%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU550^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:32:24 AM UTC 2026
% Result : Theorem 0.19s 0.33s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 14
% Syntax : Number of formulae : 200 ( 13 unt; 0 typ; 12 def)
% Number of atoms : 2300 ( 611 equ; 0 cnn)
% Maximal formula atoms : 69 ( 11 avg)
% Number of connectives : 1773 ( 298 ~; 405 |; 232 &; 444 @)
% ( 18 <=>; 328 =>; 0 <=; 0 <~>)
% Maximal formula depth : 76 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 159 ( 154 usr; 84 con; 0-4 aty)
% ( 34 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 224 ( 0 sgn 122 !; 6 ?; 224 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_80,type,
vAND: $o > $o > $o ).
thf(func_def_81,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_82,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_83,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_84,type,
vIMP: $o > $o > $o ).
thf(func_def_85,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_86,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_87,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_88,type,
vIFF: $o > $o > $o ).
thf(func_def_89,type,
vNOT: $o > $o ).
thf(func_def_90,type,
vOR: $o > $o > $o ).
thf(func_def_91,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_92,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_95,type,
sK0: $i > $o ).
thf(func_def_96,type,
sK1: $i > $o ).
thf(func_def_97,type,
sK2: $i > $i ).
thf(func_def_98,type,
sK3: $i > $i ).
thf(func_def_101,type,
sK6: ( $i > $o ) > $i > $i ).
thf(func_def_102,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_103,type,
sK8: ( $i > $o ) > $i > $i ).
thf(func_def_104,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_105,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_106,type,
sK11: ( $i > $o ) > $i ).
thf(func_def_107,type,
sK12: ( $i > $o ) > $i ).
thf(func_def_108,type,
sK13: ( $i > $o ) > $i > $i ).
thf(func_def_109,type,
sK14: ( $i > $o ) > $i > $i ).
thf(func_def_110,type,
sK15: ( $i > $o ) > $i > $i ).
thf(func_def_111,type,
sK16: ( $i > $o ) > $i > $i ).
thf(func_def_112,type,
sK17: ( $i > $o ) > $i > $i ).
thf(func_def_113,type,
sK18: ( $i > $o ) > $i > $i ).
thf(func_def_114,type,
sK19: ( $i > $o ) > $i > $i ).
thf(func_def_115,type,
sK20: $i > $i ).
thf(func_def_116,type,
sK21: ( $i > $o ) > $i ).
thf(func_def_117,type,
sK22: ( $i > $o ) > $i > $i ).
thf(func_def_118,type,
sK23: $o > $i > $i > $i ).
thf(func_def_119,type,
sK24: $i > $i > $i ).
thf(func_def_120,type,
sK25: $i > $i ).
thf(func_def_121,type,
sK26: $i > $i ).
thf(func_def_122,type,
sK27: $i > $i ).
thf(func_def_123,type,
sK28: $i > $i > $i ).
thf(func_def_124,type,
sK29: $i > $i > $i ).
thf(func_def_125,type,
sK30: ( $i > $o ) > $i ).
thf(func_def_126,type,
sK31: ( $i > $o ) > $i > $i ).
thf(func_def_127,type,
sK32: ( $i > $o ) > $i ).
thf(func_def_128,type,
sK33: ( $i > $o ) > $i > $i ).
thf(func_def_129,type,
sK34: ( $i > $o ) > $i > $i ).
thf(func_def_130,type,
sK35: $i > $i ).
thf(func_def_131,type,
sK36: $i > $i > $i > $i ).
thf(func_def_132,type,
sK37: $i > $i > $i ).
thf(func_def_133,type,
sK38: $i > $i > $i ).
thf(func_def_134,type,
sK39: $i > $i > $i ).
thf(func_def_135,type,
sK40: $i > $i ).
thf(func_def_136,type,
sK41: $i > ( $i > $i > $o ) > $i ).
thf(func_def_137,type,
sK42: $i > ( $i > $i > $o ) > $i ).
thf(func_def_138,type,
sK43: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_139,type,
sK44: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_140,type,
sK45: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_141,type,
sK46: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_142,type,
sK47: $i > $i ).
thf(func_def_143,type,
sK48: $i > $i > $i ).
thf(func_def_144,type,
sK49: $i > $i > $i ).
thf(func_def_145,type,
sK50: $i > $i > $i ).
thf(f1,axiom,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(f69,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
=> ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X0 @ X2 )
<=> ( X1 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X0 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(f70,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
=> ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X0 @ X2 )
<=> ( X1 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X0 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f69]) ).
thf(f71,plain,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f72,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f202,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
=> ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X0 @ X2 )
<=> ( X1 @ X3 ) ) )
=> ( ( exu
@ ^ [X4: $i] : ( X0 @ X4 ) )
<=> ( exu
@ ^ [X5: $i] : ( X1 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f70]) ).
thf(f203,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X0 @ X2 )
= ( X1 @ X3 ) ) )
=> ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f202]) ).
