%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU550^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:30:01 AM UTC 2026
% Result : Theorem 0.18s 0.35s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 13
% Syntax : Number of formulae : 181 ( 13 unt; 0 typ; 11 def)
% Number of atoms : 2407 ( 666 equ; 0 cnn)
% Maximal formula atoms : 69 ( 13 avg)
% Number of connectives : 1775 ( 269 ~; 371 |; 297 &; 444 @)
% ( 17 <=>; 327 =>; 0 <=; 0 <~>)
% Maximal formula depth : 76 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 212 ( 207 usr; 90 con; 0-4 aty)
% ( 36 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 236 ( 0 sgn 131 !; 8 ?; 236 :)
% 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_81,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_82,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_83,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_84,type,
vNOT: $o > $o ).
thf(func_def_85,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_86,type,
vAND: $o > $o > $o ).
thf(func_def_87,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_88,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_89,type,
vIMP: $o > $o > $o ).
thf(func_def_90,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_91,type,
sP0: $i > $i > $o ).
thf(func_def_92,type,
sP1: $i > $o ).
thf(func_def_93,type,
sP2: $i > $i > $o ).
thf(func_def_94,type,
sP3: $i > $i > $o ).
thf(func_def_95,type,
sP4: $o ).
thf(func_def_96,type,
sK5: $i > $i > $i ).
thf(func_def_97,type,
sK6: $i > $i > $i ).
thf(func_def_98,type,
sK7: $i > $i > $i ).
thf(func_def_99,type,
sK8: $i > $i > $i ).
thf(func_def_100,type,
sK9: $i > $i > $i ).
thf(func_def_101,type,
sK10: $i > $i > $i > $i ).
thf(func_def_102,type,
sK11: $i > $i ).
thf(func_def_103,type,
sK12: $i > $i ).
thf(func_def_104,type,
sK13: $i > $i ).
thf(func_def_105,type,
sK14: $i > $i ).
thf(func_def_106,type,
sK15: $i > $i > $i > $i ).
thf(func_def_107,type,
sK16: $i > $i > $i > $i ).
thf(func_def_108,type,
sK17: $i > $i > $i ).
thf(func_def_109,type,
sK18: $i > $i > $i ).
thf(func_def_110,type,
sK19: $i > $i > $i ).
thf(func_def_112,type,
sK21: $i > $i ).
thf(func_def_113,type,
sK22: $i > $i ).
thf(func_def_114,type,
sK23: $i > $i ).
thf(func_def_117,type,
sK26: $i > $i > $i ).
thf(func_def_124,type,
sK33: $i > $o ).
thf(func_def_126,type,
sK35: $i > ( $i > $o ) > $i ).
thf(func_def_129,type,
sK38: $i > $i ).
thf(func_def_130,type,
sK39: $i > $i ).
thf(func_def_134,type,
sK43: $i > $i ).
thf(func_def_136,type,
sK45: $o ).
thf(func_def_137,type,
sK46: $i > $o ).
thf(func_def_139,type,
sK48: ( $i > $o ) > $i ).
thf(func_def_140,type,
sK49: ( $i > $o ) > $i ).
thf(func_def_142,type,
sK51: $o ).
thf(func_def_145,type,
sK54: $i > $i ).
thf(func_def_153,type,
sK62: $i > $i > $i ).
thf(func_def_157,type,
sK66: $i > ( $i > $o ) > $i ).
thf(func_def_158,type,
sK67: $i > $o ).
thf(func_def_162,type,
sK71: $i > $o ).
thf(func_def_166,type,
sK75: $o ).
thf(func_def_167,type,
sK76: $o ).
thf(func_def_168,type,
sK77: $i > ( $i > $o ) > $i ).
thf(func_def_169,type,
sK78: $i > $o ).
thf(func_def_172,type,
sK81: ( $i > $o ) > $i > $i ).
thf(func_def_174,type,
sK83: $i > $o ).
thf(func_def_176,type,
sK85: $i > $o ).
thf(func_def_179,type,
sK88: $i > $i ).
thf(func_def_187,type,
sK96: $i > $i ).
thf(func_def_188,type,
sK97: $i > $o ).
thf(func_def_189,type,
sK98: $i > $o ).
thf(func_def_190,type,
sK99: ( $i > $o ) > $i ).
thf(func_def_191,type,
sK100: $i > $o ).
thf(func_def_193,type,
sK102: $i > $i ).
thf(func_def_198,type,
sK107: $i > $o ).
thf(func_def_200,type,
sK109: $i > $o ).
thf(func_def_201,type,
sK110: $i > $i ).
thf(func_def_202,type,
sK111: ( $i > $o ) > $i ).
thf(func_def_205,type,
sK114: $i > $o ).
thf(func_def_208,type,
sK117: $i > $i > $i ).
thf(func_def_210,type,
sK119: $i > $o ).
thf(func_def_213,type,
sK122: $i > $o ).
thf(func_def_217,type,
sK126: $i > $o ).
thf(func_def_219,type,
sK128: $o > $i > $i > $i ).
thf(func_def_222,type,
sK131: $o ).
thf(func_def_224,type,
sK133: $i > $o ).
thf(func_def_225,type,
sK134: $i > $i ).
thf(func_def_226,type,
sK135: ( $i > $o ) > $i ).
thf(func_def_233,type,
sK142: $o ).
thf(func_def_242,type,
sK151: $i > $i > $i ).
thf(func_def_243,type,
sK152: $i > $i > $i ).
thf(func_def_253,type,
sK162: $i > $o ).
thf(func_def_255,type,
sK164: ( $i > $o ) > $i > $i ).
thf(func_def_257,type,
sK166: $i > ( $i > $o ) > $i ).
thf(func_def_258,type,
sK167: $i > $o ).
thf(func_def_264,type,
sK173: $i > $o ).
thf(func_def_267,type,
sK176: $i > $o ).
thf(func_def_269,type,
sK178: ( $i > $o ) > $i > $i ).
thf(func_def_271,type,
sK180: $i > $i > $o ).
thf(func_def_272,type,
sK181: $i > $i ).
thf(func_def_273,type,
sK182: $i > $i ).
thf(func_def_274,type,
sK183: ( $i > $i > $o ) > $i > $i ).
thf(func_def_275,type,
sK184: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_276,type,
sK185: ( $i > $i > $o ) > $i > $i ).
thf(func_def_277,type,
sK186: $i > $i > $i ).
thf(func_def_283,type,
sK192: $i > ( $i > $o ) > $i ).
thf(func_def_284,type,
sK193: $i > $o ).
thf(func_def_287,type,
sK196: $i > $o ).
thf(func_def_288,type,
sK197: ( $i > $o ) > $i > $i ).
thf(func_def_289,type,
sK198: ( $i > $o ) > $i ).
thf(func_def_290,type,
sK199: ( $i > $o ) > $i ).
thf(func_def_291,type,
sK200: $i > $i ).
thf(func_def_292,type,
sK201: $i > $i ).
