%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU667^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:30:37 AM UTC 2026
% Result : Theorem 0.37s 0.31s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 3469 ( 955 equ; 0 cnn)
% Maximal formula atoms : 184 ( 111 avg)
% Number of connectives : 1957 ( 10 ~; 0 |; 771 &; 407 @)
% ( 0 <=>; 732 =>; 0 <=; 0 <~>)
% Maximal formula depth : 194 ( 50 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 293 ( 288 usr; 189 con; 0-4 aty)
% ( 15 !!; 22 ??; 0 @@+; 0 @@-)
% Number of variables : 161 ( 118 ^; 30 !; 13 ?; 161 :)
% 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,
dpsetconstrSub: $o ).
thf(func_def_217,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_218,type,
vIMP: $o > $o > $o ).
thf(func_def_219,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_220,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_221,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_222,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_223,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_224,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_225,type,
vAND: $o > $o > $o ).
thf(func_def_226,type,
vNOT: $o > $o ).
thf(func_def_227,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_228,type,
vIFF: $o > $o > $o ).
thf(func_def_229,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_232,type,
vOR: $o > $o > $o ).
thf(func_def_234,type,
sK1: $i > $i > $o ).
thf(func_def_236,type,
sK3: ( $i > $o ) > $i > $i ).
thf(func_def_237,type,
sK4: ( $i > $o ) > $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 > ( $i > $o ) > $i ).
thf(func_def_241,type,
sK8: $i > $i ).
thf(func_def_242,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_243,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_244,type,
sK9: $i > $i > $i ).
thf(func_def_245,type,
sK10: $i > $i > $i ).
thf(func_def_246,type,
sK11: $i > $i > $i ).
thf(func_def_247,type,
sK12: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_248,type,
sK13: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_249,type,
sK14: ( $i > $o ) > $i ).
thf(func_def_250,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_251,type,
sK16: ( $i > $o ) > $i ).
thf(func_def_252,type,
sK17: $i > ( $i > $o ) > $i ).
thf(func_def_253,type,
sK18: $i > $i > $i ).
thf(func_def_254,type,
sK19: ( $i > $o ) > $i ).
thf(func_def_255,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_256,type,
sK20: $i > $i ).
thf(func_def_257,type,
sK21: $i > $i > $i ).
thf(func_def_258,type,
sK22: $i > $i > $i ).
thf(func_def_259,type,
sK23: $i > $i > $i ).
thf(func_def_260,type,
sK24: $i > $i > $i > $i ).
thf(func_def_261,type,
sK25: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_262,type,
sK26: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_263,type,
sK27: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_264,type,
sK28: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_265,type,
sK29: $i > $i ).
thf(func_def_266,type,
sK30: $i > $i > $i ).
thf(func_def_267,type,
sK31: $i > $i > $i ).
thf(func_def_268,type,
sK32: ( $i > $o ) > $i > $i ).
thf(func_def_269,type,
sK33: $i > $o > $i > $i ).
thf(func_def_270,type,
sK34: $i > ( $i > $o ) > $i ).
thf(func_def_271,type,
sK35: $i > ( $i > $o ) > $i ).
thf(func_def_272,type,
sK36: ( $i > $o ) > $i > $i ).
thf(func_def_273,type,
sK37: ( $i > $i > $o ) > $i > $i ).
thf(func_def_274,type,
sK38: ( $i > $i > $o ) > $i > $i ).
thf(func_def_275,type,
sK39: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_276,type,
sK40: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_277,type,
sK41: ( $i > $o ) > $i > $i ).
thf(func_def_278,type,
sK42: ( $i > $o ) > $i > $i ).
thf(func_def_279,type,
sK43: $i > $i ).
thf(func_def_280,type,
sK44: $i > $i > $i ).
thf(func_def_281,type,
sK45: $i > $i ).
thf(func_def_282,type,
sK46: ( $i > $o ) > $i > $i > $i ).
thf(func_def_283,type,
sK47: $i > ( $i > $o ) > $i ).
thf(func_def_284,type,
sK48: $i > $i > $i ).
thf(func_def_285,type,
sK49: $i > $i > $i ).
thf(func_def_286,type,
sK50: $i > $i > $i ).
thf(func_def_287,type,
sK51: ( $i > $o ) > $i > $i ).
thf(func_def_288,type,
sK52: $i > $i ).
thf(func_def_289,type,
sK53: $i > $i > $i > $i ).
thf(func_def_290,type,
sK54: $i > $i > $i > $i ).
thf(func_def_291,type,
sK55: $i > ( $i > $o ) > $i ).
thf(f186,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) )
= breln ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(f187,axiom,
( dpsetconstr
= ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ? [X5: $i] :
( ( X2 @ X4 @ X5 )
& ( in @ X5 @ X1 )
& ( X3
= ( kpair @ X4 @ X5 ) ) )
& ( in @ X4 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstr) ).
thf(f189,axiom,
! [X0: $i,X2: $i > $i > $o,X1: $i] :
( ( subset
@ ( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] : ( X2 @ X3 @ X4 ) )
@ ( cartprod @ X0 @ X1 ) )
= dpsetconstrSub ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(f190,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
=> ( dpsetconstrSub
=> ! [X1: $i,X2: $i > $i > $o,X0: $i] :
( breln @ X0 @ X1
@ ( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(f191,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
=> ( dpsetconstrSub
=> ! [X1: $i,X2: $i > $i > $o,X0: $i] :
( breln @ X0 @ X1
@ ( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f190]) ).
thf(f273,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f186]) ).
