%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU660^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:30:34 AM UTC 2026
% Result : Theorem 0.66s 0.45s
% Output : Refutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 20 unt; 0 typ; 6 def)
% Number of atoms : 3475 ( 957 equ; 0 cnn)
% Maximal formula atoms : 178 ( 58 avg)
% Number of connectives : 1765 ( 57 ~; 47 |; 717 &; 224 @)
% ( 9 <=>; 711 =>; 0 <=; 0 <~>)
% Maximal formula depth : 187 ( 28 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 350 ( 347 usr; 202 con; 0-4 aty)
% Number of variables : 84 ( 0 sgn 62 !; 22 ?; 84 :)
% 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,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_162,type,
singletoninpowerset: $o ).
thf(func_def_163,type,
singletoninpowunion: $o ).
thf(func_def_164,type,
upairset2E: $o ).
thf(func_def_165,type,
upairsubunion: $o ).
thf(func_def_166,type,
upairinpowunion: $o ).
thf(func_def_167,type,
ubforcartprodlem1: $o ).
thf(func_def_168,type,
ubforcartprodlem2: $o ).
thf(func_def_169,type,
ubforcartprodlem3: $o ).
thf(func_def_170,type,
cartprodpairin: $o ).
thf(func_def_171,type,
cartprodmempair1: $o ).
thf(func_def_172,type,
cartprodmempair: $o ).
thf(func_def_173,type,
setunionE2: $o ).
thf(func_def_174,type,
setunionsingleton1: $o ).
thf(func_def_175,type,
setunionsingleton2: $o ).
thf(func_def_176,type,
setunionsingleton: $o ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_178,type,
singletonprop: $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_180,type,
ex1E1: $o ).
thf(func_def_181,type,
ex1I: $o ).
thf(func_def_182,type,
ex1I2: $o ).
thf(func_def_183,type,
singletonsuniq: $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_188,type,
setukpairinjL1: $o ).
thf(func_def_189,type,
kfstsingleton: $o ).
thf(func_def_190,type,
theprop: $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_192,type,
kfstpairEq: $o ).
thf(func_def_193,type,
cartprodfstin: $o ).
thf(func_def_194,type,
setukpairinjL2: $o ).
thf(func_def_195,type,
setukpairinjL: $o ).
thf(func_def_196,type,
setukpairinjR11: $o ).
thf(func_def_197,type,
setukpairinjR12: $o ).
thf(func_def_198,type,
setukpairinjR1: $o ).
thf(func_def_199,type,
upairequniteq: $o ).
thf(func_def_200,type,
setukpairinjR2: $o ).
thf(func_def_201,type,
setukpairinjR: $o ).
thf(func_def_202,type,
ksndsingleton: $o ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_204,type,
ksndpairEq: $o ).
thf(func_def_205,type,
kpairsurjEq: $o ).
thf(func_def_206,type,
cartprodsndin: $o ).
thf(func_def_207,type,
cartprodpairmemEL: $o ).
thf(func_def_210,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_211,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_212,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_213,type,
vAND: $o > $o > $o ).
thf(func_def_214,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_215,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_216,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_217,type,
vIMP: $o > $o > $o ).
thf(func_def_218,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_219,type,
vNOT: $o > $o ).
thf(func_def_220,type,
sP0: $i > $i > $o ).
thf(func_def_221,type,
sP1: $i > $o ).
thf(func_def_222,type,
sP2: $o ).
thf(func_def_224,type,
sK4: $i > $i ).
thf(func_def_231,type,
sK11: $o > $i > $i > $i ).
thf(func_def_234,type,
sK14: $o ).
thf(func_def_247,type,
sK27: $i > ( $i > $o ) > $i ).
thf(func_def_248,type,
sK28: $i > $o ).
thf(func_def_251,type,
sK31: ( $i > $o ) > $i ).
thf(func_def_252,type,
sK32: ( $i > $o ) > $i ).
thf(func_def_253,type,
sK33: $i > $o ).
thf(func_def_257,type,
sK37: $i > $o ).
thf(func_def_260,type,
sK40: $i > ( $i > $o ) > $i ).
thf(func_def_278,type,
sK58: $i > $i > $i ).
thf(func_def_280,type,
sK60: $i > $i > $i ).
thf(func_def_290,type,
sK70: $o ).
thf(func_def_300,type,
sK80: $i > $o ).
thf(func_def_301,type,
sK81: $i > $o ).
thf(func_def_302,type,
sK82: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_303,type,
sK83: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_335,type,
sK115: $i > $o ).
thf(func_def_336,type,
sK116: ( $i > $o ) > $i ).
thf(func_def_350,type,
sK130: $i > $o ).
thf(func_def_353,type,
sK133: $i > ( $i > $o ) > $i ).
thf(func_def_354,type,
sK134: $i > ( $i > $o ) > $i ).
thf(func_def_358,type,
sK138: $i > $i ).
thf(func_def_361,type,
sK141: $i > $i > $o ).
thf(func_def_363,type,
sK143: $i > $i ).
thf(func_def_364,type,
sK144: $i > $i ).
thf(func_def_365,type,
sK145: $i > ( $i > $i > $o ) > $i ).
thf(func_def_366,type,
sK146: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_367,type,
sK147: $i > ( $i > $i > $o ) > $i ).
thf(func_def_372,type,
sK152: $i > $i > $i ).
thf(func_def_373,type,
sK153: $i > $i > $i ).
thf(func_def_376,type,
sK156: $i > $o ).
thf(func_def_380,type,
sK160: $i > $i ).
thf(func_def_384,type,
sK164: $i > $o ).
thf(func_def_385,type,
sK165: $i > $o ).
thf(func_def_386,type,
sK166: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_387,type,
sK167: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_389,type,
sK169: $i > $o ).
thf(func_def_391,type,
sK171: ( $i > $o ) > $i > $i ).
thf(func_def_403,type,
sK183: $i > $i > $i ).
thf(func_def_409,type,
sK189: $o ).
thf(func_def_419,type,
sK199: $i > $i ).
thf(func_def_421,type,
sK201: $i > $i ).
thf(func_def_431,type,
sK211: $o ).
thf(func_def_437,type,
sK217: $i > $i > $i ).
thf(func_def_447,type,
sK227: ( $i > $o ) > $i > $i > $i ).
thf(func_def_450,type,
sK230: $i > $o ).
thf(func_def_455,type,
sK235: ( $i > $o ) > $i ).
thf(func_def_456,type,
sK236: $i > $o ).
thf(func_def_457,type,
sK237: $i > $i ).
thf(func_def_463,type,
sK243: $i > $o ).
thf(func_def_464,type,
sK244: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_465,type,
sK245: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_466,type,
sK246: $i > $o ).
thf(func_def_467,type,
sK247: $i > $o ).
thf(func_def_469,type,
sK249: $i > $o ).
thf(func_def_482,type,
sK262: $o ).
thf(func_def_491,type,
sK271: $i > $o ).
thf(func_def_494,type,
sK274: $i > $o ).
thf(func_def_514,type,
sK294: $i > $i ).
thf(func_def_522,type,
sK302: $o ).
thf(func_def_528,type,
sK308: $i > $o ).
thf(func_def_532,type,
sK312: $i > $o ).
