%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU666^1 : 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 : n008.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 08:30:36 AM UTC 2026
% Result : Theorem 1.29s 0.48s
% Output : Refutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 3394 ( 938 equ; 0 cnn)
% Maximal formula atoms : 183 ( 130 avg)
% Number of connectives : 1742 ( 10 ~; 0 |; 746 &; 242 @)
% ( 0 <=>; 728 =>; 0 <=; 0 <~>)
% Maximal formula depth : 194 ( 59 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 293 ( 288 usr; 188 con; 0-4 aty)
% ( 8 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 100 ( 65 ^; 22 !; 13 ?; 100 :)
% 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_208,type,
cartprodpairmemER: $o ).
thf(func_def_209,type,
cartprodmempaircEq: $o ).
thf(func_def_210,type,
cartprodfstpairEq: $o ).
thf(func_def_211,type,
cartprodsndpairEq: $o ).
thf(func_def_212,type,
cartprodpairsurjEq: $o ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
dpsetconstrI: $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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_219,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_220,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_221,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_222,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_223,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_224,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_225,type,
vAND: $o > $o > $o ).
thf(func_def_228,type,
vNOT: $o > $o ).
thf(func_def_229,type,
vOR: $o > $o > $o ).
thf(func_def_230,type,
vIFF: $o > $o > $o ).
thf(func_def_231,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_232,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_233,type,
sK0: $i > $i > $o ).
thf(func_def_236,type,
sK3: $i > $i > $i ).
thf(func_def_237,type,
sK4: $i > $i > $i ).
thf(func_def_238,type,
sK5: ( $i > $o ) > $i > $i ).
thf(func_def_239,type,
sK6: $i > $i ).
thf(func_def_240,type,
sK7: ( $i > $o ) > $i > $i ).
thf(func_def_241,type,
sK8: ( $i > $o ) > $i > $i ).
thf(func_def_242,type,
sK9: ( $i > $o ) > $i > $i ).
thf(func_def_243,type,
sK10: $i > $i ).
thf(func_def_244,type,
sK11: $i > $i ).
thf(func_def_245,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_246,type,
sK13: $i > $i > $i ).
thf(func_def_247,type,
sK14: $i > $i ).
thf(func_def_248,type,
sK15: $i > $i > $i ).
thf(func_def_249,type,
sK16: $i > $i > $i ).
thf(func_def_250,type,
sK17: $i > $i > $i ).
thf(func_def_251,type,
sK18: $i > $i > $i ).
thf(func_def_252,type,
sK19: $i > $i > $i > $i ).
thf(func_def_253,type,
sK20: $i > $i > $i ).
thf(func_def_254,type,
sK21: $i > $i > $i ).
thf(func_def_255,type,
sK22: $i > $i > $i ).
thf(func_def_256,type,
sK23: $i > $i > $i ).
thf(func_def_257,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_258,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_259,type,
sK24: ( $i > $o ) > $i > $i ).
thf(func_def_260,type,
sK25: $i > $i > $i ).
thf(func_def_261,type,
sK26: ( $i > $o ) > $i ).
thf(func_def_262,type,
sK27: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_263,type,
sK28: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_264,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_265,type,
sK30: ( $i > $o ) > $i > $i ).
thf(func_def_266,type,
sK31: $i > $i > $i > $i ).
thf(func_def_267,type,
sK32: $i > $i > $i > $i ).
thf(func_def_268,type,
sK33: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_269,type,
sK34: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_270,type,
sK35: $i > ( $i > $i > $o ) > $i ).
thf(func_def_271,type,
sK36: $i > ( $i > $i > $o ) > $i ).
thf(func_def_272,type,
sK37: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_273,type,
sK38: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_274,type,
sK39: ( $i > $o ) > $i ).
thf(func_def_275,type,
sK40: ( $i > $o ) > $i > $i ).
thf(func_def_276,type,
sK41: ( $i > $o ) > $i ).
thf(func_def_277,type,
sK42: $i > ( $i > $o ) > $i ).
thf(func_def_278,type,
sK43: $i > $i > ( $i > $o ) > $i ).
thf(func_def_279,type,
sK44: $i > $i ).
thf(func_def_280,type,
sK45: $i > $i > $i ).
thf(func_def_281,type,
sK46: ( $i > $o ) > $i ).
thf(func_def_282,type,
sK47: ( $i > $o ) > $i ).
thf(func_def_283,type,
sK48: $i > $i ).
thf(func_def_284,type,
sK49: ( $i > $o ) > $i > $i ).
thf(func_def_285,type,
sK50: ( $i > $o ) > $i > $i ).
thf(func_def_286,type,
sK51: $i > $i ).
thf(func_def_287,type,
sK52: ( $i > $o ) > $i > $i ).
thf(func_def_288,type,
sK53: $i > $i > $i ).
thf(func_def_289,type,
sK54: $o > $i > $i > $i ).
thf(func_def_290,type,
sK55: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_291,type,
sK56: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(f100,axiom,
( sepSubset
= ( ! [X0: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
thf(f187,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ( in @ X4 @ X0 )
& ? [X5: $i] :
( ( X2 @ X4 @ X5 )
& ( X3
= ( kpair @ X4 @ X5 ) )
& ( in @ X5 @ X1 ) ) ) ) )
= dpsetconstr ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstr) ).
thf(f189,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
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ! [X0: $i,X1: $i,X2: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] : ( X2 @ X3 @ X4 ) )
@ ( cartprod @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(f190,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
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ! [X0: $i,X1: $i,X2: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] : ( X2 @ X3 @ X4 ) )
@ ( cartprod @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f189]) ).
thf(f382,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
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ! [X0: $i,X1: $i,X2: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] : ( X2 @ X3 @ X4 ) )
@ ( cartprod @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f190]) ).
thf(f383,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 )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ! [X1: $i,X2: $i > $i > $o,X0: $i] :
( ( subset
@ ( dpsetconstr @ X0 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) )
@ ( cartprod @ X0 @ X1 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f382]) ).
