%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU593^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 08:32:35 AM UTC 2026
% Result : Theorem 10.81s 2.03s
% Output : Refutation 13.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 104 ( 58 unt; 0 typ; 6 def)
% Number of atoms : 2279 ( 613 equ; 0 cnn)
% Maximal formula atoms : 111 ( 21 avg)
% Number of connectives : 1516 ( 9 ~; 56 |; 330 &; 569 @)
% ( 0 <=>; 494 =>; 0 <=; 0 <~>)
% Maximal formula depth : 116 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 580 ( 576 usr; 225 con; 0-4 aty)
% ( 58 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 204 ( 121 ^; 79 !; 4 ?; 204 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_128,type,
vAND: $o > $o > $o ).
thf(func_def_129,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_131,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_132,type,
vIMP: $o > $o > $o ).
thf(func_def_133,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_134,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_135,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_136,type,
vIFF: $o > $o > $o ).
thf(func_def_137,type,
vNOT: $o > $o ).
thf(func_def_138,type,
vOR: $o > $o > $o ).
thf(func_def_139,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_140,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_143,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_146,type,
sF2: $o ).
thf(func_def_147,type,
sF3: $o ).
thf(func_def_148,type,
sF4: $o ).
thf(func_def_149,type,
sF5: $o ).
thf(func_def_150,type,
sF6: $o ).
thf(func_def_151,type,
sF7: $o ).
thf(func_def_152,type,
sF8: $o ).
thf(func_def_153,type,
sF9: $o ).
thf(func_def_154,type,
sF10: $o ).
thf(func_def_155,type,
sF11: $o ).
thf(func_def_156,type,
sF12: $o ).
thf(func_def_157,type,
sF13: $o ).
thf(func_def_158,type,
sF14: $o ).
thf(func_def_159,type,
sF15: $o ).
thf(func_def_160,type,
sF16: $o ).
thf(func_def_161,type,
sF17: $o ).
thf(func_def_162,type,
sF18: $o ).
thf(func_def_163,type,
sF19: $o ).
thf(func_def_164,type,
sF20: $o ).
thf(func_def_165,type,
sF21: $o ).
thf(func_def_166,type,
sF22: $o ).
thf(func_def_167,type,
sF23: $o ).
thf(func_def_168,type,
sF24: $o ).
thf(func_def_169,type,
sF25: $o ).
thf(func_def_170,type,
sF26: $o ).
thf(func_def_171,type,
sF27: $o ).
thf(func_def_172,type,
sF28: $o ).
thf(func_def_173,type,
sF29: $o ).
thf(func_def_175,type,
sF31: $o ).
thf(func_def_176,type,
sF32: $o ).
thf(func_def_177,type,
sF33: $o ).
thf(func_def_178,type,
sF34: $o ).
thf(func_def_179,type,
sF35: $o ).
thf(func_def_180,type,
sF36: $o ).
thf(func_def_181,type,
sF37: $o ).
thf(func_def_182,type,
sF38: $o ).
thf(func_def_183,type,
sF39: $o ).
thf(func_def_184,type,
sF40: $o ).
thf(func_def_185,type,
sF41: $o ).
thf(func_def_186,type,
sF42: $o ).
thf(func_def_187,type,
sF43: $o ).
thf(func_def_188,type,
sF44: $o ).
thf(func_def_189,type,
sF45: $o ).
thf(func_def_190,type,
sF46: $o ).
thf(func_def_191,type,
sF47: $o ).
thf(func_def_192,type,
sF48: $o ).
thf(func_def_193,type,
sF49: $o ).
thf(func_def_194,type,
sF50: $o ).
thf(func_def_195,type,
sF51: $o ).
thf(func_def_196,type,
sF52: $o ).
thf(func_def_197,type,
sF53: $o ).
thf(func_def_198,type,
sF54: $o ).
thf(func_def_199,type,
sF55: $o ).
thf(func_def_200,type,
sF56: $o ).
thf(func_def_201,type,
sF57: $o ).
thf(func_def_202,type,
sF58: $o ).
thf(func_def_203,type,
sF59: $o ).
thf(func_def_204,type,
sF60: $o ).
thf(func_def_205,type,
sF61: $o ).
thf(func_def_206,type,
sF62: $o ).
thf(func_def_207,type,
sF63: $o ).
thf(func_def_208,type,
sF64: $o ).
thf(func_def_209,type,
sF65: $o ).
thf(func_def_210,type,
sF66: $o ).
thf(func_def_211,type,
sF67: $o ).
thf(func_def_212,type,
sF68: $o ).
thf(func_def_213,type,
sF69: $o ).
thf(func_def_214,type,
sF70: $o ).
thf(func_def_215,type,
sF71: $o ).
thf(func_def_216,type,
sF72: $o ).
thf(func_def_217,type,
sF73: $o ).
thf(func_def_218,type,
sF74: $o ).
thf(func_def_219,type,
sF75: $o ).
thf(func_def_220,type,
sF76: $o ).
thf(func_def_221,type,
sF77: $o ).
thf(func_def_222,type,
sF78: $o ).
thf(func_def_223,type,
sF79: $o ).
thf(func_def_224,type,
sF80: $o ).
thf(func_def_225,type,
sF81: $o ).
thf(func_def_226,type,
sF82: $o ).
thf(func_def_227,type,
sF83: $o ).
thf(func_def_228,type,
sF84: $o ).
thf(func_def_229,type,
sF85: $o ).
thf(func_def_230,type,
sF86: $o ).
thf(func_def_231,type,
sF87: $o ).
thf(func_def_232,type,
sF88: $o ).
thf(func_def_233,type,
sF89: $o ).
thf(func_def_234,type,
sF90: $o ).
thf(func_def_235,type,
sF91: $o ).
thf(func_def_236,type,
sF92: $o ).
thf(func_def_237,type,
sF93: $o ).
thf(func_def_238,type,
sF94: $o ).
thf(func_def_239,type,
sF95: $o ).
thf(func_def_240,type,
sF96: $o ).
thf(func_def_241,type,
sF97: $o ).
thf(func_def_242,type,
sF98: $o ).
thf(func_def_243,type,
sF99: $o ).
thf(func_def_244,type,
sF100: $o ).
thf(func_def_245,type,
sF101: $o ).
thf(func_def_246,type,
sF102: $o ).
thf(func_def_247,type,
sF103: $o ).
thf(func_def_248,type,
sF104: $o ).
thf(func_def_250,type,
sF106: $o ).
thf(func_def_253,type,
sK109: $i > $i > $i ).
thf(func_def_261,type,
sK117: $i > $i > $i ).
thf(func_def_265,type,
sK121: $i > $i > $i ).
thf(func_def_269,type,
sK125: $i > $i ).
thf(func_def_271,type,
sK127: $i > $i > $o ).
thf(func_def_272,type,
sK128: $i > $i ).
thf(func_def_273,type,
sK129: $i > $i ).
thf(func_def_274,type,
sK130: $i > $i ).
thf(func_def_275,type,
sK131: $i > ( $i > $i > $o ) > $i ).
