%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP409_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:33:49 AM UTC 2026
% Result : Theorem 4.86s 1.80s
% Output : Refutation 6.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 22
% Syntax : Number of formulae : 86 ( 18 unt; 0 typ; 19 def)
% Number of atoms : 248 ( 21 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 265 ( 103 ~; 112 |; 21 &)
% ( 20 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 102 ( 60 atm; 19 fun; 19 num; 4 var)
% Number of types : 12 ( 10 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 23 ( 19 usr; 16 prp; 0-2 aty)
% Number of functors : 244 ( 242 usr; 24 con; 0-3 aty)
% Number of variables : 40 ( 34 !; 6 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Int_bool_fun$': $tType ).
tff(type_def_6,type,
'Nat_nat_bool_fun_fun$': $tType ).
tff(type_def_7,type,
'Int_int_fun$': $tType ).
tff(type_def_8,type,
'Nat_nat_fun$': $tType ).
tff(type_def_9,type,
'Int_nat_fun$': $tType ).
tff(type_def_10,type,
'Nat$': $tType ).
tff(type_def_11,type,
tlbool: $tType ).
tff(type_def_12,type,
'Int_int_bool_fun_fun$': $tType ).
tff(type_def_13,type,
'Nat_bool_fun$': $tType ).
tff(type_def_14,type,
'Nat_int_fun$': $tType ).
tff(func_def_0,type,
'n_0$': 'Nat$' ).
tff(func_def_1,type,
'fun_app$d': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).
tff(func_def_2,type,
'uu$': 'Int_int_bool_fun_fun$' ).
tff(func_def_3,type,
'zero$': 'Nat$' ).
tff(func_def_4,type,
'of_nat$a': 'Nat_nat_fun$' ).
tff(func_def_5,type,
'nat$': 'Int_nat_fun$' ).
tff(func_def_6,type,
'times$a': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_7,type,
'of_nat$': 'Nat_int_fun$' ).
tff(func_def_8,type,
'fun_app$a': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).
tff(func_def_9,type,
'fun_app$f': ( 'Int_nat_fun$' * $int ) > 'Nat$' ).
tff(func_def_10,type,
'of_int$': 'Int_int_fun$' ).
tff(func_def_11,type,
'times$': $int > 'Int_int_fun$' ).
tff(func_def_12,type,
'less$': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_13,type,
tltrue: tlbool ).
tff(func_def_14,type,
'greatest$': 'Int_bool_fun$' > $int ).
tff(func_def_15,type,
'one$': 'Nat$' ).
tff(func_def_16,type,
'fun_app$e': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_17,type,
'fun_app$g': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_18,type,
'less_eq$': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_19,type,
'p$': 'Nat_bool_fun$' ).
tff(func_def_20,type,
tlfalse: tlbool ).
tff(func_def_21,type,
'greatest$a': 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_22,type,
'fun_app$b': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).
tff(func_def_28,type,
sK0: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_29,type,
sK1: $int > 'Nat$' ).
tff(func_def_30,type,
sK2: $int > 'Nat$' ).
tff(func_def_31,type,
sK3: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_32,type,
sK4: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_33,type,
sK5: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_34,type,
sK6: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_35,type,
sK7: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_36,type,
sK8: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_37,type,
sK9: 'Int_int_fun$' > $int ).
tff(func_def_38,type,
sK10: 'Int_int_fun$' > $int ).
tff(func_def_39,type,
sK11: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_40,type,
sK12: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_41,type,
sK13: 'Nat$' > 'Nat$' ).
tff(func_def_42,type,
sK14: 'Int_nat_fun$' > $int ).
tff(func_def_43,type,
sK15: 'Int_nat_fun$' > $int ).
tff(func_def_44,type,
sK16: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_45,type,
sK17: $int > 'Nat$' ).
tff(func_def_46,type,
sK18: $int > 'Nat$' ).
tff(func_def_47,type,
sK19: ( $int * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_48,type,
sK20: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_49,type,
sK21: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_50,type,
sK22: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_51,type,
sK23: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_52,type,
sK24: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_53,type,
sK25: 'Int_nat_fun$' > $int ).
tff(func_def_54,type,
sK26: 'Int_nat_fun$' > $int ).
tff(func_def_55,type,
sK27: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_56,type,
sK28: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_57,type,
sK29: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_58,type,
sK30: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_59,type,
sK31: 'Int_nat_fun$' > $int ).
tff(func_def_60,type,
sK32: 'Int_nat_fun$' > $int ).
tff(func_def_61,type,
sK33: 'Nat$' ).
tff(func_def_62,type,
sK34: 'Nat$' ).
tff(func_def_63,type,
sK35: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_64,type,
sK36: $int > 'Nat$' ).
tff(func_def_65,type,
sK37: 'Int_int_fun$' > $int ).
tff(func_def_66,type,
sK38: 'Int_int_fun$' > $int ).
tff(func_def_67,type,
sK39: 'Int_int_fun$' > $int ).
tff(func_def_68,type,
sK40: 'Int_int_fun$' > $int ).
tff(func_def_69,type,
sK41: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_70,type,
sK42: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_71,type,
sK43: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_72,type,
sK44: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_73,type,
sK45: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_74,type,
sK46: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_75,type,
sK47: ( 'Nat$' * 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_76,type,
sK48: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_77,type,
sK49: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_78,type,
sK50: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_79,type,
sK51: 'Int_int_fun$' > $int ).
tff(func_def_80,type,
sK52: 'Int_int_fun$' > $int ).
tff(func_def_81,type,
sK53: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_82,type,
sK54: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_83,type,
sK55: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_84,type,
sK56: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_85,type,
sK57: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_86,type,
sK58: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_87,type,
sK59: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_88,type,
sK60: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_89,type,
sK61: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_90,type,
sK62: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_91,type,
sK63: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_92,type,
sK64: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_93,type,
sK65: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_94,type,
sK66: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_95,type,
sK67: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_96,type,
sK68: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_97,type,
sK69: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_98,type,
sK70: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_99,type,
sK71: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_100,type,
sK72: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_101,type,
sK73: ( 'Nat$' * 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_102,type,
sK74: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_103,type,
sK75: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_104,type,
sK76: 'Int_int_fun$' > $int ).
