%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP195^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:11:04 AM UTC 2026
% Result : Theorem 0.20s 0.36s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 65 ( 16 unt; 0 typ; 5 def)
% Number of atoms : 277 ( 89 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 451 ( 61 ~; 53 |; 10 &; 292 @)
% ( 5 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 12 ( 11 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 275 ( 272 usr; 20 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
poly_poly_poly_real: $tType ).
thf(type_def_6,type,
poly_poly_real: $tType ).
thf(type_def_7,type,
poly_poly_nat: $tType ).
thf(type_def_8,type,
poly_poly_int: $tType ).
thf(type_def_9,type,
poly_real: $tType ).
thf(type_def_10,type,
poly_nat: $tType ).
thf(type_def_11,type,
poly_int: $tType ).
thf(type_def_12,type,
set_real: $tType ).
thf(type_def_13,type,
real: $tType ).
thf(type_def_14,type,
nat: $tType ).
thf(type_def_15,type,
int: $tType ).
thf(type_def_16,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
one_one_nat: nat ).
thf(func_def_1,type,
zero_zero_int: int ).
thf(func_def_2,type,
zero_zero_nat: nat ).
thf(func_def_3,type,
zero_zero_poly_int: poly_int ).
thf(func_def_4,type,
zero_zero_poly_nat: poly_nat ).
thf(func_def_5,type,
zero_z1549157189ly_int: poly_poly_int ).
thf(func_def_6,type,
zero_z1059985641ly_nat: poly_poly_nat ).
thf(func_def_7,type,
zero_z935034829y_real: poly_poly_poly_real ).
thf(func_def_8,type,
zero_z1423781445y_real: poly_poly_real ).
thf(func_def_9,type,
zero_zero_poly_real: poly_real ).
thf(func_def_10,type,
zero_zero_real: real ).
thf(func_def_11,type,
suc: nat > nat ).
thf(func_def_12,type,
ord_less_int: int > int > $o ).
thf(func_def_13,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_14,type,
ord_less_poly_int: poly_int > poly_int > $o ).
thf(func_def_15,type,
ord_le38482960y_real: poly_poly_real > poly_poly_real > $o ).
thf(func_def_16,type,
ord_less_poly_real: poly_real > poly_real > $o ).
thf(func_def_17,type,
ord_less_real: real > real > $o ).
thf(func_def_18,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_19,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_20,type,
ord_less_eq_poly_int: poly_int > poly_int > $o ).
thf(func_def_21,type,
ord_le893774876y_real: poly_poly_real > poly_poly_real > $o ).
thf(func_def_22,type,
ord_le1180086932y_real: poly_real > poly_real > $o ).
thf(func_def_23,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_24,type,
is_zero_int: poly_int > $o ).
thf(func_def_25,type,
is_zero_nat: poly_nat > $o ).
thf(func_def_26,type,
is_zero_poly_real: poly_poly_real > $o ).
thf(func_def_27,type,
is_zero_real: poly_real > $o ).
thf(func_def_28,type,
order_int: int > poly_int > nat ).
thf(func_def_29,type,
order_poly_int: poly_int > poly_poly_int > nat ).
thf(func_def_30,type,
order_poly_poly_real: poly_poly_real > poly_poly_poly_real > nat ).
thf(func_def_31,type,
order_poly_real: poly_real > poly_poly_real > nat ).
thf(func_def_32,type,
order_real: real > poly_real > nat ).
thf(func_def_33,type,
pderiv_int: poly_int > poly_int ).
thf(func_def_34,type,
pderiv_nat: poly_nat > poly_nat ).
thf(func_def_35,type,
pderiv_poly_real: poly_poly_real > poly_poly_real ).
thf(func_def_36,type,
pderiv_real: poly_real > poly_real ).
thf(func_def_37,type,
poly_int2: poly_int > int > int ).
thf(func_def_38,type,
poly_nat2: poly_nat > nat > nat ).
thf(func_def_39,type,
poly_poly_int2: poly_poly_int > poly_int > poly_int ).
thf(func_def_40,type,
poly_poly_nat2: poly_poly_nat > poly_nat > poly_nat ).
