%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU652^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:30:31 AM UTC 2026
% Result : Theorem 0.55s 0.44s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 84 ( 27 unt; 0 typ; 9 def)
% Number of atoms : 3468 ( 957 equ; 0 cnn)
% Maximal formula atoms : 170 ( 41 avg)
% Number of connectives : 1808 ( 98 ~; 80 |; 688 &; 248 @)
% ( 14 <=>; 680 =>; 0 <=; 0 <~>)
% Maximal formula depth : 174 ( 20 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 : 345 ( 342 usr; 198 con; 0-4 aty)
% Number of variables : 92 ( 0 sgn 71 !; 21 ?; 92 :)
% 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_201,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_202,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_203,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_204,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_205,type,
vAND: $o > $o > $o ).
thf(func_def_206,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_207,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_208,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_209,type,
vIMP: $o > $o > $o ).
thf(func_def_210,type,
vNOT: $o > $o ).
thf(func_def_211,type,
sP0: $i > $i > $o ).
thf(func_def_212,type,
sP1: $i > $o ).
thf(func_def_213,type,
sP2: $o ).
thf(func_def_216,type,
sK5: $o ).
thf(func_def_221,type,
sK10: $i > $o ).
thf(func_def_228,type,
sK17: $i > $i > $i ).
thf(func_def_231,type,
sK20: $i > $o ).
thf(func_def_232,type,
sK21: $i > $o ).
thf(func_def_233,type,
sK22: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_234,type,
sK23: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_235,type,
sK24: $i > ( $i > $o ) > $i ).
thf(func_def_236,type,
sK25: $i > $o ).
thf(func_def_240,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_242,type,
sK31: $i > $o ).
thf(func_def_257,type,
sK46: $i > $o ).
thf(func_def_262,type,
sK51: $i > $i > $i ).
thf(func_def_263,type,
sK52: $i > $i > $i ).
thf(func_def_279,type,
sK68: $o ).
thf(func_def_291,type,
sK80: $i > $i > $i ).
thf(func_def_299,type,
sK88: $i > $o ).
thf(func_def_300,type,
sK89: $i > $o ).
thf(func_def_301,type,
sK90: $i > $o ).
thf(func_def_302,type,
sK91: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_303,type,
sK92: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_308,type,
sK97: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_309,type,
sK98: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_312,type,
sK101: $i > $o ).
thf(func_def_313,type,
sK102: $i > $o ).
thf(func_def_324,type,
sK113: $i > $i ).
thf(func_def_329,type,
sK118: $i > $o ).
thf(func_def_332,type,
sK121: $i > ( $i > $o ) > $i ).
thf(func_def_333,type,
sK122: $i > ( $i > $o ) > $i ).
thf(func_def_334,type,
sK123: $i > $i ).
thf(func_def_341,type,
sK130: $i > $i > $i ).
thf(func_def_359,type,
sK148: ( $i > $o ) > $i ).
thf(func_def_360,type,
sK149: $i > $o ).
thf(func_def_367,type,
sK156: $i > $o ).
thf(func_def_378,type,
sK167: ( $i > $o ) > $i > $i ).
thf(func_def_380,type,
sK169: $i > $o ).
thf(func_def_382,type,
sK171: $i > $o ).
thf(func_def_385,type,
sK174: $i > ( $i > $o ) > $i ).
thf(func_def_394,type,
sK183: $i > $i ).
thf(func_def_397,type,
sK186: $o ).
thf(func_def_403,type,
sK192: $i > $i > $i ).
thf(func_def_420,type,
sK209: ( $i > $o ) > $i ).
thf(func_def_421,type,
sK210: $i > $o ).
thf(func_def_422,type,
sK211: $i > $i ).
thf(func_def_429,type,
sK218: $o ).
thf(func_def_439,type,
sK228: ( $i > $o ) > $i > $i ).
thf(func_def_441,type,
sK230: $i > $o ).
thf(func_def_445,type,
sK234: $i > $o ).
thf(func_def_448,type,
sK237: $i > ( $i > $o ) > $i ).
thf(func_def_449,type,
sK238: $i > ( $i > $o ) > $i ).
thf(func_def_450,type,
sK239: ( $i > $i > $o ) > $i > $i ).
thf(func_def_451,type,
sK240: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_452,type,
sK241: ( $i > $i > $o ) > $i > $i ).
thf(func_def_454,type,
sK243: $i > $i > $o ).
thf(func_def_455,type,
sK244: $i > $i ).
thf(func_def_456,type,
sK245: $i > $i ).
thf(func_def_457,type,
sK246: $i > $o ).
thf(func_def_463,type,
sK252: $i > $o ).
thf(func_def_464,type,
sK253: $i > $i ).
thf(func_def_465,type,
sK254: ( $i > $o ) > $i ).
thf(func_def_467,type,
sK256: $i > $i ).
thf(func_def_468,type,
sK257: $i > $i ).
thf(func_def_469,type,
sK258: $i > $i ).
thf(func_def_470,type,
sK259: $i > $i ).
thf(func_def_471,type,
sK260: $i > $i ).
thf(func_def_472,type,
sK261: $i > $i > $i > $i ).
thf(func_def_473,type,
sK262: $i > $i ).
thf(func_def_474,type,
sK263: $i > $i ).
thf(func_def_475,type,
sK264: $i > $i ).
thf(func_def_476,type,
sK265: $i > $i ).
thf(func_def_477,type,
sK266: $i > $i > $i ).
thf(func_def_478,type,
sK267: $i > $i > $i ).
thf(func_def_479,type,
sK268: $i > $i > $i > $i ).
thf(func_def_480,type,
sK269: $i > $i > $i > $i ).
thf(func_def_481,type,
sK270: $i > $i > $i > $i ).
thf(func_def_482,type,
sK271: $i > $i > $i ).
thf(func_def_483,type,
sK272: $i > $i > $i ).
thf(func_def_484,type,
sK273: $i > $i > $i ).
thf(func_def_502,type,
sK291: $i > $i ).
thf(func_def_503,type,
sK292: $i > $o ).
thf(func_def_514,type,
sK303: $i > $o ).
thf(func_def_518,type,
sK307: $o ).
thf(func_def_524,type,
sK313: $o ).
thf(func_def_525,type,
sK314: $o > $i > $i > $i ).
