%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU652^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:32:50 AM UTC 2026
% Result : Theorem 1.85s 0.53s
% Output : Refutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 51 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 2761 ( 746 equ; 0 cnn)
% Maximal formula atoms : 170 ( 54 avg)
% Number of connectives : 1503 ( 29 ~; 6 |; 507 &; 252 @)
% ( 0 <=>; 685 =>; 0 <=; 0 <~>)
% Maximal formula depth : 174 ( 25 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 311 ( 307 usr; 175 con; 0-4 aty)
% ( 24 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 86 ( 30 ^; 50 !; 6 ?; 86 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_200,type,
vAND: $o > $o > $o ).
thf(func_def_201,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_202,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_203,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_204,type,
vIMP: $o > $o > $o ).
thf(func_def_205,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_206,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_207,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_208,type,
vIFF: $o > $o > $o ).
thf(func_def_209,type,
vNOT: $o > $o ).
thf(func_def_210,type,
vOR: $o > $o > $o ).
thf(func_def_211,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_212,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_215,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_219,type,
sK3: $i > $i ).
thf(func_def_220,type,
sK4: ( $i > $o ) > $i > $i ).
thf(func_def_221,type,
sK5: ( $i > $o ) > $i > $i ).
thf(func_def_222,type,
sK6: ( $i > $o ) > $i > $i ).
thf(func_def_223,type,
sK7: $i > $i > ( $i > $o ) > $i ).
thf(func_def_224,type,
sK8: $i > ( $i > $o ) > $i ).
thf(func_def_225,type,
sK9: ( $i > $o ) > $i > $i ).
thf(func_def_226,type,
sK10: ( $i > $o ) > $i > $i ).
thf(func_def_227,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_228,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_229,type,
sK13: $i > $i > $i ).
thf(func_def_230,type,
sK14: $i > $i ).
thf(func_def_231,type,
sK15: $i > $i ).
thf(func_def_232,type,
sK16: $i > $i > $i > $i ).
thf(func_def_233,type,
sK17: $i > $i > $i > $i ).
thf(func_def_234,type,
sK18: $i > $i > $i ).
thf(func_def_235,type,
sK19: $i > $i > $i ).
thf(func_def_236,type,
sK20: $i > $i > $i ).
thf(func_def_237,type,
sK21: $i > $i > $i ).
thf(func_def_238,type,
sK22: $i > $i > $i ).
thf(func_def_239,type,
sK23: $i > $i > $i ).
thf(func_def_240,type,
sK24: $i > $i > $i ).
thf(func_def_241,type,
sK25: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_242,type,
sK26: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_243,type,
sK27: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_244,type,
sK28: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_245,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_246,type,
sK30: ( $i > $o ) > $i > $i ).
thf(func_def_247,type,
sK31: ( $i > $o ) > $i > $i ).
thf(func_def_248,type,
sK32: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_249,type,
sK33: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_250,type,
sK34: ( $i > $o ) > $i ).
thf(func_def_251,type,
sK35: ( $i > $o ) > $i > $i ).
thf(func_def_252,type,
sK36: ( $i > $o ) > $i ).
thf(func_def_253,type,
sK37: ( $i > $o ) > $i > $i ).
thf(func_def_254,type,
sK38: ( $i > $o ) > $i > $i ).
thf(func_def_255,type,
sK39: ( $i > $o ) > $i ).
thf(func_def_256,type,
sK40: ( $i > $o ) > $i > $i ).
thf(func_def_257,type,
sK41: ( $i > $o ) > $i ).
thf(func_def_258,type,
sK42: ( $i > $o ) > $i > $i ).
thf(func_def_259,type,
sK43: ( $i > $o ) > $i > $i ).
thf(func_def_260,type,
sK44: ( $i > $o ) > $i ).
thf(func_def_261,type,
sK45: ( $i > $o ) > $i > $i ).
thf(func_def_262,type,
sK46: ( $i > $o ) > $i ).
thf(func_def_263,type,
sK47: ( $i > $o ) > $i > $i ).
thf(func_def_264,type,
sK48: ( $i > $o ) > $i > $i ).
thf(func_def_265,type,
sK49: ( $i > $o ) > $i > $i ).
thf(func_def_266,type,
sK50: ( $i > $o ) > $i ).
thf(func_def_267,type,
sK51: ( $i > $o ) > $i > $i ).
thf(func_def_268,type,
sK52: ( $i > $o ) > $i ).