thf(func_def_41,type,
poly_poly_poly_real2: poly_poly_poly_real > poly_poly_real > poly_poly_real ).
thf(func_def_42,type,
poly_poly_real2: poly_poly_real > poly_real > poly_real ).
thf(func_def_43,type,
poly_real2: poly_real > real > real ).
thf(func_def_44,type,
poly_cutoff_int: nat > poly_int > poly_int ).
thf(func_def_45,type,
poly_cutoff_nat: nat > poly_nat > poly_nat ).
thf(func_def_46,type,
poly_c1404107022y_real: nat > poly_poly_real > poly_poly_real ).
thf(func_def_47,type,
poly_cutoff_real: nat > poly_real > poly_real ).
thf(func_def_48,type,
poly_shift_int: nat > poly_int > poly_int ).
thf(func_def_49,type,
poly_shift_nat: nat > poly_nat > poly_nat ).
thf(func_def_50,type,
poly_shift_poly_real: nat > poly_poly_real > poly_poly_real ).
thf(func_def_51,type,
poly_shift_real: nat > poly_real > poly_real ).
thf(func_def_52,type,
reflect_poly_int: poly_int > poly_int ).
thf(func_def_53,type,
reflect_poly_nat: poly_nat > poly_nat ).
thf(func_def_54,type,
reflec943087998ly_int: poly_poly_int > poly_poly_int ).
thf(func_def_55,type,
reflec781175074ly_nat: poly_poly_nat > poly_poly_nat ).
thf(func_def_56,type,
reflec144234502y_real: poly_poly_poly_real > poly_poly_poly_real ).
thf(func_def_57,type,
reflec1522834046y_real: poly_poly_real > poly_poly_real ).
thf(func_def_58,type,
reflect_poly_real: poly_real > poly_real ).
thf(func_def_59,type,
rsquarefree_real: poly_real > $o ).
thf(func_def_60,type,
collect_real: ( real > $o ) > set_real ).
thf(func_def_61,type,
sturm_1953858694_cross: poly_real > real > real > int ).
thf(func_def_62,type,
sturm_469514713_r_pos: poly_real > real > $o ).
thf(func_def_63,type,
sturm_1279781401iation: real > real > int ).
thf(func_def_64,type,
member_real: real > set_real > $o ).
thf(func_def_65,type,
p: poly_real ).
thf(func_def_66,type,
x: real ).
thf(func_def_70,type,
vNOT: $o > $o ).
thf(func_def_71,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_72,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_73,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_74,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_75,type,
vAND: $o > $o > $o ).
thf(func_def_76,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_77,type,
vOR: $o > $o > $o ).
thf(func_def_78,type,
vIMP: $o > $o > $o ).
thf(func_def_79,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_80,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_81,type,
sP0: real > real > real > $o ).
thf(func_def_82,type,
sP1: real > real > real > $o ).
thf(func_def_83,type,
sP2: real > real > real > $o ).
thf(func_def_84,type,
sP3: nat > nat > nat > $o ).
thf(func_def_85,type,
sP4: nat > nat > nat > $o ).
thf(func_def_86,type,
sP5: nat > nat > nat > $o ).
thf(func_def_87,type,
sP6: int > int > int > $o ).
thf(func_def_88,type,
sP7: int > int > int > $o ).
thf(func_def_89,type,
sP8: int > int > int > $o ).
thf(func_def_90,type,
sK9: poly_real > real > real > real ).
thf(func_def_91,type,
sK10: poly_real > real > real > real ).
thf(func_def_92,type,
sK11: real > real > real ).
thf(func_def_93,type,
sK12: poly_real > real > real > real ).
thf(func_def_94,type,
sK13: real > poly_real > real ).
thf(func_def_95,type,
sK14: real > poly_real > real ).
thf(func_def_96,type,
sK15: set_real > real ).
thf(func_def_97,type,
sK16: real > set_real > real ).
thf(func_def_98,type,
sK17: real > set_real > real ).
thf(func_def_99,type,
sK18: real > real ).