thf(func_def_534,type,
sK323: $i > $o ).
thf(func_def_537,type,
sK326: $i > $i > $i ).
thf(func_def_544,type,
sK333: $o ).
thf(func_def_547,type,
sK336: $i > ( $i > $o ) > $i ).
thf(func_def_548,type,
sK337: $i > $o ).
thf(func_def_550,type,
sK339: $i > $o ).
thf(func_def_559,type,
sK348: $i > $i > $i ).
thf(func_def_575,type,
sK364: $i > $i > $i ).
thf(func_def_583,type,
sK372: $i > $i > $i ).
thf(func_def_599,type,
sK388: $i > $o ).
thf(func_def_602,type,
sK391: $i > ( $i > $o ) > $i ).
thf(func_def_604,type,
sK393: $i > $o ).
thf(func_def_605,type,
sK394: ( $i > $o ) > $i > $i ).
thf(func_def_606,type,
sK395: $i > $i ).
thf(func_def_610,type,
sK399: $i > $o ).
thf(func_def_622,type,
sK411: ( $i > $o ) > $i ).
thf(func_def_623,type,
sK412: ( $i > $o ) > $i ).
thf(func_def_624,type,
sK413: $i > $o ).
thf(func_def_627,type,
sK416: $i > $o ).
thf(func_def_629,type,
sK418: $i > ( $i > $o ) > $i > $i ).
thf(func_def_631,type,
sK420: $i > $o ).
thf(func_def_633,type,
sK422: ( $i > $o ) > $i > $i ).
thf(func_def_643,type,
sK432: $i > $i > $i > $i ).
thf(func_def_644,type,
sK433: $i > $i > $i > $i ).
thf(func_def_655,type,
sK444: $i > $i ).
thf(func_def_657,type,
sK446: $i > $i ).
thf(func_def_659,type,
sK448: $i > $o ).
thf(func_def_670,type,
sK459: $o ).
thf(func_def_673,type,
sK462: $i > $o ).
thf(f31,axiom,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f47,axiom,
! [X0: $i,X1: $i] :
( ( ( X0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= notinsingleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(f52,axiom,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= upairsetIR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(f175,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
=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairequniteq) ).
thf(f176,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
=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f175]) ).
thf(f185,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= upairsetIR ),
inference(rectify,[],[f52]) ).
thf(f186,plain,
( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
<=> ( upairsetIR = $true ) ),
inference(fool_elimination,[],[f185]) ).
thf(f292,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f176]) ).
thf(f293,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 )
=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f292]) ).
thf(f345,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f31]) ).
thf(f346,plain,
( ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
<=> ( setadjoinIL = $true ) ),
inference(fool_elimination,[],[f345]) ).
thf(f368,plain,
! [X0: $i,X1: $i] :
( ( ( X0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= notinsingleton ),
inference(rectify,[],[f47]) ).
thf(f369,plain,
( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true ) )
<=> ( notinsingleton = $true ) ),
inference(fool_elimination,[],[f368]) ).
thf(f540,plain,
( ! [X1: $i,X0: $i] :
( ( X0 != X1 )
=> ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true ) )
<=> ( notinsingleton = $true ) ),
inference(flattening,[],[f369]) ).
thf(f562,plain,
( ? [X1: $i,X2: $i,X0: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
& ( X1 != X2 ) )
& ( 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,[],[f293]) ).
thf(f563,plain,
( ( setminusI = $true )
& ( powersetI1 = $true )
& ( binintersectLsub = $true )
& ( wellorderingAx = $true )
& ( emptyInPowerset = $true )
& ( notdexE = $true )
& ( bs114d = $true )
& ( setoftrueEq = $true )
& ( notinemptyset = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusSubset2 = $true )
& ( powersetsubset = $true )
& ( notequalI1 = $true )
& ( emptyE1 = $true )
& ( disjointsetsI1 = $true )
& ( setunionE = $true )
& ( setukpairinjR1 = $true )
& ( kpairiskpair = $true )
& ( exu__Cong = $true )
& ( singletonsswitch = $true )
& ( cartprodmempair1 = $true )
& ( setunionsingleton1 = $true )
& ( binunionLsub = $true )
& ( powerset__Cong = $true )
& ( binintersectSubset2 = $true )
& ( omegaIndAx = $true )
& ( setminusERneg = $true )
& ( powersetAx = $true )
& ( emptysetE = $true )
& ( binintersectSubset4 = $true )
& ( exuE2 = $true )
& ( powersetI = $true )
& ( setadjoinIL = $true )
& ( binunionIR = $true )
& ( subset2powerset = $true )
& ( notsubsetI = $true )
& ( setextAx = $true )
& ( setadjoinE = $true )
& ( exuE3u = $true )
& ( binintersectSubset5 = $true )
& ( noeltsimpempty = $true )
& ( binunionRsub = $true )
& ( setadjoinOr = $true )
& ( prop2setE = $true )
& ( setunionAx = $true )
& ( omegaSAx = $true )
& ( emptyI = $true )
& ( binunionE = $true )
& ( emptysetAx = $true )
& ( notequalI2 = $true )
& ? [X1: $i,X2: $i,X0: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
& ( X1 != X2 ) )
& ( setextsub = $true )
& ( sepSubset = $true )
& ( quantDeMorgan2 = $true )
& ( upairsubunion = $true )
& ( in__Cong = $true )
& ( descr__Cong = $true )
& ( emptysetsubset = $true )
& ( binintersectSubset1 = $true )
& ( emptyset__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( symdiffIneg1 = $true )
& ( dsetconstr__Cong = $true )
& ( setunionI = $true )
& ( inCongP = $true )
& ( emptyinunitempty = $true )
& ( binintersectEL = $true )
& ( secondinupair = $true )
& ( kpairp = $true )
& ( exuE3e = $true )
& ( sepInPowerset = $true )
& ( setadjoin__Cong = $true )
& ( notinsingleton = $true )
