(f320,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X204: 'S3'] :
( ( f3(X204,f6(f7,$product(2,f11(f12,X1)))) = f3(f4(f65,f3(X204,X1)),f6(f7,2)) )
& ( f4(f65,X0) = X204 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_320) ).
tff(f3690,plain,
spl331_176,
inference(avatar_split_clause,[],[f1809,f3688]) ).
tff(f3688,plain,
( spl331_176
<=> ! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK90(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_176])]) ).
tff(f1809,plain,
! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK90(X0,X1) ),
inference(cnf_transformation,[],[f1094]) ).
tff(f1094,plain,
! [X0: 'S2',X1: 'S2'] :
( ( f3(f4(f54,X0),f3(sK90(X0,X1),X1)) = f3(sK90(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f4(f65,X0) = sK90(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK90])],[f672,f1093]) ).
tff(f1093,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: 'S3'] :
( ( f3(f4(f54,X0),f3(X2,X1)) = f3(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f4(f65,X0) = X2 ) )
=> ( ( f3(f4(f54,X0),f3(sK90(X0,X1),X1)) = f3(sK90(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f4(f65,X0) = sK90(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f672,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S3'] :
( ( f3(f4(f54,X0),f3(X2,X1)) = f3(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f4(f65,X0) = X2 ) ),
inference(rectify,[],[f336]) ).
tff(f336,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X212: 'S3'] :
( ( f3(X212,f6(f7,$sum(f11(f12,X1),1))) = f3(f4(f54,X0),f3(X212,X1)) )
& ( f4(f65,X0) = X212 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_336) ).
tff(f3686,plain,
spl331_175,
inference(avatar_split_clause,[],[f1807,f3684]) ).
tff(f3684,plain,
( spl331_175
<=> ! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK89(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_175])]) ).
tff(f1807,plain,
! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK89(X0,X1) ),
inference(cnf_transformation,[],[f1092]) ).
tff(f1092,plain,
! [X0: 'S2',X1: 'S2'] :
( ( f3(sK89(X0,X1),f6(f7,$sum(f11(f12,X1),1))) = f3(f4(f54,f3(sK89(X0,X1),X1)),X0) )
& ( f4(f65,X0) = sK89(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK89])],[f671,f1091]) ).
tff(f1091,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: 'S3'] :
( ( f3(X2,f6(f7,$sum(f11(f12,X1),1))) = f3(f4(f54,f3(X2,X1)),X0) )
& ( f4(f65,X0) = X2 ) )
=> ( ( f3(sK89(X0,X1),f6(f7,$sum(f11(f12,X1),1))) = f3(f4(f54,f3(sK89(X0,X1),X1)),X0) )
& ( f4(f65,X0) = sK89(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f671,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S3'] :
( ( f3(X2,f6(f7,$sum(f11(f12,X1),1))) = f3(f4(f54,f3(X2,X1)),X0) )
& ( f4(f65,X0) = X2 ) ),
inference(rectify,[],[f316]) ).
tff(f316,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X200: 'S3'] :
( ( f3(f4(f54,f3(X200,X1)),X0) = f3(X200,f6(f7,$sum(f11(f12,X1),1))) )
& ( f4(f65,X0) = X200 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_316) ).
tff(f3682,plain,
spl331_174,
inference(avatar_split_clause,[],[f1805,f3680]) ).
tff(f3680,plain,
( spl331_174
<=> ! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK88(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_174])]) ).
tff(f1805,plain,
! [X0: 'S2',X1: 'S2'] : ( f4(f65,X0) = sK88(X0,X1) ),
inference(cnf_transformation,[],[f1090]) ).
tff(f1090,plain,
! [X0: 'S2',X1: 'S2'] :
( ( f3(f4(f54,X0),f3(sK88(X0,X1),X1)) = f3(sK88(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f4(f65,X0) = sK88(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK88])],[f670,f1089]) ).
tff(f1089,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: 'S3'] :
( ( f3(f4(f54,X0),f3(X2,X1)) = f3(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f4(f65,X0) = X2 ) )
=> ( ( f3(f4(f54,X0),f3(sK88(X0,X1),X1)) = f3(sK88(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f4(f65,X0) = sK88(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f670,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S3'] :
( ( f3(f4(f54,X0),f3(X2,X1)) = f3(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f4(f65,X0) = X2 ) ),
inference(rectify,[],[f324]) ).
tff(f324,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X208: 'S3'] :
( ( f3(f4(f54,X0),f3(X208,X1)) = f3(X208,f6(f7,$sum(f11(f12,X1),1))) )
& ( f4(f65,X0) = X208 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_324) ).
tff(f3678,plain,
spl331_173,
inference(avatar_split_clause,[],[f1802,f3676]) ).
tff(f3676,plain,
( spl331_173
<=> ! [X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK86(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_173])]) ).
tff(f1802,plain,
! [X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK86(X0,X1) ),
inference(cnf_transformation,[],[f1088]) ).
tff(f3674,plain,
spl331_172,
inference(avatar_split_clause,[],[f1799,f3672]) ).
tff(f3672,plain,
( spl331_172
<=> ! [X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK84(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_172])]) ).
tff(f1799,plain,
! [X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK84(X0,X1) ),
inference(cnf_transformation,[],[f1085]) ).
tff(f3670,plain,
( spl331_171
| ~ spl331_74 ),
inference(avatar_split_clause,[],[f3385,f3244,f3668]) ).
tff(f3668,plain,
( spl331_171
<=> ! [X0: 'S2',X1: 'S2'] : ( sK35(X0) = sK35(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_171])]) ).
tff(f3244,plain,
( spl331_74
<=> ! [X0: 'S2'] : ( f6(f7,1) = sK35(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_74])]) ).
tff(f3385,plain,
( ! [X0: 'S2',X1: 'S2'] : ( sK35(X0) = sK35(X1) )
| ~ spl331_74 ),
inference(superposition,[],[f3245,f3245]) ).
tff(f3245,plain,
( ! [X0: 'S2'] : ( f6(f7,1) = sK35(X0) )
| ~ spl331_74 ),
inference(avatar_component_clause,[],[f3244]) ).
tff(f3666,plain,
spl331_170,
inference(avatar_split_clause,[],[f1797,f3664]) ).
tff(f3664,plain,
( spl331_170
<=> ! [X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK83(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_170])]) ).
tff(f1797,plain,
! [X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK83(X0,X1) ),
inference(cnf_transformation,[],[f1082]) ).
tff(f1082,plain,
! [X0: $real,X1: 'S2'] :
( ( f19(sK83(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f22(f49(f50,X0),f19(f59(f60,f19(sK83(X0,X1),X1)),f6(f7,2))) )
& ( f59(f60,X0) = sK83(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK83])],[f667,f1081]) ).
tff(f1081,plain,
! [X0: $real,X1: 'S2'] :
( ? [X2: 'S13'] :
( ( f19(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f22(f49(f50,X0),f19(f59(f60,f19(X2,X1)),f6(f7,2))) )
& ( f59(f60,X0) = X2 ) )
=> ( ( f19(sK83(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f22(f49(f50,X0),f19(f59(f60,f19(sK83(X0,X1),X1)),f6(f7,2))) )
& ( f59(f60,X0) = sK83(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f667,plain,
! [X0: $real,X1: 'S2'] :
? [X2: 'S13'] :
( ( f19(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f22(f49(f50,X0),f19(f59(f60,f19(X2,X1)),f6(f7,2))) )
& ( f59(f60,X0) = X2 ) ),
inference(rectify,[],[f403]) ).
tff(f403,axiom,
! [X0: $real,X1: 'S2'] :
? [X256: 'S13'] :
( ( f19(X256,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f22(f49(f50,X0),f19(f59(f60,f19(X256,X1)),f6(f7,2))) )
& ( f59(f60,X0) = X256 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_403) ).
tff(f3662,plain,
spl331_169,
inference(avatar_split_clause,[],[f1795,f3660]) ).
tff(f3660,plain,
( spl331_169
<=> ! [X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK82(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_169])]) ).
tff(f1795,plain,
! [X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK82(X0,X1) ),
inference(cnf_transformation,[],[f1080]) ).
tff(f1080,plain,
! [X0: $real,X1: 'S2'] :
( ( f19(sK82(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f19(f59(f60,f19(sK82(X0,X1),X1)),f6(f7,2)) )
& ( f59(f60,X0) = sK82(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK82])],[f666,f1079]) ).
tff(f1079,plain,
! [X0: $real,X1: 'S2'] :
( ? [X2: 'S13'] :
( ( f19(X2,f6(f7,$product(2,f11(f12,X1)))) = f19(f59(f60,f19(X2,X1)),f6(f7,2)) )
& ( f59(f60,X0) = X2 ) )
=> ( ( f19(sK82(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f19(f59(f60,f19(sK82(X0,X1),X1)),f6(f7,2)) )
& ( f59(f60,X0) = sK82(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f666,plain,
! [X0: $real,X1: 'S2'] :
? [X2: 'S13'] :
( ( f19(X2,f6(f7,$product(2,f11(f12,X1)))) = f19(f59(f60,f19(X2,X1)),f6(f7,2)) )
& ( f59(f60,X0) = X2 ) ),
inference(rectify,[],[f319]) ).
tff(f319,axiom,
! [X0: $real,X1: 'S2'] :
? [X203: 'S13'] :
( ( f19(X203,f6(f7,$product(2,f11(f12,X1)))) = f19(f59(f60,f19(X203,X1)),f6(f7,2)) )
& ( f59(f60,X0) = X203 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_319) ).
tff(f3658,plain,
spl331_168,
inference(avatar_split_clause,[],[f1793,f3656]) ).
tff(f3656,plain,
( spl331_168
<=> ! [X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK81(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_168])]) ).
tff(f1793,plain,
! [X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK81(X0,X1) ),
inference(cnf_transformation,[],[f1078]) ).
tff(f1078,plain,
! [X0: $real,X1: 'S2'] :
( ( f22(f49(f50,X0),f19(sK81(X0,X1),X1)) = f19(sK81(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f59(f60,X0) = sK81(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK81])],[f665,f1077]) ).
tff(f1077,plain,
! [X0: $real,X1: 'S2'] :
( ? [X2: 'S13'] :
( ( f22(f49(f50,X0),f19(X2,X1)) = f19(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f59(f60,X0) = X2 ) )
=> ( ( f22(f49(f50,X0),f19(sK81(X0,X1),X1)) = f19(sK81(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f59(f60,X0) = sK81(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f665,plain,
! [X0: $real,X1: 'S2'] :
? [X2: 'S13'] :
( ( f22(f49(f50,X0),f19(X2,X1)) = f19(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f59(f60,X0) = X2 ) ),
inference(rectify,[],[f335]) ).
tff(f335,axiom,
! [X0: $real,X1: 'S2'] :
? [X211: 'S13'] :
( ( f19(X211,f6(f7,$sum(f11(f12,X1),1))) = f22(f49(f50,X0),f19(X211,X1)) )
& ( f59(f60,X0) = X211 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_335) ).
tff(f3654,plain,
spl331_167,
inference(avatar_split_clause,[],[f1791,f3652]) ).
tff(f3652,plain,
( spl331_167
<=> ! [X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK80(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_167])]) ).
tff(f1791,plain,
! [X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK80(X0,X1) ),
inference(cnf_transformation,[],[f1076]) ).
tff(f1076,plain,
! [X0: $real,X1: 'S2'] :
( ( f19(sK80(X0,X1),f6(f7,$sum(f11(f12,X1),1))) = f22(f49(f50,f19(sK80(X0,X1),X1)),X0) )
& ( f59(f60,X0) = sK80(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK80])],[f664,f1075]) ).
tff(f1075,plain,
! [X0: $real,X1: 'S2'] :
( ? [X2: 'S13'] :
( ( f19(X2,f6(f7,$sum(f11(f12,X1),1))) = f22(f49(f50,f19(X2,X1)),X0) )
& ( f59(f60,X0) = X2 ) )
=> ( ( f19(sK80(X0,X1),f6(f7,$sum(f11(f12,X1),1))) = f22(f49(f50,f19(sK80(X0,X1),X1)),X0) )
& ( f59(f60,X0) = sK80(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f664,plain,
! [X0: $real,X1: 'S2'] :
? [X2: 'S13'] :
( ( f19(X2,f6(f7,$sum(f11(f12,X1),1))) = f22(f49(f50,f19(X2,X1)),X0) )
& ( f59(f60,X0) = X2 ) ),
inference(rectify,[],[f315]) ).
tff(f315,axiom,
! [X0: $real,X1: 'S2'] :
? [X199: 'S13'] :
( ( f22(f49(f50,f19(X199,X1)),X0) = f19(X199,f6(f7,$sum(f11(f12,X1),1))) )
& ( f59(f60,X0) = X199 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_315) ).
tff(f3650,plain,
spl331_166,
inference(avatar_split_clause,[],[f1789,f3648]) ).
tff(f3648,plain,
( spl331_166
<=> ! [X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK79(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_166])]) ).
tff(f1789,plain,
! [X0: $real,X1: 'S2'] : ( f59(f60,X0) = sK79(X0,X1) ),
inference(cnf_transformation,[],[f1074]) ).
tff(f1074,plain,
! [X0: $real,X1: 'S2'] :
( ( f22(f49(f50,X0),f19(sK79(X0,X1),X1)) = f19(sK79(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f59(f60,X0) = sK79(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79])],[f663,f1073]) ).
tff(f1073,plain,
! [X0: $real,X1: 'S2'] :
( ? [X2: 'S13'] :
( ( f22(f49(f50,X0),f19(X2,X1)) = f19(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f59(f60,X0) = X2 ) )
=> ( ( f22(f49(f50,X0),f19(sK79(X0,X1),X1)) = f19(sK79(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f59(f60,X0) = sK79(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f663,plain,
! [X0: $real,X1: 'S2'] :
? [X2: 'S13'] :
( ( f22(f49(f50,X0),f19(X2,X1)) = f19(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f59(f60,X0) = X2 ) ),
inference(rectify,[],[f323]) ).
tff(f323,axiom,
! [X0: $real,X1: 'S2'] :
? [X207: 'S13'] :
( ( f22(f49(f50,X0),f19(X207,X1)) = f19(X207,f6(f7,$sum(f11(f12,X1),1))) )
& ( f59(f60,X0) = X207 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_323) ).
tff(f3646,plain,
spl331_165,
inference(avatar_split_clause,[],[f1787,f3644]) ).
tff(f3644,plain,
( spl331_165
<=> ! [X0: $real,X1: $real] : ( f17(f18,X0) = sK78(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_165])]) ).
tff(f1787,plain,
! [X0: $real,X1: $real] : ( f17(f18,X0) = sK78(X0,X1) ),
inference(cnf_transformation,[],[f1072]) ).
tff(f1072,plain,
! [X0: $real,X1: $real] :
( ( f34(f35,f16(sK78(X0,X1),X1)) = f16(sK78(X0,X1),$uminus(X1)) )
& ( f17(f18,X0) = sK78(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK78])],[f662,f1071]) ).
tff(f1071,plain,
! [X0: $real,X1: $real] :
( ? [X2: 'S11'] :
( ( f34(f35,f16(X2,X1)) = f16(X2,$uminus(X1)) )
& ( f17(f18,X0) = X2 ) )
=> ( ( f34(f35,f16(sK78(X0,X1),X1)) = f16(sK78(X0,X1),$uminus(X1)) )
& ( f17(f18,X0) = sK78(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f662,plain,
! [X0: $real,X1: $real] :
? [X2: 'S11'] :
( ( f34(f35,f16(X2,X1)) = f16(X2,$uminus(X1)) )
& ( f17(f18,X0) = X2 ) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X0: $real,X1: $real] :
? [X13: 'S11'] :
( ( f34(f35,f16(X13,X1)) = f16(X13,$uminus(X1)) )
& ( f17(f18,X0) = X13 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_41) ).
tff(f3642,plain,
spl331_164,
inference(avatar_split_clause,[],[f1784,f3640]) ).
tff(f3640,plain,
( spl331_164
<=> ! [X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK76(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_164])]) ).
tff(f1784,plain,
! [X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK76(X0,X1) ),
inference(cnf_transformation,[],[f1070]) ).
tff(f3638,plain,
spl331_163,
inference(avatar_split_clause,[],[f1781,f3636]) ).
tff(f3636,plain,
( spl331_163
<=> ! [X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK74(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_163])]) ).
tff(f1781,plain,
! [X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK74(X0,X1) ),
inference(cnf_transformation,[],[f1067]) ).
tff(f3634,plain,
spl331_162,
inference(avatar_split_clause,[],[f1778,f3632]) ).
tff(f3632,plain,
( spl331_162
<=> ! [X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK72(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_162])]) ).
tff(f1778,plain,
! [X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK72(X0,X1) ),
inference(cnf_transformation,[],[f1064]) ).
tff(f3630,plain,
spl331_161,
inference(avatar_split_clause,[],[f1775,f3628]) ).
tff(f3628,plain,
( spl331_161
<=> ! [X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK70(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_161])]) ).
tff(f1775,plain,
! [X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK70(X0,X1) ),
inference(cnf_transformation,[],[f1061]) ).
tff(f3626,plain,
( spl331_160
| ~ spl331_60
| ~ spl331_62 ),
inference(avatar_split_clause,[],[f3373,f3196,f3188,f3624]) ).
tff(f3624,plain,
( spl331_160
<=> ! [X4: $real,X5: 'S10'] : ( sK14(X4) = sK16(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_160])]) ).
tff(f3188,plain,
( spl331_60
<=> ! [X0: $real] : ( f6(f7,2) = sK14(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_60])]) ).
tff(f3196,plain,
( spl331_62
<=> ! [X0: 'S10'] : ( f6(f7,2) = sK16(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_62])]) ).
tff(f3373,plain,
( ! [X4: $real,X5: 'S10'] : ( sK14(X4) = sK16(X5) )
| ~ spl331_60
| ~ spl331_62 ),
inference(superposition,[],[f3197,f3189]) ).
tff(f3189,plain,
( ! [X0: $real] : ( f6(f7,2) = sK14(X0) )
| ~ spl331_60 ),
inference(avatar_component_clause,[],[f3188]) ).
tff(f3197,plain,
( ! [X0: 'S10'] : ( f6(f7,2) = sK16(X0) )
| ~ spl331_62 ),
inference(avatar_component_clause,[],[f3196]) ).
tff(f3622,plain,
spl331_159,
inference(avatar_split_clause,[],[f1773,f3620]) ).
tff(f3620,plain,
( spl331_159
<=> ! [X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK69(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_159])]) ).
tff(f1773,plain,
! [X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK69(X0,X1) ),
inference(cnf_transformation,[],[f1058]) ).
tff(f1058,plain,
! [X0: $int,X1: 'S2'] :
( ( f11(sK69(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f8(f9(f10,X0),f11(f63(f64,f11(sK69(X0,X1),X1)),f6(f7,2))) )
& ( f63(f64,X0) = sK69(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f657,f1057]) ).
tff(f1057,plain,
! [X0: $int,X1: 'S2'] :
( ? [X2: 'S8'] :
( ( f11(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f8(f9(f10,X0),f11(f63(f64,f11(X2,X1)),f6(f7,2))) )
& ( f63(f64,X0) = X2 ) )
=> ( ( f11(sK69(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f8(f9(f10,X0),f11(f63(f64,f11(sK69(X0,X1),X1)),f6(f7,2))) )
& ( f63(f64,X0) = sK69(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f657,plain,
! [X0: $int,X1: 'S2'] :
? [X2: 'S8'] :
( ( f11(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f8(f9(f10,X0),f11(f63(f64,f11(X2,X1)),f6(f7,2))) )
& ( f63(f64,X0) = X2 ) ),
inference(rectify,[],[f402]) ).
tff(f402,axiom,
! [X0: $int,X1: 'S2'] :
? [X255: 'S8'] :
( ( f11(X255,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f8(f9(f10,X0),f11(f63(f64,f11(X255,X1)),f6(f7,2))) )
& ( f63(f64,X0) = X255 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_402) ).
tff(f3618,plain,
spl331_158,
inference(avatar_split_clause,[],[f1771,f3616]) ).
tff(f3616,plain,
( spl331_158
<=> ! [X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK68(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_158])]) ).
tff(f1771,plain,
! [X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK68(X0,X1) ),
inference(cnf_transformation,[],[f1056]) ).
tff(f1056,plain,
! [X0: 'S10',X1: 'S2'] :
( ( f13(sK68(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f34(f39(f52,X0),f13(f66(f67,f13(sK68(X0,X1),X1)),f6(f7,2))) )
& ( f66(f67,X0) = sK68(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK68])],[f656,f1055]) ).
tff(f1055,plain,
! [X0: 'S10',X1: 'S2'] :
( ? [X2: 'S9'] :
( ( f13(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f34(f39(f52,X0),f13(f66(f67,f13(X2,X1)),f6(f7,2))) )
& ( f66(f67,X0) = X2 ) )
=> ( ( f13(sK68(X0,X1),f6(f7,$sum($product(2,f11(f12,X1)),1))) = f34(f39(f52,X0),f13(f66(f67,f13(sK68(X0,X1),X1)),f6(f7,2))) )
& ( f66(f67,X0) = sK68(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f656,plain,
! [X0: 'S10',X1: 'S2'] :
? [X2: 'S9'] :
( ( f13(X2,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f34(f39(f52,X0),f13(f66(f67,f13(X2,X1)),f6(f7,2))) )
& ( f66(f67,X0) = X2 ) ),
inference(rectify,[],[f405]) ).
tff(f405,axiom,
! [X0: 'S10',X1: 'S2'] :
? [X258: 'S9'] :
( ( f13(X258,f6(f7,$sum($product(2,f11(f12,X1)),1))) = f34(f39(f52,X0),f13(f66(f67,f13(X258,X1)),f6(f7,2))) )
& ( f66(f67,X0) = X258 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_405) ).
tff(f3614,plain,
spl331_157,
inference(avatar_split_clause,[],[f1769,f3612]) ).
tff(f3612,plain,
( spl331_157
<=> ! [X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK67(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_157])]) ).