thf(f384,plain,
! [X0: $i,X1: $i > $i > $o,X2: $i] :
( ( subset
@ ( dpsetconstr @ X0 @ X2
@ ^ [X3: $i,X4: $i] : ( X1 @ X3 @ X4 ) )
@ ( cartprod @ X0 @ X2 ) )
= dpsetconstrSub ),
inference(rectify,[],[f189]) ).
thf(f385,plain,
( dpsetconstrSub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( subset
@ ( dpsetconstr @ Y2 @ Y0
@ ^ [Y3: $i,Y4: $i] : ( Y1 @ Y3 @ Y4 ) )
@ ( cartprod @ Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f384]) ).
thf(f423,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
=> ( dpsetconstrSub
=> ! [X0: $i,X1: $i > $i > $o,X2: $i] :
( breln @ X2 @ X0
@ ( dpsetconstr @ X2 @ X0
@ ^ [X3: $i,X4: $i] : ( X1 @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f191]) ).
thf(f424,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 )
=> ( ( dpsetconstrSub = $true )
=> ! [X2: $i,X1: $i > $i > $o,X0: $i] :
( $true
= ( breln @ X2 @ X0
@ ( dpsetconstr @ X2 @ X0
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f423]) ).
thf(f487,plain,
( dpsetconstr
= ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ? [X5: $i] :
( ( X2 @ X4 @ X5 )
& ( in @ X5 @ X1 )
& ( X3
= ( kpair @ X4 @ X5 ) ) )
& ( in @ X4 @ X0 ) ) ) ) ),
inference(rectify,[],[f187]) ).
thf(f488,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( ( kpair @ Y4 @ Y5 )
= Y3 )
& ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f487]) ).
thf(f559,plain,
( ? [X2: $i,X1: $i > $i > $o,X0: $i] :
( $true
!= ( breln @ X2 @ X0
@ ( dpsetconstr @ X2 @ X0
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
& ( dpsetconstrSub = $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,[],[f424]) ).
thf(f560,plain,
( ( ksndpairEq = $true )
& ( setadjoinAx = $true )
& ( exuE2 = $true )
& ( binintersectLsub = $true )
& ( vacuousDall = $true )
& ( setminusERneg = $true )
& ( omegaIndAx = $true )
& ( setbeta = $true )
& ? [X2: $i,X1: $i > $i > $o,X0: $i] :
( $true
!= ( breln @ X2 @ X0
@ ( dpsetconstr @ X2 @ X0
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
& ( powersetI = $true )
& ( upairsetIR = $true )
& ( powersetsubset = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodmempair1 = $true )
& ( exuI1 = $true )
& ( symdiffIneg2 = $true )
& ( setunionsingleton = $true )
& ( ksndsingleton = $true )
& ( notdexE = $true )
& ( setextAx = $true )
& ( notequalI1 = $true )
& ( setukpairinjR = $true )
& ( setminusI = $true )
& ( setunionsingleton1 = $true )
& ( nonemptyE1 = $true )
& ( upairsubunion = $true )
& ( emptyI = $true )
& ( nonemptyI = $true )
& ( dsetconstrEL = $true )
& ( upairsetIL = $true )
& ( bs114d = $true )
& ( binintersectI = $true )
& ( setukpairinjL2 = $true )
& ( kpairsurjEq = $true )
& ( prop2setI = $true )
& ( kpairiskpair = $true )
& ( quantDeMorgan2 = $true )
& ( setunionE2 = $true )
& ( sepSubset = $true )
& ( quantDeMorgan1 = $true )
& ( setminusLsub = $true )
& ( exuE3u = $true )
& ( prop2set2propI = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyE1 = $true )
& ( uniqinunit = $true )
& ( setext = $true )
& ( binintersectSubset5 = $true )
& ( cartprodmempair = $true )
& ( binintersectSubset4 = $true )
& ( descrp = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( setminusILneg = $true )
& ( foundationAx = $true )
& ( binintersectSubset3 = $true )
& ( emptyInPowerset = $true )
& ( ex1E1 = $true )
& ( binunionIR = $true )
& ( emptysetsubset = $true )
& ( symdiffIneg1 = $true )
& ( notinsingleton = $true )
& ( setunionsingleton2 = $true )
& ( singletonsswitch = $true )
& ( ubforcartprodlem2 = $true )
& ( secondinupair = $true )
& ( ex1I2 = $true )
& ( symdiffI2 = $true )
& ( cartprodsndpairEq = $true )
& ( ex1I = $true )
& ( setukpairinjL1 = $true )
& ( omega__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( setunionE = $true )
& ( cartprodfstpairEq = $true )
& ( upairinpowunion = $true )
& ( exu__Cong = $true )
& ( cartprodfstin = $true )
& ( omegaSAx = $true )
& ( setadjoinSub = $true )
& ( subsetI1 = $true )
& ( ubforcartprodlem1 = $true )
& ( binunionEcases = $true )
& ( setminusSubset2 = $true )
& ( dpsetconstrSub = $true )
& ( exuI3 = $true )
& ( exuEu = $true )
& ( setminusELneg = $true )
& ( emptyinunitempty = $true )
& ( setunionI = $true )
& ( cartprodpairmemER = $true )
& ( omega0Ax = $true )
& ( upairsetE = $true )
& ( dpsetconstrI = $true )
& ( exuI2 = $true )
& ( setadjoin__Cong = $true )
& ( notdallE = $true )
& ( powersetE = $true )
& ( subset2powerset = $true )
& ( binintersectRsub = $true )