thf(func_def_534,type,
sK314: $i > ( $i > $o ) > $i ).
thf(func_def_535,type,
sK315: $i > $o ).
thf(func_def_538,type,
sK318: $i > ( $i > $o ) > $i ).
thf(func_def_552,type,
sK332: $i > $o ).
thf(func_def_554,type,
sK334: $i > $i > $i > $i ).
thf(func_def_555,type,
sK335: $i > $i > $i > $i ).
thf(func_def_562,type,
sK342: ( $i > $o ) > $i > $i ).
thf(func_def_564,type,
sK344: $i > $o ).
thf(func_def_574,type,
sK354: $i > $o ).
thf(func_def_577,type,
sK357: $i > ( $i > $o ) > $i ).
thf(func_def_578,type,
sK358: $i > ( $i > $o ) > $i ).
thf(func_def_583,type,
sK363: $i > $i > $i ).
thf(func_def_586,type,
sK366: $i > $i ).
thf(func_def_588,type,
sK368: $i > $o ).
thf(func_def_590,type,
sK370: ( $i > $o ) > $i > $i ).
thf(func_def_592,type,
sK372: $i > $o ).
thf(func_def_598,type,
sK378: $i > $o ).
thf(func_def_605,type,
sK385: $i > $i > $i ).
thf(func_def_609,type,
sK389: $i > $i > $i ).
thf(func_def_612,type,
sK392: $i > $i > $i ).
thf(func_def_618,type,
sK398: $i > $o ).
thf(func_def_619,type,
sK399: $i > $i ).
thf(func_def_620,type,
sK400: ( $i > $o ) > $i ).
thf(func_def_628,type,
sK408: $i > $o ).
thf(func_def_641,type,
sK421: $o ).
thf(func_def_643,type,
sK423: $i > $o ).
thf(func_def_656,type,
sK436: $i > $o ).
thf(func_def_662,type,
sK442: $i > $i ).
thf(func_def_663,type,
sK443: $i > $i ).
thf(func_def_664,type,
sK444: $i > $i ).
thf(func_def_665,type,
sK445: $i > $i ).
thf(func_def_666,type,
sK446: $i > $i ).
thf(func_def_667,type,
sK447: $i > $i > $i > $i ).
thf(func_def_668,type,
sK448: $i > $i ).
thf(func_def_669,type,
sK449: $i > $i ).
thf(func_def_670,type,
sK450: $i > $i ).
thf(func_def_671,type,
sK451: $i > $i ).
thf(func_def_672,type,
sK452: $i > $i > $i ).
thf(func_def_673,type,
sK453: $i > $i > $i ).
thf(func_def_674,type,
sK454: $i > $i > $i > $i ).
thf(func_def_675,type,
sK455: $i > $i > $i > $i ).
thf(func_def_676,type,
sK456: $i > $i > $i > $i ).
thf(func_def_677,type,
sK457: $i > $i > $i ).
thf(func_def_678,type,
sK458: $i > $i > $i ).
thf(func_def_679,type,
sK459: $i > $i > $i ).
thf(func_def_685,type,
sK465: $o ).
thf(func_def_690,type,
sK470: $i > ( $i > $o ) > $i ).
thf(func_def_691,type,
sK471: $i > $o ).
thf(func_def_696,type,
sK476: $i > $o ).
thf(func_def_698,type,
sK478: $i > ( $i > $o ) > $i ).
thf(f177,axiom,
! [X0: $i,X1: $i] :
( ( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 )
= ksndpairEq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(f179,axiom,
( cartprodsndin
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ( in @ ( ksnd @ X2 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(f181,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
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ! [X1: $i,X3: $i,X0: $i,X2: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) )
=> ( in @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(f182,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
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ! [X1: $i,X3: $i,X0: $i,X2: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) )
=> ( in @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f181]) ).
thf(f297,plain,
( ! [X1: $i,X0: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 )
<=> ( ksndpairEq = $true ) ),
inference(fool_elimination,[],[f177]) ).
thf(f403,plain,
( cartprodsndin
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X1 @ X0 ) )
=> ( in @ ( ksnd @ X2 ) @ X0 ) ) ) ),
inference(rectify,[],[f179]) ).
thf(f404,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X2 @ ( cartprod @ X1 @ X0 ) ) )
=> ( ( in @ ( ksnd @ X2 ) @ X0 )
= $true ) )
<=> ( cartprodsndin = $true ) ),
inference(fool_elimination,[],[f403]) ).
thf(f480,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
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X3 @ X1 ) @ ( cartprod @ X2 @ X0 ) )
=> ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f182]) ).
thf(f481,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 )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ! [X1: $i,X3: $i,X0: $i,X2: $i] :
( ( ( in @ ( kpair @ X3 @ X1 ) @ ( cartprod @ X2 @ X0 ) )
= $true )
=> ( ( in @ X1 @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f480]) ).
thf(f726,plain,
( ? [X1: $i,X0: $i,X2: $i,X3: $i] :
( ( ( in @ ( kpair @ X3 @ X1 ) @ ( cartprod @ X2 @ X0 ) )
= $true )
& ( ( in @ X1 @ X0 )
!= $true ) )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $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,[],[f481]) ).