thf(func_def_276,type,
sK132: $i > ( $i > $i > $o ) > $i ).
thf(func_def_277,type,
sK133: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_278,type,
sK134: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_279,type,
sK135: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_280,type,
sK136: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_283,type,
sK139: $i > $i ).
thf(func_def_284,type,
sK140: $i > $i ).
thf(func_def_286,type,
sK142: $i > $i ).
thf(func_def_287,type,
sK143: $i > $i ).
thf(func_def_288,type,
sK144: $i > $i ).
thf(func_def_289,type,
sK145: $i > $i ).
thf(func_def_290,type,
sK146: $i > $i ).
thf(func_def_291,type,
sK147: $i > $i ).
thf(func_def_292,type,
sK148: $i > $i ).
thf(func_def_293,type,
sK149: $i > $i ).
thf(func_def_294,type,
sK150: $i > $i ).
thf(func_def_295,type,
sK151: $i > $i ).
thf(func_def_296,type,
sK152: $i > $i ).
thf(func_def_297,type,
sK153: $i > $i ).
thf(func_def_298,type,
sK154: $i > $i ).
thf(func_def_299,type,
sK155: $i > $i ).
thf(func_def_300,type,
sK156: $i > $i ).
thf(func_def_301,type,
sK157: $i > $i ).
thf(func_def_302,type,
sK158: $i > $i ).
thf(func_def_303,type,
sK159: $i > $i ).
thf(func_def_304,type,
sK160: $i > $i ).
thf(func_def_305,type,
sK161: $i > $i ).
thf(func_def_306,type,
sK162: $i > $i ).
thf(func_def_307,type,
sK163: $i > $i > $i > $i ).
thf(func_def_308,type,
sK164: $i > $i > $i ).
thf(func_def_309,type,
sK165: $i > $i > $i > $i ).
thf(func_def_310,type,
sK166: $i > $i > $i > $i ).
thf(func_def_311,type,
sK167: $i > $i > $i ).
thf(func_def_312,type,
sK168: $i > $i > $i > $i ).
thf(func_def_313,type,
sK169: $i > $i > $i > $i ).
thf(func_def_314,type,
sK170: $i > $i > $i ).
thf(func_def_315,type,
sK171: $i > $i > $i > $i ).
thf(func_def_316,type,
sK172: $i > $i > $i > $i ).
thf(func_def_317,type,
sK173: $i > $i > $i ).
thf(func_def_318,type,
sK174: $i > $i > $i > $i ).
thf(func_def_319,type,
sK175: $i > $i > $i > $i ).
thf(func_def_320,type,
sK176: $i > $i > $i ).
thf(func_def_321,type,
sK177: $i > $i > $i > $i ).
thf(func_def_322,type,
sK178: $i > $i > $i > $i ).
thf(func_def_323,type,
sK179: $i > $i > $i ).
thf(func_def_324,type,
sK180: $i > $i > $i > $i ).
thf(func_def_325,type,
sK181: $i > $i > $i > $i ).
thf(func_def_326,type,
sK182: $i > $i > $i ).
thf(func_def_327,type,
sK183: $i > $i > $i > $i ).
thf(func_def_328,type,
sK184: $i > $i > $i > $i ).
thf(func_def_329,type,
sK185: $i > $i > $i ).
thf(func_def_330,type,
sK186: $i > $i > $i > $i ).
thf(func_def_331,type,
sK187: $i > $i ).
thf(func_def_332,type,
sK188: $i > $i > $i > $i ).
thf(func_def_333,type,
sK189: $i > $i > $i ).
thf(func_def_334,type,
sK190: $i > $i > $i > $i ).
thf(func_def_335,type,
sK191: $i > $i > $i ).
thf(func_def_336,type,
sK192: $i > $i > $i > $i ).
thf(func_def_337,type,
sK193: $i > $i > $i > $i ).
thf(func_def_338,type,
sK194: $i > $i > $i ).
thf(func_def_339,type,
sK195: $i > $i > $i > $i ).
thf(func_def_340,type,
sK196: $i > $i > $i ).
thf(func_def_341,type,
sK197: $i > $i > $i > $i ).
thf(func_def_342,type,
sK198: $i > $i > $i > $i ).
thf(func_def_343,type,
sK199: $i > $i > $i ).
thf(func_def_344,type,
sK200: $i > $i > $i > $i ).
thf(func_def_345,type,
sK201: $i > $i > $i ).
thf(func_def_346,type,
sK202: $i > $i > $i > $i ).
thf(func_def_347,type,
sK203: $i > $i > $i > $i ).
thf(func_def_348,type,
sK204: $i > $i > $i ).
thf(func_def_349,type,
sK205: $i > $i > $i > $i ).
thf(func_def_350,type,
sK206: $i > $i > $i ).
thf(func_def_351,type,
sK207: $i > $i > $i > $i ).
thf(func_def_352,type,
sK208: $i > $i ).
thf(func_def_353,type,
sK209: $i > $i > $i > $i ).
thf(func_def_354,type,
sK210: $i > $i > $i ).
thf(func_def_355,type,
sK211: $i > $i > $i > $i ).
thf(func_def_356,type,
sK212: $i > $i > $i ).
thf(func_def_357,type,
sK213: $i > $i > $i > $i ).
thf(func_def_358,type,
sK214: $i > $i > $i > $i ).
thf(func_def_359,type,
sK215: $i > $i > $i ).
thf(func_def_360,type,
sK216: $i > $i > $i > $i ).
thf(func_def_361,type,
sK217: $i > $i > $i ).
thf(func_def_362,type,
sK218: $i > $i > $i > $i ).
thf(func_def_363,type,
sK219: $i > $i > $i > $i ).
thf(func_def_364,type,
sK220: $i > $i > $i ).
thf(func_def_365,type,
sK221: $i > $i > $i > $i ).
thf(func_def_366,type,
sK222: $i > $i > $i ).
thf(func_def_367,type,
sK223: $i > $i > $i > $i ).
thf(func_def_368,type,
sK224: $i > $i > $i > $i ).
thf(func_def_369,type,
sK225: $i > $i > $i ).
thf(func_def_370,type,
sK226: $i > $i > $i > $i ).
thf(func_def_371,type,
sK227: $i > $i > $i ).
thf(func_def_372,type,
sK228: $i > $i > $i > $i ).
thf(func_def_373,type,
sK229: $i > $i ).
thf(func_def_374,type,
sK230: $i > $i > $i > $i ).
thf(func_def_375,type,
sK231: $i > $i > $i ).
thf(func_def_376,type,
sK232: $i > $i > $i > $i ).
thf(func_def_377,type,
sK233: $i > $i > $i > $i ).
thf(func_def_378,type,
sK234: $i > $i > $i ).
thf(func_def_379,type,
sK235: $i > $i > $i > $i ).
thf(func_def_380,type,
sK236: $i > $i > $i > $i ).
thf(func_def_381,type,
sK237: $i > $i > $i ).
thf(func_def_382,type,
sK238: $i > $i > $i > $i ).
