%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:18 AM UTC 2026
% Result : Theorem 3.07s 0.84s
% Output : Refutation 3.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 155
% Number of leaves : 19
% Syntax : Number of formulae : 299 ( 186 unt; 0 typ; 14 def)
% Number of atoms : 11689 ( 269 equ; 0 cnn)
% Maximal formula atoms : 132 ( 39 avg)
% Number of connectives : 15913 ( 716 ~; 307 |; 0 &;4194 @)
% ( 14 <=>;10072 =>; 0 <=; 0 <~>)
% Maximal formula depth : 140 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 187 ( 183 usr; 148 con; 0-4 aty)
% ( 610 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 862 ( 0 sgn 78 !; 0 ?; 862 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_149,type,
vIMP: $o > $o > $o ).
thf(func_def_150,type,
vNOT: $o > $o ).
thf(func_def_151,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_152,type,
vAND: $o > $o > $o ).
thf(func_def_153,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_154,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_155,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_156,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_157,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_158,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_161,type,
vIFF: $o > $o > $o ).
thf(func_def_162,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_163,type,
vOR: $o > $o > $o ).
thf(func_def_164,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_169,type,
sK4: $o ).
thf(func_def_170,type,
sK5: $i > $i ).
thf(func_def_171,type,
sK6: $i > $i ).
thf(func_def_172,type,
sK7: $i > $i > $i ).
thf(func_def_173,type,
sK8: $i > $i > $i ).
thf(f15,axiom,
( dsetconstrEL
= ( ! [X1: $i > $o,X2: $i,X0: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(f16,axiom,
! [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f105,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
| ( in @ X2 @ X1 ) ) )
= binunionE ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(f130,axiom,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( binunion @ X0 @ X1 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X1 )
| ~ ( in @ X2 @ X0 ) ) ) )
= symdiff ),
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(f190,plain,
( dsetconstrEL
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( in @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f191,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f190]) ).
thf(f224,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(f225,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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( symdiff @ Y2 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f224]) ).
thf(f239,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( binunion @ X0 @ X1 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X1 )
| ~ ( in @ X2 @ X0 ) ) ) )
= symdiff ),
inference(rectify,[],[f130]) ).
thf(f240,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
| ~ ( in @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f239]) ).
thf(f252,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X2 ) )
= dsetconstrER ),
inference(rectify,[],[f16]) ).
thf(f253,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f252]) ).
thf(f282,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
=> ( ( in @ X0 @ X2 )
| ( in @ X0 @ X1 ) ) )
= binunionE ),
inference(rectify,[],[f105]) ).
thf(f283,plain,
( binunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binunion @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( in @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f282]) ).
thf(f423,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
| ~ ( in @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f240]) ).
thf(f448,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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( symdiff @ Y2 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f225]) ).
thf(f480,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f191]) ).
thf(f490,plain,
( binunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binunion @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( in @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f283]) ).
thf(f507,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f253]) ).
thf(f531,plain,
( $true
= ( ~ ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ ( binunion @ Y3 @ Y4 )
@ ^ [Y5: $i] :
( ~ ( in @ Y5 @ Y3 )
| ~ ( in @ Y5 @ Y4 ) ) )
@ Y2
@ Y1 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f448,f423]) ).
thf(f542,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f480]) ).
thf(f550,plain,
( $true
= ( ~ ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f531]) ).
thf(f564,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f507]) ).
thf(f587,plain,
( ( dsetconstrEL = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( in @ Y1 @ Y0 ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f542]) ).
thf(f660,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f550]) ).
thf(f710,plain,
( ( binunionE = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binunion @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( in @ Y2 @ Y0 ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f490]) ).
thf(f772,plain,
( ( dsetconstrER = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f564]) ).
thf(f950,definition,
( spl0_29
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( in @ Y1 @ Y0 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
thf(f952,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( in @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f950]) ).
thf(f954,definition,
( spl0_30
<=> ( dsetconstrEL = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
thf(f956,plain,
( ( dsetconstrEL = $false )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f954]) ).
thf(f957,plain,
( spl0_29
| spl0_30 ),
inference(avatar_split_clause,[],[f587,f954,f950]) ).
thf(f959,definition,
( spl0_31
<=> ( dsetconstrEL = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
thf(f961,plain,
( ( dsetconstrEL = $true )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f959]) ).
thf(f1599,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f660]) ).
thf(f2034,definition,
( spl0_269
<=> ( binunionE = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_269])],[avatar_definition]) ).
thf(f2036,plain,
( ( binunionE = $false )
| ~ spl0_269 ),
inference(avatar_component_clause,[],[f2034]) ).
thf(f2038,definition,
( spl0_270
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binunion @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( in @ Y2 @ Y0 ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_270])],[avatar_definition]) ).
thf(f2040,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binunion @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( in @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_270 ),
inference(avatar_component_clause,[],[f2038]) ).
thf(f2041,plain,
( spl0_269
| spl0_270 ),
inference(avatar_split_clause,[],[f710,f2038,f2034]) ).
thf(f2047,definition,
( spl0_272
<=> ( binunionE = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_272])],[avatar_definition]) ).
thf(f2049,plain,
( ( binunionE = $true )
| ~ spl0_272 ),
inference(avatar_component_clause,[],[f2047]) ).
thf(f2568,definition,
( spl0_387
<=> ( dsetconstrER = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_387])],[avatar_definition]) ).
thf(f2570,plain,
( ( dsetconstrER = $true )
| ~ spl0_387 ),
inference(avatar_component_clause,[],[f2568]) ).
thf(f2577,definition,
( spl0_389
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_389])],[avatar_definition]) ).
thf(f2579,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_389 ),
inference(avatar_component_clause,[],[f2577]) ).
thf(f2581,definition,
( spl0_390
<=> ( dsetconstrER = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_390])],[avatar_definition]) ).
thf(f2583,plain,
( ( dsetconstrER = $false )
| ~ spl0_390 ),
inference(avatar_component_clause,[],[f2581]) ).
thf(f2584,plain,
( spl0_389
| spl0_390 ),
inference(avatar_split_clause,[],[f772,f2581,f2577]) ).
thf(f3020,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f1599]) ).
thf(f3023,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3020]) ).
thf(f3026,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3023]) ).
thf(f3029,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3026]) ).
thf(f3032,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3029]) ).
thf(f3035,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3032]) ).
thf(f3037,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3035]) ).
thf(f3040,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3037]) ).
thf(f3044,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3040]) ).
thf(f3047,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3044]) ).
thf(f3050,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3047]) ).
thf(f3052,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3050]) ).
thf(f3055,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3052]) ).
thf(f3056,plain,
dsetconstrEL = $true,
inference(imp_proxy_clausification,[],[f3052]) ).
thf(f3058,plain,
spl0_31,
inference(avatar_split_clause,[],[f3056,f959]) ).
thf(f3059,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3055]) ).
thf(f3060,plain,
dsetconstrER = $true,
inference(imp_proxy_clausification,[],[f3055]) ).
thf(f3061,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3059]) ).
thf(f3063,plain,
spl0_387,
inference(avatar_split_clause,[],[f3060,f2568]) ).
thf(f3064,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3061]) ).
thf(f3067,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3064]) ).
thf(f3071,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3067]) ).
thf(f3073,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3071]) ).
thf(f3077,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3073]) ).
thf(f3079,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3077]) ).
thf(f3082,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3079]) ).
thf(f3086,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3082]) ).
thf(f3088,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3086]) ).
thf(f3092,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3088]) ).
thf(f3095,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3092]) ).
thf(f3098,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3095]) ).
thf(f3101,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3098]) ).
thf(f3103,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3101]) ).
thf(f3107,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3103]) ).
thf(f3110,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3107]) ).
thf(f3112,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3110]) ).
thf(f3116,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3112]) ).
thf(f3118,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3116]) ).
thf(f3121,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3118]) ).
thf(f3125,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3121]) ).
thf(f3128,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3125]) ).
thf(f3130,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3128]) ).
thf(f3133,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3130]) ).
thf(f3137,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3133]) ).
thf(f3139,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3137]) ).
thf(f3142,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3139]) ).
