%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU615^1 : 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 : 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 08:32:41 AM UTC 2026
% Result : Theorem 5.68s 1.12s
% Output : Refutation 5.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 7
% Syntax : Number of formulae : 78 ( 40 unt; 0 typ; 2 def)
% Number of atoms : 2859 ( 779 equ; 0 cnn)
% Maximal formula atoms : 134 ( 36 avg)
% Number of connectives : 1799 ( 86 ~; 45 |; 399 &; 445 @)
% ( 2 <=>; 785 =>; 0 <=; 0 <~>)
% Maximal formula depth : 142 ( 17 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 : 248 ( 243 usr; 141 con; 0-4 aty)
% ( 31 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 156 ( 0 sgn 97 !; 8 ?; 156 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_153,type,
vAND: $o > $o > $o ).
thf(func_def_154,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_155,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_156,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_157,type,
vIMP: $o > $o > $o ).
thf(func_def_158,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_159,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_160,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_161,type,
vIFF: $o > $o > $o ).
thf(func_def_162,type,
vNOT: $o > $o ).
thf(func_def_163,type,
vOR: $o > $o > $o ).
thf(func_def_164,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_165,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_168,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_172,type,
sK3: $i > $i > $i ).
thf(func_def_173,type,
sK4: $i > $i > $i ).
thf(func_def_174,type,
sK5: $i > $i > $i ).
thf(func_def_175,type,
sK6: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_176,type,
sK7: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_177,type,
sK8: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_178,type,
sK9: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_179,type,
sK10: ( $i > $o ) > $i > $i ).
thf(func_def_180,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_181,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_182,type,
sK13: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_183,type,
sK14: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_184,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_185,type,
sK16: ( $i > $o ) > $i > $i ).
thf(func_def_186,type,
sK17: ( $i > $o ) > $i ).
thf(func_def_187,type,
sK18: ( $i > $o ) > $i > $i ).
thf(func_def_188,type,
sK19: ( $i > $o ) > $i > $i ).
thf(func_def_189,type,
sK20: ( $i > $o ) > $i ).
thf(func_def_190,type,
sK21: ( $i > $o ) > $i > $i ).
thf(func_def_191,type,
sK22: ( $i > $o ) > $i ).
thf(func_def_192,type,
sK23: ( $i > $o ) > $i > $i ).
thf(func_def_193,type,
sK24: ( $i > $o ) > $i > $i ).
thf(func_def_194,type,
sK25: ( $i > $o ) > $i ).
thf(func_def_195,type,
sK26: ( $i > $o ) > $i > $i ).
thf(func_def_196,type,
sK27: ( $i > $o ) > $i ).
thf(func_def_197,type,
sK28: ( $i > $o ) > $i > $i ).
thf(func_def_198,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_199,type,
sK30: ( $i > $o ) > $i > $i ).
thf(func_def_200,type,
sK31: ( $i > $o ) > $i ).
thf(func_def_201,type,
sK32: ( $i > $o ) > $i > $i ).
thf(func_def_202,type,
sK33: ( $i > $o ) > $i ).
thf(func_def_203,type,
sK34: ( $i > $o ) > $i ).
thf(func_def_204,type,
sK35: ( $i > $o ) > $i ).
thf(func_def_205,type,
sK36: ( $i > $o ) > $i ).
thf(func_def_206,type,
sK37: ( $i > $o ) > $i > $i ).
thf(func_def_207,type,
sK38: ( $i > $o ) > $i > $i ).
thf(func_def_208,type,
sK39: ( $i > $o ) > $i > $i ).
thf(func_def_209,type,
sK40: ( $i > $o ) > $i > $i ).
thf(func_def_210,type,
sK41: ( $i > $o ) > $i > $i ).
thf(func_def_211,type,
sK42: ( $i > $o ) > $i > $i ).
thf(func_def_212,type,
sK43: ( $i > $o ) > $i > $i ).