thf(f204,plain,
( ? [X0: $i > $o,X1: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( X0 @ X2 )
= ( X1 @ X3 ) )
| ( X2 != X3 ) ) )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f203]) ).
thf(f205,plain,
( ? [X0: $i > $o,X1: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( X0 @ X2 )
= ( X1 @ X3 ) )
| ( X2 != X3 ) ) )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(flattening,[],[f204]) ).
thf(f206,plain,
( ( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( sK0 @ X2 )
= ( sK1 @ X3 ) )
| ( X2 != X3 ) )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f205]) ).
thf(f207,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f341,plain,
! [X2: $i,X3: $i] :
( ( ( sK0 @ X2 )
= ( sK1 @ X3 ) )
| ( X2 != X3 ) ),
inference(cnf_transformation,[],[f206]) ).
thf(f342,plain,
( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f206]) ).
thf(f411,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ),
inference(definition_unfolding,[],[f342,f207,f207]) ).
thf(f412,plain,
! [X3: $i] :
( ( sK1 @ X3 )
= ( sK0 @ X3 ) ),
inference(equality_resolution,[],[f341]) ).
thf(f413,plain,
! [X3: $i] :
( ( $true
= ( sK1 @ X3 ) )
| ( $false
= ( sK0 @ X3 ) ) ),
inference(iff_proxy_clausification,[],[f412]) ).
thf(f414,plain,
! [X3: $i] :
( ( $false
= ( sK1 @ X3 ) )
| ( $true
= ( sK0 @ X3 ) ) ),
inference(iff_proxy_clausification,[],[f412]) ).
thf(f415,plain,
( ( $true
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
| ( $true
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) ),
inference(xor_proxy_clausification,[],[f411]) ).
thf(f416,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) ),
inference(xor_proxy_clausification,[],[f411]) ).
thf(f417,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f416]) ).
thf(f418,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f417]) ).
thf(f419,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f418]) ).
thf(f420,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) ) ) ) )
| ( $false
= ( ( sK1 @ X2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X2 = Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f419]) ).
thf(f421,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) ) ) )
| ( $false
= ( ( sK1 @ X2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X2 = Y0 ) ) ) ) )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f420]) ).
thf(f422,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( ( sK1 @ X2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X2 = Y0 ) ) ) ) )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f421]) ).
thf(f423,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X2 = Y0 ) ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f422]) ).
thf(f424,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X2 = Y0 ) )
@ ( sK3 @ X2 ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f423]) ).
thf(f425,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK0 @ ( sK2 @ X1 ) )
=> ( X1
= ( sK2 @ X1 ) ) ) )
| ( $false
= ( ( sK1 @ ( sK3 @ X2 ) )
=> ( X2
= ( sK3 @ X2 ) ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f424]) ).
thf(f426,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( X1
= ( sK2 @ X1 ) ) )
| ( $false
= ( ( sK1 @ ( sK3 @ X2 ) )
=> ( X2
= ( sK3 @ X2 ) ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f425]) ).
thf(f427,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ ( sK2 @ X1 ) ) )
| ( $false
= ( ( sK1 @ ( sK3 @ X2 ) )
=> ( X2
= ( sK3 @ X2 ) ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f425]) ).
thf(f428,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ ( sK2 @ X1 ) ) )
| ( $false
= ( X2
= ( sK3 @ X2 ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f427]) ).
thf(f429,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ ( sK2 @ X1 ) ) )
| ( $true
= ( sK1 @ ( sK3 @ X2 ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f427]) ).
thf(f430,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ ( sK2 @ X1 ) ) )
| ( ( sK3 @ X2 )
!= X2 )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f428]) ).
thf(f431,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ X1 )
!= X1 )
| ( $false
= ( ( sK1 @ ( sK3 @ X2 ) )
=> ( X2
= ( sK3 @ X2 ) ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f426]) ).
thf(f432,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ X1 )
!= X1 )
| ( $false
= ( X2
= ( sK3 @ X2 ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f431]) ).
thf(f433,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ X1 )
!= X1 )
| ( $true
= ( sK1 @ ( sK3 @ X2 ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f431]) ).
thf(f434,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ X1 )
!= X1 )
| ( ( sK3 @ X2 )
!= X2 )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f432]) ).
thf(f435,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f415]) ).
thf(f436,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK4 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f435]) ).
thf(f437,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f436]) ).
thf(f438,plain,
( ( $true
= ( ( sK0 @ sK4 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK5 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f437]) ).
thf(f439,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) ) ) )
| ( $true
= ( ( sK1 @ sK5 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f438]) ).
thf(f440,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( ( sK1 @ sK5 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f438]) ).
thf(f441,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f440]) ).
thf(f442,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f440]) ).
thf(f443,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f441]) ).
thf(f444,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( ( sK1 @ X1 )
=> ( sK5 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f443]) ).
thf(f445,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK4 ) )
| ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( sK5 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f444]) ).
