%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP118^1 : 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 : n014.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 08:10:46 AM UTC 2026
% Result : Theorem 2.83s 0.65s
% Output : Refutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 24 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 142 ( 9 ~; 0 |; 0 &; 133 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 17 ( 16 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 205 ( 203 usr; 18 con; 0-4 aty)
% Number of variables : 11 ( 0 ^; 10 !; 1 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
finite463740460l_num1: $tType ).
thf(type_def_6,type,
finite121157254l_num1: $tType ).
thf(type_def_7,type,
finite337957458num1_n: $tType ).
thf(type_def_8,type,
finite318270636al_n_n: $tType ).
thf(type_def_9,type,
set_Fi1257234438l_num1: $tType ).
thf(type_def_10,type,
finite1183840848l_num1: $tType ).
thf(type_def_11,type,
finite2063899472l_num1: $tType ).
thf(type_def_12,type,
set_Fi1058188332real_n: $tType ).
thf(type_def_13,type,
finite1489363574real_n: $tType ).
thf(type_def_14,type,
finite964658038_int_n: $tType ).
thf(type_def_15,type,
set_real: $tType ).
thf(type_def_16,type,
set_int: $tType ).
thf(type_def_17,type,
numeral_num1: $tType ).
thf(type_def_18,type,
real: $tType ).
thf(type_def_19,type,
int: $tType ).
thf(type_def_20,type,
n: $tType ).
thf(type_def_21,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
archim1371465213g_real: real > int ).
thf(func_def_1,type,
archim1031974863r_real: real > int ).
thf(func_def_2,type,
finite627713486m1_int: numeral_num1 > int > finite2063899472l_num1 ).
thf(func_def_3,type,
finite15144922381_real: numeral_num1 > real > finite1183840848l_num1 ).
thf(func_def_4,type,
finite1888777460_n_int: n > int > finite964658038_int_n ).
thf(func_def_5,type,
finite703491444n_real: n > real > finite1489363574real_n ).
thf(func_def_6,type,
finite1470207077l_num1: int > finite2063899472l_num1 ).
thf(func_def_7,type,
finite55766923_int_n: int > finite964658038_int_n ).
thf(func_def_8,type,
finite1329045861l_num1: real > finite1183840848l_num1 ).
thf(func_def_9,type,
finite667548811real_n: real > finite1489363574real_n ).
thf(func_def_10,type,
finite1449546019l_num1: finite463740460l_num1 > numeral_num1 > finite1183840848l_num1 ).
thf(func_def_11,type,
finite1639785033num1_n: finite337957458num1_n > n > finite1183840848l_num1 ).
thf(func_def_12,type,
finite1503577981l_num1: finite121157254l_num1 > numeral_num1 > finite1489363574real_n ).
thf(func_def_13,type,
finite625646243al_n_n: finite318270636al_n_n > n > finite1489363574real_n ).
thf(func_def_14,type,
finite1800583751l_num1: finite2063899472l_num1 > numeral_num1 > int ).
thf(func_def_15,type,
finite566214509_int_n: finite964658038_int_n > n > int ).
thf(func_def_16,type,
finite1106245191l_num1: finite1183840848l_num1 > numeral_num1 > real ).
thf(func_def_17,type,
finite772340589real_n: finite1489363574real_n > n > real ).
thf(func_def_18,type,
finite1961675766l_num1: real > finite1183840848l_num1 > finite1183840848l_num1 ).
thf(func_def_19,type,
finite2053577756real_n: real > finite1489363574real_n > finite1489363574real_n ).
thf(func_def_20,type,
abs_ab948591917l_num1: finite1183840848l_num1 > finite1183840848l_num1 ).
thf(func_def_21,type,
abs_ab1599551059real_n: finite1489363574real_n > finite1489363574real_n ).
thf(func_def_22,type,
abs_abs_int: int > int ).
thf(func_def_23,type,
abs_abs_real: real > real ).