tff(func_def_105,type,
sK77: 'Int_int_fun$' > $int ).
tff(func_def_106,type,
sK78: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_107,type,
sK79: $int > 'Nat$' ).
tff(func_def_108,type,
sK80: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_109,type,
sK81: 'Nat$' > 'Nat$' ).
tff(func_def_110,type,
sK82: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_111,type,
sK83: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_112,type,
sK84: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_113,type,
sK85: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_114,type,
sK86: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_115,type,
sK87: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_116,type,
sK88: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_117,type,
sK89: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_118,type,
sK90: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_119,type,
sK91: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_120,type,
sK92: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_121,type,
sK93: $int > 'Nat$' ).
tff(func_def_122,type,
sK94: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_123,type,
sK95: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_124,type,
sK96: 'Int_int_fun$' > $int ).
tff(func_def_125,type,
sK97: 'Int_int_fun$' > $int ).
tff(func_def_126,type,
sK98: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_127,type,
sK99: ( 'Int_bool_fun$' * $int ) > $int ).
tff(func_def_128,type,
sK100: $int > 'Nat$' ).
tff(func_def_129,type,
sK101: $int > 'Nat$' ).
tff(func_def_130,type,
sK102: 'Int_int_fun$' > $int ).
tff(func_def_131,type,
sK103: 'Int_int_fun$' > $int ).
tff(func_def_132,type,
sK104: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_133,type,
sK105: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_134,type,
sK106: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_135,type,
sK107: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_136,type,
sK108: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_137,type,
sK109: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_138,type,
sK110: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_139,type,
sK111: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_140,type,
sK112: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_141,type,
sK113: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_142,type,
sK114: $int > $int ).
tff(func_def_143,type,
sK115: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_144,type,
sK116: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_145,type,
sK117: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_146,type,
sK118: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_147,type,
sK119: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_148,type,
sK120: 'Nat$' ).
tff(func_def_149,type,
sK121: 'Nat$' ).
tff(func_def_150,type,
sK122: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_151,type,
sK123: ( 'Nat_bool_fun$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_152,type,
sK124: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_153,type,
sK125: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_154,type,
sK126: 'Int_nat_fun$' > $int ).
tff(func_def_155,type,
sK127: 'Int_nat_fun$' > $int ).
tff(func_def_156,type,
sK128: 'Int_nat_fun$' > $int ).
tff(func_def_157,type,
sK129: 'Int_nat_fun$' > $int ).
tff(func_def_158,type,
sK130: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_159,type,
sK131: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_160,type,
sK132: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_161,type,
sK133: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_162,type,
sK134: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_163,type,
sK135: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_164,type,
sK136: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_165,type,
sK137: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_166,type,
sK138: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_167,type,
sK139: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_168,type,
sK140: 'Int_nat_fun$' > $int ).
tff(func_def_169,type,
sK141: 'Int_nat_fun$' > $int ).
tff(func_def_170,type,
sK142: 'Int_bool_fun$' > 'Nat$' ).
tff(func_def_171,type,
sK143: 'Int_bool_fun$' > 'Nat$' ).
tff(func_def_172,type,
sK144: 'Int_int_fun$' > $int ).
tff(func_def_173,type,
sK145: 'Int_int_fun$' > $int ).
tff(func_def_174,type,
sK146: ( 'Int_bool_fun$' * $int ) > $int ).
tff(func_def_175,type,
sK147: ( 'Int_bool_fun$' * 'Int_bool_fun$' ) > $int ).
tff(func_def_176,type,
sK148: 'Nat$' > 'Nat$' ).
tff(func_def_177,type,
sK149: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_178,type,
sK150: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_179,type,
sK151: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_180,type,
sK152: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_181,type,
sK153: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_182,type,
sK154: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_183,type,
sK155: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_184,type,
sK156: 'Int_int_fun$' > $int ).
tff(func_def_185,type,
sK157: 'Int_int_fun$' > $int ).
tff(func_def_186,type,
sK158: 'Int_nat_fun$' > $int ).
tff(func_def_187,type,
sK159: 'Int_nat_fun$' > $int ).
tff(func_def_188,type,
sK160: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_189,type,
sK161: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_190,type,
sK162: 'Int_nat_fun$' > $int ).
tff(func_def_191,type,
sK163: 'Int_nat_fun$' > $int ).
tff(func_def_192,type,
sK164: $int > 'Nat$' ).
tff(func_def_193,type,
sK165: 'Nat$' ).
tff(func_def_194,type,
sK166: 'Nat$' ).
tff(func_def_195,type,
sK167: 'Int_int_fun$' > $int ).
tff(func_def_196,type,
sK168: 'Int_int_fun$' > $int ).
tff(func_def_197,type,
sK169: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_198,type,
sK170: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_199,type,
sK171: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_200,type,
sK172: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_201,type,
sK173: 'Int_int_fun$' > $int ).
tff(func_def_202,type,
sK174: 'Int_int_fun$' > $int ).
tff(func_def_203,type,
sK175: 'Int_int_fun$' > $int ).
tff(func_def_204,type,
sK176: 'Int_int_fun$' > $int ).
tff(func_def_205,type,
sK177: 'Int_int_fun$' > $int ).
tff(func_def_206,type,
sK178: 'Int_int_fun$' > $int ).
tff(func_def_207,type,
sK179: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_208,type,
sK180: 'Int_nat_fun$' > $int ).
tff(func_def_209,type,
sK181: 'Int_nat_fun$' > $int ).
tff(func_def_210,type,
sK182: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_211,type,
sK183: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_212,type,
sK184: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_213,type,
sK185: $int > 'Nat$' ).
tff(func_def_214,type,
sK186: $int > 'Nat$' ).
tff(func_def_215,type,
sK187: 'Int_nat_fun$' > $int ).
tff(func_def_216,type,
sK188: 'Int_nat_fun$' > $int ).