thf(func_def_100,type,
sK19: nat > nat ).
thf(func_def_101,type,
sK20: int > int ).
thf(func_def_102,type,
sK21: real > real ).
thf(func_def_103,type,
sK22: nat > nat ).
thf(func_def_104,type,
sK23: int > int ).
thf(func_def_105,type,
sK24: real > real ).
thf(func_def_106,type,
sK25: nat > nat ).
thf(func_def_107,type,
sK26: int > int ).
thf(func_def_108,type,
sK27: real > real ).
thf(func_def_109,type,
sK28: nat > nat ).
thf(func_def_110,type,
sK29: int > int ).
thf(func_def_111,type,
sK30: ( nat > nat ) > nat ).
thf(func_def_112,type,
sK31: ( nat > nat ) > nat ).
thf(func_def_113,type,
sK32: ( nat > $o ) > nat ).
thf(func_def_114,type,
sK33: ( nat > $o ) > nat ).
thf(func_def_115,type,
sK34: nat > ( nat > $o ) > nat ).
thf(func_def_116,type,
sK35: ( real > real ) > real ).
thf(func_def_117,type,
sK36: ( real > real ) > real ).
thf(func_def_118,type,
sK37: ( nat > real ) > nat ).
thf(func_def_119,type,
sK38: ( nat > real ) > nat ).
thf(func_def_120,type,
sK39: ( int > real ) > int ).
thf(func_def_121,type,
sK40: ( int > real ) > int ).
thf(func_def_122,type,
sK41: ( real > nat ) > real ).
thf(func_def_123,type,
sK42: ( real > nat ) > real ).
thf(func_def_124,type,
sK43: ( nat > nat ) > nat ).
thf(func_def_125,type,
sK44: ( nat > nat ) > nat ).
thf(func_def_126,type,
sK45: ( int > nat ) > int ).
thf(func_def_127,type,
sK46: ( int > nat ) > int ).
thf(func_def_128,type,
sK47: ( real > int ) > real ).
thf(func_def_129,type,
sK48: ( real > int ) > real ).
thf(func_def_130,type,
sK49: ( nat > int ) > nat ).
thf(func_def_131,type,
sK50: ( nat > int ) > nat ).
thf(func_def_132,type,
sK51: ( int > int ) > int ).
thf(func_def_133,type,
sK52: ( int > int ) > int ).
thf(func_def_134,type,
sK53: ( real > real ) > real ).
thf(func_def_135,type,
sK54: ( real > real ) > real ).
thf(func_def_136,type,
sK55: ( real > nat ) > real ).
thf(func_def_137,type,
sK56: ( real > nat ) > real ).
thf(func_def_138,type,
sK57: ( real > int ) > real ).
thf(func_def_139,type,
sK58: ( real > int ) > real ).
thf(func_def_140,type,
sK59: ( nat > real ) > nat ).
thf(func_def_141,type,
sK60: ( nat > real ) > nat ).
thf(func_def_142,type,
sK61: ( nat > nat ) > nat ).
thf(func_def_143,type,
sK62: ( nat > nat ) > nat ).
thf(func_def_144,type,
sK63: ( nat > int ) > nat ).
thf(func_def_145,type,
sK64: ( nat > int ) > nat ).
thf(func_def_146,type,
sK65: ( int > real ) > int ).
thf(func_def_147,type,
sK66: ( int > real ) > int ).
thf(func_def_148,type,
sK67: ( int > nat ) > int ).
thf(func_def_149,type,
sK68: ( int > nat ) > int ).
thf(func_def_150,type,
sK69: ( int > int ) > int ).
thf(func_def_151,type,
sK70: ( int > int ) > int ).
thf(func_def_152,type,
sK71: ( real > real ) > real ).
thf(func_def_153,type,
sK72: ( real > real ) > real ).
thf(func_def_154,type,
sK73: ( real > nat ) > real ).
thf(func_def_155,type,
sK74: ( real > nat ) > real ).
thf(func_def_156,type,
sK75: ( real > int ) > real ).
thf(func_def_157,type,
sK76: ( real > int ) > real ).
