%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU586^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 08:32:33 AM UTC 2026
% Result : Theorem 5.78s 1.10s
% Output : Refutation 5.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 76 ( 42 unt; 0 typ; 2 def)
% Number of atoms : 1974 ( 523 equ; 0 cnn)
% Maximal formula atoms : 105 ( 25 avg)
% Number of connectives : 1296 ( 38 ~; 44 |; 312 &; 363 @)
% ( 2 <=>; 501 =>; 0 <=; 0 <~>)
% Maximal formula depth : 111 ( 13 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 : 214 ( 209 usr; 112 con; 0-4 aty)
% ( 30 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 149 ( 0 sgn 91 !; 8 ?; 149 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_120,type,
vAND: $o > $o > $o ).
thf(func_def_121,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_122,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_123,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_124,type,
vIMP: $o > $o > $o ).
thf(func_def_125,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_127,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_128,type,
vIFF: $o > $o > $o ).
thf(func_def_129,type,
vNOT: $o > $o ).
thf(func_def_130,type,
vOR: $o > $o > $o ).
thf(func_def_131,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_135,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_139,type,
sK3: $i > $i > $i ).
thf(func_def_140,type,
sK4: $i > $i > $i ).
thf(func_def_141,type,
sK5: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_142,type,
sK6: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_143,type,
sK7: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_144,type,
sK8: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_145,type,
sK9: ( $i > $o ) > $i > $i ).
thf(func_def_146,type,
sK10: ( $i > $o ) > $i > $i ).
thf(func_def_147,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_148,type,
sK12: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_149,type,
sK13: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_150,type,
sK14: ( $i > $o ) > $i ).
thf(func_def_151,type,
sK15: ( $i > $o ) > $i > $i ).
thf(func_def_152,type,
sK16: ( $i > $o ) > $i ).
thf(func_def_153,type,
sK17: ( $i > $o ) > $i > $i ).
thf(func_def_154,type,
sK18: ( $i > $o ) > $i > $i ).
thf(func_def_155,type,
sK19: ( $i > $o ) > $i ).
thf(func_def_156,type,
sK20: ( $i > $o ) > $i > $i ).
thf(func_def_157,type,
sK21: ( $i > $o ) > $i ).
thf(func_def_158,type,
sK22: ( $i > $o ) > $i > $i ).
thf(func_def_159,type,
sK23: ( $i > $o ) > $i > $i ).
thf(func_def_160,type,
sK24: ( $i > $o ) > $i ).
thf(func_def_161,type,
sK25: ( $i > $o ) > $i > $i ).
thf(func_def_162,type,
sK26: ( $i > $o ) > $i ).
thf(func_def_163,type,
sK27: ( $i > $o ) > $i > $i ).
thf(func_def_164,type,
sK28: ( $i > $o ) > $i > $i ).
thf(func_def_165,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_166,type,
sK30: ( $i > $o ) > $i ).
thf(func_def_167,type,
sK31: ( $i > $o ) > $i > $i ).
thf(func_def_168,type,
sK32: ( $i > $o ) > $i ).
thf(func_def_169,type,
sK33: ( $i > $o ) > $i ).
thf(func_def_170,type,
sK34: ( $i > $o ) > $i ).
thf(func_def_171,type,
sK35: ( $i > $o ) > $i ).
thf(func_def_172,type,
sK36: ( $i > $o ) > $i > $i ).
thf(func_def_173,type,
sK37: ( $i > $o ) > $i > $i ).
thf(func_def_174,type,
sK38: ( $i > $o ) > $i > $i ).
thf(func_def_175,type,
sK39: ( $i > $o ) > $i > $i ).
thf(func_def_176,type,
sK40: ( $i > $o ) > $i > $i ).
thf(func_def_177,type,
sK41: ( $i > $o ) > $i > $i ).
thf(func_def_178,type,
sK42: ( $i > $o ) > $i > $i ).
thf(func_def_179,type,
sK43: $i > $i ).
thf(func_def_180,type,
sK44: ( $i > $o ) > $i ).
thf(func_def_181,type,
sK45: ( $i > $o ) > $i > $i ).
thf(func_def_182,type,
sK46: $i > $o > $i > $i ).
thf(func_def_183,type,
sK47: $i > $i > $i ).
thf(func_def_184,type,
sK48: $i > $i ).