tff(f1769,plain,
! [X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK67(X0,X1) ),
inference(cnf_transformation,[],[f1054]) ).
tff(f1054,plain,
! [X0: $int,X1: 'S2'] :
( ( f11(sK67(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f11(f63(f64,f11(sK67(X0,X1),X1)),f6(f7,2)) )
& ( f63(f64,X0) = sK67(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67])],[f655,f1053]) ).
tff(f1053,plain,
! [X0: $int,X1: 'S2'] :
( ? [X2: 'S8'] :
( ( f11(X2,f6(f7,$product(2,f11(f12,X1)))) = f11(f63(f64,f11(X2,X1)),f6(f7,2)) )
& ( f63(f64,X0) = X2 ) )
=> ( ( f11(sK67(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f11(f63(f64,f11(sK67(X0,X1),X1)),f6(f7,2)) )
& ( f63(f64,X0) = sK67(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f655,plain,
! [X0: $int,X1: 'S2'] :
? [X2: 'S8'] :
( ( f11(X2,f6(f7,$product(2,f11(f12,X1)))) = f11(f63(f64,f11(X2,X1)),f6(f7,2)) )
& ( f63(f64,X0) = X2 ) ),
inference(rectify,[],[f318]) ).
tff(f318,axiom,
! [X0: $int,X1: 'S2'] :
? [X202: 'S8'] :
( ( f11(X202,f6(f7,$product(2,f11(f12,X1)))) = f11(f63(f64,f11(X202,X1)),f6(f7,2)) )
& ( f63(f64,X0) = X202 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_318) ).
tff(f3610,plain,
spl331_156,
inference(avatar_split_clause,[],[f1767,f3608]) ).
tff(f3608,plain,
( spl331_156
<=> ! [X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK66(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_156])]) ).
tff(f1767,plain,
! [X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK66(X0,X1) ),
inference(cnf_transformation,[],[f1052]) ).
tff(f1052,plain,
! [X0: 'S10',X1: 'S2'] :
( ( f13(sK66(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f13(f66(f67,f13(sK66(X0,X1),X1)),f6(f7,2)) )
& ( f66(f67,X0) = sK66(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f654,f1051]) ).
tff(f1051,plain,
! [X0: 'S10',X1: 'S2'] :
( ? [X2: 'S9'] :
( ( f13(X2,f6(f7,$product(2,f11(f12,X1)))) = f13(f66(f67,f13(X2,X1)),f6(f7,2)) )
& ( f66(f67,X0) = X2 ) )
=> ( ( f13(sK66(X0,X1),f6(f7,$product(2,f11(f12,X1)))) = f13(f66(f67,f13(sK66(X0,X1),X1)),f6(f7,2)) )
& ( f66(f67,X0) = sK66(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f654,plain,
! [X0: 'S10',X1: 'S2'] :
? [X2: 'S9'] :
( ( f13(X2,f6(f7,$product(2,f11(f12,X1)))) = f13(f66(f67,f13(X2,X1)),f6(f7,2)) )
& ( f66(f67,X0) = X2 ) ),
inference(rectify,[],[f321]) ).
tff(f321,axiom,
! [X0: 'S10',X1: 'S2'] :
? [X205: 'S9'] :
( ( f13(X205,f6(f7,$product(2,f11(f12,X1)))) = f13(f66(f67,f13(X205,X1)),f6(f7,2)) )
& ( f66(f67,X0) = X205 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_321) ).
tff(f3606,plain,
spl331_155,
inference(avatar_split_clause,[],[f1765,f3604]) ).
tff(f3604,plain,
( spl331_155
<=> ! [X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK65(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_155])]) ).
tff(f1765,plain,
! [X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK65(X0,X1) ),
inference(cnf_transformation,[],[f1050]) ).
tff(f1050,plain,
! [X0: $int,X1: 'S2'] :
( ( f8(f9(f10,X0),f11(sK65(X0,X1),X1)) = f11(sK65(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f63(f64,X0) = sK65(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f653,f1049]) ).
tff(f1049,plain,
! [X0: $int,X1: 'S2'] :
( ? [X2: 'S8'] :
( ( f8(f9(f10,X0),f11(X2,X1)) = f11(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f63(f64,X0) = X2 ) )
=> ( ( f8(f9(f10,X0),f11(sK65(X0,X1),X1)) = f11(sK65(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f63(f64,X0) = sK65(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f653,plain,
! [X0: $int,X1: 'S2'] :
? [X2: 'S8'] :
( ( f8(f9(f10,X0),f11(X2,X1)) = f11(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f63(f64,X0) = X2 ) ),
inference(rectify,[],[f334]) ).
tff(f334,axiom,
! [X0: $int,X1: 'S2'] :
? [X210: 'S8'] :
( ( f11(X210,f6(f7,$sum(f11(f12,X1),1))) = f8(f9(f10,X0),f11(X210,X1)) )
& ( f63(f64,X0) = X210 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_334) ).
tff(f3602,plain,
spl331_154,
inference(avatar_split_clause,[],[f1763,f3600]) ).
tff(f3600,plain,
( spl331_154
<=> ! [X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK64(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_154])]) ).
tff(f1763,plain,
! [X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK64(X0,X1) ),
inference(cnf_transformation,[],[f1048]) ).
tff(f1048,plain,
! [X0: 'S10',X1: 'S2'] :
( ( f34(f39(f52,X0),f13(sK64(X0,X1),X1)) = f13(sK64(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f66(f67,X0) = sK64(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK64])],[f652,f1047]) ).
tff(f1047,plain,
! [X0: 'S10',X1: 'S2'] :
( ? [X2: 'S9'] :
( ( f34(f39(f52,X0),f13(X2,X1)) = f13(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f66(f67,X0) = X2 ) )
=> ( ( f34(f39(f52,X0),f13(sK64(X0,X1),X1)) = f13(sK64(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f66(f67,X0) = sK64(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f652,plain,
! [X0: 'S10',X1: 'S2'] :
? [X2: 'S9'] :
( ( f34(f39(f52,X0),f13(X2,X1)) = f13(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f66(f67,X0) = X2 ) ),
inference(rectify,[],[f337]) ).
tff(f337,axiom,
! [X0: 'S10',X1: 'S2'] :
? [X213: 'S9'] :
( ( f13(X213,f6(f7,$sum(f11(f12,X1),1))) = f34(f39(f52,X0),f13(X213,X1)) )
& ( f66(f67,X0) = X213 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_337) ).
tff(f3598,plain,
spl331_153,
inference(avatar_split_clause,[],[f1761,f3596]) ).
tff(f3596,plain,
( spl331_153
<=> ! [X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK63(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_153])]) ).
tff(f1761,plain,
! [X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK63(X0,X1) ),
inference(cnf_transformation,[],[f1046]) ).
tff(f1046,plain,
! [X0: 'S10',X1: 'S2'] :
( ( f13(sK63(X0,X1),f6(f7,$sum(f11(f12,X1),1))) = f34(f39(f52,f13(sK63(X0,X1),X1)),X0) )
& ( f66(f67,X0) = sK63(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63])],[f651,f1045]) ).
tff(f1045,plain,
! [X0: 'S10',X1: 'S2'] :
( ? [X2: 'S9'] :
( ( f13(X2,f6(f7,$sum(f11(f12,X1),1))) = f34(f39(f52,f13(X2,X1)),X0) )
& ( f66(f67,X0) = X2 ) )
=> ( ( f13(sK63(X0,X1),f6(f7,$sum(f11(f12,X1),1))) = f34(f39(f52,f13(sK63(X0,X1),X1)),X0) )
& ( f66(f67,X0) = sK63(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f651,plain,
! [X0: 'S10',X1: 'S2'] :
? [X2: 'S9'] :
( ( f13(X2,f6(f7,$sum(f11(f12,X1),1))) = f34(f39(f52,f13(X2,X1)),X0) )
& ( f66(f67,X0) = X2 ) ),
inference(rectify,[],[f317]) ).
tff(f317,axiom,
! [X0: 'S10',X1: 'S2'] :
? [X201: 'S9'] :
( ( f34(f39(f52,f13(X201,X1)),X0) = f13(X201,f6(f7,$sum(f11(f12,X1),1))) )
& ( f66(f67,X0) = X201 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_317) ).
tff(f3594,plain,
spl331_152,
inference(avatar_split_clause,[],[f1759,f3592]) ).
tff(f3592,plain,
( spl331_152
<=> ! [X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK62(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_152])]) ).
tff(f1759,plain,
! [X0: 'S10',X1: 'S2'] : ( f66(f67,X0) = sK62(X0,X1) ),
inference(cnf_transformation,[],[f1044]) ).
tff(f1044,plain,
! [X0: 'S10',X1: 'S2'] :
( ( f34(f39(f52,X0),f13(sK62(X0,X1),X1)) = f13(sK62(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f66(f67,X0) = sK62(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62])],[f650,f1043]) ).
tff(f1043,plain,
! [X0: 'S10',X1: 'S2'] :
( ? [X2: 'S9'] :
( ( f34(f39(f52,X0),f13(X2,X1)) = f13(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f66(f67,X0) = X2 ) )
=> ( ( f34(f39(f52,X0),f13(sK62(X0,X1),X1)) = f13(sK62(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f66(f67,X0) = sK62(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f650,plain,
! [X0: 'S10',X1: 'S2'] :
? [X2: 'S9'] :
( ( f34(f39(f52,X0),f13(X2,X1)) = f13(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f66(f67,X0) = X2 ) ),
inference(rectify,[],[f325]) ).
tff(f325,axiom,
! [X0: 'S10',X1: 'S2'] :
? [X209: 'S9'] :
( ( f34(f39(f52,X0),f13(X209,X1)) = f13(X209,f6(f7,$sum(f11(f12,X1),1))) )
& ( f66(f67,X0) = X209 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_325) ).
tff(f3590,plain,
spl331_151,
inference(avatar_split_clause,[],[f1757,f3588]) ).
tff(f3588,plain,
( spl331_151
<=> ! [X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK61(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_151])]) ).
tff(f1757,plain,
! [X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK61(X0,X1) ),
inference(cnf_transformation,[],[f1042]) ).
tff(f1042,plain,
! [X0: $int,X1: 'S2'] :
( ( f11(sK61(X0,X1),f6(f7,$sum(f11(f12,X1),1))) = f8(f9(f10,f11(sK61(X0,X1),X1)),X0) )
& ( f63(f64,X0) = sK61(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61])],[f649,f1041]) ).
tff(f1041,plain,
! [X0: $int,X1: 'S2'] :
( ? [X2: 'S8'] :
( ( f11(X2,f6(f7,$sum(f11(f12,X1),1))) = f8(f9(f10,f11(X2,X1)),X0) )
& ( f63(f64,X0) = X2 ) )
=> ( ( f11(sK61(X0,X1),f6(f7,$sum(f11(f12,X1),1))) = f8(f9(f10,f11(sK61(X0,X1),X1)),X0) )
& ( f63(f64,X0) = sK61(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f649,plain,
! [X0: $int,X1: 'S2'] :
? [X2: 'S8'] :
( ( f11(X2,f6(f7,$sum(f11(f12,X1),1))) = f8(f9(f10,f11(X2,X1)),X0) )
& ( f63(f64,X0) = X2 ) ),
inference(rectify,[],[f314]) ).
tff(f314,axiom,
! [X0: $int,X1: 'S2'] :
? [X198: 'S8'] :
( ( f8(f9(f10,f11(X198,X1)),X0) = f11(X198,f6(f7,$sum(f11(f12,X1),1))) )
& ( f63(f64,X0) = X198 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_314) ).
tff(f3586,plain,
spl331_150,
inference(avatar_split_clause,[],[f1755,f3584]) ).
tff(f3584,plain,
( spl331_150
<=> ! [X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK60(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_150])]) ).
tff(f1755,plain,
! [X0: $int,X1: 'S2'] : ( f63(f64,X0) = sK60(X0,X1) ),
inference(cnf_transformation,[],[f1040]) ).
tff(f1040,plain,
! [X0: $int,X1: 'S2'] :
( ( f8(f9(f10,X0),f11(sK60(X0,X1),X1)) = f11(sK60(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f63(f64,X0) = sK60(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60])],[f648,f1039]) ).
tff(f1039,plain,
! [X0: $int,X1: 'S2'] :
( ? [X2: 'S8'] :
( ( f8(f9(f10,X0),f11(X2,X1)) = f11(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f63(f64,X0) = X2 ) )
=> ( ( f8(f9(f10,X0),f11(sK60(X0,X1),X1)) = f11(sK60(X0,X1),f6(f7,$sum(f11(f12,X1),1))) )
& ( f63(f64,X0) = sK60(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f648,plain,
! [X0: $int,X1: 'S2'] :
? [X2: 'S8'] :
( ( f8(f9(f10,X0),f11(X2,X1)) = f11(X2,f6(f7,$sum(f11(f12,X1),1))) )
& ( f63(f64,X0) = X2 ) ),
inference(rectify,[],[f322]) ).
tff(f322,axiom,
! [X0: $int,X1: 'S2'] :
? [X206: 'S8'] :
( ( f8(f9(f10,X0),f11(X206,X1)) = f11(X206,f6(f7,$sum(f11(f12,X1),1))) )
& ( f63(f64,X0) = X206 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_322) ).
tff(f3582,plain,
( spl331_149
| ~ spl331_61
| ~ spl331_62 ),
inference(avatar_split_clause,[],[f3372,f3196,f3192,f3580]) ).
tff(f3580,plain,
( spl331_149
<=> ! [X2: $int,X3: 'S10'] : ( sK15(X2) = sK16(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_149])]) ).
tff(f3192,plain,
( spl331_61
<=> ! [X0: $int] : ( f6(f7,2) = sK15(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_61])]) ).
tff(f3372,plain,
( ! [X2: $int,X3: 'S10'] : ( sK15(X2) = sK16(X3) )
| ~ spl331_61
| ~ spl331_62 ),
inference(superposition,[],[f3197,f3193]) ).
tff(f3193,plain,
( ! [X0: $int] : ( f6(f7,2) = sK15(X0) )
| ~ spl331_61 ),
inference(avatar_component_clause,[],[f3192]) ).
tff(f3578,plain,
spl331_148,
inference(avatar_split_clause,[],[f1751,f3576]) ).
tff(f3576,plain,
( spl331_148
<=> ! [X0: 'S2',X1: 'S2'] : ( f6(f7,1) = sK59(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_148])]) ).
tff(f1751,plain,
! [X0: 'S2',X1: 'S2'] : ( f6(f7,1) = sK59(X0,X1) ),
inference(cnf_transformation,[],[f1038]) ).
tff(f1038,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = sK59(X0,X1) )
| ( sK59(X0,X1) != X1 )
| ( sK59(X0,X1) != X0 ) )
& ( ( ( sK59(X0,X1) = X1 )
& ( sK59(X0,X1) = X0 ) )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != sK59(X0,X1) ) )
& ( f6(f7,1) = sK59(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59])],[f1036,f1037]) ).
tff(f1037,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
| ( X1 != X2 )
| ( X0 != X2 ) )
& ( ( ( X1 = X2 )
& ( X0 = X2 ) )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != X2 ) )
& ( f6(f7,1) = X2 ) )
=> ( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = sK59(X0,X1) )
| ( sK59(X0,X1) != X1 )
| ( sK59(X0,X1) != X0 ) )
& ( ( ( sK59(X0,X1) = X1 )
& ( sK59(X0,X1) = X0 ) )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != sK59(X0,X1) ) )
& ( f6(f7,1) = sK59(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1036,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
| ( X1 != X2 )
| ( X0 != X2 ) )
& ( ( ( X1 = X2 )
& ( X0 = X2 ) )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != X2 ) )
& ( f6(f7,1) = X2 ) ),
inference(flattening,[],[f1035]) ).
tff(f1035,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
| ( X1 != X2 )
| ( X0 != X2 ) )
& ( ( ( X1 = X2 )
& ( X0 = X2 ) )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != X2 ) )
& ( f6(f7,1) = X2 ) ),
inference(nnf_transformation,[],[f647]) ).
tff(f647,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
<=> ( ( X1 = X2 )
& ( X0 = X2 ) ) )
& ( f6(f7,1) = X2 ) ),
inference(rectify,[],[f137]) ).
tff(f137,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X27: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X27 )
<=> ( ( X1 = X27 )
& ( X0 = X27 ) ) )
& ( f6(f7,1) = X27 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_137) ).
tff(f3574,plain,
spl331_147,
inference(avatar_split_clause,[],[f1747,f3572]) ).
tff(f3572,plain,
( spl331_147
<=> ! [X0: 'S2',X1: 'S2'] : ( f6(f7,1) = sK58(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_147])]) ).
tff(f1747,plain,
! [X0: 'S2',X1: 'S2'] : ( f6(f7,1) = sK58(X0,X1) ),
inference(cnf_transformation,[],[f1034]) ).
tff(f1034,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = sK58(X0,X1) )
| ( sK58(X0,X1) != X1 )
| ( sK58(X0,X1) != X0 ) )
& ( ( ( sK58(X0,X1) = X1 )
& ( sK58(X0,X1) = X0 ) )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != sK58(X0,X1) ) )
& ( f6(f7,1) = sK58(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58])],[f1032,f1033]) ).
tff(f1033,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
| ( X1 != X2 )
| ( X0 != X2 ) )
& ( ( ( X1 = X2 )
& ( X0 = X2 ) )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != X2 ) )
& ( f6(f7,1) = X2 ) )
=> ( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = sK58(X0,X1) )
| ( sK58(X0,X1) != X1 )
| ( sK58(X0,X1) != X0 ) )
& ( ( ( sK58(X0,X1) = X1 )
& ( sK58(X0,X1) = X0 ) )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != sK58(X0,X1) ) )
& ( f6(f7,1) = sK58(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1032,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
| ( X1 != X2 )
| ( X0 != X2 ) )
& ( ( ( X1 = X2 )
& ( X0 = X2 ) )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != X2 ) )
& ( f6(f7,1) = X2 ) ),
inference(flattening,[],[f1031]) ).
tff(f1031,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
| ( X1 != X2 )
| ( X0 != X2 ) )
& ( ( ( X1 = X2 )
& ( X0 = X2 ) )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != X2 ) )
& ( f6(f7,1) = X2 ) ),
inference(nnf_transformation,[],[f646]) ).
tff(f646,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
<=> ( ( X1 = X2 )
& ( X0 = X2 ) ) )
& ( f6(f7,1) = X2 ) ),
inference(rectify,[],[f146]) ).
tff(f146,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X44: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X44 )
<=> ( ( X1 = X44 )
& ( X0 = X44 ) ) )
& ( f6(f7,1) = X44 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_146) ).
tff(f3570,plain,
spl331_146,
inference(avatar_split_clause,[],[f1743,f3568]) ).
tff(f3568,plain,
( spl331_146
<=> ! [X0: 'S2',X1: 'S2'] : ( f6(f7,0) = sK57(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_146])]) ).
tff(f1743,plain,
! [X0: 'S2',X1: 'S2'] : ( f6(f7,0) = sK57(X0,X1) ),
inference(cnf_transformation,[],[f1030]) ).
tff(f1030,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = sK57(X0,X1) )
| ( ( sK57(X0,X1) != X1 )
& ( sK57(X0,X1) != X0 ) ) )
& ( ( sK57(X0,X1) = X1 )
| ( sK57(X0,X1) = X0 )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != sK57(X0,X1) ) )
& ( f6(f7,0) = sK57(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f1028,f1029]) ).
tff(f1029,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
| ( ( X1 != X2 )
& ( X0 != X2 ) ) )
& ( ( X1 = X2 )
| ( X0 = X2 )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != X2 ) )
& ( f6(f7,0) = X2 ) )
=> ( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = sK57(X0,X1) )
| ( ( sK57(X0,X1) != X1 )
& ( sK57(X0,X1) != X0 ) ) )
& ( ( sK57(X0,X1) = X1 )
| ( sK57(X0,X1) = X0 )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != sK57(X0,X1) ) )
& ( f6(f7,0) = sK57(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1028,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
| ( ( X1 != X2 )
& ( X0 != X2 ) ) )
& ( ( X1 = X2 )
| ( X0 = X2 )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != X2 ) )
& ( f6(f7,0) = X2 ) ),
inference(flattening,[],[f1027]) ).
tff(f1027,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
| ( ( X1 != X2 )
& ( X0 != X2 ) ) )
& ( ( X1 = X2 )
| ( X0 = X2 )
| ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) != X2 ) )
& ( f6(f7,0) = X2 ) ),
inference(nnf_transformation,[],[f645]) ).
tff(f645,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X2 )
<=> ( ( X1 = X2 )
| ( X0 = X2 ) ) )
& ( f6(f7,0) = X2 ) ),
inference(rectify,[],[f147]) ).
tff(f147,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X45: 'S2'] :
( ( ( f6(f7,f8(f9(f10,f11(f12,X0)),f11(f12,X1))) = X45 )
<=> ( ( X1 = X45 )
| ( X0 = X45 ) ) )
& ( f6(f7,0) = X45 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_147) ).
tff(f3566,plain,
spl331_145,
inference(avatar_split_clause,[],[f1741,f3564]) ).
tff(f3564,plain,
( spl331_145
<=> ! [X0: $real,X1: $real] : ( f6(f7,2) = sK56(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_145])]) ).
tff(f1741,plain,
! [X0: $real,X1: $real] : ( f6(f7,2) = sK56(X0,X1) ),
inference(cnf_transformation,[],[f1026]) ).
tff(f1026,plain,
! [X0: $real,X1: $real] :
( ( f19(f59(f60,$sum(X0,X1)),sK56(X0,X1)) = $sum($sum(f19(f59(f60,X0),sK56(X0,X1)),f19(f59(f60,X1),sK56(X0,X1))),f22(f49(f50,$product(2.0,X0)),X1)) )
& ( f6(f7,2) = sK56(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56])],[f644,f1025]) ).