thf(f414,plain,
( sepSubset
= ( ! [X0: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 ) ) ),
inference(rectify,[],[f100]) ).
thf(f415,plain,
( sepSubset
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ Y1 ) ) ) ),
inference(fool_elimination,[],[f414]) ).
thf(f451,plain,
( ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ( in @ X4 @ X0 )
& ? [X5: $i] :
( ( X2 @ X4 @ X5 )
& ( X3
= ( kpair @ X4 @ X5 ) )
& ( in @ X5 @ X1 ) ) ) ) )
= dpsetconstr ),
inference(rectify,[],[f187]) ).
thf(f452,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 )
& ( Y2 @ Y4 @ Y5 ) ) )
& ( in @ Y4 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f451]) ).
thf(f555,plain,
( ? [X2: $i > $i > $o,X0: $i,X1: $i] :
( ( subset
@ ( dpsetconstr @ X0 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) )
@ ( cartprod @ X0 @ X1 ) )
!= $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $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,[],[f383]) ).
thf(f556,plain,
( ( powersetE = $true )
& ( exuI1 = $true )
& ( setunion__Cong = $true )
& ( subsetI2 = $true )
& ( binintersectRsub = $true )
& ( dsetconstrER = $true )
& ( nonemptyI1 = $true )
& ( setminusLsub = $true )
& ( binintersectI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( cartprodfstpairEq = $true )
& ( quantDeMorgan2 = $true )
& ( singletonsuniq = $true )
& ( setadjoinSub = $true )
& ( binunionIR = $true )
& ( nonemptyI = $true )
& ( subsetI1 = $true )
& ( setukpairinjL = $true )
& ( notsubsetI = $true )
& ( quantDeMorgan4 = $true )
& ( binunionE = $true )
& ( ex1I = $true )
& ( cartprodsndpairEq = $true )
& ( prop2setE = $true )
& ( setminusI = $true )
& ( prop2setI = $true )
& ( dsetconstrEL = $true )
& ? [X2: $i > $i > $o,X0: $i,X1: $i] :
( ( subset
@ ( dpsetconstr @ X0 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) )
@ ( cartprod @ X0 @ X1 ) )
!= $true )
& ( binintersectEL = $true )
& ( upairsubunion = $true )
& ( setukpairIL = $true )
& ( eqimpsubset1 = $true )
& ( omega__Cong = $true )
& ( setunionE = $true )
& ( binintersectSubset2 = $true )
& ( powerset__Cong = $true )
& ( exuI2 = $true )
& ( binintersectER = $true )
& ( eqimpsubset2 = $true )
& ( sepInPowerset = $true )
& ( bs114d = $true )
& ( exuE1 = $true )
& ( cartprodmempair = $true )
& ( notequalI2 = $true )
& ( kpairiskpair = $true )
& ( emptysetsubset = $true )
& ( subsetRefl = $true )
& ( foundationAx = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIL = $true )
& ( exuE2 = $true )
& ( emptyE1 = $true )
& ( secondinupair = $true )
& ( ksndpairEq = $true )
& ( powersetI = $true )
& ( cartprodfstin = $true )
& ( upairset2E = $true )
& ( dpsetconstrI = $true )
& ( quantDeMorgan3 = $true )
& ( emptysetAx = $true )
& ( setukpairinjR2 = $true )
& ( cartprodmempaircEq = $true )
& ( exuE3e = $true )
& ( setoftrueEq = $true )
& ( setunionE2 = $true )
& ( setadjoinAx = $true )
& ( setadjoinIR = $true )
& ( descrp = $true )
& ( setminusSubset1 = $true )
& ( ubforcartprodlem3 = $true )
& ( emptysetimpfalse = $true )
& ( cartprodmempair1 = $true )
& ( symdiffIneg2 = $true )
& ( binintersectSubset3 = $true )
& ( cartprodpairmemER = $true )
& ( exuI3 = $true )
& ( setext = $true )
& ( setunionI = $true )
& ( setukpairinjL2 = $true )
& ( kfstpairEq = $true )
& ( setminusEL = $true )
& ( singletonprop = $true )
& ( powersetAx = $true )
& ( setunionAx = $true )
& ( emptyInPowerset = $true )
& ( disjointsetsI1 = $true )
& ( exu__Cong = $true )
& ( emptyinPowerset = $true )
& ( setminusIRneg = $true )
& ( cartprodpairin = $true )
& ( binintersectSubset1 = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( wellorderingAx = $true )
& ( setextAx = $true )
& ( upairinpowunion = $true )
& ( kpairsurjEq = $true )
& ( sepSubset = $true )
& ( setminusER = $true )
& ( notinemptyset = $true )
& ( ubforcartprodlem2 = $true )
& ( binunionEcases = $true )
& ( nonemptyImpWitness = $true )
& ( upairequniteq = $true )
& ( emptyset__Cong = $true )
& ( setukpairinjR1 = $true )
& ( symdiffI2 = $true )
& ( vacuousDall = $true )
& ( setunionsingleton = $true )
& ( setbeta = $true )
& ( omega0Ax = $true )
& ( subsetTrans = $true )
& ( setextsub = $true )
& ( notequalI1 = $true )
& ( upairsetIR = $true )
& ( symdiffIneg1 = $true )
& ( kpairp = $true )
& ( emptysetE = $true )
& ( descr__Cong = $true )
& ( singletonsubset = $true )
& ( in__Cong = $true )
& ( setukpairinjL1 = $true )
& ( binunionIL = $true )
& ( nonemptyE1 = $true )
& ( subset2powerset = $true )
& ( cartprodpairsurjEq = $true )
& ( emptyI = $true )
& ( setadjoinIL = $true )
& ( setadjoinE = $true )
& ( ksndsingleton = $true )
& ( cartprodsndin = $true )
& ( cartprodpairmemEL = $true )
& ( notdallE = $true )
& ( binintersectSubset5 = $true )
& ( setukpairIR = $true )
& ( upairset2IR = $true )
& ( exuE3u = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusERneg = $true )
& ( singletoninpowunion = $true )
& ( exuEu = $true )
& ( symdiffE = $true )
& ( singletoninpowerset = $true )
& ( dsetconstrI = $true )
& ( setunionsingleton1 = $true )
& ( theprop = $true )
& ( symdiffI1 = $true )
& ( ex1I2 = $true )
& ( omegaSAx = $true )
& ( subPowSU = $true )
& ( binunionRsub = $true )
& ( setadjoinSub2 = $true )
& ( uniqinunit = $true )
& ( singletonsswitch = $true )
& ( powersetE1 = $true )
& ( setminusILneg = $true )
& ( setukpairinjR = $true )
& ( notdexE = $true )
& ( setunionsingleton2 = $true )
& ( binintersectLsub = $true )
& ( ex1E1 = $true )
& ( inCongP = $true )
& ( emptyinunitempty = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoin__Cong = $true )
& ( setukpairinjR11 = $true )
& ( replAx = $true )
& ( setminusSubset2 = $true )
& ( setukpairinjR12 = $true )
& ( binunionLsub = $true )
& ( omegaIndAx = $true )
& ( quantDeMorgan1 = $true )
& ( kfstsingleton = $true )
& ( setadjoinOr = $true )
& ( inPowerset = $true )
& ( noeltsimpempty = $true )
& ( upairsetE = $true )
& ( binintersectSubset4 = $true )
& ( powersetsubset = $true )
& ( powersetI1 = $true )
& ( prop2set2propI = $true )
& ( setminusELneg = $true ) ),
inference(flattening,[],[f555]) ).
