%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU638^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:27 AM UTC 2026
% Result : Theorem 1.85s 0.77s
% Output : Refutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 57 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 3079 ( 848 equ; 0 cnn)
% Maximal formula atoms : 157 ( 54 avg)
% Number of connectives : 1697 ( 15 ~; 9 |; 479 &; 362 @)
% ( 0 <=>; 797 =>; 0 <=; 0 <~>)
% Maximal formula depth : 163 ( 24 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 293 ( 288 usr; 161 con; 0-4 aty)
% ( 30 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 155 ( 88 ^; 56 !; 11 ?; 155 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_181,type,
vIMP: $o > $o > $o ).
thf(func_def_182,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_183,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_184,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_185,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_186,type,
vNOT: $o > $o ).
thf(func_def_187,type,
vIFF: $o > $o > $o ).
thf(func_def_188,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_189,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_190,type,
vAND: $o > $o > $o ).
thf(func_def_191,type,
vOR: $o > $o > $o ).
thf(func_def_192,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_193,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_196,type,
sK0: $i > $o ).
thf(func_def_198,type,
sK2: $i > $i > $i > $i ).
thf(func_def_199,type,
sK3: $i > $i > $i > $i ).
thf(func_def_200,type,
sK4: $i > $i > $i ).
thf(func_def_201,type,
sK5: $i > $i ).
thf(func_def_202,type,
sK6: $i > $i ).
thf(func_def_203,type,
sK7: $i > $i ).
thf(func_def_204,type,
sK8: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_205,type,
sK9: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_206,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_207,type,
sK11: $i > ( $i > $o ) > $i ).
thf(func_def_208,type,
sK12: $i > ( $i > $o ) > $i ).
thf(func_def_209,type,
sK13: ( $i > $o ) > $i ).
thf(func_def_210,type,
sK14: $i > ( $i > $o ) > $i ).
thf(func_def_211,type,
sK15: $i > ( $i > $o ) > $i ).
thf(func_def_212,type,
sK16: ( $i > $o ) > $i ).
thf(func_def_213,type,
sK17: $i > ( $i > $o ) > $i ).
thf(func_def_214,type,
sK18: $i > ( $i > $o ) > $i ).
thf(func_def_215,type,
sK19: ( $i > $o ) > $i ).
thf(func_def_216,type,
sK20: $i > ( $i > $o ) > $i ).
thf(func_def_217,type,
sK21: $i > ( $i > $o ) > $i ).
thf(func_def_218,type,
sK22: ( $i > $o ) > $i ).
thf(func_def_219,type,
sK23: $i > ( $i > $o ) > $i ).
thf(func_def_220,type,
sK24: $i > ( $i > $o ) > $i ).
thf(func_def_221,type,
sK25: ( $i > $o ) > $i ).
thf(func_def_222,type,
sK26: $i > ( $i > $o ) > $i ).
thf(func_def_223,type,
sK27: $i > ( $i > $o ) > $i ).
thf(func_def_224,type,
sK28: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_225,type,
sK29: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_226,type,
sK30: $i > ( $i > $o ) > $i ).
thf(func_def_227,type,
sK31: $i > ( $i > $o ) > $i ).
thf(func_def_228,type,
sK32: $i > ( $i > $o ) > $i ).
thf(func_def_229,type,
sK33: $i > ( $i > $o ) > $i ).
thf(func_def_230,type,
sK34: $i > $i > $i ).
thf(func_def_231,type,
sK35: $i > $i > $i ).
thf(func_def_232,type,
sK36: $i > $i > $i ).
thf(func_def_233,type,
sK37: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_234,type,
sK38: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_236,type,
sK40: $i > $i > $i ).
thf(func_def_237,type,
sK41: $i > $i > $i ).
thf(func_def_238,type,
sK42: $i > $i > $i ).
thf(func_def_239,type,
sK43: ( $i > $o ) > $i > $i ).
thf(func_def_240,type,
sK44: $i > $i > $i ).
thf(func_def_241,type,
sK45: $i > $i ).
thf(func_def_242,type,
sK46: ( $i > $o ) > $i ).
thf(func_def_243,type,
sK47: ( $i > $o ) > $i > $i ).
thf(func_def_244,type,
sK48: ( $i > $o ) > $i > $i ).
thf(func_def_245,type,
sK49: ( $i > $o ) > $i ).
thf(func_def_246,type,
sK50: ( $i > $o ) > $i ).
thf(func_def_247,type,
sK51: ( $i > $o ) > $i ).
thf(func_def_248,type,
sK52: ( $i > $o ) > $i ).
thf(func_def_249,type,
sK53: $i > $o > $i > $i ).
thf(func_def_250,type,
sK54: $i > $i ).
thf(func_def_251,type,
sK55: $i > ( $i > $o ) > $i ).
thf(func_def_252,type,
sK56: $i > ( $i > $o ) > $i ).
thf(func_def_253,type,
sK57: $i > ( $i > $o ) > $i ).
thf(func_def_254,type,
sK58: $i > ( $i > $o ) > $i ).
thf(func_def_255,type,
sK59: ( $i > $o ) > $i > $i ).