thf(func_def_213,type,
sK44: $i > $i ).
thf(func_def_214,type,
sK45: ( $i > $o ) > $i ).
thf(func_def_215,type,
sK46: ( $i > $o ) > $i > $i ).
thf(func_def_216,type,
sK47: $i > $o > $i > $i ).
thf(func_def_217,type,
sK48: $i > $i > $i ).
thf(func_def_218,type,
sK49: $i > $i ).
thf(func_def_219,type,
sK50: $i > $i ).
thf(func_def_220,type,
sK51: $i > $i ).
thf(func_def_221,type,
sK52: $i > $i > $i ).
thf(func_def_222,type,
sK53: $i > $i > $i ).
thf(func_def_223,type,
sK54: ( $i > $o ) > $i ).
thf(func_def_224,type,
sK55: ( $i > $o ) > $i > $i ).
thf(func_def_225,type,
sK56: ( $i > $o ) > $i ).
thf(func_def_226,type,
sK57: ( $i > $o ) > $i > $i ).
thf(func_def_227,type,
sK58: ( $i > $o ) > $i > $i ).
thf(func_def_228,type,
sK59: $i > $i ).
thf(func_def_229,type,
sK60: $i > $i > $i > $i ).
thf(func_def_230,type,
sK61: $i > $i > $i ).
thf(func_def_231,type,
sK62: $i > $i > $i ).
thf(func_def_232,type,
sK63: $i > $i > $i ).
thf(func_def_233,type,
sK64: $i > $i ).
thf(func_def_234,type,
sK65: $i > ( $i > $i > $o ) > $i ).
thf(func_def_235,type,
sK66: $i > ( $i > $i > $o ) > $i ).
thf(func_def_236,type,
sK67: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_237,type,
sK68: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_238,type,
sK69: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_239,type,
sK70: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_240,type,
sK71: $i > $i ).
thf(func_def_241,type,
sK72: $i > $i > $i ).
thf(func_def_242,type,
sK73: $i > $i > $i ).
thf(func_def_243,type,
sK74: $i > $i > $i ).
thf(f27,axiom,
( nonempty
= ( ^ [X0: $i] : ( X0 != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(f30,axiom,
( nonemptyI1
= ( ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ( nonempty @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(f94,axiom,
( subsetemptysetimpeq
= ( ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(f130,axiom,
( symdiffE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> X3 ) )
=> ( ( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> X3 ) )
=> X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(f134,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( symdiff @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(f135,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( symdiff @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f134]) ).
thf(f186,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f191,plain,
( nonemptyI1
= ( ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ( nonempty @ X0 ) ) ) ),
inference(rectify,[],[f30]) ).
thf(f192,plain,
( nonemptyI1
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( nonempty @ Y0 ) ) ) ),
inference(fool_elimination,[],[f191]) ).
thf(f312,plain,
( subsetemptysetimpeq
= ( ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) ) ) ),
inference(rectify,[],[f94]) ).
thf(f313,plain,
( subsetemptysetimpeq
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) ) ),
inference(fool_elimination,[],[f312]) ).
thf(f383,plain,
( symdiffE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> X3 ) )
=> ( ( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> X3 ) )
=> X3 ) ) ) ) ),
inference(rectify,[],[f130]) ).
thf(f384,plain,
( symdiffE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( symdiff @ Y2 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f383]) ).
thf(f391,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( symdiff @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f135]) ).
thf(f392,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f391]) ).
thf(f393,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f392]) ).
thf(f394,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
!= $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,[],[f393]) ).
thf(f395,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
!= $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,[],[f394]) ).
thf(f396,plain,
( ( $true
= ( in @ sK2 @ ( symdiff @ sK0 @ sK1 ) ) )
& ( $true
!= ( in @ sK2 @ sK1 ) )
& ( $true
!= ( in @ sK2 @ sK0 ) )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f395]) ).
thf(f423,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[],[f186]) ).