thf(f557,plain,
( ( powersetE = $true )
& ( exuI1 = $true )
& ( setunion__Cong = $true )
& ( subsetI2 = $true )
& ( binintersectRsub = $true )
& ( dsetconstrER = $true )
& ( nonemptyI1 = $true )
& ( setminusLsub = $true )
& ( binintersectI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( cartprodfstpairEq = $true )
& ( quantDeMorgan2 = $true )
& ( singletonsuniq = $true )
& ( setadjoinSub = $true )
& ( binunionIR = $true )
& ( nonemptyI = $true )
& ( subsetI1 = $true )
& ( setukpairinjL = $true )
& ( notsubsetI = $true )
& ( quantDeMorgan4 = $true )
& ( binunionE = $true )
& ( ex1I = $true )
& ( cartprodsndpairEq = $true )
& ( prop2setE = $true )
& ( setminusI = $true )
& ( prop2setI = $true )
& ( dsetconstrEL = $true )
& ? [X0: $i > $i > $o,X1: $i,X2: $i] :
( $true
!= ( subset
@ ( dpsetconstr @ X1 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) )
@ ( cartprod @ X1 @ X2 ) ) )
& ( binintersectEL = $true )
& ( upairsubunion = $true )
& ( setukpairIL = $true )
& ( eqimpsubset1 = $true )
& ( omega__Cong = $true )
& ( setunionE = $true )
& ( binintersectSubset2 = $true )
& ( powerset__Cong = $true )
& ( exuI2 = $true )
& ( binintersectER = $true )
& ( eqimpsubset2 = $true )
& ( sepInPowerset = $true )
& ( bs114d = $true )
& ( exuE1 = $true )
& ( cartprodmempair = $true )
& ( notequalI2 = $true )
& ( kpairiskpair = $true )
& ( emptysetsubset = $true )
& ( subsetRefl = $true )
& ( foundationAx = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIL = $true )
& ( exuE2 = $true )
& ( emptyE1 = $true )
& ( secondinupair = $true )
& ( ksndpairEq = $true )
& ( powersetI = $true )
& ( cartprodfstin = $true )
& ( upairset2E = $true )
& ( dpsetconstrI = $true )
& ( quantDeMorgan3 = $true )
& ( emptysetAx = $true )
& ( setukpairinjR2 = $true )
& ( cartprodmempaircEq = $true )
& ( exuE3e = $true )
& ( setoftrueEq = $true )
& ( setunionE2 = $true )
& ( setadjoinAx = $true )
& ( setadjoinIR = $true )
& ( descrp = $true )
& ( setminusSubset1 = $true )
& ( ubforcartprodlem3 = $true )
& ( emptysetimpfalse = $true )
& ( cartprodmempair1 = $true )
& ( symdiffIneg2 = $true )
& ( binintersectSubset3 = $true )
& ( cartprodpairmemER = $true )
& ( exuI3 = $true )
& ( setext = $true )
& ( setunionI = $true )
& ( setukpairinjL2 = $true )
& ( kfstpairEq = $true )
& ( setminusEL = $true )
& ( singletonprop = $true )
& ( powersetAx = $true )
& ( setunionAx = $true )
& ( emptyInPowerset = $true )
& ( disjointsetsI1 = $true )
& ( exu__Cong = $true )
& ( emptyinPowerset = $true )
& ( setminusIRneg = $true )
& ( cartprodpairin = $true )
& ( binintersectSubset1 = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( wellorderingAx = $true )
& ( setextAx = $true )
& ( upairinpowunion = $true )
& ( kpairsurjEq = $true )
& ( sepSubset = $true )
& ( setminusER = $true )
& ( notinemptyset = $true )
& ( ubforcartprodlem2 = $true )
& ( binunionEcases = $true )
& ( nonemptyImpWitness = $true )
& ( upairequniteq = $true )
& ( emptyset__Cong = $true )
& ( setukpairinjR1 = $true )
& ( symdiffI2 = $true )
& ( vacuousDall = $true )
& ( setunionsingleton = $true )
& ( setbeta = $true )
& ( omega0Ax = $true )
& ( subsetTrans = $true )
& ( setextsub = $true )
& ( notequalI1 = $true )
& ( upairsetIR = $true )
& ( symdiffIneg1 = $true )
& ( kpairp = $true )
& ( emptysetE = $true )
& ( descr__Cong = $true )
& ( singletonsubset = $true )
& ( in__Cong = $true )
& ( setukpairinjL1 = $true )
& ( binunionIL = $true )
& ( nonemptyE1 = $true )
& ( subset2powerset = $true )
& ( cartprodpairsurjEq = $true )
& ( emptyI = $true )
& ( setadjoinIL = $true )
& ( setadjoinE = $true )
& ( ksndsingleton = $true )
& ( cartprodsndin = $true )
& ( cartprodpairmemEL = $true )
& ( notdallE = $true )
& ( binintersectSubset5 = $true )
& ( setukpairIR = $true )
& ( upairset2IR = $true )
& ( exuE3u = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusERneg = $true )
& ( singletoninpowunion = $true )
& ( exuEu = $true )
& ( symdiffE = $true )
& ( singletoninpowerset = $true )
& ( dsetconstrI = $true )
& ( setunionsingleton1 = $true )
& ( theprop = $true )
& ( symdiffI1 = $true )
& ( ex1I2 = $true )
& ( omegaSAx = $true )
& ( subPowSU = $true )
& ( binunionRsub = $true )
& ( setadjoinSub2 = $true )
& ( uniqinunit = $true )
& ( singletonsswitch = $true )
& ( powersetE1 = $true )
& ( setminusILneg = $true )
& ( setukpairinjR = $true )
& ( notdexE = $true )
& ( setunionsingleton2 = $true )
& ( binintersectLsub = $true )
& ( ex1E1 = $true )
& ( inCongP = $true )
& ( emptyinunitempty = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoin__Cong = $true )
