%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU611^1 : 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 : n005.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 08:32:40 AM UTC 2026
% Result : Theorem 3.79s 0.84s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 7
% Syntax : Number of formulae : 95 ( 51 unt; 0 typ; 2 def)
% Number of atoms : 2905 ( 768 equ; 0 cnn)
% Maximal formula atoms : 135 ( 30 avg)
% Number of connectives : 1863 ( 69 ~; 75 |; 390 &; 579 @)
% ( 2 <=>; 703 =>; 0 <=; 0 <~>)
% Maximal formula depth : 140 ( 14 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 243 ( 239 usr; 136 con; 0-4 aty)
% ( 45 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 178 ( 0 sgn 86 !; 8 ?; 178 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_149,type,
vAND: $o > $o > $o ).
thf(func_def_150,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_151,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_152,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_153,type,
vIMP: $o > $o > $o ).
thf(func_def_154,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_155,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_156,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_157,type,
vIFF: $o > $o > $o ).
thf(func_def_158,type,
vNOT: $o > $o ).
thf(func_def_159,type,
vOR: $o > $o > $o ).
thf(func_def_160,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_161,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_164,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_168,type,
sK3: $o ).
thf(func_def_169,type,
sK4: $i > $i > $i ).
thf(func_def_170,type,
sK5: $i > $i > $i ).
thf(func_def_171,type,
sK6: $i > $i > $i ).
thf(func_def_172,type,
sK7: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_173,type,
sK8: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_174,type,
sK9: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_175,type,
sK10: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_176,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_177,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_178,type,
sK13: ( $i > $o ) > $i > $i ).
thf(func_def_179,type,
sK14: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_180,type,
sK15: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_181,type,
sK16: ( $i > $o ) > $i ).
thf(func_def_182,type,
sK17: ( $i > $o ) > $i > $i ).
thf(func_def_183,type,
sK18: ( $i > $o ) > $i ).
thf(func_def_184,type,
sK19: ( $i > $o ) > $i > $i ).
thf(func_def_185,type,
sK20: ( $i > $o ) > $i > $i ).
thf(func_def_186,type,
sK21: ( $i > $o ) > $i ).
thf(func_def_187,type,
sK22: ( $i > $o ) > $i > $i ).
thf(func_def_188,type,
sK23: ( $i > $o ) > $i ).
thf(func_def_189,type,
sK24: ( $i > $o ) > $i > $i ).
thf(func_def_190,type,
sK25: ( $i > $o ) > $i > $i ).
thf(func_def_191,type,
sK26: ( $i > $o ) > $i ).
thf(func_def_192,type,
sK27: ( $i > $o ) > $i > $i ).
thf(func_def_193,type,
sK28: ( $i > $o ) > $i ).
thf(func_def_194,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_195,type,
sK30: ( $i > $o ) > $i > $i ).
thf(func_def_196,type,
sK31: ( $i > $o ) > $i > $i ).
thf(func_def_197,type,
sK32: ( $i > $o ) > $i ).
thf(func_def_198,type,
sK33: ( $i > $o ) > $i > $i ).
thf(func_def_199,type,
sK34: ( $i > $o ) > $i ).
thf(func_def_200,type,
sK35: ( $i > $o ) > $i ).
thf(func_def_201,type,
sK36: ( $i > $o ) > $i ).
thf(func_def_202,type,
sK37: ( $i > $o ) > $i ).
thf(func_def_203,type,
sK38: ( $i > $o ) > $i > $i ).
thf(func_def_204,type,
sK39: ( $i > $o ) > $i > $i ).
thf(func_def_205,type,
sK40: ( $i > $o ) > $i > $i ).
thf(func_def_206,type,
sK41: ( $i > $o ) > $i > $i ).
thf(func_def_207,type,
sK42: ( $i > $o ) > $i > $i ).
thf(func_def_208,type,
sK43: ( $i > $o ) > $i > $i ).
thf(func_def_209,type,
sK44: ( $i > $o ) > $i > $i ).
thf(func_def_210,type,
sK45: $i > $i ).
thf(func_def_211,type,
sK46: ( $i > $o ) > $i ).
thf(func_def_212,type,
sK47: ( $i > $o ) > $i > $i ).
thf(func_def_213,type,
sK48: $i > $o > $i > $i ).