thf(f3146,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3142]) ).
thf(f3149,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3146]) ).
thf(f3152,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3149]) ).
thf(f3154,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3152]) ).
thf(f3157,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3154]) ).
thf(f3160,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3157]) ).
thf(f3164,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3160]) ).
thf(f3167,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3164]) ).
thf(f3169,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3167]) ).
thf(f3172,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3169]) ).
thf(f3175,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3172]) ).
thf(f3178,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3175]) ).
thf(f3181,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3178]) ).
thf(f3185,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3181]) ).
thf(f3188,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3185]) ).
thf(f3191,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3188]) ).
thf(f3194,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3191]) ).
thf(f3197,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3194]) ).
thf(f3200,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3197]) ).
thf(f3203,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3200]) ).
thf(f3206,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3203]) ).
thf(f3208,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3206]) ).
thf(f3212,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3208]) ).
thf(f3214,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3212]) ).
thf(f3218,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3214]) ).
thf(f3220,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3218]) ).
thf(f3223,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3220]) ).
thf(f3226,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3223]) ).
thf(f3228,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3226]) ).
thf(f3231,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3228]) ).
thf(f3233,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3231]) ).
thf(f3237,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3233]) ).
thf(f3240,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3237]) ).
thf(f3243,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3240]) ).
thf(f3245,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3243]) ).
thf(f3248,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3245]) ).
thf(f3251,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3248]) ).
thf(f3254,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3251]) ).
thf(f3257,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3254]) ).
thf(f3261,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3257]) ).
thf(f3264,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3261]) ).
thf(f3267,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3264]) ).
thf(f3269,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3267]) ).
thf(f3272,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3269]) ).
thf(f3275,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3272]) ).
thf(f3279,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3275]) ).
thf(f3282,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3279]) ).
thf(f3285,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3282]) ).
thf(f3287,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3285]) ).
thf(f3291,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3287]) ).
thf(f3294,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3291]) ).
thf(f3296,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3294]) ).
thf(f3299,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3296]) ).
thf(f3303,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3299]) ).
thf(f3306,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3303]) ).
thf(f3308,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3306]) ).
thf(f3312,plain,
( ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3308]) ).
thf(f3314,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3312]) ).
thf(f3317,plain,
( $false
= ( 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
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3314]) ).
thf(f3320,plain,
( ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3317]) ).
thf(f3321,plain,
binunionE = $true,
inference(imp_proxy_clausification,[],[f3317]) ).
thf(f3323,plain,
spl0_272,
inference(avatar_split_clause,[],[f3321,f2047]) ).
thf(f3324,plain,
( ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3320]) ).
thf(f3327,plain,
( $false
= ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3324]) ).
thf(f3329,plain,
( $false
= ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3327]) ).
thf(f3333,plain,
( $false
= ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3329]) ).
thf(f3336,plain,
( $false
= ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3333]) ).
thf(f3338,plain,
( $false
= ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3336]) ).
thf(f3341,plain,
( $false
= ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3338]) ).
thf(f3345,plain,
( ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3341]) ).
thf(f3347,plain,
( ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3345]) ).
thf(f3350,plain,
( $false
= ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3347]) ).
thf(f3353,plain,
( $false
= ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3350]) ).
thf(f3357,plain,
( ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3353]) ).
thf(f3359,plain,
( ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3357]) ).
thf(f3363,plain,
( ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3359]) ).
thf(f3366,plain,
( ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3363]) ).
thf(f3368,plain,
( ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3366]) ).
thf(f3372,plain,
( $false
= ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3368]) ).
thf(f3374,plain,
( $false
= ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3372]) ).
thf(f3377,plain,
( ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3374]) ).
thf(f3381,plain,
( ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3377]) ).
thf(f3384,plain,
( ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3381]) ).
thf(f3387,plain,
( ( setminusLsub
=> ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3384]) ).
thf(f3389,plain,
( ( setminusSubset1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3387]) ).
thf(f3392,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f3389]) ).
thf(f3396,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( binunion @ Y2 @ Y1 )
@ ^ [Y3: $i] :
( ~ ( in @ Y3 @ Y2 )
| ~ ( in @ Y3 @ Y1 ) ) ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y3 ) )
=> ( ( ~ ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> Y3 ) )
=> Y3 ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f3392]) ).
thf(f3397,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ sK1
@ ( dsetconstr @ ( binunion @ Y1 @ Y0 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( ( in @ sK1 @ Y1 )
=> ( ~ ( in @ sK1 @ Y0 )
=> Y2 ) )
=> ( ( ~ ( in @ sK1 @ Y1 )
=> ( ( in @ sK1 @ Y0 )
=> Y2 ) )
=> Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3396]) ).
thf(f3398,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ sK1
@ ( dsetconstr @ ( binunion @ Y1 @ Y0 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( ( in @ sK1 @ Y1 )
=> ( ~ ( in @ sK1 @ Y0 )
=> Y2 ) )
=> ( ( ~ ( in @ sK1 @ Y1 )
=> ( ( in @ sK1 @ Y0 )
=> Y2 ) )
=> Y2 ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f3397]) ).
thf(f3399,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ sK1
@ ( dsetconstr @ ( binunion @ Y0 @ sK2 )
@ ^ [Y1: $i] :
( ~ ( in @ Y1 @ Y0 )
| ~ ( in @ Y1 @ sK2 ) ) ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( ( in @ sK1 @ Y0 )
=> ( ~ ( in @ sK1 @ sK2 )
=> Y1 ) )
=> ( ( ~ ( in @ sK1 @ Y0 )
=> ( ( in @ sK1 @ sK2 )
=> Y1 ) )
=> Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3398]) ).
thf(f3411,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ sK1
@ ( dsetconstr @ ( binunion @ Y0 @ sK2 )
@ ^ [Y1: $i] :
( ~ ( in @ Y1 @ Y0 )
| ~ ( in @ Y1 @ sK2 ) ) ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( ( in @ sK1 @ Y0 )
=> ( ~ ( in @ sK1 @ sK2 )
=> Y1 ) )
=> ( ( ~ ( in @ sK1 @ Y0 )
=> ( ( in @ sK1 @ sK2 )
=> Y1 ) )
=> Y1 ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f3399]) ).
thf(f3414,plain,
( $false
= ( ( in @ sK1
@ ( dsetconstr @ ( binunion @ sK3 @ sK2 )
@ ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK3 )
| ~ ( in @ Y0 @ sK2 ) ) ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( ( ( in @ sK1 @ sK3 )
=> ( ~ ( in @ sK1 @ sK2 )
=> Y0 ) )
=> ( ( ~ ( in @ sK1 @ sK3 )
=> ( ( in @ sK1 @ sK2 )
=> Y0 ) )
=> Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f3411]) ).
thf(f3415,plain,
( $false
= ( !! @ $o
@ ^ [Y0: $o] :
( ( ( in @ sK1 @ sK3 )
=> ( ~ ( in @ sK1 @ sK2 )
=> Y0 ) )
=> ( ( ~ ( in @ sK1 @ sK3 )
=> ( ( in @ sK1 @ sK2 )
=> Y0 ) )
=> Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f3414]) ).
thf(f3416,plain,
( ( in @ sK1
@ ( dsetconstr @ ( binunion @ sK3 @ sK2 )
@ ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK3 )
| ~ ( in @ Y0 @ sK2 ) ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f3414]) ).
thf(f3419,plain,
( $false
= ( ^ [Y0: $o] :
( ( ( in @ sK1 @ sK3 )
=> ( ~ ( in @ sK1 @ sK2 )
=> Y0 ) )
=> ( ( ~ ( in @ sK1 @ sK3 )
=> ( ( in @ sK1 @ sK2 )
=> Y0 ) )
=> Y0 ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f3415]) ).
thf(f3422,plain,
( ( ( ( in @ sK1 @ sK3 )
=> ( ~ ( in @ sK1 @ sK2 )
=> sK4 ) )
=> ( ( ~ ( in @ sK1 @ sK3 )
=> ( ( in @ sK1 @ sK2 )
=> sK4 ) )
=> sK4 ) )
= $false ),
inference(beta-eta_normalization,[],[f3419]) ).