& ( setukpairinjR11 = $true )
& ( replAx = $true )
& ( setminusSubset2 = $true )
& ( setukpairinjR12 = $true )
& ( binunionLsub = $true )
& ( omegaIndAx = $true )
& ( quantDeMorgan1 = $true )
& ( kfstsingleton = $true )
& ( setadjoinOr = $true )
& ( inPowerset = $true )
& ( noeltsimpempty = $true )
& ( upairsetE = $true )
& ( binintersectSubset4 = $true )
& ( powersetsubset = $true )
& ( powersetI1 = $true )
& ( prop2set2propI = $true )
& ( setminusELneg = $true ) ),
inference(rectify,[],[f556]) ).
thf(f558,plain,
( ( powersetE = $true )
& ( exuI1 = $true )
& ( setunion__Cong = $true )
& ( subsetI2 = $true )
& ( binintersectRsub = $true )
& ( dsetconstrER = $true )
& ( nonemptyI1 = $true )
& ( setminusLsub = $true )
& ( binintersectI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( cartprodfstpairEq = $true )
& ( quantDeMorgan2 = $true )
& ( singletonsuniq = $true )
& ( setadjoinSub = $true )
& ( binunionIR = $true )
& ( nonemptyI = $true )
& ( subsetI1 = $true )
& ( setukpairinjL = $true )
& ( notsubsetI = $true )
& ( quantDeMorgan4 = $true )
& ( binunionE = $true )
& ( ex1I = $true )
& ( cartprodsndpairEq = $true )
& ( prop2setE = $true )
& ( setminusI = $true )
& ( prop2setI = $true )
& ( dsetconstrEL = $true )
& ( ( subset
@ ( dpsetconstr @ sK1 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK0 @ Y0 @ Y1 ) )
@ ( cartprod @ sK1 @ sK2 ) )
!= $true )
& ( binintersectEL = $true )
& ( upairsubunion = $true )
& ( setukpairIL = $true )
& ( eqimpsubset1 = $true )
& ( omega__Cong = $true )
& ( setunionE = $true )
& ( binintersectSubset2 = $true )
& ( powerset__Cong = $true )
& ( exuI2 = $true )
& ( binintersectER = $true )
& ( eqimpsubset2 = $true )
& ( sepInPowerset = $true )
& ( bs114d = $true )
& ( exuE1 = $true )
& ( cartprodmempair = $true )
& ( notequalI2 = $true )
& ( kpairiskpair = $true )
& ( emptysetsubset = $true )
& ( subsetRefl = $true )
& ( foundationAx = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIL = $true )
& ( exuE2 = $true )
& ( emptyE1 = $true )
& ( secondinupair = $true )
& ( ksndpairEq = $true )
& ( powersetI = $true )
& ( cartprodfstin = $true )
& ( upairset2E = $true )
& ( dpsetconstrI = $true )
& ( quantDeMorgan3 = $true )
& ( emptysetAx = $true )
& ( setukpairinjR2 = $true )
& ( cartprodmempaircEq = $true )
& ( exuE3e = $true )
& ( setoftrueEq = $true )
& ( setunionE2 = $true )
& ( setadjoinAx = $true )
& ( setadjoinIR = $true )
& ( descrp = $true )
& ( setminusSubset1 = $true )
& ( ubforcartprodlem3 = $true )
& ( emptysetimpfalse = $true )
& ( cartprodmempair1 = $true )
& ( symdiffIneg2 = $true )
& ( binintersectSubset3 = $true )
& ( cartprodpairmemER = $true )
& ( exuI3 = $true )
& ( setext = $true )
& ( setunionI = $true )
& ( setukpairinjL2 = $true )
& ( kfstpairEq = $true )
& ( setminusEL = $true )
& ( singletonprop = $true )
& ( powersetAx = $true )
& ( setunionAx = $true )
& ( emptyInPowerset = $true )
& ( disjointsetsI1 = $true )
& ( exu__Cong = $true )
& ( emptyinPowerset = $true )
& ( setminusIRneg = $true )
& ( cartprodpairin = $true )
& ( binintersectSubset1 = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( wellorderingAx = $true )
& ( setextAx = $true )
& ( upairinpowunion = $true )
& ( kpairsurjEq = $true )
& ( sepSubset = $true )
& ( setminusER = $true )
& ( notinemptyset = $true )
& ( ubforcartprodlem2 = $true )
& ( binunionEcases = $true )
& ( nonemptyImpWitness = $true )
& ( upairequniteq = $true )
& ( emptyset__Cong = $true )
& ( setukpairinjR1 = $true )
& ( symdiffI2 = $true )
& ( vacuousDall = $true )
& ( setunionsingleton = $true )
& ( setbeta = $true )
& ( omega0Ax = $true )
& ( subsetTrans = $true )
& ( setextsub = $true )
& ( notequalI1 = $true )
& ( upairsetIR = $true )
& ( symdiffIneg1 = $true )
& ( kpairp = $true )
& ( emptysetE = $true )
& ( descr__Cong = $true )
& ( singletonsubset = $true )
& ( in__Cong = $true )
& ( setukpairinjL1 = $true )
& ( binunionIL = $true )
& ( nonemptyE1 = $true )
& ( subset2powerset = $true )
& ( cartprodpairsurjEq = $true )
& ( emptyI = $true )
& ( setadjoinIL = $true )
& ( setadjoinE = $true )
& ( ksndsingleton = $true )
& ( cartprodsndin = $true )
& ( cartprodpairmemEL = $true )
& ( notdallE = $true )
& ( binintersectSubset5 = $true )
& ( setukpairIR = $true )
& ( upairset2IR = $true )
& ( exuE3u = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusERneg = $true )
& ( singletoninpowunion = $true )
& ( exuEu = $true )
& ( symdiffE = $true )
& ( singletoninpowerset = $true )
& ( dsetconstrI = $true )
& ( setunionsingleton1 = $true )
