%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP105^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:10:42 AM UTC 2026
% Result : Theorem 0.75s 0.47s
% Output : Refutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 31 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 115 ( 10 ~; 3 |; 0 &; 99 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 388 ( 385 usr; 14 con; 0-4 aty)
% Number of variables : 31 ( 10 ^; 21 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
list_l2071841302list_a: $tType ).
thf(type_def_6,type,
option_list_list_a: $tType ).
thf(type_def_7,type,
list_list_list_a: $tType ).
thf(type_def_8,type,
option_list_a: $tType ).
thf(type_def_9,type,
list_list_a: $tType ).
thf(type_def_10,type,
set_real: $tType ).
thf(type_def_11,type,
set_nat: $tType ).
thf(type_def_12,type,
option_a: $tType ).
thf(type_def_13,type,
list_a: $tType ).
thf(type_def_14,type,
real: $tType ).
thf(type_def_15,type,
nat: $tType ).
thf(type_def_16,type,
int: $tType ).
thf(type_def_17,type,
a: $tType ).
thf(type_def_18,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
inverse_inverse_real: real > real ).
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_real: real ).
thf(func_def_4,type,
if_nat: $o > nat > nat > nat ).
thf(func_def_5,type,
listSl162220270list_a: list_list_a > nat > list_list_list_a ).
thf(func_def_6,type,
listSl97544552lice_a: list_a > nat > list_list_a ).
thf(func_def_7,type,
listSl856612276list_a: list_list_a > nat > nat > list_list_list_a ).
thf(func_def_8,type,
listSl1495374126_aux_a: list_a > nat > nat > list_list_a ).
thf(func_def_9,type,
bind_l311701255list_a: list_list_list_a > ( list_list_a > list_list_list_a ) > list_list_list_a ).
thf(func_def_10,type,
bind_l94945665list_a: list_list_list_a > ( list_list_a > list_list_a ) > list_list_a ).
thf(func_def_11,type,
bind_list_list_a_a: list_list_list_a > ( list_list_a > list_a ) > list_a ).
thf(func_def_12,type,
bind_l971853709list_a: list_list_a > ( list_a > list_list_list_a ) > list_list_list_a ).
thf(func_def_13,type,
bind_list_a_list_a: list_list_a > ( list_a > list_list_a ) > list_list_a ).
thf(func_def_14,type,
bind_list_a_a: list_list_a > ( list_a > list_a ) > list_a ).
thf(func_def_15,type,
bind_a_list_list_a: list_a > ( a > list_list_list_a ) > list_list_list_a ).
thf(func_def_16,type,
bind_a_list_a: list_a > ( a > list_list_a ) > list_list_a ).
thf(func_def_17,type,
bind_a_a: list_a > ( a > list_a ) > list_a ).
thf(func_def_18,type,
concat_list_list_a: list_l2071841302list_a > list_list_list_a ).
thf(func_def_19,type,
concat_list_a: list_list_list_a > list_list_a ).
thf(func_def_20,type,
concat_a: list_list_a > list_a ).
thf(func_def_21,type,
count_429956358list_a: list_list_list_a > list_list_a > nat ).
thf(func_def_22,type,
count_list_list_a: list_list_a > list_a > nat ).
thf(func_def_23,type,
count_list_a: list_a > a > nat ).
thf(func_def_24,type,
gen_le840878749list_a: nat > list_list_list_a > nat ).
thf(func_def_25,type,
gen_length_list_a: nat > list_list_a > nat ).
thf(func_def_26,type,
gen_length_a: nat > list_a > nat ).
thf(func_def_27,type,
nil_list_list_list_a: list_l2071841302list_a ).
thf(func_def_28,type,
nil_list_list_a: list_list_list_a ).
thf(func_def_29,type,
nil_list_a: list_list_a ).
thf(func_def_30,type,
nil_a: list_a ).
thf(func_def_31,type,
list_ex1_list_list_a: ( list_list_a > $o ) > list_list_list_a > $o ).
thf(func_def_32,type,
list_ex1_list_a: ( list_a > $o ) > list_list_a > $o ).
thf(func_def_33,type,
list_ex1_a: ( a > $o ) > list_a > $o ).
thf(func_def_34,type,
map_fi824137674list_a: ( list_list_a > option_list_list_a ) > list_list_list_a > list_list_list_a ).
thf(func_def_35,type,
map_fi213215172list_a: ( list_list_a > option_list_a ) > list_list_list_a > list_list_a ).
thf(func_def_36,type,
map_fi1574988606st_a_a: ( list_list_a > option_a ) > list_list_list_a > list_a ).
thf(func_def_37,type,
map_fi1090123216list_a: ( list_a > option_list_list_a ) > list_list_a > list_list_list_a ).
thf(func_def_38,type,
map_fi461586634list_a: ( list_a > option_list_a ) > list_list_a > list_list_a ).