thf(func_def_256,type,
sK60: ( $i > $i > $o ) > $i > $i ).
thf(func_def_257,type,
sK61: ( $i > $i > $o ) > $i > $i ).
thf(func_def_258,type,
sK62: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_259,type,
sK63: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_260,type,
sK64: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_261,type,
sK65: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_262,type,
sK66: $i > $i > $i ).
thf(func_def_263,type,
sK67: ( $i > $o ) > $i ).
thf(func_def_264,type,
sK68: ( $i > $o ) > $i > $i ).
thf(func_def_265,type,
sK69: ( $i > $o ) > $i > $i ).
thf(func_def_266,type,
sK70: ( $i > $o ) > $i ).
thf(func_def_267,type,
sK71: ( $i > $o ) > $i > $i ).
thf(func_def_268,type,
sK72: ( $i > $o ) > $i > $i ).
thf(func_def_269,type,
sK73: $i > $i ).
thf(func_def_270,type,
sK74: ( $i > $o ) > $i ).
thf(func_def_271,type,
sK75: ( $i > $o ) > $i > $i ).
thf(func_def_272,type,
sK76: $i > $i ).
thf(func_def_273,type,
sK77: $i > $i > $i > $i ).
thf(func_def_274,type,
sK78: $i > $i > $i ).
thf(func_def_275,type,
sK79: $i > $i > $i ).
thf(func_def_276,type,
sK80: $i > $i > $i ).
thf(func_def_277,type,
sK81: $i > $i ).
thf(func_def_278,type,
sK82: $i > $i > $i ).
thf(func_def_279,type,
sK83: $i > $i > $i ).
thf(func_def_280,type,
sK84: $i > ( $i > $o ) > $i ).
thf(func_def_281,type,
sK85: ( $i > $o ) > $i > $i ).
thf(func_def_282,type,
sK86: $i > ( $i > $o ) > $i ).
thf(func_def_283,type,
sK87: ( $i > $o ) > $i > $i ).
thf(func_def_284,type,
sK88: $i > $i > $i ).
thf(func_def_285,type,
sK89: $i > $i > $i ).
thf(func_def_286,type,
sK90: $i > $i > $i ).
thf(func_def_287,type,
sK91: $i > $i ).
thf(func_def_288,type,
sK92: $i > ( $i > $o ) > $i ).
thf(func_def_289,type,
sK93: ( $i > $o ) > $i ).
thf(func_def_290,type,
sK94: ( $i > $o ) > $i > $i ).
thf(f15,axiom,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) )
= dsetconstrEL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(f16,axiom,
! [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f158,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( X0
= ( setadjoin @ X1 @ emptyset ) ) ) )
= singleton ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(f160,axiom,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(f161,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
=> ! [X1: $i > $o,X0: $i] :
( ( ex1 @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(f162,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
=> ! [X1: $i > $o,X0: $i] :
( ( ex1 @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f161]) ).
thf(f187,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X2 ) )
= dsetconstrER ),
inference(rectify,[],[f16]) ).
thf(f188,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f187]) ).
thf(f285,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) )
= dsetconstrEL ),
inference(rectify,[],[f15]) ).
thf(f286,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f285]) ).
thf(f413,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f160]) ).
thf(f414,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f413]) ).
thf(f442,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( X0
= ( setadjoin @ X1 @ emptyset ) ) ) )
= singleton ),
inference(rectify,[],[f158]) ).
thf(f443,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f442]) ).
thf(f456,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
=> ! [X0: $i > $o,X1: $i] :
( ( ex1 @ X1
@ ^ [X2: $i] : ( X0 @ X2 ) )
=> ? [X3: $i] :
( ( X0 @ X3 )
& ( in @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f162]) ).
thf(f457,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 )
=> ! [X0: $i > $o,X1: $i] :
( ( $true
= ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ? [X3: $i] :
( ( $true
= ( X0 @ X3 ) )
& ( ( in @ X3 @ X1 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f456]) ).
thf(f474,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 )
=> ! [X1: $i,X0: $i > $o] :
( ( $true
= ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f457]) ).
thf(f475,plain,
( ? [X0: $i > $o,X1: $i] :
( ( $true
= ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X2: $i] :
( ( ( X0 @ X2 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $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,[],[f474]) ).