& ( setadjoinOr = $true )
& ( eqimpsubset1 = $true )
& ( setunionAx = $true )
& ( setunion__Cong = $true )
& ( setminusEL = $true )
& ( exuE3e = $true )
& ( cartprodpairin = $true )
& ( binunionLsub = $true )
& ( setadjoinIR = $true )
& ( in__Cong = $true )
& ( setadjoinIL = $true )
& ( emptysetE = $true )
& ( setukpairinjR11 = $true )
& ( exuE1 = $true )
& ( setminusIRneg = $true )
& ( symdiffI1 = $true )
& ( nonemptyI1 = $true )
& ( powersetAx = $true )
& ( dsetconstr__Cong = $true )
& ( emptysetAx = $true )
& ( singletoninpowerset = $true )
& ( symdiffE = $true )
& ( binintersectSubset2 = $true )
& ( singletonsubset = $true )
& ( subsetTrans = $true )
& ( setukpairinjR2 = $true )
& ( setukpairIR = $true )
& ( setminusER = $true )
& ( dsetconstrI = $true )
& ( singletonprop = $true )
& ( setukpairinjR12 = $true )
& ( setadjoinSub2 = $true )
& ( cartprodsndin = $true )
& ( powersetI1 = $true )
& ( emptyinPowerset = $true )
& ( upairequniteq = $true )
& ( kpairp = $true )
& ( notequalI2 = $true )
& ( eqinunit = $true )
& ( inCongP = $true )
& ( prop2setE = $true )
& ( binintersectEL = $true )
& ( descr__Cong = $true )
& ( emptysetimpfalse = $true )
& ( subsetI2 = $true )
& ( quantDeMorgan4 = $true )
& ( singletonsuniq = $true )
& ( setoftrueEq = $true )
& ( emptyset__Cong = $true )
& ( sepInPowerset = $true )
& ( subsetE2 = $true )
& ( kfstsingleton = $true )
& ( quantDeMorgan3 = $true )
& ( notinemptyset = $true )
& ( wellorderingAx = $true )
& ( notsubsetI = $true )
& ( singletoninpowunion = $true )
& ( setadjoinE = $true )
& ( subsetRefl = $true )
& ( setextsub = $true )
& ( replAx = $true )
& ( binunionIL = $true )
& ( binintersectER = $true )
& ( upairset2E = $true )
& ( subsetE = $true )
& ( noeltsimpempty = $true )
& ( setukpairIL = $true )
& ( powersetE1 = $true )
& ( setminusSubset1 = $true )
& ( subPowSU = $true )
& ( inPowerset = $true )
& ( disjointsetsI1 = $true )
& ( cartprodpairmemEL = $true )
& ( powerset__Cong = $true )
& ( binunionRsub = $true )
& ( binunionE = $true )
& ( binintersectSubset1 = $true )
& ( setukpairinjL = $true )
& ( dsetconstrER = $true )
& ( upairset2IR = $true )
& ( cartprodpairsurjEq = $true )
& ( setukpairinjR1 = $true )
& ( ubforcartprodlem3 = $true )
& ( eqimpsubset2 = $true ) ),
inference(flattening,[],[f559]) ).
thf(f561,plain,
( ( ksndpairEq = $true )
& ( setadjoinAx = $true )
& ( exuE2 = $true )
& ( binintersectLsub = $true )
& ( vacuousDall = $true )
& ( setminusERneg = $true )
& ( omegaIndAx = $true )
& ( setbeta = $true )
& ? [X0: $i,X1: $i > $i > $o,X2: $i] :
( $true
!= ( breln @ X0 @ X2
@ ( dpsetconstr @ X0 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
& ( powersetI = $true )
& ( upairsetIR = $true )
& ( powersetsubset = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodmempair1 = $true )
& ( exuI1 = $true )
& ( symdiffIneg2 = $true )
& ( setunionsingleton = $true )
& ( ksndsingleton = $true )
& ( notdexE = $true )
& ( setextAx = $true )
& ( notequalI1 = $true )
& ( setukpairinjR = $true )
& ( setminusI = $true )
& ( setunionsingleton1 = $true )
& ( nonemptyE1 = $true )
& ( upairsubunion = $true )
& ( emptyI = $true )
& ( nonemptyI = $true )
& ( dsetconstrEL = $true )
& ( upairsetIL = $true )
& ( bs114d = $true )
& ( binintersectI = $true )
& ( setukpairinjL2 = $true )
& ( kpairsurjEq = $true )
& ( prop2setI = $true )
& ( kpairiskpair = $true )
& ( quantDeMorgan2 = $true )
& ( setunionE2 = $true )
& ( sepSubset = $true )
& ( quantDeMorgan1 = $true )
& ( setminusLsub = $true )
& ( exuE3u = $true )
& ( prop2set2propI = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyE1 = $true )
& ( uniqinunit = $true )
& ( setext = $true )
& ( binintersectSubset5 = $true )
& ( cartprodmempair = $true )
& ( binintersectSubset4 = $true )
& ( descrp = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( setminusILneg = $true )
& ( foundationAx = $true )
& ( binintersectSubset3 = $true )
& ( emptyInPowerset = $true )
& ( ex1E1 = $true )
& ( binunionIR = $true )
& ( emptysetsubset = $true )
& ( symdiffIneg1 = $true )
& ( notinsingleton = $true )
& ( setunionsingleton2 = $true )
& ( singletonsswitch = $true )
& ( ubforcartprodlem2 = $true )
& ( secondinupair = $true )
& ( ex1I2 = $true )
& ( symdiffI2 = $true )
& ( cartprodsndpairEq = $true )
& ( ex1I = $true )
& ( setukpairinjL1 = $true )
& ( omega__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( setunionE = $true )