thf(func_def_295,type,
sK204: $i > ( $i > $o ) > $i ).
thf(func_def_296,type,
sK205: ( $i > $o ) > $i > $i ).
thf(func_def_297,type,
sK206: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_298,type,
sK207: ( $i > $o ) > $i > $i ).
thf(func_def_299,type,
sK208: ( $i > $o ) > $i ).
thf(func_def_300,type,
sK209: ( $i > $o ) > $i > $i ).
thf(func_def_301,type,
sK210: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_302,type,
sK211: ( $i > $o ) > $i ).
thf(func_def_303,type,
sK212: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_304,type,
sK213: ( $i > $o ) > $i ).
thf(func_def_305,type,
sK214: $i > $i ).
thf(func_def_306,type,
sK215: $i > ( $i > $o ) > $i ).
thf(func_def_307,type,
sK216: ( $i > $o ) > $i ).
thf(func_def_308,type,
sK217: $i > ( $i > $o ) > $i ).
thf(func_def_309,type,
sK218: ( $i > $o ) > $i ).
thf(f1,axiom,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) )
= exu ),
file('/export/starexec/sandbox/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
=> ! [X1: $i > $o,X0: $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/sandbox/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
=> ! [X1: $i > $o,X0: $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(f128,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 )
=> ( ( X1 @ X2 )
<=> ( X0 @ X3 ) ) )
=> ( ( exu
@ ^ [X4: $i] : ( X1 @ X4 ) )
<=> ( exu
@ ^ [X5: $i] : ( X0 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f70]) ).
thf(f129,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] :
( ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
= ( X0 @ X3 ) ) )
=> ( ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f128]) ).
thf(f188,plain,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) )
= exu ),
inference(rectify,[],[f1]) ).
thf(f189,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f188]) ).
thf(f285,plain,
( ? [X1: $i > $o,X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X3: $i,X2: $i] :
( ( ( X1 @ X2 )
= ( X0 @ 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,[],[f129]) ).
thf(f286,plain,
( ( exuE3u = $true )
& ( notdexE = $true )
& ( quantDeMorgan2 = $true )
& ( nonemptyI1 = $true )
& ( setunionE = $true )
& ( descrp = $true )
& ( quantDeMorgan4 = $true )
& ( setunionI = $true )
& ( emptyinPowerset = $true )
& ( omega0Ax = $true )
& ( setextAx = $true )
& ( dsetconstrI = $true )
& ( in__Cong = $true )
& ( prop2set2propI = $true )
& ( notdallE = $true )
& ( exuE3e = $true )
& ( setoftrueEq = $true )
& ( emptysetimpfalse = $true )
& ( emptyI = $true )
& ( emptysetAx = $true )
& ( singletonsswitch = $true )
& ( omegaIndAx = $true )
& ( exuE1 = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinOr = $true )
& ( replAx = $true )
& ( powersetI = $true )
& ( exuI3 = $true )
& ( setbeta = $true )
& ( emptysetE = $true )
& ( upairsetIR = $true )
& ( powersetE = $true )
& ( notinemptyset = $true )
& ( setadjoinIL = $true )
& ( exuI2 = $true )
& ( setadjoinAx = $true )
& ( setunionAx = $true )
& ( emptyE1 = $true )
& ( subPowSU = $true )
& ( emptyinunitempty = $true )
& ( eqinunit = $true )
& ( dsetconstrER = $true )
& ( setext = $true )
& ( upairsetE = $true )
& ( omegaSAx = $true )
& ( vacuousDall = $true )
& ( nonemptyI = $true )
& ( setadjoinE = $true )
& ( prop2setI = $true )
& ( wellorderingAx = $true )
& ( setadjoinIR = $true )
& ( inCongP = $true )
& ( upairsetIL = $true )
& ( notinsingleton = $true )
& ( noeltsimpempty = $true )
& ( nonemptyImpWitness = $true )
& ( quantDeMorgan1 = $true )
& ( powersetAx = $true )
& ( exuI1 = $true )
& ( uniqinunit = $true )
& ? [X1: $i > $o,X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X3: $i,X2: $i] :
( ( ( X1 @ X2 )
= ( X0 @ X3 ) )
| ( X2 != X3 ) ) )
& ( dsetconstrEL = $true )
& ( nonemptyE1 = $true )
& ( emptyInPowerset = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( exuE2 = $true ) ),
inference(flattening,[],[f285]) ).
thf(f403,plain,
( ( exuE3u = $true )
& ( notdexE = $true )
& ( quantDeMorgan2 = $true )
& ( nonemptyI1 = $true )
& ( setunionE = $true )
& ( descrp = $true )
& ( quantDeMorgan4 = $true )
& ( setunionI = $true )
& ( emptyinPowerset = $true )
& ( omega0Ax = $true )
& ( setextAx = $true )
& ( dsetconstrI = $true )
& ( in__Cong = $true )
& ( prop2set2propI = $true )
& ( notdallE = $true )
& ( exuE3e = $true )
& ( setoftrueEq = $true )
& ( emptysetimpfalse = $true )
& ( emptyI = $true )
& ( emptysetAx = $true )
& ( singletonsswitch = $true )
& ( omegaIndAx = $true )
& ( exuE1 = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinOr = $true )
& ( replAx = $true )
& ( powersetI = $true )
& ( exuI3 = $true )
& ( setbeta = $true )
& ( emptysetE = $true )
& ( upairsetIR = $true )
& ( powersetE = $true )
& ( notinemptyset = $true )
& ( setadjoinIL = $true )
& ( exuI2 = $true )
& ( setadjoinAx = $true )
& ( setunionAx = $true )
& ( emptyE1 = $true )
& ( subPowSU = $true )
& ( emptyinunitempty = $true )
& ( eqinunit = $true )
& ( dsetconstrER = $true )
& ( setext = $true )
& ( upairsetE = $true )
& ( omegaSAx = $true )
& ( vacuousDall = $true )
& ( nonemptyI = $true )
& ( setadjoinE = $true )
& ( prop2setI = $true )
& ( wellorderingAx = $true )
& ( setadjoinIR = $true )
& ( inCongP = $true )
& ( upairsetIL = $true )
& ( notinsingleton = $true )
& ( noeltsimpempty = $true )
& ( nonemptyImpWitness = $true )
& ( quantDeMorgan1 = $true )
& ( powersetAx = $true )
& ( exuI1 = $true )
& ( uniqinunit = $true )
& ? [X0: $i > $o,X1: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( X1 @ X2 )
= ( X0 @ X3 ) )
| ( X2 != X3 ) ) )
& ( dsetconstrEL = $true )
& ( nonemptyE1 = $true )
& ( emptyInPowerset = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( exuE2 = $true ) ),
inference(rectify,[],[f286]) ).