thf(f426,plain,
( nonemptyI1
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( nonempty @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f192]) ).
thf(f490,plain,
( subsetemptysetimpeq
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) ) ),
inference(cnf_transformation,[],[f313]) ).
thf(f526,plain,
( symdiffE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( symdiff @ Y2 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f384]) ).
thf(f557,plain,
nonemptyI1 = $true,
inference(cnf_transformation,[],[f396]) ).
thf(f621,plain,
subsetemptysetimpeq = $true,
inference(cnf_transformation,[],[f396]) ).
thf(f657,plain,
symdiffE = $true,
inference(cnf_transformation,[],[f396]) ).
thf(f661,plain,
( $true
!= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f396]) ).
thf(f662,plain,
( $true
!= ( in @ sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f396]) ).
thf(f663,plain,
( $true
= ( in @ sK2 @ ( symdiff @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f396]) ).
thf(f693,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ^ [Y1: $i] : ( emptyset != Y1 )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f426,f557,f423]) ).
thf(f757,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) ) ),
inference(definition_unfolding,[],[f490,f621]) ).
thf(f793,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( symdiff @ Y2 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f526,f657]) ).
thf(f824,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( symdiff @ Y2 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f793]) ).
thf(f825,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( symdiff @ Y1 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( ( in @ X1 @ Y1 )
=> ( ~ ( in @ X1 @ Y0 )
=> Y2 ) )
=> ( ( ~ ( in @ X1 @ Y1 )
=> ( ( in @ X1 @ Y0 )
=> Y2 ) )
=> Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f824]) ).
thf(f826,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( symdiff @ Y1 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( ( in @ X1 @ Y1 )
=> ( ~ ( in @ X1 @ Y0 )
=> Y2 ) )
=> ( ( ~ ( in @ X1 @ Y1 )
=> ( ( in @ X1 @ Y0 )
=> Y2 ) )
=> Y2 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f825]) ).
thf(f827,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( symdiff @ Y0 @ X2 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( ( in @ X1 @ Y0 )
=> ( ~ ( in @ X1 @ X2 )
=> Y1 ) )
=> ( ( ~ ( in @ X1 @ Y0 )
=> ( ( in @ X1 @ X2 )
=> Y1 ) )
=> Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f826]) ).
thf(f828,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( symdiff @ Y0 @ X2 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( ( in @ X1 @ Y0 )
=> ( ~ ( in @ X1 @ X2 )
=> Y1 ) )
=> ( ( ~ ( in @ X1 @ Y0 )
=> ( ( in @ X1 @ X2 )
=> Y1 ) )
=> Y1 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f827]) ).
thf(f829,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( symdiff @ X3 @ X2 ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X2 )
=> Y0 ) )
=> ( ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> Y0 ) )
=> Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f828]) ).
thf(f830,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X2 )
=> Y0 ) )
=> ( ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> Y0 ) )
=> Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f829]) ).
thf(f831,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $o] :
( ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X2 )
=> Y0 ) )
=> ( ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> Y0 ) )
=> Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f830]) ).
thf(f832,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( $true
= ( ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X2 )
=> X4 ) )
=> ( ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> X4 ) )
=> X4 ) ) ) ),
inference(beta-eta_normalization,[],[f831]) ).
thf(f833,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( $false
= ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X2 )
=> X4 ) ) )
| ( $true
= ( ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> X4 ) )
=> X4 ) ) ),
inference(imp_proxy_clausification,[],[f832]) ).
thf(f835,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X3 )
= $true )
| ( $true
= ( ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> X4 ) )
=> X4 ) ) ),
inference(imp_proxy_clausification,[],[f833]) ).
thf(f836,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X3 )
= $true )
| ( $false
= ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> X4 ) ) )
| ( $true = X4 ) ),
inference(imp_proxy_clausification,[],[f835]) ).