thf(f3423,plain,
( ( ( ~ ( in @ sK1 @ sK3 )
=> ( ( in @ sK1 @ sK2 )
=> sK4 ) )
=> sK4 )
= $false ),
inference(imp_proxy_clausification,[],[f3422]) ).
thf(f3424,plain,
( $true
= ( ( in @ sK1 @ sK3 )
=> ( ~ ( in @ sK1 @ sK2 )
=> sK4 ) ) ),
inference(imp_proxy_clausification,[],[f3422]) ).
thf(f3425,plain,
( ( ( ~ ( in @ sK1 @ sK2 )
=> sK4 )
= $true )
| ( ( in @ sK1 @ sK3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f3424]) ).
thf(f3426,plain,
$false = sK4,
inference(imp_proxy_clausification,[],[f3423]) ).
thf(f3427,plain,
( $true
= ( ~ ( in @ sK1 @ sK3 )
=> ( ( in @ sK1 @ sK2 )
=> sK4 ) ) ),
inference(imp_proxy_clausification,[],[f3423]) ).
thf(f3428,plain,
( ( ( ~ ( in @ sK1 @ sK2 ) )
= $false )
| ( $true = sK4 )
| ( ( in @ sK1 @ sK3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f3425]) ).
thf(f3429,plain,
( ( $true
= ( ( in @ sK1 @ sK2 )
=> sK4 ) )
| ( ( ~ ( in @ sK1 @ sK3 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3427]) ).
thf(f3430,plain,
( ( $true = sK4 )
| ( ( in @ sK1 @ sK3 )
= $false )
| ( ( in @ sK1 @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f3428]) ).
thf(f3431,plain,
( ( ( ~ ( in @ sK1 @ sK3 ) )
= $false )
| ( $true = sK4 )
| ( $false
= ( in @ sK1 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f3429]) ).
thf(f3433,definition,
( spl0_487
<=> ( $true = sK4 ) ),
introduced(definition,[new_symbols(definition,[spl0_487])],[avatar_definition]) ).
thf(f3435,plain,
( ( $true = sK4 )
| ~ spl0_487 ),
inference(avatar_component_clause,[],[f3433]) ).
thf(f3437,definition,
( spl0_488
<=> ( ( in @ sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_488])],[avatar_definition]) ).
thf(f3438,plain,
( ( ( in @ sK1 @ sK2 )
!= $true )
| spl0_488 ),
inference(avatar_component_clause,[],[f3437]) ).
thf(f3439,plain,
( ( ( in @ sK1 @ sK2 )
= $true )
| ~ spl0_488 ),
inference(avatar_component_clause,[],[f3437]) ).
thf(f3441,definition,
( spl0_489
<=> ( ( in @ sK1 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl0_489])],[avatar_definition]) ).
thf(f3443,plain,
( ( ( in @ sK1 @ sK3 )
= $false )
| ~ spl0_489 ),
inference(avatar_component_clause,[],[f3441]) ).
thf(f3444,plain,
( spl0_487
| spl0_488
| spl0_489 ),
inference(avatar_split_clause,[],[f3430,f3441,f3437,f3433]) ).
thf(f3445,plain,
( ( $true = sK4 )
| ( ( in @ sK1 @ sK3 )
= $true )
| ( $false
= ( in @ sK1 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f3431]) ).
thf(f3447,definition,
( spl0_490
<=> ( ( in @ sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_490])],[avatar_definition]) ).
thf(f3449,plain,
( ( ( in @ sK1 @ sK3 )
= $true )
| ~ spl0_490 ),
inference(avatar_component_clause,[],[f3447]) ).
thf(f3451,definition,
( spl0_491
<=> ( $false
= ( in @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_491])],[avatar_definition]) ).
thf(f3453,plain,
( ( $false
= ( in @ sK1 @ sK2 ) )
| ~ spl0_491 ),
inference(avatar_component_clause,[],[f3451]) ).
thf(f3454,plain,
( spl0_487
| spl0_490
| spl0_491 ),
inference(avatar_split_clause,[],[f3445,f3451,f3447,f3433]) ).
thf(f3460,plain,
( ( $false = $true )
| ~ spl0_487 ),
inference(superposition,[],[f3435,f3426]) ).
thf(f3464,plain,
( $false
| ~ spl0_487 ),
inference(trivial_inequality_removal,[],[f3460]) ).
thf(f3465,plain,
~ spl0_487,
inference(avatar_contradiction_clause,[],[f3464]) ).
thf(f3749,plain,
( ( $false = $true )
| ~ spl0_269
| ~ spl0_272 ),
inference(forward_demodulation,[],[f2049,f2036]) ).
thf(f3750,plain,
( $false
| ~ spl0_269
| ~ spl0_272 ),
inference(trivial_inequality_removal,[],[f3749]) ).
thf(f3751,plain,
( ~ spl0_269
| ~ spl0_272 ),
inference(avatar_contradiction_clause,[],[f3750]) ).
thf(f4892,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_389 ),
inference(pi_proxy_clausification,[],[f2579]) ).
thf(f4893,plain,
( ! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ X1 ) ) ) )
= $true )
| ~ spl0_389 ),
inference(beta-eta_normalization,[],[f4892]) ).
thf(f4894,plain,
( ! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl0_389 ),
inference(pi_proxy_clausification,[],[f4893]) ).
thf(f4895,plain,
( ! [X2: $i,X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( Y0 @ X1 ) ) )
= $true )
| ~ spl0_389 ),
inference(beta-eta_normalization,[],[f4894]) ).
thf(f4896,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( Y0 @ X1 ) )
@ X3 )
= $true )
| ~ spl0_389 ),
inference(pi_proxy_clausification,[],[f4895]) ).
thf(f4897,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) )
=> ( X3 @ X1 ) ) )
| ~ spl0_389 ),
inference(beta-eta_normalization,[],[f4896]) ).
thf(f4898,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) ) )
| ( ( X3 @ X1 )
= $true ) )
| ~ spl0_389 ),
inference(imp_proxy_clausification,[],[f4897]) ).
thf(f4901,plain,
( ( $false = $true )
| ( ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK3 )
| ~ ( in @ Y0 @ sK2 ) )
@ sK1 )
= $true )
| ~ spl0_389 ),
inference(superposition,[],[f4898,f3416]) ).
thf(f4911,plain,
( ( ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK3 )
| ~ ( in @ Y0 @ sK2 ) )
@ sK1 )
= $true )
| ~ spl0_389 ),
inference(trivial_inequality_removal,[],[f4901]) ).
thf(f4912,plain,
( ( ( ~ ( in @ sK1 @ sK3 )
| ~ ( in @ sK1 @ sK2 ) )
= $true )
| ~ spl0_389 ),
inference(beta-eta_normalization,[],[f4911]) ).
thf(f4921,plain,
( ( ( ~ $true
| ~ ( in @ sK1 @ sK2 ) )
= $true )
| ~ spl0_389
| ~ spl0_490 ),
inference(forward_demodulation,[],[f4912,f3449]) ).
thf(f4922,plain,
( ( ( $false
| ~ ( in @ sK1 @ sK2 ) )
= $true )
| ~ spl0_389
| ~ spl0_490 ),
inference(boolean_simplification,[],[f4921]) ).
thf(f4923,plain,
( ( ( ~ ( in @ sK1 @ sK2 ) )
= $true )
| ~ spl0_389
| ~ spl0_490 ),
inference(boolean_simplification,[],[f4922]) ).
thf(f4928,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_389
| ~ spl0_488
| ~ spl0_490 ),
inference(forward_demodulation,[],[f4923,f3439]) ).
thf(f4929,plain,
( ( $false = $true )
| ~ spl0_389
| ~ spl0_488
| ~ spl0_490 ),
inference(boolean_simplification,[],[f4928]) ).
thf(f4930,plain,
( $false
| ~ spl0_389
| ~ spl0_488
| ~ spl0_490 ),
inference(trivial_inequality_removal,[],[f4929]) ).
thf(f4931,plain,
( ~ spl0_389
| ~ spl0_488
| ~ spl0_490 ),
inference(avatar_contradiction_clause,[],[f4930]) ).