thf(func_def_24,type,
minus_779068585l_num1: finite2063899472l_num1 > finite2063899472l_num1 > finite2063899472l_num1 ).
thf(func_def_25,type,
minus_1196255695_int_n: finite964658038_int_n > finite964658038_int_n > finite964658038_int_n ).
thf(func_def_26,type,
minus_249161513l_num1: finite1183840848l_num1 > finite1183840848l_num1 > finite1183840848l_num1 ).
thf(func_def_27,type,
minus_1037315151real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).
thf(func_def_28,type,
minus_minus_int: int > int > int ).
thf(func_def_29,type,
minus_minus_real: real > real > real ).
thf(func_def_30,type,
one_on601734293l_num1: finite2063899472l_num1 ).
thf(func_def_31,type,
one_on1516019131_int_n: finite964658038_int_n ).
thf(func_def_32,type,
one_on1961019669l_num1: finite1183840848l_num1 ).
thf(func_def_33,type,
one_on1253059131real_n: finite1489363574real_n ).
thf(func_def_34,type,
one_one_int: int ).
thf(func_def_35,type,
one_one_Numeral_num1: numeral_num1 ).
thf(func_def_36,type,
one_one_real: real ).
thf(func_def_37,type,
if_Fin1570437642l_num1: $o > finite2063899472l_num1 > finite2063899472l_num1 > finite2063899472l_num1 ).
thf(func_def_38,type,
if_Fin1767949360_int_n: $o > finite964658038_int_n > finite964658038_int_n > finite964658038_int_n ).
thf(func_def_39,type,
if_Fin1668193290l_num1: $o > finite1183840848l_num1 > finite1183840848l_num1 > finite1183840848l_num1 ).
thf(func_def_40,type,
if_Fin127821360real_n: $o > finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).
thf(func_def_41,type,
ring_11529266783l_num1: set_Fi1257234438l_num1 ).
thf(func_def_42,type,
ring_1723899781real_n: set_Fi1058188332real_n ).
thf(func_def_43,type,
ring_1_Ints_int: set_int ).
thf(func_def_44,type,
ring_1_Ints_real: set_real ).
thf(func_def_45,type,
ring_1154201247l_num1: int > finite1183840848l_num1 ).
thf(func_def_46,type,
ring_11737179077real_n: int > finite1489363574real_n ).
thf(func_def_47,type,
ring_1_of_int_int: int > int ).
thf(func_def_48,type,
ring_1_of_int_real: int > real ).
thf(func_def_49,type,
minkow781993583real_n: finite2063899472l_num1 > finite121157254l_num1 ).
thf(func_def_50,type,
minkow2063319845m1_int: finite2063899472l_num1 > finite2063899472l_num1 ).
thf(func_def_51,type,
minkow19073400691_real: finite2063899472l_num1 > finite1183840848l_num1 ).
thf(func_def_52,type,
minkow371489429real_n: finite964658038_int_n > finite318270636al_n_n ).
thf(func_def_53,type,
minkow1468704075_n_int: finite964658038_int_n > finite964658038_int_n ).
thf(func_def_54,type,
minkow1134813771n_real: finite964658038_int_n > finite1489363574real_n ).
thf(func_def_55,type,
ord_le2035778724l_num1: finite1183840848l_num1 > finite1183840848l_num1 > $o ).
thf(func_def_56,type,
ord_le1017090250real_n: finite1489363574real_n > finite1489363574real_n > $o ).
thf(func_def_57,type,
ord_less_int: int > int > $o ).
thf(func_def_58,type,
ord_less_real: real > real > $o ).
thf(func_def_59,type,
ord_le1202326448l_num1: finite2063899472l_num1 > finite2063899472l_num1 > $o ).
thf(func_def_60,type,
ord_le1908593622_int_n: finite964658038_int_n > finite964658038_int_n > $o ).
thf(func_def_61,type,
ord_le1724070576l_num1: finite1183840848l_num1 > finite1183840848l_num1 > $o ).