thf(func_def_158,type,
sK77: ( nat > real ) > nat ).
thf(func_def_159,type,
sK78: ( nat > real ) > nat ).
thf(func_def_160,type,
sK79: ( nat > nat ) > nat ).
thf(func_def_161,type,
sK80: ( nat > nat ) > nat ).
thf(func_def_162,type,
sK81: ( nat > int ) > nat ).
thf(func_def_163,type,
sK82: ( nat > int ) > nat ).
thf(func_def_164,type,
sK83: ( int > real ) > int ).
thf(func_def_165,type,
sK84: ( int > real ) > int ).
thf(func_def_166,type,
sK85: ( int > nat ) > int ).
thf(func_def_167,type,
sK86: ( int > nat ) > int ).
thf(func_def_168,type,
sK87: ( int > int ) > int ).
thf(func_def_169,type,
sK88: ( int > int ) > int ).
thf(func_def_170,type,
sK89: ( real > real ) > real ).
thf(func_def_171,type,
sK90: ( real > real ) > real ).
thf(func_def_172,type,
sK91: ( real > nat ) > real ).
thf(func_def_173,type,
sK92: ( real > nat ) > real ).
thf(func_def_174,type,
sK93: ( real > int ) > real ).
thf(func_def_175,type,
sK94: ( real > int ) > real ).
thf(func_def_176,type,
sK95: ( nat > real ) > nat ).
thf(func_def_177,type,
sK96: ( nat > real ) > nat ).
thf(func_def_178,type,
sK97: ( nat > nat ) > nat ).
thf(func_def_179,type,
sK98: ( nat > nat ) > nat ).
thf(func_def_180,type,
sK99: ( nat > int ) > nat ).
thf(func_def_181,type,
sK100: ( nat > int ) > nat ).
thf(func_def_182,type,
sK101: ( int > real ) > int ).
thf(func_def_183,type,
sK102: ( int > real ) > int ).
thf(func_def_184,type,
sK103: ( int > nat ) > int ).
thf(func_def_185,type,
sK104: ( int > nat ) > int ).
thf(func_def_186,type,
sK105: ( int > int ) > int ).
thf(func_def_187,type,
sK106: ( int > int ) > int ).
thf(func_def_188,type,
sK107: ( real > real > $o ) > real ).
thf(func_def_189,type,
sK108: ( real > real > $o ) > real ).
thf(func_def_190,type,
sK109: ( real > real > $o ) > real ).
thf(func_def_191,type,
sK110: ( real > real > $o ) > real ).
thf(func_def_192,type,
sK111: ( nat > nat > $o ) > nat ).
thf(func_def_193,type,
sK112: ( nat > nat > $o ) > nat ).
thf(func_def_194,type,
sK113: ( nat > nat > $o ) > nat ).
thf(func_def_195,type,
sK114: ( nat > nat > $o ) > nat ).
thf(func_def_196,type,
sK115: ( int > int > $o ) > int ).
thf(func_def_197,type,
sK116: ( int > int > $o ) > int ).
thf(func_def_198,type,
sK117: ( int > int > $o ) > int ).
thf(func_def_199,type,
sK118: ( int > int > $o ) > int ).
thf(func_def_200,type,
sK119: ( real > real > $o ) > real ).
thf(func_def_201,type,
sK120: ( real > real > $o ) > real ).
thf(func_def_202,type,
sK121: ( real > real > $o ) > real ).
thf(func_def_203,type,
sK122: ( real > real > $o ) > real ).
thf(func_def_204,type,
sK123: ( real > real > $o ) > real ).
thf(func_def_205,type,
sK124: ( nat > nat > $o ) > nat ).
thf(func_def_206,type,
sK125: ( nat > nat > $o ) > nat ).
thf(func_def_207,type,
sK126: ( nat > nat > $o ) > nat ).
thf(func_def_208,type,
sK127: ( nat > nat > $o ) > nat ).
thf(func_def_209,type,
sK128: ( nat > nat > $o ) > nat ).
thf(func_def_210,type,
sK129: ( nat > $o ) > nat ).