thf(f837,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X3 )
= $true )
| ( $false
= ( ( in @ X1 @ X2 )
=> X4 ) )
| ( $true = X4 ) ),
inference(imp_proxy_clausification,[],[f836]) ).
thf(f841,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X3 )
= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( $true = X4 ) ),
inference(imp_proxy_clausification,[],[f837]) ).
thf(f1093,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f757]) ).
thf(f1094,plain,
! [X1: $i] :
( $true
= ( ( subset @ X1 @ emptyset )
=> ( emptyset = X1 ) ) ),
inference(beta-eta_normalization,[],[f1093]) ).
thf(f1095,plain,
! [X1: $i] :
( ( $false
= ( subset @ X1 @ emptyset ) )
| ( $true
= ( emptyset = X1 ) ) ),
inference(imp_proxy_clausification,[],[f1094]) ).
thf(f1096,plain,
! [X1: $i] :
( ( $false
= ( subset @ X1 @ emptyset ) )
| ( emptyset = X1 ) ),
inference(equality_proxy_clausification,[],[f1095]) ).
thf(f1876,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ^ [Y1: $i] : ( emptyset != Y1 )
@ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f693]) ).
thf(f1877,plain,
! [X1: $i] :
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) )
=> ( emptyset != X1 ) ) ),
inference(beta-eta_normalization,[],[f1876]) ).
thf(f1878,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) )
| ( $true
= ( emptyset != X1 ) ) ),
inference(imp_proxy_clausification,[],[f1877]) ).
thf(f1879,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] : ( in @ Y0 @ X1 )
@ X2 ) )
| ( $true
= ( emptyset != X1 ) ) ),
inference(pi_proxy_clausification,[],[f1878]) ).
thf(f1880,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] : ( in @ Y0 @ X1 )
@ X2 ) )
| ( $false
= ( emptyset = X1 ) ) ),
inference(not_proxy_clausification,[],[f1879]) ).
thf(f1881,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] : ( in @ Y0 @ X1 )
@ X2 ) )
| ( emptyset != X1 ) ),
inference(equality_proxy_clausification,[],[f1880]) ).
thf(f1882,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( emptyset != X1 ) ),
inference(beta-eta_normalization,[],[f1881]) ).
thf(f2252,definition,
( spl75_1
<=> ! [X4: $o] : ( $true = X4 ) ),
introduced(definition,[new_symbols(definition,[spl75_1])],[avatar_definition]) ).
thf(f2253,plain,
( ! [X4: $o] : ( $true = X4 )
| ~ spl75_1 ),
inference(avatar_component_clause,[],[f2252]) ).
thf(f2259,definition,
( spl75_3
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl75_3])],[avatar_definition]) ).
thf(f2260,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( symdiff @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X3 )
= $true ) )
| ~ spl75_3 ),
inference(avatar_component_clause,[],[f2259]) ).
thf(f2261,plain,
( spl75_1
| spl75_3 ),
inference(avatar_split_clause,[],[f841,f2259,f2252]) ).
thf(f5865,plain,
( ( $false = $true )
| ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK0 ) )
| ~ spl75_3 ),
inference(constrained_superposition,[],[f663,f2260]) ).
thf(f5876,plain,
( ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK0 ) )
| ~ spl75_3 ),
inference(trivial_inequality_removal,[],[f5865]) ).
thf(f5878,plain,
( ( $true
= ( in @ sK2 @ sK0 ) )
| ~ spl75_3 ),
inference(forward_subsumption_resolution,[],[f5876,f662]) ).
thf(f5883,plain,
( $false
| ~ spl75_3 ),
inference(forward_subsumption_resolution,[],[f5878,f661]) ).
thf(f5884,plain,
~ spl75_3,
inference(avatar_contradiction_clause,[],[f5883]) ).
thf(f5901,plain,
( ! [X1: $i] :
( ( $false = $true )
| ( emptyset != X1 ) )
| ~ spl75_1 ),
inference(constrained_superposition,[],[f1882,f2253]) ).