thf(func_def_185,type,
sK49: $i > $i ).
thf(func_def_186,type,
sK50: $i > $i ).
thf(func_def_187,type,
sK51: $i > $i > $i ).
thf(func_def_188,type,
sK52: $i > $i > $i ).
thf(func_def_189,type,
sK53: ( $i > $o ) > $i ).
thf(func_def_190,type,
sK54: ( $i > $o ) > $i > $i ).
thf(func_def_191,type,
sK55: ( $i > $o ) > $i ).
thf(func_def_192,type,
sK56: ( $i > $o ) > $i > $i ).
thf(func_def_193,type,
sK57: ( $i > $o ) > $i > $i ).
thf(func_def_194,type,
sK58: $i > $i ).
thf(func_def_195,type,
sK59: $i > $i > $i > $i ).
thf(func_def_196,type,
sK60: $i > $i > $i ).
thf(func_def_197,type,
sK61: $i > $i > $i ).
thf(func_def_198,type,
sK62: $i > $i > $i ).
thf(func_def_199,type,
sK63: $i > $i ).
thf(func_def_200,type,
sK64: $i > ( $i > $i > $o ) > $i ).
thf(func_def_201,type,
sK65: $i > ( $i > $i > $o ) > $i ).
thf(func_def_202,type,
sK66: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_203,type,
sK67: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_204,type,
sK68: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_205,type,
sK69: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_206,type,
sK70: $i > $i ).
thf(func_def_207,type,
sK71: $i > $i > $i ).
thf(func_def_208,type,
sK72: $i > $i > $i ).
thf(func_def_209,type,
sK73: $i > $i > $i ).
thf(f27,axiom,
( nonempty
= ( ^ [X0: $i] : ( X0 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(f30,axiom,
( nonemptyI1
= ( ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ( nonempty @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(f94,axiom,
( subsetemptysetimpeq
= ( ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(f104,axiom,
( binunionEcases
= ( ! [X0: $i,X1: $i,X2: $i,X3: $o] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( ( in @ X2 @ X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(f105,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(f106,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f105]) ).
thf(f157,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f162,plain,
( nonemptyI1
= ( ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ( nonempty @ X0 ) ) ) ),
inference(rectify,[],[f30]) ).
thf(f163,plain,
( nonemptyI1
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( nonempty @ Y0 ) ) ) ),
inference(fool_elimination,[],[f162]) ).
thf(f283,plain,
( subsetemptysetimpeq
= ( ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) ) ) ),
inference(rectify,[],[f94]) ).
thf(f284,plain,
( subsetemptysetimpeq
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) ) ),
inference(fool_elimination,[],[f283]) ).
thf(f303,plain,
( binunionEcases
= ( ! [X0: $i,X1: $i,X2: $i,X3: $o] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( ( in @ X2 @ X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ) ),
inference(rectify,[],[f104]) ).
thf(f304,plain,
( binunionEcases
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ ( binunion @ Y3 @ Y2 ) )
=> ( ( ( in @ Y1 @ Y3 )
=> Y0 )
=> ( ( ( in @ Y1 @ Y2 )
=> Y0 )
=> Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f303]) ).
thf(f305,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f106]) ).
thf(f306,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f305]) ).
thf(f307,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $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,[],[f306]) ).
thf(f308,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $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,[],[f307]) ).
thf(f309,plain,
( ( $true
!= ( in @ sK2 @ sK1 ) )
& ( $true
!= ( in @ sK2 @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( binunion @ sK0 @ sK1 ) ) )
& ( 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)],[f308]) ).
thf(f336,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[],[f157]) ).
thf(f339,plain,
( nonemptyI1
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( nonempty @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f163]) ).
thf(f403,plain,
( subsetemptysetimpeq
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) ) ),
inference(cnf_transformation,[],[f284]) ).
thf(f413,plain,
( binunionEcases
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ ( binunion @ Y3 @ Y2 ) )
=> ( ( ( in @ Y1 @ Y3 )
=> Y0 )
=> ( ( ( in @ Y1 @ Y2 )
=> Y0 )
=> Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f304]) ).
thf(f441,plain,
nonemptyI1 = $true,
inference(cnf_transformation,[],[f309]) ).
thf(f505,plain,
subsetemptysetimpeq = $true,
inference(cnf_transformation,[],[f309]) ).