thf(func_def_269,type,
sK53: ( $i > $o ) > $i ).
thf(func_def_270,type,
sK54: ( $i > $o ) > $i ).
thf(func_def_271,type,
sK55: ( $i > $o ) > $i ).
thf(func_def_272,type,
sK56: ( $i > $o ) > $i > $i ).
thf(func_def_273,type,
sK57: ( $i > $o ) > $i > $i ).
thf(func_def_274,type,
sK58: ( $i > $o ) > $i > $i ).
thf(func_def_275,type,
sK59: ( $i > $o ) > $i > $i ).
thf(func_def_276,type,
sK60: ( $i > $o ) > $i > $i ).
thf(func_def_277,type,
sK61: ( $i > $o ) > $i > $i ).
thf(func_def_278,type,
sK62: ( $i > $o ) > $i > $i ).
thf(func_def_279,type,
sK63: $i > $i ).
thf(func_def_280,type,
sK64: ( $i > $o ) > $i ).
thf(func_def_281,type,
sK65: ( $i > $o ) > $i > $i ).
thf(func_def_282,type,
sK66: $i > $o > $i > $i ).
thf(func_def_283,type,
sK67: $i > $i > $i ).
thf(func_def_284,type,
sK68: $i > $i ).
thf(func_def_285,type,
sK69: $i > $i ).
thf(func_def_286,type,
sK70: $i > $i ).
thf(func_def_287,type,
sK71: $i > $i > $i ).
thf(func_def_288,type,
sK72: $i > $i > $i ).
thf(func_def_289,type,
sK73: ( $i > $o ) > $i ).
thf(func_def_290,type,
sK74: ( $i > $o ) > $i > $i ).
thf(func_def_291,type,
sK75: ( $i > $o ) > $i ).
thf(func_def_292,type,
sK76: ( $i > $o ) > $i > $i ).
thf(func_def_293,type,
sK77: ( $i > $o ) > $i > $i ).
thf(func_def_294,type,
sK78: $i > $i ).
thf(func_def_295,type,
sK79: $i > $i > $i > $i ).
thf(func_def_296,type,
sK80: $i > $i > $i ).
thf(func_def_297,type,
sK81: $i > $i > $i ).
thf(func_def_298,type,
sK82: $i > $i > $i ).
thf(func_def_299,type,
sK83: $i > $i ).
thf(func_def_300,type,
sK84: $i > ( $i > $i > $o ) > $i ).
thf(func_def_301,type,
sK85: $i > ( $i > $i > $o ) > $i ).
thf(func_def_302,type,
sK86: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_303,type,
sK87: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_304,type,
sK88: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_305,type,
sK89: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_306,type,
sK90: $i > $i ).
thf(func_def_307,type,
sK91: $i > $i > $i ).
thf(func_def_308,type,
sK92: $i > $i > $i ).
thf(func_def_309,type,
sK93: $i > $i > $i ).
thf(f31,axiom,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f47,axiom,
( notinsingleton
= ( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(f136,axiom,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(f175,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(f176,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f175]) ).
thf(f234,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f31]) ).
thf(f235,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f234]) ).
thf(f264,plain,
( notinsingleton
= ( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(rectify,[],[f47]) ).
thf(f265,plain,
( notinsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 != Y0 )
=> ~ ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[],[f264]) ).
thf(f436,plain,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(rectify,[],[f136]) ).
thf(f437,plain,
( secondinupair
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[],[f436]) ).
thf(f505,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f176]) ).
thf(f506,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f505]) ).
thf(f507,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( X0 != X1 )
& ( ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) )
& ( 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,[],[f506]) ).
thf(f508,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( X0 != X1 )
& ( ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) )
& ( 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(flattening,[],[f507]) ).
thf(f509,plain,
( ( sK0 != sK1 )
& ( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK2 @ emptyset ) )
& ( 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(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f508]) ).
thf(f540,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f235]) ).
thf(f556,plain,
( notinsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 != Y0 )
=> ~ ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[],[f265]) ).
thf(f645,plain,
( secondinupair
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[],[f437]) ).
thf(f712,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f509]) ).
thf(f728,plain,
notinsingleton = $true,
inference(cnf_transformation,[],[f509]) ).
thf(f816,plain,
secondinupair = $true,
inference(cnf_transformation,[],[f509]) ).
thf(f852,plain,
( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK2 @ emptyset ) ),
inference(cnf_transformation,[],[f509]) ).