thf(func_def_39,type,
map_filter_list_a_a: ( list_a > option_a ) > list_list_a > list_a ).
thf(func_def_40,type,
map_fi2089402454list_a: ( a > option_list_list_a ) > list_a > list_list_list_a ).
thf(func_def_41,type,
map_filter_a_list_a: ( a > option_list_a ) > list_a > list_list_a ).
thf(func_def_42,type,
map_filter_a_a: ( a > option_a ) > list_a > list_a ).
thf(func_def_43,type,
maps_l57963201list_a: ( list_list_a > list_list_list_a ) > list_list_list_a > list_list_list_a ).
thf(func_def_44,type,
maps_l2025957947list_a: ( list_list_a > list_list_a ) > list_list_list_a > list_list_a ).
thf(func_def_45,type,
maps_list_list_a_a: ( list_list_a > list_a ) > list_list_list_a > list_a ).
thf(func_def_46,type,
maps_l755382343list_a: ( list_a > list_list_list_a ) > list_list_a > list_list_list_a ).
thf(func_def_47,type,
maps_list_a_list_a: ( list_a > list_list_a ) > list_list_a > list_list_a ).
thf(func_def_48,type,
maps_list_a_a: ( list_a > list_a ) > list_list_a > list_a ).
thf(func_def_49,type,
maps_a_list_list_a: ( a > list_list_list_a ) > list_a > list_list_list_a ).
thf(func_def_50,type,
maps_a_list_a: ( a > list_list_a ) > list_a > list_list_a ).
thf(func_def_51,type,
maps_a_a: ( a > list_a ) > list_a > list_a ).
thf(func_def_52,type,
member_list_list_a: list_list_list_a > list_list_a > $o ).
thf(func_def_53,type,
member_list_a: list_list_a > list_a > $o ).
thf(func_def_54,type,
member_a: list_a > a > $o ).
thf(func_def_55,type,
null_list_list_a: list_list_list_a > $o ).
thf(func_def_56,type,
null_list_a: list_list_a > $o ).
thf(func_def_57,type,
null_a: list_a > $o ).
thf(func_def_58,type,
semiri2019852685at_int: nat > int ).
thf(func_def_59,type,
semiri1382578993at_nat: nat > nat ).
thf(func_def_60,type,
semiri2110766477t_real: nat > real ).
thf(func_def_61,type,
size_s575106428list_a: list_list_list_a > nat ).
thf(func_def_62,type,
size_s1427607542list_a: list_list_a > nat ).
thf(func_def_63,type,
size_size_list_a: list_a > nat ).
thf(func_def_64,type,
ord_less_int: int > int > $o ).
thf(func_def_65,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_66,type,
ord_less_real: real > real > $o ).
thf(func_def_67,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_68,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_69,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_70,type,
power_power_int: int > nat > int ).
thf(func_def_71,type,
power_power_nat: nat > nat > nat ).
thf(func_def_72,type,
power_power_real: real > nat > real ).
thf(func_def_73,type,
divide_divide_int: int > int > int ).
thf(func_def_74,type,
divide_divide_nat: nat > nat > nat ).
thf(func_def_75,type,
divide_divide_real: real > real > real ).
thf(func_def_76,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_77,type,
collect_real: ( real > $o ) > set_real ).
thf(func_def_78,type,
member_nat: nat > set_nat > $o ).
thf(func_def_79,type,
member_real: real > set_real > $o ).
thf(func_def_80,type,
k: nat ).
thf(func_def_84,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_85,type,
vNOT: $o > $o ).
thf(func_def_86,type,
vOR: $o > $o > $o ).
thf(func_def_87,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_88,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_89,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_90,type,
vAND: $o > $o > $o ).
thf(func_def_91,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_92,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_93,type,
vIMP: $o > $o > $o ).
thf(func_def_94,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_95,type,
sK0: ( list_a > $o ) > list_a ).
thf(func_def_96,type,
sK1: nat > list_a ).
thf(func_def_97,type,
sK2: ( nat > $o ) > nat ).
thf(func_def_98,type,
sK3: ( nat > $o ) > nat ).
thf(func_def_99,type,
sK4: ( nat > $o ) > nat ).
thf(func_def_100,type,
sK5: real > real > real ).
thf(func_def_101,type,
sK6: ( nat > $o ) > set_nat > nat ).
thf(func_def_102,type,
sK7: ( nat > $o ) > set_nat > nat ).
thf(func_def_103,type,
sK8: ( nat > $o ) > set_nat > nat ).
thf(func_def_104,type,
sK9: ( nat > $o ) > set_nat > nat ).
thf(func_def_105,type,
sK10: int > nat ).
thf(func_def_106,type,
sK11: int > nat ).
thf(func_def_107,type,
sK12: real > nat ).