thf(f446,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK4 ) )
| ( $false
= ( sK1 @ X1 ) )
| ( sK5 = X1 ) ),
inference(equality_proxy_clausification,[],[f445]) ).
thf(f447,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) )
@ X1 ) )
| ( $true
= ( ( sK1 @ sK5 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f439]) ).
thf(f448,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f447]) ).
thf(f449,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) )
@ X1 ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f447]) ).
thf(f450,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ X1 )
=> ( sK4 = X1 ) ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(beta-eta_normalization,[],[f449]) ).
thf(f451,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK4 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f450]) ).
thf(f452,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( sK4 = X1 ) ),
inference(equality_proxy_clausification,[],[f451]) ).
thf(f453,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f448]) ).
thf(f454,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( sK0 @ X1 )
=> ( sK4 = X1 ) ) )
| ( $true
= ( ( sK1 @ X2 )
=> ( sK5 = X2 ) ) ) ),
inference(beta-eta_normalization,[],[f453]) ).
thf(f455,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ( sK1 @ X2 )
=> ( sK5 = X2 ) ) )
| ( $true
= ( sK4 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f454]) ).
thf(f456,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) )
| ( $true
= ( sK4 = X1 ) )
| ( $true
= ( sK5 = X2 ) ) ),
inference(imp_proxy_clausification,[],[f455]) ).
thf(f457,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) )
| ( sK4 = X1 )
| ( $true
= ( sK5 = X2 ) ) ),
inference(equality_proxy_clausification,[],[f456]) ).
thf(f458,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) )
| ( sK4 = X1 )
| ( sK5 = X2 ) ),
inference(equality_proxy_clausification,[],[f457]) ).
thf(f1230,definition,
( spl51_1
<=> ! [X2: $i] :
( ( $true
= ( sK1 @ ( sK3 @ X2 ) ) )
| ( $false
= ( sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl51_1])],[avatar_definition]) ).
thf(f1231,plain,
( ! [X2: $i] :
( ( $true
= ( sK1 @ ( sK3 @ X2 ) ) )
| ( $false
= ( sK1 @ X2 ) ) )
| ~ spl51_1 ),
inference(avatar_component_clause,[],[f1230]) ).
thf(f1233,definition,
( spl51_2
<=> ! [X1: $i] :
( ( $true
= ( sK0 @ ( sK2 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl51_2])],[avatar_definition]) ).
thf(f1234,plain,
( ! [X1: $i] :
( ( $true
= ( sK0 @ ( sK2 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl51_2 ),
inference(avatar_component_clause,[],[f1233]) ).
thf(f1235,plain,
( spl51_1
| spl51_2 ),
inference(avatar_split_clause,[],[f429,f1233,f1230]) ).
thf(f1237,definition,
( spl51_3
<=> ! [X2: $i] :
( ( ( sK3 @ X2 )
!= X2 )
| ( $false
= ( sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl51_3])],[avatar_definition]) ).
thf(f1238,plain,
( ! [X2: $i] :
( ( ( sK3 @ X2 )
!= X2 )
| ( $false
= ( sK1 @ X2 ) ) )
| ~ spl51_3 ),
inference(avatar_component_clause,[],[f1237]) ).
thf(f1239,plain,
( spl51_3
| spl51_2 ),
inference(avatar_split_clause,[],[f430,f1233,f1237]) ).
thf(f1241,definition,
( spl51_4
<=> ! [X1: $i] :
( ( ( sK2 @ X1 )
!= X1 )
| ( $false
= ( sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl51_4])],[avatar_definition]) ).
thf(f1242,plain,
( ! [X1: $i] :
( ( ( sK2 @ X1 )
!= X1 )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl51_4 ),
inference(avatar_component_clause,[],[f1241]) ).
thf(f1243,plain,
( spl51_1
| spl51_4 ),
inference(avatar_split_clause,[],[f433,f1241,f1230]) ).
thf(f1244,plain,
( spl51_3
| spl51_4 ),
inference(avatar_split_clause,[],[f434,f1241,f1237]) ).
thf(f1246,definition,
( spl51_5
<=> ( $true
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl51_5])],[avatar_definition]) ).
thf(f1248,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl51_5 ),
inference(avatar_component_clause,[],[f1246]) ).
thf(f1250,definition,
( spl51_6
<=> ( $true
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl51_6])],[avatar_definition]) ).
thf(f1252,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ~ spl51_6 ),
inference(avatar_component_clause,[],[f1250]) ).
thf(f1253,plain,
( spl51_5
| spl51_6 ),
inference(avatar_split_clause,[],[f442,f1250,f1246]) ).
thf(f1255,definition,
( spl51_7
<=> ! [X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( sK5 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl51_7])],[avatar_definition]) ).
thf(f1256,plain,
( ! [X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( sK5 = X1 ) )
| ~ spl51_7 ),
inference(avatar_component_clause,[],[f1255]) ).