& ( symdiffI2 = $true )
& ( nonemptyI = $true )
& ( binintersectI = $true )
& ( cartprodmempair = $true )
& ( setminusER = $true )
& ( ubforcartprodlem2 = $true )
& ( exuE1 = $true )
& ( omega0Ax = $true )
& ( omega__Cong = $true )
& ( setminusELneg = $true )
& ( vacuousDall = $true )
& ( setunionsingleton2 = $true )
& ( exuI3 = $true )
& ( subPowSU = $true )
& ( singletonprop = $true )
& ( singletonsubset = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIL = $true )
& ( cartprodfstin = $true )
& ( singletoninpowerset = $true )
& ( symdiffE = $true )
& ( exuI2 = $true )
& ( binintersectER = $true )
& ( emptyinPowerset = $true )
& ( singletoninpowunion = $true )
& ( ubforcartprodlem3 = $true )
& ( dsetconstrI = $true )
& ( setext = $true )
& ( setadjoinIR = $true )
& ( binunionIL = $true )
& ( upairinpowunion = $true )
& ( setukpairinjR12 = $true )
& ( inPowerset = $true )
& ( replAx = $true )
& ( singletonsuniq = $true )
& ( foundationAx = $true )
& ( setukpairinjL = $true )
& ( prop2setI = $true )
& ( setukpairIL = $true )
& ( dsetconstrEL = $true )
& ( uniqinunit = $true )
& ( setminusLsub = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan4 = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( prop2set2propI = $true )
& ( upairsetIR = $true )
& ( subsetE = $true )
& ( setukpairinjL2 = $true )
& ( upairset2E = $true )
& ( eqinunit = $true )
& ( exuEu = $true )
& ( binintersectSubset3 = $true )
& ( kfstpairEq = $true )
& ( setukpairinjL1 = $true )
& ( setadjoinSub2 = $true )
& ( setunionE2 = $true )
& ( setunionsingleton = $true )
& ( dsetconstrER = $true )
& ( setukpairIR = $true )
& ( setminusSubset1 = $true )
& ( setminusEL = $true )
& ( subsetTrans = $true )
& ( cartprodpairin = $true )
& ( setadjoinSub = $true )
& ( symdiffIneg2 = $true )
& ( setukpairinjR11 = $true )
& ( subsetI1 = $true )
& ( nonemptyE1 = $true )
& ( binunionEcases = $true )
& ( quantDeMorgan3 = $true )
& ( ex1I2 = $true )
& ( subsetE2 = $true )
& ( theprop = $true )
& ( subsetRefl = $true )
& ( kfstsingleton = $true )
& ( upairsetE = $true )
& ( eqimpsubset2 = $true )
& ( quantDeMorgan1 = $true )
& ( powersetE = $true )
& ( setbeta = $true )
& ( setminusIRneg = $true )
& ( notdallE = $true )
& ( descrp = $true )
& ( powersetE1 = $true )
& ( symdiffI1 = $true )
& ( setadjoinAx = $true )
& ( exuI1 = $true )
& ( nonemptyI1 = $true )
& ( ex1E1 = $true )
& ( ex1I = $true )
& ( upairset2IR = $true )
& ( setminusILneg = $true )
& ( setunion__Cong = $true )
& ( binintersectRsub = $true ) ),
inference(flattening,[],[f562]) ).
thf(f717,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
<=> ( notinsingleton = $true ) ),
inference(ennf_transformation,[],[f540]) ).
thf(f741,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( upairsetIR != $true ) )
& ( ( upairsetIR = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true ) ) ),
inference(nnf_transformation,[],[f186]) ).
thf(f742,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( upairsetIR != $true ) )
& ( ( upairsetIR = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f741]) ).
thf(f743,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( upairsetIR != $true ) )
& ( ( upairsetIR = $true )
| ( ( in @ sK9 @ ( setadjoin @ sK8 @ ( setadjoin @ sK9 @ emptyset ) ) )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X2,sK8),skolemize(X3,sK9)],[f742]) ).
thf(f759,plain,
( ( ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) ) ),
inference(nnf_transformation,[],[f346]) ).
thf(f760,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
!= $true ) ) ),
inference(rectify,[],[f759]) ).
thf(f761,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ( $true
!= ( in @ sK28 @ ( setadjoin @ sK28 @ sK27 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27,sK28]),skolemize(X2,sK27),skolemize(X3,sK28)],[f760]) ).
thf(f919,plain,
( ( setminusI = $true )
& ( powersetI1 = $true )
& ( binintersectLsub = $true )
& ( wellorderingAx = $true )
& ( emptyInPowerset = $true )
& ( notdexE = $true )
& ( bs114d = $true )
& ( setoftrueEq = $true )
& ( notinemptyset = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusSubset2 = $true )
& ( powersetsubset = $true )
& ( notequalI1 = $true )
& ( emptyE1 = $true )
& ( disjointsetsI1 = $true )
& ( setunionE = $true )
& ( setukpairinjR1 = $true )
& ( kpairiskpair = $true )
& ( exu__Cong = $true )
& ( singletonsswitch = $true )
& ( cartprodmempair1 = $true )
& ( setunionsingleton1 = $true )
& ( binunionLsub = $true )
& ( powerset__Cong = $true )
& ( binintersectSubset2 = $true )
& ( omegaIndAx = $true )
& ( setminusERneg = $true )
& ( powersetAx = $true )
& ( emptysetE = $true )
& ( binintersectSubset4 = $true )
& ( exuE2 = $true )
& ( powersetI = $true )
& ( setadjoinIL = $true )
& ( binunionIR = $true )
& ( subset2powerset = $true )
& ( notsubsetI = $true )
& ( setextAx = $true )
& ( setadjoinE = $true )
& ( exuE3u = $true )
& ( binintersectSubset5 = $true )
& ( noeltsimpempty = $true )
& ( binunionRsub = $true )
& ( setadjoinOr = $true )
& ( prop2setE = $true )
& ( setunionAx = $true )
& ( omegaSAx = $true )
& ( emptyI = $true )
& ( binunionE = $true )
& ( emptysetAx = $true )
& ( notequalI2 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
& ( X0 != X1 ) )
& ( setextsub = $true )
& ( sepSubset = $true )