& ( theprop = $true )
& ( symdiffI1 = $true )
& ( ex1I2 = $true )
& ( omegaSAx = $true )
& ( subPowSU = $true )
& ( binunionRsub = $true )
& ( setadjoinSub2 = $true )
& ( uniqinunit = $true )
& ( singletonsswitch = $true )
& ( powersetE1 = $true )
& ( setminusILneg = $true )
& ( setukpairinjR = $true )
& ( notdexE = $true )
& ( setunionsingleton2 = $true )
& ( binintersectLsub = $true )
& ( ex1E1 = $true )
& ( inCongP = $true )
& ( emptyinunitempty = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoin__Cong = $true )
& ( setukpairinjR11 = $true )
& ( replAx = $true )
& ( setminusSubset2 = $true )
& ( setukpairinjR12 = $true )
& ( binunionLsub = $true )
& ( omegaIndAx = $true )
& ( quantDeMorgan1 = $true )
& ( kfstsingleton = $true )
& ( setadjoinOr = $true )
& ( inPowerset = $true )
& ( noeltsimpempty = $true )
& ( upairsetE = $true )
& ( binintersectSubset4 = $true )
& ( powersetsubset = $true )
& ( powersetI1 = $true )
& ( prop2set2propI = $true )
& ( setminusELneg = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f557]) ).
thf(f735,plain,
sepSubset = $true,
inference(cnf_transformation,[],[f558]) ).
thf(f805,plain,
( ( subset
@ ( dpsetconstr @ sK1 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK0 @ Y0 @ Y1 ) )
@ ( cartprod @ sK1 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[],[f558]) ).
thf(f836,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 )
& ( Y2 @ Y4 @ Y5 ) ) )
& ( in @ Y4 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f452]) ).
thf(f866,plain,
( sepSubset
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ Y1 ) ) ) ),
inference(cnf_transformation,[],[f415]) ).
thf(f1019,plain,
( $true
!= ( subset
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 )
& ( Y2 @ Y4 @ Y5 ) ) )
& ( in @ Y4 @ Y0 ) ) ) )
@ sK1
@ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK0 @ Y0 @ Y1 ) )
@ ( cartprod @ sK1 @ sK2 ) ) ),
inference(definition_unfolding,[],[f805,f836]) ).
thf(f1051,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ Y1 ) ) )
= $true ),
inference(definition_unfolding,[],[f866,f735]) ).
thf(f1778,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ Y1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1051]) ).
thf(f1779,plain,
! [X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ ( dsetconstr @ Y0 @ X1 ) @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f1778]) ).
thf(f1780,plain,
! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] : ( subset @ ( dsetconstr @ Y0 @ X1 ) @ Y0 )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f1779]) ).
thf(f1781,plain,
! [X2: $i,X1: $i > $o] :
( ( subset @ ( dsetconstr @ X2 @ X1 ) @ X2 )
= $true ),
inference(beta-eta_normalization,[],[f1780]) ).
thf(f1949,plain,
( ( subset
@ ( dsetconstr @ ( cartprod @ sK1 @ sK2 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 )
& ( sK0 @ Y1 @ Y2 ) ) )
& ( in @ Y1 @ sK1 ) ) ) )
@ ( cartprod @ sK1 @ sK2 ) )
!= $true ),
inference(beta-eta_normalization,[],[f1019]) ).
thf(f2720,plain,
$false,
inference(forward_subsumption_resolution,[],[f1949,f1781]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU666^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n008.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:07:24 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.22/0.28 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
% 0.54/0.40 % (3210673)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.54/0.40 % (3210678)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=141349453:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.54/0.40 % (3210684)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.54/0.40 % (3210684)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
% 0.54/0.40 % (3210679)lrs+10_16_si=on:nwc=1.5:random_seed=1910260368:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.54/0.40 % (3210680)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4224337797:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.54/0.40 % (3210684)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=148363052:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.54/0.40 % (3210681)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=563800141: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)
% 0.54/0.40 % (3210682)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4051283202:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.54/0.40 % (3210683)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=602108057:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.54/0.40 % (3210680)Instruction limit reached!
