%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU651^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 7.63s 1.88s
% Output : Refutation 7.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 9
% Syntax : Number of formulae : 102 ( 74 unt; 0 typ; 1 def)
% Number of atoms : 3174 ( 834 equ; 0 cnn)
% Maximal formula atoms : 170 ( 31 avg)
% Number of connectives : 2240 ( 32 ~; 38 |; 507 &; 922 @)
% ( 1 <=>; 695 =>; 0 <=; 0 <~>)
% Maximal formula depth : 175 ( 14 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 312 ( 308 usr; 176 con; 0-4 aty)
% ( 45 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 160 ( 0 sgn 86 !; 8 ?; 160 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_199,type,
vAND: $o > $o > $o ).
thf(func_def_200,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_201,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_202,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_203,type,
vIMP: $o > $o > $o ).
thf(func_def_204,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_205,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_206,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_207,type,
vIFF: $o > $o > $o ).
thf(func_def_208,type,
vNOT: $o > $o ).
thf(func_def_209,type,
vOR: $o > $o > $o ).
thf(func_def_210,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_211,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_214,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_219,type,
sK4: $i > $i ).
thf(func_def_220,type,
sK5: ( $i > $o ) > $i > $i ).
thf(func_def_221,type,
sK6: ( $i > $o ) > $i > $i ).
thf(func_def_222,type,
sK7: ( $i > $o ) > $i > $i ).
thf(func_def_223,type,
sK8: $i > $i > ( $i > $o ) > $i ).
thf(func_def_224,type,
sK9: $i > ( $i > $o ) > $i ).
thf(func_def_225,type,
sK10: ( $i > $o ) > $i > $i ).
thf(func_def_226,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_227,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_228,type,
sK13: ( $i > $o ) > $i > $i ).
thf(func_def_229,type,
sK14: $i > $i > $i ).
thf(func_def_230,type,
sK15: $i > $i ).
thf(func_def_231,type,
sK16: $i > $i ).
thf(func_def_232,type,
sK17: $i > $i > $i > $i ).
thf(func_def_233,type,
sK18: $i > $i > $i > $i ).
thf(func_def_234,type,
sK19: $i > $i > $i ).
thf(func_def_235,type,
sK20: $i > $i > $i ).
thf(func_def_236,type,
sK21: $i > $i > $i ).
thf(func_def_237,type,
sK22: $i > $i > $i ).
thf(func_def_238,type,
sK23: $i > $i > $i ).
thf(func_def_239,type,
sK24: $i > $i > $i ).
thf(func_def_240,type,
sK25: $i > $i > $i ).
thf(func_def_241,type,
sK26: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_242,type,
sK27: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_243,type,
sK28: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_244,type,
sK29: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_245,type,
sK30: ( $i > $o ) > $i > $i ).
thf(func_def_246,type,
sK31: ( $i > $o ) > $i > $i ).
thf(func_def_247,type,
sK32: ( $i > $o ) > $i > $i ).
thf(func_def_248,type,
sK33: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_249,type,
sK34: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_250,type,
sK35: ( $i > $o ) > $i ).
thf(func_def_251,type,
sK36: ( $i > $o ) > $i > $i ).
thf(func_def_252,type,
sK37: ( $i > $o ) > $i ).
thf(func_def_253,type,
sK38: ( $i > $o ) > $i > $i ).
thf(func_def_254,type,
sK39: ( $i > $o ) > $i > $i ).
thf(func_def_255,type,
sK40: ( $i > $o ) > $i ).
thf(func_def_256,type,
sK41: ( $i > $o ) > $i > $i ).
thf(func_def_257,type,
sK42: ( $i > $o ) > $i ).
thf(func_def_258,type,
sK43: ( $i > $o ) > $i > $i ).
thf(func_def_259,type,
sK44: ( $i > $o ) > $i > $i ).
thf(func_def_260,type,
sK45: ( $i > $o ) > $i ).
thf(func_def_261,type,
sK46: ( $i > $o ) > $i > $i ).
thf(func_def_262,type,
sK47: ( $i > $o ) > $i ).
thf(func_def_263,type,
sK48: ( $i > $o ) > $i > $i ).
thf(func_def_264,type,
sK49: ( $i > $o ) > $i > $i ).
thf(func_def_265,type,
sK50: ( $i > $o ) > $i > $i ).
thf(func_def_266,type,
sK51: ( $i > $o ) > $i ).