& ( quantDeMorgan2 = $true )
& ( upairsubunion = $true )
& ( in__Cong = $true )
& ( descr__Cong = $true )
& ( emptysetsubset = $true )
& ( binintersectSubset1 = $true )
& ( emptyset__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( symdiffIneg1 = $true )
& ( dsetconstr__Cong = $true )
& ( setunionI = $true )
& ( inCongP = $true )
& ( emptyinunitempty = $true )
& ( binintersectEL = $true )
& ( secondinupair = $true )
& ( kpairp = $true )
& ( exuE3e = $true )
& ( sepInPowerset = $true )
& ( setadjoin__Cong = $true )
& ( notinsingleton = $true )
& ( symdiffI2 = $true )
& ( nonemptyI = $true )
& ( binintersectI = $true )
& ( cartprodmempair = $true )
& ( setminusER = $true )
& ( ubforcartprodlem2 = $true )
& ( exuE1 = $true )
& ( omega0Ax = $true )
& ( omega__Cong = $true )
& ( setminusELneg = $true )
& ( vacuousDall = $true )
& ( setunionsingleton2 = $true )
& ( exuI3 = $true )
& ( subPowSU = $true )
& ( singletonprop = $true )
& ( singletonsubset = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIL = $true )
& ( cartprodfstin = $true )
& ( singletoninpowerset = $true )
& ( symdiffE = $true )
& ( exuI2 = $true )
& ( binintersectER = $true )
& ( emptyinPowerset = $true )
& ( singletoninpowunion = $true )
& ( ubforcartprodlem3 = $true )
& ( dsetconstrI = $true )
& ( setext = $true )
& ( setadjoinIR = $true )
& ( binunionIL = $true )
& ( upairinpowunion = $true )
& ( setukpairinjR12 = $true )
& ( inPowerset = $true )
& ( replAx = $true )
& ( singletonsuniq = $true )
& ( foundationAx = $true )
& ( setukpairinjL = $true )
& ( prop2setI = $true )
& ( setukpairIL = $true )
& ( dsetconstrEL = $true )
& ( uniqinunit = $true )
& ( setminusLsub = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan4 = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( prop2set2propI = $true )
& ( upairsetIR = $true )
& ( subsetE = $true )
& ( setukpairinjL2 = $true )
& ( upairset2E = $true )
& ( eqinunit = $true )
& ( exuEu = $true )
& ( binintersectSubset3 = $true )
& ( kfstpairEq = $true )
& ( setukpairinjL1 = $true )
& ( setadjoinSub2 = $true )
& ( setunionE2 = $true )
& ( setunionsingleton = $true )
& ( dsetconstrER = $true )
& ( setukpairIR = $true )
& ( setminusSubset1 = $true )
& ( setminusEL = $true )
& ( subsetTrans = $true )
& ( cartprodpairin = $true )
& ( setadjoinSub = $true )
& ( symdiffIneg2 = $true )
& ( setukpairinjR11 = $true )
& ( subsetI1 = $true )
& ( nonemptyE1 = $true )
& ( binunionEcases = $true )
& ( quantDeMorgan3 = $true )
& ( ex1I2 = $true )
& ( subsetE2 = $true )
& ( theprop = $true )
& ( subsetRefl = $true )
& ( kfstsingleton = $true )
& ( upairsetE = $true )
& ( eqimpsubset2 = $true )
& ( quantDeMorgan1 = $true )
& ( powersetE = $true )
& ( setbeta = $true )
& ( setminusIRneg = $true )
& ( notdallE = $true )
& ( descrp = $true )
& ( powersetE1 = $true )
& ( symdiffI1 = $true )
& ( setadjoinAx = $true )
& ( exuI1 = $true )
& ( nonemptyI1 = $true )
& ( ex1E1 = $true )
& ( ex1I = $true )
& ( upairset2IR = $true )
& ( setminusILneg = $true )
& ( setunion__Cong = $true )
& ( binintersectRsub = $true ) ),
inference(rectify,[],[f563]) ).
thf(f920,plain,
( ( setminusI = $true )
& ( powersetI1 = $true )
& ( binintersectLsub = $true )
& ( wellorderingAx = $true )
& ( emptyInPowerset = $true )
& ( notdexE = $true )
& ( bs114d = $true )
& ( setoftrueEq = $true )
& ( notinemptyset = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusSubset2 = $true )
& ( powersetsubset = $true )
& ( notequalI1 = $true )
& ( emptyE1 = $true )
& ( disjointsetsI1 = $true )
& ( setunionE = $true )
& ( setukpairinjR1 = $true )
& ( kpairiskpair = $true )
& ( exu__Cong = $true )
& ( singletonsswitch = $true )
& ( cartprodmempair1 = $true )
& ( setunionsingleton1 = $true )
& ( binunionLsub = $true )
& ( powerset__Cong = $true )
& ( binintersectSubset2 = $true )
& ( omegaIndAx = $true )
& ( setminusERneg = $true )
& ( powersetAx = $true )
& ( emptysetE = $true )
& ( binintersectSubset4 = $true )
& ( exuE2 = $true )
& ( powersetI = $true )
& ( setadjoinIL = $true )
& ( binunionIR = $true )
& ( subset2powerset = $true )
& ( notsubsetI = $true )
& ( setextAx = $true )
& ( setadjoinE = $true )
& ( exuE3u = $true )
& ( binintersectSubset5 = $true )
& ( noeltsimpempty = $true )
& ( binunionRsub = $true )
& ( setadjoinOr = $true )
& ( prop2setE = $true )
& ( setunionAx = $true )
& ( omegaSAx = $true )
& ( emptyI = $true )
& ( binunionE = $true )
& ( emptysetAx = $true )
& ( notequalI2 = $true )
& ( ( setadjoin @ sK177 @ emptyset )
= ( setadjoin @ sK176 @ ( setadjoin @ sK175 @ emptyset ) ) )
& ( sK176 != sK175 )
& ( setextsub = $true )
& ( sepSubset = $true )
& ( quantDeMorgan2 = $true )
& ( upairsubunion = $true )
& ( in__Cong = $true )
& ( descr__Cong = $true )
& ( emptysetsubset = $true )
& ( binintersectSubset1 = $true )
& ( emptyset__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( symdiffIneg1 = $true )
& ( dsetconstr__Cong = $true )
& ( setunionI = $true )
& ( inCongP = $true )
& ( emptyinunitempty = $true )
& ( binintersectEL = $true )
& ( secondinupair = $true )
& ( kpairp = $true )
& ( exuE3e = $true )
& ( sepInPowerset = $true )
& ( setadjoin__Cong = $true )
& ( notinsingleton = $true )
& ( symdiffI2 = $true )
& ( nonemptyI = $true )
& ( binintersectI = $true )
& ( cartprodmempair = $true )
& ( setminusER = $true )