& ( cartprodfstpairEq = $true )
& ( upairinpowunion = $true )
& ( exu__Cong = $true )
& ( cartprodfstin = $true )
& ( omegaSAx = $true )
& ( setadjoinSub = $true )
& ( subsetI1 = $true )
& ( ubforcartprodlem1 = $true )
& ( binunionEcases = $true )
& ( setminusSubset2 = $true )
& ( dpsetconstrSub = $true )
& ( exuI3 = $true )
& ( exuEu = $true )
& ( setminusELneg = $true )
& ( emptyinunitempty = $true )
& ( setunionI = $true )
& ( cartprodpairmemER = $true )
& ( omega0Ax = $true )
& ( upairsetE = $true )
& ( dpsetconstrI = $true )
& ( exuI2 = $true )
& ( setadjoin__Cong = $true )
& ( notdallE = $true )
& ( powersetE = $true )
& ( subset2powerset = $true )
& ( binintersectRsub = $true )
& ( setadjoinOr = $true )
& ( eqimpsubset1 = $true )
& ( setunionAx = $true )
& ( setunion__Cong = $true )
& ( setminusEL = $true )
& ( exuE3e = $true )
& ( cartprodpairin = $true )
& ( binunionLsub = $true )
& ( setadjoinIR = $true )
& ( in__Cong = $true )
& ( setadjoinIL = $true )
& ( emptysetE = $true )
& ( setukpairinjR11 = $true )
& ( exuE1 = $true )
& ( setminusIRneg = $true )
& ( symdiffI1 = $true )
& ( nonemptyI1 = $true )
& ( powersetAx = $true )
& ( dsetconstr__Cong = $true )
& ( emptysetAx = $true )
& ( singletoninpowerset = $true )
& ( symdiffE = $true )
& ( binintersectSubset2 = $true )
& ( singletonsubset = $true )
& ( subsetTrans = $true )
& ( setukpairinjR2 = $true )
& ( setukpairIR = $true )
& ( setminusER = $true )
& ( dsetconstrI = $true )
& ( singletonprop = $true )
& ( setukpairinjR12 = $true )
& ( setadjoinSub2 = $true )
& ( cartprodsndin = $true )
& ( powersetI1 = $true )
& ( emptyinPowerset = $true )
& ( upairequniteq = $true )
& ( kpairp = $true )
& ( notequalI2 = $true )
& ( eqinunit = $true )
& ( inCongP = $true )
& ( prop2setE = $true )
& ( binintersectEL = $true )
& ( descr__Cong = $true )
& ( emptysetimpfalse = $true )
& ( subsetI2 = $true )
& ( quantDeMorgan4 = $true )
& ( singletonsuniq = $true )
& ( setoftrueEq = $true )
& ( emptyset__Cong = $true )
& ( sepInPowerset = $true )
& ( subsetE2 = $true )
& ( kfstsingleton = $true )
& ( quantDeMorgan3 = $true )
& ( notinemptyset = $true )
& ( wellorderingAx = $true )
& ( notsubsetI = $true )
& ( singletoninpowunion = $true )
& ( setadjoinE = $true )
& ( subsetRefl = $true )
& ( setextsub = $true )
& ( replAx = $true )
& ( binunionIL = $true )
& ( binintersectER = $true )
& ( upairset2E = $true )
& ( subsetE = $true )
& ( noeltsimpempty = $true )
& ( setukpairIL = $true )
& ( powersetE1 = $true )
& ( setminusSubset1 = $true )
& ( subPowSU = $true )
& ( inPowerset = $true )
& ( disjointsetsI1 = $true )
& ( cartprodpairmemEL = $true )
& ( powerset__Cong = $true )
& ( binunionRsub = $true )
& ( binunionE = $true )
& ( binintersectSubset1 = $true )
& ( setukpairinjL = $true )
& ( dsetconstrER = $true )
& ( upairset2IR = $true )
& ( cartprodpairsurjEq = $true )
& ( setukpairinjR1 = $true )
& ( ubforcartprodlem3 = $true )
& ( eqimpsubset2 = $true ) ),
inference(rectify,[],[f560]) ).
thf(f562,plain,
( ( ksndpairEq = $true )
& ( setadjoinAx = $true )
& ( exuE2 = $true )
& ( binintersectLsub = $true )
& ( vacuousDall = $true )
& ( setminusERneg = $true )
& ( omegaIndAx = $true )
& ( setbeta = $true )
& ( $true
!= ( breln @ sK0 @ sK2
@ ( dpsetconstr @ sK0 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) )
& ( powersetI = $true )
& ( upairsetIR = $true )
& ( powersetsubset = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodmempair1 = $true )
& ( exuI1 = $true )
& ( symdiffIneg2 = $true )
& ( setunionsingleton = $true )
& ( ksndsingleton = $true )
& ( notdexE = $true )
& ( setextAx = $true )
& ( notequalI1 = $true )
& ( setukpairinjR = $true )
& ( setminusI = $true )
& ( setunionsingleton1 = $true )
& ( nonemptyE1 = $true )
& ( upairsubunion = $true )
& ( emptyI = $true )
& ( nonemptyI = $true )
& ( dsetconstrEL = $true )
& ( upairsetIL = $true )
& ( bs114d = $true )
& ( binintersectI = $true )
& ( setukpairinjL2 = $true )
& ( kpairsurjEq = $true )
& ( prop2setI = $true )
& ( kpairiskpair = $true )
& ( quantDeMorgan2 = $true )
& ( setunionE2 = $true )
& ( sepSubset = $true )
& ( quantDeMorgan1 = $true )
& ( setminusLsub = $true )
& ( exuE3u = $true )
& ( prop2set2propI = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyE1 = $true )
& ( uniqinunit = $true )
& ( setext = $true )
& ( binintersectSubset5 = $true )