thf(func_def_267,type,
sK52: ( $i > $o ) > $i > $i ).
thf(func_def_268,type,
sK53: ( $i > $o ) > $i ).
thf(func_def_269,type,
sK54: ( $i > $o ) > $i ).
thf(func_def_270,type,
sK55: ( $i > $o ) > $i ).
thf(func_def_271,type,
sK56: ( $i > $o ) > $i ).
thf(func_def_272,type,
sK57: ( $i > $o ) > $i > $i ).
thf(func_def_273,type,
sK58: ( $i > $o ) > $i > $i ).
thf(func_def_274,type,
sK59: ( $i > $o ) > $i > $i ).
thf(func_def_275,type,
sK60: ( $i > $o ) > $i > $i ).
thf(func_def_276,type,
sK61: ( $i > $o ) > $i > $i ).
thf(func_def_277,type,
sK62: ( $i > $o ) > $i > $i ).
thf(func_def_278,type,
sK63: ( $i > $o ) > $i > $i ).
thf(func_def_279,type,
sK64: $i > $i ).
thf(func_def_280,type,
sK65: ( $i > $o ) > $i ).
thf(func_def_281,type,
sK66: ( $i > $o ) > $i > $i ).
thf(func_def_282,type,
sK67: $i > $o > $i > $i ).
thf(func_def_283,type,
sK68: $i > $i > $i ).
thf(func_def_284,type,
sK69: $i > $i ).
thf(func_def_285,type,
sK70: $i > $i ).
thf(func_def_286,type,
sK71: $i > $i ).
thf(func_def_287,type,
sK72: $i > $i > $i ).
thf(func_def_288,type,
sK73: $i > $i > $i ).
thf(func_def_289,type,
sK74: ( $i > $o ) > $i ).
thf(func_def_290,type,
sK75: ( $i > $o ) > $i > $i ).
thf(func_def_291,type,
sK76: ( $i > $o ) > $i ).
thf(func_def_292,type,
sK77: ( $i > $o ) > $i > $i ).
thf(func_def_293,type,
sK78: ( $i > $o ) > $i > $i ).
thf(func_def_294,type,
sK79: $i > $i ).
thf(func_def_295,type,
sK80: $i > $i > $i > $i ).
thf(func_def_296,type,
sK81: $i > $i > $i ).
thf(func_def_297,type,
sK82: $i > $i > $i ).
thf(func_def_298,type,
sK83: $i > $i > $i ).
thf(func_def_299,type,
sK84: $i > $i ).
thf(func_def_300,type,
sK85: $i > ( $i > $i > $o ) > $i ).
thf(func_def_301,type,
sK86: $i > ( $i > $i > $o ) > $i ).
thf(func_def_302,type,
sK87: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_303,type,
sK88: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_304,type,
sK89: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_305,type,
sK90: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_306,type,
sK91: $i > $i ).
thf(func_def_307,type,
sK92: $i > $i > $i ).
thf(func_def_308,type,
sK93: $i > $i > $i ).
thf(func_def_309,type,
sK94: $i > $i > $i ).
thf(f21,axiom,
( notinemptyset
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(f35,axiom,
( setadjoinOr
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( X2 = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(f138,axiom,
( setukpairIR
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR) ).
thf(f140,axiom,
( kpair
= ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpair) ).
thf(f157,axiom,
( setunionsingleton
= ( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
thf(f168,axiom,
( kfstpairEq
= ( ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(f173,axiom,
( setukpairinjR12
= ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(f174,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
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X2 = X3 )
=> ( X1 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(f175,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
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X2 = X3 )
=> ( X1 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f174]) ).
thf(f214,plain,
( notinemptyset
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
inference(rectify,[],[f21]) ).
thf(f215,plain,
( notinemptyset
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset ) ) ),
inference(fool_elimination,[],[f214]) ).
thf(f239,plain,
( setadjoinOr
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( X2 = X0 ) ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f240,plain,
( setadjoinOr
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) )
=> ( ( Y2 = Y0 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f239]) ).
thf(f439,plain,
( setukpairIR
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f138]) ).
thf(f440,plain,
( setukpairIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fool_elimination,[],[f439]) ).
thf(f443,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[],[f140]) ).
thf(f476,plain,
( setunionsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( ( setunion @ ( setadjoin @ Y0 @ emptyset ) )
= Y0 ) ) ),
inference(fool_elimination,[],[f157]) ).