tff(f1025,plain,
! [X0: $real,X1: $real] :
( ? [X2: 'S2'] :
( ( f19(f59(f60,$sum(X0,X1)),X2) = $sum($sum(f19(f59(f60,X0),X2),f19(f59(f60,X1),X2)),f22(f49(f50,$product(2.0,X0)),X1)) )
& ( f6(f7,2) = X2 ) )
=> ( ( f19(f59(f60,$sum(X0,X1)),sK56(X0,X1)) = $sum($sum(f19(f59(f60,X0),sK56(X0,X1)),f19(f59(f60,X1),sK56(X0,X1))),f22(f49(f50,$product(2.0,X0)),X1)) )
& ( f6(f7,2) = sK56(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f644,plain,
! [X0: $real,X1: $real] :
? [X2: 'S2'] :
( ( f19(f59(f60,$sum(X0,X1)),X2) = $sum($sum(f19(f59(f60,X0),X2),f19(f59(f60,X1),X2)),f22(f49(f50,$product(2.0,X0)),X1)) )
& ( f6(f7,2) = X2 ) ),
inference(rectify,[],[f364]) ).
tff(f364,axiom,
! [X0: $real,X1: $real] :
? [X218: 'S2'] :
( ( f19(f59(f60,$sum(X0,X1)),X218) = $sum($sum(f19(f59(f60,X0),X218),f19(f59(f60,X1),X218)),f22(f49(f50,$product(2.0,X0)),X1)) )
& ( f6(f7,2) = X218 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_364) ).
tff(f3562,plain,
spl331_144,
inference(avatar_split_clause,[],[f1739,f3560]) ).
tff(f3560,plain,
( spl331_144
<=> ! [X0: $real,X1: $real] : ( f6(f7,2) = sK55(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_144])]) ).
tff(f1739,plain,
! [X0: $real,X1: $real] : ( f6(f7,2) = sK55(X0,X1) ),
inference(cnf_transformation,[],[f1024]) ).
tff(f1024,plain,
! [X0: $real,X1: $real] :
( ~ $less(f19(f59(f60,X1),sK55(X0,X1)),$uminus(f19(f59(f60,X0),sK55(X0,X1))))
& ( f6(f7,2) = sK55(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55])],[f643,f1023]) ).
tff(f1023,plain,
! [X0: $real,X1: $real] :
( ? [X2: 'S2'] :
( ~ $less(f19(f59(f60,X1),X2),$uminus(f19(f59(f60,X0),X2)))
& ( f6(f7,2) = X2 ) )
=> ( ~ $less(f19(f59(f60,X1),sK55(X0,X1)),$uminus(f19(f59(f60,X0),sK55(X0,X1))))
& ( f6(f7,2) = sK55(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f643,plain,
! [X0: $real,X1: $real] :
? [X2: 'S2'] :
( ~ $less(f19(f59(f60,X1),X2),$uminus(f19(f59(f60,X0),X2)))
& ( f6(f7,2) = X2 ) ),
inference(rectify,[],[f506]) ).
tff(f506,plain,
! [X0: $real,X1: $real] :
? [X272: 'S2'] :
( ~ $less(f19(f59(f60,X1),X272),$uminus(f19(f59(f60,X0),X272)))
& ( f6(f7,2) = X272 ) ),
inference(theory_normalization,[],[f429]) ).
tff(f429,axiom,
! [X0: $real,X1: $real] :
? [X272: 'S2'] :
( $lesseq($uminus(f19(f59(f60,X0),X272)),f19(f59(f60,X1),X272))
& ( f6(f7,2) = X272 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_429) ).
tff(f3558,plain,
spl331_143,
inference(avatar_split_clause,[],[f1609,f3556]) ).
tff(f3556,plain,
( spl331_143
<=> ! [X0: $int] : ( sK41(X0) = f8(f21,sK41(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_143])]) ).
tff(f1609,plain,
! [X0: $int] : ( sK41(X0) = f8(f21,sK41(X0)) ),
inference(cnf_transformation,[],[f980]) ).
tff(f3554,plain,
spl331_142,
inference(avatar_split_clause,[],[f1607,f3552]) ).
tff(f3552,plain,
( spl331_142
<=> ! [X0: $real] : ( sK40(X0) = f22(f23,sK40(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_142])]) ).
tff(f1607,plain,
! [X0: $real] : ( sK40(X0) = f22(f23,sK40(X0)) ),
inference(cnf_transformation,[],[f978]) ).
tff(f3549,plain,
spl331_141,
inference(avatar_split_clause,[],[f1589,f3547]) ).
tff(f1589,plain,
! [X0: 'S2'] : ( f9(f10,sK31(X0)) = sK32(X0) ),
inference(cnf_transformation,[],[f962]) ).
tff(f962,plain,
! [X0: 'S2'] :
( ~ $less(f8(sK32(X0),f8(sK32(X0),sK31(X0))),sK31(X0))
& ( f9(f10,sK31(X0)) = sK32(X0) )
& ( f11(f12,X0) = sK31(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32])],[f630,f961,f960]) ).
tff(f960,plain,
! [X0: 'S2'] :
( ? [X1: $int] :
( ? [X2: 'S6'] :
( ~ $less(f8(X2,f8(X2,X1)),X1)
& ( f9(f10,X1) = X2 ) )
& ( f11(f12,X0) = X1 ) )
=> ( ? [X2: 'S6'] :
( ~ $less(f8(X2,f8(X2,sK31(X0))),sK31(X0))
& ( f9(f10,sK31(X0)) = X2 ) )
& ( f11(f12,X0) = sK31(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f961,plain,
! [X0: 'S2'] :
( ? [X2: 'S6'] :
( ~ $less(f8(X2,f8(X2,sK31(X0))),sK31(X0))
& ( f9(f10,sK31(X0)) = X2 ) )
=> ( ~ $less(f8(sK32(X0),f8(sK32(X0),sK31(X0))),sK31(X0))
& ( f9(f10,sK31(X0)) = sK32(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f630,plain,
! [X0: 'S2'] :
? [X1: $int] :
( ? [X2: 'S6'] :
( ~ $less(f8(X2,f8(X2,X1)),X1)
& ( f9(f10,X1) = X2 ) )
& ( f11(f12,X0) = X1 ) ),
inference(rectify,[],[f474]) ).
tff(f474,plain,
! [X0: 'S2'] :
? [X23: $int] :
( ? [X24: 'S6'] :
( ~ $less(f8(X24,f8(X24,X23)),X23)
& ( f9(f10,X23) = X24 ) )
& ( f11(f12,X0) = X23 ) ),
inference(theory_normalization,[],[f133]) ).
tff(f133,axiom,
! [X0: 'S2'] :
? [X23: $int] :
( ? [X24: 'S6'] :
( $lesseq(X23,f8(X24,f8(X24,X23)))
& ( f9(f10,X23) = X24 ) )
& ( f11(f12,X0) = X23 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_133) ).
tff(f3545,plain,
spl331_140,
inference(avatar_split_clause,[],[f1581,f3543]) ).
tff(f1581,plain,
! [X0: 'S2'] : ( sK27(X0) = f8(f21,sK27(X0)) ),
inference(cnf_transformation,[],[f953]) ).
tff(f3540,plain,
spl331_139,
inference(avatar_split_clause,[],[f1566,f3538]) ).
tff(f1566,plain,
! [X0: 'S2'] : ( sK21(X0) = f22(f30,sK21(X0)) ),
inference(cnf_transformation,[],[f941]) ).
tff(f941,plain,
! [X0: 'S2'] :
( ( sK21(X0) = f22(f30,sK21(X0)) )
& ( f19(f20,X0) = sK21(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f620,f940]) ).
tff(f940,plain,
! [X0: 'S2'] :
( ? [X1: $real] :
( ( f22(f30,X1) = X1 )
& ( f19(f20,X0) = X1 ) )
=> ( ( sK21(X0) = f22(f30,sK21(X0)) )
& ( f19(f20,X0) = sK21(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f620,plain,
! [X0: 'S2'] :
? [X1: $real] :
( ( f22(f30,X1) = X1 )
& ( f19(f20,X0) = X1 ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: 'S2'] :
? [X6: $real] :
( ( f22(f30,X6) = X6 )
& ( f19(f20,X0) = X6 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_15) ).
tff(f3536,plain,
( spl331_138
| ~ spl331_62 ),
inference(avatar_split_clause,[],[f3371,f3196,f3534]) ).
tff(f3534,plain,
( spl331_138
<=> ! [X0: 'S10',X1: 'S10'] : ( sK16(X0) = sK16(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_138])]) ).
tff(f3371,plain,
( ! [X0: 'S10',X1: 'S10'] : ( sK16(X0) = sK16(X1) )
| ~ spl331_62 ),
inference(superposition,[],[f3197,f3197]) ).
tff(f3531,plain,
spl331_137,
inference(avatar_split_clause,[],[f1564,f3529]) ).
tff(f1564,plain,
! [X0: 'S2'] : ( sK20(X0) = f22(f33,sK20(X0)) ),
inference(cnf_transformation,[],[f939]) ).
tff(f939,plain,
! [X0: 'S2'] :
( ( sK20(X0) = f22(f33,sK20(X0)) )
& ( f19(f20,X0) = sK20(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f619,f938]) ).
tff(f938,plain,
! [X0: 'S2'] :
( ? [X1: $real] :
( ( f22(f33,X1) = X1 )
& ( f19(f20,X0) = X1 ) )
=> ( ( sK20(X0) = f22(f33,sK20(X0)) )
& ( f19(f20,X0) = sK20(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f619,plain,
! [X0: 'S2'] :
? [X1: $real] :
( ( f22(f33,X1) = X1 )
& ( f19(f20,X0) = X1 ) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X0: 'S2'] :
? [X7: $real] :
( ( f22(f33,X7) = X7 )
& ( f19(f20,X0) = X7 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_18) ).
tff(f3527,plain,
spl331_136,
inference(avatar_split_clause,[],[f1562,f3525]) ).
tff(f1562,plain,
! [X0: 'S2'] : ( sK19(X0) = f22(f23,sK19(X0)) ),
inference(cnf_transformation,[],[f937]) ).
tff(f937,plain,
! [X0: 'S2'] :
( ( sK19(X0) = f22(f23,sK19(X0)) )
& ( f19(f20,X0) = sK19(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f618,f936]) ).
tff(f936,plain,
! [X0: 'S2'] :
( ? [X1: $real] :
( ( f22(f23,X1) = X1 )
& ( f19(f20,X0) = X1 ) )
=> ( ( sK19(X0) = f22(f23,sK19(X0)) )
& ( f19(f20,X0) = sK19(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f618,plain,
! [X0: 'S2'] :
? [X1: $real] :
( ( f22(f23,X1) = X1 )
& ( f19(f20,X0) = X1 ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: 'S2'] :
? [X5: $real] :
( ( f22(f23,X5) = X5 )
& ( f19(f20,X0) = X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_6) ).
tff(f3523,plain,
spl331_135,
inference(avatar_split_clause,[],[f1560,f3521]) ).
tff(f3521,plain,
( spl331_135
<=> ! [X0: $real] : ( sK18(X0) = f34(f35,sK18(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_135])]) ).
tff(f1560,plain,
! [X0: $real] : ( sK18(X0) = f34(f35,sK18(X0)) ),
inference(cnf_transformation,[],[f935]) ).
tff(f3519,plain,
spl331_134,
inference(avatar_split_clause,[],[f1558,f3517]) ).
tff(f3517,plain,
( spl331_134
<=> ! [X0: 'S2'] : ( sK17(X0) = f34(f35,sK17(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_134])]) ).
tff(f1558,plain,
! [X0: 'S2'] : ( sK17(X0) = f34(f35,sK17(X0)) ),
inference(cnf_transformation,[],[f933]) ).
tff(f933,plain,
! [X0: 'S2'] :
( ( sK17(X0) = f34(f35,sK17(X0)) )
& ( f13(f14,X0) = sK17(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f616,f932]) ).
tff(f932,plain,
! [X0: 'S2'] :
( ? [X1: 'S10'] :
( ( f34(f35,X1) = X1 )
& ( f13(f14,X0) = X1 ) )
=> ( ( sK17(X0) = f34(f35,sK17(X0)) )
& ( f13(f14,X0) = sK17(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f616,plain,
! [X0: 'S2'] :
? [X1: 'S10'] :
( ( f34(f35,X1) = X1 )
& ( f13(f14,X0) = X1 ) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X0: 'S2'] :
? [X8: 'S10'] :
( ( f34(f35,X8) = X8 )
& ( f13(f14,X0) = X8 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_19) ).
tff(f3514,plain,
( spl331_133
| ~ spl331_67
| ~ spl331_68
| ~ spl331_132 ),
inference(avatar_split_clause,[],[f3510,f3506,f3220,f3216,f3512]) ).
tff(f3506,plain,
( spl331_132
<=> ! [X0: 'S10'] : ~ $less(f27(f31,X0),f27(f28,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_132])]) ).
tff(f3510,plain,
( ! [X0: 'S10'] : ~ $less(sK24(X0),sK23(X0))
| ~ spl331_67
| ~ spl331_68
| ~ spl331_132 ),
inference(forward_demodulation,[],[f3509,f3221]) ).
tff(f3509,plain,
( ! [X0: 'S10'] : ~ $less(f27(f31,X0),sK23(X0))
| ~ spl331_67
| ~ spl331_132 ),
inference(forward_demodulation,[],[f3507,f3217]) ).
tff(f3507,plain,
( ! [X0: 'S10'] : ~ $less(f27(f31,X0),f27(f28,X0))
| ~ spl331_132 ),
inference(avatar_component_clause,[],[f3506]) ).
tff(f3508,plain,
spl331_132,
inference(avatar_split_clause,[],[f1482,f3506]) ).
tff(f1482,plain,
! [X0: 'S10'] : ~ $less(f27(f31,X0),f27(f28,X0)),
inference(cnf_transformation,[],[f460]) ).
tff(f460,plain,
! [X0: 'S10'] : ~ $less(f27(f31,X0),f27(f28,X0)),
inference(theory_normalization,[],[f24]) ).
tff(f24,axiom,
! [X0: 'S10'] : $lesseq(f27(f28,X0),f27(f31,X0)),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_24) ).
tff(f3504,plain,
spl331_131,
inference(avatar_split_clause,[],[f1481,f3502]) ).
tff(f1481,plain,
! [X0: 'S2'] : ~ $less(f19(f59(f60,2.0),X0),1.0),
inference(cnf_transformation,[],[f459]) ).
tff(f459,plain,
! [X0: 'S2'] : ~ $less(f19(f59(f60,2.0),X0),1.0),
inference(theory_normalization,[],[f428]) ).
tff(f428,axiom,
! [X0: 'S2'] : $lesseq(1.0,f19(f59(f60,2.0),X0)),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_428) ).
tff(f3500,plain,
spl331_130,
inference(avatar_split_clause,[],[f1480,f3498]) ).
tff(f3498,plain,
( spl331_130
<=> ! [X0: 'S10'] : ( f34(f35,f34(f35,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_130])]) ).
tff(f1480,plain,
! [X0: 'S10'] : ( f34(f35,f34(f35,X0)) = X0 ),
inference(cnf_transformation,[],[f26]) ).
tff(f26,axiom,
! [X0: 'S10'] : ( f34(f35,f34(f35,X0)) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_26) ).
tff(f3496,plain,
( spl331_129
| ~ spl331_60
| ~ spl331_61 ),
inference(avatar_split_clause,[],[f3369,f3192,f3188,f3494]) ).
tff(f3494,plain,
( spl331_129
<=> ! [X2: $real,X3: $int] : ( sK14(X2) = sK15(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_129])]) ).
tff(f3369,plain,
( ! [X2: $real,X3: $int] : ( sK14(X2) = sK15(X3) )
| ~ spl331_60
| ~ spl331_61 ),
inference(superposition,[],[f3193,f3189]) ).
tff(f3492,plain,
( spl331_128
| ~ spl331_71
| ~ spl331_127 ),
inference(avatar_split_clause,[],[f3488,f3485,f3232,f3490]) ).
tff(f3490,plain,
( spl331_128
<=> ! [X0: 'S2'] : ( f6(f7,sK27(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_128])]) ).
tff(f3232,plain,
( spl331_71
<=> ! [X0: 'S2'] : ( f11(f12,X0) = sK27(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_71])]) ).
tff(f3485,plain,
( spl331_127
<=> ! [X0: 'S2'] : ( f6(f7,f11(f12,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_127])]) ).
tff(f3488,plain,
( ! [X0: 'S2'] : ( f6(f7,sK27(X0)) = X0 )
| ~ spl331_71
| ~ spl331_127 ),
inference(forward_demodulation,[],[f3486,f3233]) ).
tff(f3233,plain,
( ! [X0: 'S2'] : ( f11(f12,X0) = sK27(X0) )
| ~ spl331_71 ),
inference(avatar_component_clause,[],[f3232]) ).
tff(f3486,plain,
( ! [X0: 'S2'] : ( f6(f7,f11(f12,X0)) = X0 )
| ~ spl331_127 ),
inference(avatar_component_clause,[],[f3485]) ).
tff(f3487,plain,
spl331_127,
inference(avatar_split_clause,[],[f1479,f3485]) ).
tff(f1479,plain,
! [X0: 'S2'] : ( f6(f7,f11(f12,X0)) = X0 ),
inference(cnf_transformation,[],[f454]) ).
tff(f454,axiom,
! [X0: 'S2'] : ( f6(f7,f11(f12,X0)) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_454) ).
tff(f3481,plain,
( spl331_126
| ~ spl331_64
| ~ spl331_125 ),
inference(avatar_split_clause,[],[f3477,f3474,f3204,f3479]) ).
tff(f3474,plain,
( spl331_125
<=> ! [X0: $real] : ( f27(f28,f16(f32,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_125])]) ).
tff(f3477,plain,
( ! [X0: $real] : ( f27(f28,sK18(X0)) = X0 )
| ~ spl331_64
| ~ spl331_125 ),
inference(forward_demodulation,[],[f3475,f3205]) ).
tff(f3475,plain,
( ! [X0: $real] : ( f27(f28,f16(f32,X0)) = X0 )
| ~ spl331_125 ),
inference(avatar_component_clause,[],[f3474]) ).
tff(f3476,plain,
spl331_125,
inference(avatar_split_clause,[],[f1478,f3474]) ).
tff(f1478,plain,
! [X0: $real] : ( f27(f28,f16(f32,X0)) = X0 ),
inference(cnf_transformation,[],[f25]) ).
tff(f25,axiom,
! [X0: $real] : ( f27(f28,f16(f32,X0)) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_25) ).
tff(f3470,plain,
( spl331_124
| ~ spl331_64
| ~ spl331_123 ),
inference(avatar_split_clause,[],[f3466,f3463,f3204,f3468]) ).
tff(f3463,plain,
( spl331_123
<=> ! [X0: $real] : ( 0.0 = f27(f36,f16(f32,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_123])]) ).
tff(f3466,plain,
( ! [X0: $real] : ( 0.0 = f27(f36,sK18(X0)) )
| ~ spl331_64
| ~ spl331_123 ),
inference(forward_demodulation,[],[f3464,f3205]) ).
tff(f3464,plain,
( ! [X0: $real] : ( 0.0 = f27(f36,f16(f32,X0)) )
| ~ spl331_123 ),
inference(avatar_component_clause,[],[f3463]) ).
tff(f3465,plain,
spl331_123,
inference(avatar_split_clause,[],[f1477,f3463]) ).
tff(f1477,plain,
! [X0: $real] : ( 0.0 = f27(f36,f16(f32,X0)) ),
inference(cnf_transformation,[],[f62]) ).
tff(f62,axiom,
! [X0: $real] : ( 0.0 = f27(f36,f16(f32,X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_62) ).
tff(f3459,plain,
( spl331_122
| ~ spl331_63
| ~ spl331_120 ),
inference(avatar_split_clause,[],[f3451,f3448,f3200,f3457]) ).
tff(f3448,plain,
( spl331_120
<=> ! [X0: 'S2'] : ( 0.0 = f27(f36,f13(f14,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_120])]) ).
tff(f3451,plain,
( ! [X0: 'S2'] : ( 0.0 = f27(f36,sK17(X0)) )
| ~ spl331_63
| ~ spl331_120 ),
inference(forward_demodulation,[],[f3449,f3201]) ).
tff(f3449,plain,
( ! [X0: 'S2'] : ( 0.0 = f27(f36,f13(f14,X0)) )
| ~ spl331_120 ),
inference(avatar_component_clause,[],[f3448]) ).
tff(f3455,plain,
( spl331_121
| ~ spl331_61 ),
inference(avatar_split_clause,[],[f3368,f3192,f3453]) ).
tff(f3453,plain,
( spl331_121
<=> ! [X0: $int,X1: $int] : ( sK15(X0) = sK15(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_121])]) ).
tff(f3368,plain,
( ! [X0: $int,X1: $int] : ( sK15(X0) = sK15(X1) )
| ~ spl331_61 ),
inference(superposition,[],[f3193,f3193]) ).
tff(f3450,plain,
spl331_120,
inference(avatar_split_clause,[],[f1476,f3448]) ).
tff(f1476,plain,
! [X0: 'S2'] : ( 0.0 = f27(f36,f13(f14,X0)) ),
inference(cnf_transformation,[],[f57]) ).
tff(f57,axiom,
! [X0: 'S2'] : ( 0.0 = f27(f36,f13(f14,X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_57) ).
tff(f3446,plain,
( spl331_119
| ~ spl331_71
| ~ spl331_118 ),
inference(avatar_split_clause,[],[f3442,f3439,f3232,f3444]) ).
tff(f3444,plain,
( spl331_119
<=> ! [X0: 'S2'] : ( f1 = f41(sK27(X0),f42) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_119])]) ).
tff(f3439,plain,
( spl331_118
<=> ! [X0: 'S2'] : ( f1 = f41(f11(f12,X0),f42) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_118])]) ).
tff(f3442,plain,
( ! [X0: 'S2'] : ( f1 = f41(sK27(X0),f42) )
| ~ spl331_71
| ~ spl331_118 ),
inference(forward_demodulation,[],[f3440,f3233]) ).
tff(f3440,plain,
( ! [X0: 'S2'] : ( f1 = f41(f11(f12,X0),f42) )
| ~ spl331_118 ),
inference(avatar_component_clause,[],[f3439]) ).