thf(func_def_214,type,
sK49: $i > $i > $i ).
thf(func_def_215,type,
sK50: $i > $i ).
thf(func_def_216,type,
sK51: $i > $i ).
thf(func_def_217,type,
sK52: $i > $i ).
thf(func_def_218,type,
sK53: $i > $i > $i ).
thf(func_def_219,type,
sK54: $i > $i > $i ).
thf(func_def_220,type,
sK55: ( $i > $o ) > $i ).
thf(func_def_221,type,
sK56: ( $i > $o ) > $i > $i ).
thf(func_def_222,type,
sK57: ( $i > $o ) > $i ).
thf(func_def_223,type,
sK58: ( $i > $o ) > $i > $i ).
thf(func_def_224,type,
sK59: ( $i > $o ) > $i > $i ).
thf(func_def_225,type,
sK60: $i > $i ).
thf(func_def_226,type,
sK61: $i > $i > $i > $i ).
thf(func_def_227,type,
sK62: $i > $i > $i ).
thf(func_def_228,type,
sK63: $i > $i > $i ).
thf(func_def_229,type,
sK64: $i > $i > $i ).
thf(func_def_230,type,
sK65: $i > $i ).
thf(func_def_231,type,
sK66: $i > ( $i > $i > $o ) > $i ).
thf(func_def_232,type,
sK67: $i > ( $i > $i > $o ) > $i ).
thf(func_def_233,type,
sK68: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_234,type,
sK69: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_235,type,
sK70: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_236,type,
sK71: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_237,type,
sK72: $i > $i ).
thf(func_def_238,type,
sK73: $i > $i > $i ).
thf(func_def_239,type,
sK74: $i > $i > $i ).
thf(func_def_240,type,
sK75: $i > $i > $i ).
thf(f15,axiom,
( dsetconstrEL
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(f16,axiom,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f105,axiom,
( binunionE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(f130,axiom,
( symdiff
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( binunion @ X0 @ X1 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X1 )
| ~ ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiff) ).
thf(f131,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
=> ! [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(f132,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
=> ! [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(negated_conjecture,[status(cth)],[f131]) ).
thf(f159,plain,
( dsetconstrEL
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f160,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f159]) ).
thf(f161,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f162,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f161]) ).
thf(f331,plain,
( binunionE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f105]) ).
thf(f332,plain,
( binunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f331]) ).
thf(f380,plain,
( symdiff
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( binunion @ X0 @ X1 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X1 )
| ~ ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f130]) ).
thf(f381,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
| ~ ( in @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f380]) ).
thf(f382,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
=> ! [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,[],[f132]) ).
thf(f383,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true )
=> ! [X3: $o] :
( ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( ( in @ X2 @ X0 )
!= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f382]) ).
thf(f384,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true )
=> ! [X3: $o] :
( ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( ( in @ X2 @ X0 )
!= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f383]) ).
thf(f385,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( $true = X3 )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $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,[],[f384]) ).
thf(f386,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( $true = X3 )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $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,[],[f385]) ).
thf(f387,plain,
( ( $true != sK3 )
& ( ( $true = sK3 )
| ( $true
!= ( in @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK0 ) ) )
& ( ( $true = sK3 )
| ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true
!= ( in @ sK2 @ sK0 ) ) )
& ( $true
= ( in @ sK2 @ ( symdiff @ sK0 @ sK1 ) ) )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f386]) ).
thf(f402,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f160]) ).
thf(f403,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f162]) ).
thf(f492,plain,
( binunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f332]) ).
thf(f517,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
| ~ ( in @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f381]) ).
thf(f531,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[],[f387]) ).
thf(f532,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f387]) ).
thf(f620,plain,
binunionE = $true,
inference(cnf_transformation,[],[f387]) ).
thf(f645,plain,
( $true
= ( in @ sK2 @ ( symdiff @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f387]) ).
thf(f646,plain,
( ( $true = sK3 )
| ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true
!= ( in @ sK2 @ sK0 ) ) ),
inference(cnf_transformation,[],[f387]) ).
thf(f647,plain,
( ( $true = sK3 )
| ( $true
!= ( in @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK0 ) ) ),
inference(cnf_transformation,[],[f387]) ).