thf(func_def_383,type,
sK239: $i > $i > $i > $i ).
thf(func_def_384,type,
sK240: $i > $i > $i ).
thf(func_def_385,type,
sK241: $i > $i > $i > $i ).
thf(func_def_386,type,
sK242: $i > $i > $i > $i ).
thf(func_def_387,type,
sK243: $i > $i > $i ).
thf(func_def_388,type,
sK244: $i > $i > $i > $i ).
thf(func_def_389,type,
sK245: $i > $i > $i > $i ).
thf(func_def_390,type,
sK246: $i > $i > $i ).
thf(func_def_391,type,
sK247: $i > $i > $i > $i ).
thf(func_def_392,type,
sK248: $i > $i > $i > $i ).
thf(func_def_393,type,
sK249: $i > $i > $i ).
thf(func_def_394,type,
sK250: $i > $i > $i > $i ).
thf(func_def_395,type,
sK251: $i > $i > $i > $i ).
thf(func_def_396,type,
sK252: $i > $i > $i ).
thf(func_def_397,type,
sK253: $i > $i > $i > $i ).
thf(func_def_398,type,
sK254: $i > $i > $i > $i ).
thf(func_def_399,type,
sK255: $i > $i > $i ).
thf(func_def_400,type,
sK256: $i > $i > $i > $i ).
thf(func_def_401,type,
sK257: $i > $i > $i > $i ).
thf(func_def_402,type,
sK258: $i > $i > $i ).
thf(func_def_403,type,
sK259: $i > $i > $i > $i ).
thf(func_def_404,type,
sK260: $i > $i > $i > $i ).
thf(func_def_405,type,
sK261: $i > $i > $i ).
thf(func_def_406,type,
sK262: $i > $i > $i > $i ).
thf(func_def_407,type,
sK263: $i > $i > $i > $i ).
thf(func_def_408,type,
sK264: $i > $i > $i ).
thf(func_def_409,type,
sK265: $i > $i > $i > $i ).
thf(func_def_410,type,
sK266: $i > $i > $i > $i ).
thf(func_def_411,type,
sK267: $i > $i > $i ).
thf(func_def_412,type,
sK268: $i > $i > $i > $i ).
thf(func_def_413,type,
sK269: $i > $i > $i > $i ).
thf(func_def_414,type,
sK270: $i > $i > $i ).
thf(func_def_415,type,
sK271: $i > $i > $i > $i ).
thf(func_def_416,type,
sK272: $i > $i > $i > $i ).
thf(func_def_417,type,
sK273: $i > $i > $i ).
thf(func_def_418,type,
sK274: $i > $i > $i > $i ).
thf(func_def_419,type,
sK275: $i > $i > $i > $i ).
thf(func_def_420,type,
sK276: $i > $i > $i ).
thf(func_def_421,type,
sK277: $i > $i > $i > $i ).
thf(func_def_422,type,
sK278: $i > $i ).
thf(func_def_423,type,
sK279: $i > $i > $i > $i ).
thf(func_def_424,type,
sK280: $i > $i > $i ).
thf(func_def_425,type,
sK281: $i > $i > $i > $i ).
thf(func_def_426,type,
sK282: $i > $i > $i ).
thf(func_def_427,type,
sK283: $i > $i > $i > $i ).
thf(func_def_428,type,
sK284: $i > $i > $i > $i ).
thf(func_def_429,type,
sK285: $i > $i > $i ).
thf(func_def_430,type,
sK286: $i > $i > $i > $i ).
thf(func_def_431,type,
sK287: $i > $i > $i ).
thf(func_def_432,type,
sK288: $i > $i > $i > $i ).
thf(func_def_433,type,
sK289: $i > $i > $i > $i ).
thf(func_def_434,type,
sK290: $i > $i > $i ).
thf(func_def_435,type,
sK291: $i > $i > $i > $i ).
thf(func_def_436,type,
sK292: $i > $i > $i ).
thf(func_def_437,type,
sK293: $i > $i > $i > $i ).
thf(func_def_438,type,
sK294: $i > $i > $i > $i ).
thf(func_def_439,type,
sK295: $i > $i > $i ).
thf(func_def_440,type,
sK296: $i > $i > $i > $i ).
thf(func_def_441,type,
sK297: $i > $i > $i ).
thf(func_def_442,type,
sK298: $i > $i > $i > $i ).
thf(func_def_443,type,
sK299: $i > $i > $i > $i ).
thf(func_def_444,type,
sK300: $i > $i > $i ).
thf(func_def_445,type,
sK301: $i > $i > $i > $i ).
thf(func_def_446,type,
sK302: $i > $i > $i ).
thf(func_def_447,type,
sK303: $i > $i > $i > $i ).
thf(func_def_448,type,
sK304: $i > $i > $i > $i ).
thf(func_def_449,type,
sK305: $i > $i > $i ).
thf(func_def_450,type,
sK306: $i > $i > $i > $i ).
thf(func_def_451,type,
sK307: $i > $i > $i ).
thf(func_def_452,type,
sK308: $i > $i > $i > $i ).
thf(func_def_453,type,
sK309: $i > $i > $i > $i ).
thf(func_def_454,type,
sK310: $i > $i > $i ).
thf(func_def_455,type,
sK311: $i > $i > $i > $i ).
thf(func_def_456,type,
sK312: $i > $i > $i ).
thf(func_def_457,type,
sK313: $i > $i > $i > $i ).
thf(func_def_458,type,
sK314: $i > $i > $i > $i ).
thf(func_def_459,type,
sK315: $i > $i > $i ).
thf(func_def_460,type,
sK316: $i > $i > $i > $i ).
thf(func_def_461,type,
sK317: $i > $i > $i ).
thf(func_def_462,type,
sK318: $i > $i > $i > $i ).
thf(func_def_463,type,
sK319: $i > $i ).
thf(func_def_464,type,
sK320: $i > $i > $i > $i ).
thf(func_def_465,type,
sK321: $i > $i > $i ).
thf(func_def_466,type,
sK322: $i > $i > $i > $i ).
thf(func_def_467,type,
sK323: $i > $i > $i ).
thf(func_def_468,type,
sK324: $i > $i > $i > $i ).
thf(func_def_469,type,
sK325: $i > $i > $i > $i ).
thf(func_def_470,type,
sK326: $i > $i > $i ).
thf(func_def_471,type,
sK327: $i > $i > $i > $i ).
thf(func_def_472,type,
sK328: $i > $i > $i ).
thf(func_def_473,type,
sK329: $i > $i > $i > $i ).
thf(func_def_474,type,
sK330: $i > $i > $i > $i ).
thf(func_def_475,type,
sK331: $i > $i > $i ).
thf(func_def_476,type,
sK332: $i > $i > $i > $i ).
thf(func_def_477,type,
sK333: $i > $i > $i ).
thf(func_def_478,type,
sK334: $i > $i > $i > $i ).
thf(func_def_479,type,
sK335: $i > $i > $i > $i ).