thf(f853,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f509]) ).
thf(f885,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f540,f712]) ).
thf(f901,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 != Y0 )
=> ~ ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(definition_unfolding,[],[f556,f728]) ).
thf(f989,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(definition_unfolding,[],[f645,f816]) ).
thf(f1406,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f989]) ).
thf(f1407,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f1406]) ).
thf(f1408,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f1407]) ).
thf(f1409,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(beta-eta_normalization,[],[f1408]) ).
thf(f2363,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 != Y0 )
=> ~ ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f901]) ).
thf(f2364,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f2363]) ).
thf(f2365,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( Y0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f2364]) ).
thf(f2366,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( X2 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(beta-eta_normalization,[],[f2365]) ).
thf(f2367,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( X2 != X1 ) )
| ( $true
= ( ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2366]) ).
thf(f2368,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( X2 = X1 ) )
| ( $true
= ( ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(not_proxy_clausification,[],[f2367]) ).
thf(f2369,plain,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( $true
= ( ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(equality_proxy_clausification,[],[f2368]) ).
thf(f2370,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
| ( X1 = X2 ) ),
inference(not_proxy_clausification,[],[f2369]) ).
thf(f2496,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f885]) ).
thf(f2497,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f2496]) ).
thf(f2498,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f2497]) ).
thf(f2499,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2498]) ).
thf(f3496,plain,
( $true
= ( in @ sK0 @ ( setadjoin @ sK2 @ emptyset ) ) ),
inference(constrained_superposition,[],[f2499,f852]) ).
thf(f3514,plain,
( $true
= ( in @ sK1 @ ( setadjoin @ sK2 @ emptyset ) ) ),
inference(constrained_superposition,[],[f1409,f852]) ).
thf(f6503,plain,
( ( $false = $true )
| ( sK0 = sK2 ) ),
inference(constrained_superposition,[],[f2370,f3496]) ).
thf(f6508,plain,
sK0 = sK2,
inference(trivial_inequality_removal,[],[f6503]) ).
thf(f6517,plain,
( ( $false = $true )
| ( sK1 = sK2 ) ),
inference(constrained_superposition,[],[f2370,f3514]) ).
thf(f6522,plain,
sK1 = sK2,
inference(trivial_inequality_removal,[],[f6517]) ).
thf(f6535,plain,
sK0 = sK1,
inference(forward_demodulation,[],[f6522,f6508]) ).
thf(f6536,plain,
$false,
inference(forward_subsumption_resolution,[],[f6535,f853]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU652^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n010.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:03:03 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.85/0.53 % (2907090)Will run a generic schedule for satisfiability detection.
% 1.85/0.53 % (2907097)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3282916191:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.85/0.53 % (2907096)% WARNING: option uhcvi not known.
% 1.85/0.53 % (2907095)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=947955687_2999 on theBenchmark for (2999ds/0Mi)
% 1.85/0.53 % (2907096)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1522935240:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.85/0.53 % (2907098)dis+10_1_sil=32000:sp=arity:random_seed=983220826:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.85/0.53 % (2907099)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2377737712:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.85/0.53 % (2907096)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.85/0.53 % (2907099)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.85/0.53 % (2907100)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3043248529:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.85/0.53 % (2907101)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4237516912:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.85/0.53 % Exception at run slice level
% 1.85/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.85/0.53 % (2907096)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.85/0.53 % (2907098)Instruction limit reached!
% 1.85/0.53 % (2907098)------------------------------
% 1.85/0.53 % (2907098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.53 % (2907098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.53 % (2907098)CaDiCaL version: 2.1.3
% 1.85/0.53 % (2907098)Termination reason: Instruction limit
% 1.85/0.53 % (2907098)Termination phase: Saturation
% 1.85/0.53 % (2907098)Time elapsed: 0.044 s
% 1.85/0.53 % (2907098)Peak memory usage: 13 MB
% 1.85/0.53 % (2907098)Instructions burned: 103 (million)
% 1.85/0.53 % (2907099)Instruction limit reached!