tff(func_def_217,type,
sK189: 'Nat$' > 'Nat$' ).
tff(func_def_218,type,
sK190: $int > 'Nat$' ).
tff(func_def_219,type,
sK191: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_220,type,
sK192: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_221,type,
sK193: $int > $int ).
tff(func_def_222,type,
sK194: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_223,type,
sK195: 'Int_int_fun$' > $int ).
tff(func_def_224,type,
sK196: 'Int_int_fun$' > $int ).
tff(func_def_225,type,
sK197: 'Nat$' > 'Nat$' ).
tff(func_def_226,type,
sK198: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_227,type,
sK199: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_228,type,
sK200: 'Int_nat_fun$' > $int ).
tff(func_def_229,type,
sK201: 'Int_nat_fun$' > $int ).
tff(func_def_230,type,
sK202: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_231,type,
sK203: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_232,type,
sK204: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_233,type,
sK205: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_234,type,
sK206: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_235,type,
sK207: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_236,type,
sK208: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_237,type,
sK209: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_238,type,
sK210: $int > 'Nat$' ).
tff(func_def_239,type,
sK211: $int > 'Nat$' ).
tff(func_def_240,type,
sK212: 'Int_nat_fun$' > $int ).
tff(func_def_241,type,
sK213: 'Int_nat_fun$' > $int ).
tff(func_def_242,type,
sK214: 'Nat$' > 'Nat$' ).
tff(func_def_243,type,
sF215: $int ).
tff(func_def_244,type,
sF216: $int ).
tff(func_def_245,type,
sF217: $int ).
tff(func_def_246,type,
sF218: $int ).
tff(pred_def_1,type,
'fun_app$c': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_2,type,
'fun_app$': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_3,type,
'antimono$': 'Nat_int_fun$' > $o ).
tff(pred_def_4,type,
'antimono$a': 'Int_int_fun$' > $o ).
tff(f2,conjecture,
( ( ! [X0: 'Nat$'] :
( $lesseq($sum('fun_app$b'('of_nat$','n_0$'),1),'fun_app$b'('of_nat$',X0))
=> 'fun_app$c'('p$',X0) )
& 'fun_app$c'('p$','n_0$') )
<=> ! [X0: 'Nat$'] :
( $lesseq('fun_app$b'('of_nat$','n_0$'),'fun_app$b'('of_nat$',X0))
=> 'fun_app$c'('p$',X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture1) ).
tff(f3,negated_conjecture,
~ ( ( ! [X0: 'Nat$'] :
( $lesseq($sum('fun_app$b'('of_nat$','n_0$'),1),'fun_app$b'('of_nat$',X0))
=> 'fun_app$c'('p$',X0) )
& 'fun_app$c'('p$','n_0$') )
<=> ! [X0: 'Nat$'] :
( $lesseq('fun_app$b'('of_nat$','n_0$'),'fun_app$b'('of_nat$',X0))
=> 'fun_app$c'('p$',X0) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f294,axiom,
! [X0: $int] :
( $less(X0,X0)
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom292) ).
tff(f615,axiom,
! [X0: 'Nat$'] : ( 'fun_app$f'('nat$','fun_app$b'('of_nat$',X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom613) ).
tff(f826,plain,
~ ( ( ! [X0: 'Nat$'] :
( ~ $less('fun_app$b'('of_nat$',X0),$sum('fun_app$b'('of_nat$','n_0$'),1))
=> 'fun_app$c'('p$',X0) )
& 'fun_app$c'('p$','n_0$') )
<=> ! [X0: 'Nat$'] :
( ~ $less('fun_app$b'('of_nat$',X0),'fun_app$b'('of_nat$','n_0$'))
=> 'fun_app$c'('p$',X0) ) ),
inference(theory_normalization,[],[f3]) ).
tff(f1116,plain,
! [X0: $int] : ~ $less(X0,X0),
inference(true_and_false_elimination,[],[f294]) ).
tff(f1117,plain,
! [X0: $int] : ~ $less(X0,X0),
inference(flattening,[],[f1116]) ).
tff(f1216,plain,
~ ( ! [X1: 'Nat$'] :
( ~ $less('fun_app$b'('of_nat$',X1),'fun_app$b'('of_nat$','n_0$'))
=> 'fun_app$c'('p$',X1) )
<=> ( ! [X0: 'Nat$'] :
( ~ $less('fun_app$b'('of_nat$',X0),$sum('fun_app$b'('of_nat$','n_0$'),1))
=> 'fun_app$c'('p$',X0) )
& 'fun_app$c'('p$','n_0$') ) ),
inference(rectify,[],[f826]) ).
tff(f1423,plain,
( ! [X1: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X1),'fun_app$b'('of_nat$','n_0$'))
| 'fun_app$c'('p$',X1) )
<~> ( ! [X0: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X0),$sum('fun_app$b'('of_nat$','n_0$'),1))
| 'fun_app$c'('p$',X0) )
& 'fun_app$c'('p$','n_0$') ) ),
inference(ennf_transformation,[],[f1216]) ).
tff(f1900,plain,
( ( ? [X0: 'Nat$'] :
( ~ $less('fun_app$b'('of_nat$',X0),$sum('fun_app$b'('of_nat$','n_0$'),1))
& ~ 'fun_app$c'('p$',X0) )
| ~ 'fun_app$c'('p$','n_0$')
| ? [X1: 'Nat$'] :
( ~ $less('fun_app$b'('of_nat$',X1),'fun_app$b'('of_nat$','n_0$'))
& ~ 'fun_app$c'('p$',X1) ) )
& ( ( ! [X0: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X0),$sum('fun_app$b'('of_nat$','n_0$'),1))
| 'fun_app$c'('p$',X0) )
& 'fun_app$c'('p$','n_0$') )
| ! [X1: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X1),'fun_app$b'('of_nat$','n_0$'))
| 'fun_app$c'('p$',X1) ) ) ),
inference(nnf_transformation,[],[f1423]) ).