% 0.54/0.40 % (3210680)------------------------------
% 0.54/0.40 % (3210680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.40 % (3210680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.40 % (3210680)CaDiCaL version: 2.1.3
% 0.54/0.40 % (3210680)Termination reason: Instruction limit
% 0.54/0.40 % (3210680)Termination phase: shuffling
% 0.54/0.40 % (3210680)Time elapsed: 0.005 s
% 0.54/0.40 % (3210680)Peak memory usage: 10 MB
% 0.54/0.40 % (3210680)Instructions burned: 11 (million)
% 0.54/0.40 % (3210679)Instruction limit reached!
% 0.54/0.40 % (3210679)------------------------------
% 0.54/0.40 % (3210679)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.40 % (3210679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.40 % (3210679)CaDiCaL version: 2.1.3
% 0.54/0.40 % (3210679)Termination reason: Instruction limit
% 0.54/0.40 % (3210679)Termination phase: shuffling
% 0.54/0.40 % (3210679)Time elapsed: 0.010 s
% 0.54/0.40 % (3210679)Peak memory usage: 10 MB
% 0.54/0.40 % (3210679)Instructions burned: 18 (million)
% 0.54/0.40 % (3210682)Instruction limit reached!
% 0.54/0.40 % (3210682)------------------------------
% 0.54/0.40 % (3210682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.40 % (3210682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.40 % (3210682)CaDiCaL version: 2.1.3
% 0.54/0.40 % (3210682)Termination reason: Instruction limit
% 0.54/0.40 % (3210682)Termination phase: Preprocessing 1
% 0.54/0.40 % (3210682)Time elapsed: 0.010 s
% 0.54/0.40 % (3210682)Peak memory usage: 10 MB
% 0.54/0.40 % (3210682)Instructions burned: 24 (million)
% 0.54/0.40 % (3210678)Instruction limit reached!
% 0.54/0.40 % (3210678)------------------------------
% 0.54/0.40 % (3210678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.40 % (3210678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.40 % (3210678)CaDiCaL version: 2.1.3
% 0.54/0.40 % (3210678)Termination reason: Instruction limit
% 0.54/0.40 % (3210678)Termination phase: Property scanning
% 0.54/0.40 % (3210678)Time elapsed: 0.022 s
% 0.54/0.40 % (3210678)Peak memory usage: 13 MB
% 0.54/0.40 % (3210678)Instructions burned: 90 (million)
% 0.54/0.40 % (3210695)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=752644052:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.54/0.40 % (3210692)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=34751356:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.44 % (3210694)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.44 % (3210695)Instruction limit reached!
% 0.54/0.44 % (3210695)------------------------------
% 0.54/0.44 % (3210695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3210695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3210695)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3210695)Termination reason: Instruction limit
% 0.54/0.44 % (3210695)Termination phase: shuffling
% 0.54/0.44 % (3210695)Time elapsed: 0.003 s
% 0.54/0.44 % (3210695)Peak memory usage: 10 MB
% 0.54/0.44 % (3210695)Instructions burned: 14 (million)
% 0.54/0.44 % (3210692)Instruction limit reached!
% 0.54/0.44 % (3210692)------------------------------
% 0.54/0.44 % (3210692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3210692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3210692)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3210692)Termination reason: Instruction limit
% 0.54/0.44 % (3210692)Termination phase: shuffling
% 0.54/0.44 % (3210692)Time elapsed: 0.003 s
% 0.54/0.44 % (3210692)Peak memory usage: 10 MB
% 0.54/0.44 % (3210692)Instructions burned: 6 (million)
% 0.54/0.44 % (3210693)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1277348288:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.54/0.44 % (3210694)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3059526742:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.54/0.44 % (3210693)Instruction limit reached!
% 0.54/0.44 % (3210693)------------------------------
% 0.54/0.44 % (3210693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3210693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3210693)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3210693)Termination reason: Instruction limit
% 0.54/0.44 % (3210693)Termination phase: shuffling
% 0.54/0.44 % (3210693)Time elapsed: 0.003 s
% 0.54/0.44 % (3210693)Peak memory usage: 10 MB
% 0.54/0.44 % (3210693)Instructions burned: 5 (million)
% 0.54/0.44 % (3210694)Instruction limit reached!
% 0.54/0.44 % (3210694)------------------------------
% 0.54/0.44 % (3210694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3210694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3210694)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3210694)Termination reason: Instruction limit
% 0.54/0.44 % (3210694)Termination phase: shuffling
% 0.54/0.44 % (3210694)Time elapsed: 0.004 s
% 0.54/0.44 % (3210694)Peak memory usage: 10 MB
% 0.54/0.44 % (3210694)Instructions burned: 8 (million)
% 0.54/0.44 % (3210683)Instruction limit reached!
% 0.54/0.44 % (3210683)------------------------------
% 0.54/0.44 % (3210683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3210683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3210683)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3210683)Termination reason: Instruction limit
% 0.54/0.44 % (3210683)Termination phase: Property scanning
% 0.54/0.44 % (3210683)Time elapsed: 0.035 s
% 0.54/0.44 % (3210683)Peak memory usage: 12 MB
% 0.54/0.44 % (3210683)Instructions burned: 77 (million)
% 0.54/0.44 % (3210699)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=4111110695:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.54/0.44 % (3210698)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
% 0.54/0.44 % (3210698)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.44 % (3210698)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2895928691:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.54/0.44 % (3210703)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.29/0.47 % (3210702)lrs+10_1_si=on:cs=on:random_seed=1895794788:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.29/0.47 % (3210703)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=490735845:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.29/0.47 % (3210704)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2766760377:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.29/0.47 % (3210703)Instruction limit reached!