thf(f496,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[],[f168]) ).
thf(f502,plain,
( setukpairinjR12
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[],[f173]) ).
thf(f503,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
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X2 = X3 )
=> ( X1 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f175]) ).
thf(f504,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 )
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X2 = X3 )
=> ( X1 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f503]) ).
thf(f505,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 != X3 )
& ( X2 = X3 )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( 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,[],[f504]) ).
thf(f506,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 != X3 )
& ( X2 = X3 )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( 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,[],[f505]) ).
thf(f507,plain,
( ( sK1 != sK3 )
& ( sK2 = sK3 )
& ( ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) )
& ( 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,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f506]) ).
thf(f528,plain,
( notinemptyset
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset ) ) ),
inference(cnf_transformation,[],[f215]) ).
thf(f542,plain,
( setadjoinOr
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) )
=> ( ( Y2 = Y0 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f240]) ).
thf(f645,plain,
( setukpairIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f440]) ).
thf(f647,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f443]) ).
thf(f664,plain,
( setunionsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( ( setunion @ ( setadjoin @ Y0 @ emptyset ) )
= Y0 ) ) ),
inference(cnf_transformation,[],[f476]) ).
thf(f675,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[],[f496]) ).
thf(f680,plain,
( setukpairinjR12
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[],[f502]) ).
thf(f700,plain,
notinemptyset = $true,
inference(cnf_transformation,[],[f507]) ).
thf(f713,plain,
setadjoinOr = $true,
inference(cnf_transformation,[],[f507]) ).
thf(f815,plain,
setukpairIR = $true,
inference(cnf_transformation,[],[f507]) ).
thf(f833,plain,
setunionsingleton = $true,
inference(cnf_transformation,[],[f507]) ).
thf(f842,plain,
kfstpairEq = $true,
inference(cnf_transformation,[],[f507]) ).
thf(f847,plain,
setukpairinjR12 = $true,
inference(cnf_transformation,[],[f507]) ).
thf(f848,plain,
( ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ),
inference(cnf_transformation,[],[f507]) ).
thf(f849,plain,
sK2 = sK3,
inference(cnf_transformation,[],[f507]) ).
thf(f850,plain,
sK1 != sK3,
inference(cnf_transformation,[],[f507]) ).
thf(f873,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset ) )
= $true ),
inference(definition_unfolding,[],[f528,f700]) ).
thf(f886,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) )
=> ( ( Y2 = Y0 )
| ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f542,f713]) ).
thf(f988,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f645,f815]) ).
thf(f1006,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( setunion @ ( setadjoin @ Y0 @ emptyset ) )
= Y0 ) ) ),
inference(definition_unfolding,[],[f664,f833]) ).
thf(f1015,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 ) )
= Y1 ) ) ) ),
inference(definition_unfolding,[],[f675,f842,f647]) ).
thf(f1020,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ emptyset ) ) ) ) ) ),
inference(definition_unfolding,[],[f680,f847]) ).
thf(f1021,plain,
( ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ),
inference(definition_unfolding,[],[f848,f849,f849]) ).
thf(f1022,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1020]) ).
thf(f1023,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f1022]) ).
thf(f1024,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ emptyset ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f1023]) ).
thf(f1025,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( X2 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
inference(beta-eta_normalization,[],[f1024]) ).
thf(f1026,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( X2 = X1 ) )
| ( $true
= ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
inference(imp_proxy_clausification,[],[f1025]) ).
thf(f1027,plain,
! [X2: $i,X1: $i] :
( ( X1 != X2 )
| ( $true
= ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
inference(equality_proxy_clausification,[],[f1026]) ).
thf(f1028,plain,
! [X2: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[],[f1027]) ).
thf(f1065,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 ) )
= Y1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1015]) ).
thf(f1066,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= Y0 ) ) ),
inference(beta-eta_normalization,[],[f1065]) ).
thf(f1067,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= Y0 )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f1066]) ).
thf(f1068,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( kfst @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X2 ) ),
inference(beta-eta_normalization,[],[f1067]) ).
thf(f1069,plain,
! [X2: $i,X1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X2 ),
inference(equality_proxy_clausification,[],[f1068]) ).
thf(f1221,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( setunion @ ( setadjoin @ Y0 @ emptyset ) )
= Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1006]) ).