thf(f4934,plain,
( ( $false = $true )
| ~ spl0_387
| ~ spl0_390 ),
inference(superposition,[],[f2570,f2583]) ).
thf(f4937,plain,
( $false
| ~ spl0_387
| ~ spl0_390 ),
inference(trivial_inequality_removal,[],[f4934]) ).
thf(f4938,plain,
( ~ spl0_387
| ~ spl0_390 ),
inference(avatar_contradiction_clause,[],[f4937]) ).
thf(f5213,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( in @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_29 ),
inference(pi_proxy_clausification,[],[f952]) ).
thf(f5214,plain,
( ! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) )
=> ( in @ Y0 @ X1 ) ) ) )
= $true )
| ~ spl0_29 ),
inference(beta-eta_normalization,[],[f5213]) ).
thf(f5215,plain,
( ! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) )
=> ( in @ Y0 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl0_29 ),
inference(pi_proxy_clausification,[],[f5214]) ).
thf(f5216,plain,
( ! [X2: $i,X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( in @ X2 @ X1 ) ) )
= $true )
| ~ spl0_29 ),
inference(beta-eta_normalization,[],[f5215]) ).
thf(f5217,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( in @ X2 @ X1 ) )
@ X3 )
= $true )
| ~ spl0_29 ),
inference(pi_proxy_clausification,[],[f5216]) ).
thf(f5218,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) )
=> ( in @ X2 @ X1 ) ) )
| ~ spl0_29 ),
inference(beta-eta_normalization,[],[f5217]) ).
thf(f5219,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( ( $false
= ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) )
| ( ( in @ X2 @ X1 )
= $true ) )
| ~ spl0_29 ),
inference(imp_proxy_clausification,[],[f5218]) ).
thf(f5229,plain,
( ( $true
= ( in @ sK1 @ ( binunion @ sK3 @ sK2 ) ) )
| ( $false = $true )
| ~ spl0_29 ),
inference(superposition,[],[f3416,f5219]) ).
thf(f5232,plain,
( ( $true
= ( in @ sK1 @ ( binunion @ sK3 @ sK2 ) ) )
| ~ spl0_29 ),
inference(trivial_inequality_removal,[],[f5229]) ).
thf(f5691,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binunion @ Y0 @ Y1 ) )
=> ( ( in @ Y2 @ Y1 )
| ( in @ Y2 @ Y0 ) ) ) ) )
@ X1 )
= $true )
| ~ spl0_270 ),
inference(pi_proxy_clausification,[],[f2040]) ).
thf(f5692,plain,
( ! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( binunion @ X1 @ Y0 ) )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y1 @ X1 ) ) ) ) )
= $true )
| ~ spl0_270 ),
inference(beta-eta_normalization,[],[f5691]) ).
thf(f5693,plain,
( ! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( binunion @ X1 @ Y0 ) )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y1 @ X1 ) ) ) )
@ X2 )
= $true )
| ~ spl0_270 ),
inference(pi_proxy_clausification,[],[f5692]) ).
thf(f5694,plain,
( ! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binunion @ X1 @ X2 ) )
=> ( ( in @ Y0 @ X2 )
| ( in @ Y0 @ X1 ) ) ) )
= $true )
| ~ spl0_270 ),
inference(beta-eta_normalization,[],[f5693]) ).
thf(f5747,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( binunion @ X1 @ X2 ) )
=> ( ( in @ Y0 @ X2 )
| ( in @ Y0 @ X1 ) ) )
@ X3 )
= $true )
| ~ spl0_270 ),
inference(pi_proxy_clausification,[],[f5694]) ).
thf(f5748,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ( ( in @ X3 @ X2 )
| ( in @ X3 @ X1 ) ) )
= $true )
| ~ spl0_270 ),
inference(beta-eta_normalization,[],[f5747]) ).
thf(f5749,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
= $false )
| ( ( ( in @ X3 @ X2 )
| ( in @ X3 @ X1 ) )
= $true ) )
| ~ spl0_270 ),
inference(imp_proxy_clausification,[],[f5748]) ).
thf(f5750,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
= $false )
| ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X2 )
= $true ) )
| ~ spl0_270 ),
inference(or_proxy_clausification,[],[f5749]) ).
thf(f5753,plain,
( ( ( in @ sK1 @ sK2 )
= $true )
| ( $false = $true )
| ( ( in @ sK1 @ sK3 )
= $true )
| ~ spl0_29
| ~ spl0_270 ),
inference(superposition,[],[f5750,f5232]) ).
thf(f5778,plain,
( ( ( in @ sK1 @ sK3 )
= $true )
| ( ( in @ sK1 @ sK2 )
= $true )
| ~ spl0_29
| ~ spl0_270 ),
inference(trivial_inequality_removal,[],[f5753]) ).
thf(f5784,plain,
( ( ( in @ sK1 @ sK3 )
= $true )
| ~ spl0_29
| ~ spl0_270
| spl0_488 ),
inference(forward_subsumption_resolution,[],[f5778,f3438]) ).
thf(f5788,plain,
( ( $false = $true )
| ~ spl0_29
| ~ spl0_270
| spl0_488
| ~ spl0_489 ),
inference(forward_demodulation,[],[f5784,f3443]) ).
thf(f5789,plain,
( $false
| ~ spl0_29
| ~ spl0_270
| spl0_488
| ~ spl0_489 ),
inference(trivial_inequality_removal,[],[f5788]) ).
thf(f5790,plain,
( ~ spl0_29
| ~ spl0_270
| spl0_488
| ~ spl0_489 ),
inference(avatar_contradiction_clause,[],[f5789]) ).
thf(f5793,plain,
( ( $false = $true )
| ~ spl0_30
| ~ spl0_31 ),
inference(superposition,[],[f961,f956]) ).
thf(f5797,plain,
( $false
| ~ spl0_30
| ~ spl0_31 ),
inference(trivial_inequality_removal,[],[f5793]) ).
thf(f5798,plain,
( ~ spl0_30
| ~ spl0_31 ),
inference(avatar_contradiction_clause,[],[f5797]) ).
thf(f5818,plain,
( ( $false = $true )
| ~ spl0_488
| ~ spl0_491 ),
inference(forward_demodulation,[],[f3439,f3453]) ).
thf(f5819,plain,
( $false
| ~ spl0_488
| ~ spl0_491 ),
inference(trivial_inequality_removal,[],[f5818]) ).
thf(f5820,plain,
( ~ spl0_488
| ~ spl0_491 ),
inference(avatar_contradiction_clause,[],[f5819]) ).
cnf(s15,plain,
( spl0_29
| spl0_30 ),
inference(sat_conversion,[],[f957]) ).
cnf(s137,plain,
( spl0_269
| spl0_270 ),
inference(sat_conversion,[],[f2041]) ).
cnf(s200,plain,
( spl0_389
| spl0_390 ),
inference(sat_conversion,[],[f2584]) ).
cnf(s264,plain,
spl0_31,
inference(sat_conversion,[],[f3058]) ).
cnf(s265,plain,
spl0_387,
inference(sat_conversion,[],[f3063]) ).
cnf(s351,plain,
spl0_272,
inference(sat_conversion,[],[f3323]) ).
cnf(s376,plain,
( spl0_487
| spl0_488
| spl0_489 ),
inference(sat_conversion,[],[f3444]) ).
cnf(s377,plain,
( spl0_487
| spl0_490
| spl0_491 ),
inference(sat_conversion,[],[f3454]) ).
cnf(s380,plain,
~ spl0_487,
inference(sat_conversion,[],[f3465]) ).
cnf(s435,plain,
( ~ spl0_269
| ~ spl0_272 ),
inference(sat_conversion,[],[f3751]) ).
cnf(s495,plain,
( ~ spl0_389
| ~ spl0_488
| ~ spl0_490 ),
inference(sat_conversion,[],[f4931]) ).
cnf(s497,plain,
( ~ spl0_387
| ~ spl0_390 ),
inference(sat_conversion,[],[f4938]) ).