thf(f404,plain,
( ( exuE3u = $true )
& ( notdexE = $true )
& ( quantDeMorgan2 = $true )
& ( nonemptyI1 = $true )
& ( setunionE = $true )
& ( descrp = $true )
& ( quantDeMorgan4 = $true )
& ( setunionI = $true )
& ( emptyinPowerset = $true )
& ( omega0Ax = $true )
& ( setextAx = $true )
& ( dsetconstrI = $true )
& ( in__Cong = $true )
& ( prop2set2propI = $true )
& ( notdallE = $true )
& ( exuE3e = $true )
& ( setoftrueEq = $true )
& ( emptysetimpfalse = $true )
& ( emptyI = $true )
& ( emptysetAx = $true )
& ( singletonsswitch = $true )
& ( omegaIndAx = $true )
& ( exuE1 = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinOr = $true )
& ( replAx = $true )
& ( powersetI = $true )
& ( exuI3 = $true )
& ( setbeta = $true )
& ( emptysetE = $true )
& ( upairsetIR = $true )
& ( powersetE = $true )
& ( notinemptyset = $true )
& ( setadjoinIL = $true )
& ( exuI2 = $true )
& ( setadjoinAx = $true )
& ( setunionAx = $true )
& ( emptyE1 = $true )
& ( subPowSU = $true )
& ( emptyinunitempty = $true )
& ( eqinunit = $true )
& ( dsetconstrER = $true )
& ( setext = $true )
& ( upairsetE = $true )
& ( omegaSAx = $true )
& ( vacuousDall = $true )
& ( nonemptyI = $true )
& ( setadjoinE = $true )
& ( prop2setI = $true )
& ( wellorderingAx = $true )
& ( setadjoinIR = $true )
& ( inCongP = $true )
& ( upairsetIL = $true )
& ( notinsingleton = $true )
& ( noeltsimpempty = $true )
& ( nonemptyImpWitness = $true )
& ( quantDeMorgan1 = $true )
& ( powersetAx = $true )
& ( exuI1 = $true )
& ( uniqinunit = $true )
& ( ( exu
@ ^ [Y0: $i] : ( sK98 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( sK97 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( sK98 @ X2 )
= ( sK97 @ X3 ) )
| ( X2 != X3 ) )
& ( dsetconstrEL = $true )
& ( nonemptyE1 = $true )
& ( emptyInPowerset = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( exuE2 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97,sK98]),skolemize(X0,sK97),skolemize(X1,sK98)],[f403]) ).
thf(f658,plain,
! [X2: $i,X3: $i] :
( ( ( sK98 @ X2 )
= ( sK97 @ X3 ) )
| ( X2 != X3 ) ),
inference(cnf_transformation,[],[f404]) ).
thf(f659,plain,
( ( exu
@ ^ [Y0: $i] : ( sK98 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( sK97 @ Y0 ) ) ),
inference(cnf_transformation,[],[f404]) ).
thf(f858,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f189]) ).
thf(f985,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK97 @ Y0 ) )
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK98 @ Y0 ) ) ),
inference(definition_unfolding,[],[f659,f858,f858]) ).
thf(f1132,plain,
! [X3: $i] :
( ( sK98 @ X3 )
= ( sK97 @ X3 ) ),
inference(equality_resolution,[],[f658]) ).
thf(f1184,plain,
( ( $true
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK98 @ Y0 ) ) )
| ( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK97 @ Y0 ) )
= $true ) ),
inference(xor_proxy_clausification,[],[f985]) ).
thf(f1185,plain,
( ( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK97 @ Y0 ) )
= $false )
| ( $false
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK98 @ Y0 ) ) ) ),
inference(xor_proxy_clausification,[],[f985]) ).
thf(f1186,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK98 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK98 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $false )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK97 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK97 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1185]) ).
thf(f1187,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK98 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK98 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X1 )
= $false )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK97 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK97 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1186]) ).
thf(f1188,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK98 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK98 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK97 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK97 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1187]) ).
thf(f1189,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK97 @ X2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK97 @ Y0 )
=> ( X2 = Y0 ) ) ) )
= $false )
| ( ( ( sK98 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK98 @ Y0 )
=> ( X1 = Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1188]) ).
thf(f1190,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK98 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK98 @ Y0 )
=> ( X1 = Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK97 @ Y0 )
=> ( X2 = Y0 ) ) )
= $false )
| ( ( sK97 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f1189]) ).
thf(f1191,plain,
! [X2: $i,X1: $i] :
( ( ( sK98 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK97 @ Y0 )
=> ( X2 = Y0 ) ) )
= $false )
| ( ( sK97 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK98 @ Y0 )
=> ( X1 = Y0 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f1190]) ).
thf(f1192,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK98 @ Y0 )
=> ( X1 = Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK97 @ Y0 )
=> ( X2 = Y0 ) )
@ ( sK200 @ X2 ) )
= $false )
| ( ( sK97 @ X2 )
= $false )
| ( ( sK98 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1191]) ).
thf(f1193,plain,
! [X2: $i,X1: $i] :
( ( ( sK97 @ X2 )
= $false )
| ( ( sK98 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK98 @ Y0 )
=> ( X1 = Y0 ) )
@ ( sK201 @ X1 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK97 @ Y0 )
=> ( X2 = Y0 ) )
@ ( sK200 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1192]) ).
thf(f1194,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK97 @ ( sK200 @ X2 ) )
=> ( X2
= ( sK200 @ X2 ) ) )
= $false )
| ( ( sK97 @ X2 )
= $false )
| ( ( ( sK98 @ ( sK201 @ X1 ) )
=> ( X1
= ( sK201 @ X1 ) ) )
= $false )
| ( ( sK98 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f1193]) ).
thf(f1195,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( X2
= ( sK200 @ X2 ) ) )
| ( ( sK97 @ X2 )
= $false )
| ( ( ( sK98 @ ( sK201 @ X1 ) )
=> ( X1
= ( sK201 @ X1 ) ) )
= $false )
| ( ( sK98 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1194]) ).
thf(f1196,plain,
! [X2: $i,X1: $i] :
( ( ( sK97 @ X2 )
= $false )
| ( ( sK97 @ ( sK200 @ X2 ) )
= $true )
| ( ( sK98 @ X1 )
= $false )
| ( ( ( sK98 @ ( sK201 @ X1 ) )
=> ( X1
= ( sK201 @ X1 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1194]) ).
thf(f1197,plain,
! [X2: $i,X1: $i] :
( ( ( X1
= ( sK201 @ X1 ) )
= $false )
| ( ( sK97 @ X2 )
= $false )
| ( ( sK98 @ X1 )
= $false )
| ( ( sK97 @ ( sK200 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1196]) ).
thf(f1198,plain,
! [X2: $i,X1: $i] :
( ( ( sK98 @ ( sK201 @ X1 ) )
= $true )
| ( ( sK97 @ ( sK200 @ X2 ) )
= $true )
| ( ( sK97 @ X2 )
= $false )
| ( ( sK98 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1196]) ).
thf(f1199,plain,
! [X2: $i,X1: $i] :
( ( ( sK201 @ X1 )
!= X1 )
| ( ( sK97 @ X2 )
= $false )
| ( ( sK97 @ ( sK200 @ X2 ) )
= $true )
| ( ( sK98 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[],[f1197]) ).