thf(func_def_62,type,
ord_le866583254real_n: finite1489363574real_n > finite1489363574real_n > $o ).
thf(func_def_63,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_64,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_65,type,
real_V1974343547l_num1: finite463740460l_num1 > finite463740460l_num1 > real ).
thf(func_def_66,type,
real_V845814485l_num1: finite121157254l_num1 > finite121157254l_num1 > real ).
thf(func_def_67,type,
real_V488409631l_num1: finite1183840848l_num1 > finite1183840848l_num1 > real ).
thf(func_def_68,type,
real_V783965509real_n: finite1489363574real_n > finite1489363574real_n > real ).
thf(func_def_69,type,
real_V1934908667t_real: real > real > real ).
thf(func_def_70,type,
real_V316032763l_num1: finite463740460l_num1 > real ).
thf(func_def_71,type,
real_V1121707553num1_n: finite337957458num1_n > real ).
thf(func_def_72,type,
real_V400292255l_num1: finite1183840848l_num1 > real ).
thf(func_def_73,type,
real_V739724485real_n: finite1489363574real_n > real ).
thf(func_def_74,type,
real_V646646907m_real: real > real ).
thf(func_def_75,type,
collec321817931real_n: ( finite1489363574real_n > $o ) > set_Fi1058188332real_n ).
thf(func_def_76,type,
collect_real: ( real > $o ) > set_real ).
thf(func_def_77,type,
member1413569767l_num1: finite1183840848l_num1 > set_Fi1257234438l_num1 > $o ).
thf(func_def_78,type,
member1352538125real_n: finite1489363574real_n > set_Fi1058188332real_n > $o ).
thf(func_def_79,type,
member_int: int > set_int > $o ).
thf(func_def_80,type,
member_real: real > set_real > $o ).
thf(func_def_81,type,
a: set_Fi1058188332real_n ).
thf(func_def_82,type,
i: n ).
thf(func_def_83,type,
m: int ).
thf(func_def_84,type,
x: finite1489363574real_n ).
thf(func_def_85,type,
y: finite1489363574real_n ).
thf(func_def_89,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_90,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_91,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_92,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_93,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_94,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_95,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_96,type,
vIMP: $o > $o > $o ).
thf(func_def_97,type,
vAND: $o > $o > $o ).
thf(func_def_98,type,
vOR: $o > $o > $o ).
thf(func_def_99,type,
vNOT: $o > $o ).
thf(func_def_100,type,
sP0: int > ( int > $o ) > $o ).
thf(func_def_101,type,
sP1: int > ( int > $o ) > $o ).
thf(func_def_102,type,
sP2: int > int > ( int > $o ) > $o ).
thf(func_def_103,type,
sP3: int > int > ( int > $o ) > $o ).
thf(func_def_104,type,
sP4: real > real > ( real > $o ) > $o ).
thf(func_def_105,type,
sP5: real > real > ( real > $o ) > $o ).
thf(func_def_106,type,
sP6: set_real > real > $o ).
thf(func_def_107,type,
sP7: set_real > $o ).
thf(func_def_108,type,
sP8: ( int > int > $o ) > $o ).
thf(func_def_109,type,
sP9: ( real > real > $o ) > $o ).
thf(func_def_110,type,
sP10: int > int > int > $o ).
thf(func_def_111,type,
sP11: int > int > int > $o ).
thf(func_def_112,type,
sP12: int > int > int > $o ).
thf(func_def_113,type,
sP13: int > int > int > $o ).
thf(func_def_114,type,
sP14: int > int > int > $o ).
thf(func_def_115,type,
sP15: real > real > real > $o ).
thf(func_def_116,type,
sP16: real > real > real > $o ).
thf(func_def_117,type,
sP17: real > real > real > $o ).
thf(func_def_118,type,
sP18: real > real > real > $o ).
thf(func_def_119,type,
sP19: real > real > real > $o ).
thf(func_def_120,type,
sK20: int ).
thf(func_def_121,type,
sK21: ( real > $o ) > int ).