tff(f3441,plain,
spl331_118,
inference(avatar_split_clause,[],[f1475,f3439]) ).
tff(f1475,plain,
! [X0: 'S2'] : ( f1 = f41(f11(f12,X0),f42) ),
inference(cnf_transformation,[],[f47]) ).
tff(f47,axiom,
! [X0: 'S2'] : ( f1 = f41(f11(f12,X0),f42) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_47) ).
tff(f3437,plain,
( spl331_117
| ~ spl331_65
| ~ spl331_116 ),
inference(avatar_split_clause,[],[f3433,f3430,f3208,f3435]) ).
tff(f3435,plain,
( spl331_117
<=> ! [X0: 'S2'] : ( f1 = f43(sK19(X0),f44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_117])]) ).
tff(f3430,plain,
( spl331_116
<=> ! [X0: 'S2'] : ( f1 = f43(f19(f20,X0),f44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_116])]) ).
tff(f3433,plain,
( ! [X0: 'S2'] : ( f1 = f43(sK19(X0),f44) )
| ~ spl331_65
| ~ spl331_116 ),
inference(forward_demodulation,[],[f3431,f3209]) ).
tff(f3431,plain,
( ! [X0: 'S2'] : ( f1 = f43(f19(f20,X0),f44) )
| ~ spl331_116 ),
inference(avatar_component_clause,[],[f3430]) ).
tff(f3432,plain,
spl331_116,
inference(avatar_split_clause,[],[f1474,f3430]) ).
tff(f1474,plain,
! [X0: 'S2'] : ( f1 = f43(f19(f20,X0),f44) ),
inference(cnf_transformation,[],[f48]) ).
tff(f48,axiom,
! [X0: 'S2'] : ( f1 = f43(f19(f20,X0),f44) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_48) ).
tff(f3428,plain,
( spl331_115
| ~ spl331_63
| ~ spl331_114 ),
inference(avatar_split_clause,[],[f3424,f3421,f3200,f3426]) ).
tff(f3426,plain,
( spl331_115
<=> ! [X0: 'S2'] : ( f1 = f45(sK17(X0),f46) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_115])]) ).
tff(f3421,plain,
( spl331_114
<=> ! [X0: 'S2'] : ( f1 = f45(f13(f14,X0),f46) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_114])]) ).
tff(f3424,plain,
( ! [X0: 'S2'] : ( f1 = f45(sK17(X0),f46) )
| ~ spl331_63
| ~ spl331_114 ),
inference(forward_demodulation,[],[f3422,f3201]) ).
tff(f3422,plain,
( ! [X0: 'S2'] : ( f1 = f45(f13(f14,X0),f46) )
| ~ spl331_114 ),
inference(avatar_component_clause,[],[f3421]) ).
tff(f3423,plain,
spl331_114,
inference(avatar_split_clause,[],[f1473,f3421]) ).
tff(f1473,plain,
! [X0: 'S2'] : ( f1 = f45(f13(f14,X0),f46) ),
inference(cnf_transformation,[],[f49]) ).
tff(f49,axiom,
! [X0: 'S2'] : ( f1 = f45(f13(f14,X0),f46) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_49) ).
tff(f3419,plain,
( spl331_113
| ~ spl331_60 ),
inference(avatar_split_clause,[],[f3367,f3188,f3417]) ).
tff(f3417,plain,
( spl331_113
<=> ! [X0: $real,X1: $real] : ( sK14(X0) = sK14(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_113])]) ).
tff(f3367,plain,
( ! [X0: $real,X1: $real] : ( sK14(X0) = sK14(X1) )
| ~ spl331_60 ),
inference(superposition,[],[f3189,f3189]) ).
tff(f3415,plain,
spl331_112,
inference(avatar_split_clause,[],[f1472,f3413]) ).
tff(f3413,plain,
( spl331_112
<=> ! [X0: 'S2'] : ( f1 = f47(f3(f24,X0),f48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_112])]) ).
tff(f1472,plain,
! [X0: 'S2'] : ( f1 = f47(f3(f24,X0),f48) ),
inference(cnf_transformation,[],[f50]) ).
tff(f50,axiom,
! [X0: 'S2'] : ( f1 = f47(f3(f24,X0),f48) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_50) ).
tff(f3411,plain,
spl331_111,
inference(avatar_split_clause,[],[f1465,f3408]) ).
tff(f3408,plain,
( spl331_111
<=> ( f51 = f16(f17(f18,0.0),1.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_111])]) ).
tff(f1465,plain,
f51 = f16(f17(f18,0.0),1.0),
inference(cnf_transformation,[],[f58]) ).
tff(f58,axiom,
f51 = f16(f17(f18,0.0),1.0),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_58) ).
tff(f3406,plain,
spl331_110,
inference(avatar_split_clause,[],[f597,f3404]) ).
tff(f597,plain,
! [X0: $real,X1: $real] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(theory_axiom_138,[]) ).
tff(f3402,plain,
spl331_109,
inference(avatar_split_clause,[],[f586,f3400]) ).
tff(f586,plain,
! [X0: $real,X1: $real] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_138,[]) ).
tff(f3398,plain,
spl331_108,
inference(avatar_split_clause,[],[f579,f3396]) ).
tff(f579,plain,
! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(theory_axiom_138,[]) ).
tff(f3394,plain,
spl331_107,
inference(avatar_split_clause,[],[f568,f3392]) ).
tff(f568,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_138,[]) ).
tff(f3390,plain,
( spl331_106
| ~ spl331_38
| ~ spl331_67 ),
inference(avatar_split_clause,[],[f3378,f3216,f3097,f3387]) ).
tff(f3387,plain,
( spl331_106
<=> ( 0.0 = sK23(f51) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_106])]) ).
tff(f3097,plain,
( spl331_38
<=> ( 0.0 = f27(f28,f51) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_38])]) ).
tff(f3378,plain,
( ( 0.0 = sK23(f51) )
| ~ spl331_38
| ~ spl331_67 ),
inference(superposition,[],[f3217,f3099]) ).
tff(f3099,plain,
( ( 0.0 = f27(f28,f51) )
| ~ spl331_38 ),
inference(avatar_component_clause,[],[f3097]) ).
tff(f3384,plain,
( spl331_105
| ~ spl331_37
| ~ spl331_66 ),
inference(avatar_split_clause,[],[f3376,f3212,f3092,f3381]) ).
tff(f3092,plain,
( spl331_37
<=> ( 1.0 = f27(f36,f51) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_37])]) ).
tff(f3376,plain,
( ( 1.0 = sK22(f51) )
| ~ spl331_37
| ~ spl331_66 ),
inference(superposition,[],[f3213,f3094]) ).
tff(f3094,plain,
( ( 1.0 = f27(f36,f51) )
| ~ spl331_37 ),
inference(avatar_component_clause,[],[f3092]) ).
tff(f3366,plain,
spl331_104,
inference(avatar_split_clause,[],[f2675,f3364]) ).
tff(f3364,plain,
( spl331_104
<=> ! [X0: 'S10',X1: 'S10'] : ( sK149(X0,X1) = sK22(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_104])]) ).
tff(f2675,plain,
! [X0: 'S10',X1: 'S10'] : ( sK149(X0,X1) = sK22(X1) ),
inference(forward_demodulation,[],[f1914,f1567]) ).
tff(f1914,plain,
! [X0: 'S10',X1: 'S10'] : ( f27(f36,X1) = sK149(X0,X1) ),
inference(cnf_transformation,[],[f1172]) ).
tff(f3362,plain,
spl331_103,
inference(avatar_split_clause,[],[f2673,f3360]) ).
tff(f3360,plain,
( spl331_103
<=> ! [X0: 'S10',X1: 'S10'] : ( sK151(X0,X1) = sK23(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_103])]) ).
tff(f2673,plain,
! [X0: 'S10',X1: 'S10'] : ( sK151(X0,X1) = sK23(X1) ),
inference(forward_demodulation,[],[f1916,f1570]) ).
tff(f1916,plain,
! [X0: 'S10',X1: 'S10'] : ( f27(f28,X1) = sK151(X0,X1) ),
inference(cnf_transformation,[],[f1172]) ).
tff(f3358,plain,
spl331_102,
inference(avatar_split_clause,[],[f2671,f3356]) ).
tff(f3356,plain,
( spl331_102
<=> ! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK145(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_102])]) ).
tff(f2671,plain,
! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK145(X0,X1) ),
inference(forward_demodulation,[],[f1907,f1580]) ).
tff(f1907,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK145(X0,X1) ),
inference(cnf_transformation,[],[f1170]) ).
tff(f1170,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ~ $less(f8(f9(f10,sK145(X0,X1)),sK146(X0,X1)),sK147(X0,X1))
| $less(sK146(X0,X1),sK147(X0,X1))
| $less(sK145(X0,X1),sK147(X0,X1)) )
& ( ( ~ $less(sK146(X0,X1),sK147(X0,X1))
& ~ $less(sK145(X0,X1),sK147(X0,X1)) )
| $less(f8(f9(f10,sK145(X0,X1)),sK146(X0,X1)),sK147(X0,X1)) )
& ( $sum(0,1) = sK147(X0,X1) )
& ( f11(f12,X1) = sK146(X0,X1) )
& ( f11(f12,X0) = sK145(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK145,sK146,sK147])],[f1168,f1169]) ).
tff(f1169,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: $int,X3: $int,X4: $int] :
( ( ~ $less(f8(f9(f10,X2),X3),X4)
| $less(X3,X4)
| $less(X2,X4) )
& ( ( ~ $less(X3,X4)
& ~ $less(X2,X4) )
| $less(f8(f9(f10,X2),X3),X4) )
& ( $sum(0,1) = X4 )
& ( f11(f12,X1) = X3 )
& ( f11(f12,X0) = X2 ) )
=> ( ( ~ $less(f8(f9(f10,sK145(X0,X1)),sK146(X0,X1)),sK147(X0,X1))
| $less(sK146(X0,X1),sK147(X0,X1))
| $less(sK145(X0,X1),sK147(X0,X1)) )
& ( ( ~ $less(sK146(X0,X1),sK147(X0,X1))
& ~ $less(sK145(X0,X1),sK147(X0,X1)) )
| $less(f8(f9(f10,sK145(X0,X1)),sK146(X0,X1)),sK147(X0,X1)) )
& ( $sum(0,1) = sK147(X0,X1) )
& ( f11(f12,X1) = sK146(X0,X1) )
& ( f11(f12,X0) = sK145(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1168,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int,X4: $int] :
( ( ~ $less(f8(f9(f10,X2),X3),X4)
| $less(X3,X4)
| $less(X2,X4) )
& ( ( ~ $less(X3,X4)
& ~ $less(X2,X4) )
| $less(f8(f9(f10,X2),X3),X4) )
& ( $sum(0,1) = X4 )
& ( f11(f12,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(flattening,[],[f1167]) ).
tff(f1167,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int,X4: $int] :
( ( ~ $less(f8(f9(f10,X2),X3),X4)
| $less(X3,X4)
| $less(X2,X4) )
& ( ( ~ $less(X3,X4)
& ~ $less(X2,X4) )
| $less(f8(f9(f10,X2),X3),X4) )
& ( $sum(0,1) = X4 )
& ( f11(f12,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(nnf_transformation,[],[f703]) ).
tff(f703,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int,X4: $int] :
( ( ~ $less(f8(f9(f10,X2),X3),X4)
<=> ( ~ $less(X3,X4)
& ~ $less(X2,X4) ) )
& ( $sum(0,1) = X4 )
& ( f11(f12,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(rectify,[],[f520]) ).
tff(f520,plain,
! [X0: 'S2',X1: 'S2'] :
? [X39: $int,X40: $int,X41: $int] :
( ( ~ $less(f8(f9(f10,X39),X40),X41)
<=> ( ~ $less(X40,X41)
& ~ $less(X39,X41) ) )
& ( $sum(0,1) = X41 )
& ( f11(f12,X1) = X40 )
& ( f11(f12,X0) = X39 ) ),
inference(theory_normalization,[],[f144]) ).
tff(f144,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X39: $int,X40: $int,X41: $int] :
( ( $lesseq(X41,f8(f9(f10,X39),X40))
<=> ( $lesseq(X41,X40)
& $lesseq(X41,X39) ) )
& ( $sum(0,1) = X41 )
& ( f11(f12,X1) = X40 )
& ( f11(f12,X0) = X39 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_144) ).
tff(f3354,plain,
spl331_101,
inference(avatar_split_clause,[],[f2670,f3352]) ).
tff(f3352,plain,
( spl331_101
<=> ! [X0: 'S2',X1: 'S2'] : ( sK146(X0,X1) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_101])]) ).
tff(f2670,plain,
! [X0: 'S2',X1: 'S2'] : ( sK146(X0,X1) = sK27(X1) ),
inference(forward_demodulation,[],[f1908,f1580]) ).
tff(f1908,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK146(X0,X1) ),
inference(cnf_transformation,[],[f1170]) ).
tff(f3350,plain,
spl331_100,
inference(avatar_split_clause,[],[f2669,f3348]) ).
tff(f3348,plain,
( spl331_100
<=> ! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK143(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_100])]) ).
tff(f2669,plain,
! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK143(X0,X1) ),
inference(forward_demodulation,[],[f1903,f1580]) ).
tff(f1903,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK143(X0,X1) ),
inference(cnf_transformation,[],[f1166]) ).
tff(f3346,plain,
spl331_99,
inference(avatar_split_clause,[],[f2668,f3344]) ).
tff(f3344,plain,
( spl331_99
<=> ! [X0: 'S2',X1: 'S2'] : ( sK144(X0,X1) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_99])]) ).
tff(f2668,plain,
! [X0: 'S2',X1: 'S2'] : ( sK144(X0,X1) = sK27(X1) ),
inference(forward_demodulation,[],[f1904,f1580]) ).
tff(f1904,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK144(X0,X1) ),
inference(cnf_transformation,[],[f1166]) ).
tff(f3342,plain,
spl331_98,
inference(avatar_split_clause,[],[f2663,f3340]) ).
tff(f3340,plain,
( spl331_98
<=> ! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK140(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_98])]) ).
tff(f2663,plain,
! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK140(X0,X1) ),
inference(forward_demodulation,[],[f1899,f1580]) ).
tff(f1899,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK140(X0,X1) ),
inference(cnf_transformation,[],[f1164]) ).
tff(f1164,plain,
! [X0: 'S2',X1: 'S2'] :
( ( $less(sK140(X0,X1),f8(f9(f10,sK141(X0,X1)),sK140(X0,X1)))
| ~ $less(sK139(X0,X1),sK141(X0,X1))
| ~ $less(sK139(X0,X1),sK140(X0,X1)) )
& ( f11(f12,X1) = sK141(X0,X1) )
& ( f11(f12,X0) = sK140(X0,X1) )
& ( $sum(0,1) = sK139(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK139,sK140,sK141])],[f871,f1163]) ).
tff(f1163,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: $int,X3: $int,X4: $int] :
( ( $less(X3,f8(f9(f10,X4),X3))
| ~ $less(X2,X4)
| ~ $less(X2,X3) )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 )
& ( $sum(0,1) = X2 ) )
=> ( ( $less(sK140(X0,X1),f8(f9(f10,sK141(X0,X1)),sK140(X0,X1)))
| ~ $less(sK139(X0,X1),sK141(X0,X1))
| ~ $less(sK139(X0,X1),sK140(X0,X1)) )
& ( f11(f12,X1) = sK141(X0,X1) )
& ( f11(f12,X0) = sK140(X0,X1) )
& ( $sum(0,1) = sK139(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f871,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int,X4: $int] :
( ( $less(X3,f8(f9(f10,X4),X3))
| ~ $less(X2,X4)
| ~ $less(X2,X3) )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 )
& ( $sum(0,1) = X2 ) ),
inference(flattening,[],[f870]) ).
tff(f870,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int,X4: $int] :
( ( $less(X3,f8(f9(f10,X4),X3))
| ~ $less(X2,X4)
| ~ $less(X2,X3) )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 )
& ( $sum(0,1) = X2 ) ),
inference(ennf_transformation,[],[f701]) ).
tff(f701,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int,X4: $int] :
( ( $less(X2,X3)
=> ( $less(X2,X4)
=> $less(X3,f8(f9(f10,X4),X3)) ) )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 )
& ( $sum(0,1) = X2 ) ),
inference(rectify,[],[f167]) ).
tff(f167,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X96: $int,X97: $int,X98: $int] :
( ( $less(X96,X97)
=> ( $less(X96,X98)
=> $less(X97,f8(f9(f10,X98),X97)) ) )
& ( f11(f12,X1) = X98 )
& ( f11(f12,X0) = X97 )
& ( $sum(0,1) = X96 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_167) ).
tff(f3338,plain,
spl331_97,
inference(avatar_split_clause,[],[f2662,f3336]) ).
tff(f3336,plain,
( spl331_97
<=> ! [X0: 'S2',X1: 'S2'] : ( sK141(X0,X1) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_97])]) ).
tff(f2662,plain,
! [X0: 'S2',X1: 'S2'] : ( sK141(X0,X1) = sK27(X1) ),
inference(forward_demodulation,[],[f1900,f1580]) ).
tff(f1900,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK141(X0,X1) ),
inference(cnf_transformation,[],[f1164]) ).
tff(f3334,plain,
spl331_96,
inference(avatar_split_clause,[],[f2661,f3332]) ).
tff(f3332,plain,
( spl331_96
<=> ! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK137(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_96])]) ).
tff(f2661,plain,
! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK137(X0,X1) ),
inference(forward_demodulation,[],[f1895,f1580]) ).
tff(f1895,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK137(X0,X1) ),
inference(cnf_transformation,[],[f1162]) ).
tff(f1162,plain,
! [X0: 'S2',X1: 'S2'] :
( ( $less(sK137(X0,X1),f8(f9(f10,sK137(X0,X1)),sK138(X0,X1)))
| ~ $less(sK136(X0,X1),sK138(X0,X1))
| ~ $less(sK136(X0,X1),sK137(X0,X1)) )
& ( f11(f12,X1) = sK138(X0,X1) )
& ( f11(f12,X0) = sK137(X0,X1) )
& ( $sum(0,1) = sK136(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK136,sK137,sK138])],[f869,f1161]) ).
tff(f1161,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: $int,X3: $int,X4: $int] :
( ( $less(X3,f8(f9(f10,X3),X4))
| ~ $less(X2,X4)
| ~ $less(X2,X3) )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 )
& ( $sum(0,1) = X2 ) )
=> ( ( $less(sK137(X0,X1),f8(f9(f10,sK137(X0,X1)),sK138(X0,X1)))
| ~ $less(sK136(X0,X1),sK138(X0,X1))
| ~ $less(sK136(X0,X1),sK137(X0,X1)) )
& ( f11(f12,X1) = sK138(X0,X1) )
& ( f11(f12,X0) = sK137(X0,X1) )
& ( $sum(0,1) = sK136(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f869,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int,X4: $int] :
( ( $less(X3,f8(f9(f10,X3),X4))
| ~ $less(X2,X4)
| ~ $less(X2,X3) )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 )
& ( $sum(0,1) = X2 ) ),
inference(flattening,[],[f868]) ).
tff(f868,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int,X4: $int] :
( ( $less(X3,f8(f9(f10,X3),X4))
| ~ $less(X2,X4)
| ~ $less(X2,X3) )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 )
& ( $sum(0,1) = X2 ) ),
inference(ennf_transformation,[],[f700]) ).
tff(f700,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int,X4: $int] :
( ( $less(X2,X3)
=> ( $less(X2,X4)
=> $less(X3,f8(f9(f10,X3),X4)) ) )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 )
& ( $sum(0,1) = X2 ) ),
inference(rectify,[],[f168]) ).
tff(f168,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X99: $int,X100: $int,X101: $int] :
( ( $less(X99,X100)
=> ( $less(X99,X101)
=> $less(X100,f8(f9(f10,X100),X101)) ) )
& ( f11(f12,X1) = X101 )
& ( f11(f12,X0) = X100 )
& ( $sum(0,1) = X99 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_168) ).
tff(f3330,plain,
spl331_95,
inference(avatar_split_clause,[],[f2660,f3328]) ).
tff(f3328,plain,
( spl331_95
<=> ! [X0: 'S2',X1: 'S2'] : ( sK138(X0,X1) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_95])]) ).
tff(f2660,plain,
! [X0: 'S2',X1: 'S2'] : ( sK138(X0,X1) = sK27(X1) ),
inference(forward_demodulation,[],[f1896,f1580]) ).
tff(f1896,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK138(X0,X1) ),
inference(cnf_transformation,[],[f1162]) ).
tff(f3326,plain,
spl331_94,
inference(avatar_split_clause,[],[f2658,f3324]) ).
tff(f3324,plain,
( spl331_94
<=> ! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK134(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_94])]) ).
tff(f2658,plain,
! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK134(X0,X1) ),
inference(forward_demodulation,[],[f1891,f1580]) ).
tff(f1891,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK134(X0,X1) ),
inference(cnf_transformation,[],[f1160]) ).
tff(f1160,plain,
! [X0: 'S2',X1: 'S2'] :
( ( $less(sK133(X0,X1),f8(f9(f10,sK135(X0,X1)),sK134(X0,X1)))
| ~ $less(sK133(X0,X1),sK135(X0,X1))
| ~ $less(sK133(X0,X1),sK134(X0,X1)) )
& ( f11(f12,X1) = sK135(X0,X1) )
& ( f11(f12,X0) = sK134(X0,X1) )
& ( $sum(0,1) = sK133(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK133,sK134,sK135])],[f867,f1159]) ).
tff(f1159,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: $int,X3: $int,X4: $int] :
( ( $less(X2,f8(f9(f10,X4),X3))
| ~ $less(X2,X4)
| ~ $less(X2,X3) )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 )
& ( $sum(0,1) = X2 ) )
=> ( ( $less(sK133(X0,X1),f8(f9(f10,sK135(X0,X1)),sK134(X0,X1)))
| ~ $less(sK133(X0,X1),sK135(X0,X1))
| ~ $less(sK133(X0,X1),sK134(X0,X1)) )
& ( f11(f12,X1) = sK135(X0,X1) )
& ( f11(f12,X0) = sK134(X0,X1) )
& ( $sum(0,1) = sK133(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f867,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int,X4: $int] :
( ( $less(X2,f8(f9(f10,X4),X3))
| ~ $less(X2,X4)
| ~ $less(X2,X3) )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 )
& ( $sum(0,1) = X2 ) ),
inference(flattening,[],[f866]) ).