thf(f476,plain,
( ( subsetRefl = $true )
& ( setminusERneg = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyImpWitness = $true )
& ( setadjoinSub = $true )
& ( dsetconstrER = $true )
& ( exu__Cong = $true )
& ( symdiffE = $true )
& ( upairsetE = $true )
& ( setminusI = $true )
& ( symdiffI1 = $true )
& ( quantDeMorgan4 = $true )
& ( omega__Cong = $true )
& ( setadjoinIR = $true )
& ( descrp = $true )
& ( in__Cong = $true )
& ( uniqinunit = $true )
& ( powersetE1 = $true )
& ( kpairp = $true )
& ( binintersectER = $true )
& ( setextAx = $true )
& ( emptysetsubset = $true )
& ( binunionIR = $true )
& ( emptysetE = $true )
& ( emptyInPowerset = $true )
& ( eqimpsubset1 = $true )
& ( setextsub = $true )
& ( emptyset__Cong = $true )
& ( secondinupair = $true )
& ( dsetconstrEL = $true )
& ( inCongP = $true )
& ( setunionE2 = $true )
& ( inPowerset = $true )
& ( setbeta = $true )
& ( binunionRsub = $true )
& ( emptyinPowerset = $true )
& ( replAx = $true )
& ( subPowSU = $true )
& ( binunionEcases = $true )
& ( powersetsubset = $true )
& ( setminusSubset2 = $true )
& ( setminusSubset1 = $true )
& ( cartprodmempair = $true )
& ( binunionE = $true )
& ( sepSubset = $true )
& ( descr__Cong = $true )
& ( upairsetIL = $true )
& ( setminusEL = $true )
& ( setadjoinSub2 = $true )
& ( exuEu = $true )
& ( omega0Ax = $true )
& ( foundationAx = $true )
& ( emptysetimpfalse = $true )
& ( emptyI = $true )
& ( dsetconstr__Cong = $true )
& ( subsetI1 = $true )
& ( emptysetAx = $true )
& ( bs114d = $true )
& ( setadjoinAx = $true )
& ( singletonprop = $true )
& ( binintersectSubset1 = $true )
& ( powersetE = $true )
& ( dsetconstrI = $true )
& ( binunionIL = $true )
& ( ubforcartprodlem2 = $true )
& ( binintersectSubset2 = $true )
& ( prop2setI = $true )
& ( vacuousDall = $true )
& ( setminusER = $true )
& ( setunionsingleton1 = $true )
& ( powersetAx = $true )
& ( eqimpsubset2 = $true )
& ( exuE2 = $true )
& ( binintersectLsub = $true )
& ( quantDeMorgan1 = $true )
& ( cartprodmempair1 = $true )
& ( exuE3u = $true )
& ( setminusIRneg = $true )
& ( symdiffIneg2 = $true )
& ( binintersectRsub = $true )
& ( emptyinunitempty = $true )
& ( setunionsingleton = $true )
& ( symdiffI2 = $true )
& ( exuE3e = $true )
& ( setadjoinE = $true )
& ( binintersectEL = $true )
& ( subsetE = $true )
& ( setunionI = $true )
& ( kpairiskpair = $true )
& ( binunionLsub = $true )
& ( nonemptyI = $true )
& ( singletonsswitch = $true )
& ( setoftrueEq = $true )
& ( noeltsimpempty = $true )
& ( subsetI2 = $true )
& ( nonemptyI1 = $true )
& ( prop2set2propI = $true )
& ( setminusLsub = $true )
& ( binintersectSubset3 = $true )
& ( omegaIndAx = $true )
& ( setunionAx = $true )
& ( powersetI = $true )
& ( exuI2 = $true )
& ( setadjoinIL = $true )
& ( subset2powerset = $true )
& ( subsetTrans = $true )
& ( setukpairIL = $true )
& ( setunionE = $true )
& ( setadjoinOr = $true )
& ( sepInPowerset = $true )
& ( ubforcartprodlem3 = $true )
& ( powerset__Cong = $true )
& ( binintersectI = $true )
& ( setadjoin__Cong = $true )
& ( omegaSAx = $true )
& ( notinsingleton = $true )
& ( exuE1 = $true )
& ( setukpairIR = $true )
& ( notequalI2 = $true )
& ( upairset2IR = $true )
& ( binintersectSubset4 = $true )
& ( binintersectSubset5 = $true )
& ( singletonsubset = $true )
& ? [X0: $i > $o,X1: $i] :
( ( $true
= ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X2: $i] :
( ( ( X0 @ X2 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( notdexE = $true )
& ( exuI3 = $true )
& ( singletoninpowunion = $true )
& ( setminusELneg = $true )
& ( setminusILneg = $true )
& ( cartprodpairin = $true )
& ( quantDeMorgan2 = $true )
& ( upairsetIR = $true )
& ( upairset2E = $true )
& ( eqinunit = $true )
& ( nonemptyE1 = $true )
& ( symdiffIneg1 = $true )
& ( upairinpowunion = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( wellorderingAx = $true )
& ( exuI1 = $true )
& ( emptyE1 = $true )
& ( singletoninpowerset = $true )
& ( setunionsingleton2 = $true )
& ( subsetE2 = $true )
& ( prop2setE = $true )
& ( setunion__Cong = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsubunion = $true )
& ( ubforcartprodlem1 = $true )
& ( notinemptyset = $true )
& ( notdallE = $true )
& ( setext = $true )
& ( quantDeMorgan3 = $true ) ),
inference(flattening,[],[f475]) ).