thf(func_def_480,type,
sK336: $i > $i > $i ).
thf(func_def_481,type,
sK337: $i > $i > $i > $i ).
thf(func_def_482,type,
sK338: $i > $i > $i ).
thf(func_def_483,type,
sK339: $i > $i > $i > $i ).
thf(func_def_484,type,
sK340: $i > $i > $i > $i ).
thf(func_def_485,type,
sK341: $i > $i > $i ).
thf(func_def_486,type,
sK342: $i > $i > $i > $i ).
thf(func_def_487,type,
sK343: $i > $i > $i ).
thf(func_def_488,type,
sK344: $i > $i > $i > $i ).
thf(func_def_489,type,
sK345: $i > $i > $i > $i ).
thf(func_def_490,type,
sK346: $i > $i > $i ).
thf(func_def_491,type,
sK347: $i > $i > $i > $i ).
thf(func_def_492,type,
sK348: $i > $i > $i ).
thf(func_def_493,type,
sK349: $i > $i > $i > $i ).
thf(func_def_494,type,
sK350: $i > $i > $i > $i ).
thf(func_def_495,type,
sK351: $i > $i > $i ).
thf(func_def_496,type,
sK352: $i > $i > $i > $i ).
thf(func_def_497,type,
sK353: $i > $i > $i ).
thf(func_def_498,type,
sK354: $i > $i > $i > $i ).
thf(func_def_499,type,
sK355: $i > $i > $i > $i ).
thf(func_def_500,type,
sK356: $i > $i > $i ).
thf(func_def_501,type,
sK357: $i > $i > $i > $i ).
thf(func_def_502,type,
sK358: $i > $i > $i ).
thf(func_def_503,type,
sK359: $i > $i > $i > $i ).
thf(func_def_504,type,
sK360: $i > $i ).
thf(func_def_505,type,
sK361: $i > $i > $i > $i ).
thf(func_def_506,type,
sK362: $i > $i > $i ).
thf(func_def_507,type,
sK363: $i > $i > $i ).
thf(func_def_508,type,
sK364: $i > $i > $i ).
thf(func_def_509,type,
sK365: $i > $o ).
thf(func_def_511,type,
sK367: ( $i > $o ) > $i > $i ).
thf(func_def_513,type,
sK369: $i > $o ).
thf(func_def_516,type,
sK372: $i > $o ).
thf(func_def_519,type,
sK375: $i > $o ).
thf(func_def_521,type,
sK377: $i > $o ).
thf(func_def_523,type,
sK379: $i > $i ).
thf(func_def_524,type,
sK380: ( $i > $o ) > $i ).
thf(func_def_525,type,
sK381: ( $i > $o ) > $i > $i ).
thf(func_def_527,type,
sK383: $o ).
thf(func_def_528,type,
sK384: $o ).
thf(func_def_531,type,
sK387: $i > $o ).
thf(func_def_533,type,
sK389: ( $i > $o ) > $i ).
thf(func_def_534,type,
sK390: ( $i > $o ) > $i > $i ).
thf(func_def_537,type,
sK393: $i > $i > $i ).
thf(func_def_538,type,
sK394: $i > $i > $i ).
thf(func_def_540,type,
sK396: $i > $i ).
thf(func_def_542,type,
sK398: $i > $o ).
thf(func_def_545,type,
sK401: $i > $i ).
thf(func_def_547,type,
sK403: $i > $o ).
thf(func_def_559,type,
sK415: $o ).
thf(func_def_566,type,
sK422: $i > $i > $i ).
thf(func_def_576,type,
sK432: $o ).
thf(func_def_577,type,
sK433: $o > $i > $i > $i ).
thf(func_def_580,type,
sK436: $i > $o ).
thf(func_def_582,type,
sK438: $i > $i ).
thf(func_def_583,type,
sK439: ( $i > $o ) > $i ).
thf(func_def_584,type,
sK440: ( $i > $o ) > $i > $i ).
thf(func_def_586,type,
sK442: $i > $i ).
thf(func_def_602,type,
sK458: $i > $o ).
thf(func_def_606,type,
sK462: $i > $o ).
thf(func_def_607,type,
sK463: $i > $o ).
thf(func_def_610,type,
sK466: ( $i > $o ) > $i > $i ).
thf(func_def_611,type,
sK467: $i > $o ).
thf(func_def_614,type,
sK470: ( $i > $o ) > $i > $i ).
thf(func_def_615,type,
sK471: $i > $o ).
thf(func_def_618,type,
sK474: ( $i > $o ) > $i > $i ).
thf(func_def_619,type,
sK475: $i > $o ).
thf(func_def_622,type,
sK478: ( $i > $o ) > $i > $i ).
thf(func_def_623,type,
sK479: $o ).
thf(func_def_624,type,
sK480: $o ).
thf(func_def_625,type,
sK481: $i > $o ).
thf(func_def_627,type,
sK483: $i > $i ).
thf(func_def_628,type,
sK484: ( $i > $o ) > $i ).
thf(func_def_629,type,
sK485: ( $i > $o ) > $i > $i ).
thf(func_def_630,type,
sK486: $i > $o ).
thf(func_def_632,type,
sK488: $i > $i ).
thf(func_def_633,type,
sK489: ( $i > $o ) > $i ).
thf(func_def_634,type,
sK490: ( $i > $o ) > $i ).
thf(func_def_635,type,
sK491: ( $i > $o ) > $i ).
thf(func_def_636,type,
sK492: $i > $o ).
thf(func_def_638,type,
sK494: $i > $i ).
thf(func_def_639,type,
sK495: ( $i > $o ) > $i ).
thf(func_def_640,type,
sK496: ( $i > $o ) > $i > $i ).
thf(func_def_649,type,
sK505: $i > $o ).
thf(func_def_653,type,
sK509: ( $i > $o ) > $i > $i ).
thf(func_def_654,type,
sK510: $i > $o ).
thf(func_def_655,type,
sK511: $i > $o ).
thf(func_def_656,type,
sK512: $i > $i ).
thf(func_def_657,type,
sK513: $i > $i ).
thf(func_def_660,type,
sK516: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_661,type,
sK517: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_662,type,
sK518: ( $i > $o ) > $i ).
thf(func_def_663,type,
sK519: $i > ( $i > $o ) > $i ).
thf(func_def_664,type,
sK520: ( $i > $o ) > $i ).
thf(func_def_665,type,
sK521: $i > ( $i > $o ) > $i ).
thf(func_def_666,type,
sK522: $i > ( $i > $o ) > $i ).
thf(func_def_667,type,
sK523: ( $i > $o ) > $i ).
thf(func_def_668,type,
sK524: $i > ( $i > $o ) > $i ).
thf(func_def_669,type,
sK525: ( $i > $o ) > $i ).
thf(func_def_670,type,
sK526: $i > ( $i > $o ) > $i ).
thf(func_def_671,type,
sK527: $i > ( $i > $o ) > $i ).
thf(func_def_672,type,
sK528: ( $i > $o ) > $i ).
thf(func_def_673,type,
sK529: $i > ( $i > $o ) > $i ).