tff(f866,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int,X4: $int] :
( ( $less(X2,f8(f9(f10,X4),X3))
| ~ $less(X2,X4)
| ~ $less(X2,X3) )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 )
& ( $sum(0,1) = X2 ) ),
inference(ennf_transformation,[],[f699]) ).
tff(f699,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int,X4: $int] :
( ( $less(X2,X3)
=> ( $less(X2,X4)
=> $less(X2,f8(f9(f10,X4),X3)) ) )
& ( f11(f12,X1) = X4 )
& ( f11(f12,X0) = X3 )
& ( $sum(0,1) = X2 ) ),
inference(rectify,[],[f169]) ).
tff(f169,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X102: $int,X103: $int,X104: $int] :
( ( $less(X102,X103)
=> ( $less(X102,X104)
=> $less(X102,f8(f9(f10,X104),X103)) ) )
& ( f11(f12,X1) = X104 )
& ( f11(f12,X0) = X103 )
& ( $sum(0,1) = X102 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_169) ).
tff(f3322,plain,
spl331_93,
inference(avatar_split_clause,[],[f2657,f3320]) ).
tff(f3320,plain,
( spl331_93
<=> ! [X0: 'S2',X1: 'S2'] : ( sK135(X0,X1) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_93])]) ).
tff(f2657,plain,
! [X0: 'S2',X1: 'S2'] : ( sK135(X0,X1) = sK27(X1) ),
inference(forward_demodulation,[],[f1892,f1580]) ).
tff(f1892,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK135(X0,X1) ),
inference(cnf_transformation,[],[f1160]) ).
tff(f3318,plain,
spl331_92,
inference(avatar_split_clause,[],[f2655,f3316]) ).
tff(f3316,plain,
( spl331_92
<=> ! [X0: 'S2',X1: 'S2'] : ( sK130(X0,X1) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_92])]) ).
tff(f2655,plain,
! [X0: 'S2',X1: 'S2'] : ( sK130(X0,X1) = sK27(X1) ),
inference(forward_demodulation,[],[f1886,f1580]) ).
tff(f1886,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK130(X0,X1) ),
inference(cnf_transformation,[],[f1158]) ).
tff(f1158,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ( sK132(X0,X1) = f11(f12,f6(f7,sK132(X0,X1))) )
| $less(sK130(X0,X1),sK131(X0,X1)) )
& ( $sum(sK130(X0,X1),$uminus(sK131(X0,X1))) = sK132(X0,X1) )
& ( f11(f12,X0) = sK131(X0,X1) )
& ( f11(f12,X1) = sK130(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK130,sK131,sK132])],[f865,f1157,f1156]) ).
tff(f1156,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: $int,X3: $int] :
( ? [X4: $int] :
( ( ( f11(f12,f6(f7,X4)) = X4 )
| $less(X2,X3) )
& ( $sum(X2,$uminus(X3)) = X4 ) )
& ( f11(f12,X0) = X3 )
& ( f11(f12,X1) = X2 ) )
=> ( ? [X4: $int] :
( ( ( f11(f12,f6(f7,X4)) = X4 )
| $less(sK130(X0,X1),sK131(X0,X1)) )
& ( $sum(sK130(X0,X1),$uminus(sK131(X0,X1))) = X4 ) )
& ( f11(f12,X0) = sK131(X0,X1) )
& ( f11(f12,X1) = sK130(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1157,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X4: $int] :
( ( ( f11(f12,f6(f7,X4)) = X4 )
| $less(sK130(X0,X1),sK131(X0,X1)) )
& ( $sum(sK130(X0,X1),$uminus(sK131(X0,X1))) = X4 ) )
=> ( ( ( sK132(X0,X1) = f11(f12,f6(f7,sK132(X0,X1))) )
| $less(sK130(X0,X1),sK131(X0,X1)) )
& ( $sum(sK130(X0,X1),$uminus(sK131(X0,X1))) = sK132(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f865,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int] :
( ? [X4: $int] :
( ( ( f11(f12,f6(f7,X4)) = X4 )
| $less(X2,X3) )
& ( $sum(X2,$uminus(X3)) = X4 ) )
& ( f11(f12,X0) = X3 )
& ( f11(f12,X1) = X2 ) ),
inference(ennf_transformation,[],[f698]) ).
tff(f698,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int] :
( ? [X4: $int] :
( ( ~ $less(X2,X3)
=> ( f11(f12,f6(f7,X4)) = X4 ) )
& ( $sum(X2,$uminus(X3)) = X4 ) )
& ( f11(f12,X0) = X3 )
& ( f11(f12,X1) = X2 ) ),
inference(rectify,[],[f518]) ).
tff(f518,plain,
! [X0: 'S2',X1: 'S2'] :
? [X223: $int,X224: $int] :
( ? [X225: $int] :
( ( ~ $less(X223,X224)
=> ( f11(f12,f6(f7,X225)) = X225 ) )
& ( $sum(X223,$uminus(X224)) = X225 ) )
& ( f11(f12,X0) = X224 )
& ( f11(f12,X1) = X223 ) ),
inference(theory_normalization,[],[f374]) ).
tff(f374,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X223: $int,X224: $int] :
( ? [X225: $int] :
( ( $lesseq(X224,X223)
=> ( f11(f12,f6(f7,X225)) = X225 ) )
& ( $difference(X223,X224) = X225 ) )
& ( f11(f12,X0) = X224 )
& ( f11(f12,X1) = X223 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_374) ).
tff(f3314,plain,
spl331_91,
inference(avatar_split_clause,[],[f2654,f3312]) ).
tff(f3312,plain,
( spl331_91
<=> ! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK131(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_91])]) ).
tff(f2654,plain,
! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK131(X0,X1) ),
inference(forward_demodulation,[],[f1887,f1580]) ).
tff(f1887,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK131(X0,X1) ),
inference(cnf_transformation,[],[f1158]) ).
tff(f3310,plain,
spl331_90,
inference(avatar_split_clause,[],[f2652,f3308]) ).
tff(f3308,plain,
( spl331_90
<=> ! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK128(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_90])]) ).
tff(f2652,plain,
! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK128(X0,X1) ),
inference(forward_demodulation,[],[f1881,f1580]) ).
tff(f1881,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK128(X0,X1) ),
inference(cnf_transformation,[],[f1155]) ).
tff(f1155,plain,
! [X0: 'S2',X1: 'S2'] :
( ( $less(0,f8(f9(f10,sK128(X0,X1)),sK129(X0,X1)))
| ~ $less(0,sK129(X0,X1))
| ~ $less(0,sK128(X0,X1)) )
& ( ( $less(0,sK129(X0,X1))
& $less(0,sK128(X0,X1)) )
| ~ $less(0,f8(f9(f10,sK128(X0,X1)),sK129(X0,X1))) )
& ( f11(f12,X1) = sK129(X0,X1) )
& ( f11(f12,X0) = sK128(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK128,sK129])],[f1153,f1154]) ).
tff(f1154,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: $int,X3: $int] :
( ( $less(0,f8(f9(f10,X2),X3))
| ~ $less(0,X3)
| ~ $less(0,X2) )
& ( ( $less(0,X3)
& $less(0,X2) )
| ~ $less(0,f8(f9(f10,X2),X3)) )
& ( f11(f12,X1) = X3 )
& ( f11(f12,X0) = X2 ) )
=> ( ( $less(0,f8(f9(f10,sK128(X0,X1)),sK129(X0,X1)))
| ~ $less(0,sK129(X0,X1))
| ~ $less(0,sK128(X0,X1)) )
& ( ( $less(0,sK129(X0,X1))
& $less(0,sK128(X0,X1)) )
| ~ $less(0,f8(f9(f10,sK128(X0,X1)),sK129(X0,X1))) )
& ( f11(f12,X1) = sK129(X0,X1) )
& ( f11(f12,X0) = sK128(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1153,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int] :
( ( $less(0,f8(f9(f10,X2),X3))
| ~ $less(0,X3)
| ~ $less(0,X2) )
& ( ( $less(0,X3)
& $less(0,X2) )
| ~ $less(0,f8(f9(f10,X2),X3)) )
& ( f11(f12,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(flattening,[],[f1152]) ).
tff(f1152,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int] :
( ( $less(0,f8(f9(f10,X2),X3))
| ~ $less(0,X3)
| ~ $less(0,X2) )
& ( ( $less(0,X3)
& $less(0,X2) )
| ~ $less(0,f8(f9(f10,X2),X3)) )
& ( f11(f12,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(nnf_transformation,[],[f697]) ).
tff(f697,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int] :
( ( $less(0,f8(f9(f10,X2),X3))
<=> ( $less(0,X3)
& $less(0,X2) ) )
& ( f11(f12,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(rectify,[],[f136]) ).
tff(f136,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X25: $int,X26: $int] :
( ( $less(0,f8(f9(f10,X25),X26))
<=> ( $less(0,X26)
& $less(0,X25) ) )
& ( f11(f12,X1) = X26 )
& ( f11(f12,X0) = X25 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_136) ).
tff(f3306,plain,
spl331_89,
inference(avatar_split_clause,[],[f2651,f3304]) ).
tff(f3304,plain,
( spl331_89
<=> ! [X0: 'S2',X1: 'S2'] : ( sK129(X0,X1) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_89])]) ).
tff(f2651,plain,
! [X0: 'S2',X1: 'S2'] : ( sK129(X0,X1) = sK27(X1) ),
inference(forward_demodulation,[],[f1882,f1580]) ).
tff(f1882,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK129(X0,X1) ),
inference(cnf_transformation,[],[f1155]) ).
tff(f3302,plain,
spl331_88,
inference(avatar_split_clause,[],[f2650,f3300]) ).
tff(f3300,plain,
( spl331_88
<=> ! [X0: 'S2',X1: 'S2'] : ( sK126(X0,X1) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_88])]) ).
tff(f2650,plain,
! [X0: 'S2',X1: 'S2'] : ( sK126(X0,X1) = sK27(X1) ),
inference(forward_demodulation,[],[f1878,f1580]) ).
tff(f1878,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK126(X0,X1) ),
inference(cnf_transformation,[],[f1151]) ).
tff(f1151,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ( f34(f39(f61,f13(f14,X1)),f13(f14,X0)) = f13(f14,f6(f7,$sum(sK126(X0,X1),$uminus(sK127(X0,X1))))) )
| $less(sK126(X0,X1),sK127(X0,X1)) )
& ( f11(f12,X0) = sK127(X0,X1) )
& ( f11(f12,X1) = sK126(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK126,sK127])],[f864,f1150]) ).
tff(f1150,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: $int,X3: $int] :
( ( ( f34(f39(f61,f13(f14,X1)),f13(f14,X0)) = f13(f14,f6(f7,$sum(X2,$uminus(X3)))) )
| $less(X2,X3) )
& ( f11(f12,X0) = X3 )
& ( f11(f12,X1) = X2 ) )
=> ( ( ( f34(f39(f61,f13(f14,X1)),f13(f14,X0)) = f13(f14,f6(f7,$sum(sK126(X0,X1),$uminus(sK127(X0,X1))))) )
| $less(sK126(X0,X1),sK127(X0,X1)) )
& ( f11(f12,X0) = sK127(X0,X1) )
& ( f11(f12,X1) = sK126(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f864,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int] :
( ( ( f34(f39(f61,f13(f14,X1)),f13(f14,X0)) = f13(f14,f6(f7,$sum(X2,$uminus(X3)))) )
| $less(X2,X3) )
& ( f11(f12,X0) = X3 )
& ( f11(f12,X1) = X2 ) ),
inference(ennf_transformation,[],[f696]) ).
tff(f696,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int] :
( ( ~ $less(X2,X3)
=> ( f34(f39(f61,f13(f14,X1)),f13(f14,X0)) = f13(f14,f6(f7,$sum(X2,$uminus(X3)))) ) )
& ( f11(f12,X0) = X3 )
& ( f11(f12,X1) = X2 ) ),
inference(rectify,[],[f517]) ).
tff(f517,plain,
! [X0: 'S2',X1: 'S2'] :
? [X226: $int,X227: $int] :
( ( ~ $less(X226,X227)
=> ( f34(f39(f61,f13(f14,X1)),f13(f14,X0)) = f13(f14,f6(f7,$sum(X226,$uminus(X227)))) ) )
& ( f11(f12,X0) = X227 )
& ( f11(f12,X1) = X226 ) ),
inference(theory_normalization,[],[f375]) ).
tff(f375,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X226: $int,X227: $int] :
( ( $lesseq(X227,X226)
=> ( f13(f14,f6(f7,$difference(X226,X227))) = f34(f39(f61,f13(f14,X1)),f13(f14,X0)) ) )
& ( f11(f12,X0) = X227 )
& ( f11(f12,X1) = X226 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_375) ).
tff(f3298,plain,
spl331_87,
inference(avatar_split_clause,[],[f2649,f3296]) ).
tff(f3296,plain,
( spl331_87
<=> ! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK127(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_87])]) ).
tff(f2649,plain,
! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK127(X0,X1) ),
inference(forward_demodulation,[],[f1879,f1580]) ).
tff(f1879,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK127(X0,X1) ),
inference(cnf_transformation,[],[f1151]) ).
tff(f3294,plain,
spl331_86,
inference(avatar_split_clause,[],[f2645,f3292]) ).
tff(f3292,plain,
( spl331_86
<=> ! [X0: 'S2',X1: 'S2'] : ( sK124(X0,X1) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_86])]) ).
tff(f2645,plain,
! [X0: 'S2',X1: 'S2'] : ( sK124(X0,X1) = sK27(X1) ),
inference(forward_demodulation,[],[f1875,f1580]) ).
tff(f1875,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK124(X0,X1) ),
inference(cnf_transformation,[],[f1149]) ).
tff(f1149,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ( $sum(f19(f20,X1),$uminus(f19(f20,X0))) = f19(f20,f6(f7,$sum(sK124(X0,X1),$uminus(sK125(X0,X1))))) )
| $less(sK124(X0,X1),sK125(X0,X1)) )
& ( f11(f12,X0) = sK125(X0,X1) )
& ( f11(f12,X1) = sK124(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK124,sK125])],[f863,f1148]) ).
tff(f1148,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: $int,X3: $int] :
( ( ( $sum(f19(f20,X1),$uminus(f19(f20,X0))) = f19(f20,f6(f7,$sum(X2,$uminus(X3)))) )
| $less(X2,X3) )
& ( f11(f12,X0) = X3 )
& ( f11(f12,X1) = X2 ) )
=> ( ( ( $sum(f19(f20,X1),$uminus(f19(f20,X0))) = f19(f20,f6(f7,$sum(sK124(X0,X1),$uminus(sK125(X0,X1))))) )
| $less(sK124(X0,X1),sK125(X0,X1)) )
& ( f11(f12,X0) = sK125(X0,X1) )
& ( f11(f12,X1) = sK124(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f863,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int] :
( ( ( $sum(f19(f20,X1),$uminus(f19(f20,X0))) = f19(f20,f6(f7,$sum(X2,$uminus(X3)))) )
| $less(X2,X3) )
& ( f11(f12,X0) = X3 )
& ( f11(f12,X1) = X2 ) ),
inference(ennf_transformation,[],[f695]) ).
tff(f695,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int] :
( ( ~ $less(X2,X3)
=> ( $sum(f19(f20,X1),$uminus(f19(f20,X0))) = f19(f20,f6(f7,$sum(X2,$uminus(X3)))) ) )
& ( f11(f12,X0) = X3 )
& ( f11(f12,X1) = X2 ) ),
inference(rectify,[],[f516]) ).
tff(f516,plain,
! [X0: 'S2',X1: 'S2'] :
? [X221: $int,X222: $int] :
( ( ~ $less(X221,X222)
=> ( f19(f20,f6(f7,$sum(X221,$uminus(X222)))) = $sum(f19(f20,X1),$uminus(f19(f20,X0))) ) )
& ( f11(f12,X0) = X222 )
& ( f11(f12,X1) = X221 ) ),
inference(theory_normalization,[],[f373]) ).
tff(f373,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X221: $int,X222: $int] :
( ( $lesseq(X222,X221)
=> ( f19(f20,f6(f7,$difference(X221,X222))) = $difference(f19(f20,X1),f19(f20,X0)) ) )
& ( f11(f12,X0) = X222 )
& ( f11(f12,X1) = X221 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_373) ).
tff(f3290,plain,
spl331_85,
inference(avatar_split_clause,[],[f2644,f3288]) ).
tff(f3288,plain,
( spl331_85
<=> ! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK125(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_85])]) ).
tff(f2644,plain,
! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK125(X0,X1) ),
inference(forward_demodulation,[],[f1876,f1580]) ).
tff(f1876,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK125(X0,X1) ),
inference(cnf_transformation,[],[f1149]) ).
tff(f3286,plain,
spl331_84,
inference(avatar_split_clause,[],[f2640,f3284]) ).
tff(f3284,plain,
( spl331_84
<=> ! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK122(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_84])]) ).
tff(f2640,plain,
! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK122(X0,X1) ),
inference(forward_demodulation,[],[f1872,f1580]) ).
tff(f1872,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK122(X0,X1) ),
inference(cnf_transformation,[],[f1147]) ).
tff(f1147,plain,
! [X0: 'S2',X1: 'S2'] :
( ( f6(f7,f8(f9(f10,$sum(sK122(X0,X1),1)),sK123(X0,X1))) = f6(f7,$sum(sK123(X0,X1),f8(f9(f10,sK122(X0,X1)),sK123(X0,X1)))) )
& ( f11(f12,X1) = sK123(X0,X1) )
& ( f11(f12,X0) = sK122(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK122,sK123])],[f694,f1146]) ).
tff(f1146,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: $int,X3: $int] :
( ( f6(f7,f8(f9(f10,$sum(X2,1)),X3)) = f6(f7,$sum(X3,f8(f9(f10,X2),X3))) )
& ( f11(f12,X1) = X3 )
& ( f11(f12,X0) = X2 ) )
=> ( ( f6(f7,f8(f9(f10,$sum(sK122(X0,X1),1)),sK123(X0,X1))) = f6(f7,$sum(sK123(X0,X1),f8(f9(f10,sK122(X0,X1)),sK123(X0,X1)))) )
& ( f11(f12,X1) = sK123(X0,X1) )
& ( f11(f12,X0) = sK122(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f694,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int] :
( ( f6(f7,f8(f9(f10,$sum(X2,1)),X3)) = f6(f7,$sum(X3,f8(f9(f10,X2),X3))) )
& ( f11(f12,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(rectify,[],[f145]) ).
tff(f145,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X42: $int,X43: $int] :
( ( f6(f7,f8(f9(f10,$sum(X42,1)),X43)) = f6(f7,$sum(X43,f8(f9(f10,X42),X43))) )
& ( f11(f12,X1) = X43 )
& ( f11(f12,X0) = X42 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_145) ).
tff(f3282,plain,
spl331_83,
inference(avatar_split_clause,[],[f2639,f3280]) ).
tff(f3280,plain,
( spl331_83
<=> ! [X0: 'S2',X1: 'S2'] : ( sK123(X0,X1) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_83])]) ).
tff(f2639,plain,
! [X0: 'S2',X1: 'S2'] : ( sK123(X0,X1) = sK27(X1) ),
inference(forward_demodulation,[],[f1873,f1580]) ).
tff(f1873,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK123(X0,X1) ),
inference(cnf_transformation,[],[f1147]) ).
tff(f3278,plain,
spl331_82,
inference(avatar_split_clause,[],[f2636,f3276]) ).
tff(f3276,plain,
( spl331_82
<=> ! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK120(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_82])]) ).
tff(f2636,plain,
! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK120(X0,X1) ),
inference(forward_demodulation,[],[f1869,f1580]) ).
tff(f1869,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK120(X0,X1) ),
inference(cnf_transformation,[],[f1145]) ).
tff(f1145,plain,
! [X0: 'S2',X1: 'S2'] :
( ( f6(f7,f8(f9(f10,sK120(X0,X1)),sK121(X0,X1))) = f6(f7,f8(f9(f10,sK121(X0,X1)),sK120(X0,X1))) )
& ( f11(f12,X1) = sK121(X0,X1) )
& ( f11(f12,X0) = sK120(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK120,sK121])],[f693,f1144]) ).
tff(f1144,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: $int,X3: $int] :
( ( f6(f7,f8(f9(f10,X2),X3)) = f6(f7,f8(f9(f10,X3),X2)) )
& ( f11(f12,X1) = X3 )
& ( f11(f12,X0) = X2 ) )
=> ( ( f6(f7,f8(f9(f10,sK120(X0,X1)),sK121(X0,X1))) = f6(f7,f8(f9(f10,sK121(X0,X1)),sK120(X0,X1))) )
& ( f11(f12,X1) = sK121(X0,X1) )
& ( f11(f12,X0) = sK120(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f693,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int,X3: $int] :
( ( f6(f7,f8(f9(f10,X2),X3)) = f6(f7,f8(f9(f10,X3),X2)) )
& ( f11(f12,X1) = X3 )
& ( f11(f12,X0) = X2 ) ),
inference(rectify,[],[f140]) ).
tff(f140,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X28: $int,X29: $int] :
( ( f6(f7,f8(f9(f10,X28),X29)) = f6(f7,f8(f9(f10,X29),X28)) )
& ( f11(f12,X1) = X29 )
& ( f11(f12,X0) = X28 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_140) ).
tff(f3274,plain,
spl331_81,
inference(avatar_split_clause,[],[f2635,f3272]) ).
tff(f3272,plain,
( spl331_81
<=> ! [X0: 'S2',X1: 'S2'] : ( sK121(X0,X1) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_81])]) ).