thf(func_def_108,type,
sK13: real > nat ).
thf(func_def_109,type,
sK14: int > nat ).
thf(func_def_110,type,
sK15: int > nat ).
thf(func_def_111,type,
sK16: real > nat ).
thf(func_def_112,type,
sK17: ( real > $o ) > nat ).
thf(func_def_113,type,
sK18: ( real > $o ) > real ).
thf(func_def_114,type,
sK19: ( real > $o ) > real ).
thf(func_def_115,type,
sK20: ( nat > nat ) > nat ).
thf(func_def_116,type,
sK21: ( nat > nat ) > nat ).
thf(func_def_117,type,
sK22: nat > ( nat > $o ) > nat ).
thf(func_def_118,type,
sK23: ( nat > $o ) > nat ).
thf(func_def_119,type,
sK24: nat > ( nat > $o ) > nat ).
thf(func_def_120,type,
sK25: real > real ).
thf(func_def_121,type,
sK26: real > real ).
thf(func_def_122,type,
sK27: set_real > real ).
thf(func_def_123,type,
sK28: real > set_real > real ).
thf(func_def_124,type,
sK29: real > set_real > real ).
thf(func_def_125,type,
sK30: real > nat > real ).
thf(func_def_126,type,
sK31: real > nat > real ).
thf(func_def_127,type,
sK32: nat > nat > nat ).
thf(func_def_128,type,
sK33: nat > nat > nat > nat ).
thf(func_def_129,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
sK34: real > real ).
thf(func_def_131,type,
sK35: nat > nat ).
thf(func_def_132,type,
sK36: real > real ).
thf(func_def_133,type,
sK37: nat > nat ).
thf(func_def_134,type,
sK38: real > real ).
thf(func_def_135,type,
sK39: nat > nat ).
thf(func_def_136,type,
sK40: real > real ).
thf(func_def_137,type,
sK41: nat > nat ).
thf(func_def_138,type,
sK42: real > real ).
thf(func_def_139,type,
sK43: real > nat > real ).
thf(func_def_140,type,
sK44: nat > nat ).
thf(func_def_141,type,
sK45: int > int ).
thf(func_def_142,type,
sK46: int > int ).
thf(func_def_143,type,
sK47: int > int ).
thf(func_def_144,type,
sK48: int > int ).
thf(func_def_145,type,
sK49: int > int > int ).
thf(func_def_146,type,
sK50: int > int ).
thf(func_def_147,type,
sK51: int > int ).
thf(func_def_148,type,
sK52: int > int ).
thf(func_def_149,type,
sK53: int > int ).
thf(func_def_150,type,
sK54: int > int ).
thf(func_def_151,type,
sK55: int > int ).
thf(func_def_152,type,
sK56: int > int ).
thf(func_def_153,type,
sK57: int > int ).
thf(func_def_154,type,
sK58: int > int > int ).
thf(func_def_155,type,
sK59: int > int > int ).
thf(func_def_156,type,
sK60: int > int ).
thf(func_def_157,type,
sK61: int > int ).
thf(func_def_158,type,
sK62: int > int > int ).
thf(func_def_159,type,
sK63: int > int ).
thf(func_def_160,type,
sK64: int > int ).
thf(func_def_161,type,
sK65: int > int ).
thf(func_def_162,type,
sK66: int > int ).
thf(func_def_163,type,
sK67: int > int ).
thf(func_def_164,type,
sK68: int > int ).
thf(func_def_165,type,
sK69: int > int > int ).
thf(func_def_166,type,
sK70: int > int ).
thf(func_def_167,type,
sK71: int > int ).
thf(func_def_168,type,
sK72: int > int ).
thf(func_def_169,type,
sK73: int > int ).
thf(func_def_170,type,
sK74: int > int > int ).
thf(func_def_171,type,
sK75: int > int > int ).
thf(func_def_172,type,
sK76: int > int ).
thf(func_def_173,type,
sK77: nat > nat ).
thf(func_def_174,type,
sK78: nat > nat > nat ).
thf(func_def_175,type,
sK79: nat > nat > nat ).
thf(func_def_176,type,
sK80: nat > nat ).
thf(func_def_177,type,
sK81: nat > nat > nat ).
thf(func_def_178,type,
sK82: real > real ).
thf(func_def_179,type,
sK83: real > real > real ).
thf(func_def_180,type,
sK84: real > real ).
thf(func_def_181,type,
sK85: real > real > real ).
thf(func_def_182,type,
sK86: real > real ).
thf(func_def_183,type,
sK87: real > real > real ).
thf(func_def_184,type,
sK88: real > real ).
thf(func_def_185,type,
sK89: real > real > real ).
thf(func_def_186,type,
sK90: real > real > real ).
thf(func_def_187,type,
sK91: real > real > real ).
thf(func_def_188,type,
sK92: real > real > real ).