thf(f515,plain,
binunionEcases = $true,
inference(cnf_transformation,[],[f309]) ).
thf(f516,plain,
( $true
= ( in @ sK2 @ ( binunion @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f309]) ).
thf(f517,plain,
( $true
!= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f309]) ).
thf(f518,plain,
( $true
!= ( in @ sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f309]) ).
thf(f548,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ^ [Y1: $i] : ( emptyset != Y1 )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f339,f441,f336]) ).
thf(f612,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) ) ),
inference(definition_unfolding,[],[f403,f505]) ).
thf(f622,plain,
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ ( binunion @ Y3 @ Y2 ) )
=> ( ( ( in @ Y1 @ Y3 )
=> Y0 )
=> ( ( ( in @ Y1 @ Y2 )
=> Y0 )
=> Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f413,f515]) ).
thf(f623,plain,
! [X1: $o] :
( $true
= ( ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ ( binunion @ Y3 @ Y2 ) )
=> ( ( ( in @ Y1 @ Y3 )
=> Y0 )
=> ( ( ( in @ Y1 @ Y2 )
=> Y0 )
=> Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f622]) ).
thf(f624,plain,
! [X1: $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( ( in @ Y0 @ Y2 )
=> X1 )
=> ( ( ( in @ Y0 @ Y1 )
=> X1 )
=> X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f623]) ).
thf(f625,plain,
! [X2: $i,X1: $o] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( ( in @ Y0 @ Y2 )
=> X1 )
=> ( ( ( in @ Y0 @ Y1 )
=> X1 )
=> X1 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f624]) ).
thf(f626,plain,
! [X2: $i,X1: $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X2 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( ( in @ X2 @ Y1 )
=> X1 )
=> ( ( ( in @ X2 @ Y0 )
=> X1 )
=> X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f625]) ).
thf(f627,plain,
! [X2: $i,X3: $i,X1: $o] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X2 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( ( in @ X2 @ Y1 )
=> X1 )
=> ( ( ( in @ X2 @ Y0 )
=> X1 )
=> X1 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f626]) ).
thf(f628,plain,
! [X2: $i,X3: $i,X1: $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( binunion @ Y0 @ X3 ) )
=> ( ( ( in @ X2 @ Y0 )
=> X1 )
=> ( ( ( in @ X2 @ X3 )
=> X1 )
=> X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f627]) ).
thf(f629,plain,
! [X2: $i,X3: $i,X1: $o,X4: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ ( binunion @ Y0 @ X3 ) )
=> ( ( ( in @ X2 @ Y0 )
=> X1 )
=> ( ( ( in @ X2 @ X3 )
=> X1 )
=> X1 ) ) )
@ X4 ) ),
inference(pi_proxy_clausification,[],[f628]) ).
thf(f630,plain,
! [X2: $i,X3: $i,X1: $o,X4: $i] :
( $true
= ( ( in @ X2 @ ( binunion @ X4 @ X3 ) )
=> ( ( ( in @ X2 @ X4 )
=> X1 )
=> ( ( ( in @ X2 @ X3 )
=> X1 )
=> X1 ) ) ) ),
inference(beta-eta_normalization,[],[f629]) ).
thf(f631,plain,
! [X2: $i,X3: $i,X1: $o,X4: $i] :
( ( $false
= ( in @ X2 @ ( binunion @ X4 @ X3 ) ) )
| ( $true
= ( ( ( in @ X2 @ X4 )
=> X1 )
=> ( ( ( in @ X2 @ X3 )
=> X1 )
=> X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f630]) ).
thf(f632,plain,
! [X2: $i,X3: $i,X1: $o,X4: $i] :
( ( $false
= ( in @ X2 @ ( binunion @ X4 @ X3 ) ) )
| ( $false
= ( ( in @ X2 @ X4 )
=> X1 ) )
| ( $true
= ( ( ( in @ X2 @ X3 )
=> X1 )
=> X1 ) ) ),
inference(imp_proxy_clausification,[],[f631]) ).
thf(f634,plain,
! [X2: $i,X3: $i,X1: $o,X4: $i] :
( ( $false
= ( in @ X2 @ ( binunion @ X4 @ X3 ) ) )
| ( ( in @ X2 @ X4 )
= $true )
| ( $true
= ( ( ( in @ X2 @ X3 )
=> X1 )
=> X1 ) ) ),
inference(imp_proxy_clausification,[],[f632]) ).