cnf(s520,plain,
( ~ spl0_29
| ~ spl0_270
| spl0_488
| ~ spl0_489 ),
inference(sat_conversion,[],[f5790]) ).
cnf(s522,plain,
( ~ spl0_30
| ~ spl0_31 ),
inference(sat_conversion,[],[f5798]) ).
cnf(s523,plain,
( ~ spl0_488
| ~ spl0_491 ),
inference(sat_conversion,[],[f5820]) ).
cnf(s528,plain,
( spl0_490
| spl0_491 ),
inference(rat,[],[s377,s380]) ).
cnf(s529,plain,
( spl0_488
| spl0_489 ),
inference(rat,[],[s376,s380]) ).
cnf(s543,plain,
~ spl0_269,
inference(rat,[],[s435,s351]) ).
cnf(s588,plain,
~ spl0_390,
inference(rat,[],[s497,s265]) ).
cnf(s589,plain,
~ spl0_30,
inference(rat,[],[s522,s264]) ).
cnf(s612,plain,
spl0_389,
inference(rat,[],[s200,s588]) ).
cnf(s628,plain,
spl0_270,
inference(rat,[],[s137,s543]) ).
cnf(s660,plain,
spl0_29,
inference(rat,[],[s15,s589]) ).
cnf(s665,plain,
spl0_488,
inference(rat,[],[s520,s529,s628,s660]) ).
cnf(s666,plain,
~ spl0_491,
inference(rat,[],[s523,s665]) ).
cnf(s667,plain,
~ spl0_490,
inference(rat,[],[s495,s612,s665]) ).
cnf(s668,plain,
$false,
inference(rat,[],[s528,s666,s667]) ).
thf(f5840,plain,
$false,
inference(avatar_sat_refutation,[],[s668]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.10/0.20 % Computer : n011.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:57:46 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.21/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.63/0.43 % (134774)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.63/0.43 % (134781)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=44093036:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.63/0.43 % (134780)lrs+10_16_si=on:nwc=1.5:random_seed=1064855850:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.63/0.43 % (134779)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4127861712:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.63/0.43 % (134782)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3760835787:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.63/0.43 % (134785)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.63/0.43 % (134785)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.63/0.43 % (134783)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=35513191:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.63/0.43 % (134781)Instruction limit reached!
% 0.63/0.43 % (134781)------------------------------
% 0.63/0.43 % (134781)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.43 % (134781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.43 % (134781)CaDiCaL version: 2.1.3
% 0.63/0.43 % (134781)Termination reason: Instruction limit
% 0.63/0.43 % (134781)Termination phase: shuffling
% 0.63/0.43 % (134781)Time elapsed: 0.002 s
% 0.63/0.43 % (134781)Peak memory usage: 9 MB
% 0.63/0.43 % (134781)Instructions burned: 4 (million)
% 0.63/0.43 % (134785)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3184763945:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.63/0.43 % (134780)Instruction limit reached!
% 0.63/0.43 % (134780)------------------------------
% 0.63/0.43 % (134780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.43 % (134780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.43 % (134780)CaDiCaL version: 2.1.3
% 0.63/0.43 % (134780)Termination reason: Instruction limit
% 0.63/0.43 % (134780)Termination phase: Property scanning
% 0.63/0.43 % (134780)Time elapsed: 0.008 s
% 0.63/0.43 % (134780)Peak memory usage: 10 MB
% 0.63/0.43 % (134780)Instructions burned: 18 (million)
% 0.63/0.43 % (134783)Instruction limit reached!
% 0.63/0.43 % (134783)------------------------------
% 0.63/0.43 % (134783)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.43 % (134783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.43 % (134783)CaDiCaL version: 2.1.3
% 0.63/0.43 % (134783)Termination reason: Instruction limit
% 0.63/0.43 % (134783)Termination phase: Preprocessing 3
% 0.63/0.43 % (134783)Time elapsed: 0.012 s
% 0.63/0.43 % (134783)Peak memory usage: 11 MB
% 0.63/0.43 % (134783)Instructions burned: 26 (million)
% 0.63/0.43 % (134784)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1671777463:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.63/0.43 % (134794)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.63/0.43 % (134793)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3542358846:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.63/0.43 % (134794)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1924449036:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.63/0.43 % (134793)Instruction limit reached!
% 0.63/0.43 % (134793)------------------------------
% 0.63/0.43 % (134793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.43 % (134793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.43 % (134793)CaDiCaL version: 2.1.3
% 0.63/0.43 % (134793)Termination reason: Instruction limit
% 1.32/0.50 % (134793)Termination phase: shuffling
% 1.32/0.50 % (134793)Time elapsed: 0.003 s
% 1.32/0.50 % (134793)Peak memory usage: 10 MB
% 1.32/0.50 % (134793)Instructions burned: 5 (million)
% 1.32/0.50 % (134794)Instruction limit reached!
% 1.32/0.50 % (134794)------------------------------
% 1.32/0.50 % (134794)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.50 % (134794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.50 % (134794)CaDiCaL version: 2.1.3
% 1.32/0.50 % (134794)Termination reason: Instruction limit
% 1.32/0.50 % (134794)Termination phase: shuffling
% 1.32/0.50 % (134794)Time elapsed: 0.003 s
% 1.32/0.50 % (134794)Peak memory usage: 10 MB
% 1.32/0.50 % (134794)Instructions burned: 8 (million)
% 1.32/0.50 % (134779)Instruction limit reached!
% 1.32/0.50 % (134779)------------------------------
% 1.32/0.50 % (134779)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.50 % (134779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.50 % (134779)CaDiCaL version: 2.1.3
% 1.32/0.50 % (134779)Termination reason: Instruction limit
% 1.32/0.50 % (134779)Termination phase: Saturation
% 1.32/0.50 % (134779)Time elapsed: 0.040 s
% 1.32/0.50 % (134779)Peak memory usage: 13 MB
% 1.32/0.50 % (134779)Instructions burned: 88 (million)
% 1.32/0.50 % (134791)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1561450236:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.32/0.50 % (134791)Instruction limit reached!
% 1.32/0.50 % (134791)------------------------------
% 1.32/0.50 % (134791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.50 % (134791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.50 % (134791)CaDiCaL version: 2.1.3
% 1.32/0.50 % (134791)Termination reason: Instruction limit
% 1.32/0.50 % (134791)Termination phase: shuffling
% 1.32/0.50 % (134791)Time elapsed: 0.003 s
% 1.32/0.50 % (134791)Peak memory usage: 10 MB
% 1.32/0.50 % (134791)Instructions burned: 6 (million)
% 1.32/0.50 % (134798)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2176814584:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.32/0.50 % (134798)Instruction limit reached!
% 1.32/0.50 % (134798)------------------------------
% 1.32/0.50 % (134798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.50 % (134798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.50 % (134798)CaDiCaL version: 2.1.3
% 1.32/0.50 % (134798)Termination reason: Instruction limit
% 1.32/0.50 % (134798)Termination phase: shuffling
% 1.32/0.50 % (134798)Time elapsed: 0.006 s
% 1.32/0.50 % (134798)Peak memory usage: 10 MB
% 1.32/0.50 % (134798)Instructions burned: 13 (million)
% 1.32/0.50 % (134799)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.32/0.50 % (134799)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.32/0.50 % (134801)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=4031129783:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.32/0.50 % (134799)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=50754160:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.32/0.50 % (134802)lrs+10_1_si=on:cs=on:random_seed=734541614:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.32/0.50 % (134802)Instruction limit reached!
% 1.32/0.50 % (134802)------------------------------
% 1.32/0.50 % (134802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.50 % (134802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.50 % (134802)CaDiCaL version: 2.1.3
% 1.32/0.50 % (134802)Termination reason: Instruction limit
% 1.32/0.50 % (134802)Termination phase: shuffling
% 1.32/0.50 % (134802)Time elapsed: 0.004 s
% 1.32/0.50 % (134802)Peak memory usage: 10 MB
% 1.32/0.50 % (134802)Instructions burned: 9 (million)
% 1.32/0.50 % (134804)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.32/0.56 % (134804)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2201715095:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.32/0.56 % (134785)Instruction limit reached!