thf(f648,plain,
$true != sK3,
inference(cnf_transformation,[],[f387]) ).
thf(f664,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f402,f531]) ).
thf(f665,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f403,f532]) ).
thf(f753,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f492,f620]) ).
thf(f778,plain,
( $true
= ( in @ sK2
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
| ~ ( in @ Y2 @ Y1 ) ) )
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[],[f645,f517]) ).
thf(f779,plain,
( $true
= ( in @ sK2
@ ( dsetconstr @ ( binunion @ sK0 @ sK1 )
@ ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK0 )
| ~ ( in @ Y0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f778]) ).
thf(f945,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f753]) ).
thf(f946,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( in @ X1 @ Y1 )
| ( in @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f945]) ).
thf(f947,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( in @ X1 @ Y1 )
| ( in @ X1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f946]) ).
thf(f948,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( binunion @ Y0 @ X2 ) )
=> ( ( in @ X1 @ Y0 )
| ( in @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f947]) ).
thf(f949,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( binunion @ Y0 @ X2 ) )
=> ( ( in @ X1 @ Y0 )
| ( in @ X1 @ X2 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f948]) ).
thf(f950,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( binunion @ X3 @ X2 ) )
=> ( ( in @ X1 @ X3 )
| ( in @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f949]) ).
thf(f951,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( binunion @ X3 @ X2 ) ) )
| ( $true
= ( ( in @ X1 @ X3 )
| ( in @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f950]) ).
thf(f952,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( binunion @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X3 )
= $true ) ),
inference(or_proxy_clausification,[],[f951]) ).
thf(f1914,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f665]) ).
thf(f1915,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1914]) ).
thf(f1916,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f1915]) ).
thf(f1917,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f1916]) ).
thf(f1918,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f1917]) ).
thf(f1919,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1918]) ).
thf(f1920,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1919]) ).
thf(f1921,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f664]) ).
thf(f1922,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1921]) ).
thf(f1923,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f1922]) ).
thf(f1924,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f1923]) ).
thf(f1925,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f1924]) ).
thf(f1926,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( in @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f1925]) ).
thf(f1927,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1926]) ).
thf(f2429,plain,
( ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true
!= ( in @ sK2 @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f646,f648]) ).
thf(f2431,definition,
( spl76_1
<=> ( $true
= ( in @ sK2 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl76_1])],[avatar_definition]) ).
thf(f2432,plain,
( ( $true
= ( in @ sK2 @ sK0 ) )
| ~ spl76_1 ),
inference(avatar_component_clause,[],[f2431]) ).
thf(f2433,plain,
( ( $true
!= ( in @ sK2 @ sK0 ) )
| spl76_1 ),
inference(avatar_component_clause,[],[f2431]) ).
thf(f2435,definition,
( spl76_2
<=> ( $true
= ( in @ sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl76_2])],[avatar_definition]) ).
thf(f2436,plain,
( ( $true
!= ( in @ sK2 @ sK1 ) )
| spl76_2 ),
inference(avatar_component_clause,[],[f2435]) ).
thf(f2437,plain,
( ( $true
= ( in @ sK2 @ sK1 ) )
| ~ spl76_2 ),
inference(avatar_component_clause,[],[f2435]) ).
thf(f2438,plain,
( ~ spl76_1
| spl76_2 ),
inference(avatar_split_clause,[],[f2429,f2435,f2431]) ).
thf(f2441,plain,
( ( $true
!= ( in @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f647,f648]) ).
thf(f2442,plain,
( ( $true
!= ( in @ sK2 @ sK1 ) )
| spl76_1 ),
inference(forward_subsumption_resolution,[],[f2441,f2433]) ).
thf(f2443,plain,
( ~ spl76_2
| spl76_1 ),
inference(avatar_split_clause,[],[f2442,f2431,f2435]) ).
thf(f4253,plain,
( ( $false = $true )
| ( $true
= ( in @ sK2 @ ( binunion @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f1927,f779]) ).
thf(f4254,plain,
( ( $false = $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK0 )
| ~ ( in @ Y0 @ sK1 ) )
@ sK2 ) ) ),
inference(constrained_superposition,[],[f1920,f779]) ).
thf(f4259,plain,
( $true
= ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK0 )
| ~ ( in @ Y0 @ sK1 ) )
@ sK2 ) ),
inference(trivial_inequality_removal,[],[f4254]) ).