thf(f635,plain,
! [X2: $i,X3: $i,X1: $o,X4: $i] :
( ( $false
= ( in @ X2 @ ( binunion @ X4 @ X3 ) ) )
| ( ( in @ X2 @ X4 )
= $true )
| ( $false
= ( ( in @ X2 @ X3 )
=> X1 ) )
| ( $true = X1 ) ),
inference(imp_proxy_clausification,[],[f634]) ).
thf(f637,plain,
! [X2: $i,X3: $i,X1: $o,X4: $i] :
( ( $false
= ( in @ X2 @ ( binunion @ X4 @ X3 ) ) )
| ( ( in @ X2 @ X4 )
= $true )
| ( $true
= ( in @ X2 @ X3 ) )
| ( $true = X1 ) ),
inference(imp_proxy_clausification,[],[f635]) ).
thf(f685,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f612]) ).
thf(f686,plain,
! [X1: $i] :
( $true
= ( ( subset @ X1 @ emptyset )
=> ( emptyset = X1 ) ) ),
inference(beta-eta_normalization,[],[f685]) ).
thf(f687,plain,
! [X1: $i] :
( ( $false
= ( subset @ X1 @ emptyset ) )
| ( $true
= ( emptyset = X1 ) ) ),
inference(imp_proxy_clausification,[],[f686]) ).
thf(f688,plain,
! [X1: $i] :
( ( $false
= ( subset @ X1 @ emptyset ) )
| ( emptyset = X1 ) ),
inference(equality_proxy_clausification,[],[f687]) ).
thf(f1468,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) )
=> ( ^ [Y1: $i] : ( emptyset != Y1 )
@ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f548]) ).
thf(f1469,plain,
! [X1: $i] :
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) )
=> ( emptyset != X1 ) ) ),
inference(beta-eta_normalization,[],[f1468]) ).
thf(f1470,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) )
| ( $true
= ( emptyset != X1 ) ) ),
inference(imp_proxy_clausification,[],[f1469]) ).
thf(f1471,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] : ( in @ Y0 @ X1 )
@ X2 ) )
| ( $true
= ( emptyset != X1 ) ) ),
inference(pi_proxy_clausification,[],[f1470]) ).
thf(f1472,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] : ( in @ Y0 @ X1 )
@ X2 ) )
| ( $false
= ( emptyset = X1 ) ) ),
inference(not_proxy_clausification,[],[f1471]) ).
thf(f1473,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] : ( in @ Y0 @ X1 )
@ X2 ) )
| ( emptyset != X1 ) ),
inference(equality_proxy_clausification,[],[f1472]) ).
thf(f1474,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( emptyset != X1 ) ),
inference(beta-eta_normalization,[],[f1473]) ).
thf(f1844,definition,
( spl74_1
<=> ! [X1: $o] : ( $true = X1 ) ),
introduced(definition,[new_symbols(definition,[spl74_1])],[avatar_definition]) ).
thf(f1845,plain,
( ! [X1: $o] : ( $true = X1 )
| ~ spl74_1 ),
inference(avatar_component_clause,[],[f1844]) ).
thf(f1847,definition,
( spl74_2
<=> ! [X4: $i,X2: $i,X3: $i] :
( ( $false
= ( in @ X2 @ ( binunion @ X4 @ X3 ) ) )
| ( $true
= ( in @ X2 @ X3 ) )
| ( ( in @ X2 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl74_2])],[avatar_definition]) ).
thf(f1848,plain,
( ! [X2: $i,X3: $i,X4: $i] :
( ( $false
= ( in @ X2 @ ( binunion @ X4 @ X3 ) ) )
| ( $true
= ( in @ X2 @ X3 ) )
| ( ( in @ X2 @ X4 )
= $true ) )
| ~ spl74_2 ),
inference(avatar_component_clause,[],[f1847]) ).
thf(f1849,plain,
( spl74_1
| spl74_2 ),
inference(avatar_split_clause,[],[f637,f1847,f1844]) ).
thf(f5160,plain,
( ( $false = $true )
| ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK0 ) )
| ~ spl74_2 ),
inference(constrained_superposition,[],[f516,f1848]) ).