thf(f5906,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( emptyset = X0 ) )
| ~ spl75_1 ),
inference(constrained_superposition,[],[f1096,f2253]) ).
thf(f5907,plain,
( ! [X0: $i] : ( emptyset = X0 )
| ~ spl75_1 ),
inference(trivial_inequality_removal,[],[f5906]) ).
thf(f5916,plain,
( ! [X1: $i] : ( emptyset != X1 )
| ~ spl75_1 ),
inference(trivial_inequality_removal,[],[f5901]) ).
thf(f5930,plain,
( $false
| ~ spl75_1 ),
inference(forward_subsumption_resolution,[],[f5916,f5907]) ).
thf(f5931,plain,
~ spl75_1,
inference(avatar_contradiction_clause,[],[f5930]) ).
cnf(s2,plain,
( spl75_1
| spl75_3 ),
inference(sat_conversion,[],[f2261]) ).
cnf(s18,plain,
~ spl75_3,
inference(sat_conversion,[],[f5884]) ).
cnf(s25,plain,
~ spl75_1,
inference(sat_conversion,[],[f5931]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s2,s18,s25]) ).
thf(f5932,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU615^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n011.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:58:16 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 4.36/1.02 % (136263)Will run a generic schedule for satisfiability detection.
% 4.36/1.02 % (136279)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=930042861:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.36/1.02 % (136276)% WARNING: option uhcvi not known.
% 4.36/1.02 % (136279)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.36/1.02 % (136278)dis+10_1_sil=32000:sp=arity:random_seed=3624421986:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.36/1.02 % (136275)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3448542202_2999 on theBenchmark for (2999ds/0Mi)
% 4.36/1.02 % (136277)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3328940963:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.36/1.02 % (136276)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4190976392:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.36/1.02 % (136281)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2509696124:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.36/1.02 % (136280)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=346066351:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.36/1.02 % (136276)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.36/1.02 % (136279)Instruction limit reached!
% 4.36/1.02 % (136279)------------------------------
% 4.36/1.02 % (136279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.36/1.02 % (136279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.36/1.02 % (136279)CaDiCaL version: 2.1.3
% 4.36/1.02 % (136279)Termination reason: Instruction limit
% 4.36/1.02 % (136279)Termination phase: Saturation
% 4.36/1.02 % (136279)Time elapsed: 0.029 s
% 4.36/1.02 % (136279)Peak memory usage: 13 MB
% 4.36/1.02 % (136279)Instructions burned: 119 (million)
% 4.36/1.02 % Exception at run slice level
% 4.36/1.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.36/1.02 % (136276)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.36/1.02 % (136309)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1431447815:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.36/1.02 % (136310)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2291458212:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.36/1.02 % Exception at run slice level
% 4.36/1.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.36/1.02 % (136278)Instruction limit reached!
% 4.36/1.02 % (136278)------------------------------
% 4.36/1.02 % (136278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.36/1.02 % (136278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.36/1.02 % (136278)CaDiCaL version: 2.1.3
% 4.36/1.02 % (136278)Termination reason: Instruction limit
% 4.36/1.02 % (136278)Termination phase: Saturation
% 4.36/1.02 % (136278)Time elapsed: 0.047 s
% 4.36/1.02 % (136278)Peak memory usage: 13 MB
% 4.36/1.02 % (136278)Instructions burned: 103 (million)
% 4.36/1.02 % (136328)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=1799093737:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.36/1.02 % (136280)Instruction limit reached!
% 4.36/1.02 % (136280)------------------------------
% 4.36/1.02 % (136280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.36/1.02 % (136280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.36/1.02 % (136280)CaDiCaL version: 2.1.3
% 4.36/1.02 % (136280)Termination reason: Instruction limit
% 4.36/1.02 % (136280)Termination phase: Saturation
% 4.36/1.02 % (136280)Time elapsed: 0.060 s
% 4.36/1.02 % (136280)Peak memory usage: 13 MB
% 4.36/1.02 % (136280)Instructions burned: 131 (million)
% 4.36/1.02 % (136328)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.36/1.02 % (136330)ott-21_1_sil=16000:fs=off:random_seed=2840530774:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.36/1.02 % (136328)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.36/1.02 % (136281)Instruction limit reached!