thf(f1222,plain,
! [X1: $i] :
( $true
= ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ) ),
inference(beta-eta_normalization,[],[f1221]) ).
thf(f1223,plain,
! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ),
inference(equality_proxy_clausification,[],[f1222]) ).
thf(f1382,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f988]) ).
thf(f1383,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1382]) ).
thf(f1384,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f1383]) ).
thf(f1385,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f1384]) ).
thf(f2444,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ Y1 ) )
=> ( ( Y2 = Y0 )
| ( in @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f886]) ).
thf(f2445,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setadjoin @ Y1 @ Y0 ) )
=> ( ( Y1 = X1 )
| ( in @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2444]) ).
thf(f2446,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setadjoin @ Y1 @ Y0 ) )
=> ( ( Y1 = X1 )
| ( in @ X1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f2445]) ).
thf(f2447,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ X2 ) )
=> ( ( Y0 = X1 )
| ( in @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2446]) ).
thf(f2448,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ X2 ) )
=> ( ( Y0 = X1 )
| ( in @ X1 @ X2 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f2447]) ).
thf(f2449,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( setadjoin @ X3 @ X2 ) )
=> ( ( X3 = X1 )
| ( in @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2448]) ).
thf(f2450,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( $true
= ( ( X3 = X1 )
| ( in @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f2449]) ).
thf(f2451,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X2 )
= $true )
| ( $true
= ( X3 = X1 ) ) ),
inference(or_proxy_clausification,[],[f2450]) ).
thf(f2452,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X2 )
= $true )
| ( X1 = X3 ) ),
inference(equality_proxy_clausification,[],[f2451]) ).
thf(f2560,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f873]) ).
thf(f2561,plain,
! [X1: $i] :
( $true
= ( ~ ( in @ X1 @ emptyset ) ) ),
inference(beta-eta_normalization,[],[f2560]) ).
thf(f2562,plain,
! [X1: $i] :
( ( in @ X1 @ emptyset )
= $false ),
inference(not_proxy_clausification,[],[f2561]) ).
thf(f6724,plain,
( sK0
= ( kfst @ ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ),
inference(constrained_superposition,[],[f1069,f1021]) ).
thf(f6725,plain,
sK0 = sK3,
inference(forward_demodulation,[],[f6724,f1069]) ).
thf(f6731,definition,
( spl95_18
<=> ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[spl95_18])],[avatar_definition]) ).
thf(f6732,plain,
( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ emptyset ) )
| spl95_18 ),
inference(avatar_component_clause,[],[f6731]) ).
thf(f6733,plain,
( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ emptyset ) )
| ~ spl95_18 ),
inference(avatar_component_clause,[],[f6731]) ).
thf(f6826,plain,
( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ emptyset ) )
| ~ spl95_18 ),
inference(forward_demodulation,[],[f6733,f6725]) ).
thf(f7017,plain,
( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ),
inference(constrained_superposition,[],[f1021,f6725]) ).
thf(f7018,plain,
( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
| ~ spl95_18 ),
inference(forward_demodulation,[],[f7017,f6826]) ).
thf(f7719,plain,
( ( $true
= ( in @ sK1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ emptyset ) ) ) )
| ~ spl95_18 ),
inference(constrained_superposition,[],[f1385,f7018]) ).
thf(f7725,plain,
( ( $true
= ( in @ sK1 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl95_18 ),
inference(forward_demodulation,[],[f7719,f1223]) ).
thf(f7737,plain,
( ( $false = $true )
| ( $true
= ( in @ sK1 @ emptyset ) )
| ( sK1 = sK3 )
| ~ spl95_18 ),
inference(constrained_superposition,[],[f7725,f2452]) ).
thf(f7764,plain,
( ( $true
= ( in @ sK1 @ emptyset ) )
| ( sK1 = sK3 )
| ~ spl95_18 ),
inference(trivial_inequality_removal,[],[f7737]) ).
thf(f7770,plain,
( ( $true
= ( in @ sK1 @ emptyset ) )
| ~ spl95_18 ),
inference(forward_subsumption_resolution,[],[f7764,f850]) ).
thf(f7774,plain,
( ( $false = $true )
| ~ spl95_18 ),
inference(forward_demodulation,[],[f7770,f2562]) ).
thf(f7775,plain,
( $false
| ~ spl95_18 ),
inference(trivial_inequality_removal,[],[f7774]) ).