thf(func_def_122,type,
sK22: ( int > $o ) > int ).
thf(func_def_123,type,
sK23: ( finite1489363574real_n > $o ) > int ).
thf(func_def_124,type,
sK24: real > int ).
thf(func_def_125,type,
sK25: int > int ).
thf(func_def_126,type,
sK26: finite1489363574real_n > int ).
thf(func_def_127,type,
sK27: real > int ).
thf(func_def_128,type,
sK28: real > int ).
thf(func_def_129,type,
sK29: int > ( int > $o ) > int ).
thf(func_def_130,type,
sK30: int > ( int > $o ) > int ).
thf(func_def_131,type,
sK31: real > int ).
thf(func_def_132,type,
sK32: finite1489363574real_n > finite337957458num1_n > n ).
thf(func_def_133,type,
sK33: finite1183840848l_num1 > finite463740460l_num1 > numeral_num1 ).
thf(func_def_134,type,
sK34: finite337957458num1_n > finite1489363574real_n > n ).
thf(func_def_135,type,
sK35: finite1489363574real_n > finite1489363574real_n > n ).
thf(func_def_136,type,
sK36: finite463740460l_num1 > finite1183840848l_num1 > numeral_num1 ).
thf(func_def_137,type,
sK37: finite1183840848l_num1 > finite1183840848l_num1 > numeral_num1 ).
thf(func_def_138,type,
sK38: int > int > ( int > $o ) > int ).
thf(func_def_139,type,
sK39: int > int > ( int > $o ) > int ).
thf(func_def_140,type,
sK40: real > real > ( real > $o ) > real ).
thf(func_def_141,type,
sK41: real > real > ( real > $o ) > real ).
thf(func_def_142,type,
sK42: real > set_real > real ).
thf(func_def_143,type,
sK43: real > set_real > real ).
thf(func_def_144,type,
sK44: set_real > real ).
thf(func_def_145,type,
sK45: ( int > int > $o ) > int ).
thf(func_def_146,type,
sK46: ( int > int > $o ) > int ).
thf(func_def_147,type,
sK47: ( int > int > $o ) > int ).
thf(func_def_148,type,
sK48: ( int > int > $o ) > int ).
thf(func_def_149,type,
sK49: ( real > real > $o ) > real ).
thf(func_def_150,type,
sK50: ( real > real > $o ) > real ).
thf(func_def_151,type,
sK51: ( real > real > $o ) > real ).
thf(func_def_152,type,
sK52: ( real > real > $o ) > real ).
thf(func_def_153,type,
sK53: ( int > int ) > int ).
thf(func_def_154,type,
sK54: ( int > int ) > int ).
thf(func_def_155,type,
sK55: ( int > real ) > int ).
thf(func_def_156,type,
sK56: ( int > real ) > int ).
thf(func_def_157,type,
sK57: ( real > int ) > real ).
thf(func_def_158,type,
sK58: ( real > int ) > real ).
thf(func_def_159,type,
sK59: ( real > real ) > real ).
thf(func_def_160,type,
sK60: ( real > real ) > real ).
thf(func_def_161,type,
sK61: ( int > int ) > int ).
thf(func_def_162,type,
sK62: ( int > int ) > int ).
thf(func_def_163,type,
sK63: ( int > real ) > int ).
thf(func_def_164,type,
sK64: ( int > real ) > int ).
thf(func_def_165,type,
sK65: ( real > int ) > real ).
thf(func_def_166,type,
sK66: ( real > int ) > real ).
thf(func_def_167,type,
sK67: ( real > real ) > real ).
thf(func_def_168,type,
sK68: ( real > real ) > real ).
thf(func_def_169,type,
sK69: set_Fi1257234438l_num1 > finite1183840848l_num1 > finite1183840848l_num1 > finite1183840848l_num1 ).
thf(func_def_170,type,
sK70: set_real > real > real > real ).
thf(func_def_171,type,
sK71: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).