thf(func_def_211,type,
sK130: real > real > real ).
thf(func_def_212,type,
sK131: real > real ).
thf(func_def_213,type,
sK132: nat > nat ).
thf(func_def_214,type,
sK133: real > real ).
thf(func_def_215,type,
sK134: ( real > real ) > real ).
thf(func_def_216,type,
sK135: ( real > real ) > real ).
thf(func_def_217,type,
sK136: ( real > nat ) > real ).
thf(func_def_218,type,
sK137: ( real > nat ) > real ).
thf(func_def_219,type,
sK138: ( nat > real ) > nat ).
thf(func_def_220,type,
sK139: ( nat > real ) > nat ).
thf(func_def_221,type,
sK140: ( nat > nat ) > nat ).
thf(func_def_222,type,
sK141: ( nat > nat ) > nat ).
thf(func_def_223,type,
sK142: ( real > real ) > real ).
thf(func_def_224,type,
sK143: ( real > real ) > real ).
thf(func_def_225,type,
sK144: ( nat > real ) > nat ).
thf(func_def_226,type,
sK145: ( nat > real ) > nat ).
thf(func_def_227,type,
sK146: ( real > nat ) > real ).
thf(func_def_228,type,
sK147: ( real > nat ) > real ).
thf(func_def_229,type,
sK148: ( nat > nat ) > nat ).
thf(func_def_230,type,
sK149: ( nat > nat ) > nat ).
thf(func_def_231,type,
sK150: ( real > real ) > real ).
thf(func_def_232,type,
sK151: ( real > real ) > real ).
thf(func_def_233,type,
sK152: ( real > nat ) > real ).
thf(func_def_234,type,
sK153: ( real > nat ) > real ).
thf(func_def_235,type,
sK154: ( nat > real ) > nat ).
thf(func_def_236,type,
sK155: ( nat > real ) > nat ).
thf(func_def_237,type,
sK156: ( nat > nat ) > nat ).
thf(func_def_238,type,
sK157: ( nat > nat ) > nat ).
thf(func_def_239,type,
sK158: ( real > real ) > real ).
thf(func_def_240,type,
sK159: ( real > real ) > real ).
thf(func_def_241,type,
sK160: ( real > nat ) > real ).
thf(func_def_242,type,
sK161: ( real > nat ) > real ).
thf(func_def_243,type,
sK162: ( nat > real ) > nat ).
thf(func_def_244,type,
sK163: ( nat > real ) > nat ).
thf(func_def_245,type,
sK164: ( nat > nat ) > nat ).
thf(func_def_246,type,
sK165: ( nat > nat ) > nat ).
thf(func_def_247,type,
sK166: ( nat > $o ) > nat ).
thf(func_def_248,type,
sK167: ( nat > nat > $o ) > nat ).
thf(func_def_249,type,
sK168: ( nat > nat > $o ) > nat ).
thf(func_def_250,type,
sK169: ( nat > nat > $o ) > nat ).
thf(func_def_251,type,
sK170: ( nat > nat > $o ) > nat ).
thf(func_def_252,type,
sK171: ( nat > nat > $o ) > nat ).
thf(func_def_253,type,
sK172: ( nat > $o ) > nat > nat ).
thf(func_def_254,type,
sK173: ( nat > $o ) > nat ).
thf(func_def_255,type,
sK174: nat > ( nat > $o ) > nat ).
thf(func_def_256,type,
sK175: ( nat > $o ) > nat ).
thf(func_def_257,type,
sK176: nat > nat ).
thf(func_def_258,type,
sK177: real > real > poly_real > real ).
thf(func_def_259,type,
sK178: real > real > poly_real > real ).
thf(func_def_260,type,
sK179: real > real > poly_real > real ).
thf(func_def_261,type,
sK180: real > real > poly_real > real ).
thf(func_def_262,type,
sK181: real > real > poly_real > real ).
thf(func_def_263,type,
sK182: real > real > poly_real > real ).
thf(func_def_264,type,
sK183: poly_int > int ).
thf(func_def_265,type,
sK184: poly_poly_real > poly_real ).