% 4.36/1.02 % (136281)------------------------------
% 5.68/1.12 % (136281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.68/1.12 % (136281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.12 % (136281)CaDiCaL version: 2.1.3
% 5.68/1.12 % (136281)Termination reason: Instruction limit
% 5.68/1.12 % (136281)Termination phase: Saturation
% 5.68/1.12 % (136281)Time elapsed: 0.073 s
% 5.68/1.12 % (136281)Peak memory usage: 14 MB
% 5.68/1.12 % (136281)Instructions burned: 160 (million)
% 5.68/1.12 % (136334)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3759232343:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 5.68/1.12 % (136340)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1714031119:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 5.68/1.12 % (136310)Instruction limit reached!
% 5.68/1.12 % (136310)------------------------------
% 5.68/1.12 % (136310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.68/1.12 % (136310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.12 % (136310)CaDiCaL version: 2.1.3
% 5.68/1.12 % (136310)Termination reason: Instruction limit
% 5.68/1.12 % (136310)Termination phase: Saturation
% 5.68/1.12 % (136310)Time elapsed: 0.060 s
% 5.68/1.12 % (136310)Peak memory usage: 13 MB
% 5.68/1.12 % (136310)Instructions burned: 132 (million)
% 5.68/1.12 % Exception at run slice level
% 5.68/1.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.68/1.12 % (136343)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=705968621:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 5.68/1.12 % (136344)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2638979869:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 5.68/1.12 % (136330)Instruction limit reached!
% 5.68/1.12 % (136330)------------------------------
% 5.68/1.12 % (136330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.68/1.12 % (136330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.12 % (136330)CaDiCaL version: 2.1.3
% 5.68/1.12 % (136330)Termination reason: Instruction limit
% 5.68/1.12 % (136330)Termination phase: Saturation
% 5.68/1.12 % (136330)Time elapsed: 0.085 s
% 5.68/1.12 % (136330)Peak memory usage: 13 MB
% 5.68/1.12 % (136330)Instructions burned: 181 (million)
% 5.68/1.12 % Exception at run slice level
% 5.68/1.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.68/1.12 % (136347)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=664219664:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 5.68/1.12 % (136348)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4121244227:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 5.68/1.12 % (136347)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.68/1.12 % (136348)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.68/1.12 % (136328)Instruction limit reached!
% 5.68/1.12 % (136328)------------------------------
% 5.68/1.12 % (136328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.68/1.12 % (136328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.12 % (136328)CaDiCaL version: 2.1.3
% 5.68/1.12 % (136328)Termination reason: Instruction limit
% 5.68/1.12 % (136328)Termination phase: Saturation
% 5.68/1.12 % (136328)Time elapsed: 0.142 s
% 5.68/1.12 % (136328)Peak memory usage: 14 MB
% 5.68/1.12 % (136328)Instructions burned: 689 (million)
% 5.68/1.12 % (136351)fmb+10_1_sil=64000:random_seed=711000801:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 5.68/1.12 % (136351)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.68/1.12 % Exception at run slice level
% 5.68/1.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.68/1.12 % (136353)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3014522081:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 5.68/1.12 % Exception at run slice level
% 5.68/1.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.68/1.12 % (136355)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2053479718:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 5.68/1.12 % Exception at run slice level
% 5.68/1.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.68/1.12 % (136357)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=115514502:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 5.68/1.12 % (136357)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.68/1.12 % (136334)Instruction limit reached!