thf(f477,plain,
( ( subsetRefl = $true )
& ( setminusERneg = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyImpWitness = $true )
& ( setadjoinSub = $true )
& ( dsetconstrER = $true )
& ( exu__Cong = $true )
& ( symdiffE = $true )
& ( upairsetE = $true )
& ( setminusI = $true )
& ( symdiffI1 = $true )
& ( quantDeMorgan4 = $true )
& ( omega__Cong = $true )
& ( setadjoinIR = $true )
& ( descrp = $true )
& ( in__Cong = $true )
& ( uniqinunit = $true )
& ( powersetE1 = $true )
& ( kpairp = $true )
& ( binintersectER = $true )
& ( setextAx = $true )
& ( emptysetsubset = $true )
& ( binunionIR = $true )
& ( emptysetE = $true )
& ( emptyInPowerset = $true )
& ( eqimpsubset1 = $true )
& ( setextsub = $true )
& ( emptyset__Cong = $true )
& ( secondinupair = $true )
& ( dsetconstrEL = $true )
& ( inCongP = $true )
& ( setunionE2 = $true )
& ( inPowerset = $true )
& ( setbeta = $true )
& ( binunionRsub = $true )
& ( emptyinPowerset = $true )
& ( replAx = $true )
& ( subPowSU = $true )
& ( binunionEcases = $true )
& ( powersetsubset = $true )
& ( setminusSubset2 = $true )
& ( setminusSubset1 = $true )
& ( cartprodmempair = $true )
& ( binunionE = $true )
& ( sepSubset = $true )
& ( descr__Cong = $true )
& ( upairsetIL = $true )
& ( setminusEL = $true )
& ( setadjoinSub2 = $true )
& ( exuEu = $true )
& ( omega0Ax = $true )
& ( foundationAx = $true )
& ( emptysetimpfalse = $true )
& ( emptyI = $true )
& ( dsetconstr__Cong = $true )
& ( subsetI1 = $true )
& ( emptysetAx = $true )
& ( bs114d = $true )
& ( setadjoinAx = $true )
& ( singletonprop = $true )
& ( binintersectSubset1 = $true )
& ( powersetE = $true )
& ( dsetconstrI = $true )
& ( binunionIL = $true )
& ( ubforcartprodlem2 = $true )
& ( binintersectSubset2 = $true )
& ( prop2setI = $true )
& ( vacuousDall = $true )
& ( setminusER = $true )
& ( setunionsingleton1 = $true )
& ( powersetAx = $true )
& ( eqimpsubset2 = $true )
& ( exuE2 = $true )
& ( binintersectLsub = $true )
& ( quantDeMorgan1 = $true )
& ( cartprodmempair1 = $true )
& ( exuE3u = $true )
& ( setminusIRneg = $true )
& ( symdiffIneg2 = $true )
& ( binintersectRsub = $true )
& ( emptyinunitempty = $true )
& ( setunionsingleton = $true )
& ( symdiffI2 = $true )
& ( exuE3e = $true )
& ( setadjoinE = $true )
& ( binintersectEL = $true )
& ( subsetE = $true )
& ( setunionI = $true )
& ( kpairiskpair = $true )
& ( binunionLsub = $true )
& ( nonemptyI = $true )
& ( singletonsswitch = $true )
& ( setoftrueEq = $true )
& ( noeltsimpempty = $true )
& ( subsetI2 = $true )
& ( nonemptyI1 = $true )
& ( prop2set2propI = $true )
& ( setminusLsub = $true )
& ( binintersectSubset3 = $true )
& ( omegaIndAx = $true )
& ( setunionAx = $true )
& ( powersetI = $true )
& ( exuI2 = $true )
& ( setadjoinIL = $true )
& ( subset2powerset = $true )
& ( subsetTrans = $true )
& ( setukpairIL = $true )
& ( setunionE = $true )
& ( setadjoinOr = $true )
& ( sepInPowerset = $true )
& ( ubforcartprodlem3 = $true )
& ( powerset__Cong = $true )
& ( binintersectI = $true )
& ( setadjoin__Cong = $true )
& ( omegaSAx = $true )
& ( notinsingleton = $true )
& ( exuE1 = $true )
& ( setukpairIR = $true )
& ( notequalI2 = $true )
& ( upairset2IR = $true )
& ( binintersectSubset4 = $true )
& ( binintersectSubset5 = $true )
& ( singletonsubset = $true )
& ( ( ex1 @ sK1
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true )
& ! [X2: $i] :
( ( $true
!= ( sK0 @ X2 ) )
| ( $true
!= ( in @ X2 @ sK1 ) ) )
& ( notdexE = $true )
& ( exuI3 = $true )
& ( singletoninpowunion = $true )
& ( setminusELneg = $true )
& ( setminusILneg = $true )
& ( cartprodpairin = $true )
& ( quantDeMorgan2 = $true )
& ( upairsetIR = $true )
& ( upairset2E = $true )
& ( eqinunit = $true )
& ( nonemptyE1 = $true )
& ( symdiffIneg1 = $true )
& ( upairinpowunion = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( wellorderingAx = $true )
& ( exuI1 = $true )
& ( emptyE1 = $true )
& ( singletoninpowerset = $true )
& ( setunionsingleton2 = $true )
& ( subsetE2 = $true )
& ( prop2setE = $true )
& ( setunion__Cong = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsubunion = $true )
& ( ubforcartprodlem1 = $true )
& ( notinemptyset = $true )
& ( notdallE = $true )
& ( setext = $true )
& ( quantDeMorgan3 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f476]) ).
thf(f497,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f188]) ).
thf(f530,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f443]) ).