thf(f5167,plain,
( ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK0 ) )
| ~ spl74_2 ),
inference(trivial_inequality_removal,[],[f5160]) ).
thf(f5169,plain,
( ( $true
= ( in @ sK2 @ sK0 ) )
| ~ spl74_2 ),
inference(forward_subsumption_resolution,[],[f5167,f518]) ).
thf(f5174,plain,
( $false
| ~ spl74_2 ),
inference(forward_subsumption_resolution,[],[f5169,f517]) ).
thf(f5175,plain,
~ spl74_2,
inference(avatar_contradiction_clause,[],[f5174]) ).
thf(f5191,plain,
( ! [X1: $i] :
( ( $false = $true )
| ( emptyset != X1 ) )
| ~ spl74_1 ),
inference(constrained_superposition,[],[f1474,f1845]) ).
thf(f5196,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( emptyset = X0 ) )
| ~ spl74_1 ),
inference(constrained_superposition,[],[f688,f1845]) ).
thf(f5197,plain,
( ! [X0: $i] : ( emptyset = X0 )
| ~ spl74_1 ),
inference(trivial_inequality_removal,[],[f5196]) ).
thf(f5206,plain,
( ! [X1: $i] : ( emptyset != X1 )
| ~ spl74_1 ),
inference(trivial_inequality_removal,[],[f5191]) ).
thf(f5219,plain,
( $false
| ~ spl74_1 ),
inference(forward_subsumption_resolution,[],[f5206,f5197]) ).
thf(f5220,plain,
~ spl74_1,
inference(avatar_contradiction_clause,[],[f5219]) ).
cnf(s1,plain,
( spl74_1
| spl74_2 ),
inference(sat_conversion,[],[f1849]) ).
cnf(s11,plain,
~ spl74_2,
inference(sat_conversion,[],[f5175]) ).
cnf(s18,plain,
~ spl74_1,
inference(sat_conversion,[],[f5220]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s11,s18]) ).
thf(f5221,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU586^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.17 % Computer : n020.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 13:53:35 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.20 Running first-order model finding
% 0.06/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.28/0.98 % (1091543)Will run a generic schedule for satisfiability detection.
% 4.28/0.98 % (1091548)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1662520731_2999 on theBenchmark for (2999ds/0Mi)
% 4.28/0.98 % (1091551)dis+10_1_sil=32000:sp=arity:random_seed=3233287944:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.28/0.98 % (1091550)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1443221646:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.28/0.98 % (1091552)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4166484292:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.28/0.98 % (1091553)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3566525424:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.28/0.98 % (1091554)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1246837699:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.28/0.98 % (1091549)% WARNING: option uhcvi not known.
% 4.28/0.98 % (1091549)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3385442449:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.28/0.98 % (1091549)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.28/0.98 % (1091552)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.28/0.98 % (1091549)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.28/0.98 % Exception at run slice level
% 4.28/0.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.28/0.98 % (1091562)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2331214170:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.28/0.98 % (1091551)Instruction limit reached!
% 4.28/0.98 % (1091551)------------------------------
% 4.28/0.98 % (1091551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.28/0.98 % (1091551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/0.98 % (1091551)CaDiCaL version: 2.1.3
% 4.28/0.98 % (1091551)Termination reason: Instruction limit
% 4.28/0.98 % (1091551)Termination phase: Saturation
% 4.28/0.98 % (1091551)Time elapsed: 0.049 s
% 4.28/0.98 % (1091551)Peak memory usage: 13 MB
% 4.28/0.98 % (1091551)Instructions burned: 103 (million)
% 4.28/0.98 % (1091552)Instruction limit reached!
% 4.28/0.98 % (1091552)------------------------------
% 4.28/0.98 % (1091552)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.28/0.98 % (1091552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/0.98 % (1091552)CaDiCaL version: 2.1.3
% 4.28/0.98 % (1091552)Termination reason: Instruction limit
% 4.28/0.98 % (1091552)Termination phase: Saturation
% 4.28/0.98 % (1091552)Time elapsed: 0.054 s
% 4.28/0.98 % (1091552)Peak memory usage: 13 MB
% 4.28/0.98 % (1091552)Instructions burned: 116 (million)
% 4.28/0.98 % Exception at run slice level
% 4.28/0.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.28/0.98 % (1091553)Instruction limit reached!