thf(f1200,plain,
! [X2: $i,X1: $i] :
( ( ( sK97 @ X2 )
= $false )
| ( ( sK200 @ X2 )
!= X2 )
| ( ( ( sK98 @ ( sK201 @ X1 ) )
=> ( X1
= ( sK201 @ X1 ) ) )
= $false )
| ( ( sK98 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[],[f1195]) ).
thf(f1201,plain,
! [X2: $i,X1: $i] :
( ( ( sK200 @ X2 )
!= X2 )
| ( ( sK98 @ X1 )
= $false )
| ( ( X1
= ( sK201 @ X1 ) )
= $false )
| ( ( sK97 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1200]) ).
thf(f1202,plain,
! [X2: $i,X1: $i] :
( ( ( sK98 @ X1 )
= $false )
| ( ( sK200 @ X2 )
!= X2 )
| ( ( sK98 @ ( sK201 @ X1 ) )
= $true )
| ( ( sK97 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1200]) ).
thf(f1203,plain,
! [X2: $i,X1: $i] :
( ( ( sK200 @ X2 )
!= X2 )
| ( ( sK98 @ X1 )
= $false )
| ( ( sK97 @ X2 )
= $false )
| ( ( sK201 @ X1 )
!= X1 ) ),
inference(equality_proxy_clausification,[],[f1201]) ).
thf(f1204,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK97 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK97 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK98 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK98 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1184]) ).
thf(f1205,plain,
( ( ( ^ [Y0: $i] :
( ( sK97 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK97 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK202 )
= $true )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK98 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK98 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f1204]) ).
thf(f1206,plain,
( ( ( ^ [Y0: $i] :
( ( sK97 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK97 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK202 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK98 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK98 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK203 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f1205]) ).
thf(f1207,plain,
( ( ( ( sK98 @ sK203 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK98 @ Y0 )
=> ( sK203 = Y0 ) ) ) )
= $true )
| ( ( ( sK97 @ sK202 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK97 @ Y0 )
=> ( sK202 = Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1206]) ).
thf(f1208,plain,
( ( ( ( sK97 @ sK202 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK97 @ Y0 )
=> ( sK202 = Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK98 @ Y0 )
=> ( sK203 = Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1207]) ).
thf(f1209,plain,
( ( ( sK98 @ sK203 )
= $true )
| ( ( ( sK97 @ sK202 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK97 @ Y0 )
=> ( sK202 = Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1207]) ).
thf(f1211,plain,
( ( ( sK98 @ sK203 )
= $true )
| ( ( sK97 @ sK202 )
= $true ) ),
inference(and_proxy_clausification,[],[f1209]) ).
thf(f1216,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK98 @ Y0 )
=> ( sK203 = Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK97 @ Y0 )
=> ( sK202 = Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1208]) ).
thf(f1217,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK98 @ Y0 )
=> ( sK203 = Y0 ) ) )
= $true )
| ( ( sK97 @ sK202 )
= $true ) ),
inference(and_proxy_clausification,[],[f1208]) ).
thf(f1218,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK98 @ Y0 )
=> ( sK203 = Y0 ) )
@ X1 ) )
| ( ( sK97 @ sK202 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1217]) ).
thf(f1219,plain,
! [X1: $i] :
( ( ( ( sK98 @ X1 )
=> ( sK203 = X1 ) )
= $true )
| ( ( sK97 @ sK202 )
= $true ) ),
inference(beta-eta_normalization,[],[f1218]) ).
thf(f1220,plain,
! [X1: $i] :
( ( ( sK98 @ X1 )
= $false )
| ( ( sK97 @ sK202 )
= $true )
| ( ( sK203 = X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1219]) ).
thf(f1221,plain,
! [X1: $i] :
( ( ( sK97 @ sK202 )
= $true )
| ( ( sK98 @ X1 )
= $false )
| ( sK203 = X1 ) ),
inference(equality_proxy_clausification,[],[f1220]) ).
thf(f1222,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK98 @ Y0 )
=> ( sK203 = Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK97 @ Y0 )
=> ( sK202 = Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1216]) ).
thf(f1223,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK97 @ Y0 )
=> ( sK202 = Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK98 @ Y0 )
=> ( sK203 = Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1222]) ).
thf(f1224,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK97 @ X2 )
=> ( sK202 = X2 ) )
= $true )
| ( ( ( sK98 @ X1 )
=> ( sK203 = X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1223]) ).
thf(f1225,plain,
! [X2: $i,X1: $i] :
( ( ( sK202 = X2 )
= $true )
| ( ( sK97 @ X2 )
= $false )
| ( ( ( sK98 @ X1 )
=> ( sK203 = X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1224]) ).
thf(f1226,plain,
! [X2: $i,X1: $i] :
( ( ( sK97 @ X2 )
= $false )
| ( ( ( sK98 @ X1 )
=> ( sK203 = X1 ) )
= $true )
| ( sK202 = X2 ) ),
inference(equality_proxy_clausification,[],[f1225]) ).
thf(f1227,plain,
! [X2: $i,X1: $i] :
( ( sK202 = X2 )
| ( ( sK97 @ X2 )
= $false )
| ( ( sK98 @ X1 )
= $false )
| ( ( sK203 = X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1226]) ).
thf(f1228,plain,
! [X2: $i,X1: $i] :
( ( sK203 = X1 )
| ( ( sK98 @ X1 )
= $false )
| ( ( sK97 @ X2 )
= $false )
| ( sK202 = X2 ) ),
inference(equality_proxy_clausification,[],[f1227]) ).
thf(f1416,plain,
! [X3: $i] :
( ( ( sK97 @ X3 )
= $false )
| ( ( sK98 @ X3 )
= $true ) ),
inference(iff_proxy_clausification,[],[f1132]) ).
thf(f1417,plain,
! [X3: $i] :
( ( $true
= ( sK97 @ X3 ) )
| ( ( sK98 @ X3 )
= $false ) ),
inference(iff_proxy_clausification,[],[f1132]) ).
thf(f1489,definition,
( spl219_3
<=> ! [X1: $i] :
( ( ( sK98 @ ( sK201 @ X1 ) )
= $true )
| ( ( sK98 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl219_3])],[avatar_definition]) ).
thf(f1490,plain,
( ! [X1: $i] :
( ( ( sK98 @ ( sK201 @ X1 ) )
= $true )
| ( ( sK98 @ X1 )
= $false ) )
| ~ spl219_3 ),
inference(avatar_component_clause,[],[f1489]) ).
thf(f1492,definition,
( spl219_4
<=> ! [X2: $i] :
( ( ( sK97 @ ( sK200 @ X2 ) )
= $true )
| ( ( sK97 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl219_4])],[avatar_definition]) ).
thf(f1493,plain,
( ! [X2: $i] :
( ( ( sK97 @ ( sK200 @ X2 ) )
= $true )
| ( ( sK97 @ X2 )
= $false ) )
| ~ spl219_4 ),
inference(avatar_component_clause,[],[f1492]) ).