thf(func_def_172,type,
sK72: finite1183840848l_num1 > finite1183840848l_num1 > numeral_num1 ).
thf(func_def_173,type,
sK73: finite1183840848l_num1 > finite1183840848l_num1 > numeral_num1 ).
thf(func_def_174,type,
sK74: finite1489363574real_n > finite1489363574real_n > n ).
thf(func_def_175,type,
sK75: finite1489363574real_n > finite1489363574real_n > n ).
thf(func_def_176,type,
sK76: finite1183840848l_num1 > finite1183840848l_num1 > numeral_num1 ).
thf(func_def_177,type,
sK77: finite1489363574real_n > finite1489363574real_n > n ).
thf(func_def_178,type,
sK78: finite1183840848l_num1 > finite1183840848l_num1 > numeral_num1 ).
thf(func_def_179,type,
sK79: finite1489363574real_n > finite1489363574real_n > n ).
thf(func_def_180,type,
sK80: finite1183840848l_num1 > finite1183840848l_num1 > numeral_num1 ).
thf(func_def_181,type,
sK81: finite1183840848l_num1 > finite1183840848l_num1 > numeral_num1 ).
thf(func_def_182,type,
sK82: finite1489363574real_n > finite1489363574real_n > n ).
thf(func_def_183,type,
sK83: finite1489363574real_n > finite1489363574real_n > n ).
thf(func_def_184,type,
sK84: real > ( int > $o ) > int ).
thf(func_def_185,type,
sK85: real > int ).
thf(func_def_186,type,
sK86: real > int ).
thf(func_def_187,type,
sK87: ( n > int > $o ) > n ).
thf(func_def_188,type,
sK88: ( n > int > $o ) > finite964658038_int_n ).
thf(func_def_189,type,
sK89: n > ( n > int > $o ) > int ).
thf(func_def_190,type,
sK90: ( n > int > $o ) > finite964658038_int_n > n ).
thf(func_def_191,type,
sK91: ( numeral_num1 > int > $o ) > numeral_num1 ).
thf(func_def_192,type,
sK92: ( numeral_num1 > int > $o ) > finite2063899472l_num1 ).
thf(func_def_193,type,
sK93: numeral_num1 > ( numeral_num1 > int > $o ) > int ).
thf(func_def_194,type,
sK94: ( numeral_num1 > int > $o ) > finite2063899472l_num1 > numeral_num1 ).
thf(func_def_195,type,
sK95: ( numeral_num1 > real > $o ) > numeral_num1 ).
thf(func_def_196,type,
sK96: ( numeral_num1 > real > $o ) > finite1183840848l_num1 ).
thf(func_def_197,type,
sK97: numeral_num1 > ( numeral_num1 > real > $o ) > real ).
thf(func_def_198,type,
sK98: ( numeral_num1 > real > $o ) > finite1183840848l_num1 > numeral_num1 ).
thf(func_def_199,type,
sK99: ( n > real > $o ) > n ).
thf(func_def_200,type,
sK100: ( n > real > $o ) > finite1489363574real_n ).
thf(func_def_201,type,
sK101: n > ( n > real > $o ) > real ).
thf(func_def_202,type,
sK102: ( n > real > $o ) > finite1489363574real_n > n ).
thf(func_def_203,type,
sK103: ( numeral_num1 > $o ) > numeral_num1 ).
thf(func_def_204,type,
sK104: ( numeral_num1 > $o ) > numeral_num1 ).
thf(f3,axiom,
( ( ring_1_of_int_real @ m )
= ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_m) ).
thf(f4,axiom,
~ ! [X0: int] :
( ( ring_1_of_int_real @ X0 )
!= ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_Areal__of__int_Am_A_061_Ax_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(f7,axiom,
! [X0: finite1489363574real_n,X1: finite1489363574real_n,X2: n] :
( ( finite772340589real_n @ ( minus_1037315151real_n @ X0 @ X1 ) @ X2 )
= ( minus_minus_real @ ( finite772340589real_n @ X0 @ X2 ) @ ( finite772340589real_n @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_vector__minus__component) ).