% 1.29/0.47 % (3210703)------------------------------
% 1.29/0.47 % (3210703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.47 % (3210703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.47 % (3210703)CaDiCaL version: 2.1.3
% 1.29/0.47 % (3210703)Termination reason: Instruction limit
% 1.29/0.47 % (3210703)Termination phase: shuffling
% 1.29/0.47 % (3210703)Time elapsed: 0.002 s
% 1.29/0.47 % (3210703)Peak memory usage: 10 MB
% 1.29/0.47 % (3210703)Instructions burned: 4 (million)
% 1.29/0.47 % (3210702)Instruction limit reached!
% 1.29/0.47 % (3210702)------------------------------
% 1.29/0.47 % (3210702)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.47 % (3210702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.47 % (3210702)CaDiCaL version: 2.1.3
% 1.29/0.47 % (3210702)Termination reason: Instruction limit
% 1.29/0.47 % (3210702)Termination phase: shuffling
% 1.29/0.47 % (3210702)Time elapsed: 0.004 s
% 1.29/0.47 % (3210702)Peak memory usage: 10 MB
% 1.29/0.47 % (3210702)Instructions burned: 9 (million)
% 1.29/0.47 % (3210699)Instruction limit reached!
% 1.29/0.47 % (3210699)------------------------------
% 1.29/0.47 % (3210699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.47 % (3210699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.47 % (3210699)CaDiCaL version: 2.1.3
% 1.29/0.47 % (3210699)Termination reason: Instruction limit
% 1.29/0.47 % (3210699)Termination phase: Saturation
% 1.29/0.47 % (3210699)Time elapsed: 0.019 s
% 1.29/0.47 % (3210699)Peak memory usage: 12 MB
% 1.29/0.47 % (3210699)Instructions burned: 90 (million)
% 1.29/0.47 % (3210698)Instruction limit reached!
% 1.29/0.47 % (3210698)------------------------------
% 1.29/0.47 % (3210698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.47 % (3210698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.47 % (3210698)CaDiCaL version: 2.1.3
% 1.29/0.47 % (3210698)Termination reason: Instruction limit
% 1.29/0.47 % (3210698)Termination phase: Property scanning
% 1.29/0.47 % (3210698)Time elapsed: 0.013 s
% 1.29/0.47 % (3210698)Peak memory usage: 10 MB
% 1.29/0.47 % (3210698)Instructions burned: 30 (million)
% 1.29/0.47 % (3210684)Instruction limit reached!
% 1.29/0.47 % (3210684)------------------------------
% 1.29/0.47 % (3210684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.47 % (3210684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.47 % (3210684)CaDiCaL version: 2.1.3
% 1.29/0.47 % (3210684)Termination reason: Instruction limit
% 1.29/0.47 % (3210684)Termination phase: Saturation
% 1.29/0.47 % (3210684)Time elapsed: 0.066 s
% 1.29/0.47 % (3210684)Peak memory usage: 14 MB
% 1.29/0.47 % (3210684)Instructions burned: 157 (million)
% 1.29/0.47 % (3210712)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4114736294:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.29/0.47 % (3210704)Instruction limit reached!
% 1.29/0.47 % (3210704)------------------------------
% 1.29/0.47 % (3210704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.47 % (3210704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.47 % (3210704)CaDiCaL version: 2.1.3
% 1.29/0.47 % (3210704)Termination reason: Instruction limit
% 1.29/0.47 % (3210704)Termination phase: Preprocessing 3
% 1.29/0.47 % (3210704)Time elapsed: 0.017 s
% 1.29/0.47 % (3210704)Peak memory usage: 11 MB
% 1.29/0.47 % (3210704)Instructions burned: 38 (million)
% 1.29/0.47 % (3210712)Instruction limit reached!
% 1.29/0.47 % (3210712)------------------------------
% 1.29/0.47 % (3210712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.47 % (3210712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.48 % (3210712)CaDiCaL version: 2.1.3
% 1.29/0.48 % (3210712)Termination reason: Instruction limit
% 1.29/0.48 % (3210712)Termination phase: shuffling
% 1.29/0.48 % (3210712)Time elapsed: 0.004 s
% 1.29/0.48 % (3210712)Peak memory usage: 10 MB
% 1.29/0.48 % (3210712)Instructions burned: 18 (million)
% 1.29/0.48 % (3210710)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=78809876:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.29/0.48 % (3210711)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2573653739:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.29/0.48 % (3210713)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1519680199:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.29/0.48 % (3210714)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2493237945:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.29/0.48 % (3210711)Instruction limit reached!
% 1.29/0.48 % (3210711)------------------------------
% 1.29/0.48 % (3210711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.48 % (3210711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.48 % (3210711)CaDiCaL version: 2.1.3
% 1.29/0.48 % (3210711)Termination reason: Instruction limit
% 1.29/0.48 % (3210711)Termination phase: SInE selection
% 1.29/0.48 % (3210711)Time elapsed: 0.011 s
% 1.29/0.48 % (3210711)Peak memory usage: 11 MB
% 1.29/0.48 % (3210711)Instructions burned: 26 (million)
% 1.29/0.48 % (3210716)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=4079281648: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)
% 1.29/0.48 % (3210714)Instruction limit reached!
% 1.29/0.48 % (3210714)------------------------------
% 1.29/0.48 % (3210714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.48 % (3210714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.48 % (3210714)CaDiCaL version: 2.1.3
% 1.29/0.48 % (3210714)Termination reason: Instruction limit
% 1.29/0.48 % (3210714)Termination phase: shuffling
% 1.29/0.48 % (3210714)Time elapsed: 0.007 s
% 1.29/0.48 % (3210714)Peak memory usage: 10 MB
% 1.29/0.48 % (3210714)Instructions burned: 16 (million)
% 1.29/0.48 % (3210717)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3745604278:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.29/0.48 % (3210716)Instruction limit reached!
% 1.29/0.48 % (3210716)------------------------------
% 1.29/0.48 % (3210716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.48 % (3210716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.48 % (3210716)CaDiCaL version: 2.1.3
% 1.29/0.48 % (3210716)Termination reason: Instruction limit
% 1.29/0.48 % (3210716)Termination phase: shuffling
% 1.29/0.48 % (3210716)Time elapsed: 0.002 s
% 1.29/0.48 % (3210716)Peak memory usage: 10 MB
% 1.29/0.48 % (3210716)Instructions burned: 4 (million)
% 1.29/0.48 % (3210717)Instruction limit reached!