thf(f1257,plain,
( spl51_7
| spl51_6 ),
inference(avatar_split_clause,[],[f446,f1250,f1255]) ).
thf(f1259,definition,
( spl51_8
<=> ! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( sK4 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl51_8])],[avatar_definition]) ).
thf(f1260,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( sK4 = X1 ) )
| ~ spl51_8 ),
inference(avatar_component_clause,[],[f1259]) ).
thf(f1261,plain,
( spl51_5
| spl51_8 ),
inference(avatar_split_clause,[],[f452,f1259,f1246]) ).
thf(f1262,plain,
( spl51_7
| spl51_8 ),
inference(avatar_split_clause,[],[f458,f1259,f1255]) ).
thf(f1301,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( sK5 = X0 )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl51_7 ),
inference(constrained_superposition,[],[f1256,f413]) ).
thf(f1302,plain,
( ! [X0: $i] :
( ( sK5 = X0 )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl51_7 ),
inference(trivial_inequality_removal,[],[f1301]) ).
thf(f1313,plain,
( ( $false = $true )
| ( $true
= ( sK0 @ sK5 ) )
| ~ spl51_5 ),
inference(constrained_superposition,[],[f1248,f414]) ).
thf(f1316,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ~ spl51_5 ),
inference(trivial_inequality_removal,[],[f1313]) ).
thf(f1385,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( sK5
= ( sK2 @ X0 ) )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl51_2
| ~ spl51_7 ),
inference(constrained_superposition,[],[f1302,f1234]) ).
thf(f1386,plain,
( ! [X0: $i] :
( ( sK5
= ( sK2 @ X0 ) )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl51_2
| ~ spl51_7 ),
inference(trivial_inequality_removal,[],[f1385]) ).
thf(f1405,plain,
( ! [X0: $i] :
( ( sK5 != X0 )
| ( $false
= ( sK0 @ X0 ) )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl51_2
| ~ spl51_4
| ~ spl51_7 ),
inference(constrained_superposition,[],[f1242,f1386]) ).
thf(f1407,plain,
( ( $false = $true )
| ( sK5
= ( sK2 @ sK5 ) )
| ~ spl51_2
| ~ spl51_5
| ~ spl51_7 ),
inference(constrained_superposition,[],[f1316,f1386]) ).
thf(f1408,plain,
( ( sK5
= ( sK2 @ sK5 ) )
| ~ spl51_2
| ~ spl51_5
| ~ spl51_7 ),
inference(trivial_inequality_removal,[],[f1407]) ).
thf(f1410,plain,
( ! [X0: $i] :
( ( sK5 != X0 )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl51_2
| ~ spl51_4
| ~ spl51_7 ),
inference(duplicate_literal_removal,[],[f1405]) ).
thf(f1419,plain,
( ( sK5 != sK5 )
| ( $false
= ( sK0 @ sK5 ) )
| ~ spl51_2
| ~ spl51_4
| ~ spl51_5
| ~ spl51_7 ),
inference(constrained_superposition,[],[f1242,f1408]) ).
thf(f1420,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ~ spl51_2
| ~ spl51_4
| ~ spl51_5
| ~ spl51_7 ),
inference(trivial_inequality_removal,[],[f1419]) ).
thf(f1425,plain,
( ( $false = $true )
| ~ spl51_2
| ~ spl51_4
| ~ spl51_5
| ~ spl51_7 ),
inference(constrained_superposition,[],[f1420,f1316]) ).
thf(f1429,plain,
( $false
| ~ spl51_2
| ~ spl51_4
| ~ spl51_5
| ~ spl51_7 ),
inference(trivial_inequality_removal,[],[f1425]) ).
thf(f1430,plain,
( ~ spl51_2
| ~ spl51_4
| ~ spl51_5
| ~ spl51_7 ),
inference(avatar_contradiction_clause,[],[f1429]) ).
thf(f1434,definition,
( spl51_14
<=> ! [X0: $i] :
( $false
= ( sK0 @ X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl51_14])],[avatar_definition]) ).
thf(f1435,plain,
( ! [X0: $i] :
( $false
= ( sK0 @ X0 ) )
| ~ spl51_14 ),
inference(avatar_component_clause,[],[f1434]) ).
thf(f1437,definition,
( spl51_15
<=> ( $true
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl51_15])],[avatar_definition]) ).
thf(f1439,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ~ spl51_15 ),
inference(avatar_component_clause,[],[f1437]) ).
thf(f1448,plain,
( ( $false = $true )
| ~ spl51_6
| ~ spl51_14 ),
inference(constrained_superposition,[],[f1435,f1252]) ).
thf(f1449,plain,
( ( $false = $true )
| ~ spl51_6
| ~ spl51_14 ),
inference(constrained_superposition,[],[f1252,f1435]) ).
thf(f1450,plain,
( $false
| ~ spl51_6
| ~ spl51_14 ),
inference(trivial_inequality_removal,[],[f1449]) ).