% 4.28/0.98 % (1091553)------------------------------
% 4.28/0.98 % (1091553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.28/0.98 % (1091553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/0.98 % (1091553)CaDiCaL version: 2.1.3
% 4.28/0.98 % (1091553)Termination reason: Instruction limit
% 4.28/0.98 % (1091553)Termination phase: Saturation
% 4.28/0.98 % (1091553)Time elapsed: 0.061 s
% 4.28/0.98 % (1091553)Peak memory usage: 13 MB
% 4.28/0.98 % (1091553)Instructions burned: 133 (million)
% 4.28/0.98 % (1091554)Instruction limit reached!
% 4.28/0.98 % (1091554)------------------------------
% 4.28/0.98 % (1091554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.28/0.98 % (1091554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.28/0.98 % (1091554)CaDiCaL version: 2.1.3
% 4.28/0.98 % (1091554)Termination reason: Instruction limit
% 4.28/0.98 % (1091554)Termination phase: Saturation
% 4.28/0.98 % (1091554)Time elapsed: 0.069 s
% 4.28/0.98 % (1091554)Peak memory usage: 13 MB
% 4.28/0.98 % (1091554)Instructions burned: 160 (million)
% 4.28/0.98 % (1091565)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=3226804874:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 5.78/1.10 % (1091566)ott-21_1_sil=16000:fs=off:random_seed=1884881494:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 5.78/1.10 % (1091564)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1971706261:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.78/1.10 % (1091567)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=493697462:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 5.78/1.10 % (1091565)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.78/1.10 % (1091568)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3951300041:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 5.78/1.10 % (1091565)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.78/1.10 % Exception at run slice level
% 5.78/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.78/1.10 % (1091574)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1551396978:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 5.78/1.10 % (1091564)Instruction limit reached!
% 5.78/1.10 % (1091564)------------------------------
% 5.78/1.10 % (1091564)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.78/1.10 % (1091564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.10 % (1091564)CaDiCaL version: 2.1.3
% 5.78/1.10 % (1091564)Termination reason: Instruction limit
% 5.78/1.10 % (1091564)Termination phase: Saturation
% 5.78/1.10 % (1091564)Time elapsed: 0.075 s
% 5.78/1.10 % (1091564)Peak memory usage: 13 MB
% 5.78/1.10 % (1091564)Instructions burned: 132 (million)
% 5.78/1.10 % (1091566)Instruction limit reached!
% 5.78/1.10 % (1091566)------------------------------
% 5.78/1.10 % (1091566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.78/1.10 % (1091566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.10 % (1091566)CaDiCaL version: 2.1.3
% 5.78/1.10 % (1091566)Termination reason: Instruction limit
% 5.78/1.10 % (1091566)Termination phase: Saturation
% 5.78/1.10 % (1091566)Time elapsed: 0.086 s
% 5.78/1.10 % (1091566)Peak memory usage: 13 MB
% 5.78/1.10 % (1091566)Instructions burned: 181 (million)
% 5.78/1.10 % (1091576)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=161308255:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 5.78/1.10 % (1091577)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=4123164669: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)
% 5.78/1.10 % (1091577)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.78/1.10 % Exception at run slice level
% 5.78/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.78/1.10 % (1091580)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3130457529:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 5.78/1.10 % (1091580)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.78/1.10 % (1091565)Instruction limit reached!
% 5.78/1.10 % (1091565)------------------------------
% 5.78/1.10 % (1091565)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.78/1.10 % (1091565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.10 % (1091565)CaDiCaL version: 2.1.3
% 5.78/1.10 % (1091565)Termination reason: Instruction limit
% 5.78/1.10 % (1091565)Termination phase: Saturation
% 5.78/1.10 % (1091565)Time elapsed: 0.260 s
% 5.78/1.10 % (1091565)Peak memory usage: 14 MB
% 5.78/1.10 % (1091565)Instructions burned: 685 (million)
% 5.78/1.10 % (1091567)Instruction limit reached!