% 1.32/0.56 % (134785)------------------------------
% 1.32/0.56 % (134785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.56 % (134785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.56 % (134785)CaDiCaL version: 2.1.3
% 1.32/0.56 % (134785)Termination reason: Instruction limit
% 1.32/0.56 % (134785)Termination phase: Saturation
% 1.32/0.56 % (134785)Time elapsed: 0.072 s
% 1.32/0.56 % (134785)Peak memory usage: 14 MB
% 1.32/0.56 % (134785)Instructions burned: 167 (million)
% 1.32/0.56 % (134784)Instruction limit reached!
% 1.32/0.56 % (134784)------------------------------
% 1.32/0.56 % (134784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.56 % (134784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.56 % (134784)CaDiCaL version: 2.1.3
% 1.32/0.56 % (134784)Termination reason: Instruction limit
% 1.32/0.56 % (134784)Termination phase: Saturation
% 1.32/0.56 % (134784)Time elapsed: 0.063 s
% 1.32/0.56 % (134784)Peak memory usage: 13 MB
% 1.32/0.56 % (134784)Instructions burned: 75 (million)
% 1.32/0.56 % (134804)Instruction limit reached!
% 1.32/0.56 % (134804)------------------------------
% 1.32/0.56 % (134804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.56 % (134804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.56 % (134804)CaDiCaL version: 2.1.3
% 1.32/0.56 % (134804)Termination reason: Instruction limit
% 1.32/0.56 % (134804)Termination phase: shuffling
% 1.32/0.56 % (134804)Time elapsed: 0.001 s
% 1.32/0.56 % (134804)Peak memory usage: 10 MB
% 1.32/0.56 % (134804)Instructions burned: 2 (million)
% 1.32/0.56 % (134799)Instruction limit reached!
% 1.32/0.56 % (134799)------------------------------
% 1.32/0.56 % (134799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.56 % (134799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.56 % (134799)CaDiCaL version: 2.1.3
% 1.32/0.56 % (134799)Termination reason: Instruction limit
% 1.32/0.56 % (134799)Termination phase: Property scanning
% 1.32/0.56 % (134799)Time elapsed: 0.023 s
% 1.32/0.56 % (134799)Peak memory usage: 11 MB
% 1.32/0.56 % (134799)Instructions burned: 29 (million)
% 1.32/0.56 % (134808)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3284397948:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.32/0.56 % (134810)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2337619570:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.32/0.56 % (134811)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=392876397:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.32/0.56 % (134801)Instruction limit reached!
% 1.32/0.56 % (134801)------------------------------
% 1.32/0.56 % (134801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.56 % (134801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.56 % (134801)CaDiCaL version: 2.1.3
% 1.32/0.56 % (134801)Termination reason: Instruction limit
% 1.32/0.56 % (134801)Termination phase: Saturation
% 1.32/0.56 % (134801)Time elapsed: 0.037 s
% 1.32/0.56 % (134801)Peak memory usage: 13 MB
% 1.32/0.56 % (134801)Instructions burned: 86 (million)
% 1.32/0.56 % (134812)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1987968619:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.32/0.56 % (134812)Instruction limit reached!
% 1.32/0.56 % (134812)------------------------------
% 1.32/0.56 % (134812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.56 % (134812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.56 % (134812)CaDiCaL version: 2.1.3
% 1.32/0.56 % (134812)Termination reason: Instruction limit
% 1.32/0.56 % (134812)Termination phase: Property scanning
% 1.32/0.56 % (134812)Time elapsed: 0.006 s
% 1.32/0.56 % (134812)Peak memory usage: 10 MB
% 1.32/0.56 % (134812)Instructions burned: 14 (million)
% 1.32/0.56 % (134811)Instruction limit reached!
% 1.32/0.56 % (134811)------------------------------
% 1.93/0.62 % (134811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.62 % (134811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.62 % (134811)CaDiCaL version: 2.1.3
% 1.93/0.62 % (134811)Termination reason: Instruction limit
% 1.93/0.62 % (134811)Termination phase: Preprocessing 3
% 1.93/0.62 % (134811)Time elapsed: 0.012 s
% 1.93/0.62 % (134811)Peak memory usage: 11 MB
% 1.93/0.62 % (134811)Instructions burned: 25 (million)
% 1.93/0.62 % (134808)Instruction limit reached!
% 1.93/0.62 % (134808)------------------------------
% 1.93/0.62 % (134808)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.62 % (134808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.62 % (134808)CaDiCaL version: 2.1.3
% 1.93/0.62 % (134808)Termination reason: Instruction limit
% 1.93/0.62 % (134808)Termination phase: Property scanning
% 1.93/0.62 % (134808)Time elapsed: 0.018 s
% 1.93/0.62 % (134808)Peak memory usage: 12 MB
% 1.93/0.62 % (134808)Instructions burned: 39 (million)
% 1.93/0.62 % (134813)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2668206066:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.93/0.62 % (134820)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=767282788:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.93/0.62 % (134818)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3172887431:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.93/0.62 % (134821)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=166441676:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.93/0.62 % (134820)Instruction limit reached!
% 1.93/0.62 % (134820)------------------------------
% 1.93/0.62 % (134820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.62 % (134820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.62 % (134820)CaDiCaL version: 2.1.3
% 1.93/0.62 % (134820)Termination reason: Instruction limit
% 1.93/0.62 % (134820)Termination phase: Property scanning
% 1.93/0.62 % (134820)Time elapsed: 0.011 s
% 1.93/0.62 % (134820)Peak memory usage: 10 MB
% 1.93/0.62 % (134820)Instructions burned: 26 (million)
% 1.93/0.62 % (134818)Instruction limit reached!
% 1.93/0.62 % (134818)------------------------------
% 1.93/0.62 % (134818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.62 % (134818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.62 % (134818)CaDiCaL version: 2.1.3
% 1.93/0.62 % (134818)Termination reason: Instruction limit
% 1.93/0.62 % (134818)Termination phase: Property scanning
% 1.93/0.62 % (134818)Time elapsed: 0.014 s
% 1.93/0.62 % (134818)Peak memory usage: 10 MB
% 1.93/0.62 % (134818)Instructions burned: 16 (million)
% 1.93/0.62 % (134819)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=795243104:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.93/0.62 % (134819)Instruction limit reached!
% 1.93/0.62 % (134819)------------------------------
% 1.93/0.62 % (134819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.62 % (134819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.62 % (134819)CaDiCaL version: 2.1.3
% 1.93/0.62 % (134819)Termination reason: Instruction limit
% 1.93/0.62 % (134819)Termination phase: shuffling
% 1.93/0.62 % (134819)Time elapsed: 0.002 s
% 1.93/0.62 % (134819)Peak memory usage: 10 MB
% 1.93/0.62 % (134819)Instructions burned: 2 (million)
% 1.93/0.62 % (134821)Instruction limit reached!
% 1.93/0.62 % (134821)------------------------------
% 1.93/0.62 % (134821)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.62 % (134821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.62 % (134821)CaDiCaL version: 2.1.3
% 1.93/0.62 % (134821)Termination reason: Instruction limit
% 1.93/0.62 % (134821)Termination phase: Property scanning
% 1.93/0.62 % (134821)Time elapsed: 0.020 s
% 1.93/0.62 % (134821)Peak memory usage: 10 MB
% 1.93/0.62 % (134821)Instructions burned: 23 (million)
% 1.93/0.62 % (134826)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2263529838:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.93/0.62 % (134827)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.58/0.71 % (134827)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.58/0.71 % (134827)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=1035858695:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.58/0.71 % (134829)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.58/0.71 % (134826)Instruction limit reached!
% 2.58/0.71 % (134826)------------------------------
% 2.58/0.71 % (134826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.71 % (134826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.71 % (134826)CaDiCaL version: 2.1.3
% 2.58/0.71 % (134826)Termination reason: Instruction limit
% 2.58/0.71 % (134826)Termination phase: Property scanning
% 2.58/0.71 % (134826)Time elapsed: 0.028 s
% 2.58/0.71 % (134826)Peak memory usage: 12 MB
% 2.58/0.71 % (134826)Instructions burned: 61 (million)
% 2.58/0.71 % (134831)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=984914754:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.58/0.71 % (134829)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=2915637560:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.58/0.71 % (134827)Instruction limit reached!