thf(f727,plain,
( ( wellorderingAx = $true )
& ( in__Cong = $true )
& ( exuE3e = $true )
& ( singletonsubset = $true )
& ( setukpairinjR2 = $true )
& ( subsetE2 = $true )
& ( setunionAx = $true )
& ( symdiffIneg1 = $true )
& ( omegaIndAx = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI1 = $true )
& ( symdiffI1 = $true )
& ( exuE1 = $true )
& ( dsetconstr__Cong = $true )
& ( singletonsswitch = $true )
& ( replAx = $true )
& ( emptysetAx = $true )
& ( exuI2 = $true )
& ( setadjoinE = $true )
& ( nonemptyImpWitness = $true )
& ( emptyE1 = $true )
& ( nonemptyE1 = $true )
& ( omega0Ax = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( emptysetE = $true )
& ( descr__Cong = $true )
& ( cartprodsndin = $true )
& ( setadjoinSub2 = $true )
& ( symdiffI2 = $true )
& ( setukpairinjR1 = $true )
& ( powersetI = $true )
& ( prop2setE = $true )
& ( setukpairinjL2 = $true )
& ( symdiffIneg2 = $true )
& ( cartprodfstin = $true )
& ( powersetAx = $true )
& ( emptyset__Cong = $true )
& ( eqimpsubset1 = $true )
& ( setunionE = $true )
& ( ex1I = $true )
& ( setminusIRneg = $true )
& ( ex1I2 = $true )
& ( sepSubset = $true )
& ( notdexE = $true )
& ( subPowSU = $true )
& ( binunionIR = $true )
& ( binintersectSubset4 = $true )
& ( singletoninpowerset = $true )
& ( quantDeMorgan2 = $true )
& ( setminusSubset2 = $true )
& ( setukpairinjR12 = $true )
& ( kpairiskpair = $true )
& ( binunionEcases = $true )
& ( setadjoinSub = $true )
& ( notinsingleton = $true )
& ( dsetconstrI = $true )
& ( omega__Cong = $true )
& ( upairsetIR = $true )
& ( quantDeMorgan4 = $true )
& ( theprop = $true )
& ( setunionsingleton = $true )
& ( powerset__Cong = $true )
& ( upairsetE = $true )
& ( binintersectRsub = $true )
& ( setbeta = $true )
& ( cartprodpairmemEL = $true )
& ( ex1E1 = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionRsub = $true )
& ( setminusERneg = $true )
& ( setminusEL = $true )
& ( setextsub = $true )
& ( exuE2 = $true )
& ( exuI1 = $true )
& ( setunionsingleton1 = $true )
& ( ubforcartprodlem1 = $true )
& ( emptysetimpfalse = $true )
& ( prop2set2propI = $true )
& ( uniqinunit = $true )
& ( notinemptyset = $true )
& ( sepInPowerset = $true )
& ( kpairp = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset1 = $true )
& ( symdiffE = $true )
& ( kfstpairEq = $true )
& ( vacuousDall = $true )
& ( setminusSubset1 = $true )
& ( binunionLsub = $true )
& ( setukpairinjL1 = $true )
& ( exu__Cong = $true )
& ( subsetI2 = $true )
& ( emptysetsubset = $true )
& ( setadjoinAx = $true )
& ( exuE3u = $true )
& ( setukpairinjL = $true )
& ( cartprodmempair = $true )
& ( upairequniteq = $true )
& ( quantDeMorgan1 = $true )
& ( setminusLsub = $true )
& ( setminusER = $true )
& ( setunionE2 = $true )
& ( binunionIL = $true )
& ( kpairsurjEq = $true )
& ( setadjoinIR = $true )
& ( exuI3 = $true )
& ( upairset2IR = $true )
& ( setunionsingleton2 = $true )
& ( powersetE1 = $true )
& ( inPowerset = $true )
& ( setoftrueEq = $true )
& ( upairsubunion = $true )
& ( emptyinunitempty = $true )
& ( descrp = $true )
& ( singletonsuniq = $true )
& ( exuEu = $true )
& ( upairset2E = $true )
& ( quantDeMorgan3 = $true )
& ( bs114d = $true )
& ( setextAx = $true )
& ( emptyInPowerset = $true )
& ( eqinunit = $true )
& ( emptyI = $true )
& ( powersetsubset = $true )
& ( binintersectI = $true )
& ( powersetI1 = $true )
& ( cartprodmempair1 = $true )
& ( ksndsingleton = $true )
& ( kfstsingleton = $true )
& ( setunionI = $true )
& ( notdallE = $true )
& ( inCongP = $true )
& ( setadjoinOr = $true )
& ( secondinupair = $true )
& ( setukpairinjR11 = $true )
& ( subset2powerset = $true )
& ( ubforcartprodlem2 = $true )
& ( setext = $true )
& ( setunion__Cong = $true )
& ( dsetconstrEL = $true )
& ( binintersectER = $true )
& ( setminusILneg = $true )
& ( subsetI1 = $true )
& ( singletoninpowunion = $true )
& ( upairinpowunion = $true )
& ( notequalI1 = $true )
& ( subsetE = $true )
& ( subsetRefl = $true )
& ( ubforcartprodlem3 = $true )
& ( singletonprop = $true )
& ( foundationAx = $true )
& ( setminusI = $true )
& ( cartprodpairin = $true )
& ( setukpairIL = $true )
& ( ksndpairEq = $true )
& ? [X1: $i,X0: $i,X2: $i,X3: $i] :
( ( ( in @ ( kpair @ X3 @ X1 ) @ ( cartprod @ X2 @ X0 ) )
= $true )
& ( ( in @ X1 @ X0 )
!= $true ) )
& ( setukpairinjR = $true )
& ( notsubsetI = $true )
& ( setadjoinIL = $true )
& ( eqimpsubset2 = $true )
& ( dsetconstrER = $true )
& ( omegaSAx = $true )
& ( binintersectSubset2 = $true )
& ( binunionE = $true )
& ( binintersectLsub = $true )
& ( disjointsetsI1 = $true )
& ( powersetE = $true )
& ( prop2setI = $true )
& ( setukpairIR = $true )
& ( setadjoin__Cong = $true )
& ( notequalI2 = $true )
& ( nonemptyI = $true )
& ( setminusELneg = $true )
& ( subsetTrans = $true )
& ( upairsetIL = $true )
& ( noeltsimpempty = $true ) ),
inference(flattening,[],[f726]) ).
thf(f739,plain,
( ( cartprodsndin = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( cartprod @ X1 @ X0 ) ) )
| ( ( in @ ( ksnd @ X2 ) @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f404]) ).
thf(f829,plain,
( ( ( cartprodsndin = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( cartprod @ X1 @ X0 ) ) )
& ( ( in @ ( ksnd @ X2 ) @ X0 )
!= $true ) ) )
& ( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( cartprod @ X1 @ X0 ) ) )
| ( ( in @ ( ksnd @ X2 ) @ X0 )
= $true ) )
| ( cartprodsndin != $true ) ) ),
inference(nnf_transformation,[],[f739]) ).
thf(f830,plain,
( ( ( cartprodsndin = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X2 @ X1 ) ) )
& ( ( in @ ( ksnd @ X0 ) @ X1 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( cartprod @ X5 @ X4 ) ) )
| ( $true
= ( in @ ( ksnd @ X3 ) @ X4 ) ) )
| ( cartprodsndin != $true ) ) ),
inference(rectify,[],[f829]) ).
thf(f831,plain,
( ( ( cartprodsndin = $true )
| ( ( $true
= ( in @ sK74 @ ( cartprod @ sK76 @ sK75 ) ) )
& ( ( in @ ( ksnd @ sK74 ) @ sK75 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( cartprod @ X5 @ X4 ) ) )
| ( $true
= ( in @ ( ksnd @ X3 ) @ X4 ) ) )
| ( cartprodsndin != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74,sK75,sK76]),skolemize(X0,sK74),skolemize(X1,sK75),skolemize(X2,sK76)],[f830]) ).