% 1.85/0.53 % (2907099)------------------------------
% 1.85/0.53 % (2907099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.53 % (2907099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.53 % (2907099)CaDiCaL version: 2.1.3
% 1.85/0.53 % (2907099)Termination reason: Instruction limit
% 1.85/0.53 % (2907099)Termination phase: Saturation
% 1.85/0.53 % (2907099)Time elapsed: 0.049 s
% 1.85/0.53 % (2907099)Peak memory usage: 13 MB
% 1.85/0.53 % (2907099)Instructions burned: 117 (million)
% 1.85/0.53 % (2907109)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1254178601:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.85/0.53 % (2907110)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4090782855:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.85/0.53 % (2907112)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2540809210:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.85/0.53 % Exception at run slice level
% 1.85/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.85/0.53 % (2907112)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.85/0.53 % (2907101)Instruction limit reached!
% 1.85/0.53 % (2907101)------------------------------
% 1.85/0.53 % (2907101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.53 % (2907101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.53 % (2907101)CaDiCaL version: 2.1.3
% 1.85/0.53 % (2907101)Termination reason: Instruction limit
% 1.85/0.53 % (2907101)Termination phase: Saturation
% 1.85/0.53 % (2907101)Time elapsed: 0.075 s
% 1.85/0.53 % (2907101)Peak memory usage: 14 MB
% 1.85/0.53 % (2907101)Instructions burned: 159 (million)
% 1.85/0.53 % (2907115)ott-21_1_sil=16000:fs=off:random_seed=176559169:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.85/0.53 % (2907112)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.85/0.53 % (2907100)Instruction limit reached!
% 1.85/0.53 % (2907100)------------------------------
% 1.85/0.53 % (2907100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.53 % (2907100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.53 % (2907100)CaDiCaL version: 2.1.3
% 1.85/0.53 % (2907100)Termination reason: Instruction limit
% 1.85/0.53 % (2907100)Termination phase: Saturation
% 1.85/0.53 % (2907100)Time elapsed: 0.090 s
% 1.85/0.53 % (2907100)Peak memory usage: 13 MB
% 1.85/0.53 % (2907100)Instructions burned: 132 (million)
% 1.85/0.53 % (2907116)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2826638752:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.85/0.53 % (2907110)Instruction limit reached!
% 1.85/0.53 % (2907110)------------------------------
% 1.85/0.53 % (2907110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.53 % (2907110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.53 % (2907110)CaDiCaL version: 2.1.3
% 1.85/0.53 % (2907110)Termination reason: Instruction limit
% 1.85/0.53 % (2907110)Termination phase: Saturation
% 1.85/0.53 % (2907110)Time elapsed: 0.057 s
% 1.85/0.53 % (2907110)Peak memory usage: 13 MB
% 1.85/0.53 % (2907110)Instructions burned: 132 (million)
% 1.85/0.53 % (2907118)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=469115183:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.85/0.53 % (2907120)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2825354373:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.85/0.53 % Exception at run slice level
% 1.85/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.85/0.53 % (2907115)Instruction limit reached!
% 1.85/0.53 % (2907115)------------------------------
% 1.85/0.53 % (2907115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.53 % (2907115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.53 % (2907115)CaDiCaL version: 2.1.3
% 1.85/0.53 % (2907115)Termination reason: Instruction limit
% 1.85/0.53 % (2907115)Termination phase: Saturation
% 1.85/0.53 % (2907115)Time elapsed: 0.082 s
% 1.85/0.53 % (2907115)Peak memory usage: 14 MB
% 1.85/0.53 % (2907115)Instructions burned: 181 (million)
% 1.85/0.53 % (2907123)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1895846960:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 1.85/0.53 % (2907124)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1015501207:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 1.85/0.53 % (2907124)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.85/0.53 % Exception at run slice level
% 1.85/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.85/0.53 % (2907096) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2907090-2907096"...
% 1.85/0.53 % (2907096)...printing done.
% 1.85/0.53 % (2907096)Refutation found. Thanks to Tanya!
% 1.85/0.53 % SZS status Theorem for theBenchmark
% 1.85/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 1.85/0.54 % (2907096)------------------------------
% 1.85/0.54 % (2907096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.54 % (2907096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.54 % (2907096)CaDiCaL version: 2.1.3
% 1.85/0.54 % (2907096)Termination reason: Refutation
% 1.85/0.54 % (2907096)Time elapsed: 0.255 s
% 1.85/0.54 % (2907096)Peak memory usage: 15 MB
% 1.85/0.54 % (2907096)Instructions burned: 530 (million)
% 1.85/0.54 % (2907090)Success in time 0.307 s
% 1.85/0.54 % Vampire exiting
%------------------------------------------------------------------------------