thf(f7776,plain,
~ spl95_18,
inference(avatar_contradiction_clause,[],[f7775]) ).
thf(f7777,plain,
( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ emptyset ) )
| spl95_18 ),
inference(forward_demodulation,[],[f6732,f6725]) ).
thf(f7792,plain,
( ( ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ emptyset ) )
| ( sK3 != sK3 )
| spl95_18 ),
inference(constrained_superposition,[],[f7777,f1028]) ).
thf(f7793,plain,
( $false
| spl95_18 ),
inference(trivial_inequality_removal,[],[f7792]) ).
thf(f7794,plain,
spl95_18,
inference(avatar_contradiction_clause,[],[f7793]) ).
cnf(s36,plain,
~ spl95_18,
inference(sat_conversion,[],[f7776]) ).
cnf(s37,plain,
spl95_18,
inference(sat_conversion,[],[f7794]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s36,s37]) ).
thf(f7797,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU651^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.25 % Computer : n007.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Tue Sep 29 14:00:41 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.27/0.31 Running first-order model finding
% 0.27/0.31 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.74/1.47 % (3415875)Will run a generic schedule for satisfiability detection.
% 6.74/1.47 % (3415886)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2001561593:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.74/1.47 % (3415881)% WARNING: option uhcvi not known.
% 6.74/1.47 % (3415880)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2855591880_2999 on theBenchmark for (2999ds/0Mi)
% 6.74/1.47 % (3415885)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1469961629:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.74/1.47 % (3415884)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3869064751:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.74/1.47 % (3415881)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1764310722:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.74/1.47 % (3415883)dis+10_1_sil=32000:sp=arity:random_seed=2921727925:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.74/1.47 % (3415882)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3376404008:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.74/1.47 % (3415881)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.74/1.47 % (3415884)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.74/1.47 % Exception at run slice level
% 6.74/1.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.74/1.47 % (3415886)Instruction limit reached!
% 6.74/1.47 % (3415886)------------------------------
% 6.74/1.47 % (3415886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.74/1.47 % (3415886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/1.47 % (3415886)CaDiCaL version: 2.1.3
% 6.74/1.47 % (3415886)Termination reason: Instruction limit
% 6.74/1.47 % (3415886)Termination phase: Saturation
% 6.74/1.47 % (3415886)Time elapsed: 0.070 s
% 6.74/1.47 % (3415886)Peak memory usage: 14 MB
% 6.74/1.47 % (3415886)Instructions burned: 161 (million)
% 6.74/1.47 % (3415881)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.74/1.47 % (3415894)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1035560517:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 6.74/1.47 % (3415883)Instruction limit reached!
% 6.74/1.47 % (3415883)------------------------------
% 6.74/1.47 % (3415883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.74/1.47 % (3415883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/1.47 % (3415883)CaDiCaL version: 2.1.3
% 6.74/1.47 % (3415883)Termination reason: Instruction limit
% 6.74/1.47 % (3415883)Termination phase: Saturation
% 6.74/1.47 % (3415883)Time elapsed: 0.082 s
% 6.74/1.47 % (3415883)Peak memory usage: 13 MB
% 6.74/1.47 % (3415883)Instructions burned: 103 (million)
% 6.74/1.47 % (3415895)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2865924599:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 6.74/1.47 % (3415884)Instruction limit reached!
% 6.74/1.47 % (3415884)------------------------------
% 6.74/1.47 % (3415884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.74/1.47 % (3415884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/1.47 % (3415884)CaDiCaL version: 2.1.3
% 6.74/1.47 % (3415884)Termination reason: Instruction limit
% 6.74/1.47 % (3415884)Termination phase: Saturation
% 6.74/1.47 % (3415884)Time elapsed: 0.094 s
% 6.74/1.47 % (3415884)Peak memory usage: 13 MB
% 6.74/1.47 % (3415884)Instructions burned: 116 (million)
% 6.74/1.47 % (3415885)Instruction limit reached!