thf(f934,plain,
( ( wellorderingAx = $true )
& ( in__Cong = $true )
& ( exuE3e = $true )
& ( singletonsubset = $true )
& ( setukpairinjR2 = $true )
& ( subsetE2 = $true )
& ( setunionAx = $true )
& ( symdiffIneg1 = $true )
& ( omegaIndAx = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI1 = $true )
& ( symdiffI1 = $true )
& ( exuE1 = $true )
& ( dsetconstr__Cong = $true )
& ( singletonsswitch = $true )
& ( replAx = $true )
& ( emptysetAx = $true )
& ( exuI2 = $true )
& ( setadjoinE = $true )
& ( nonemptyImpWitness = $true )
& ( emptyE1 = $true )
& ( nonemptyE1 = $true )
& ( omega0Ax = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( emptysetE = $true )
& ( descr__Cong = $true )
& ( cartprodsndin = $true )
& ( setadjoinSub2 = $true )
& ( symdiffI2 = $true )
& ( setukpairinjR1 = $true )
& ( powersetI = $true )
& ( prop2setE = $true )
& ( setukpairinjL2 = $true )
& ( symdiffIneg2 = $true )
& ( cartprodfstin = $true )
& ( powersetAx = $true )
& ( emptyset__Cong = $true )
& ( eqimpsubset1 = $true )
& ( setunionE = $true )
& ( ex1I = $true )
& ( setminusIRneg = $true )
& ( ex1I2 = $true )
& ( sepSubset = $true )
& ( notdexE = $true )
& ( subPowSU = $true )
& ( binunionIR = $true )
& ( binintersectSubset4 = $true )
& ( singletoninpowerset = $true )
& ( quantDeMorgan2 = $true )
& ( setminusSubset2 = $true )
& ( setukpairinjR12 = $true )
& ( kpairiskpair = $true )
& ( binunionEcases = $true )
& ( setadjoinSub = $true )
& ( notinsingleton = $true )
& ( dsetconstrI = $true )
& ( omega__Cong = $true )
& ( upairsetIR = $true )
& ( quantDeMorgan4 = $true )
& ( theprop = $true )
& ( setunionsingleton = $true )
& ( powerset__Cong = $true )
& ( upairsetE = $true )
& ( binintersectRsub = $true )
& ( setbeta = $true )
& ( cartprodpairmemEL = $true )
& ( ex1E1 = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionRsub = $true )
& ( setminusERneg = $true )
& ( setminusEL = $true )
& ( setextsub = $true )
& ( exuE2 = $true )
& ( exuI1 = $true )
& ( setunionsingleton1 = $true )
& ( ubforcartprodlem1 = $true )
& ( emptysetimpfalse = $true )
& ( prop2set2propI = $true )
& ( uniqinunit = $true )
& ( notinemptyset = $true )
& ( sepInPowerset = $true )
& ( kpairp = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset1 = $true )
& ( symdiffE = $true )
& ( kfstpairEq = $true )
& ( vacuousDall = $true )
& ( setminusSubset1 = $true )
& ( binunionLsub = $true )
& ( setukpairinjL1 = $true )
& ( exu__Cong = $true )
& ( subsetI2 = $true )
& ( emptysetsubset = $true )
& ( setadjoinAx = $true )
& ( exuE3u = $true )
& ( setukpairinjL = $true )
& ( cartprodmempair = $true )
& ( upairequniteq = $true )
& ( quantDeMorgan1 = $true )
& ( setminusLsub = $true )
& ( setminusER = $true )
& ( setunionE2 = $true )
& ( binunionIL = $true )
& ( kpairsurjEq = $true )
& ( setadjoinIR = $true )
& ( exuI3 = $true )
& ( upairset2IR = $true )
& ( setunionsingleton2 = $true )
& ( powersetE1 = $true )
& ( inPowerset = $true )
& ( setoftrueEq = $true )
& ( upairsubunion = $true )
& ( emptyinunitempty = $true )
& ( descrp = $true )
& ( singletonsuniq = $true )
& ( exuEu = $true )
& ( upairset2E = $true )
& ( quantDeMorgan3 = $true )
& ( bs114d = $true )
& ( setextAx = $true )
& ( emptyInPowerset = $true )
& ( eqinunit = $true )
& ( emptyI = $true )
& ( powersetsubset = $true )
& ( binintersectI = $true )
& ( powersetI1 = $true )
& ( cartprodmempair1 = $true )
& ( ksndsingleton = $true )
& ( kfstsingleton = $true )
& ( setunionI = $true )
& ( notdallE = $true )
& ( inCongP = $true )
& ( setadjoinOr = $true )
& ( secondinupair = $true )
& ( setukpairinjR11 = $true )
& ( subset2powerset = $true )
& ( ubforcartprodlem2 = $true )
& ( setext = $true )
& ( setunion__Cong = $true )
& ( dsetconstrEL = $true )
& ( binintersectER = $true )
& ( setminusILneg = $true )
& ( subsetI1 = $true )
& ( singletoninpowunion = $true )
& ( upairinpowunion = $true )
& ( notequalI1 = $true )
& ( subsetE = $true )
& ( subsetRefl = $true )
& ( ubforcartprodlem3 = $true )
& ( singletonprop = $true )
& ( foundationAx = $true )
& ( setminusI = $true )
& ( cartprodpairin = $true )
& ( setukpairIL = $true )
& ( ksndpairEq = $true )
& ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X0 ) @ ( cartprod @ X2 @ X1 ) ) )
& ( ( in @ X0 @ X1 )
!= $true ) )
& ( setukpairinjR = $true )
& ( notsubsetI = $true )
& ( setadjoinIL = $true )
& ( eqimpsubset2 = $true )
& ( dsetconstrER = $true )
& ( omegaSAx = $true )
& ( binintersectSubset2 = $true )
& ( binunionE = $true )
& ( binintersectLsub = $true )
& ( disjointsetsI1 = $true )
& ( powersetE = $true )
& ( prop2setI = $true )
& ( setukpairIR = $true )
& ( setadjoin__Cong = $true )
& ( notequalI2 = $true )
& ( nonemptyI = $true )
& ( setminusELneg = $true )
& ( subsetTrans = $true )
& ( upairsetIL = $true )
& ( noeltsimpempty = $true ) ),
inference(rectify,[],[f727]) ).