thf(func_def_189,type,
sK93: real > real > real ).
thf(func_def_190,type,
sK94: real > real ).
thf(func_def_191,type,
sK95: real > real ).
thf(func_def_192,type,
sK96: real > real ).
thf(func_def_193,type,
sK97: real > real ).
thf(func_def_194,type,
sK98: real > real > real > real ).
thf(func_def_195,type,
sK99: real > real ).
thf(func_def_196,type,
sK100: real > real > real > real ).
thf(func_def_197,type,
sK101: real > real ).
thf(func_def_198,type,
sK102: real > real > real > real ).
thf(func_def_199,type,
sK103: real > real > real ).
thf(func_def_200,type,
sK104: real > real > real ).
thf(func_def_201,type,
sK105: real > real > real ).
thf(func_def_202,type,
sK106: real > real > real ).
thf(func_def_203,type,
sK107: real > real > real ).
thf(func_def_204,type,
sK108: real > real > real ).
thf(func_def_205,type,
sK109: real > real > real ).
thf(func_def_206,type,
sK110: real > real > real ).
thf(func_def_207,type,
sK111: real > real ).
thf(func_def_208,type,
sK112: real > real ).
thf(func_def_209,type,
sK113: real > real ).
thf(func_def_210,type,
sK114: real > real ).
thf(func_def_211,type,
sK115: real > real ).
thf(func_def_212,type,
sK116: real > real ).
thf(func_def_213,type,
sK117: real > real ).
thf(func_def_214,type,
sK118: real > real ).
thf(func_def_215,type,
sK119: real > real ).
thf(func_def_216,type,
sK120: real > real ).
thf(func_def_217,type,
sK121: real > real ).
thf(func_def_218,type,
sK122: real > real ).
thf(func_def_219,type,
sK123: int > int > int ).
thf(func_def_220,type,
sK124: int > int > int ).
thf(func_def_221,type,
sK125: real > real > real ).
thf(func_def_222,type,
sK126: real > real ).
thf(func_def_223,type,
sK127: real > real ).
thf(func_def_224,type,
sK128: real > real ).
thf(func_def_225,type,
sK129: real > real ).
thf(func_def_226,type,
sK130: real > real > real ).
thf(func_def_227,type,
sK131: real > real > real ).
thf(func_def_228,type,
sK132: real > real ).
thf(func_def_229,type,
sK133: real > real ).
thf(func_def_230,type,
sK134: real > real ).
thf(func_def_231,type,
sK135: real > real ).
thf(func_def_232,type,
sK136: real > real > real ).
thf(func_def_233,type,
sK137: real > real ).
thf(func_def_234,type,
sK138: real > real ).
thf(func_def_235,type,
sK139: real > real ).
thf(func_def_236,type,
sK140: real > real ).
thf(func_def_237,type,
sK141: nat > nat > nat ).
thf(func_def_238,type,
sK142: real > real ).
thf(func_def_239,type,
sK143: real > real ).
thf(func_def_240,type,
sK144: real > real ).
thf(func_def_241,type,
sK145: real > real ).
thf(func_def_242,type,
sK146: real > real ).
thf(func_def_243,type,
sK147: real > real ).
thf(func_def_244,type,
sK148: real > real ).
thf(func_def_245,type,
sK149: real > real ).
thf(func_def_246,type,
sK150: nat > nat > ( nat > $o ) > nat ).
thf(func_def_247,type,
sK151: nat > nat ).
thf(func_def_248,type,
sK152: nat > nat ).
thf(func_def_249,type,
sK153: nat > nat ).
thf(func_def_250,type,
sK154: nat > nat ).
thf(func_def_251,type,
sK155: real > real > real ).
thf(func_def_252,type,
sK156: nat > nat ).
thf(func_def_253,type,
sK157: int > int > int ).
thf(func_def_254,type,
sK158: nat > nat ).
thf(func_def_255,type,
sK159: nat > nat > nat ).
thf(func_def_256,type,
sK160: nat > nat > nat > nat ).
thf(func_def_257,type,
sK161: nat > nat ).
thf(func_def_258,type,
sK162: real > real ).
thf(func_def_259,type,
sK163: int > int ).
thf(func_def_260,type,
sK164: nat > nat ).
thf(func_def_261,type,
sK165: nat > nat > nat ).
thf(func_def_262,type,
sK166: nat > nat > nat ).
thf(func_def_263,type,
sK167: ( nat > nat ) > nat ).
thf(func_def_264,type,
sK168: real > real ).
thf(func_def_265,type,
sK169: real > real ).
thf(func_def_266,type,
sK170: real > real ).
thf(func_def_267,type,
sK171: real > real ).
thf(func_def_268,type,
sK172: real > real ).
thf(func_def_269,type,
sK173: real > real ).
thf(func_def_270,type,
sK174: real > nat ).