thf(func_def_266,type,
sK185: poly_real > real ).
thf(func_def_267,type,
sK186: poly_poly_poly_real > poly_poly_real ).
thf(func_def_268,type,
sK187: poly_poly_int > poly_int ).
thf(f1,axiom,
( ( poly_real2 @ p @ x )
!= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_False) ).
thf(f2,axiom,
( ( sturm_469514713_r_pos @ p @ x )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062) ).
thf(f3,axiom,
( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
=> ( sturm_469514713_r_pos @ p @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062) ).
thf(f346,conjecture,
( ( sturm_469514713_r_pos @ p @ x )
!= ( ~ ( ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) )
& ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f347,negated_conjecture,
~ ( ( ( sturm_469514713_r_pos @ p @ x )
!= ( ~ ( ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) )
& ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f346]) ).
thf(f348,plain,
( ( sturm_469514713_r_pos @ p @ x )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ),
inference(rectify,[],[f2]) ).
thf(f349,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $true )
=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
= $true ) ),
inference(fool_elimination,[],[f348]) ).
thf(f350,plain,
( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
=> ( sturm_469514713_r_pos @ p @ x ) ),
inference(rectify,[],[f3]) ).
thf(f351,plain,
( ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
= $true )
=> ( ( sturm_469514713_r_pos @ p @ x )
= $true ) ),
inference(fool_elimination,[],[f350]) ).
thf(f921,plain,
~ ( ( ( sturm_469514713_r_pos @ p @ x )
!= ( ~ ( ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) )
& ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) ) ) ) ) ),
inference(rectify,[],[f347]) ).
thf(f922,plain,
~ ( ( ( sturm_469514713_r_pos @ p @ x )
!= ( ~ ( ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
& ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ) ) ) ) ),
inference(fool_elimination,[],[f921]) ).
thf(f981,plain,
( ( sturm_469514713_r_pos @ p @ x )
= ( ~ ( ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
& ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ) ) ) ),
inference(flattening,[],[f922]) ).
thf(f982,plain,
( ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
= $true )
| ( ( sturm_469514713_r_pos @ p @ x )
!= $true ) ),
inference(ennf_transformation,[],[f349]) ).
thf(f983,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
!= $true ) ),
inference(ennf_transformation,[],[f351]) ).
thf(f1421,plain,
( ( poly_real2 @ p @ x )
!= zero_zero_real ),
inference(cnf_transformation,[],[f1]) ).
thf(f1422,plain,
( ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
= $true )
| ( ( sturm_469514713_r_pos @ p @ x )
!= $true ) ),
inference(cnf_transformation,[],[f982]) ).
thf(f1423,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
!= $true ) ),
inference(cnf_transformation,[],[f983]) ).
thf(f1907,plain,
( ( sturm_469514713_r_pos @ p @ x )
= ( ~ ( ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
& ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ) ) ) ),
inference(cnf_transformation,[],[f981]) ).
thf(f2189,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $true )
| ( ( ~ ( ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
& ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f1907]) ).
thf(f2190,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $false )
| ( $true
= ( ~ ( ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
& ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f1907]) ).
thf(f2191,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $false )
| ( ( ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
& ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f2190]) ).
thf(f2192,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $false )
| ( ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) )
= $false )
| ( ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
= $false ) ),
inference(and_proxy_clausification,[],[f2191]) ).
thf(f2193,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
= $false )
| ( ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f2192]) ).
thf(f2201,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
= $false )
| ( $true
= ( ( poly_real2 @ p @ x )
= zero_zero_real ) ) ),
inference(imp_proxy_clausification,[],[f2193]) ).
thf(f2202,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
= $false )
| ( ( poly_real2 @ p @ x )
= zero_zero_real ) ),
inference(equality_proxy_clausification,[],[f2201]) ).
thf(f2203,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $true )
| ( $true
= ( ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
& ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f2189]) ).
thf(f2204,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $true )
| ( $true
= ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ) ) ),
inference(and_proxy_clausification,[],[f2203]) ).
thf(f2208,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $true )
| ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2204]) ).