thf(f935,plain,
( ( wellorderingAx = $true )
& ( in__Cong = $true )
& ( exuE3e = $true )
& ( singletonsubset = $true )
& ( setukpairinjR2 = $true )
& ( subsetE2 = $true )
& ( setunionAx = $true )
& ( symdiffIneg1 = $true )
& ( omegaIndAx = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI1 = $true )
& ( symdiffI1 = $true )
& ( exuE1 = $true )
& ( dsetconstr__Cong = $true )
& ( singletonsswitch = $true )
& ( replAx = $true )
& ( emptysetAx = $true )
& ( exuI2 = $true )
& ( setadjoinE = $true )
& ( nonemptyImpWitness = $true )
& ( emptyE1 = $true )
& ( nonemptyE1 = $true )
& ( omega0Ax = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( emptysetE = $true )
& ( descr__Cong = $true )
& ( cartprodsndin = $true )
& ( setadjoinSub2 = $true )
& ( symdiffI2 = $true )
& ( setukpairinjR1 = $true )
& ( powersetI = $true )
& ( prop2setE = $true )
& ( setukpairinjL2 = $true )
& ( symdiffIneg2 = $true )
& ( cartprodfstin = $true )
& ( powersetAx = $true )
& ( emptyset__Cong = $true )
& ( eqimpsubset1 = $true )
& ( setunionE = $true )
& ( ex1I = $true )
& ( setminusIRneg = $true )
& ( ex1I2 = $true )
& ( sepSubset = $true )
& ( notdexE = $true )
& ( subPowSU = $true )
& ( binunionIR = $true )
& ( binintersectSubset4 = $true )
& ( singletoninpowerset = $true )
& ( quantDeMorgan2 = $true )
& ( setminusSubset2 = $true )
& ( setukpairinjR12 = $true )
& ( kpairiskpair = $true )
& ( binunionEcases = $true )
& ( setadjoinSub = $true )
& ( notinsingleton = $true )
& ( dsetconstrI = $true )
& ( omega__Cong = $true )
& ( upairsetIR = $true )
& ( quantDeMorgan4 = $true )
& ( theprop = $true )
& ( setunionsingleton = $true )
& ( powerset__Cong = $true )
& ( upairsetE = $true )
& ( binintersectRsub = $true )
& ( setbeta = $true )
& ( cartprodpairmemEL = $true )
& ( ex1E1 = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionRsub = $true )
& ( setminusERneg = $true )
& ( setminusEL = $true )
& ( setextsub = $true )
& ( exuE2 = $true )
& ( exuI1 = $true )
& ( setunionsingleton1 = $true )
& ( ubforcartprodlem1 = $true )
& ( emptysetimpfalse = $true )
& ( prop2set2propI = $true )
& ( uniqinunit = $true )
& ( notinemptyset = $true )
& ( sepInPowerset = $true )
& ( kpairp = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset1 = $true )
& ( symdiffE = $true )
& ( kfstpairEq = $true )
& ( vacuousDall = $true )
& ( setminusSubset1 = $true )
& ( binunionLsub = $true )
& ( setukpairinjL1 = $true )
& ( exu__Cong = $true )
& ( subsetI2 = $true )
& ( emptysetsubset = $true )
& ( setadjoinAx = $true )
& ( exuE3u = $true )
& ( setukpairinjL = $true )
& ( cartprodmempair = $true )
& ( upairequniteq = $true )
& ( quantDeMorgan1 = $true )
& ( setminusLsub = $true )
& ( setminusER = $true )
& ( setunionE2 = $true )
& ( binunionIL = $true )
& ( kpairsurjEq = $true )
& ( setadjoinIR = $true )
& ( exuI3 = $true )
& ( upairset2IR = $true )
& ( setunionsingleton2 = $true )
& ( powersetE1 = $true )
& ( inPowerset = $true )
& ( setoftrueEq = $true )
& ( upairsubunion = $true )
& ( emptyinunitempty = $true )
& ( descrp = $true )
& ( singletonsuniq = $true )
& ( exuEu = $true )
& ( upairset2E = $true )
& ( quantDeMorgan3 = $true )
& ( bs114d = $true )
& ( setextAx = $true )
& ( emptyInPowerset = $true )
& ( eqinunit = $true )
& ( emptyI = $true )
& ( powersetsubset = $true )
& ( binintersectI = $true )
& ( powersetI1 = $true )
& ( cartprodmempair1 = $true )
& ( ksndsingleton = $true )
& ( kfstsingleton = $true )
& ( setunionI = $true )
& ( notdallE = $true )
& ( inCongP = $true )
& ( setadjoinOr = $true )
& ( secondinupair = $true )
& ( setukpairinjR11 = $true )
& ( subset2powerset = $true )
& ( ubforcartprodlem2 = $true )
& ( setext = $true )
& ( setunion__Cong = $true )
& ( dsetconstrEL = $true )
& ( binintersectER = $true )
& ( setminusILneg = $true )
& ( subsetI1 = $true )
& ( singletoninpowunion = $true )
& ( upairinpowunion = $true )
& ( notequalI1 = $true )
& ( subsetE = $true )
& ( subsetRefl = $true )
& ( ubforcartprodlem3 = $true )
& ( singletonprop = $true )
& ( foundationAx = $true )
& ( setminusI = $true )
& ( cartprodpairin = $true )
& ( setukpairIL = $true )
& ( ksndpairEq = $true )
& ( $true
= ( in @ ( kpair @ sK175 @ sK172 ) @ ( cartprod @ sK174 @ sK173 ) ) )
& ( $true
!= ( in @ sK172 @ sK173 ) )
& ( setukpairinjR = $true )
& ( notsubsetI = $true )
& ( setadjoinIL = $true )
& ( eqimpsubset2 = $true )
& ( dsetconstrER = $true )
& ( omegaSAx = $true )
& ( binintersectSubset2 = $true )
& ( binunionE = $true )
& ( binintersectLsub = $true )
& ( disjointsetsI1 = $true )
& ( powersetE = $true )
& ( prop2setI = $true )
& ( setukpairIR = $true )
& ( setadjoin__Cong = $true )
& ( notequalI2 = $true )
& ( nonemptyI = $true )
& ( setminusELneg = $true )
& ( subsetTrans = $true )
& ( upairsetIL = $true )
& ( noeltsimpempty = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK172,sK173,sK174,sK175]),skolemize(X0,sK172),skolemize(X1,sK173),skolemize(X2,sK174),skolemize(X3,sK175)],[f934]) ).
thf(f997,plain,
( ( ! [X1: $i,X0: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 )
| ( ksndpairEq != $true ) )
& ( ( ksndpairEq = $true )
| ? [X1: $i,X0: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
!= X1 ) ) ),
inference(nnf_transformation,[],[f297]) ).
thf(f998,plain,
( ( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 )
| ( ksndpairEq != $true ) )
& ( ( ksndpairEq = $true )
| ? [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X3 @ X2 ) )
!= X2 ) ) ),
inference(rectify,[],[f997]) ).
thf(f999,plain,
( ( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 )
| ( ksndpairEq != $true ) )
& ( ( ksndpairEq = $true )
| ( ( ksnd @ ( kpair @ sK234 @ sK233 ) )
!= sK233 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK233,sK234]),skolemize(X2,sK233),skolemize(X3,sK234)],[f998]) ).
thf(f1379,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( cartprod @ X5 @ X4 ) ) )
| ( cartprodsndin != $true )
| ( $true
= ( in @ ( ksnd @ X3 ) @ X4 ) ) ),
inference(cnf_transformation,[],[f831]) ).
thf(f1532,plain,
( $true
!= ( in @ sK172 @ sK173 ) ),
inference(cnf_transformation,[],[f935]) ).
thf(f1533,plain,
( $true
= ( in @ ( kpair @ sK175 @ sK172 ) @ ( cartprod @ sK174 @ sK173 ) ) ),
inference(cnf_transformation,[],[f935]) ).
thf(f1534,plain,
ksndpairEq = $true,
inference(cnf_transformation,[],[f935]) ).
thf(f1662,plain,
cartprodsndin = $true,
inference(cnf_transformation,[],[f935]) ).
thf(f1777,plain,
! [X0: $i,X1: $i] :
( ( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 )
| ( ksndpairEq != $true ) ),
inference(cnf_transformation,[],[f999]) ).
thf(f2770,definition,
( spl489_106
<=> ( $true
= ( in @ ( kpair @ sK175 @ sK172 ) @ ( cartprod @ sK174 @ sK173 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl489_106])],[avatar_definition]) ).
thf(f2772,plain,
( ( $true
= ( in @ ( kpair @ sK175 @ sK172 ) @ ( cartprod @ sK174 @ sK173 ) ) )
| ~ spl489_106 ),
inference(avatar_component_clause,[],[f2770]) ).
thf(f2773,plain,
spl489_106,
inference(avatar_split_clause,[],[f1533,f2770]) ).
thf(f3211,definition,
( spl489_206
<=> ( cartprodsndin = $true ) ),
introduced(definition,[new_symbols(definition,[spl489_206])],[avatar_definition]) ).
thf(f4101,definition,
( spl489_397
<=> ( $true
= ( in @ sK172 @ sK173 ) ) ),
introduced(definition,[new_symbols(definition,[spl489_397])],[avatar_definition]) ).