& ( cartprodmempair = $true )
& ( binintersectSubset4 = $true )
& ( descrp = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( setminusILneg = $true )
& ( foundationAx = $true )
& ( binintersectSubset3 = $true )
& ( emptyInPowerset = $true )
& ( ex1E1 = $true )
& ( binunionIR = $true )
& ( emptysetsubset = $true )
& ( symdiffIneg1 = $true )
& ( notinsingleton = $true )
& ( setunionsingleton2 = $true )
& ( singletonsswitch = $true )
& ( ubforcartprodlem2 = $true )
& ( secondinupair = $true )
& ( ex1I2 = $true )
& ( symdiffI2 = $true )
& ( cartprodsndpairEq = $true )
& ( ex1I = $true )
& ( setukpairinjL1 = $true )
& ( omega__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( setunionE = $true )
& ( cartprodfstpairEq = $true )
& ( upairinpowunion = $true )
& ( exu__Cong = $true )
& ( cartprodfstin = $true )
& ( omegaSAx = $true )
& ( setadjoinSub = $true )
& ( subsetI1 = $true )
& ( ubforcartprodlem1 = $true )
& ( binunionEcases = $true )
& ( setminusSubset2 = $true )
& ( dpsetconstrSub = $true )
& ( exuI3 = $true )
& ( exuEu = $true )
& ( setminusELneg = $true )
& ( emptyinunitempty = $true )
& ( setunionI = $true )
& ( cartprodpairmemER = $true )
& ( omega0Ax = $true )
& ( upairsetE = $true )
& ( dpsetconstrI = $true )
& ( exuI2 = $true )
& ( setadjoin__Cong = $true )
& ( notdallE = $true )
& ( powersetE = $true )
& ( subset2powerset = $true )
& ( binintersectRsub = $true )
& ( setadjoinOr = $true )
& ( eqimpsubset1 = $true )
& ( setunionAx = $true )
& ( setunion__Cong = $true )
& ( setminusEL = $true )
& ( exuE3e = $true )
& ( cartprodpairin = $true )
& ( binunionLsub = $true )
& ( setadjoinIR = $true )
& ( in__Cong = $true )
& ( setadjoinIL = $true )
& ( emptysetE = $true )
& ( setukpairinjR11 = $true )
& ( exuE1 = $true )
& ( setminusIRneg = $true )
& ( symdiffI1 = $true )
& ( nonemptyI1 = $true )
& ( powersetAx = $true )
& ( dsetconstr__Cong = $true )
& ( emptysetAx = $true )
& ( singletoninpowerset = $true )
& ( symdiffE = $true )
& ( binintersectSubset2 = $true )
& ( singletonsubset = $true )
& ( subsetTrans = $true )
& ( setukpairinjR2 = $true )
& ( setukpairIR = $true )
& ( setminusER = $true )
& ( dsetconstrI = $true )
& ( singletonprop = $true )
& ( setukpairinjR12 = $true )
& ( setadjoinSub2 = $true )
& ( cartprodsndin = $true )
& ( powersetI1 = $true )
& ( emptyinPowerset = $true )
& ( upairequniteq = $true )
& ( kpairp = $true )
& ( notequalI2 = $true )
& ( eqinunit = $true )
& ( inCongP = $true )
& ( prop2setE = $true )
& ( binintersectEL = $true )
& ( descr__Cong = $true )
& ( emptysetimpfalse = $true )
& ( subsetI2 = $true )
& ( quantDeMorgan4 = $true )
& ( singletonsuniq = $true )
& ( setoftrueEq = $true )
& ( emptyset__Cong = $true )
& ( sepInPowerset = $true )
& ( subsetE2 = $true )
& ( kfstsingleton = $true )
& ( quantDeMorgan3 = $true )
& ( notinemptyset = $true )
& ( wellorderingAx = $true )
& ( notsubsetI = $true )
& ( singletoninpowunion = $true )
& ( setadjoinE = $true )
& ( subsetRefl = $true )
& ( setextsub = $true )
& ( replAx = $true )
& ( binunionIL = $true )
& ( binintersectER = $true )
& ( upairset2E = $true )
& ( subsetE = $true )
& ( noeltsimpempty = $true )
& ( setukpairIL = $true )
& ( powersetE1 = $true )
& ( setminusSubset1 = $true )
& ( subPowSU = $true )
& ( inPowerset = $true )
& ( disjointsetsI1 = $true )
& ( cartprodpairmemEL = $true )
& ( powerset__Cong = $true )
& ( binunionRsub = $true )
& ( binunionE = $true )
& ( binintersectSubset1 = $true )
& ( setukpairinjL = $true )
& ( dsetconstrER = $true )
& ( upairset2IR = $true )
& ( cartprodpairsurjEq = $true )
& ( setukpairinjR1 = $true )
& ( ubforcartprodlem3 = $true )
& ( eqimpsubset2 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f561]) ).
thf(f625,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( ( kpair @ Y4 @ Y5 )
= Y3 )
& ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f488]) ).
thf(f627,plain,
( dpsetconstrSub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( subset
@ ( dpsetconstr @ Y2 @ Y0
@ ^ [Y3: $i,Y4: $i] : ( Y1 @ Y3 @ Y4 ) )
@ ( cartprod @ Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f385]) ).
thf(f797,plain,
dpsetconstrSub = $true,
inference(cnf_transformation,[],[f562]) ).
thf(f873,plain,
( $true
!= ( breln @ sK0 @ sK2
@ ( dpsetconstr @ sK0 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f562]) ).
thf(f919,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f273]) ).