thf(f2209,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $true )
| ( $true
= ( ( poly_real2 @ p @ x )
= zero_zero_real ) )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
= $true ) ),
inference(not_proxy_clausification,[],[f2208]) ).
thf(f2210,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $true )
| ( ( poly_real2 @ p @ x )
= zero_zero_real )
| ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
= $true ) ),
inference(equality_proxy_clausification,[],[f2209]) ).
thf(f4350,definition,
( spl188_2
<=> ( ( poly_real2 @ p @ x )
= zero_zero_real ) ),
introduced(definition,[new_symbols(definition,[spl188_2])],[avatar_definition]) ).
thf(f4354,definition,
( spl188_3
<=> ( ( sturm_469514713_r_pos @ p @ x )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl188_3])],[avatar_definition]) ).
thf(f4356,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $false )
| ~ spl188_3 ),
inference(avatar_component_clause,[],[f4354]) ).
thf(f4359,definition,
( spl188_4
<=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl188_4])],[avatar_definition]) ).
thf(f4361,plain,
( ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
= $false )
| ~ spl188_4 ),
inference(avatar_component_clause,[],[f4359]) ).
thf(f4362,plain,
( spl188_2
| spl188_4
| spl188_3 ),
inference(avatar_split_clause,[],[f2202,f4354,f4359,f4350]) ).
thf(f4369,definition,
( spl188_6
<=> ( ( sturm_469514713_r_pos @ p @ x )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl188_6])],[avatar_definition]) ).
thf(f4371,plain,
( ( ( sturm_469514713_r_pos @ p @ x )
= $true )
| ~ spl188_6 ),
inference(avatar_component_clause,[],[f4369]) ).
thf(f4374,definition,
( spl188_7
<=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl188_7])],[avatar_definition]) ).
thf(f4376,plain,
( ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
= $true )
| ~ spl188_7 ),
inference(avatar_component_clause,[],[f4374]) ).
thf(f4377,plain,
( spl188_7
| spl188_2
| spl188_6 ),
inference(avatar_split_clause,[],[f2210,f4369,f4350,f4374]) ).
thf(f4419,plain,
( ~ spl188_7
| spl188_6 ),
inference(avatar_split_clause,[],[f1423,f4369,f4374]) ).
thf(f4420,plain,
( ~ spl188_6
| spl188_7 ),
inference(avatar_split_clause,[],[f1422,f4374,f4369]) ).
thf(f4421,plain,
~ spl188_2,
inference(avatar_split_clause,[],[f1421,f4350]) ).
thf(f4423,plain,
( ( $true = $false )
| ~ spl188_4
| ~ spl188_7 ),
inference(constrained_superposition,[],[f4361,f4376]) ).
thf(f4427,plain,
( $false
| ~ spl188_4
| ~ spl188_7 ),
inference(trivial_inequality_removal,[],[f4423]) ).
thf(f4428,plain,
( ~ spl188_4
| ~ spl188_7 ),
inference(avatar_contradiction_clause,[],[f4427]) ).
thf(f4430,plain,
( ( $true = $false )
| ~ spl188_3
| ~ spl188_6 ),
inference(constrained_superposition,[],[f4371,f4356]) ).
thf(f4431,plain,
( $false
| ~ spl188_3
| ~ spl188_6 ),
inference(trivial_inequality_removal,[],[f4430]) ).
thf(f4432,plain,
( ~ spl188_3
| ~ spl188_6 ),
inference(avatar_contradiction_clause,[],[f4431]) ).
cnf(s2,plain,
( spl188_2
| spl188_3
| spl188_4 ),
inference(sat_conversion,[],[f4362]) ).
cnf(s5,plain,
( spl188_2
| spl188_6
| spl188_7 ),
inference(sat_conversion,[],[f4377]) ).
cnf(s28,plain,
( spl188_6
| ~ spl188_7 ),
inference(sat_conversion,[],[f4419]) ).
cnf(s29,plain,
( ~ spl188_6
| spl188_7 ),
inference(sat_conversion,[],[f4420]) ).
cnf(s30,plain,
~ spl188_2,
inference(sat_conversion,[],[f4421]) ).