thf(f4103,plain,
( ( $true
!= ( in @ sK172 @ sK173 ) )
| spl489_397 ),
inference(avatar_component_clause,[],[f4101]) ).
thf(f4104,plain,
~ spl489_397,
inference(avatar_split_clause,[],[f1532,f4101]) ).
thf(f4281,definition,
( spl489_434
<=> ( ksndpairEq = $true ) ),
introduced(definition,[new_symbols(definition,[spl489_434])],[avatar_definition]) ).
thf(f4544,plain,
spl489_434,
inference(avatar_split_clause,[],[f1534,f4281]) ).
thf(f5433,definition,
( spl489_668
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ ( cartprod @ X5 @ X4 ) ) )
| ( $true
= ( in @ ( ksnd @ X3 ) @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl489_668])],[avatar_definition]) ).
thf(f5434,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( cartprod @ X5 @ X4 ) ) )
| ( $true
= ( in @ ( ksnd @ X3 ) @ X4 ) ) )
| ~ spl489_668 ),
inference(avatar_component_clause,[],[f5433]) ).
thf(f5435,plain,
( spl489_668
| ~ spl489_206 ),
inference(avatar_split_clause,[],[f1379,f3211,f5433]) ).
thf(f5773,definition,
( spl489_740
<=> ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 ) ),
introduced(definition,[new_symbols(definition,[spl489_740])],[avatar_definition]) ).
thf(f5774,plain,
( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X1 @ X0 ) )
= X0 )
| ~ spl489_740 ),
inference(avatar_component_clause,[],[f5773]) ).
thf(f5775,plain,
( spl489_740
| ~ spl489_434 ),
inference(avatar_split_clause,[],[f1777,f4281,f5773]) ).
thf(f5786,plain,
spl489_206,
inference(avatar_split_clause,[],[f1662,f3211]) ).
thf(f7181,plain,
( ( $true != $true )
| ( $true
= ( in @ ( ksnd @ ( kpair @ sK175 @ sK172 ) ) @ sK173 ) )
| ~ spl489_106
| ~ spl489_668 ),
inference(superposition,[],[f5434,f2772]) ).
thf(f7203,plain,
( ( $true
= ( in @ ( ksnd @ ( kpair @ sK175 @ sK172 ) ) @ sK173 ) )
| ~ spl489_106
| ~ spl489_668 ),
inference(trivial_inequality_removal,[],[f7181]) ).
thf(f7209,plain,
( ( $true
= ( in @ sK172 @ sK173 ) )
| ~ spl489_106
| ~ spl489_668
| ~ spl489_740 ),
inference(forward_demodulation,[],[f7203,f5774]) ).
thf(f7210,plain,
( $false
| ~ spl489_106
| spl489_397
| ~ spl489_668
| ~ spl489_740 ),
inference(forward_subsumption_resolution,[],[f7209,f4103]) ).
thf(f7211,plain,
( ~ spl489_106
| spl489_397
| ~ spl489_668
| ~ spl489_740 ),
inference(avatar_contradiction_clause,[],[f7210]) ).
cnf(s58,plain,
spl489_106,
inference(sat_conversion,[],[f2773]) ).
cnf(s306,plain,
~ spl489_397,
inference(sat_conversion,[],[f4104]) ).
cnf(s415,plain,
spl489_434,
inference(sat_conversion,[],[f4544]) ).
cnf(s651,plain,
( ~ spl489_206
| spl489_668 ),
inference(sat_conversion,[],[f5435]) ).
cnf(s739,plain,
( ~ spl489_434
| spl489_740 ),
inference(sat_conversion,[],[f5775]) ).
cnf(s743,plain,
spl489_206,
inference(sat_conversion,[],[f5786]) ).
cnf(s850,plain,
( ~ spl489_106
| spl489_397
| ~ spl489_668
| ~ spl489_740 ),
inference(sat_conversion,[],[f7211]) ).
cnf(s857,plain,
spl489_668,
inference(rat,[],[s651,s743]) ).
cnf(s913,plain,
spl489_740,
inference(rat,[],[s739,s415]) ).
cnf(s942,plain,
~ spl489_106,
inference(rat,[],[s850,s913,s857,s306]) ).
cnf(s1048,plain,
$false,
inference(rat,[],[s58,s942]) ).
thf(f7212,plain,
$false,
inference(avatar_sat_refutation,[],[s1048]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU660^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:03:49 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.66/0.38 % (767724)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.66/0.38 % (767734)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2928540351:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.66/0.38 % (767735)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.66/0.38 % (767735)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.66/0.38 % (767729)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1024259625:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.66/0.38 % (767730)lrs+10_16_si=on:nwc=1.5:random_seed=1709704140:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.66/0.38 % (767731)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4018186386:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.66/0.38 % (767732)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3477198037:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.66/0.38 % (767733)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1595624761:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.66/0.38 % (767735)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1436901491:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.66/0.38 % (767731)Instruction limit reached!
% 0.66/0.38 % (767731)------------------------------
% 0.66/0.38 % (767731)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (767731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (767731)CaDiCaL version: 2.1.3
% 0.66/0.38 % (767731)Termination reason: Instruction limit
% 0.66/0.38 % (767731)Termination phase: shuffling
% 0.66/0.38 % (767731)Time elapsed: 0.002 s
% 0.66/0.38 % (767731)Peak memory usage: 10 MB
% 0.66/0.38 % (767731)Instructions burned: 3 (million)
% 0.66/0.38 % (767730)Instruction limit reached!
% 0.66/0.38 % (767730)------------------------------
% 0.66/0.38 % (767730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (767730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (767730)CaDiCaL version: 2.1.3
% 0.66/0.38 % (767730)Termination reason: Instruction limit
% 0.66/0.38 % (767730)Termination phase: shuffling
% 0.66/0.38 % (767730)Time elapsed: 0.008 s
% 0.66/0.38 % (767730)Peak memory usage: 10 MB
% 0.66/0.38 % (767730)Instructions burned: 18 (million)
% 0.66/0.38 % (767734)Instruction limit reached!
% 0.66/0.38 % (767734)------------------------------
% 0.66/0.38 % (767734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (767734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (767734)CaDiCaL version: 2.1.3
% 0.66/0.38 % (767734)Termination reason: Instruction limit
% 0.66/0.38 % (767734)Termination phase: Property scanning
% 0.66/0.38 % (767734)Time elapsed: 0.019 s
% 0.66/0.38 % (767734)Peak memory usage: 12 MB
% 0.66/0.38 % (767734)Instructions burned: 79 (million)
% 0.66/0.38 % (767733)Instruction limit reached!
% 0.66/0.38 % (767733)------------------------------
% 0.66/0.38 % (767733)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (767733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (767733)CaDiCaL version: 2.1.3
% 0.66/0.38 % (767733)Termination reason: Instruction limit
% 0.66/0.38 % (767733)Termination phase: Preprocessing 3
% 0.66/0.38 % (767733)Time elapsed: 0.012 s
% 0.66/0.38 % (767733)Peak memory usage: 11 MB
% 0.66/0.38 % (767733)Instructions burned: 25 (million)
% 0.66/0.38 % (767745)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.66/0.38 % (767743)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2406104455:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.66/0.38 % (767745)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1970149181:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.66/0.42 % (767743)Instruction limit reached!