& ( ubforcartprodlem2 = $true )
& ( exuE1 = $true )
& ( omega0Ax = $true )
& ( omega__Cong = $true )
& ( setminusELneg = $true )
& ( vacuousDall = $true )
& ( setunionsingleton2 = $true )
& ( exuI3 = $true )
& ( subPowSU = $true )
& ( singletonprop = $true )
& ( singletonsubset = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIL = $true )
& ( cartprodfstin = $true )
& ( singletoninpowerset = $true )
& ( symdiffE = $true )
& ( exuI2 = $true )
& ( binintersectER = $true )
& ( emptyinPowerset = $true )
& ( singletoninpowunion = $true )
& ( ubforcartprodlem3 = $true )
& ( dsetconstrI = $true )
& ( setext = $true )
& ( setadjoinIR = $true )
& ( binunionIL = $true )
& ( upairinpowunion = $true )
& ( setukpairinjR12 = $true )
& ( inPowerset = $true )
& ( replAx = $true )
& ( singletonsuniq = $true )
& ( foundationAx = $true )
& ( setukpairinjL = $true )
& ( prop2setI = $true )
& ( setukpairIL = $true )
& ( dsetconstrEL = $true )
& ( uniqinunit = $true )
& ( setminusLsub = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan4 = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( prop2set2propI = $true )
& ( upairsetIR = $true )
& ( subsetE = $true )
& ( setukpairinjL2 = $true )
& ( upairset2E = $true )
& ( eqinunit = $true )
& ( exuEu = $true )
& ( binintersectSubset3 = $true )
& ( kfstpairEq = $true )
& ( setukpairinjL1 = $true )
& ( setadjoinSub2 = $true )
& ( setunionE2 = $true )
& ( setunionsingleton = $true )
& ( dsetconstrER = $true )
& ( setukpairIR = $true )
& ( setminusSubset1 = $true )
& ( setminusEL = $true )
& ( subsetTrans = $true )
& ( cartprodpairin = $true )
& ( setadjoinSub = $true )
& ( symdiffIneg2 = $true )
& ( setukpairinjR11 = $true )
& ( subsetI1 = $true )
& ( nonemptyE1 = $true )
& ( binunionEcases = $true )
& ( quantDeMorgan3 = $true )
& ( ex1I2 = $true )
& ( subsetE2 = $true )
& ( theprop = $true )
& ( subsetRefl = $true )
& ( kfstsingleton = $true )
& ( upairsetE = $true )
& ( eqimpsubset2 = $true )
& ( quantDeMorgan1 = $true )
& ( powersetE = $true )
& ( setbeta = $true )
& ( setminusIRneg = $true )
& ( notdallE = $true )
& ( descrp = $true )
& ( powersetE1 = $true )
& ( symdiffI1 = $true )
& ( setadjoinAx = $true )
& ( exuI1 = $true )
& ( nonemptyI1 = $true )
& ( ex1E1 = $true )
& ( ex1I = $true )
& ( upairset2IR = $true )
& ( setminusILneg = $true )
& ( setunion__Cong = $true )
& ( binintersectRsub = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK175,sK176,sK177]),skolemize(X0,sK175),skolemize(X1,sK176),skolemize(X2,sK177)],[f919]) ).
thf(f969,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( notinsingleton != $true ) )
& ( ( notinsingleton = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
& ( X0 != X1 ) ) ) ),
inference(nnf_transformation,[],[f717]) ).
thf(f970,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( notinsingleton != $true ) )
& ( ( notinsingleton = $true )
| ? [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= $true )
& ( X2 != X3 ) ) ) ),
inference(rectify,[],[f969]) ).
thf(f971,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( notinsingleton != $true ) )
& ( ( notinsingleton = $true )
| ( ( ( in @ sK219 @ ( setadjoin @ sK220 @ emptyset ) )
= $true )
& ( sK219 != sK220 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK219,sK220]),skolemize(X2,sK219),skolemize(X3,sK220)],[f970]) ).
thf(f1246,plain,
! [X0: $i,X1: $i] :
( ( upairsetIR != $true )
| ( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true ) ),
inference(cnf_transformation,[],[f743]) ).
thf(f1272,plain,
! [X0: $i,X1: $i] :
( ( setadjoinIL != $true )
| ( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(cnf_transformation,[],[f761]) ).
thf(f1516,plain,
upairsetIR = $true,
inference(cnf_transformation,[],[f920]) ).
thf(f1564,plain,
notinsingleton = $true,
inference(cnf_transformation,[],[f920]) ).
thf(f1586,plain,
sK176 != sK175,
inference(cnf_transformation,[],[f920]) ).
thf(f1587,plain,
( ( setadjoin @ sK177 @ emptyset )
= ( setadjoin @ sK176 @ ( setadjoin @ sK175 @ emptyset ) ) ),
inference(cnf_transformation,[],[f920]) ).
thf(f1605,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f920]) ).
thf(f1695,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( notinsingleton != $true )
| ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) ),
inference(cnf_transformation,[],[f971]) ).
thf(f3137,definition,
( spl466_203
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl466_203])],[avatar_definition]) ).
thf(f3138,plain,
( ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) )
= $true )
| ~ spl466_203 ),
inference(avatar_component_clause,[],[f3137]) ).
thf(f3149,definition,
( spl466_206
<=> ( setadjoinIL = $true ) ),
introduced(definition,[new_symbols(definition,[spl466_206])],[avatar_definition]) ).
thf(f3410,definition,
( spl466_265
<=> ( ( setadjoin @ sK177 @ emptyset )
= ( setadjoin @ sK176 @ ( setadjoin @ sK175 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[spl466_265])],[avatar_definition]) ).
thf(f3412,plain,
( ( ( setadjoin @ sK177 @ emptyset )
= ( setadjoin @ sK176 @ ( setadjoin @ sK175 @ emptyset ) ) )
| ~ spl466_265 ),
inference(avatar_component_clause,[],[f3410]) ).
thf(f3413,plain,
spl466_265,
inference(avatar_split_clause,[],[f1587,f3410]) ).
thf(f3564,plain,
spl466_206,
inference(avatar_split_clause,[],[f1605,f3149]) ).