% 1.29/0.48 % (3210717)------------------------------
% 1.29/0.48 % (3210717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.48 % (3210717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.48 % (3210717)CaDiCaL version: 2.1.3
% 1.29/0.48 % (3210717)Termination reason: Instruction limit
% 1.29/0.48 % (3210717)Termination phase: Property scanning
% 1.29/0.48 % (3210717)Time elapsed: 0.011 s
% 1.29/0.48 % (3210717)Peak memory usage: 10 MB
% 1.29/0.48 % (3210717)Instructions burned: 26 (million)
% 1.29/0.48 % (3210722)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1723929719:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.29/0.48 % (3210726)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
% 1.29/0.48 % (3210726)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.29/0.48 % (3210726)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=1090464641:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.29/0.48 % (3210725)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1547570785:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.29/0.48 % (3210726)Instruction limit reached!
% 1.29/0.48 % (3210726)------------------------------
% 1.29/0.48 % (3210726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.48 % (3210726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.48 % (3210726)CaDiCaL version: 2.1.3
% 1.29/0.48 % (3210726)Termination reason: Instruction limit
% 1.29/0.48 % (3210726)Termination phase: shuffling
% 1.29/0.48 % (3210726)Time elapsed: 0.004 s
% 1.29/0.48 % (3210726)Peak memory usage: 10 MB
% 1.29/0.48 % (3210726)Instructions burned: 17 (million)
% 1.29/0.48 % (3210722)Instruction limit reached!
% 1.29/0.48 % (3210722)------------------------------
% 1.29/0.48 % (3210722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.48 % (3210722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.48 % (3210722)CaDiCaL version: 2.1.3
% 1.29/0.48 % (3210722)Termination reason: Instruction limit
% 1.29/0.48 % (3210722)Termination phase: Property scanning
% 1.29/0.48 % (3210722)Time elapsed: 0.011 s
% 1.29/0.48 % (3210722)Peak memory usage: 10 MB
% 1.29/0.48 % (3210722)Instructions burned: 24 (million)
% 1.29/0.48 % (3210727)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.29/0.48 % (3210731)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=946311938:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.29/0.48 % (3210727)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=1421569832:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.29/0.48 % (3210727)Instruction limit reached!
% 1.29/0.48 % (3210727)------------------------------
% 1.29/0.48 % (3210727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.48 % (3210727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.48 % (3210727)CaDiCaL version: 2.1.3
% 1.29/0.48 % (3210727)Termination reason: Instruction limit
% 1.29/0.48 % (3210727)Termination phase: shuffling
% 1.29/0.48 % (3210727)Time elapsed: 0.004 s
% 1.29/0.48 % (3210727)Peak memory usage: 10 MB
% 1.29/0.48 % (3210727)Instructions burned: 9 (million)
% 1.29/0.48 % (3210731)Instruction limit reached!
% 1.29/0.48 % (3210731)------------------------------
% 1.29/0.48 % (3210731)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.48 % (3210731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.48 % (3210731)CaDiCaL version: 2.1.3
% 1.29/0.48 % (3210731)Termination reason: Instruction limit
% 1.29/0.48 % (3210731)Termination phase: Property scanning
% 1.29/0.48 % (3210731)Time elapsed: 0.008 s
% 1.29/0.48 % (3210731)Peak memory usage: 10 MB
% 1.29/0.48 % (3210731)Instructions burned: 35 (million)
% 1.29/0.48 % (3210732)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3857069912:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.29/0.48 % (3210710) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3210673-3210710"...
% 1.29/0.48 % (3210732)Instruction limit reached!
% 1.29/0.48 % (3210732)------------------------------
% 1.29/0.48 % (3210732)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.48 % (3210732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.48 % (3210732)CaDiCaL version: 2.1.3
% 1.29/0.48 % (3210732)Termination reason: Instruction limit
% 1.29/0.48 % (3210732)Termination phase: shuffling
% 1.29/0.48 % (3210732)Time elapsed: 0.004 s
% 1.29/0.48 % (3210732)Peak memory usage: 10 MB
% 1.29/0.48 % (3210732)Instructions burned: 8 (million)
% 1.29/0.48 % (3210725)Instruction limit reached!
% 1.29/0.48 % (3210725)------------------------------
% 1.29/0.48 % (3210725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.48 % (3210725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.48 % (3210725)CaDiCaL version: 2.1.3
% 1.29/0.48 % (3210725)Termination reason: Instruction limit
% 1.29/0.48 % (3210725)Termination phase: Property scanning
% 1.29/0.48 % (3210725)Time elapsed: 0.029 s
% 1.29/0.48 % (3210725)Peak memory usage: 12 MB
% 1.29/0.48 % (3210725)Instructions burned: 62 (million)
% 1.29/0.48 % (3210736)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=474498192:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.29/0.48 % (3210710)...printing done.
% 1.29/0.48 % (3210710)Refutation found. Thanks to Tanya!
% 1.29/0.48 % SZS status Theorem for theBenchmark
% 1.29/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 1.29/0.48 % (3210710)------------------------------
% 1.29/0.48 % (3210710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.48 % (3210710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.48 % (3210710)CaDiCaL version: 2.1.3
% 1.29/0.48 % (3210710)Termination reason: Refutation
% 1.29/0.48 % (3210710)Time elapsed: 0.067 s
% 1.29/0.48 % (3210710)Peak memory usage: 14 MB
% 1.29/0.48 % (3210710)Instructions burned: 152 (million)
% 1.29/0.48 % (3210673)Success in time 0.192 s
% 1.29/0.48 % Vampire exiting
%------------------------------------------------------------------------------