tff(f2635,plain,
! [X0: 'S2',X1: 'S2'] : ( sK121(X0,X1) = sK27(X1) ),
inference(forward_demodulation,[],[f1870,f1580]) ).
tff(f1870,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK121(X0,X1) ),
inference(cnf_transformation,[],[f1145]) ).
tff(f3270,plain,
spl331_80,
inference(avatar_split_clause,[],[f2634,f3268]) ).
tff(f3268,plain,
( spl331_80
<=> ! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK118(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_80])]) ).
tff(f2634,plain,
! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK118(X0,X1) ),
inference(forward_demodulation,[],[f1866,f1580]) ).
tff(f1866,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK118(X0,X1) ),
inference(cnf_transformation,[],[f1143]) ).
tff(f3266,plain,
spl331_79,
inference(avatar_split_clause,[],[f2631,f3264]) ).
tff(f3264,plain,
( spl331_79
<=> ! [X0: 'S2',X1: $real] : ( sK27(X0) = sK116(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_79])]) ).
tff(f2631,plain,
! [X0: 'S2',X1: $real] : ( sK27(X0) = sK116(X0,X1) ),
inference(forward_demodulation,[],[f1863,f1580]) ).
tff(f1863,plain,
! [X0: 'S2',X1: $real] : ( f11(f12,X0) = sK116(X0,X1) ),
inference(cnf_transformation,[],[f1141]) ).
tff(f3262,plain,
spl331_78,
inference(avatar_split_clause,[],[f2628,f3260]) ).
tff(f3260,plain,
( spl331_78
<=> ! [X0: 'S2',X1: 'S10'] : ( sK27(X0) = sK114(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_78])]) ).
tff(f2628,plain,
! [X0: 'S2',X1: 'S10'] : ( sK27(X0) = sK114(X0,X1) ),
inference(forward_demodulation,[],[f1860,f1580]) ).
tff(f1860,plain,
! [X0: 'S2',X1: 'S10'] : ( f11(f12,X0) = sK114(X0,X1) ),
inference(cnf_transformation,[],[f1139]) ).
tff(f3258,plain,
spl331_77,
inference(avatar_split_clause,[],[f2625,f3256]) ).
tff(f3256,plain,
( spl331_77
<=> ! [X0: 'S2',X1: $int] : ( sK27(X0) = sK112(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_77])]) ).
tff(f2625,plain,
! [X0: 'S2',X1: $int] : ( sK27(X0) = sK112(X0,X1) ),
inference(forward_demodulation,[],[f1857,f1580]) ).
tff(f1857,plain,
! [X0: 'S2',X1: $int] : ( f11(f12,X0) = sK112(X0,X1) ),
inference(cnf_transformation,[],[f1137]) ).
tff(f3254,plain,
spl331_76,
inference(avatar_split_clause,[],[f2599,f3252]) ).
tff(f2599,plain,
! [X0: 'S2',X1: 'S2'] : ( sK27(X0) = sK98(X0,X1) ),
inference(forward_demodulation,[],[f1824,f1580]) ).
tff(f1824,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X0) = sK98(X0,X1) ),
inference(cnf_transformation,[],[f1109]) ).
tff(f3250,plain,
spl331_75,
inference(avatar_split_clause,[],[f2598,f3248]) ).
tff(f3248,plain,
( spl331_75
<=> ! [X0: 'S2',X1: 'S2'] : ( sK100(X0,X1) = sK27(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_75])]) ).
tff(f2598,plain,
! [X0: 'S2',X1: 'S2'] : ( sK100(X0,X1) = sK27(X1) ),
inference(forward_demodulation,[],[f1826,f1580]) ).
tff(f1826,plain,
! [X0: 'S2',X1: 'S2'] : ( f11(f12,X1) = sK100(X0,X1) ),
inference(cnf_transformation,[],[f1109]) ).
tff(f3246,plain,
spl331_74,
inference(avatar_split_clause,[],[f2330,f3244]) ).
tff(f2330,plain,
! [X0: 'S2'] : ( f6(f7,1) = sK35(X0) ),
inference(evaluation,[],[f1596]) ).
tff(f1596,plain,
! [X0: 'S2'] : ( f6(f7,$sum(0,1)) = sK35(X0) ),
inference(cnf_transformation,[],[f968]) ).
tff(f3242,plain,
spl331_73,
inference(avatar_split_clause,[],[f1593,f3240]) ).
tff(f3238,plain,
spl331_72,
inference(avatar_split_clause,[],[f1591,f3236]) ).
tff(f1591,plain,
! [X0: $real] : ( f22(f23,X0) = sK33(X0) ),
inference(cnf_transformation,[],[f964]) ).
tff(f964,plain,
! [X0: $real] :
( ( f22(f49(f50,X0),X0) = f22(f49(f50,sK33(X0)),sK33(X0)) )
& ( f22(f23,X0) = sK33(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f631,f963]) ).
tff(f963,plain,
! [X0: $real] :
( ? [X1: $real] :
( ( f22(f49(f50,X0),X0) = f22(f49(f50,X1),X1) )
& ( f22(f23,X0) = X1 ) )
=> ( ( f22(f49(f50,X0),X0) = f22(f49(f50,sK33(X0)),sK33(X0)) )
& ( f22(f23,X0) = sK33(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f631,plain,
! [X0: $real] :
? [X1: $real] :
( ( f22(f49(f50,X0),X0) = f22(f49(f50,X1),X1) )
& ( f22(f23,X0) = X1 ) ),
inference(rectify,[],[f236]) ).
tff(f236,axiom,
! [X0: $real] :
? [X136: $real] :
( ( f22(f49(f50,X136),X136) = f22(f49(f50,X0),X0) )
& ( f22(f23,X0) = X136 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_236) ).
tff(f3234,plain,
spl331_71,
inference(avatar_split_clause,[],[f1580,f3232]) ).
tff(f3230,plain,
spl331_70,
inference(avatar_split_clause,[],[f1578,f3228]) ).
tff(f1578,plain,
! [X0: $int] : ( f8(f21,X0) = sK26(X0) ),
inference(cnf_transformation,[],[f951]) ).
tff(f951,plain,
! [X0: $int] :
( ( f8(f9(f10,X0),X0) = f8(f9(f10,sK26(X0)),sK26(X0)) )
& ( f8(f21,X0) = sK26(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f625,f950]) ).
tff(f950,plain,
! [X0: $int] :
( ? [X1: $int] :
( ( f8(f9(f10,X0),X0) = f8(f9(f10,X1),X1) )
& ( f8(f21,X0) = X1 ) )
=> ( ( f8(f9(f10,X0),X0) = f8(f9(f10,sK26(X0)),sK26(X0)) )
& ( f8(f21,X0) = sK26(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f625,plain,
! [X0: $int] :
? [X1: $int] :
( ( f8(f9(f10,X0),X0) = f8(f9(f10,X1),X1) )
& ( f8(f21,X0) = X1 ) ),
inference(rectify,[],[f237]) ).
tff(f237,axiom,
! [X0: $int] :
? [X137: $int] :
( ( f8(f9(f10,X137),X137) = f8(f9(f10,X0),X0) )
& ( f8(f21,X0) = X137 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_237) ).
tff(f3226,plain,
spl331_69,
inference(avatar_split_clause,[],[f1574,f3224]) ).
tff(f3224,plain,
( spl331_69
<=> ! [X0: 'S10'] : ~ $less(sK24(X0),$uminus(sK24(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_69])]) ).
tff(f1574,plain,
! [X0: 'S10'] : ~ $less(sK24(X0),$uminus(sK24(X0))),
inference(cnf_transformation,[],[f947]) ).
tff(f3222,plain,
spl331_68,
inference(avatar_split_clause,[],[f1573,f3220]) ).
tff(f3218,plain,
spl331_67,
inference(avatar_split_clause,[],[f1570,f3216]) ).
tff(f3214,plain,
spl331_66,
inference(avatar_split_clause,[],[f1567,f3212]) ).
tff(f3210,plain,
spl331_65,
inference(avatar_split_clause,[],[f1561,f3208]) ).
tff(f1561,plain,
! [X0: 'S2'] : ( f19(f20,X0) = sK19(X0) ),
inference(cnf_transformation,[],[f937]) ).
tff(f3206,plain,
spl331_64,
inference(avatar_split_clause,[],[f1559,f3204]) ).
tff(f3202,plain,
spl331_63,
inference(avatar_split_clause,[],[f1557,f3200]) ).
tff(f1557,plain,
! [X0: 'S2'] : ( f13(f14,X0) = sK17(X0) ),
inference(cnf_transformation,[],[f933]) ).
tff(f3198,plain,
spl331_62,
inference(avatar_split_clause,[],[f1555,f3196]) ).
tff(f1555,plain,
! [X0: 'S10'] : ( f6(f7,2) = sK16(X0) ),
inference(cnf_transformation,[],[f931]) ).
tff(f931,plain,
! [X0: 'S10'] :
( ( f34(f39(f52,X0),f34(f35,X0)) = f16(f32,$sum(f19(f59(f60,f27(f28,X0)),sK16(X0)),f19(f59(f60,f27(f36,X0)),sK16(X0)))) )
& ( f6(f7,2) = sK16(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f615,f930]) ).
tff(f930,plain,
! [X0: 'S10'] :
( ? [X1: 'S2'] :
( ( f34(f39(f52,X0),f34(f35,X0)) = f16(f32,$sum(f19(f59(f60,f27(f28,X0)),X1),f19(f59(f60,f27(f36,X0)),X1))) )
& ( f6(f7,2) = X1 ) )
=> ( ( f34(f39(f52,X0),f34(f35,X0)) = f16(f32,$sum(f19(f59(f60,f27(f28,X0)),sK16(X0)),f19(f59(f60,f27(f36,X0)),sK16(X0)))) )
& ( f6(f7,2) = sK16(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f615,plain,
! [X0: 'S10'] :
? [X1: 'S2'] :
( ( f34(f39(f52,X0),f34(f35,X0)) = f16(f32,$sum(f19(f59(f60,f27(f28,X0)),X1),f19(f59(f60,f27(f36,X0)),X1))) )
& ( f6(f7,2) = X1 ) ),
inference(rectify,[],[f299]) ).
tff(f299,axiom,
! [X0: 'S10'] :
? [X189: 'S2'] :
( ( f34(f39(f52,X0),f34(f35,X0)) = f16(f32,$sum(f19(f59(f60,f27(f28,X0)),X189),f19(f59(f60,f27(f36,X0)),X189))) )
& ( f6(f7,2) = X189 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_299) ).
tff(f3194,plain,
spl331_61,
inference(avatar_split_clause,[],[f1553,f3192]) ).
tff(f1553,plain,
! [X0: $int] : ( f6(f7,2) = sK15(X0) ),
inference(cnf_transformation,[],[f929]) ).
tff(f929,plain,
! [X0: $int] :
( ( f11(f63(f64,X0),sK15(X0)) = f11(f63(f64,f8(f21,X0)),sK15(X0)) )
& ( f6(f7,2) = sK15(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f614,f928]) ).
tff(f928,plain,
! [X0: $int] :
( ? [X1: 'S2'] :
( ( f11(f63(f64,X0),X1) = f11(f63(f64,f8(f21,X0)),X1) )
& ( f6(f7,2) = X1 ) )
=> ( ( f11(f63(f64,X0),sK15(X0)) = f11(f63(f64,f8(f21,X0)),sK15(X0)) )
& ( f6(f7,2) = sK15(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f614,plain,
! [X0: $int] :
? [X1: 'S2'] :
( ( f11(f63(f64,X0),X1) = f11(f63(f64,f8(f21,X0)),X1) )
& ( f6(f7,2) = X1 ) ),
inference(rectify,[],[f348]) ).
tff(f348,axiom,
! [X0: $int] :
? [X216: 'S2'] :
( ( f11(f63(f64,f8(f21,X0)),X216) = f11(f63(f64,X0),X216) )
& ( f6(f7,2) = X216 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_348) ).
tff(f3190,plain,
spl331_60,
inference(avatar_split_clause,[],[f1551,f3188]) ).
tff(f1551,plain,
! [X0: $real] : ( f6(f7,2) = sK14(X0) ),
inference(cnf_transformation,[],[f927]) ).
tff(f927,plain,
! [X0: $real] :
( ( f19(f59(f60,X0),sK14(X0)) = f19(f59(f60,f22(f23,X0)),sK14(X0)) )
& ( f6(f7,2) = sK14(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f613,f926]) ).
tff(f926,plain,
! [X0: $real] :
( ? [X1: 'S2'] :
( ( f19(f59(f60,X0),X1) = f19(f59(f60,f22(f23,X0)),X1) )
& ( f6(f7,2) = X1 ) )
=> ( ( f19(f59(f60,X0),sK14(X0)) = f19(f59(f60,f22(f23,X0)),sK14(X0)) )
& ( f6(f7,2) = sK14(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f613,plain,
! [X0: $real] :
? [X1: 'S2'] :
( ( f19(f59(f60,X0),X1) = f19(f59(f60,f22(f23,X0)),X1) )
& ( f6(f7,2) = X1 ) ),
inference(rectify,[],[f349]) ).
tff(f349,axiom,
! [X0: $real] :
? [X217: 'S2'] :
( ( f19(f59(f60,f22(f23,X0)),X217) = f19(f59(f60,X0),X217) )
& ( f6(f7,2) = X217 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_349) ).
tff(f3186,plain,
spl331_59,
inference(avatar_split_clause,[],[f590,f3184]) ).
tff(f3184,plain,
( spl331_59
<=> ! [X0: $real] : ( 0.0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_59])]) ).
tff(f590,plain,
! [X0: $real] : ( 0.0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_143,[]) ).
tff(f3182,plain,
spl331_58,
inference(avatar_split_clause,[],[f572,f3180]) ).
tff(f3180,plain,
( spl331_58
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_58])]) ).
tff(f572,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_143,[]) ).
tff(f3178,plain,
spl331_57,
inference(avatar_split_clause,[],[f2342,f3176]) ).
tff(f2342,plain,
! [X0: 'S2'] : ( sK27(X0) = sK31(X0) ),
inference(forward_demodulation,[],[f1588,f1580]) ).
tff(f1588,plain,
! [X0: 'S2'] : ( f11(f12,X0) = sK31(X0) ),
inference(cnf_transformation,[],[f962]) ).
tff(f3174,plain,
spl331_56,
inference(avatar_split_clause,[],[f2341,f3172]) ).
tff(f3172,plain,
( spl331_56
<=> ! [X0: 'S2'] : ( sK27(X0) = sK30(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_56])]) ).
tff(f2341,plain,
! [X0: 'S2'] : ( sK27(X0) = sK30(X0) ),
inference(forward_demodulation,[],[f1586,f1580]) ).
tff(f1586,plain,
! [X0: 'S2'] : ( f11(f12,X0) = sK30(X0) ),
inference(cnf_transformation,[],[f959]) ).
tff(f959,plain,
! [X0: 'S2'] :
( ( f6(f7,$sum(sK30(X0),sK30(X0))) = f6(f7,$product(2,sK30(X0))) )
& ( f11(f12,X0) = sK30(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f629,f958]) ).
tff(f958,plain,
! [X0: 'S2'] :
( ? [X1: $int] :
( ( f6(f7,$sum(X1,X1)) = f6(f7,$product(2,X1)) )
& ( f11(f12,X0) = X1 ) )
=> ( ( f6(f7,$sum(sK30(X0),sK30(X0))) = f6(f7,$product(2,sK30(X0))) )
& ( f11(f12,X0) = sK30(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f629,plain,
! [X0: 'S2'] :
? [X1: $int] :
( ( f6(f7,$sum(X1,X1)) = f6(f7,$product(2,X1)) )
& ( f11(f12,X0) = X1 ) ),
inference(rectify,[],[f276]) ).
tff(f276,axiom,
! [X0: 'S2'] :
? [X172: $int] :
( ( f6(f7,$product(2,X172)) = f6(f7,$sum(X172,X172)) )
& ( f11(f12,X0) = X172 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_276) ).
tff(f3170,plain,
spl331_55,
inference(avatar_split_clause,[],[f2340,f3168]) ).
tff(f3168,plain,
( spl331_55
<=> ! [X0: 'S2'] : ( sK27(X0) = sK29(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_55])]) ).
tff(f2340,plain,
! [X0: 'S2'] : ( sK27(X0) = sK29(X0) ),
inference(forward_demodulation,[],[f1584,f1580]) ).
tff(f1584,plain,
! [X0: 'S2'] : ( f11(f12,X0) = sK29(X0) ),
inference(cnf_transformation,[],[f957]) ).
tff(f957,plain,
! [X0: 'S2'] :
( ( f6(f7,$product(sK29(X0),2)) = f6(f7,$sum(sK29(X0),sK29(X0))) )
& ( f11(f12,X0) = sK29(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f628,f956]) ).
tff(f956,plain,
! [X0: 'S2'] :
( ? [X1: $int] :
( ( f6(f7,$product(X1,2)) = f6(f7,$sum(X1,X1)) )
& ( f11(f12,X0) = X1 ) )
=> ( ( f6(f7,$product(sK29(X0),2)) = f6(f7,$sum(sK29(X0),sK29(X0))) )
& ( f11(f12,X0) = sK29(X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f628,plain,
! [X0: 'S2'] :
? [X1: $int] :
( ( f6(f7,$product(X1,2)) = f6(f7,$sum(X1,X1)) )
& ( f11(f12,X0) = X1 ) ),
inference(rectify,[],[f277]) ).
tff(f277,axiom,
! [X0: 'S2'] :
? [X173: $int] :
( ( f6(f7,$product(X173,2)) = f6(f7,$sum(X173,X173)) )
& ( f11(f12,X0) = X173 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_277) ).
tff(f3166,plain,
spl331_54,
inference(avatar_split_clause,[],[f2338,f3164]) ).
tff(f2338,plain,
! [X0: 'S2'] : ( sK27(X0) = sK28(X0) ),
inference(forward_demodulation,[],[f1582,f1580]) ).
tff(f1582,plain,
! [X0: 'S2'] : ( f11(f12,X0) = sK28(X0) ),
inference(cnf_transformation,[],[f955]) ).
tff(f3162,plain,
spl331_53,
inference(avatar_split_clause,[],[f2337,f3160]) ).
tff(f3160,plain,
( spl331_53
<=> ! [X0: 'S10'] : ( sK24(X0) = sK25(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_53])]) ).
tff(f2337,plain,
! [X0: 'S10'] : ( sK24(X0) = sK25(X0) ),
inference(forward_demodulation,[],[f1575,f1573]) ).
tff(f1575,plain,
! [X0: 'S10'] : ( f27(f31,X0) = sK25(X0) ),
inference(cnf_transformation,[],[f949]) ).
tff(f3158,plain,
spl331_52,
inference(avatar_split_clause,[],[f2336,f3156]) ).
tff(f2336,plain,
! [X0: 'S2'] : ( sK19(X0) = sK21(X0) ),
inference(forward_demodulation,[],[f1565,f1561]) ).
tff(f1565,plain,
! [X0: 'S2'] : ( f19(f20,X0) = sK21(X0) ),
inference(cnf_transformation,[],[f941]) ).
tff(f3154,plain,
spl331_51,
inference(avatar_split_clause,[],[f2335,f3152]) ).
tff(f2335,plain,
! [X0: 'S2'] : ( sK19(X0) = sK20(X0) ),
inference(forward_demodulation,[],[f1563,f1561]) ).
tff(f1563,plain,
! [X0: 'S2'] : ( f19(f20,X0) = sK20(X0) ),
inference(cnf_transformation,[],[f939]) ).
tff(f3150,plain,
spl331_50,
inference(avatar_split_clause,[],[f2329,f3148]) ).
tff(f3148,plain,
( spl331_50
<=> ! [X0: 'S2',X1: 'S2'] : ( 1 = sK54(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_50])]) ).
tff(f2329,plain,
! [X0: 'S2',X1: 'S2'] : ( 1 = sK54(X0,X1) ),
inference(evaluation,[],[f1737]) ).
tff(f1737,plain,
! [X0: 'S2',X1: 'S2'] : ( $sum(0,1) = sK54(X0,X1) ),
inference(cnf_transformation,[],[f1022]) ).
tff(f1022,plain,
! [X0: 'S2',X1: 'S2'] :
( ( ~ $less(f11(f12,f3(f4(f65,X0),X1)),sK54(X0,X1))
| $less(f11(f12,X0),sK54(X0,X1)) )
& ( $sum(0,1) = sK54(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54])],[f855,f1021]) ).
tff(f1021,plain,
! [X0: 'S2',X1: 'S2'] :
( ? [X2: $int] :
( ( ~ $less(f11(f12,f3(f4(f65,X0),X1)),X2)
| $less(f11(f12,X0),X2) )
& ( $sum(0,1) = X2 ) )
=> ( ( ~ $less(f11(f12,f3(f4(f65,X0),X1)),sK54(X0,X1))
| $less(f11(f12,X0),sK54(X0,X1)) )
& ( $sum(0,1) = sK54(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f855,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int] :
( ( ~ $less(f11(f12,f3(f4(f65,X0),X1)),X2)
| $less(f11(f12,X0),X2) )
& ( $sum(0,1) = X2 ) ),
inference(ennf_transformation,[],[f642]) ).
tff(f642,plain,
! [X0: 'S2',X1: 'S2'] :
? [X2: $int] :
( ( ~ $less(f11(f12,X0),X2)
=> ~ $less(f11(f12,f3(f4(f65,X0),X1)),X2) )
& ( $sum(0,1) = X2 ) ),
inference(rectify,[],[f505]) ).
tff(f505,plain,
! [X0: 'S2',X1: 'S2'] :
? [X287: $int] :
( ( ~ $less(f11(f12,X0),X287)
=> ~ $less(f11(f12,f3(f4(f65,X0),X1)),X287) )
& ( $sum(0,1) = X287 ) ),
inference(theory_normalization,[],[f443]) ).
tff(f443,axiom,
! [X0: 'S2',X1: 'S2'] :
? [X287: $int] :
( ( $lesseq(X287,f11(f12,X0))
=> $lesseq(X287,f11(f12,f3(f4(f65,X0),X1))) )
& ( $sum(0,1) = X287 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_443) ).