thf(f1451,plain,
( ~ spl51_6
| ~ spl51_14 ),
inference(avatar_contradiction_clause,[],[f1450]) ).
thf(f1452,plain,
( $false
| ~ spl51_6
| ~ spl51_14 ),
inference(trivial_inequality_removal,[],[f1448]) ).
thf(f1453,plain,
( ~ spl51_6
| ~ spl51_14 ),
inference(avatar_contradiction_clause,[],[f1452]) ).
thf(f1465,plain,
( ( $false = $true )
| ( sK4 = sK5 )
| ~ spl51_8
| ~ spl51_15 ),
inference(constrained_superposition,[],[f1260,f1439]) ).
thf(f1487,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ~ spl51_2
| ~ spl51_4
| ~ spl51_7 ),
inference(equality_resolution,[],[f1410]) ).
thf(f1488,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl51_2
| ~ spl51_4
| ~ spl51_7 ),
inference(constrained_superposition,[],[f1487,f1302]) ).
thf(f1498,plain,
( ! [X0: $i] :
( $false
= ( sK0 @ X0 ) )
| ~ spl51_2
| ~ spl51_4
| ~ spl51_7 ),
inference(duplicate_literal_removal,[],[f1488]) ).
thf(f1499,plain,
( spl51_14
| ~ spl51_2
| ~ spl51_4
| ~ spl51_7 ),
inference(avatar_split_clause,[],[f1498,f1255,f1241,f1233,f1434]) ).
thf(f1510,plain,
( spl51_15
| ~ spl51_5 ),
inference(avatar_split_clause,[],[f1316,f1246,f1437]) ).
thf(f1516,plain,
( ( $false = $true )
| ~ spl51_14
| ~ spl51_15 ),
inference(constrained_superposition,[],[f1439,f1435]) ).
thf(f1520,plain,
( $false
| ~ spl51_14
| ~ spl51_15 ),
inference(trivial_inequality_removal,[],[f1516]) ).
thf(f1521,plain,
( ~ spl51_14
| ~ spl51_15 ),
inference(avatar_contradiction_clause,[],[f1520]) ).
thf(f1614,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $true
= ( sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl51_1 ),
inference(constrained_superposition,[],[f414,f1231]) ).
thf(f1615,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( sK5
= ( sK3 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl51_1
| ~ spl51_7 ),
inference(constrained_superposition,[],[f1256,f1231]) ).
thf(f1616,plain,
( ! [X0: $i] :
( ( sK5
= ( sK3 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl51_1
| ~ spl51_7 ),
inference(trivial_inequality_removal,[],[f1615]) ).
thf(f1617,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl51_1 ),
inference(trivial_inequality_removal,[],[f1614]) ).
thf(f1639,plain,
( ( $false = $true )
| ( sK5
= ( sK3 @ sK5 ) )
| ~ spl51_1
| ~ spl51_5
| ~ spl51_7 ),
inference(constrained_superposition,[],[f1248,f1616]) ).
thf(f1644,plain,
( ( sK5
= ( sK3 @ sK5 ) )
| ~ spl51_1
| ~ spl51_5
| ~ spl51_7 ),
inference(trivial_inequality_removal,[],[f1639]) ).
thf(f1655,plain,
( ( sK5 != sK5 )
| ( $false
= ( sK1 @ sK5 ) )
| ~ spl51_1
| ~ spl51_3
| ~ spl51_5
| ~ spl51_7 ),
inference(constrained_superposition,[],[f1238,f1644]) ).
thf(f1656,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ~ spl51_1
| ~ spl51_3
| ~ spl51_5
| ~ spl51_7 ),
inference(trivial_inequality_removal,[],[f1655]) ).
thf(f1661,plain,
( ( $false = $true )
| ~ spl51_1
| ~ spl51_3
| ~ spl51_5
| ~ spl51_7 ),
inference(constrained_superposition,[],[f1656,f1248]) ).
thf(f1669,plain,
( $false
| ~ spl51_1
| ~ spl51_3
| ~ spl51_5
| ~ spl51_7 ),
inference(trivial_inequality_removal,[],[f1661]) ).
thf(f1670,plain,
( ~ spl51_1
| ~ spl51_3
| ~ spl51_5
| ~ spl51_7 ),
inference(avatar_contradiction_clause,[],[f1669]) ).
thf(f1673,plain,
( ( sK4 = sK5 )
| ~ spl51_8
| ~ spl51_15 ),
inference(trivial_inequality_removal,[],[f1465]) ).
thf(f1740,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( sK4
= ( sK2 @ X0 ) )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl51_2
| ~ spl51_8 ),
inference(constrained_superposition,[],[f1260,f1234]) ).
thf(f1741,plain,
( ! [X0: $i] :
( ( sK4
= ( sK2 @ X0 ) )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl51_2
| ~ spl51_8 ),
inference(trivial_inequality_removal,[],[f1740]) ).