thf(func_def_674,type,
sK530: ( $i > $o ) > $i ).
thf(func_def_675,type,
sK531: $i > ( $i > $o ) > $i ).
thf(func_def_676,type,
sK532: $i > ( $i > $o ) > $i ).
thf(func_def_685,type,
sK541: $i > $o ).
thf(func_def_686,type,
sK542: $i > $o ).
thf(func_def_689,type,
sK545: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_690,type,
sK546: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_691,type,
sK547: $i > ( $i > $o ) > $i ).
thf(func_def_692,type,
sK548: ( $i > $o ) > $i > $i ).
thf(func_def_695,type,
sK551: $i > $o ).
thf(func_def_696,type,
sK552: $i > $o ).
thf(func_def_697,type,
sK553: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_698,type,
sK554: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_701,type,
sK557: $i > $i > $i ).
thf(func_def_742,type,
sK598: $i > $o ).
thf(func_def_744,type,
sK600: $i > $o ).
thf(func_def_752,type,
sK608: $o ).
thf(f88,axiom,
( subsetRefl
= ( ! [X0: $i] : ( subset @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(f93,axiom,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(f100,axiom,
( sepSubset
= ( ! [X0: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
thf(f108,axiom,
( binintersect
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersect) ).
thf(f110,axiom,
( binintersectSubset5
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X2 @ X0 )
=> ( ( subset @ X2 @ X1 )
=> ( subset @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(f113,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(f114,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f113]) ).
thf(f279,plain,
( subsetRefl
= ( ! [X0: $i] : ( subset @ X0 @ X0 ) ) ),
inference(rectify,[],[f88]) ).
thf(f280,plain,
( subsetRefl
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ Y0 @ Y0 ) ) ),
inference(fool_elimination,[],[f279]) ).
thf(f289,plain,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[],[f93]) ).
thf(f290,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f289]) ).
thf(f303,plain,
( sepSubset
= ( ! [X0: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 ) ) ),
inference(rectify,[],[f100]) ).
thf(f304,plain,
( sepSubset
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ Y1 ) ) ) ),
inference(fool_elimination,[],[f303]) ).
thf(f319,plain,
( binintersect
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f108]) ).
thf(f320,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f319]) ).
thf(f323,plain,
( binintersectSubset5
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X2 @ X0 )
=> ( ( subset @ X2 @ X1 )
=> ( subset @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f110]) ).
thf(f324,plain,
( binintersectSubset5
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( subset @ Y0 @ Y1 )
=> ( subset @ Y0 @ ( binintersect @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f323]) ).
thf(f329,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f114]) ).
thf(f330,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f329]) ).
thf(f331,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X0 )
& ( ( subset @ X0 @ X1 )
= $true ) )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f330]) ).
thf(f332,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X0 )
& ( ( subset @ X0 @ X1 )
= $true ) )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(flattening,[],[f331]) ).
thf(f333,plain,
( ( sK0
!= ( binintersect @ sK0 @ sK1 ) )
& ( $true
= ( subset @ sK0 @ sK1 ) )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f332]) ).
thf(f421,plain,
( subsetRefl
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ Y0 @ Y0 ) ) ),
inference(cnf_transformation,[],[f280]) ).
thf(f426,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f290]) ).
thf(f433,plain,
( sepSubset
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ Y1 ) ) ) ),
inference(cnf_transformation,[],[f304]) ).
thf(f441,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f320]) ).
thf(f443,plain,
( binintersectSubset5
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( subset @ Y0 @ Y1 )
=> ( subset @ Y0 @ ( binintersect @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f324]) ).
thf(f531,plain,
subsetRefl = $true,
inference(cnf_transformation,[],[f333]) ).
thf(f536,plain,
setextsub = $true,
inference(cnf_transformation,[],[f333]) ).
thf(f543,plain,
sepSubset = $true,
inference(cnf_transformation,[],[f333]) ).
thf(f552,plain,
binintersectSubset5 = $true,
inference(cnf_transformation,[],[f333]) ).
thf(f555,plain,
( $true
= ( subset @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f333]) ).
thf(f556,plain,
( sK0
!= ( binintersect @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f333]) ).
thf(f644,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ Y0 @ Y0 ) ) ),
inference(definition_unfolding,[],[f421,f531]) ).
thf(f649,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f426,f536]) ).
thf(f656,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f433,f543]) ).
thf(f665,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( subset @ Y0 @ Y1 )
=> ( subset @ Y0
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f443,f552,f441]) ).
thf(f668,plain,
( sK0
!= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f556,f441]) ).
thf(f914,definition,
( sF82
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ Y0 @ Y0 ) ) ),
introduced(definition,[new_symbols(definition,[sF82])],[function_definition]) ).
thf(f915,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( subset @ Y0 @ Y0 ) )
= sF82 ),
inference(reorient_equations,[],[f914]) ).
thf(f916,plain,
$true = sF82,
inference(definition_folding,[],[f644,f915]) ).
thf(f929,definition,
( sF87
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF87])],[function_definition]) ).
thf(f930,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) )
= sF87 ),
inference(reorient_equations,[],[f929]) ).
thf(f931,plain,
$true = sF87,
inference(definition_folding,[],[f649,f930]) ).
thf(f950,definition,
( sF94
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ Y1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sF94])],[function_definition]) ).
thf(f951,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ Y1 ) ) )
= sF94 ),
inference(reorient_equations,[],[f950]) ).
thf(f952,plain,
$true = sF94,
inference(definition_folding,[],[f656,f951]) ).
thf(f975,definition,
( sF102
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( subset @ Y0 @ Y1 )
=> ( subset @ Y0
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF102])],[function_definition]) ).
thf(f976,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( subset @ Y0 @ Y1 )
=> ( subset @ Y0
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ) )
= sF102 ),
inference(reorient_equations,[],[f975]) ).
thf(f977,plain,
$true = sF102,
inference(definition_folding,[],[f665,f976]) ).
thf(f984,definition,
( sF105
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK0
@ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF105])],[function_definition]) ).
thf(f985,plain,
( ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK0
@ sK1 )
= sF105 ),
inference(reorient_equations,[],[f984]) ).
thf(f986,plain,
sK0 != sF105,
inference(definition_folding,[],[f668,f985]) ).
thf(f987,definition,
( sF106
= ( subset @ sK0 @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF106])],[function_definition]) ).
thf(f988,plain,
( ( subset @ sK0 @ sK1 )
= sF106 ),
inference(reorient_equations,[],[f987]) ).
thf(f989,plain,
$true = sF106,
inference(definition_folding,[],[f555,f988]) ).
thf(f5989,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ Y0 @ Y0 ) ) )
| ( $false = sF82 ) ),
inference(iff_proxy_clausification,[],[f915]) ).
thf(f5993,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] : ( subset @ Y0 @ Y0 )
@ X1 ) )
| ( $false = sF82 ) ),
inference(pi_proxy_clausification,[],[f5989]) ).