thf(f4260,plain,
( $true
= ( ~ ( in @ sK2 @ sK0 )
| ~ ( in @ sK2 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f4259]) ).
thf(f4261,plain,
( ( $true
= ( ~ ( in @ sK2 @ sK1 ) ) )
| ( $true
= ( ~ ( in @ sK2 @ sK0 ) ) ) ),
inference(or_proxy_clausification,[],[f4260]) ).
thf(f4262,plain,
( ( $false
= ( in @ sK2 @ sK1 ) )
| ( $true
= ( ~ ( in @ sK2 @ sK0 ) ) ) ),
inference(not_proxy_clausification,[],[f4261]) ).
thf(f4263,plain,
( ( $false
= ( in @ sK2 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK0 ) ) ),
inference(not_proxy_clausification,[],[f4262]) ).
thf(f4264,plain,
( $true
= ( in @ sK2 @ ( binunion @ sK0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f4253]) ).
thf(f4742,plain,
( ( $false = $true )
| ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK0 ) ) ),
inference(constrained_superposition,[],[f4264,f952]) ).
thf(f4753,plain,
( ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f4742]) ).
thf(f4755,plain,
( ( $true
= ( in @ sK2 @ sK0 ) )
| spl76_2 ),
inference(forward_subsumption_resolution,[],[f4753,f2436]) ).
thf(f4758,plain,
( $false
| spl76_1
| spl76_2 ),
inference(forward_subsumption_resolution,[],[f4755,f2433]) ).
thf(f4759,plain,
( spl76_1
| spl76_2 ),
inference(avatar_contradiction_clause,[],[f4758]) ).
thf(f5258,plain,
( ( $false = $true )
| ( $false
= ( in @ sK2 @ sK1 ) )
| ~ spl76_1 ),
inference(forward_demodulation,[],[f4263,f2432]) ).
thf(f5259,plain,
( ( $false
= ( in @ sK2 @ sK1 ) )
| ~ spl76_1 ),
inference(trivial_inequality_removal,[],[f5258]) ).
thf(f5263,plain,
( ( $false = $true )
| ~ spl76_1
| ~ spl76_2 ),
inference(constrained_superposition,[],[f5259,f2437]) ).
thf(f5271,plain,
( $false
| ~ spl76_1
| ~ spl76_2 ),
inference(trivial_inequality_removal,[],[f5263]) ).
thf(f5272,plain,
( ~ spl76_1
| ~ spl76_2 ),
inference(avatar_contradiction_clause,[],[f5271]) ).
cnf(s1,plain,
( ~ spl76_1
| spl76_2 ),
inference(sat_conversion,[],[f2438]) ).
cnf(s2,plain,
( spl76_1
| ~ spl76_2 ),
inference(sat_conversion,[],[f2443]) ).
cnf(s4,plain,
( spl76_1
| spl76_2 ),
inference(sat_conversion,[],[f4759]) ).
cnf(s6,plain,
( ~ spl76_1
| ~ spl76_2 ),
inference(sat_conversion,[],[f5272]) ).
cnf(s7,plain,
spl76_1,
inference(rat,[],[s2,s4]) ).
cnf(s8,plain,
~ spl76_2,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8,s7]) ).
thf(f5276,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU611^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n005.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 13:57:55 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 3.79/0.84 % (1706536)Will run a generic schedule for satisfiability detection.
% 3.79/0.84 % (1706543)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1012124460:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.79/0.84 % (1706542)% WARNING: option uhcvi not known.
% 3.79/0.84 % (1706541)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3423958485_2999 on theBenchmark for (2999ds/0Mi)
% 3.79/0.84 % (1706542)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=757858464:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.79/0.84 % (1706544)dis+10_1_sil=32000:sp=arity:random_seed=932839506:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.79/0.84 % (1706545)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2800853334:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.79/0.84 % (1706546)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1039155791:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.79/0.84 % (1706547)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3898634908:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.79/0.84 % (1706542)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.79/0.84 % (1706545)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.79/0.84 % Exception at run slice level
% 3.79/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.79/0.84 % (1706542)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.79/0.84 % (1706555)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3445683659:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.79/0.84 % (1706544)Instruction limit reached!