tff(f1901,plain,
( ( ? [X0: 'Nat$'] :
( ~ $less('fun_app$b'('of_nat$',X0),$sum('fun_app$b'('of_nat$','n_0$'),1))
& ~ 'fun_app$c'('p$',X0) )
| ~ 'fun_app$c'('p$','n_0$')
| ? [X1: 'Nat$'] :
( ~ $less('fun_app$b'('of_nat$',X1),'fun_app$b'('of_nat$','n_0$'))
& ~ 'fun_app$c'('p$',X1) ) )
& ( ( ! [X0: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X0),$sum('fun_app$b'('of_nat$','n_0$'),1))
| 'fun_app$c'('p$',X0) )
& 'fun_app$c'('p$','n_0$') )
| ! [X1: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X1),'fun_app$b'('of_nat$','n_0$'))
| 'fun_app$c'('p$',X1) ) ) ),
inference(flattening,[],[f1900]) ).
tff(f1902,plain,
( ( ? [X0: 'Nat$'] :
( ~ $less('fun_app$b'('of_nat$',X0),$sum('fun_app$b'('of_nat$','n_0$'),1))
& ~ 'fun_app$c'('p$',X0) )
| ~ 'fun_app$c'('p$','n_0$')
| ? [X1: 'Nat$'] :
( ~ $less('fun_app$b'('of_nat$',X1),'fun_app$b'('of_nat$','n_0$'))
& ~ 'fun_app$c'('p$',X1) ) )
& ( ( ! [X2: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X2),$sum('fun_app$b'('of_nat$','n_0$'),1))
| 'fun_app$c'('p$',X2) )
& 'fun_app$c'('p$','n_0$') )
| ! [X3: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X3),'fun_app$b'('of_nat$','n_0$'))
| 'fun_app$c'('p$',X3) ) ) ),
inference(rectify,[],[f1901]) ).
tff(f1903,plain,
( ( ( ~ $less('fun_app$b'('of_nat$',sK33),$sum('fun_app$b'('of_nat$','n_0$'),1))
& ~ 'fun_app$c'('p$',sK33) )
| ~ 'fun_app$c'('p$','n_0$')
| ( ~ $less('fun_app$b'('of_nat$',sK34),'fun_app$b'('of_nat$','n_0$'))
& ~ 'fun_app$c'('p$',sK34) ) )
& ( ( ! [X2: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X2),$sum('fun_app$b'('of_nat$','n_0$'),1))
| 'fun_app$c'('p$',X2) )
& 'fun_app$c'('p$','n_0$') )
| ! [X3: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X3),'fun_app$b'('of_nat$','n_0$'))
| 'fun_app$c'('p$',X3) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33,sK34]),skolemize(X0,sK33),skolemize(X1,sK34)],[f1902]) ).
tff(f2651,plain,
! [X0: $int] : ~ $less(X0,X0),
inference(cnf_transformation,[],[f1117]) ).
tff(f2654,plain,
! [X3: 'Nat$'] :
( 'fun_app$c'('p$','n_0$')
| $less('fun_app$b'('of_nat$',X3),'fun_app$b'('of_nat$','n_0$'))
| 'fun_app$c'('p$',X3) ),
inference(cnf_transformation,[],[f1903]) ).
tff(f2655,plain,
! [X2: 'Nat$',X3: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X2),$sum('fun_app$b'('of_nat$','n_0$'),1))
| 'fun_app$c'('p$',X2)
| $less('fun_app$b'('of_nat$',X3),'fun_app$b'('of_nat$','n_0$'))
| 'fun_app$c'('p$',X3) ),
inference(cnf_transformation,[],[f1903]) ).
tff(f2656,plain,
( ~ 'fun_app$c'('p$',sK34)
| ~ 'fun_app$c'('p$','n_0$')
| ~ 'fun_app$c'('p$',sK33) ),
inference(cnf_transformation,[],[f1903]) ).
tff(f2657,plain,
( ~ 'fun_app$c'('p$',sK33)
| ~ 'fun_app$c'('p$','n_0$')
| ~ $less('fun_app$b'('of_nat$',sK34),'fun_app$b'('of_nat$','n_0$')) ),
inference(cnf_transformation,[],[f1903]) ).
tff(f2658,plain,
( ~ $less('fun_app$b'('of_nat$',sK33),$sum('fun_app$b'('of_nat$','n_0$'),1))
| ~ 'fun_app$c'('p$','n_0$')
| ~ 'fun_app$c'('p$',sK34) ),
inference(cnf_transformation,[],[f1903]) ).
tff(f2659,plain,
( ~ $less('fun_app$b'('of_nat$',sK33),$sum('fun_app$b'('of_nat$','n_0$'),1))
| ~ 'fun_app$c'('p$','n_0$')
| ~ $less('fun_app$b'('of_nat$',sK34),'fun_app$b'('of_nat$','n_0$')) ),
inference(cnf_transformation,[],[f1903]) ).
tff(f3549,plain,
! [X0: 'Nat$'] : ( 'fun_app$f'('nat$','fun_app$b'('of_nat$',X0)) = X0 ),
inference(cnf_transformation,[],[f615]) ).
tff(f3813,definition,
sF215 = 'fun_app$b'('of_nat$',sK33),
introduced(definition,[new_symbols(definition,[sF215])],[function_definition]) ).
tff(f3814,plain,
'fun_app$b'('of_nat$',sK33) = sF215,
inference(reorient_equations,[],[f3813]) ).
tff(f3815,definition,
sF216 = 'fun_app$b'('of_nat$','n_0$'),
introduced(definition,[new_symbols(definition,[sF216])],[function_definition]) ).
tff(f3816,plain,
'fun_app$b'('of_nat$','n_0$') = sF216,
inference(reorient_equations,[],[f3815]) ).
tff(f3817,definition,
sF217 = $sum(sF216,1),
introduced(definition,[new_symbols(definition,[sF217])],[function_definition]) ).
tff(f3818,plain,
$sum(sF216,1) = sF217,
inference(reorient_equations,[],[f3817]) ).
tff(f3819,definition,
sF218 = 'fun_app$b'('of_nat$',sK34),
introduced(definition,[new_symbols(definition,[sF218])],[function_definition]) ).