thf(f5994,plain,
! [X1: $i] :
( ( $true
= ( subset @ X1 @ X1 ) )
| ( $false = sF82 ) ),
inference(beta-eta_normalization,[],[f5993]) ).
thf(f6055,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) )
| ( $false = sF87 ) ),
inference(iff_proxy_clausification,[],[f930]) ).
thf(f6066,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) )
@ X1 ) )
| ( $false = sF87 ) ),
inference(pi_proxy_clausification,[],[f6055]) ).
thf(f6067,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) ) ) )
| ( $false = sF87 ) ),
inference(beta-eta_normalization,[],[f6066]) ).
thf(f6068,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) )
@ X2 ) )
| ( $false = sF87 ) ),
inference(pi_proxy_clausification,[],[f6067]) ).
thf(f6069,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( subset @ X2 @ X1 )
=> ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) ) ) )
| ( $false = sF87 ) ),
inference(beta-eta_normalization,[],[f6068]) ).
thf(f6070,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $false )
| ( $false = sF87 )
| ( $true
= ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f6069]) ).
thf(f6071,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $false )
| ( $false = sF87 )
| ( ( subset @ X1 @ X2 )
= $false )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f6070]) ).
thf(f6072,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $false )
| ( $false = sF87 )
| ( ( subset @ X1 @ X2 )
= $false )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f6071]) ).
thf(f6139,plain,
( ( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ Y1 ) ) ) )
| ( $false = sF94 ) ),
inference(iff_proxy_clausification,[],[f951]) ).
thf(f6145,plain,
! [X1: $i > $o] :
( ( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ Y1 ) )
@ X1 ) )
| ( $false = sF94 ) ),
inference(pi_proxy_clausification,[],[f6139]) ).
thf(f6146,plain,
! [X1: $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ ( dsetconstr @ Y0 @ X1 ) @ Y0 ) ) )
| ( $false = sF94 ) ),
inference(beta-eta_normalization,[],[f6145]) ).
thf(f6147,plain,
! [X2: $i,X1: $i > $o] :
( ( $true
= ( ^ [Y0: $i] : ( subset @ ( dsetconstr @ Y0 @ X1 ) @ Y0 )
@ X2 ) )
| ( $false = sF94 ) ),
inference(pi_proxy_clausification,[],[f6146]) ).
thf(f6148,plain,
! [X2: $i,X1: $i > $o] :
( ( $true
= ( subset @ ( dsetconstr @ X2 @ X1 ) @ X2 ) )
| ( $false = sF94 ) ),
inference(beta-eta_normalization,[],[f6147]) ).
thf(f6280,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( subset @ Y0 @ Y1 )
=> ( subset @ Y0
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ) ) )
| ( $false = sF102 ) ),
inference(iff_proxy_clausification,[],[f976]) ).
thf(f6292,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( subset @ Y0 @ Y1 )
=> ( subset @ Y0
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) )
@ X1 ) )
| ( $false = sF102 ) ),
inference(pi_proxy_clausification,[],[f6280]) ).
thf(f6293,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ Y1 )
=> ( ( subset @ X1 @ Y0 )
=> ( subset @ X1
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
| ( $false = sF102 ) ),
inference(beta-eta_normalization,[],[f6292]) ).
thf(f6294,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ Y1 )
=> ( ( subset @ X1 @ Y0 )
=> ( subset @ X1
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( in @ Y2 @ Y0 ) ) ) ) ) )
@ X2 ) )
| ( $false = sF102 ) ),
inference(pi_proxy_clausification,[],[f6293]) ).
thf(f6295,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ X1
@ ( dsetconstr @ Y0
@ ^ [Y1: $i] : ( in @ Y1 @ X2 ) ) ) ) ) ) )
| ( $false = sF102 ) ),
inference(beta-eta_normalization,[],[f6294]) ).
thf(f6296,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ X1
@ ( dsetconstr @ Y0
@ ^ [Y1: $i] : ( in @ Y1 @ X2 ) ) ) ) )
@ X3 ) )
| ( $false = sF102 ) ),
inference(pi_proxy_clausification,[],[f6295]) ).
thf(f6297,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( subset @ X1 @ X3 )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ X1
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) ) ) ) ) )
| ( $false = sF102 ) ),
inference(beta-eta_normalization,[],[f6296]) ).
thf(f6298,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X1 @ X3 ) )
| ( $false = sF102 )
| ( $true
= ( ( subset @ X1 @ X2 )
=> ( subset @ X1
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f6297]) ).
thf(f6299,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X1 @ X3 ) )
| ( $false = sF102 )
| ( ( subset @ X1 @ X2 )
= $false )
| ( $true
= ( subset @ X1
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f6298]) ).
thf(f6327,plain,
( sF105
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ Y0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f985]) ).
thf(f6328,plain,
( ( $true
= ( subset @ sK0 @ sK1 ) )
| ( $false = sF106 ) ),
inference(iff_proxy_clausification,[],[f988]) ).
thf(f6682,plain,
! [X1: $i] :
( ( $false = $true )
| ( $true
= ( subset @ X1 @ X1 ) ) ),
inference(forward_demodulation,[],[f5994,f916]) ).
thf(f6683,plain,
! [X1: $i] :
( $true
= ( subset @ X1 @ X1 ) ),
inference(trivial_inequality_removal,[],[f6682]) ).
thf(f6692,plain,
! [X2: $i,X1: $i] :
( ( $false = $true )
| ( ( subset @ X2 @ X1 )
= $false )
| ( ( subset @ X1 @ X2 )
= $false )
| ( X1 = X2 ) ),
inference(forward_demodulation,[],[f6072,f931]) ).
thf(f6693,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $false )
| ( ( subset @ X1 @ X2 )
= $false )
| ( X1 = X2 ) ),
inference(trivial_inequality_removal,[],[f6692]) ).
thf(f6706,plain,
! [X2: $i,X1: $i > $o] :
( ( $false = $true )
| ( $true
= ( subset @ ( dsetconstr @ X2 @ X1 ) @ X2 ) ) ),
inference(forward_demodulation,[],[f6148,f952]) ).
thf(f6707,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( subset @ ( dsetconstr @ X2 @ X1 ) @ X2 ) ),
inference(trivial_inequality_removal,[],[f6706]) ).
thf(f6722,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( subset @ X1 @ X3 ) )
| ( ( subset @ X1 @ X2 )
= $false )
| ( $true
= ( subset @ X1
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) ) ) ) ),
inference(forward_demodulation,[],[f6299,f977]) ).
thf(f6723,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( subset @ X1
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) ) ) )
| ( ( subset @ X1 @ X2 )
= $false )
| ( $false
= ( subset @ X1 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f6722]) ).
thf(f6728,plain,
( ( $false = $true )
| ( $true
= ( subset @ sK0 @ sK1 ) ) ),
inference(forward_demodulation,[],[f6328,f989]) ).
thf(f6729,plain,
( $true
= ( subset @ sK0 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f6728]) ).
thf(f6887,plain,
( $true
= ( subset @ sF105 @ sK0 ) ),
inference(constrained_superposition,[],[f6707,f6327]) ).