thf(func_def_271,type,
sK175: real > real ).
thf(func_def_272,type,
sK176: nat > real > real ).
thf(func_def_273,type,
sK177: nat > real ).
thf(func_def_274,type,
sK178: nat > nat ).
thf(func_def_275,type,
sK179: nat > nat ).
thf(func_def_276,type,
sK180: nat > nat ).
thf(func_def_277,type,
sK181: nat > nat ).
thf(func_def_278,type,
sK182: nat > nat ).
thf(func_def_279,type,
sK183: nat > nat ).
thf(func_def_280,type,
sK184: nat > nat ).
thf(func_def_281,type,
sK185: nat > nat ).
thf(func_def_282,type,
sK186: nat > nat ).
thf(func_def_283,type,
sK187: int ).
thf(func_def_284,type,
sK188: nat > real > real > real ).
thf(func_def_285,type,
sK189: nat > int > int > int ).
thf(func_def_286,type,
sK190: nat > nat > nat > nat ).
thf(func_def_287,type,
sK191: nat > nat ).
thf(func_def_288,type,
sK192: nat > nat ).
thf(func_def_289,type,
sK193: nat > nat ).
thf(func_def_290,type,
sK194: nat > nat ).
thf(func_def_291,type,
sK195: nat > nat ).
thf(func_def_292,type,
sK196: nat > nat ).
thf(func_def_293,type,
sK197: nat > nat > nat > nat ).
thf(func_def_294,type,
sK198: nat > nat > nat > real ).
thf(func_def_295,type,
sK199: nat > nat > nat > nat ).
thf(func_def_296,type,
sK200: nat > nat > nat > int ).
thf(func_def_297,type,
sK201: nat > nat > nat > nat ).
thf(func_def_298,type,
sK202: nat > nat > nat > nat ).
thf(func_def_299,type,
sK203: nat > nat > nat > nat ).
thf(func_def_300,type,
sK204: nat > nat > nat > real ).
thf(func_def_301,type,
sK205: nat > nat > nat > nat ).
thf(func_def_302,type,
sK206: nat > nat > nat > int ).
thf(func_def_303,type,
sK207: nat > nat > nat > nat ).
thf(func_def_304,type,
sK208: nat > nat > nat > nat ).
thf(func_def_305,type,
sK209: nat > nat ).
thf(func_def_306,type,
sK210: nat > nat ).
thf(func_def_307,type,
sK211: nat > nat ).
thf(func_def_308,type,
sK212: nat > nat ).
thf(func_def_309,type,
sK213: nat > nat > nat ).
thf(func_def_310,type,
sK214: real > real ).
thf(func_def_311,type,
sK215: real > real ).
thf(func_def_312,type,
sK216: nat > nat ).
thf(func_def_313,type,
sK217: nat > nat > real ).
thf(func_def_314,type,
sK218: nat > nat ).
thf(func_def_315,type,
sK219: nat > nat > int ).
thf(func_def_316,type,
sK220: nat > nat > nat ).
thf(func_def_317,type,
sK221: nat > nat ).
thf(func_def_318,type,
sK222: int > int ).
thf(func_def_319,type,
sK223: int > int ).
thf(func_def_320,type,
sK224: int > int ).
thf(func_def_321,type,
sK225: int > int ).
thf(func_def_322,type,
sK226: nat > ( nat > $o ) > set_nat > nat ).
thf(func_def_323,type,
sK227: nat > set_nat > ( nat > $o ) > nat ).
thf(func_def_324,type,
sK228: nat > nat > real ).
thf(func_def_325,type,
sK229: nat > nat > int ).
thf(func_def_326,type,
sK230: nat > nat > nat ).
thf(func_def_327,type,
sK231: nat > nat > nat ).
thf(func_def_328,type,
sK232: nat > nat > nat ).
thf(func_def_329,type,
sK233: nat > nat > nat ).
thf(func_def_330,type,
sK234: nat > real ).
thf(func_def_331,type,
sK235: nat > int ).
thf(func_def_332,type,
sK236: nat > nat ).
thf(func_def_333,type,
sK237: nat > nat > nat ).
thf(func_def_334,type,
sK238: nat > nat > real ).
thf(func_def_335,type,
sK239: nat > nat > nat ).
thf(func_def_336,type,
sK240: nat > nat > int ).
thf(func_def_337,type,
sK241: nat > nat > nat ).
thf(func_def_338,type,
sK242: nat > nat > nat ).
thf(func_def_339,type,
sK243: ( nat > $o ) > set_nat > nat > nat ).
thf(func_def_340,type,
sK244: ( nat > $o ) > set_nat > nat > nat ).
thf(func_def_341,type,
sK245: nat > nat ).
thf(func_def_342,type,
sK246: nat > real ).
thf(func_def_343,type,
sK247: nat > nat ).