thf(f1760,plain,
( ( $false = $true )
| ( sK4
= ( sK2 @ sK4 ) )
| ~ spl51_2
| ~ spl51_6
| ~ spl51_8 ),
inference(constrained_superposition,[],[f1252,f1741]) ).
thf(f1761,plain,
( ( $false = $true )
| ( sK4
= ( sK2 @ sK5 ) )
| ~ spl51_2
| ~ spl51_8
| ~ spl51_15 ),
inference(constrained_superposition,[],[f1439,f1741]) ).
thf(f1762,plain,
( ( sK4
= ( sK2 @ sK5 ) )
| ~ spl51_2
| ~ spl51_8
| ~ spl51_15 ),
inference(trivial_inequality_removal,[],[f1761]) ).
thf(f1763,plain,
( ( sK4
= ( sK2 @ sK4 ) )
| ~ spl51_2
| ~ spl51_6
| ~ spl51_8 ),
inference(trivial_inequality_removal,[],[f1760]) ).
thf(f1771,plain,
( ! [X0: $i] :
( ( ( sK2 @ X0 )
= X0 )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl51_2
| ~ spl51_6
| ~ spl51_8 ),
inference(constrained_superposition,[],[f1763,f1260]) ).
thf(f1830,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK1 @ X0 ) )
| ( sK4
= ( sK3 @ X0 ) ) )
| ~ spl51_1
| ~ spl51_8 ),
inference(constrained_superposition,[],[f1617,f1260]) ).
thf(f1918,definition,
( spl51_17
<=> ( sK4 = sK5 ) ),
introduced(definition,[new_symbols(definition,[spl51_17])],[avatar_definition]) ).
thf(f1920,plain,
( ( sK4 != sK5 )
| spl51_17 ),
inference(avatar_component_clause,[],[f1918]) ).
thf(f1924,plain,
( ( sK4 != sK4 )
| ~ spl51_8
| ~ spl51_15
| spl51_17 ),
inference(constrained_superposition,[],[f1920,f1673]) ).
thf(f1925,plain,
( $false
| ~ spl51_8
| ~ spl51_15
| spl51_17 ),
inference(trivial_inequality_removal,[],[f1924]) ).
thf(f1926,plain,
( ~ spl51_8
| ~ spl51_15
| spl51_17 ),
inference(avatar_contradiction_clause,[],[f1925]) ).
thf(f1958,plain,
( ! [X0: $i] :
( ( X0 != X0 )
| ( $false
= ( sK0 @ X0 ) )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl51_2
| ~ spl51_4
| ~ spl51_6
| ~ spl51_8 ),
inference(constrained_superposition,[],[f1242,f1771]) ).
thf(f1962,plain,
( ( sK4 != sK5 )
| ( $false
= ( sK0 @ sK5 ) )
| ~ spl51_2
| ~ spl51_4
| ~ spl51_8
| ~ spl51_15 ),
inference(constrained_superposition,[],[f1242,f1762]) ).
thf(f1966,plain,
( ! [X0: $i] :
( ( X0 != X0 )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl51_2
| ~ spl51_4
| ~ spl51_6
| ~ spl51_8 ),
inference(duplicate_literal_removal,[],[f1958]) ).
thf(f1967,plain,
( ! [X0: $i] :
( $false
= ( sK0 @ X0 ) )
| ~ spl51_2
| ~ spl51_4
| ~ spl51_6
| ~ spl51_8 ),
inference(trivial_inequality_removal,[],[f1966]) ).
thf(f1970,definition,
( spl51_18
<=> ( $false
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl51_18])],[avatar_definition]) ).
thf(f1972,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ~ spl51_18 ),
inference(avatar_component_clause,[],[f1970]) ).
thf(f1973,plain,
( spl51_18
| ~ spl51_17
| ~ spl51_2
| ~ spl51_4
| ~ spl51_8
| ~ spl51_15 ),
inference(avatar_split_clause,[],[f1962,f1437,f1259,f1241,f1233,f1918,f1970]) ).
thf(f1975,plain,
( spl51_14
| ~ spl51_2
| ~ spl51_4
| ~ spl51_6
| ~ spl51_8 ),
inference(avatar_split_clause,[],[f1967,f1259,f1250,f1241,f1233,f1434]) ).
thf(f1976,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( sK4
= ( sK3 @ X0 ) ) )
| ~ spl51_1
| ~ spl51_8 ),
inference(trivial_inequality_removal,[],[f1830]) ).
thf(f2004,plain,
( ( $false = $true )
| ~ spl51_15
| ~ spl51_18 ),
inference(constrained_superposition,[],[f1972,f1439]) ).
thf(f2008,plain,
( $false
| ~ spl51_15
| ~ spl51_18 ),
inference(trivial_inequality_removal,[],[f2004]) ).
thf(f2009,plain,
( ~ spl51_15
| ~ spl51_18 ),
inference(avatar_contradiction_clause,[],[f2008]) ).