thf(f1494,plain,
( spl219_3
| spl219_4 ),
inference(avatar_split_clause,[],[f1198,f1492,f1489]) ).
thf(f1496,definition,
( spl219_5
<=> ! [X1: $i] :
( ( ( sK201 @ X1 )
!= X1 )
| ( ( sK98 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl219_5])],[avatar_definition]) ).
thf(f1497,plain,
( ! [X1: $i] :
( ( ( sK201 @ X1 )
!= X1 )
| ( ( sK98 @ X1 )
= $false ) )
| ~ spl219_5 ),
inference(avatar_component_clause,[],[f1496]) ).
thf(f1498,plain,
( spl219_4
| spl219_5 ),
inference(avatar_split_clause,[],[f1199,f1496,f1492]) ).
thf(f1500,definition,
( spl219_6
<=> ! [X2: $i] :
( ( ( sK200 @ X2 )
!= X2 )
| ( ( sK97 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl219_6])],[avatar_definition]) ).
thf(f1501,plain,
( ! [X2: $i] :
( ( ( sK200 @ X2 )
!= X2 )
| ( ( sK97 @ X2 )
= $false ) )
| ~ spl219_6 ),
inference(avatar_component_clause,[],[f1500]) ).
thf(f1502,plain,
( spl219_3
| spl219_6 ),
inference(avatar_split_clause,[],[f1202,f1500,f1489]) ).
thf(f1503,plain,
( spl219_6
| spl219_5 ),
inference(avatar_split_clause,[],[f1203,f1496,f1500]) ).
thf(f1505,definition,
( spl219_7
<=> ( ( sK97 @ sK202 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl219_7])],[avatar_definition]) ).
thf(f1507,plain,
( ( ( sK97 @ sK202 )
= $true )
| ~ spl219_7 ),
inference(avatar_component_clause,[],[f1505]) ).
thf(f1509,definition,
( spl219_8
<=> ( ( sK98 @ sK203 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl219_8])],[avatar_definition]) ).
thf(f1511,plain,
( ( ( sK98 @ sK203 )
= $true )
| ~ spl219_8 ),
inference(avatar_component_clause,[],[f1509]) ).
thf(f1512,plain,
( spl219_7
| spl219_8 ),
inference(avatar_split_clause,[],[f1211,f1509,f1505]) ).
thf(f1514,definition,
( spl219_9
<=> ! [X1: $i] :
( ( sK202 = X1 )
| ( ( sK97 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl219_9])],[avatar_definition]) ).
thf(f1515,plain,
( ! [X1: $i] :
( ( ( sK97 @ X1 )
= $false )
| ( sK202 = X1 ) )
| ~ spl219_9 ),
inference(avatar_component_clause,[],[f1514]) ).
thf(f1518,definition,
( spl219_10
<=> ! [X1: $i] :
( ( ( sK98 @ X1 )
= $false )
| ( sK203 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl219_10])],[avatar_definition]) ).
thf(f1519,plain,
( ! [X1: $i] :
( ( ( sK98 @ X1 )
= $false )
| ( sK203 = X1 ) )
| ~ spl219_10 ),
inference(avatar_component_clause,[],[f1518]) ).
thf(f1520,plain,
( spl219_10
| spl219_7 ),
inference(avatar_split_clause,[],[f1221,f1505,f1518]) ).
thf(f1521,plain,
( spl219_9
| spl219_10 ),
inference(avatar_split_clause,[],[f1228,f1518,f1514]) ).
thf(f1576,plain,
( ( $true = $false )
| ( ( sK98 @ sK202 )
= $true )
| ~ spl219_7 ),
inference(constrained_superposition,[],[f1507,f1416]) ).
thf(f1577,plain,
( ( ( sK98 @ sK202 )
= $true )
| ~ spl219_7 ),
inference(trivial_inequality_removal,[],[f1576]) ).
thf(f1580,plain,
( ! [X0: $i] :
( ( ( sK98 @ X0 )
= $false )
| ( sK202 = X0 )
| ( $true = $false ) )
| ~ spl219_9 ),
inference(constrained_superposition,[],[f1417,f1515]) ).
thf(f1583,plain,
( ! [X0: $i] :
( ( ( sK98 @ X0 )
= $false )
| ( sK202 = X0 ) )
| ~ spl219_9 ),
inference(trivial_inequality_removal,[],[f1580]) ).
thf(f1592,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( sK201 @ X0 )
= sK202 )
| ( ( sK98 @ X0 )
= $false ) )
| ~ spl219_3
| ~ spl219_9 ),
inference(constrained_superposition,[],[f1490,f1583]) ).
thf(f1594,plain,
( ! [X0: $i] :
( ( ( sK201 @ X0 )
= sK202 )
| ( ( sK98 @ X0 )
= $false ) )
| ~ spl219_3
| ~ spl219_9 ),
inference(trivial_inequality_removal,[],[f1592]) ).
thf(f1597,plain,
( ! [X0: $i] :
( ( sK202 != X0 )
| ( ( sK98 @ X0 )
= $false )
| ( ( sK98 @ X0 )
= $false ) )
| ~ spl219_3
| ~ spl219_5
| ~ spl219_9 ),
inference(constrained_superposition,[],[f1497,f1594]) ).
thf(f1599,plain,
( ! [X0: $i] :
( ( sK202 != X0 )
| ( ( sK98 @ X0 )
= $false ) )
| ~ spl219_3
| ~ spl219_5
| ~ spl219_9 ),
inference(duplicate_literal_removal,[],[f1597]) ).
thf(f1600,plain,
( ! [X0: $i] :
( ( sK98 @ X0 )
= $false )
| ~ spl219_3
| ~ spl219_5
| ~ spl219_9 ),
inference(forward_subsumption_resolution,[],[f1599,f1583]) ).
thf(f1603,plain,
( ( $true = $false )
| ~ spl219_3
| ~ spl219_5
| ~ spl219_7
| ~ spl219_9 ),
inference(constrained_superposition,[],[f1577,f1600]) ).
thf(f1609,plain,
( $false
| ~ spl219_3
| ~ spl219_5
| ~ spl219_7
| ~ spl219_9 ),
inference(trivial_inequality_removal,[],[f1603]) ).
thf(f1610,plain,
( ~ spl219_3
| ~ spl219_5
| ~ spl219_7
| ~ spl219_9 ),
inference(avatar_contradiction_clause,[],[f1609]) ).
thf(f1611,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( sK98 @ X0 )
= $false )
| ( sK203
= ( sK201 @ X0 ) ) )
| ~ spl219_3
| ~ spl219_10 ),
inference(constrained_superposition,[],[f1519,f1490]) ).
thf(f1612,plain,
( ( $true = $false )
| ( sK203 = sK202 )
| ~ spl219_7
| ~ spl219_10 ),
inference(constrained_superposition,[],[f1519,f1577]) ).
thf(f1615,plain,
( ( sK203 = sK202 )
| ~ spl219_7
| ~ spl219_10 ),
inference(trivial_inequality_removal,[],[f1612]) ).