% 6.74/1.47 % (3415885)------------------------------
% 6.74/1.47 % (3415885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.74/1.47 % (3415885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/1.47 % (3415885)CaDiCaL version: 2.1.3
% 6.74/1.47 % (3415885)Termination reason: Instruction limit
% 6.74/1.47 % (3415885)Termination phase: Saturation
% 6.74/1.47 % (3415885)Time elapsed: 0.106 s
% 6.74/1.47 % (3415885)Peak memory usage: 13 MB
% 6.74/1.47 % (3415885)Instructions burned: 131 (million)
% 6.74/1.47 % Exception at run slice level
% 6.74/1.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.74/1.47 % (3415897)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=607315595:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 7.63/1.88 % (3415901)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3625661651:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 7.63/1.88 % (3415899)ott-21_1_sil=16000:fs=off:random_seed=1358918068:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 7.63/1.88 % (3415900)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3427517158:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 7.63/1.88 % (3415897)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.63/1.88 % Exception at run slice level
% 7.63/1.88 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.63/1.88 % (3415897)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.63/1.88 % (3415906)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2574731978:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 7.63/1.88 % (3415895)Instruction limit reached!
% 7.63/1.88 % (3415895)------------------------------
% 7.63/1.88 % (3415895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.63/1.88 % (3415895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/1.88 % (3415895)CaDiCaL version: 2.1.3
% 7.63/1.88 % (3415895)Termination reason: Instruction limit
% 7.63/1.88 % (3415895)Termination phase: Saturation
% 7.63/1.88 % (3415895)Time elapsed: 0.109 s
% 7.63/1.88 % (3415895)Peak memory usage: 13 MB
% 7.63/1.88 % (3415895)Instructions burned: 135 (million)
% 7.63/1.88 % (3415908)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2058305806:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 7.63/1.88 % (3415899)Instruction limit reached!
% 7.63/1.88 % (3415899)------------------------------
% 7.63/1.88 % (3415899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.63/1.88 % (3415899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/1.88 % (3415899)CaDiCaL version: 2.1.3
% 7.63/1.88 % (3415899)Termination reason: Instruction limit
% 7.63/1.88 % (3415899)Termination phase: Saturation
% 7.63/1.88 % (3415899)Time elapsed: 0.118 s
% 7.63/1.88 % (3415899)Peak memory usage: 13 MB
% 7.63/1.88 % (3415899)Instructions burned: 181 (million)
% 7.63/1.88 % (3415910)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=2304591695: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)
% 7.63/1.88 % Exception at run slice level
% 7.63/1.88 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.63/1.88 % (3415912)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1597501859:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 7.63/1.88 % (3415910)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.63/1.88 % (3415912)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.63/1.88 % (3415900)Instruction limit reached!
% 7.63/1.88 % (3415900)------------------------------
% 7.63/1.88 % (3415900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.63/1.88 % (3415900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/1.88 % (3415900)CaDiCaL version: 2.1.3
% 7.63/1.88 % (3415900)Termination reason: Instruction limit
% 7.63/1.88 % (3415900)Termination phase: Saturation
% 7.63/1.88 % (3415900)Time elapsed: 0.430 s
% 7.63/1.88 % (3415900)Peak memory usage: 14 MB
% 7.63/1.88 % (3415900)Instructions burned: 478 (million)
% 7.63/1.88 % (3415914)fmb+10_1_sil=64000:random_seed=2070991283:i=22061:nm=2:gsp=on_2993 on theBenchmark for (2993ds/22061Mi)
% 7.63/1.88 % (3415897)Instruction limit reached!
% 7.63/1.88 % (3415897)------------------------------
% 7.63/1.88 % (3415897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.63/1.88 % (3415897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/1.88 % (3415897)CaDiCaL version: 2.1.3
% 7.63/1.88 % (3415897)Termination reason: Instruction limit
% 7.63/1.88 % (3415897)Termination phase: Saturation
% 7.63/1.88 % (3415897)Time elapsed: 0.499 s
% 7.63/1.88 % (3415897)Peak memory usage: 15 MB
% 7.63/1.88 % (3415897)Instructions burned: 684 (million)
% 7.63/1.88 % (3415914)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.63/1.88 % (3415916)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1099658031:i=9515:nm=5_2993 on theBenchmark for (2993ds/9515Mi)
% 7.63/1.88 % Exception at run slice level
% 7.63/1.88 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.63/1.88 % (3415918)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1003799385:fmbsr=1.7:i=920_2992 on theBenchmark for (2992ds/920Mi)
% 7.63/1.88 % Exception at run slice level
% 7.63/1.88 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.63/1.88 % (3415906)Instruction limit reached!