thf(f3770,definition,
( spl466_341
<=> ( sK176 = sK175 ) ),
introduced(definition,[new_symbols(definition,[spl466_341])],[avatar_definition]) ).
thf(f3772,plain,
( ( sK176 != sK175 )
| spl466_341 ),
inference(avatar_component_clause,[],[f3770]) ).
thf(f3773,plain,
~ spl466_341,
inference(avatar_split_clause,[],[f1586,f3770]) ).
thf(f3927,definition,
( spl466_376
<=> ! [X2: $i,X1: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X1 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl466_376])],[avatar_definition]) ).
thf(f3928,plain,
( ! [X2: $i,X1: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X1 ) )
= $true )
| ~ spl466_376 ),
inference(avatar_component_clause,[],[f3927]) ).
thf(f4229,definition,
( spl466_441
<=> ( upairsetIR = $true ) ),
introduced(definition,[new_symbols(definition,[spl466_441])],[avatar_definition]) ).
thf(f4307,definition,
( spl466_457
<=> ( notinsingleton = $true ) ),
introduced(definition,[new_symbols(definition,[spl466_457])],[avatar_definition]) ).
thf(f4451,plain,
( ~ spl466_441
| spl466_203 ),
inference(avatar_split_clause,[],[f1246,f3137,f4229]) ).
thf(f4816,plain,
spl466_457,
inference(avatar_split_clause,[],[f1564,f4307]) ).
thf(f5224,definition,
( spl466_643
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl466_643])],[avatar_definition]) ).
thf(f5225,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ~ spl466_643 ),
inference(avatar_component_clause,[],[f5224]) ).
thf(f5240,plain,
( spl466_376
| ~ spl466_206 ),
inference(avatar_split_clause,[],[f1272,f3149,f3927]) ).
thf(f5542,plain,
( spl466_643
| ~ spl466_457 ),
inference(avatar_split_clause,[],[f1695,f4307,f5224]) ).
thf(f5882,plain,
spl466_441,
inference(avatar_split_clause,[],[f1516,f4229]) ).
thf(f6193,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ sK176 @ ( setadjoin @ sK175 @ emptyset ) ) )
!= $true )
| ( sK177 = X0 ) )
| ~ spl466_265
| ~ spl466_643 ),
inference(superposition,[],[f5225,f3412]) ).
thf(f6206,plain,
( ( sK176 = sK177 )
| ( $true != $true )
| ~ spl466_265
| ~ spl466_376
| ~ spl466_643 ),
inference(superposition,[],[f6193,f3928]) ).
thf(f6214,plain,
( ( sK176 = sK177 )
| ~ spl466_265
| ~ spl466_376
| ~ spl466_643 ),
inference(trivial_inequality_removal,[],[f6206]) ).
thf(f6220,definition,
( spl466_788
<=> ( sK176 = sK177 ) ),
introduced(definition,[new_symbols(definition,[spl466_788])],[avatar_definition]) ).
thf(f6222,plain,
( ( sK176 = sK177 )
| ~ spl466_788 ),
inference(avatar_component_clause,[],[f6220]) ).
thf(f6223,plain,
( spl466_788
| ~ spl466_265
| ~ spl466_376
| ~ spl466_643 ),
inference(avatar_split_clause,[],[f6214,f5224,f3927,f3410,f6220]) ).
thf(f6420,plain,
( ( $true != $true )
| ( sK175 = sK177 )
| ~ spl466_203
| ~ spl466_265
| ~ spl466_643 ),
inference(superposition,[],[f6193,f3138]) ).
thf(f6423,plain,
( ( sK175 = sK177 )
| ~ spl466_203
| ~ spl466_265
| ~ spl466_643 ),
inference(trivial_inequality_removal,[],[f6420]) ).
thf(f6426,plain,
( ( sK176 = sK175 )
| ~ spl466_203
| ~ spl466_265
| ~ spl466_643
| ~ spl466_788 ),
inference(forward_demodulation,[],[f6423,f6222]) ).
thf(f6428,plain,
( $false
| ~ spl466_203
| ~ spl466_265
| spl466_341
| ~ spl466_643
| ~ spl466_788 ),
inference(forward_subsumption_resolution,[],[f6426,f3772]) ).
thf(f6429,plain,
( ~ spl466_203
| ~ spl466_265
| spl466_341
| ~ spl466_643
| ~ spl466_788 ),
inference(avatar_contradiction_clause,[],[f6428]) ).
cnf(s185,plain,
spl466_265,
inference(sat_conversion,[],[f3413]) ).
cnf(s215,plain,
spl466_206,
inference(sat_conversion,[],[f3564]) ).
cnf(s264,plain,
~ spl466_341,
inference(sat_conversion,[],[f3773]) ).
cnf(s411,plain,
( spl466_203
| ~ spl466_441 ),
inference(sat_conversion,[],[f4451]) ).
cnf(s507,plain,
spl466_457,
inference(sat_conversion,[],[f4816]) ).
cnf(s617,plain,
( ~ spl466_206
| spl466_376 ),
inference(sat_conversion,[],[f5240]) ).
cnf(s699,plain,
( ~ spl466_457
| spl466_643 ),
inference(sat_conversion,[],[f5542]) ).
cnf(s796,plain,
spl466_441,
inference(sat_conversion,[],[f5882]) ).
cnf(s810,plain,
( ~ spl466_265
| ~ spl466_376
| ~ spl466_643
| spl466_788 ),
inference(sat_conversion,[],[f6223]) ).
cnf(s824,plain,
( ~ spl466_203
| ~ spl466_265
| spl466_341
| ~ spl466_643
| ~ spl466_788 ),
inference(sat_conversion,[],[f6429]) ).
cnf(s856,plain,
spl466_643,
inference(rat,[],[s699,s507]) ).
cnf(s885,plain,
spl466_203,
inference(rat,[],[s411,s796]) ).
cnf(s947,plain,
spl466_376,
inference(rat,[],[s617,s215]) ).
cnf(s958,plain,
~ spl466_788,
inference(rat,[],[s824,s264,s856,s885,s185]) ).
cnf(s959,plain,
$false,
inference(rat,[],[s810,s947,s856,s958,s185]) ).
thf(f6430,plain,
$false,
inference(avatar_sat_refutation,[],[s959]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU652^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n020.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 14:03:35 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.21/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.40 % (1103936)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.55/0.40 % (1103941)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3609696034:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.55/0.40 % (1103947)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.55/0.40 % (1103947)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
% 0.55/0.40 % (1103942)lrs+10_16_si=on:nwc=1.5:random_seed=874703326:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.55/0.40 % (1103945)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=221903688:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.55/0.40 % (1103943)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=992678754:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.55/0.40 % (1103944)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=4035986548: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)
% 0.55/0.40 % (1103946)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2572885373:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.55/0.40 % (1103947)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=3535321194:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.55/0.40 % (1103943)Instruction limit reached!