tff(f3820,plain,
'fun_app$b'('of_nat$',sK34) = sF218,
inference(reorient_equations,[],[f3819]) ).
tff(f3821,plain,
( ~ 'fun_app$c'('p$','n_0$')
| ~ $less(sF215,sF217)
| ~ $less(sF218,sF216) ),
inference(definition_folding,[],[f2659,f3816,f3820,f3818,f3816,f3814]) ).
tff(f3822,plain,
( ~ 'fun_app$c'('p$','n_0$')
| ~ 'fun_app$c'('p$',sK34)
| ~ $less(sF215,sF217) ),
inference(definition_folding,[],[f2658,f3818,f3816,f3814]) ).
tff(f3823,plain,
( ~ 'fun_app$c'('p$',sK33)
| ~ $less(sF218,sF216)
| ~ 'fun_app$c'('p$','n_0$') ),
inference(definition_folding,[],[f2657,f3816,f3820]) ).
tff(f3824,plain,
! [X2: 'Nat$',X3: 'Nat$'] :
( 'fun_app$c'('p$',X3)
| $less('fun_app$b'('of_nat$',X3),sF216)
| $less('fun_app$b'('of_nat$',X2),sF217)
| 'fun_app$c'('p$',X2) ),
inference(definition_folding,[],[f2655,f3816,f3818,f3816]) ).
tff(f3825,plain,
! [X3: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X3),sF216)
| 'fun_app$c'('p$',X3)
| 'fun_app$c'('p$','n_0$') ),
inference(definition_folding,[],[f2654,f3816]) ).
tff(f3928,definition,
( spl219_7
<=> ( $sum(sF216,1) = sF217 ) ),
introduced(definition,[new_symbols(definition,[spl219_7])],[avatar_definition]) ).
tff(f3931,plain,
spl219_7,
inference(avatar_split_clause,[],[f3818,f3928]) ).
tff(f3933,definition,
( spl219_8
<=> 'fun_app$c'('p$','n_0$') ),
introduced(definition,[new_symbols(definition,[spl219_8])],[avatar_definition]) ).
tff(f3968,definition,
( spl219_15
<=> ( 'fun_app$b'('of_nat$',sK34) = sF218 ) ),
introduced(definition,[new_symbols(definition,[spl219_15])],[avatar_definition]) ).
tff(f3970,plain,
( ( 'fun_app$b'('of_nat$',sK34) = sF218 )
| ~ spl219_15 ),
inference(avatar_component_clause,[],[f3968]) ).
tff(f3971,plain,
spl219_15,
inference(avatar_split_clause,[],[f3820,f3968]) ).
tff(f3973,definition,
( spl219_16
<=> $less(sF215,sF217) ),
introduced(definition,[new_symbols(definition,[spl219_16])],[avatar_definition]) ).
tff(f3975,plain,
( ~ $less(sF215,sF217)
| spl219_16 ),
inference(avatar_component_clause,[],[f3973]) ).
tff(f3977,definition,
( spl219_17
<=> $less(sF218,sF216) ),
introduced(definition,[new_symbols(definition,[spl219_17])],[avatar_definition]) ).
tff(f3980,plain,
( ~ spl219_16
| ~ spl219_17
| ~ spl219_8 ),
inference(avatar_split_clause,[],[f3821,f3933,f3977,f3973]) ).
tff(f3982,definition,
( spl219_18
<=> 'fun_app$c'('p$',sK34) ),
introduced(definition,[new_symbols(definition,[spl219_18])],[avatar_definition]) ).
tff(f3984,plain,
( ~ 'fun_app$c'('p$',sK34)
| spl219_18 ),
inference(avatar_component_clause,[],[f3982]) ).
tff(f3986,definition,
( spl219_19
<=> 'fun_app$c'('p$',sK33) ),
introduced(definition,[new_symbols(definition,[spl219_19])],[avatar_definition]) ).
tff(f3988,plain,
( ~ 'fun_app$c'('p$',sK33)
| spl219_19 ),
inference(avatar_component_clause,[],[f3986]) ).
tff(f3989,plain,
( ~ spl219_18
| ~ spl219_19
| ~ spl219_8 ),
inference(avatar_split_clause,[],[f2656,f3933,f3986,f3982]) ).
tff(f3995,plain,
( ~ spl219_19
| ~ spl219_17
| ~ spl219_8 ),
inference(avatar_split_clause,[],[f3823,f3933,f3977,f3986]) ).
tff(f4012,definition,
( spl219_24
<=> ! [X2: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X2),sF217)
| 'fun_app$c'('p$',X2) ) ),
introduced(definition,[new_symbols(definition,[spl219_24])],[avatar_definition]) ).
tff(f4013,plain,
( ! [X2: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X2),sF217)
| 'fun_app$c'('p$',X2) )
| ~ spl219_24 ),
inference(avatar_component_clause,[],[f4012]) ).
tff(f4015,definition,
( spl219_25
<=> ! [X3: 'Nat$'] :
( 'fun_app$c'('p$',X3)
| $less('fun_app$b'('of_nat$',X3),sF216) ) ),
introduced(definition,[new_symbols(definition,[spl219_25])],[avatar_definition]) ).
tff(f4016,plain,
( ! [X3: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X3),sF216)
| 'fun_app$c'('p$',X3) )
| ~ spl219_25 ),
inference(avatar_component_clause,[],[f4015]) ).
tff(f4017,plain,
( spl219_24
| spl219_25 ),
inference(avatar_split_clause,[],[f3824,f4015,f4012]) ).
tff(f4022,plain,
( ~ spl219_16
| ~ spl219_8
| ~ spl219_18 ),
inference(avatar_split_clause,[],[f3822,f3982,f3933,f3973]) ).
tff(f4032,plain,
( spl219_8
| spl219_25 ),
inference(avatar_split_clause,[],[f3825,f4015,f3933]) ).
tff(f4035,definition,
( spl219_29
<=> ( 'fun_app$b'('of_nat$',sK33) = sF215 ) ),
introduced(definition,[new_symbols(definition,[spl219_29])],[avatar_definition]) ).