% 5.68/1.12 % (136334)------------------------------
% 5.68/1.12 % (136334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.68/1.12 % (136334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.12 % (136334)CaDiCaL version: 2.1.3
% 5.68/1.12 % (136334)Termination reason: Instruction limit
% 5.68/1.12 % (136334)Termination phase: Saturation
% 5.68/1.12 % (136334)Time elapsed: 0.259 s
% 5.68/1.12 % (136334)Peak memory usage: 14 MB
% 5.68/1.12 % (136334)Instructions burned: 478 (million)
% 5.68/1.12 % (136359)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1295981464:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 5.68/1.12 % (136359)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.68/1.12 % (136359)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.68/1.12 % (136347)Instruction limit reached!
% 5.68/1.12 % (136347)------------------------------
% 5.68/1.12 % (136347)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.68/1.12 % (136347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.12 % (136347)CaDiCaL version: 2.1.3
% 5.68/1.12 % (136347)Termination reason: Instruction limit
% 5.68/1.12 % (136347)Termination phase: Saturation
% 5.68/1.12 % (136347)Time elapsed: 0.289 s
% 5.68/1.12 % (136347)Peak memory usage: 15 MB
% 5.68/1.12 % (136347)Instructions burned: 693 (million)
% 5.68/1.12 % (136361)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=547973197:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 5.68/1.12 % Exception at run slice level
% 5.68/1.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.68/1.12 % (136363)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2029169369:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 5.68/1.12 % Exception at run slice level
% 5.68/1.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.68/1.12 % (136365)ott-2_1_sil=16000:newcnf=on:random_seed=533330740:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 5.68/1.12 % (136365)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.68/1.12 % (136348)Instruction limit reached!
% 5.68/1.12 % (136348)------------------------------
% 5.68/1.12 % (136348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.68/1.12 % (136348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.12 % (136348)CaDiCaL version: 2.1.3
% 5.68/1.12 % (136348)Termination reason: Instruction limit
% 5.68/1.12 % (136348)Termination phase: Saturation
% 5.68/1.12 % (136348)Time elapsed: 0.433 s
% 5.68/1.12 % (136348)Peak memory usage: 17 MB
% 5.68/1.12 % (136348)Instructions burned: 881 (million)
% 5.68/1.12 % (136367)ott+10_1_sil=32000:tgt=ground:random_seed=2098060724:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 5.68/1.12 % (136343)Instruction limit reached!
% 5.68/1.12 % (136343)------------------------------
% 5.68/1.12 % (136343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.68/1.12 % (136343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.12 % (136343)CaDiCaL version: 2.1.3
% 5.68/1.12 % (136343)Termination reason: Instruction limit
% 5.68/1.12 % (136343)Termination phase: Saturation
% 5.68/1.12 % (136343)Time elapsed: 0.572 s
% 5.68/1.12 % (136343)Peak memory usage: 18 MB
% 5.68/1.12 % (136343)Instructions burned: 1180 (million)
% 5.68/1.12 % (136369)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3916594655:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 5.68/1.12 % Exception at run slice level
% 5.68/1.12 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.68/1.12 % (136371)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=423508693:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 5.68/1.12 % (136371)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.68/1.12 % (136365) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-136263-136365"...
% 5.68/1.12 % (136365)...printing done.
% 5.68/1.12 % (136365)Refutation found. Thanks to Tanya!
% 5.68/1.12 % SZS status Theorem for theBenchmark
% 5.68/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 5.68/1.12 % (136365)------------------------------
% 5.68/1.12 % (136365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.68/1.12 % (136365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.12 % (136365)CaDiCaL version: 2.1.3
% 5.68/1.12 % (136365)Termination reason: Refutation
% 5.68/1.12 % (136365)Time elapsed: 0.293 s
% 5.68/1.12 % (136365)Peak memory usage: 16 MB
% 5.68/1.12 % (136365)Instructions burned: 621 (million)
% 5.68/1.12 % (136263)Success in time 0.9 s
% 5.68/1.12 % Vampire exiting
%------------------------------------------------------------------------------