% 0.55/0.40 % (1103943)------------------------------
% 0.55/0.40 % (1103943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (1103943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (1103943)CaDiCaL version: 2.1.3
% 0.55/0.40 % (1103943)Termination reason: Instruction limit
% 0.55/0.40 % (1103943)Termination phase: shuffling
% 0.55/0.40 % (1103943)Time elapsed: 0.002 s
% 0.55/0.40 % (1103943)Peak memory usage: 10 MB
% 0.55/0.40 % (1103943)Instructions burned: 3 (million)
% 0.55/0.40 % (1103942)Instruction limit reached!
% 0.55/0.40 % (1103942)------------------------------
% 0.55/0.40 % (1103942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (1103942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (1103942)CaDiCaL version: 2.1.3
% 0.55/0.40 % (1103942)Termination reason: Instruction limit
% 0.55/0.40 % (1103942)Termination phase: shuffling
% 0.55/0.40 % (1103942)Time elapsed: 0.009 s
% 0.55/0.40 % (1103942)Peak memory usage: 10 MB
% 0.55/0.40 % (1103942)Instructions burned: 19 (million)
% 0.55/0.40 % (1103945)Instruction limit reached!
% 0.55/0.40 % (1103945)------------------------------
% 0.55/0.40 % (1103945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (1103945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (1103945)CaDiCaL version: 2.1.3
% 0.55/0.40 % (1103945)Termination reason: Instruction limit
% 0.55/0.40 % (1103945)Termination phase: Preprocessing 3
% 0.55/0.40 % (1103945)Time elapsed: 0.012 s
% 0.55/0.40 % (1103945)Peak memory usage: 11 MB
% 0.55/0.40 % (1103945)Instructions burned: 25 (million)
% 0.55/0.40 % (1103941)Instruction limit reached!
% 0.55/0.40 % (1103941)------------------------------
% 0.55/0.40 % (1103941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (1103941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (1103941)CaDiCaL version: 2.1.3
% 0.55/0.40 % (1103941)Termination reason: Instruction limit
% 0.55/0.40 % (1103941)Termination phase: Property scanning
% 0.55/0.40 % (1103941)Time elapsed: 0.022 s
% 0.55/0.40 % (1103941)Peak memory usage: 13 MB
% 0.55/0.40 % (1103941)Instructions burned: 88 (million)
% 0.55/0.40 % (1103955)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4272610623:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.55/0.40 % (1103955)Instruction limit reached!
% 0.55/0.40 % (1103955)------------------------------
% 0.55/0.40 % (1103955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103955)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103955)Termination reason: Instruction limit
% 0.55/0.44 % (1103955)Termination phase: shuffling
% 0.55/0.44 % (1103955)Time elapsed: 0.002 s
% 0.55/0.44 % (1103955)Peak memory usage: 10 MB
% 0.55/0.44 % (1103955)Instructions burned: 3 (million)
% 0.55/0.44 % (1103958)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2029099145:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.55/0.44 % (1103957)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.55/0.44 % (1103958)Instruction limit reached!
% 0.55/0.44 % (1103958)------------------------------
% 0.55/0.44 % (1103958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103958)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103958)Termination reason: Instruction limit
% 0.55/0.44 % (1103958)Termination phase: shuffling
% 0.55/0.44 % (1103958)Time elapsed: 0.003 s
% 0.55/0.44 % (1103958)Peak memory usage: 10 MB
% 0.55/0.44 % (1103958)Instructions burned: 12 (million)
% 0.55/0.44 % (1103956)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=473086507:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.55/0.44 % (1103957)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2416204762:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.55/0.44 % (1103946)Instruction limit reached!
% 0.55/0.44 % (1103946)------------------------------
% 0.55/0.44 % (1103946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103946)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103946)Termination reason: Instruction limit
% 0.55/0.44 % (1103946)Termination phase: Property scanning
% 0.55/0.44 % (1103946)Time elapsed: 0.034 s
% 0.55/0.44 % (1103946)Peak memory usage: 12 MB
% 0.55/0.44 % (1103946)Instructions burned: 75 (million)
% 0.55/0.44 % (1103957)Instruction limit reached!
% 0.55/0.44 % (1103957)------------------------------
% 0.55/0.44 % (1103957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103956)Instruction limit reached!
% 0.55/0.44 % (1103956)------------------------------
% 0.55/0.44 % (1103956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103957)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103957)Termination reason: Instruction limit
% 0.55/0.44 % (1103957)Termination phase: shuffling
% 0.55/0.44 % (1103956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103957)Time elapsed: 0.005 s
% 0.55/0.44 % (1103957)Peak memory usage: 10 MB
% 0.55/0.44 % (1103957)Instructions burned: 10 (million)
% 0.55/0.44 % (1103956)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103956)Termination reason: Instruction limit
% 0.55/0.44 % (1103956)Termination phase: shuffling
% 0.55/0.44 % (1103956)Time elapsed: 0.005 s
% 0.55/0.44 % (1103956)Peak memory usage: 10 MB
% 0.55/0.44 % (1103956)Instructions burned: 10 (million)
% 0.55/0.44 % (1103961)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
% 0.55/0.44 % (1103961)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.55/0.44 % (1103964)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=2668511851:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.55/0.44 % (1103961)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=665541880:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.55/0.44 % (1103966)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.55/0.44 % (1103966)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=1818906604:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.55/0.44 % (1103967)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2692822844:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.55/0.44 % (1103965)lrs+10_1_si=on:cs=on:random_seed=4162647966:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.55/0.44 % (1103966)Instruction limit reached!