tff(f3146,plain,
spl331_49,
inference(avatar_split_clause,[],[f2318,f3144]) ).
tff(f3144,plain,
( spl331_49
<=> ! [X0: 'S2',X1: 'S2'] : ( 1 = sK133(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_49])]) ).
tff(f2318,plain,
! [X0: 'S2',X1: 'S2'] : ( 1 = sK133(X0,X1) ),
inference(evaluation,[],[f1890]) ).
tff(f1890,plain,
! [X0: 'S2',X1: 'S2'] : ( $sum(0,1) = sK133(X0,X1) ),
inference(cnf_transformation,[],[f1160]) ).
tff(f3142,plain,
spl331_48,
inference(avatar_split_clause,[],[f2317,f3140]) ).
tff(f3140,plain,
( spl331_48
<=> ! [X0: 'S2',X1: 'S2'] : ( 1 = sK136(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_48])]) ).
tff(f2317,plain,
! [X0: 'S2',X1: 'S2'] : ( 1 = sK136(X0,X1) ),
inference(evaluation,[],[f1894]) ).
tff(f1894,plain,
! [X0: 'S2',X1: 'S2'] : ( $sum(0,1) = sK136(X0,X1) ),
inference(cnf_transformation,[],[f1162]) ).
tff(f3138,plain,
spl331_47,
inference(avatar_split_clause,[],[f2316,f3136]) ).
tff(f3136,plain,
( spl331_47
<=> ! [X0: 'S2',X1: 'S2'] : ( 1 = sK139(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_47])]) ).
tff(f2316,plain,
! [X0: 'S2',X1: 'S2'] : ( 1 = sK139(X0,X1) ),
inference(evaluation,[],[f1898]) ).
tff(f1898,plain,
! [X0: 'S2',X1: 'S2'] : ( $sum(0,1) = sK139(X0,X1) ),
inference(cnf_transformation,[],[f1164]) ).
tff(f3134,plain,
spl331_46,
inference(avatar_split_clause,[],[f2314,f3132]) ).
tff(f3132,plain,
( spl331_46
<=> ! [X0: 'S2',X1: 'S2'] : ( 1 = sK147(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_46])]) ).
tff(f2314,plain,
! [X0: 'S2',X1: 'S2'] : ( 1 = sK147(X0,X1) ),
inference(evaluation,[],[f1909]) ).
tff(f1909,plain,
! [X0: 'S2',X1: 'S2'] : ( $sum(0,1) = sK147(X0,X1) ),
inference(cnf_transformation,[],[f1170]) ).
tff(f3130,plain,
spl331_45,
inference(avatar_split_clause,[],[f1852,f3128]) ).
tff(f3128,plain,
( spl331_45
<=> ! [X0: $real,X1: $real] : ( 0.0 = sK110(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_45])]) ).
tff(f1852,plain,
! [X0: $real,X1: $real] : ( 0.0 = sK110(X0,X1) ),
inference(cnf_transformation,[],[f1135]) ).
tff(f3126,plain,
spl331_44,
inference(avatar_split_clause,[],[f1733,f3124]) ).
tff(f3124,plain,
( spl331_44
<=> ! [X0: $real,X1: $real] : ( 0.0 = sK53(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_44])]) ).
tff(f1733,plain,
! [X0: $real,X1: $real] : ( 0.0 = sK53(X0,X1) ),
inference(cnf_transformation,[],[f1020]) ).
tff(f1020,plain,
! [X0: $real,X1: $real] :
( ( ( $sum(f22(f49(f50,X0),X0),f22(f49(f50,X1),X1)) = sK53(X0,X1) )
| ( sK53(X0,X1) != X1 )
| ( sK53(X0,X1) != X0 ) )
& ( ( ( sK53(X0,X1) = X1 )
& ( sK53(X0,X1) = X0 ) )
| ( $sum(f22(f49(f50,X0),X0),f22(f49(f50,X1),X1)) != sK53(X0,X1) ) )
& ( 0.0 = sK53(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f1018,f1019]) ).
tff(f1019,plain,
! [X0: $real,X1: $real] :
( ? [X2: $real] :
( ( ( $sum(f22(f49(f50,X0),X0),f22(f49(f50,X1),X1)) = X2 )
| ( X1 != X2 )
| ( X0 != X2 ) )
& ( ( ( X1 = X2 )
& ( X0 = X2 ) )
| ( $sum(f22(f49(f50,X0),X0),f22(f49(f50,X1),X1)) != X2 ) )
& ( 0.0 = X2 ) )
=> ( ( ( $sum(f22(f49(f50,X0),X0),f22(f49(f50,X1),X1)) = sK53(X0,X1) )
| ( sK53(X0,X1) != X1 )
| ( sK53(X0,X1) != X0 ) )
& ( ( ( sK53(X0,X1) = X1 )
& ( sK53(X0,X1) = X0 ) )
| ( $sum(f22(f49(f50,X0),X0),f22(f49(f50,X1),X1)) != sK53(X0,X1) ) )
& ( 0.0 = sK53(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1018,plain,
! [X0: $real,X1: $real] :
? [X2: $real] :
( ( ( $sum(f22(f49(f50,X0),X0),f22(f49(f50,X1),X1)) = X2 )
| ( X1 != X2 )
| ( X0 != X2 ) )
& ( ( ( X1 = X2 )
& ( X0 = X2 ) )
| ( $sum(f22(f49(f50,X0),X0),f22(f49(f50,X1),X1)) != X2 ) )
& ( 0.0 = X2 ) ),
inference(flattening,[],[f1017]) ).
tff(f1017,plain,
! [X0: $real,X1: $real] :
? [X2: $real] :
( ( ( $sum(f22(f49(f50,X0),X0),f22(f49(f50,X1),X1)) = X2 )
| ( X1 != X2 )
| ( X0 != X2 ) )
& ( ( ( X1 = X2 )
& ( X0 = X2 ) )
| ( $sum(f22(f49(f50,X0),X0),f22(f49(f50,X1),X1)) != X2 ) )
& ( 0.0 = X2 ) ),
inference(nnf_transformation,[],[f641]) ).
tff(f641,plain,
! [X0: $real,X1: $real] :
? [X2: $real] :
( ( ( $sum(f22(f49(f50,X0),X0),f22(f49(f50,X1),X1)) = X2 )
<=> ( ( X1 = X2 )
& ( X0 = X2 ) ) )
& ( 0.0 = X2 ) ),
inference(rectify,[],[f420]) ).
tff(f420,axiom,
! [X0: $real,X1: $real] :
? [X267: $real] :
( ( ( $sum(f22(f49(f50,X0),X0),f22(f49(f50,X1),X1)) = X267 )
<=> ( ( X1 = X267 )
& ( X0 = X267 ) ) )
& ( 0.0 = X267 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_420) ).
tff(f3122,plain,
spl331_43,
inference(avatar_split_clause,[],[f1731,f3120]) ).
tff(f3120,plain,
( spl331_43
<=> ! [X0: $real,X1: $real] : ( 0.0 = sK52(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_43])]) ).
tff(f1731,plain,
! [X0: $real,X1: $real] : ( 0.0 = sK52(X0,X1) ),
inference(cnf_transformation,[],[f1016]) ).
tff(f1016,plain,
! [X0: $real,X1: $real] :
( ( $less(sK52(X0,X1),f22(f49(f50,X0),X1))
| ~ $less(sK52(X0,X1),X1)
| ~ $less(sK52(X0,X1),X0) )
& ( 0.0 = sK52(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f854,f1015]) ).
tff(f1015,plain,
! [X0: $real,X1: $real] :
( ? [X2: $real] :
( ( $less(X2,f22(f49(f50,X0),X1))
| ~ $less(X2,X1)
| ~ $less(X2,X0) )
& ( 0.0 = X2 ) )
=> ( ( $less(sK52(X0,X1),f22(f49(f50,X0),X1))
| ~ $less(sK52(X0,X1),X1)
| ~ $less(sK52(X0,X1),X0) )
& ( 0.0 = sK52(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f854,plain,
! [X0: $real,X1: $real] :
? [X2: $real] :
( ( $less(X2,f22(f49(f50,X0),X1))
| ~ $less(X2,X1)
| ~ $less(X2,X0) )
& ( 0.0 = X2 ) ),
inference(flattening,[],[f853]) ).
tff(f853,plain,
! [X0: $real,X1: $real] :
? [X2: $real] :
( ( $less(X2,f22(f49(f50,X0),X1))
| ~ $less(X2,X1)
| ~ $less(X2,X0) )
& ( 0.0 = X2 ) ),
inference(ennf_transformation,[],[f640]) ).
tff(f640,plain,
! [X0: $real,X1: $real] :
? [X2: $real] :
( ( $less(X2,X0)
=> ( $less(X2,X1)
=> $less(X2,f22(f49(f50,X0),X1)) ) )
& ( 0.0 = X2 ) ),
inference(rectify,[],[f426]) ).
tff(f426,axiom,
! [X0: $real,X1: $real] :
? [X270: $real] :
( ( $less(X270,X0)
=> ( $less(X270,X1)
=> $less(X270,f22(f49(f50,X0),X1)) ) )
& ( 0.0 = X270 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_426) ).
tff(f3118,plain,
( spl331_42
| ~ spl331_41 ),
inference(avatar_split_clause,[],[f3114,f3111,f3116]) ).
tff(f3116,plain,
( spl331_42
<=> ! [X0: $real] : ~ $less(sK34(X0),0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_42])]) ).
tff(f3111,plain,
( spl331_41
<=> ! [X0: $real] : ~ $less(f22(f30,X0),0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_41])]) ).
tff(f3114,plain,
( ! [X0: $real] : ~ $less(sK34(X0),0.0)
| ~ spl331_41 ),
inference(forward_demodulation,[],[f3112,f1593]) ).
tff(f3112,plain,
( ! [X0: $real] : ~ $less(f22(f30,X0),0.0)
| ~ spl331_41 ),
inference(avatar_component_clause,[],[f3111]) ).
tff(f3113,plain,
spl331_41,
inference(avatar_split_clause,[],[f1469,f3111]) ).
tff(f1469,plain,
! [X0: $real] : ~ $less(f22(f30,X0),0.0),
inference(cnf_transformation,[],[f20]) ).
tff(f20,axiom,
! [X0: $real] : ~ $less(f22(f30,X0),0.0),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_20) ).
tff(f3109,plain,
( spl331_40
| ~ spl331_39 ),
inference(avatar_split_clause,[],[f3105,f3102,f3107]) ).
tff(f3102,plain,
( spl331_39
<=> ! [X0: 'S10'] : ~ $less(f27(f31,X0),0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_39])]) ).
tff(f3105,plain,
( ! [X0: 'S10'] : ~ $less(sK24(X0),0.0)
| ~ spl331_39 ),
inference(forward_demodulation,[],[f3103,f1573]) ).
tff(f3103,plain,
( ! [X0: 'S10'] : ~ $less(f27(f31,X0),0.0)
| ~ spl331_39 ),
inference(avatar_component_clause,[],[f3102]) ).
tff(f3104,plain,
spl331_39,
inference(avatar_split_clause,[],[f1468,f3102]) ).
tff(f1468,plain,
! [X0: 'S10'] : ~ $less(f27(f31,X0),0.0),
inference(cnf_transformation,[],[f21]) ).
tff(f21,axiom,
! [X0: 'S10'] : ~ $less(f27(f31,X0),0.0),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_21) ).
tff(f3100,plain,
spl331_38,
inference(avatar_split_clause,[],[f1464,f3097]) ).
tff(f1464,plain,
0.0 = f27(f28,f51),
inference(cnf_transformation,[],[f122]) ).
tff(f122,axiom,
0.0 = f27(f28,f51),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_122) ).
tff(f3095,plain,
spl331_37,
inference(avatar_split_clause,[],[f1463,f3092]) ).
tff(f1463,plain,
1.0 = f27(f36,f51),
inference(cnf_transformation,[],[f60]) ).
tff(f60,axiom,
1.0 = f27(f36,f51),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_60) ).
tff(f3090,plain,
spl331_36,
inference(avatar_split_clause,[],[f600,f3088]) ).
tff(f600,plain,
! [X0: $real] : ( 0.0 = $product(X0,0.0) ),
introduced(theory_axiom_152,[]) ).
tff(f3086,plain,
spl331_35,
inference(avatar_split_clause,[],[f599,f3084]) ).
tff(f3084,plain,
( spl331_35
<=> ! [X0: $real] : ( $product(X0,1.0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_35])]) ).
tff(f599,plain,
! [X0: $real] : ( $product(X0,1.0) = X0 ),
introduced(theory_axiom_140,[]) ).
tff(f3082,plain,
spl331_34,
inference(avatar_split_clause,[],[f596,f3080]) ).
tff(f3080,plain,
( spl331_34
<=> ! [X0: $real] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_34])]) ).
tff(f596,plain,
! [X0: $real] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_151,[]) ).
tff(f3078,plain,
spl331_33,
inference(avatar_split_clause,[],[f588,f3076]) ).
tff(f3076,plain,
( spl331_33
<=> ! [X0: $real] : ( $sum(X0,0.0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_33])]) ).
tff(f588,plain,
! [X0: $real] : ( $sum(X0,0.0) = X0 ),
introduced(theory_axiom_140,[]) ).
tff(f3074,plain,
spl331_32,
inference(avatar_split_clause,[],[f582,f3072]) ).
tff(f582,plain,
! [X0: $int] : ( 0 = $product(X0,0) ),
introduced(theory_axiom_152,[]) ).
tff(f3070,plain,
spl331_31,
inference(avatar_split_clause,[],[f581,f3068]) ).
tff(f3068,plain,
( spl331_31
<=> ! [X0: $int] : ( $product(X0,1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_31])]) ).
tff(f581,plain,
! [X0: $int] : ( $product(X0,1) = X0 ),
introduced(theory_axiom_140,[]) ).
tff(f3066,plain,
spl331_30,
inference(avatar_split_clause,[],[f578,f3064]) ).
tff(f3064,plain,
( spl331_30
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_30])]) ).
tff(f578,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_151,[]) ).
tff(f3062,plain,
spl331_29,
inference(avatar_split_clause,[],[f570,f3060]) ).
tff(f3060,plain,
( spl331_29
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_29])]) ).
tff(f570,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_140,[]) ).
tff(f3058,plain,
spl331_28,
inference(avatar_split_clause,[],[f1549,f3056]) ).
tff(f3056,plain,
( spl331_28
<=> ! [X0: $real] : ~ $less(sK13(X0),0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_28])]) ).
tff(f1549,plain,
! [X0: $real] : ~ $less(sK13(X0),0.0),
inference(cnf_transformation,[],[f925]) ).
tff(f925,plain,
! [X0: $real] :
( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),sK13(X0)),f22(f30,f22(f49(f50,X2),X0)))
& ~ $less(sK13(X0),0.0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f469,f924]) ).
tff(f924,plain,
! [X0: $real] :
( ? [X1: $real] :
( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),X1),f22(f30,f22(f49(f50,X2),X0)))
& ~ $less(X1,0.0) )
=> ( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),sK13(X0)),f22(f30,f22(f49(f50,X2),X0)))
& ~ $less(sK13(X0),0.0) ) ),
introduced(choice_axiom,[]) ).
tff(f469,plain,
! [X0: $real] :
? [X1: $real] :
( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),X1),f22(f30,f22(f49(f50,X2),X0)))
& ~ $less(X1,0.0) ),
inference(theory_normalization,[],[f184]) ).
tff(f184,axiom,
! [X0: $real] :
? [X1: $real] :
( ! [X2: $real] : $lesseq(f22(f30,f22(f49(f50,X2),X0)),f22(f49(f50,f22(f30,X2)),X1))
& $lesseq(0.0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_184) ).
tff(f3054,plain,
spl331_27,
inference(avatar_split_clause,[],[f1547,f3052]) ).
tff(f3052,plain,
( spl331_27
<=> ! [X0: $real] : ~ $less(sK12(X0),0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_27])]) ).
tff(f1547,plain,
! [X0: $real] : ~ $less(sK12(X0),0.0),
inference(cnf_transformation,[],[f923]) ).
tff(f923,plain,
! [X0: $real] :
( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),sK12(X0)),f22(f30,f22(f49(f50,X0),X2)))
& ~ $less(sK12(X0),0.0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f468,f922]) ).
tff(f922,plain,
! [X0: $real] :
( ? [X1: $real] :
( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),X1),f22(f30,f22(f49(f50,X0),X2)))
& ~ $less(X1,0.0) )
=> ( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),sK12(X0)),f22(f30,f22(f49(f50,X0),X2)))
& ~ $less(sK12(X0),0.0) ) ),
introduced(choice_axiom,[]) ).
tff(f468,plain,
! [X0: $real] :
? [X1: $real] :
( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),X1),f22(f30,f22(f49(f50,X0),X2)))
& ~ $less(X1,0.0) ),
inference(theory_normalization,[],[f188]) ).
tff(f188,axiom,
! [X0: $real] :
? [X1: $real] :
( ! [X2: $real] : $lesseq(f22(f30,f22(f49(f50,X0),X2)),f22(f49(f50,f22(f30,X2)),X1))
& $lesseq(0.0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_188) ).
tff(f3050,plain,
spl331_26,
inference(avatar_split_clause,[],[f1545,f3048]) ).
tff(f3048,plain,
( spl331_26
<=> ! [X0: 'S10'] : ~ $less(sK11(X0),0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_26])]) ).
tff(f1545,plain,
! [X0: 'S10'] : ~ $less(sK11(X0),0.0),
inference(cnf_transformation,[],[f921]) ).
tff(f921,plain,
! [X0: 'S10'] :
( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),sK11(X0)),f27(f31,f34(f39(f52,X0),X2)))
& ~ $less(sK11(X0),0.0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f467,f920]) ).
tff(f920,plain,
! [X0: 'S10'] :
( ? [X1: $real] :
( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),X1),f27(f31,f34(f39(f52,X0),X2)))
& ~ $less(X1,0.0) )
=> ( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),sK11(X0)),f27(f31,f34(f39(f52,X0),X2)))
& ~ $less(sK11(X0),0.0) ) ),
introduced(choice_axiom,[]) ).
tff(f467,plain,
! [X0: 'S10'] :
? [X1: $real] :
( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),X1),f27(f31,f34(f39(f52,X0),X2)))
& ~ $less(X1,0.0) ),
inference(theory_normalization,[],[f189]) ).
tff(f189,axiom,
! [X0: 'S10'] :
? [X1: $real] :
( ! [X2: 'S10'] : $lesseq(f27(f31,f34(f39(f52,X0),X2)),f22(f49(f50,f27(f31,X2)),X1))
& $lesseq(0.0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_189) ).
tff(f3046,plain,
spl331_25,
inference(avatar_split_clause,[],[f1543,f3044]) ).
tff(f3044,plain,
( spl331_25
<=> ! [X0: 'S10'] : ~ $less(sK10(X0),0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_25])]) ).
tff(f1543,plain,
! [X0: 'S10'] : ~ $less(sK10(X0),0.0),
inference(cnf_transformation,[],[f919]) ).
tff(f919,plain,
! [X0: 'S10'] :
( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),sK10(X0)),f27(f31,f34(f39(f52,X2),X0)))
& ~ $less(sK10(X0),0.0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f466,f918]) ).
tff(f918,plain,
! [X0: 'S10'] :
( ? [X1: $real] :
( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),X1),f27(f31,f34(f39(f52,X2),X0)))
& ~ $less(X1,0.0) )
=> ( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),sK10(X0)),f27(f31,f34(f39(f52,X2),X0)))
& ~ $less(sK10(X0),0.0) ) ),
introduced(choice_axiom,[]) ).
tff(f466,plain,
! [X0: 'S10'] :
? [X1: $real] :
( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),X1),f27(f31,f34(f39(f52,X2),X0)))
& ~ $less(X1,0.0) ),
inference(theory_normalization,[],[f185]) ).
tff(f185,axiom,
! [X0: 'S10'] :
? [X1: $real] :
( ! [X2: 'S10'] : $lesseq(f27(f31,f34(f39(f52,X2),X0)),f22(f49(f50,f27(f31,X2)),X1))
& $lesseq(0.0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_185) ).
tff(f3042,plain,
spl331_24,
inference(avatar_split_clause,[],[f1541,f3040]) ).
tff(f3040,plain,
( spl331_24
<=> ! [X0: $real] : $less(0.0,sK9(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_24])]) ).
tff(f1541,plain,
! [X0: $real] : $less(0.0,sK9(X0)),
inference(cnf_transformation,[],[f917]) ).
tff(f917,plain,
! [X0: $real] :
( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),sK9(X0)),f22(f30,f22(f49(f50,X0),X2)))
& $less(0.0,sK9(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f465,f916]) ).
tff(f916,plain,
! [X0: $real] :
( ? [X1: $real] :
( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),X1),f22(f30,f22(f49(f50,X0),X2)))
& $less(0.0,X1) )
=> ( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),sK9(X0)),f22(f30,f22(f49(f50,X0),X2)))
& $less(0.0,sK9(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f465,plain,
! [X0: $real] :
? [X1: $real] :
( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),X1),f22(f30,f22(f49(f50,X0),X2)))
& $less(0.0,X1) ),
inference(theory_normalization,[],[f190]) ).
tff(f190,axiom,
! [X0: $real] :
? [X1: $real] :
( ! [X2: $real] : $lesseq(f22(f30,f22(f49(f50,X0),X2)),f22(f49(f50,f22(f30,X2)),X1))
& $less(0.0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_190) ).
tff(f3038,plain,
spl331_23,
inference(avatar_split_clause,[],[f1539,f3036]) ).
tff(f3036,plain,
( spl331_23
<=> ! [X0: $real] : $less(0.0,sK8(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_23])]) ).
tff(f1539,plain,
! [X0: $real] : $less(0.0,sK8(X0)),
inference(cnf_transformation,[],[f915]) ).
tff(f915,plain,
! [X0: $real] :
( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),sK8(X0)),f22(f30,f22(f49(f50,X2),X0)))
& $less(0.0,sK8(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f464,f914]) ).