% 2.58/0.71 % (134827)------------------------------
% 2.58/0.71 % (134827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.71 % (134827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.71 % (134827)CaDiCaL version: 2.1.3
% 2.58/0.71 % (134827)Termination reason: Instruction limit
% 2.58/0.71 % (134827)Termination phase: shuffling
% 2.58/0.71 % (134827)Time elapsed: 0.013 s
% 2.58/0.71 % (134827)Peak memory usage: 10 MB
% 2.58/0.71 % (134827)Instructions burned: 14 (million)
% 2.58/0.71 % (134829)Instruction limit reached!
% 2.58/0.71 % (134829)------------------------------
% 2.58/0.71 % (134829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.71 % (134829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.71 % (134829)CaDiCaL version: 2.1.3
% 2.58/0.71 % (134829)Termination reason: Instruction limit
% 2.58/0.71 % (134829)Termination phase: shuffling
% 2.58/0.71 % (134829)Time elapsed: 0.008 s
% 2.58/0.71 % (134829)Peak memory usage: 10 MB
% 2.58/0.71 % (134829)Instructions burned: 10 (million)
% 2.58/0.71 % (134831)Instruction limit reached!
% 2.58/0.71 % (134831)------------------------------
% 2.58/0.71 % (134831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.71 % (134831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.71 % (134831)CaDiCaL version: 2.1.3
% 2.58/0.71 % (134831)Termination reason: Instruction limit
% 2.58/0.71 % (134831)Termination phase: Property scanning
% 2.58/0.71 % (134831)Time elapsed: 0.013 s
% 2.58/0.71 % (134831)Peak memory usage: 10 MB
% 2.58/0.71 % (134831)Instructions burned: 31 (million)
% 2.58/0.71 % (134833)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=4088452031:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.58/0.71 % (134833)Instruction limit reached!
% 2.58/0.71 % (134833)------------------------------
% 2.58/0.71 % (134833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.71 % (134833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.71 % (134833)CaDiCaL version: 2.1.3
% 2.58/0.71 % (134833)Termination reason: Instruction limit
% 2.58/0.71 % (134833)Termination phase: shuffling
% 2.58/0.71 % (134833)Time elapsed: 0.004 s
% 2.58/0.71 % (134833)Peak memory usage: 10 MB
% 2.58/0.71 % (134833)Instructions burned: 8 (million)
% 2.58/0.71 % (134836)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1000224609:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.58/0.71 % (134840)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3578656880:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.58/0.77 % (134837)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2674971579:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.58/0.77 % (134836)Instruction limit reached!
% 2.58/0.77 % (134836)------------------------------
% 2.58/0.77 % (134836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.77 % (134836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.77 % (134836)CaDiCaL version: 2.1.3
% 2.58/0.77 % (134836)Termination reason: Instruction limit
% 2.58/0.77 % (134836)Termination phase: Property scanning
% 2.58/0.77 % (134836)Time elapsed: 0.018 s
% 2.58/0.77 % (134836)Peak memory usage: 10 MB
% 2.58/0.77 % (134836)Instructions burned: 25 (million)
% 2.58/0.77 % (134838)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1021879122:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.58/0.77 % (134837)Instruction limit reached!
% 2.58/0.77 % (134837)------------------------------
% 2.58/0.77 % (134837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.77 % (134837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.77 % (134837)CaDiCaL version: 2.1.3
% 2.58/0.77 % (134837)Termination reason: Instruction limit
% 2.58/0.77 % (134837)Termination phase: Property scanning
% 2.58/0.77 % (134837)Time elapsed: 0.022 s
% 2.58/0.77 % (134837)Peak memory usage: 10 MB
% 2.58/0.77 % (134837)Instructions burned: 20 (million)
% 2.58/0.77 % (134810)Instruction limit reached!
% 2.58/0.77 % (134810)------------------------------
% 2.58/0.77 % (134810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.77 % (134810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.77 % (134810)CaDiCaL version: 2.1.3
% 2.58/0.77 % (134810)Termination reason: Instruction limit
% 2.58/0.77 % (134810)Termination phase: Saturation
% 2.58/0.77 % (134810)Time elapsed: 0.171 s
% 2.58/0.77 % (134810)Peak memory usage: 13 MB
% 2.58/0.77 % (134810)Instructions burned: 249 (million)
% 2.58/0.77 % (134845)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2475271969:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.58/0.77 % (134846)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3239887931:i=42:hud=10:rtra=on_2996 on theBenchmark for (2996ds/42Mi)
% 2.58/0.77 % (134847)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.58/0.77 % (134847)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2180961056:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2996 on theBenchmark for (2996ds/7Mi)
% 2.58/0.77 % (134847)Instruction limit reached!
% 2.58/0.77 % (134847)------------------------------
% 2.58/0.77 % (134847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.77 % (134847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.77 % (134847)CaDiCaL version: 2.1.3
% 2.58/0.77 % (134847)Termination reason: Instruction limit
% 2.58/0.77 % (134847)Termination phase: shuffling
% 2.58/0.77 % (134847)Time elapsed: 0.004 s
% 2.58/0.77 % (134847)Peak memory usage: 10 MB
% 2.58/0.77 % (134847)Instructions burned: 8 (million)
% 2.58/0.77 % (134840)Instruction limit reached!
% 2.58/0.77 % (134840)------------------------------
% 2.58/0.77 % (134840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.77 % (134840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.77 % (134840)CaDiCaL version: 2.1.3
% 2.58/0.77 % (134840)Termination reason: Instruction limit
% 2.58/0.77 % (134840)Termination phase: Saturation
% 2.58/0.77 % (134840)Time elapsed: 0.060 s
% 2.58/0.77 % (134840)Peak memory usage: 13 MB
% 2.58/0.77 % (134840)Instructions burned: 144 (million)
% 2.58/0.77 % (134846)Instruction limit reached!
% 2.58/0.77 % (134846)------------------------------
% 2.58/0.77 % (134846)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.77 % (134846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.77 % (134846)CaDiCaL version: 2.1.3
% 2.58/0.77 % (134846)Termination reason: Instruction limit
% 2.58/0.77 % (134846)Termination phase: Property scanning
% 3.07/0.84 % (134846)Time elapsed: 0.018 s
% 3.07/0.84 % (134846)Peak memory usage: 11 MB
% 3.07/0.84 % (134846)Instructions burned: 43 (million)
% 3.07/0.84 % (134851)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2652643422:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 3.07/0.84 % (134852)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=1490121756:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 3.07/0.84 % (134853)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 3.07/0.84 % (134853)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=941740782:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 3.07/0.84 % (134853)Instruction limit reached!
% 3.07/0.84 % (134853)------------------------------
% 3.07/0.84 % (134853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.84 % (134853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.84 % (134853)CaDiCaL version: 2.1.3
% 3.07/0.84 % (134853)Termination reason: Instruction limit
% 3.07/0.84 % (134853)Termination phase: shuffling
% 3.07/0.84 % (134853)Time elapsed: 0.003 s
% 3.07/0.84 % (134853)Peak memory usage: 10 MB
% 3.07/0.84 % (134853)Instructions burned: 7 (million)
% 3.07/0.84 % (134782)Instruction limit reached!
% 3.07/0.84 % (134782)------------------------------
% 3.07/0.84 % (134782)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.84 % (134782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.84 % (134782)CaDiCaL version: 2.1.3
% 3.07/0.84 % (134782)Termination reason: Instruction limit
% 3.07/0.84 % (134782)Termination phase: Saturation
% 3.07/0.84 % (134782)Time elapsed: 0.336 s
% 3.07/0.84 % (134782)Peak memory usage: 18 MB
% 3.07/0.84 % (134782)Instructions burned: 636 (million)
% 3.07/0.84 % (134857)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3435558496:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 3.07/0.84 % (134857)Instruction limit reached!