thf(f997,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( subset
@ ( ^ [Y3: $i,Y4: $i,Y5: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y3 @ Y4 )
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( in @ Y7 @ Y3 )
& ( ?? @ $i
@ ^ [Y8: $i] :
( ( ( kpair @ Y7 @ Y8 )
= Y6 )
& ( in @ Y8 @ Y4 )
& ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
@ Y2
@ Y0
@ ^ [Y3: $i,Y4: $i] : ( Y1 @ Y3 @ Y4 ) )
@ ( cartprod @ Y2 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f627,f797,f625]) ).
thf(f1068,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
@ sK0
@ sK2
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( ( kpair @ Y4 @ Y5 )
= Y3 )
& ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
@ sK0
@ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f873,f919,f625]) ).
thf(f1347,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( subset
@ ( ^ [Y3: $i,Y4: $i,Y5: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y3 @ Y4 )
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( in @ Y7 @ Y3 )
& ( ?? @ $i
@ ^ [Y8: $i] :
( ( ( kpair @ Y7 @ Y8 )
= Y6 )
& ( in @ Y8 @ Y4 )
& ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
@ Y2
@ Y0
@ ^ [Y3: $i,Y4: $i] : ( Y1 @ Y3 @ Y4 ) )
@ ( cartprod @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f997]) ).
thf(f1348,plain,
! [X1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ ( cartprod @ Y1 @ X1 )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( kpair @ Y3 @ Y4 )
= Y2 )
& ( in @ Y4 @ X1 )
& ( Y0 @ Y3 @ Y4 ) ) ) ) ) )
@ ( cartprod @ Y1 @ X1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f1347]) ).
thf(f1349,plain,
! [X2: $i > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ ( cartprod @ Y1 @ X1 )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( kpair @ Y3 @ Y4 )
= Y2 )
& ( in @ Y4 @ X1 )
& ( Y0 @ Y3 @ Y4 ) ) ) ) ) )
@ ( cartprod @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f1348]) ).
thf(f1350,plain,
! [X2: $i > $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( subset
@ ( dsetconstr @ ( cartprod @ Y0 @ X1 )
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y2 @ Y3 )
= Y1 )
& ( in @ Y3 @ X1 )
& ( X2 @ Y2 @ Y3 ) ) ) ) ) )
@ ( cartprod @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f1349]) ).
thf(f1351,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( subset
@ ( dsetconstr @ ( cartprod @ Y0 @ X1 )
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( kpair @ Y2 @ Y3 )
= Y1 )
& ( in @ Y3 @ X1 )
& ( X2 @ Y2 @ Y3 ) ) ) ) ) )
@ ( cartprod @ Y0 @ X1 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f1350]) ).
thf(f1352,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( $true
= ( subset
@ ( dsetconstr @ ( cartprod @ X3 @ X1 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( kpair @ Y1 @ Y2 )
= Y0 )
& ( in @ Y2 @ X1 )
& ( X2 @ Y1 @ Y2 ) ) ) ) ) )
@ ( cartprod @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1351]) ).
thf(f2680,plain,
( $true
!= ( subset
@ ( dsetconstr @ ( cartprod @ sK0 @ sK2 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( kpair @ Y1 @ Y2 )
= Y0 )
& ( in @ Y2 @ sK2 )
& ( sK1 @ Y1 @ Y2 ) ) ) ) ) )
@ ( cartprod @ sK0 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f1068]) ).
thf(f2748,plain,
$false,
inference(forward_subsumption_resolution,[],[f2680,f1352]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU667^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.12 % Computer : n012.cluster.edu
% 0.00/0.12 % Model : x86_64 x86_64
% 0.00/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.12 % Memory : 8046.5625MB
% 0.00/0.12 % OS : Linux 6.8.0-71-generic
% 0.00/0.12 % CPULimit : 300
% 0.00/0.12 % WCLimit : 300
% 0.00/0.12 % DateTime : Tue Sep 29 14:06:18 UTC 2026
% 0.00/0.12 % CPUTime :
% 0.00/0.12 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.14 Running higher-order theorem proving
% 0.10/0.16 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/0.28 % (157371)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.37/0.28 % (157376)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3877199290:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.37/0.28 % (157377)lrs+10_16_si=on:nwc=1.5:random_seed=1854903963:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.37/0.28 % (157378)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=166808238:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.37/0.28 % (157378)Instruction limit reached!
% 0.37/0.28 % (157378)------------------------------
% 0.37/0.28 % (157378)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.28 % (157378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.28 % (157378)CaDiCaL version: 2.1.3
% 0.37/0.28 % (157378)Termination reason: Instruction limit
% 0.37/0.28 % (157378)Termination phase: shuffling
% 0.37/0.28 % (157378)Time elapsed: 0.003 s
% 0.37/0.28 % (157378)Peak memory usage: 10 MB
% 0.37/0.28 % (157378)Instructions burned: 10 (million)
% 0.37/0.28 % (157377)Instruction limit reached!
% 0.37/0.28 % (157377)------------------------------
% 0.37/0.28 % (157377)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.28 % (157377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.28 % (157377)CaDiCaL version: 2.1.3
% 0.37/0.28 % (157377)Termination reason: Instruction limit
% 0.37/0.28 % (157377)Termination phase: shuffling
% 0.37/0.28 % (157377)Time elapsed: 0.005 s
% 0.37/0.28 % (157377)Peak memory usage: 10 MB
% 0.37/0.28 % (157377)Instructions burned: 21 (million)
% 0.37/0.28 % (157380)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1946267260:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.37/0.28 % (157386)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2001860786:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.37/0.28 % (157387)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4059198747:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.37/0.28 % (157386)Instruction limit reached!