tff(f914,plain,
! [X0: $real] :
( ? [X1: $real] :
( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),X1),f22(f30,f22(f49(f50,X2),X0)))
& $less(0.0,X1) )
=> ( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),sK8(X0)),f22(f30,f22(f49(f50,X2),X0)))
& $less(0.0,sK8(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f464,plain,
! [X0: $real] :
? [X1: $real] :
( ! [X2: $real] : ~ $less(f22(f49(f50,f22(f30,X2)),X1),f22(f30,f22(f49(f50,X2),X0)))
& $less(0.0,X1) ),
inference(theory_normalization,[],[f186]) ).
tff(f186,axiom,
! [X0: $real] :
? [X1: $real] :
( ! [X2: $real] : $lesseq(f22(f30,f22(f49(f50,X2),X0)),f22(f49(f50,f22(f30,X2)),X1))
& $less(0.0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_186) ).
tff(f3034,plain,
spl331_22,
inference(avatar_split_clause,[],[f1537,f3032]) ).
tff(f3032,plain,
( spl331_22
<=> ! [X0: 'S10'] : $less(0.0,sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_22])]) ).
tff(f1537,plain,
! [X0: 'S10'] : $less(0.0,sK7(X0)),
inference(cnf_transformation,[],[f913]) ).
tff(f913,plain,
! [X0: 'S10'] :
( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),sK7(X0)),f27(f31,f34(f39(f52,X0),X2)))
& $less(0.0,sK7(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f463,f912]) ).
tff(f912,plain,
! [X0: 'S10'] :
( ? [X1: $real] :
( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),X1),f27(f31,f34(f39(f52,X0),X2)))
& $less(0.0,X1) )
=> ( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),sK7(X0)),f27(f31,f34(f39(f52,X0),X2)))
& $less(0.0,sK7(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f463,plain,
! [X0: 'S10'] :
? [X1: $real] :
( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),X1),f27(f31,f34(f39(f52,X0),X2)))
& $less(0.0,X1) ),
inference(theory_normalization,[],[f191]) ).
tff(f191,axiom,
! [X0: 'S10'] :
? [X1: $real] :
( ! [X2: 'S10'] : $lesseq(f27(f31,f34(f39(f52,X0),X2)),f22(f49(f50,f27(f31,X2)),X1))
& $less(0.0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_191) ).
tff(f3030,plain,
spl331_21,
inference(avatar_split_clause,[],[f1535,f3028]) ).
tff(f3028,plain,
( spl331_21
<=> ! [X0: 'S10'] : $less(0.0,sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_21])]) ).
tff(f1535,plain,
! [X0: 'S10'] : $less(0.0,sK6(X0)),
inference(cnf_transformation,[],[f911]) ).
tff(f911,plain,
! [X0: 'S10'] :
( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),sK6(X0)),f27(f31,f34(f39(f52,X2),X0)))
& $less(0.0,sK6(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f462,f910]) ).
tff(f910,plain,
! [X0: 'S10'] :
( ? [X1: $real] :
( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),X1),f27(f31,f34(f39(f52,X2),X0)))
& $less(0.0,X1) )
=> ( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),sK6(X0)),f27(f31,f34(f39(f52,X2),X0)))
& $less(0.0,sK6(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f462,plain,
! [X0: 'S10'] :
? [X1: $real] :
( ! [X2: 'S10'] : ~ $less(f22(f49(f50,f27(f31,X2)),X1),f27(f31,f34(f39(f52,X2),X0)))
& $less(0.0,X1) ),
inference(theory_normalization,[],[f187]) ).
tff(f187,axiom,
! [X0: 'S10'] :
? [X1: $real] :
( ! [X2: 'S10'] : $lesseq(f27(f31,f34(f39(f52,X2),X0)),f22(f49(f50,f27(f31,X2)),X1))
& $less(0.0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_187) ).
tff(f3026,plain,
spl331_20,
inference(avatar_split_clause,[],[f1462,f3023]) ).
tff(f3023,plain,
( spl331_20
<=> ( f1 = f38(f36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_20])]) ).
tff(f1462,plain,
f1 = f38(f36),
inference(cnf_transformation,[],[f59]) ).
tff(f59,axiom,
f1 = f38(f36),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_59) ).
tff(f3021,plain,
spl331_19,
inference(avatar_split_clause,[],[f1461,f3018]) ).
tff(f3018,plain,
( spl331_19
<=> ( f1 = f38(f28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_19])]) ).
tff(f1461,plain,
f1 = f38(f28),
inference(cnf_transformation,[],[f44]) ).
tff(f44,axiom,
f1 = f38(f28),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_44) ).
tff(f3016,plain,
spl331_18,
inference(avatar_split_clause,[],[f1460,f3013]) ).
tff(f3013,plain,
( spl331_18
<=> ( f1 = f37(f35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_18])]) ).
tff(f1460,plain,
f1 = f37(f35),
inference(cnf_transformation,[],[f43]) ).
tff(f43,axiom,
f1 = f37(f35),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_43) ).
tff(f3011,plain,
~ spl331_17,
inference(avatar_split_clause,[],[f2305,f3008]) ).
tff(f2305,plain,
~ $less(sK323,0.0),
inference(cnf_transformation,[],[f1444]) ).
tff(f1444,plain,
( ! [X1: $real,X2: $real] : ~ $less(f22(f49(f50,f22(f49(f50,f22(f30,X1)),f22(f30,X2))),sK323),f22(f30,f22(f49(f50,X1),X2)))
& ~ $less(sK323,0.0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK323])],[f560,f1443]) ).
tff(f1443,plain,
( ? [X0: $real] :
( ! [X1: $real,X2: $real] : ~ $less(f22(f49(f50,f22(f49(f50,f22(f30,X1)),f22(f30,X2))),X0),f22(f30,f22(f49(f50,X1),X2)))
& ~ $less(X0,0.0) )
=> ( ! [X2: $real,X1: $real] : ~ $less(f22(f49(f50,f22(f49(f50,f22(f30,X1)),f22(f30,X2))),sK323),f22(f30,f22(f49(f50,X1),X2)))
& ~ $less(sK323,0.0) ) ),
introduced(choice_axiom,[]) ).
tff(f560,plain,
? [X0: $real] :
( ! [X1: $real,X2: $real] : ~ $less(f22(f49(f50,f22(f49(f50,f22(f30,X1)),f22(f30,X2))),X0),f22(f30,f22(f49(f50,X1),X2)))
& ~ $less(X0,0.0) ),
inference(theory_normalization,[],[f192]) ).
tff(f192,axiom,
? [X0: $real] :
( ! [X1: $real,X2: $real] : $lesseq(f22(f30,f22(f49(f50,X1),X2)),f22(f49(f50,f22(f49(f50,f22(f30,X1)),f22(f30,X2))),X0))
& $lesseq(0.0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_192) ).
tff(f3006,plain,
~ spl331_16,
inference(avatar_split_clause,[],[f2303,f3003]) ).
tff(f2303,plain,
~ $less(sK322,0.0),
inference(cnf_transformation,[],[f1442]) ).
tff(f1442,plain,
( ! [X1: 'S10',X2: 'S10'] : ~ $less(f22(f49(f50,f22(f49(f50,f27(f31,X1)),f27(f31,X2))),sK322),f27(f31,f34(f39(f52,X1),X2)))
& ~ $less(sK322,0.0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK322])],[f559,f1441]) ).
tff(f1441,plain,
( ? [X0: $real] :
( ! [X1: 'S10',X2: 'S10'] : ~ $less(f22(f49(f50,f22(f49(f50,f27(f31,X1)),f27(f31,X2))),X0),f27(f31,f34(f39(f52,X1),X2)))
& ~ $less(X0,0.0) )
=> ( ! [X2: 'S10',X1: 'S10'] : ~ $less(f22(f49(f50,f22(f49(f50,f27(f31,X1)),f27(f31,X2))),sK322),f27(f31,f34(f39(f52,X1),X2)))
& ~ $less(sK322,0.0) ) ),
introduced(choice_axiom,[]) ).
tff(f559,plain,
? [X0: $real] :
( ! [X1: 'S10',X2: 'S10'] : ~ $less(f22(f49(f50,f22(f49(f50,f27(f31,X1)),f27(f31,X2))),X0),f27(f31,f34(f39(f52,X1),X2)))
& ~ $less(X0,0.0) ),
inference(theory_normalization,[],[f193]) ).
tff(f193,axiom,
? [X0: $real] :
( ! [X1: 'S10',X2: 'S10'] : $lesseq(f27(f31,f34(f39(f52,X1),X2)),f22(f49(f50,f22(f49(f50,f27(f31,X1)),f27(f31,X2))),X0))
& $lesseq(0.0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_193) ).
tff(f3001,plain,
~ spl331_15,
inference(avatar_split_clause,[],[f2301,f2998]) ).
tff(f2301,plain,
~ $less(sK321,0.0),
inference(cnf_transformation,[],[f1440]) ).
tff(f1440,plain,
( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK321),f22(f30,f22(f33,X1)))
& ~ $less(sK321,0.0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK321])],[f558,f1439]) ).
tff(f1439,plain,
( ? [X0: $real] :
( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),X0),f22(f30,f22(f33,X1)))
& ~ $less(X0,0.0) )
=> ( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK321),f22(f30,f22(f33,X1)))
& ~ $less(sK321,0.0) ) ),
introduced(choice_axiom,[]) ).
tff(f558,plain,
? [X0: $real] :
( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),X0),f22(f30,f22(f33,X1)))
& ~ $less(X0,0.0) ),
inference(theory_normalization,[],[f56]) ).
tff(f56,axiom,
? [X0: $real] :
( ! [X1: $real] : $lesseq(f22(f30,f22(f33,X1)),f22(f49(f50,f22(f30,X1)),X0))
& $lesseq(0.0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_56) ).
tff(f2996,plain,
~ spl331_14,
inference(avatar_split_clause,[],[f2299,f2993]) ).
tff(f2299,plain,
~ $less(sK320,0.0),
inference(cnf_transformation,[],[f1438]) ).
tff(f2991,plain,
~ spl331_13,
inference(avatar_split_clause,[],[f2297,f2988]) ).
tff(f2297,plain,
~ $less(sK319,0.0),
inference(cnf_transformation,[],[f1436]) ).
tff(f2986,plain,
~ spl331_12,
inference(avatar_split_clause,[],[f2295,f2983]) ).
tff(f2295,plain,
~ $less(sK318,0.0),
inference(cnf_transformation,[],[f1434]) ).
tff(f2981,plain,
~ spl331_11,
inference(avatar_split_clause,[],[f2293,f2978]) ).
tff(f2293,plain,
~ $less(sK317,0.0),
inference(cnf_transformation,[],[f1432]) ).
tff(f2976,plain,
spl331_10,
inference(avatar_split_clause,[],[f2291,f2973]) ).
tff(f2973,plain,
( spl331_10
<=> $less(0.0,sK316) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_10])]) ).
tff(f2291,plain,
$less(0.0,sK316),
inference(cnf_transformation,[],[f1430]) ).
tff(f1430,plain,
( ! [X1: $real,X2: $real] : ~ $less(f22(f49(f50,f22(f49(f50,f22(f30,X1)),f22(f30,X2))),sK316),f22(f30,f22(f49(f50,X1),X2)))
& $less(0.0,sK316) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK316])],[f553,f1429]) ).
tff(f1429,plain,
( ? [X0: $real] :
( ! [X1: $real,X2: $real] : ~ $less(f22(f49(f50,f22(f49(f50,f22(f30,X1)),f22(f30,X2))),X0),f22(f30,f22(f49(f50,X1),X2)))
& $less(0.0,X0) )
=> ( ! [X2: $real,X1: $real] : ~ $less(f22(f49(f50,f22(f49(f50,f22(f30,X1)),f22(f30,X2))),sK316),f22(f30,f22(f49(f50,X1),X2)))
& $less(0.0,sK316) ) ),
introduced(choice_axiom,[]) ).
tff(f553,plain,
? [X0: $real] :
( ! [X1: $real,X2: $real] : ~ $less(f22(f49(f50,f22(f49(f50,f22(f30,X1)),f22(f30,X2))),X0),f22(f30,f22(f49(f50,X1),X2)))
& $less(0.0,X0) ),
inference(theory_normalization,[],[f200]) ).
tff(f200,axiom,
? [X0: $real] :
( ! [X1: $real,X2: $real] : $lesseq(f22(f30,f22(f49(f50,X1),X2)),f22(f49(f50,f22(f49(f50,f22(f30,X1)),f22(f30,X2))),X0))
& $less(0.0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_200) ).
tff(f2971,plain,
spl331_9,
inference(avatar_split_clause,[],[f2289,f2968]) ).
tff(f2968,plain,
( spl331_9
<=> $less(0.0,sK315) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_9])]) ).
tff(f2289,plain,
$less(0.0,sK315),
inference(cnf_transformation,[],[f1428]) ).
tff(f1428,plain,
( ! [X1: 'S10',X2: 'S10'] : ~ $less(f22(f49(f50,f22(f49(f50,f27(f31,X1)),f27(f31,X2))),sK315),f27(f31,f34(f39(f52,X1),X2)))
& $less(0.0,sK315) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK315])],[f552,f1427]) ).
tff(f1427,plain,
( ? [X0: $real] :
( ! [X1: 'S10',X2: 'S10'] : ~ $less(f22(f49(f50,f22(f49(f50,f27(f31,X1)),f27(f31,X2))),X0),f27(f31,f34(f39(f52,X1),X2)))
& $less(0.0,X0) )
=> ( ! [X2: 'S10',X1: 'S10'] : ~ $less(f22(f49(f50,f22(f49(f50,f27(f31,X1)),f27(f31,X2))),sK315),f27(f31,f34(f39(f52,X1),X2)))
& $less(0.0,sK315) ) ),
introduced(choice_axiom,[]) ).
tff(f552,plain,
? [X0: $real] :
( ! [X1: 'S10',X2: 'S10'] : ~ $less(f22(f49(f50,f22(f49(f50,f27(f31,X1)),f27(f31,X2))),X0),f27(f31,f34(f39(f52,X1),X2)))
& $less(0.0,X0) ),
inference(theory_normalization,[],[f201]) ).
tff(f201,axiom,
? [X0: $real] :
( ! [X1: 'S10',X2: 'S10'] : $lesseq(f27(f31,f34(f39(f52,X1),X2)),f22(f49(f50,f22(f49(f50,f27(f31,X1)),f27(f31,X2))),X0))
& $less(0.0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_201) ).
tff(f2966,plain,
spl331_8,
inference(avatar_split_clause,[],[f2287,f2963]) ).
tff(f2963,plain,
( spl331_8
<=> $less(0.0,sK314) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_8])]) ).
tff(f2287,plain,
$less(0.0,sK314),
inference(cnf_transformation,[],[f1426]) ).
tff(f1426,plain,
( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK314),f22(f30,f22(f33,X1)))
& $less(0.0,sK314) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK314])],[f551,f1425]) ).
tff(f1425,plain,
( ? [X0: $real] :
( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),X0),f22(f30,f22(f33,X1)))
& $less(0.0,X0) )
=> ( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),sK314),f22(f30,f22(f33,X1)))
& $less(0.0,sK314) ) ),
introduced(choice_axiom,[]) ).
tff(f551,plain,
? [X0: $real] :
( ! [X1: $real] : ~ $less(f22(f49(f50,f22(f30,X1)),X0),f22(f30,f22(f33,X1)))
& $less(0.0,X0) ),
inference(theory_normalization,[],[f54]) ).
tff(f54,axiom,
? [X0: $real] :
( ! [X1: $real] : $lesseq(f22(f30,f22(f33,X1)),f22(f49(f50,f22(f30,X1)),X0))
& $less(0.0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_54) ).
tff(f2961,plain,
spl331_7,
inference(avatar_split_clause,[],[f2285,f2958]) ).
tff(f2958,plain,
( spl331_7
<=> $less(0.0,sK313) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_7])]) ).
tff(f2285,plain,
$less(0.0,sK313),
inference(cnf_transformation,[],[f1424]) ).
tff(f2956,plain,
spl331_6,
inference(avatar_split_clause,[],[f2283,f2953]) ).
tff(f2953,plain,
( spl331_6
<=> $less(0.0,sK312) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_6])]) ).
tff(f2283,plain,
$less(0.0,sK312),
inference(cnf_transformation,[],[f1422]) ).
tff(f2951,plain,
spl331_5,
inference(avatar_split_clause,[],[f2281,f2948]) ).
tff(f2948,plain,
( spl331_5
<=> $less(0.0,sK311) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_5])]) ).
tff(f2281,plain,
$less(0.0,sK311),
inference(cnf_transformation,[],[f1420]) ).
tff(f2946,plain,
spl331_4,
inference(avatar_split_clause,[],[f2279,f2943]) ).
tff(f2943,plain,
( spl331_4
<=> $less(0.0,sK310) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_4])]) ).
tff(f2279,plain,
$less(0.0,sK310),
inference(cnf_transformation,[],[f1418]) ).
tff(f2941,plain,
~ spl331_3,
inference(avatar_split_clause,[],[f1459,f2938]) ).
tff(f2938,plain,
( spl331_3
<=> ( f1 = f2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl331_3])]) ).
tff(f1459,plain,
f1 != f2,
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
f1 != f2,
file('/export/starexec/sandbox2/tmp/tmp.0nnSHvV2f2/Vampire---4.8_13359',formula_1) ).
tff(f2936,plain,
spl331_2,
inference(avatar_split_clause,[],[f591,f2934]) ).
tff(f591,plain,
! [X0: $real] : ~ $less(X0,X0),
introduced(theory_axiom_145,[]) ).
tff(f2932,plain,
spl331_1,
inference(avatar_split_clause,[],[f573,f2930]) ).
tff(f573,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_145,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.18 % Problem : SWW822_1 : TPTP v8.1.2. Released v7.0.0.
% 0.21/0.20 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.21/0.42 % Computer : n024.cluster.edu
% 0.21/0.42 % Model : x86_64 x86_64
% 0.21/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.42 % Memory : 8042.1875MB
% 0.21/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.21/0.42 % CPULimit : 300
% 0.21/0.42 % WCLimit : 300
% 0.21/0.42 % DateTime : Wed Aug 30 16:37:38 EDT 2023
% 0.21/0.43 % CPUTime :
% 0.21/0.49 % (13514)Running in auto input_syntax mode. Trying TPTP
% 0.28/0.53 % (13520)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.28/0.53 % (13516)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.28/0.53 % (13515)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.28/0.53 % (13521)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.28/0.53 % (13524)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.28/0.53 % (13517)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.28/0.53 % (13525)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.28/0.55 % (13515)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.28/0.55 % (13516)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.28/0.55 % (13515)Terminated due to inappropriate strategy.
% 0.28/0.55 % (13515)------------------------------
% 0.28/0.55 % (13515)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.28/0.55 % (13515)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.28/0.55 % (13515)Termination reason: Inappropriate
% 0.28/0.55
% 0.28/0.55 % (13515)Memory used [KB]: 2942
% 0.28/0.55 % (13515)Time elapsed: 0.025 s
% 0.28/0.55 % (13515)------------------------------
% 0.28/0.55 % (13515)------------------------------
% 0.28/0.55 % (13520)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.28/0.55 % (13520)Terminated due to inappropriate strategy.
% 0.28/0.55 % (13520)------------------------------
% 0.28/0.55 % (13520)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.28/0.55 % (13520)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.28/0.55 % (13520)Termination reason: Inappropriate
% 0.28/0.55
% 0.28/0.55 % (13520)Memory used [KB]: 2942
% 0.28/0.55 % (13520)Time elapsed: 0.025 s
% 0.28/0.55 % (13520)------------------------------
% 0.28/0.55 % (13520)------------------------------
% 0.28/0.55 % (13516)Terminated due to inappropriate strategy.
% 0.28/0.55 % (13516)------------------------------
% 0.28/0.55 % (13516)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.28/0.55 % (13516)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.28/0.55 % (13516)Termination reason: Inappropriate
% 0.28/0.55
% 0.28/0.55 % (13516)Memory used [KB]: 2942
% 0.28/0.55 % (13516)Time elapsed: 0.025 s
% 0.28/0.55 % (13516)------------------------------
% 0.28/0.55 % (13516)------------------------------
% 0.28/0.56 % (13528)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on Vampire---4 for (367ds/0Mi)
% 0.28/0.56 % (13527)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on Vampire---4 for (382ds/0Mi)
% 0.37/0.56 % (13526)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on Vampire---4 for (411ds/0Mi)
% 0.37/0.59 % (13526)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.37/0.59 % (13526)Terminated due to inappropriate strategy.
% 0.37/0.59 % (13526)------------------------------
% 0.37/0.59 % (13526)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.37/0.59 % (13526)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.37/0.59 % (13526)Termination reason: Inappropriate
% 0.37/0.59
% 0.37/0.59 % (13526)Memory used [KB]: 2942
% 0.37/0.59 % (13526)Time elapsed: 0.024 s
% 0.37/0.59 % (13526)------------------------------
% 0.37/0.59 % (13526)------------------------------
% 0.37/0.59 % (13529)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on Vampire---4 for (354ds/0Mi)
% 0.37/0.66 % (13521)First to succeed.
% 0.47/0.71 % (13529)Also succeeded, but the first one will report.
% 0.47/0.71 % (13521)Refutation found. Thanks to Tanya!
% 0.47/0.71 % SZS status Unsatisfiable for Vampire---4
% 0.47/0.71 % SZS output start Proof for Vampire---4
% See solution above
% 0.47/0.73 % (13521)------------------------------
% 0.47/0.73 % (13521)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.47/0.73 % (13521)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.47/0.73 % (13521)Termination reason: Refutation
% 0.47/0.73
% 0.47/0.73 % (13521)Memory used [KB]: 10618
% 0.47/0.73 % (13521)Time elapsed: 0.180 s
% 0.47/0.73 % (13521)------------------------------
% 0.47/0.73 % (13521)------------------------------
% 0.47/0.73 % (13514)Success in time 0.293 s
% 0.47/0.73 % Vampire---4.8 exiting
%------------------------------------------------------------------------------