thf(f2032,plain,
( ! [X0: $i] :
( ( sK4 != X0 )
| ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl51_1
| ~ spl51_3
| ~ spl51_8 ),
inference(constrained_superposition,[],[f1238,f1976]) ).
thf(f2033,plain,
( ! [X0: $i] :
( ( sK4 != X0 )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl51_1
| ~ spl51_3
| ~ spl51_8 ),
inference(duplicate_literal_removal,[],[f2032]) ).
thf(f2039,plain,
( ( $false
= ( sK1 @ sK4 ) )
| ~ spl51_1
| ~ spl51_3
| ~ spl51_8 ),
inference(equality_resolution,[],[f2033]) ).
thf(f2044,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK4 ) )
| ~ spl51_1
| ~ spl51_3
| ~ spl51_8 ),
inference(constrained_superposition,[],[f413,f2039]) ).
thf(f2045,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ~ spl51_1
| ~ spl51_3
| ~ spl51_8 ),
inference(trivial_inequality_removal,[],[f2044]) ).
thf(f2049,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl51_1
| ~ spl51_3
| ~ spl51_8 ),
inference(constrained_superposition,[],[f2045,f1260]) ).
thf(f2051,plain,
( ( $false = $true )
| ~ spl51_1
| ~ spl51_3
| ~ spl51_6
| ~ spl51_8 ),
inference(constrained_superposition,[],[f2045,f1252]) ).
thf(f2055,plain,
( $false
| ~ spl51_1
| ~ spl51_3
| ~ spl51_6
| ~ spl51_8 ),
inference(trivial_inequality_removal,[],[f2051]) ).
thf(f2056,plain,
( ~ spl51_1
| ~ spl51_3
| ~ spl51_6
| ~ spl51_8 ),
inference(avatar_contradiction_clause,[],[f2055]) ).
thf(f2058,plain,
( ! [X0: $i] :
( $false
= ( sK0 @ X0 ) )
| ~ spl51_1
| ~ spl51_3
| ~ spl51_8 ),
inference(duplicate_literal_removal,[],[f2049]) ).
thf(f2059,plain,
( spl51_14
| ~ spl51_1
| ~ spl51_3
| ~ spl51_8 ),
inference(avatar_split_clause,[],[f2058,f1259,f1237,f1230,f1434]) ).
cnf(s1,plain,
( spl51_1
| spl51_2 ),
inference(sat_conversion,[],[f1235]) ).
cnf(s2,plain,
( spl51_2
| spl51_3 ),
inference(sat_conversion,[],[f1239]) ).
cnf(s3,plain,
( spl51_1
| spl51_4 ),
inference(sat_conversion,[],[f1243]) ).
cnf(s4,plain,
( spl51_3
| spl51_4 ),
inference(sat_conversion,[],[f1244]) ).
cnf(s5,plain,
( spl51_5
| spl51_6 ),
inference(sat_conversion,[],[f1253]) ).
cnf(s6,plain,
( spl51_6
| spl51_7 ),
inference(sat_conversion,[],[f1257]) ).
cnf(s7,plain,
( spl51_5
| spl51_8 ),
inference(sat_conversion,[],[f1261]) ).
cnf(s8,plain,
( spl51_7
| spl51_8 ),
inference(sat_conversion,[],[f1262]) ).
cnf(s15,plain,
( ~ spl51_2
| ~ spl51_4
| ~ spl51_5
| ~ spl51_7 ),
inference(sat_conversion,[],[f1430]) ).
cnf(s17,plain,
( ~ spl51_6
| ~ spl51_14 ),
inference(sat_conversion,[],[f1451]) ).
cnf(s18,plain,
( ~ spl51_6
| ~ spl51_14 ),
inference(sat_conversion,[],[f1453]) ).
cnf(s21,plain,
( ~ spl51_2
| ~ spl51_4
| ~ spl51_7
| spl51_14 ),
inference(sat_conversion,[],[f1499]) ).
cnf(s25,plain,
( ~ spl51_5
| spl51_15 ),
inference(sat_conversion,[],[f1510]) ).
cnf(s27,plain,
( ~ spl51_14
| ~ spl51_15 ),
inference(sat_conversion,[],[f1521]) ).
cnf(s29,plain,
( ~ spl51_1
| ~ spl51_3
| ~ spl51_5
| ~ spl51_7 ),
inference(sat_conversion,[],[f1670]) ).
cnf(s31,plain,
( ~ spl51_8
| ~ spl51_15
| spl51_17 ),
inference(sat_conversion,[],[f1926]) ).
cnf(s34,plain,
( ~ spl51_2
| ~ spl51_4
| ~ spl51_8
| ~ spl51_15
| ~ spl51_17
| spl51_18 ),
inference(sat_conversion,[],[f1973]) ).
cnf(s36,plain,
( ~ spl51_2
| ~ spl51_4
| ~ spl51_6
| ~ spl51_8
| spl51_14 ),
inference(sat_conversion,[],[f1975]) ).