cnf(s33,plain,
( ~ spl188_4
| ~ spl188_7 ),
inference(sat_conversion,[],[f4428]) ).
cnf(s34,plain,
( ~ spl188_3
| ~ spl188_6 ),
inference(sat_conversion,[],[f4432]) ).
cnf(s36,plain,
( spl188_6
| spl188_7 ),
inference(rat,[],[s5,s30]) ).
cnf(s37,plain,
( spl188_3
| spl188_4 ),
inference(rat,[],[s2,s30]) ).
cnf(s38,plain,
spl188_7,
inference(rat,[],[s36,s29]) ).
cnf(s39,plain,
~ spl188_4,
inference(rat,[],[s33,s38]) ).
cnf(s40,plain,
spl188_6,
inference(rat,[],[s28,s38]) ).
cnf(s41,plain,
spl188_3,
inference(rat,[],[s37,s39]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s34,s40,s41]) ).
thf(f4435,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP195^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n004.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 20:10:22 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.36 % (1781912)Will run a generic schedule for satisfiability detection.
% 0.20/0.36 % (1781918)% WARNING: option uhcvi not known.
% 0.20/0.36 % (1781922)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3583840940:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.36 % (1781918)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=52194459:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.36 % (1781919)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=635850663:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.36 % (1781917)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3854437537_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.36 % (1781920)dis+10_1_sil=32000:sp=arity:random_seed=2554873297:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.36 % (1781918)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.36 % (1781921)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2252640023:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.36 % (1781923)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2919754724:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.36 % (1781921)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.36 % (1781918)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.36 % Exception at run slice level
% 0.20/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.36 % (1781920)Instruction limit reached!
% 0.20/0.36 % (1781920)------------------------------
% 0.20/0.36 % (1781920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1781920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1781920)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1781920)Termination reason: Instruction limit
% 0.20/0.36 % (1781920)Termination phase: Property scanning
% 0.20/0.36 % (1781920)Time elapsed: 0.043 s
% 0.20/0.36 % (1781920)Peak memory usage: 11 MB
% 0.20/0.36 % (1781920)Instructions burned: 103 (million)
% 0.20/0.36 % (1781922)Instruction limit reached!
% 0.20/0.36 % (1781922)------------------------------
% 0.20/0.36 % (1781922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1781922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1781922)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1781922)Termination reason: Instruction limit
% 0.20/0.36 % (1781922)Termination phase: Saturation
% 0.20/0.36 % (1781922)Time elapsed: 0.053 s
% 0.20/0.36 % (1781922)Peak memory usage: 13 MB
% 0.20/0.36 % (1781922)Instructions burned: 132 (million)
% 0.20/0.36 % (1781933)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1480062992:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.20/0.36 % (1781921)Instruction limit reached!
% 0.20/0.36 % (1781921)------------------------------
% 0.20/0.36 % (1781921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1781921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1781921)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1781921)Termination reason: Instruction limit
% 0.20/0.36 % (1781921)Termination phase: Saturation
% 0.20/0.36 % (1781921)Time elapsed: 0.048 s
% 0.20/0.36 % (1781921)Peak memory usage: 13 MB
% 0.20/0.36 % (1781921)Instructions burned: 117 (million)
% 0.20/0.36 % (1781918) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1781912-1781918"...
% 0.20/0.36 % (1781931)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3327951549:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.36 % (1781918)...printing done.
% 0.20/0.36 % (1781918)Refutation found. Thanks to Tanya!
% 0.20/0.36 % SZS status Theorem for theBenchmark
% 0.20/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.36 % (1781918)------------------------------
% 0.20/0.36 % (1781918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1781918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1781918)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1781918)Termination reason: Refutation
% 0.20/0.36 % (1781918)Time elapsed: 0.070 s
% 0.20/0.36 % (1781918)Peak memory usage: 14 MB
% 0.20/0.36 % (1781918)Instructions burned: 161 (million)
% 0.20/0.36 % (1781912)Success in time 0.116 s
% 0.20/0.36 % Vampire exiting
%------------------------------------------------------------------------------