% 3.07/0.84 % (134857)------------------------------
% 3.07/0.84 % (134857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.84 % (134857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.84 % (134857)CaDiCaL version: 2.1.3
% 3.07/0.84 % (134857)Termination reason: Instruction limit
% 3.07/0.84 % (134857)Termination phase: Property scanning
% 3.07/0.84 % (134857)Time elapsed: 0.009 s
% 3.07/0.84 % (134857)Peak memory usage: 10 MB
% 3.07/0.84 % (134857)Instructions burned: 22 (million)
% 3.07/0.84 % (134858)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2087949624:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 3.07/0.84 % (134858)Instruction limit reached!
% 3.07/0.84 % (134858)------------------------------
% 3.07/0.84 % (134858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.84 % (134858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.84 % (134858)CaDiCaL version: 2.1.3
% 3.07/0.84 % (134858)Termination reason: Instruction limit
% 3.07/0.84 % (134858)Termination phase: Property scanning
% 3.07/0.84 % (134858)Time elapsed: 0.008 s
% 3.07/0.84 % (134858)Peak memory usage: 10 MB
% 3.07/0.84 % (134858)Instructions burned: 20 (million)
% 3.07/0.84 % (134845)Instruction limit reached!
% 3.07/0.84 % (134845)------------------------------
% 3.07/0.84 % (134845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.84 % (134845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.84 % (134845)CaDiCaL version: 2.1.3
% 3.07/0.84 % (134845)Termination reason: Instruction limit
% 3.07/0.84 % (134845)Termination phase: Saturation
% 3.07/0.84 % (134845)Time elapsed: 0.098 s
% 3.07/0.84 % (134845)Peak memory usage: 13 MB
% 3.07/0.84 % (134845)Instructions burned: 193 (million)
% 3.07/0.84 % (134860)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=3728966698:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 3.07/0.84 % (134862)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3085034112:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2995 on theBenchmark for (2995ds/853Mi)
% 3.07/0.84 % (134863)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=1216867115:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2995 on theBenchmark for (2995ds/45Mi)
% 3.07/0.84 % (134813)Instruction limit reached!
% 3.07/0.84 % (134813)------------------------------
% 3.07/0.84 % (134813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.84 % (134813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.84 % (134813)CaDiCaL version: 2.1.3
% 3.07/0.84 % (134813)Termination reason: Instruction limit
% 3.07/0.84 % (134813)Termination phase: Saturation
% 3.07/0.84 % (134813)Time elapsed: 0.282 s
% 3.07/0.84 % (134813)Peak memory usage: 14 MB
% 3.07/0.84 % (134813)Instructions burned: 327 (million)
% 3.07/0.84 % (134863)Instruction limit reached!
% 3.07/0.84 % (134863)------------------------------
% 3.07/0.84 % (134863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.84 % (134863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.84 % (134863)CaDiCaL version: 2.1.3
% 3.07/0.84 % (134863)Termination reason: Instruction limit
% 3.07/0.84 % (134863)Termination phase: Property scanning
% 3.07/0.84 % (134863)Time elapsed: 0.022 s
% 3.07/0.84 % (134863)Peak memory usage: 12 MB
% 3.07/0.84 % (134863)Instructions burned: 46 (million)
% 3.07/0.84 % (134852)Instruction limit reached!
% 3.07/0.84 % (134852)------------------------------
% 3.07/0.84 % (134852)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.84 % (134852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.84 % (134852)CaDiCaL version: 2.1.3
% 3.07/0.84 % (134852)Termination reason: Instruction limit
% 3.07/0.84 % (134852)Termination phase: Saturation
% 3.07/0.84 % (134852)Time elapsed: 0.104 s
% 3.07/0.84 % (134852)Peak memory usage: 13 MB
% 3.07/0.84 % (134852)Instructions burned: 169 (million)
% 3.07/0.84 % (134851)Instruction limit reached!
% 3.07/0.84 % (134851)------------------------------
% 3.07/0.84 % (134851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.84 % (134851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.84 % (134851)CaDiCaL version: 2.1.3
% 3.07/0.84 % (134851)Termination reason: Instruction limit
% 3.07/0.84 % (134851)Termination phase: Saturation
% 3.07/0.84 % (134851)Time elapsed: 0.115 s
% 3.07/0.84 % (134851)Peak memory usage: 14 MB
% 3.07/0.84 % (134851)Instructions burned: 181 (million)
% 3.07/0.84 % (134868)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=1826188288:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2995 on theBenchmark for (2995ds/21Mi)
% 3.07/0.84 % (134869)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.07/0.84 % (134869)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=1235356957:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/200Mi)
% 3.07/0.84 % (134868)Instruction limit reached!
% 3.07/0.84 % (134868)------------------------------
% 3.07/0.84 % (134868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.84 % (134868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.84 % (134868)CaDiCaL version: 2.1.3
% 3.07/0.84 % (134868)Termination reason: Instruction limit
% 3.07/0.84 % (134868)Termination phase: Property scanning
% 3.07/0.84 % (134868)Time elapsed: 0.010 s
% 3.07/0.84 % (134868)Peak memory usage: 10 MB
% 3.07/0.84 % (134868)Instructions burned: 23 (million)
% 3.07/0.84 % (134867)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=716552399:i=480:rtra=on_2995 on theBenchmark for (2995ds/480Mi)
% 3.07/0.84 % (134870)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=97481905:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 3.07/0.84 % (134870)Instruction limit reached!
% 3.07/0.84 % (134870)------------------------------
% 3.07/0.84 % (134870)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.84 % (134870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.84 % (134870)CaDiCaL version: 2.1.3
% 3.07/0.84 % (134870)Termination reason: Instruction limit
% 3.07/0.84 % (134870)Termination phase: shuffling
% 3.07/0.84 % (134870)Time elapsed: 0.006 s
% 3.07/0.84 % (134870)Peak memory usage: 10 MB
% 3.07/0.84 % (134870)Instructions burned: 13 (million)
% 3.07/0.84 % (134838) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-134774-134838"...
% 3.07/0.84 % (134873)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3985271660:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 3.07/0.84 % (134876)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=2707886473:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 3.07/0.84 % (134873)Instruction limit reached!
% 3.07/0.84 % (134873)------------------------------
% 3.07/0.84 % (134873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.84 % (134873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.84 % (134873)CaDiCaL version: 2.1.3
% 3.07/0.84 % (134873)Termination reason: Instruction limit
% 3.07/0.84 % (134873)Termination phase: Saturation
% 3.07/0.84 % (134873)Time elapsed: 0.028 s
% 3.07/0.84 % (134873)Peak memory usage: 12 MB
% 3.07/0.84 % (134873)Instructions burned: 66 (million)
% 3.07/0.84 % (134876)Instruction limit reached!
% 3.07/0.84 % (134876)------------------------------
% 3.07/0.84 % (134876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.84 % (134876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.84 % (134876)CaDiCaL version: 2.1.3
% 3.07/0.84 % (134876)Termination reason: Instruction limit
% 3.07/0.84 % (134876)Termination phase: Property scanning
% 3.07/0.84 % (134876)Time elapsed: 0.023 s
% 3.07/0.84 % (134876)Peak memory usage: 11 MB
% 3.07/0.84 % (134876)Instructions burned: 52 (million)
% 3.07/0.84 % (134879)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1784060675:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/31Mi)
% 3.07/0.84 % (134838)...printing done.
% 3.07/0.84 % (134838)Refutation found. Thanks to Tanya!
% 3.07/0.84 % SZS status Theorem for theBenchmark
% 3.07/0.84 % SZS output start Proof for theBenchmark
% See solution above
% 3.07/0.85 % (134838)------------------------------
% 3.07/0.85 % (134838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.85 % (134838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.85 % (134838)CaDiCaL version: 2.1.3
% 3.07/0.85 % (134838)Termination reason: Refutation
% 3.07/0.85 % (134838)Time elapsed: 0.261 s
% 3.07/0.85 % (134838)Peak memory usage: 16 MB
% 3.07/0.85 % (134838)Instructions burned: 526 (million)
% 3.07/0.85 % (134774)Success in time 0.56 s
% 3.07/0.85 % Vampire exiting
%------------------------------------------------------------------------------