tff(f4037,plain,
( ( 'fun_app$b'('of_nat$',sK33) = sF215 )
| ~ spl219_29 ),
inference(avatar_component_clause,[],[f4035]) ).
tff(f4038,plain,
spl219_29,
inference(avatar_split_clause,[],[f3814,f4035]) ).
tff(f4043,definition,
( spl219_30
<=> ( 'fun_app$b'('of_nat$','n_0$') = sF216 ) ),
introduced(definition,[new_symbols(definition,[spl219_30])],[avatar_definition]) ).
tff(f4045,plain,
( ( 'fun_app$b'('of_nat$','n_0$') = sF216 )
| ~ spl219_30 ),
inference(avatar_component_clause,[],[f4043]) ).
tff(f4046,plain,
spl219_30,
inference(avatar_split_clause,[],[f3816,f4043]) ).
tff(f4053,plain,
( 'fun_app$c'('p$',sK34)
| $less(sF218,sF217)
| ~ spl219_15
| ~ spl219_24 ),
inference(superposition,[],[f4013,f3970]) ).
tff(f4060,definition,
( spl219_33
<=> $less(sF218,sF217) ),
introduced(definition,[new_symbols(definition,[spl219_33])],[avatar_definition]) ).
tff(f4065,plain,
( $less(sF215,sF217)
| 'fun_app$c'('p$',sK33)
| ~ spl219_24
| ~ spl219_29 ),
inference(superposition,[],[f4013,f4037]) ).
tff(f4071,plain,
( 'fun_app$c'('p$',sK33)
| spl219_16
| ~ spl219_24
| ~ spl219_29 ),
inference(forward_subsumption_resolution,[],[f4065,f3975]) ).
tff(f4074,plain,
( 'fun_app$c'('p$',sK34)
| $less(sF218,sF216)
| ~ spl219_15
| ~ spl219_25 ),
inference(superposition,[],[f4016,f3970]) ).
tff(f4075,plain,
( 'fun_app$c'('p$',sK33)
| $less(sF215,sF216)
| ~ spl219_25
| ~ spl219_29 ),
inference(superposition,[],[f4016,f4037]) ).
tff(f4076,plain,
( $less(sF215,sF216)
| spl219_19
| ~ spl219_25
| ~ spl219_29 ),
inference(forward_subsumption_resolution,[],[f4075,f3988]) ).
tff(f4079,definition,
( spl219_35
<=> $less(sF215,sF216) ),
introduced(definition,[new_symbols(definition,[spl219_35])],[avatar_definition]) ).
tff(f4082,plain,
( spl219_35
| spl219_19
| ~ spl219_25
| ~ spl219_29 ),
inference(avatar_split_clause,[],[f4076,f4035,f4015,f3986,f4079]) ).
tff(f4083,plain,
( spl219_33
| spl219_18
| ~ spl219_15
| ~ spl219_24 ),
inference(avatar_split_clause,[],[f4053,f4012,f3968,f3982,f4060]) ).
tff(f4085,plain,
( spl219_19
| spl219_16
| ~ spl219_24
| ~ spl219_29 ),
inference(avatar_split_clause,[],[f4071,f4035,f4012,f3973,f3986]) ).
tff(f4205,plain,
( ( sK34 = 'fun_app$f'('nat$',sF218) )
| ~ spl219_15 ),
inference(superposition,[],[f3549,f3970]) ).
tff(f4207,plain,
( ( 'n_0$' = 'fun_app$f'('nat$',sF216) )
| ~ spl219_30 ),
inference(superposition,[],[f3549,f4045]) ).
tff(f4209,definition,
( spl219_50
<=> ( 'n_0$' = 'fun_app$f'('nat$',sF216) ) ),
introduced(definition,[new_symbols(definition,[spl219_50])],[avatar_definition]) ).
tff(f4212,plain,
( spl219_50
| ~ spl219_30 ),
inference(avatar_split_clause,[],[f4207,f4043,f4209]) ).
tff(f4219,definition,
( spl219_52
<=> ( sK34 = 'fun_app$f'('nat$',sF218) ) ),
introduced(definition,[new_symbols(definition,[spl219_52])],[avatar_definition]) ).
tff(f4222,plain,
( spl219_52
| ~ spl219_15 ),
inference(avatar_split_clause,[],[f4205,f3968,f4219]) ).
tff(f4223,plain,
( $less(sF218,sF216)
| ~ spl219_15
| spl219_18
| ~ spl219_25 ),
inference(forward_subsumption_resolution,[],[f4074,f3984]) ).
tff(f4234,plain,
( spl219_17
| ~ spl219_15
| spl219_18
| ~ spl219_25 ),
inference(avatar_split_clause,[],[f4223,f4015,f3982,f3968,f3977]) ).
tff(f4246,plain,
( 'fun_app$c'('p$','n_0$')
| $less(sF216,sF216)
| ~ spl219_25
| ~ spl219_30 ),
inference(superposition,[],[f4016,f4045]) ).
tff(f4247,plain,
( 'fun_app$c'('p$','n_0$')
| ~ spl219_25
| ~ spl219_30 ),
inference(forward_subsumption_resolution,[],[f4246,f2651]) ).
tff(f4248,plain,
( spl219_8
| ~ spl219_25
| ~ spl219_30 ),
inference(avatar_split_clause,[],[f4247,f4043,f4015,f3933]) ).
tff(f4249,plain,
$false,
inference(avatar_smt_refutation,[],[f4248,f4234,f4222,f4212,f4085,f4083,f4082,f4046,f4038,f4032,f4022,f4017,f3995,f3989,f3980,f3971,f3931]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP409_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 % Computer : n008.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 12:58:24 UTC 2026
% 0.13/0.42 % CPUTime :
% 0.13/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.86/1.80 % (1201668)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.86/1.80 % (1201673)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3921182577:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.86/1.80 % (1201673)Instruction limit reached!