% 0.55/0.44 % (1103966)------------------------------
% 0.55/0.44 % (1103966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103966)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103966)Termination reason: Instruction limit
% 0.55/0.44 % (1103966)Termination phase: shuffling
% 0.55/0.44 % (1103966)Time elapsed: 0.002 s
% 0.55/0.44 % (1103966)Peak memory usage: 10 MB
% 0.55/0.44 % (1103966)Instructions burned: 4 (million)
% 0.55/0.44 % (1103961)Instruction limit reached!
% 0.55/0.44 % (1103961)------------------------------
% 0.55/0.44 % (1103961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103961)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103961)Termination reason: Instruction limit
% 0.55/0.44 % (1103961)Termination phase: Property scanning
% 0.55/0.44 % (1103961)Time elapsed: 0.013 s
% 0.55/0.44 % (1103961)Peak memory usage: 10 MB
% 0.55/0.44 % (1103961)Instructions burned: 30 (million)
% 0.55/0.44 % (1103965)Instruction limit reached!
% 0.55/0.44 % (1103965)------------------------------
% 0.55/0.44 % (1103965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103965)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103965)Termination reason: Instruction limit
% 0.55/0.44 % (1103965)Termination phase: shuffling
% 0.55/0.44 % (1103965)Time elapsed: 0.004 s
% 0.55/0.44 % (1103965)Peak memory usage: 10 MB
% 0.55/0.44 % (1103965)Instructions burned: 9 (million)
% 0.55/0.44 % (1103964)Instruction limit reached!
% 0.55/0.44 % (1103964)------------------------------
% 0.55/0.44 % (1103964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103964)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103964)Termination reason: Instruction limit
% 0.55/0.44 % (1103964)Termination phase: Saturation
% 0.55/0.44 % (1103964)Time elapsed: 0.019 s
% 0.55/0.44 % (1103964)Peak memory usage: 12 MB
% 0.55/0.44 % (1103964)Instructions burned: 88 (million)
% 0.55/0.44 % (1103947)Instruction limit reached!
% 0.55/0.44 % (1103947)------------------------------
% 0.55/0.44 % (1103947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103947)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103947)Termination reason: Instruction limit
% 0.55/0.44 % (1103947)Termination phase: Saturation
% 0.55/0.44 % (1103947)Time elapsed: 0.067 s
% 0.55/0.44 % (1103947)Peak memory usage: 14 MB
% 0.55/0.44 % (1103947)Instructions burned: 159 (million)
% 0.55/0.44 % (1103976)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=110851342:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.55/0.44 % (1103967)Instruction limit reached!
% 0.55/0.44 % (1103967)------------------------------
% 0.55/0.44 % (1103967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103967)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103967)Termination reason: Instruction limit
% 0.55/0.44 % (1103967)Termination phase: Preprocessing 3
% 0.55/0.44 % (1103967)Time elapsed: 0.019 s
% 0.55/0.44 % (1103967)Peak memory usage: 11 MB
% 0.55/0.44 % (1103967)Instructions burned: 39 (million)
% 0.55/0.44 % (1103974)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2404115585:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.55/0.44 % (1103973)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1058974679:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.55/0.44 % (1103975)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=667758084:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.55/0.44 % (1103975)Instruction limit reached!
% 0.55/0.44 % (1103975)------------------------------
% 0.55/0.44 % (1103975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103975)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103975)Termination reason: Instruction limit
% 0.55/0.44 % (1103975)Termination phase: shuffling
% 0.55/0.44 % (1103975)Time elapsed: 0.007 s
% 0.55/0.44 % (1103975)Peak memory usage: 10 MB
% 0.55/0.44 % (1103975)Instructions burned: 16 (million)
% 0.55/0.44 % (1103977)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2499989021:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.55/0.44 % (1103974)Instruction limit reached!
% 0.55/0.44 % (1103974)------------------------------
% 0.55/0.44 % (1103974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103974)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103974)Termination reason: Instruction limit
% 0.55/0.44 % (1103974)Termination phase: Preprocessing 1
% 0.55/0.44 % (1103974)Time elapsed: 0.012 s
% 0.55/0.44 % (1103974)Peak memory usage: 10 MB
% 0.55/0.44 % (1103974)Instructions burned: 26 (million)
% 0.55/0.44 % (1103979)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=321008211: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)
% 0.55/0.44 % (1103977)Instruction limit reached!
% 0.55/0.44 % (1103977)------------------------------
% 0.55/0.44 % (1103977)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103977)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103977)Termination reason: Instruction limit
% 0.55/0.44 % (1103977)Termination phase: shuffling
% 0.55/0.44 % (1103977)Time elapsed: 0.007 s
% 0.55/0.44 % (1103977)Peak memory usage: 10 MB
% 0.55/0.44 % (1103977)Instructions burned: 16 (million)
% 0.55/0.44 % (1103979)Instruction limit reached!
% 0.55/0.44 % (1103979)------------------------------
% 0.55/0.44 % (1103979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103979)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103979)Termination reason: Instruction limit
% 0.55/0.44 % (1103979)Termination phase: shuffling
% 0.55/0.44 % (1103979)Time elapsed: 0.002 s
% 0.55/0.44 % (1103979)Peak memory usage: 10 MB
% 0.55/0.44 % (1103979)Instructions burned: 3 (million)
% 0.55/0.44 % (1103984)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2739717200:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.55/0.44 % (1103944) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1103936-1103944"...
% 0.55/0.44 % (1103985)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=908633964:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.55/0.44 % (1103988)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
% 0.55/0.44 % (1103988)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.55/0.44 % (1103944)...printing done.
% 0.55/0.44 % (1103988)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=841185370:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.55/0.44 % (1103987)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3137379242:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.55/0.44 % (1103944)Refutation found. Thanks to Tanya!
% 0.55/0.44 % SZS status Theorem for theBenchmark
% 0.55/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.55/0.44 % (1103944)------------------------------
% 0.55/0.44 % (1103944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.44 % (1103944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.44 % (1103944)CaDiCaL version: 2.1.3
% 0.55/0.44 % (1103944)Termination reason: Refutation
% 0.55/0.44 % (1103944)Time elapsed: 0.112 s
% 0.55/0.44 % (1103944)Peak memory usage: 17 MB
% 0.55/0.44 % (1103944)Instructions burned: 217 (million)
% 0.55/0.44 % (1103936)Success in time 0.158 s
% 0.55/0.44 % Vampire exiting
%------------------------------------------------------------------------------