thf(f1616,plain,
( ! [X0: $i] :
( ( ( sK98 @ X0 )
= $false )
| ( sK203
= ( sK201 @ X0 ) ) )
| ~ spl219_3
| ~ spl219_10 ),
inference(trivial_inequality_removal,[],[f1611]) ).
thf(f1619,plain,
( ! [X0: $i] :
( ( ( sK201 @ X0 )
= sK202 )
| ( ( sK98 @ X0 )
= $false ) )
| ~ spl219_3
| ~ spl219_7
| ~ spl219_10 ),
inference(forward_demodulation,[],[f1616,f1615]) ).
thf(f1623,plain,
( ! [X0: $i] :
( ( ( sK98 @ X0 )
= $false )
| ( ( sK98 @ X0 )
= $false )
| ( sK202 != X0 ) )
| ~ spl219_3
| ~ spl219_5
| ~ spl219_7
| ~ spl219_10 ),
inference(constrained_superposition,[],[f1497,f1619]) ).
thf(f1624,plain,
( ! [X0: $i] :
( ( sK202 != X0 )
| ( ( sK98 @ X0 )
= $false ) )
| ~ spl219_3
| ~ spl219_5
| ~ spl219_7
| ~ spl219_10 ),
inference(duplicate_literal_removal,[],[f1623]) ).
thf(f1626,plain,
( ( sK202 != sK202 )
| ( ( sK98 @ sK202 )
= $false )
| ~ spl219_3
| ~ spl219_5
| ~ spl219_7
| ~ spl219_10 ),
inference(imitation,[],[f1624]) ).
thf(f1628,plain,
( ( ( sK98 @ sK202 )
= $false )
| ~ spl219_3
| ~ spl219_5
| ~ spl219_7
| ~ spl219_10 ),
inference(trivial_inequality_removal,[],[f1626]) ).
thf(f1632,plain,
( ( $true = $false )
| ~ spl219_3
| ~ spl219_5
| ~ spl219_7
| ~ spl219_10 ),
inference(forward_demodulation,[],[f1628,f1577]) ).
thf(f1633,plain,
( $false
| ~ spl219_3
| ~ spl219_5
| ~ spl219_7
| ~ spl219_10 ),
inference(trivial_inequality_removal,[],[f1632]) ).
thf(f1634,plain,
( ~ spl219_3
| ~ spl219_5
| ~ spl219_7
| ~ spl219_10 ),
inference(avatar_contradiction_clause,[],[f1633]) ).
thf(f1636,plain,
( ! [X0: $i] :
( ( ( sK98 @ ( sK200 @ X0 ) )
= $true )
| ( $true = $false )
| ( ( sK97 @ X0 )
= $false ) )
| ~ spl219_4 ),
inference(constrained_superposition,[],[f1493,f1416]) ).
thf(f1638,plain,
( ! [X0: $i] :
( ( ( sK98 @ ( sK200 @ X0 ) )
= $true )
| ( ( sK97 @ X0 )
= $false ) )
| ~ spl219_4 ),
inference(trivial_inequality_removal,[],[f1636]) ).
thf(f1641,plain,
( ! [X0: $i] :
( ( ( sK200 @ X0 )
= sK203 )
| ( $true = $false )
| ( ( sK97 @ X0 )
= $false ) )
| ~ spl219_4
| ~ spl219_10 ),
inference(constrained_superposition,[],[f1519,f1638]) ).
thf(f1642,plain,
( ! [X0: $i] :
( ( ( sK200 @ X0 )
= sK203 )
| ( ( sK97 @ X0 )
= $false ) )
| ~ spl219_4
| ~ spl219_10 ),
inference(trivial_inequality_removal,[],[f1641]) ).
thf(f1644,plain,
( ! [X0: $i] :
( ( ( sK200 @ X0 )
= sK202 )
| ( ( sK97 @ X0 )
= $false ) )
| ~ spl219_4
| ~ spl219_7
| ~ spl219_10 ),
inference(forward_demodulation,[],[f1642,f1615]) ).
thf(f1648,plain,
( ! [X0: $i] :
( ( sK202 != X0 )
| ( ( sK97 @ X0 )
= $false )
| ( ( sK97 @ X0 )
= $false ) )
| ~ spl219_4
| ~ spl219_6
| ~ spl219_7
| ~ spl219_10 ),
inference(constrained_superposition,[],[f1501,f1644]) ).
thf(f1651,plain,
( ! [X0: $i] :
( ( sK202 != X0 )
| ( ( sK97 @ X0 )
= $false ) )
| ~ spl219_4
| ~ spl219_6
| ~ spl219_7
| ~ spl219_10 ),
inference(duplicate_literal_removal,[],[f1648]) ).
thf(f1653,plain,
( ( ( sK97 @ sK202 )
= $false )
| ~ spl219_4
| ~ spl219_6
| ~ spl219_7
| ~ spl219_10 ),
inference(equality_resolution,[],[f1651]) ).
thf(f1658,plain,
( ( $true = $false )
| ~ spl219_4
| ~ spl219_6
| ~ spl219_7
| ~ spl219_10 ),
inference(forward_demodulation,[],[f1653,f1507]) ).
thf(f1659,plain,
( $false
| ~ spl219_4
| ~ spl219_6
| ~ spl219_7
| ~ spl219_10 ),
inference(trivial_inequality_removal,[],[f1658]) ).
thf(f1660,plain,
( ~ spl219_4
| ~ spl219_6
| ~ spl219_7
| ~ spl219_10 ),
inference(avatar_contradiction_clause,[],[f1659]) ).
thf(f1664,plain,
( ! [X0: $i] :
( ( ( sK97 @ X0 )
= $false )
| ( $true = $false )
| ( ( sK200 @ X0 )
= sK202 ) )
| ~ spl219_4
| ~ spl219_9 ),
inference(constrained_superposition,[],[f1515,f1493]) ).
thf(f1667,plain,
( ! [X0: $i] :
( ( ( sK200 @ X0 )
= sK202 )
| ( ( sK97 @ X0 )
= $false ) )
| ~ spl219_4
| ~ spl219_9 ),
inference(trivial_inequality_removal,[],[f1664]) ).
thf(f1686,plain,
( ! [X0: $i] :
( ( ( sK97 @ X0 )
= $false )
| ( sK202 != X0 )
| ( ( sK97 @ X0 )
= $false ) )
| ~ spl219_4
| ~ spl219_6
| ~ spl219_9 ),
inference(constrained_superposition,[],[f1501,f1667]) ).
thf(f1688,plain,
( ! [X0: $i] :
( ( sK202 != X0 )
| ( ( sK97 @ X0 )
= $false ) )
| ~ spl219_4
| ~ spl219_6
| ~ spl219_9 ),
inference(duplicate_literal_removal,[],[f1686]) ).
thf(f1690,plain,
( ! [X0: $i] :
( ( sK97 @ X0 )
= $false )
| ~ spl219_4
| ~ spl219_6
| ~ spl219_9 ),
inference(forward_subsumption_resolution,[],[f1688,f1515]) ).