% 3.79/0.84 % (1706544)------------------------------
% 3.79/0.84 % (1706544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.79/0.84 % (1706544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/0.84 % (1706544)CaDiCaL version: 2.1.3
% 3.79/0.84 % (1706544)Termination reason: Instruction limit
% 3.79/0.84 % (1706544)Termination phase: Saturation
% 3.79/0.84 % (1706544)Time elapsed: 0.047 s
% 3.79/0.84 % (1706544)Peak memory usage: 13 MB
% 3.79/0.84 % (1706544)Instructions burned: 104 (million)
% 3.79/0.84 % (1706545)Instruction limit reached!
% 3.79/0.84 % (1706545)------------------------------
% 3.79/0.84 % (1706545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.79/0.84 % (1706545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/0.84 % (1706545)CaDiCaL version: 2.1.3
% 3.79/0.84 % (1706545)Termination reason: Instruction limit
% 3.79/0.84 % (1706545)Termination phase: Saturation
% 3.79/0.84 % (1706545)Time elapsed: 0.053 s
% 3.79/0.84 % (1706545)Peak memory usage: 13 MB
% 3.79/0.84 % (1706545)Instructions burned: 117 (million)
% 3.79/0.84 % (1706546)Instruction limit reached!
% 3.79/0.84 % (1706546)------------------------------
% 3.79/0.84 % (1706546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.79/0.84 % (1706546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/0.84 % (1706546)CaDiCaL version: 2.1.3
% 3.79/0.84 % (1706546)Termination reason: Instruction limit
% 3.79/0.84 % (1706546)Termination phase: Saturation
% 3.79/0.84 % (1706546)Time elapsed: 0.061 s
% 3.79/0.84 % (1706546)Peak memory usage: 13 MB
% 3.79/0.84 % (1706546)Instructions burned: 132 (million)
% 3.79/0.84 % Exception at run slice level
% 3.79/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.79/0.84 % (1706557)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2448198136:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.79/0.84 % (1706558)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=2307782982:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.79/0.84 % (1706547)Instruction limit reached!
% 3.79/0.84 % (1706547)------------------------------
% 3.79/0.84 % (1706547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.79/0.84 % (1706547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/0.84 % (1706547)CaDiCaL version: 2.1.3
% 3.79/0.84 % (1706547)Termination reason: Instruction limit
% 3.79/0.84 % (1706547)Termination phase: Saturation
% 3.79/0.84 % (1706547)Time elapsed: 0.072 s
% 3.79/0.84 % (1706547)Peak memory usage: 14 MB
% 3.79/0.84 % (1706547)Instructions burned: 159 (million)
% 3.79/0.84 % (1706559)ott-21_1_sil=16000:fs=off:random_seed=95095841:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 3.79/0.84 % (1706560)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3272959100:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 3.79/0.84 % (1706558)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.79/0.84 % (1706563)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2689649834:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.79/0.84 % (1706558)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.79/0.84 % Exception at run slice level
% 3.79/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.79/0.84 % (1706557)Instruction limit reached!
% 3.79/0.84 % (1706557)------------------------------
% 3.79/0.84 % (1706557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.79/0.84 % (1706557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/0.84 % (1706557)CaDiCaL version: 2.1.3
% 3.79/0.84 % (1706557)Termination reason: Instruction limit
% 3.79/0.84 % (1706557)Termination phase: Saturation
% 3.79/0.84 % (1706557)Time elapsed: 0.060 s
% 3.79/0.84 % (1706557)Peak memory usage: 13 MB
% 3.79/0.84 % (1706557)Instructions burned: 131 (million)
% 3.79/0.84 % (1706567)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2538821620:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.79/0.84 % (1706568)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1042982170:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.79/0.84 % (1706559)Instruction limit reached!
% 3.79/0.84 % (1706559)------------------------------
% 3.79/0.84 % (1706559)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.79/0.84 % (1706559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/0.84 % (1706559)CaDiCaL version: 2.1.3
% 3.79/0.84 % (1706559)Termination reason: Instruction limit
% 3.79/0.84 % (1706559)Termination phase: Saturation
% 3.79/0.84 % (1706559)Time elapsed: 0.087 s
% 3.79/0.84 % (1706559)Peak memory usage: 13 MB
% 3.79/0.84 % (1706559)Instructions burned: 181 (million)
% 3.79/0.84 % Exception at run slice level
% 3.79/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.79/0.84 % (1706571)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=1385382547:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 3.79/0.84 % (1706572)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1996062242:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 3.79/0.84 % (1706572)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.79/0.84 % (1706571)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.79/0.84 % (1706558)Instruction limit reached!