% 4.86/1.80 % (1201673)------------------------------
% 4.86/1.80 % (1201673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.80 % (1201673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.80 % (1201673)CaDiCaL version: 2.1.3
% 4.86/1.80 % (1201673)Termination reason: Instruction limit
% 4.86/1.80 % (1201673)Termination phase: Property scanning
% 4.86/1.80 % (1201673)Time elapsed: 0.006 s
% 4.86/1.80 % (1201673)Peak memory usage: 86 MB
% 4.86/1.80 % (1201673)Instructions burned: 14 (million)
% 4.86/1.80 % (1201675)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1635537343:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.86/1.80 % (1201679)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3768480348:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.86/1.80 % (1201674)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=852585916:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.86/1.80 % (1201678)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1250922315:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.86/1.80 % (1201677)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1658009553:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.86/1.80 % (1201676)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1704007016:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.86/1.80 % (1201677)Instruction limit reached!
% 4.86/1.80 % (1201677)------------------------------
% 4.86/1.80 % (1201677)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.80 % (1201677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.80 % (1201677)CaDiCaL version: 2.1.3
% 4.86/1.80 % (1201677)Termination reason: Instruction limit
% 4.86/1.80 % (1201677)Termination phase: Property scanning
% 4.86/1.80 % (1201677)Time elapsed: 0.005 s
% 4.86/1.80 % (1201677)Peak memory usage: 86 MB
% 4.86/1.80 % (1201677)Instructions burned: 5 (million)
% 4.86/1.80 % (1201676)Instruction limit reached!
% 4.86/1.80 % (1201676)------------------------------
% 4.86/1.80 % (1201676)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.80 % (1201676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.80 % (1201676)CaDiCaL version: 2.1.3
% 4.86/1.80 % (1201676)Termination reason: Instruction limit
% 4.86/1.80 % (1201676)Termination phase: Property scanning
% 4.86/1.80 % (1201676)Time elapsed: 0.007 s
% 4.86/1.80 % (1201676)Peak memory usage: 86 MB
% 4.86/1.80 % (1201676)Instructions burned: 7 (million)
% 4.86/1.80 % (1201679)Instruction limit reached!
% 4.86/1.80 % (1201679)------------------------------
% 4.86/1.80 % (1201679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.80 % (1201679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.80 % (1201679)CaDiCaL version: 2.1.3
% 4.86/1.80 % (1201679)Termination reason: Instruction limit
% 4.86/1.80 % (1201679)Termination phase: Preprocessing 3
% 4.86/1.80 % (1201679)Time elapsed: 0.030 s
% 4.86/1.80 % (1201679)Peak memory usage: 88 MB
% 4.86/1.80 % (1201679)Instructions burned: 33 (million)
% 4.86/1.80 % (1201678)Instruction limit reached!
% 4.86/1.80 % (1201678)------------------------------
% 4.86/1.80 % (1201678)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.80 % (1201678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.80 % (1201678)CaDiCaL version: 2.1.3
% 4.86/1.80 % (1201678)Termination reason: Instruction limit
% 4.86/1.80 % (1201678)Termination phase: Property scanning
% 4.86/1.80 % (1201678)Time elapsed: 0.043 s
% 4.86/1.80 % (1201678)Peak memory usage: 88 MB
% 4.86/1.80 % (1201678)Instructions burned: 46 (million)
% 4.86/1.80 % (1201674)First to succeed.
% 4.86/1.80 % (1201674)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1201668"
% 4.86/1.80 % (1201681)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1564171109:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 4.86/1.80 % (1201689)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=3205762622:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/16Mi)
% 4.86/1.80 % (1201681)Instruction limit reached!
% 4.86/1.80 % (1201681)------------------------------
% 4.86/1.80 % (1201681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.80 % (1201681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.80 % (1201681)CaDiCaL version: 2.1.3
% 4.86/1.80 % (1201681)Termination reason: Instruction limit
% 4.86/1.80 % (1201681)Termination phase: SInE selection
% 4.86/1.80 % (1201681)Time elapsed: 0.014 s
% 4.86/1.80 % (1201681)Peak memory usage: 85 MB
% 4.86/1.80 % (1201681)Instructions burned: 14 (million)
% 4.86/1.80 % (1201689)Instruction limit reached!
% 4.86/1.80 % (1201689)------------------------------
% 4.86/1.80 % (1201689)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.80 % (1201689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.80 % (1201689)CaDiCaL version: 2.1.3
% 4.86/1.80 % (1201689)Termination reason: Instruction limit
% 4.86/1.80 % (1201689)Termination phase: Preprocessing 3
% 4.86/1.80 % (1201689)Time elapsed: 0.010 s
% 4.86/1.80 % (1201689)Peak memory usage: 87 MB
% 4.86/1.80 % (1201689)Instructions burned: 19 (million)
% 4.86/1.80 % (1201675)Instruction limit reached!
% 4.86/1.80 % (1201675)------------------------------
% 4.86/1.80 % (1201675)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.80 % (1201675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.80 % (1201675)CaDiCaL version: 2.1.3
% 4.86/1.80 % (1201675)Termination reason: Instruction limit
% 4.86/1.80 % (1201675)Termination phase: Saturation
% 4.86/1.80 % (1201675)Time elapsed: 0.236 s
% 4.86/1.80 % (1201675)Peak memory usage: 118 MB
% 4.86/1.80 % (1201675)Instructions burned: 203 (million)
% 4.86/1.80 % (1201690)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=775597173:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 4.86/1.80 % (1201690)Instruction limit reached!
% 4.86/1.80 % (1201690)------------------------------
% 4.86/1.80 % (1201690)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.80 % (1201690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.80 % (1201690)CaDiCaL version: 2.1.3
% 4.86/1.80 % (1201690)Termination reason: Instruction limit
% 4.86/1.80 % (1201690)Termination phase: shuffling
% 4.86/1.80 % (1201690)Time elapsed: 0.015 s
% 4.86/1.80 % (1201690)Peak memory usage: 86 MB
% 4.86/1.80 % (1201690)Instructions burned: 25 (million)
% 4.86/1.80 % (1201688)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=3402049837:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2996 on theBenchmark for (2996ds/29Mi)
% 4.86/1.80 % (1201688)Instruction limit reached!