thf(f10,axiom,
! [X0: int] :
( ( ring_1_of_int_real @ ( abs_abs_int @ X0 ) )
= ( abs_abs_real @ ( ring_1_of_int_real @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_of__int__abs) ).
thf(f157,axiom,
real_V646646907m_real = abs_abs_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_real__norm__def) ).
thf(f364,conjecture,
( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
= ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f365,negated_conjecture,
( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
!= ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ),
inference(negated_conjecture,[status(cth)],[f364]) ).
thf(f824,plain,
( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
!= ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ),
inference(flattening,[],[f365]) ).
thf(f825,plain,
? [X0: int] :
( ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) )
= ( ring_1_of_int_real @ X0 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f1037,plain,
( ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) )
= ( ring_1_of_int_real @ sK20 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X0,sK20)],[f825]) ).
thf(f1117,plain,
( ( ring_1_of_int_real @ m )
= ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ),
inference(cnf_transformation,[],[f3]) ).
thf(f1118,plain,
( ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) )
= ( ring_1_of_int_real @ sK20 ) ),
inference(cnf_transformation,[],[f1037]) ).
thf(f1121,plain,
! [X2: n,X0: finite1489363574real_n,X1: finite1489363574real_n] :
( ( finite772340589real_n @ ( minus_1037315151real_n @ X0 @ X1 ) @ X2 )
= ( minus_minus_real @ ( finite772340589real_n @ X0 @ X2 ) @ ( finite772340589real_n @ X1 @ X2 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f1124,plain,
! [X0: int] :
( ( ring_1_of_int_real @ ( abs_abs_int @ X0 ) )
= ( abs_abs_real @ ( ring_1_of_int_real @ X0 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f1275,plain,
abs_abs_real = real_V646646907m_real,
inference(cnf_transformation,[],[f157]) ).
thf(f1544,plain,
( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
!= ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ),
inference(cnf_transformation,[],[f824]) ).
thf(f1554,plain,
! [X0: int] :
( ( ring_1_of_int_real @ ( abs_abs_int @ X0 ) )
= ( real_V646646907m_real @ ( ring_1_of_int_real @ X0 ) ) ),
inference(definition_unfolding,[],[f1124,f1275]) ).
thf(f1713,plain,
( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
!= ( real_V646646907m_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ),
inference(definition_unfolding,[],[f1544,f1275]) ).
thf(f2770,plain,
( ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i )
= ( ring_1_of_int_real @ sK20 ) ),
inference(forward_demodulation,[],[f1118,f1121]) ).
thf(f2771,plain,
( ( ring_1_of_int_real @ m )
= ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ),
inference(forward_demodulation,[],[f1117,f1121]) ).
thf(f2772,plain,
( ( ring_1_of_int_real @ m )
= ( ring_1_of_int_real @ sK20 ) ),
inference(forward_demodulation,[],[f2771,f2770]) ).
thf(f3984,plain,
( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
!= ( real_V646646907m_real @ ( ring_1_of_int_real @ sK20 ) ) ),
inference(constrained_superposition,[],[f1713,f2770]) ).
thf(f3985,plain,
( ( real_V646646907m_real @ ( ring_1_of_int_real @ m ) )
!= ( real_V646646907m_real @ ( ring_1_of_int_real @ sK20 ) ) ),
inference(forward_demodulation,[],[f3984,f1554]) ).
thf(f3986,plain,
( ( real_V646646907m_real @ ( ring_1_of_int_real @ sK20 ) )
!= ( real_V646646907m_real @ ( ring_1_of_int_real @ sK20 ) ) ),
inference(forward_demodulation,[],[f3985,f2772]) ).
thf(f3987,plain,
$false,
inference(trivial_inequality_removal,[],[f3986]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP118^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 19:56:15 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 2.40/0.65 % (3132135)Will run a generic schedule for satisfiability detection.