thf(f535,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f286]) ).
thf(f650,plain,
! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK1 ) )
| ( $true
!= ( sK0 @ X2 ) ) ),
inference(cnf_transformation,[],[f477]) ).
thf(f651,plain,
( ( ex1 @ sK1
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true ),
inference(cnf_transformation,[],[f477]) ).
thf(f745,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[],[f477]) ).
thf(f769,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f477]) ).
thf(f780,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f414]) ).
thf(f796,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f780,f530]) ).
thf(f815,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f497,f769]) ).
thf(f851,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(definition_unfolding,[],[f535,f745]) ).
thf(f933,plain,
( $true
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) )
@ sK1
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(definition_unfolding,[],[f651,f796]) ).
thf(f1517,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK1 @ sK0 ) )
& ( in @ Y0 @ ( dsetconstr @ sK1 @ sK0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f933]) ).
thf(f1518,plain,
( $true
= ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK1 @ sK0 ) )
& ( in @ Y0 @ ( dsetconstr @ sK1 @ sK0 ) ) )
@ sK39 ) ),
inference(sigma_proxy_clausification,[],[f1517]) ).
thf(f1519,plain,
( $true
= ( ( ( setadjoin @ sK39 @ emptyset )
= ( dsetconstr @ sK1 @ sK0 ) )
& ( in @ sK39 @ ( dsetconstr @ sK1 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f1518]) ).
thf(f1520,plain,
( ( in @ sK39 @ ( dsetconstr @ sK1 @ sK0 ) )
= $true ),
inference(and_proxy_clausification,[],[f1519]) ).
thf(f2380,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f815]) ).
thf(f2381,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2380]) ).
thf(f2382,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f2381]) ).
thf(f2383,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f2382]) ).
thf(f2384,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f2383]) ).
thf(f2385,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) )
=> ( X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2384]) ).
thf(f2386,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) )
= $false )
| ( ( X3 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2385]) ).
thf(f2547,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f851]) ).
thf(f2548,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2547]) ).
thf(f2549,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f2548]) ).
thf(f2550,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f2549]) ).
thf(f2551,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f2550]) ).
thf(f2552,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( in @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f2551]) ).
thf(f2553,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2552]) ).
thf(f4438,plain,
( ( $true = $false )
| ( $true
= ( in @ sK39 @ sK1 ) ) ),
inference(superposition,[],[f2553,f1520]) ).
thf(f4439,plain,
( ( $true
= ( sK0 @ sK39 ) )
| ( $true = $false ) ),
inference(superposition,[],[f2386,f1520]) ).
thf(f4441,plain,
( $true
= ( sK0 @ sK39 ) ),
inference(trivial_inequality_removal,[],[f4439]) ).
thf(f4442,plain,
( $true
= ( in @ sK39 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f4438]) ).
thf(f4699,plain,
( ( $true
!= ( sK0 @ sK39 ) )
| ( $true != $true ) ),
inference(superposition,[],[f650,f4442]) ).
thf(f4705,plain,
( $true
!= ( sK0 @ sK39 ) ),
inference(trivial_inequality_removal,[],[f4699]) ).
thf(f4706,plain,
$false,
inference(forward_subsumption_resolution,[],[f4705,f4441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU638^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.29 % Computer : n011.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8046.5625MB
% 0.11/0.29 % OS : Linux 6.8.0-71-generic
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Sep 29 14:00:46 UTC 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.29/0.35 Running higher-order theorem proving
% 0.36/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.78/0.64 % (141334)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.78/0.64 % (141345)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.78/0.64 % (141345)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.78/0.64 % (141345)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1974422500:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.78/0.64 % (141340)lrs+10_16_si=on:nwc=1.5:random_seed=2505738750:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.78/0.64 % (141339)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1989706611:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.78/0.64 % (141341)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3091739110:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.78/0.64 % (141343)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3622954145:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.78/0.64 % (141344)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1036591429:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.78/0.64 % (141342)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4107679548:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.78/0.64 % (141341)Instruction limit reached!
% 0.78/0.64 % (141341)------------------------------
% 0.78/0.64 % (141341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.64 % (141341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.64 % (141341)CaDiCaL version: 2.1.3
% 0.78/0.64 % (141341)Termination reason: Instruction limit
% 0.78/0.64 % (141341)Termination phase: shuffling
% 0.78/0.64 % (141341)Time elapsed: 0.004 s
% 0.78/0.64 % (141341)Peak memory usage: 10 MB
% 0.78/0.64 % (141341)Instructions burned: 3 (million)
% 0.78/0.64 % (141340)Instruction limit reached!
% 0.78/0.64 % (141340)------------------------------
% 0.78/0.64 % (141340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.64 % (141340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.64 % (141340)CaDiCaL version: 2.1.3
% 0.78/0.64 % (141340)Termination reason: Instruction limit
% 0.78/0.64 % (141340)Termination phase: Property scanning
% 0.78/0.64 % (141340)Time elapsed: 0.015 s
% 0.78/0.64 % (141340)Peak memory usage: 10 MB
% 0.78/0.64 % (141340)Instructions burned: 18 (million)
% 0.78/0.64 % (141343)Instruction limit reached!