% 3.79/0.84 % (1706558)------------------------------
% 3.79/0.84 % (1706558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.79/0.84 % (1706558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/0.84 % (1706558)CaDiCaL version: 2.1.3
% 3.79/0.84 % (1706558)Termination reason: Instruction limit
% 3.79/0.84 % (1706558)Termination phase: Saturation
% 3.79/0.84 % (1706558)Time elapsed: 0.262 s
% 3.79/0.84 % (1706558)Peak memory usage: 14 MB
% 3.79/0.84 % (1706558)Instructions burned: 686 (million)
% 3.79/0.84 % (1706560)Instruction limit reached!
% 3.79/0.84 % (1706560)------------------------------
% 3.79/0.84 % (1706560)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.79/0.84 % (1706560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/0.84 % (1706560)CaDiCaL version: 2.1.3
% 3.79/0.84 % (1706560)Termination reason: Instruction limit
% 3.79/0.84 % (1706560)Termination phase: Saturation
% 3.79/0.84 % (1706560)Time elapsed: 0.256 s
% 3.79/0.84 % (1706560)Peak memory usage: 14 MB
% 3.79/0.84 % (1706560)Instructions burned: 478 (million)
% 3.79/0.84 % (1706575)fmb+10_1_sil=64000:random_seed=1577482920:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 3.79/0.84 % (1706576)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3468078449:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 3.79/0.84 % (1706575)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.79/0.84 % Exception at run slice level
% 3.79/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.79/0.84 % Exception at run slice level
% 3.79/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.79/0.84 % (1706579)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=4190625026:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 3.79/0.84 % (1706580)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3461881395:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 3.79/0.84 % (1706580)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.79/0.84 % Exception at run slice level
% 3.79/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.79/0.84 % (1706583)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2509577018:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 3.79/0.84 % (1706583)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.79/0.84 % (1706583)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.79/0.84 % (1706571)Instruction limit reached!
% 3.79/0.84 % (1706571)------------------------------
% 3.79/0.84 % (1706571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.79/0.84 % (1706571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/0.84 % (1706571)CaDiCaL version: 2.1.3
% 3.79/0.84 % (1706571)Termination reason: Instruction limit
% 3.79/0.84 % (1706571)Termination phase: Saturation
% 3.79/0.84 % (1706571)Time elapsed: 0.280 s
% 3.79/0.84 % (1706571)Peak memory usage: 16 MB
% 3.79/0.84 % (1706571)Instructions burned: 692 (million)
% 3.79/0.84 % (1706585)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=171109353:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 3.79/0.84 % Exception at run slice level
% 3.79/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.79/0.84 % (1706587)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=213348544:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 3.79/0.84 % Exception at run slice level
% 3.79/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.79/0.84 % (1706589)ott-2_1_sil=16000:newcnf=on:random_seed=1993633658:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 3.79/0.84 % (1706580) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1706536-1706580"...
% 3.79/0.84 % (1706580)...printing done.
% 3.79/0.84 % (1706589)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.79/0.84 % (1706580)Refutation found. Thanks to Tanya!
% 3.79/0.84 % SZS status Theorem for theBenchmark
% 3.79/0.84 % SZS output start Proof for theBenchmark
% See solution above
% 3.79/0.85 % (1706580)------------------------------
% 3.79/0.85 % (1706580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.79/0.85 % (1706580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/0.85 % (1706580)CaDiCaL version: 2.1.3
% 3.79/0.85 % (1706580)Termination reason: Refutation
% 3.79/0.85 % (1706580)Time elapsed: 0.180 s
% 3.79/0.85 % (1706580)Peak memory usage: 15 MB
% 3.79/0.85 % (1706580)Instructions burned: 373 (million)
% 3.79/0.85 % (1706536)Success in time 0.619 s
% 3.79/0.85 % Vampire exiting
%------------------------------------------------------------------------------