thf(f7006,plain,
( ( $false = $true )
| ( $false
= ( subset @ sK0 @ sF105 ) )
| ( sK0 = sF105 ) ),
inference(constrained_superposition,[],[f6693,f6887]) ).
thf(f7007,plain,
( ( $false
= ( subset @ sK0 @ sF105 ) )
| ( sK0 = sF105 ) ),
inference(trivial_inequality_removal,[],[f7006]) ).
thf(f7011,plain,
( $false
= ( subset @ sK0 @ sF105 ) ),
inference(forward_subsumption_resolution,[],[f7007,f986]) ).
thf(f8038,plain,
! [X0: $i] :
( ( $true
= ( subset @ X0 @ sF105 ) )
| ( $false
= ( subset @ X0 @ sK1 ) )
| ( $false
= ( subset @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f6723,f6327]) ).
thf(f22255,plain,
( ( $false = $true )
| ( $false
= ( subset @ sK0 @ sK1 ) )
| ( $false
= ( subset @ sK0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f7011,f8038]) ).
thf(f22274,plain,
( ( $false
= ( subset @ sK0 @ sK1 ) )
| ( $false
= ( subset @ sK0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f22255]) ).
thf(f22318,plain,
( ( $false = $true )
| ( $false
= ( subset @ sK0 @ sK0 ) ) ),
inference(forward_demodulation,[],[f22274,f6729]) ).
thf(f22319,plain,
( $false
= ( subset @ sK0 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f22318]) ).
thf(f22322,plain,
$false = $true,
inference(forward_demodulation,[],[f22319,f6683]) ).
thf(f22323,plain,
$false,
inference(trivial_inequality_removal,[],[f22322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU593^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.16 % Computer : n019.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 13:53:48 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 Running first-order model finding
% 0.10/0.18 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
% 4.28/0.97 % (805801)Will run a generic schedule for satisfiability detection.
% 4.28/0.97 % (805808)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3583682370:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.28/0.97 % (805807)% WARNING: option uhcvi not known.
% 4.28/0.97 % (805806)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=647333687_2999 on theBenchmark for (2999ds/0Mi)
% 4.28/0.97 % (805809)dis+10_1_sil=32000:sp=arity:random_seed=326646078:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.28/0.97 % (805807)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3404928770:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.28/0.97 % (805810)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1150953109:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.28/0.97 % (805811)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1397303262:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.28/0.97 % (805812)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=314212068:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.28/0.98 % (805807)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.28/0.98 % (805810)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.28/0.98 % Exception at run slice level
% 4.28/0.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.28/0.98 % (805807)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.28/0.98 % (805820)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=475996162:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.28/0.98 % (805809)Instruction limit reached!
% 4.28/0.98 % (805809)------------------------------
% 4.28/0.98 % (805809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.28/0.98 % (805809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/0.98 % (805809)CaDiCaL version: 2.1.3
% 4.28/0.98 % (805809)Termination reason: Instruction limit
% 4.28/0.98 % (805809)Termination phase: Saturation
% 4.28/0.98 % (805809)Time elapsed: 0.048 s
% 4.28/0.98 % (805809)Peak memory usage: 13 MB
% 4.28/0.98 % (805809)Instructions burned: 103 (million)
% 4.28/0.98 % (805810)Instruction limit reached!
% 4.28/0.98 % (805810)------------------------------
% 4.28/0.98 % (805810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.28/0.98 % (805810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/0.98 % (805810)CaDiCaL version: 2.1.3
% 4.28/0.98 % (805810)Termination reason: Instruction limit
% 4.28/0.98 % (805810)Termination phase: Saturation
% 4.28/0.98 % (805810)Time elapsed: 0.055 s
% 4.28/0.98 % (805810)Peak memory usage: 13 MB
% 4.28/0.98 % (805810)Instructions burned: 116 (million)
% 4.28/0.98 % Exception at run slice level
% 4.28/0.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.28/0.98 % (805811)Instruction limit reached!
% 4.28/0.98 % (805811)------------------------------
% 4.28/0.98 % (805811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.28/0.98 % (805811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/0.98 % (805811)CaDiCaL version: 2.1.3
% 4.28/0.98 % (805811)Termination reason: Instruction limit
% 4.28/0.98 % (805811)Termination phase: Saturation
% 4.28/0.98 % (805811)Time elapsed: 0.061 s
% 4.28/0.98 % (805811)Peak memory usage: 13 MB
% 4.28/0.98 % (805811)Instructions burned: 133 (million)
% 4.28/0.98 % (805822)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3022430493:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.28/0.98 % (805812)Instruction limit reached!
% 4.28/0.98 % (805812)------------------------------
% 4.28/0.98 % (805812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.28/0.98 % (805812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/0.98 % (805812)CaDiCaL version: 2.1.3
% 4.28/0.98 % (805812)Termination reason: Instruction limit
% 4.28/0.98 % (805812)Termination phase: Saturation
% 4.28/0.98 % (805812)Time elapsed: 0.069 s
% 4.28/0.98 % (805812)Peak memory usage: 13 MB
% 4.28/0.98 % (805812)Instructions burned: 160 (million)
% 4.28/0.98 % (805824)ott-21_1_sil=16000:fs=off:random_seed=338562251:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 10.81/2.03 % (805823)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=3973688720:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 10.81/2.03 % (805825)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1618214295:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 10.81/2.03 % (805823)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.81/2.03 % (805827)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=219049654:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 10.81/2.03 % (805823)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 10.81/2.03 % Exception at run slice level
% 10.81/2.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.81/2.03 % (805832)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2140021860:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 10.81/2.03 % (805822)Instruction limit reached!
% 10.81/2.03 % (805822)------------------------------
% 10.81/2.03 % (805822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.81/2.03 % (805822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.81/2.03 % (805822)CaDiCaL version: 2.1.3
% 10.81/2.03 % (805822)Termination reason: Instruction limit
% 10.81/2.03 % (805822)Termination phase: Saturation
% 10.81/2.03 % (805822)Time elapsed: 0.062 s
% 10.81/2.03 % (805822)Peak memory usage: 13 MB
% 10.81/2.03 % (805822)Instructions burned: 133 (million)
% 10.81/2.03 % (805834)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=245614337:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 10.81/2.03 % (805824)Instruction limit reached!
% 10.81/2.03 % (805824)------------------------------
% 10.81/2.03 % (805824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.81/2.03 % (805824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.81/2.03 % (805824)CaDiCaL version: 2.1.3
% 10.81/2.03 % (805824)Termination reason: Instruction limit
% 10.81/2.03 % (805824)Termination phase: Saturation
% 10.81/2.03 % (805824)Time elapsed: 0.085 s
% 10.81/2.03 % (805824)Peak memory usage: 13 MB
% 10.81/2.03 % (805824)Instructions burned: 182 (million)
% 10.81/2.03 % Exception at run slice level
% 10.81/2.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.81/2.03 % (805836)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=1603664131:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 10.81/2.03 % (805837)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=641089944:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 10.81/2.03 % (805836)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.81/2.03 % (805837)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.81/2.03 % (805825)Instruction limit reached!