% 0.78/0.64 % (141343)------------------------------
% 0.78/0.64 % (141343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.64 % (141343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.64 % (141343)CaDiCaL version: 2.1.3
% 0.78/0.64 % (141343)Termination reason: Instruction limit
% 0.78/0.64 % (141343)Termination phase: Preprocessing 3
% 0.78/0.64 % (141343)Time elapsed: 0.022 s
% 0.78/0.64 % (141343)Peak memory usage: 11 MB
% 0.78/0.64 % (141343)Instructions burned: 25 (million)
% 0.78/0.64 % (141354)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1460985013:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.78/0.64 % (141355)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.78/0.64 % (141345)Instruction limit reached!
% 0.78/0.64 % (141345)------------------------------
% 0.78/0.64 % (141345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.64 % (141345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.64 % (141345)CaDiCaL version: 2.1.3
% 0.78/0.64 % (141345)Termination reason: Instruction limit
% 0.78/0.64 % (141345)Termination phase: Saturation
% 0.78/0.64 % (141345)Time elapsed: 0.067 s
% 0.78/0.64 % (141345)Peak memory usage: 13 MB
% 0.78/0.64 % (141345)Instructions burned: 157 (million)
% 0.78/0.64 % (141354)Instruction limit reached!
% 1.85/0.70 % (141354)------------------------------
% 1.85/0.70 % (141354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.70 % (141354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.70 % (141354)CaDiCaL version: 2.1.3
% 1.85/0.70 % (141354)Termination reason: Instruction limit
% 1.85/0.70 % (141354)Termination phase: shuffling
% 1.85/0.70 % (141354)Time elapsed: 0.005 s
% 1.85/0.70 % (141354)Peak memory usage: 10 MB
% 1.85/0.70 % (141354)Instructions burned: 6 (million)
% 1.85/0.70 % (141355)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3882227808:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.85/0.70 % (141355)Instruction limit reached!
% 1.85/0.70 % (141355)------------------------------
% 1.85/0.70 % (141355)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.70 % (141355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.70 % (141355)CaDiCaL version: 2.1.3
% 1.85/0.70 % (141355)Termination reason: Instruction limit
% 1.85/0.70 % (141355)Termination phase: shuffling
% 1.85/0.70 % (141355)Time elapsed: 0.006 s
% 1.85/0.70 % (141355)Peak memory usage: 10 MB
% 1.85/0.70 % (141355)Instructions burned: 7 (million)
% 1.85/0.70 % (141353)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=846609650:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.85/0.70 % (141344)Instruction limit reached!
% 1.85/0.70 % (141344)------------------------------
% 1.85/0.70 % (141344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.70 % (141344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.70 % (141344)CaDiCaL version: 2.1.3
% 1.85/0.70 % (141344)Termination reason: Instruction limit
% 1.85/0.70 % (141344)Termination phase: Property scanning
% 1.85/0.70 % (141344)Time elapsed: 0.065 s
% 1.85/0.70 % (141344)Peak memory usage: 12 MB
% 1.85/0.70 % (141344)Instructions burned: 75 (million)
% 1.85/0.70 % (141353)Instruction limit reached!
% 1.85/0.70 % (141353)------------------------------
% 1.85/0.70 % (141353)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.70 % (141353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.70 % (141353)CaDiCaL version: 2.1.3
% 1.85/0.70 % (141353)Termination reason: Instruction limit
% 1.85/0.70 % (141353)Termination phase: shuffling
% 1.85/0.70 % (141353)Time elapsed: 0.003 s
% 1.85/0.70 % (141353)Peak memory usage: 10 MB
% 1.85/0.70 % (141353)Instructions burned: 3 (million)
% 1.85/0.70 % (141357)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3865475984:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/12Mi)
% 1.85/0.70 % (141339)Instruction limit reached!
% 1.85/0.70 % (141339)------------------------------
% 1.85/0.70 % (141339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.70 % (141339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.70 % (141339)CaDiCaL version: 2.1.3
% 1.85/0.70 % (141339)Termination reason: Instruction limit
% 1.85/0.70 % (141339)Termination phase: Property scanning
% 1.85/0.70 % (141339)Time elapsed: 0.074 s
% 1.85/0.70 % (141339)Peak memory usage: 12 MB
% 1.85/0.70 % (141339)Instructions burned: 92 (million)
% 1.85/0.70 % (141357)Instruction limit reached!
% 1.85/0.70 % (141357)------------------------------
% 1.85/0.70 % (141357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.70 % (141357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.70 % (141357)CaDiCaL version: 2.1.3
% 1.85/0.70 % (141357)Termination reason: Instruction limit
% 1.85/0.70 % (141357)Termination phase: shuffling
% 1.85/0.70 % (141357)Time elapsed: 0.008 s
% 1.85/0.70 % (141357)Peak memory usage: 10 MB
% 1.85/0.70 % (141357)Instructions burned: 17 (million)
% 1.85/0.70 % (141359)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.85/0.70 % (141359)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.85/0.70 % (141359)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4031144003:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 1.85/0.76 % (141361)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2143622354:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.85/0.76 % (141363)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.85/0.76 % (141362)lrs+10_1_si=on:cs=on:random_seed=242367462:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.85/0.76 % (141363)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1138667045:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.85/0.76 % (141365)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3307948695:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.85/0.76 % (141362)Instruction limit reached!