% 4.86/1.80 % (1201688)------------------------------
% 4.86/1.80 % (1201688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.80 % (1201688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.80 % (1201688)CaDiCaL version: 2.1.3
% 4.86/1.80 % (1201688)Termination reason: Instruction limit
% 4.86/1.80 % (1201688)Termination phase: Preprocessing 3
% 4.86/1.80 % (1201688)Time elapsed: 0.029 s
% 4.86/1.80 % (1201688)Peak memory usage: 87 MB
% 4.86/1.80 % (1201688)Instructions burned: 29 (million)
% 4.86/1.80 % (1201691)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=2266945785:i=27:canc=cautious:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/27Mi)
% 4.86/1.80 % (1201691)Instruction limit reached!
% 4.86/1.80 % (1201691)------------------------------
% 4.86/1.80 % (1201691)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.80 % (1201691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.80 % (1201691)CaDiCaL version: 2.1.3
% 4.86/1.80 % (1201691)Termination reason: Instruction limit
% 4.86/1.80 % (1201691)Termination phase: Preprocessing 3
% 4.86/1.80 % (1201691)Time elapsed: 0.025 s
% 4.86/1.80 % (1201691)Peak memory usage: 87 MB
% 4.86/1.80 % (1201691)Instructions burned: 27 (million)
% 4.86/1.80 % (1201695)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=1054183103:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2994 on theBenchmark for (2994ds/2Mi)
% 4.86/1.80 % (1201695)Instruction limit reached!
% 4.86/1.80 % (1201695)------------------------------
% 4.86/1.80 % (1201695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.80 % (1201695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.80 % (1201695)CaDiCaL version: 2.1.3
% 4.86/1.80 % (1201695)Termination reason: Instruction limit
% 4.86/1.80 % (1201695)Termination phase: shuffling
% 4.86/1.80 % (1201695)Time elapsed: 0.003 s
% 4.86/1.80 % (1201695)Peak memory usage: 85 MB
% 4.86/1.80 % (1201695)Instructions burned: 2 (million)
% 4.86/1.80 % (1201694)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=2592022485:i=85:gtgl=4:rtra=on:gtg=exists_sym_2994 on theBenchmark for (2994ds/85Mi)
% 4.86/1.80 % (1201697)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=1496579909:i=181:rtra=on:ss=axioms:ev=cautious_2994 on theBenchmark for (2994ds/181Mi)
% 4.86/1.80 % (1201700)dis+1010_128_isp=bottom:to=lpo:thi=overlap:prc=on:sas=z3:si=on:fd=preordered:random_seed=2920036475:i=66:thsqd=64:thsqc=16:rtra=on:thsq=on:ev=force_2994 on theBenchmark for (2994ds/66Mi)
% 4.86/1.80 % (1201698)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=2226951275:i=4:ep=RST:ins=2:rtra=on_2994 on theBenchmark for (2994ds/4Mi)
% 4.86/1.80 % (1201698)Instruction limit reached!
% 4.86/1.80 % (1201698)------------------------------
% 4.86/1.80 % (1201698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.80 % (1201698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.80 % (1201698)CaDiCaL version: 2.1.3
% 4.86/1.80 % (1201698)Termination reason: Instruction limit
% 4.86/1.80 % (1201698)Termination phase: Property scanning
% 4.86/1.80 % (1201698)Time elapsed: 0.005 s
% 4.86/1.80 % (1201698)Peak memory usage: 85 MB
% 4.86/1.80 % (1201698)Instructions burned: 4 (million)
% 4.86/1.80 % (1201700)Instruction limit reached!
% 4.86/1.80 % (1201700)------------------------------
% 4.86/1.80 % (1201700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.80 % (1201700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.80 % (1201700)CaDiCaL version: 2.1.3
% 4.86/1.80 % (1201700)Termination reason: Instruction limit
% 4.86/1.80 % (1201700)Termination phase: Saturation
% 4.86/1.80 % (1201700)Time elapsed: 0.030 s
% 4.86/1.80 % (1201700)Peak memory usage: 88 MB
% 4.86/1.80 % (1201700)Instructions burned: 68 (million)
% 4.86/1.80 % (1201694)Instruction limit reached!
% 4.86/1.80 % (1201694)------------------------------
% 4.86/1.80 % (1201694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.80 % (1201694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.80 % (1201694)CaDiCaL version: 2.1.3
% 4.86/1.80 % (1201694)Termination reason: Instruction limit
% 4.86/1.80 % (1201694)Termination phase: Property scanning
% 4.86/1.80 % (1201694)Time elapsed: 0.076 s
% 4.86/1.80 % (1201694)Peak memory usage: 88 MB
% 4.86/1.80 % (1201694)Instructions burned: 85 (million)
% 4.86/1.80 % (1201702)lrs+10_1_thi=all:si=on:fd=off:random_seed=430909992:i=53:rtra=on:gtg=all_2993 on theBenchmark for (2993ds/53Mi)
% 4.86/1.80 % (1201674)Refutation found. Thanks to Tanya!
% 4.86/1.80 % SZS status Theorem for theBenchmark
% 4.86/1.80 % SZS output start Proof for theBenchmark
% See solution above
% 6.63/2.03 % (1201674)------------------------------
% 6.63/2.03 % (1201674)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/2.03 % (1201674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/2.03 % (1201674)CaDiCaL version: 2.1.3
% 6.63/2.03 % (1201674)Termination reason: Refutation
% 6.63/2.03 % (1201674)Time elapsed: 0.172 s
% 6.63/2.03 % (1201674)Peak memory usage: 119 MB
% 6.63/2.03 % (1201674)Instructions burned: 137 (million)
% 6.63/2.03 % (1201674)------------------------------
% 6.63/2.03 % (1201674)------------------------------
% 6.63/2.03 % (1201668)Success in time 0.884 s
% 6.63/2.03 % Vampire exiting
%------------------------------------------------------------------------------