% 0.37/0.28 % (157386)------------------------------
% 0.37/0.28 % (157386)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.28 % (157386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.28 % (157386)CaDiCaL version: 2.1.3
% 0.37/0.28 % (157386)Termination reason: Instruction limit
% 0.37/0.28 % (157386)Termination phase: shuffling
% 0.37/0.28 % (157386)Time elapsed: 0.002 s
% 0.37/0.28 % (157386)Peak memory usage: 10 MB
% 0.37/0.28 % (157386)Instructions burned: 5 (million)
% 0.37/0.28 % (157380)Instruction limit reached!
% 0.37/0.28 % (157380)------------------------------
% 0.37/0.28 % (157380)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.28 % (157380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.28 % (157380)CaDiCaL version: 2.1.3
% 0.37/0.28 % (157380)Termination reason: Instruction limit
% 0.37/0.28 % (157380)Termination phase: shuffling
% 0.37/0.28 % (157380)Time elapsed: 0.011 s
% 0.37/0.28 % (157380)Peak memory usage: 11 MB
% 0.37/0.28 % (157380)Instructions burned: 26 (million)
% 0.37/0.28 % (157382)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.37/0.28 % (157382)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
% 0.37/0.28 % (157387)Instruction limit reached!
% 0.37/0.28 % (157387)------------------------------
% 0.37/0.28 % (157387)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.28 % (157387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.28 % (157387)CaDiCaL version: 2.1.3
% 0.37/0.28 % (157387)Termination reason: Instruction limit
% 0.37/0.28 % (157387)Termination phase: shuffling
% 0.37/0.28 % (157387)Time elapsed: 0.003 s
% 0.37/0.28 % (157387)Peak memory usage: 10 MB
% 0.37/0.28 % (157387)Instructions burned: 11 (million)
% 0.37/0.28 % (157382)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=435442611:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.37/0.28 % (157376)Instruction limit reached!
% 0.37/0.31 % (157376)------------------------------
% 0.37/0.31 % (157376)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157376)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157376)Termination reason: Instruction limit
% 0.37/0.31 % (157376)Termination phase: Function definition elimination
% 0.37/0.31 % (157376)Time elapsed: 0.022 s
% 0.37/0.31 % (157376)Peak memory usage: 12 MB
% 0.37/0.31 % (157376)Instructions burned: 88 (million)
% 0.37/0.31 % (157391)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.37/0.31 % (157379)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=640409827: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)
% 0.37/0.31 % (157391)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3847677551:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.37/0.31 % (157381)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4143544991:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.37/0.31 % (157391)Instruction limit reached!
% 0.37/0.31 % (157391)------------------------------
% 0.37/0.31 % (157391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157391)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157391)Termination reason: Instruction limit
% 0.37/0.31 % (157391)Termination phase: shuffling
% 0.37/0.31 % (157391)Time elapsed: 0.002 s
% 0.37/0.31 % (157391)Peak memory usage: 10 MB
% 0.37/0.31 % (157391)Instructions burned: 7 (million)
% 0.37/0.31 % (157393)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
% 0.37/0.31 % (157393)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.37/0.31 % (157395)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=1709597434:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.37/0.31 % (157393)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3943225509:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.37/0.31 % (157399)lrs+10_1_si=on:cs=on:random_seed=463745938:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.37/0.31 % (157399)Instruction limit reached!
% 0.37/0.31 % (157399)------------------------------
% 0.37/0.31 % (157399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157399)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157399)Termination reason: Instruction limit
% 0.37/0.31 % (157399)Termination phase: shuffling
% 0.37/0.31 % (157399)Time elapsed: 0.003 s
% 0.37/0.31 % (157399)Peak memory usage: 10 MB
% 0.37/0.31 % (157399)Instructions burned: 13 (million)
% 0.37/0.31 % (157393)Instruction limit reached!
% 0.37/0.31 % (157393)------------------------------
% 0.37/0.31 % (157393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157393)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157393)Termination reason: Instruction limit
% 0.37/0.31 % (157393)Termination phase: Property scanning
% 0.37/0.31 % (157393)Time elapsed: 0.012 s
% 0.37/0.31 % (157393)Peak memory usage: 10 MB
% 0.37/0.31 % (157393)Instructions burned: 33 (million)
% 0.37/0.31 % (157395)Instruction limit reached!
% 0.37/0.31 % (157395)------------------------------
% 0.37/0.31 % (157395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157395)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157395)Termination reason: Instruction limit
% 0.37/0.31 % (157395)Termination phase: Property scanning
% 0.37/0.31 % (157395)Time elapsed: 0.019 s
% 0.37/0.31 % (157395)Peak memory usage: 11 MB
% 0.37/0.31 % (157395)Instructions burned: 88 (million)
% 0.37/0.31 % (157403)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.37/0.31 % (157403)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=1514146765:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.37/0.31 % (157392)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1350972299:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.37/0.31 % (157403)Instruction limit reached!
% 0.37/0.31 % (157403)------------------------------
% 0.37/0.31 % (157403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157403)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157403)Termination reason: Instruction limit
% 0.37/0.31 % (157403)Termination phase: shuffling
% 0.37/0.31 % (157403)Time elapsed: 0.001 s
% 0.37/0.31 % (157403)Peak memory usage: 10 MB
% 0.37/0.31 % (157403)Instructions burned: 5 (million)
% 0.37/0.31 % (157392)Instruction limit reached!
% 0.37/0.31 % (157392)------------------------------
% 0.37/0.31 % (157392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157392)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157392)Termination reason: Instruction limit
% 0.37/0.31 % (157392)Termination phase: shuffling
% 0.37/0.31 % (157392)Time elapsed: 0.007 s
% 0.37/0.31 % (157392)Peak memory usage: 10 MB
% 0.37/0.31 % (157392)Instructions burned: 14 (million)
% 0.37/0.31 % (157404)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3386946746:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.37/0.31 % (157405)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3831882206:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.37/0.31 % (157408)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1880354292:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.37/0.31 % (157381)Instruction limit reached!