% 1.85/0.76 % (141362)------------------------------
% 1.85/0.76 % (141362)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.76 % (141362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.76 % (141362)CaDiCaL version: 2.1.3
% 1.85/0.76 % (141362)Termination reason: Instruction limit
% 1.85/0.76 % (141362)Termination phase: shuffling
% 1.85/0.76 % (141362)Time elapsed: 0.007 s
% 1.85/0.76 % (141362)Peak memory usage: 10 MB
% 1.85/0.76 % (141362)Instructions burned: 8 (million)
% 1.85/0.76 % (141363)Instruction limit reached!
% 1.85/0.76 % (141363)------------------------------
% 1.85/0.76 % (141363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.76 % (141363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.76 % (141363)CaDiCaL version: 2.1.3
% 1.85/0.76 % (141363)Termination reason: Instruction limit
% 1.85/0.76 % (141363)Termination phase: shuffling
% 1.85/0.76 % (141363)Time elapsed: 0.007 s
% 1.85/0.76 % (141363)Peak memory usage: 10 MB
% 1.85/0.76 % (141363)Instructions burned: 2 (million)
% 1.85/0.76 % (141366)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=892995659:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.85/0.76 % (141359)Instruction limit reached!
% 1.85/0.76 % (141359)------------------------------
% 1.85/0.76 % (141359)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.76 % (141359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.76 % (141359)CaDiCaL version: 2.1.3
% 1.85/0.76 % (141359)Termination reason: Instruction limit
% 1.85/0.76 % (141359)Termination phase: Property scanning
% 1.85/0.76 % (141359)Time elapsed: 0.023 s
% 1.85/0.76 % (141359)Peak memory usage: 10 MB
% 1.85/0.76 % (141359)Instructions burned: 28 (million)
% 1.85/0.76 % (141375)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2146751239:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.85/0.76 % (141372)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1715040656:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.85/0.76 % (141374)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2628029151:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.85/0.76 % (141365)Instruction limit reached!
% 1.85/0.76 % (141365)------------------------------
% 1.85/0.76 % (141365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.76 % (141365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.76 % (141365)CaDiCaL version: 2.1.3
% 1.85/0.76 % (141365)Termination reason: Instruction limit
% 1.85/0.76 % (141365)Termination phase: Preprocessing 3
% 1.85/0.76 % (141365)Time elapsed: 0.034 s
% 1.85/0.76 % (141365)Peak memory usage: 11 MB
% 1.85/0.76 % (141365)Instructions burned: 38 (million)
% 1.85/0.76 % (141374)Instruction limit reached!
% 1.85/0.76 % (141374)------------------------------
% 1.85/0.76 % (141374)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.76 % (141374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.76 % (141374)CaDiCaL version: 2.1.3
% 1.85/0.76 % (141374)Termination reason: Instruction limit
% 1.85/0.76 % (141374)Termination phase: shuffling
% 1.85/0.76 % (141374)Time elapsed: 0.016 s
% 1.85/0.76 % (141374)Peak memory usage: 10 MB
% 1.85/0.76 % (141374)Instructions burned: 17 (million)
% 1.85/0.76 % (141372)Instruction limit reached!
% 1.85/0.76 % (141372)------------------------------
% 1.85/0.76 % (141372)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.76 % (141372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.76 % (141372)CaDiCaL version: 2.1.3
% 1.85/0.76 % (141372)Termination reason: Instruction limit
% 1.85/0.76 % (141372)Termination phase: Unused predicate definition removal
% 1.85/0.76 % (141372)Time elapsed: 0.021 s
% 1.85/0.76 % (141372)Peak memory usage: 10 MB
% 1.85/0.76 % (141372)Instructions burned: 25 (million)
% 1.85/0.76 % (141361)Instruction limit reached!
% 1.85/0.76 % (141361)------------------------------
% 1.85/0.76 % (141361)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.76 % (141361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.76 % (141361)CaDiCaL version: 2.1.3
% 1.85/0.76 % (141361)Termination reason: Instruction limit
% 1.85/0.76 % (141361)Termination phase: Saturation
% 1.85/0.76 % (141361)Time elapsed: 0.070 s
% 1.85/0.76 % (141361)Peak memory usage: 12 MB
% 1.85/0.76 % (141361)Instructions burned: 86 (million)
% 1.85/0.76 % (141379)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=237740661:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.85/0.76 % (141380)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3174539097:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2997 on theBenchmark for (2997ds/2Mi)
% 1.85/0.76 % (141379)Instruction limit reached!
% 1.85/0.76 % (141379)------------------------------
% 1.85/0.76 % (141379)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.76 % (141379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.76 % (141379)CaDiCaL version: 2.1.3
% 1.85/0.76 % (141379)Termination reason: Instruction limit
% 1.85/0.76 % (141379)Termination phase: shuffling
% 1.85/0.76 % (141379)Time elapsed: 0.013 s
% 1.85/0.76 % (141379)Peak memory usage: 10 MB
% 1.85/0.76 % (141379)Instructions burned: 14 (million)
% 1.85/0.76 % (141380)Instruction limit reached!