thf(func_def_344,type,
sK248: nat > int ).
thf(func_def_345,type,
sK249: nat > nat ).
thf(func_def_346,type,
sK250: nat > nat ).
thf(func_def_347,type,
sK251: real ).
thf(func_def_348,type,
sK252: int ).
thf(func_def_349,type,
sK253: nat ).
thf(func_def_350,type,
sK254: real > real ).
thf(func_def_351,type,
sK255: real > real ).
thf(func_def_352,type,
sK256: real > real ).
thf(func_def_353,type,
sK257: real > real ).
thf(func_def_354,type,
sK258: real > real ).
thf(func_def_355,type,
sK259: real > real ).
thf(func_def_356,type,
sK260: nat > nat > nat ).
thf(func_def_357,type,
sK261: nat > ( nat > $o ) > nat ).
thf(func_def_358,type,
sK262: nat > nat ).
thf(func_def_359,type,
sK263: nat > nat ).
thf(func_def_360,type,
sK264: nat > nat ).
thf(func_def_361,type,
sK265: nat > nat ).
thf(func_def_362,type,
sK266: nat > nat > nat ).
thf(func_def_363,type,
sK267: nat > nat > nat ).
thf(func_def_364,type,
sK268: nat > nat ).
thf(func_def_365,type,
sK269: nat > nat ).
thf(func_def_366,type,
sK270: nat > nat ).
thf(func_def_367,type,
sK271: nat > nat ).
thf(func_def_368,type,
sK272: nat > ( nat > $o ) > nat ).
thf(func_def_369,type,
sK273: nat > ( nat > $o ) > nat ).
thf(func_def_370,type,
sK274: nat > nat ).
thf(func_def_371,type,
sK275: nat > nat ).
thf(func_def_372,type,
sK276: nat > nat ).
thf(func_def_373,type,
sK277: nat > nat ).
thf(func_def_374,type,
sK278: nat > nat ).
thf(func_def_375,type,
sK279: nat > nat ).
thf(func_def_376,type,
sK280: nat > nat ).
thf(func_def_377,type,
sK281: nat > nat ).
thf(func_def_378,type,
sK282: nat > nat ).
thf(func_def_379,type,
sK283: nat > nat ).
thf(func_def_380,type,
sK284: nat > nat ).
thf(func_def_381,type,
sK285: list_a > ( list_a > $o ) > nat ).
thf(func_def_382,type,
sK286: list_a > nat ).
thf(func_def_383,type,
sK287: list_list_list_a > nat ).
thf(func_def_384,type,
sK288: list_list_a > nat ).
thf(func_def_385,type,
sK289: nat > list_a > nat ).
thf(func_def_386,type,
sK290: nat > list_list_a > nat ).
thf(f24,axiom,
! [X0: nat] :
( ( gen_length_a @ X0 @ nil_a )
= X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_gen__length__code_I1_J) ).
thf(f60,axiom,
( size_size_list_a
= ( gen_length_a @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_length__code) ).
thf(f103,axiom,
! [X0: list_a,X1: nat] :
( ( listSl1495374126_aux_a @ X0 @ X1 @ zero_zero_nat )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_list__slice__aux_Osimps_I1_J) ).
thf(f142,axiom,
( listSl97544552lice_a
= ( ^ [X0: list_a,X1: nat] : ( listSl1495374126_aux_a @ X0 @ X1 @ ( divide_divide_nat @ ( size_size_list_a @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_list__slice__def) ).
thf(f233,axiom,
! [X0: nat] :
( ( ord_less_eq_nat @ X0 @ zero_zero_nat )
=> ( X0 = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_bot__nat__0_Oextremum__uniqueI) ).
thf(f291,axiom,
! [X0: nat,X1: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ X0 @ X1 ) @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_div__le__dividend) ).
thf(f350,conjecture,
( ( listSl97544552lice_a @ nil_a @ k )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f351,negated_conjecture,
( ( listSl97544552lice_a @ nil_a @ k )
!= nil_list_a ),
inference(negated_conjecture,[status(cth)],[f350]) ).
thf(f491,plain,
( listSl97544552lice_a
= ( ^ [Y0: list_a,Y1: nat] : ( listSl1495374126_aux_a @ Y0 @ Y1 @ ( divide_divide_nat @ ( size_size_list_a @ Y0 ) @ Y1 ) ) ) ),
inference(fool_elimination,[],[f142]) ).
thf(f611,plain,
! [X0: nat] :
( ( ord_less_eq_nat @ X0 @ zero_zero_nat )
=> ( X0 = zero_zero_nat ) ),
inference(rectify,[],[f233]) ).
thf(f612,plain,
! [X0: nat] :
( ( ( ord_less_eq_nat @ X0 @ zero_zero_nat )
= $true )
=> ( zero_zero_nat = X0 ) ),
inference(fool_elimination,[],[f611]) ).