% 0.66/0.42 % (767743)------------------------------
% 0.66/0.42 % (767743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.42 % (767743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.42 % (767743)CaDiCaL version: 2.1.3
% 0.66/0.42 % (767743)Termination reason: Instruction limit
% 0.66/0.42 % (767743)Termination phase: shuffling
% 0.66/0.42 % (767743)Time elapsed: 0.002 s
% 0.66/0.42 % (767743)Peak memory usage: 10 MB
% 0.66/0.42 % (767743)Instructions burned: 4 (million)
% 0.66/0.42 % (767745)Instruction limit reached!
% 0.66/0.42 % (767745)------------------------------
% 0.66/0.42 % (767745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.42 % (767745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.42 % (767745)CaDiCaL version: 2.1.3
% 0.66/0.42 % (767745)Termination reason: Instruction limit
% 0.66/0.42 % (767745)Termination phase: shuffling
% 0.66/0.42 % (767745)Time elapsed: 0.002 s
% 0.66/0.42 % (767745)Peak memory usage: 10 MB
% 0.66/0.42 % (767745)Instructions burned: 9 (million)
% 0.66/0.42 % (767744)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2878937213:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.66/0.42 % (767744)Instruction limit reached!
% 0.66/0.42 % (767744)------------------------------
% 0.66/0.42 % (767744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.42 % (767744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.42 % (767744)CaDiCaL version: 2.1.3
% 0.66/0.42 % (767744)Termination reason: Instruction limit
% 0.66/0.42 % (767744)Termination phase: shuffling
% 0.66/0.42 % (767744)Time elapsed: 0.003 s
% 0.66/0.42 % (767744)Peak memory usage: 10 MB
% 0.66/0.42 % (767744)Instructions burned: 6 (million)
% 0.66/0.42 % (767746)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2830758969:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.66/0.42 % (767750)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2832610541:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.66/0.42 % (767746)Instruction limit reached!
% 0.66/0.42 % (767746)------------------------------
% 0.66/0.42 % (767746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.42 % (767746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.42 % (767746)CaDiCaL version: 2.1.3
% 0.66/0.42 % (767746)Termination reason: Instruction limit
% 0.66/0.42 % (767746)Termination phase: shuffling
% 0.66/0.42 % (767746)Time elapsed: 0.006 s
% 0.66/0.42 % (767746)Peak memory usage: 10 MB
% 0.66/0.42 % (767746)Instructions burned: 14 (million)
% 0.66/0.42 % (767749)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.66/0.42 % (767749)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.66/0.42 % (767729)Instruction limit reached!
% 0.66/0.42 % (767729)------------------------------
% 0.66/0.42 % (767729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.42 % (767729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.42 % (767729)CaDiCaL version: 2.1.3
% 0.66/0.42 % (767729)Termination reason: Instruction limit
% 0.66/0.42 % (767729)Termination phase: Property scanning
% 0.66/0.42 % (767729)Time elapsed: 0.040 s
% 0.66/0.42 % (767729)Peak memory usage: 13 MB
% 0.66/0.42 % (767729)Instructions burned: 88 (million)
% 0.66/0.42 % (767749)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2477174219:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.66/0.42 % (767753)lrs+10_1_si=on:cs=on:random_seed=2425489177:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.66/0.42 % (767755)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.66/0.45 % (767750)Instruction limit reached!
% 0.66/0.45 % (767750)------------------------------
% 0.66/0.45 % (767750)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767750)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767750)Termination reason: Instruction limit
% 0.66/0.45 % (767750)Termination phase: Saturation
% 0.66/0.45 % (767750)Time elapsed: 0.019 s
% 0.66/0.45 % (767750)Peak memory usage: 12 MB
% 0.66/0.45 % (767750)Instructions burned: 90 (million)
% 0.66/0.45 % (767749)Instruction limit reached!
% 0.66/0.45 % (767749)------------------------------
% 0.66/0.45 % (767749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767749)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767749)Termination reason: Instruction limit
% 0.66/0.45 % (767749)Termination phase: Property scanning
% 0.66/0.45 % (767749)Time elapsed: 0.013 s
% 0.66/0.45 % (767749)Peak memory usage: 10 MB
% 0.66/0.45 % (767749)Instructions burned: 29 (million)
% 0.66/0.45 % (767753)Instruction limit reached!
% 0.66/0.45 % (767753)------------------------------
% 0.66/0.45 % (767753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767753)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767753)Termination reason: Instruction limit
% 0.66/0.45 % (767753)Termination phase: shuffling
% 0.66/0.45 % (767753)Time elapsed: 0.005 s
% 0.66/0.45 % (767753)Peak memory usage: 10 MB
% 0.66/0.45 % (767753)Instructions burned: 9 (million)
% 0.66/0.45 % (767755)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3252383736:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.66/0.45 % (767756)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2439114984:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.66/0.45 % (767755)Instruction limit reached!
% 0.66/0.45 % (767755)------------------------------
% 0.66/0.45 % (767755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767755)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767755)Termination reason: Instruction limit
% 0.66/0.45 % (767755)Termination phase: shuffling
% 0.66/0.45 % (767755)Time elapsed: 0.003 s
% 0.66/0.45 % (767755)Peak memory usage: 10 MB
% 0.66/0.45 % (767755)Instructions burned: 6 (million)
% 0.66/0.45 % (767759)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3072712758:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.66/0.45 % (767735)Instruction limit reached!
% 0.66/0.45 % (767735)------------------------------
% 0.66/0.45 % (767735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767735)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767735)Termination reason: Instruction limit
% 0.66/0.45 % (767735)Termination phase: Saturation
% 0.66/0.45 % (767735)Time elapsed: 0.067 s
% 0.66/0.45 % (767735)Peak memory usage: 14 MB
% 0.66/0.45 % (767735)Instructions burned: 158 (million)
% 0.66/0.45 % (767761)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3263116279:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.66/0.45 % (767760)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3263115994:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.66/0.45 % (767756)Instruction limit reached!
% 0.66/0.45 % (767756)------------------------------
% 0.66/0.45 % (767756)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767756)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767756)Termination reason: Instruction limit
% 0.66/0.45 % (767756)Termination phase: Preprocessing 3
% 0.66/0.45 % (767756)Time elapsed: 0.018 s
% 0.66/0.45 % (767756)Peak memory usage: 11 MB
% 0.66/0.45 % (767756)Instructions burned: 40 (million)
% 0.66/0.45 % (767764)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1973295053:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.66/0.45 % (767761)Instruction limit reached!
% 0.66/0.45 % (767761)------------------------------
% 0.66/0.45 % (767761)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767761)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767761)Termination reason: Instruction limit
% 0.66/0.45 % (767761)Termination phase: shuffling
% 0.66/0.45 % (767761)Time elapsed: 0.007 s
% 0.66/0.45 % (767761)Peak memory usage: 10 MB
% 0.66/0.45 % (767761)Instructions burned: 16 (million)
% 0.66/0.45 % (767766)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=380355925:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.66/0.45 % (767760)Instruction limit reached!