% 7.63/1.88 % (3415906)------------------------------
% 7.63/1.88 % (3415906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.63/1.88 % (3415906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/1.88 % (3415906)CaDiCaL version: 2.1.3
% 7.63/1.88 % (3415906)Termination reason: Instruction limit
% 7.63/1.88 % (3415906)Termination phase: Saturation
% 7.63/1.88 % (3415906)Time elapsed: 0.526 s
% 7.63/1.88 % (3415906)Peak memory usage: 18 MB
% 7.63/1.88 % (3415906)Instructions burned: 1180 (million)
% 7.63/1.88 % (3415920)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3097427411:i=5131_2992 on theBenchmark for (2992ds/5131Mi)
% 7.63/1.88 % (3415920)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.63/1.88 % Exception at run slice level
% 7.63/1.88 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.63/1.88 % (3415921)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=143144286:i=1472:ins=7:fdi=8:gsp=on_2992 on theBenchmark for (2992ds/1472Mi)
% 7.63/1.88 % (3415923)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=4256246378:i=6324_2992 on theBenchmark for (2992ds/6324Mi)
% 7.63/1.88 % (3415921)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.63/1.88 % (3415921)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.63/1.88 % Exception at run slice level
% 7.63/1.88 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.63/1.88 % (3415910)Instruction limit reached!
% 7.63/1.88 % (3415910)------------------------------
% 7.63/1.88 % (3415910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.63/1.88 % (3415910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/1.88 % (3415910)CaDiCaL version: 2.1.3
% 7.63/1.88 % (3415910)Termination reason: Instruction limit
% 7.63/1.88 % (3415910)Termination phase: Saturation
% 7.63/1.88 % (3415910)Time elapsed: 0.531 s
% 7.63/1.88 % (3415910)Peak memory usage: 16 MB
% 7.63/1.88 % (3415910)Instructions burned: 692 (million)
% 7.63/1.88 % (3415926)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2055944588:fmbsr=2.30978:i=2174_2991 on theBenchmark for (2991ds/2174Mi)
% 7.63/1.88 % (3415927)ott-2_1_sil=16000:newcnf=on:random_seed=1380811830:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2991 on theBenchmark for (2991ds/869Mi)
% 7.63/1.88 % Exception at run slice level
% 7.63/1.88 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.63/1.88 % (3415927)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.63/1.88 % (3415930)ott+10_1_sil=32000:tgt=ground:random_seed=201826820:i=5114:av=off_2990 on theBenchmark for (2990ds/5114Mi)
% 7.63/1.88 % (3415912)Instruction limit reached!
% 7.63/1.88 % (3415912)------------------------------
% 7.63/1.88 % (3415912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.63/1.88 % (3415912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/1.88 % (3415912)CaDiCaL version: 2.1.3
% 7.63/1.88 % (3415912)Termination reason: Instruction limit
% 7.63/1.88 % (3415912)Termination phase: Saturation
% 7.63/1.88 % (3415912)Time elapsed: 0.732 s
% 7.63/1.88 % (3415912)Peak memory usage: 16 MB
% 7.63/1.88 % (3415912)Instructions burned: 880 (million)
% 7.63/1.88 % (3415932)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3933620263:i=54282_2989 on theBenchmark for (2989ds/54282Mi)
% 7.63/1.88 % Exception at run slice level
% 7.63/1.88 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.63/1.88 % (3415934)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1330500410:i=3512:aac=none_2988 on theBenchmark for (2988ds/3512Mi)
% 7.63/1.88 % (3415934)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.63/1.88 % (3415927) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3415875-3415927"...
% 7.63/1.88 % (3415927)...printing done.
% 7.63/1.88 % (3415927)Refutation found. Thanks to Tanya!
% 7.63/1.88 % SZS status Theorem for theBenchmark
% 7.63/1.88 % SZS output start Proof for theBenchmark
% See solution above
% 7.63/1.89 % (3415927)------------------------------
% 7.63/1.89 % (3415927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.63/1.89 % (3415927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/1.89 % (3415927)CaDiCaL version: 2.1.3
% 7.63/1.89 % (3415927)Termination reason: Refutation
% 7.63/1.89 % (3415927)Time elapsed: 0.666 s
% 7.63/1.89 % (3415927)Peak memory usage: 17 MB
% 7.63/1.89 % (3415927)Instructions burned: 778 (million)
% 7.63/1.89 % (3415875)Success in time 1.567 s
% 7.63/1.89 % Vampire exiting
%------------------------------------------------------------------------------