thf(f700,plain,
! [X0: nat,X1: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ X0 @ X1 ) @ X0 ),
inference(rectify,[],[f291]) ).
thf(f701,plain,
! [X0: nat,X1: nat] :
( ( ord_less_eq_nat @ ( divide_divide_nat @ X0 @ X1 ) @ X0 )
= $true ),
inference(fool_elimination,[],[f700]) ).
thf(f828,plain,
( nil_list_a
!= ( listSl97544552lice_a @ nil_a @ k ) ),
inference(flattening,[],[f351]) ).
thf(f912,plain,
! [X0: nat] :
( ( zero_zero_nat = X0 )
| ( ( ord_less_eq_nat @ X0 @ zero_zero_nat )
!= $true ) ),
inference(ennf_transformation,[],[f612]) ).
thf(f1075,plain,
! [X0: nat] :
( ( gen_length_a @ X0 @ nil_a )
= X0 ),
inference(cnf_transformation,[],[f24]) ).
thf(f1111,plain,
( size_size_list_a
= ( gen_length_a @ zero_zero_nat ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f1161,plain,
! [X0: list_a,X1: nat] :
( nil_list_a
= ( listSl1495374126_aux_a @ X0 @ X1 @ zero_zero_nat ) ),
inference(cnf_transformation,[],[f103]) ).
thf(f1208,plain,
( listSl97544552lice_a
= ( ^ [Y0: list_a,Y1: nat] : ( listSl1495374126_aux_a @ Y0 @ Y1 @ ( divide_divide_nat @ ( size_size_list_a @ Y0 ) @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f491]) ).
thf(f1305,plain,
! [X0: nat] :
( ( ( ord_less_eq_nat @ X0 @ zero_zero_nat )
!= $true )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f912]) ).
thf(f1370,plain,
! [X0: nat,X1: nat] :
( ( ord_less_eq_nat @ ( divide_divide_nat @ X0 @ X1 ) @ X0 )
= $true ),
inference(cnf_transformation,[],[f701]) ).
thf(f1438,plain,
( nil_list_a
!= ( listSl97544552lice_a @ nil_a @ k ) ),
inference(cnf_transformation,[],[f828]) ).
thf(f1441,plain,
( listSl97544552lice_a
= ( ^ [Y0: list_a,Y1: nat] : ( listSl1495374126_aux_a @ Y0 @ Y1 @ ( divide_divide_nat @ ( gen_length_a @ zero_zero_nat @ Y0 ) @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f1208,f1111]) ).
thf(f1628,plain,
( nil_list_a
!= ( ^ [Y0: list_a,Y1: nat] : ( listSl1495374126_aux_a @ Y0 @ Y1 @ ( divide_divide_nat @ ( gen_length_a @ zero_zero_nat @ Y0 ) @ Y1 ) )
@ nil_a
@ k ) ),
inference(definition_unfolding,[],[f1438,f1441]) ).
thf(f1642,plain,
( nil_list_a
!= ( listSl1495374126_aux_a @ nil_a @ k @ ( divide_divide_nat @ ( gen_length_a @ zero_zero_nat @ nil_a ) @ k ) ) ),
inference(beta-eta_normalization,[],[f1628]) ).
thf(f5383,plain,
( nil_list_a
!= ( listSl1495374126_aux_a @ nil_a @ k @ ( divide_divide_nat @ zero_zero_nat @ k ) ) ),
inference(constrained_superposition,[],[f1642,f1075]) ).
thf(f5590,plain,
! [X0: nat] :
( ( $true != $true )
| ( zero_zero_nat
= ( divide_divide_nat @ zero_zero_nat @ X0 ) ) ),
inference(constrained_superposition,[],[f1305,f1370]) ).
thf(f5591,plain,
! [X0: nat] :
( zero_zero_nat
= ( divide_divide_nat @ zero_zero_nat @ X0 ) ),
inference(trivial_inequality_removal,[],[f5590]) ).
thf(f7105,plain,
( nil_list_a
!= ( listSl1495374126_aux_a @ nil_a @ k @ zero_zero_nat ) ),
inference(constrained_superposition,[],[f5383,f5591]) ).
thf(f7106,plain,
$false,
inference(forward_subsumption_resolution,[],[f7105,f1161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP105^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n015.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 19:57:34 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.75/0.47 % (4033055)Will run a generic schedule for satisfiability detection.
% 0.75/0.47 % (4033060)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4017218436_2999 on theBenchmark for (2999ds/0Mi)
% 0.75/0.47 % (4033061)% WARNING: option uhcvi not known.