cnf(s41,plain,
( ~ spl51_15
| ~ spl51_18 ),
inference(sat_conversion,[],[f2009]) ).
cnf(s45,plain,
( ~ spl51_1
| ~ spl51_3
| ~ spl51_6
| ~ spl51_8 ),
inference(sat_conversion,[],[f2056]) ).
cnf(s46,plain,
( ~ spl51_1
| ~ spl51_3
| ~ spl51_8
| spl51_14 ),
inference(sat_conversion,[],[f2059]) ).
cnf(s47,plain,
( ~ spl51_8
| ~ spl51_6
| ~ spl51_2
| ~ spl51_4 ),
inference(rat,[],[s17,s36]) ).
cnf(s48,plain,
( spl51_5
| spl51_1 ),
inference(rat,[],[s47,s5,s7,s3,s1]) ).
cnf(s49,plain,
spl51_1,
inference(rat,[],[s34,s31,s8,s41,s15,s25,s48,s1,s3]) ).
cnf(s50,plain,
( ~ spl51_6
| ~ spl51_4
| ~ spl51_2 ),
inference(rat,[],[s8,s21,s47,s18]) ).
cnf(s51,plain,
( ~ spl51_4
| ~ spl51_2 ),
inference(rat,[],[s15,s5,s6,s50]) ).
cnf(s52,plain,
( spl51_8
| ~ spl51_3 ),
inference(rat,[],[s29,s7,s8,s49]) ).
cnf(s53,plain,
( ~ spl51_8
| ~ spl51_3 ),
inference(rat,[],[s25,s5,s27,s45,s46,s49]) ).
cnf(s54,plain,
~ spl51_3,
inference(rat,[],[s53,s52]) ).
cnf(s55,plain,
spl51_4,
inference(rat,[],[s4,s54]) ).
cnf(s56,plain,
spl51_2,
inference(rat,[],[s2,s54]) ).
cnf(s57,plain,
$false,
inference(rat,[],[s51,s56,s55]) ).
thf(f2060,plain,
$false,
inference(avatar_sat_refutation,[],[s57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU550^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n015.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:53:03 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.33 % (3558374)Will run a generic schedule for satisfiability detection.
% 0.19/0.33 % (3558380)% WARNING: option uhcvi not known.
% 0.19/0.33 % (3558380)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2062559774:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.33 % (3558380)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.33 % (3558380)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.33 % (3558379)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2677423934_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.33 % (3558383)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=624888456:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.33 % (3558381)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3004323318:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.33 % (3558382)dis+10_1_sil=32000:sp=arity:random_seed=3659025235:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.33 % (3558385)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3701670746:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.33 % (3558383)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.33 % Exception at run slice level
% 0.19/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.33 % (3558384)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4087416728:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.33 % (3558392)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2736564501:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.33 % Exception at run slice level
% 0.19/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.33 % (3558382)Instruction limit reached!
% 0.19/0.33 % (3558382)------------------------------
% 0.19/0.33 % (3558382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (3558382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (3558382)CaDiCaL version: 2.1.3
% 0.19/0.33 % (3558382)Termination reason: Instruction limit
% 0.19/0.33 % (3558382)Termination phase: Saturation
% 0.19/0.33 % (3558382)Time elapsed: 0.051 s
% 0.19/0.33 % (3558382)Peak memory usage: 13 MB
% 0.19/0.33 % (3558382)Instructions burned: 103 (million)
% 0.19/0.33 % (3558383)Instruction limit reached!
% 0.19/0.33 % (3558383)------------------------------
% 0.19/0.33 % (3558383)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (3558383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (3558383)CaDiCaL version: 2.1.3
% 0.19/0.33 % (3558383)Termination reason: Instruction limit
% 0.19/0.33 % (3558383)Termination phase: Saturation
% 0.19/0.33 % (3558383)Time elapsed: 0.058 s
% 0.19/0.33 % (3558383)Peak memory usage: 13 MB
% 0.19/0.33 % (3558383)Instructions burned: 117 (million)
% 0.19/0.33 % (3558385) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3558374-3558385"...
% 0.19/0.33 % (3558395)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3908428071:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.33 % (3558385)...printing done.
% 0.19/0.33 % (3558385)Refutation found. Thanks to Tanya!
% 0.19/0.33 % SZS status Theorem for theBenchmark
% 0.19/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.33 % (3558385)------------------------------
% 0.19/0.33 % (3558385)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (3558385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (3558385)CaDiCaL version: 2.1.3
% 0.19/0.33 % (3558385)Termination reason: Refutation
% 0.19/0.33 % (3558385)Time elapsed: 0.060 s
% 0.19/0.33 % (3558385)Peak memory usage: 14 MB
% 0.19/0.33 % (3558385)Instructions burned: 117 (million)
% 0.19/0.33 % (3558374)Success in time 0.106 s
% 0.19/0.33 % Vampire exiting
%------------------------------------------------------------------------------