% 1.85/0.76 % (141380)------------------------------
% 1.85/0.76 % (141380)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.76 % (141380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.76 % (141380)CaDiCaL version: 2.1.3
% 1.85/0.76 % (141380)Termination reason: Instruction limit
% 1.85/0.76 % (141380)Termination phase: shuffling
% 1.85/0.76 % (141380)Time elapsed: 0.003 s
% 1.85/0.76 % (141380)Peak memory usage: 10 MB
% 1.85/0.76 % (141380)Instructions burned: 3 (million)
% 1.85/0.76 % (141381)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2763723202:i=26:ep=R:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/26Mi)
% 1.85/0.76 % (141382)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2498773161:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.85/0.76 % (141382)Instruction limit reached!
% 1.85/0.76 % (141382)------------------------------
% 1.85/0.76 % (141382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.76 % (141382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.76 % (141382)CaDiCaL version: 2.1.3
% 1.85/0.76 % (141382)Termination reason: Instruction limit
% 1.85/0.76 % (141382)Termination phase: Property scanning
% 1.85/0.76 % (141382)Time elapsed: 0.020 s
% 1.85/0.76 % (141382)Peak memory usage: 10 MB
% 1.85/0.76 % (141382)Instructions burned: 23 (million)
% 1.85/0.76 % (141381)Instruction limit reached!
% 1.85/0.76 % (141381)------------------------------
% 1.85/0.76 % (141381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.76 % (141381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.76 % (141381)CaDiCaL version: 2.1.3
% 1.85/0.76 % (141381)Termination reason: Instruction limit
% 1.85/0.76 % (141381)Termination phase: Property scanning
% 1.85/0.76 % (141381)Time elapsed: 0.023 s
% 1.85/0.76 % (141381)Peak memory usage: 10 MB
% 1.85/0.76 % (141381)Instructions burned: 29 (million)
% 1.85/0.76 % (141386)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.85/0.77 % (141386)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.85/0.77 % (141386)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=1154096844:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 1.85/0.77 % (141385)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=512360410:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 1.85/0.77 % (141386)Instruction limit reached!
% 1.85/0.77 % (141386)------------------------------
% 1.85/0.77 % (141386)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.77 % (141386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.77 % (141386)CaDiCaL version: 2.1.3
% 1.85/0.77 % (141386)Termination reason: Instruction limit
% 1.85/0.77 % (141386)Termination phase: shuffling
% 1.85/0.77 % (141386)Time elapsed: 0.013 s
% 1.85/0.77 % (141386)Peak memory usage: 10 MB
% 1.85/0.77 % (141386)Instructions burned: 15 (million)
% 1.85/0.77 % (141389)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.85/0.77 % (141389)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=3954743808:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 1.85/0.77 % (141390)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=881265848:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 1.85/0.77 % (141389)Instruction limit reached!
% 1.85/0.77 % (141389)------------------------------
% 1.85/0.77 % (141389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.77 % (141389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.77 % (141389)CaDiCaL version: 2.1.3
% 1.85/0.77 % (141389)Termination reason: Instruction limit
% 1.85/0.77 % (141389)Termination phase: shuffling
% 1.85/0.77 % (141389)Time elapsed: 0.007 s
% 1.85/0.77 % (141389)Peak memory usage: 10 MB
% 1.85/0.77 % (141389)Instructions burned: 8 (million)
% 1.85/0.77 % (141375) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-141334-141375"...
% 1.85/0.77 % (141393)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2221949309:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 1.85/0.77 % (141390)Instruction limit reached!
% 1.85/0.77 % (141390)------------------------------
% 1.85/0.77 % (141390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.77 % (141390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.77 % (141390)CaDiCaL version: 2.1.3
% 1.85/0.77 % (141390)Termination reason: Instruction limit
% 1.85/0.77 % (141390)Termination phase: Property scanning
% 1.85/0.77 % (141390)Time elapsed: 0.026 s
% 1.85/0.77 % (141390)Peak memory usage: 10 MB
% 1.85/0.77 % (141390)Instructions burned: 32 (million)
% 1.85/0.77 % (141375)...printing done.
% 1.85/0.77 % (141375)Refutation found. Thanks to Tanya!
% 1.85/0.77 % SZS status Theorem for theBenchmark
% 1.85/0.77 % SZS output start Proof for theBenchmark
% See solution above
% 1.85/0.77 % (141375)------------------------------
% 1.85/0.77 % (141375)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.77 % (141375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.77 % (141375)CaDiCaL version: 2.1.3
% 1.85/0.77 % (141375)Termination reason: Refutation
% 1.85/0.77 % (141375)Time elapsed: 0.150 s
% 1.85/0.77 % (141375)Peak memory usage: 15 MB
% 1.85/0.77 % (141375)Instructions burned: 323 (million)
% 1.85/0.77 % (141334)Success in time 0.34 s
% 1.85/0.77 % Vampire exiting
%------------------------------------------------------------------------------