% 0.75/0.47 % (4033061)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=658104474:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.75/0.47 % Exception at run slice level
% 0.75/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.75/0.47 % (4033061)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.75/0.47 % (4033062)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1785896983:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.75/0.47 % (4033069)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3483129397:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.75/0.47 % (4033061)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.75/0.47 % Exception at run slice level
% 0.75/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.75/0.47 % (4033073)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2698690025:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.75/0.47 % (4033064)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3261279514:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.75/0.47 % (4033066)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4029162926:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.75/0.47 % (4033063)dis+10_1_sil=32000:sp=arity:random_seed=3771839685:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.75/0.47 % (4033065)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2641134374:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.75/0.47 % (4033073)Instruction limit reached!
% 0.75/0.47 % (4033073)------------------------------
% 0.75/0.47 % (4033073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.47 % (4033073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.47 % (4033073)CaDiCaL version: 2.1.3
% 0.75/0.47 % (4033073)Termination reason: Instruction limit
% 0.75/0.47 % (4033073)Termination phase: Saturation
% 0.75/0.47 % (4033073)Time elapsed: 0.030 s
% 0.75/0.47 % (4033073)Peak memory usage: 13 MB
% 0.75/0.47 % (4033073)Instructions burned: 132 (million)
% 0.75/0.47 % (4033064)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.75/0.47 % (4033079)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=2805937513:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.75/0.47 % (4033079)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.75/0.47 % (4033079)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.75/0.47 % (4033065)Instruction limit reached!
% 0.75/0.47 % (4033065)------------------------------
% 0.75/0.47 % (4033065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.47 % (4033065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.47 % (4033065)CaDiCaL version: 2.1.3
% 0.75/0.47 % (4033065)Termination reason: Instruction limit
% 0.75/0.47 % (4033065)Termination phase: Saturation
% 0.75/0.47 % (4033065)Time elapsed: 0.064 s
% 0.75/0.47 % (4033065)Peak memory usage: 13 MB
% 0.75/0.47 % (4033065)Instructions burned: 133 (million)
% 0.75/0.47 % (4033081)ott-21_1_sil=16000:fs=off:random_seed=1178769284:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.75/0.47 % (4033064)Instruction limit reached!
% 0.75/0.47 % (4033064)------------------------------
% 0.75/0.47 % (4033064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.47 % (4033064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.47 % (4033064)CaDiCaL version: 2.1.3
% 0.75/0.47 % (4033064)Termination reason: Instruction limit
% 0.75/0.47 % (4033064)Termination phase: Saturation
% 0.75/0.47 % (4033064)Time elapsed: 0.083 s
% 0.75/0.47 % (4033064)Peak memory usage: 13 MB
% 0.75/0.47 % (4033064)Instructions burned: 116 (million)
% 0.75/0.47 % (4033063)Instruction limit reached!
% 0.75/0.47 % (4033063)------------------------------
% 0.75/0.47 % (4033063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.47 % (4033063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.47 % (4033063)CaDiCaL version: 2.1.3
% 0.75/0.47 % (4033063)Termination reason: Instruction limit
% 0.75/0.47 % (4033063)Termination phase: Saturation
% 0.75/0.47 % (4033063)Time elapsed: 0.093 s
% 0.75/0.47 % (4033063)Peak memory usage: 13 MB
% 0.75/0.47 % (4033063)Instructions burned: 107 (million)
% 0.75/0.47 % (4033083)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3163396139:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.75/0.47 % (4033084)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3659353975:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 0.75/0.47 % (4033066)Instruction limit reached!
% 0.75/0.47 % (4033066)------------------------------
% 0.75/0.47 % (4033066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.47 % (4033066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.47 % (4033066)CaDiCaL version: 2.1.3
% 0.75/0.47 % (4033066)Termination reason: Instruction limit
% 0.75/0.47 % (4033066)Termination phase: Saturation
% 0.75/0.47 % (4033066)Time elapsed: 0.129 s
% 0.75/0.47 % (4033066)Peak memory usage: 14 MB
% 0.75/0.47 % (4033066)Instructions burned: 159 (million)
% 0.75/0.47 % (4033061) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4033055-4033061"...
% 0.75/0.47 % (4033061)...printing done.
% 0.75/0.47 % (4033079) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4033055-4033079"...
% 0.75/0.47 % (4033061)Refutation found. Thanks to Tanya!
% 0.75/0.47 % SZS status Theorem for theBenchmark
% 0.75/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.75/0.47 % (4033061)------------------------------
% 0.75/0.47 % (4033061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.47 % (4033061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.47 % (4033061)CaDiCaL version: 2.1.3
% 0.75/0.47 % (4033061)Termination reason: Refutation
% 0.75/0.47 % (4033061)Time elapsed: 0.193 s
% 0.75/0.47 % (4033061)Peak memory usage: 15 MB
% 0.75/0.47 % (4033061)Instructions burned: 394 (million)
% 0.75/0.47 % (4033055)Success in time 0.242 s
% 0.75/0.47 % Vampire exiting
%------------------------------------------------------------------------------