% 5.78/1.10 % (1091567)------------------------------
% 5.78/1.10 % (1091567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.78/1.10 % (1091567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.10 % (1091567)CaDiCaL version: 2.1.3
% 5.78/1.10 % (1091567)Termination reason: Instruction limit
% 5.78/1.10 % (1091567)Termination phase: Saturation
% 5.78/1.10 % (1091567)Time elapsed: 0.258 s
% 5.78/1.10 % (1091567)Peak memory usage: 13 MB
% 5.78/1.10 % (1091567)Instructions burned: 478 (million)
% 5.78/1.10 % (1091582)fmb+10_1_sil=64000:random_seed=4010585049:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 5.78/1.10 % (1091583)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3434034024:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 5.78/1.10 % (1091582)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.78/1.10 % Exception at run slice level
% 5.78/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.78/1.10 % Exception at run slice level
% 5.78/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.78/1.10 % (1091586)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2369660913:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 5.78/1.10 % (1091587)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=724651424:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 5.78/1.10 % (1091587)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.78/1.10 % Exception at run slice level
% 5.78/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.78/1.10 % (1091590)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1461649420:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 5.78/1.10 % (1091590)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.78/1.10 % (1091590)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.78/1.10 % (1091577)Instruction limit reached!
% 5.78/1.10 % (1091577)------------------------------
% 5.78/1.10 % (1091577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.78/1.10 % (1091577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.10 % (1091577)CaDiCaL version: 2.1.3
% 5.78/1.10 % (1091577)Termination reason: Instruction limit
% 5.78/1.10 % (1091577)Termination phase: Saturation
% 5.78/1.10 % (1091577)Time elapsed: 0.306 s
% 5.78/1.10 % (1091577)Peak memory usage: 15 MB
% 5.78/1.10 % (1091577)Instructions burned: 693 (million)
% 5.78/1.10 % (1091592)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1150525784:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 5.78/1.10 % Exception at run slice level
% 5.78/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.78/1.10 % (1091594)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2865916212:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 5.78/1.10 % Exception at run slice level
% 5.78/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.78/1.10 % (1091596)ott-2_1_sil=16000:newcnf=on:random_seed=1007948388:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 5.78/1.10 % (1091596)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.78/1.10 % (1091580)Instruction limit reached!
% 5.78/1.10 % (1091580)------------------------------
% 5.78/1.10 % (1091580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.78/1.10 % (1091580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.10 % (1091580)CaDiCaL version: 2.1.3
% 5.78/1.10 % (1091580)Termination reason: Instruction limit
% 5.78/1.10 % (1091580)Termination phase: Saturation
% 5.78/1.10 % (1091580)Time elapsed: 0.430 s
% 5.78/1.10 % (1091580)Peak memory usage: 17 MB
% 5.78/1.10 % (1091580)Instructions burned: 880 (million)
% 5.78/1.10 % (1091598)ott+10_1_sil=32000:tgt=ground:random_seed=2670156504:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 5.78/1.10 % (1091574)Instruction limit reached!
% 5.78/1.10 % (1091574)------------------------------
% 5.78/1.10 % (1091574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.78/1.10 % (1091574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.10 % (1091574)CaDiCaL version: 2.1.3
% 5.78/1.10 % (1091574)Termination reason: Instruction limit
% 5.78/1.10 % (1091574)Termination phase: Saturation
% 5.78/1.10 % (1091574)Time elapsed: 0.570 s
% 5.78/1.10 % (1091574)Peak memory usage: 18 MB
% 5.78/1.10 % (1091574)Instructions burned: 1180 (million)
% 5.78/1.10 % (1091600)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3591009956:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 5.78/1.10 % Exception at run slice level
% 5.78/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.78/1.10 % (1091602)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2356167293:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 5.78/1.10 % (1091602)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.78/1.10 % (1091596) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1091543-1091596"...
% 5.78/1.10 % (1091596)...printing done.
% 5.78/1.10 % (1091596)Refutation found. Thanks to Tanya!
% 5.78/1.10 % SZS status Theorem for theBenchmark
% 5.78/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 5.78/1.10 % (1091596)------------------------------
% 5.78/1.10 % (1091596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.78/1.10 % (1091596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.10 % (1091596)CaDiCaL version: 2.1.3
% 5.78/1.10 % (1091596)Termination reason: Refutation
% 5.78/1.10 % (1091596)Time elapsed: 0.271 s
% 5.78/1.10 % (1091596)Peak memory usage: 16 MB
% 5.78/1.10 % (1091596)Instructions burned: 580 (million)
% 5.78/1.10 % (1091543)Success in time 0.887 s
% 5.78/1.10 % Vampire exiting
%------------------------------------------------------------------------------