% 2.40/0.65 % (3132143)dis+10_1_sil=32000:sp=arity:random_seed=1801383909:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.40/0.65 % (3132141)% WARNING: option uhcvi not known.
% 2.40/0.65 % (3132140)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1839127211_2999 on theBenchmark for (2999ds/0Mi)
% 2.40/0.65 % (3132141)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3438744479:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.40/0.65 % (3132142)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2944812898:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.40/0.65 % (3132144)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=245827737:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.40/0.65 % (3132145)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=866162537:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.40/0.65 % (3132146)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3211877059:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.40/0.65 % (3132141)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.40/0.65 % (3132144)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.40/0.65 % (3132143)Instruction limit reached!
% 2.40/0.65 % (3132143)------------------------------
% 2.40/0.65 % (3132143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.40/0.65 % (3132143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.65 % (3132143)CaDiCaL version: 2.1.3
% 2.40/0.65 % (3132143)Termination reason: Instruction limit
% 2.40/0.65 % (3132143)Termination phase: Saturation
% 2.40/0.65 % (3132143)Time elapsed: 0.023 s
% 2.40/0.65 % (3132143)Peak memory usage: 12 MB
% 2.40/0.65 % (3132143)Instructions burned: 105 (million)
% 2.40/0.65 % (3132154)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1143058053:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.40/0.65 % (3132141)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.40/0.65 % Exception at run slice level
% 2.40/0.65 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.40/0.65 % Exception at run slice level
% 2.40/0.65 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.40/0.65 % (3132144)Instruction limit reached!
% 2.40/0.65 % (3132144)------------------------------
% 2.40/0.65 % (3132144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.40/0.65 % (3132144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.65 % (3132144)CaDiCaL version: 2.1.3
% 2.40/0.65 % (3132144)Termination reason: Instruction limit
% 2.40/0.65 % (3132144)Termination phase: Saturation
% 2.40/0.65 % (3132144)Time elapsed: 0.052 s
% 2.40/0.65 % (3132144)Peak memory usage: 13 MB
% 2.40/0.65 % (3132144)Instructions burned: 123 (million)
% 2.40/0.65 % (3132157)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=3343850471:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.40/0.65 % (3132145)Instruction limit reached!
% 2.40/0.65 % (3132145)------------------------------
% 2.40/0.65 % (3132145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.40/0.65 % (3132145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.65 % (3132145)CaDiCaL version: 2.1.3
% 2.40/0.65 % (3132145)Termination reason: Instruction limit
% 2.40/0.65 % (3132145)Termination phase: Saturation
% 2.40/0.65 % (3132145)Time elapsed: 0.056 s
% 2.40/0.65 % (3132145)Peak memory usage: 13 MB
% 2.40/0.65 % (3132145)Instructions burned: 133 (million)
% 2.40/0.65 % (3132157)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.40/0.65 % (3132146)Instruction limit reached!
% 2.40/0.65 % (3132146)------------------------------
% 2.40/0.65 % (3132146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.40/0.65 % (3132146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.65 % (3132146)CaDiCaL version: 2.1.3
% 2.40/0.65 % (3132146)Termination reason: Instruction limit
% 2.40/0.65 % (3132146)Termination phase: Saturation
% 2.40/0.65 % (3132146)Time elapsed: 0.070 s
% 2.40/0.65 % (3132158)ott-21_1_sil=16000:fs=off:random_seed=564922981:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.40/0.65 % (3132146)Peak memory usage: 14 MB
% 2.40/0.65 % (3132146)Instructions burned: 160 (million)
% 2.40/0.65 % (3132160)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2822052480:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.40/0.65 % (3132156)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3497206342:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.40/0.65 % (3132157)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.40/0.65 % (3132162)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2647739020:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.40/0.65 % Exception at run slice level
% 2.40/0.65 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.40/0.65 % (3132156)Instruction limit reached!