thf(f1691,plain,
( ( $true = $false )
| ~ spl219_4
| ~ spl219_6
| ~ spl219_7
| ~ spl219_9 ),
inference(constrained_superposition,[],[f1690,f1507]) ).
thf(f1703,plain,
( $false
| ~ spl219_4
| ~ spl219_6
| ~ spl219_7
| ~ spl219_9 ),
inference(trivial_inequality_removal,[],[f1691]) ).
thf(f1704,plain,
( ~ spl219_4
| ~ spl219_6
| ~ spl219_7
| ~ spl219_9 ),
inference(avatar_contradiction_clause,[],[f1703]) ).
thf(f1724,definition,
( spl219_24
<=> ! [X0: $i] :
( ( sK97 @ X0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl219_24])],[avatar_definition]) ).
thf(f1725,plain,
( ! [X0: $i] :
( ( sK97 @ X0 )
= $false )
| ~ spl219_24 ),
inference(avatar_component_clause,[],[f1724]) ).
thf(f1734,definition,
( spl219_26
<=> ! [X0: $i] :
( ( sK98 @ X0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl219_26])],[avatar_definition]) ).
thf(f1735,plain,
( ! [X0: $i] :
( ( sK98 @ X0 )
= $false )
| ~ spl219_26 ),
inference(avatar_component_clause,[],[f1734]) ).
thf(f1749,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( sK98 @ X0 )
= $false ) )
| ~ spl219_24 ),
inference(constrained_superposition,[],[f1725,f1417]) ).
thf(f1756,plain,
( ! [X0: $i] :
( ( sK98 @ X0 )
= $false )
| ~ spl219_24 ),
inference(trivial_inequality_removal,[],[f1749]) ).
thf(f1759,plain,
( ( $true = $false )
| ~ spl219_8
| ~ spl219_26 ),
inference(constrained_superposition,[],[f1735,f1511]) ).
thf(f1762,plain,
( ( $true = $false )
| ~ spl219_8
| ~ spl219_26 ),
inference(constrained_superposition,[],[f1511,f1735]) ).
thf(f1768,plain,
( $false
| ~ spl219_8
| ~ spl219_26 ),
inference(trivial_inequality_removal,[],[f1762]) ).
thf(f1769,plain,
( ~ spl219_8
| ~ spl219_26 ),
inference(avatar_contradiction_clause,[],[f1768]) ).
thf(f1770,plain,
( $false
| ~ spl219_8
| ~ spl219_26 ),
inference(trivial_inequality_removal,[],[f1759]) ).
thf(f1771,plain,
( ~ spl219_8
| ~ spl219_26 ),
inference(avatar_contradiction_clause,[],[f1770]) ).
thf(f1776,plain,
( spl219_26
| ~ spl219_24 ),
inference(avatar_split_clause,[],[f1756,f1724,f1734]) ).
thf(f1786,plain,
( ! [X0: $i] :
( ( ( sK97 @ X0 )
= $false )
| ( ( sK97 @ X0 )
= $false )
| ( sK203 != X0 ) )
| ~ spl219_4
| ~ spl219_6
| ~ spl219_10 ),
inference(constrained_superposition,[],[f1501,f1642]) ).
thf(f1788,plain,
( ! [X0: $i] :
( ( $true
= ( sK97 @ sK203 ) )
| ( ( sK97 @ X0 )
= $false )
| ( ( sK97 @ X0 )
= $false ) )
| ~ spl219_4
| ~ spl219_10 ),
inference(constrained_superposition,[],[f1493,f1642]) ).
thf(f1789,plain,
( ! [X0: $i] :
( ( sK203 != X0 )
| ( ( sK97 @ X0 )
= $false ) )
| ~ spl219_4
| ~ spl219_6
| ~ spl219_10 ),
inference(duplicate_literal_removal,[],[f1786]) ).
thf(f1790,plain,
( ! [X0: $i] :
( ( ( sK97 @ X0 )
= $false )
| ( $true
= ( sK97 @ sK203 ) ) )
| ~ spl219_4
| ~ spl219_10 ),
inference(duplicate_literal_removal,[],[f1788]) ).
thf(f1793,definition,
( spl219_27
<=> ( $true
= ( sK97 @ sK203 ) ) ),
introduced(definition,[new_symbols(definition,[spl219_27])],[avatar_definition]) ).
thf(f1795,plain,
( ( $true
= ( sK97 @ sK203 ) )
| ~ spl219_27 ),
inference(avatar_component_clause,[],[f1793]) ).
thf(f1796,plain,
( spl219_27
| spl219_24
| ~ spl219_4
| ~ spl219_10 ),
inference(avatar_split_clause,[],[f1790,f1518,f1492,f1724,f1793]) ).
thf(f1802,plain,
( ( $false
= ( sK97 @ sK203 ) )
| ~ spl219_4
| ~ spl219_6
| ~ spl219_10 ),
inference(equality_resolution,[],[f1789]) ).
thf(f1807,plain,
( ( $true = $false )
| ~ spl219_4
| ~ spl219_6
| ~ spl219_10
| ~ spl219_27 ),
inference(forward_demodulation,[],[f1802,f1795]) ).
thf(f1808,plain,
( $false
| ~ spl219_4
| ~ spl219_6
| ~ spl219_10
| ~ spl219_27 ),
inference(trivial_inequality_removal,[],[f1807]) ).
thf(f1809,plain,
( ~ spl219_4
| ~ spl219_6
| ~ spl219_10
| ~ spl219_27 ),
inference(avatar_contradiction_clause,[],[f1808]) ).
thf(f1810,plain,
( ! [X0: $i] :
( ( sK203
= ( sK201 @ X0 ) )
| ( ( sK98 @ X0 )
= $false ) )
| ~ spl219_3
| ~ spl219_10 ),
inference(trivial_inequality_removal,[],[f1611]) ).
thf(f1812,plain,
( ! [X0: $i] :
( ( ( sK98 @ X0 )
= $false )
| ( ( sK98 @ X0 )
= $false )
| ( sK203 != X0 ) )
| ~ spl219_3
| ~ spl219_5
| ~ spl219_10 ),
inference(constrained_superposition,[],[f1497,f1810]) ).
thf(f1813,plain,
( ! [X0: $i] :
( ( sK203 != X0 )
| ( ( sK98 @ X0 )
= $false ) )
| ~ spl219_3
| ~ spl219_5
| ~ spl219_10 ),
inference(duplicate_literal_removal,[],[f1812]) ).
thf(f1814,plain,
( ! [X0: $i] :
( ( sK98 @ X0 )
= $false )
| ~ spl219_3
| ~ spl219_5
| ~ spl219_10 ),
inference(forward_subsumption_resolution,[],[f1813,f1519]) ).
thf(f1815,plain,
( spl219_26
| ~ spl219_3
| ~ spl219_5
| ~ spl219_10 ),
inference(avatar_split_clause,[],[f1814,f1518,f1496,f1489,f1734]) ).