% 0.37/0.31 % (157381)------------------------------
% 0.37/0.31 % (157381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157381)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157381)Termination reason: Instruction limit
% 0.37/0.31 % (157381)Termination phase: Property scanning
% 0.37/0.31 % (157381)Time elapsed: 0.045 s
% 0.37/0.31 % (157381)Peak memory usage: 12 MB
% 0.37/0.31 % (157381)Instructions burned: 76 (million)
% 0.37/0.31 % (157408)Instruction limit reached!
% 0.37/0.31 % (157408)------------------------------
% 0.37/0.31 % (157408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157408)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157408)Termination reason: Instruction limit
% 0.37/0.31 % (157408)Termination phase: SInE selection
% 0.37/0.31 % (157408)Time elapsed: 0.006 s
% 0.37/0.31 % (157408)Peak memory usage: 11 MB
% 0.37/0.31 % (157408)Instructions burned: 25 (million)
% 0.37/0.31 % (157404)Instruction limit reached!
% 0.37/0.31 % (157404)------------------------------
% 0.37/0.31 % (157404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157404)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157404)Termination reason: Instruction limit
% 0.37/0.31 % (157404)Termination phase: Preprocessing 3
% 0.37/0.31 % (157404)Time elapsed: 0.010 s
% 0.37/0.31 % (157404)Peak memory usage: 11 MB
% 0.37/0.31 % (157404)Instructions burned: 42 (million)
% 0.37/0.31 % (157409)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2423361803:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.37/0.31 % (157382)Instruction limit reached!
% 0.37/0.31 % (157382)------------------------------
% 0.37/0.31 % (157382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157382)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157382)Termination reason: Instruction limit
% 0.37/0.31 % (157382)Termination phase: Saturation
% 0.37/0.31 % (157382)Time elapsed: 0.067 s
% 0.37/0.31 % (157382)Peak memory usage: 14 MB
% 0.37/0.31 % (157409)Instruction limit reached!
% 0.37/0.31 % (157409)------------------------------
% 0.37/0.31 % (157409)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157382)Instructions burned: 158 (million)
% 0.37/0.31 % (157409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157409)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157409)Termination reason: Instruction limit
% 0.37/0.31 % (157409)Termination phase: shuffling
% 0.37/0.31 % (157409)Time elapsed: 0.004 s
% 0.37/0.31 % (157409)Peak memory usage: 10 MB
% 0.37/0.31 % (157409)Instructions burned: 14 (million)
% 0.37/0.31 % (157415)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3626662252: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)
% 0.37/0.31 % (157415)Instruction limit reached!
% 0.37/0.31 % (157415)------------------------------
% 0.37/0.31 % (157415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157415)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157415)Termination reason: Instruction limit
% 0.37/0.31 % (157415)Termination phase: shuffling
% 0.37/0.31 % (157415)Time elapsed: 0.001 s
% 0.37/0.31 % (157415)Peak memory usage: 10 MB
% 0.37/0.31 % (157415)Instructions burned: 3 (million)
% 0.37/0.31 % (157418)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=4197672155:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.37/0.31 % (157419)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2342607560:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.37/0.31 % (157413)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2282655680:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.37/0.31 % (157414)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2255993928:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.37/0.31 % (157418)Instruction limit reached!
% 0.37/0.31 % (157418)------------------------------
% 0.37/0.31 % (157418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157418)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157418)Termination reason: Instruction limit
% 0.37/0.31 % (157418)Termination phase: Property scanning
% 0.37/0.31 % (157418)Time elapsed: 0.007 s
% 0.37/0.31 % (157418)Peak memory usage: 10 MB
% 0.37/0.31 % (157418)Instructions burned: 29 (million)
% 0.37/0.31 % (157419)Instruction limit reached!
% 0.37/0.31 % (157419)------------------------------
% 0.37/0.31 % (157419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157419)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157419)Termination reason: Instruction limit
% 0.37/0.31 % (157419)Termination phase: Property scanning
% 0.37/0.31 % (157419)Time elapsed: 0.006 s
% 0.37/0.31 % (157419)Peak memory usage: 10 MB
% 0.37/0.31 % (157419)Instructions burned: 24 (million)
% 0.37/0.31 % (157405) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-157371-157405"...
% 0.37/0.31 % (157405)...printing done.
% 0.37/0.31 % (157414)Instruction limit reached!
% 0.37/0.31 % (157414)------------------------------
% 0.37/0.31 % (157414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157414)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157414)Termination reason: Instruction limit
% 0.37/0.31 % (157414)Termination phase: shuffling
% 0.37/0.31 % (157414)Time elapsed: 0.008 s
% 0.37/0.31 % (157414)Peak memory usage: 10 MB
% 0.37/0.31 % (157414)Instructions burned: 17 (million)
% 0.37/0.31 % (157405)Refutation found. Thanks to Tanya!
% 0.37/0.31 % SZS status Theorem for theBenchmark
% 0.37/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.37/0.31 % (157405)------------------------------
% 0.37/0.31 % (157405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.31 % (157405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.31 % (157405)CaDiCaL version: 2.1.3
% 0.37/0.31 % (157405)Termination reason: Refutation
% 0.37/0.31 % (157405)Time elapsed: 0.040 s
% 0.37/0.31 % (157405)Peak memory usage: 14 MB
% 0.37/0.31 % (157405)Instructions burned: 164 (million)
% 0.37/0.31 % (157371)Success in time 0.142 s
% 0.37/0.31 % Vampire exiting
%------------------------------------------------------------------------------