% 2.40/0.65 % (3132156)------------------------------
% 2.40/0.65 % (3132156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.40/0.65 % (3132156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.65 % (3132156)CaDiCaL version: 2.1.3
% 2.40/0.65 % (3132156)Termination reason: Instruction limit
% 2.40/0.65 % (3132156)Termination phase: Saturation
% 2.40/0.65 % (3132156)Time elapsed: 0.069 s
% 2.40/0.65 % (3132156)Peak memory usage: 13 MB
% 2.40/0.65 % (3132156)Instructions burned: 132 (million)
% 2.40/0.65 % (3132166)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1483457794:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.40/0.65 % (3132167)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3406495672:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 2.40/0.65 % (3132158)Instruction limit reached!
% 2.40/0.65 % (3132158)------------------------------
% 2.40/0.65 % (3132158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.40/0.65 % (3132158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.65 % (3132158)CaDiCaL version: 2.1.3
% 2.40/0.65 % (3132158)Termination reason: Instruction limit
% 2.40/0.65 % (3132158)Termination phase: Saturation
% 2.40/0.65 % (3132158)Time elapsed: 0.103 s
% 2.40/0.65 % (3132158)Peak memory usage: 13 MB
% 2.40/0.65 % (3132158)Instructions burned: 181 (million)
% 2.40/0.65 % (3132170)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2511986134:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 2.40/0.65 % (3132170)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.40/0.65 % (3132157)Instruction limit reached!
% 2.40/0.65 % (3132157)------------------------------
% 2.40/0.65 % (3132157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.40/0.65 % (3132157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.65 % (3132157)CaDiCaL version: 2.1.3
% 2.40/0.65 % (3132157)Termination reason: Instruction limit
% 2.40/0.65 % (3132157)Termination phase: Saturation
% 2.40/0.65 % (3132157)Time elapsed: 0.158 s
% 2.40/0.65 % (3132157)Peak memory usage: 15 MB
% 2.40/0.65 % (3132157)Instructions burned: 687 (million)
% 2.83/0.65 % (3132172)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=200432016:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.83/0.65 % (3132172)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.83/0.65 % Exception at run slice level
% 2.83/0.65 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.83/0.65 % (3132174)fmb+10_1_sil=64000:random_seed=2191621452:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 2.83/0.65 % (3132160)Instruction limit reached!
% 2.83/0.65 % (3132160)------------------------------
% 2.83/0.65 % (3132160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.83/0.65 % (3132160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/0.65 % (3132160)CaDiCaL version: 2.1.3
% 2.83/0.65 % (3132160)Termination reason: Instruction limit
% 2.83/0.65 % (3132160)Termination phase: Saturation
% 2.83/0.65 % (3132160)Time elapsed: 0.244 s
% 2.83/0.65 % (3132160)Peak memory usage: 14 MB
% 2.83/0.65 % (3132160)Instructions burned: 477 (million)
% 2.83/0.65 % (3132174)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.83/0.65 % (3132176)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2860555976:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 2.83/0.65 % Exception at run slice level
% 2.83/0.65 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.83/0.65 % (3132170) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3132135-3132170"...
% 2.83/0.65 % (3132170)...printing done.
% 2.83/0.65 % (3132170)Refutation found. Thanks to Tanya!
% 2.83/0.65 % SZS status Theorem for theBenchmark
% 2.83/0.65 % SZS output start Proof for theBenchmark
% See solution above
% 2.83/0.66 % (3132170)------------------------------
% 2.83/0.66 % (3132170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.83/0.66 % (3132170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/0.66 % (3132170)CaDiCaL version: 2.1.3
% 2.83/0.66 % (3132170)Termination reason: Refutation
% 2.83/0.66 % (3132170)Time elapsed: 0.163 s
% 2.83/0.66 % (3132170)Peak memory usage: 16 MB
% 2.83/0.66 % (3132170)Instructions burned: 332 (million)
% 2.83/0.66 % (3132135)Success in time 0.417 s
% 2.83/0.66 % Vampire exiting
%------------------------------------------------------------------------------