cnf(s2,plain,
( spl219_3
| spl219_4 ),
inference(sat_conversion,[],[f1494]) ).
cnf(s3,plain,
( spl219_4
| spl219_5 ),
inference(sat_conversion,[],[f1498]) ).
cnf(s4,plain,
( spl219_3
| spl219_6 ),
inference(sat_conversion,[],[f1502]) ).
cnf(s5,plain,
( spl219_5
| spl219_6 ),
inference(sat_conversion,[],[f1503]) ).
cnf(s6,plain,
( spl219_7
| spl219_8 ),
inference(sat_conversion,[],[f1512]) ).
cnf(s8,plain,
( spl219_7
| spl219_10 ),
inference(sat_conversion,[],[f1520]) ).
cnf(s9,plain,
( spl219_9
| spl219_10 ),
inference(sat_conversion,[],[f1521]) ).
cnf(s25,plain,
( ~ spl219_3
| ~ spl219_5
| ~ spl219_7
| ~ spl219_9 ),
inference(sat_conversion,[],[f1610]) ).
cnf(s27,plain,
( ~ spl219_3
| ~ spl219_5
| ~ spl219_7
| ~ spl219_10 ),
inference(sat_conversion,[],[f1634]) ).
cnf(s29,plain,
( ~ spl219_4
| ~ spl219_6
| ~ spl219_7
| ~ spl219_10 ),
inference(sat_conversion,[],[f1660]) ).
cnf(s31,plain,
( ~ spl219_4
| ~ spl219_6
| ~ spl219_7
| ~ spl219_9 ),
inference(sat_conversion,[],[f1704]) ).
cnf(s43,plain,
( ~ spl219_8
| ~ spl219_26 ),
inference(sat_conversion,[],[f1769]) ).
cnf(s44,plain,
( ~ spl219_8
| ~ spl219_26 ),
inference(sat_conversion,[],[f1771]) ).
cnf(s46,plain,
( ~ spl219_24
| spl219_26 ),
inference(sat_conversion,[],[f1776]) ).
cnf(s48,plain,
( ~ spl219_4
| ~ spl219_10
| spl219_24
| spl219_27 ),
inference(sat_conversion,[],[f1796]) ).
cnf(s50,plain,
( ~ spl219_4
| ~ spl219_6
| ~ spl219_10
| ~ spl219_27 ),
inference(sat_conversion,[],[f1809]) ).
cnf(s51,plain,
( ~ spl219_3
| ~ spl219_5
| ~ spl219_10
| spl219_26 ),
inference(sat_conversion,[],[f1815]) ).
cnf(s61,plain,
( spl219_7
| spl219_3 ),
inference(rat,[],[s46,s48,s44,s50,s6,s8,s4,s2]) ).
cnf(s62,plain,
( ~ spl219_7
| ~ spl219_4
| ~ spl219_6 ),
inference(rat,[],[s9,s29,s31]) ).
cnf(s63,plain,
spl219_3,
inference(rat,[],[s62,s61,s2,s4]) ).
cnf(s64,plain,
( ~ spl219_6
| ~ spl219_4 ),
inference(rat,[],[s46,s48,s44,s50,s6,s8,s62]) ).
cnf(s65,plain,
( spl219_7
| ~ spl219_5 ),
inference(rat,[],[s43,s51,s6,s8,s63]) ).
cnf(s66,plain,
( ~ spl219_7
| ~ spl219_5 ),
inference(rat,[],[s9,s27,s25,s63]) ).
cnf(s67,plain,
~ spl219_5,
inference(rat,[],[s66,s65]) ).
cnf(s68,plain,
spl219_6,
inference(rat,[],[s5,s67]) ).
cnf(s69,plain,
spl219_4,
inference(rat,[],[s3,s67]) ).
cnf(s70,plain,
$false,
inference(rat,[],[s64,s69,s68]) ).
thf(f1816,plain,
$false,
inference(avatar_sat_refutation,[],[s70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU550^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 % Computer : n014.cluster.edu
% 0.06/0.22 % Model : x86_64 x86_64
% 0.06/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.22 % Memory : 8046.5625MB
% 0.06/0.22 % OS : Linux 6.8.0-71-generic
% 0.06/0.22 % CPULimit : 300
% 0.06/0.22 % WCLimit : 300
% 0.06/0.23 % DateTime : Tue Sep 29 13:49:30 UTC 2026
% 0.06/0.23 % CPUTime :
% 0.06/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.26 Running higher-order theorem proving
% 0.18/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.35 % (2692596)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.35 % (2692610)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4273351370:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.18/0.35 % (2692611)lrs+10_16_si=on:nwc=1.5:random_seed=59140419:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.18/0.35 % (2692612)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3203918327:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.18/0.35 % (2692612)Instruction limit reached!
% 0.18/0.35 % (2692612)------------------------------
% 0.18/0.35 % (2692612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.35 % (2692612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.35 % (2692612)CaDiCaL version: 2.1.3
% 0.18/0.35 % (2692612)Termination reason: Instruction limit
% 0.18/0.35 % (2692612)Termination phase: shuffling
% 0.18/0.35 % (2692612)Time elapsed: 0.002 s
% 0.18/0.35 % (2692612)Peak memory usage: 10 MB
% 0.18/0.35 % (2692612)Instructions burned: 3 (million)
% 0.18/0.35 % (2692613)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=1199343275: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)
% 0.18/0.35 % (2692611)Instruction limit reached!
% 0.18/0.35 % (2692611)------------------------------
% 0.18/0.35 % (2692611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.35 % (2692611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.35 % (2692611)CaDiCaL version: 2.1.3
% 0.18/0.35 % (2692611)Termination reason: Instruction limit
% 0.18/0.35 % (2692611)Termination phase: Property scanning
% 0.18/0.35 % (2692611)Time elapsed: 0.008 s
% 0.18/0.35 % (2692611)Peak memory usage: 10 MB
% 0.18/0.35 % (2692611)Instructions burned: 18 (million)
% 0.18/0.35 % (2692614)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4000402438:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.18/0.35 % (2692610) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2692596-2692610"...
% 0.18/0.35 % (2692616)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.18/0.35 % (2692616)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
% 0.18/0.35 % (2692610)...printing done.
% 0.18/0.35 % (2692610)Refutation found. Thanks to Tanya!
% 0.18/0.35 % SZS status Theorem for theBenchmark
% 0.18/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.35 % (2692610)------------------------------
% 0.18/0.35 % (2692610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.35 % (2692610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.35 % (2692610)CaDiCaL version: 2.1.3
% 0.18/0.35 % (2692610)Termination reason: Refutation
% 0.18/0.35 % (2692610)Time elapsed: 0.025 s
% 0.18/0.35 % (2692610)Peak memory usage: 14 MB
% 0.18/0.35 % (2692610)Instructions burned: 91 (million)
% 0.18/0.35 % (2692596)Success in time 0.056 s
% 0.18/0.35 % Vampire exiting
%------------------------------------------------------------------------------