% 0.66/0.45 % (767760)------------------------------
% 0.66/0.45 % (767760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767760)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767760)Termination reason: Instruction limit
% 0.66/0.45 % (767760)Termination phase: SInE selection
% 0.66/0.45 % (767760)Time elapsed: 0.012 s
% 0.66/0.45 % (767760)Peak memory usage: 11 MB
% 0.66/0.45 % (767760)Instructions burned: 27 (million)
% 0.66/0.45 % (767766)Instruction limit reached!
% 0.66/0.45 % (767766)------------------------------
% 0.66/0.45 % (767766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767766)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767766)Termination reason: Instruction limit
% 0.66/0.45 % (767766)Termination phase: shuffling
% 0.66/0.45 % (767766)Time elapsed: 0.006 s
% 0.66/0.45 % (767766)Peak memory usage: 10 MB
% 0.66/0.45 % (767766)Instructions burned: 14 (million)
% 0.66/0.45 % (767769)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1196048715:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.66/0.45 % (767769)Instruction limit reached!
% 0.66/0.45 % (767769)------------------------------
% 0.66/0.45 % (767769)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767769)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767769)Termination reason: Instruction limit
% 0.66/0.45 % (767769)Termination phase: shuffling
% 0.66/0.45 % (767769)Time elapsed: 0.002 s
% 0.66/0.45 % (767769)Peak memory usage: 10 MB
% 0.66/0.45 % (767769)Instructions burned: 3 (million)
% 0.66/0.45 % (767771)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=490774590:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.66/0.45 % (767773)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=883990660:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.66/0.45 % (767774)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=723149562:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.66/0.45 % (767771)Instruction limit reached!
% 0.66/0.45 % (767771)------------------------------
% 0.66/0.45 % (767771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767771)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767771)Termination reason: Instruction limit
% 0.66/0.45 % (767771)Termination phase: Property scanning
% 0.66/0.45 % (767771)Time elapsed: 0.012 s
% 0.66/0.45 % (767771)Peak memory usage: 10 MB
% 0.66/0.45 % (767771)Instructions burned: 27 (million)
% 0.66/0.45 % (767776)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.66/0.45 % (767776)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.66/0.45 % (767773)Instruction limit reached!
% 0.66/0.45 % (767773)------------------------------
% 0.66/0.45 % (767773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767773)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767773)Termination reason: Instruction limit
% 0.66/0.45 % (767773)Termination phase: Property scanning
% 0.66/0.45 % (767773)Time elapsed: 0.010 s
% 0.66/0.45 % (767773)Peak memory usage: 10 MB
% 0.66/0.45 % (767773)Instructions burned: 24 (million)
% 0.66/0.45 % (767776)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=227697114:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.66/0.45 % (767776)Instruction limit reached!
% 0.66/0.45 % (767776)------------------------------
% 0.66/0.45 % (767776)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767776)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767776)Termination reason: Instruction limit
% 0.66/0.45 % (767776)Termination phase: shuffling
% 0.66/0.45 % (767776)Time elapsed: 0.006 s
% 0.66/0.45 % (767776)Peak memory usage: 10 MB
% 0.66/0.45 % (767776)Instructions burned: 14 (million)
% 0.66/0.45 % (767780)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.66/0.45 % (767759)Instruction limit reached!
% 0.66/0.45 % (767759)------------------------------
% 0.66/0.45 % (767759)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767759)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767759)Termination reason: Instruction limit
% 0.66/0.45 % (767759)Termination phase: Saturation
% 0.66/0.45 % (767759)Time elapsed: 0.067 s
% 0.66/0.45 % (767759)Peak memory usage: 15 MB
% 0.66/0.45 % (767759)Instructions burned: 258 (million)
% 0.66/0.45 % (767780)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=32152213:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.66/0.45 % (767781)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1565905202:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 0.66/0.45 % (767780)Instruction limit reached!
% 0.66/0.45 % (767780)------------------------------
% 0.66/0.45 % (767780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767780)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767780)Termination reason: Instruction limit
% 0.66/0.45 % (767780)Termination phase: shuffling
% 0.66/0.45 % (767780)Time elapsed: 0.004 s
% 0.66/0.45 % (767780)Peak memory usage: 10 MB
% 0.66/0.45 % (767780)Instructions burned: 10 (million)
% 0.66/0.45 % (767774)Instruction limit reached!
% 0.66/0.45 % (767774)------------------------------
% 0.66/0.45 % (767774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767774)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767774)Termination reason: Instruction limit
% 0.66/0.45 % (767774)Termination phase: Property scanning
% 0.66/0.45 % (767774)Time elapsed: 0.028 s
% 0.66/0.45 % (767774)Peak memory usage: 12 MB
% 0.66/0.45 % (767774)Instructions burned: 62 (million)
% 0.66/0.45 % (767732) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-767724-767732"...
% 0.66/0.45 % (767785)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1935264299:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.66/0.45 % (767783)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=394783771:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 0.66/0.45 % (767783)Instruction limit reached!
% 0.66/0.45 % (767783)------------------------------
% 0.66/0.45 % (767783)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767783)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767783)Termination reason: Instruction limit
% 0.66/0.45 % (767783)Termination phase: shuffling
% 0.66/0.45 % (767783)Time elapsed: 0.004 s
% 0.66/0.45 % (767783)Peak memory usage: 10 MB
% 0.66/0.45 % (767783)Instructions burned: 9 (million)
% 0.66/0.45 % (767732)...printing done.
% 0.66/0.45 % (767785)Instruction limit reached!
% 0.66/0.45 % (767785)------------------------------
% 0.66/0.45 % (767785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767785)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767785)Termination reason: Instruction limit
% 0.66/0.45 % (767785)Termination phase: Property scanning
% 0.66/0.45 % (767785)Time elapsed: 0.006 s
% 0.66/0.45 % (767785)Peak memory usage: 10 MB
% 0.66/0.45 % (767785)Instructions burned: 25 (million)
% 0.66/0.45 % (767781)Instruction limit reached!
% 0.66/0.45 % (767781)------------------------------
% 0.66/0.45 % (767781)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.45 % (767781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.45 % (767781)CaDiCaL version: 2.1.3
% 0.66/0.45 % (767781)Termination reason: Instruction limit
% 0.66/0.45 % (767781)Termination phase: Property scanning
% 0.66/0.45 % (767781)Time elapsed: 0.013 s
% 0.66/0.45 % (767781)Peak memory usage: 10 MB
% 0.66/0.45 % (767781)Instructions burned: 31 (million)
% 0.66/0.45 % (767732)Refutation found. Thanks to Tanya!
% 0.66/0.45 % SZS status Theorem for theBenchmark
% 0.66/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.66/0.46 % (767732)------------------------------
% 0.66/0.46 % (767732)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.46 % (767732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.46 % (767732)CaDiCaL version: 2.1.3
% 0.66/0.46 % (767732)Termination reason: Refutation
% 0.66/0.46 % (767732)Time elapsed: 0.147 s
% 0.66/0.46 % (767732)Peak memory usage: 18 MB
% 0.66/0.46 % (767732)Instructions burned: 282 (million)
% 0.66/0.46 % (767724)Success in time 0.194 s
% 0.66/0.46 % Vampire exiting
%------------------------------------------------------------------------------