% 10.81/2.03 % (805825)------------------------------
% 10.81/2.03 % (805825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.81/2.03 % (805825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.81/2.03 % (805825)CaDiCaL version: 2.1.3
% 10.81/2.03 % (805825)Termination reason: Instruction limit
% 10.81/2.03 % (805825)Termination phase: Saturation
% 10.81/2.03 % (805825)Time elapsed: 0.252 s
% 10.81/2.03 % (805825)Peak memory usage: 13 MB
% 10.81/2.03 % (805825)Instructions burned: 477 (million)
% 10.81/2.03 % (805823)Instruction limit reached!
% 10.81/2.03 % (805823)------------------------------
% 10.81/2.03 % (805823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.81/2.03 % (805823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.81/2.03 % (805823)CaDiCaL version: 2.1.3
% 10.81/2.03 % (805823)Termination reason: Instruction limit
% 10.81/2.03 % (805823)Termination phase: Saturation
% 10.81/2.03 % (805823)Time elapsed: 0.259 s
% 10.81/2.03 % (805823)Peak memory usage: 14 MB
% 10.81/2.03 % (805823)Instructions burned: 686 (million)
% 10.81/2.03 % (805840)fmb+10_1_sil=64000:random_seed=2303653309:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 10.81/2.03 % (805841)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2793292846:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 10.81/2.03 % (805840)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 10.81/2.03 % Exception at run slice level
% 10.81/2.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.81/2.03 % Exception at run slice level
% 10.81/2.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.81/2.03 % (805844)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2650125178:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 10.81/2.03 % (805845)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2121208283:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 10.81/2.03 % (805845)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.81/2.03 % Exception at run slice level
% 10.81/2.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.81/2.03 % (805848)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2169541288:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 10.81/2.03 % (805848)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 10.81/2.03 % (805848)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 10.81/2.03 % (805836)Instruction limit reached!
% 10.81/2.03 % (805836)------------------------------
% 10.81/2.03 % (805836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.81/2.03 % (805836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.81/2.03 % (805836)CaDiCaL version: 2.1.3
% 10.81/2.03 % (805836)Termination reason: Instruction limit
% 10.81/2.03 % (805836)Termination phase: Saturation
% 10.81/2.03 % (805836)Time elapsed: 0.284 s
% 10.81/2.03 % (805836)Peak memory usage: 15 MB
% 10.81/2.03 % (805836)Instructions burned: 694 (million)
% 10.81/2.03 % (805850)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1076209595:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 10.81/2.03 % Exception at run slice level
% 10.81/2.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.81/2.03 % (805852)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=737764610:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 10.81/2.03 % Exception at run slice level
% 10.81/2.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.81/2.03 % (805854)ott-2_1_sil=16000:newcnf=on:random_seed=2189836492:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 10.81/2.03 % (805854)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 10.81/2.03 % (805837)Instruction limit reached!
% 10.81/2.03 % (805837)------------------------------
% 10.81/2.03 % (805837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.81/2.03 % (805837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.81/2.03 % (805837)CaDiCaL version: 2.1.3
% 10.81/2.03 % (805837)Termination reason: Instruction limit
% 10.81/2.03 % (805837)Termination phase: Saturation
% 10.81/2.03 % (805837)Time elapsed: 0.439 s
% 10.81/2.03 % (805837)Peak memory usage: 17 MB
% 10.81/2.03 % (805837)Instructions burned: 881 (million)
% 10.81/2.03 % (805856)ott+10_1_sil=32000:tgt=ground:random_seed=3087190579:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 10.81/2.03 % (805832)Instruction limit reached!
% 10.81/2.03 % (805832)------------------------------
% 10.81/2.03 % (805832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.81/2.03 % (805832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.81/2.03 % (805832)CaDiCaL version: 2.1.3
% 10.81/2.03 % (805832)Termination reason: Instruction limit
% 10.81/2.03 % (805832)Termination phase: Saturation
% 10.81/2.03 % (805832)Time elapsed: 0.567 s
% 10.81/2.03 % (805832)Peak memory usage: 18 MB
% 10.81/2.03 % (805832)Instructions burned: 1180 (million)
% 10.81/2.03 % (805858)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1053269361:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 10.81/2.03 % Exception at run slice level
% 10.81/2.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 10.81/2.03 % (805860)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3410684516:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 10.81/2.03 % (805860)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 10.81/2.03 % (805854)Instruction limit reached!
% 10.81/2.03 % (805854)------------------------------
% 10.81/2.03 % (805854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.81/2.03 % (805854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.81/2.03 % (805854)CaDiCaL version: 2.1.3
% 10.81/2.03 % (805854)Termination reason: Instruction limit
% 10.81/2.03 % (805854)Termination phase: Saturation
% 10.81/2.03 % (805854)Time elapsed: 0.430 s
% 10.81/2.03 % (805854)Peak memory usage: 15 MB
% 10.81/2.03 % (805854)Instructions burned: 869 (million)
% 10.81/2.03 % (805862)dis+21_1_sil=32000:sas=cadical:random_seed=186669572:i=3773:amm=off_2989 on theBenchmark for (2989ds/3773Mi)
% 10.81/2.03 % (805848)Instruction limit reached!
% 10.81/2.03 % (805848)------------------------------
% 10.81/2.03 % (805848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.81/2.03 % (805848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.81/2.03 % (805848)CaDiCaL version: 2.1.3
% 10.81/2.03 % (805848)Termination reason: Instruction limit
% 10.81/2.03 % (805848)Termination phase: Saturation
% 10.81/2.03 % (805848)Time elapsed: 0.660 s
% 10.81/2.03 % (805848)Peak memory usage: 24 MB
% 10.81/2.03 % (805848)Instructions burned: 1474 (million)
% 10.81/2.03 % (805864)ott+11_1_sil=16000:gs=on:random_seed=1774442739:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2988 on theBenchmark for (2988ds/2251Mi)
% 10.81/2.03 % (805864)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 10.81/2.03 % (805856) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-805801-805856"...
% 10.81/2.03 % (805856)...printing done.
% 10.81/2.03 % (805856)Refutation found. Thanks to Tanya!
% 10.81/2.03 % SZS status Theorem for theBenchmark
% 10.81/2.03 % SZS output start Proof for theBenchmark
% See solution above
% 13.10/2.04 % (805856)------------------------------
% 13.10/2.04 % (805856)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.10/2.04 % (805856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.10/2.04 % (805856)CaDiCaL version: 2.1.3
% 13.10/2.04 % (805856)Termination reason: Refutation
% 13.10/2.04 % (805856)Time elapsed: 1.153 s
% 13.10/2.04 % (805856)Peak memory usage: 23 MB
% 13.10/2.04 % (805856)Instructions burned: 2488 (million)
% 13.10/2.04 % (805801)Success in time 1.842 s
% 13.10/2.04 % Vampire exiting
%------------------------------------------------------------------------------